sub-Hz Differential Rotational Spectroscopy of Enantiomers
Lincoln Satterthwaite, Greta Koumarianou, Daniel Sorensen, David Patterson
Subject: Physical Sciences, Atomic & Molecular Physics Keywords: chirality; microwave spectroscopy; electroweak force; precision measurement; differential spectroscopy; parity violation
Observation of parity-violating effects in chiral molecules is a long-standing challenge of the molecular spectroscopy community. In the microwave regime, the difference in transition frequencies between enantiomers is predicted to be below the mHz level, which is considerably beyond current experimental capabilities. The most promising future efforts combine vibrational spectroscopy, buffer gas cooling, and carefully chosen molecular candidates with large predicted parity-violating shifts. Here, we demonstrate for the first time high-precision differential microwave spectroscopy, achieving sub-Hz precision by coupling a cryogenic buffer gas cell with a tunable microwave Fabry-Perot cavity. We report statistically limited sub-Hz precision of (0.08±0.72) Hz, observed between enantiopure samples of (R)-1,2-propanediol and (S)-1,2-propanediol at frequencies near 15 GHz. We confirm highly repeatable spectroscopic measurements compared to traditional pulsed-jet methods, opening up new capabilities in probing subtle molecular structural effects at the 10−10 level and providing a platform for exploring sources of systematic error in parity-violation searches. We discuss dominant systematic effects at this level and propose possible extensions of the technique for higher precision.
Optical Energy Variability Induced by Speckle: The Cases of MERLIN and CHARM-F IPDA Lidar
Vincent Casse, Fabien Gibert, Dimitri Edouart, Olivier Chomette, Cyril Crevoisier
Subject: Earth Sciences, Atmospheric Science Keywords: speckle; coherence; interference; differential absorption lidar; radiometry; space mission
In the context of the French-German space lidar mission MERLIN dedicated to the determination of the atmospheric methane content, an end-to-end mission simulator is being developed. In order to check whether the instrument design meets the performance requirements, simulations have to count all the sources of noise on the measurements like the optical energy variability induced by speckle. Speckle is due to interference as the lidar beam are quasi monochromatic. Speckle contribution to the error budget has to be estimated but also simulated. In this paper, the speckle theory is revisited and applied to MERLIN double pulsed IPDA lidar and also to the DLR demonstrator CHARM-F. Results show: on the signal path, speckle noise depends mainly on the size of the illuminating area on ground; on the solar flux, speckle is fully negligible both because the pixel size and the optical filter spectral width; on energy monitoring path a decorrelation mechanism is needed to reduce speckle noise on averaged data. Speckle noises for MERLIN and CHARM-F can be simulated by Gaussian noises with only one random draw by shot separately for energy monitoring and signal paths.
Using Dielectric Relaxation Spectroscopy to Characterize the Glass Transition and Onset of Crystallinity of Skim-Milk Powder
Martin G. Buehler
Subject: Chemistry, Food Chemistry Keywords: DRS dielectric relaxation; DSC differential scanning calorimetry; SMP skim milk powder; boundary curves
This paper describes the dielectric relaxation spectroscopy (DRS) method for obtaining glass transition temperature and the onset of crystallinity of skim milk powder (SMP). The methodology consists of exposing SMP samples to numerous constant temperatures, T, and water activities, aw, and measuring the relaxation time. Measurements are based on changes in the loss-tangent height at its peak frequency. Glass transition times are identified at peaks in the loss-tangent height versus time curve and the onset of crystallinity times are identified when the loss-tangent height collapses. The analysis leads to two boundary curves: glass transition Tg, aw curve and the onset of crystallinity Tc, aw curve. They separate the SMP stable (long shelf life) and unstable (short shelf life) regions. Two curve fitting algorithms were developed for (a) aw2, tg curve where tg is the time to glass transition and aw2, tc curve where time tc is the time to onset of crystallinity and (b) Tg, aw and Tc, aw boundary curves. Finally, the DRS data are compared to differential scanning calorimetry (DSC) results.
Twisted Few-Mode Optical Fiber with Improved Height of Quasi-Step Refractive Index Profile
Anton V. Bourdine, Vladimir V. Demidov, Artem A. Kuznetsov, Alexander A. Vasilets, Egishe V. Ter-Nersesyants, Alexander V. Khokhlov, Alexandra S. Matrosova, Grigori A. Pchelkin, Michael V. Dashkov, Elena S. Zaitseva, Azat R. Gizatulin, Ivan K. Meshkov, Airat Zh. Sakhabutdinov, Eugeniy V. Dmitriev, Oleg G. Morozov, Vladimir A. Burdin, Konstantin V. Dukelskii, Yaseera Ismail, Francesco Petruccione, Ghanshyam Singh, Manish Tiwari, Juan Yin
Subject: Engineering, Other Keywords: twisted optical fiber; chirality; laser beam profile; differential mode delay; laser-based few-mode optical signal transmission; fiber Bragg grating; few-mode effects
Online: 30 March 2022 (15:17:48 CEST)
This work presents results of property researches of fabricated samples of silica few-mode optical fiber (FMF) with induced chirality under twisting 10 and 66 revolutions per meter, core diameter 11 µm, typical "telecommunication" cladding diameter 125 µm and improved height of quasi-step refractive index profile. Proposed FMF supports 4 guided modes over "C"-band. We represent results of computed characteristics, as well as experimentally measured spectral responses of laser-excited optical signals, including researches and analysis of few-mode effects, occurring after fiber Bragg grating writing.
Particulate Exotica
Subject: Physical Sciences, Acoustics Keywords: geometrodynamics; differential topology
Recent advances in differential topology single out four-dimensions as being special, allowing for vast varieties of exotic smoothness (differential) structures, distinguished by their handlebody decompositions, even as the coarser algebraic topology is fixed. Should the spacetime we reside in takes up one of the more exotic choices, and there is no obvious reason why it shouldn't, apparent pathologies would inevitably plague calculus-based physical theories assuming the standard vanilla structure, due to the non-existence of a diffeomorphism and the consequent lack of a suitable portal through which to transfer the complete information regarding the exotic physical dynamics into the vanilla theories. An obvious plausible consequence of this deficiency would be the uncertainty permeating our attempted description of the microscopic world. We tentatively argue here, that a re-inspection of the key ingredients of the phenomenological particle models, from the perspective of exotica, could possibly yield interesting insights. Our short and rudimentary discussion is qualitative and speculative, because the necessary mathematical tools have only just began to be developed.
Approximate Analytical Solution of Unstable Ordinary Differential Equation Using Differential Evolution Algorithm
Ashiribo Wusu, Olusola Olabanjo
Subject: Mathematics & Computer Science, Applied Mathematics Keywords: Unstable; Ordinary Differential Equation; Initial Value Problems; Optimization; Differential Evolution
Online: 7 July 2022 (09:29:01 CEST)
The application of evolutionary optimization algorithms in problem solving is currently gaining wide popularity. Use of Differential Evolution (DE) algorithm in obtaining analytically approximate solution of unstable second order initial value Ordinary Differential Equation (ODE) is presented in this work. The methodology involves solving an associated problem of optimization with con-strains to get an analytically approximate solution for the ODE under consider-ation. Three test cases were used to demonstrate the efficiency of our method. In comparison with other methods discussed in the literature, our method gave significant improvement on the accuracy of the obtained results.
Oscillatory Behavior of Three Dimensional α-Fractional Delay Differential Systems
Adem Kilicman, V. Sadhasivam, M. Deepa, N. Nagajothi
Subject: Mathematics & Computer Science, Applied Mathematics Keywords: oscillation; nonlinear differential system; delay differential system; α-fractional derivative
In this article, we consider the three dimensional $\alpha$-fractional nonlinear delay differential system of the form \begin{align*} D^{\alpha}\left(u(t)\right)&=p(t)g\left(v(\sigma(t))\right),\\D^{\alpha}\left(v(t)\right)&=-q(t)h\left(w(t))\right),\\D^{\alpha}\left(w(t)\right)&=r(t)f\left(u(\tau(t))\right),~ t \geq t_0, \end{align*} where $0 < \alpha \leq 1$, $D^{\alpha}$ denotes the Katugampola fractional derivative of order $\alpha$. We have established some new oscillation criteria of solutions of differential system by using generalized Riccati transformation and inequality technique. The obtained results are illustrated with suitable examples.
An Improvement Differential Evolution Algorithms for the Crop Planning in the Northeastern Region of Thailand
Udompong Ketsripongsa, Rapeepan Pitakaso, Kanchana Sethanan, Tassin Srivarapongse
Subject: Mathematics & Computer Science, Computational Mathematics Keywords: Differential Evolution Algorithm; Crop Planning; Economic Crops; Improvement Differential Evolution algorithm
This research presents a solution to the problem of planning the optimum area for economic crops by developed mathematical models and developed an algorithm to solve the problem of planning the optimum area by considered economic value for the maximize profit of farmers. The data were collected from farmers in 8 provinces in the northeastern region of Thailand. The 3 economic crops studied were rice, cassava and sugarcane. The solving problem methods were 1) Created mathematical models and solved the problems with Lingo V.11. 2) Improved Differential Evolution algorithms (I-DE) to solve the problems, which had 3 local search methods included (Swap, Cyclic Move and K-variable moves). The results of this study showed that in the small and medium problems instances, Lingo V.11 and DE provided equal profit outcome but DE was faster but in the large size of test instances DE generated better solution than that of Lingo v.11 when Lingo simulation time is set to 250 hours and DE simulation time has set to maximum 21.82 minutes. 2) Comparing DE and I-DE , I-DE outperforms DE in finding the better solution for all size of test instances (small, medium and large).
Univalent Functions Defined by a Generalized Multipler Differential Operator
Adnan Ghazy Alamoush
Subject: Mathematics & Computer Science, Geometry & Topology Keywords: Analytic functions; univalent function; differential operator; differential subordination; convex functions; structural formula
In this paper, we investigate a new subclass of univalent functions defined by a generalized differential operator, and obtain some interesting properties of functions belonging to the class Rm λµ ( α, β, γ, υ ).
Fuzzy Sumudu Transform for Solving System of Linear Fuzzy Differential Equations with Fuzzy Constant Coefficients
Norazrizal Aswad Abdul Rahman, Muhammad Zaini Ahmad
Subject: Mathematics & Computer Science, Artificial Intelligence & Robotics Keywords: fuzzy Sumudu transform; fuzzy linear differential equations; system of fuzzy differential equations
In this paper, we employ fuzzy Sumudu transform for solving system of linear fuzzy differential equations with fuzzy constant coefficients. The system with fuzzy constant coefficients is interpreted under strongly generalized differentiability. For this purpose, new procedures for solving the system are proposed. A numerical example is carried out for solving system adapted from fuzzy radioactive decay model. Conclusion is drawn in the last section and some potential research directions are given.
Existence of Fractional Impulsive Functional Integro-Differential Equations in Banach Spaces
Dimplekumar Chalishajar, C. Ravichandran, S. Dhanalakshmi, R. Murugesu
Subject: Mathematics & Computer Science, Applied Mathematics Keywords: fractional differential equations: impulse; integro-differential equations; non local conditions; fixed point theorem
In this paper, we established the existence of PC-mild solutions for non local fractional impulsive functional integro-differential equations with finite delay. The proofs are obtained by using the techniques of fixed point theorems, semi-group theory and generalized Bellman inequality. In this paper, we have used the distributed characteristic operators to define the mild solution of the system. Results obtained here improve and extend some known results.
Preprint ESSAY | doi:10.20944/preprints202210.0364.v1
An Expository Medley on the Probabilistic Aspects and Insights of the Schrödinger Systems
Chaoyi Sheng
Subject: Mathematics & Computer Science, General Mathematics Keywords: Schrödinger systems; Differential equations; Evolutions
Calculus, as a starting point to everyone's study of mathematics, was developed along with classical mechanics. Though not rigorously formulated, the intuition for differential form and infinitesimal motion makes calculus not hard to understand. And hence it does not require great effort to grasp the principles of classical mechanics. However, the situation becomes quite different when it comes to the quantum world. Given a particle system, what of interest is always the physical quantity of this system, such as energy, position, momentum, entropy, etc. But it is no longer straightforward.
Can miRNA Indicate Risk of Illness After Continuous Exposure to M. tuberculosis?
Cleonardo Augusto Silva, Arthur Ribeiro-dos-Santos, Wanderson Gonçalves Gonçalves, Pablo Pinto, Rafael Pompeu Pantoja, Tatiana Vinasco-Sandoval, André Ribeiro-dos-Santos, Mara Helena Hutz, Amanda Vidal, Gilderlanio Santana Araújo, Ândrea Ribeiro-dos-Santos, Sidney Santos
Subject: Life Sciences, Biochemistry Keywords: miRNA; Tuberculosis; differential expression analysis
Molecular studies regarding regulatory elements such as small ncRNAs and their mechanisms are poorly understood in infectious diseases. Tuberculosis is one of the oldest infectious diseases of humanity, and it is still a challenge to prevent and treat it. The control of the infection as well as its diagnosis are still complex, and treatments used are linked to several side effects. This study aimed to investigate miRNA's expression profile to identify possible biomarkers for tuberculosis. We applied NGS techniques to investigate miRNA's global expression profile from blood samples of infected patients with tuberculosis, their respective healthy physicians, and external healthy individuals as controls. Samples from 22 individuals run through a differential expression, target genes, gene set enrichment, and miRNA-gene network analysis. We observed 153 altered miRNAs, among which, only three DEmiRNAs (hsa-let-7g-5p, hsa-miR-486-3p and hsa-miR-4732-5p) were found between the investigated patients and their respective physicians. These DEmiRNAs are suggested to play an important role in granuloma regulation and their immune physiopathology. Our results propose that miRNAs may be involved in immune modulation, regulating the repertoire of genes expressed in the immune system's cells. Our findings encourage the application of miRNAs as potential biomarkers for tuberculosis.
Numerical Solutions of the Hattendorff Differential Equation for Multi-state Markov Insurance Models
Nathan Ritchey, Rajeev Rajaram
Subject: Mathematics & Computer Science, Computational Mathematics Keywords: Policy Value; Kolmogorov forward equations; Multi-state model; Thiele's differential equation; Hattendorff differential equation
We provide methodology and numerical results for the Hattendorff differential equa- tion for the continuous time evolution of the variance of L(j)t , the loss at time t random variable for a multi-state process, given that the state at time t is j.
Application of Differential Transform to Multi-Term Fractional Differential Equations with Non-Commensurate Orders
Josef Rebenda
Subject: Mathematics & Computer Science, Computational Mathematics Keywords: fractional differential equation; non-commensurate orders; initial value problem; differential transform; fractional power series
The differential transformation, an approach based on Taylor's theorem, is proposed as convenient for finding exact or approximate solution to the initial value problem with multiple Caputo fractional derivatives of generally non-commensurate orders. The multi-term differential equation is first transformed into a multi-order system and then into a system of recurrence relations for coefficients of formal fractional power series. The order of the fractional power series is discussed in relation to orders of derivatives appearing in the original equation. Application of the algorithm to an initial value problem results in a reliable and expected outcome.
DGJ Method for Linear and Nonlinear Third order Fractional Differential Equation
Mahmut Modanli
Subject: Mathematics & Computer Science, Applied Mathematics Keywords: DGJ method, third order fractional differential equation, nonlinear differential equation, convergence of the method.
DGJ (Daftardar-Gejii-Jafaris) method is used to obtain numerical solution of the third order fractional differential equation. Providing the DGJ method converges, the approximate solution is a good and effective numerical result which is close to the exact solution or the exact solution. For this,the examples of the explaning the method are presented. The proposed method is implemented for the approximation solution of the third order nonlinear fractional partial differential equations. The method was shown to be unsuitable and inconsistent for an example of a nonlinear fractional partial differential equation depend on initial-boundary value conditions. The fact that these numerical results are not consistent can be explained by the fact that the method is not convergent.
$(q,\sigma,\tau)$-Differential Graded Algebras
Viktor Abramov, Olga Liivapuu, Abdenacer Makhlouf
Subject: Mathematics & Computer Science, Algebra & Number Theory Keywords: q-differential graded algebra; (σ,τ)-differential graded algebra; generalized Clifford algebra; pre-cosimplicial complex
We propose a notion of $(q,\sigma,\tau)$-differential graded algebra, which generalizes the notions of $(\sigma,\tau)$-differential graded algebra and $q$-differential graded algebra. We construct two examples of $(q,\sigma,\tau)$-differential graded algebra, where the first one is constructed by means of generalized Clifford algebra with two generators (reduced quantum plane), where we use a $(\sigma,\tau)$-twisted graded $q$-commutator. In order to construct the second example, we introduce a notion of $(\sigma,\tau)$-pre-cosimplicial algebra.
Preprint SHORT NOTE | doi:10.20944/preprints202109.0217.v1
Harmonisation of Classical Wave Equation
Alireza Jamali
Subject: Mathematics & Computer Science, Applied Mathematics Keywords: harmonic analysis; nonlinear partial differential equation
In this short note we present a technique using which one attributes frequency and wavevector to (almost) arbitrary scalar fields. Our proposed definition is then applied to the classical wave equation to yield a novel nonlinear PDE.
Modified SPWM Control for the Single-Stage Differential Boost Inverter Applying in Battery Energy Storage System
Yu-Lin Lee, Kun-Feng Chen, Kai-Jun Pai, Chang-Hua Lin, Yuan-Hong Cheng
Subject: Engineering, Electrical & Electronic Engineering Keywords: boost inverter; modified SPWM; differential inverter
This study aims to implement a SSDBI (single-stage differential boost inverter, SSDBI) applying in a single-stage BESS (battery energy storage system, BESS) topology, which can supply power from lower voltage battery module to AC load. Compared with the common two-stage topology, which has a two-stage converter and higher voltage battery module array, the single-stage topology can reduce the number of cells and components, and improve the power density. In addition, a modified SPWM control was proposed to reduce the control complexity of the SSDBI while improving the THD of the inverter. The modified SPWM control can reduce the duty ratio of the SSDBI and the stress on the components to improve the AC voltage output waveform and reduce the THD value about 2.654%.
The Active Segmentation Platform for Microscopic Image Classification and Segmentation
Sumit Vohra, Dimiter Prodanov
Subject: Life Sciences, Biochemistry Keywords: scale spaces; differential invariants; segmentation; classification
Image segmentation and classification still represent an active area of research since no universal solution can be identified. Established segmentation algorithms like thresholding are problem specific, treat well the easy cases and mostly relied on single parameter i.e intensity. Machine learning approaches offer alternatives where predefined features are combined into different classifiers. On the other hand, the outcome of machine learning is only as good as the underlying feature space. Differential geometry can substantially improve the outcome of machine learning since it can enrich the underlying feature space with new geometrical objects, called invariants. In this way, the geometrical features form a high-dimensional feature space for each pixel, where original objects can be resolved. Alternatives based on the geometry of the image scale-invariant interest points have been exploited successfully in the field of computer vision. Here, we integrate geometrical feature extraction based on signal processing, machine learning, and input relying on domain knowledge. The approach is exemplified on the ISBI 2012 image segmentation challenge data set. As a second application, we demonstrate powerful image classification functionality based on the same principles, which was applied to the HeLa and HEp-2 data sets. Obtained results demonstrate that feature space enrichment properly balanced with feature selection functionality can achieve performance comparable to deep learning approaches.
Entropic Ranks: A Methodology for Enhanced, Threshold-Free, Information-Rich Data Partition and Interpretation
Hector - Xavier de Lastic, Irene Liampa, Alexandros G. Georgakilas, Michalis Zervakis, Aristotelis Chatziioannou
Subject: Mathematics & Computer Science, Artificial Intelligence & Robotics Keywords: data analysis; threshold-free; differential analysis
Background: Traditional omic analysis relies on p-value and fold change as selection criteria. There is an ongoing debate on their effectiveness in delivering systemic and robust interpretation, due to their dependence on assumptions of conformity with various parametric distributions.Here, we propose a threshold-free selection method based on robust, non-parametric statistics, ensuring independence from the statistical distribution properties and broad applicability. Such methods could adapt to different initial data distributions, contrary to statistical techniques based on fixed thresholds. Methods: Our work extends the Rank Products methodology with a neutral selection method of high information-extraction capacity. We introduce the calculation of the RP distribution's entropy to isolate the features of interest by their contribution to the distribution's information content. The aim is a methodology performing threshold-free identification of the differentially expressed features, which are highly informative about the phenomenon under scrutiny. Conclusions: Applying the proposed method on microarray (transcriptomic and DNA methylation) and RNAseq count data of varying sizes and noise presence, we observe robust convergence for the different parameterisations to stable cutoff points. Functional analysis through BioInfoMiner and EnrichR was used to evaluate the information potency of the resulting feature lists. Overall, the derived functional terms provide a systemic description highly compatible with the results of traditional statistical hypothesis testing techniques. The methodology behaves consistently across different data types. The feature lists are compact and information-rich, indicating phenotypic aspects specific to the tissue and biological phenomenon i nvestigated. Selection by information content measures efficiently addresses problems, emerging from arbitrary thresholding, thus facilitating the full automation of the analysis.
On-Board Correction of Systematic Odometry Errors in Differential Robots
Saturnino Maldonado-Bascón, Roberto J. López Sastre, Fco. Javier Acevedo-Rodríguez, Pedro Gil Jiménez
Subject: Engineering, Electrical & Electronic Engineering Keywords: differential drive robot; calibration; systematic error
An easier method for the calibration of differential drive robots is presented. Most of the calibration is done on-board and it is not necessary to expend too much time taking note of the robot's position. The calibration method does not need a big free space to perform the tests. The bigger space is just in a straight line, which is easy to find. Results with the proposed method are compared with those from UMB as a reference, and they show very little deviation while the proposed calibration is much simpler.
Dynkin Game under G-Expectation in Continuous Time
Helin Wu, Yong Ren, Feng Hu
Subject: Mathematics & Computer Science, Probability And Statistics Keywords: Dynkin game; Ambiguity; Backward stochastic differential equation (BSDE); Reflected backward stochastic differential equation (Reflected BSDE); Constraint
In this paper, we investigate some kind of Dynkin game under $g$-expectation induced by backward stochastic differential equation (shortly for BSDE). We define the lower and upper value functions $\underline{V}_t=ess\sup\limits_{\tau\in{\mathcal{T}_t}} ess\inf\limits_{\sigma\in{\mathcal{T}_t}}\mathcal{E}^g_t[R(\tau,\sigma)]$ and $\overline{V}_t=ess\inf\limits_{\sigma\in{\mathcal{T}_t}}ess\sup\limits_{\tau\in{\mathcal{T}_t}}\mathcal{E}^g_t[R(\tau,\sigma)]$, respectively. Under some regular assumptions, a pair of saddle point is obtained and the value function of Dynkin game $V(t)=\underline{V}_t=\overline{V}_t$ follows. Furthermore, the constrained case of Dynkin game is also considered.
Fourier Transform on the Homogeneous Space of 3D Positions and Orientations for Exact Solutions to PDEs
Remco Duits, Erik J. Bekkers, Alexey Mashtakov
Subject: Mathematics & Computer Science, Analysis Keywords: Fourier transform; rigid body motions; partial differential equations; Lévy processes; lie groups; homogeneous spaces; stochastic differential equations
Fokker-Planck PDEs (incl. diffusions) for stable Lévy processes (incl. Wiener processes) on the joint space of positions and orientations play a major role in mechanics, robotics, image analysis, directional statistics and probability theory. Exact analytic designs and solutions are known in the 2D case, where they have been obtained using Fourier transform on $SE(2)$. Here we extend these approaches to 3D using Fourier transform on the Lie group $SE(3)$ of rigid body motions. More precisely, we define the homogeneous space of 3D positions and orientations $\mathbb{R}^{3}\rtimes S^{2}:=SE(3)/(\{\mathbf{0}\} \times SO(2))$ as the quotient in $SE(3)$. In our construction, two group elements are equivalent if they are equal up to a rotation around the reference axis. On this quotient we design a specific Fourier transform. We apply this Fourier transform to derive new exact solutions to Fokker-Planck PDEs of $\alpha$-stable Lévy processes on $\mathbb{R}^{3}\rtimes S^{2}$. This reduces classical analysis computations and provides an explicit algebraic spectral decomposition of the solutions. We compare the exact probability kernel for $\alpha = 1$ (the diffusion kernel) to the kernel for $\alpha=\frac12$ (the Poisson kernel). We set up SDEs for the Lévy processes on the quotient and derive corresponding Monte-Carlo methods. We verify that the exact probability kernels arise as the limit of the Monte-Carlo approximations.
Differentially Private Block Coordinate Descent for Linear Regression on Vertically Partitioned Data
Jins De Jong, Bart Kamphorst, Shannon Kroes
Subject: Mathematics & Computer Science, Applied Mathematics Keywords: Differential privacy; Federated learning; Vertically partitioned data
We present a differentially private extension of the block coordinate descent based on objective perturbation. The algorithm iteratively performs linear regression in a federated setting on vertically partitioned data. In addition to a privacy guarantee, the algorithm also offers a utility guarantee; a tolerance parameter indicates how much the differentially private regression may deviate from an analysis without differential privacy. The algorithm's performance is compared with the standard block coordinate descent algorithm and the trade-off between utility and privacy is studied. The performance is studied using both artificial test data and the forest fires data set. We find that the algorithm is fast and able to generate practical predictions with single-digit privacy budgets, albeit with some accuracy loss.
Identification of Drought-Responsive microRNAs from Roots and Leaves of Alfalfa by High-Throughput Sequencing
Yue Li, Liqiang Wan, Shuyi Bi, Xiufu Wan, Zhenyi Li, Jing Cao, Zongyong Tong, Hongyu Xu, Feng He, Xianglin Li
Subject: Life Sciences, Molecular Biology Keywords: alfalfa; drought; microRNA; small RNA; differential expression
Alfalfa, an important legume forage, is an ideal crop for sustainable agriculture and a potential bioenergy plant. Drought, one of the most common environmental stresses, substantially affects plants' growth, development and productivity. MicroRNAs (miRNAs) are newly discovered gene expression regulators that have been linked to several plant stress responses. To elucidate the role of miRNAs in drought stress regulation of alfalfa, a high-throughput sequencing approach was used to analyze 12 small RNA libraries comprising of 4 samples, each with 3 biological replicates. We identified 348 known miRNAs, belonging to 80 miRNA families, from the 12 libraries and 281 novel miRNAs using Mireap software. 18 known miRNAs in roots and 12 known miRNAs in leaves were screened out as drought-responsive miRNAs. Except for miR319d and miR157a which were upregulated under drought stress, the expression pattern of drought-responsive miRNAs were different between roots and leaves in alfalfa. This is the first study discovering miR157a, miR1507, miR3512, miR3630, miR5213, miR5294, miR5368 and miR6173 are drought-responsive miRNAs. Target transcripts of drought-responsive miRNAs were computationally predicted. All 447 target genes for the known miRNAs were predicted using an online tool. This study provides a significant insight on understanding drought-responsive mechanisms of alfalfa.
On Inner Expansions for A Singularly Perturbed Cauchy Problem with Confluent Fuchsian Singularities
Stephane Malek
Subject: Mathematics & Computer Science, Analysis Keywords: asymptotic expansion; Borel-Laplace transform; Cauchy problem; formal power series; integro-differential equation; partial differential equation; singular perturbation
A nonlinear singularly perturbed Cauchy problem with confluent fuchsian singularities is examined. This problem involves coefficients with polynomial dependence in time. A similar initial value problem with logarithmic reliance in time has been investigated by the author in a recent work, for which sets of holomorphic inner and outer solutions were built up and expressed as a Laplace transform with logarithmic kernel. Here, a family of holomorphic inner solutions are constructed by means of exponential transseries expansions containing infinitely many Laplace transforms with special kernel. Furthermore, asymptotic expansions of Gevrey type for these solutions relatively to the perturbation parameter are established.
The (k, s)-Fractional Calculus of Class of a Function
Gauhar Rahman, Abdul Ghaffar, K. S. Nisar, Azeema Azeema
Subject: Mathematics & Computer Science, Analysis Keywords: fractional integral operators; fractional differential operators; generalized (k, s)-fractional integral operators; generalized (k, s)-fractional differential operators
In this present paper, we deal with the generalized (k, s)-fractional integral and differential operators recently defined by Nisar et al. and obtain some generalized (k, s)-fractional integral and differential formulas involving the class of a function as its kernels. Also, we investigate a certain number of their consequences containing the said function in their kernels.
Modeling The Sport Differential Mechanism
Maksym Diachuk, Said M. Easa
Subject: Engineering, Automotive Engineering Keywords: sport differential; torque vectoring; friction clutch; vehicle kinematics
The study is devoted to the issues of mathematical modeling and simulating the sport differential mechanism (DM) with controllable torque redistribution. The issue is caused by the elaboration of ADAS systems with the automated torque vectoring for transmissions of all-wheel-drive (AWD) vehicles and the inclusion of such devices in the combined autonomous vehicle trajectory control scheme. At the article's beginning, the use of devices for redistributing traction forces is reasoned by analyzing the curvilinear vehicle motion, where they could ensure the accuracy of vehicle steerability. The literature review highlights modern developments in the field of modeling and researching such DMs. Considering the vehicle turn with a minimum radius, the conditions corresponding to passing greater torque over the outrunning rear axle are determined. All the mechanism's components and loads acting between them are described in detail. To form an original method of mathematical description of the mechanism functioning, the system of differential equations, systems of kinematic and force connections are considered separately. The article details the mathematical approach to generalize the way for automating the equation compilation for rotational mechanical systems such as vehicle transmissions. In the simulation section, a Simulink model reflecting the functional components and calculation procedures is presented. A series of testing and simulations on the DM operation with forcible torque distribution is carried out. Modeling data are presented, and the analysis of simulation results is performed. In the completion, conclusions are made regarding the scope and use of this model and the prospects for further developing the method proposed to automate the formation of equation systems.
Diagnostic Tools for Autism Spectrum Disorders by Sex: Analysis of Current Status and Future Lines
Esperanza Navarro-Pardo, Fernanda López-Ramón, Yurena Alonso-Esteban, Francisco Alcantud-Marín
Subject: Behavioral Sciences, Applied Psychology Keywords: Autism Spectrum Disorders; Diagnostic Tools; Sex; Differential Diagnostic.
Online: 2 March 2021 (10:05:57 CET)
Studies on the prevalence of Autism Spectrum Disorders show a gender disproportion. In the last years, there has been an increasing interest in the search for an explanation. There are two main lines of research; the first one looks for sex-related biological reasons that justifies the low prevalence of ASD in women (some protective factor related to hormones or immune system among others), and the second line of studies is related to the possible biases introduced in the diagnostic tools or procedures. In this article, a review of the latter line of research is made. Theoretical analysis following two objectives: a) Analysis of possible biases in diagnostic tools and b) Other non-biological explanations for gender differences in the prevalence of ASD. The literature analyzed provides contradictory results although it evidences the possible bias both in the construction of the diagnostic tools and in the assessment and determination of their standards. It is necessary to develop specific or complementary tools and diagnostic procedures differentiated by gender in order to control for this bias.
ChemNODE: A Neural Ordinary Differential Equations Approach for Chemical Kinetics Solvers
Opeoluwa Owoyele, Pinaki Pal
Subject: Mathematics & Computer Science, Algebra & Number Theory Keywords: neural ordinary differential equations; machine learning; chemical kinetics
The main bottleneck when performing computational fluid dynamics (CFD) simulations of combustion systems is the computation and integration of the highly non-linear and stiff chemical source terms. In recent times, machine learning has emerged as a promising tool to accelerate combustion chemistry, involving the use of regression models to predict the chemical source terms as functions of the thermochemical state of the system. However, combustion is a highly nonlinear phenomenon, and this often leads to divergence from the true solution when the neural network representation of chemical kinetics is integrated in time. This is because these approaches minimize the error during training without guaranteeing successful integration with ordinary differential equation (ODE) solvers. In this work, a novel neural ODE approach to combustion modeling, ChemNODE, is developed to address this issue. The source terms predicted by the neural network are integrated during training, and by backpropagating errors through the ODE solver, the neural network weights are adjusted accordingly to minimize the difference between the predicted and actual ODE solutions. It is shown that even when the dimensionality of the thermochemical manifold is trimmed to remove redundant species, the proposed approach accurately captures the correct physical behavior and reproduces the results obtained using the full chemical kinetic mechanism.
Effect of an Illegal Open Dump in an Urban Forest on Landscape Appreciation
Ernest Bielinis, Emilia Janeczko, Krzysztof Janeczko, Lidia Bielinis
Subject: Earth Sciences, Environmental Sciences Keywords: forestry; forests; restorativeness; semantic differential method; waste management
Rubbish in a forest environment is a great threat to this ecosystem, but this threat may also apply to the lost benefits for visitors to the forest. Previous studies proved that forest areas have a positive effect on obtaining psychological relaxation in the people visiting them. However, it was not known whether this restorative experience could be disturbed in any way by the presence of an open dump in the forest. To check how the presence of a landfill affects the visitors, an experiment was planned in which the respondents observed a forest area with a landfill and a forest landscape without a landfill for 15 minutes (control). The respondents then assessed the landscape using the semantic differential method and the Perceived Restorativeness Scale (PRS). An analysis of these observations showed that the presence of a landfill in the forest significantly changed the appreciation of the landscape by the respondents, the values of positive experiences decreased, and the negative experiences increased. Restorativeness was also reduced. Based on the results, it can be concluded that the presence of garbage in the forest may interrupt the restorative experience of its visitors.
A New Block Structural Index Reduction Approach for Large-scale Differential Algebraic Equations
Juan Tang, Yongsheng Rao
Subject: Mathematics & Computer Science, Computational Mathematics Keywords: differential algebraic equations; index reduction; block triangular forms
A new generation of universal tools and languages for modeling and simulation multi-physical domain applications emerged and became widely accepted, which generate large-scale systems of differential algebraic equations (DAEs) automatically. Motivated by the characteristics of DAEs systems with large dimension, high index or block structures, we first propose a modified Pantelides' algorithm (MPA) for any high order DAEs based on its Σ matrix, which is similar to Pryce's Σ method. By introducing a vital parameter vector, a modified Pantelides' algorithm with parameter has been presented.It leads to a block Pantelides' algorithm (BPA) naturally which can immediately compute the crucial canonical offsets for whole (coupled) systems with block-triangular form. We illustrate these algorithms by some examples. And numerical experiments show that the time complexity of BPA can be reduced by at least O(ℓ) compared to the MPA, which is mainly consistent with the results of our analysis.
Unusual Faces of Bladder Cancer
Claudia Manini, José I. López
Subject: Medicine & Pharmacology, Allergology Keywords: Bladder cancer; diagnosis; differential diagnosis; prognosis; histopathology; immunohistochemistry
The overwhelming majority of bladder cancers are transitional cell carcinomas. Albeit mostly monotonous, carcinomas in the bladder may occasionally display a broad spectrum of histological features that should be recognized by pathologists because some of them represent a diagnostic problem and/or lead prognostic implications. Sometimes these features are focal in the context of conventional transitional cell carcinomas, but some others are generalized across the tumor making its recognition a challenge. For practical purposes, the review distributes the morphologic spectrum of changes in architectural and cytological. So, nested and large nested, micropapillary, myxoid stroma, small tubules and adenoma nephrogenic-like, microcystic, verrucous, and diffuse lymphoepithelioma-like, on one hand, and plasmacytoid, signet ring, basaloid-squamous, yolk-sac, trophoblastic, rhabdoid, lipid/lipoblastic, giant, clear, eosinophilic (oncocytoid), and sarcomatoid, on the other, are revisited. Key histological and immunohistochemical features useful in the differential diagnosis are mentioned. In selected cases, molecular data associated with the diagnosis, prognosis, and/or treatment are also included.
Mathematical Model Describing HIV Infection with Time-Delayed CD4 T-Cell Activation
Hernán Darío Toro-Zapata, Carlos Andrés Trujillo-Salazar, Edwin Mauricio Carranza-Mayorga
Subject: Materials Science, Other Keywords: mathematical model; delay differential equations; HIV; immune system
A mathematical model, composed of two non-linear differential equations that describe the population dynamics of CD4 T cells in the human immune system, as well as viral HIV particles, is proposed. The invariance region is determined, classical equilibria stability analysis is performed using the basic reproduction number, and numerical simulations are carried out, in order to illustrate stability results. Later, the model is modified with a delay term, which describes the time that cells require for immunological activation. This generates a two-dimensional integro-differential system, which is transformed into a system with three ordinary differential equations, via auxiliary variable use. For the new model, equilibrium points are determined, their local stability is examined, and results are studied by way of numerical simulation.
A Topological Perspective for Interval Type-2 Fuzzy Hedges
Hime Oliveira
Subject: Mathematics & Computer Science, Artificial Intelligence & Robotics Keywords: type-2 fuzzy sets; fiber bundles; differential topology
Type-2 fuzzy sets were introduced by L. Zadeh aiming at modelling some settings in which fuzzy sets (usually called type-1 fuzzy sets) are not sufficient to reflect certain uncertainty degrees - loosely speaking, they are fuzzy sets whose membership degrees are ordinary fuzzy sets. On the other hand, fiber bundles are topological entities of extreme importance in Mathematics itself and many other scientific areas, like Physics (General Relativity, Field Theory etc.), finance modelling, and statistical inference. The present work introduces a conceptual link between the two ideas and conjectures about the potential mutual benefits that can be obtained from this viewpoint.As an objective and usable product of the presented ideas, it is described a framework for defining type-2 fuzzy hedges, proper to operate on interval type-2 fuzzy sets.
Finding Exact Forms on a Thermodynamic Manifold
Chao Ju, Mark Stalzer
Subject: Physical Sciences, Other Keywords: thermodynamics; entropy; artificial intelligence; differential geometry; computational physics
Because only two variables are needed to characterize a simple thermodynamic system in equilibrium, any such system is constrained on a 2D manifold. Of particular interest are the exact 1-forms on the cotangent space of that manifold, since the integral of exact 1-forms is path-independent, a crucial property satisfied by state variables such as internal energy dE and entropy dS. Our prior work [1] shows that given an appropriate language of vector calculus, a machine can re-discover the Maxwell equations and the incompressible Navier-Stokes equations from data. In this paper, We enhance this language by including differential forms and show that machines can re-discover the equation for entropy dS given data. Since entropy appears in various fields of science in different guises, a potential extension of this work is to use the machinery developed in this paper to let machines discover the expressions for entropy from data in fields other than classical thermodynamics.
A Generalized Fractional Power Series for Solving a Class of Nonlinear Fractional Integro-Differential Equation
Sirunya Thanompolkrang, Duangkamol Poltem
Subject: Mathematics & Computer Science, Applied Mathematics Keywords: fractional power series; integro-differential equations; conformable derivative
In this paper, we investigate an analytical solution of a class of nonlinear fractional integro-differential equation base on a generalized fractional power series expansion. The fractional derivatives are described in the conformable's type. The new approach is a modified form of the well-known Taylor series expansion. The illustrative examples are presented to demonstrate the accuracy and effectiveness of the proposed method
Kelly's Criterion in Portfolio Optimization: A Decoupled Problem
Zachariah Peterson
Subject: Mathematics & Computer Science, Applied Mathematics Keywords: portfolio optimization; Kelly criterion; differential evolution; mean-variance
Kelly's Criterion is well known among gamblers and investors as a method for maximizing the returns one would expect to observe over long periods of betting or investing. These ideas are conspicuously absent from portfolio optimization problems in the financial and automation literature. This paper will show how Kelly's Criterion can be incorporated into standard portfolio optimization models. The model developed here combines risk and return into a single objective function by incorporating a risk parameter. This model is then solved for a portfolio of 10 stocks from a major stock exchange using a differential evolution algorithm. Monte Carlo calculations are used to verify the accuracy of the results obtained from differential evolution. The results show that evolutionary algorithms can be successfully applied to solve a portfolio optimization problem where returns are calculated by applying Kelly's Criterion to each of the assets in the portfolio.
Culture of Cancer Cells at Physiological Oxygen Levels Affects Gene Expression in a Cell-Type Specific Manner
Ricardo Alva, Fereshteh Moradi, Ping Liang, Jeff Stuart
Subject: Life Sciences, Biochemistry Keywords: oxygen; physioxia; hyperoxia; cell culture; transcriptomics; differential gene expression
Standard cell culture is routinely performed at supraphysiological oxygen concentrations (~18% O2). Conversely, oxygen levels in most tissues range from 1%–6% (physioxia). Such hyperoxic conditions can alter reactive oxygen species (ROS) production, energy metabolism, mitochondrial network dynamics, and response to drugs and hormones. The aim of this project was to investigate the transcriptional response to different oxygen levels and whether it is similar across cell lines, or cell-line specific. Using RNA-seq, we performed differential gene expression and functional enrichment analyses in four human cancer cell lines, LNCaP, Huh-7, PC-3, and SH-SY5Y cultured at either 5% or 18% oxygen for 14 days. We found that oxygen levels affected transcript abundance of hundreds of genes, with the affected genes having little overlap between cell lines. Functional enrichment analysis also revealed different processes and pathways being affected in each cell line. Interestingly, we found that the top differentially expressed genes are involved in cancer biology. Further, we observed several hypoxia-inducible factor (HIF) targets upregulated at 5% oxygen, suggesting a role of HIF at physiological oxygen conditions. Finally, oxygen strongly induced transcription of mitochondrial genes in most cell lines, in a cell-type specific manner too. We conclude that cellular response to oxygen is widely cell-type specific, emphasizing the importance of maintaining physioxia in cell culture.
Recognizing and Distinguising the Phenomenon Referred to as Meningioma
Bruce M. Rothschild
Subject: Life Sciences, Other Keywords: meningioma; hemangioma; cranial pathology; porotic hyperostosis; differential diagnosis; osteosarcoma
Background: The reliability of a recent review of meningiomas in the archeologic record was difficult to assess, given the inverted sex ratio of the report and other contents apparently at variance with anatomical/medical findings in scientifically-identified cases. It therefore seemed appropriate to reexamine the nature of meningiomas and derive improve criteria for their recognition in the archeologic record and distinguish them from hemangiomas and bone marrow hyperplasia (recognized in the form of porotic hyperostosis). Methods: Medically-documented cases of meningiomas, hemangiomas and cranial bone marrow hyperplasia were examined to establish a macroscopic standard that distinguishing among them. Alleged cases in the archeologic record were examined for conformity with those criteria. Results: An en face pattern of uniform mesh with contained whorls appears pathognomonic for meningiomas. This contrasts with the non-uniform marrow expansion displacement of trabeculae in porotic hyperostosis and non-uniform vascular displacement of trabeculae in hemangiomas. Reassessment of past attributions revealed few cases of meningiomas that could be confidently diagnosed. Those identified has sex ratios parsimonious with medical literature reports. Conclusions: Criteria suggested for identifying meningiomas permits distinguishing from hemangiomas, bone marrow hyperplasia (porotic hyperostosis) and from the macroscopically-observable surface spicules characteristic of osteosarcomas. Examination for fulfillment of criteria for meningiomas and hemangiomas seems to provide a picture (including sex ratios) more parsimonious with the clinical literature, concluding that Cook and Danforth's disparate ratios were related to less fastidious case selection. Additionally, confidence in recognizing porotic hyperostosis may be compromised because of apparent similar macroscopic alterations to those seen with hemangiomas.
The Real Cause of Differential Aging in the Twin "paradox"
Subject: Physical Sciences, General & Theoretical Physics Keywords: Twin paradox; Relativity; Space-time; Time dilation; Differential aging
Physicists have employed various approaches to solve the "paradox" and offered a consistent conclusion that the traveller twin is younger than the homebody twin. However, some authors attribute the cause of differential aging to acceleration, while others believe that acceleration should not be regarded as the source of differential aging, but frame switch is. So far there is no agreement on this issue. Actually, acceleration and frame switch should not be regarded as the source of differential aging. The author will introduce a thought experiment in which two very long spacecraft are moving in opposite directions at a speed close to the speed of light to discuss the real cause of differential aging. The author found that the real cause of differential aging in the twin "paradox" is because of the asymmetry of destination choice. People always choose their destinations in the universe rather than in spacecraft. The destinations are always stationary relative to the homebody twin and moving relative to the traveller twin. Once we choose a destination in a reference frame, the distance is the proper length in this reference frame, but the distance will contract in another moving reference frame, thus the recording time will be shorter.
The System of Differential Equations Associated With Involutions
Farrukh Nuriddin ugli Dekhkonov
Subject: Mathematics & Computer Science, General Mathematics Keywords: Involution; linear differential equation; fixed point; boundary value problem
In this paper, we consider with a class of system of differential equations whose argument transforms are involution. In this an initial value problem for a differential equation with involution is reduced to an initial value problem for a higher order ordinary differential equation. Than either two initial conditions are necessary for a solution, the equation is then reduced to a boundary value problem for a higher order ODE.
ANNs-Based Method for Solving Partial Differential Equations : A Survey
Danang Adi Pratama, Maharani Abu Bakar, Mustafa Man, M. Mashuri
Subject: Mathematics & Computer Science, Algebra & Number Theory Keywords: artificial neural networks; discretization; machine learning; partial differential equations
Conventionally, partial differential equations (PDE) problems are solved numerically through discretization process by using finite difference approximations. The algebraic systems generated by this process are then finalized by using an iterative method. Recently, scientists invented a short cut approach, without discretization process, to solve the PDE problems, namely by using machine learning (ML). This is potential to make scientific machine learning as a new sub-field of research. Thus, given the interest in developing ML for solving PDEs, it makes an abundance of an easy-to-use methods that allows researchers to quickly set up and solve problems. In this review paper, we discussed at least three methods for solving high dimensional of PDEs, namely PyDEns, NeuroDiffEq, and Nangs, which are all based on artificial neural networks (ANNs). ANN is one of the methods under ML which proven to be a universal estimator function. Comparison of numerical results presented in solving the classical PDEs such as heat, wave, and Poisson equations, to look at the accuracy and efficiency of the methods. The results showed that the NeuroDiffEq and Nangs algorithms performed better to solve higher dimensional of PDEs than the PyDEns.
Glassy Carbon Electrode Modified by Molybdenum to Detection Hydrochlorothiazide
Ahmad Khalaf Alkhawaldeh, Rawia Alkhawaldeh
Subject: Chemistry, Analytical Chemistry Keywords: Hydrochlorothiazide; Differential pulse voltammograms; Cyclic Voltammetry; Molybdenum; Modified electrode
Molybdenum oxides is well-known electro-catalysts in fuel cells systems, they are usually used as anodic materials for the oxidation of low molecular weight alcohols. The utilization of Mo as catalysts in the pharmaceutical analysis is not common yet. In this study, bare glassy carbon electrodes were modified by the oxides by means of electrochemical deposition and the modified electrodes were used as catalysts for the electrochemical oxidation of hydrochlorothiazide (HCT). Well-resolved anodic peaks were reported for the analyzed pharmaceuticals when the Mo/GCE was utilized for the analysis of HCT. Analytical performance of the modified electrodes was evaluated based on the following statistical parameters; linearity ranges, correlation coefficients, limits of detection and quantitation, and recovery values. The prepared electrodes were used for the determination of the active ingredients in their pharmaceutical formulations and the reported activity was correlated to influence of the utilized pH on both structures of the used electrodes and the detected analytes.
Mathematical Model for Secondary Transport of Cations at the Root of Plants
Byunghyun Ban
Subject: Biology, Agricultural Sciences & Agronomy Keywords: aquaculture; computational biology; differential equation; ion transport; systems biology
A mathematical expression to describe cation absorption of root is expressed with simulation results. The root cells selectively emit H+ ions with active transport consuming ATPs to establish electrical gradient. The gradient promotes external positive ions to flow into the roots, while carries negatively charged particles with symport. In this paper, a mathematical model whose independent variables are the concentrations of external and internal cation is presented. This differential equation is induced from Ohm's law. The equation has terms for plant physiology, ion's physical and electrical properties, growth of plant, and interaction between the root and the surroundings. Simulation showed that the physiology-related coefficient has important role on nutrition absorption.
Conformable Laplace Transform of Fractional Differential Equations
Fernando S. Silva, Davidson M. Moreira, Marcelo A. Moret
Subject: Mathematics & Computer Science, Applied Mathematics Keywords: fractional differential equations; conformable derivative; Bernoulli equation; exact solution
In this paper we use the conformable fractional derivative to discuss some fractional linear differential equations with constant coefficients. By applying some similar arguments to the theory of ordinary differential equations, we establish a sufficient condition to guarantee the reliability of solving constant coefficient fractional differential equations by the conformable Laplace transform method. Finally, we analyze the analytical solution for a class of fractional models associated with Logistic model, Von Foerster model and Bertalanffy model is presented graphically for various fractional orders and solution of corresponding classical model is recovered as a particular case.
On Boundary Layer Expansions for a Singularly Perturbed Problem with Confluent Fuchsian Singularities
Subject: Mathematics & Computer Science, Analysis Keywords: asymptotic expansion; Borel-Laplace transform; Fourier transform; initial value problem; formal power series; linear integro-differential equation; partial differential equation; singular perturbation
We consider a family of nonlinear singularly perturbed PDEs whose coefficients involve a logarithmic dependence in time with confluent Fuchsian singularities that unfold an irregular singularity at the origin and rely on a single perturbation parameter. We exhibit two distinguished finite sets of holomorphic solutions, so-called outer and inner solutions, by means of a Laplace transform with special kernel and Fourier integral. We analyze the asymptotic expansions of these solutions relatively to the perturbation parameter and show that they are (at most) of Gevrey order 1 for the first set of solutions and of some Gevrey order that hinges on the unfolding of the irregular singularity for the second.
Completeness of Bethe Ansatz for Gaudin Models with gl(1|1) Symmetry and Diagonal Twists
Kang Lu
Subject: Physical Sciences, Mathematical Physics Keywords: Gaudin models; Lie superalgebras; Bethe ansatz; Pseudo-differential operators; Berezinian
We study the Gaudin models with gl(1|1) symmetry that are twisted by a diagonal matrix and defined on tensor products of polynomial evaluation gl(1|1)[t]-modules, extending all the results of to the twisted case. Namely, we give an explicit description of the algebra of Hamiltonians (Gaudin Hamiltonians) acting on tensor products of polynomial evaluation gl(1|1)[t]-modules and show that there exists a bijection between common eigenvectors (up to proportionality) of the algebra of Hamiltonians and monic divisors of an explicit polynomial written in terms of the highest weights and evaluation parameters. In particular, our result implies that each common eigenspace of the algebra of Hamiltonians has dimension one. We also give dimensions of the generalized eigenspaces.
Inferring Bona Fide Differentially Expressed Genes and Their Variants Associated With Vitamin K Deficiency Using Systems Genetics Approach
Shalini Rajagopal, Akanksha Sharma, Anita Simlot, Praveen Mathur, Sumita Mehta, Sudhir Mehta, Jalaja Naravula, Krishna Mohan Medicherla, Anil Kumar, Uma Kanga, Renuka Suravajhala, Ramji Bhandari, Bipin Nair, Kavi Kishor PB, Prashanth Suravajhala
Subject: Life Sciences, Genetics Keywords: RNA-Seq; Vitamin K; Comorbidities; Differential Expressed Genes; Variant analysis
Systems genetics is key for integrating a large number of variants associated with diseases. Vitamin K (VK) is one of the scarcely studied conditions in lieu of ascertaining either the differentially expressed genes (DEGs) or variants in an individual subpopulation of diseased phenotypes associated with VK, viz. myocardial infarction, renal failure, prostate cancer, thrombosis, thrombocytopenia, coagulation related diseases to name a few. In this work, we have screened characteristic DEGs common to three VK-related diseases, viz. myocardial infarction, renal failure and prostate cancer and asked whether or not any DEGs in addition to pathogenic variants are common to these conditions. We attempt to bridge the gap in finding characteristic biomarkers and discuss the role of long noncoding RNAs (lncRNAs) in the biogenesis of VK deficiencies.
An Integrative Analysis Identified Schizophrenia-Associated Brain Cell Types and Gene Expression Changes
Wenxiang Cai, Weichen Song, Zhe Liu, Dhruba Tara Maharjan, Jisheng Liang, Guan Ning Lin
Subject: Medicine & Pharmacology, Psychiatry & Mental Health Studies Keywords: Schizophrenia; cell types proportions; differential expression genes; functional pathways; CIBERSORTx
Schizophrenia (SCZ) is a severe mental disorder that may result in hallucinations, delusions, and extremely disordered thinking. How each cell type in the brain contributes to SCZ occurrence is still unclear. Here, we leveraged the human dorsolateral prefrontal cortex bulk RNA-seq data, then used the RNA-seq deconvolution algorithm CIBERSORTx to generate SCZ brain single-cell RNA-seq data for a comprehensive analysis to understand SCZ-associated brain cell types and gene expression changes. Firstly, we observed that the proportions of brain cell types in SCZ differed from normal samples. Among these cell types, astrocyte, pericyte, and PAX6 cells were found to have a higher proportion in SCZ patients (astrocyte: SCZ = 0.163, Control = 0.145, P.adj = 4.9×10-4; pericyte: SCZ = 0.057, Control = 0.066, P.adj = 1.1×10-4; PAX6 : SCZ = 0.014, Control = 0.011, P.adj = 0.014), while the L5/6_IT_CAR3 cells and LAMP5 cells are the exact opposite (L5/6_IT_Car3 : SCZ = 0.102, Control = 0.108, P.adj = 0.016; LAMP5 : SCZ = 0.057, Control = 0.066, P.adj = 2.2×10-6). Next, we investigated gene expression in cell types and functional pathways in SCZ. We observed chemical synaptic transmission dysregulation in two types of GABAergic neurons (PVALB and LAMP5), and immune reaction involvement in GABAergic neurons (SST) and non-neuronal cell types (endothelial and oligodendrocyte). Furthermore, we observed that some differential expression genes from bulk RNA-seq displayed cell-type-specific abnormal in the expression of molecules in SCZ. Finally, the cell types with the SCZ-related transcriptomic changes could be considered to belong to the same module since we observed two major similar coordinated transcriptomic changes across these cell types. Together, our results offer novel insights into cellular heterogeneity and the molecular mechanisms underlying SCZ.
A Comparative Study of Three Mathematical Models for the Interaction between the Human Immune System and a Virus
Florian Munteanu
Subject: Mathematics & Computer Science, Applied Mathematics Keywords: mathematical models; systems of ordinary differential equations; dynamical systems; stability
In this paper it will be considered three deterministic models for the study of the interaction between the human immune system and a virus: the logistic model, the Gompertz model, and the generalized logistic model (or Richards model). A qualitative analysis of this models based on dynamical systems theory will be performed, by studying the local behavior of the equilibria and obtaining local dynamics properties from the linear stability point of view. Also, we will compare this models in order to understanding which is more appropriate to models the interaction between the human immune system and a virus. It will be obtained some natural medical interpretations which are available for all three models and can be useful to the medical community.
SIR-Solution for Slowly Time-Dependent Ratio between Recovery and Infection Rates
Martin Kröger, Reinhard Schlickeiser
Subject: Physical Sciences, Mathematical Physics Keywords: epidemiology; statistical analysis; time-scale separation; differential equations; adiabatic approximation
The temporal evolution of pandemics described by the susceptible-infectious-recovered (SIR)-compartment model is sensitively determined by the time dependence of the infection (a(t)) and recovery (u(t)) rates regulating the transitions from the susceptible to the infected and from the infected to the recovered compartment, respectively. Here approximated SIR-solutions for different time dependencies of the infection and recovery rates are derived which are based on the adiabatic approximation assuming time-dependent ratios k(t)=u(t)/a(t) varying slowly in comparison to the typical time characteristics of the pandemic wave. For such slow variations the available analytical approximations from the KSSIR-model, valid for a stationary value of the ratio k, are used to insert a-posteriori the adopted time-dependent ratio of the two rates. Instead of investigating endless different combinations of the time dependencies of the two rates a(t) and u(t) a suitably parameterized reduced time dependence of the ratio k(tau) is adopted. Together with the definition of the reduced time this parameterized ratio k(tau) allows us to cover a great variety of different time dependencies of the infection and recovery rates. The agreement between the solutions from the adiabatic approximation in its four different studied variants and the exact numerical solutions of the SIR-equations is remarkably good providing strong confidence in the accuracy of the proposed adiabatic approximation.
Tandem Recurrence Relations for Coefficients of Logarithmic Frobenius Series Solutions about Regular Singular Points
Ramses Van Der Toorn
Subject: Mathematics & Computer Science, General Mathematics Keywords: ordinary differential equations; Frobenius method; tandem recurrence relations; Bessel's equation
We enhance Frobenius' method for solving linear ordinary differential equations about regular singular points. Key to Frobenius' approach is the exploration of the derivative with respect to a single parameter; this parameter is introduced through the powers of generalized power series. Extending this approach, we discover that tandem recurrence relations can be derived. These relations render coefficients for series occurring in logarithmic solutions. The method applies to the, practically important, exceptional cases in which the roots of the indicial equation are equal, or differ by a non-zero integer. We demonstrate the method on Bessel's equation and derive previously unknown tandem recurrence relations for coefficients of solutions of the second kind, for Bessel equations of all integer and half-integer order.
Delta Fractional Sturm--Liouville Problems: From Discrete to Continuous
Ramazan Ozarslan, Erdal Bas
Subject: Mathematics & Computer Science, Algebra & Number Theory Keywords: Delta fractional equations; Fractional differential equations; Sturm--Liouville; Eigenfunctions; Eigenvalues
In this study, we consider delta fractional Sturm--Liouville (DFSL) initial value problems in the sense of delta Caputo and delta Riemann-Liouville (R--L) operators. One of the properties of delta fractional difference operators which makes it different from nabla counterpart is to shift its domain. This feature makes it more complex than the nabla fractional operator. We obtain sum representation of solutions for DFSL initial value problems with the help of $\mathcal{Z}-$ transformation. Moreover, we get analytical solutions of homogeneous DFSL problem within Riemann-Liouville (R--L) and Caputo sense, discrete Sturm--Liouville (DSL) problem, continuous fractional Sturm--Liouville (FSL) problem in the sense of R--L and Caputo operators, and continuous Sturm--Liouville (SL) differential problem. From this point of view, we compare all the solutions with each other. Consequently, we show that all results for these four eigenvalue problems are compatible with each other and approach to each other while the orders tends to one, i.e. $\Delta^{\mu }\left( \Delta x\left( t-\mu \right) \right)\cong D_{0^{+}}^{\mu }\left( x^{\prime }\left( t\right) \right)\cong \Delta^2x(n-1) \cong x^{\prime \prime }\left( t\right) =\lambda x\left( t\right),\ \mu\rightarrow1 $ . We support our results comparatively by tables and simulations in detail.
Biofilm Early Stages of Growth and Accumulation Theoretical Model
José Carvalho, Manuel Carrondo, Luis Bonilla
Subject: Engineering, Automotive Engineering Keywords: biofilm; Miller recurrent algorithm; Bessel functions; differential-difference master equations
A theoretical model to translate the evolution over time, in early stages, of growth and accumulation of biofilm bacterial mass is introduced. The model implies the solution of a system of differential-difference master equations. The application of an algorithm like Miller´s tree term recurrence, already known for Bessel functions of first kind, allows an exact calculation of the solutions of such equations, for a wide range of parameters values and time. For biofilm model a five term recurrence is deduced and applied in a backwards computation. A suitable normalisation condition completes the reach of the solution.
Hamiltonian form for General Autonomous ODE Systems: Introductory Results
Artur Kobus
Subject: Physical Sciences, Acoustics Keywords: classical dynamics; conservation laws; ordinary differential equations; phase-space geometry
New class of conserved quantities is constructed. These quantities find direct application in mechanics of dissipative (generally non-conservative) dynamical systems. Approach demands formulation in the language of geometric mechanics, providing theoretical framework for situations with energy flow in and out of the system. As a by product, we suggest possibility of existence of Hamiltonian form for every autonomous ODE system, evolution of which is governed by non-potential generator of motion. Various examples are provided, ranging from physics and mathematics, to chemical kinetics and population dynamics in biology. Applications of these ideas in geometric integration techniques (GNI) of numerical analysis are discussed, and as an example of such, new discrete gradient-based numerical method is introduced.
Infeasibility and Structural Bias in Differential Evolution
Fabio Caraffini, Anna Kononova, David Corne
Subject: Mathematics & Computer Science, Numerical Analysis & Optimization Keywords: structural bias, algorithmic design, differential evolution, population-based algorithms, optimisation
This paper investigates a range of popular differential evolution (DE) configurations to identify components responsible for emergence of structural bias – a recently identified tendency of algorithms to prefer some regions of search space over others, for reasons unrelated to objective function values. Previous work has explored this tendency for genetic algorithms (GA) and particle swarm optimisation (PSO), finding a relationship between population size and extent of structural bias, hence highlighting potential weaknesses of those algorithms. In current article, we focus on DE, extend the investigation to include consideration of an algorithmic component that is often overlooked – constraint handling mechanism. Towards this end, a wide range of DE configurations was tested here. Results suggest that DE is generally robust to structural bias. Unlike the case with GA and PSO, population size seems to have no influence on DE structural bias. Only one of variants studied – DE/current-to-best/1/bin – shows clear signs of bias, however, we show that this effect is mitigated by a judicious choice of constraint handling technique. These findings contribute towards explaining widespread success of DE variants in algorithm comparison studies; its robustness to structural bias represents the absence of a factor that may confound other algorithms.
Research of Power Control for Grid-connected Wind Turbine with Differential Speed Regulation
Su Rui, Zhang Huan, Wang Fujun, Li Gangjun
Subject: Engineering, Industrial & Manufacturing Engineering Keywords: Grid-connected wind turbine; Differential speed regulation; Power control; Simulation
The differential gear train and speed regulating motor constitute the variable ratio transmission for grid-connected wind turbine with differential speed regulation. The synchronous generator in the system can accessing the power grid without frequency converter. The transmission can realize the mode of variable speed constant frequency that the wind rotor speed is varying and the generator rotor speed is constant. The power control method is studied under the different wind speed which is lower or higher than rated wind speed with using the relational expression of utilization rate of wind energy Cp, pitch angle β and the tip speed ratio λ. The SIMULINK software is used to build the 1500 kW wind turbine model with differential speed regulation. Some different wind speed is made as input. The feasibility of power control method for grid-connected wind turbine with differential speed regulation is verified by the comparison between the simulation results and the theoretical value of the key parameters.
Mixed of Elzaki Transform and Projected Differential Transform Method for a Nonlinear Wave-Like Equations with Variable Coefficients
Ali Khalouta, Abdelouahab Kadem
Subject: Mathematics & Computer Science, Applied Mathematics Keywords: nonlinear wave-like equations; Elzaki transform; projected differential transform method
In this work, a mixture of Elzaki transform and projected differential transform method is applied to solve a nonlinear wave-like equations with variable coefficients. Nonlinear terms can be easily manipulated by using the projected differential transformation method. The method gives the results show that the proposed method is very efficient, simple and can be applied to other applications.
A Study of Second Order Impulsive Neutral Evolution Differential Control Systems with an Infinite Delay
P. Palani, T. Gunasekar, M. Angayarkanni, D. Kesavan
Subject: Mathematics & Computer Science, Applied Mathematics Keywords: nonlinear ordinary differential operators; impulsive optimal control problems; evolution equations
This article, we study the sufficient conditions for the controllability of second-order impulsive partial neutral evolution differential systems with infinite delay in Banach spaces by using the theory of cosine families of bounded linear operators and fixed point theorem.
Arsenate-Resistant Genes in Egyptian Rice Cultivars as Soil Pollution Sensors
Elsayed Hafez, Ebtesam A. El. Bestawy, Mohamed A. Rashad, Sayed Hassan
Subject: Biology, Plant Sciences Keywords: arsenic pollution; differential display; genes; resistance; rice crop; soil contamination
The main objective of the present study was to investigate arsenate [As (V)] resistance genes in rice cultivars grown in arsenic contaminated Egyptian soil in order to genetically induce resistance against arsenic in the local rice varieties as well as defining contaminated rice grains and/or soil. Three local rice cultivars; Sakha 102-104 were cultivated on modified Murashige and Skoog Basal Medium (MS medium) containing elevated concentrations of arsenate (0.1, 1 and 10 mg/l). The three varieties showed different resistant attitudes against arsenate with Sakha 104 being the most resistant. Extracted messenger RNA (mRNA) from treated and untreated Sakha 104 plantlets was scanned using differential display to demonstrate the arsenate resistant genes using three different arbitrary primers. About 100 different RNAs with (1500 bp - 50 bp) were obtained from which seven were up-regulated genes, subjected to DNA cloning using TOPO TA system and the selected clones were sequenced. The sequence analysis described four genes out of the seven namely disease resistance protein RPM1, Epstein-Barr virus EBNA-1-like, CwfJ family protein and outer membrane lipoprotein OmlA while the other three genes were hypothetical proteins. It is concluded the four induced genes in the resistant rice cultivar considered as a direct response to arsenic soil pollution. Genes detected in the present study can be used as geno-sensors for rice grains and soil contamination with As (V). Moreover, local rice cultivars may be genetically modified with such genes to induce high resistance and to overcome arsenic soil pollution.
Notes on a Family of Inhomogeneous Linear Ordinary Differential Equations
Feng Qi, Jing-Lin Wang, Bai-Ni Guo
Subject: Mathematics & Computer Science, Analysis Keywords: simple form; explicit form; differential equation; Lerch transcendent; logarithmic function
In the note, the authors find several simple and explicit forms for a family of inhomogeneous linear ordinary differential equations studied in "D. Lim, Differential equations for Daehee polynomials and their applications, J. Nonlinear Sci. Appl. 10 (2017), no. 4, 1303-1315; Available online at http://dx.doi.org/10.22436/jnsa.010.04.02".
Lobatto-Milstein Numerical Method in Application of Uncertainty Investment of Solar Power Projects
Mahmoud A. Eissa, Boping Tian
Subject: Mathematics & Computer Science, Applied Mathematics Keywords: stochastic differential equation; numerical simulation; real option; renewable energy; Egypt
Recently, there has been a growing interest in the production of electricity from renewable energy sources (RES). The RES investment is characterized by uncertainty, which is long-term, costly, depend on feed-in-tariff and support schemes. In this paper, we address the real option valuation (ROV) of a solar power plant investment. The real option framework is investigated. This framework considers the renewable certificate price, furthermore the cost of delay between establishing and operating the solar power plant. The optimal time of launching the project and assess the value of deferred option are discussed. The new three stage numerical methods are constructed, the Lobatto3C-Milstein (L3CM) methods. The numerical methods are integrated with concept of Black-Scholes option pricing theory, and applied in option valuation for solar energy investment with uncertainty. The numerical results of L3CM, finite difference and Monte Carlo methods are compared to show the efficiency of our methods. Our data set refers to the Arab Republic of Egypt.
Local Polynomial Smoother for Solving Bagley-Torvik Fractional Differential Equations
Tianshun Yan, Shuanghua Luo
Subject: Mathematics & Computer Science, Computational Mathematics Keywords: numerical solution; Bagley-Torvik fractional differential equations; local polynomial smoother
Local polynomial smoother (LPS) is a weighted local least-squares nonparametric method. It provides a local Taylor series fit of the data at any location and can be directly used in a differential equation to provide a numerical scheme. In this article, we introduce this new nonparametric idea based on local polynomial smoother, for acquiring the numerical solution of the Bagley-Torvik fractional-order differential equations. Furthermore, this paper will present a numerical comparison with some methods, such as legendre operational matrix and pseudo-spectral method. The efficiency and accuracy of the LPS method are demonstrated by two numerical examples.
Mean-Field Type Games between Two Players Driven by Backward Stochastic Differential Equations
Alexander Aurell
Subject: Mathematics & Computer Science, Numerical Analysis & Optimization Keywords: mean-field type game; non-zero-sum differential game; cooperative game; backward stochastic differential equations; linear-quadratic stochastic control; social cost; price of anarchy
In this paper, mean-field type games between two players with backward stochastic dynamics are defined and studied. They make up a class of non-zero-sum differential games where the players' state dynamics solve backward stochastic differential equations (BSDEs) that depend on the marginal distributions of player states. Players try to minimize their individual cost functionals, also depending on the marginal state distributions. Under some regularity conditions, we derive necessary and sufficient conditions for existence of Nash equilibria. Player behavior is illustrated by numerical examples, and is compared to a centrally planned solution where the social cost, the sum of player costs, is minimized. The inefficiency of a Nash equilibrium, compared to socially optimal behavior, is quantified by the so-called price of anarchy. Numerical simulations of the price of anarchy indicate how the improvement in social cost achievable by a central planner depends on problem parameters.
Recognition of Micro-Expressions using the Spatiotemporal Capsule Network
Muhammad Mugees Asif, Sana Asif, Rabia Hussain, Imtnan Khalid
Subject: Mathematics & Computer Science, Artificial Intelligence & Robotics Keywords: Capsule network; differential features; deep learning; micro-expression recognition; spatiotemporal features
Micro-expression (ME) is one of the key psychological stress reactions. It is a modest, spontaneous facial mechanism. ME has significant applicability in a variety of psychologically-related sectors because to its precision and unpredictability with regard to psychological manifestations. Nevertheless, the current Micro-expression recognition (MER) algorithms have poor accuracy and a limited quantity of ME data, and this study issue has not been thoroughly investigated. Therefore, we present an approach for deep learning based on a Spatio-temporal capsule network (STCP-Net). STCP-Net has four components: a jitter reduction module, a differential feature extraction module, an STCP module, and a fully linked layer. The first two modules are aimed to extract diversifying differential features more precisely and to limit the influence of head jitter. The STCP module is used to extract Spatio-temporal features layer by layer, taking the temporal and geographical connection between features into account. This research runs sufficient trials using the Leave One Subject Out (LOSO) methodology for cross-validation using the CASMEII dataset. The conclusion and analysis demonstrate that the algorithm is innovative and efficient.
A Reliability-Enhanced Differential Sensing Amplifier for Hybrid CMOS/MTJ Logic Circuits
Chengzhi Wang, Huiquan Wang, Dognsheng Wang, Jian Fang, Lu Wang, Guangda Zhang
Subject: Engineering, Electrical & Electronic Engineering Keywords: hybrid logic circuits; magnetic tunnel junction; differential sensing amplifier; sensing margin
Recently, hybrid logic circuits based on magnetic tunnel junctions (MTJs) have been widely investigated to realize zero standby power. However, such hybrid CMOS/MTJ logic circuits suffer from a severe sensing reliability due to the limited tunnel magnetoresistance ratio (TMR≤150%) of the MTJ and the large process variation in the deep sub-micrometer technology node. In this paper, a novel differential sensing amplifier (DSA) is proposed, in which two PMOS transistors are added to connect the discharging branches and evaluation branches. Owing to the positive feedback realized by these two added PMOS transistors, it can achieve a large sensing margin. By using an industrial CMOS 40 nm design kit and a physics-based MTJ compact model, hybrid CMOS/MTJ simulations have been performed to demonstrate its functionality and evaluate its performance. Simulation results show that it can achieve a smaller sensing error rate of 9% in comparison with the previously proposed DSAs with the TMR ratio of 100% and process variation of 10%, while maintaining almost the same sensing delay of 74.5 ps and sensing energy of 1.92 fJ/bit.
On the Operator Method for Solving Linear Integro-Differential Equations with Fractional Conformable Derivatives
Batirkhan kh. Turmetov, Kairat I. Usmanov, Kulzina Zh. Nazarova
Subject: Mathematics & Computer Science, Algebra & Number Theory Keywords: integro-differential equation; fractional derivatives; fractional conformable derivatives; normalized systems method.
The methods for constructing solutions to integro-differential equations of the Volterra type are considered. The equations are related to fractional conformable derivatives. Explicit solutions of homogeneous and inhomogeneous equations are constructed and a Cauchy-type problem is studied. It should be noted that the considered method is based on the construction of normalized systems of functions with respect to a differential operator of fractional order.
On a Coupled System of Random and Stochastic Differential Equations with Nonlocal Stochastic Integral Conditions
A. M. A. El-Sayed, Hoda A. Foued
Subject: Mathematics & Computer Science, Algebra & Number Theory Keywords: Stochastic processes; stochastic differential equation; coupled system; nonlocal stochastic integral conditions.
Here we are concerning with two problems of a coupled system of random and stochastic nonlinear differential equations with two coupled systems of nonlinear nonlocal random and stochastic integral conditions. The existence of solutions will be studied. The sufficient condition for the uniqueness of the solution will be given. The continuous dependence of the unique solution on the nonlocal conditions will be proved.
The Mapping of the Main Functions and Different Variations of YH-DIE
Gilbert Mason, Yuanjue Chou, Springer Pind
Subject: Mathematics & Computer Science, Analysis Keywords: complete Riemannian manifolds; entire solutions; minimal graphs; differential equat; algebraic variety
YH-DIE must have continuity . Given the basic algebraic clusters of homogeneous configurations,we can get the basic three equations: \begin{array}{l} {\mathop{\int}\nolimits_{0}\nolimits^{{x}_{i}}{\frac{{G}\left({{x}_{i}\mathrm{,}s}\right)}{{\left({{x}_{i}\mathrm{{-}}{s}}\right)}^{\mathit{\alpha}}}\mathrm{\varphi}\left({s}\right){ds}}\mathrm{{=}}{f}\left({{x}_{i}}\right)}\ ;\ {\frac{\mathrm{\partial}}{\mathrm{\partial}{x}_{i}}\left({\frac{{\mathrm{\partial}}_{{x}_{i}}G}{\sqrt{{1}\mathrm{{+}}{\left|{\mathrm{\nabla}{G}}\right|}^{2}}}}\right)\mathrm{{=}}{0}}\ ;\ {{i}\mathrm{{=}}\mathop{\sum}\limits_{{x}_{i}\mathrm{{=}}{1}}\limits^{\mathrm{\infty}}{\arccos\hspace{0.33em}\mathrm{\varphi}\left({{x}_{i}}\right)}\mathrm{{=}}{f}\left({\fbox{${Yuh}$}}\right)} \end{array} YH-DIE has become a fusion point and access point in the fields of algebraic geometry and partial differential equations, and its mapping on multidimensional algebraic clusters or manifolds is very special. The minimal surface equation is a special case.
Solution of Volterra's Integro-Differential Equations by Using Variational Iteration Method
Abdulla - Al - Mamun, Weidong Tao, Md. Asaduzzaman
Subject: Mathematics & Computer Science, Computational Mathematics Keywords: Variational iteration method, Integro-differential equation, Lagrange multiplier, Homotopy perturbation method.
In this paper, we introduce some basic idea of Variational iteration method for short (VIM) to solve the Volterra's integro-differential equations. The VIM is used to solve effectively, easily, and accurately a large class of non-linear problems with approximations which converge rapidly to accurate solutions. For linear problems, it's exact solution can be obtained by only one iteration step due to the fact that the Lagrange multiplier can be exactly identified. It is to be noted that the Lagrange multiplier reduces the iteration on integral operator and also minimizes the computational time. The method requires no transformation or linearization of any forms. Two numerical examples are presented to show the effectiveness and efficiency of the method. Also, we compare the result with the result from Homotopy perturbation method (HPM). Finally, we investigate the absolute difference between variational iteration method and homotopy perturbation method and draw the graph of difference function by using Mathematica.
Growth of the Entire or Meromorphic Solutions of Differential-Difference Equations
Rajshree Dhar
Subject: Keywords: entire and meromorphic functions; differential-difference polynomial; shared value; Nevanlinna theory
In this paper, we study the entire or meromorphic solutions for differential-difference equations in f(z) , its shifts, its derivatives and derivatives of its shifts. and study some Hayman's results for differential-difference polynomials.
Normal Calculus on Moving Surfaces
Keith C. Afas
Subject: Mathematics & Computer Science, General Mathematics Keywords: calculus of moving surfaces; CMS; differential geometry; normal; tensor; hypersurfaces; dynamic
This paper presents an extension for principles of Differential Geometry on Surfaces (re-hashed through the budding field of CMS, the Calculus of Moving Surfaces). It analyzes mostly 2D Hypersurfaces with Riemannian Geometry and proposes the construction of a 3D Static Frame combining the Surface Basis Vectors with the Orthogonal Normal Field as a 3D Orthogonal Vector Frame. The paper introduces conventions for manipulating Tensors defined using this 3D Orthogonal Vector Frame as well as Curvature Connections associated with this Vector Frame. It then finally introduces Symbols and Tensors to describe Inner Products and Variance within the 3D Vector Frame and then extends all the above concepts to a surface which is Dynamic utilizing principles from CMS. This formulation has potential to extend identities and concepts from CMS and from Differential Geometry in a compact Tensorial Framework, which agrees with the new Framework proposed by CMS.
Tumbling-Snake Model for Polymeric Liquids Subjected to Biaxial Elongational Flows with a Focus on Planar Elongation
Pavlos S. Stephanou, Martin Kröger
Subject: Engineering, Other Keywords: polymer melt; stochastic differential equation; link tension coefficient; entanglements; biaxial flow
We have recently solved the tumbling-snake model for concentrated polymer solutions and entangled melts in the presence of both steady-state and transient shear and uniaxial elongational flows, supplemented by a variable link tension coefficient. Here, we provide the transient and stationary solutions of the tumbling-snake model under biaxial elongation both analytically, for small and large elongation rates, and via Brownian dynamics simulations, for the case of planar elongational flow over a wide range of rates, times, and the model parameters. We show that both the steady-state and transient first planar viscosity predictions are similar to their uniaxial counterparts, in accord with recent experimental data. The second planar viscosity seems to behave in all aspects similarly to the shear viscosity, if shear rate is replaced by elongation rate.
On the Analysis of Mixed-Index Time Fractional Differential Equation Systems
Kevin Burrage, Pamela Burrage, Ian Turner, Fanhai Zeng
Subject: Mathematics & Computer Science, Computational Mathematics Keywords: time fractional differential equations; mixed-index problems; analytical solutions; asymptotic stability
In this paper we study the class of mixed-index time fractional differential equations in which different components of the problem have different time fractional derivatives on the left hand side. We prove a theorem on the solution of the linear system of equations, which collapses to the well-known Mittag-Leffler solution in the case the indices are the same, and also generalises the solution of the so-called linear sequential class of time fractional problems. We also investigate the asymptotic stability properties of this class of problems using Laplace transforms and show how Laplace transforms can be used to write solutions as linear combinations of generalisedMittag-Leffler functions in some cases. Finally we illustrate our results with some numerical simulations.
Cuprous Oxide Thin Film Non-Enzymatic Glucose Sensor Using Differential Pulse Voltammetry (DPV) and Other Voltammetry Methods and Comparing to Different Thin Film Electrodes on the Detection of Glucose in an Alkaline Solution
Yifan Dai, Alireza Molazemhosseini, Kevin Abbasi, Chung Chiun Liu
Subject: Engineering, Biomedical & Chemical Engineering Keywords: cuprous oxide; non-enzymatic glucose sensor; alkaline solution; differential pulse voltammetry
A cuprous oxide (Cu2O) thin layer served as the base for a non-enzymatic glucose sensor in an alkaline medium, 0.1 NaOH solution, with a linear range of 50-200 mg/dL using differential pulse voltammetry (DPV) measurement. An X-ray photoelectron spectroscopy (XPS) study confirmed the formation of the cuprous oxide layer on the thin gold film sensor prototype. Quantitative detection of glucose in both phosphate-buffered saline (PBS) and undiluted human serum were carried out. Neither ascorbic acid nor uric acid even at a relatively high concentration level of 100mg/dL in serum interfered with the glucose detection, demonstrating the excellent selectivity of this non-enzymatic cuprous oxide thin layer based glucose sensor. Chronoamperometry (CA) and single potential amperometric voltammetry were used to verify the measurements obtained by differential pulse voltammetry (DPV), and the positive results validated that the detection of glucose in a 0.1 M NaOH alkaline medium by DPV measurement was effective. Nickel, platinum and copper are commonly used metals for non-enzymatic glucose detection. The performance of these metal-based sensors for glucose detection using DPV were also evaluated. Cuprous oxide (Cu2O) thin layer based sensor showed the best sensitivity for glucose detection among the sensors evaluated.
Imperfection Sensitivity of Nonlinear Vibration of Curved Single-Walled Carbon Nanotubes Based on Nonlocal Timoshenko Beam Theory
Iman Eshraghi, Seyed K. Jalali, Nicola Maria Pugno
Subject: Engineering, Mechanical Engineering Keywords: nonlinear vibration; imperfection; curved SWCNT; nonlocal theory; differential quadrature method (DQ)
Imperfection sensitivity of large amplitude vibration of curved single-walled carbon nanotubes (SWCNTs) is considered in this study. The SWCNT is modeled as a Timoshenko nano-beam and its curved shape is included as an initial geometric imperfection term in the displacement field. Geometric nonlinearities of von Kármán type and nonlocal elasticity theory of Eringen are employed to derive governing equations of motion of nano-beam. Spatial discretization of governing equations and associated boundary conditions is performed using differential quadrature (DQ) method and the corresponding nonlinear eigenvalue problem is iteratively solved. Effects of value and location of the geometric imperfection, and the nonlocal small-scale parameter on the nonlinear frequency ratio and imperfection sensitivity of a curved SWCNT for various boundary conditions are investigated. The results show that the geometric imperfection plays a significant role in the nonlinear vibration characteristics of curved SWCNTs.
MOMMI-MP: A Comprehensive Database for Integrated Analysis of Metabolic and Microbiome Profiling of Mouse Pregnancy
Kaustubh Pachpor, Medha Priyadarshini, Derek Reiman, Brian T Layden, Yang Dai
Subject: Medicine & Pharmacology, Gastroenterology Keywords: Gestational diabetes mellitus; Insulin resistance; Microbiome; Metabolome; Database; Differential abundance; Correlation; Pathways
Pregnancy is a dynamic state with multiple metabolic changes occurring including insulin resistance. Gestational diabetes mellitus (GDM), a form of diabetes that appears during pregnancy, develops if metabolic aberrations occur, in particular, in normal pregnancy-induced insulin resistance. Multi-omics is a powerful approach for uncovering the mechanisms driving metabolic change in different physiologic and pathologic states. A recent study demonstrated that the gestational gut microbiome mediates pregnancy metabolic adaptations through effects on gut indoleamine-2,3 dioxygenase 1 activity and the production of kynurenine. Using the dataset generated from this highly controlled study, we performed a comprehensive analysis of the pregnancy-specific physiological and metabolic profiles, 16S rRNA microbiome, and plasma untargeted LC-MS metabolome data. To facilitate the utilization of these analysis results by other researchers, we developed MOMMI-MP, a database that provides an easy-to-use platform to browse and search differential abundant microbial taxa and metabolites, and to examine metabolic pathways. The datasets consist of data collected from 3 genetically diverse strains of mice (C57BL/6J, CD1, and NIH-Swiss) over 6 time points during the gestational (days 0, 10, 15, and 19 during gestation) and postpartum (days 3 and 20 after delivery) states, totaling 180 samples for each strain. The computational results are presented in various tables and plots, and organized in MOMMI-MP to empower exploratory analyses by other researchers. In conclusion, MOMMI-MP is a resource to facilitate the investigation of novel mechanisms governing metabolic changes during pregnancy.
Calibrating a Process-based Model to Enhance Robustness in Carbon Sequestration Simulations: the Sase of Cedrus Atlantica (Endl.) Manetti ex Carrière
Issam Boukhris, Said Lahssini, Alessio Collalti, Said Moukrim, Monia Santini, Tommaso Chiti, Riccardo Valentini
Subject: Biology, Forestry Keywords: Cedrus altlantica; carbon sequestration; DE-MC (Differential Evolution - Markov chains); parameter optimization
To assess the degree to which it has met its commitments under the Paris Agreement, Morocco is called upon to carry out carbon assessments and transparent evaluations. Within the forestry sector, little is known about the role of Morocco's forests in contributing to carbon uptake. With this aim, we applied for the first time in literature the 3-PG model to Cedrus atlantica ((Endl.) Manetti ex Carrière, 1855), which represents about 131.800 ha of Morocco's forest area (i.e. Azrou forest). Through the Differential Evolution - Markov Chains (DE-MC) we tested and assessed the sensitivity and calibrated the 3-PG model. This process-based model provided significant results regarding the carbon sequestration capacity. The results showed the following: i- Parameters related to stand properties, canopy structure, and processes, as well as biomass partitioning, are the most important or sensitive for the performance of the model; ii- The DE-MC method optimized the values of the 3-PG parameters which was confirmed by the means of Gelman-Rubin convergence test; iii- According to the predictions of the calibrated 3-PG, the Net Primary Production in the pure Azrou forest varies between 0.32 and 7.88 tC.ha−1.yr−1, it is equal in average to 4.9 tC.ha−1.yr−1, which given the total area corresponds to 7078 tC.yr−1.
Asymptotics and Confluence for a Singular Nonlinear Q-Difference-Differential Cauchy Problem
Subject: Mathematics & Computer Science, Analysis Keywords: asymptotic expansion; confluence; formal power series; partial differential equation; q-difference equation
We examine a family of nonlinear q-difference-differential Cauchy problems obtained as a coupling of linear Cauchy problems containing dilation q-difference operators, recently investigated by the author, and quasi-linear Kowalevski type problems that involve contraction q-difference operators. We build up local holomorphic solutions to these problems. Two aspects of these solutions are explored. One facet deals with asymptotic expansions in the complex time variable for which a mixed type Gevrey and q-Gevrey structure is exhibited. The other feature concerns the problem of confluence of these solutions as q tends to 1.
Differential Gene Expression Analysis of Resistant and Susceptible Flax Cultivars in Response to Fusarium oxysporum Stress
He Rui, Chang Yin Dong, Wang Jian Ming
Subject: Biology, Agricultural Sciences & Agronomy Keywords: flax; Fusarium oxysporum; differential expression genes; GO enrichment analysis; KEGG enrichment analysis
A plant's early response to pathogen stress is a vital indicator of its disease resistance. In order to study the response mechanism of resistant and susceptible flax cultivars to Fusarium oxysporum f. sp. lini (Foln), we applied RNA-sequencing to analyze transcriptomes of flax with Foln 0.5, 2 and 8 hours post inoculation (hpi). We found a significant difference in the number of differential expression genes (DEGs) between resistant and susceptible flax clutivars. The number of DEGs in the Fusarium-resistant cultivar increased dramatically at 2 hpi, and a large number of DEGs participated in the Fusarium-susceptible cultivar response to Foln infection 0.5 hpi. GO enrichment analysis determined that the up-regulated DEGs of both flax cultivars were enriched such as oxidoreductase activity and oxidation-reduction process. At the same time, the genes involved in diterpenoid synthesis were up-regulated in resistant cultivar, while those involved in extracellular region, cell wall and organophosphate ester transport were down-regulated in susceptible cultivar. KEGG enrichment analysis showed the genes encoded WRKY 22 and WRKY33 which involved in MAPK signaling pathway were up-regulated expressed in S-29 and down-regulated expressed in R-7, negatively regulated the disease resistance of flax; The genes encoded Hsp 90 family which in involved in plant pathogen interaction pathway were up-regulated in R-7 and down-regulated in S-29, which positively regulated the disease resistance of flax; The genes encoded MYC2 transcription factor and TIFY proteins which involved in plant hormone signaling pathway were up-regulated in R-7, and regulated the jasmonic acid metabolism of flax and the signal transduction of plant hormones. Meanwhile seven regulatory genes with the most correlation were screened out, Among Lus10025000.g and Lus10026447.g regulated other genes expressed both in plant hormone signal transduction pathway and MAPK signal pathway. In conclusion, these findings will facilitate further studies on the function of these candidate genes in flax of response to Fusarium stress, and the breeding of disease-resistant flax cultivar.
Optimal Power Flow Considering Intermittent Solar and Wind Generation using Multi-Operator Differential Evolution Algorithm
Md Alamgir Hossain, Karam M. Sallam, Seham S. Elsayed, Ripon K. Chakrabortty, Michael J. Ryan
Subject: Engineering, Automotive Engineering Keywords: Evolutionary Algorithms; differential evolution; constraints handling techniques; optimal power flow; renewable energy
In this paper, a multi-operator differential evolution algorithm (MODE) is proposed to solve the Optimal Power Flow (OPF) problem and is called MODE-OPF. The MODE-OPF utilizes the strengths of more than one differential evolution (DE) operator in a single algorithmic framework. Additionally, an adaptive method (AM) is proposed to update the number of solutions evolved by each DE operator based on both the diversity of population and quality of solutions. This adaptive method has the ability to maintain diversity at the early stages of the optimization process and boost convergence at the later ones. The performance of the proposed MODE-OPF is tested by solving OPF problems for both small and large IEEE bus systems (i.e., IEEE-30 and IEEE-118) while considering the intermittent solar and wind power generation. To prove the suitability of this proposed algorithm, its performance has been compared against several state-of-the-art optimization algorithms, where MODE-OPF outperforms other algorithms in all experimental results and thereby improving a network's performance with lower cost. MODE-OPF decreases the total generation cost up to 24.08%, the real power loss up to 6.80% and the total generation cost with emission up to 8.56%.
New Study of Existence and Dimension of the Set of Solutions for Nonlocal Impulsive Differential Inclusions With Sectorial Operator
Salvatore Sessa, Nawal Alsarori, Kirtiwant Ghadle, Hayel Saleh
Subject: Mathematics & Computer Science, Algebra & Number Theory Keywords: Impulsive fractional differential inclusions; Nonlocal conditions; Fixed point theorems; 10 Mild solutions
In this article, we are interested in a new generic class of nonlocal fractional impulsive differential inclusions with linear sectorial operator and Lipschitz multivalued function in the setting of finite dimensional Banach spaces. By modifying the definition of PC-mild solutions initiated by Shu, we succeeded to determine new conditions that sufficiently guarantee the existence of the solutions. The results are obtained by combining techniques of fractional calculus and fixed point theorem for contraction maps. We also characterize the topological structure of the set of solutions. Finally, we provide a demonstration to address the applicability of the theoretical results.
Asymptotics and Confluence for Some Linear q-Difference-Differential Cauchy Problem
Subject: Mathematics & Computer Science, Algebra & Number Theory Keywords: asymptotic expansion; confluence; formal power series; partial differential equation; q-difference equation
A linear Cauchy problem with polynomial coefficients wich combines q-difference operators for q>1 and differential operators of irregular type is examined. A finite set of sectorial holomorphic solutions w.r.t the complex time is constructed by means of classical Laplace transforms. These functions share a common asymptotic expansion in the time variable which turns out to carry a double layers structure which couples q-Gevrey and Gevrey bounds. In the last part of the work, the problem of confluence of these solutions as q tends to 1 is investigated.
A Math Approach with Brief Cases towards Reducing Computational and Time Complexity in the Industrial Systems
Yaroslav Matviychuk, Tomáš Peráček, Natalya Shakhovska
Subject: Mathematics & Computer Science, Information Technology & Data Management Keywords: mathematical model; reduction; identification procedure; incorrectness; neural network; ordinary differential equation (ODE)
The paper proposes a new principle of finding and removing elements of mathematical model, redundant in terms of parametric identification of the model. It allows reducing computational and time complexity of the applications built on the model. Especially this is important for AI based systems, systems based on IoT solutions, distributed systems etc. Besides, the complexity reduction allows increasing an accuracy of mathematical models implemented. Despite the model order reduction methods are well known, they are extremely depended however on the problem area. Thus, proposed reduction principles can be used in different areas, what is demonstrated in this paper. The proposed method for the reduction of mathematical models of dynamic systems allows also the assessment of the requirements for the parameters of the simulator elements to ensure the specified accuracy of dynamic similarity. Efficiency of the principle is shown on the ordinary differential equations and on the neural network model. The given examples demonstrate efficient normalizing properties of the reduction principle for the mathematical models in the form of neural networks.
Integer Versus Fractional Order SEIR Deterministic and Stochastic Models of Measles
Md Rafiul Islam, Angela Peace, Daniel Medina, Tamer Oraby
Subject: Life Sciences, Other Keywords: fractional SEIR stochastic model; Caputo fractional order differential equations; measles; parameter estimation
In this paper, we compare the performance between systems of ordinary and (Caputo) fractional differential equations depicting the susceptible-exposed-infectious-recovered (SEIR) models of diseases. In order to understand the origins of both approaches as mean-field approximations of integer and fractional stochastic processes, we introduce the fractional differential equations as approximations of some type of fractional nonlinear birth--death processes. Then, we examine validity of the two approaches against empirical courses of epidemics; we fit both of them to case counts of three measles epidemics that occurred during the pre-vaccination era in three different locations. While FDEs appear more flexible in fitting empirical data, our ODEs offered better fits to two out of three data sets. Important differences in transient dynamics between these modeling approaches are discussed.
A Fractional-Order Predator-Prey Model with Ratio-Dependent Functional Response and Linear Harvesting
Agus Suryanto, Isnani Darti, Hasan S. Panigoro, Adem Kilicman
Subject: Mathematics & Computer Science, Applied Mathematics Keywords: fractional order differential equation; linear harvesting; stability analysis; lyapunov function; hopf bifurcation
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We consider a model of predator-prey interaction at fractional-order where the predation obeys the ratio-dependent functional response and the prey is linearly harvested. For the proposed model, we show the existence, uniqueness, non-negativity as well as the boundedness of the solutions. Conditions for the existence of all possible equilibrium points and their stability criteria, both locally and globally, are also investigated. The local stability conditions are derived using the Magtinon's theorem, while the global stability is proven by formulating an appropriate Lyapunov function. The occurance of Hopf bifurcation around the interior point is also shown analytically. At the end, we implement the Predictor-Corrector scheme to perform some numerical simulations.
An Integrated Pan-Cancer Analysis and Structure-Based Virtual Screening of GPR15
Yanjing Wang, Xiangeng Wang, Yi Xiong, Cheng‐Dong Li, Qin Xu, Lu Shen, Aman Chandra Kaushik, Dong-Qing Wei
Subject: Medicine & Pharmacology, Oncology & Oncogenics Keywords: GPR15, pan-cancer, TCGA, cancer immunity, differential gene expression, prognosis, virtual screening
G protein-coupled receptor 15 (GPR15, also known as BOB) is an extensively studied orphan GPCR involving HIV infection, colonic inflammation and smoking-related diseases. Recently, GPR15 was deorphanized and its corresponding natural ligand demonstrated an ability of inhibiting cancer cell growth. However, no study reported the potential role of GPR15 in a pan-cancer manner. Using large-scale publicly available data from the Cancer Genome Atlas (TCGA) and the Genotype-Tissue Expression (GTEx) databases, we found that GPR15 expression is significantly lower in colon adenocarcinoma (COAD) than in normal tissues. And among 33 cancer types, GPR15 expression is significantly correlated with the prognoses of COAD, neck squamous carcinoma (HNSC), lung adenocarcinoma (LUAD) positively and stomach adenocarcinoma (STAD) negatively. This study also revealed that commonly upregulated gene set in the high GPR15 expression group (stratified via median) of COAD, HNSC, LUAD and STAD are enriched in immune systems, indicating that GPR15 might be considered as a potential target for cancer immunotherapy. Furthermore, we modelled the 3D structure of GPR15 and conducted the structure-based virtual screening. The top 8 hits compounds were screened and then subjected to molecular dynamics (MD) simulation for stability analysis. Our study provided novel insights into the role of GPR15 in a pan-cancer manner and discovered a potential hit compound for GPR15 antagonists.
Certain Generating Matrix Functions of Charlier Matrix Polynomials Using Weisner's Group Theoretic Method
Ayman Shehata
Subject: Mathematics & Computer Science, Analysis Keywords: Charlier matrix polynomials; generating matrix functions; Charlier matrix differential equations; Lie algebra
The present paper discusses a study of a class of Charlier matrix polynomials and its generalized analogue. Certain generating matrix functions, recurrence matrix relations, matrix differential equation, summation formulas and many new results have been discussed for these matrix polynomials. Weisner's group theoretic method is used to obtain matrix generating relations for Charlier matrix polynomials and the details of this method were given in this paper. Finally, we will discuss only briefly the procedure followed.
On Some Classes of Spirallike Functions Defined by the Salagean Operator
Mohammad Mehdi Shabani, Saeed Hashemi Sababe
Subject: Mathematics & Computer Science, Analysis Keywords: analytic function; Hadamard product; Starlike function; Convex function; Subordination; Salagean differential operator
Online: 9 May 2019 (12:31:19 CEST)
In this paper, we introduce two subclasses of analytic and Spirallike functions and investigate convolution properties, the necessary and sufficient condition, coefficient estimates and inclusion properties for these classes .
Microscopic Change in Hardened Cement Paste Due to High-Speed Impact
Yuya Sakai, Ivwananji Sikombe, Keiko Watanabe, Hiroyuki Inoue
Subject: Engineering, Civil Engineering Keywords: cement paste; impact test; pore structure; thermograveimetry analysis; X-ray differential analysis
Online: 6 December 2018 (05:24:33 CET)
Impact load was applied to hardened cement paste (HCP) specimens using a gas gun to investigate microscopic changes in the specimens and develop a better response model of concrete subjected to impact load. Plasma emission was observed at the moment of impact at 420 m/s and the colour of the portion near the impact point turned brighter. This brighter portion was analysed, and it was observed that the pore structure was coarser compared to the other portion; however, the results of thermogravimetry and X-ray diffraction analysis were similar. A possible reason is that the generated heat was instantaneous and the rate of the temperature increase in the HCP decreased due to evaporation of water in the HCP. These results indicate that during impact at a few hundred m/s, porosity increase due to heat effect is more dominant than porosity decrease due to mechanical compaction.
Degenerate Daehee Numbers of the Third Kind
Sung-Soo Pyo, Taekyun Kim, Seog-Hoon Rim
Subject: Mathematics & Computer Science, Algebra & Number Theory Keywords: degenerate log function; degenerate Daehee numbers of the thirdkind; nonlinear differential equation.
In this paper, we define new kind of Daehee numbers, the degenerate Daehee numbers of the third kind, using degenerate log function as generating function. We obtain some identities for the degenerate Daehee numbers of the third kind associated with the Daehee, degenerate Daehee and degenerate Daehee numbers of the second kind. In addition, we derive a differential equation associated with the degenerate log function. We deduce some identities from the differential equation.
Cut-off Values of Hematologic Parameters to Predict the Number of Alpha Genes Deleted in Subjects with Deletional Alpha Thalassemia
Diego Velasco-Rodríguez, Carlos Blas, Juan-Manuel Alonso-Domínguez, Gala Vega, Carlos Soto, Aránzazu García-Raso, Pilar Llamas-Sillero
Subject: Medicine & Pharmacology, Other Keywords: alpha; thalassemia; deletional; cut-off; number of genes; microcytic anemia; differential diagnosis
Most of α-thalassemia cases are caused by deletions of the structural α-globin genes. The degree of microcytosis and hypochromia has been correlated with the number of affected α-globin genes, suggesting a promising role of hematologic parameters as predictive diagnostic tools. However, specific cut-off points for these parameters to discriminate between the different subtypes of α-thalassemia remain to be clearly defined. Six hematologic parameters (total number of erythrocytes, hemoglobin concentration, mean corpuscular volume, mean corpuscular hemoglobin, mean corpuscular hemoglobin concentration and red cell distribution width) were evaluated in 174 cases of deletional α-thalassemia (92 heterozygous α+ thalassemia, 39 homozygous α+ thalassemia, 34 heterozygous α0 thalassemia and 9 cases of Hb H disease). A good correlation between the number of deleted alpha genes and MCV (r = -0.672, p<0.001), MCH (r = -0.788, p<0.001) and RDW (r = 0.633, p<0.001) was observed. The deletion of at least two alpha genes in adult individuals with microcytosis without iron deficiency and normal values of Hb A2 and Hb F should be discarded when MCH levels are lower than 23.15 pg. Furthermore, MCH <21.90 pg and/or MCV <70.80 fL are strongly suggestive of the presence of one α0 allele. Finally, an accurate presumptive diagnosis of Hb H disease can be made if both RDW ≥20% and MCH <18.45 pg are seen.
CHAGSKODE Algorithm for Solving Real World Constrained Optimization Problems
Debanjan Saha, Karam M. Sallam, Shuvodeep De, Ali W. Mohamed
Subject: Engineering, Other Keywords: Differential Evolution; APGSK algorithm; Constrained Optimization; transformation; parameter adaptation; multi-operator; Evolutionary Algorithms
Real-world optimization problems are often gov- erned by one or more constraints. Over the last few decades, extensive research has been performed in Constrained Opti- mization Problems (COPs) fueled by advances in computational power. In particular, Evolutionary Algorithms (EAs) are a preferred tool for practitioners for solving these COPs within practicable time limits. We propose a novel hybrid Evolutionary Algorithm based on the Differential Evolution algorithm and Adaptive Parameter Gaining Sharing Knowledge-based algo- rithm to solve global real-world constrained parameter space. The proposed CHAGSKODE algorithm leverages the power of multiple adaptation strategies concerning the control parameters, search mechanisms, as well as uses knowledge sharing between junior and senior phases. We test our method on the benchmark functions taken from the CEC2020 special session & competition on real-world constrained optimization. Experimental results indicate that CHAGSKODE is able to achieve state-of-the- art performance on real-world constrained global optimization when compared against other well-known real-world constrained optimizers.
Chebfun Solutions to a Class of 1D Singular and Nonlinear Boundary Value Problems
Călin-Ioan Gheorghiu
Subject: Mathematics & Computer Science, Computational Mathematics Keywords: Chebfun; differential equation; non-linearity; singularity; convergence; Bernstein growth; improper integrals; boundary layer
The Chebyshev collocation method (ChC) implemented as Chebfun is used in order to solve a class of second order one-dimensional singular and genuinely nonlinear boundary value problems. Efforts to solve these problems with conventional ChC have generally failed, and the outcomes obtained by finite differences or finite elements are seldom satisfactory. We try to fix this situation using the new Chebfun programming environment. However, for toughest problems we have to loosen the default Chebfun tolerance in Newton's solver as the ChC runs into trouble with ill-conditioning of the spectral differentiation matrices. Although in such cases the convergence is not quadratic the Newton updates decrease monotonically. This fact, along with the decreasing behaviour of Chebyshev coefficients of solutions, suggests that the outcomes are trustworthy, i.e., the collocation method has exponential (geometric) rate of convergence or at least an algebraic rate. We consider first a set of problems that have exact solutions or prime integrals and then another set of benchmark problems that do not possess these properties. Actually, for each test problem carried out we have determined how Chebfun solution converges, its length, the accuracy of the Newton method and especially how well the numerical results overlap with the analytical ones (existence and uniqueness).
Force Estimation during Cell Migration Using Mathematical Modelling
Feng Wei Yang, Chandrasekar Venkataraman, Sai Gu, Vanessa Styles, Anotida Madzvamuse
Subject: Mathematics & Computer Science, Computational Mathematics Keywords: cell migration; optimal control; geometric partial differential equations; mechanical membrane forces; cell polarisation
Cell migration is essential for physiological, pathological and biomedical processes such as, in embryogenesis, wound healing, immune response, cancer metastasis, tumour invasion and inflammation. In light of this, quantifying mechanical properties during the process of cell migration is of great interest in experimental sciences, yet few theoretical approaches in this direction have been studied. In this work, we propose a theoretical and computational approach based on the optimal control of geometric partial differential equations to estimate cell membrane forces associated with cell polarisation during migration. Specifically, cell membrane forces are inferred or estimated by fitting a mathematical model to a sequence of images, allowing us to capture dynamics of the cell migration. Our approach offers a robust and potentially accurate framework to compute geometric mechanical membrane forces associated with cell polarisation during migration and also yields geometric information of independent interest, we illustrate one such example that involves quantifying cell proliferation levels which are associated with cell division, cell fusion or cell death.
Some Examples of Nonassociative Coalgebras and Supercoalgebras
Daniyar Kozybaev, Ualbai Umirbaev, Viktor Zhelyabin
Subject: Mathematics & Computer Science, Algebra & Number Theory Keywords: coalgebra; coderivation; differential algebra; Novikov algebra; Lie algebra; Jordan superalgebra; right-alternative algebra
Locally finiteness of some varieties of nonassociative coalgebras is studied and the Gelfand-Dorfman construction for Novikov coalgebras and the Kantor construction for Jordan super-coalgebras are given. We give examples of a non-locally finite differential coalgebra, Novikov coalgebra, Lie coalgebra, Jordan super-coalgebra, and right-alternative coalgebra. The dual algebra of each of these examples satisfies very strong additional identities. We also constructed examples of an infinite dimensional simple differential coalgebra, Novikov coalgebra, Lie coalgebra, and Jordan super-coalgebra over a field of characteristic zero.
Molecular Pathogenesis and Immune Evasion of Vesicular Stomatitis Virus Inferred from Genes Expression Changes in Infected Porcine Macrophages
Lauro Velazquez-Salinas, Jessica A. Canter, James J. Zhu, Luis L. Rodriguez
Subject: Life Sciences, Biochemistry Keywords: Vesicular Stomatitis Virus; macrophage; microarray analysis; differential gene expression; molecular pathogenesis; immune evasion
Molecular mechanisms associated with the pathogenesis of Vesicular stomatitis virus (VSV) in livestock remain poorly understood. Several studies have highlighted the relevant role of macrophages in controlling the systemic dissemination of VSV during infection in different animal models, including mice, cattle and pigs. To gain more insight on the molecular mechanisms used by VSV to impair the immune response in macrophages, we used microarrays to determine the transcriptomic changes produced by VSV infection in primary cultures of porcine macrophages. The results indicated that VSV infection induced the massive expression of multiple anorexic, pyrogenic, proinflammatory and immunosuppressive genes. Overall, the interferon (IFN) response appeared suppressed, leading to the absence of stimulation of interferon-stimulated genes (ISG). Interestingly, VSV infection promoted the expression of several genes known to downregulate the expression of IFNb. This represents an alternate mechanism for VSV control of the IFN response, beyond the recognized mechanisms mediated by the matrix protein. Although there was no significant differential gene expression in macrophages infected with a highly virulent epidemic strain compared to a less virulent endemic strain, the endemic strain consistently induced higher expression of all upregulated cytokines and chemokines. Collectively, this study provides novel insights into VSV molecular pathogenesis and immune evasion that warrants further investigation
Time Optimal Control for Semilinear Stochastic Functional Differential Equations With Delays
Yong Han Kang, Jin-Mun Jeong
Subject: Mathematics & Computer Science, Algebra & Number Theory Keywords: stochastic differential equation; retarded control system; time optimal control; admissible set; analytic semigroup.
The purpose of this paper is to find the time optimal control to a target set for semilinear stochastic functional differential equations involving time delays or memories under general conditions on a target set and nonlinear terms even though the equations contain unbounded principal operators. Our research approach is construct a fundamental solution for corresponding linear systems and establish variations of constant formula of solutions for given stochastic equations. The existence result of time optimal controls for one point target set governed by the given semilinear stochastic equation is also established.