  We study the evolution of an initially random distribution of particles on a
square lattice, under certain rules for `growing' and `culling' of particles.
In one version we allow the particles to move laterally along the surface
(mobile layer) and in the other version this motion is not allowed (immobile
case). In the former case both analytical and computer simulation results are
presented, while in the latter only simulation is possible. We introduce growth
and culling probabilities appropriate for condensation and evaporation on a
two-dimensional surface, and compare results with existing models for this
problem. Our results show very interesting behaviour, under certain conditions
quite different from earlier models. We find a possibility of hysteresis not
reported earlier for such models. ~


  Let $p$ be an odd prime number. In this paper, we characterize the nonabelian
composition factors of a finite group with odd $p$-Sylow automizers, and then
prove that the McKay conjecture, the Alperin weight conjecture and the
Alperin-McKay conjecture hold for such group.


  Jets at high energy colliders are complicated objects to identify. Even if
jets are widely separated, there is no reason for jets to have the same size. A
single reconstruction, or interpretation, of each event can only extract a
limited amount of information. Motivated by the recently proposed Qjet
algorithms, which give multiple interpretations for each event using
nondeterministic jet clustering, we propose a simple, fast and powerful method
to give multiple event interpretations by varying the parameter R in the jet
definition. With multiple interpretations we can redefine the weight of each
event in a counting experiment to be the fraction of interpretations passing
the experimental cuts, instead of 0 or 1 in a conventional analysis. We show
that the statistical power of an analysis can be dramatically increased. In
particular, we can have a 46% improvement in the statistical significance for
the Higgs search with an associated Z boson (ZH\rightarrow \nu {\bar \nu}b
{\bar b}) at the 8 TeV LHC.


  A novel two-state, Reversible Cellular Automata (RCA) is described. This
three-dimensional RCA is shown to be capable of universal computation.
Additionally, evidence is offered that this RCA Is capable of universal
construction.


  Optimality Theory is a constraint-based theory of phonology which allows
constraints to be violated. Consequently, implementing the theory presents
problems for declarative constraint-based processing frameworks. On the basis
of two regularity assumptions, that candidate sets are regular and that
constraints can be modelled by transducers, this paper presents and proves
correct algorithms for computing the action of constraints, and hence deriving
surface forms.


  Hybrid energy storage systems (HESS) combine different energy storage
technologies aiming at overall system performance and lifetime improvement
compared to a single technology system. In this work, control combinations for
a vanadium redox flow battery (VRFB, 5/60 kW/kWh) and a lithium-ion battery
(LIB, 3.3/9.8 kW/kWh) are investigated for the design of a HESS. Four real-time
energy management/power allocation scenarios are considered for the operation
of the hybrid storage solution through a 15-year economic and energetic
analysis. The results obtained for each scenario are compared with a single
technology battery performance. In the definition of the scenarios, real
electricity generation is considered from two solar photovoltaic installations
(3.2 kWp and 6.7 kWp) and an estimated representative load of a services
building. HESS performance is evaluated through specific energy and economic
key performance indicators. The results obtained indicate that the use of
customized energy management strategies (EMSs) renders the VRFB and LIB
characteristics complementary, besides enhancing the competitiveness of VRFB,
as a single technology. Moreover, the HESS management impacts the seasonality
factor, contributing to the overall electric system smart management.


  It is shown that the fault testing for quantum circuits does not follow
conventional classical techniques. If probabilistic gate like Hadamard gate is
included in a circuit then the classical notion of test vector is shown to
fail. We have reported several new and distinguishing features of quantum fault
and also presented a general methodology for detection of functional faults in
a quantum circuit. The technique can generate test vectors for detection of
different kinds of fault. Specific examples are given and time complexity of
the proposed quantum fault detection algorithm is reported.


  The observation of Higgs pair production at high-energy colliders can give
evidence for the presence of a triple Higgs coupling. However, the actual
determination of the value of this coupling is more difficult. In the context
of general models for new physics, double Higgs production processes can
receive contributions from many possible beyond-Standard-Model effects. This
dependence must be understood if one is to make a definite statement about the
deviation of the Higgs field potential from the Standard Model. In this paper,
we study the extraction of the triple Higgs coupling from the process
$e^+e^-\to Zhh$. We show that, by combining the measurement of this process
with other measurements available at a 500 GeV $e^+e^-$ collider, it is
possible to quote model-independent limits on the Effective Field Theory
parameter c6 that parametrizes modifications of the Higgs potential. We present
precise error estimates based on the anticipated ILC physics program, studied
with full simulation. Our analysis also gives new insight into the
model-independent extraction of the Higgs boson coupling constants and total
width from $e^+e^-$ data.


  The catalyst development for N2 electroreduction reaction (NRR) with low
onset potential and high Faradaic efficiency is highly desired, but remains
challenging. Machine learning (ML) recently emerged as a complementary tool to
accelerate material discovery; however a ML model for NRR has yet to be
developed. Here, we develop and report slab-graph convolutional neural network
(SGCNN), an accurate and flexible ML model that is applicable to catalytic
surface reactions. With the self-accumulated database of 2,699 surface
calculations, SGCNN predict binding energies, ranging over 8 eV, of five key
adsorbates (*H, *N2, *N2H, *NH, *NH2) related to NRR performance with the
mean-absolute-error of only 0.23eV. Unlike previously available models, SGCNN
avoids using ab initio level inputs, instead is solely based on elemental
properties that are all readily available in Periodic-Table-of-Elements; true
accelerations can be realized. t-distributed stochastic neighbor embedding
(t-SNE) analysis reveals that binary intermetallics of averaged d-electron
occupation between 4 and 5 could potentially lower the onset potential in N2
electroreduction.


  Training neural networks with many processors can reduce time-to-solution;
however, it is challenging to maintain convergence and efficiency at large
scales. The Kronecker-factored Approximate Curvature (K-FAC) was recently
proposed as an approximation of the Fisher Information Matrix that can be used
in natural gradient optimizers. We investigate here a scalable K-FAC design and
its applicability in convolutional neural network (CNN) training at scale. We
study optimization techniques such as layer-wise distribution strategies,
inverse-free second-order gradient evaluation, and dynamic K-FAC update
decoupling to reduce training time while preserving convergence. We use
residual neural networks (ResNet) applied to the CIFAR-10 and ImageNet-1k
datasets to evaluate the correctness and scalability of our K-FAC gradient
preconditioner. With ResNet-50 on the ImageNet-1k dataset, our distributed
K-FAC implementation converges to the 75.9% MLPerf baseline in 18-25% less time
than does the classic stochastic gradient descent (SGD) optimizer across scales
on a GPU cluster.


  Galaxies congregate in clusters and along filaments, and are missing from
large regions referred to as voids. These structures are seen in maps derived
from spectroscopic surveys that reveal networks of structure that are
interconnected with no clear boundaries. Extended regions with a high
concentration of galaxies are called 'superclusters', although this term is not
precise. There is, however, another way to analyse the structure. If the
distance to each galaxy from Earth is directly measured, then the peculiar
velocity can be derived from the subtraction of the mean cosmic expansion, the
product of distance times the Hubble constant, from observed velocity. The
peculiar velocity is the line-of-sight departure from the cosmic expansion and
arises from gravitational perturbations; a map of peculiar velocities can be
translated into a map of the distribution of matter. Here we report a map of
structure made using a catalogue of peculiar velocities. We find locations
where peculiar velocity flows diverge, as water does at watershed divides, and
we trace the surface of divergent points that surrounds us. Within the volume
enclosed by this surface, the motions of galaxies are inward after removal of
the mean cosmic expansion and long range flows. We define a supercluster to be
the volume within such a surface, and so we are defining the extent of our home
supercluster, which we call Laniakea. A key component of this paper is an
accompanying movie that can be viewed (also in 3D) and downloaded at
http://irfu.cea.fr/laniakea or http://vimeo.com/pomarede/laniakea


  This graduate textbook on machine learning tells a story of how patterns in
data support predictions and consequential actions. Starting with the
foundations of decision making, we cover representation, optimization, and
generalization as the constituents of supervised learning. A chapter on
datasets as benchmarks examines their histories and scientific bases.
Self-contained introductions to causality, the practice of causal inference,
sequential decision making, and reinforcement learning equip the reader with
concepts and tools to reason about actions and their consequences. Throughout,
the text discusses historical context and societal impact. We invite readers
from all backgrounds; some experience with probability, calculus, and linear
algebra suffices.


  An analogue of the classical Mecke formula for Poisson point processes is
proved for the class of space-time STIT tessellation processes. From this key
identity the Markov property of a class of associated random processes is
derived. This in turn is used to determine the distribution of the number of
internal vertices of the typical maximal tessellation segment.


  Minimax optimization problems arises from both modern machine learning
including generative adversarial networks, adversarial training and multi-agent
reinforcement learning, as well as from tradition research areas such as saddle
point problems, numerical partial differential equations and optimality
conditions of equality constrained optimization. For the unconstrained
continuous nonconvex-nonconcave situation, Jin, Netrapalli and Jordan (2019)
carefully considered the very basic question: what is a proper definition of
local optima of a minimax optimization problem, and proposed a proper
definition of local optimality called local minimax. We shall extend the
definition of local minimax point to constrained nonconvex-nonconcave minimax
optimization problems. By analyzing Jacobian uniqueness conditions for the
lower-level maximization problem and the strong regularity of
Karush-Kuhn-Tucker conditions of the maximization problem, we provide both
necessary optimality conditions and sufficient optimality conditions for the
local minimax points of constrained minimax optimization problems.


  Sr$_2$RuO$_4$ is the best candidate for spin-triplet superconductivity, an
unusual and elusive superconducting state of fundamental importance. In the
last three decades Sr$_2$RuO$_4$ has been very carefully studied and despite
its apparent simplicity when compared with strongly correlated high-$T_{c}$
cuprates, for which the pairing symmetry is understood, there is no scenario
that can explain all the major experimental observations, a conundrum that has
generated tremendous interest. Here we present a density-functional based
analysis of magnetic interactions in Sr$_{2}$RuO$_{4}$ and discuss the role of
magnetic anisotropy in its unconventional superconductivity. Our goal is
twofold. First, we access the possibility of the superconducting order
parameter rotation in an external magnetic field of 200 Oe, and conclude that
the spin-orbit interaction in this material is several orders of magnitude too
strong to be consistent with this hypothesis. Thus, the observed invariance of
the Knight shift across $T_{c}$ has no plausible explanation, and casts doubt
on using the Knight shift as an ultimate litmus paper for the pairing symmetry.
Second, we propose a quantitative double-exchange-like model for combining
itinerant fermions with an anisotropic Heisenberg magnetic Hamiltonian. This
model is complementary to the Hubbard-model-based calculations published so
far, and forms an alternative framework for exploring superconducting symmetry
in Sr$_{2}$RuO$_{4}.$ As an example, we use this model to analyze the
degeneracy between various $p-$triplet states in the simplest mean-field
approximation, and show that it splits into a single and two doublets with the
ground state defined by the competition between the "Ising" and "compass"
anisotropic terms.


  As part of an on-going radio supernova monitoring program, we have discovered
a variable, compact steep spectrum radio source ~65 arcsec (~4 kpc) from the
centre of the starburst galaxy NGC 3310. If the source is at the distance of
NGC 3310, then its 5 GHz luminosity is ~3 x 10^{19} WHz^-1. The source
luminosity, together with its variability characteristics, compact structure
(<17 mas) and its association with a group of HII regions, leads us to propose
that it is a previously uncatalogued type II radio supernova. A search of
archival data also shows an associated X-ray source with a luminosity similar
to known radio supernova.


  Speech enhancement models have greatly progressed in recent years, but still
show limits in perceptual quality of their speech outputs. We propose an
objective for perceptual quality based on temporal acoustic parameters. These
are fundamental speech features that play an essential role in various
applications, including speaker recognition and paralinguistic analysis. We
provide a differentiable estimator for four categories of low-level acoustic
descriptors involving: frequency-related parameters, energy or
amplitude-related parameters, spectral balance parameters, and temporal
features. Unlike prior work that looks at aggregated acoustic parameters or a
few categories of acoustic parameters, our temporal acoustic parameter (TAP)
loss enables auxiliary optimization and improvement of many fine-grain speech
characteristics in enhancement workflows. We show that adding TAPLoss as an
auxiliary objective in speech enhancement produces speech with improved
perceptual quality and intelligibility. We use data from the Deep Noise
Suppression 2020 Challenge to demonstrate that both time-domain models and
time-frequency domain models can benefit from our method.


  Monte Carlo simulations of a Miyazawa-Jernigan lattice-polymer model indicate
that, depending on the native's structure geometry, the model exhibits two
broad classes of folding mechanisms for two-state folders. Folding to native
structures of low contact order is driven by contact range and is characterised
by progressive accumulation of structure towards the native fold. By contrast,
folding to high contact order targets is largely dominated by intermediate
stage contacts which are not present in the native fold, yielding a more
cooperative folding process.


  Recent research underscores the pivotal role of the Out-of-Distribution (OOD)
feature representation field scale in determining the efficacy of models in OOD
detection. Consequently, the adoption of model ensembles has emerged as a
prominent strategy to augment this feature representation field, capitalizing
on anticipated model diversity.
  However, our introduction of novel qualitative and quantitative model
ensemble evaluation methods, specifically Loss Basin/Barrier Visualization and
the Self-Coupling Index, reveals a critical drawback in existing ensemble
methods. We find that these methods incorporate weights that are
affine-transformable, exhibiting limited variability and thus failing to
achieve the desired diversity in feature representation.
  To address this limitation, we elevate the dimensions of traditional model
ensembles, incorporating various factors such as different weight
initializations, data holdout, etc., into distinct supervision tasks. This
innovative approach, termed Multi-Comprehension (MC) Ensemble, leverages
diverse training tasks to generate distinct comprehensions of the data and
labels, thereby extending the feature representation field.
  Our experimental results demonstrate the superior performance of the MC
Ensemble strategy in OOD detection compared to both the naive Deep Ensemble
method and a standalone model of comparable size. This underscores the
effectiveness of our proposed approach in enhancing the model's capability to
detect instances outside its training distribution.


  We showed that there is a complete analogue of a representation of the
quantum plane B_q where |q|=1, with the classical ax+b group. We showed that
the Fourier Transform of the representation of B_q on H=L^2(R) has a limit (in
the dual co-representation) towards the Mellin transform of the unitary
representation of the ax+b group, and furthermore the intertwiners of the
tensor products representation has a limit towards the intertwiners of the
Mellin transform of the classical ax+b representation. We also wrote explicitly
the multiplicative unitary defining the quantum ax+b semigroup and showed that
it defines the co-representation that is dual to the representation of B_q
above, and also correspond precisely to the classical family of unitary
representation of the ax+b group.


  Wave propagation control is of fundamental interest in many areas of Physics.
It can be achieved with wavelength-scaled photonic crystals, hence avoiding low
frequency applications. By contrast, metamaterials are structured on a
deep-subwavelength scale, and therefore usually described through
homogenization, neglecting the unit-cell structuration. Here, we show with
microwaves that, by considering their inherent crystallinity, we can induce
wave propagation carrying angular momenta within a subwavelength-scaled
collection of wires. Then, inspired by the Quantum Valley-Hall Effect in
condensed matter physics, we exploit this bulk circular polarization to create
modes propagating along particular interfaces. The latter also carry an edge
angular momentum whose conservation during the propagation allows wave routing
by design in specific directions. This experimental study not only evidences
that crystalline metamaterials are a straightforward tabletop platform to
emulate exciting solid-state physics phenomena at the macroscopic scale, but it
also opens the door to crystalline polarized subwavelength waveguides.


  A simple, general and practically exact method is developed to calculate the
ground states of 1D macroscopic quantum systems with translational symmetry.
Applied to the Hubbard model, a modest calculation reproduces the Bethe Ansatz
results.


  Quantum cryptography is set to become a key technology for future secure
communications. However, to get maximum benefit in communication networks,
transmission links will need to be shared among several quantum keys for
several independent users. Such links will enable switching in quantum network
nodes of the quantum keys to their respective destinations. In this paper we
present an experimental demonstration of a photonic integrated silicon chip
quantum key distribution protocols based on space division multiplexing (SDM),
through multicore fiber technology. Parallel and independent quantum keys are
obtained, which are useful in crypto-systems and future quantum network.


  The extended $\gamma$-ray halos around pulsars are unique probe of
transportation of high-energy electrons (and positrons) in vicinities of such
pulsars. Observations of morphologies of several such halos indicate that
particles diffuse very slowly around pulsars, compared with that in the Milky
Way halo. The energy-dependent morphologies are expected to be very important
in studying the energy-dependence of the diffusion coefficient. In this work we
point out that the spectrum of high-energy electrons takes effect in shaping
the $\gamma$-ray morphologies at the ultra-high-energy bands, and thus results
in a degeneracy between the electron spectrum and the energy-dependence of the
diffusion coefficient. The reasons for such a degeneracy include both the
Klein-Nishina effect of the inverse Compton scattering and the curvature (if
any) of the electron spectrum. It it thus necessary to take into account the
spectral shape of electrons when deriving the energy-dependence of diffusion
coefficient using ultra-high-energy $\gamma$-ray measurements of extended
pulsar halos.


  This paper proposes a new RWO-Sampling (Random Walk Over-Sampling) based on
graphs for imbalanced datasets. In this method, two schemes based on
under-sampling and over-sampling methods are introduced to keep the proximity
information robust to noises and outliers. After constructing the first graph
on minority class, RWO-Sampling will be implemented on selected samples, and
the rest will remain unchanged. The second graph is constructed for the
majority class, and the samples in a low-density area (outliers) are removed.
Finally, in the proposed method, samples of the majority class in a
high-density area are selected, and the rest are eliminated. Furthermore,
utilizing RWO-sampling, the boundary of minority class is increased though the
outliers are not raised. This method is tested, and the number of evaluation
measures is compared to previous methods on nine continuous attribute datasets
with different over-sampling rates and one data set for the diagnosis of
COVID-19 disease. The experimental results indicated the high efficiency and
flexibility of the proposed method for the classification of imbalanced data


  This paper presents the first experimental analysis of polarized synchrotron
emission from relativistic runaway electrons (REs) in a tokamak plasma.
Importantly, we show that the polarization information of synchrotron radiation
can be used to diagnose spatially-localized RE pitch angle distributions.
Synchrotron-producing REs were generated during low density, Ohmic, diverted
plasma discharges in the Alcator C-Mod tokamak. The ten-channel Motional Stark
Effect diagnostic was used to measure spatial profiles of the polarization
angle $\theta_{\mathrm{pol}}$ and the fraction $\mathrm{f}_{\mathrm{pol}}$ of
detected light that was linearly-polarized. Spatial transitions in
$\theta_{\mathrm{pol}}$ of 90$\deg$---from horizontal to vertical polarization
and vice versa---are observed in experimental data and are well-explained by
the gyro-motion of REs and high directionality of synchrotron radiation.
Polarized synchrotron emission is modeled with the synthetic diagnostic SOFT;
its output Green's (or detector response) functions reveal a critical RE pitch
angle at which $\theta_{\mathrm{pol}}$ flips by 90$\deg$ and
$\mathrm{f}_{\mathrm{pol}}$ is minimal. Using SOFT, we determine the dominant
RE pitch angle which reproduces measured $\theta_{\mathrm{pol}}$ and
$\mathrm{f}_{\mathrm{pol}}$ values. The spatiotemporal evolutions of
$\theta_{\mathrm{pol}}$ and $\mathrm{f}_{\mathrm{pol}}$ are explored in detail
for one C-Mod discharge. For channels viewing REs near the magnetic axis and
flux surfaces $q$ = 1 and 4/3, disagreements between synthetic and experimental
signals suggest that the sawtooth instability may be influencing RE dynamics.
Furthermore, other sources of pitch angle scattering, not considered in this
analysis, could help explain discrepancies between simulation and experiment.


  This paper proposes a new bootstrap method to compute predictive intervals
for nonlinear autoregressive time series model forecast. This method we call
the splice boobstrap as it involves splicing the last p values of a given
series to a suitably simulated series. This ensures that each simulated series
will have the same set of p time series values in common, a necessary
requirement for computing conditional predictive intervals. Using simulation
studies we show the methods gives 90% intervals intervals that are similar to
those expected from theory for simple linear and SETAR model driven by normal
and non-normal noise. Furthermore, we apply the method to some economic data
and demonstrate the intervals compare favourably with cross-validation based
intervals.


  Spurious correlations in training data significantly hinder the
generalization capability of machine learning models when faced with
distribution shifts in real-world scenarios. To tackle the problem, numerous
debias approaches have been proposed and benchmarked on datasets intentionally
designed with severe biases. However, it remains to be asked: \textit{1. Do
existing benchmarks really capture biases in the real world? 2. Can existing
debias methods handle biases in the real world?} To answer the questions, we
revisit biased distributions in existing benchmarks and real-world datasets,
and propose a fine-grained framework for analyzing dataset bias by
disentangling it into the magnitude and prevalence of bias. We observe and
theoretically demonstrate that existing benchmarks poorly represent real-world
biases. We further introduce two novel biased distributions to bridge this gap,
forming a nuanced evaluation framework for real-world debiasing. Building upon
these results, we evaluate existing debias methods with our evaluation
framework. Results show that existing methods are incapable of handling
real-world biases. Through in-depth analysis, we propose a simple yet effective
approach that can be easily applied to existing debias methods, named Debias in
Destruction (DiD). Empirical results demonstrate the superiority of DiD,
improving the performance of existing methods on all types of biases within the
proposed evaluation framework.


  Previous research underscored the potential of danmaku--a text-based
commenting feature on videos--in engaging hearing audiences. Yet, for many Deaf
and hard-of-hearing (DHH) individuals, American Sign Language (ASL) takes
precedence over English. To improve inclusivity, we introduce "Signmaku," a new
commenting mechanism that uses ASL, serving as a sign language counterpart to
danmaku. Through a need-finding study (N=12) and a within-subject experiment
(N=20), we evaluated three design styles: real human faces, cartoon-like
figures, and robotic representations. The results showed that cartoon-like
signmaku not only entertained but also encouraged participants to create and
share ASL comments, with fewer privacy concerns compared to the other designs.
Conversely, the robotic representations faced challenges in accurately
depicting hand movements and facial expressions, resulting in higher cognitive
demands on users. Signmaku featuring real human faces elicited the lowest
cognitive load and was the most comprehensible among all three types. Our
findings offered novel design implications for leveraging generative AI to
create signmaku comments, enriching co-learning experiences for DHH
individuals.


  Spatial modulation (SM) is a transmission scheme that uses multiple transmit
antennas but only one transmit RF chain. At each time instant, only one among
the transmit antennas will be active and the others remain silent. The index of
the active transmit antenna will also convey information bits in addition to
the information bits conveyed through modulation symbols (e.g.,QAM).
Pseudo-random phase precoding (PRPP) is a technique that can achieve high
diversity orders even in single antenna systems without the need for channel
state information at the transmitter (CSIT) and transmit power control (TPC).
In this paper, we exploit the advantages of both SM and PRPP simultaneously. We
propose a pseudo-random phase precoded SM (PRPP-SM) scheme, where both the
modulation bits and the antenna index bits are precoded by pseudo-random
phases. The proposed PRPP-SM system gives significant performance gains over SM
system without PRPP and PRPP system without SM. Since maximum likelihood (ML)
detection becomes exponentially complex in large dimensions, we propose low
complexity local search based detection (LSD) algorithm suited for PRPP-SM
systems with large precoder sizes. Our simulation results show that with 4
transmit antennas, 1 receive antenna, $5\times 20$ pseudo-random phase precoder
matrix and BPSK modulation, the performance of PRPP-SM using ML detection is
better than SM without PRPP with ML detection by about 9 dB at $10^{-2}$ BER.
This performance advantage gets even better for large precoding sizes.


  The rapid advancement of AI-generated singing voices, which now closely mimic
natural human singing and align seamlessly with musical scores, has led to
heightened concerns for artists and the music industry. Unlike spoken voice,
singing voice presents unique challenges due to its musical nature and the
presence of strong background music, making singing voice deepfake detection
(SVDD) a specialized field requiring focused attention. To promote SVDD
research, we recently proposed the "SVDD Challenge," the very first research
challenge focusing on SVDD for lab-controlled and in-the-wild bonafide and
deepfake singing voice recordings. The challenge will be held in conjunction
with the 2024 IEEE Spoken Language Technology Workshop (SLT 2024).


  This paper introduces a hypothesis space for deep learning that employs deep
neural networks (DNNs). By treating a DNN as a function of two variables, the
physical variable and parameter variable, we consider the primitive set of the
DNNs for the parameter variable located in a set of the weight matrices and
biases determined by a prescribed depth and widths of the DNNs. We then
complete the linear span of the primitive DNN set in a weak* topology to
construct a Banach space of functions of the physical variable. We prove that
the Banach space so constructed is a reproducing kernel Banach space (RKBS) and
construct its reproducing kernel. We investigate two learning models,
regularized learning and minimum interpolation problem in the resulting RKBS,
by establishing representer theorems for solutions of the learning models. The
representer theorems unfold that solutions of these learning models can be
expressed as linear combination of a finite number of kernel sessions
determined by given data and the reproducing kernel.


  Multimedia traffic is predicted to account for 82% of the total data traffic
by the year 2020. With the increasing popularity of video streaming
applications like YouTube, Netflix, Amazon Prime Video, popular video content
is often required to be delivered to a large number of users simultaneously.
Multicast transmission can be used for catering to such applications
efficiently. The common content can be transmitted to the users on the same
resources resulting in considerable resource conservation. This paper proposes
various schemes for efficient grouping and resource allocation for multicast
transmission in LTE. The optimal grouping and resource allocation problems are
shown to be NP-hard and so, we propose heuristic algorithms for both these
problems. We also formulate a Simulated Annealing based algorithm to
approximate the optimal resource allocation for our problem. The LP-relaxation
based resource allocation proposed by us results in allocations very close to
the estimated optimal.


  We present an one-dimensional particle-in-cell Monte-Carlo model for
capacitively coupled radio-frequency discharges in oxygen. The model
quantitatively describes the central part of the discharge. For a given voltage
and pressure, it self-consistently determines the electric potential and the
distribution functions for electrons, negatively charged atomic oxygen, and
positively charged molecular oxygen. Previously used collision cross sections
are critically assessed and in some cases modified. Provided associative
detachment due to metastable oxygen molecules is included in the model, the
electro-negativities in the center of the discharge are in excellent agreement
with experiments. Due to lack of empirical data for the cross section of this
process, we propose a simple model and discuss its limitations.


  Let R be rational map. Critical point c is called summable if series
$\sum_i\frac{1}{(R^i)'(R(c))}$ is absolutely convergent. Under some topological
condition on postcritical set we prove that R can not be structurally stable if
summable critical point $c \in J(R)$.


  In this article, we provide a detailed survey of techniques for hexahedral
mesh generation. We cover the whole spectrum of alternative approaches to mesh
generation, as well as post processing algorithms for connectivity editing and
mesh optimization. For each technique, we highlight capabilities and
limitations, also pointing out the associated unsolved challenges. Recent
relaxed approaches, aiming to generate not pure-hex but hex-dominant meshes,
are also discussed. The required background, pertaining to geometrical as well
as combinatorial aspects, is introduced along the way.


  Completion is one of the most studied techniques in term rewriting and
fundamental to automated reasoning with equalities. In this paper we present
new correctness proofs of abstract completion, both for finite and infinite
runs. For the special case of ground completion we present a new proof based on
random descent. We moreover extend the results to ordered completion, an
important extension of completion that aims to produce ground-complete
presentations of the initial equations. We present new proofs concerning the
completeness of ordered completion for two settings. Moreover, we revisit and
extend results of M\'etivier concerning canonicity of rewrite systems. All
proofs presented in the paper have been formalized in Isabelle/HOL.


  Ephemeral Fast Radio Bursts (FRBs) must be powered by some of the most
energetic processes in the Universe. That makes them highly interesting in
their own right and as precise probes for estimating cosmological parameters.
This field thus poses a unique challenge: FRBs must be detected promptly and
immediately localised and studied based only on that single
millisecond-duration flash. The problem is that the burst occurrence is highly
unpredictable and that their distance strongly suppresses their brightness.
Since the discovery of FRBs in single-dish archival data in 2007, detection
software has evolved tremendously. Pipelines now detect bursts in real-time
within a matter of seconds, operate on interferometers, buffer high-time and
frequency resolution data, and issue real-time alerts to other observatories
for rapid multi-wavelength follow-up. In this paper, we review the components
that comprise a FRB search software pipeline, we discuss the proven techniques
that were adopted from pulsar searches, we highlight newer, more efficient
techniques for detecting FRBs, and we conclude by discussing the proposed novel
future methodologies that may power the search for FRBs in the era of big data
astronomy.


  The un-reduction procedure introduced previously in the context of Mechanics
is extended to covariant Field Theory. The new covariant un-reduction procedure
is applied to the problem of shape matching of images which depend on more than
one independent variable (for instance, time and an additional labelling
parameter). Other possibilities are also explored: non-linear $\sigma$-models
and the hyperbolic flows of curves.


  The nonlinear interaction of x-rays with matter is at the heart of
understanding and controlling ultrafast molecular dynamics from an
atom-specific viewpoint, providing new scientific and analytical opportunities
to explore the structure and dynamics of small quantum systems. At increasingly
high x-ray intensity, the sensitivity of ultrashort x-ray pulses to specific
electronic states and emerging short-lived transient intermediates is of
particular relevance for our understanding of fundamental multi-photon
absorption processes. In this work, intense x-ray free-electron laser (XFEL)
pulses at the European XFEL (EuXFEL) are combined with a gas cell and grating
spectrometer for a high-intensity transmission spectroscopy study of
multiphoton-induced ultrafast molecular fragmentation dynamics in CF$_4$. This
approach unlocks the direct intra-pulse observation of transient fragments,
including neutral atoms, by their characteristic absorption lines in the
transmitted broad-band x-ray spectrum. The dynamics with and without initially
producing fluorine K-shell holes are studied by tuning the central photon
energy. The absorption spectra are measured at different FEL intensities to
observe nonlinear effects. Transient isolated fluorine atoms and ions are
spectroscopically recorded within the ultrashort pulse duration of few tens of
femtoseconds. An isosbestic point that signifies the correlated transition
between intact neutral CF$_4$ molecules and charged atomic fragments is
observed near the fluorine K-edge. The dissociation dynamics and the
multiphoton absorption-induced dynamics encoded in the spectra are
theoretically interpreted. Overall, this study demonstrates the potential of
high-intensity x-ray transmission spectroscopy to study ultrafast molecular
dynamics with sensitivity to specific intermediate species and their electronic
structure.


  We study the distances, called spacings, between pairs of neighboring energy
levels for the quantum harmonic oscillator. Specifically, we consider all
energy levels falling between E and E+1, and study how the spacings between
these levels change for various choices of E, particularly when E goes to
infinity. Primarily, we study the case in which the spring constant is a badly
approximable vector. We first give the proof by Boshernitzan-Dyson that the
number of distinct spacings has a uniform bound independent of E. Then, if the
spring constant has components forming a basis of an algebraic number field, we
show that, when normalized up to a unit, the spacings are from a finite set.
Moreover, in the specific case that the field has one fundamental unit, the
probability distribution of these spacings behaves quasiperiodically in log E.
We conclude by studying the spacings in the case that the spring constant is
not badly approximable, providing examples for which the number of distinct
spacings is unbounded.


  The three-rotor system concerns equally massive point particles moving on a
circle subject to attractive cosine potentials of strength $g$. The quantum
theory models chains of coupled Josephson junctions. Classically, it displays
order-chaos-order behavior with increasing energy $E$ along with a seemingly
globally chaotic phase for $5.33g \lesssim E \lesssim 5.6g$. It is also known
to admit pendulum and isosceles breather families of periodic orbits at all
energies. While pendula display a doubly infinite sequence of stability
transitions accumulating at their libration to rotation threshold at $E = 4g$,
breathers undergo only one stability transition. Here, we show that these
stability transitions are associated to forward and reverse fork-like
isochronous and period-doubling bifurcations. The new family of periodic orbits
born at each of these bifurcations is found using an efficient search algorithm
starting from a transverse perturbation to the parent orbit. The graphs of
stability indices of various classes of orbits born at pendulum bifurcations
meet at $E = 4g$ forming `fans'. The transitions in the librational and
rotational phases are related by an asymptotic duality between bifurcation
energies and shapes of newly born periodic orbits. The latter are captured by
solutions to a Lam\'e equation. We also find and numerically validate values of
scaling constants for self-similarity in (a) stability indices of librational
and rotational pendula and (b) shapes of newly born orbits as $E \to 4g$.
Finally, we argue that none of the infinitely many families of periodic orbits
we have found is stable for $5.33g \lesssim E \lesssim 5.6g$, providing further
evidence for global chaos in this energy band.


  We used chemical equilibrium calculations to model thermal outgassing of
ordinary chondritic material as a function of temperature, pressure, and bulk
compositions and use our results to discuss outgassing on asteroids and the
early Earth. The calculations include ~1,000 solids and gases of the elements
Al, C, Ca, Cl, Co, Cr, F, Fe, H, K, Mg, Mn, N, Na, Ni, O, P, S, Si, and Ti. The
major outgassed volatiles from ordinary chondritic material are CH4, H2, H2O,
N2, and NH3(the latter at conditions where hydrous minerals form). Contrary to
widely held assumptions, CO is never the major C-bearing gas during ordinary
chondrite metamorphism. The calculated oxygen fugacity (partial pressure) of
ordinary chondritic material is close to that of the quartz-fayalite-iron (QFI)
buffer. Our results are insensitive to variable total pressure, variable
volatile element abundances, and kinetic inhibition of C and N dissolution in
Fe metal. Our results predict that Earth's early atmosphere contained CH4, H2,
H2O, N2, and NH3; similar to that used in Miller-Urey synthesis of organic
compounds.


  Three-dimensional numerical simulations in a square duct were conducted to
investigate entrance lengths of normal fluid and superfluid flows in a thermal
counterflow of superfluid $^4$He. The two fluids were coarse-grained by using
the Hall-Vinen-Bekharevich-Khalatnikov (HVBK) model and were coupled through
mutual friction. We solved the HVBK equations by parameterizing the coefficient
of the mutual friction to consider the vortex line density. A uniform mutual
friction parameter was assumed in the streamwise direction. Our simulation
showed that the entrance length of the normal fluid from a hot end becomes
shorter than that of a single normal fluid due to the mutual friction with the
parabolically developed superfluid flow near the hot end. As the mutual
friction increases, the entrance length decreases. Same as that, the entrance
length of the superfluid from a cold end is affected by the strength of the
mutual friction due to the parabolically developed normal fluid flow near the
cold end. Aside from the entrance effect, the realized condition of a
tail-flattened flow is discussed by parameterizing the superfluid turbulent
eddy viscosity and the mutual friction.


  We present deep optical 18-medium-band photometry from the Subaru telescope
over the ~30' x 30' Extended Chandra Deep Field-South (ECDF-S), as part of the
Multiwavelength Survey by Yale-Chile (MUSYC). This field has a wealth of
ground- and space-based ancillary data, and contains the GOODS-South field and
the Hubble Ultra Deep Field. We combine the Subaru imaging with existing
UBVRIzJHK and Spitzer IRAC images to create a uniform catalog. Detecting
sources in the MUSYC BVR image we find ~40,000 galaxies with R_AB<25.3, the
median 5 sigma limit of the 18 medium bands. Photometric redshifts are
determined using the EAZY code and compared to ~2000 spectroscopic redshifts in
this field. The medium band filters provide very accurate redshifts for the
(bright) subset of galaxies with spectroscopic redshifts, particularly at 0.1 <
z < 1.2 and at z > 3.5. For 0.1 < z < 1.2, we find a 1 sigma scatter in \Delta
z/(1+z) of 0.007, similar to results obtained with a similar filter set in the
COSMOS field. As a demonstration of the data quality, we show that the red
sequence and blue cloud can be cleanly identified in rest-frame color-magnitude
diagrams at 0.1 < z < 1.2. We find that ~20% of the red-sequence-galaxies show
evidence of dust-emission at longer rest-frame wavelengths. The reduced images,
photometric catalog, and photometric redshifts are provided through the public
MUSYC website.


  Combining the characteristic method and the local discontinuous Galerkin
method with carefully constructing numerical fluxes, we design the variational
formulations for the time-dependent convection-dominated Navier-Stokes
equations in $\mathbb{R}^2$. The proposed symmetric variational formulation is
strictly proved to be unconditionally stable; and the scheme has the striking
benefit that the conditional number of the matrix of the corresponding matrix
equation does not increase with the refining of the meshes. The presented
scheme works well for a wide range of Reynolds numbers, e.g., the scheme still
has good error convergence when $Re=0.5 e+005$ or $1.0 e+ 008$. Extensive
numerical experiments are performed to show the optimal convergence orders and
the contours of the solutions of the equation with given initial and boundary
conditions.


  We propose a new, data-driven approach for efficient pricing of - fixed- and
float-strike - discrete arithmetic Asian and Lookback options when the
underlying process is driven by the Heston model dynamics. The method proposed
in this article constitutes an extension of our previous work, where the
problem of sampling from time-integrated stochastic bridges was addressed. The
model relies on the Seven-League scheme, where artificial neural networks are
employed to "learn" the distribution of the random variable of interest
utilizing stochastic collocation points. The method results in a robust
procedure for Monte Carlo pricing. Furthermore, semi-analytic formulae for
option pricing are provided in a simplified, yet general, framework. The model
guarantees high accuracy and a reduction of the computational time up to
thousands of times compared to classical Monte Carlo pricing schemes.


  Let $W_{g,n}$ be the correlators computed by Topological Recursion for some
given spectral curve $(x,y)$ and $W^\vee_{g,n}$ for $(y,x)$, where the role of
$x,y$ is inverted. These two sets of correlators $W_{g,n}$ and $W^\vee_{g,n}$
are related by the $x$-$y$ symplectic transformation. Bychkov, Dunin-Barkowski,
Kazarian and Shadrin computed a functional relation between two slightly
different sets of correlators. Together with Alexandrov, they proved that their
functional relation is indeed the $x$-$y$ symplectic transformation in
Topological Recursion. This article provides a fairly simple formula directly
between $W_{g,n}$ and $W^\vee_{g,n}$ which holds by their theorem for
meromorphic $x$ and $y$ with simple and distinct ramification points. Due to
the recent connection between free probability and fully simple vs ordinary
maps, we conclude a simplified moment-cumulant relation for moments and higher
order free cumulants.


  We show that two-dimensional sigma models are equivalent to certain perturbed
conformal field theories. When the fields in the sigma model take values in a
space G/H for a group G and a maximal subgroup H, the corresponding conformal
field theory is the $k\to\infty$ limit of the coset model $(G/H)_k$, and the
perturbation is related to the current of G. This correspondence allows us for
example to find the free energy for the "O(n)" (=O(n)/O(n-1)) sigma model at
non-zero temperature. It also results in a new approach to the CP^{n} model.


  We present a method for obtaining congruences modulo powers of a prime
number~$p$ for combinatorial sequences whose generating function satisfies an
algebraic differential equation. This method generalises the one by Kauers and
the authors [Electron. J. Combin. 8(2) (2012), Art. P37; arXiv:1107.2015] from
$p=2$ to arbitrary primes. Our applications include congruences for numbers of
non-crossing graphs and numbers of Kreweras walks modulo powers of~$3$, as well
as congruences for Fu\ss-Catalan numbers and blossom tree numbers modulo powers
of arbitrary primes.


  As statements regarding the soft limit of cosmological correlation functions,
consistency relations are known to exist in any flat FRW universe. In this
letter we explore the possibility of finding such relations in a spatially
closed universe, where the soft limit $\textbf{q}\rightarrow 0$ does not exist
in any rigorous sense. Despite the absence of spatial infinity of the spatial
slices, we find the adiabatic modes and their associated consistency relations
in a toy universe with background topology $R\times S^2$. Flat FRW universe
adiabatic modes are recovered via taking the large radius limit $R\gg
\mathcal{H}^{-1}$, for which we are living in a small local patch of Hubble
size on the sphere. It is shown that both dilation and translation adiabatic
modes in the local patch are recovered by a global dilation on the sphere,
acting at different places.


  We elaborate the description of the semi-classical gravity sector of
Yang-Mills matrix models on a covariant quantum FLRW background. The basic
geometric structure is a frame, which arises from the Poisson structure on an
underlying $S^2$ bundle over space-time. The equations of motion for the
associated Weitzenb\"ock torsion obtained in arXiv:2002.02742 are rewritten in
the form of Yang-Mills-type equations for the frame. An effective action is
found which reproduces these equations of motion, which contains an
Einstein-Hilbert term coupled to a dilaton, an axion and a Maxwell-type term
for the dynamical frame. An explicit rotationally invariant solution is found,
which describes a gravitational field coupled to the dilaton.


  The author (physicist)has observed the very strange,beautiful and frightening
Lightning Ball (LB). He has never forgotten this phenomenon. During his working
life he could not devote himself to the problem of LB-formation.Only two years
ago as he has been reading different unbelievable models of LB-formation, he
decided to work on this problem. By studying the literature and the crucial
points of his observation the author succeeded in creating a completely new
model of Lightning Ball(LB) and Ball Lightning(BL)-formation based on the
symmetry breaking of the hydrodynamic vortex ring.This agrees fully with the
observation and overcomes the shortcomings of current models of LB formation.
This model provides answers to the questions: Why are LBs so rarely
observed,why do BLs in rare cases have such a high energy and how can we
generate LB in the laboratory? Moreover the author differentiates between LB
and BL, the latter having a high energy and occuring in 5 % of the
observations. Keywords: ball lightning, hydrodynamic vortex ring, symmetry
breaking, electroluminescence, triboelectrification.


  Strain relaxation of thick InGaN layers was studied in order to develop
technology of InGaN templates for deposition of InGaN Quantum Wells (QWs) and
InGaN layers of high-In-content. In this paper, we show that InGaN layers grown
on misoriented (0001)-GaN substrates relax by preferential activation of
certain glide planes for misfit dislocation formation. Substrate misorientation
changes resolved shear stresses, affecting the distribution of misfit
dislocations within each dislocation set. We demonstrate that this mechanism
leads to an anisotropic strain as well as a tilt of the InGaN layer with
respect to the GaN substrate. It appears that these phenomena are more
pronounced in structures grown on substrates misoriented toward <11-20>
direction than corresponding structures with <-1100> misorientation. These
features would influence the properties of the overgrown InGaN QWs and should
be taken into consideration during designing structures grown on relaxed InGaN
templates. We reveal that the lattice of partially relaxed InGaN has a
triclinic deformation, thus requiring advanced XRD analysis. The presentation
of just a single asymmetric reciprocal space map commonly practiced in the
literature can lead to misleading information regarding the relaxation state of
partially relaxed wurtzite structures.


  Pure and bright single photon sources have recently been obtained by
inserting solid-state emitters in photonic nanowires or microcavities. The
cavity approach presents the attractive possibility to greatly increase the
source operation frequency. However, it is perceived as technologically
demanding because the emitter resonance must match the cavity resonance. Here
we show that the spectral matching requirement is actually strongly lifted by
the intrinsic coupling of the emitter to its environment. A single photon
source consisting of a single InGaAs quantum dot inserted in a micropillar
cavity is studied. Phonon coupling results in a large Purcell effect even when
the quantum dot is detuned from the cavity resonance. The phonon-assisted
cavity enhanced emission is shown to be a good single-photon source, with a
brightness exceeding $40$ \% for a detuning range covering 15 cavity
linewidths.


  Adaptability is a significant property which enables software systems to
continuously provide the required functionality and achieve optimal
performance. The recognised importance of adaptability makes its evaluation an
essential task. However, the various adaptability dimensions and implementation
mechanisms make adaptive strategies difficult to evaluate. In service oriented
computing, several frameworks that extend the WS-BPEL, the de facto standard in
composing distributed business applications, focus on enabling the adaptability
of processes. We aim to evaluate the adaptability of processes specified from
the extended-BPEL frameworks. In this paper, we propose metrics to measure the
adaptability of an AO4BPEL process. The metrics is grounded in the perspective
that a process is capable of dynamically adapting to changes in business
requirements. This opens potential future work on evaluating the adaptability
of processes specified from various aspect-oriented WS-BPEL frameworks.


  A recently reported phase sensitive Brillouin light scattering technique is
improved by use of a magnetic modulator. This modulator is based on Brillouin
light scattering in a thin ferrite film. Using this magnetic modulator in time-
and space Brillouin light scattering measurements we have increased phase
contrast and excluded influence of optical inhomogeneities in the sample. We
also demonstrate that the quality of the resulting interference patterns can be
improved by data postprocessing using the simultaneously recorded information
about the reference light.


  The utilization of large language models (LLMs) in the Healthcare domain has
generated both excitement and concern due to their ability to effectively
respond to freetext queries with certain professional knowledge. This survey
outlines the capabilities of the currently developed LLMs for Healthcare and
explicates their development process, with the aim of providing an overview of
the development roadmap from traditional Pretrained Language Models (PLMs) to
LLMs. Specifically, we first explore the potential of LLMs to enhance the
efficiency and effectiveness of various Healthcare applications highlighting
both the strengths and limitations. Secondly, we conduct a comparison between
the previous PLMs and the latest LLMs, as well as comparing various LLMs with
each other. Then we summarize related Healthcare training data, training
methods, optimization strategies, and usage. Finally, the unique concerns
associated with deploying LLMs in Healthcare settings are investigated,
particularly regarding fairness, accountability, transparency and ethics. Our
survey provide a comprehensive investigation from perspectives of both computer
science and Healthcare specialty. Besides the discussion about Healthcare
concerns, we supports the computer science community by compiling a collection
of open source resources, such as accessible datasets, the latest
methodologies, code implementations, and evaluation benchmarks in the Github.
Summarily, we contend that a significant paradigm shift is underway,
transitioning from PLMs to LLMs. This shift encompasses a move from
discriminative AI approaches to generative AI approaches, as well as a shift
from model-centered methodologies to data-centered methodologies. Also, we
determine that the biggest obstacle of using LLMs in Healthcare are fairness,
accountability, transparency and ethics.


  Measuring the stability of conclusions derived from Ordinary Least Squares
linear regression is critically important, but most metrics either only measure
local stability (i.e. against infinitesimal changes in the data), or are only
interpretable under statistical assumptions. Recent work proposes a simple,
global, finite-sample stability metric: the minimum number of samples that need
to be removed so that rerunning the analysis overturns the conclusion,
specifically meaning that the sign of a particular coefficient of the estimated
regressor changes. However, besides the trivial exponential-time algorithm, the
only approach for computing this metric is a greedy heuristic that lacks
provable guarantees under reasonable, verifiable assumptions; the heuristic
provides a loose upper bound on the stability and also cannot certify lower
bounds on it.
  We show that in the low-dimensional regime where the number of covariates is
a constant but the number of samples is large, there are efficient algorithms
for provably estimating (a fractional version of) this metric. Applying our
algorithms to the Boston Housing dataset, we exhibit regression analyses where
we can estimate the stability up to a factor of $3$ better than the greedy
heuristic, and analyses where we can certify stability to dropping even a
majority of the samples.


  Let $g$ be a map from the set of positive integers into itself defined as
follows: Let $x$ be a positive integer. If $x$ is odd, then $g(x)=3x+1$, and if
$x$ is even, then $g(x)=x/2$. The $3x+1$ conjecture, also called the Collatz
conjecture, states: For any positive integer $x$ there exists another positive
integer $m$ such that the $m$-iterate of $x$ under the map $g$ is equal to $1$,
i.e. $g^m(x)=1$. We provide some information related with this conjecture.


  The standard cosmological model, based on general relativity with an
inflationary era, is very effective in accounting for a broad range of observed
features of the universe. However, the ongoing puzzles about the nature of dark
matter and dark energy, together with the problem of a fundamental theoretical
framework for inflation, indicate that cosmology may be probing the limits of
validity of general relativity. The early universe provides a testing ground
for theories of gravity, since gravitational dynamics can lead to
characteristic imprints on the CMB and other cosmological observations.
Precision cosmology is in principle a means to constrain and possibly falsify
candidate quantum gravity theories like M theory. Generalized Randall-Sundrum
brane-worlds provide a phenomenological means to test aspects of M theory. I
outline the 1+3-covariant approach to cosmological perturbations in these
brane-worlds, and its application to CMB anisotropies.


  We show that C.J.Read's example of an operator T on l_1 which does not have
any non-trivial invariant subspaces is not the adjoint of an operator on a
predual of l_1. Furthermore, we present a bounded diagonal operator D such that
even though its inverse is unbounded, but D^{-1}TD is a bounded operator with
invariant subspaces, and is adjoint to an operator on c_0.


  We study a process of slow mixing in stars with convective envelopes, which
is driven by the settling of cool downward plumes below the base of the
convection zone. If a small fraction (of order $10^{-7}$) of the material
cooled at the surface retains a significant entropy deficit while descending in
plumes, it can reach the depth where lithium burning takes place. The model
calculates the thermal response and mixing below the convection zone due to the
settling process, assuming that the plumes arrive at the base of the convection
zone with a broad range of entropy contrasts. We obtain a good fit to the
observed lithium depletion in the Sun by assuming that the settling mass flux
is distributed with respect to the entropy contrast as a power law with a slope
around -2. We find convective settling to have a negligible influence on the
stratification below the convection zone, although mixing induced by it could
modify the gradient of helium concentration.


  The conventional method of glucose measurement such as pricking blood from
the body is prevalent which brings pain and trauma. Invasive methods of
measurement sometimes raise the risk of blood infection to the patient.
Sometimes, some of the physiological parameters such as body temperature and
systolic blood pressure (SBP) are responsible for blood glucose level
fluctuations. Moreover, diabetes for a long duration usually becomes a critical
issue. In such situation, patients need to consult diabetologist frequently,
which is not possible in normal life. Therefore, it is required to develop
non-invasive glucose balancing paradigm, which measures blood glucose without
pricking blood along with physiological parameters measurement and decision
model. The proposed paradigm helps to doctor, who is even available at remote
location. There will not be any need to consult frequently. In the way of
optimized non-invasive system design, an NIRS technique with specific
wavelengths along with physiological parameters is taken to predict the precise
glucose value. The all parameters (glucose, Blood pressure and body
temperature), food intake and insulin levels are parts of decision model, which
would help to the doctor to take decision related to the further medicine doses
and diet plan. The patients would have suggestions according to maintain their
blood glucose level. The proposed system demonstrated an accurate model with
MARD and AvgE 12.50% and 12.10% respectively using DNN model. Coefficient of
determination R2 has been found 0.97.


  We present the theoretical basis and sample Monte Carlo data for the YFS
exponentiated calculation of $e^+e^- \to Z Z \to f_1\bar f_1 + \bar f_2 f_2$ at
and beyond LEP2 energies, where the left-handed part of $f_i$ is a component of
an $SU_{2L}$ doublet, $i=1,2$. The calculation is performed for both SM
couplings and for anomalous $ZZV$ triple gauge boson couplings in the
conventions of Hagiwara et al.. Our formulas, which are gauge invariant, are
illustrated in a proto-typical YFS Monte Carlo event generator YFSZZ.


  We present the statistics of faint submillimeter/millimeter galaxies (SMGs)
and serendipitous detections of a submillimeter/millimeter line emitter (SLE)
with no multi-wavelength continuum counterpart revealed by the deep ALMA
observations. We identify faint SMGs with flux densities of 0.1-1.0 mJy in the
deep Band 6 and Band 7 maps of 10 independent fields that reduce cosmic
variance effects. The differential number counts at 1.2 mm are found to
increase with decreasing flux density down to 0.1 mJy. Our number counts
indicate that the faint (0.1-1.0 mJy, or SFR_IR ~ 30-300 Msun/yr) SMGs
contribute nearly a half of the extragalactic background light (EBL), while the
remaining half of the EBL is mostly contributed by very faint sources with flux
densities of <0.1 mJy (SFR_IR <~ 30 Msun/yr). We conduct counts-in-cells
analysis with the multifield ALMA data for the faint SMGs, and obtain a coarse
estimate of galaxy bias, b_g <4. The galaxy bias suggests that the dark halo
masses of the faint SMGs are <~ 7x10^12 Msun, which is smaller than those of
bright (>1 mJy) SMGs, but consistent with abundant high-z star-forming
populations such as sBzKs, LBGs, and LAEs. Finally, we report the serendipitous
detection of SLE-1 with continuum counterparts neither in our 1.2 mm-band nor
multi-wavelength images including ultra deep HST/WFC3 and Spitzer data. The SLE
has a significant line at 249.9 GHz with a signal-to-noise ratio of 7.1. If the
SLE is not a spurious source made by unknown systematic noise of ALMA, the
strong upper limits of our multi-wavelength data suggest that the SLE would be
a faint galaxy at z >~ 6.


  Ab initio quantum chemical calculations of Heisenberg exchange in linear
cuprate antiferromagnets are reported. For Sr2CuO3 I obtain Ja=-119 meV for the
intrachain coupling and Jb=-0.28 meV for the interchain coupling. For Ca2CuO3 I
find Ja=-119 meV and Jb=-0.52 meV. With these values, recent mean field theory
gives the staggered magnetic moments as 0.069 and 0.095 mB, in full agreement
with recent experiments. The experimental Neel temperatures are found to be
proportional to the ratio Jb/Ja to a high accuracy. This indicates that the
isolated chain is an antiferromagnet with vanishing Tn.


  Let $p$ be a prime number. We develop a theory of $p$-adic Mahler measure of
polynomials and apply it to the study of $\mathbb{Z}$-covers of rational
homology 3-spheres branched over links. We obtain a $p$-adic analogue of the
asymptotic formula of the torsion homology growth and a balance formula among
the leading coefficient of the Alexander polynomial, the $p$-adic entropy, and
the Iwasawa $\mu_p$-invariant. We also apply the purely $p$-adic theory of
Besser--Deninger to $\mathbb{Z}$-covers of links. In addition, we study the
entropies of profinite cyclic covers of links. We examine various examples
throughout the paper.


  The domestication and development of cattle has considerably impacted human
societies, but the histories of cattle breeds have been poorly understood
especially for African, Asian, and American breeds. Using genotypes from 43,043
autosomal single nucleotide polymorphism markers scored in 1,543 animals, we
evaluate the population structure of 134 domesticated bovid breeds. Regardless
of the analytical method or sample subset, the three major groups of Asian
indicine, Eurasian taurine, and African taurine were consistently observed.
Patterns of geographic dispersal resulting from co-migration with humans and
exportation are recognizable in phylogenetic networks. All analytical methods
reveal patterns of hybridization which occurred after divergence. Using 19
breeds, we map the cline of indicine introgression into Africa. We infer that
African taurine possess a large portion of wild African auroch ancestry,
causing their divergence from Eurasian taurine. We detect exportation patterns
in Asia and identify a cline of Eurasian taurine/indicine hybridization in
Asia. We also identify the influence of species other than Bos taurus in the
formation of Asian breeds. We detect the pronounced influence of Shorthorn
cattle in the formation of European breeds. Iberian and Italian cattle possess
introgression from African taurine. American Criollo cattle are shown to be of
Iberian, and not African, decent. Indicine introgression into American cattle
occurred in the Americas, and not Europe. We argue that cattle migration,
movement and trading followed by admixture have been important forces in
shaping modern bovine genomic variation.


  This work summarizes part of current knowledge on High-level Cognitive
process and its relation with biological hardware. Thus, it is possible to
identify some paradoxes which could impact the development of future
technologies and artificial intelligence: we may make a High-level Cognitive
Machine, sacrificing the principal attribute of a machine, its accuracy.


  Monolayer transition metal dichalcogenides (TMDs) hold great promise for
future information processing applications utilizing a combination of electron
spin and valley pseudospin. This unique spin system has led to observation of
the valley Zeeman effect in neutral and charged excitonic resonances under
applied magnetic fields. However, reported values of the trion valley Zeeman
splitting remain highly inconsistent across studies. Here, we utilize high
quality hBN encapsulated monolayer WSe$_2$ to enable simultaneous measurement
of both intervalley and intravalley trion photoluminescence. We find the valley
Zeeman splitting of each trion state to be describable only by a combination of
three distinct g-factors, one arising from the exciton-like valley Zeeman
effect, the other two, trion specific, g-factors associated with recoil of the
excess electron. This complex picture goes significantly beyond the valley
Zeeman effect reported for neutral excitons, and eliminates the ambiguity
surrounding the magneto-optical response of trions in tungsten based TMD
monolayers.


  We prove general necessary optimality conditions for delta-nabla
isoperimetric problems of the calculus of variations.


  We consider a simple dynamic model of the vibrating screen operating in the
parametric resonance (PR) mode. This model was used in the course of designing
and setting of such a screen in LPMC. The PR-based screen compares favorably
with conventional types of such machines, where the transverse oscillations are
excited directly. It is characterized by larger values of the amplitude and by
insensitivity to damping in a rather wide range. The model represents an
initially strained system of two equal masses connected by a linearly elastic
string. Self-equilibrated, longitudinal, harmonic forces act on the masses.
Under certain conditions this results in transverse, finite-amplitude
oscillations of the string. The problem is reduced to a system of two ordinary
differential equations coupled by the geometric nonlinearity. Damping in both
the transverse and longitudinal oscillations is taken into account. Free and
forced oscillations of this mass-string system are examined analytically and
numerically. The energy exchange between the longitudinal and transverse modes
of free oscillations is demonstrated. An exact analytical solution is found for
the forced oscillations, where the coupling plays the role of a stabilizer. In
a more general case, the harmonic analysis is used with neglect of the higher
harmonics. Explicit expressions for all parameters of the steady nonlinear
oscillations are determined. The domains are found where the analytically
obtained steady oscillation regimes are stable. Over the frequency ranges,
where the steady oscillations exist, a perfect correspondence is found between
the amplitudes obtained analytically and numerically. Illustrations based on
the analytical and numerical simulations are presented.


  In this paper, we present a meshless method belonging to the family of
element-free Galerkin (EFG) methods. The distinguishing feature of the
presented meshless method is that it allows accurate enforcement of essential
boundary conditions. The method uses total Lagrangian formulation with explicit
time integration to facilitate code simplicity and robust computations in
applications that involve large deformations and non-linear materials. We use a
regularized weight function, which closely approximates the Kronecker delta, to
generate interpolating shape functions. The imposition of the prescribed
displacements on the boundary becomes as straightforward as in the finite
element (FE) method. The effectiveness and accuracy of the proposed method is
demonstrated using 3D numerical examples that include cylinder indentation by
70% of its initial height, and indentation of the brain.


  The Internet of things (IoT), which is the network of physical devices
embedded with sensors, actuators, and connec- tivity, is being accelerated into
the mainstream by the emergence of 5G wireless networking. This paper presents
an uncoordinated non-orthogonal random access protocol, an enhancement to the
recently introduced Aloha-NOMA protocol, which provides high throughput, while
being matched to the low complexity requirements and the sporadic traffic
pattern of IoT devices. Under ideal conditions it has been shown that
Aloha-NOMA, using power-domain orthogonality, can significantly increase the
throughput using SIC (Successive Interference Cancellation) to enable correct
reception of multiple simultaneous transmitted signals. For this ideal
performance, the enhanced Aloha-NOMA receiver adaptively learns the number of
active devices (which is not known a priori) using a form of multi-hypothesis
testing. For small numbers of simultaneous transmissions, it is shown that
there can be substantial throughput gain of 6.9 dB relative to pure Aloha for
0.25 probability of transmission and up to 3 active transmitters.


  Consider a system of $N$ non-intersecting Brownian bridges in $[0,1]$, and
let $\mathcal M_N(p)$ be the maximal height attained by the top path in the
interval $[0,p]$, $p\in[0,1]$. It is known that, under a suitable rescaling,
the distribution of $\mathcal M_N(p)$ converges, as $N\to\infty$, to a
one-parameter family of distributions interpolating between the Tracy-Widom
distributions for the Gaussian Orthogonal and Unitary Ensembles (corresponding,
respectively, to $p\to1$ and $p\to0$). It is also known that, for fixed $N$,
$\mathcal M_N(1)$ is distributed as the top eigenvalue of a random matrix drawn
from the Laguerre Orthogonal Ensemble. Here we show a version of these results
for $\mathcal M_N(p)$ for fixed $N$, showing that $\mathcal M_N(p)/\sqrt{p}$
converges in distribution, as $p\to0$, to the rightmost charge in a generalized
Laguerre Unitary Ensemble, which coincides with the top eigenvalue of a random
matrix drawn from the Antisymmetric Gaussian Ensemble.


  We propose a framework for joint entropy coding and encryption using Chaotic
maps. We begin by observing that the message symbols can be treated as the
symbolic sequence of a discrete dynamical system. For an appropriate choice of
the dynamical system, we could back-iterate and encode the message as the
initial condition of the dynamical system. We show that such an encoding
achieves Shannon's entropy and hence optimal for compression. It turns out that
the appropriate discrete dynamical system to achieve optimality is the
piecewise-linear Generalized Luroth Series (GLS) and further that such an
entropy coding technique is exactly equivalent to the popular Arithmetic Coding
algorithm. GLS is a generalization of Arithmetic Coding with different modes of
operation.
  GLS preserves the Lebesgue measure and is ergodic. We show that these
properties of GLS enable a framework for joint compression and encryption and
thus give a justification of the recent work of Grangetto et al. and Wen et al.
Both these methods have the obvious disadvantage of the key length being equal
to the message length for strong security. We derive measure preserving
piece-wise non-linear GLS (nGLS) and their skewed cousins, which exhibit Robust
Chaos. We propose a joint entropy coding and encryption framework using
skewed-nGLS and demonstrate Shannon's desired sensitivity to the key parameter.
Potentially, our method could improve the security and key efficiency over
Grangetto's method while still maintaining the total compression ratio. This is
a new area of research with promising applications in communications.


  A key question to QCD is what mechanism generates the hadron mass in the
light quark sector, where both confinement and chiral symmetry breaking are in
the game. Are confinement and chiral symmetry breaking in the vacuum uniquely
interconnected? Can hadrons survive chiral symmetry restoration? If yes, what
happens with their mass and what symmetries beyond the chiral symmetry are
there? We review our recent insights. In particular, in a dynamical lattice
simulation we artificially restore chiral symmetry by removing the low-lying
Dirac modes of the valence quark propagators, which is a well defined procedure
and keep gluodynamics intact. Hadrons survive this artificial chiral
restoration and their mass is surprisingly large. All hadrons fall into chiral
multiplets and some of them are degenerate, i.e. the spectrum reveals some
higher symmetry, that includes the chiral symmetry as a subgroup. The U(1)_A
symmetry does not get restored after removal of the chiral modes from the
valence quarks.


  The widespread use of the noninteracting ground state as the initial state
for the digital quantum simulation of the Fermi-Hubbard model is largely due to
the scarcity of alternative easy-to-prepare approximations to the exact ground
state in the literature. Exploiting the fact that the spin-$\frac{1}{2}$
Heisenberg model is the effective low-energy theory of the Fermi-Hubbard model
at half-filling in the strongly interacting limit, here we propose a three-step
deterministic quantum routine to prepare an educated guess of the ground state
of the Fermi-Hubbard model through a shallow circuit suitable for near-term
quantum hardware. First, the ground state of the Heisenberg model is
initialized via a hybrid variational method using an ansatz that explores only
the correct symmetry subspace. Second, a general method is devised to convert a
multi-spin-$\frac{1}{2}$ wave function into its fermionic version. Third,
taking inspiration from the Baeriswyl ansatz, a constant-depth single-parameter
layer that adds doublon-holon pairs is applied to this fermionic state.
Numerical simulations on chains and ladders with up to 12 sites confirm the
improvement over the noninteracting ground state of the overlap with the exact
ground state for the intermediate values of the interaction strength at which
quantum simulation is bound to be most relevant.


  We prove a quantitative propagation of chaos, uniformly in time, for the
spatially homogeneous Landau equation in the case of Maxwellian molecules. We
improve the results of Fontbona, Gu\'erin and M\'el\'eard \cite{FonGueMe} and
Fournier \cite{Fournier} where the propagation of chaos is proved for finite
time. Moreover, we prove a quantitative estimate on the rate of convergence to
equilibrium uniformly in the number of particles.


  The abrupt and permanent changes of photospheric magnetic field in the
localized regions of active regions during solar flares called magnetic
imprints (MIs), have been observed for the past nearly three decades. The well
known "coronal implosion" model is assumed to explain such flare associated
changes but the complete physical understanding is still missing and debatable.
In this study, we made a systematic analysis of flare-related changes of
photospheric magnetic field during 21 flares (14 eruptive and 7 non-eruptive)
using the high-cadence (\texttt{135s}) vector-magnetogram data obtained from
Helioseismic and Magnetic Imager. The MI regions for eruptive flares are found
to be strongly localised, whereas the majority of non-eruptive events
($>70~\%$) have scattered imprint regions. To quantify the strength of the MIs,
we derived the integrated change of horizontal field and total change of
Lorentz force over an area. These quantities correlate well with the flare
strength, irrespective of whether flares being eruptive or not, short or long
duration. Further, the free-energy (FE), determined from virial-theorem
estimates, exhibits statistically significant downward trend which starts
around the flare time is observed in majority of flares. The change of FE
during flares do not depend on eruptivity but have a strong positive
correlation ($\approx 0.8$) with the Lorentz force change, indicating that the
part of FE released would penetrate into the photosphere. While these results
strongly favor the idea of significant feedback from corona on the photospheric
magnetic field, the characteristics of MIs are quite indistinguishable for
flares being eruptive or not.


  We show that the excess in the Galactic electron flux recently published by
Chang, et al. (Nature, 20 Nov. 2008) can have a simple methodical origin due to
a contribution from misidentified proton induced electron-like events in the
ATIC detector. A subtraction of the cosmic ray proton component from the
published ATIC electron flux eliminates this excess in the range of 300 to 800
GeV.


  A polynomial form is established for the off-shell CHY scattering equations
proposed by Lam and Yao. Re-expressing this in terms of independent Mandelstam
invariants provides a new expression for the polynomial scattering equations,
immediately valid off shell, which makes it evident that they yield the
off-shell amplitudes given by massless $\phi^3$ Feynman graphs. A CHY
expression for individual Feynman graphs, valid even off shell, is established
through a recurrence relation.


  Let K be a variety of (commutative, integral) residuated lattices. The
substructural logic usually associated with K is an algebraizable logic that
has K as its equivalent algebraic semantics, and is a logic that preserves
truth, i.e., 1 is the only truth value preserved by the inferences of the
logic. In this paper we introduce another logic associated with K, namely the
logic that preserves degrees of truth, in the sense that it preserves lower
bounds of truth values in inferences. We study this second logic mainly from
the point of view of abstract algebraic logic. We determine its algebraic
models and we classify it in the Leibniz and the Frege hierarchies: we show
that it is always fully selfextensional, that for most varieties K it is
non-protoalgebraic, and that it is algebraizable if and only K is a variety of
generalized Heyting algebras, in which case it coincides with the logic that
preserves truth. We also characterize the new logic in three ways: by a Hilbert
style axiomatic system, by a Gentzen style sequent calculus, and by a set of
conditions on its closure operator. Concerning the relation between the two
logics, we prove that the truth preserving logic is the purely inferential
extension of the one that preserves degrees of truth with either the rule of
Modus Ponens or the rule of Adjunction for the fusion connective.


  The main purpose of this article is to give the integral cohomology of
classical principal congruence subgroups in SL(2,Z) as well as their analogues
in the third braid group with local coefficients in symmetric powers of the
natural symplectic representation. The resulting answers (1) correspond to
certain modular forms in characteristic zero, and (2) the cohomology of certain
spaces in homotopy theory in characteristic p. The torsion is given in terms of
the structure of a "p-divided power algebra".
  The work is an extension of the work in arXiv:1204.5390v1 as well as
extensions of a classical computation of Shimura to integral coefficients. The
results here contrast the local coefficients such as that in [Looijenga, J.
Alg. Geom., 5, '96] and [Tillmann, Q. J. Math., 61, '10].


  A popular tool for unsupervised modelling and mining multi-aspect data is
tensor decomposition. In an exploratory setting, where and no labels or ground
truth are available how can we automatically decide how many components to
extract? How can we assess the quality of our results, so that a domain expert
can factor this quality measure in the interpretation of our results? In this
paper, we introduce AutoTen, a novel automatic unsupervised tensor mining
algorithm with minimal user intervention, which leverages and improves upon
heuristics that assess the result quality. We extensively evaluate AutoTen's
performance on synthetic data, outperforming existing baselines on this very
hard problem. Finally, we apply AutoTen on a variety of real datasets,
providing insights and discoveries. We view this work as a step towards a fully
automated, unsupervised tensor mining tool that can be easily adopted by
practitioners in academia and industry.


  The stability of a sheared magnetic field is analyzed in two-dimensional
magnetohydrodynamics with resistive and viscous dissipation. Using a
multiple-scale analysis, it is shown that at large enough Reynolds numbers the
basic state describing a motionless fluid and a layered magnetic field, becomes
unstable with respect to large scale perturbations. The exact expressions for
eddy-viscosity and eddy-resistivity are derived in the nearby of the critical
point where the instability sets in. In this marginally unstable case the
nonlinear phase of perturbation growth obeys to a Cahn-Hilliard-like dynamics
characterized by coalescence of magnetic islands leading to a final new
equilibrium state. High resolution numerical simulations confirm quantitatively
the predictions of multiscale analysis.


  Machine Learning models incorporating multiple layered learning networks have
been seen to provide effective models for various classification problems. The
resulting optimization problem to solve for the optimal vector minimizing the
empirical risk is, however, highly nonlinear. This presents a challenge to
application and development of appropriate optimization algorithms for solving
the problem. In this paper, we summarize the primary challenges involved and
present the case for a Newton-based method incorporating directions of negative
curvature, including promising numerical results on data arising from security
anomally deetection.


  Ultracool stellar atmospheres show absorption by alkali resonance lines
severely broadened by collisions with neutral perturbers. In the coolest and
densest atmospheres, such as those of T dwarfs, Na I and K I broadened by
molecular hydrogen and helium can come to dominate the entire optical spectrum.
The effects of NaHe collision broadening are also central to understanding the
opacity of cool DZ white dwarf stars. In order to be able to construct
synthetic spectra of brown dwarfs and cool DZ white dwarfs, where helium
density can reach several 10^21~cm-3 NaHe line profiles of the resonance lines
have been computed over a wide range of densities and temperatures. Unified
line profiles that are valid from the core to the far wings at high densities
are calculated in the semiclassical approach using up-to-date molecular data
including in particular electronic spin-orbit coupling from the sodium atom. We
present a comprehensive study of Na-He collisional profiles at high density,
and temperatures from 5000~K, the temperature prevailing in the atmosphere of
ultra-cool DZ white dwarf stars, down to 1~K, the temperature in liquid helium
clusters. Collision broadening and shift parameters within the impact
approximation obtained in the semiclassical and quantum theory using our new
accurate molecular data are presented.


  Let (M,g) be a compact Riemannian manifold of dimension >2. We show that
there is a metric h conformal to g and of volume 1 such that the first positive
eigenvalue the conformal Laplacian with repect to h is arbitrarily large. A
similar statement is proven for the first positive eigenvalue of the Dirac
operator on a spin manifold of dimension >1.


  There is a venerable position in the philosophy of space and time that holds
that the geometry of spacetime is conventional, provided one is willing to
postulate a "universal force field". Here we ask a more focused question,
inspired by this literature: in the context of our best classical theories of
space and time, if one understands "force" in the standard way, can one
accommodate different geometries by postulating a new force field? We argue
that the answer depends on one's theory. In Newtonian gravitation the answer is
"yes"; in relativity theory, it is "no".


  We address the problem of achieving persistent surveillance over an
environment by using energy-constrained unmanned aerial vehicles (UAVs), which
are supported by unmanned ground vehicles (UGVs) serving as mobile charging
stations. Specifically, we plan the trajectories of all vehicles and the
charging schedule of UAVs to minimize the long-term maximum age, where age is
defined as the time between two consecutive visits to regions of interest in a
partitioned environment. We introduce a scalable planning strategy based on 1)
creating UAV- UGV teams, 2) decomposing the environment into optimal partitions
that can be covered by any of the teams in a single fuel cycle, 3) uniformly
distributing the teams over a cyclic path traversing those partitions, and 4)
having the UAVs in each team cover their current partition and be transported
to the next partition while being recharged by the UGV. We show some results
related to the safety and performance of the proposed strategy.


  In a schematic model with equidistant fourfold degenerate single-nucleon
levels, a conventional isovector pairing force and a symmetry force, the RPA
correlation energy rises almost linearly with the isospin T, thus producing a
Wigner term in accordance with the empirical proportionality of the symmetry
energy to T(T+1).


  When a large group of pedestrians moves around a corner, most pedestrians do
not follow the shortest path, which is to stay as close as possible to the
inner wall, but try to minimize the travel time. For this they accept to move
on a longer path with some distance to the corner, to avoid large densities and
by this succeed in maintaining a comparatively high speed. In many models of
pedestrian dynamics the basic rule of motion is often either "move as far as
possible toward the destination" or - reformulated - "of all coordinates
accessible in this time step move to the one with the smallest distance to the
destination". Atop of this rule modifications are placed to make the motion
more realistic. These modifications usually focus on local behavior and neglect
long-ranged effects. Compared to real pedestrians this leads to agents in a
simulation valuing the shortest path a lot better than the quickest. So, in a
situation as the movement of a large crowd around a corner, one needs an
additional element in a model of pedestrian dynamics that makes the agents
deviate from the rule of the shortest path. In this work it is shown, how this
can be achieved by using a flood fill dynamic potential field method, where
during the filling process the value of a field cell is not increased by 1, but
by a larger value, if it is occupied by an agent. This idea may be an obvious
one, however, the tricky part - and therefore in a strict sense the
contribution of this work - is a) to minimize unrealistic artifacts, as naive
flood fill metrics deviate considerably from the Euclidean metric and in this
respect yield large errors, b) do this with limited computational effort, and
c) keep agents' movement at very low densities unaltered.


  Understanding the resilience of infrastructures such as transportation
network has significant importance for our daily life. Recently, a homogeneous
spatial network model was developed for studying spatial embedded networks with
characteristic link length such as power-grids and the brain. However, although
many real-world networks are spatially embedded and their links have
characteristics length such as pipelines, power lines or ground transportation
lines they are not homogeneous but rather heterogeneous. For example, density
of links within cities are significantly higher than between cities. Here we
present and study numerically and analytically a similar realistic
heterogeneous spatial modular model using percolation process to better
understand the effect of heterogeneity on such networks. The model assumes that
inside a city there are many lines connecting different locations, while long
lines between the cities are sparse and usually directly connecting only a few
nearest neighbours cities in a two dimensional plane. We find that this model
experiences two distinct continues transitions, one when the cities disconnect
from each other and the second when each city breaks apart. Although the
critical threshold for site percolation in 2D grid remains an open question we
analytically find the critical threshold for site percolation in this model. In
addition, while the homogeneous model experience a single transition having a
unique phenomenon called \textit{critical stretching} where a geometric
crossover from random to spatial structure in different scales found to stretch
non-linearly with the characteristic length at criticality. Here we show that
the heterogeneous model does not experience such a phenomenon indicating that
critical stretching strongly depends on the network structure.


  We propose the experimental realization of (3+1) relativistic Dirac fermions
using ultracold atoms in a rotating optical lattice or, alternatively, in a
synthetic magnetic field. This approach has the advantage to give mass to the
Dirac fermions by coupling the ultracold atoms to a Bragg pulse. A dimensional
crossover from (3+1) to (2+1) Dirac fermions can be obtained by varying the
anisotropy of the lattice. We also discuss under which conditions the
interatomic potentials give rise to relativistically invariant interactions
among the Dirac fermions.


  We investigate the flux flow state in a two-gap superconductor in which two
s-wave gaps with different amplitudes exist on two separate Fermi surfaces. The
flux flow resistivity is obtained on the basis of the Bardeen-Stephen relation
and the result agrees well with the anomalous field dependence of the flow
resistivity recently observed in the two-gap superconductor MgB2. Some typical
properties of the vortex in this system are also discussed.


  This paper analyzes stealthy attacks, particularly the zero-dynamics attack
(ZDA) in networked control systems. ZDA hides the attack signal in the
null-space of the state-space representation of the control system and hence it
cannot be detected via conventional detection methods. A natural defense
strategy builds on changing the null-space via switching through a set of
topologies. In this paper, we propose a realistic ZDA variation where the
attacker is aware of this topology-switching strategy, and hence employs the
policy to avoid detection: "pause (update and resume) attack" before (after)
topology switching to evade detection. We first systematically study the
proposed ZDA variation, and then develop defense strategies under the realistic
assumptions. Particularly, we characterize conditions for detectability of the
proposed ZDA variation, in terms of the network topologies to be maintained,
the set of agents to be monitored, and the measurements of the monitored agents
that should be extracted. We provide numerical results that demonstrate our
theoretical findings.


  We study Cheeger and $p$-eigenvalue partition problems depending on a given
evaluation function $\Phi$ for $p\in[1,\infty)$. We prove existence and
regularity of minima, relations among the problems, convergence, and stability
with respect to $p$ and to $\Phi$.


  The paper is devoted to the large scale geometry of the Heisenberg group
$\mathbb H$ equipped with left-invariant Riemannian distances.
  We prove that two such distances have bounded difference if and only if they
are asymptotic, i.e., their ratio goes to one, at infinity.
  Moreover, we show that for every left-invariant Riemannian distance $d$ on
$\mathbb H$ there is a unique subRiemanniann metric $d'$ for which $d-d'$ goes
to zero at infinity, and we estimate the rate of convergence.
  As a first immediate consequence we get that the Riemannian Heisenberg group
is at bounded distance from its asymptotic cone.
  The second consequence, which was our aim, is the explicit description of the
horoboundary of the Riemannian Heisenberg group.


  Two-state models provide phenomenological descriptions of many different
systems, ranging from physics to chemistry and biology. We investigate work
fluctuations in an ensemble of two-state systems driven out of equilibrium
under the action of an external perturbation. We calculate the probability
density P(W) that a work equal to W is exerted upon the system along a given
non-equilibrium trajectory and introduce a trajectory thermodynamics formalism
to quantify work fluctuations in the large-size limit. We then define a
trajectory entropy S(W) that counts the number of non-equilibrium trajectories
P(W)=exp(S(W)/kT) with work equal to W. A trajectory free-energy F(W) can also
be defined, which has a minimum at a value of the work that has to be
efficiently sampled to quantitatively test the Jarzynski equality. Within this
formalism a Lagrange multiplier is also introduced, the inverse of which plays
the role of a trajectory temperature. Our solution for P(W) exactly satisfies
the fluctuation theorem by Crooks and allows us to investigate
heat-fluctuations for a protocol that is invariant under time reversal. The
heat distribution is then characterized by a Gaussian component (describing
small and frequent heat exchange events) and exponential tails (describing the
statistics of large deviations and rare events). For the latter, the width of
the exponential tails is related to the aforementioned trajectory temperature.
Finite-size effects to the large-N theory and the recovery of work
distributions for finite N are also discussed. Finally, we pay particular
attention to the case of magnetic nanoparticle systems under the action of a
magnetic field H where work and heat fluctuations are predicted to be
observable in ramping experiments in micro-SQUIDs.


  A defensive alliance in an undirected graph $G=(V,E)$ is a non-empty set of
vertices $S$ satisfying the condition that every vertex $v\in S$ has at least
as many neighbours (including itself) in $S$ as it has in $V\setminus S$. We
consider the notion of global minimality in this paper. We are interested in
globally minimal defensive alliance of maximum size. This problem is known to
be NP-hard but its parameterized complexity remains open until now. We enhance
our understanding of the problem from the viewpoint of parameterized complexity
by showing that the Globally Minimal Defensive Alliance problem is FPT
parameterized by the neighbourhood diversity of the input graph. The result for
neighborhood diversity implies that the problem is FPT parameterized by vertex
cover number also. We prove that the problem parameterized by the vertex cover
number of the input graph does not admit a polynomial compression unless coNP
$\subseteq$ NP/poly. We show that the problem is W[1]-hard parameterized by a
wide range of fairly restrictive structural parameters such as the feedback
vertex set number, pathwidth, treewidth and treedepth. We also proved that,
given a vertex $r \in V(G)$, deciding if $G$ has a globally minimal defensive
alliance of any size containing vertex $r$ is NP-complete.


  We have studied the temperature-dependent electronic structure near the Fermi
level (EF) of the layered cobaltate superconductor, Na0.35CoO2.1.3H2O, and
related materials, using laser-excited ultrahigh-resolution photoemission
spectroscopy. We observe the formation of a pseudogap with an energy scale of ~
20 meV in Na0.35CoO2.1.3H2O and Na0.35CoO2.0.7H2O, which is clearly absent in
Na0.7CoO2. The energy scale of the pseudogap is larger than the expected value
for the superconducting gap, suggesting an additional competing order parameter
at low temperatures. We discuss implications of the pseudogap in relation to
available transport and magnetic susceptibility results.