  We have derived the general solution of a wave equation describing the
dynamics of two-layere viscoelastic polymer materials of arbitrary thickness
deposited on solid (quartz) surfaces in a fluid environment. Within the Voight
model of viscoelastic element, we calculate the acoustic response of the system
to an applied shear stress, i.e. we find the shift of the quartz generator
resonance frequency and of the dissipation factor, and show that it strongly
depends on the viscous loading of the adsorbed layers and on the shear storage
and loss moduli of the overlayers. These results can readily be applied to
quartz crystal acoustical measurements of the viscoelasticity of polymers,
which conserve their shape under the shear deformations and do not flow, and
layered structures such as protein films adsorbed from solution onto the
surface of self-assembled monolayres.


  Let $\mathcal{B}(H)$ be the bounded, linear operators on a separable Hilbert
space equipped with the norm topology. A property is called typical if the set
of operators fulfilling the property is co-meager. We show that having
non-empty continuous spectrum is a typical property and that the operators with
non-empty point spectrum form a nowhere dense set. In addition we show that the
set of operators with empty point spectrum is dense and characterize the
closure of the set of those operators for which the spectrum and the point
spectrum coincide.


  Let $\mathfrak a \subset \mathscr O_X$ be a coherent ideal sheaf on a normal
complex variety $X$, and let $c \ge 0$ be a real number. De Fernex and Hacon
associated a multiplier ideal sheaf to the pair $(X, \mathfrak a^c)$ which
coincides with the usual notion whenever the canonical divisor $K_X$ is
$\mathbb Q$-Cartier. We investigate the properties of the jumping numbers
associated to these multiplier ideals.
  We show that the set of jumping numbers of a pair is unbounded, countable and
satisfies a certain periodicity property. We then prove that the jumping
numbers form a discrete set of real numbers if the locus where $K_X$ fails to
be $\mathbb Q$-Cartier is zero-dimensional. It follows that discreteness holds
whenever $X$ is a threefold with rational singularities.
  Furthermore, we show that the jumping numbers are rational and discrete if
one removes from $X$ a closed subset $W \subset X$ of codimension at least
three, which does not depend on $\mathfrak a$. We also obtain that outside of
$W$, the multiplier ideal reduces to the test ideal modulo sufficiently large
primes $p \gg 0$.


  Reinforcement learning from human feedback plays a crucial role in aligning
language models towards human preferences, traditionally represented through
comparisons between pairs or sets of responses within a given context. While
many studies have enhanced algorithmic techniques to optimize learning from
such data, this work shifts focus to improving preference learning through a
data-centric approach. Specifically, we propose enriching existing preference
datasets with machine-generated rationales that explain the reasons behind
choices. We develop a simple and principled framework to augment current
preference learning methods with rationale information. Our comprehensive
analysis highlights how rationales enhance learning efficiency. Extensive
experiments reveal that rationale-enriched preference learning offers multiple
advantages: it improves data efficiency, accelerates convergence to
higher-performing models, and reduces verbosity bias and hallucination.
Furthermore, this framework is versatile enough to integrate with various
preference optimization algorithms. Overall, our findings highlight the
potential of re-imagining data design for preference learning, demonstrating
that even freely available machine-generated rationales can significantly boost
performance across multiple dimensions. The code repository is available at
https: //github.com/reds-lab/preference-learning-with-rationales


  Background: Modern Code Review (MCR) is a lightweight alternative to
traditional code inspections. While secondary studies on MCR exist, it is
unknown whether the research community has targeted themes that practitioners
consider important. Objectives: The objectives are to provide an overview of
MCR research, analyze the practitioners' opinions on the importance of MCR
research, investigate the alignment between research and practice, and propose
future MCR research avenues. Method: We conducted a systematic mapping study to
survey state of the art until and including 2021, employed the Q-Methodology to
analyze the practitioners' perception of the relevance of MCR research, and
analyzed the primary studies' research impact. Results: We analyzed 244 primary
studies, resulting in five themes. As a result of the 1,300 survey data points,
we found that the respondents are positive about research investigating the
impact of MCR on product quality and MCR process properties. In contrast, they
are negative about human factor- and support systems-related research.
Conclusion: These results indicate a misalignment between the state of the art
and the themes deemed important by most survey respondents. Researchers should
focus on solutions that can improve the state of MCR practice. We provide an
MCR research agenda that can potentially increase the impact of MCR research.


  Many-body interactions (MBIs) such as exciton-exciton interactions
significantly affect the optical response of semiconductor nanostructures.
These interactions can be rigorously modeled through microscopic calculations.
However, these calculations can be computationally intensive and often lack
physical insights. An alternative is to use phenomenological many-body
interaction models such as the modified optical Bloch equations (MOBEs) and the
anharmonic oscillator (AO) model. While both these models have separately been
used to interpret experimental data, to the best of our knowledge, an explicit
and direct correspondence between these models has not been established. Here,
we show the empirical equivalence between these two complimentary MBI models
through two-dimensional coherent spectroscopy simulations. A quantitative
correspondence between the MBI parameters used in the two models are obtained.
We also perform a quantitative comparison of these MBI models with experiments,
which highlights the usefulness of these phenomenological models in
interpreting experimental results.


  In this paper, we prove the energy conservation for the weak solutions of the
compressible Navier-Stokes equations for any time $t>0$, under certain
conditions. The results hold for the renormalized solutions of the equations
with constant viscosities, as well as the weak solutions of the equations with
degenerate viscosity. Our conditions do not depend on the dimensions. The
energy may conserve on the vacuum for the compressible Navier-Stokes equations
with constant viscosities. Our results are the first ones on the energy
conservation for the weak solutions of the compressible Navier-Stokes
equations.


  The thickness of the cortical band is linked to various neurological and
psychiatric conditions, and is often estimated through surface-based methods
such as Freesurfer in MRI studies. The DiReCT method, which calculates cortical
thickness using a diffeomorphic deformation of the gray-white matter interface
towards the pial surface, offers an alternative to surface-based methods.
Recent studies using a synthetic cortical thickness phantom have demonstrated
that the combination of DiReCT and deep-learning-based segmentation is more
sensitive to subvoxel cortical thinning than Freesurfer.
  While anatomical segmentation of a T1-weighted image now takes seconds,
existing implementations of DiReCT rely on iterative image registration methods
which can take up to an hour per volume. On the other hand, learning-based
deformable image registration methods like VoxelMorph have been shown to be
faster than classical methods while improving registration accuracy. This paper
proposes CortexMorph, a new method that employs unsupervised deep learning to
directly regress the deformation field needed for DiReCT. By combining
CortexMorph with a deep-learning-based segmentation model, it is possible to
estimate region-wise thickness in seconds from a T1-weighted image, while
maintaining the ability to detect cortical atrophy. We validate this claim on
the OASIS-3 dataset and the synthetic cortical thickness phantom of Rusak et
al.


  Reduction of comparison cycles leads to power savings of a
successive-approximation-register (SAR) analog-to-digital converters (ADC). We
establish that the lowest average number of comparison cycles of a SAR ADC
approaches the entropy of the ADC output, and proposed a simple adaptive
algorithm that approaches this lower bound. Today's SAR ADC uses binary search,
which consumes more power than necessary for non-uniform input distributions
commonly found in practice. We refer to a SAR ADC employing such algorithm the
maximal entropy reduction (MER) ADC.


  Let F be an orthonormal basis of weight 2 cusp forms on Gamma_0(N). We show
that various weighted averages of special values L(f \tensor chi, 1) over f in
F are equal to 4 pi + O(N^{-1 + epsilon}). A previous result of Duke gives an
error term of O(N^{-1/2} log N).
  The bound here is used in the author's paper "Galois representations attached
to Q-curves and the generalized Fermat equation A^4 + B^2 = C^p," (to appear,
Amer. J. Math.) to show that certain spaces of cuspforms arising there contain
forms whose L-functions have nonvanishing special value.
  Version of May 2005: Nathan Ng found an error in the earlier version which
yielded a bound too strong by a factor of log N; this is the corrected version,
as it will appear in Canad. Math. Bull. The change does not affect the
application to the Amer. J. Math. paper.


  In this paper we study an asymptotic expansion for the distribution of a
random motion of a particle driven by a Markov process in diffusion
approximation. We show that the singularly perturbed equation of a Markovian
random motion can be reduced to the regularly perturbed equation for the
distribution of the random motion.


  The geometric Fierz identities are here employed to generate new emergent
fermionic fields on the parallelizable (curvatureless, torsionfull) 7-sphere
($S^7$). Employing recently found new classes of spinor fields on the $S^7$
spin bundle, new classes of fermionic fields are obtained from their bilinear
covariants by a generalized reconstruction theorem, on the parallelizable
$S^7$. Using a generalized non-associative product on the octonionic bundle on
the parallelizable $S^7$, these new classes of algebraic spinor fields, lifted
onto the parallelizable $S^7$, are shown to correctly transform under the
Moufang loop generators on $S^7$.


  We prove asymptotic stability of trapped solitons in the generalized
nonlinear Schr\"odinger equation with a potential in dimension 1 and for even
potential and even initial conditions.


  This paper introduces "OPTOTEACH", a new teaching system for photonics lab
work, designed by Harz University and successfully released on the German
market by HarzOptics. OPTOTEACH is the first POF-WDM teaching system,
specifically designed to cover a multitude of lab experiments in the field of
optical communication technology.
  It is illustrated, how this lab system is supplemented by a newly developed
optical teaching software - "OPTOSOFT" - and how the combination of system and
software creates a unique augmented learning environment. The paper details,
how the didactic concept for the software was conceptualised and introduces the
latest beta version. OPTOSOFT is specifically designed not only as an
attachment to OPTOTEACH, it also allows students to rehearse various aspects of
theoretical optics and experience a fully interactive and feature-rich
self-learning environment.
  The paper further details the first experiences educators at Harz University
have made working with the lab system as well as the teaching software. So far,
the augmented learning concept was received mostly positive, although there is
some potential for further optimisation concerning integration and pacing of
various interactive modules.


  We numerically investigate the propelled motions of a Janus particle in a
periodically phase-separating binary fluid mixture. In this study, the surface
of the particle tail prefers one of the binary fluid components and the
particle head is neutral in the wettability. During the demixing period, the
more wettable phase is selectively adsorbed to the particle tail. Growths of
the adsorbed domains induce the hydrodynamic flow in the vicinity of the
particle tail, and this asymmetric pumping flow drives the particle toward the
particle head. During the mixing period, the particle motion almost ceases
because the mixing primarily occurs via diffusion and the resulting
hydrodynamic flow is negligibly small. Repeating this cycle unboundedly moves
the Janus particle toward the head. The dependencies of the composition and the
repeat frequency on the particle motion are discussed.


  The linear cosmological perturbation theory of an almost homogeneous and
isotropic perfect fluid universe is reconsidered and formally simplified by
introducing new covariant and gauge-invariant variables with physical
interpretations on hypersurfaces of constant expansion, constant curvature or
constant energy density. The existence of conserved perturbation quantities on
scales larger than the Hubble scale is discussed. The quantity which is
conserved on large scales in a flat background universe may be expressed in
terms of the fractional, spatial gradient of the energy density on constant
expansion hypersurfaces or, alternatively, with the help of expansion or
curvature perturbation variables on hypersurfaces of constant energy density.
For nonvanishing background curvature the perturbation dynamics is most
suitably described in terms of energy density perturbations on hypersurfaces of
constant curvature.


  We consider a subanalytic subset A of a complex analytic manifold M (when M
is viewed as a real manifold) and formulate conditions under which A is a
complex analytic subset of M.


  Radiation transport plays important roles in stellar atmospheres, but the
effects of turbulence are being obscured by other effects such as
stratification. Using radiative hydrodynamic simulations of forced turbulence,
we determine the decay rates of sinusoidal large-scale temperature
perturbations of different wavenumbers in the optically thick and thin regimes.
Increasing the wavenumber increases the rate of decay in both regimes, but this
effect is much weaker than for the usual turbulent diffusion of passive
scalars, where the increase is quadratic for small wavenumbers. The turbulent
decay is well described by an enhanced Newtonian cooling process in the
optically thin limit, which is found to show a weak increase proportional to
the square root of the wavenumber. In the optically thick limit, the increase
in turbulent decay is somewhat steeper for wavenumbers below the
energy-carrying wavenumber of the turbulence, but levels off toward larger
wavenumbers. In the presence of turbulence, the typical cooling time is
comparable to the turbulent turnover time. We observe that the temperature
takes a long time to reach equilibrium in both the optically thin and thick
cases, but in the former, the temperature retains smaller scale structures for
longer.


  In this paper we propose a new family of RRT based algorithms, named RRT+ ,
that are able to find faster solutions in high-dimensional configuration spaces
compared to other existing RRT variants by finding paths in lower dimensional
subspaces of the configuration space. The method can be easily applied to
complex hyper-redundant systems and can be adapted by other RRT based planners.
We introduce RRT+ and develop some variants, called PrioritizedRRT+ ,
PrioritizedRRT+-Connect, and PrioritizedBidirectionalT-RRT+ , that use the new
sampling technique and we show that our method provides faster results than the
corresponding original algorithms. Experiments using the state-of-the-art
planners available in OMPL show superior performance of RRT+ for
high-dimensional motion planning problems.


  Bias in word embeddings such as Word2Vec has been widely investigated, and
many efforts made to remove such bias. We show how to use conceptors debiasing
to post-process both traditional and contextualized word embeddings. Our
conceptor debiasing can simultaneously remove racial and gender biases and,
unlike standard debiasing methods, can make effect use of heterogeneous lists
of biased words. We show that conceptor debiasing diminishes racial and gender
bias of word representations as measured using the Word Embedding Association
Test (WEAT) of Caliskan et al. (2017).


  The Seebeck coefficient and electrical conductivity are two critical
quantities to optimize simultaneously in designing thermoelectric materials,
and they are determined by the dynamics of carrier scattering. We uncover a new
regime where the co-existence at the Fermi level of multiple bands with
different effective masses leads to strongly energy-dependent carrier lifetimes
due to intrinsic electron-phonon scattering. In this anomalous regime,
electrical conductivity decreases with carrier concentration, Seebeck
coefficient reverses sign even at high doping, and power factor exhibits an
unusual second peak. We discuss the origin and magnitude of this effect using
first-principles Boltzmann transport calculations and simplified models. We
also identify general design rules for using this paradigm to engineer enhanced
performance in thermoelectric materials.


  In this paper, the paradigm of sphere decoding (SD) based on lattice Gaussian
distribution is studied, where the sphere radius $D>0$ in the sense of
Euclidean distance is characterized by the initial pruning size $K>1$, the
standard deviation $\sigma>0$ and a regularization term
$\rho_{\sigma,\mathbf{y}}(\Lambda)>0$ ($\Lambda$ denotes the lattice,
$\mathbf{y}$ is the query point). In this way, extra freedom is obtained for
analytical diagnosis of both the decoding performance and complexity. Based on
it, the equivalent SD (ESD) algorithm is firstly proposed, and we show it is
exactly the same with the classic Fincke-Pohst SD but characterizes the sphere
radius with $D=\sigma\sqrt{2\ln K}$. By fixing $\sigma$ properly, we show that
the complexity of ESD measured by the number of visited nodes is upper bounded
by $|S|<nK$, thus resulting in a tractable decoding trade-off solely determined
by $K$. In order to further exploit the decoding potential, the regularized SD
(RSD) algorithm based on Klein's sampling probability is proposed, which
achieves a better decoding trade-off than the equivalent SD by fully utilizing
the regularization terms. Moreover, besides the designed criterion of pruning
threshold, another decoding criterion named as candidate protection is proposed
to solve the decoding problems in the cases of small $K$, which generalizes
both the regularized SD and equivalent SD from maximum likelihood (ML) decoding
to bounded distance decoding (BDD). Finally, simulation results based on MIMO
detection are presented to confirm the tractable decoding trade-off of the
proposed lattice Gaussian distribution-based SD algorithms.


  We present an analysis of different sets of gravitational N-body simulations,
all describing the dynamics of discrete particles with a small initial velocity
dispersion. They encompass very different initial particle configurations,
different numerical algorithms for the computation of the force, with or
without the space expansion of cosmological models. Despite these differences
we find in all cases that the non-linear clustering which results is
essentially the same, with a well-defined simple power-law behaviour in the
two-point correlations in the range from a few times the lower cut-off in the
gravitational force to the scale at which fluctuations are of order one. We
argue, presenting quantitative evidence, that this apparently universal
behaviour can be understood by the domination of the small scale contribution
to the gravitational force, coming initially from nearest neighbor particles.


  (Abridged) The purpose of this paper is to explore and compare the physical
and chemical structure of Class I low-mass protostellar sources on
protoplanetary disc scales. We present a study of the dust and gas emission
towards a representative sample of 12 Class I protostars from the Ophiuchus
molecular cloud with the Atacama Large Millimeter/submillimeter Array (ALMA).
The continuum at 0.87 mm and molecular transitions from C17O, C34S, H13CO+,
CH3OH, SO2 , and C2H were observed at high angular resolution (0.4", ~60 au
diameter) towards each source. Disc and stellar masses are estimated from the
continuum flux and position-velocity diagrams, and six of the sources show
disc-like structures. Towards the more luminous sources, compact emission and
large line widths are seen for transitions of SO2 that probe warm gas (Eu ~200
K). In contrast, C17O emission is detected towards the least evolved and less
luminous systems. No emission of CH3OH is detected towards any of the continuum
peaks, indicating an absence of warm CH3OH gas towards these sources. A
power-law relation is seen between the stellar mass and the bolometric
luminosity, corresponding to a mass accretion rate of (2.4 +/- 0.6) x 10^-7
Msun/year for the Class I sources. This mass accretion rate is lower than the
expected value if the accretion is constant in time and rather points to a
scenario of accretion occurring in bursts. The differentiation between C17O and
SO2 suggests that they trace different physical components: C17O traces the
densest and colder regions of the disc-envelope system, while SO2 may be
associated with regions of higher temperature, such as accretion shocks. The
lack of warm CH3OH emission suggests that there is no hot-core-like region
around any of the sources and that the CH3OH column density averaged over the
disc is low.


  We have studied the correlation between 2357 Chandra X-ray point sources in a
40 x 40 parsec field and ~20,000 infrared sources we observed in the
corresponding subset of our 2 x 1.4 degree Spitzer/IRAC Galactic Center Survey
at 3.6-8.0 um, using various spatial and X-ray hardness thresholds. The
correlation was determined for source separations of less than 0.5", 1" or 2".
Only the soft X-ray sources show any correlation with infrared point sources on
these scales, and that correlation is very weak. The upper limit on hard X-ray
sources that have infrared counterparts is <1.7% (3 sigma). However, because of
the confusion limit of the IR catalog, we only detect IR sources with absolute
magnitudes < ~1. As a result, a stronger correlation with fainter sources
cannot be ruled out. Only one compact infrared source, IRS 13, coincides with
any of the dozen prominent X-ray emission features in the 3 x 3 parsec region
centered on Sgr A*, and the diffuse X-ray and infrared emission around Sgr A*
seems to be anti-correlated on a few-arcsecond scale. We compare our results
with previous identifications of near-infrared companions to Chandra X-ray
sources.


  We consider the gauging of space translations with time-dependent gauge
functions. Using fixed time gauge of relativistic theory, we consider the
gauge-invariant model describing the motion of nonrelativistic particles. When
we use gauge-invariant nonrelativistic velocities as independent variables the
translation gauge fields enter the equations through a d\times (d+1) matrix of
vielbein fields and their Abelian field strengths, which can be identified with
the torsion tensors of teleparallel formulation of relativity theory. We
consider the planar case (d=2) in some detail, with the assumption that the
action for the dreibein fields is given by the translational Chern-Simons term.
We fix the asymptotic transformations in such a way that the space part of the
metric becomes asymptotically Euclidean. The residual symmetries are (local in
time) translations and rigid rotations. We describe the effective interaction
of the d=2 N-particle problem and discuss its classical solution for N=2. The
phase space Hamiltonian H describing two-body interactions satisfies a
nonlinear equation H={\cal H}(\vec x,\vec p;H) which implies, after
quantization, a nonstandard form of the Schr\"odinger equation with energy
dependent fractional angular momentum eigenvalues. Quantum solutions of the
two-body problem are discussed. The bound states with discrete energy levels
correspond to a confined classical motion (for the planar distance between two
particles r\le r_0) and the scattering states with continuum energy correspond
to the classical motion for r>r_0. We extend our considerations by introducing
an external constant magnetic field and, for N=2, provide the classical and
quantum solutions in the confined and unconfined regimes.


  The Holme-Kim random graph processes is a variant of the Barabasi-Albert
scale-free graph that was designed to exhibit clustering. In this paper we show
that whether the model does indeed exhibit clustering depends on how we define
the clustering coefficient. In fact, we find that local clustering coefficient
remains typically positive whereas global clustering tends to 0 at a slow rate.
These and other results are proven via martingale techniques, such as
Freedman's concentration inequality combined with a bootstrapping argument.


  Retinal images have the highest resolution and clarity among medical images.
Thus, vessel analysis in retinal images may facilitate early diagnosis and
treatment of many chronic diseases. In this paper, we propose a novel
multi-scale residual convolutional neural network structure based on a
\emph{scale-space approximation (SSA)} block of layers, comprising subsampling
and subsequent upsampling, for multi-scale representation. Through analysis in
the frequency domain, we show that this block structure is a close
approximation of Gaussian filtering, the operation to achieve scale variations
in scale-space theory. Experimental evaluations demonstrate that the proposed
network outperforms current state-of-the-art methods. Ablative analysis shows
that the SSA is indeed an important factor in performance improvement.


  Ballistic electrons confined to a billiard and subject to spin--orbit
coupling of the Rashba type are investigated, using both approximate
semiclassical and exact quantum--mechanical methods. We focus on the
low--energy part of the spectrum that has negative eigenvalues. When the spin
precession length is smaller than the radius of the billiard, the low--lying
energy eigenvalues turn out to be well described semiclassically. Corresponding
eigenspinors are found to have a finite spin polarization in the direction
perpendicular to the billiard plane.


  We prove that the extended mapping class group, $\rm Mod^{*}(\Sigma_{g})$, of
a connected orientable surface of genus $g$, can be generated by three
involutions for $g\geq 5$. In the presence of punctures, we prove that $\rm
Mod^{*}(\Sigma_{g,p})$ can be generated by three involutions for $g\geq 10$ and
$p\geq 6$ (with the exception that for $g\geq 11$, $p$ should be at least
$15$).


  Single crystals of MgB2 have been grown with a high-pressure cubic anvil
technique. They grow via the peritectic decomposition of the MgNB9 ternary
nitride. The crystals are of a size up to 2x1x0.1mm3 with a weight up to 230
micrograms. Typically they have transition temperatures between 38 and 38.6 K
with a width of 0.3-0.5 K. Investigations of the P-T phase diagram prove that
the MgB2 phase is stable at least up to 2190C at high hydrostatic pressure in
the presence of Mg vapor under high pressure. Substitution of aluminum for
magnesium in single crystals leads to stepwise decrease of Tc. This indicates a
possible appearance of superstructures or phases with different Tc's. The upper
critical field decreases with Al doping.


  We study the growth of the rank of subgroups of finite index in residually
finite groups, by relating it to the notion of cost.
  As a by-product, we show that the `Rank vs. Heegaard genus' conjecture on
hyperbolic 3-manifolds is incompatible with the `Fixed Price problem' in
topological dynamics.


  A study of the relation between topology change, energy and Lie algebra
representations for fuzzy geometry in connection to $M$-theory is presented. We
encounter two different types of topology change, related to the different
features of the Lie algebra representations appearing in the matrix models of
$M$-theory. From these studies, we propose a new method of obtaining
non-commutative solutions for the non-Abelian $D$-brane action found by Myers.
This mechanism excludes one of the two topology changing processes previously
found in other non-commutative solutions of many matrix-based models in
$M$-theory i.e. in M(atrix) theory, Matrix string theory and non-Abelian
$D$-brane physics.


  Classical chaos refers to the property of trajectories to diverge
exponentially as time tends to infinity. It is characterized by a positive
Lyapunov exponent.
  There are many different descriptions of quantum chaos. The one related to
the notion of generalized (quantum) Lyapunov exponent is based either on
qualitative physical considerations or on the so-called symplectic tomography
map.
  The purpose of this note is to show how the definition of quantum Lyapunov
exponent naturally arises in the framework of the Moyal phase space formulation
of quantum mechanics and is based on the notions of quantum trajectories and
the family of quantizers. The role of the Heisenberg uncertainty principle in
the statement of the criteria for quantum chaos is made explicit.


  The natural world is replete with examples of multistable systems, known to
respond to periodic modulations and produce a signal, which exhibits resonance
with noise amplitude. This is a concept not demonstrated in pure materials,
which involve a measured physical property. In a thermoremanent magnetization
experiment with a common magnetic material, Fe, in the nanoparticulate form, we
establish how magnetization in a system of dilute spins during dissipation of
stored magnetic energy, breaks up into spontaneous oscillatory behavior.
Starting at 175 K and aided by temperature (stochastic noise) the oscillation
amplitude goes through a maximum, reminiscent of stochastic resonance. Our
observation of thermal noise induced coherent resonance is due to intrinsic
self-organizing magnetic dynamics of the Fe nanoperticle system without
applying any external periodic force. These results yield new possibilities in
design of magnetic materials and a platform to understand stochastic
interference and phase synchronization in neural activity, as models for neural
communication.


  Strong static type systems help programmers eliminate many errors without
much burden of supplying type annotations. However, this flexibility makes it
highly non-trivial to diagnose ill-typed programs, especially for novice
programmers. Compared to classic constraint solving and optimization-based
approaches, the data-driven approach has shown great promise in identifying the
root causes of type errors with higher accuracy. Instead of relying on
hand-engineered features, this work explores natural language models for type
error localization, which can be trained in an end-to-end fashion without
requiring any features. We demonstrate that, for novice type error diagnosis,
the language model-based approach significantly outperforms the previous
state-of-the-art data-driven approach. Specifically, our model could predict
type errors correctly 62% of the time, outperforming the state-of-the-art
Nate's data-driven model by 11%, in a more rigorous accuracy metric.
Furthermore, we also apply structural probes to explain the performance
difference between different language models.


  The implementation of a Cloud Radio Access Network (C-RAN) with Full
Dimensional (FD)-MIMO is faced with the challenge of controlling the fronthaul
overhead for the transmission of baseband signals as the number of horizontal
and vertical antennas grows larger. This work proposes to leverage the special
low-rank structure of FD-MIMO channel, which is characterized by a
time-invariant elevation component and a time-varying azimuth component, by
means of a layered precoding approach, so as to reduce the fronthaul overhead.
According to this scheme, separate precoding matrices are applied for the
azimuth and elevation channel components, with different rates of adaptation to
the channel variations and correspondingly different impacts on the fronthaul
capacity. Moreover, we consider two different Central Unit (CU) - Radio Unit
(RU) functional splits at the physical layer, namely the conventional C-RAN
implementation and an alternative one in which coding and precoding are
performed at the RUs. Via numerical results, it is shown that the layered
schemes significantly outperform conventional non-layered schemes, especially
in the regime of low fronthaul capacity and large number of vertical antennas.


  We reconsider the problem of the interpretation of the Quantum Theory (QT) in
the perspective of the entire universe and of Bphr idea that the classical
language is the language of our experience and QT acquires a meaning only with
a reference to it. We distinguish a classical or macroscopic level, and a
quantum or microscopic one that is perceived only through the modifications
that it induces in the first. The macroscopic state of the universe is assumed
to be specified by a set of variables, a classical energy momentum tensor and
some conserved currents, which are supposed to have a well defined value across
the entire space-time. To the energy-momentum tensor a classical metric is
related by the Einstein equation. The quantum state and dynamics are expressed
by the usual QT formalism in terms of a density operator and the ordinary
quantum operators in Heisenberg picture. For the macroscopic variables a basic
distribution of probability is postulated in terms of a density and the
corresponding quantum operators, so in some way their evolution is driven by
the underlying QT. Such postulate essentially replaces the usual elfadjoint
operators correspondence. For the Universe we adopt a variance of the
{\Lambda}CDM model with Omega=1, one single inflaton with an Higgs type
potential, the initial time at t=minus infinite. The expectation values of all
fundamental fields are supposed to vanish for time going to minus infinite. In
the framework the scalar fluctuation in the Cosmic Microwave Background are
correctly explained giving appropriate calue to the parameters in the
potential. As in more conventional models the absence of the tensor
fluctuations remains not understood, if even a quantum metric is introduced.
This seems to suggest that Gravity is a pure classical phenomenon, what could
be consistently accommodated in our formalism by an appropriate even if
somewhat ad hoc assumption


  We construct Baxter operators for the homogeneous closed $\mathrm{XXX}$ spin
chain with the quantum space carrying infinite or finite dimensional $s\ell_2$
representations. All algebraic relations of Baxter operators and transfer
matrices are deduced uniformly from Yang-Baxter relations of the local building
blocks of these operators. This results in a systematic and very transparent
approach where the cases of finite and infinite dimensional representations are
treated in analogy. Simple relations between the Baxter operators of both cases
are obtained. We represent the quantum spaces by polynomials and build the
operators from elementary differentiation and multiplication operators. We
present compact explicit formulae for the action of Baxter operators on
polynomials.


  We have investigated the effect of doping by Te on the anomalous Hall effect
in Ga1-xMnxAs (x = 0.085). For this relatively high value of x the temperature
dependence of resistivity shows an insulating behavior. It is well known that
in Ga1-xMnxAs the Mn ions naturally act as acceptors. Additional doping by Te
donors decreases the Curie temperature and increases the anomalous Hall
resistivity. With increasing Te concentration the long-range ferromagnetic
order in Ga1-xMnxAs eventually disappears, and paramagnetic-to-spin glass
transition is observed instead. The critical concentration of holes required
for establishing ferromagnetic order in Ga1-xMnxAs (x = 0.085) has been
estimated by using the magnetic polaron percolation theory proposed by Kaminski
and Das Sarma [Phys.Rev.Lett. 88, 247202 (2002)].


  A fundamental question, first raised by Langlands, is to know whether the
Rankin-Selberg product of two (not necessarily holomorphic) cusp forms f and g
is modular, i.e., if there exists an automorphic form f box g on GL(4)/Q whose
standard L-function equals L^*(s, f x g) after removing the ramified and
archimedean factors. The first main result of this paper is to answer it in the
affirmative, in fact with the base field Q replaced by any number field F. Our
proof uses a mixture of converse theorems, base change and descent, and it also
appeals to the local regularity properties of Eisenstein series and the scalar
products of their truncations.
  One of the applications of this result is that the space of cusp forms on
SL(2) has multiplicity one. Concretely this means the following: If f, g are
newforms of holomorphic or Maass type with trivial character such that the
squares of the p-th coeficients of f and g are the same at almost all primes p,
then g must be a twist of f by a quadratic Dirichlet character.


  We give a detailed proof for Gordan-Noether's results in "Ueber die
algebraischen Formen, deren Hesse'sche Determinante identisch verschwindet"
published in 1876 in Mathematische Annahlen. C. Lossen has written a paper in a
similar direction as the present paper, but did not provide a proof for every
result. In our paper, every result is proved. Furthermore, our paper is
independent of Lossen's paper and includes a considerable number of new
observations.
  An earlier version of this paper has been printed in Proceedings of the
School of Science of Tokai University, Vol.49, Mar. 2014. In this version, a
serious error has been corrected and some new results have been added.


  Data-driven control has gained significant attention in recent years,
particularly regarding feedback linearization of nonlinear systems. However,
existing approaches face limitations when it comes to implementing them on
hardware. The main challenges include the need for very small sampling times,
which strain hardware capabilities, and the requirement of an initial open-loop
data set, which can be impractical for stabilizing unstable equilibrium points.
To address these issues, we propose a two-stage model-free approach that
combines a high-gain observer and a dynamic controller. This eliminates the
hardware implementation difficulties mentioned earlier. The high-gain observer
acts as a robust state estimator, offering superior noise attenuation and lower
computational costs, crucial factors for digital hardware implementation.
Unlike data-driven methods, our design's stability and performance depend on a
tunable software parameter, simplifying digital implementation without
overburdening hardware resources. Experimental results on a Twin Rotor system
demonstrate the effectiveness of our approach compared to the state-of-the-art
data-driven method.


  Stochastic Gradient Descent is used for large datasets to train models to
reduce the training time. On top of that data parallelism is widely used as a
method to efficiently train neural networks using multiple worker nodes in
parallel. Synchronous and asynchronous approach to data parallelism is used by
most systems to train the model in parallel. However, both of them have their
drawbacks. We propose a third approach to data parallelism which is a hybrid
between synchronous and asynchronous approaches, using both approaches to train
the neural network. When the threshold function is selected appropriately to
gradually shift all parameter aggregation from asynchronous to synchronous, we
show that in a given time period our hybrid approach outperforms both
asynchronous and synchronous approaches.


  This article is based on recent works done in collaboration with M. Mintchev,
E. Ragoucy and P. Sorba. It aims at presenting the latest developments in the
subject of factorization for integrable field theories with a reflecting and
transmitting impurity.


  A detailed study of the semiclassical expansion of the world line path
integral for a charged relativistic particle in a constant external electric
field is presented. We show that the Schwinger formula for charged particle
pair production is reproduced exactly by the semiclassical expansion around
classical instanton solutions when the leading order of fluctuations is taken
into account. We prove that all corrections to this leading approximation
vanish and that the WKB approximation to the world line path integral is exact.


  The forward--backward path integral describing a charged particle moving in a
thermal bath of photons is expressed in terms of the solution of a
Langevin-type of equation. Approximate methods for solving this equation are
discussed.


  In this paper, we study a dynamic analogue of the Path Cover problem, which
can be solved in polynomial-time in directed acyclic graphs. A temporal digraph
has an arc set that changes over discrete time-steps, if the underlying digraph
(the union of all the arc sets) is acyclic, then we have a temporal DAG. A
temporal path is a directed path in the underlying digraph, such that the
time-steps of arcs are strictly increasing along the path. Two temporal paths
are temporally disjoint if they do not occupy any vertex at the same time. A
temporal (resp. temporally disjoint) path cover is a collection of (resp.
temporally disjoint) temporal paths that covers all vertices. In this paper, we
study the computational complexities of the problems of finding a temporal
(disjoint) path cover with minimum cardinality, denoted as Temporal Path Cover
(TPC) and Temporally Disjoint Path Cover (TD-PC). We show that both problems
are NP-hard even when the underlying DAG is planar, bipartite, subcubic, and
there are only two arc-disjoint time-steps. Moreover, TD-PC remains NP-hard
even on temporal oriented trees. In contrast, we show that TPC is
polynomial-time solvable on temporal oriented trees by a reduction to Clique
Cover for (static undirected) weakly chordal graphs (a subclass of perfect
graphs for which Clique Cover admits an efficient algorithm). This highlights
an interesting algorithmic difference between the two problems. Although it is
NP-hard on temporal oriented trees, TD-PC becomes polynomial-time solvable on
temporal oriented lines and temporal rooted directed trees. We also show that
TPC (resp. TD-PC) admits an XP (resp. FPT) time algorithm with respect to
parameter tmax + tw, where tmax is the maximum time-step, and tw is the
treewidth of the underlying static undirected graph.


  We consider a refracted jump diffusion process having two-sided jumps with
rational Laplace transforms. For such a process, by applying a straightforward
but interesting approach, we derive formulas for the Laplace transform of its
distribution. Our formulas are presented in an attractive form and the approach
is novel. In particular, the idea in the application of an approximating
procedure is remarkable. Besides, the results are used to price Variable
Annuities with state-dependent fees.


  This paper proposes a technique to manipulate an object with a nonholonomic
mobile robot by pushing, which is a nonprehensile manipulation motion
primitive. Such a primitive involves unilateral constraints associated with the
friction between the robot and the manipulated object. Violating this
constraint produces the slippage of the object during the manipulation,
preventing the correct achievement of the task. A linear time-varying model
predictive control is designed to include the unilateral constraint within the
control action properly. The approach is verified in a dynamic simulation
environment through a Pioneer 3-DX wheeled robot executing the pushing
manipulation of a package.


  A straightforward application of the variational principle to null strings
meets difficulties since string's world-sheets are degenerate. It is known that
the variational principle in this case can be formulted with the help of
two-vector density on the string world-sheet which plays a role of Lagrange
multipliers. It is shown that recently suggested stress-energy tensor of null
strings can be derived by variation over the background metric of the action
used to describe tensionless limit in the string theory. One of the Lagrange
multipliers is related to the energy of the null string.


  A geometric approach to understanding recursion relations for scattering
amplitudes is developed. We achieve this by studying intersection numbers of
triangulated accordiohedra presented as hyperplane arrangements. The
cancellation of spurious divergences is subsequently realized as a topological
no-boundary condition.


  In this paper, we prove $L^p$ estimates for the fractional derivatives of
solutions to elliptic fractional partial differential equations whose
coefficients are $VMO$. In particular, our work extends the optimal regularity
known in the second order elliptic setting to a spectrum of fractional order
elliptic equations.


  For a given network, a backbone is an overlay network consisting of a
connected dominating set with additional accessibility properties. Once a
backbone is created for a network, it can be utilized for fast communication
amongst the nodes of the network.
  The Signal-to-Interference-plus-Noise-Ratio (SINR) model has become the
standard for modeling communication among devices in wireless networks. For
this model, the community has pondered what the most realistic solutions for
communication problems in wireless networks would look like. Such solutions
would have the characteristic that they would make the least number of
assumptions about the availability of information about the participating
nodes. Solving problems when nothing at all is known about the network and
having nodes just start participating would be ideal. However, this is quite
challenging and most likely not feasible. The pragmatic approach is then to
make meaningful assumptions about the available information and present
efficient solutions based on this information.
  We present a solution for creation of backbone in the SINR model, when nodes
do not have access to their physical coordinates or the coordinates of other
nodes in the network. This restriction models the deployment of nodes in
various situations for sensing hurricanes, cyclones, and so on, where only
information about nodes prior to their deployment may be known but not their
actual locations post deployment. We assume that nodes have access to knowledge
of their label, the labels of nodes within their neighborhood, the range from
which labels are taken $[N]$ and the total number of participating nodes $n$.
We also assume that nodes wake up spontaneously. We present an efficient
deterministic protocol to create a backbone with a round complexity of
$O(\Delta \lg^2 N)$.


  Ultracold bosons in optical superlattices are expected to exhibit
fractional-filling insulating phases for sufficiently large repulsive
interactions. On strictly 1D systems, the exact mapping between hard-core
bosons and free spinless fermions shows that any periodic modulation in the
lattice parameters causes the presence of fractional-filling insulator domains.
Here, we focus on two recently proposed realistic 2D structures where such
mapping does not hold, i.e. the two-leg ladder and the trimerized kagome'
lattice. Based on a cell strong-coupling perturbation technique, we provide
quantitatively satisfactory phase diagrams for these structures, and give
estimates for the occurrence of the fractional-filling insulator domains in
terms of the inter-cell/intra-cell hopping amplitude ratio.


  We study metrics with positive scalar curvatures in domains with corners and
suggest possible extensions of the concept of positive scalar curvature to
singular spaces.


  Collapse, or a gravitational-like phase transition is studied in a
microcanonical ensemble of particles with an attractive $1/r^{\alpha}$
potential. A mean field continuous integral equation is used to determine a
saddle-point density profile that extremizes the entropy functional. For all
$0<\alpha<3$, a critical energy is determined below which the entropy of the
system exhibits a discontinuous jump. If an effective short-range cutoff is
applied, the entropy jump is finite; if not, the entropy diverges to $+\infty$.
A stable integral equation solution represents a state with maximal entropy;
the reverse is always true only for a modified integral equation introduced
here.


  The gravitational field of Spiral galaxies is well traced by their rotation
curves. Only recently it has become of extreme interest that the latter form a
family ruled by two parameters of the {\it luminous} component: the disk
length-scale $R_D$ and the magnitude $M_I$. This evidence is so strong and
consequential that it must be taken as the starting point for the investigation
on the issue of the dark matter in galaxies. The emerging fact is that
structural quantities deeply rooted in the luminous components, like the disk
length scales are found to tightly correlate with structural quantities deeply
rooted in the dark component, like the DM halo core radii. This unexpected
evidence may strongly call for a shift of paradigm with respect to the current
Cold collisionless Dark Matter one.


  Motivated by recent works on the high-dimensional logistic regression, we
establish that the existence of the maximum likelihood estimate exhibits a
phase transition for a wide range of generalized linear models with binary
outcome and elliptical covariates. This extends a previous result of Cand\`es
and Sur who proved the phase transition for the logistic regression with
Gaussian covariates. Our result reveals a rich structure in the phase
transition phenomenon, which is simply overlooked by Gaussianity. The main
tools for deriving the result are data separation, convex geometry and
stochastic approximation. We also conduct simulation studies to corroborate our
theoretical findings, and explore other features of the problem.


  Incorporating full duplex operation in Multiple Input Multiple Output (MIMO)
systems provides the potential of boosting throughput performance. However, the
hardware complexity of the analog self-interference canceller scales with the
number of transmit and receive antennas, thus exploiting the benefits of analog
cancellation becomes impractical for full duplex MIMO transceivers. In this
paper, we present a novel architecture for the analog canceller comprising of
reduced number of taps (tap refers to a line of fixed delay and variable phase
shifter and attenuator) and simple multiplexers for efficient signal routing
among the transmit and receive radio frequency chains. In contrast to the
available analog cancellation architectures, the values for each tap and the
configuration of the multiplexers are jointly designed with the digital
beamforming filters according to certain performance objectives. Focusing on a
narrowband flat fading channel model as an example, we present a general
optimization framework for the joint design of analog cancellation and digital
beamforming. We also detail a particular optimization objective together with
its derived solution for the latter architectural components. Representative
computer simulation results demonstrate the superiority of the proposed low
complexity full duplex MIMO system over lately available ones.


  Manual material handling tasks have the potential to be highly unsafe from an
ergonomic viewpoint. Safety inspections to monitor body postures can help
mitigate ergonomic risks of material handling. However, the real effect of
awkward muscle movements, strains, and excessive forces that may result in an
injury may not be identified by external cues. This paper evaluates the ability
of surface electromyogram (EMG)-based systems together with machine learning
algorithms to automatically detect body movements that may harm muscles in
material handling. The analysis utilized a lifting equation developed by the
U.S. National Institute for Occupational Safety and Health (NIOSH). This
equation determines a Recommended Weight Limit, which suggests the maximum
acceptable weight that a healthy worker can lift and carry as well as a Lifting
Index value to assess the risk extent. Four different machine learning models,
namely Decision Tree, Support Vector Machine, K-Nearest Neighbor, and Random
Forest are developed to classify the risk assessments calculated based on the
NIOSH lifting equation. The sensitivity of the models to various parameters is
also evaluated to find the best performance using each algorithm. Results
indicate that Decision Tree models have the potential to predict the risk level
with close to 99.35% accuracy.


  This paper presents a class of one-dimensional cellular automata (CA) models
on traffic flows, featuring nonlocal look-ahead interactions. We develop
kinetic Monte Carlo (KMC) algorithms to simulate the dynamics. The standard KMC
method can be inefficient for models with global interactions. We design an
accelerated KMC method to reduce the computational complexity in the evaluation
of the nonlocal transition rates. We investigate several numerical experiments
to demonstrate the efficiency of the accelerated algorithm, and obtain the
fundamental diagrams of the dynamics under various parameter settings.


  The monitoring of Cs-137 in seawater using scintillation detector relies on
the spectrum analysis method to extract the Cs-137 concentration. And when in
poor statistic situation, the calculation result of the traditional net peak
area (NPA) method has a large uncertainty. We present a machine learning based
method to better analyze the gamma-ray spectrum with low Cs-137 concentration.
We apply multilayer perceptron (MLP) to analyze the 662 keV full energy peak of
Cs-137 in the seawater spectrum. And the MLP can be trained with a few measured
background spectrums by combining the simulated Cs-137 signal with measured
background spectrums. Thus, it can save the time of preparing and measuring the
standard samples for generating the training dataset. To validate the MLP-based
method, we use Geant4 and background gamma-ray spectrums measured by a seaborne
monitoring device to generate an independent test dataset to test the result by
our method and the traditional NPA method. We find that the MLP-based method
achieves a root mean squared error of 0.159, 2.3 times lower than that of the
traditional net peak area method, indicating the MLP-based method improves the
precision of Cs-137 concentration calculation


  A theorem, usually attributed to Barr, yields that (A) geometric implications
deduced in classical L_{\infty\omega} logic from geometric theories also have
intuitionistic proofs. Barr's theorem is of a topos-theoretic nature and its
proof is non-constructive. In the literature one also finds mysterious comments
about the capacity of this theorem to remove the axiom of choice from
derivations. This article investigates the proof-theoretic side of Barr's
theorem and also aims to shed some light on the axiom of choice part. More
concretely, a constructive proof of the Hauptsatz for L_{\infty\omega} is given
and is put to use to arrive at a simple proof of (A) that is formalizable in
constructive set theory and Martin-Loef type theory.


  Safety-critical infrastructures must operate safely and reliably. Fault tree
analysis is a widespread method used to assess risks in these systems: fault
trees (FTs) are required - among others - by the Federal Aviation Authority,
the Nuclear Regulatory Commission, in the ISO26262 standard for autonomous
driving and for software development in aerospace systems. Although popular
both in industry and academia, FTs lack a systematic way to formulate powerful
and understandable analysis queries. In this paper, we aim to fill this gap and
introduce Boolean Fault tree Logic (BFL), a logic to reason about FTs. BFL is a
simple, yet expressive logic that supports easier formulation of complex
scenarios and specification of FT properties. Alongside BFL, we present model
checking algorithms based on binary decision diagrams (BDDs) to analyse
specified properties in BFL, patterns and an algorithm to construct
counterexamples. Finally, we propose a case-study application of BFL by
analysing a COVID19-related FT.


  We solve the Ginzburg-Landau equation (GLE) for the mesoscopic thin film of
the square shape in the magnetic field. In the limit of Ginzburg-Landau
parameter $\kappa \to \infty$ we find a series of first and second order phase
transitions as temperature and/or magnetic field changes. First order phase
transitions between giant flux states can be described with a simple
variational procedure. We discuss the similarity with rotating liquid $He^4$
and derive a simple formula for $H_{c1}$. We identify order parameters based on
symmetry arguments and we propose Landau functional describing the second order
phase transition.


  The Dressed K-matrix Model, developed previously for low- and
intermediate-energy Compton scattering, is generalized to calculate the
photon-nucleon vertex with a virtual photon and an off-shell nucleon. Using
this model, the ratio of the proton electromagnetic form factors is computed.
The calculated ratio is in excellent agreement with the ratio measured in
polarized electron-proton scattering.


  Results of numerical Monte Carlo simulations for the Stark-tuned F\"orster
resonance and dipole blockade between two to five cold rubidium Rydberg atoms
in various spatial configurations are presented. The effects of the atoms'
spatial uncertainties on the resonance amplitude and spectra are investigated.
The feasibility of observing coherent Rabi-like population oscillations at a
F\"orster resonance between two cold Rydberg atoms is analyzed. Spectra and the
fidelity of the Rydberg dipole blockade are calculated for various experimental
conditions, including nonzero detuning from the F\"orster resonance and finite
laser linewidth. The results are discussed in the context of
quantum-information processing with Rydberg atoms.


  Animating 3D characters using motion capture data requires basic expertise
and manual labor. To support the creativity of animation design and make it
easier for common users, we present a sketch-based interface DualMotion, with
rough sketches as input for designing daily-life animations of characters, such
as walking and jumping.Our approach enables to combine global motions of lower
limbs and the local motion of the upper limbs in a database by utilizing a
two-stage design strategy. Users are allowed to design a motion by starting
with drawing a rough trajectory of a body/lower limb movement in the global
design stage. The upper limb motions are then designed by drawing several more
relative motion trajectories in the local design stage. We conduct a user study
and verify the effectiveness and convenience of the proposed system in creative
activities.


  We present a class of static, spherically symmetric, non-singular solutions
of the tree-level string effective action, truncated to first order in
$\alpha'$. In the string frame the solutions approach asymptotically (at $r\to
0$ and $r\to \infty$) two different anti-de Sitter configurations, thus
interpolating between two maximally symmetric states of different constant
curvature. The radial-dependent dilaton defines a string coupling which is
everywhere finite, with a peak value that can be chosen arbitrarily small so as
to neglect quantum-loop corrections. This example stresses the possible
importance of finite-size $\alpha'$ corrections, typical of string theory, in
avoiding space-time singularities.


  This paper is devoted to the analysis of the complex damage of DNA irradiated
by ions. The analysis and assessment of complex damage is important because
cells in which it occurs are less likely to survive because the DNA repair
mechanisms may not be sufficiently effective. We studied the flux of secondary
electrons through the surface of nucleosomes and calculated the radial dose and
the distribution of clustered damage around the ion's track. The calculated
radial dose distribution is compared to simulations. The radial distribution of
the complex damage is found to be different from that of the dose. Comparison
with experiments may solve the question of what is more lethal for the cell,
damage complexity or absorbed energy. We suggest a way to calculate the
probability of cell death based on the complexity of the damage. This work is
done within the framework of the phenomenon-based multiscale approach to
radiation damage by ions.


  Knowledge distillation is one of the methods for model compression, and
existing knowledge distillation techniques focus on how to improve the
distillation algorithm so as to enhance the distillation efficiency. This paper
introduces dynamic incremental learning into knowledge distillation and
proposes a distillation strategy for education distillation. Specifically, it
is proposed to take fragmented student models divided from the complete student
model as lower-grade models. As the grade level rises, fragmented student
models deepen in conjunction with designed teaching reference layers, while
learning and distilling from more teacher models. By moving from lower to
higher grades, fragmented student models were gradually integrated into a
complete target student model, and the performance of the student models
gradually improved from lower to higher grades of the stage. Education
distillation strategies combined with distillation algorithms outperform the
results of single distillation algorithms on the public dataset
CIFAR100,Caltech256, Food-101 dataset.


  Consider a fiber bundle in which the total space, the base space and the
fiber are all symplectic manifolds. We study the relations between the
quantization of these spaces. In particular, we discuss the geometric
quantization of a vector bundle, as oppose to a line bundle, over the base
space that recovers the standard geometric quantization of the total space.


  By analyzing $e^+e^-$ annihilation data with an integrated luminosity of
$2.93~\rm fb^{-1}$ collected at the center-of-mass energy $\sqrt s=$ 3.773 GeV
with the BESIII detector, we present the first absolute measurements of the
branching fractions of twenty Cabibbo-suppressed hadronic $D^{0(+)}$ decays
involving multiple pions. The largest four branching fractions obtained are
$\mathcal{B}(D^0\to\pi^+\pi^-\pi^0)= (1.343\pm0.013_{\rm stat}\pm0.016_{\rm
syst})\%$, $\mathcal{B}(D^0\to\pi^+\pi^-2\pi^0)= (0.998\pm0.019_{\rm
stat}\pm0.024_{\rm syst})\%$, $\mathcal{B}(D^+\to 2\pi^+\pi^-\pi^0)=
(1.174\pm0.021_{\rm stat}\pm0.021_{\rm syst})\%$, and $\mathcal{B}(D^+\to
2\pi^+\pi^-2\pi^0)=(1.074\pm0.040_{\rm stat}\pm0.030_{\rm syst})\%$. The $CP$
asymmetries for the six decays with highest event yields are also determined.


  In the canonical approach of loop quantum gravity, arguably the most
important outstanding problem is finding and interpreting solutions to the
Hamiltonian constraint. In this work, we demonstrate that methods of machine
learning are in principle applicable to this problem. We consider U(1) BF
theory in 3 dimensions, quantized with loop quantum gravity methods. In
particular, we formulate a master constraint corresponding to Hamilton and
Gauss constraints using loop quantum gravity methods. To make the problem
amenable for numerical simulation we fix a graph and introduce a cutoff on the
kinematical degrees of freedom, effectively considering U$_q$(1) BF theory at a
root of unity. We show that the Neural Network Quantum State (NNQS) ansatz can
be used to numerically solve the constraints efficiently and accurately. We
compute expectation values and fluctuations of certain observables and compare
them with exact results or exact numerical methods where possible. We also
study the dependence on the cutoff.


  The waiting time distribution has, in recent years, proven to be a useful
statistical tool for characterising transport in nanoscale quantum transport.
In particular, as opposed to moments of the distribution of transferred charge,
which have historically been calculated in the long-time limit, waiting times
are able to detect non-renewal behaviour in mesoscopic systems. They have
failed, however, to correctly incorporate backtunneling events. Recently, a
method has been developed that can describe unidirectional and bidirectional
transport on an equal footing: the distribution of first-passage times. Rather
than the time between successive electron tunnelings, the first-passage refers
to the first time the number of extra electrons in the drain reaches $+1$.
Here, we demonstrate the differences between first-passage time statistics and
waiting time statistics in transport scenarios where the waiting time either
cannot correctly reproduce the higher order current cumulants or cannot be
calculated at all. To this end, we examine electron transport through a
molecule coupled to two macroscopic metal electrodes. We model the molecule
with strong electron-electron and electron-phonon interactions in three
regimes: (i) sequential tunneling and cotunneling for a finite bias voltage
through the Anderson model, (ii) sequential tunneling with no temperature
gradient and a bias voltage through the Holstein model, and (iii) sequential
tunneling at zero bias voltage and a temperature gradient through the Holstein
model. We show that, for each transport scenario, backtunneling events play a
significant role; consequently, the waiting time statistics do not correctly
predict the renewal and non-renewal behaviour, whereas the first-passage time
distribution does.


  Loop under-approximation is a technique that enriches C programs with
additional branches that represent the effect of a (limited) range of loop
iterations. While this technique can speed up the detection of bugs
significantly, it introduces redundant execution traces which may complicate
the verification of the program. This holds particularly true for verification
tools based on Bounded Model Checking, which incorporate simplistic heuristics
to determine whether all feasible iterations of a loop have been considered.
  We present a technique that uses \emph{trace automata} to eliminate redundant
executions after performing loop acceleration. The method reduces the diameter
of the program under analysis, which is in certain cases sufficient to allow a
safety proof using Bounded Model Checking. Our transformation is precise---it
does not introduce false positives, nor does it mask any errors. We have
implemented the analysis as a source-to-source transformation, and present
experimental results showing the applicability of the technique.


  Utilizing realistic simulations of high-harmonic generation (HHG) in several
materials, we study how different regions of the Brillouin zone contribute to
the nonlinear response. It is often assumed that only the vicinity of the Gamma
point is predominantly responsible for the HHG spectrum, but it is shown here
that such an approximation is inaccurate in general. While examples can be
identified where merely 0.4% of the Brillouin zone produces semi-quantitatively
accurate HHG-spectra, in most situations one must include at least thirty to
fifty percent of the Brillouin-zone volume to obtain accurate above-the-gap
harmonics. For the harmonic peaks below the bandgap energy, the current-density
responses from the entire Brillouin zone must always be integrated. We also
identify the minimal set of electronic bands necessary for the construction of
reduced but still realistic HHG-models. The results should be useful for a
number of HHG applications, including all-optical reconstructions of the
band-structure and light-matter couplings, or considerations involving
semi-classical approaches to solid-state high-harmonic radiation.


  A $q$-bic hypersurface is a hypersurface in projective space of degree $q+1$,
where $q$ is a power of the positive ground field characteristic, whose
equation consists of monomials which are products of a $q$-power and a linear
power; the Fermat hypersurface is an example. I identify $q$-bics as moduli
spaces of isotropic vectors for an intrinsically defined bilinear form, and use
this to study their Fano schemes of linear spaces. Amongst other things, I
prove that the scheme of $m$-planes in a smooth $(2m+1)$-dimensional $q$-bic
hypersurface is an $(m+1)$-dimensional smooth projective variety of general
type which admits a purely inseparable covering by a complete intersection; I
compute its Betti numbers by relating it to Deligne--Lusztig varieties for the
finite unitary group; and I prove that its Albanese variety is purely
inseparably isogenous via an Abel--Jacobi map to a certain conjectural
intermediate Jacobian of the hypersurface. The case $m = 1$ may be viewed as an
analogue of results of Clemens and Griffiths regarding cubic threefolds.


  To understand and interpret the observed Spectral Energy Distributions (SEDs)
of starbursts, theoretical or semi-empirical SED models are necessary. Yet,
while they are well-founded in theory, independent verification and calibration
of these models, including the exploration of possible degeneracies between
their parameters, are rarely made. As a consequence, a robust fitting method
that leads to unique and reproducible results has been lacking. Here we
introduce a novel approach based on Bayesian analysis to fit the Spitzer-IRS
spectra of starbursts using the SED models proposed by Groves et al. (2008). We
demonstrate its capabilities and verify the agreement between the derived best
fit parameters and actual physical conditions by modelling the nearby,
well-studied, giant HII region 30 Dor in the LMC. The derived physical
parameters, such as cluster mass, cluster age, ISM pressure and covering
fraction of photodissociation regions, are representative of the 30 Dor region.
The inclusion of the emission lines in the modelling is crucial to break
degeneracies. We investigate the limitations and uncertainties by modelling
sub-regions, which are dominated by single components, within 30 Dor. A
remarkable result for 30 Doradus in particular is a considerable contribution
to its mid-infrared spectrum from hot ({\simeq} 300K) dust. The demonstrated
success of our approach will allow us to derive the physical conditions in more
distant, spatially unresolved starbursts.


  We investigate the semantic knowledge of language models (LMs), focusing on
(1) whether these LMs create categories of linguistic environments based on
their semantic monotonicity properties, and (2) whether these categories play a
similar role in LMs as in human language understanding, using negative polarity
item licensing as a case study. We introduce a series of experiments consisting
of probing with diagnostic classifiers (DCs), linguistic acceptability tasks,
as well as a novel DC ranking method that tightly connects the probing results
to the inner workings of the LM. By applying our experimental pipeline to LMs
trained on various filtered corpora, we are able to gain stronger insights into
the semantic generalizations that are acquired by these models.


  An aperiodic and irreducible Markov chain on a finite state space converges
to its stationary distribution. When convergence to equilibrium is measured by
total variation distance, there exists an optimal coupling and a maximal
coupling time. In this article, the maximal coupling time is compared to the
hitting time of a specific state or set. Such sets, named halting sets, are
studied in the case of symmetric birth-and-death chains and in some other
examples. Some applications to the cutoff phenomenon are given. These results
yield new methods to calculate cutoff times for some monotone birth-and death
chains without the lazy hypothesis .


  In this paper, the notion of universal enveloping algebra introduced in [A.
Ardizzoni, \emph{A First Sight Towards Primitively Generated Connected Braided
Bialgebras}, submitted. (arXiv:0805.3391v3)] is specialized to the case of
braided vector spaces whose Nichols algebra is quadratic as an algebra. In this
setting a classification of universal enveloping algebras for braided vector
spaces of dimension not greater than 2 is handled. As an application, we
investigate the structure of primitively generated connected braided bialgebras
whose braided vector space of primitive elements forms a Nichols algebra which
is quadratic algebra.


  In the first part of this paper, we present a unified framework for analyzing
the algorithmic complexity of any optimization problem, whether it be
continuous or discrete in nature. This helps to formalize notions like "input",
"size" and "complexity" in the context of general mathematical optimization,
avoiding context dependent definitions which is one of the sources of
difference in the treatment of complexity within continuous and discrete
optimization. In the second part of the paper, we employ the language developed
in the first part to study information theoretic and algorithmic complexity of
{\em mixed-integer convex optimization}, which contains as a special case
continuous convex optimization on the one hand and pure integer optimization on
the other. We strive for the maximum possible generality in our exposition.
  We hope that this paper contains material that both continuous optimizers and
discrete optimizers find new and interesting, even though almost all of the
material presented is common knowledge in one or the other community. We see
the main merit of this paper as bringing together all of this information under
one unifying umbrella with the hope that this will act as yet another catalyst
for more interaction across the continuous-discrete divide. In fact, our
motivation behind Part I of the paper is to provide a common language for both
communities.


  We present Transformation Invariance and Covariance Contrast (TiCo) for
self-supervised visual representation learning. Similar to other recent
self-supervised learning methods, our method is based on maximizing the
agreement among embeddings of different distorted versions of the same image,
which pushes the encoder to produce transformation invariant representations.
To avoid the trivial solution where the encoder generates constant vectors, we
regularize the covariance matrix of the embeddings from different images by
penalizing low rank solutions. By jointly minimizing the transformation
invariance loss and covariance contrast loss, we get an encoder that is able to
produce useful representations for downstream tasks. We analyze our method and
show that it can be viewed as a variant of MoCo with an implicit memory bank of
unlimited size at no extra memory cost. This makes our method perform better
than alternative methods when using small batch sizes. TiCo can also be seen as
a modification of Barlow Twins. By connecting the contrastive and
redundancy-reduction methods together, TiCo gives us new insights into how
joint embedding methods work.


  Systems of particles in a confining potential exhibit a spatially dependent
density which fundamentally alters the nature of phase transitions that occur.
A specific instance of this situation, which is being extensively explored
currently, concerns the properties of ultra-cold, optically trapped atoms. Of
interest is how the superfluid-insulator transition is modified by the
inhomogeneity, and, indeed, the extent to which a sharp transition survives at
all. This paper explores a classical analog of these systems, the Blume-Capel
model with a spatially varying single ion anisotropy and/or temperature
gradient. We present results both for the nature of the critical properties and
for the validity of the "local density approximation" which is often used to
model the inhomogeneous case. We compare situations when the underlying uniform
transition is first and second order.


  We prove two sufficient conditions of quasi-normality in which each pair $f$
and $g$ of $\mathcal{F}$ shares some holomorphic functions.


  We introduce a Milnor type $K$-group associated to commutative algebraic
groups over a perfect field. It is an additive variant of Somekawa's $K$-group.
We show that the $K$-group associated to the additive group and $q$
multiplicative groups of a field is isomorphic to the space of absolute
K\"ahler differentials of degree $q$ of the field, thus giving us a geometric
interpretation of the space of absolute K\"ahler differentials. We also show
that the $K$-group associated to the additive group and Jacobian variety of a
curve is isomorphic to the homology group of a certain complex.


  We review Quasi Maximum Likelihood estimation of factor models for
high-dimensional panels of time series. We consider two cases: (1) estimation
when no dynamic model for the factors is specified (Bai and Li, 2012, 2016);
(2) estimation based on the Kalman smoother and the Expectation Maximization
algorithm thus allowing to model explicitly the factor dynamics (Doz et al.,
2012, Barigozzi and Luciani, 2019). Our interest is in approximate factor
models, i.e., when we allow for the idiosyncratic components to be mildly
cross-sectionally, as well as serially, correlated. Although such setting
apparently makes estimation harder, we show, in fact, that factor models do not
suffer of the {\it curse of dimensionality} problem, but instead they enjoy a
{\it blessing of dimensionality} property. In particular, given an approximate
factor structure, if the cross-sectional dimension of the data, $N$, grows to
infinity, we show that: (i) identification of the model is still possible, (ii)
the mis-specification error due to the use of an exact factor model
log-likelihood vanishes. Moreover, if we let also the sample size, $T$, grow to
infinity, we can also consistently estimate all parameters of the model and
make inference. The same is true for estimation of the latent factors which can
be carried out by weighted least-squares, linear projection, or Kalman
filtering/smoothing. We also compare the approaches presented with: Principal
Component analysis and the classical, fixed $N$, exact Maximum Likelihood
approach. We conclude with a discussion on efficiency of the considered
estimators.


  We find the most general supersymmetric solutions of ungauged N=1,d=4
supergravity coupled to an arbitrary number of vector and chiral
supermultiplets, which turn out to be essentially pp-waves and strings. We also
introduce magnetic 1-forms and their supersymmetry transformations and 2-forms
associated to the isometries of the scalar manifold and their supersymmetry
transformations. Only the latter can couple to BPS objects (strings), in
agreement with our results.


  We propose a method for explicit computation of the Chern character form of a
holomorphic Hermitian vector bundle $(E,h)$ over a complex manifold $X$ in a
local holomorphic frame. First, we use the descent equations arising in the
double complex of $(p,q)$-forms on $X$ and find explicit degree decomposition
of the Chern-Simons form $\mathrm{cs}_{k}$ associated to the Chern character
form $\mathrm{ch}_{k}$ of $(E,h)$. Second, we introduce the `ascent' equations
that start from the $(2k-1,0)$ component of $\mathrm{cs}_{k}$, and use Cholesky
decomposition of the Hermitian metric $h$ to represent the Chern-Simons form,
modulo $d$-exact forms, as a $\partial$-exact form. This yields a formula for
the Bott-Chern form $\mathrm{bc}_{k}$ of type $(k-1,k-1)$ such that
$\mathrm{ch}_{k}=\frac{\sqrt{-1}}{2\pi}\bar{\partial}\partial\,\mathrm{bc}_{k}$.
Explicit computation is presented for the cases $k=2$ and $3$.


  We define a notion for unfolding smooth, ruled surfaces, and prove that every
smooth prismatoid (the convex hull of two smooth curves lying in parallel
planes), has a nonoverlapping "volcano unfolding." These unfoldings keep the
base intact, unfold the sides outward, splayed around the base, and attach the
top to the tip of some side rib. Our result answers a question for smooth
prismatoids whose analog for polyhedral prismatoids remains unsolved.


  Bayesian optimization (BO) has well-documented merits for optimizing
black-box functions with an expensive evaluation cost. Such functions emerge in
applications as diverse as hyperparameter tuning, drug discovery, and robotics.
BO hinges on a Bayesian surrogate model to sequentially select query points so
as to balance exploration with exploitation of the search space. Most existing
works rely on a single Gaussian process (GP) based surrogate model, where the
kernel function form is typically preselected using domain knowledge. To bypass
such a design process, this paper leverages an ensemble (E) of GPs to
adaptively select the surrogate model fit on-the-fly, yielding a GP mixture
posterior with enhanced expressiveness for the sought function. Acquisition of
the next evaluation input using this EGP-based function posterior is then
enabled by Thompson sampling (TS) that requires no additional design
parameters. To endow function sampling with scalability, random feature-based
kernel approximation is leveraged per GP model. The novel EGP-TS readily
accommodates parallel operation. To further establish convergence of the
proposed EGP-TS to the global optimum, analysis is conducted based on the
notion of Bayesian regret for both sequential and parallel settings. Tests on
synthetic functions and real-world applications showcase the merits of the
proposed method.


  Stochastic Gradient Descent (SGD) is a central tool in machine learning. We
prove that SGD converges to zero loss, even with a fixed (non-vanishing)
learning rate - in the special case of homogeneous linear classifiers with
smooth monotone loss functions, optimized on linearly separable data. Previous
works assumed either a vanishing learning rate, iterate averaging, or loss
assumptions that do not hold for monotone loss functions used for
classification, such as the logistic loss. We prove our result on a fixed
dataset, both for sampling with or without replacement. Furthermore, for
logistic loss (and similar exponentially-tailed losses), we prove that with SGD
the weight vector converges in direction to the $L_2$ max margin vector as
$O(1/\log(t))$ for almost all separable datasets, and the loss converges as
$O(1/t)$ - similarly to gradient descent. Lastly, we examine the case of a
fixed learning rate proportional to the minibatch size. We prove that in this
case, the asymptotic convergence rate of SGD (with replacement) does not depend
on the minibatch size in terms of epochs, if the support vectors span the data.
These results may suggest an explanation to similar behaviors observed in deep
networks, when trained with SGD.


  Spoken language change detection (LCD) refers to detecting language switching
points in a multilingual speech signal. Speaker change detection (SCD) refers
to locating the speaker change points in a multispeaker speech signal. The
objective of this work is to understand the challenges in LCD task by comparing
it with SCD task. Human subjective study for change detection is performed for
LCD and SCD. This study demonstrates that LCD requires larger duration
spectro-temporal information around the change point compared to SCD. Based on
this, the work explores automatic distance based and model based LCD
approaches. The model based ones include Gaussian mixture model and universal
background model (GMM-UBM), attention, and Generative adversarial network (GAN)
based approaches. Both the human and automatic LCD tasks infer that the
performance of the LCD task improves by incorporating more and more
spectro-temporal duration.


  In the problem of generalized zero-shot learning, the datapoints from unknown
classes are not available during training. The main challenge for generalized
zero-shot learning is the unbalanced data distribution which makes it hard for
the classifier to distinguish if a given testing sample comes from a seen or
unseen class. However, using Generative Adversarial Network (GAN) to generate
auxiliary datapoints by the semantic embeddings of unseen classes alleviates
the above problem. Current approaches combine the auxiliary datapoints and
original training data to train the generalized zero-shot learning model and
obtain state-of-the-art results. Inspired by such models, we propose to feed
the generated data via a model selection mechanism. Specifically, we leverage
two sources of datapoints (observed and auxiliary) to train some classifier to
recognize which test datapoints come from seen and which from unseen classes.
This way, generalized zero-shot learning can be divided into two disjoint
classification tasks, thus reducing the negative influence of the unbalanced
data distribution. Our evaluations on four publicly available datasets for
generalized zero-shot learning show that our model obtains state-of-the-art
results.


  Shesop is an integrated system to make human lives more easily and to help
people in terms of healthcare. Stress and influenza classification is a part of
Shesop's application for a healthcare devices such as smartwatch, polar and
fitbit. The main objective of this paper is to create a proper application to
implement the stress and influenza classification. The application use Android
studio, XML and Java. Also, while creating this application, all design and
program is considered to be available for future updates. The application needs
an android smartphone with Bluetooth Low Energy technology (bluetooth v4.0 or
above). SheSop application will accommodate data entry, device picker, data
gathering process, result and saving the result. In the end, we could use the
polar H7 and this application to get a real-time heart rate, Heart rate
variability and diagnose our stress and influenza condition.


  This short survey paper is concerned with a new method to prove global
well-posedness results for dispersive equations below energy spaces, namely
$H^{1}$ for the Schr\"odinger equation and $L^{2}$ for the KdV equation. The
main ingredient of this method is the definition of a family of what we call
almost conservation laws. In particular we analyze the Korteweg-de Vries
initial value problem and we illustrate in general terms how the ``algorithm''
that we use to formally generate almost conservation laws can be used to
recover the infinitely many conserved integrals that make the KdV an integrable
system.


  We carry out hydrodynamical simulation of the evolution of fluid in
relativistic heavy-ion collisions with random initial fluctuations. The time
evolution of power spectrum of momentum anisotropies shows very strong
correspondence with the physics of cosmic microwave anisotropies as was earlier
predicted by some of us. In particular our results demonstrate suppression of
superhorizon fluctuations and the correspondence between the location of the
first peak in the power spectrum of momentum anisotropies and the length scale
of fluctuations and expected freezeout time scale (more precisely, the sound
horizon size at freezeout).


  We investigate the spectral properties of the Wilson Dirac operator in
quenched QCD in the microscopic regime. We distinguish the topological sectors
using the index as determined by the Wilson flow method. Consequently, the
distributions of the low-lying eigenvalues of the Wilson Dirac operator can be
compared in each of the topological sectors to predictions from random matrix
theory applied to the $\epsilon$-regime of chiral perturbation theory. We find
rather good agreement for volumes as small as $(1.5 \, \text{fm})^4$ and
lattice spacings as coarse as $0.1\, \text{fm}$, and demonstrate that it is
indeed possible to extract low-energy constants for Wilson fermions from the
spectral properties of the Wilson Dirac operator.


  We prove the absence of a universal diameter bound on lengths of curves in a
sweep-out of a Riemannian 2-sphere. If such bound existed it would yield a
simple proof of existence of short geodesic segments and closed geodesics on a
sphere of small diameter.


  We use recently acquired geomagnetic archival data to extend our long-term
reconstruction of the HMF strength. The 1835-2009 HMF series is based on an
updated and substantiated IDV series from 1872-onwards and on Bartels'
extension, by proxy, of his u-series from 1835-1871. The new IDV series, termed
IDV09, has excellent agreement (R^2 = 0.98; RMS = 0.3 nT) with the earlier
IDV05 series, and also with the negative component of Love's extended (to 1905)
Dst series (R^2 = 0.91). Of greatest importance to the community, in an area of
research that has been contentious, comparison of the extended HMF series with
other recent reconstructions of solar wind B for the last ~100 years yields a
strong consensus between series based on geomagnetic data. Differences exist
from ~1900-1910 but they are far smaller than the previous disagreement for
this key interval of low solar wind B values which closely resembles current
solar activity. Equally encouraging, a discrepancy with an HMF reconstruction
based on 10Be data for the first half of the 20th century has largely been
removed by a revised 10Be-based reconstruction published after we submitted
this paper, although a remaining discrepancy for the years ~1885-1905 will need
to be resolved.


  We numerically study the interacting quantum Hall skyrmion system based on
the Chern-Simons action. By noticing that the action is invariant under global
spin rotations in the spin space with respect to the magnetic field direction,
we obtain the low-energy effective action for a many skyrmion system.
Performing extensive molecular dynamics simulations, we establish the
thermodynamic phase diagram for a many skyrmion system.


  Low-textured image stitching remains a challenging problem. It is difficult
to achieve good alignment and it is easy to break image structures due to
insufficient and unreliable point correspondences. Moreover, because of the
viewpoint variations between multiple images, the stitched images suffer from
projective distortions. To solve these problems, this paper presents a
line-guided local warping method with a global similarity constraint for image
stitching. Line features which serve well for geometric descriptions and scene
constraints, are employed to guide image stitching accurately. On one hand, the
line features are integrated into a local warping model through a designed
weight function. On the other hand, line features are adopted to impose strong
geometric constraints, including line correspondence and line colinearity, to
improve the stitching performance through mesh optimization. To mitigate
projective distortions, we adopt a global similarity constraint, which is
integrated with the projective warps via a designed weight strategy. This
constraint causes the final warp to slowly change from a projective to a
similarity transformation across the image. Finally, the images undergo a
two-stage alignment scheme that provides accurate alignment and reduces
projective distortion. We evaluate our method on a series of images and compare
it with several other methods. The experimental results demonstrate that the
proposed method provides a convincing stitching performance and that it
outperforms other state-of-the-art methods.


  An interval edge t-coloring of a graph G is a proper edge coloring of G with
colors 1,2...,t such that at least one edge of G is colored by color
i,i=1,2...,t, and the edges incident with each vertex v are colored by d_{G}(v)
consecutive colors, where d_{G}(v) is the degree of the vertex v in G. In this
paper interval edge colorings of bipartite cylinders and bipartite tori are
investigated.


  The nervous system, more specifically, the brain, is capable of solving
complex problems simply and efficiently, far surpassing modern computers. In
this regard, neuromorphic engineering is a research field that focuses on
mimicking the basic principles that govern the brain in order to develop
systems that achieve such computational capabilities. Within this field,
bio-inspired learning and memory systems are still a challenge to be solved,
and this is where the hippocampus is involved. It is the region of the brain
that acts as a short-term memory, allowing the learning and unstructured and
rapid storage of information from all the sensory nuclei of the cerebral cortex
and its subsequent recall. In this work, we propose a novel bio-inspired memory
model based on the hippocampus with the ability to learn memories, recall them
from a cue (a part of the memory associated with the rest of the content) and
even forget memories when trying to learn others with the same cue. This model
has been implemented on the SpiNNaker hardware platform using Spiking Neural
Networks, and a set of experiments and tests were performed to demonstrate its
correct and expected operation. The proposed spike-based memory model generates
spikes only when it receives an input, being energy efficient, and it needs 7
timesteps for the learning step and 6 timesteps for recalling a
previously-stored memory. This work presents the first hardware implementation
of a fully functional bio-inspired spike-based hippocampus memory model, paving
the road for the development of future more complex neuromorphic systems.


  The evaporation of a drop from a liquid subphase is investigated. The two
liquids are immiscible, and the contact angles between them are given by the
Neumann construction. The evaporation of the drop gives rise to flows in both
liquids, which are coupled by the continuity of velocity and shear-stress
conditions. We derive self-similar solutions to the velocity fields in both
liquids close to the three-phase contact line, where the drop geometry can be
approximated by a wedge. We focus on the case where Marangoni stresses are
negligible, for which the flow field consists of three contributions: flow
driven by the evaporative flux from the drop surface, flow induced by the
receding motion of the contact line, and an eigenmode flow that satisfies the
homogeneous boundary conditions. The eigenmode flow is asymptotically
subdominant for all contact angles. The moving contact-line flow dominates when
the angle between the liquid drop and the horizontal surface of the liquid
subphase is smaller than $90^\circ$, while the evaporative-flux driven flow
dominates for larger angles. A parametric study is performed to show how the
velocity fields in the two liquids depend on the contact angles between the
liquids and their viscosity ratio.


  We unravel the existence and stability properties of dark soliton solutions
as they extend from the regime of trapped quantum droplets towards the
Thomas-Fermi limit in homonuclear symmetric Bose mixtures. Leveraging a
phase-plane analysis, we identify the regimes of existence of different types
of quantum droplets and subsequently examine the possibility of black and gray
solitons and kink-type structures in this system. Moreover, we employ the
Landau dynamics approach to extract an analytical estimate of the oscillation
frequency of a single dark soliton in the relevant extended Gross-Pitaevskii
model. Within this framework, we also find that the single soliton immersed in
a droplet is stable, while multisoliton configurations exhibit parametric
windows of oscillatory instabilities. Our results pave the way for studying
dynamical features of nonlinear multisoliton excitations in a droplet
environment in contemporary experimental settings.


  We present a new method for quantum state tomography within a
single-excitation subspace of two-qubit states in an open waveguide. The system
under investigation consists of three qubits in an open waveguide, separated by
a distance comparable to the wavelength of the electromagnetic field. We show
that the modulation of the frequency of the central ancillary qubit allows us
to obtain unambiguous information about the initial phase difference
$\varphi_1-\varphi_3$ of the edge qubits via the measurement of the evolution
of their probability amplitudes.


  We analyze and simulate a two dimensional Brownian multi-type particle system
with death and branching (birth) depending on the position of particles of
different types. The system is confined in the two dimensional box, whose
boundaries act as the sink of Brownian particles. The branching rate matches
the death rate so that the total number of particles is kept constant. In the
case of m types of particles in the rectangular box of size a,b and elongated
shape $a\gg b$ we observe that the stationary distribution of particles
corresponds to the m-th Laplacian eigenfunction. For smaller elongations $a>b$
we find a configurational transition to a new limiting distribution. The ratio
a/b for which the transition occurs is related to the value of the m-th
eigenvalue of the Laplacian with rectangular boundaries.


  We introduce consideration of dispersive aspects of standard perfect fluid
Friedmann cosmology and study the new qualitative behaviours of cosmological
solutions that emerge as the fluid parameter changes and zero eigenvalues
appear in the linear part of the Friedmann equations. We find that due to their
insufficient degeneracy, the Milne, flat, Einstein-static, and de Sitter
solutions cannot properly bifurcate. However, the dispersive versions of Milne
and flat universes contained in the versal unfolding of the standard Friedmann
equations possess novel long-term properties not met in their standard
counterparts. We apply these results to the horizon problem and show that
unlike their hyperbolic versions, the dispersive Milne and flat solutions
completely synchronize in the future, hence offering a solution to the
homogeneity, isotropy, and causal connectedness puzzles.


  We present a formalism to study adiabatic pumping through a superconductor -
normal - superconductor weak link. At zero temperature, the pumped charge is
related to the Berry phase accumulated, in a pumping cycle, by the Andreev
bound states. We analyze in detail the case when the normal region is short
compared to the superconducting coherence length. The pumped charge turns out
to be an even function of the superconducting phase difference. Hence, it can
be distinguished from the charge transferred due to the standard Josephson
effect.