  This paper investigates the distributionally robust filtering of signals
generated by state-space models driven by exogenous disturbances with noisy
observations in finite and infinite horizon scenarios. The exact joint
probability distribution of the disturbances and noise is unknown but assumed
to reside within a Wasserstein-2 ambiguity ball centered around a given nominal
distribution. We aim to derive a causal estimator that minimizes the worst-case
mean squared estimation error among all possible distributions within this
ambiguity set. We remove the iid restriction in prior works by permitting
arbitrarily time-correlated disturbances and noises. In the finite horizon
setting, we reduce this problem to a semi-definite program (SDP), with
computational complexity scaling with the time horizon. For infinite horizon
settings, we characterize the optimal estimator using Karush-Kuhn-Tucker (KKT)
conditions. Although the optimal estimator lacks a rational form, i.e., a
finite-dimensional state-space realization, it can be fully described by a
finite-dimensional parameter. {Leveraging this parametrization, we propose
efficient algorithms that compute the optimal estimator with arbitrary fidelity
in the frequency domain.} Moreover, given any finite degree, we provide an
efficient convex optimization algorithm that finds the finite-dimensional
state-space estimator that best approximates the optimal non-rational filter in
${\cal H}_\infty$ norm. This facilitates the practical implementation of the
infinite horizon filter without having to grapple with the ill-scaled SDP from
finite time. Finally, numerical simulations demonstrate the effectiveness of
our approach in practical scenarios.


  Breakup of a liquid jet in a high speed gaseous crossflow finds wide range of
engineering and technological applications, especially in the combustors of the
gas turbine engines in aerospace industry. In this study, we present
volume-of-fluid method based direct numerical simulations of a liquid jet
injected into a swirling crossflow of gas. The liquid is injected radially
outwards from a central tube to a confined annular space with a swirling gas
crossflow. The essential features of the jet breakup involving jet flattening,
surface waves and stripping of droplets from the edges of the jet are captured
in the simulations. We discuss the effect of swirl on the spray characteristics
such as jet trajectory, column breakup-length, and size, shape-factor and
velocity distribution of the drops. Drop size increases with swirl and
penetration is slightly reduced. Moreover, the trajectory follows an angle
(azimuthal) that is smaller than the geometric angle of the swirl at the inlet.
Interestingly, we also observe coalescence events downstream of the jet that
affect the final droplet size distribution for the geometry considered in this
study.


  The Doctoral thesis of William Naylor. Gives the background of the three
papers included, specifically introducing both the quark meson model and the
NJL model, the basic formalism of thermal field theory, and functional
renormalization group (including some details on numerically solving the FRG
equation for the QM model).


  We address light propagation in segmented waveguide arrays where the
refractive index is longitudinally modulated with an out-of-phase modulation in
adjacent waveguides, so that the coupling strength varies along propagation
direction. Thus in resonant segments coupling may be inhibited hence light
remains localized, while in detuned segments coupling results in complex
switching scenarios that may be controlled by stacking several resonant and
nonresonant segments. By tuning the modulation frequency and lengths of
waveguide segments one may control the distribution of light among the output
guides, including loca-lizing all light in the selected output channel.


  For a coalgebra $C_k$ over field $k$, we define the "coalgebra extension
problem" as the question: what multiplication laws can we define on $C_k$ to
make it a bialgebra over $k$? This paper answers this existence-uniqueness
question for certain coalgebras called "circulant coalgebras". We begin with
the trigonometric coalgebra, comparing and contrasting with the
group-(bi)algebra $k[\mathbb Z/2]$. This leads to a generalization, the dual
coalgebra to the group-algebra $k[\mathbb Z/p]$, which we then investigate. We
show connections with other questions, motivating us to answer to the coalgebra
extension problem for these families. The answer depends interestingly on the
base field $k$'s characteristic.
  Along similar lines, we investigate the algebraic group $S^1$ over arbitrary
$k$. We find that similar complications arise in characteristic 2. We explore
this, motivated (by quantum groups) by the question of whether or not
$\mathcal{O}(S^1)$ is pointed. We give a very explicit conjecture in terms of
the Chebyshev polynomials of trigonometry. We end by constructing a formal
group object, in a certain monoidal category of modules of $k[[h]]$, as a
$2^{\text{nd}}$ order deformation of $k[t]$.


  Determining the distance between a controllable system to the set of
uncontrollable systems, namely, the controllability radius problem, has been
extensively studied in the past. However, the opposite direction, that is,
determining the `distance' between an uncontrollable system to the set of
controllable systems, has seldom been considered. In this paper, we address
this problem by defining the notion of zero-norm distance to controllability
(ZNDC) to be the smallest number of entries (parameters) in the system matrices
that need to be perturbed to make the original system controllable. We show
genericity exists in this problem, so that other matrix norms (such as the
$2$-norm or the Frobenius norm) adopted in this notion are nonsense. For ZNDC,
we show it is NP-hard to compute, even when only the state matrix can be
perturbed. We then provide some nontrivial lower and upper bounds. For its
computation, we provide two heuristic algorithms. The first one is by
transforming the ZNDC into a problem of structural controllability of linearly
parameterized systems, and then greedily selecting the candidate links
according to a suitable objective function. The second one is based on the
weighted $l_1$-norm relaxation and the convex-concave procedure, which is
tailored for ZNDC when additional structural constraints are involved in the
perturbed parameters. Finally, we examine the performance of our proposed
algorithms in several typical uncontrollable networks in multi-agent systems.


  In this paper, we develop a new method to produce explicit formulas for the
number $f_{G}(n)$ of rooted spanning forests in the circulant graphs $
G=C_{n}(s_1,s_2,\ldots,s_k)$ and $ G=C_{2n}(s_1,s_2,\ldots,s_k,n).$ These
formulas are expressed through Chebyshev polynomials. We prove that in both
cases the number of rooted spanning forests can be represented in the form
$f_{G}(n)=p\,a(n)^2,$ where $a(n)$ is an integer sequence and $p$ is a
prescribed natural number depending on the parity of $n$. Finally, we find an
asymptotic formula for $f_{G}(n)$ through the Mahler measure of the associated
Laurent polynomial $P(z)=2k+1-\sum\limits_{i=1}^k(z^{s_i}+z^{-s_i}).$


  When one combines multiverse predictions by Bousso, Hall, and Nomura for the
observed age and size of the universe in terms of the proton and electron
charge and masses with anthropic predictions of Carter, Carr, and Rees for
these masses in terms of the charge, one gets that the age of the universe
should be roughly the inverse 64th power, and the cosmological constant should
be around the 128th power, of the proton charge. Combining these with a further
renormalization group argument gives a single approximate equation for the
proton charge, with no continuous adjustable or observed parameters, and with a
solution that is within 8% of the observed value. Using this solution gives
large logarithms for the age and size of the universe and for the cosmological
constant that agree with the observed values within 17%.


  Very recently, NiTe2 has been reported to be a type II Dirac semimetal with
Dirac nodes near the Fermi surface. Furthermore, it is unveiled that NiTe2
presents the Hall Effect, which is ascribed to orbital magnetoresistance. The
physical properties behavior of NiTe2 under high pressure attracts us. In this
paper, we investigate the electrical properties of polycrystalline NiTe2 by
application of pressure ranging from 3.4GPa to 54.45Gpa. Superconductivity
emerges at critical pressure 12GPa with a transition temperature of 3.7K, and
Tc reaches its maximum, 6.4 K, at the pressure of 52.8GPa. Comparing with the
superconductivity in MoP, we purposed the possibility of topological
superconductivity in NiTe2. Two superconductivity transitions are observed with
pressure increasing in single crystal.


  In few-body physics, Efimov states are an infinite series of three-body bound
states that obey universal discrete scaling symmetry when pairwise interactions
are resonantly enhanced. Despite abundant reports of Efimov states in recent
cold atom experiments, direct observation of the discrete scaling symmetry
remains an elusive goal. Here we report the observation of three consecutive
Efimov resonances in a heteronuclear Li-Cs mixture near a broad interspecies
Feshbach resonance. The positions of the resonances closely follow a geometric
series $1$, $\lambda$, $\lambda^2$. The observed scaling constant $\lambda_{\rm
exp} = 4.9(4)$ is in good agreement with the predicted value of 4.88.


  We give a pedagogical review of the recently-introduced notion of a "scalar
product" between Feynman integrals and how it helps us understand the analytic
structure of the perturbative S-matrix. (This article is a contribution to the
proceedings of the workshop "MathemAmplitudes 2019: Intersection Theory and
Feynman Integrals" held in Padova, Italy on 18-20 December 2019.)


  Recent angle-resolved photoemission experiments have observed a
proximity-induced superconducting gap in the helical surface states of a thin
film of the 3D topological insulator Bi$_2$Se$_3$ grown on a superconducting
NbSe$_2$ substrate. The superconducting coherence peaks in the electronic
density of states are strongly suppressed when the topological insulator is
doped with magnetic Mn impurities, which was interpreted as the complete
destruction of helical superconductivity in the topological surface states.
Motivated by these experiments, we explore a different possibility: gapless
helical superconductivity, where a gapless electronic density of states
coexists with a nonzero helical superconducting order parameter. We study a
model of superconducting Dirac fermions coupled to random magnetic impurities
within the Abrikosov-Gor'kov framework, and find finite regions of gapless
helical superconductivity in the phase diagram of the system for both
proximity-induced and intrinsic superconductivity. For the latter, we derive
universal rates of supression of the superconducting transition temperature due
to magnetic scattering and, for a Fermi level at the Dirac point, a universal
rate of increase of the quantum critical attraction strength.


  With the observations of the CS 5-4 line toward a sample of 24 infrared
bright galaxies using HHSMT, we detected CS 5-4 emission in 14 galaxies,
including 12 ULIRGs/LIRGs and 2 nearby normal galaxies. As a good dense gas
tracer, which has been well used for studying star formation in the Milky Way,
CS 5-4 can trace the active star forming gas in galaxies. The correlation
between CS 5-4 luminosity, which is estimated with detected CS 5-4 line
emission, and infrared luminosity in these 14 galaxies is fitted with
correlation coefficient of 0.939 and the slope close to unity. This correlation
confirmed that dense gas, which is closely linked to star formation, is very
important for understanding star formation in galaxies.


  Dozens of planets are now discovered with large orbital obliquity, and have
become the proof for the dynamical evolution of planetary orbits. In the
current samples, there is an apparent clustering of planets around $90^\circ$,
and also an absence of planets around $180^\circ$ although the latter is
expected by some theories. Statistical extrapolation using Hierarchical
Bayesian Analysis have recently refuted the significant clustering around
$90^\circ$ and suggested that the distribution may actually be broader. In this
work, the symmetric TESS transit light curve of KELT-19Ab is analyzed using
gravity darkening to measure its true obliquity. Its large sky projected
obliquity $\lambda = -179.7^{\circ+3.7^\circ}_{\,\,-3.8^\circ}$ makes KELT-19Ab
the only currently known planet with obliquity potentially close to
$180^\circ$. We apply spectroscopic constraints on $v\mathrm{sin}i$ and
$\lambda$ as well as theoretical constraints on the limb-darkening coefficients
to find that the KELT-19Ab's obliquity is $\psi =
155^{\circ+17^\circ}_{\,\,-21^\circ}$, in favor of a flipped orbit. The result
is consistent with the statistically inferred uniformity of obliquity
distribution, and also highlights the applicability of the gravity darkening
technique to symmetric light curves.


  Direct photon production data at fixed target and collider experiments from
$pp$ and $\bar{p}p$ collisions are analysed in NLO QCD. The results are grouped
into three sets having $\sqrt{s}=20-30$ GeV, 630 GeV and 1.8 TeV. It is seen
that at the lowest energies considered, the theory systematically underpredicts
the results for all the values of the transverse momentum. At the intermediate
energy of the UA2 experiment, the data are more accurately described at high
$p_T$, and at the highest collider energies no significant underprediction is
seen even at low $p_T$, when using recent structure functions as measured at
HERA.


  We show that coherence between two excited ro-vibrational states belonging to
the same molecular electronic configuration arises quite naturally due to their
interaction with electromagnetic vacuum. For initial preparation of a molecule
in the desired ro-vibrational states, we propose to employ the method of
ultracold photoassociation. Spontaneous decay of the excited molecule then
gives rise to vacuum induced coherence between the excited ro-vibrational
states. We demonstrate theoretically an interesting interplay of effects due to
vacuum induced coherence and photoassociation. We apply our theory to
photoassociation of bosonic Ytterbium (^{174}Yb) atoms which appear to be a
promising system for exploring such interplay. The effects discussed here can
be important for controlling decoherence and dissipation in molecular systems.


  Given a holomorphic submersion of reduced complex spaces, we prove that the
basic Oka property of the submersion implies the parametric Oka property. This
generalizes the corresponding result for complex manifolds (F. Forstneric, Oka
Manifolds, C. R. Acad. Sci. Paris, Ser. I, 347 (2009) 1017-1020). It follows
that a stratified elliptic (or subelliptic) holomorphic submersion, or a
stratified holomorphic fiber bundle whose fibers are Oka manifolds, enjoys the
parametric Oka property. As an application we give a parametric version of the
factorization theorem due to Ivarsson and Kutzschebauch (A solution of Gromov's
Vaserstein problem, C. R. Acad. Sci. Paris, Ser. I 346 (2008) 1239-1243) for
holomorphic maps from finite dimensional reduced Stein spaces to the special
linear group SL_n(C).


  Application of electronic railway systems as well as the implication of
Automatic Train Control (ATC) System has increased the safety of rail
transportation. However, one of the most important causes of accidents on the
railway is rail damage and breakage. In this paper, we have proposed a method
that the rail region is first recognized from the observation area, then by
investigating the image texture processing data, the types of rail defects
including cracks, wear, peeling, disintegration, and breakage are detected. In
order to reduce the computational cost, the image is changed from the RGB color
spectrum to the gray spectrum. Image texture processing data is obtained by the
two-dimensional Gray Levels Co-occurrence Matrix (GLCM) at different angles;
this data demonstrates second-order features of the images. Large data of
features has a negative effect on the overall accuracy of the classifiers. To
tackle this issue and acquire faster response, Principal Component Analysis
(PCA) algorithm is used, before entering the band into the classifier. Then the
features extracted from the images are compared by three different classifiers
including Support Vector Machine (SVM), Random Forest (RF), and K-Nearest
Neighbor (KNN) classification. The results obtained from this method indicate
that the Random Forest classifier has better performance (accuracy 97%,
precision 96%, and recall 96%) than other classifiers.


  Linear spectral transformations of orthogonal polynomials in the real line,
and in particular Geronimus transformations, are extended to orthogonal
polynomials depending on several real variables. Multivariate
Christoffel-Geronimus-Uvarov formulae for the perturbed orthogonal polynomials
and their quasi-tau matrices are found for each perturbation of the original
linear functional. These expressions are given in terms of quasi-determinants
of bordered truncated block matrices and the 1D Christoffel-Geronimus-Uvarov
formulae in terms of quotient of determinants of combinations of the original
orthogonal polynomials and their Cauchy transforms, are recovered. A new
multispectral Toda hierarchy of nonlinear partial differential equations, for
which the multivariate orthogonal polynomials are reductions, is proposed. This
new integrable hierachy is associated with non-standard multivariate
biorthogonality. Wave and Baker functions, linear equations, Lax and
Zakharov-Shabat equations, KP type equations, appropriate reductions,
Darboux/linear spectral transformations, and bilinear equations involving
linear spectral transformations are presented.


  It is supposed that $\beta$-decay can be slightly suppressed at an atomic
substance - plasma transition under a plasma electron gas action. The
estimation shows that this effect can give a relative difference of the decay
amount on a level of $10^{-4}$.


  We show that the pattern of tunnelling rates can display a vivid and regular
pattern when the classical dynamics is of mixed chaotic/regular type. We
consider the situation in which the dominant tunnelling route connects to a
stable periodic orbit and this orbit is surrounded by a regular island which
supports a number of quantum states. We derive an explicit semiclassical
expression for the positions and tunnelling rates of these states by use of a
complexified trace formula.


  We perform a detailed classification of the Lie point symmetries and of the
resulting similarity transformations for the Generalized Boiti-Leon-Pempinelli
equations. The latter equations for a system of two nonlinear 1+2 partial
differential equations of second- and third-order. The nonlinear equations
depend of two parameters, namely $n$ and $m$, from where we find that for
various values of these two parameters the resulting systems admit different
number of Lie point symmetries. For every case, we present the complete
analysis for the admitted Lie group as also we determine all the possible
similarity solutions which follow from the one-dimensional optimal system.
Finally, we summarize the results by presenting them in a tabular way.


  The dynamics of an electronic two-level system coupled to an electromagnetic
field are simulated explicitly for one and three dimensional systems through
semiclassical propagation of the Maxwell-Liouville equations. We consider three
flavors of mixed quantum-classical dynamics: the classical path approximation
(CPA), Ehrenfest dynamics, and symmetrical quantum-classical (SQC) dynamics.
The CPA fails to recover a consistent description of spontaneous emission. A
consistent "spontaneous" emission can be obtained from Ehrenfest
dynamics--provided that one starts in an electronic superposition state.
Spontaneous emission is always obtained using SQC dynamics. Using the SQC and
Ehrenfest frameworks, we further calculate the dynamics following an incoming
pulse, but here we find very different responses: SQC and Ehrenfest dynamics
deviate sometimes strongly in the calculated rate of decay of the transient
excited state. Nevertheless, our work confirms the earlier observations by W.
Miller [J. Chem. Phys. 69, 2188-2195, 1978] that Ehrenfest dynamics can
effectively describe some aspects of spontaneous emission and highlights new
possibilities for studying light-matter interactions with semiclassical
mechanics.


  In Ref.~\cite{Guo:2021rre}, we proposed to replace the final dark matter (DM)
particle in the semi-annihilation mode $\rm DM+DM\to antiDM+Higgs~boson$ with
its $Z_{N\geq 3}$ companion, thus reducing DM number density without DM-nucleon
scattering. In this work, we study the indirect detection signals from DM
annihilation, the Higgs boson pair with one of them from the companion decay
being on- or off- shell, depending on the DM-companion mass splitting. We
generate the photon spectrum by using PYTHIA8 and study the properties of the
spectrum, to find that the hard part of the spectrum in our model is mainly
shaped by the direct Higgs boson and thus does not differ much from that of the
conventional semi-annihilation mode. Using the Fermi-LAT data of white dwarfs,
we derive the current limit of the DM annihilation cross section for ${\rm
DM+DM\to companion^*+Higgs~ boson}$, and for the relatively light DM, it
reaches the typical thermal cross section. However, for the TeV scale DM, we
have to rely on the Cherenkov Telescope Array, which is able to rule out the
whole parameter space except for the coannihilation region.


  In this contribution, we recall the derivation of the anti bounce back
boundary condition for the D2Q9 lattice Boltzmann scheme. We recall various
elements of the state of the art for anti bounce back applied to linear heat
and acoustics equations and in particular the possibility to take into account
curved boundaries. We present an asymptotic analysis that allows an expansion
of all the fields in the boundary cells. This analysis based on the Taylor
expansion method confirms the well known behaviour of anti bounce back boundary
for the heat equation. The analysis puts also in evidence a hidden differential
boundary condition in the case of linear acoustics. Indeed, we observe
discrepancies in the first layers near the boundary. To reduce these
discrepancies, we propose a new boundary condition mixing bounce back for the
oblique links and anti bounce back for the normal link. This boundary condition
is able to enforce both pressure and tangential velocity on the boundary.
Numerical tests for the Poiseuille flow illustrate our theoretical analysis and
show improvements in the quality of the flow.


  A fourth-order multi-exponential scheme is proposed for the Zakharov-Shabat
system. The scheme represents a product of 13 exponential operators. The
construction of the scheme is based on a fourth-order three-exponential scheme,
which contains only one exponent with a spectral parameter. This exponent is
factorized to the fourth-order with the Suzuki formula of 11 exponents. The
obtained scheme allows the use of a fast algorithm in calculating the initial
problem for a large number of spectral parameters and conserves the quadratic
invariant exactly for real spectral parameters.


  Optimal two-dimensional (2D), three-dimensional (3D) wave launching
configurations are proposed for enhanced acceleration of charged particles in
magnetized plasmas. A primary wave is launched obliquely with respect to the
magnetic field and a secondary, low amplitude, wave is launched
perpendicularly. The effect of both the launching angle of the primary wave,
and the presence of the secondary wave is investigated. Theoretical predictions
of the highest performances of the three-dimensional (3D) configurations are
proposed using a Resonance Moments Method (RMM) based on estimates for the
moments of the velocity distribution function calculated inside the resonance
layers (RL). They suggest the existence of an optimal angle corresponding to
non parallel launching. Direct statistical simulations show that it is possible
to rise the mean electron velocity up to the order of magnitude as compared to
the primary wave launching alone. It is a quite promising result because the
amplitude of the secondary wave is ten times lower the one of the first wave.
The parameters used are related to magnetic plasma fusion experiments in
electron cyclotron resonance heating and electron acceleration in planetary
ionospheres and magnetospheres.


  For information transmission a discrete time channel with independent
additive Gaussian noise is used. There is also feedback channel with
independent additive Gaussian noise, and the transmitter observes without delay
all outputs of the forward channel via that feedback channel. Transmission of
nonexponential number of messages is considered and the achievable decoding
error exponent for such a combination of channels is investigated. It is shown
that for any finite noise in the feedback channel the achievable error exponent
is better than similar error exponent of the no-feedback channel. Method of
transmission/decoding used in the paper strengthens the earlier method used by
authors for BSC. In particular, for small feedback noise, it allows to get the
gain of 23.6% (instead of 14.3% earlier for BSC).


  A numerical technique for calculating effective actions of electromagnetic
backgrounds is proposed, which is based on the string-inspired worldline
formalism. As examples, we consider scalar electrodynamics in three and four
dimensions to one-loop order. Beyond the constant-magnetic-field case, we
analyze a step-function-like magnetic field exhibiting a nonlocal and
nonperturbative phenomenon: ``magnetic-field diffusion''. Finally,
generalizations to fermionic loops and systems at finite temperature are
discussed.


  Minimal surfaces in Euclidean space provide examples of possible non-compact
horizon geometries and topologies in asymptotically flat space-time. On the
other hand, the existence of limiting surfaces in the space-time provides a
simple mechanism for making these configurations compact. Limiting surfaces
appear naturally in a given space-time by making minimal surfaces rotate but
they are also inherent to plane wave or de Sitter space-times in which case
minimal surfaces can be static and compact. We use the blackfold approach in
order to scan for possible black hole horizon geometries and topologies in
asymptotically flat, plane wave and de Sitter space-times. In the process we
uncover several new configurations, such as black helicoids and catenoids, some
of which have an asymptotically flat counterpart. In particular, we find that
the ultraspinning regime of singly-spinning Myers-Perry black holes, described
in terms of the simplest minimal surface (the plane), can be obtained as a
limit of a black helicoid, suggesting that these two families of black holes
are connected. We also show that minimal surfaces embedded in spheres rather
than Euclidean space can be used to construct static compact horizons in
asymptotically de Sitter space-times.


  The risk of conflict is exasperated by a multitude of internal and external
factors. Current multivariate analysis paints diverse causal risk profiles that
vary with time. However, these profiles evolve and a universal model to
understand that evolution remains absent. Most of the current conflict analysis
is data-driven and conducted at the individual country or region level, often
in isolation. Consistent consideration of multi-scale interactions and their
non-linear dynamics is missing. Here, we develop a multiplexed network model,
where each city is modelled as a non-linear bi-stable system with stable states
in either war or peace. The causal factor categories which exasperate the risk
of conflict are each modelled as a network layer. We consider 3 layers: (1)
core geospatial network of interacting cities reflecting ground level
interactions, (2) cultural network of interacting countries reflecting cultural
groupings, and (3) political network of interacting countries reflecting
alliances. Together, they act as drivers to push cities towards or pull cities
away from war. Using a variety of data sources relative to 2002-2016, we show,
that our model correctly predicts the transitions from war to peace and peace
to war with F1 score of 0.78 to 0.92 worldwide at the city scale resolution. As
many conflicts during this period are auto-regressive (e.g. the War on Terror
in Afghanistan and Iraq, the Narco War across the Americas), we can predict the
emergence of new war or new peace. We demonstrate successful predictions across
a wide range of conflict genres and we perform causal discovery by identifying
which model component led to the correct prediction. In the cases of Somalia
(2008-13), Myanmar (2013-15), Colombia (2011-14), Libya (2014-16), and Yemen
(2011-13) we identify the set of most likely causal factors and how it may
differ across a country and change over time.


  In this paper, we address the problem of speaker verification in conditions
unseen or unknown during development. A standard method for speaker
verification consists of extracting speaker embeddings with a deep neural
network and processing them through a backend composed of probabilistic linear
discriminant analysis (PLDA) and global logistic regression score calibration.
This method is known to result in systems that work poorly on conditions
different from those used to train the calibration model. We propose to modify
the standard backend, introducing an adaptive calibrator that uses duration and
other automatically extracted side-information to adapt to the conditions of
the inputs. The backend is trained discriminatively to optimize binary
cross-entropy. When trained on a number of diverse datasets that are labeled
only with respect to speaker, the proposed backend consistently and, in some
cases, dramatically improves calibration, compared to the standard PLDA
approach, on a number of held-out datasets, some of which are markedly
different from the training data. Discrimination performance is also
consistently improved. We show that joint training of the PLDA and the adaptive
calibrator is essential -- the same benefits cannot be achieved when freezing
PLDA and fine-tuning the calibrator. To our knowledge, the results in this
paper are the first evidence in the literature that it is possible to develop a
speaker verification system with robust out-of-the-box performance on a large
variety of conditions.


  We study the nuclear medium effects in the weak structure functions
$F_2(x,Q^2)$ and $F_3(x,Q^2)$ in the deep inelastic neutrino/antineutrino
reactions in nuclei.
  We use a theoretical model for the nuclear spectral functions which
incorporates the conventional nuclear effects, such as Fermi motion, binding
and nucleon correlations.
  We also consider the pion and rho meson cloud contributions calculated from a
microscopic model for meson-nucleus self-energies. The calculations have been
performed using relativistic nuclear spectral functions which include nucleon
correlations. Our results are compared with the experimental data of NuTeV and
CDHSW.


  We combine the Macroscopic Fluctuation Theory and the Inverse Scattering
Method to determine the full long-time statistics of the energy density
$u(x,t)$ averaged over a given spatial interval, $$ U
=\frac{1}{2L}\int_{-L}^{L}dx\, u(x,t)\,, $$ in a freely expanding
Kipnis-Marchioro-Presutti (KMP) lattice gas on the line, following the release
at $t=0$ of a finite amount of energy at the origin. In particular, we show
that, as time $t$ goes to infinity at fixed $L$, the large deviation function
of $U$ approaches a universal form when expressed in terms of the energy
content of the interval $|x|<L$ at time $t$. A key part of the solution is the
determination of the most likely configuration of the energy density at time
$t$, conditional on $U$.


  We consider linear one-dimensional parabolic equations with space dependent
coefficients that are only measurable and that may be degenerate or
singular.Considering generalized Robin-Neumann boundary conditions at both
extremities, we prove the null controllability with one boundary control by
following the flatness approach, which providesexplicitly the control and the
associated trajectory as series. Both the control and the trajectory have a
Gevrey regularity in time related to the $L^p$ class of the coefficient in
front of $u\_t$.The approach applies in particular to the (possibly degenerate
or singular) heat equation $(a(x)u\_x)\_x-u\_t=0$ with $a(x)\textgreater{}0$
for a.e. $x\in (0,1)$ and $a+1/a \in L^1(0,1)$, or to the heat equation with
inverse square potential $u\_{xx}+(\mu / |x|^2)u-u\_t=0$with $\mu\ge 1/4$.


  In this paper, we consider gradient estimates for two type of nonlinear
parabolic equations under the Ricci flow: one is the equation $$u_t=\Delta
u+au\log u+bu$$ with $a,b$ two real constants, the other is $$u_t=\Delta
u+\lambda u^{\alpha}$$ with $\lambda,\alpha$ two real constants. By a suitable
scaling for the above two equations, we obtain Hamilton-Souplet-Zhang type
gradient estimates.


  Advanced embedded algorithms are growing in complexity and they are an
essential contributor to the growth of autonomy in many areas. However, the
promise held by these algorithms cannot be kept without proper attention to the
considerably stronger design constraints that arise when the applications of
interest, such as aerospace systems, are safety-critical. Formal verification
is the process of proving or disproving the ''correctness'' of an algorithm
with respect to a certain mathematical description of it by means of a
computer. This article discusses the formal verification of the Ellipsoid
method, a convex optimization algorithm, and its code implementation as it
applies to receding horizon control. Options for encoding code properties and
their proofs are detailed. The applicability and limitations of those code
properties and proofs are presented as well. Finally, floating-point errors are
taken into account in a numerical analysis of the Ellipsoid algorithm.
Modifications to the algorithm are presented which can be used to control its
numerical stability.


  Interfacial segregation and chemical short-range ordering influence the
behavior of grain boundaries in complex concentrated alloys. In this study, we
use atomistic modeling of a NbMoTaW refractory complex concentrated alloy to
provide insight into the interplay between these two phenomena. Hybrid Monte
Carlo and molecular dynamics simulations are performed on columnar grain models
to identify equilibrium grain boundary structures. Our results reveal extended
near-boundary segregation zones that are much larger than traditional
segregation regions, which also exhibit chemical patterning that bridges the
interfacial and grain interior regions. Furthermore, structural transitions
pertaining to an A2-to-B2 transformation are observed within these extended
segregation zones. Both grain size and temperature are found to significantly
alter the widths of these regions. Analysis of chemical short-range order
indicates that not all pairwise elemental interactions are affected by the
presence of a grain boundary equally, as only a subset of elemental clustering
types are more likely to reside near certain boundaries. The results emphasize
the increased chemical complexity that is associated with near-boundary
segregation zones and demonstrate the unique nature of interfacial segregation
in complex concentrated alloys.


  Recent advancements in language modeling have led to the emergence of Large
Language Models (LLMs) capable of various natural language processing tasks.
Despite their success in text-based tasks, applying LLMs to the speech domain
remains limited and challenging. This paper presents BLOOMZMMS, a novel model
that integrates a multilingual LLM with a multilingual speech encoder, aiming
to harness the capabilities of LLMs for speech recognition and beyond.
Utilizing a multi-instructional training approach, we demonstrate the
transferability of linguistic knowledge from the text to the speech modality.
Our experiments, conducted on 1900 hours of transcribed data from 139
languages, establish that a multilingual speech representation can be
effectively learned and aligned with a multilingual LLM. While this learned
representation initially shows limitations in task generalization, we address
this issue by generating synthetic targets in a multi-instructional style. Our
zero-shot evaluation results confirm the robustness of our approach across
multiple tasks, including speech translation and multilingual spoken language
understanding, thereby opening new avenues for applying LLMs in the speech
domain.


  The pursuit of a comprehensive understanding of the dynamical nature of
intertwined orders in quantum matter has fueled the development of several new
experimental techniques, including time- and angle-resolved photoemission
spectroscopy (TR-ARPES). In this regard, the study of copper-oxide
high-temperature superconductors, prototypical quantum materials, has furthered
both the technical advancement of the experimental technique, as well as the
understanding of their correlated dynamical properties. Here, we provide a
brief historical overview of the TR-ARPES investigations of cuprates, and
review what specific information can be accessed via this approach. We then
present a detailed discussion of the transient evolution of the low-energy
spectral function both along the gapless nodal direction and in the near-nodal
superconducting gap region, as probed by TR-ARPES on Bi-based cuprates.


  We report the discovery of two massive eccentric systems with BRITE data,
$\tau$ Ori and $\tau$ Lib, showing heartbeat effects close to the periastron
passage. $\tau$ Lib exhibits shallow eclipses that will soon vanish due to the
apsidal motion in the system. In neither system, tidally excited oscillations
were detected.


  The microscopic studies on nuclear fission require the evaluation of the
potential energy surface as a function of the collective coordinates. A
reasonable choice of constraints on multipole moments should be made to
describe the topography of the surface completely within a reasonable amount of
computing time. We present a detailed analysis of fission barriers in the
self-consistent Hartree-Fock-Bogoliubov approach with the D1S parametrization
of the Gogny nucleon-nucleon interaction. Two heavy isotopes representing
different spontaneous fission modes - $^{252}$Cf (asymmetric) and $^{258}$No
(bimodal) - have been chosen for the analysis. We have shown the existence of
complicated structures on the energy surface that can not be fully described in
two-dimensional calculations. We analyze apparent problems that can be
encountered in this type of calculations: multiple solutions for given
constraints and transitions between various potential energy surfaces. We
present possible solutions on how to deal with these issues.


  Decade-long timing observations of arrays of millisecond pulsars have placed
highly constraining upper limits on the amplitude of the nanohertz
gravitational-wave stochastic signal from the mergers of supermassive
black-hole binaries ($\sim 10^{-15}$ strain at $f = 1/\mathrm{yr}$). These
limits suggest that binary merger rates have been overestimated, or that
environmental influences from nuclear gas or stars accelerate orbital decay,
reducing the gravitational-wave signal at the lowest, most sensitive
frequencies. This prompts the question whether nanohertz gravitational waves
are likely to be detected in the near future. In this letter, we answer this
question quantitatively using simple statistical estimates, deriving the range
of true signal amplitudes that are compatible with current upper limits, and
computing expected detection probabilities as a function of observation time.
We conclude that small arrays consisting of the pulsars with the least timing
noise, which yield the tightest upper limits, have discouraging prospects of
making a detection in the next two decades. By contrast, we find large arrays
are crucial to detection because the quadrupolar spatial correlations induced
by gravitational waves can be well sampled by many pulsar pairs. Indeed, timing
programs which monitor a large and expanding set of pulsars have an $\sim 80\%$
probability of detecting gravitational waves within the next ten years, under
assumptions on merger rates and environmental influences ranging from
optimistic to conservative. Even in the extreme case where $90\%$ of binaries
stall before merger and environmental coupling effects diminish low-frequency
gravitational-wave power, detection is delayed by at most a few years.


  Luminous blue variables (LBVs) are expected to play an important role in
massive stellar evolution as well as being the progenitors of some of the most
luminous supernovae known. In this paper we provide a multiwavelength study of
the population of (candidate) LBVs identified within M33. New spectra provide
an observational baseline of >4yr with respect to published data, which is well
suited to identifying LBV outbursts. Multi-epoch optical and mid-IR surveys of
M33 further constrain the variability of the sample and permit a search for
dusty circumstellar ejecta. Spectroscopic and photometric variability appears
common amongst the sample, although in many cases further observations will be
required to determine its physical origin. Nevertheless, we report a new
outburst of M33 Var C, while the transition of the WNLh star B517 to a cooler B
supergiant phase between 1993-2010 confirms an LBV classification.
Proof-of-concept quantitative analysis is provided for Romano's star; the
results being consistent with the finding that its bolometric luminosity varies
during its LBV excursions. The combination of the temperature and luminosity of
two stars, the B hypergiant [HS80] 110A and the cool hypergiant B324, appears
to be in violation of the empirical Humphreys-Davidson limit. Mid-IR
observations demonstrate that a number of candidates appear associated with hot
circumstellar dust, although no objects as extreme as Eta Carinae are
identified. The combined multiwavelength dataset suggests that the population
of LBVs studied is contaminated by stars demonstrating the B[e] phenomenon. Of
these, a subset of optically faint, low luminosity stars associated with hot
dust are of particular interest since they appear similar to the likely
progenitors of SN 2008S and the 2008 NGC300 transient, albeit suffering less
intrinsic extinction. [ABRIDGED]


  We show that the time dependent single electron, nuclear density matrix of an
interacting electronic system coupled to nuclear degrees of freedom can be
exactly reproduced by that of an electronic system with arbitrarily specified
electron-electron interactions coupled to the same nuclear degrees of freedom,
given the initial density matrix of the interacting system. This formalism
enables the construction of rigorous time dependent density functional theories
to study nonadiabatic electronic dynamics. We obtain the Runge-Gross and Van
Leeuwen theorems as special cases in the adiabatic limit.


  A new type of compact high resolution high sensitivity gamma ray spectrometer
for short pulse intense 250 keV to 50 MeV gamma rays has been developed by
combining the principles of scintillators and attenuation spectrometers. The
first prototype of this scintillator attenuation spectrometer or SAS was tested
successfully in Trident laser experiments at LANL. Later versions have been
used extensively in the Texas Petawatt laser experiments in Austin TX, and more
recently in OMEGAEP laser experiments at LLE, Rochester, NY. The SAS is
particularly useful for high repetition rate laser applications. Here we give a
concise description of the design principles, capabilities and sample
preliminary results of the SAS.


  We obtain an asymptotic formula for the number of circles of curvature at
most T in any given bounded Apollonian circle packing. For an integral packing,
we obtain the upper bounds for the number of circles with prime curvature as
well as of pairs of circles with prime curvatures, which are sharp up constant
multiples. The main ingredient of our proof is the effective equidistribution
of expanding horospheres on geometrically finite hyperbolic 3-manifolds under
the assumption that the critical exponent of its fundamental group exceeds one.


  Recent self-supervised pre-training methods on Heterogeneous Information
Networks (HINs) have shown promising competitiveness over traditional
semi-supervised Heterogeneous Graph Neural Networks (HGNNs). Unfortunately,
their performance heavily depends on careful customization of various
strategies for generating high-quality positive examples and negative examples,
which notably limits their flexibility and generalization ability. In this
work, we present SHGP, a novel Self-supervised Heterogeneous Graph Pre-training
approach, which does not need to generate any positive examples or negative
examples. It consists of two modules that share the same attention-aggregation
scheme. In each iteration, the Att-LPA module produces pseudo-labels through
structural clustering, which serve as the self-supervision signals to guide the
Att-HGNN module to learn object embeddings and attention coefficients. The two
modules can effectively utilize and enhance each other, promoting the model to
learn discriminative embeddings. Extensive experiments on four real-world
datasets demonstrate the superior effectiveness of SHGP against
state-of-the-art unsupervised baselines and even semi-supervised baselines. We
release our source code at: https://github.com/kepsail/SHGP.


  In this paper, we consider the connectedness of planar self-affine set
$T(A,\mathcal{D})$ arising from an integral expanding matrix $A$ with
characteristic polynomial $f(x)=x^2+bx+c$ and a digit set
$\mathcal{D}=\{0,1,\dots, m\}v$. The necessary and sufficient conditions only
depending on $b,c,m$ are given for the $T(A,\mathcal{D})$ to be connected.
Moreover, we also consider the case that ${\mathcal D}$ is non-consecutively
collinear.


  Explainability techniques for Graph Neural Networks still have a long way to
go compared to explanations available for both neural and decision decision
tree-based models trained on tabular data. Using a task that straddles both
graphs and tabular data, namely Entity Matching, we comment on key aspects of
explainability that are missing in GNN model explanations.


  The high-order accurate continuous Galerkin finite element method offers
attractive computational efficiency for computational fluid dynamics. A
challenge is however spurious oscillations which result for convection
dominated flows over discontinuities. To derive a continuous Galerkin scheme
for both smooth and discontinuous fields we start by first writing the scheme
in Summation-by-Parts (SBP) form for a single element mesh. Boundary conditions
are applied weakly via Simultaneous-Approximation-Terms (SAT) and Gauss-Labotto
quadrature employed in the interest of computational efficiency. We then show
that the stable single element baseline scheme in SBP-SAT form extends
trivially to a provably stable multi-element formulation. Next, we develop
provably stable element based Galerkin-weighted artificial dissipation
operators to deal with spurious oscillations over shocks while retaining high
order accuracy elsewhere. The resulting scheme achieves super-convergence with
accuracy of Order(p+2) when using p^th order Lagrange polynomials for smooth
fields. The developed dissipation operators furnish WENO like behaviour over
discontinuities while retaining high order accuracy elsewhere for both linear
and non-linear wave propagation problems.


  We consider a networked linear dynamical system with $p$ agents/nodes. We
study the problem of learning the underlying graph of interactions/dependencies
from observations of the nodal trajectories over a time-interval $T$. We
present a regularized non-casual consistent estimator for this problem and
analyze its sample complexity over two regimes: (a) where the interval $T$
consists of $n$ i.i.d. observation windows of length $T/n$ (restart and
record), and (b) where $T$ is one continuous observation window (consecutive).
Using the theory of $M$-estimators, we show that the estimator recovers the
underlying interactions, in either regime, in a time-interval that is
logarithmic in the system size $p$. To the best of our knowledge, this is the
first work to analyze the sample complexity of learning linear dynamical
systems \emph{driven by unobserved not-white wide-sense stationary (WSS)
inputs}.


  We study the relation between two kinds of topological amplitudes of
non-compact D-branes on conifold. In the A-model, D-branes are represented by
fermion operators in the melting crystal picture and the amplitudes are given
by the quantum dilogarithm. In the mirror B-model, D-branes correspond to the
determinant operator det(x-M) in the Chern-Simons matrix model and the
amplitudes are given by the Stieltjes-Wigert polynomial. We show that these two
amplitudes are related by a certain integral transformation. We argue that this
transformation represents the deformation of closed string background due to
the presence of D-branes.


  Although contemporary model theory has been called "algebraic geometry minus
fields", the formal methods of the two fields are radically different. This
dissertation aims to shrink that gap by presenting a theory of logical schemes,
geometric entities which relate to first-order logical theories in much the
same way that algebraic schemes relate to commutative rings.
  The construction relies on a Grothendieck-style representation theorem which
associates every coherent or classical first-order theory with an affine
scheme: a topological groupoid (the spectrum of the theory) together with a
sheaf of (local) syntactic categories. The groupoid is constructed from the
semantics of the theory (models and isomorphisms) and topologized using a
Stone-type construction. The sheaf of categories can be regarded as a logical
theory varying over the spectrum, and its global sections recover the theory up
to semantic equivalence. These affine pieces can be glued together to give more
general logical schemes and these are studied using methods from algebraic
geometry. The final chapter also presents some connections between schemes and
other areas of logic such as model theory, type theory and topos theory.


  We provide a brief review of human mobility science and present three key
areas where we expect to see substantial advancements. We start from the mind
and discuss the need to better understand how spatial cognition shapes mobility
patterns. We then move to societies and argue the importance of better
understanding new forms of transportation. We conclude by discussing how
algorithms shape mobility behaviour and provide useful tools for modellers.
Finally, we discuss how progress in these research directions may help us
address some of the challenges our society faces today.


  An electrically charged black hole solution with scalar hair in four
dimensions is presented. The self-interacting scalar field is real and it is
minimally coupled to gravity and electromagnetism. The event horizon is a
surface of negative constant curvature and the asymptotic region is locally an
AdS spacetime. The asymptotic fall-off of the fields is slower than the
standard one. The scalar field is regular everywhere except at the origin, and
is supported by the presence of electric charge which is bounded from above by
the AdS radius. In turn, the presence of the real scalar field smooths the
electromagnetic potential everywhere. Regardless the value of the electric
charge, the black hole is massless and has a fixed temperature. The entropy
follows the usual area law. It is shown that there is a nonvanishing
probability for the decay of the hairy black hole into a charged black hole
without scalar field. Furthermore, it is found that an extremal black hole
without scalar field is likely to undergo a spontaneous dressing up with a
nontrivial scalar field, provided the electric charge is below a critical
value.


  We report the discovery of the fifth self-lensing binary in which a low-mass
white dwarf (WD) gravitationally magnifies its 15th magnitude G-star companion,
KIC 8145411, during eclipses. The system was identified from a pair of such
self-lensing events in the Kepler photometry, and was followed up with the
Tillinghast Reflector Echelle Spectrograph (TRES) on the 1.5m telescope at the
Fred Lawrence Whipple Observatory and the High-Dispersion Spectrograph (HDS) on
the Subaru 8.2m telescope. A joint analysis of the TRES radial velocities, the
HDS spectrum, and the Kepler photometry of the primary star determines the WD
mass $0.20\pm0.01\,M_\odot$, orbital semi-major axis
$1.28\pm0.03\,\mathrm{au}$, and orbital eccentricity $0.14\pm0.02$. Because
such extremely low-mass WDs cannot be formed in isolation within the age of the
Galaxy, their formation is believed to involve binary interactions that
truncated evolution of the WD progenitor. However, the observed orbit of the
KIC 8145411 system is at least ten times wider than required for this scenario
to work. The presence of this system in the Kepler sample, along with its
similarities to field blue straggler binaries presumably containing WDs, may
suggest that some 10% of post-AGB binaries with Sun-like primaries contain such
anomalous WDs.


  Novel liquid crystalline (LC) compositions are suggested and studied as
elements of LC-nose. This allows for optical detection of several volatile
organic compounds (VOCs). Ethanol, toluene, pyridine and acetic acid were
detected by means of colorimetric and spectroscopic techniques during their
diffusion inside chiral elements of LC-nose. Selectivity to different VOCs is
enhanced by means of components of liquid crystal matrix with different
viscosity, affinities to the solvents, and abilities to form hydrogen bonding.


  In many sports, it is commonly believed that the home team has an advantage
over the visiting team, known as the home field advantage. Yet its causal
effect on team performance is largely unknown. In this paper, we propose a
novel causal inference approach to study the causal effect of home field
advantage in English Premier League. We develop a hierarchical causal model and
show that both league level and team level causal effects are identifiable and
can be conveniently estimated. We further develop an inference procedure for
the proposed estimators and demonstrate its excellent numerical performance via
simulation studies. We implement our method on the 2020-21 English Premier
League data and assess the causal effect of home advantage on eleven summary
statistics that measure the offensive and defensive performance and referee
bias. We find that the home field advantage resides more heavily in offensive
statistics than it does in defensive or referee statistics. We also find
evidence that teams that had lower rankings retain a higher home field
advantage.


  Refractive-index (RI) sensing plays a pivotal role in various domains,
encompassing applications like glucose sensing, biosensing, and gas detection.
Despite the advantages of optical fiber sensors, such as their compact size,
flexibility, and immunity to electromagnetic interference, they are often
plagued by temperature-induced drift, which adversely impacts the accuracy of
RI measurements. This study introduces an innovative approach to alleviate
temperature-induced drift in RI-sensing optical frequency combs (OFCs) by
employing active-dummy compensation. The central idea revolves around the
utilization of a dual-comb setup, comprising an active-sensing OFC that
monitors both sample RI and environmental temperature, and a dummy-sensing OFC
that exclusively tracks environmental temperature. The disparity between these
sensor signals, denoted as delta_frep, effectively nullifies the effects of
temperature variations, yielding a temperature-independent sensor signal for
precise RI measurements. This investigation delves into the relationship
between active-dummy temperature compensation and delta_frep. It becomes
evident that diminishing delta_frep values enhance temperature compensation,
thereby diminishing fluctuations in delta_frep caused by environmental
temperature shifts. This compensation technique establishes a direct link
between delta_frep and sample RI, paving the way for absolute RI measurements
based on delta_frep. The findings of this research are a valuable contribution
to the advancement of accurate and temperature-compensated RI sensing
methodologies using dual-comb setup. The insights gained regarding delta_frep
dependency and the strategies proposed for enhancing measurement precision and
stability hold significant promise for applications in fields of product
quality control and biosensing.


  Bosonic quantum error-correcting codes offer a viable direction towards
reducing the hardware overhead required for fault-tolerant quantum information
processing. A broad class of bosonic codes, namely rotation-symmetric codes,
can be characterized by their phase-space rotation symmetry. However, their
performance has been examined to date only within an idealistic noise model.
Here, we further analyze the error-correction capabilities of
rotation-symmetric codes using a teleportation-based error-correction circuit.
To this end, we numerically compute the average gate fidelity, including
measurement errors into the noise model of the data qubit. Focusing on physical
measurement models, we assess the performance of heterodyne and adaptive
homodyne detection in comparison to the previously studied canonical phase
measurement. This setting allows us to shed light on the role of different
currently available measurement schemes when decoding the encoded information.
We find that with the currently achievable measurement efficiencies in
microwave optics, bosonic rotation codes undergo a substantial decrease in
their break-even potential. In addition, we perform a detailed analysis of
Gottesman-Kitaev-Preskill (GKP) codes using a similar error-correction circuit
that allows us to analyze the effect of realistic measurement models on
different codes. In comparison to RSB codes, we find for GKP codes an even
greater reduction in performance together with a vulnerability to photon-number
dephasing. Our results show that highly efficient measurement protocols
constitute a crucial building block towards error-corrected quantum information
processing with bosonic continuous-variable systems.


  Borrowing ideas from tight binding model, we propose a board class of Lattice
QFT models that are classified by the ADE Lie algebras. In the case of su(N)
series, we show that the couplings between the quantum states living at the
first nearest neighbor sites of the lattice $\mathcal{L}_{su(N)}$ are governed
by the complex fundamental representations \underline{${{\mathbf{N}}}$} and
$\bar{{\mathbf{N}}}$ of $su(N)$; and the second nearest neighbor interactions
are described by its adjoint $\underline{\mathbf{N}} \otimes \bar{\mathbf{N}}$.
The lattice models associated with the leading su(2), su(3) and su(4) cases are
explicitly studied and their fermionic field realizations are given. It is also
shown that the su(2) and su(3) models describe respectively the electronic
properties of the acetylene chain and the graphene. It is established as well
that the energy dispersion of the first nearest neighbor couplings is
completely determined by the $A_{N}$ roots $ \mathbf{\alpha}$ through the
typical dependence $N/2+\sum_{roots}\cos(\mathbf{k}.\alpha) $ with $\mathbf{k}$
the wave vector. Other features such as DE extension and other applications are
also discussed.
  Keywords: Tight Binding Model, Graphene, Lattice QFT, ADE Symmetries.


  Converse effect of spin photocurrent and current induced spin polarization
are experimentally demonstrated in the same two-dimensional electron gas system
with Rashba spin splitting. Their consistency with the strength of the Rashba
coupling as measured from beating of the Shubnikov-de Haas oscillations reveals
a unified picture for the spin photocurrent, current-induced spin polarization
and spin orbit coupling. In addition, the observed spectral inversion of the
spin photocurrent indicates the system with dominating structure inversion
asymmetry.


  Recently the power of positive partial transpose preserving (PPTp) and
no-signalling (NS) codes in quantum communication has been studied. We continue
with this line of research and show that the NS/PPTp/NS$\cap$PPTp codes
assisted zero-error quantum capacity depends only on the non-commutative
bipartite graph of the channel and the one-shot case can be computed
efficiently by semidefinite programming (SDP). As an example, the activated
PPTp codes assisted zero-error quantum capacity is carefully studied. We then
present a general SDP upper bound $Q_\Gamma$ of quantum capacity and show it is
always smaller than or equal to the "Partial transposition bound" introduced by
Holevo and Werner, and the inequality could be strict. This upper bound is
found to be additive, and thus is an upper bound of the potential PPTp assisted
quantum capacity as well. We further demonstrate that $Q_\Gamma$ is strictly
better than several previously known upper bounds for an explicit class of
quantum channels. Finally, we show that $Q_\Gamma$ can be used to bound the
super-activation of quantum capacity.


  Breast cancer is a common cancer for women. Early detection of breast cancer
can considerably increase the survival rate of women. This paper mainly focuses
on transfer learning process to detect breast cancer. Modified VGG (MVGG),
residual network, mobile network is proposed and implemented in this paper.
DDSM dataset is used in this paper. Experimental results show that our proposed
hybrid transfers learning model (Fusion of MVGG16 and ImageNet) provides an
accuracy of 88.3% where the number of epoch is 15. On the other hand, only
modified VGG 16 architecture (MVGG 16) provides an accuracy 80.8% and MobileNet
provides an accuracy of 77.2%. So, it is clearly stated that the proposed
hybrid pre-trained network outperforms well compared to single architecture.
This architecture can be considered as an effective tool for the radiologists
in order to reduce the false negative and false positive rate. Therefore, the
efficiency of mammography analysis will be improved.


  The problem of $\rho$- and $\omega$- mesons contributions to the background
for $\eta \to \pi^0 e^+e^-$ decay and to the asymmetries in the decays $\eta
\to \pi^+\pi^-\pi^0$ and $\eta \to \pi^+\pi^-\gamma$ is considered.


  Caching networks can reduce the routing costs of accessing contents by
caching contents closer to users. However, cache nodes may belong to different
entities and behave selfishly to maximize their own benefits, which often lead
to performance degradation for the overall network. While there has been
extensive literature on allocating contents to caches to maximize the social
welfare, the analysis of selfish caching behaviors remains largely unexplored.
In this paper, we model the selfish behaviors of cache nodes as selfish caching
games on arbitrary directed graphs with heterogeneous content popularity. We
study the existence of a pure strategy Nash equilibrium (PSNE) in selfish
caching games, and analyze its efficiency in terms of social welfare. We show
that a PSNE does not always exist in arbitrary-topology caching networks.
However, if the network does not have a mixed request loop, i.e., a directed
loop in which each edge is traversed by at least one content request, we show
that a PSNE always exists and can be found in polynomial time. Furthermore, we
can avoid mixed request loops by properly choosing request forwarding paths. We
then show that the efficiency of Nash equilibria, captured by the price of
anarchy (PoA), can be arbitrarily poor if we allow arbitrary content request
patterns, and adding extra cache nodes can make the PoA worse, i.e., cache
paradox happens. However, when cache nodes have homogeneous request patterns,
we show that the PoA is bounded even allowing arbitrary topologies. We further
analyze the selfish caching games for cache nodes with limited computational
capabilities, and show that an approximate PSNE exists with bounded PoA in
certain cases of interest. Simulation results show that increasing the cache
capacity in the network improves the efficiency of Nash equilibria, while
adding extra cache nodes can degrade the efficiency of Nash equilibria.


  Let M be a surface with conical singularities, and consider a degenerating
family of surfaces obtained from M by removing disks of smaller and smaller
radius around a subset of the conical singularities. Such families arise
naturally in the study of the moduli space of flat metrics on higher-genus
surfaces with boundary. In particular, they have been used by Khuri to prove
that the determinant of the Laplacian is not a proper map on this moduli space
when the genus of M is positive. Khuri's work is closely related to the
isospectral compactness results of Osgood, Phillips, and Sarnak. Our main
theorem is an asymptotic formula for the determinant of the Laplacian on the
degenerating family of surfaces, up to terms which vanish in the singular
limit. We then apply this theorem to extend and sharpen the results of Khuri.
The proof uses the determinant gluing formula of Burghelea, Friedlander, and
Kappeler along with an observation of Wentworth on the asymptotics of
Dirichlet-to-Neumann operators.


  Quantum chaos is a subject whose major goal is to identify and to investigate
different quantum signatures of classical chaos. Here we study entanglement
production in coupled chaotic systems as a possible quantum indicator of
classical chaos. We use coupled kicked tops as a model for our extensive
numerical studies. We find that, in general, presence of chaos in the system
produces more entanglement. However, coupling strength between two subsystems
is also very important parameter for the entanglement production. Here we show
how chaos can lead to large entanglement which is universal and describable by
random matrix theory (RMT). We also explain entanglement production in coupled
strongly chaotic systems by deriving a formula based on RMT. This formula is
valid for arbitrary coupling strengths, as well as for sufficiently long time.
Here we investigate also the effect of chaos on the entanglement production for
the mixed initial state. We find that many properties of the mixed state
entanglement production are qualitatively similar to the pure state
entanglement production. We however still lack an analytical understanding of
the mixed state entanglement production in chaotic systems.


  We analyze chiral interactions to N2LO on the light of proton-proton and
neutron-proton scattering data published from 1950 till 2013 and discuss
conditions under which the chiral coefficients can be extracted


  We study sample path deviations of the Wiener process from three different
representations of its bridge: anticipative version, integral representation
and space-time transform. Although these representations of the Wiener bridge
are equal in law, their sample path behavior is quite different. Our results
nicely demonstrate this fact. We calculate and compare the expected absolute,
quadratic and conditional quadratic path deviations of the different
representations of the Wiener bridge from the original Wiener process. It is
further shown that the presented qualitative behavior of sample path deviations
is not restricted only to the Wiener process and its bridges. Sample path
deviations of the Ornstein-Uhlenbeck process from its bridge versions are also
considered and we give some quantitative answers also in this case.


  We classify the harmonic morphisms with one-dimensional fibres (1) from
real-analytic conformally-flat Riemannian manifolds of dimension at least four,
and (2) between conformally-flat Riemannian manifolds of dimensions at least
three.


  This paper proposes an optimized mapping of the FIR filter algorithm that
enhances the rate of a reconfigurable computer over a basic mapping previously
proposed [1]. It also presents a new interconnection scheme in the
reconfigurable part of MorphoSys, a reconfigurable computing system [2].
Reconfigurable computing (RC) is introduced, followed by the MorphoSys RC
system. Two optimized FIR mappings are then presented which deliver enhanced
speed. A spreadsheet model will detail the modification and the improvement.
The speedup achieved is also explained as well as the advantages in the mapping
of the application.


  We perform a femtosecond-THz optical pump-probe spectroscopy to investigate
the cooling dynamics of hot carriers in quasi-free standing bilayer epitaxial
graphene. We observed longer decay time constants, in the range of 2.6 to 6.4
ps, compared to previous studies on monolayer graphene, which increase
nonlinearly with excitation intensity. The increased relaxation times are due
to the decoupling of the graphene layer from the SiC substrate after hydrogen
intercalation which increases the distance between graphene and substrate.
Furthermore, our measurements do not show that the supercollision mechanism is
related to the cooling process of the hot carriers, which is ultimately
achieved by electron-optical phonon scattering.


  Integrating automatic speech scoring/assessment systems has become a critical
aspect of second-language speaking education. With self-supervised learning
advancements, end-to-end speech scoring approaches have exhibited promising
results. However, this study highlights the significant decrease in the
performance of speech scoring systems in new question contexts, thereby
identifying this as a cold start problem in terms of items. With the finding of
cold-start phenomena, this paper seeks to alleviate the problem by following
methods: 1) prompt embeddings, 2) question context embeddings using BERT or
CLIP models, and 3) choice of the pretrained acoustic model. Experiments are
conducted on TOEIC speaking test datasets collected from
English-as-a-second-language (ESL) learners rated by professional TOEIC
speaking evaluators. The results demonstrate that the proposed framework not
only exhibits robustness in a cold-start environment but also outperforms the
baselines for known content.


  The triplet or type-II seesaw mechanism is the simplest way to endow
neutrinos with mass in the Standard Model (SM). Here we review its associated
theory and phenomenology, including restrictions from $S$, $T$, $U$ parameters,
neutrino experiments, charged lepton flavour violations as well as collider
searches. We also examine restrictions coming from requiring consistency of
electroweak symmetry breaking, i.e. perturbative unitarity and stability of the
vacuum. Finally, we discuss novel effects associated to the scalar mediator of
neutrino mass generation namely, (i) rare processes, e.g. $l_\alpha \to l_\beta
\gamma$ decays, at the intensity frontier, and also (ii) four-lepton signatures
in colliders at the high-energy frontier. These can be used to probe neutrino
properties in an important way, providing a test of the absolute neutrino mass
and mass-ordering, as well as of the atmospheric octant. They may also provide
the first evidence for charged lepton flavour violation in nature. In contrast,
neutrino non-standard interaction strengths are found to lie below current
detectability.


  We study quantum phase transitions involving fractional quantum Hall states,
using numerical calculations of entanglements and related quantities. We tune
finite-size wavefunctions on spherical geometries, by varying the interaction
potential away from the Coulomb interaction. We uncover signatures of quantum
phase transitions contained in the scaling behavior of the entropy of
entanglement between two parts of the sphere. In addition to the entanglement
entropy, we show that signatures of quantum phase transitions also appear in
other aspects of the reduced density matrix of one part of the sphere.


  This tutorial covers a few recent papers in the field of network embedding.
Network embedding is a collective term for techniques for mapping graph nodes
to vectors of real numbers in a multidimensional space. To be useful, a good
embedding should preserve the structure of the graph. The vectors can then be
used as input to various network and graph analysis tasks, such as link
prediction. The papers discussed develop methods for the online learning of
such embeddings, and include DeepWalk, LINE, node2vec, struc2vec and
megapath2vec. These new methods and developments in online learning of network
embeddings have major applications for the analysis of graphs and networks,
including online social networks.


  In this paper, we survey the state of the art of the secure key exchange
method that is secured by the laws of classical statistical physics, and
involves the Kirchhoff's law and the generalized Johnson noise equation, too.
We discuss the major characteristics and advantages of these schemes especially
in comparison with quantum encryption, and analyze some of the technical
challenges of its implementation, too. Finally, we outline some ideas about how
to use already existing and currently used wire lines, such as power lines,
phone lines, internet lines to implement unconditionally secure information
networks.


  The present paper is devoted to analysis of the lack of compactness of
bounded sequences in \emph{inhomogeneous} Sobolev spaces, where bounded
sequences might fail to be compact due to an isometric group action, that is,
\emph{translation}. It will be proved that every bounded sequence $(u_n)$ has
(possibly infinitely many) \emph{profiles}, and then the sequence is
asymptotically decomposed into a sum of translated profiles and a
double-suffixed residual term, where the residual term becomes arbitrarily
small in appropriate Lebesgue or Sobolev spaces of lower order. To this end,
functional analytic frameworks are established in an abstract way by making use
of a group action $G$, in order to characterize profiles by $(u_n)$ and $G$.
One also finds that a decomposition of the Sobolev norm into profiles is
bounded by the supremum of the norm of $u_n$. Moreover, the profile
decomposition leads to results of decomposition of integral functionals of
subcritical order. It is noteworthy that the space where the decomposition of
integral functionals holds is the same as that where the residual term is
vanishing.


  The temperature induced phase transition is investigated in the one-component
scalar field \phi^4 model on the lattice. Using the GPU cluster a huge amount
of Monte Carlo simulation data is collected for a wide interval of coupling
values. This gives a possibility to determine the low bound on the coupling
constant \lambda_0 when the transition happens and investigate its type. We
found that for the values of \lambda close to this bound a weak-first-order
phase transition takes place. It converts into a second order one with the
increase of \lambda. A comparison with the results obtained in analytic and
numeric calculations by other authors is given.


  We consider two theorems from the theory of compressive sensing. Mainly a
theorem concerning uniform recovery of random sampling matrices, where the
number of samples needed in order to recover an $s$-sparse signal from linear
measurements (with high probability) is known to be $m\gtrsim s(\ln s)^3\ln N$.
We present new and improved constants together with what we consider to be a
more explicit proof. A proof that also allows for a slightly larger class of
$m\times N$-matrices, by considering what we call \emph{low entropy}. We also
present an improved condition on the so-called restricted isometry constants,
$\delta_s$, ensuring sparse recovery via $\ell^1$-minimization. We show that
$\delta_{2s}<4/\sqrt{41}$ is sufficient and that this can be improved further
to almost allow for a sufficient condition of the type $\delta_{2s}<2/3$.


  We extend the quantum jump method to nearly adiabatically driven open quantum
systems in a way that allows for an accurate account of the external driving in
the system-environment interaction. Using this framework, we construct the
corresponding trajectory-dependent work performed on the system and derive the
integral fluctuation theorem and the Jarzynski equality for nearly adiabatic
driving. We show that such identities hold as long as the stochastic dynamics
and work variable are consistently defined. We numerically study the emerging
work statistics for a two-level quantum system and find that the conventional
diabatic approximation is unable to capture some prominent features arising
from driving such as the continuity of the probability density of work. Our
results reveal the necessity of using accurate expressions for the
drive-dressed heat exchange in future experiments probing jump time
distributions.


  Let $\cal{F}$ be a regular codimension 1 holomorphic foliation on a compact
K\" ahler manifold. One assumes in addition that $\cal{F}$ possesses a
transverse invariant positive current. The aim of this paper is to establish
the following alternative: - There exists an invariant hypersurface. - The
foliation admits a transverse invariant hermitian metric with constant
curvature


  We study regenerated high-energy emission from the gamma-ray burst (GRB)
afterglows, and compare its flux with the direct component from the same
afterglow. When the intrinsic emission spectrum extends to TeV region, these
very high-energy photons are significantly absorbed by the cosmic infrared
background (CIB) radiation field, creating electron/positron pairs; since these
pairs are highly energetic, they can scatter the cosmic microwave background
radiation up to GeV energies, which may change the intrinsic afterglow light
curve in the GeV region. Using the theoretical modeling given in literature and
the reasonable choice of relevant parameters, we calculate the expected light
curve due to the regeneration mechanism. As the result, we find that the
regenerated emission could only slightly change the original light curve, even
if we take a rather large value for the CIB density, independently of the
density profile of surrounding medium, i.e., constant or wind-like profile.
This ensures us the reliable estimation of the intrinsic GRB parameters when
the high-energy observation is accessible, regardless of a large amount of
uncertainty concerning the CIB density as well as extragalactic magnetic field
strength.


  To scale non-parametric extensions of probabilistic topic models such as
Latent Dirichlet allocation to larger data sets, practitioners rely
increasingly on parallel and distributed systems. In this work, we study
data-parallel training for the hierarchical Dirichlet process (HDP) topic
model. Based upon a representation of certain conditional distributions within
an HDP, we propose a doubly sparse data-parallel sampler for the HDP topic
model. This sampler utilizes all available sources of sparsity found in natural
language - an important way to make computation efficient. We benchmark our
method on a well-known corpus (PubMed) with 8m documents and 768m tokens, using
a single multi-core machine in under four days.


  Ascertaining the physical state of a system is vital in order to understand
and predict its behaviour. Tomography is a standard approach used to determine
the form of an unknown state. Here we show that an alternative approach, based
on sequential weak and strong measurements, can be used to determine the
density matrix in a simple, fast, and general style. We directly measure the
probability amplitudes of a variety of pure polarisation states of light. We
then generalise this experiment to directly measure the Dirac distribution and
consequently determine the density matrix. Our work is the first to demonstrate
the direct measurement of the full description of the state of a
two-dimensional system, and it has applications to measurements in foundational
quantum mechanics, quantum information, and physical chemistry.


  We examine the dual of the so-called "hit problem", the latter being the
problem of determining a minimal generating set for the cohomology of products
of infinite projective spaces as module over the Steenrod Algebra $\mathcal{A}$
at the prime 2. The dual problem is to determine the set of $\mathcal
{A}$-annihilated elements in homology. The set of $\mathcal{A}$-annihilateds
has been shown by David Anick to be a free associative algebra. In this note we
prove that, for each $k \geq 0$, the set of {\it $k$ partially
$\mathcal{A}$-annihilateds}, the set of elements that are annihilated by $Sq^i$
for each $i\leq 2^k$, itself forms a free associative algebra.


  This work presents a harmonic design of autonomous guided vehicle (AGV)
control, edge intelligence, and human input to enable autonomous transportation
in industrial environments. The AGV has the capability to navigate between a
source and destinations and pick/place objects. The human input implicitly
provides preferences of the destination and exact drop point, which are derived
from an artificial intelligence (AI) module at the network edge and shared with
the AGV over a wireless network. The demonstration indicates that the proposed
integrated design of hardware, software, and AI design achieve a technology
readiness level (TRL) of range 4-5


  This article fits in many studies of multifractal analysis of measure. We
took as a starting point the work of F. Ben Nasr in " Calculs de dimension de
packing " to give a new inequality involving $Dim(\bar{X}^{\alpha})$ which
would be, in certain cases, finer than the inequality established by L. Olsen
in " A multifractal formalism " . Besides we elaborated an application of our
result which gives a better inequality involving $Dim(\bar{X}^{\alpha})$.


  In this work we analyse the role of low- and intermediate-mass stars in
contributing to the chemical enrichment of the interstellar medium. First we
present new sets of stellar yields basing on the results of updated
evolutionary calculations, which extend from the ZAMS up to the end of the AGB
phase (Girardi et al. 2000; Marigo et al. 1999a). These new yields, that
present a significant dependence on metallicity, are then compared to those of
other available sets (Renzini & Voli 1981; van de Hoek & Groenewegen 1997). The
resulting differences are explained in terms of different model assumptions --
i.e. treatment of convective boundaries, mass loss, dredge-up, hot-bottom
burning --, and further discussed on the basis of important empirical
constraints which should be reproduced by theory -- i.e. the initial-final mass
relation, white dwarf mass distribution, carbon star luminosity function, and
chemical abundances of planetary nebulae. We show that present models are able
to reproduce such constraints in a satisfactory way.


  The paper shows that under some conditions the totalization of a cosimplicial
space obtained from a multiplicative operad is a double loop space of the space
of derived morphisms from the associative operad to the operad itself.


  Rayleigh-Taylor-instability(RTI) induced flow and mixing are of great
importance in both nature and engineering scenarios. To capture the
underpinning physics, tracers are introduced to make a supplement to discrete
Boltzmann simulation of RTI in compressible flows. Via marking two types of
tracers with different colors, the tracer distribution provides a clear
boundary of two fluids during the RTI evolution. Fine structures of the flow
and thermodynamic nonequilibrium behavior around the interface in a miscible
two-fluid system are delineated. Distribution of tracers in its velocity phase
space makes a charming pattern showing quite dense information on the flow
behavior, which opens a new perspective for analyzing and accessing
significantly deep insights into the flow system. RTI mixing is further
investigated via tracer defined local mixedness. The appearance of
Kelvin-Helmholtz instability is quantitatively captured by mixedness averaged
align the direction of the pressure gradient. The role of compressibility and
viscosity on mixing are investigated separately, both of which show two-stage
effect. The underlying mechanism of the two-stage effect is interpreted as the
development of large structures at the initial stage and the generation of
small structures at the late stage. At the late stage, for a fixed time, a
saturation phenomenon of viscosity is found that further increase of viscosity
cannot see an evident decline in mixedness. The mixing statues of heavy and
light fluids are not synchronous and the mixing of a RTI system is
heterogenous. The results are helpful for understanding the mechanism of flow
and mixing induced by RTI.


  We extend to any dimension the quantitative fourth moment theorem on the
Poisson setting, recently proved by C. D\"obler and G. Peccati (2017). In
particular, by adapting the exchangeable pairs couplings construction
introduced by I. Nourdin and G. Zheng (2017) to the Poisson framework, we prove
our results under the weakest possible assumption of finite fourth moments.
This yields a Peccati-Tudor type theorem, as well as an optimal improvement in
the univariate case. Finally, a transfer principle "from-Poisson-to-Gaussian"
is derived, which is closely related to the universality phenomenon for
homogeneous multilinear sums.


  The paper extends basic Einstein--Hilbert action by adding a newly proposed
invariant constructed from a specific contraction between the Einstein tensor
and the energy momentum tensor, encoding a non--minimal coupling between the
space--time geometry and the matter fields. The fundamental Einstein--Hilbert
action is extended by considering a generic function ${f}(R,G_{\mu \nu}T^{\mu
\nu})$ which is further decomposed into its main constituents, a geometric
component which depends on the scalar curvature, and a second element embedding
the interplay between geometry and matter fields. Specific cosmological models
are established at the level of background dynamics, based on particular
couplings between the matter energy--momentum tensor and the Einstein tensor.
After deducing the resulting field equations, the physical aspects for the
cosmological model are investigated by employing a dynamical system analysis
for various coupling functions. The investigation showed that the present model
is compatible with different epochs in the evolution of our Universe, possible
explaining various late time historical stages.


  Niche and neutral theory are two prevailing, yet much debated, ideas in
ecology proposed to explain the patterns of biodiversity. Whereas niche theory
emphasizes selective differences between species and interspecific interactions
in shaping the community, neutral theory supposes functional equivalence
between species and points to stochasticity as the primary driver of ecological
dynamics. In this work, we draw a bridge between these two opposing theories.
Starting from a Lotka-Volterra (LV) model with demographic noise and random
symmetric interactions, we analytically derive the stationary population
statistics and species abundance distribution (SAD). Using these results, we
demonstrate that the model can exhibit three classes of SADs commonly found in
niche and neutral theories and found conditions that allow an ecosystem to
transition between these various regimes. Thus, we reconcile how neutral-like
statistics may arise from a diverse community with niche differentiation.


  The question of how quantum coherence facilitates energy transfer has been
intensively debated in the scientific community. Since natural and artificial
light-harvesting units operate under the stationary condition, we address this
question via a non-equilibrium steady-state analysis of a molecular dimer
irradiated by incoherent sunlight and then generalize the key predictions to
arbitrarily-complex exciton networks. The central result of the steady-state
analysis is the coherence-flux-efficiency relation:$\eta=c\sum_{i\neq
j}F_{ij}\kappa_j=2c\sum_{i\neq j}J_{ij}{\rm Im}[{\rho}_{ij}]\kappa_j$ with $c$
the normalization constant. In this relation, the first equality indicates that
energy transfer efficiency $\eta$ is uniquely determined by the trapping flux,
which is the product of flux $F$ and branching ratio $\kappa$ for trapping at
the reaction centers, and the second equality indicates that the energy
transfer flux $F$ is equivalent to quantum coherence measured by the imaginary
part of the off-diagonal density matrix, i.e., $F_{ij}=2J_{ij}{\rm
Im}[{\rho}_{ij}]$. Consequently, maximal steady-state coherence gives rise to
optimal efficiency. The coherence-flux-efficiency relation holds rigorously and
generally for any exciton networks of arbitrary connectivity under the
stationary condition and is not limited to incoherent radiation or incoherent
pumping. For light-harvesting systems under incoherent light, non-equilibrium
energy transfer flux (i.e. steady-state coherence) is driven by the breakdown
of detailed balance and by the quantum interference of light-excitations and
leads to the optimization of energy transfer efficiency. It should be noted
that the steady-state coherence or, equivalently, efficiency is the combined
result of light-induced transient coherence, inhomogeneous depletion, and
system-bath correlation, and is thus not necessarily correlated with quantum
beatings.


  Interest in understanding the interplay between noise and the response of a
non-linear device cuts across disciplinary boundaries. It is as relevant for
unmasking the dynamics of neurons in noisy environments as it is for designing
reliable nanoscale logic circuit elements and sensors. Most studies of noise in
non-linear devices are limited to either time-correlated noise with a
Lorentzian spectrum (of which the white noise is a limiting case) or just white
noise. We use analytical theory and numerical simulations to study the impact
of the more ubiquitous "natural" noise with a 1/f frequency spectrum.
Specifically, we study the impact of the 1/f noise on a leaky integrate and
fire model of a neuron. The impact of noise is considered on two quantities of
interest to neuron function: The spike count Fano factor and the speed of
neuron response to a small step-like stimulus. For the perfect (non-leaky)
integrate and fire model, we show that the Fano factor can be expressed as an
integral over noise spectrum weighted by a (low pass) filter function. This
result elucidates the connection between low frequency noise and disorder in
neuron dynamics. We compare our results to experimental data of single neurons
in vivo, and show how the 1/f noise model provides much better agreement than
the usual approximations based on Lorentzian noise. The low frequency noise,
however, complicates the case for information coding scheme based on interspike
intervals by introducing variability in the neuron response time. On a positive
note, the neuron response time to a step stimulus is, remarkably, nearly
optimal in the presence of 1/f noise. An explanation of this effect elucidates
how the brain can take advantage of noise to prime a subset of the neurons to
respond almost instantly to sudden stimuli.


  We report on X-ray and gamma-ray observations of the millisecond pulsar
B1937+21 taken with the Chandra X-ray Observatory, XMM-Newton, and the Fermi
Large Area Telescope. The pulsar X-ray emission shows a purely non-thermal
spectrum with a hard photon index of 0.9+/-0.1, and is nearly 100% pulsed. We
found no evidence of varying pulse profile with energy as previously claimed.
We also analyzed 5.5 yr of Fermi survey data and obtained much improved
constraints on the pulsar's timing and spectral properties in gamma-rays. The
pulsed spectrum is adequately fitted by a simple power-law with a photon index
of 2.38+/-0.07. Both the gamma-ray and X-ray pulse profiles show similar
two-peak structure and generally align with the radio peaks. We found that the
aligned profiles and the hard spectrum in X-rays seem to be common properties
among millisecond pulsars with high magnetic fields at the light cylinder. We
discuss a possible physical scenario that could give rise to these features.


  The electrostatic potential generated by a point charge at rest in a simple
static, spherically symmetric wormhole is given in the form of series of
multipoles and in closed form. The general potential which is physically
acceptable depends on a parameter due to the fact that the monopole solution is
arbitrary. When the wormhole has Z2-symmetry, the potential is completely
determined. The calculation of the electrostatic self-energy and of the
self-force is performed in all cases considered.


  We calculate the diffusion coefficients of persistent random walks on
lattices, where the direction of a walker at a given step depends on the memory
of a certain number of previous steps. In particular, we describe a simple
method which enables us to obtain explicit expressions for the diffusion
coefficients of walks with two-step memory on different classes of one-, two-
and higher-dimensional lattices.


  We prove several topological properties of linear Weingarten surfaces of
Bryant type, as wave fronts in hyperbolic 3-space. For example, we show the
orientability of such surfaces, and also co-orientability when they are not
flat. Moreover, we show an explicit formula of the non-holomorphic hyperbolic
Gauss map via another hyperbolic Gauss map which is holomorphic. Using this, we
show the orientability and co-orientability of CMC-1 faces (i.e., constant mean
curvature one surfaces with admissible singular points) in de Sitter 3-space.
(CMC-1 faces might not be wave fronts in general, but belong to a class of
linear Weingarten surfaces with singular points.) Since both linear Weingarten
fronts and CMC-1 faces may have singular points, orientability and
co-orientability are both nontrivial properties. We also remark on some
properties of non-orientable maximal surfaces in Lorentz-Minkowski 3-space,
comparing the corresponding properties of CMC-1 faces in de Sitter 3-space.


  The $N=2$ supersymmetric {\it self-dual} Yang-Mills theory and the $N=4$ and
$N=2$ {\it self-dual} supergravities in $2+2$ space-time dimensions are
formulated for the first time. These formulations utilize solutions of the
Bianchi identities subject to the super-Yang-Mills or supergravity constraints
in the relevant $N$-extended superspace with the space-time signature $(2,2)$.


  We consider the problem of discrete-time signal denoising, focusing on a
specific family of non-linear convolution-type estimators. Each such estimator
is associated with a time-invariant filter which is obtained adaptively, by
solving a certain convex optimization problem. Adaptive convolution-type
estimators were demonstrated to have favorable statistical properties. However,
the question of their computational complexity remains largely unexplored, and
in fact we are not aware of any publicly available implementation of these
estimators. Our first contribution is an efficient implementation of these
estimators via some known first-order proximal algorithms. Our second
contribution is a computational complexity analysis of the proposed procedures,
which takes into account their statistical nature and the related notion of
statistical accuracy. The proposed procedures and their analysis are
illustrated on a simulated data benchmark.


  Classical approaches to analyzing dynamical systems, including bifurcation
analysis, can provide invaluable insights into underlying structure of a
mathematical model, and the spectrum of all possible dynamical behaviors.
However, these models frequently fail to take into account population
heterogeneity, which, while critically important to understanding and
predicting the behavior of any evolving system, is a common simplification that
is made in analysis of many mathematical models of ecological systems. Attempts
to include population heterogeneity frequently result in expanding system
dimensionality, effectively preventing qualitative analysis. Reduction Theorem,
or Hidden keystone variable (HKV) method, allows incorporating population
heterogeneity while still permitting the use of previously existing classical
bifurcation analysis. A combination of these methods allows visualization of
evolutionary trajectories and making meaningful predictions about dynamics over
time of evolving populations. Here, we discuss three examples of combination of
these methods to augment understanding of evolving ecological systems. We
demonstrate what new meaningful questions can be asked through this approach,
and propose that the large existing literature of fully analyzed models can
reveal new and meaningful dynamical behaviors with the application of the
HKV-method, if the right questions are asked.


  The glass phase and its quantum analog are prominent challenges of current
non-equilibrium statistical mechanics and condensed matter physics. As a model
system to study the transition from classical to quantum glassy dynamics, we
propose a setup of laser driven three-level atoms trapped in an optical
lattice. Tuning the strength of the laser driving to the intermediate level
allows one to study the transition from a classical Kinetically Constrained
Model to the coherent regime. For strong driving, Rydberg excitations evolve
analogously to defects in the One-Spin Facilitated Model, a minimal model known
to exhibit glassy dynamics. In our setup, the constraints result from the
interplay between Rydberg interactions and the laser detuning from the Rydberg
state. The emerging heterogeneous relaxation timescales are tuneable over
several orders of magnitudes. In the opposite limit of weak driving of the
intermediate level, we find an effective cluster model which describes the
dynamics in a reduced subspace of the allowed number and positions of Rydberg
excitations. This subspace is uniquely determined by the initial state and is
characterized by a fixed number of clusters of Rydberg excitations. In
addition, we investigate the influence of random fields on the classical
relaxation. We find that the glassy dynamics can relax faster in the presence
of weak random fields.