  The realizations of spin-orbit coupling in cold atoms lead to a burst of
research activities in the searching of topological matters in ultracold atom
systems. The very recent theoretical predictions show that topological
Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) superfluids can be realized with proper
spin-orbit coupling and Zeeman fields. In this work, a comprehensive
understanding of the pairing symmetry, phase diagram and the edge modes in this
new topological matter are presented. The momentum of the Cooper pairs plays
the role of renormalizing the in-plane Zeeman field and chemical potential. The
in-plane Zeeman field and finite momentum pairing induce asymmetry to the
effective $p$-wave pairing, apart from a small fraction of higher orbital
components. The phase diagram is composed by different phases, which are
determined by the topology and band gap nature of the superfluids. Especially,
the gapped and gapless topological FFLO phase have totally different finite
size effect. These novel features show that the spin-orbit coupled cold atoms
provides an important platform in realizing topological matters which may not
be materialized with solids.


  Decentralized optimization, particularly the class of decentralized composite
convex optimization (DCCO) problems, has found many applications. Due to
ubiquitous communication congestion and random dropouts in practice, it is
highly desirable to design decentralized algorithms that can handle stochastic
communication networks. However, most existing algorithms for DCCO only work in
networks that are deterministically connected during bounded communication
rounds, and therefore cannot be extended to stochastic networks. In this paper,
we propose a new decentralized dual averaging (DDA) algorithm that can solve
DCCO in stochastic networks. Under a rather mild condition on stochastic
networks, we show that the proposed algorithm attains global linear convergence
if each local objective function is strongly convex. Our algorithm
substantially improves the existing DDA-type algorithms as the latter were only
known to converge sublinearly prior to our work. The key to achieving the
improved rate is the design of a novel dynamic averaging consensus protocol for
DDA, which intuitively leads to more accurate local estimates of the global
dual variable. To the best of our knowledge, this is the first linearly
convergent DDA-type decentralized algorithm and also the first algorithm that
attains global linear convergence for solving DCCO in stochastic networks.
Numerical results are also presented to support our design and analysis.


  Closed-form, normalizable solutions of Dirac's equation propagating within a
semi-infinite cylindrical waveguide are obtained in terms of ordinary and
modified Bessel functions. These relativistic wave packets induce quantum
backflow on a cross-section of the cylinder at practically any distance along
the waveguide, becoming spin-polarized in the nonrelativistic limit. The
predicted backflow is stable in time and is manifest regardless of the initial
wave function.


  We point out that, in a class of gauge mediation models using metastable
supersymmetry breaking vacua, the minimum of the supersymmetry breaking field
in the early universe is dynamically deviated from the one in the low energy.
The deviation induces coherent oscillations of the supersymmetry breaking
field, which decays into the gravitinos. For certain parameters, it can produce
a right amount of the gravitinos to account for the observed dark matter.


  We present a large high-resolution study of the distribution and evolution of
CIV absorbers, including the weakest population with equivalent widths
$W_r<0.3$~{\AA}. By searching 369 high-resolution, high signal-to-noise spectra
of quasars at $1.1\leq z_{em} \leq5.3$ from Keck/HIRES and VLT/UVES, we find
$1268$ CIV absorbers with $W_r \geq 0.05$~{\AA} (our $\sim50\%$ completeness
limit) at redshifts $1\leq z \leq4.75$. A Schechter function describes the
observed equivalent width distribution with a transition from power-law to
exponential decline at $W_r \gtrsim 0.5$~{\AA}. The power-law slope $\alpha$
rises by $\sim7\%$ and transition equivalent width $W_{\star}$ falls by
$\sim\!20\%$ from $\langle z \rangle=1.7$ to $\langle z \rangle=3.6$. We find
that the co-moving redshift path density, $dN/dX$, of $W_r \geq 0.05$~{\AA}
absorbers rises by $\sim1.8$ times from $z\simeq 4.0$ to $z\simeq 1.3$, while
the $W_r \geq 0.6$~{\AA} $dN/dX$ rises by a factor of $\sim8.5$. We quantify
the observed evolution by a model in which $dN/dX$ decreases linearly with
redshift. The model suggests that populations with larger $W_r$ thresholds
evolve faster with redshift and appear later in the universe. The cosmological
Technicolor Dawn simulations at $z=3-5$ over-produce the observed abundance of
absorbers with $W_r<0.3$~{\AA}, while yielding better agreement at higher
$W_r$. Our empirical linear model successfully describes {CIV evolution in the
simulations and the observed evolution of $W_r \geq 0.6$~{\AA} CIV for the past
$\sim12$ Gyr. Combining our measurements with the literature gives us a picture
of CIV-absorbing structures becoming more numerous and/or larger in physical
size over the last $\approx13$ Gyr of cosmic time ($z\sim6$ to $z\sim0$).


  The impact of surface reflection on the statistics of transmission
eigenvalues is a largely unexplored subject of fundamental and practical
importance in statistical optics. Here, we develop a first-principles theory
and confirm numerically that the distribution of transmission eigenvalues of
diffusive waves exhibits a nonanalytic `transition' as the strength of surface
reflection at one surface passes through a critical value while that at the
other is fixed. Above the critical value, the highest transmission eigenvalue
is strictly smaller than unity and decreases with increasing internal
reflection. When the input and output surfaces are equally reflective, the
highest transmission eigenvalue is unity and the transition disappears
irrespective of the strength of surface reflection.


  I introduce the problem of finding maximal sets of equiangular lines, in both
its real and complex versions, attempting to write the treatment that I would
have wanted when I first encountered the subject. Equiangular lines intersect
in the overlap region of quantum information theory, the octonions and
Hilbert's twelfth problem. The question of how many equiangular lines can fit
into a space of a given dimension is easy to pose -- a high-school student can
grasp it -- yet it is hard to answer, being as yet unresolved. This contrast of
ease and difficulty gives the problem a classic charm.


  We investigate the importance of lensing magnification for estimates of
galaxy clustering and its cross-correlation with shear for the photometric
sample of Euclid. Using updated specifications, we study the impact of lensing
magnification on the constraints and the shift in the estimation of the best
fitting cosmological parameters that we expect if this effect is neglected. We
follow the prescriptions of the official Euclid Fisher matrix forecast for the
photometric galaxy clustering analysis and the combination of photometric
clustering and cosmic shear. The slope of the luminosity function (local count
slope), which regulates the amplitude of the lensing magnification, and the
galaxy bias have been estimated from the Euclid Flagship simulation.We find
that magnification significantly affects both the best-fit estimation of
cosmological parameters and the constraints in the galaxy clustering analysis
of the photometric sample. In particular, including magnification in the
analysis reduces the 1$\sigma$ errors on $\Omega_{\text{m},0}, w_{0}, w_a$ at
the level of 20-35%, depending on how well we will be able to independently
measure the local count slope. In addition, we find that neglecting
magnification in the clustering analysis leads to shifts of up to 1.6$\sigma$
in the best-fit parameters. In the joint analysis of galaxy clustering, cosmic
shear, and galaxy-galaxy lensing, magnification does not improve precision, but
it leads to an up to 6$\sigma$ bias if neglected. Therefore, for all models
considered in this work, magnification has to be included in the analysis of
galaxy clustering and its cross-correlation with the shear signal ($3\times2$pt
analysis) for an accurate parameter estimation.


  We have performed magnetotransport experiments in the high-temperature regime
(up to 50 K) of the integer quantum Hall effect for two-dimensional electron
gases in semiconducting heterostructures. While the magnetic field dependence
of the classical Hall law presents no anomaly at high temperatures, we find a
breakdown of the Drude-Lorentz law for the longitudinal conductance beyond a
crossover magnetic field B_c ~ 1 T, which turns out to be correlated with the
onset of the integer quantum Hall effect at low temperatures. We show that the
high magnetic field regime at B > B_c can be understood in terms of classical
percolative transport in a smooth disordered potential. From the temperature
dependence of the peak longitudinal conductance, we extract scaling exponents
which are in good agreement with the theoretically expected values. We also
prove that inelastic scattering on phonons is responsible for dissipation in a
wide temperature range going from 1 to 50 K at high magnetic fields.


  We provide a sound and relatively complete Hoare-like proof system for
reasoning about partial correctness of recursive procedures in presence of
local variables and the call-by-value parameter mechanism, and in which the
correctness proofs are linear in the length of the program. We argue that in
spite of the fact that Hoare-like proof systems for recursive procedures were
intensively studied, no such proof system has been proposed in the literature.


  For the classical zero-flux chemotaxis-consumption model \begin{equation*}
u_t= \Delta u - \chi \nabla \cdot (u \nabla v) \quad \textrm{and}\quad
v_t=\Delta v- uv, \quad \text{ with } (x,t)\in \Omega \times (0,T_{max}),
\end{equation*} $\Omega$ being a bounded and smooth domain of $\mathbb{R}^n$,
$n\geq 3$, $\chi$ some positive number and $T_{max} \in (0,\infty]$, the
following was established in a paper by Tao: for every sufficiently regular
initial data $u(x,0)=u_0(x)\geq 0$ and $v(x,0)=v_0(x) \geq 0$, there is
$\chi(\lVert v_0 \rVert_{L^\infty(\Omega)})$ such that for all $0<\chi\leq
\chi(\lVert v_0 \rVert_{L^\infty(\Omega)})$, the initial-boundary value problem
has a unique classical solution in $\Omega \times (0,\infty)$ which is bounded.
In this paper, whenever $n\geq 5$, we obtain the same claim for larger values
of the constant $\chi(\|v_0\|_{L^{\infty}(\Omega)})$.


  Monocular depth estimation is fundamental for 3D scene understanding and
downstream applications. However, even under the supervised setup, it is still
challenging and ill-posed due to the lack of full geometric constraints.
Although a scene can consist of millions of pixels, there are fewer high-level
patterns. We propose iDisc to learn those patterns with internal discretized
representations. The method implicitly partitions the scene into a set of
high-level patterns. In particular, our new module, Internal Discretization
(ID), implements a continuous-discrete-continuous bottleneck to learn those
concepts without supervision. In contrast to state-of-the-art methods, the
proposed model does not enforce any explicit constraints or priors on the depth
output. The whole network with the ID module can be trained end-to-end, thanks
to the bottleneck module based on attention. Our method sets the new state of
the art with significant improvements on NYU-Depth v2 and KITTI, outperforming
all published methods on the official KITTI benchmark. iDisc can also achieve
state-of-the-art results on surface normal estimation. Further, we explore the
model generalization capability via zero-shot testing. We observe the
compelling need to promote diversification in the outdoor scenario. Hence, we
introduce splits of two autonomous driving datasets, DDAD and Argoverse. Code
is available at http://vis.xyz/pub/idisc .


  Learning approximations to smooth target functions of many variables from
finite sets of pointwise samples is an important task in scientific computing
and its many applications in computational science and engineering. Despite
well over half a century of research on high-dimensional approximation, this
remains a challenging problem. Yet, significant advances have been made in the
last decade towards efficient methods for doing this, commencing with so-called
sparse polynomial approximation methods and continuing most recently with
methods based on Deep Neural Networks (DNNs). In tandem, there have been
substantial advances in the relevant approximation theory and analysis of these
techniques. In this work, we survey this recent progress. We describe the
contemporary motivations for this problem, which stem from parametric models
and computational uncertainty quantification; the relevant function classes,
namely, classes of infinite-dimensional, Banach-valued, holomorphic functions;
fundamental limits of learnability from finite data for these classes; and
finally, sparse polynomial and DNN methods for efficiently learning such
functions from finite data. For the latter, there is currently a significant
gap between the approximation theory of DNNs and the practical performance of
deep learning. Aiming to narrow this gap, we develop the topic of practical
existence theory, which asserts the existence of dimension-independent DNN
architectures and training strategies that achieve provably near-optimal
generalization errors in terms of the amount of training data.


  We extend our previous work on simulations with the code RAMSES on accretion
driven turbulence by including self-gravity and study the effects of core
formation and collapse. We show that radial accretion onto filaments drives
turbulent motions which are not isotropic but radially dominated. In contrast
to filaments without gravity, the velocity dispersion of self-gravitating
filaments does not settle in an equilibrium. Despite showing similar amounts of
driven turbulence, they continually dissipate their velocity dispersion until
the onset of core formation. This difference is connected to the evolution of
the radius as it determines the dissipation rate. In the non-gravitational case
filament growth is not limited and its radius grows linearly with time. In
contrast, there is a maximum extent in the self-gravitational case resulting in
an increased dissipation rate. Furthermore, accretion driven turbulence shows a
radial profile which is anti-correlated with density. This leads to a constant
turbulent pressure throughout the filament. As the additional turbulent
pressure does not have a radial gradient it does not contribute to the
stability of filaments and does not increase the critical line-mass. However,
this radial turbulence does affect the radius of a filament, adding to the
extent and setting its maximum value. Moreover, the radius evolution also
affects the growth timescale of cores which compared to the timescale of
collapse of an accreting filament limits core formation to high line-masses.


  Mechanical effects have mostly been neglected so far in phase field tumour
models that are based on a Cahn-Hilliard approach. In this paper we study a
macroscopic mechanical model for tumour growth in which cell-cell adhesion
effects are taken into account with the help of a Ginzburg--Landau type energy.
In the overall model an equation of Cahn-Hilliard type is coupled to the system
of linear elasticity and a reaction-diffusion equation for a nutrient
concentration. The highly non-linear coupling between a fourth-order
Cahn-Hilliard equation and the quasi-static elasticity system lead to new
challenges which cannot be dealt within a gradient flow setting which was the
method of choice for other elastic Cahn-Hilliard systems. We show existence,
uniqueness and regularity results. In addition, several continuous dependence
results with respect to different topologies are shown. Some of these results
give uniqueness for weak solutions and other results will be helpful for
optimal control problems.


  In a recent work, Galloway [9] proved a local foliation theorem by MOTSs for
a 3-dimensional initial data set $(M,g,K)$ with mean curvature $\tau\le0$ in a
4-dimensional spacetime $(\overline M,\overline g)$ when (under suitable
assumptions) $M$ has a stable spherical MOTS $\Sigma$ which achieves an upper
bound for the area. He proved that each leaf is a round 2-sphere with the same
constant Gaussian curvature. Here, we improve his result by dropping the
hypothesis on the mean curvature of $M$ and showing that each leaf is a minimal
surface. We show that in an outer neighborhood $U$ of $\Sigma$, the metric $g$
splits as the product $([0,\varepsilon)\times\Sigma,dt^2+g_0)$, where
$(\Sigma,g_0)$ is a round 2-sphere. In fact, we prove that the outer
neighborhood $U$ can be isometrically embedded into the 4-dimensional Nariai
spacetime $(\overline N,\overline h)$ as a spacelike hypersurface so that
$g|_U$ is the induced metric from $\overline N$ and $K|_U$ is the second
fundamental form of $U$ in $\overline N$. This completely classifies the local
geometry of such initial data sets.


  We examine the MiniBooNE neutrino, MiniBooNE antineutrino and LSND
antineutrino data sets in a two-neutrino
$\stackrel{\tiny{(-)}}{\nu}_{\mu}\rightarrow\stackrel{\tiny{(-)}}{\nu}_e$
oscillation approximation subject to non-standard matter effects. We assume
those effects can be parametrized by an $L$-independent effective potential,
$V_s=\pm A_s$, experienced only by an intermediate, non-weakly-interacting
(sterile) neutrino state which we assume participates in the oscillation, where
$+/-$ corresponds to neutrino/antineutrino propagation. We discuss the
mathematical framework in which such oscillations arise in detail, and derive
the relevant oscillation probability as a function of the vacuum oscillation
parameters $\Delta m^2$ and $\sin^22\theta_{\mu e}$, and the matter effect
parameter $A_s$. We are able to successfully fit all three data sets, including
the MiniBooNE low energy excess, with the following best-fit model parameters:
$\Delta m^2=0.47$ eV$^2$, $\sin^22\theta_{\mu e}=0.010$, and
$A_s=2.0\times10^{-10}$ eV. The $\chi^2$-probability for the best fit
corresponds to 21.6%, to be compared to 6.8% for a fit where $A_s$ has been set
to zero, corresponding to a (3+1) sterile neutrino oscillation model. We find
that the compatibility between the three data sets corresponds to 17.4%, to be
compared to 2.3% for $A_s=0$. Finally, given the fit results, we examine
consequences for reactor, solar, and atmospheric oscillations. For this paper,
the presented model is empirically driven, but the results obtained can be
directly used to investigate various phenomenological interpretations such as
non-standard matter effects.


  The Turaev genus defines a natural filtration on knots where Turaev genus
zero knots are precisely the alternating knots. We show that the signature of a
Turaev genus one knot is determined by the number of components in its all-A
Kauffman state, the number of positive crossings, and its determinant. We also
show that either the leading or trailing coefficient of the Jones polynomial of
a Turaev genus one link (or an almost alternating link) has absolute value one.


  While a large body of literature suggests that large language models (LLMs)
acquire rich linguistic representations, little is known about whether they
adapt to linguistic biases in a human-like way. The present study probes this
question by asking whether LLMs display human-like referential biases using
stimuli and procedures from real psycholinguistic experiments. Recent
psycholinguistic studies suggest that humans adapt their referential biases
with recent exposure to referential patterns; closely replicating three
relevant psycholinguistic experiments from Johnson & Arnold (2022) in an
in-context learning (ICL) framework, we found that InstructGPT adapts its
pronominal interpretations in response to the frequency of referential patterns
in the local discourse, though in a limited fashion: adaptation was only
observed relative to syntactic but not semantic biases. By contrast, FLAN-UL2
fails to generate meaningful patterns. Our results provide further evidence
that contemporary LLMs discourse representations are sensitive to syntactic
patterns in the local context but less so to semantic patterns. Our data and
code are available at \url{https://github.com/zkx06111/llm_priming}.


  We report on a new class of critical states in the energy spectrum of general
Fibonacci systems. By introducing a transfer matrix renormalization technique,
we prove that the charge distribution of these states spreads over the whole
system, showing transport properties characteristic of electronic extended
states. Our analytical method is a first step to find out the link between the
spatial structure of these critical wave functions and the quasiperiodic order
of the underlying lattice.


  Using the superfield nonequilibrium Greens function technique, we derive the
spatio-temporal spin magnetization quantum transport equations (SMQTEs) for a
two-band model of semiconductors. The relevant variables are the real
(Pauli-Dirac) spin, pseudo-spin, and the total charge. The results show that
the multi-band real SMQTEs are coupled to the pseudo-spin magnetization
transport equations by virtue of the presence of two additional discrete
quantum labels besides the up and down real-spin indices, namely, the
conduction and valence band quantum labels. The SMQTEs essentially consist of
three group of terms describing the rate of change, namely, (1) a group of
terms similar to the equation for particle quantum transport, i.e., with
spin-independent transport parameters, (2) a group of terms describing various
torques influencing the spin orientation and directional flow of spin
magnetization correlations or phase-space magnetization density, and (3) a
group of terms expressing the coupling of the real spin magnetization with the
pseudo-spin magnetization. Self-consistently, the pseudo-spin magnetization
equations incorporate the pseudo-spin/real spin coupling, as well as the
pseudo-spin coupling to the total charge.


  We consider a recurrent random walk on a rooted tree in random environment
given by a branching random walk. Up to the first return to the root, its edge
local times form a Multi-type Galton-Watson tree with countably infinitely many
types. When the walk is the diffusive or sub-diffusive, by studying the maximal
type of this Galton-Watson tree, we establish the asymptotic behaviour of the
largest local times of this walk during n excursions, under the annealed law.


  The human voice conveys unique characteristics of an individual, making voice
biometrics a key technology for verifying identities in various industries.
Despite the impressive progress of speaker recognition systems in terms of
accuracy, a number of ethical and legal concerns has been raised, specifically
relating to the fairness of such systems. In this paper, we aim to explore the
disparity in performance achieved by state-of-the-art deep speaker recognition
systems, when different groups of individuals characterized by a common
sensitive attribute (e.g., gender) are considered. In order to mitigate the
unfairness we uncovered by means of an exploratory study, we investigate
whether balancing the representation of the different groups of individuals in
the training set can lead to a more equal treatment of these demographic
groups. Experiments on two state-of-the-art neural architectures and a
large-scale public dataset show that models trained with
demographically-balanced training sets exhibit a fairer behavior on different
groups, while still being accurate. Our study is expected to provide a solid
basis for instilling beyond-accuracy objectives (e.g., fairness) in speaker
recognition.


  In this paper we present an example of two polarized K3 surfaces which are
not Fundamental Group Equivalent (their fundamental groups of the complement of
the branch curves are not isomorphic; denoted by FGE) but the fundamental
groups of their related Galois covers are isomorphic. For each surface, we
consider a generic projection to CP^2 and a degenerations of the surface into a
union of planes - the "pillow" degeneration for the non-prime surface and the
"magician" degeneration for the prime surface. We compute the Braid Monodromy
Factorization (BMF) of the branch curve of each projected surface, using the
related degenerations. By these factorizations, we compute the above
fundamental groups. It is known that the two surfaces are not in the same
component of the Hilbert scheme of linearly embedded K3 surfaces. Here we prove
that furthermore they are not FGE equivalent, and thus they are not of the same
Braid Monodromy Type (BMT) (which implies that they are not a projective
deformation of each other


  Isolating the voice of a specific person while filtering out other voices or
background noises is challenging when video is shot in noisy environments. We
propose audio-visual methods to isolate the voice of a single speaker and
eliminate unrelated sounds. First, face motions captured in the video are used
to estimate the speaker's voice, by passing the silent video frames through a
video-to-speech neural network-based model. Then the speech predictions are
applied as a filter on the noisy input audio. This approach avoids using
mixtures of sounds in the learning process, as the number of such possible
mixtures is huge, and would inevitably bias the trained model. We evaluate our
method on two audio-visual datasets, GRID and TCD-TIMIT, and show that our
method attains significant SDR and PESQ improvements over the raw
video-to-speech predictions, and a well-known audio-only method.


  We discuss associated neutralino production e^+ e^- --> \tilde{\chi}^0_1
\tilde{\chi}^0_2 with both beams polarized in the MSSM, NMSSM and an E_6 model.
It is shown that neutralinos with a large singlino component can be produced at
a high luminosity linear collider in a broad parameter range. Polarization
effects in the extended models are compared over the whole parameter space
where the lightest neutralino is mainly a singlino. We explain the complete
different behavior of these models in some parameter regions, which may help to
identify the respective supersymmetric model.


  The internal and external mechanical environment plays an important role in
tumorogenesis. As a proxy of an avascular early state tumor, we use
multicellular spheroids, a composite material made of cells, extracellular
matrix and permeating fluid. We characterize its effective rheology at the
timescale of minutes to hours by compressing the aggregates with osmotic shocks
and modeling the experimental results with an active poroelastic material that
reproduces the stress and strain distributions in the aggregate. The model also
predicts how the emergent bulk modulus of the aggregate as well as the
hydraulic diffusion of the percolating interstitial fluid are modified by the
preexisting active stress within the aggregate. We further show that the value
of these two phenomenological parameters can be rationalized by considering
that, in our experimental context, the cells are effectively impermeable and
incompressible inclusions nested in a compressible and permeable matrix.


  We discuss the non-constant dilaton deformed ${\rm AdS}_5\times{\rm S}_5$
solutions of IIB supergravity where AdS sector is described by black hole. The
investigation of running gauge coupling (exponent of dilaton) of non-SUSY gauge
theory at finite temperature is presented for different regimes (high or low T,
large radius expansion). Running gauge coupling shows power-like behavior on
temperature with stable fixed point. The quark-antiquark potential at finite T
is found and possibility of confinement is established. It is shown that
non-constant dilaton affects the potential, sometimes reversing its behavior if
we compare it with the constant dilaton case (${\cal N}=4$ super Yang-Mills
theory). Thermodynamics of obtained backgrounds is studied. In particular,
next-to-leading term to free energy F is evaluated as $F=-{\tilde V_3 \over
4\pi^2}({N^2 (\pi T)^4 \over 2} + {5c^2 \over 768 g_{YM}^6 N{\alpha'}^6 (\pi
T)^4})$. Here $\tilde V_3$ is the volume of the space part in the boundary of
AdS, c is the parameter coming from the non-constant dilaton and N is the
number of the coincident D3-branes.


  We study the role played in leptogenesis by the equilibration of lepton
flavors, as could be induced in supersymmetric models by off diagonal soft
breaking masses for the scalar lepton doublets $\tilde m_{\alpha\beta}$, or
more generically by new sources of lepton flavor violation. We show that if
$\tilde m_{\alpha\beta}\gsim 1 $GeV and leptogenesis occurs below $\sim 100
$TeV, dynamical flavor effects are irrelevant and leptogenesis is correctly
described by a one-flavor Boltzmann equation. We also discuss spectator effects
in low scale leptogenesis by taking into account various chemical equilibrium
conditions enforced by the reactions that are in thermal equilibrium. We write
down the Boltzmann equation for low scale supersymmetric leptogenesis that
includes flavor and spectator effects in the presence of lepton flavor
equilibration, and we show how it reduces to a particularly simple form.


  Quasi-separable matrices are a class of rank-structured matriceswidely used
in numerical linear algebra and of growing interestin computer algebra, with
applications in e.g. the linearization ofpolynomial matrices. Various
representation formats exist for thesematrices that have rarely been
compared.We show how the most central formats SSS and HSS can beadapted to
symbolic computation, where the exact rank replacesthreshold based numerical
ranks. We clarify their links and comparethem with the Bruhat format. To this
end, we state their space andtime cost estimates based on fast matrix
multiplication, and comparethem, with their leading constants. The comparison
is supportedby software experiments.We make further progresses for the Bruhat
format, for which wegive a generation algorithm, following a Crout elimination
scheme,which specializes into fast algorithms for the construction from asparse
matrix or from the sum of Bruhat representations.


  Strong decay probabilities are calculated using the Lorentz contracted wave
functions of decay products, determined in the arbitrary dynamical scheme with
the instantaneous interaction. It is shown that the decay width obtains an
additional factor defined by the contraction coefficient $C_m(s)$, which for
two-body equal mass decays is $C^2_m(s)= 4m^2/s$ , $s= E^2$. The resulting
decay widths are compared to the experimental data, where in particular the
$\rho(770),\rho(1450) $ decay data require an additional $1/s$ dependence of
the width to fit the data. Important consequences for the dynamics of hadron
decays and scattering are shortly discussed.


  The nitrocarburization of the AISI-H13 tool steel by ion beam assisted
deposition is reported. In this technique, a carbon film is continuously
deposited over the sample by the ion beam sputtering of a carbon target while a
second ion source is used to bombard the sample with low energy nitrogen ions.
The results show that the presence of carbon has an important impact on the
crystalline and microstructural properties of the material without modification
of the case depth.


  We have observed the rotational ground-state (J = 1-0) transitions of DCO+,
HN13C and DNC with the IRAM 30m telescope toward the dark cloud LDN 1512 which
has exceptionally narrow lines permitting hyperfine splitting to be resolved in
part. The measured splittings of 50-300 kHz are used to derive nuclear
quadrupole and spin-rotation parameters for these species. The measurements are
supplemented by high-level quantum-chemical calculations using coupled-cluster
techniques and large atomic-orbital basis sets.
  We find eQq = +151.12 (400) kHz and C_I = -1.12 (43) kHz for DCO+, eQq =
272.5 (51) kHz for HN13C, and eQq(D) = 265.9 (83) kHz and eQq(N) = 288.2 (71)
kHz for DNC. The numbers for DNC are consistent with previous laboratory data,
while our constants for DCO+ are somewhat smaller than previous results based
on astronomical data. For both DCO+ and DNC, our results are more accurate than
previous determinations. Our results are in good agreement with the
corresponding best theoretical estimates. We also derive updated rotational
constants for HN13C: B = 43545.6000 (47) MHz and D = 93.7 (20) kHz.
  The hyperfine splittings of the DCO+, DNC and HN13C J = 1-0 lines range over
0.47-1.28 km/s, which is comparable to typical line widths in pre-stellar cores
and to systematic gas motions on ~1000 AU scales in protostellar cores. We
present tabular information to allow inclusion of the hyperfine splitting in
astronomical data interpretation. The large differences in the 14N quadrupole
parameters of DNC and HN13C have been traced to differences in the vibrational
corrections caused by significant non-rigidity of these molecules, particularly
along the bending coordinate.


  In [GH], Griffiths and Harris asked whether a projective complex submanifold
of codimension two is determined by the moduli of its second fundamental forms.
More precisely, given a nonsingular subvariety $X^n \subset {\mathbb P}^{n+2}$,
the second fundamental form $II_{X,x}$ at a point $x \in X$ is a pencil of
quadrics on $T_x(X)$, defining a rational map $\mu^X$ from $X$ to a suitable
moduli space of pencils of quadrics on a complex vector space of dimension $n$.
The question raised by Griffiths and Harris was whether the image of $\mu^X$
determines $X$. We study this question when $X^n \subset {\mathbb P}^{n+2}$ is
a nonsingular intersection of two quadric hypersurfaces of dimension $n >4$. In
this case, the second fundamental form $II_{X,x}$ at a general point $x \in X$
is a nonsingular pencil of quadrics. Firstly, we prove that the moduli map
$\mu^X$ is dominant over the moduli of nonsingular pencils of quadrics. This
gives a negative answer to Griffiths-Harris's question. To remedy the
situation, we consider a refined version $\widetilde\mu^X$ of the moduli map
$\mu^X$, which takes into account the infinitesimal information of $\mu^X$. Our
main result is an affirmative answer in terms of the refined moduli map: we
prove that the image of $\widetilde\mu^X$ determines $X$, among nonsingular
intersections of two quadrics.


  The rules that govern spin exchange interaction in pristine graphene
nanostructures are constrained by the bipartite character of the lattice, so
that the sign of the exchange is determined by whether magnetic moments are on
the same sublattice or else. The synthesis of graphene ribbons with perfect
zigzag edges and a fluoranthene group with a pentagon ring, a defect that
breaks the bipartite nature of the honeycomb lattice, has been recently
demonstrated. Here we address how the electronic and spin properties of these
structures are modified by such defects, both for indirect exchange
interactions as well as the emergent edge magnetism, studied both with DFT and
mean field Hubbard model calculations. In all instances we find that the local
breakdown of the bipartite nature at the defect reverts the sign of the
otherwise ferromagnetic correlations along the edge, introducing a locally
antiferromagnetic intra-edge coupling and, for narrow ribbons, also revert the
antiferromagnetic inter-edge interactions that are normally found in pristine
ribbons. Our findings show that these pentagon defects are a resource that
permits to engineer the spin exchange interactions in graphene based
nano-structures.


  This paper studies the exploitation of networked integrated sensing and
communications (ISAC) to support low-altitude economy (LAE), in which a set of
networked ground base stations (GBSs) transmit wireless signals to
cooperatively communicate with multiple authorized unmanned aerial vehicles
(UAVs) and concurrently use the echo signals to detect the invasion of
unauthorized objects in interested airspace. Under this setup, we jointly
design the cooperative transmit beamforming at multiple GBSs together with the
trajectory control of authorized UAVs and their GBS associations, for enhancing
the authorized UAVs' communication performance while ensuring the sensing
requirements for airspace monitoring. In particular, our objective is to
maximize the average sum rate of authorized UAVs over a particular flight
period, subject to the minimum illumination power constraints for sensing over
the interested airspace, the maximum transmit power constraints at individual
GBSs, and the flight constraints at UAVs. This problem is non-convex and
challenging to solve, due to the involvement of integer variables and the
coupling of optimization variables. To solve this non-convex problem, we
propose an efficient algorithm by using the techniques of alternating
optimization (AO), successive convex approximation (SCA), and semi-definite
relaxation (SDR). Numerical results show that the obtained transmit beamforming
and UAV trajectory designs in the proposed algorithm efficiently balance the
tradeoff between the sensing and communication performances, thus significantly
outperforming various benchmarks.


  SNO+ is a large multipurpose experiment with the ultimate goal of searching
for the neutrinoless double beta decay in $^{130}\mathrm{Te}$. After a
commissioning phase with water as the target medium, during which acquired data
allowed for measurements of solar neutrinos and the detection of reactor
antineutrinos, SNO+ is now filled with 780 tonnes of liquid scintillator. The
higher light yield of the scintillator enhances the physics capabilities of the
experiment, and a physics program including reactor, geo and solar neutrinos is
currently underway. The water and unloaded scintillator phases provide crucial
commissioning milestones in preparation for the tellurium loading, such as
calibrating the detector and making extensive background constraint
measurements as components of the final scintillator cocktail are gradually
added. In a first phase, 3900~kg of natural tellurium (0.5%) will be added to
the scintillator for a predicted sensitivity of about $2\times20^{26}$ years
(90% CL) with 3 years of livetime. Higher tellurium loading will follow for
predicted sensitivities above $1\times10^{27}$ years (3% loading).


  The structure of the joint phase diagram demonstrating high-$T_c$
superconductivity of copper oxides is studied on the basis of the theory of
interaction-induced flat bands. Prerequisites of an associated topological
rearrangement of the Landau state are established, and related non-Fermi-liquid
(NFL) behavior of the normal states of cuprates is investigated. We focus on
manifestations of this behavior in the electrical resistivity $\rho(T)$,
especially the observed gradual crossover from normal-state $T$-linear behavior
$\rho(T,x)=A_1(x)T$ at doping $x$ below the critical value $x_c^h$ for
termination of superconductivity, to $T$-quadratic behavior at $x>x_c^h$, which
is incompatible with predictions of the conventional quantum-critical-point
scenario. It is demonstrated that at $x<x^h_c$, in agreement with available
experimental data, the coefficient $A_1( x)$ is decomposed into the product of
two factors, one of which changes linearly with doping $x$, while the second is
universal, being of the Planckian form.


  High-energy photons are a powerful probe for astrophysics and for fundamental
physics under extreme conditions. During the recent years, our knowledge of the
most violent phenomena in the Universe has impressively progressed thanks to
the advent of new detectors for high-energy gamma-rays. Observation of
gamma-rays gives an exciting view of the high-energy universe thanks to
satellite-based telescopes (AGILE, GLAST) and to ground-based detectors like
the Cherenkov telescopes (H.E.S.S. and MAGIC in particular), which recently
discovered more than 60 new very-high-energy sources. The progress achieved
with the last generation of Cherenkov telescopes is comparable to the one drawn
by EGRET with respect to the previous gamma-ray satellite detectors. This
article reviews the present status of high-energy gamma astrophysics, with
emphasis on the recent results and on the experimental developments.


  Large-scale resistive Hall-magnetohydrodynamic (Hall-MHD) simulations of the
transition from Sweet-Parker (collisional) to Hall (collisionless) magnetic
reconnection are presented, the first to separate effects of secondary islands
from collisionless effects. Three main results are described. There exists a
regime in which secondary islands occur without collisionless effects when the
thickness of the dissipation regions exceed ion gyroscales. The reconnection
rate with secondary islands is faster than Sweet-Parker but significantly
slower than Hall reconnection. This implies that secondary islands are not the
cause of the fastest reconnection rates. Because Hall reconnection is much
faster, its onset causes the ejection of secondary islands from the vicinity of
the X-line. These results imply that most of the energy release occurs during
Hall reconnection. Coronal applications are discussed.


  The significant advancements in Large Language Models (LLMs) have resulted in
their widespread adoption across various tasks within Software Engineering
(SE), including vulnerability detection and repair. Numerous recent studies
have investigated the application of LLMs to enhance vulnerability detection
and repair tasks. Despite the increasing research interest, there is currently
no existing survey that focuses on the utilization of LLMs for vulnerability
detection and repair. In this paper, we aim to bridge this gap by offering a
systematic literature review of approaches aimed at improving vulnerability
detection and repair through the utilization of LLMs. The review encompasses
research work from leading SE, AI, and Security conferences and journals,
covering 36 papers published at 21 distinct venues. By answering three key
research questions, we aim to (1) summarize the LLMs employed in the relevant
literature, (2) categorize various LLM adaptation techniques in vulnerability
detection, and (3) classify various LLM adaptation techniques in vulnerability
repair. Based on our findings, we have identified a series of challenges that
still need to be tackled considering existing studies. Additionally, we have
outlined a roadmap highlighting potential opportunities that we believe are
pertinent and crucial for future research endeavors.


  We report Spitzer Space Telescope photometry between 3.6 microns and 24
microns and spectroscopy between 5 microns and 15 microns of GD 362, a white
dwarf with an effective temperature near 10,000 K that displays a remarkably
high concentration of metals in its photosphere and a thermal infrared excess.
We approximately reproduce both the infrared continuum and the very strong 10
micron silicate emission feature with a model of an orbiting dusty disk which
is flat out to 50 stellar radii and warped between 50 and 70 stellar radii. The
relatively small amount of cold material implied by the weak 24 mircon flux
argues that the disk lies within the Roche radius of the star, and we may be
witnessing a system where an asteroidal-size body has been tidally destroyed.
If so, determination of the photospheric metal abundances may measure the bulk
composition of an extrasolar minor planet.


  In this paper, I give an extension to the banachic - non linear- case of the
work of B. Hanouzet and J.L. Joly which is quoted below in the bibliography and
which was elaborated in the hilbertian- linear- case.


  If gravity is an emergent phenomenon, as suggested by several recent results,
then the structure of the action principle for gravity should encode this fact.
With this motivation we study several features of the Einstein-Hilbert action
and establish direct connections with horizon thermodynamics. We begin by
introducing the concept of holographically conjugate variables (HCVs) in terms
of which the surface term in the action has a specific relationship with the
bulk term. In addition to g_{ab} and its conjugate momentum \sqrt{-g} M^{cab},
this procedure allows us to (re)discover and motivate strongly the use of
f^{ab}=\sqrt{-g}g^{ab} and its conjugate momentum N^c_{ab}. The gravitational
action can then be interpreted as a momentum space action for these variables.
We also show that many expressions in classical gravity simplify considerably
in this approach. For example, the field equations can be written in a form
analogous to Hamilton's equations for a suitable Hamiltonian if we use these
variables. More importantly, the variation of the surface term, evaluated on
any null surface which acts a local Rindler horizon can be given a direct
thermodynamic interpretation. The term involving the variation of the dynamical
variable leads to T\delta S while the term involving the variation of the
conjugate momentum leads to S\delta T. We have found this correspondence only
for the choice of variables (g_{ab}, \sqrt{-g} M^{cab}) or (f^{ab}, N^c_{ab}).
We use this result to provide a direct thermodynamical interpretation of the
boundary condition in the action principle, when it is formulated in a
spacetime region bounded by the null surfaces. We analyse these features from
several different perspectives and provide a detailed description, which offers
insights about the nature of classical gravity and emergent paradigm.


  A set of differential operators acting by continuous deformations on path
dependent functionals of open and closed curves is introduced. Geometrically,
these path operators are interpreted as infinitesimal generators of curves in
the base manifold of the gauge theory. They furnish a representation with the
action of the group of loops having a fundamental role. We show that the path
derivative, which is covariant by construction, satisfies the Ricci and Bianchi
identities. Also, we provide a geometrical derivation of covariant Taylor
expansions based on particular deformations of open curves. The formalism
includes, as special cases, other path dependent operators such as end point
derivatives and area derivatives.


  In this paper, the trade-off between the quantization noise and the dynamic
range of ADCs used to acquire radar signals is revisited using the Unlimited
Sensing Framework (USF) in a practical setting. Trade-offs between saturation
and resolution arise in many applications, like radar, where sensors acquire
signals which exhibit a high degree of variability in amplitude. To solve this
issue, we propose the use of the co-design approach of the USF which acquires
folded version of the signal of interest and leverages its structure to
reconstruct it after its acquisition. We demonstrate that this method
outperforms other standard acquisition methods for Doppler radars. Taking our
theory all the way to practice, we develop a prototype USF-enabled Doppler
Radar and show the clear benefits of our method. In each experiment, we show
that using the USF increases sensitivity compared to a classic acquisition
approach.


  Insects, pick-and-place manufacturing, engineered adhesives, and soft robots
employ soft materials to stick to surfaces even in the presence of roughness.
Experiments show that the force required for making contact is lower than for
releasing it, a phenomenon known as the adhesion hysteresis. The common
explanation for this hysteresis is either contact aging or viscoelasticity.
Here, we show that adhesion hysteresis emerges even for perfectly elastic
contacts and in the absence of contact aging and viscoelasticity because of
surface roughness. We present a crack-perturbation model and experimental
observations that reveal discrete jumps of the contact perimeter. These
stick-slip instabilities are triggered by local differences in fracture energy
between roughness peaks and valleys. Pinning of the contact perimeter retards
both its advancement when coming into contact and its retraction when pulling
away. Our model quantitatively reproduces the hysteresis observed in
experiments and allows us to derive analytical predictions for its magnitude,
accounting for realistic rough geometries across orders of magnitude in length
scale. Our results explain why adhesion hysteresis is ubiquitous and reveal why
soft pads in nature and engineering are efficient in adhering even to surfaces
with significant roughness.


  This note considers linear recurrences (also called linear difference
equations) in unknowns indexed by the integers. We characterize a unique
\emph{reduced} linear recurrence with the same solutions as a given linear
recurrence, and construct a \emph{solution matrix} which parametrizes the space
of solutions. Several properties of solution matrices are shown, including a
combinatorial characterization of bases and dimension of the space of
solutions.


  In recent years there have been a number of proposals to utilize the
specificity of DNA based interactions for potential applications in
nanoscience. One interesting direction is the self-assembly of micro- and
nanoparticle clusters using DNA scaffolds. In this letter we consider a DNA
scaffold method to self-assemble clusters of "colored" particles. Stable
clusters of microspheres have recently been produced by an entirely different
method. Our DNA based approach self-assembles clusters with additional degrees
of freedom associated with particle permutation. We demonstrate that in the
non-equilibrium regime of irreversible binding the self-assembly process is
experimentally feasible. These color degrees of freedom may allow for more
diverse intercluster interactions essential for hierarchical self-assembly of
larger structures.


  The blackbody radiation in a box L^3 with periodic boundary conditions in
thermal equilibrium at a temperature T is affected by finite-size effects.
These bring about modifications of the thermodynamic functions which can be
expressed in a closed form in terms of the dimensionless parameter LT. For
instance, when LT~4 - corresponding to the value where the most reliable SU(N)
gauge lattice simulations have been performed above the deconfining temperature
T_c - the deviation of the free energy density from its thermodynamic limit is
about 5%. This may account for almost half of the pressure deficit observed in
lattice simulations at T~ 4 T_c.


  In this study, a machine learning-based technique is developed to reduce the
computational cost required to explore large design spaces of substitutional
alloys. The first advancement is based on a neural network approach to predict
the initial position of ions for both minority and majority ions before ion
relaxation. The second advancement is to allow the neural network to predict
the total energy for every possibility minority ion position and select the
most stable configuration in the absence of relaxing each trial position. In
this study, a bismuth oxide materials system, (Bi$_{x}$La$_{y}$Yb$_{z}$)$_2$
MoO$_6$, is used as the model system to demonstrate the developed method and
potential computational speedup. Comparing a brute force method that requires
the calculation of every possible minority concentration location and
subsequent relaxation there was a 1.3x speedup if the neural network (NN) was
allowed to predict the initial position prior to relaxation. This speedup is a
result in an average decrease of 4 wall hour (64 cpu-hrs) reduction in
relaxation for individual calculations. Implementation of the second
advancement allowed the NN to predict the total energy for all possible trials
prior to relaxation, resulting in a speedup of approximately 37x. Validation
was done by comparing both position and energy between the NN to DFT
calculations. A maximum vector mean squared error (MSE) of 1.6x10$^{-2}$ and a
maximum energy MSE of 2.3x10$^{-7}$ was predicted. This method demonstrates a
significant computational speedup, which has the potential for significant
computational savings for larger compositional design spaces.


  A major transition in the operation of electric power grids is the
replacement of synchronous machines by distributed generation connected via
power electronic converters. The accompanying "loss of rotational inertia" and
the fluctuations by renewable sources jeopardize the system stability, as
testified by the ever-growing number of frequency incidents. As a remedy,
numerous studies demonstrate how virtual inertia can be emulated through
various devices, but few of them address the question of "where" to place this
inertia. It is however strongly believed that the placement of virtual inertia
hugely impacts system efficiency, as demonstrated by recent case studies. In
this article, we carry out a comprehensive analysis in an attempt to address
the optimal inertia placement problem. We consider a linear network-reduced
power system model along with an H2 performance metric accounting for the
network coherency. The optimal inertia placement problem turns out to be
non-convex, yet we provide a set of closed-form global optimality results for
particular problem instances as well as a computational approach resulting in
locally optimal solutions. Further, we also consider the robust inertia
allocation problem, wherein the optimization is carried out accounting for the
worst-case disturbance location. We illustrate our results with a three-region
power grid case study and compare our locally optimal solution with different
placement heuristics in terms of different performance metrics.


  We study a topological method to calculate the first Milnor fiber cohomology
of a defining polynomial of a reduced projective hyperplane arrangement $X$ of
degree $d$. We can show the vanishing of a monodromy eigenspace of the first
Milnor fiber cohomology with eigenvalue of order $m\ge 2$ if
$X\setminus(X^{[(m)]}\cup X^{\langle 3\rangle})$ or more generally
$X\setminus(X^{[(m)]}\cup X^{\langle 3\rangle}\cup X_d)$ is connected. Here
$X^{[(m)]}$ is the set of points of $X$ with multiplicity divisible by $m$, and
$X^{\langle 3\rangle}:=\bigcup_{i,j,k}X_i\cap X_j\cap X_k$ with $X_i$ the
irreducible components of $X$, where the union is taken over $i,j,k$ with ${\rm
codim}\,X_i\cap X_j\cap X_k=3$. This hypothesis can be relaxed to some extent.
The assertion is reduced to the case of a line arrangement in ${\bf P}^2$ by
Artin's vanishing theorem (where $X^{\langle 3\rangle}=\emptyset$), and we use
a projection from ${\bf P}^2$ to ${\bf P}^1$ with center a sufficiently general
point of $X_d$. It may be expected that the assumption of an improved assertion
is always satisfied for $m\ge 5$ (and also for $m=4$ except the Hessian
arrangement). The resulting vanishing of eigenspaces has been conjectured for
$m\ge 5$.


  Recent work has shown significant progress in the direction of synthetic data
generation using Generative Adversarial Networks (GANs). GANs have been applied
in many fields of computer vision including text-to-image conversion, domain
transfer, super-resolution, and image-to-video applications. In computer
vision, traditional GANs are based on deep convolutional neural networks.
However, deep convolutional neural networks can require extensive computational
resources because they are based on multiple operations performed by
convolutional layers, which can consist of millions of trainable parameters.
Training a GAN model can be difficult and it takes a significant amount of time
to reach an equilibrium point. In this paper, we investigate the use of
depthwise separable convolutions to reduce training time while maintaining data
generation performance. Our results show that a DepthwiseGAN architecture can
generate realistic images in shorter training periods when compared to a
StarGan architecture, but that model capacity still plays a significant role in
generative modelling. In addition, we show that depthwise separable
convolutions perform best when only applied to the generator. For quality
evaluation of generated images, we use the Fr\'echet Inception Distance (FID),
which compares the similarity between the generated image distribution and that
of the training dataset.


  We present a heuristic search algorithm for solving first-order Markov
Decision Processes (FOMDPs). Our approach combines first-order state
abstraction that avoids evaluating states individually, and heuristic search
that avoids evaluating all states. Firstly, in contrast to existing systems,
which start with propositionalizing the FOMDP and then perform state
abstraction on its propositionalized version we apply state abstraction
directly on the FOMDP avoiding propositionalization. This kind of abstraction
is referred to as first-order state abstraction. Secondly, guided by an
admissible heuristic, the search is restricted to those states that are
reachable from the initial state. We demonstrate the usefulness of the above
techniques for solving FOMDPs with a system, referred to as FluCaP (formerly,
FCPlanner), that entered the probabilistic track of the 2004 International
Planning Competition (IPC2004) and demonstrated an advantage over other
planners on the problems represented in first-order terms.


  Common measures of neural representational (dis)similarity are designed to be
insensitive to rotations and reflections of the neural activation space.
Motivated by the premise that the tuning of individual units may be important,
there has been recent interest in developing stricter notions of
representational (dis)similarity that require neurons to be individually
matched across networks. When two networks have the same size (i.e. same number
of neurons), a distance metric can be formulated by optimizing over neuron
index permutations to maximize tuning curve alignment. However, it is not clear
how to generalize this metric to measure distances between networks with
different sizes. Here, we leverage a connection to optimal transport theory to
derive a natural generalization based on "soft" permutations. The resulting
metric is symmetric, satisfies the triangle inequality, and can be interpreted
as a Wasserstein distance between two empirical distributions. Further, our
proposed metric avoids counter-intuitive outcomes suffered by alternative
approaches, and captures complementary geometric insights into neural
representations that are entirely missed by rotation-invariant metrics.


  Experimental studies of spin transport in a two-dimensional electron gas
hosted by a triple GaAs/AlGaAs quantum well are reported. Using time-resolved
Kerr rotation, we observed the precession of the spin polarization about a
current-controlled spin-orbit magnetic field. Spatially-resolved imaging showed
a large variation of the electron g-factor and the drift transport of coherent
electron spins over distances exceeding half-millimetre in a direction
transverse to the electric field.


  Unsupervised domain adaptation of speech signal aims at adapting a
well-trained source-domain acoustic model to the unlabeled data from target
domain. This can be achieved by adversarial training of deep neural network
(DNN) acoustic models to learn an intermediate deep representation that is both
senone-discriminative and domain-invariant. Specifically, the DNN is trained to
jointly optimize the primary task of senone classification and the secondary
task of domain classification with adversarial objective functions. In this
work, instead of only focusing on learning a domain-invariant feature (i.e. the
shared component between domains), we also characterize the difference between
the source and target domain distributions by explicitly modeling the private
component of each domain through a private component extractor DNN. The private
component is trained to be orthogonal with the shared component and thus
implicitly increases the degree of domain-invariance of the shared component. A
reconstructor DNN is used to reconstruct the original speech feature from the
private and shared components as a regularization. This domain separation
framework is applied to the unsupervised environment adaptation task and
achieved 11.08% relative WER reduction from the gradient reversal layer
training, a representative adversarial training method, for automatic speech
recognition on CHiME-3 dataset.


  We present a systematic and realistic simulation for single and double
phosphorous donors in a silicon-based quantum computer design. A two-valley
equation is developed to describe the ground state of phosphorous donors in
strained silicon quantum well (QW), with the central cell effect treated by a
model impurity potential. We find that the increase of quantum well confinement
leads to shrinking charge distribution in all 3 dimensions. Using an
unrestricted Hartree-Fock method with Generalized Valence Bond (GVB)
single-particle wave functions, we are able to solve the two-electron
Sch${\ddot o}$dinger equation with quantum well confinement and realistic gate
potentials. The effects of QW width, gate voltages, donor separation, and donor
position are calculated and analyzed. The gate tunability and gate fidelity are
defined and evaluated, for a typical QC design. Estimates are obtained for the
duration of $\sqrt{SWAP}$ gate operation and the required accuracy in voltage
control. A strong exchange oscillation is observed as both donors are shifted
along [001] axis but with their separation unchanged. Applying a gate potential
tends to suppress the oscillation. The exchange oscillation as a function of
donor position along [100] axis is found to be completely suppressed as the
donor separation is decreased. The simulation presented in this paper is of
importance to the practical design of an exchange-based silicon quantum
computer.


  We present the complete spectrum for the Bjorken $x$ weighted Energy-Energy
Correlation in the deep inelastic scattering (DIS) process, from the target
fragmentation region to the current fragmentation region, in the Breit frame.
The corresponding collinear and transverse momentum-dependent logarithms are
resummed to all orders with the accuracy of NLL and N$^3$LL, respectively. And
the results in the full region are matched with ${\cal O}(\alpha^2_s)$
fixed-order calculation. The final numerical predictions are presented for both
EIC and CEBAF kinematics.


  In this research, we propose a novel approach for the quantification of
credit portfolio Value-at-Risk (VaR) sensitivity to asset correlations with the
use of synthetic financial correlation matrices generated with deep learning
models. In previous work Generative Adversarial Networks (GANs) were employed
to demonstrate the generation of plausible correlation matrices, that capture
the essential characteristics observed in empirical correlation matrices
estimated on asset returns. Instead of GANs, we employ Variational Autoencoders
(VAE) to achieve a more interpretable latent space representation. Through our
analysis, we reveal that the VAE latent space can be a useful tool to capture
the crucial factors impacting portfolio diversification, particularly in
relation to credit portfolio sensitivity to asset correlations changes.


  The two-dimensional n-body problem of classical mechanics is a non-integrable
Hamiltonian system for n > 2. Traditional numerical integration algorithms,
which are polynomials in the time step, typically lead to systematic drifts in
the computed value of the total energy and angular momentum. Even symplectic
integration schemes exactly conserve only an approximate Hamiltonian. We
present an algorithm that conserves the true Hamiltonian and the total angular
momentum to machine precision. It is derived by applying conventional
discretizations in a new space obtained by transformation of the dependent
variables. We develop the method first for the restricted circular three-body
problem, then for the general two-dimensional three-body problem, and finally
for the planar n-body problem. Jacobi coordinates are used to reduce the
two-dimensional n-body problem to an (n-1)-body problem that incorporates the
constant linear momentum and center of mass constraints. For a four-body
choreography, we find that a larger time step can be used with our conservative
algorithm than with symplectic and conventional integrators.


  We extract pairing gap in $^{184}$W at finite temperature for the first time
from the experimental level densities of $^{183}$W, $^{184}$W, and $^{185}$W
using "thermal" odd-even mass difference. We found the quenching of pairing gap
near the critical temperature $T_c = 0.47$ MeV in the BCS calculations. It is
shown that the monopole pairing model with a deformed Woods-Saxon potential
explains the reduction of the pairing correlation using the partition function
with the number parity projection in the static path approximation plus
random-phase approximation.


  We use very deep (R_lim=27) UGRI imaging to study the evolution of the faint
end of the UV-selected galaxy luminosity function from z~4 to z~2. We find that
the luminosity function evolves with time and that this evolution is
differential with luminosity: the number of sub-L* galaxies increases from z~4
to z~3 by at least a factor of 2.3, while the bright end of the LF remains
unchanged. Potential systematic biases restrict our ability to draw strong
conclusions at lower redshifts, z~2, but we can say that the number density of
sub-L* galaxies at z~2.2 is at least as high as it is at z~3. Turning to the UV
luminosity density of the Universe, we find that the luminosity density starts
dropping with increasing redshift already beginning at z=3 (earlier than
recently thought - Steidel et al. 1999) and that this drop is dominated by the
same sub-L* galaxies that dominate the evolution of the LF. This differential
evolution of the luminosity function suggests that differentially comparing key
diagnostics of dust, stellar populations, etc. as a function of z and L should
let us isolate the key mechanisms that drive galaxy evolution at high redshift.


  We propose a new algorithm for minimizing regularized empirical loss:
Stochastic Dual Newton Ascent (SDNA). Our method is dual in nature: in each
iteration we update a random subset of the dual variables. However, unlike
existing methods such as stochastic dual coordinate ascent, SDNA is capable of
utilizing all curvature information contained in the examples, which leads to
striking improvements in both theory and practice - sometimes by orders of
magnitude. In the special case when an L2-regularizer is used in the primal,
the dual problem is a concave quadratic maximization problem plus a separable
term. In this regime, SDNA in each step solves a proximal subproblem involving
a random principal submatrix of the Hessian of the quadratic function; whence
the name of the method. If, in addition, the loss functions are quadratic, our
method can be interpreted as a novel variant of the recently introduced
Iterative Hessian Sketch.


  Heterogeneous cellular networks provide significant improvements in terms of
increased data rates and cell coverage, and offer reduced user rate starvation.
However, there are important problems to be solved. In this paper, we identify
that the cell selection criterion is an important factor determining the user
rates especially in the uplink transmissions and apply cell breathing to
determine the user and base station assignments. We observe that the proposed
interference-based cell selection algorithm provides better load balancing
among the base stations in the system to improve the uplink user rates. We
present the implementation steps in a typical LTE network and demonstrate the
performance improvements through simulations.


  The spectra of parallel flows (that is, flows governed by first-order
differential operators parallel to one direction) are investigated, on both
$L^2$ spaces and weighted-$L^2$ spaces. As a consequence, an example of a flow
admitting a purely singular continuous spectrum is provided. For flows
admitting more regular spectra the density of states is analyzed, and spaces on
which it is uniformly bounded are identified. As an application, an ergodic
theorem with uniform convergence is proved.


  We report the result of searching for globular clusters (GCs) around 55 Milky
Way satellite dwarf galaxies within the distance of 450 kpc from the Galactic
Center except for the Large and Small Magellanic Clouds and the Sagittarius
dwarf. For each dwarf, we analyze the stellar distribution of sources in Gaia
DR2, selected by magnitude, proper motion, and source morphology. Using the
kernel density estimation of stellar number counts, we identify eleven possible
GC candidates. Crossed-matched with existing imaging data, all eleven objects
are known either GCs or galaxies and only Fornax GC 1-6 among them are
associated with the targeted dwarf galaxy. Using simulated GCs, we calculate
the GC detection limit $M_{\rm V}^{\rm lim}$ that spans the range from $M_{\rm
V}^{\rm lim} \sim -7$ for distant dwarfs to $M_{\rm V}^{\rm lim} \sim 0$ for
nearby systems. Assuming a Gaussian GC luminosity function, we compute that the
completeness of the GC search is above 90 percent for most dwarf galaxies. We
construct the 90 percent credible intervals/upper limits on the GC specific
frequency $S_{\rm N}$ of the MW dwarf galaxies: $12 < S_{\rm N} < 47$ for
Fornax, $S_{\rm N} < 20$ for the dwarfs with $-12 < M_{\rm V} < -10$, $S_{\rm
N} < 30$ for the dwarfs with $-10 < M_{\rm V} < -7$, and $S_{\rm N} < 90$ for
the dwarfs with $M_{\rm V} > -7$. Based on $S_{\rm N}$, we derive the
probability of galaxies hosting GCs given their luminosity, finding that the
probability of galaxies fainter than $M_{\rm V} = -9$ to host GCs is lower than
0.1.


  The dynamics of black hole seeds in high redshift galaxies is key to
understand their ability to grow via accretion and to pair in close binaries
during galactic mergers. To properly follow the dynamics of black holes we
develop a physically motivated model to capture unresolved dynamical friction
from stars, dark matter and gas. We first validate the model and then we use it
to investigate the dynamics of seed black holes born at $z\sim9$ in dwarf
proto-galaxies. We perform a suite of zoom cosmological simulations with
spatial resolution as high as 10 pc and with a stellar and dark matter mass
resolution of $2\times10^3 \, \textrm{M}_\odot$ and $2\times10^5 \,
\textrm{M}_\odot$ respectively. We first explore the dynamics of a seed black
hole in the galaxy where it is born and show that it is highly erratic if the
seed mass is less than $10^5\, \textrm{M}_\odot$. The dynamics is dominated by
the stellar component, whose distribution is irregular and patchy, thus
inducing stochasticity in the orbits: the black hole may be anywhere in the
proto-galaxy. When this dwarf merges into a larger galaxy, it is paramount to
simulate the process with very high spatial and mass resolution in order to
correctly account for the stripping of the stellar envelope of the satellite
black hole. The outcome of the encounter could be either a tight binary or, at
least temporary, a wandering black hole, leading to multiple black holes in a
galaxy, each inherited from a different merger.


  Online Real-Time Bidding (RTB) is a complex auction game among which
advertisers struggle to bid for ad impressions when a user request occurs.
Considering display cost, Return on Investment (ROI), and other influential Key
Performance Indicators (KPIs), large ad platforms try to balance the trade-off
among various goals in dynamics. To address the challenge, we propose a
Multi-ObjecTive Actor-Critics algorithm based on reinforcement learning (RL),
named MoTiAC, for the problem of bidding optimization with various goals. In
MoTiAC, objective-specific agents update the global network asynchronously with
different goals and perspectives, leading to a robust bidding policy. Unlike
previous RL models, the proposed MoTiAC can simultaneously fulfill
multi-objective tasks in complicated bidding environments. In addition, we
mathematically prove that our model will converge to Pareto optimality.
Finally, experiments on a large-scale real-world commercial dataset from
Tencent verify the effectiveness of MoTiAC versus a set of recent approaches


  The fact that the Korteweg-de-Vries equation offers a good approximation of
long-wave solutions of small amplitude to the one-dimensional Gross-Pitaevskii
equation was derived several years ago in the physical literature. In this
paper, we provide a rigorous proof of this fact, and compute a precise estimate
for the error term. Our proof relies on the integrability of both the
equations. In particular, we give a relation between the invariants of the two
equations, which, we hope, is of independent interest.


  Gas flows in and out of galaxies through their circumgalactic medium (CGM)
are poorly constrained and direct observations of this faint, diffuse medium
remain challenging. We use a sample of five $z$ $\sim$ 1-2 galaxy counterparts
to Damped Lyman-$\alpha$ Absorbers (DLAs) to combine data on cold gas, metals
and stellar content of the same galaxies. We present new HST/WFC3 imaging of
these fields in 3-5 broadband filters and characterise the stellar properties
of the host galaxies. By fitting the spectral energy distribution, we measure
their stellar masses to be in the range of log($M_*$/$\text{M}_{\odot}$) $\sim$
9.1$-$10.7. Combining these with IFU observations, we find a large spread of
baryon fractions inside the host galaxies, between 7 and 100 percent.
Similarly, we find gas fractions between 3 and 56 percent. Given their star
formation rates, these objects lie on the expected main sequence of galaxies.
Emission line metallicities indicate they are consistent with the
mass-metallicity relation for DLAs. We also report an apparent anti-correlation
between the stellar masses and $N$(HI), which could be due to a dust bias
effect or lower column density systems tracing more massive galaxies. We
present new ALMA observations of one of the targets leading to a molecular gas
mass of log($M_{\rm mol}$/$\text{M}_{\odot}$) < 9.89. We also investigate the
morphology of the DLA counterparts and find that most of the galaxies show a
clumpy structure and suggest ongoing tidal interaction. Thanks to our high
spatial resolution HST data, we gain new insights in the structural complexity
of the CGM.


  A non-perturbative mass of $0.2719 g^2 T$ is generated for the magnetic
sector of the $SU(2)$ gauge theory at high temperature due to the condensation
of Polyakov \cite{Pol} monopole and antimonopole which form a magnetic glue
ball. String tension for the spatial wilson loop is calculated which is of the
same order of magnitude and has same temperature dependence as obtained from
lattice simulation.


  Electroencephalography (EEG) signals are promising as alternatives to other
biometrics owing to their protection against spoofing. Previous studies have
focused on capturing individual variability by analyzing
task/condition-specific EEG. This work attempts to model biometric signatures
independent of task/condition by normalizing the associated variance. Toward
this goal, the paper extends ideas from subspace-based text-independent speaker
recognition and proposes novel modifications for modeling multi-channel EEG
data. The proposed techniques assume that biometric information is present in
the entire EEG signal and accumulate statistics across time in a high
dimensional space. These high dimensional statistics are then projected to a
lower dimensional space where the biometric information is preserved. The lower
dimensional embeddings obtained using the proposed approach are shown to be
task-independent. The best subspace system identifies individuals with
accuracies of 86.4% and 35.9% on datasets with 30 and 920 subjects,
respectively, using just nine EEG channels. The paper also provides insights
into the subspace model's scalability to unseen tasks and individuals during
training and the number of channels needed for subspace modeling.


  A cerium containing pnictide, CeNiAsO, crystallized in the ZrCuSiAs type
structure, has been investigated by measuring transport and magnetic
properties, as well as specific heat. We found that CeNiAsO is an
antiferromagnetic dense Kondo lattice metallic compound with Kondo scale $T_K
\sim$ 15 K and shows an enhanced Sommerfeld coefficient of $\gamma_0 \sim$ 203
mJ/mol$\cdot$K$^{2}$. While no superconductivity can been observed down to 30
mK, Ce ions exhibit two successive antiferromagnetic (AFM) transitions. We
propose that the magnetic moment of Ce ion could align in the G type AFM order
below the first transition at $T_{N1}$=9.3 K, and it might be modified into the
C type AFM order below a lower transition at $T_{N2}$=7.3 K. Our results
indicate that the 3$d-4f$ interlayer Kondo interactions play an important role
in Ni-based Ce-containing pnictide.


  High sensitivity MEMS pressure sensor chip for different ranges (1 to 60 kPa)
utilizing the novel electrical circuit of piezosensitive differential amplifier
with negative feedback loop (PDA-NFL) is developed. Pressure sensor chip
PDA-NFL utilizes two bipolar-junction transistors (BJT) with vertical n-p-n
type structure (V-NPN) and eight piezoresistors (p-type). Both theoretical
model of sensor response to pressure and temperature and experimental data are
presented. Data confirms the applicability of theoretical model. Introduction
of the amplifier allows for decreasing chip size while keeping the same
sensitivity as a chip with classic Wheatstone bridge circuit.


  Domain generation algorithms (DGAs) are commonly used by botnets to generate
domain names through which bots can establish a resilient communication channel
with their command and control servers. Recent publications presented deep
learning, character-level classifiers that are able to detect algorithmically
generated domain (AGD) names with high accuracy, and correspondingly,
significantly reduce the effectiveness of DGAs for botnet communication. In
this paper we present MaskDGA, a practical adversarial learning technique that
adds perturbation to the character-level representation of algorithmically
generated domain names in order to evade DGA classifiers, without the attacker
having any knowledge about the DGA classifier's architecture and parameters.
MaskDGA was evaluated using the DMD-2018 dataset of AGD names and four recently
published DGA classifiers, in which the average F1-score of the classifiers
degrades from 0.977 to 0.495 when applying the evasion technique. An additional
evaluation was conducted using the same classifiers but with adversarial
defenses implemented: adversarial re-training and distillation. The results of
this evaluation show that MaskDGA can be used for improving the robustness of
the character-level DGA classifiers against adversarial attacks, but that
ideally DGA classifiers should incorporate additional features alongside
character-level features that are demonstrated in this study to be vulnerable
to adversarial attacks.


  In this paper, we describe a reliable symbolic computational algorithm for
inverting general cyclic heptadiagonal matrices by using parallel computing
along with recursion. The algorithm is implementable to the Computer Algebra
System(CAS) such as MAPLE, Matlab and Mathematica . An example is presented for
the sake of illustration.


  We present a model as well as experimental results for a surface electrode
radio-frequency Paul trap that has a circular electrode geometry well-suited
for trapping of single ions and two-dimensional planar ion crystals. The trap
design is compatible with microfabrication and offers a simple method by which
the height of the trapped ions above the surface may be changed \emph{in situ}.
We demonstrate trapping of single and few Sr+ ions over an ion height range of
200-1000 microns for several hours under Doppler laser cooling, and use these
to characterize the trap, finding good agreement with our model.


  We propose a framework to study local gauge theories on manifolds with
boundaries and asymptotic symmetries, which is based on representing them as
so-called gauge PDEs. These objects extend the conventional BV-AKSZ
sigma-models to the case of not necessarily topological and diffeomorphism
invariant systems and are known to behave well with respect to restrictions to
submanifolds and boundaries. We introduce the notion of gauge PDE with
boundaries, which takes into account generic boundary conditions, and apply the
framework to asymptotically flat gravity. In so doing we start with a suitable
representation of gravity as a gauge PDE with boundaries which implements the
Penrose's description of asymptotically simple spacetimes. We then derive the
minimal model of the gauge PDE induced on the boundary and observe that it
provides the Cartan (frame-like) description of a (curved) conformal Carollian
structure on the boundary. Furthermore, imposing a suitable version of the
familiar boundary conditions in the induced boundary gauge PDE immediately
leads to the conventional BMS algebra of asymptotic symmetries. Finally, we
briefly sketch the construction in the case of asymptotically (A)dS gravity.


  We have developed an analytical model of angle-dependent magnetoresistance
oscillations (AMROs) in a quasi-two-dimensional metal in which magnetic
breakdown occurs. The model takes account of all the contributions from
quasiparticles undergoing both magnetic breakdown and Bragg reflection at each
junction and allows extremely efficient simulation of data which can be
compared with recent experimental results on the organic metal
kappa-ET2Cu(NCS)2. AMROs resulting from both closed and open orbits emerge
naturally at low field, and the model enables the transition to breakdown-AMROs
with increasing field to be described in detail.


  Existing bidirectional reflectance distribution function (BRDF) models are
capable of capturing the distinctive highlights produced by the fibrous nature
of wood. However, capturing parameter textures for even a single specimen
remains a laborious process requiring specialized equipment. In this paper we
take a procedural approach to generating parameters for the wood BSDF. We
characterize the elements of trees that are important for the appearance of
wood, discuss techniques appropriate for representing those features, and
present a complete procedural wood shader capable of reproducing the growth
patterns responsible for the distinctive appearance of highly prized
``figured'' wood. Our procedural wood shader is random-access, 3D, modular, and
is fast enough to generate a preview for design.


  We present a probabilistic analysis of two Krylov subspace methods for
solving linear systems. We prove a central limit theorem for norms of the
residual vectors that are produced by the conjugate gradient and MINRES
algorithms when applied to a wide class of sample covariance matrices
satisfying some standard moment conditions. The proof involves establishing a
four moment theorem for the so-called spectral measure, implying, in
particular, universality for the matrix produced by the Lanczos iteration. The
central limit theorem then implies an almost-deterministic iteration count for
the iterative methods in question.


  If a linear electron accelerator is installed into the SPPC (Super
Proton-Proton Collider) complex, ep collision options will be available in
addition to pp collisions. We consider the production of excited electrons with
spin-1/2 at the future SPPC-based electron-proton colliders with center-of-mass
energies of $8.44$, $11.66$, $26.68$ and $36.88$ TeV. In the $ep\rightarrow
e^{\star}X\rightarrow e\gamma X$ signal process, excited electrons are produced
by contact interactions and decay into the photon channel by gauge
interactions. Taking into account the corresponding background process, the
pseudorapidity and transverse momentum distributions of the final state
particles are plotted. We reported the discovery, observation and exclusion
mass limits of excited electrons by applying appropriate kinematical cuts best
suited for amplify the signal of the excited electron signature. We also
investigated the highest achievable values of the compositeness scale for the
discovery of excited electrons at these colliders.


  We present a flexible scheme to realize exact flat Landau levels on curved
spherical geometry in a system of spinful cold atoms. This is achieved by
Floquet engineering of a magnetic quadrupole field. We show that a synthetic
monopole field in real space can be created. We prove that the system can be
exactly mapped to the electron-monopole system on sphere, thus realizing
Haldane's spherical geometry for fractional quantum Hall physics. The scheme
works for either bosons or fermions. We investigate the ground state vortex
pattern for an $s$-wave interacting atomic condensate by mapping this system to
the classical Thompson's problem. We further study the distortion and stability
of the vortex pattern when dipolar interaction is present. Our scheme is
compatible with current experimental setup, and may serve as a promising route
of investigating quantum Hall physics and exotic spinor vortex matter on curved
space.


  The article deals with iterative methods of solving linear operator equations
$x = Bx + f$ and $Ax = f$ with self-adjoint operators in Hilbert space $X$ in
critical case when $\rho(B) = 1$ and $0 \in {\rm Sp}\, A$. The main results are
based on the use of M.A. Krasnosel'ski\u{i} theorem about the convergence of
the successive approximations and some its modifications and refinements.


  This paper presents a localization system for mobile robots enabling precise
localization in inaccurate building models. The approach leverages local
referencing to counteract inherent deviations between as-planned and as-built
data for locally accurate registration. We further fuse a novel image-based
robust outlier detector with LiDAR data to reject a wide range of outlier
measurements from clutter, dynamic objects, and sensor failures. We evaluate
the proposed approach on a mobile robot in a challenging real world building
construction site. It consistently outperforms the traditional ICP-based
alingment, reducing localization error by at least 30%.


  Suppose that we are given an infinite binary sequence which is random for a
Bernoulli measure of parameter $p$. By the law of large numbers, the frequency
of zeros in the sequence tends to~$p$, and thus we can get better and better
approximations of $p$ as we read the sequence. We study in this paper a similar
question, but from the viewpoint of inductive inference. We suppose now that
$p$ is a computable real, but one asks for more: as we are reading more and
more bits of our random sequence, we have to eventually guess the exact
parameter $p$ (in the form of a Turing code). Can one do such a thing uniformly
on all sequences that are random for computable Bernoulli measures, or even on
a `large enough' fraction of them? In this paper, we give a negative answer to
this question. In fact, we prove a very general negative result which extends
far beyond the class of Bernoulli measures.


  We prove that Khovanov homology with Z/2-coefficients detects the link L7n1,
and the union of a trefoil and its meridian.


  We prove that the moduli spaces of K3 surfaces with non-symplectic
involutions are unirational. As a by-product we describe configuration spaces
of 4<d<9 points in the projective plane as arithmetic quotients of type IV.


  Economic inequality is one of the pivotal issues for most of economic and
social policy makers across the world to insure the sustainable economic growth
and justice. In the mainstream school of economics, namely neoclassical
theories, economic issues are dealt with in a mechanistic manner. Such a
mainstream framework is majorly focused on investigating a socio-economic
system based on an axiomatic scheme where reductionism approach plays a vital
role. The major limitations of such theories include unbounded rationality of
economic agents, reducing the economic aggregates to a set of predictable
factors and lack of attention to adaptability and the evolutionary nature of
economic agents. In tackling deficiencies of conventional economic models, in
the past two decades, some new approaches have been recruited. One of those
novel approaches is the Complex adaptive systems (CAS) framework which has
shown a very promising performance in action. In contrast to mainstream school,
under this framework, the economic phenomena are studied in an organic manner
where the economic agents are supposed to be both boundedly rational and
adaptive. According to it, the economic aggregates emerge out of the ways
agents of a system decide and interact. As a powerful way of modeling CASs,
Agent-based models (ABMs) has found a growing application among academicians
and practitioners. ABMs show that how simple behavioral rules of agents and
local interactions among them at micro-scale can generate surprisingly complex
patterns at macro-scale. In this paper, ABMs have been used to show (1) how an
economic inequality emerges in a system and to explain (2) how sadaqah as an
Islamic charity rule can majorly help alleviating the inequality and how
resource allocation strategies taken by charity entities can accelerate this
alleviation.


  For each positive integer $n$, we introduce a monoidal category
$\mathcal{JP}(n)$ using a generalization of partition diagrams. When the
characteristic of the ground field is either 0 or at least $n$, we show
$\mathcal{JP}(n)$ is monoidally equivalent to the full subcategory of
$\operatorname{Rep}(A_n)$ whose objects are tensor powers of the natural
$n$-dimensional permutation representation of the alternating group $A_n$.


  In this note, we revisit the Rankin-Selberg integral of Shimura type for
generic representations of $\mathrm{SL}_2\times \mathrm{GL}_2$, constructed by
Ginzburg, Rallis, and Soudry. We give a different and more ``intrinsic'' proof
of the unramified computation. In contrast to their proof we avoid local
functional equation for the general linear groups but use the Casselman-Shalika
formulas for unramified Whittaker functions for $\mathrm{SL}_2$ and
$\mathrm{GL}_2$.


  One of the most powerful techniques to study the dark sector of the Universe
is weak gravitational lensing. In practice, to infer the reduced shear, weak
lensing measures galaxy shapes, which are the consequence of both the intrinsic
ellipticity of the sources and of the integrated gravitational lensing effect
along the line of sight. Hence, a very large number of galaxies is required in
order to average over their individual properties and to isolate the weak
lensing cosmic shear signal. If this `shape noise' can be reduced, significant
advances in the power of a weak lensing surveys can be expected. This paper
describes a general method for extracting the probability distributions of
parameters from catalogues of data using Voronoi cells, which has several
applications, and has synergies with Bayesian hierarchical modelling
approaches. This allows us to construct a probability distribution for the
variance of the intrinsic ellipticity as a function of galaxy property using
only photometric data, allowing a reduction of shape noise. As a proof of
concept the method is applied to the CFHTLenS survey data. We use this approach
to investigate trends of galaxy properties in the data and apply this to the
case of weak lensing power spectra.


  A fully operational loss-free quantum battery requires an inherent control
over the energy transfer process, with the ability of keeping the energy
retained with no leakage. Moreover, it also requires a stable discharge
mechanism, which entails that no energy revivals occur as the device starts its
energy distribution. Here, we provide a scalable solution for both
requirements. To this aim, we propose a general design for a quantum battery
based on an {\it{energy current}} (EC) observable quantifying the energy
transfer rate to a consumption hub. More specifically, we introduce an
instantaneous EC operator describing the energy transfer process driven by an
arbitrary interaction Hamiltonian. The EC observable is shown to be the root
for two main applications: (i) a trapping energy mechanism based on a common
eigenstate between the EC operator and the interaction Hamiltonian, in which
the battery can indefinitely retain its energy even if it is coupled to the
consumption hub; (ii) an asymptotically stable discharge mechanism, which is
achieved through an adiabatic evolution eventually yielding vanishing EC. These
two independent but complementary applications are illustrated in quantum spin
chains, where the trapping energy control is realized through Bell pairwise
entanglement and the stability arises as a general consequence of the adiabatic
spin dynamics.


  Alphabet size of auxiliary random variables in our canonical description is
derived. Our analysis improves upon estimates known in special cases, and
generalizes to an arbitrary multiterminal setup. The salient steps include
decomposition of constituent rate polytopes into orthants, translation of a
hyperplane till it becomes tangent to the achievable region at an extreme
point, and derivation of minimum auxiliary alphabet sizes based on
Caratheodory's theorem.


  The on lattice $\phi^4$ model is a paradigmatic example of continuous real
variables model undergoing a continuous symmetry braking phase transition
(SBPT). In this paper we study the $\mathbb{Z}_2$-symmetric mean-field version
without the quadratic term of the local potential. Obviously, the
simplification is directly extensible to the other symmetry groups for which
the model undergoes a SBPT. We show that the $\mathbb{Z}_2$-SBPT is not
affected by the quadratic term, and that the potential energy landscape turns
out greatly simplified. In particular, there exist only three critical points,
to confront with an amount growing as $e^N$ ($N$ is the number of degrees of
freedom) of the model with non-vanishing quadratic term. In our opinion, this
is an crucial feature because in recent years the study of the link between
statistical mechanic and geometric-topological properties of configuration
space has received an increasing attention. In this paper we study the
equipotential hypersurfaces with the aim of deepening our understanding of the
link between SBPTs and the truly essential geometric-topological properties of
the energy potential landscape.


  We develop perturbation theory approaches to model the marked correlation
function constructed to up-weight low density regions of the Universe, which
might help distinguish modified gravity models from the standard cosmology
model based on general relativity. Working within Convolution Lagrangian
Perturbation Theory, we obtain that weighted correlation functions are
expressible as double convolution integrals that we approximate using a
combination of Eulerian and Lagrangian schemes. We find that different
approaches agree within 1$\%$ on quasi non-linear scales. Compared with {\it
N}-body simulations, the perturbation theory is found to provide accurate
predictions for the marked correlation function of dark matter fields, dark
matter halos as well as Halo Occupation Distribution galaxies down to $30$
Mpc/h. These analytic approaches help to understand the degeneracy between the
mark and the galaxy bias and find a way to maximize the differences among
various cosmological models.


  We derive the generalized magneto-absorption spectra for curved graphene
nanorib- bons and carbon nanotubes by using the Peierls tight-binding model.
The main spectral characteristics and the optical selection rules result from
the cooperative or competitive relationships between the geometric structure
and a magnetic field. In curved ribbons, the dominant selection rule remains
unchanged during the variation of the curvature. When the arc angle increases,
the prominent peaks are split, with some even vanishing as the angle exceeds a
critical value. In carbon nanotubes, the angular-momentum coupling induces
extra selection rules, of which more are revealed due to the increase of either
(both) of the factors: tube diameter and field strength. Particularly once the
two factors exceed certain critical values, the optical spectra could reflect
the quasi-Landau-level structures. The identifying features of the spec- tra
provide insight into optical excitations for curved systems with either open or
closed boundary condition.


  A conservative flux postprocessing algorithm is presented for both
steady-state and dynamic flow models. The postprocessed flux is shown to have
the same convergence order as the original flux. An arbitrary flux
approximation is projected into a conservative subspace by adding a piecewise
constant correction that is minimized in a weighted $L^2$ norm. The application
of a weighted norm appears to yield better results for heterogeneous media than
the standard $L^2$ norm which has been considered in earlier works. We also
study the effect of different flux calculations on the domain boundary. In
particular we consider the continuous Galerkin finite element method for
solving Darcy flow and couple it with a discontinuous Galerkin finite element
method for an advective transport problem.


  In high-energy flash radiography, scattered photons will degrade the
acquiring image, which limits the resolving power of the interface and density
of the dense object. The application of large anti-scatter grid is capable of
remarkably decreasing scattered photons, whereas requires a very stable source
position in order to reduce the loss of signal photons in the grid structure.
The pinhole imaging technique is applied to observe spatial jitters of a
triple-pulse radiographic source produced by a linear induction accelerator.
Numerical simulations are taken to analyze the performance of the imaging
technique with same or close parameters of the pinhole object and experimental
alignment Experiments are carried out to observe spatial jitters of the source
between different measurements. Deviations of the source position between
different pulses are also measured in each experiment.


  We report muSR experiments on Mg{x}Cu{4-x}(OH)6Cl2 with x \sim 1, a new
material isostructural to Herbertsmithite exhibiting regular kagome planes of
spin 1/2 (Cu^{2+}), and therefore a candidate for a spin liquid ground state.
We evidence the absence of any magnetic ordering down to 20 mK (\sim J/10^4).
We investigate in detail the spin dynamics on well characterized samples in
zero and applied longitudinal fields and propose a low T defect based
interpretation to explain the unconventional dynamics observed in the quantum
spin liquid phase.