  We study symplectic embeddings of ellipsoids into balls. In the main
construction, we show that a given embedding of 2m-dimensional ellipsoids can
be suspended to embeddings of ellipsoids in any higher dimension. In dimension
6,s if the ratio of the areas of any two axes is sufficiently large then the
ellipsoid is flexible in the sense that it fully fills a ball. We also show
that the same property holds in all dimensions for sufficiently thin ellipsoids
E(1,..., a). A consequence of our study is that in arbitrary dimension a ball
can be fully filled by any sufficiently large number of identical smaller
balls, thus generalizing a result of Biran valid in dimension 4.


  The node-opening technique, originally designed for constructing minimal
surfaces, is adapted to construct a rich variety of new maxfaces of high genus
that are embedded outside a compact set and have arbitrarily many catenoid or
planar ends, thus removing the scarcity of examples of maxfaces. The surfaces
look like spacelike planes connected by small necks. Among the examples are
maxfaces of the Costa--Hoffman--Meeks type. Although very fruitful, the main
challenge of this paper is not the construction itself, but the analysis of the
positions and natures of singularities on these maxfaces. More specifically, we
conclude that the singular set form curves around the waists of the necks. In
generic and some symmetric cases, all but finitely many singularities are
cuspidal edges, and the non-cuspidal singularities are swallowtails evenly
distributed along the singular curves.


  In most Swiss municipalities, a curbside system consisting of heavy trucks
stopping at almost each household is used for non-recoverable waste collection.
Due to the many stops of the trucks, this strategy causes high fuel
consumption, emissions and noise. These effects can be alleviated by reducing
the number of stops performed by collection vehicles. One possibility consists
of locating collection points throughout the municipality such that residents
bring their waste to their most preferred location. The optimization problem
consists of selecting a subset of candidate locations to place the points such
that each household disposes the waste at the most preferred location. Provided
that the underlying road network is available, we refer to this optimization
problem as the capacitated multi-vehicle covering tour problem on a road
network (Cm-CTP-R). We introduce two mixed-integer linear programming (MILP)
formulations: a road-network-based formulation that exploits the sparsity of
the network and a customer-based formulation typically used in vehicle routing
problems (VRP). To solve large instances, we propose a two-phased heuristic
approach that addresses the two subproblems the Cm-CTP-R is built on: a set
covering problem to select the locations and a split-delivery VRP to determine
the routes. Computational experiments on both small and real-life instances
show that the road-network-based formulation is better suited. Furthermore, the
proposed heuristic provides good solutions with optimality gaps below 0.5% and
3.5% for 75% of the small and real-life instances respectively and is able to
find better solutions than the exact method for many real-life instances.


  We construct Lie algebras of derivations (and identify their geometrical
realization) whose Maurer-Cartan sets provide moduli spaces describing the
classes of homotopy types of rational spaces sharing either the same homotopy
Lie algebra, homology or cohomology.


  We discuss the importance for the long-term cluster evolution of the mass
loss from intermediate-mass stars (0.8-8 Msun). We present constraints on the
mass loss from red giants in clusters in the Magellanic Clouds, a search for
the intra-cluster medium in galactic globular clusters, and a simple estimate
for the cluster evolution due to red giant mass loss compared to stellar
escape.


  In this paper we consider sequences $u_j:B_2\subseteq M\to N$ of stationary
harmonic maps between smooth Riemannian manifolds with uniformly bounded energy
$E[u_j]\equiv \int |\nabla u_j|^2\leq \Lambda$ . After passing to a subsequence
it is known one can limit $u_j\to u:B_1\to N$ with the associated defect
measure $|\nabla u_j|^2 dv_g \to |\nabla u|^2dv_g+\nu$, where $\nu = e(x)\,
H^{m-2}_S$ is an $m-2$ rectifiable measure \cite{lin_stat}. For a.e. $x\in
S=\operatorname{supp}(\nu)$ one can produce a finite number of bubble maps
$b_j:S^2\to N$ by blowing up the sequence $u_j$ near $x$.
  We prove the energy identity in this paper. Namely, we have at a.e. $x\in S$
that $e(x)=\sum_j E[b_j]$ for a complete set of such bubbles. That is, the
energy density of the defect measure $\nu$ is precisely the sum of the energies
of the bubbling maps.


  This paper regards the problem of optimally placing unreliable sensors in a
one-dimensional environment. We assume that sensors can fail with a certain
probability and we minimize the expected maximum distance from any point in the
environment to the closest active sensor. We provide a computational method to
find the optimal placement and we estimate the relative quality of equispaced
and random placements. We prove that the former is asymptotically equivalent to
the optimal placement when the number of sensors goes to infinity, with a cost
ratio converging to 1, while the cost of the latter remains strictly larger.


  In the present work, some MoS2 and WS2 nanosheets were prepared and
characterized. Depending on the preparation procedures, trigonal prismatic (2H)
or octahedral (1T) coordination of the metal atoms were obtained, exhibiting
metallic (1T) or semiconducting (2H) character. Both MoS2 and WS2 nanosheets
were found exhibiting large nonlinear optical (NLO) response, strongly
dependent on their metallic (1T) or semiconducting (2H) character. So, the
semiconducting character 2H-MoS2 and 2H-WS2 exhibit positive nonlinear
absorption and strong self-focusing, while their metallic character
counterparts exhibit strong negative nonlinear absorption and important
self-defocusing. In addition, the semiconducting MoS2 and WS2 were found
exhibiting important and very broadband optical limiting action extended from
450 to 1750 nm. So, by selecting the crystalline phase of the nanosheets, i.e.,
their semiconduction/metallic character, their NLO response can be greatly
modulated. The results of the present work demonstrate unambiguously that the
control of the crystalline phase of MoS2 and WS2 provides an efficient strategy
for 2D nanostructures with custom made NLO properties for specific
optoelectronic and photonic applications.


  Mutual Information (MI) plays an important role in representation learning.
However, MI is unfortunately intractable in continuous and high-dimensional
settings. Recent advances establish tractable and scalable MI estimators to
discover useful representation. However, most of the existing methods are not
capable of providing an accurate estimation of MI with low-variance when the MI
is large. We argue that directly estimating the gradients of MI is more
appealing for representation learning than estimating MI in itself. To this
end, we propose the Mutual Information Gradient Estimator (MIGE) for
representation learning based on the score estimation of implicit
distributions. MIGE exhibits a tight and smooth gradient estimation of MI in
the high-dimensional and large-MI settings. We expand the applications of MIGE
in both unsupervised learning of deep representations based on InfoMax and the
Information Bottleneck method. Experimental results have indicated significant
performance improvement in learning useful representation.


  We investigate Sobolev spaces $W^{1,\Phi}$ associated to Musielak-Orlicz
spaces $L^\Phi$. We first present conditions for the boundedness of the Voltera
operator in $L^\Phi$. Employing this, we provide necessary and sufficient
conditions for $W^{1,\Phi}$ to contain isomorphic subspaces to $\ell^\infty$ or
$\ell^1$. Further we give necessary and sufficient conditions in terms of the
function $\Phi$ or its complementary function $\Phi^*$ for reflexivity, uniform
convexity, $B$-convexity and superreflexivity of $W^{1,\Phi}$. As corollaries
we obtain the corresponding results for Orlicz-Sobolev spaces $W^{1,\varphi}$
where $\varphi$ is an Orlicz function, the variable exponent Sobolev spaces
$W^{1,p(\cdot)}$ and the Sobolev spaces associated to double phase functionals.


  When tasked with supporting multiple languages for a given problem, two
approaches have arisen: training a model for each language with the annotation
budget divided equally among them, and training on a high-resource language
followed by zero-shot transfer to the remaining languages. In this work, we
show that the strategy of joint learning across multiple languages using a
single model performs substantially better than the aforementioned
alternatives. We also demonstrate that active learning provides additional,
complementary benefits. We show that this simple approach enables the model to
be data efficient by allowing it to arbitrate its annotation budget to query
languages it is less certain on. We illustrate the effectiveness of our
proposed method on a diverse set of tasks: a classification task with 4
languages, a sequence tagging task with 4 languages and a dependency parsing
task with 5 languages. Our proposed method, whilst simple, substantially
outperforms the other viable alternatives for building a model in a
multilingual setting under constrained budgets.


  In this work, we define an orthogonal graph on the set of equivalence classes
of $(2\nu + \delta)-$tuples over $\mathbb{Z}_{2^n}$ where $n$ and $\nu$ are
positive integers and $\delta = 0, 1$ or $2$. We classify our graph if it is
strongly regular or quasi-strongly regular and compute all parameters
precisely. We show that our graph is arc transitive. The automorphisms group is
given and the chromatic number of the graph except when $\delta = 0$ and $\nu$
is odd is determined. Moreover, we work on subconstituents of this orthogonal
graph.


  This paper presents a theoretical description of diffusion growth of a gas
bubble after its nucleation in supersaturated liquid solution. We study systems
where gas molecules completely dissociate in the solvent into two parts, thus
making Sievert's solubility law valid. We show that the difference between
Henry's and Sievert's laws for chemical equilibrium conditions causes the
difference in bubble growth dynamics. Assuming that diffusion flux is steady we
obtain a differential equation on bubble radius. Bubble dynamics equation is
solved analytically for the case of homogeneous nucleation of a bubble, which
takes place at a significant pressure drop. We also obtain conditions of
diffusion flux steadiness. The fulfillment of these conditions is studied for
the case of nucleation of water vapor bubbles in magmatic melts.


  Engineering quantum states of light represents a crucial task in the vast
majority of photonic quantum technology applications. Direct manipulation of
the number of photons in the light signal, such as single-photon subtraction
and addition, proved to be an efficient strategy for the task. Here we propose
an adaptive multi-photon subtraction scheme where a particular subtraction task
is conditioned by all previous subtraction events in order to maximize the
probability of successful subtraction. We theoretically illustrate this
technique on the model example of conversion of Fock states via photon
subtraction. We also experimentally demonstrate the core building block of the
proposal by implementing a feedforward-assisted conversion of two-photon state
to a single-photon state. Our experiment combines two elementary photon
subtraction blocks where the splitting ratio of the second subtraction beam
splitter is affected by the measurement result from the first subtraction block
in real time using an ultra-fast feedforward loop. The reported optimized
photon subtraction scheme applies to a broad range of photonic states,
including highly nonclassical Fock states and squeezed light, advancing the
photonic quantum toolbox.


  A simulated annealing algorithm is employed to generate a stochastic model
for a Berea and a Fontainebleau sandstone with prescribed two-point probability
function, lineal path function, and ``pore size'' distribution function,
respectively. We find that the temperature decrease of the annealing has to be
rather quick to yield isotropic and percolating configurations. A comparison of
simple morphological quantities indicates good agreement between the
reconstructions and the original sandstones. Also, the mean survival time of a
random walker in the pore space is reproduced with good accuracy. However, a
more detailed investigation by means of local porosity theory shows that there
may be significant differences of the geometrical connectivity between the
reconstructed and the experimental samples.


  We examine the effects of low-temperature, or $\Delta$$n = 0$, dielectronic
recombination (DR) on the ionization balance of the Fe M-Shell (Fe IX through
Fe XVI). Since $\Delta$$n = 0$ rates are not available for these ions, we have
derived estimates based on the existing rates for the first four ionization
states of the CNO sequence and newly calculated rates for L-shell ions of 3rd
row elements and Fe. For a range of ionization parameter and column density
applicable to the intrinsic absorbers detected in {\it ASCA}, {\it Chandra},
and {\it XMM-Newton} observations of Seyfert galaxies, we generated two grids
of photoionization models, with and without DR. The results show that the
ionization parameter at which the population of an Fe M-shell ion peakscan
increase in some cases by factor $>$ 2 when these rates are included. More
importantly, there are dramatic changes in the range in ionization parameter
over which individual M-shell ions contain significant fractions of the total
Fe (e.g. $>$ 10%) in the plasma. These results may explain the mismatch between
the range of Fe ionization states detected in the X-ray spectra of Seyferts,
identified by the energies of the M-Shell Unresolved Transition Array, and
those predicted by photoionization models of the X-ray absorbers that reproduce
lines of second and third row elements. The results suggest that care should be
taken in using 3rd and 4th row ions to constrain the physical conditions in
photoionized X-ray plasmas until accurate DR rates are available. This
underscores the importance of atomic physics in interpreting astronomical
spectroscopy.


  The readout electronics upgrade for the ATLAS Liquid Argon Calorimeters at
the CERN Large Hadron Collider requires a radiation-hard ADC. The design of a
radiation-hard dual-channel 12-bit 40 MS/s pipeline ADC for this use is
presented. The design consists of two pipeline A/D channels each with four
Multiplying Digital-to-Analog Converters followed by 8-bit
Successive-Approximation-Register analog-to-digital converters. The custom
design, fabricated in a commercial 130 nm CMOS process, shows a performance of
67.9 dB SNDR at 10 MHz for a single channel at 40 MS/s, with a latency of 87.5
ns (to first bit read out), while its total power consumption is 50 mW/channel.
The chip uses two power supply voltages: 1.2 and 2.5 V. The sensitivity to
single event effects during irradiation is measured and determined to meet the
system requirements.


  This paper considers the generic problem of dense alignment between two
images, whether they be two frames of a video, two widely different views of a
scene, two paintings depicting similar content, etc. Whereas each such task is
typically addressed with a domain-specific solution, we show that a simple
unsupervised approach performs surprisingly well across a range of tasks. Our
main insight is that parametric and non-parametric alignment methods have
complementary strengths. We propose a two-stage process: first, a feature-based
parametric coarse alignment using one or more homographies, followed by
non-parametric fine pixel-wise alignment. Coarse alignment is performed using
RANSAC on off-the-shelf deep features. Fine alignment is learned in an
unsupervised way by a deep network which optimizes a standard structural
similarity metric (SSIM) between the two images, plus cycle-consistency.
Despite its simplicity, our method shows competitive results on a range of
tasks and datasets, including unsupervised optical flow on KITTI, dense
correspondences on Hpatches, two-view geometry estimation on YFCC100M,
localization on Aachen Day-Night, and, for the first time, fine alignment of
artworks on the Brughel dataset. Our code and data are available at
http://imagine.enpc.fr/~shenx/RANSAC-Flow/


  The shuffle mode, where songs are played in a randomized order that is
decided upon for all tracks at once, is widely found and known to exist in
music player systems. There are only few music enthusiasts who use this mode
since it either is too random to suit their mood or it keeps on repeating the
same list every time. In this paper, we propose to build a convolutional deep
belief network(CDBN) that is trained to perform genre recognition based on
audio features retrieved from the records of the Million Song Dataset. The
learned parameters shall be used to initialize a multi-layer perceptron which
takes extracted features of user's playlist as input alongside the metadata to
classify to various categories. These categories will be shuffled
retrospectively based on the metadata to autonomously provide with a list that
is efficacious in playing songs that are desired by humans in normal
conditions.


  Atomically thin two-dimensional layer of honeycomb crystalline carbon known
as graphene is a promising system for electronics. It has a point-like Fermi
surface, which is very sensitive to external potentials. In particular, Zeeman
magnetic field parallel to the graphene layer splits electron bands and creates
fully spin-polarized and geometrically congruent circular Fermi surfaces of
particle and hole type. In the presence of electric field, particles and holes
with opposite spins drift in opposite direction. These phenomena are likely to
be of interest for developing graphene-based spintronic devices. A domain wall
(DW) separating regions with opposite spin polarizations is a basic element of
such a device. Here we consider a ballistic passage of spin-polarized charge
carriers through DW in graphene. We also discuss the analogy between the
generation of spin currents in graphene and in relativistic quark-gluon plasma,
where the spin-polarized current is responsible for the phenomenon of charge
separation studied recently at RHIC.


  The ideas presented in this proceeding aims to be a first step towards a
description of hadronic collisions where all soft processes are fundamentally
strongly coupled and the same Universal strongly coupled physics drives both
initial and final-state interactions. As it is not currently possible to derive
such a picture from first principles, instead, an attempt to generalize the
perfect liquid observation to a ``perfect QCD'' guiding principle is presented,
focusing on implications for particle production in small systems. The first
steps towards a microscopic model is taken by arguing that ``perfect QCD''
suggests that the screening in the initial state is so large that multi-parton
interactions are of little or no importance. Instead, a target and projectile
remnant is coherently excited and particle production is mainly driven by
radiation in a qualitative similar manner as $e^+e^- \rightarrow q\bar{q}$.
Finally, some of the possible implications of this ``excited remnant model''
are presented. It is argued that the time ordering of soft and hard physics can
explain the absence of jet quenching in small systems and that the coherence
scale of the projectile and target provides insights into what small systems
will exhibit flow.


  We studied the $ep\rightarrow ep+2jets$ diffractive cross section with ZEUS
phase space. Neglecting the $t$-channel momentum in the Born and gluon dipole
impact factors, we calculated the corresponding contributions to the cross
section differential in $\beta=\frac{Q^{2}}{Q^{2}+M_{2jets}^{2}}$ and the angle
$\phi$ between the leptonic and hadronic planes. The gluon dipole contribution
was obtained in the exclusive $k_{t}$-algorithm with the exclusive cut
$y_{cut}=0.15$ in the small $y_{cut}$ approximation. In the collinear
approximation we canceled singularities between real and virtual contributions
to the $q\bar{q}$ dipole configuration, keeping the exact $y_{cut}$ dependency.
We used the Golec-Biernat - W\"usthoff (GBW) parametrization for the dipole
matrix element and linearized the double dipole contributions. The results give
roughly $\frac{1}{2}$ of the observed cross section for small $\beta$ and
coincides with it for large $\beta.$


  Defining the density flow of perturbations moving at a given speed for
cellular automata, we establish equalities and inequalities between the
measurable entropy of a cellular automaton and the measurable entropy of its
associated shift.


  Multisplit is a broadly useful parallel primitive that permutes its input
data into contiguous buckets or bins, where the function that categorizes an
element into a bucket is provided by the programmer. Due to the lack of an
efficient multisplit on GPUs, programmers often choose to implement multisplit
with a sort. One way is to first generate an auxiliary array of bucket IDs and
then sort input data based on it. In case smaller indexed buckets possess
smaller valued keys, another way for multisplit is to directly sort input data.
Both methods are inefficient and require more work than necessary: the former
requires more expensive data movements while the latter spends unnecessary
effort in sorting elements within each bucket. In this work, we provide a
parallel model and multiple implementations for the multisplit problem. Our
principal focus is multisplit for a small (up to 256) number of buckets. We use
warp-synchronous programming models and emphasize warp-wide communications to
avoid branch divergence and reduce memory usage. We also hierarchically reorder
input elements to achieve better coalescing of global memory accesses. On a
GeForce GTX 1080 GPU, we can reach a peak throughput of 18.93 Gkeys/s (or 11.68
Gpairs/s) for a key-only (or key-value) multisplit. Finally, we demonstrate how
multisplit can be used as a building block for radix sort. In our
multisplit-based sort implementation, we achieve comparable performance to the
fastest GPU sort routines, sorting 32-bit keys (and key-value pairs) with a
throughput of 3.0 G keys/s (and 2.1 Gpair/s).


  In this paper, using definability of types over indiscernible sequences as a
template, we study a property of formulas and theories called "uniform
definability of types over finite sets" (UDTFS). We explore UDTFS and show how
it relates to well-known properties in model theory. We recall that stable
theories and weakly o-minimal theories have UDTFS and UDTFS implies dependence.
We then show that all dp-minimal theories have UDTFS.


  In this paper, we investigate whether text from a Community Question
Answering (QA) platform can be used to predict and describe real-world
attributes. We experiment with predicting a wide range of 62 demographic
attributes for neighbourhoods of London. We use the text from QA platform of
Yahoo! Answers and compare our results to the ones obtained from Twitter
microblogs. Outcomes show that the correlation between the predicted
demographic attributes using text from Yahoo! Answers discussions and the
observed demographic attributes can reach an average Pearson correlation
coefficient of \r{ho} = 0.54, slightly higher than the predictions obtained
using Twitter data. Our qualitative analysis indicates that there is semantic
relatedness between the highest correlated terms extracted from both datasets
and their relative demographic attributes. Furthermore, the correlations
highlight the different natures of the information contained in Yahoo! Answers
and Twitter. While the former seems to offer a more encyclopedic content, the
latter provides information related to the current sociocultural aspects or
phenomena.


  Models of the accretion disks of Young Stellar Objects show that they should
not be ionized at a few AU from the star, and thus not subject to the MHD
turbulence believed to cause accretion. This has been suggested to create a
'Dead Zone' where accretion remains unexplained. Here we show that the
existence of the Dead Zone self-consistently creates a density profile
favorable to the Rossby Wave Instability of Lovelace et al. (1999). This
instability will create and sustain Rossby vortices in the disk which could
lead to enhanced planet formation.


  Using a recently developed quantization of spherically symmetric gravity
coupled to a scalar field, we give a construction of null expansion operators
that allow a definition of general, fully dynamical quantum black holes. These
operators capture the intuitive idea that classical black holes are defined by
the presence of trapped surfaces, that is surfaces from which light cannot
escape outward. They thus provide a mechanism for classifying quantum states of
the system into those that describe quantum black holes and those that do not.
We find that quantum horizons fluctuate, confirming long-held heuristic
expectations. We also give explicit examples of quantum black hole states. The
work sets a framework for addressing the puzzles of black hole physics in a
fully quantized dynamical setting.


  The calcium-silicate-hydrate is used to model properties of cement on Earth.
We study cementitious nanoparticles and propose these structures as components
of cosmic dust grains. Quantum density functional theory methods are applied
for the calculation of infrared spectra of Ca4Si4O14H4, Ca6Si3O13H2, and
Ca12Si6O26H4 clusters. We find bands distributed over the near, mid and
far-infrared region. A specific calcium-silicate-hydrate spectral feature at 14
microns, together with the bands at 10 and 18 microns which exist for other
silicates as well, could be used for a detection of cosmic cement. We compare
calculated bands with the 14 microns features in the spectra of HD 45677, HD
44179, and IRC+10420 which were observed by Infrared Space Observatory and
classified as remaining. High abundance of oxygen atoms in cementitious
nanoparticles could partially explain observed depletion of this element from
the interstellar medium into dust grains.


  Categorical aspects of the theory of modules over trusses are studied. Tensor
product of modules over trusses is defined and its existence established. In
particular, it is shown that bimodules over trusses form a monoidal category.
Truss versions of the Eilenberg-Watts theorem and Morita equivalence are
formulated. Projective and small-projective modules over trusses are defined
and their properties studied.


  In this report, we describe the proximity effect which arises when a
quasicrystal is placed in contact with a superconductor. We consider the
simplest known model of a quasicrystal, the 1D Fibonacci chain, for which all
states are known to be critical. A hybrid ring is made by connecting a finite
piece of such a Fibonacci chain to a BCS-type superconductor. Solving the
resulting Bogoliubov-de Gennes equations self-consistently, we show that the
proximity effect in the Fibonacci chain is long ranged, and that the induced
superconducting order carries information on topological properties, namely,
the winding numbers of edge states of the Fibonacci chain.


  In this work we have investigated the orthorhombic to tetragonal phase
transition in the Ba2Cu3O4Cl2 compound. This transition was observed by X-ray
powder diffractometry carried out in samples heat treated between 700 and 750OC
and also in samples with Ba2ZnCu2O4Cl2 composition. Results of X-ray
diffractograms simulation confirm the phase transition. dc-Magnetization
measurements performed in SQUID showed the existence of diamagnetism signal.
The results suggest the existence of localized superconductivity and can
explain the different magnetic properties reported in literature for the
Ba2Cu3O4Cl2 compound.


  We study the distribution of large prime factors of a random element $u$ of
arithmetic sequences satisfying simple regularity and equidistribution
properties. We show that if such an arithmetic sequence has level of
distribution $1$ the large prime factors of $u$ tend to a Poisson-Dirichlet
process, while if the sequence has any positive level of distribution the
correlation functions of large prime factors tend to a Poisson-Dirichlet
process against test functions of restricted support. For sequences with
positive level of distribution, we also estimate the probability the largest
prime factor of $u$ is greater than $u^{1-\epsilon}$, showing that this
probability is $O(\epsilon)$.
  Examples of sequences described include shifted primes and values of
single-variable irreducible polynomials.
  The proofs involve (i) a characterization of the Poisson-Dirichlet process
due to Arratia-Kochman-Miller and (ii) an upper bound sieve.


  We study the flavor dependent $U(1)_{B_i-L_j}$ models, where an $i$th
generation of quarks and $j(\neq i)$th generation of leptons are charged. By
solving the anomaly free condition for the matter sector of the SM fermions and
three generations of right-handed (RH) neutrinos, we find that the $j$th
generation of RH neutrino is not necessarily charged under the $U(1)_{B_i-L_j}$
gauge symmetry with the charge $-1$ and the other (neither $i$th nor $j$th)
generation of RH neutrino can also be. As a general solution for the anomaly
cancellation conditions, the other two RN neutrinos than the charge $-1$ RH
neutrino may have non-vanishing charge and be stable due to the gauge
invariance, and hence it is a candidate for dark matter (DM) in our Universe.
We apply this result to a $B_3-L_2$ model and consider a light thermal DM and a
solution to the muon $g-2$ anomaly. We identify the parameter region to have
the DM mass range from MeV to sub-GeV and simultaneously solve the muon $g-2$
anomaly. We also derive the constraints on the gauge kinetic mixing parameter
by using the latest Borexino phase-II data.


  Path planning is critical for autonomous vehicles (AVs) to determine the
optimal route while considering constraints and objectives. The potential field
(PF) approach has become prevalent in path planning due to its simple structure
and computational efficiency. However, current PF methods used in AVs focus
solely on the path generation of the ego vehicle while assuming that the
surrounding obstacle vehicles drive at a preset behavior without the PF-based
path planner, which ignores the fact that the ego vehicle's PF could also
impact the path generation of the obstacle vehicles. To tackle this problem, we
propose a PF-based path planning approach where local paths are shared among
ego and obstacle vehicles via vehicle-to-vehicle (V2V) communication. Then by
integrating this shared local path into an objective function, a new
optimization function called interactive speed optimization (ISO) is designed
to allow driving safety and comfort for both ego and obstacle vehicles. The
proposed method is evaluated using MATLAB/Simulink in the urgent merging
scenarios by comparing it with conventional methods. The simulation results
indicate that the proposed method can mitigate the impact of other AVs' PFs by
slowing down in advance, effectively reducing the oscillations for both ego and
obstacle AVs.


  Equistable graphs are graphs admitting positive weights on vertices such that
a subset of vertices is a maximal stable set if and only if it is of total
weight $1$. In $1994$, Mahadev et al.~introduced a subclass of equistable
graphs, called strongly equistable graphs, as graphs such that for every $c \le
1$ and every non-empty subset $T$ of vertices that is not a maximal stable set,
there exist positive vertex weights such that every maximal stable set is of
total weight $1$ and the total weight of $T$ does not equal $c$. Mahadev et al.
conjectured that every equistable graph is strongly equistable. General
partition graphs are the intersection graphs of set systems over a finite
ground set $U$ such that every maximal stable set of the graph corresponds to a
partition of $U$. In $2009$, Orlin proved that every general partition graph is
equistable, and conjectured that the converse holds as well.
  Orlin's conjecture, if true, would imply the conjecture due to Mahadev,
Peled, and Sun. An intermediate conjecture, one that would follow from Orlin's
conjecture and would imply the conjecture by Mahadev, Peled, and Sun, was posed
by Miklavi\v{c} and Milani\v{c} in $2011$, and states that every equistable
graph has a clique intersecting all maximal stable sets. The above conjectures
have been verified for several graph classes. We introduce the notion of
equistarable graphs and based on it construct counterexamples to all three
conjectures within the class of complements of line graphs of triangle-free
graphs.


  Type U radio bursts are impulsive coherent radio emissions produced by the
Sun that indicate the presence of subrelativistic electron beams propagating
along magnetic loops in the solar corona. In this work, we present the analysis
of a type U radio burst that was exceptionally imaged on 2011 March 22 by the
Nan\c{c}ay Radioheliograph (NRH) at three different frequencies (298.7, 327.0,
and 360.8 MHz). Using a novel modelling approach, we show for the first time
that the use of high-resolution radio heliograph images of type U radio bursts
can be sufficient to both accurately reconstruct the 3D morphology of coronal
loops (without recurring to triangulation techniques) and to fully constrain
their physical parameters. At the same time, we can obtain unique information
on the dynamics of the accelerated electron beams, which provides important
clues as to the plasma mechanisms involved in their acceleration and as to why
type U radio bursts are not observed as frequently as type III radio bursts. We
finally present plausible explanations for a problematic aspect related to the
apparent lack of association between the modeled loop as inferred from radio
images and the extreme-ultraviolet (EUV) structures observed from space in the
same coronal region


  The accurate detection of lesion attributes is meaningful for both the
computeraid diagnosis system and dermatologists decisions. However, unlike
lesion segmentation and melenoma classification, there are few deep learning
methods and literatures focusing on this task. Currently, the lesion attribute
detection still remains challenging due to the extremely unbalanced class
distribution and insufficient samples, as well as large intraclass and low
interclass variations. To solve these problems, we propose a deep learning
framework named superpixel attention network (SANet). Firstly, we segment input
images into small regions and shuffle the obtained regions by the random
shuttle mechanism (RSM). Secondly, we apply the SANet to capture discriminative
features and reconstruct input images. Specifically, SANet contains two sub
modules: superpixel average pooling and superpixel at tention module. We
introduce a superpixel average pooling to reformulate the superpixel
classification problem as a superpixel segmentation problem and a SAMis
utilized to focus on discriminative superpixel regions and feature channels.
Finally, we design a novel but effective loss, namely global balancing loss to
address the serious data imbalance in ISIC 2018 Task 2 lesion attributes
detection dataset. The proposed method achieves quite good performance on the
ISIC 2018 Task 2 challenge.


  Modern machine learning methods often require more data for training than a
single expert can provide. Therefore, it has become a standard procedure to
collect data from external sources, e.g. via crowdsourcing. Unfortunately, the
quality of these sources is not always guaranteed. As additional complications,
the data might be stored in a distributed way, or might even have to remain
private. In this work, we address the question of how to learn robustly in such
scenarios. Studying the problem through the lens of statistical learning
theory, we derive a procedure that allows for learning from all available
sources, yet automatically suppresses irrelevant or corrupted data. We show by
extensive experiments that our method provides significant improvements over
alternative approaches from robust statistics and distributed optimization.


  We consider retarded settings in the context of a Bell-type experiment. The
retarded setting is defined as the value the setting would have taken were it
not for some external intervention (for example, by a human). We derive
retarded Bell inequalities that explicitly take into account the retarded
settings. These inequalities are not violated by Quantum Theory (or any other
theory) when the retarded settings are equal to the actual settings. We
construct a simple model that reproduces Quantum Theory when the retarded and
actual settings are equal, but violates it when they are not. We discuss using
humans to choose the settings in this type of experiment and the implications
of a violation of Quantum Theory (in agreement with the retarded Bell
inequalities) in this context.


  The prosperous development of both hardware and algorithms for quantum
computing (QC) potentially prompts a paradigm shift in scientific computing in
various fields. As an increasingly active topic in QC, the variational quantum
algorithm (VQA) leads a promising direction for solving partial differential
equations on Noisy Intermediate Scale Quantum (NISQ) devices. Although a clear
perspective on the advantages of QC over classical computing techniques for
specific mathematical and physical problems exists, applications of QC in
computational fluid dynamics to solve practical flow problems, though
promising, are still in an early stage of development. To explore QC in
practical simulation of flow problems, this work applies a variational hybrid
quantum-classical algorithm, namely the variational quantum linear solver
(VQLS), to resolve the heat conduction equation through finite difference
discretization of the Laplacian operator. Details of VQLS implementation are
discussed by various test instances of linear systems. Finally, the successful
statevector simulations of the heat conduction equation in one and two
dimensions demonstrate the validity of the present algorithm by
proof-of-concept results. In addition, the heuristic scaling for the heat
conduction problem indicates that the time complexity of the present approach
is logarithmically dependent on the precision {\epsilon} and linearly dependent
on the number of qubits n.


  Online volunteers are a crucial labor force that keeps many for-profit
systems afloat (e.g. social media platforms and online review sites). Despite
their substantial role in upholding highly valuable technological systems,
online volunteers have no way of knowing the value of their work. This paper
uses content moderation as a case study and measures its monetary value to make
apparent volunteer labor's value. Using a novel dataset of private logs
generated by moderators, we use linear mixed-effect regression and estimate
that Reddit moderators worked a minimum of 466 hours per day in 2020. These
hours amount to 3.4 million USD a year based on the median hourly wage for
comparable content moderation services in the U.S. We discuss how this
information may inform pathways to alleviate the one-sided relationship between
technology companies and online volunteers.


  In this paper we consider routing in random wireless-adhoc-networks (WANETs),
where each node is equipped with a single antenna. Our analysis uses a proper
model of the physical layer together with an abstraction of higher
communication layers. We assume that the nodes are distributed according to a
Poisson-point-process and consider routing schemes that select the next relay
based on the geographical locations, the channel gains of its neighbor nodes
and the statistical characterization of all other nodes. While many routing
problems are formulated as optimization problems, the optimal distributed
solution is rarely accessible. In this work, we present the exact optimal
solution for the scenario analyzed. The optimal routing is given as a
maximization of a routing metric which depends solely on the known partial
channel state information (CSI) and includes an expectation with respect to the
interference statistics. The optimal routing scheme is important because it
gives an upper bound on the performance of any other routing scheme. We also
present sub-optimal routing schemes that only use part of the available
knowledge and require much lower computational complexity. Numerical results
demonstrate that the performance of the low complexity schemes is close to
optimal and outperforms other tested routing schemes.


  Interference of standing waves in electromagnetic resonators forms the basis
of many technologies, from telecommunications and spectroscopy to detection of
gravitational waves. However, unlike the confinement of light waves in vacuum,
the interference of electronic waves in solids is complicated by boundary
properties of the crystal, notably leading to electron guiding by atomic-scale
potentials at the edges. Understanding the microscopic role of boundaries on
coherent wave interference is an unresolved question due to the challenge of
detecting charge flow with submicron resolution. Here we employ Fraunhofer
interferometry to achieve real-space imaging of cavity modes in a graphene
Fabry-Perot resonator, embedded between two superconductors to form a Josephson
junction. By directly visualizing current flow using Fourier methods, our
measurements reveal surprising redistribution of current on and off resonance.
These findings provide direct evidence of separate interference conditions for
edge and bulk currents and reveal the ballistic nature of guided edge states.
Beyond equilibrium, our measurements show strong modulation of the multiple
Andreev reflection amplitude on an off resonance, a direct measure of the
gate-tunable change of cavity transparency. These results demonstrate that,
contrary to the common belief, electron interactions with realistic disordered
edges facilitate electron wave interference and ballistic transport.


  We have performed a principal component analysis on the X-ray spectra of the
microquasar Cygnus X-3 from RXTE, INTEGRAL and Swift during a major flare
ejection event in 2006 May-July. The analysis showed that there are two main
variability components in play, i.e. two principal components explained almost
all the variability in the X-ray lightcurves. According to the spectral shape
of these components and spectral fits to the original data, the most probable
emission components corresponding to the principal components are
inverse-Compton scattering and bremsstrahlung. We find that these components
form a double-peaked profile when phase-folded with the peaks occurring in
opposite phases. This could be due to an asymmetrical wind around the companion
star with which the compact object is interacting.


  In Generalized Few-shot Segmentation (GFSS), a model is trained with a large
corpus of base class samples and then adapted on limited samples of novel
classes. This paper focuses on the relevance between base and novel classes,
and improves GFSS in two aspects: 1) mining the similarity between base and
novel classes to promote the learning of novel classes, and 2) mitigating the
class imbalance issue caused by the volume difference between the support set
and the training set. Specifically, we first propose a similarity transition
matrix to guide the learning of novel classes with base class knowledge. Then,
we leverage the Label-Distribution-Aware Margin (LDAM) loss and Transductive
Inference to the GFSS task to address the problem of class imbalance as well as
overfitting the support set. In addition, by extending the probability
transition matrix, the proposed method can mitigate the catastrophic forgetting
of base classes when learning novel classes. With a simple training phase, our
proposed method can be applied to any segmentation network trained on base
classes. We validated our methods on the adapted version of OpenEarthMap.
Compared to existing GFSS baselines, our method excels them all from 3% to 7%
and ranks second in the OpenEarthMap Land Cover Mapping Few-Shot Challenge at
the completion of this paper. Code:
https://github.com/earth-insights/ClassTrans


  Using a dark matter only Constrained Local UniversE Simulation (CLUES) we
examine the existence of subhaloes that change their affiliation from one of
the two prominent hosts in the Local Group (i.e. the Milky Way and the
Andromeda galaxy) to the other, and call these objects "renegade subhaloes". In
light of recent claims that the two Magellanic Clouds (MCs) may have originated
from another region (or even the outskirts) of the Local Group or that they
have been spawned by a major merger in the past of the Andromeda galaxy, we
investigate the nature of such events. However, we cannot confirm that renegade
subhaloes enter as deep into the potential well of their present host nor that
they share the most simplest properties with the MCs, namely mass and relative
velocity. Our simulation rather suggests that these renegade subhaloes appear
to be flying past one host before being pulled into the other. A merger is not
required to trigger such an event, it is rather the distinct environment of our
simulated Local Group facilitating such behavior. Since just a small fraction
of the full z=0 subhalo population are renegades, our study indicates that it
will be intrinsically difficult to distinguish them despite clear differences
in their velocity, radial distribution, shape and spin parameter distributions.


  It is well known that a charged particle cannot be in stable equilibrium in a
purely electrostatic field. The situation is different in a magnetostatic
field; consequently, magnetic levitation is possible while electrostatic
levitation is not. In this paper, motivated by an analogy with a mechanical
system, we show that the addition of a small oscillating electrical field to an
otherwise electrostatic configuration leads to the stabilisation of unstable
equilibrium points. Therefore, levitation becomes possible in an "almost
electrostatic" field.


  The generation of very narrow linewidth light sources is of great importance
in modern science. One such source is the superradiant laser, which relies on
collectively interacting ultra long lived dipoles driven by incoherent light.
Here we discuss a different way of generating spectrally pure light by
coherently driving such dipoles inside an optical QED cavity. The light exiting
the cavity carries information about the detuning between the driving light and
the atomic transition, but is also affected by the noise originating from all
the decoherence processes that act on the combined atom-cavity system. We
calculate these effects to obtain fundamental limits for frequency estimation
and stabilization across a range of values of input light intensities and
atom-light interaction strengths, estimate these limits in state-of-the-art
cavity experiments with alkaline-earth atoms and identify favorable operating
conditions. We find that the achievable linewidths are comparable to those of
the superradiant laser.


  We propose a hybrid architecture for systematically computing robust visual
explanation(s) encompassing hypothesis formation, belief revision, and default
reasoning with video data. The architecture consists of two tightly integrated
synergistic components: (1) (functional) answer set programming based abductive
reasoning with space-time tracklets as native entities; and (2) a visual
processing pipeline for detection based object tracking and motion analysis.
  We present the formal framework, its general implementation as a
(declarative) method in answer set programming, and an example application and
evaluation based on two diverse video datasets: the MOTChallenge benchmark
developed by the vision community, and a recently developed Movie Dataset.


  Let F be a non-archimedian local field of characteristic 0, and O the ring of
integres in F. We give an explicit formula for the Siegel series of a
half-integral matrix over O. This formula expresses the Siegel series of a
half-integral matrix $B$ explicitly in terms of the Gross-Keating invariant of
$B$ and its related invariants.


  We have conducted a highly precise doping controlled experiment on a thin
film of the single layer cuprate Bi2Sr2-xLaxCuOy (x = 0.6), in order to observe
the superconducting insulating transition (SIT). Sr2+/La3+ substitution (x =
0.6) allowed us to start from a doping state in the vicinity of the SIT, which
was further finely-tuned by varying the oxygen content in very small amounts
through a vacuum anneal process. Measurements of the Hall effect at 300K and of
the resistance vs. T, R(T), have been performed after each treatment.
Approaching the SIT from the metallic side, and with decreasing T, R(T)
exhibits a high T metallic behaviour down to a temperature Tmin, followed by a
non metallic increase (dR/dT< 0) up to a maximum at Tp before the
superconducting transition at Tc. This re-entrant behaviour in R(T), commonly
observed in cuprates close to the SIT, is attributed to a phase segregation
phenomenon in the presence of strong electronic correlations and
inhomogeneities. We present our results extracted from R(T) and Hall effect
studies in the region close to the SIT and in the insulating region. A phase
diagram shows the characteristic temperatures versus doping.


  The labels in medical diagnosis task are usually discrete and successively
distributed. For example, the Diabetic Retinopathy Diagnosis (DR) involves five
health risk levels: no DR (0), mild DR (1), moderate DR (2), severe DR (3) and
proliferative DR (4). This labeling system is common for medical disease.
Previous methods usually construct a multi-binary-classification task or
propose some re-parameter schemes in the output unit. In this paper, we target
on this task from the perspective of loss function. More specifically, the
Wasserstein distance is utilized as an alternative, explicitly incorporating
the inter-class correlations by pre-defining its ground metric. Then, the
ground metric which serves as a linear, convex or concave increasing function
w.r.t. the Euclidean distance in a line is explored from an optimization
perspective. Meanwhile, this paper also proposes of constructing the smoothed
target labels that model the inlier and outlier noises by using a
unimodal-uniform mixture distribution. Different from the one-hot setting, the
smoothed label endues the computation of Wasserstein distance with more
challenging features. With either one-hot or smoothed target label, this paper
systematically concludes the practical closed-form solution. We evaluate our
method on several medical diagnosis tasks (e.g., Diabetic Retinopathy and
Ultrasound Breast dataset) and achieve state-of-the-art performance.


  Big-bang nucleosynthesis (BBN) describes the production of the lightest
nuclides via a dynamic interplay among the four fundamental forces during the
first seconds of cosmic time. We briefly overview the essentials of this
physics, and present new calculations of light element abundances through li6
and li7, with updated nuclear reactions and uncertainties including those in
the neutron lifetime. We provide fits to these results as a function of baryon
density and of the number of neutrino flavors, N_nu. We review recent
developments in BBN, particularly new, precision Planck cosmic microwave
background (CMB) measurements that now probe the baryon density, helium
content, and the effective number of degrees of freedom, n_eff. These
measurements allow for a tight test of BBN and of cosmology using CMB data
alone. Our likelihood analysis convolves the 2015 Planck data chains with our
BBN output and observational data. Adding astronomical measurements of light
elements strengthens the power of BBN. We include a new determination of the
primordial helium abundance in our likelihood analysis. New D/H observations
are now more precise than the corresponding theoretical predictions, and are
consistent with the Standard Model and the Planck baryon density. Moreover, D/H
now provides a tight measurement of N_nu when combined with the CMB baryon
density, and provides a 2sigma upper limit N_nu < 3.2. The new precision of the
CMB and of D/H observations together leave D/H predictions as the largest
source of uncertainties. Future improvement in BBN calculations will therefore
rely on improved nuclear cross section data. In contrast with D/H and he4, li7
predictions continue to disagree with observations, perhaps pointing to new
physics.


  Current approaches to text generation largely rely on autoregressive models
and maximum likelihood estimation. This paradigm leads to (i) diverse but
low-quality samples due to mismatched learning objective and evaluation metric
(likelihood vs. quality) and (ii) exposure bias due to mismatched history
distributions (gold vs. model-generated). To alleviate these problems, we frame
text generation as an offline reinforcement learning (RL) problem with expert
demonstrations (i.e., the reference), where the goal is to maximize quality
given model-generated histories. We propose GOLD (generation by off-policy
learning from demonstrations): an easy-to-optimize algorithm that learns from
the demonstrations by importance weighting. Intuitively, GOLD upweights
confident tokens and downweights unconfident ones in the reference during
training, avoiding optimization issues faced by prior RL approaches that rely
on online data collection. According to both automatic and human evaluation,
models trained by GOLD outperform those trained by MLE and policy gradient on
summarization, question generation, and machine translation. Further, our
models are less sensitive to decoding algorithms and alleviate exposure bias.


  We present a lattice QCD study of the neutrinoless double beta decay
involving light sterile neutrinos. The calculation is performed at physical
pion mass using five gauge ensembles generated with the $2+1$-flavor domain
wall fermions. We obtain the low-energy constants
$g_{\text{LR}}^{\pi\pi}(m_\nu)$ with the neutrino mass $m_\nu$ from $0$ GeV to
$3$ GeV. The lattice results are reasonably consistent with the previous
interpolation method with a $\sim20\%$ deviation at small $m_\nu$. We provide
an explanation on the discrepancy at vanishing neutrino mass. At large $m_\nu$,
a good consistence between our results and the previous lattice determination
of $g_{4}^{\pi\pi}(\mu)$ is found at $\mu=m_\nu=3$ GeV.


  We analyze two volume limited galaxy samples from the SDSS photometric and
spectroscopic data to test the isotropy in the local Universe. We use
information entropy to quantify the global anisotropy in the galaxy
distribution at different length scales and find that the galaxy distribution
is highly anisotropic on small scales. The observed anisotropy diminishes with
increasing length scales and nearly plateaus out beyond a length scale of 200
Mpc/h in both the datasets. We compare these anisotropies with those predicted
by the mock catalogues from the N-body simulations of the Lambda CDM model and
find a fairly good agreement with the observations. We find a small residual
anisotropy on large scales which decays in a way that is consistent with the
linear perturbation theory. The slopes of the observed anisotropy converge to
the slopes predicted by the linear theory beyond a length scale of ~ 200 Mpc/h
indicating a transition to isotropy. We separately compare the anisotropies
observed across the different parts of the sky and find no evidence for a
preferred direction in the galaxy distribution.


  The decay of $\Lambda_c^+$ into $\pi^+\pi^0\Lambda(1405)$ with the
$\Lambda(1405)$ decay into $\pi^0\Sigma^0$ through a triangle diagram is
studied. This process is initiated by $ \Lambda_c^+ \to \pi^+ \bar{K}^*N $,
then the $\bar{K}^*$ decays into $\bar{K} \pi$ and $\bar{K} N$ produce the
$\Lambda(1405)$ through a triangle loop containing $\bar{K}^*N\bar{K}$ which
develops a singularity around $1890$ MeV. This process is prohibited by the
isospin symmetry, but the decay into this channel is enhanced by the
contribution of the triangle diagram, which is sensitive to the mass of the
internal particles. We find a narrow peak in the $\pi^0\Sigma^0$ invariant mass
distribution, which originates from the $\Lambda(1405)$ amplitude, but is tied
to the mass differences between the charged and neutral $\bar{K}$ or $N$
states. The observation of the unavoidable peak of the triangle singularity in
the isospin-violating $\Lambda(1405)$ production would provide further support
for hadronic molecular picture of the $\Lambda(1405)$ and further information
on the $\bar{K} N $ interaction.


  We define a new family of commuting operators $F_k$ in Khovanov-Rozansky link
homology, similar to the action of tautological classes in cohomology of
character varieties. We prove that $F_2$ satisfies ``hard Lefshetz property"
and hence exhibits the symmetry in Khovanov-Rozansky homology conjectured by
Dunfield, Gukov and Rasmussen.


  We give a new and very intuitive construction of Hyodo--Kato cohomology and
the Hyodo--Kato map, based on logarithmic rigid cohomology. We show that it is
independent of the choice of a uniformiser and study its dependence on the
choice of a branch of the $p$-adic logarithm. Moreover, we show the
compatibility with the classical construction of Hyodo--Kato cohomology and the
Hyodo--Kato map.)


  The recent discovery of superconductivity in infinite-layer nickelates has
drawn considerable attention; however, a consensus on the fundamental building
blocks and common ingredients necessary to understand and describe their ground
states and emergent properties is lacking. A series of experimental and
theoretical studies have suggested that an effective two-band Hubbard model
with Ni 3$d_{x^2-y^2}$ and rare-earth ($R$) 5$d$ character may describe the
low-energy physics. Here, we study the ground state properties of this two-band
model on four-leg cylinders using the density-matrix renormalization group
(DMRG) technique to better grasp whether such a simple model can embody the
essential physics. A key difference compared to single-band Hubbard materials
is that the system is self-doped: even at overall half-filling, the $R$-band
acts as an electron reservoir, hole-doping the Ni-layer and fundamentally
altering the physics expected from an undoped antiferromagnet. On the four-leg
cylinder, the ground state is consistent with a Luttinger liquid, with
anti-phase modulations of the charge density in the Ni- and $R$-layers having
corresponding wavevectors that lock together. Light hole doping away from 1/2
filling releases the locking between the Ni and the $R$ charge modulations, as
the electron density in the $R$-band decreases and eventually becomes exhausted
at a hole doping concentration that depends sensitively on the effective
splitting between the Ni and the $R$ orbitals. The ground state of the doped
system is consistent with a Luther-Emery liquid, possessing quasi-long-range
superconducting correlations in the Ni layer, similar to the single-band
Hubbard model. Our results are consistent with experimental observations and
may help to reveal the microscopic mechanism for pairing and other emergent
properties.


  Recent proofs of the convergence of the linear delta expansion in zero and in
one dimensions have been limited to the analogue of the vacuum generating
functional in field theory. In zero dimensions it was shown that with an
appropriate, $N$-dependent, choice of an optimizing parameter $\l$, which is an
important feature of the method, the sequence of approximants $Z_N$ tends to
$Z$ with an error proportional to ${\rm e}^{-cN}$. In the present paper we
establish the convergence of the linear delta expansion for the connected
vacuum function $W=\ln Z$. We show that with the same choice of $\l$ the
corresponding sequence $W_N$ tends to $W$ with an error proportional to ${\rm
e}^{-c\sqrt N}$. The rate of convergence of the latter sequence is governed by
the positions of the zeros of $Z_N$.


  Derived variables are variables that are constructed from one or more source
variables through established mathematical operations or algorithms. For
example, body mass index (BMI) is a derived variable constructed from two
source variables: weight and height. When using a derived variable as the
outcome in a statistical model, complications arise when some of the source
variables have missing values. In this paper, we propose how one can define a
single fully Bayesian model to simultaneously impute missing values and sample
from the posterior. We compare our proposed method with alternative approaches
that rely on multiple imputation, and, with a simulated dataset, consider how
best to estimate the risk of microcephaly in newborns exposed to the ZIKA
virus.


  Machine learning methods such as deep neural networks (DNNs), despite their
success across different domains, are known to often generate incorrect
predictions with high confidence on inputs outside their training distribution.
The deployment of DNNs in safety-critical domains requires detection of
out-of-distribution (OOD) data so that DNNs can abstain from making predictions
on those. A number of methods have been recently developed for OOD detection,
but there is still room for improvement. We propose the new method iDECODe,
leveraging in-distribution equivariance for conformal OOD detection. It relies
on a novel base non-conformity measure and a new aggregation method, used in
the inductive conformal anomaly detection framework, thereby guaranteeing a
bounded false detection rate. We demonstrate the efficacy of iDECODe by
experiments on image and audio datasets, obtaining state-of-the-art results. We
also show that iDECODe can detect adversarial examples.


  With the exponential growth of data and its crucial impact on our lives and
decision-making, the integrity of data has become a significant concern.
Malicious data poisoning attacks, where false values are injected into the
data, can disrupt machine learning processes and lead to severe consequences.
To mitigate these attacks, distance-based defenses, such as trimming, have been
proposed, but they can be easily evaded by white-box attackers. The evasiveness
and effectiveness of poisoning attack strategies are two sides of the same
coin, making game theory a promising approach. However, existing
game-theoretical models often overlook the complexities of online data
poisoning attacks, where strategies must adapt to the dynamic process of data
collection.
  In this paper, we present an interactive game-theoretical model to defend
online data manipulation attacks using the trimming strategy. Our model
accommodates a complete strategy space, making it applicable to strong evasive
and colluding adversaries. Leveraging the principle of least action and the
Euler-Lagrange equation from theoretical physics, we derive an analytical model
for the game-theoretic process. To demonstrate its practical usage, we present
a case study in a privacy-preserving data collection system under local
differential privacy where a non-deterministic utility function is adopted. Two
strategies are devised from this analytical model, namely, Tit-for-tat and
Elastic. We conduct extensive experiments on real-world datasets, which
showcase the effectiveness and accuracy of these two strategies.


  We introduce and develop a theory of limits for sequences of sparse graphs
based on $L^p$ graphons, which generalizes both the existing $L^\infty$ theory
of dense graph limits and its extension by Bollob\'as and Riordan to sparse
graphs without dense spots. In doing so, we replace the no dense spots
hypothesis with weaker assumptions, which allow us to analyze graphs with power
law degree distributions. This gives the first broadly applicable limit theory
for sparse graphs with unbounded average degrees. In this paper, we lay the
foundations of the $L^p$ theory of graphons, characterize convergence, and
develop corresponding random graph models, while we prove the equivalence of
several alternative metrics in a companion paper.


  In this paper we discuss the quantum properties for superposition of squeezed
displaced number states against multiphoton Jaynes-Cummings model (JCM). In
particular, we investigate atomic inversion, photon-number distribution,
purity, quadrature squeezing, Mandel $Q$ parameter and Wigner function. We show
that the quadrature squeezing for three-photon absorption case can exhibit
revivals and collapses typical to those occurring in the atomic inversion for
one-photon absorption case. Also we prove that for odd number absorption
parameter there is a connection between the evolution of the atomic inversion
and the evolution of the Wigner function at the origin in phase space.
Furthermore, we show that the nonclassical states whose the Wigner functions
values at the origins are negative will be always nonclassical when they are
evolving through the JCM with even absorption parameter. Also we demonstrate
that various types of cat states can be generated via this system.


  In this paper, we study the formalism of unsupervised multi-class domain
adaptation (multi-class UDA), which underlies a few recent algorithms whose
learning objectives are only motivated empirically. Multi-Class Scoring
Disagreement (MCSD) divergence is presented by aggregating the absolute margin
violations in multi-class classification, and this proposed MCSD is able to
fully characterize the relations between any pair of multi-class scoring
hypotheses. By using MCSD as a measure of domain distance, we develop a new
domain adaptation bound for multi-class UDA; its data-dependent, probably
approximately correct bound is also developed that naturally suggests
adversarial learning objectives to align conditional feature distributions
across source and target domains. Consequently, an algorithmic framework of
Multi-class Domain-adversarial learning Networks (McDalNets) is developed, and
its different instantiations via surrogate learning objectives either coincide
with or resemble a few recently popular methods, thus (partially) underscoring
their practical effectiveness. Based on our identical theory for multi-class
UDA, we also introduce a new algorithm of Domain-Symmetric Networks (SymmNets),
which is featured by a novel adversarial strategy of domain confusion and
discrimination. SymmNets affords simple extensions that work equally well under
the problem settings of either closed set, partial, or open set UDA. We conduct
careful empirical studies to compare different algorithms of McDalNets and our
newly introduced SymmNets. Experiments verify our theoretical analysis and show
the efficacy of our proposed SymmNets. In addition, we have made our
implementation code publicly available.


  The lack of proper documentation makes program comprehension a cumbersome
process for developers. Source code summarization is one of the existing
solutions to this problem. Lots of approaches have been proposed to summarize
source code in recent years. A prevalent weakness of these solutions is that
they do not pay much attention to interactions among elements of a software. An
element is simply a callable code snippet such as a method or even a clickable
button. As a result, these approaches cannot be applied to event-driven
programs, such as Android applications, because they have specific features
such as numerous interactions between their elements. To tackle this problem,
we propose a novel approach based on deep neural networks and dynamic call
graphs to generate summaries for methods of event-driven programs. First, we
collect a set of comment/code pairs from Github and train a deep neural network
on the set. Afterward, by exploiting a dynamic call graph, the Pagerank
algorithm, and the pre-trained deep neural network, we generate summaries. An
empirical evaluation with 14 real-world Android applications and 42
participants indicates 32.3% BLEU4 which is a definite improvement compared to
the existing state-of-the-art techniques. We also assessed the informativeness
and naturalness of our generated summaries from developers' perspectives and
showed they are sufficiently understandable and informative.


  In this paper, an improved strategy for automated text dependent speaker
identification system has been proposed in noisy environment. The
identification process incorporates the Neuro- Genetic hybrid algorithm with
cepstral based features. To remove the background noise from the source
utterance, wiener filter has been used. Different speech pre-processing
techniques such as start-end point detection algorithm, pre-emphasis filtering,
frame blocking and windowing have been used to process the speech utterances.
RCC, MFCC, MFCC, MFCC, LPC and LPCC have been used to extract the features.
After feature extraction of the speech, Neuro-Genetic hybrid algorithm has been
used in the learning and identification purposes. Features are extracted by
using different techniques to optimize the performance of the identification.
According to the VALID speech database, the highest speaker identification rate
of 100.000 percent for studio environment and 82.33 percent for office
environmental conditions have been achieved in the close set text dependent
speaker identification system.


  I discuss minimally doubled fermions fermions as an ultra-local formulation
on the lattice for sea quarks that realize a non-singlet chiral symmetry. I
introduce a non-singlet mass term for Karsten-Wilczek fermions and identify the
appropriate representation of the SU(2) flavor group at finite lattice spacing.
I present an algebraic proof that the symmetry of the quark determinant under
charge conjugation and reflections of the Euclidean axes is preserved for
Karsten-Wilczek fermions as sea quarks. Finally, I discuss how the flavor
components in meson correlation functions with Karsten-Wilczek fermions emerge
naturally and I show how taste-breaking can be avoided without fine tuning.


  We consider probabilistic shaping to maximize the achievable information rate
of coded modulation (CM) with hard decision decoding. The proposed scheme using
binary staircase codes outperforms its uniform CM counterpart by more than 1.3
dB for 64-QAM and 5 bits/symbol.


  Using the real time formalism of the finite temperature field theory we
calculate the 1-loop polarization tensor in the presence of a background
magnetic field in a medium. The expression is obtained to linear order in the
background field strength. We discuss the Faraday rotation as well as the
photon absorption probabilities in this context.


  We study the Page curve of an evaporating black hole using a toy model given
by Jackiw-Teitelboim gravity with Fateev-Zamolodchikov-Zamolodchikov-Teschner
(FZZT) antibranes. We treat the anti-FZZT branes as dynamical objects, taking
their back-reaction into account. We construct the entanglement entropy from
the dual matrix model and study its behavior as a function of the 't Hooft
coupling $t$ proportional to the number of branes, which plays the role of
time. By numerical computation we observe that the entropy first increases and
then decreases as $t$ grows, reproducing the well-known behavior of the Page
curve of an evaporating black hole. The system finally exhibits a phase
transition, which may be viewed as the end of the evaporation. We study the
critical behavior of the entropy near the phase transition. We also make a
conjecture about the late-time monotonically decreasing behavior of the
entropy. We prove it in a certain limit as well as give an intuitive
explanation by means of the dual matrix model.


  Existing uncertainty modeling approaches try to detect an out-of-distribution
point from the in-distribution dataset. We extend this argument to detect
finer-grained uncertainty that distinguishes between (a). certain points, (b).
uncertain points but within the data distribution, and (c). out-of-distribution
points. Our method corrects overconfident NN decisions, detects outlier points
and learns to say ``I don't know'' when uncertain about a critical point
between the top two predictions. In addition, we provide a mechanism to
quantify class distributions overlap in the decision manifold and investigate
its implications in model interpretability.
  Our method is two-step: in the first step, the proposed method builds a class
distribution using Kernel Activation Vectors (kav) extracted from the Network.
In the second step, the algorithm determines the confidence of a test point by
a hierarchical decision rule based on the chi-squared distribution of squared
Mahalanobis distances.
  Our method sits on top of a given Neural Network, requires a single scan of
training data to estimate class distribution statistics, and is highly scalable
to deep networks and wider pre-softmax layer. As a positive side effect, our
method helps to prevent adversarial attacks without requiring any additional
training. It is directly achieved when the Softmax layer is substituted by our
robust uncertainty layer at the evaluation phase.


  Natural microbial communities contain hundreds to thousands of interacting
species. For this reason, computational simulations are playing an increasingly
important role in microbial ecology. In this manuscript, we present a new
open-source, freely available Python package called Community Simulator for
simulating microbial population dynamics in a reproducible, transparent and
scalable way. The Community Simulator includes five major elements: tools for
preparing the initial states and environmental conditions for a set of samples,
automatic generation of dynamical equations based on a dictionary of modeling
assumptions, random parameter sampling with tunable levels of metabolic and
taxonomic structure, parallel integration of the dynamical equations, and
support for metacommunity dynamics with migration between samples. To
significantly speed up simulations using Community Simulator, our Python
package implements a new Expectation-Maximization (EM) algorithm for finding
equilibrium states of community dynamics that exploits a recently discovered
duality between ecological dynamics and convex optimization. We present data
showing that this EM algorithm improves performance by between one and two
orders compared to direct numerical integration of the corresponding ordinary
differential equations. We conclude by listing several recent applications of
the Community Simulator to problems in microbial ecology, and discussing
possible extensions of the package for directly analyzing microbiome
compositional data.


  Recent object detection systems rely on two critical steps: (1) a set of
object proposals is predicted as efficiently as possible, and (2) this set of
candidate proposals is then passed to an object classifier. Such approaches
have been shown they can be fast, while achieving the state of the art in
detection performance. In this paper, we propose a new way to generate object
proposals, introducing an approach based on a discriminative convolutional
network. Our model is trained jointly with two objectives: given an image
patch, the first part of the system outputs a class-agnostic segmentation mask,
while the second part of the system outputs the likelihood of the patch being
centered on a full object. At test time, the model is efficiently applied on
the whole test image and generates a set of segmentation masks, each of them
being assigned with a corresponding object likelihood score. We show that our
model yields significant improvements over state-of-the-art object proposal
algorithms. In particular, compared to previous approaches, our model obtains
substantially higher object recall using fewer proposals. We also show that our
model is able to generalize to unseen categories it has not seen during
training. Unlike all previous approaches for generating object masks, we do not
rely on edges, superpixels, or any other form of low-level segmentation.


  A novel secure communication protocol is presented, based on an entangled
pair of qubits and allowing asymptotically secure key distribution and
quasi-secure direct communication. Since the information is transferred in a
deterministic manner, no qubits have to be discarded. The transmission of
information is instantaneous, i.e. the information can be decoded during the
transmission. The security against arbitrary eavesdropping attacks is provided.
In case of eavesdropping attacks with full information gain, the detection rate
is 50% per control transmission. The experimental realization of the protocol
is feasible with relatively small effort, which also makes commercial
applications conceivable.


  A major impediment to a more complete understanding of barrier crossing and
other single-molecule processes is the inability to directly visualize the
trajectories and dynamics of atoms and molecules in reactions. Rather, the
kinetics are inferred from ensemble measurements or the position of a
transducer (e.g. an AFM cantilever) as a surrogate variable. Direct
visualization is highly desirable. Here, we achieve the direct measurement of
barrier crossing trajectories by using optical microscopy to observe position
and orientation changes of pairs of Ag nanoparticles in an optical ring trap,
i.e. passing events. A two-step mechanism similar to a bimolecular exchange
reaction is revealed by analysis that combines detailed knowledge of each
trajectory, a statistically significant number of repetitions of the passing
events, and the driving force-dependence of the process. We find that while the
total event rate increases with driving force, this increase is only due to
increased rate of encounters. There is no drive force-dependence on the rate of
barrier crossing because the key motion for the process involves a radial
motion of one particle as a thermal (random) fluctuation allowing the other to
pass. This simple experiment can readily be extended to study more complex
barrier crossing processes by replacing the spherical metal nanoparticles with
anisotropic ones or through more intricate optical trapping potentials.


  Correlated classical and quantum many-particle systems out of equilibrium are
of high interest in many fields, including dense plasmas, correlated solids,
and ultracold atoms. Accurate theoretical description of these systems is
challenging both, conceptionally and with respect to computational resources.
While for classical systems, in principle, exact simulations are possible via
molecular dynamics, this is not the case for quantum systems. Alternatively,
one can use many-particle approaches such as hydrodynamics, kinetic theory or
nonequilibrium Green functions (NEGF). However, NEGF exhibit a very unfavorable
cubic scaling of the CPU time with the number of time steps. An alternative is
the G1--G2 scheme [N. Schl\"unzen et al., Phys. Rev. Lett. \textbf{124}, 076601
(2020)] which allows for NEGF simulations with time linear scaling, however, at
the cost of large memory consumption. The reason is the need to store the
two-particle correlation function. This problem can be overcome for a number of
approximations by reformulating the kinetic equations in terms of fluctuations
-- an approach that was developed, for classical systems, by Yu.L. Klimontovich
[JETP \textbf{33}, 982 (1957)]. Here we present an overview of his ideas and
extend them to quantum systems. In particular, we demonstrate that this quantum
fluctuations approach can reproduce the nonequilibrium $GW$ approximation [E.
Schroedter \textit{et al.}, Cond. Matt. Phys. \textbf{25}, 23401 (2022)]
promising high accuracy at low computational cost which arises from an
effective semiclassical stochastic sampling procedure. We also demonstrate how
to extend the approach to the two-time exchange-correlation functions and the
density response properties. [E. Schroedter \textit{et al.}, Phys. Rev. B
\textbf{108}, 205109 (2023)].


  This paper studies the asymptotic spectral properties of the sample
covariance matrix for high dimensional compositional data, including the
limiting spectral distribution, the limit of extreme eigenvalues, and the
central limit theorem for linear spectral statistics. All asymptotic results
are derived under the high-dimensional regime where the data dimension
increases to infinity proportionally with the sample size. The findings reveal
that the limiting spectral distribution is the well-known Marchenko-Pastur law.
The largest (or smallest non-zero) eigenvalue converges almost surely to the
left (or right) endpoint of the limiting spectral distribution, respectively.
Moreover, the linear spectral statistics demonstrate a Gaussian limit.
Simulation experiments demonstrate the accuracy of theoretical results.


  In this paper we present a CAT generation algorithm for Dyck paths with a
fixed length n. It is the formalization of a method for the exhaustive
generation of this kind of paths which can be described by means of two
equivalent strategies. The former is described by a rooted tree, the latter
lists the paths by means of three operations which, as we are going to see, are
equivalent to visit the tree. These constructions are strictly connected with
ECO method and can be encoded by a rule, very similar to the succession rule in
ECO, with a finite number of labels for each n. Moreover with a slight
variation this method can be generalized to other combinatorial classes like
Grand Dyck or Motzkin paths.


  Gravitational lensing time delays offer an avenue to measure the Hubble
parameter $H_0$, with some analyses suggesting a tension with early-type probes
of $H_0$. The lensing measurements must mitigate systematic uncertainties due
to the mass modelling of lens galaxies. In particular, a core component in the
lens density profile would form an approximate local mass sheet degeneracy and
could bias $H_0$ in the right direction to solve the lensing tension. We
consider ultralight dark matter as a possible mechanism to generate such
galactic cores. We show that cores of roughly the required properties could
arise naturally if an ultralight axion of mass $m\sim10^{-25}$ eV makes up a
fraction of order ten percent of the total cosmological dark matter density. A
relic abundance of this order of magnitude could come from vacuum misalignment.
Stellar kinematics measurements of well-resolved massive galaxies (including
the Milky Way) may offer a way to test the scenario. Kinematics analyses aiming
to test the core hypothesis in massive elliptical lens galaxies should not, in
general, adopt the perfect mass sheet limit, as ignoring the finite extent of
an actual physical core could lead to significant systematic errors.


  For high-density metro traffic, nowadays the time-variant passenger flow is
the main cause of train delays and stranded passengers. Typically, the main
objective of automatic metro traffic regulation methods is to minimize the
delay time of trains while passengers' satisfaction is not considered. Instead,
in this work, a novel framework that integrates a passenger flow module (PFM)
and a train operation module (TOM) is proposed with the aim of simultaneously
minimizing traffic delays and passengers' discomfort. In particular, the PFM is
devoted to the optimization of the headway time in case of platform
overcrowding, so as to reduce the passengers waiting time at platforms and
increase the load rate of trains; while the TOM is devoted to the minimization
of trains' delays. The two modules interact with each other so that the headway
time is automatically adjusted when a platform is overcrowded, and the train
traffic is immediately regulated according to the new headway time. As a
result, the number of passengers on the platform and their total waiting time
can be significantly reduced. Numerical results are provided to show the
effectiveness of the proposed method in improving the operation performance
while minimizing the passengers' discomfort.


  A new entropy-like measure as well as a new measure of total uncertainty
pertaining to the Dempster-Shafer theory are introduced. It is argued that
these measures are better justified than any of the previously proposed
candidates.


  The dynamical parameters conventionally used to specify the orbit of a test
particle in Kerr spacetime are the energy $E$, the axial component of the
angular momentum, $L_{z}$, and Carter's constant $Q$. These parameters are
obtained by solving the Hamilton-Jacobi equation for the dynamical problem of
geodesic motion. Employing the action-angle variable formalism, on the other
hand, yields a different set of constants of motion, namely, the fundamental
frequencies $\omega_{r}$, $\omega_{\theta}$ and $\omega_{\phi}$ associated with
the radial, polar and azimuthal components of orbital motion. These
frequencies, naturally, determine the time scales of orbital motion and,
furthermore, the instantaneous gravitational wave spectrum in the adiabatic
approximation. In this article, it is shown that the fundamental frequencies
are geometric invariants and explicit formulas in terms of quadratures are
derived. The numerical evaluation of these formulas in the case of a rapidly
rotating black hole illustrates the behaviour of the fundamental frequencies as
orbital parameters such as the semi-latus rectum $p$, the eccentricity $e$ or
the inclination parameter $\theta_{-}$ are varied. The limiting cases of
circular, equatorial and Keplerian motion are investigated as well and it is
shown that known results are recovered from the general formulas.


  The Stone theorem requires that in a physical Hilbert space ${\cal H}$ the
time-evolution of a stable quantum system is unitary if and only if the
corresponding Hamiltonian $H$ is self-adjoint. Sometimes, a simpler picture of
the evolution may be constructed in a manifestly unphysical Hilbert space
${\cal K}$ in which $H$ is nonhermitian but ${\cal PT}-$symmetric. In
applications, unfortunately, one only rarely succeeds in circumventing the key
technical obstacle which lies in the necessary reconstruction of the physical
Hilbert space ${\cal H}$. For a ${\cal PT}-$symmetric version of the spiked
harmonic oscillator we show that in the dynamical regime of the unavoided level
crossings such a reconstruction of ${\cal H}$ becomes feasible and, moreover,
obtainable by non-numerical means. The general form of such a reconstruction of
${\cal H}$ enables one to render every exceptional unavoided-crossing point
tractable as a genuine, phenomenologically most appealing
quantum-phase-transition instant.


  The independence equivalence class of a graph $G$ is the set of graphs that
have the same independence polynomial as $G$. Beaton, Brown and Cameron
(arXiv:1810.05317) found the independence equivalence classes of even cycles,
and raised the problem of finding the independence equivalence class of odd
cycles. The problem is completely solved in this paper.


  We demonstrate, for the first time, m-CAP modulation using off-the-shelf LEDs
in a VLC in real time experimental setup using field programmable gate arrays
based in universal software radio peripherals (USRPs). We demonstrate
transmission speeds up to ~30 Mb/s can be achieved, which supports high
definition television streaming.


  Consider a compact Riemannian manifold with boundary endowed with a magnetic
field. A path taken by a particle of unit charge, mass, and energy is called a
magnetic geodesic. It is shown that if everything is real-analytic, the
topology, metric, and magnetic field are uniquely determined by the scattering
relation of the magnetic geodesic flow, measured at the boundary. Conjugate
points are allowed with minor restrictions. In exchange for the real-analytic
assumption, prior results in boundary rigidity are greatly generalized.


  It is well-known that perturbative quantum gravity is non-renormalizable. The
metric or vierbein has generally been used as the variable to quantize in
perturbative quantum gravity. In this essay, we show that one can use the spin
connection instead, in which case it is possible to obtain a ghost-free
renormalizable theory of quantum gravity. Furthermore in this approach,
gravitational analogs of particle physics phenomena can be studied. In
particular, we study the gravitational Higgs mechanism using spin connection as
a gauge field, and show that this provides a mechanism for the effective
reduction in the dimensionality of spacetime.


  The leading segmentation methods represent the output map as a pixel grid. We
study an alternative representation in which the object edges are modeled, per
image patch, as a polygon with $k$ vertices that is coupled with per-patch
label probabilities. The vertices are optimized by employing a differentiable
neural renderer to create a raster image. The delineated region is then
compared with the ground truth segmentation. Our method obtains multiple
state-of-the-art results: 76.26\% mIoU on the Cityscapes validation, 90.92\%
IoU on the Vaihingen building segmentation benchmark, 66.82\% IoU for the MoNU
microscopy dataset, and 90.91\% for the bird benchmark CUB. Our code for
training and reproducing these results is attached as supplementary.


  Drawing from the theory of stochastic differential equations, we introduce a
novel sampling method for known distributions and a new algorithm for diffusion
generative models with unknown distributions. Our approach is inspired by the
concept of the reverse diffusion process, widely adopted in diffusion
generative models. Additionally, we derive the explicit convergence rate based
on the smooth ODE flow. For diffusion generative models and sampling, we
establish a dimension-free particle approximation convergence result. Numerical
experiments demonstrate the effectiveness of our method. Notably, unlike the
traditional Langevin method, our sampling method does not require any
regularity assumptions about the density function of the target distribution.
Furthermore, we also apply our method to optimization problems.


  Learning the kernel functions used in kernel methods has been a vastly
explored area in machine learning. It is now widely accepted that to obtain
'good' performance, learning a kernel function is the key challenge. In this
work we focus on learning kernel representations for structured regression. We
propose use of polynomials expansion of kernels, referred to as Schoenberg
transforms and Gegenbaur transforms, which arise from the seminal result of
Schoenberg (1938). These kernels can be thought of as polynomial combination of
input features in a high dimensional reproducing kernel Hilbert space (RKHS).
We learn kernels over input and output for structured data, such that,
dependency between kernel features is maximized. We use Hilbert-Schmidt
Independence Criterion (HSIC) to measure this. We also give an efficient,
matrix decomposition-based algorithm to learn these kernel transformations, and
demonstrate state-of-the-art results on several real-world datasets.


  We study the relationship between the central ideals and the Jacobson
radicals of blocks of group algebras.In particular, we characterize the blocks
with the property that the square of the radical is a non-zero central ideal.
Moreover, we also consider the blocks with the property that the cube of the
radical becomes a non-zero central ideal.


  We prove existence of renormalized solutions to general nonlinear elliptic
equation in Musielak-Orlicz space avoiding growth restrictions. Namely, we
consider \begin{equation*} -{\rm div} A(x,\nabla u)= f\in L^1(\Omega),
\end{equation*} on a Lipschitz bounded domain in $\mathbb{R}^N$. The growth of
the monotone vector field $A$ is controlled by a generalized nonhomogeneous and
anisotropic $N$-function $M $. The approach does not require any particular
type of growth condition of $M$ or its conjugate $M^*$ (neither $\Delta_2$, nor
$\nabla_2$). The condition we impose is log-Holder continuity of $M$, which
results in good approximation properties of the space. The proof of the main
results uses truncation ideas, the Young measures methods and monotonicity
arguments.


  We investigate a gauged matrix model in the large $N$ limit which is closely
related to the superconductor fluctuation and the flux lattice melting in two
dimensions. With the use of saddle point method the free energy is expanded up
to eighth order for the coupling constant $g$. In the case that the coefficient
of quadratic term of the Ginzburg-Landau matrix model is negative, a critical
point $g=g_c$ is obtained in the large $N$ limit and the relation between this
phase transition and the 2D flux lattice melting transition is discussed.


  We study the dynamics of proliferating cell collectives whose microscopic
constituents' growth is inhibited by macroscopic growth-induced stress.
Discrete particle simulations of a growing collective show the emergence of
concentric-ring patterns in cell size whose spatio-temporal structure is
closely tied to the individual cell's stress response. Motivated by these
observations, we derive a multiscale continuum theory whose parameters map
directly to the discrete model. Analytical solutions of this theory show the
concentric patterns arise from anisotropically accumulated resistance to growth
over many cell cycles. This work shows how purely mechanical processes can
affect the internal patterning and morphology of cell collectives, and provides
a concise theoretical framework for connecting the micro- to macroscopic
dynamics of proliferating matter.


  Experimental realization of magnetic field induced quantum phase transition
(QPT) is reported for NH4CuPO4.H2O, a two spin cluster material with isotropic
Heisenberg interaction. Experimental magnetization and specific heat data have
been collected as a function of temperature and magnetic field. Experimental
data have been analyzed in terms of Heisenberg dimer model. Two quantum
complementary observables representing local and non-local properties of the
spins are constructed using the experimental data and a clear evidence of QPT
is observed through partial quantum information sharing when the magnetic field
is swept through a particular value. Signature of QPT is also observed when
specific heat is measured as a function of magnetic field at low temperature.
Furthermore, using the experimental specific heat data, magnetic energy values
are calculated and their variations are captured as a function of magnetic
field and temperature.


  Automatic program synthesis is a long-lasting dream in software engineering.
Recently, a promising Deep Learning (DL) based solution, called Copilot, has
been proposed by OpenAI and Microsoft as an industrial product. Although some
studies evaluate the correctness of Copilot solutions and report its issues,
more empirical evaluations are necessary to understand how developers can
benefit from it effectively. In this paper, we study the capabilities of
Copilot in two different programming tasks: (i) generating (and reproducing)
correct and efficient solutions for fundamental algorithmic problems, and (ii)
comparing Copilot's proposed solutions with those of human programmers on a set
of programming tasks. For the former, we assess the performance and
functionality of Copilot in solving selected fundamental problems in computer
science, like sorting and implementing data structures. In the latter, a
dataset of programming problems with human-provided solutions is used. The
results show that Copilot is capable of providing solutions for almost all
fundamental algorithmic problems, however, some solutions are buggy and
non-reproducible. Moreover, Copilot has some difficulties in combining multiple
methods to generate a solution. Comparing Copilot to humans, our results show
that the correct ratio of humans' solutions is greater than Copilot's
suggestions, while the buggy solutions generated by Copilot require less effort
to be repaired.


  In the communication problem $\mathbf{UR}$ (universal relation) [KRW95],
Alice and Bob respectively receive $x$ and $y$ in $\{0,1\}^n$ with the promise
that $x\neq y$. The last player to receive a message must output an index $i$
such that $x_i\neq y_i$. We prove that the randomized one-way communication
complexity of this problem in the public coin model is exactly $\Theta(\min\{n,
\log(1/\delta)\log^2(\frac{n}{\log(1/\delta)})\})$ bits for failure probability
$\delta$. Our lower bound holds even if promised $\mathop{support}(y)\subset
\mathop{support}(x)$. As a corollary, we obtain optimal lower bounds for
$\ell_p$-sampling in strict turnstile streams for $0\le p < 2$, as well as for
the problem of finding duplicates in a stream. Our lower bounds do not need to
use large weights, and hold even if it is promised that $x\in\{0,1\}^n$ at all
points in the stream.
  Our lower bound demonstrates that any algorithm $\mathcal{A}$ solving
sampling problems in turnstile streams in low memory can be used to encode
subsets of $[n]$ of certain sizes into a number of bits below the information
theoretic minimum. Our encoder makes adaptive queries to $\mathcal{A}$
throughout its execution, but done carefully so as to not violate correctness.
This is accomplished by injecting random noise into the encoder's interactions
with $\mathcal{A}$, which is loosely motivated by techniques in differential
privacy. Our correctness analysis involves understanding the ability of
$\mathcal{A}$ to correctly answer adaptive queries which have positive but
bounded mutual information with $\mathcal{A}$'s internal randomness, and may be
of independent interest in the newly emerging area of adaptive data analysis
with a theoretical computer science lens.


  A time-dependent optical lattice with staggered particle current in the
tight-binding regime was considered that can be described by a time-independent
effective lattice model with an artificial staggered magnetic field. The low
energy description of a single-component fermion in this lattice at
half-filling is provided by two copies of ideal two-dimensional massless Dirac
fermions. The Dirac cones are generally anisotropic and can be tuned by the
external staggered flux $\p$. For bosons, the staggered flux modifies the
single-particle spectrum such that in the weak coupling limit, depending on the
flux $\p$, distinct superfluid phases are realized. Their properties are
discussed, the nature of the phase transitions between them is establised, and
Bogoliubov theory is used to determine their excitation spectra. Then the
generalized superfluid-Mott-insulator transition is studied in the presence of
the staggered flux and the complete phase diagram is established. Finally, the
momentum distribution of the distinct superfluid phases is obtained, which
provides a clear experimental signature of each phase in ballistic expansion
experiments.