  Federated learning (FL) refers to a distributed machine learning framework
involving learning from several decentralized edge clients without sharing
local dataset. This distributed strategy prevents data leakage and enables
on-device training as it updates the global model based on the local model
updates. Despite offering several advantages, including data privacy and
scalability, FL poses challenges such as statistical and system heterogeneity
of data in federated networks, communication bottlenecks, privacy and security
issues. This survey contains a systematic summarization of previous work,
studies, and experiments on FL and presents a list of possibilities for FL
across a range of applications and use cases. Other than that, various
challenges of implementing FL and promising directions revolving around the
corresponding challenges are provided.


  The role of repulsive interactions in statistical systems of Bose particles
is investigated. Three different phenomenological frameworks are considered: a
mean field model, an excluded volume model, and a model with a medium dependent
effective mass. All three models are tuned to yield similar equations of state,
with only minor deviations from the ideal Bose gas at small chemical
potentials. Our analysis indicates, however, that these models lead to
qualitatively different results for the Bose-Einstein condensation phenomenon.
We discuss the different aspects of this phenomenon, namely, an onset of the
Bose-Einstein condensation, particle number fluctuations, and a behavior of the
Bose condensate. The obtained results can be helpful for interpreting the
lattice QCD data at small temperature and large isospin chemical potential and
the data on multiple pion production in high energy nuclear collisions.


  The coupled motion is investigated for a mechanical system consisting of
water and a body freely floating in it. Water occupies either a half-space or a
layer of constant depth into which an infinitely long surface-piercing cylinder
is immersed, thus allowing us to study two-dimensional modes. Under the
assumption that the motion is of small amplitude near equilibrium, a linear
setting is applicable and for the time-harmonic oscillations it reduces to a
spectral problem with the frequency of oscillations as the spectral parameter.
It is essential that one of the problem's relations is linear with respect to
the parameter, whereas two others are quadratic with respect to it.
  Within this framework, it is shown that the total energy of the water motion
is finite and the equipartition of energy holds for the whole system. On this
basis, it is proved that no wave modes can be trapped provided their
frequencies exceed a bound depending on cylinder's properties, whereas its
geometry is subject to some restrictions and, in some cases, certain
restrictions are imposed on the type of mode.


  We study purely nonlocal Hamiltonian structures for systems of hydrodynamic
type. In the case of a semi-Hamiltonian system, we show that such structures
are related to quadratic expansions of the diagonal metrics naturally
associated with the system.


  We extend the family non-symmetric Macdonald polynomials and define
general-basement Macdonald polynomials. We show that these also satisfy a
triangularity property with respect to the monomials bases and behave well
under the Demazure-Lusztig operators.
  The symmetric Macdonald polynomials $J_\lambda$ are expressed as a sum of
general-basement Macdonald polynomials via an explicit formula.
  By letting $q=0$, we obtain $t$-deformations of key polynomials and Demazure
atoms and we show that the Hall--Littlewood polynomials expand positively into
these. This generalizes a result by Haglund, Luoto, Mason and van Willigenburg.
  As a corollary, we prove that Schur polynomials decompose with non-negative
coefficients into $t$-deformations of general Demazure atoms and thus
generalizing the $t=0$ case which was previously known. This gives a unified
formula for the classical expansion of Schur polynomials in Hall-Littlewood
polynomials and the expansion of Schur polynomials into Demazure atoms.


  Generalized mass-action systems are power-law dynamical systems arising from
chemical reaction networks. Essentially, every nonnegative ODE model used in
chemistry and biology (for example, in ecology and epidemiology) and even in
economics and engineering can be written in this form. Previous results have
focused on existence and uniqueness of special steady states (complex-balanced
equilibria) for all rate constants, thereby ruling out multiple (special)
steady states. Recently, necessary conditions for linear stability have been
obtained.
  In this work, we provide sufficient conditions for the linear stability of
complex-balanced equilibria for all rate constants (and also for the
non-existence of other steady states). In particular, via sign-vector
conditions (on the stoichiometric coefficients and kinetic orders), we
guarantee that the Jacobian matrix is a $P$-matrix. Technically, we use a new
decomposition of the graph Laplacian which allows to consider orders of
(generalized) monomials. Alternatively, we use cycle decomposition which allows
a linear parametrization of all Jacobian matrices. In any case, we guarantee
stability without explicit computation of steady states. We illustrate our
results in examples from chemistry and biology: generalized Lotka-Volterra
systems and SIR models, a two-component signaling system, and an enzymatic
futile cycle.


  While numerous public blockchain datasets are available, their utility is
constrained by an exclusive focus on blockchain data. This constraint limits
the incorporation of relevant social network data into blockchain analysis,
thereby diminishing the breadth and depth of insight that can be derived. To
address the above limitation, we introduce EX-Graph, a novel dataset that
authentically links Ethereum and X, marking the first and largest dataset of
its kind. EX-Graph combines Ethereum transaction records (2 million nodes and
30 million edges) and X following data (1 million nodes and 3 million edges),
bonding 30,667 Ethereum addresses with verified X accounts sourced from
OpenSea. Detailed statistical analysis on EX-Graph highlights the structural
differences between X-matched and non-X-matched Ethereum addresses. Extensive
experiments, including Ethereum link prediction, wash-trading Ethereum
addresses detection, and X-Ethereum matching link prediction, emphasize the
significant role of X data in enhancing Ethereum analysis. EX-Graph is
available at \url{https://exgraph.deno.dev/}.


  Professor A. K. Raychaudhuri suddenly passed away on 18th June 2005. I have
attempted to give a glimpse of his life and work, and more specifically his
role as a great teacher and inspiring force to three generations of students of
the Presidency College, Kolkata.


  We prove the local well-posedness for the nonlinear fourth-order
Schr\"odinger equation (NL4S) in Sobolev spaces. We also studied the regularity
of solutions in the sub-critical case. A direct consequence of this regularity
is the global well-posedness above mass and energy spaces under some
assumptions. Finally, we show the ill-posedness for (NL4S) in some cases of the
super-critical range.


  The current paper reports on the implementation of a numerical solver on the
Graphic Processing Units (GPU) to model reactive gas mixture with detailed
chemical kinetics. The solver incorporates high-order finite volume methods for
solving the fluid dynamical equations coupled with stiff source terms. The
chemical kinetics are solved implicitly via an operator-splitting method. We
explored different approaches in implementing a fast kinetics solver on the
GPU. The detail of the implementation is discussed in the paper. The solver is
tested with two high-order shock capturing schemes: MP5 (Suresh, et al. (1997))
and ADERWENO (Titarev, et al. (2005)). Considering only the fluid dynamics
calculation, the speed-up factors obtained are 30 for the MP5 scheme and 55 for
ADERWENO scheme. For the fully-coupled solver, the performance gain depended on
the size of the reaction mechanism. Two different examples of chemistry were
explored. The first mechanism consisted of 9 species and 38 reactions,
resulting in a speed-up factor up to 35. The second, larger mechanism consisted
of 36 species and 308 reactions, resulting in a speed-up factor of up to 40.


  We propose Weil and Cartan models for the equivariant cohomology of
noncommutative spaces which carry a covariant action of Drinfel'd twisted
symmetries. The construction is suggested by the noncommutative Weil algebra of
Alekseev and Meinrenken; we show that one can implement a Drinfel'd twist of
their models in order to take into account the noncommutativity of the spaces
we are acting on.


  Cellular networks are becoming increasingly heterogeneous with higher base
station (BS) densities and ever more frequency bands, making BS selection and
band assignment key decisions in terms of rate and coverage. In this paper, we
decompose the mobility-aware user association task into (i) forecasting of user
rate and then (ii) convex utility maximization for user association accounting
for the effects of BS load and handover overheads. Using a linear combination
of normalized mean-squared error and normalized discounted cumulative gain as a
novel loss function, a recurrent deep neural network is trained to reliably
forecast the mobile users' future rates. Based on the forecast, the controller
optimizes the association decisions to maximize the service rate-based network
utility using our computationally efficient (speed up of 100x versus generic
convex solver) algorithm based on the Frank-Wolfe method. Using an
industry-grade network simulator developed by Meta, we show that the proposed
model predictive control (MPC) approach improves the 5th percentile service
rate by 3.5x compared to the traditional signal strength-based association,
reduces the median number of handovers by 7x compared to a handover agnostic
strategy, and achieves service rates close to a genie-aided scheme.
Furthermore, our model-based approach is significantly more sample-efficient
(needs 100x less training data) compared to model-free reinforcement learning
(RL), and generalizes well across different user drop scenarios.


  In this work we obtain the exact solution for relativistic Landau problem
plus oscillator potential in a complex symmetric gauge field in a
non-commutative complex space, using the algebraic techniques of creation and
annihilation operators. It is shown that the relativistic Landau problem in a
complex symmetric gauge field in a non-commutative complex space is similar
behavior to the Pauli equation in the presence of a symmetric gauge field in a
commutative ordinary space. We derive the exact non-commutative Landau and
oscillator energy levels, while the non-relativistic limit of the energy
spectrum is obtained. We show that the energy is not degenerate and is splitted
into two levels, as in the Zeeman effect.


  Stochastic systems are used to model a variety of phenomena in which noise
plays an essential role. In these models, one potential goal is to determine if
noise can induce transitions between states, and if so, to calculate the most
probable escape path from an attractor. In the small noise limit, the
Freidlin-Wentzell theory of large deviations provides a variational framework
to calculate these paths. This work focuses on using large deviation theory to
calculate such paths for stochastic gradient systems with non-gradient
perturbations. While for gradient systems the most probable escape paths
consist of time-reversed heteroclinic orbits, for general systems it can be a
challenging calculation. By applying Melnikov theory to the resulting
Euler-Lagrange equations recast in Hamiltonian form, we determine a condition
for when the optimal escape path is the heteroclinic orbit for the perturbed
system. We provide a numerical example to illustrate how the computed most
probable escape path compares with the theoretical result.


  Choose a topos $E$. There are several different "notions of sheafness" on
$E$. How do we visualize them?
  Let's refer to the classifier object of $E$ as $\Omega$, and to its Heyting
Algebra of truth-values, $Sub(1_E)$, as $H$; we will sometimes call $H$ the
"logic" of the topos. There is a well-known way of representing notions of
sheafness as morphisms $j:\Omega\to \Omega$, but these `$j$'s yield big
diagrams when we draw them explicitly; here we will see a way to represent
these `$j$'s as maps $J:H\to H$ in a way that is much more manageable.
  In the previous paper of this series we showed how certain toy models of
Heyting Algebras, called "ZHAs", can be used to develop visual intuition for
how Heyting Algebras and Intuitionistic Propositional Logic work; here we will
extend that to sheaves. The full idea is this: notions of sheafness correspond
to local operators and vice-versa; local operators correspond to J-operators
and vice-versa; if our Heyting Algebra $H$ is a ZHA then J-operators correspond
to slashings on $H$, and vice-versa; slashings on $H$ correspond to "sets of
question marks" and vice-versa, and each set of question marks induces a notion
of erasing and reconstructing, which induces a sheaf. Also, every ZHA $H$
corresponds to an (acyclic) 2-column graph, and vice-versa, and for any
two-column graph $(P,A)$ the logic of the topos $\mathbf{Set}^{(P,A)}$ is
exactly the ZHA $H$ associated to $(P,A)$.


  In this paper we define and study a new class of states (the empty states).
These states are the superposition of two identical states (self-superposition
state). We defined three different representations of theses states, namely,
the source, the operator, and the self-superposition representations. Then, we
apply the empty state to an elementary example state and find its three
different representations. We apply the empty state to Fock states and find an
undetermined state. Then, we apply the empty state to the coherent state to
produce the empty state of the coherent state (the EC state), and determine
some of its mathematical, statistical and nonclassical properties.


  Varying dynamics parameters in simulation is a popular Domain Randomization
(DR) approach for overcoming the reality gap in Reinforcement Learning (RL).
Nevertheless, DR heavily hinges on the choice of the sampling distribution of
the dynamics parameters, since high variability is crucial to regularize the
agent's behavior but notoriously leads to overly conservative policies when
randomizing excessively. In this paper, we propose a novel approach to address
sim-to-real transfer, which automatically shapes dynamics distributions during
training in simulation without requiring real-world data. We introduce DOmain
RAndomization via Entropy MaximizatiON (DORAEMON), a constrained optimization
problem that directly maximizes the entropy of the training distribution while
retaining generalization capabilities. In achieving this, DORAEMON gradually
increases the diversity of sampled dynamics parameters as long as the
probability of success of the current policy is sufficiently high. We
empirically validate the consistent benefits of DORAEMON in obtaining highly
adaptive and generalizable policies, i.e. solving the task at hand across the
widest range of dynamics parameters, as opposed to representative baselines
from the DR literature. Notably, we also demonstrate the Sim2Real applicability
of DORAEMON through its successful zero-shot transfer in a robotic manipulation
setup under unknown real-world parameters.


  In order to understand galaxy evolution through cosmic times it is critical
to derive the properties of the molecular gas content of galaxies, i.e. the
material out of which stars ultimately form. The last decade has seen rapid
progress in this area, with the detection of massive molecular gas reservoirs
at high redshifts in submillimeter-selected galaxies and quasars. In the latter
case, molecular gas reservoirs have been quantified out to redshifts z>6, i.e.
towards the end of cosmic reionization when the universe was less than one Gyr
old. The recent discovery of molecular gas in more normal galaxies have
extended these studies from the most extreme objects in the universe
(SFR~1000M_sun/yr; quasars and submillimeter galaxies) to more 'normal'
starforming systems at redshifts 1.5-2.5 (with SFR~100M_sun/yr). However,
detecting the molecular gas reservoirs of high-redshift galaxies that only have
moderate star formation rates (~<10 M_sun/yr, similar to the faint galaxies
seen in the Hubble Ultra Deep Field) will likely have to await the completion
of ALMA.


  The link between the fate of the most massive stars and the resulting
supernova (SN) explosion is still a matter of debate, in major part because of
the ambiguity among light-curve powering mechanisms. When stars explode as SNe,
the light-curve luminosity is typically sustained by a central engine
(radioactive decay, magnetar spin-down, or fallback accretion). However, since
massive stars eject considerable amounts of material during their evolution,
there may be a significant contribution coming from interactions with the
previously ejected circumstellar medium (CSM). Reconstructing the progenitor
configuration at the time of explosion requires a detailed analysis of the
long-term photometric and spectroscopic evolution of the related transient. In
this paper, we present the results of our follow-up campaign of SN 2020faa.
Given the high luminosity and peculiar slow light curve, it is purported to
have a massive progenitor. We present the spectro-photometric dataset and
investigate different options to explain the unusual observed properties that
support this assumption. We computed the bolometric luminosity of the supernova
and the evolution of its temperature, radius, and expansion velocity. We also
fit the observed light curve with a multi-component model to infer information
on the progenitor and the explosion mechanism. Reasonable parameters are
inferred for SN 2020faa with a magnetar of energy Ep=1.5(+0.5,-0.2)x10^50 erg
and spin-down time t(spin)=15+/-1 d, a shell mass M(shell)=2.4(+0.5,-0.4) Msun
and kinetic energy Ekin(shell)=0.9(+0.5,-0.3)x 10^51 erg, and a core with
M(core)=21.5(+1.4,-0.7) Msun and Ekin(core)=3.9(+0.1,-0.4)x10^51 erg. In
addition, we need an extra source to power the luminosity of the second peak.
We find that hidden interaction with either a CSM disc or delayed, choked jets
is a viable mechanism for supplying the required energy to achieve this effect.


  Here we show how to generate a dark two-mode squeezed state of a trapped ion,
employing a three-level ion in a V configuration with a strong decay of the
excited states. The degree of squeezing can be manipulated by choosing the
intensity of the driving fields. Our scheme is robust against the usual
dissipation mechanism and could be implemented with present-day technology. The
validity of the approximations employed in this work was tested by numerical
calculations, which agreed completely with the analytical solutions.


  In the current study easy method to synthesize C12A7 particles with cubic
morphology was investigated for the application of Transparent Conducting Oxide
layer in thinfilm solar cell. By self-combustion method with proper amount of
urea addition, cubic and foamy structures of C12A7 were achieved at 950 {\deg}C
and at 510 {\deg}C respectively. Pure C12A7 formation confirmed by P-XRD and
growth mechanism of the cubes was also understood by SEM and FT-IR analysis.
Further the band gap was measured 3.07 eV in case of 510 {\deg}C and 3.32 eV in
case of 950 {\deg}C synthesized particles with the help of UV-Vis analysis.
During PL single sharp peaks at 399 nm noticed which indicates less defective
C12A7 at 950 {\deg}C, confirmed by XRD having more crystallinity and less
strain. No trap state or radiative recombination observed in case of C12A7
synthesized at 950 {\deg}C sample. Conductivity from conductometry titration
method was found to be 9.223 mS at 26.3 {\deg}C and 747.33 mS at 26.4 {\deg}C
for 510 {\deg}C and 950 {\deg}C synthesized samples respectively.


  We address a core problem of computer vision: Detection and description of 2D
feature points for image matching. For a long time, hand-crafted designs, like
the seminal SIFT algorithm, were unsurpassed in accuracy and efficiency.
Recently, learned feature detectors emerged that implement detection and
description using neural networks. Training these networks usually resorts to
optimizing low-level matching scores, often pre-defining sets of image patches
which should or should not match, or which should or should not contain key
points. Unfortunately, increased accuracy for these low-level matching scores
does not necessarily translate to better performance in high-level vision
tasks. We propose a new training methodology which embeds the feature detector
in a complete vision pipeline, and where the learnable parameters are trained
in an end-to-end fashion. We overcome the discrete nature of key point
selection and descriptor matching using principles from reinforcement learning.
As an example, we address the task of relative pose estimation between a pair
of images. We demonstrate that the accuracy of a state-of-the-art
learning-based feature detector can be increased when trained for the task it
is supposed to solve at test time. Our training methodology poses little
restrictions on the task to learn, and works for any architecture which
predicts key point heat maps, and descriptors for key point locations.


  This is a study of H-alpha emitters in two dense galaxy proto-clusters
surrounding radio galaxies at z~2. We show that the proto-cluster surrounding
MRC 1138-262 contains 14+/-2 times more H-alpha candidates than the average
field (9 sigma significance), and the z=2.35 radio galaxy 4C+10.48 is
surrounded by 12+/-2 times more emitters than the field (5 sigma), so it is
also likely to reside in a dense proto-cluster environment. We compared these
H-alpha emitters, situated in dense environments, to a control field sample
selected from 3 separate fields forming a total area of 172 arcmin^2. We
constructed and compared H-alpha and rest-frame R continuum luminosity
functions of the emitters in both environments. The star formation density is
on average 13 times greater in the proto-clusters than the field at z~2, so the
total star formation rate within the central 1.5Mpc of the proto-clusters
exceeds 3000Msun/yr. However, we found no significant difference in the shape
of the H-alpha luminosity functions, implying that environment does not
substantially affect the strength of the H-alpha line from strongly star
forming galaxies. The proto-cluster emitters are typically 0.8mag brighter in
rest-frame R continuum than field emitters, implying they are twice as massive
as their field counterparts at the same redshift. We also show the
proto-cluster galaxies have lower specific star formation rates than field
galaxies, meaning the emitters in the dense environments formed more of their
stars earlier than the field galaxies. We conclude that galaxy growth in the
early Universe was accelerated in dense environments, and that cluster galaxies
differed from field galaxies even before the cluster had fully formed.


  The process AB --> Quarkonium + photon + X, for a heavy quarkonium state such
as J/psi or Upsilon, is considered. The ratio of the cross-sections for this
process in pp and pp(bar) collisions is shown to be a vary sensitive probe of
models of quarkonium formation.


  Despite the great success of quantum mechanics, questions regarding its
application still exist and the boundary between quantum and classical
mechanics remains unclear. Based on the philosophical assumptions of
macrorealism and noninvasive measurability, Leggett and Garg devised a series
of inequalities (LG inequalities) involving a single system with a set of
measurements at different times. Introduced as the Bell inequalities in time,
the violation of LG inequalities excludes the hidden-variable description based
on the above two assumptions. We experimentally investigated the single photon
LG inequalities under decoherence simulated by birefringent media. These
generalized LG inequalities test the evolution trajectory of the photon and are
shown to be maximally violated in a coherent evolution process. The violation
of LG inequalities becomes weaker with the increase of interaction time in the
environment. The ability to violate the LG inequalities can be used to set a
boundary of the classical realistic description.


  We present a novel method for approximately equilibrating a matrix $A \in
{\bf R}^{m \times n}$ using only multiplication by $A$ and $A^T$. Our method is
based on convex optimization and projected stochastic gradient descent, using
an unbiased estimate of a gradient obtained by a randomized method. Our method
provably converges in expectation with an $O(1/t)$ convergence rate and
empirically gets good results with a small number of iterations. We show how
the method can be applied as a preconditioner for matrix-free iterative
algorithms such as LSQR and Chambolle-Cremers-Pock, substantially reducing the
iterations required to reach a given level of precision. We also derive a novel
connection between equilibration and condition number, showing that
equilibration minimizes an upper bound on the condition number over all choices
of row and column scalings.


  We consider discrete porous medium equations of the form \partial_t \rho_t =
\Delta \phi(\rho_t), where \Delta is the generator of a reversible continuous
time Markov chain on a finite set X, and \phi is an increasing function. We
show that these equations arise as gradient flows of certain entropy
functionals with respect to suitable non-local transportation metrics. This may
be seen as a discrete analogue of the Wasserstein gradient flow structure for
porous medium equations in R^n discovered by Otto. We present a one-dimensional
counterexample to geodesic convexity and discuss Gromov-Hausdorff convergence
to the Wasserstein metric.


  Systems of interacting charges and fields are ubiquitous in physics.
Recently, it has been shown that Hamiltonians derived using different gauges
can yield different physical results when matter degrees of freedom are
truncated to a few low-lying energy eigenstates. This effect is particularly
prominent in the ultra-strong coupling regime. Such ambiguities arise because
transformations reshuffle the partition between light and matter degrees of
freedom and so level truncation is a gauge dependent approximation. To avoid
this gauge ambiguity, we redefine the electromagnetic fields in terms of
potentials for which the resulting canonical momenta and Hamiltonian are
explicitly unchanged by the gauge choice of this theory. Instead the
light/matter partition is assigned by the intuitive choice of separating an
electric field between displacement and polarisation contributions. This
approach is an attractive choice in typical cavity quantum electrodynamics
situations.


  We introduce and explore a new concept of evasive subspace with respect to a
collection of subspaces sharing a common dimension, most notably partial
spreads. We show that this concept generalises known notions of subspace
scatteredness and evasiveness. We establish various upper bounds for the
dimension of an evasive subspace with respect to arbitrary partial spreads,
obtaining improvements for the Desarguesian ones. We also establish existence
results for evasive spaces in a non-constructive way, using a graph theory
approach. The upper and lower bounds we derive have a precise interpretation as
bounds for the critical exponent of certain combinatorial geometries. Finally,
we investigate connections between the notion of evasive space we introduce and
the theory of rank-metric codes, obtaining new results on the covering radius
and on the existence of minimal vector rank-metric codes.


  Most human protein-coding genes can be transcribed into multiple possible
distinct mRNA isoforms. These alternative splicing patterns encourage molecular
diversity and dysregulation of isoform expression plays an important role in
disease etiology. However, isoforms are difficult to characterize from
short-read RNA-seq data because they share identical subsequences and exist in
tissue- and sample-specific frequencies. Here, we develop BIISQ, a Bayesian
nonparametric model to discover Isoforms and Individual Specific Quantification
from RNA-seq data. BIISQ does not require known isoform reference sequences but
instead estimates isoform composition directly with an isoform catalog shared
across samples. We develop a stochastic variational inference approach for
efficient and robust posterior inference and demonstrate superior precision and
recall for short read RNA-seq simulations and simulated short read data from
PacBio long read sequencing when compared to state-of-the-art isoform
reconstruction methods. BIISQ achieves the most significant gains for longer
(in terms of exons) isoforms and isoforms that are lowly expressed (over 500%
more transcripts correctly inferred at low coverage in simulations). Finally,
we estimate isoforms in the GEUVADIS RNA-seq data, identify genetic variants
that regulate transcript ratios, and demonstrate variant enrichment in
functional elements related to mRNA splicing regulation.


  Defect detection at commit check-in time prevents the introduction of defects
into software systems. Current defect detection approaches rely on metric-based
models which are not very accurate and whose results are not directly useful
for developers. We propose a method to detect bug-inducing commits by comparing
the incoming changes with all past commits in the project, considering both
those that introduced defects and those that did not. Our method considers
individual changes in the commit separately, at the method-level granularity.
Doing so helps developers as they are informed of specific methods that need
further attention instead of being told that the entire commit is problematic.
Our approach represents source code as abstract syntax trees and uses tree
kernels to estimate the similarity of the code with previous commits. We
experiment with subtree kernels (STK), subset tree kernels (SSTK), or partial
tree kernels (PTK). An incoming change is then classified using a K-NN
classifier on the past changes. We evaluate our approach on the BigCloneBench
benchmark and on the Technical Debt dataset, using the NiCad clone detector as
the baseline. Our experiments with the BigCloneBench benchmark show that the
tree kernel approach can detect clones with a comparable MAP to that of NiCad.
Also, on defect detection with the Technical Debt dataset, tree kernels are
least as effective as NiCad with MRR, F-score, and Accuracy of 0.87, 0.80, and
0.82 respectively.


  Deep neural networks have achieved state-of-art performance in many domains
including computer vision, natural language processing and self-driving cars.
However, they are very computationally expensive and memory intensive which
raises significant challenges when it comes to deploy or train them on strict
latency applications or resource-limited environments. As a result, many
attempts have been introduced to accelerate and compress deep learning models,
however the majority were not able to maintain the same accuracy of the
baseline models. In this paper, we describe EnSyth, a deep learning ensemble
approach to enhance the predictability of compact neural network's models.
First, we generate a set of diverse compressed deep learning models using
different hyperparameters for a pruning method, after that we utilise ensemble
learning to synthesise the outputs of the compressed models to compose a new
pool of classifiers. Finally, we apply backward elimination on the generated
pool to explore the best performing combinations of models. On CIFAR-10,
CIFAR-5 data-sets with LeNet-5, EnSyth outperforms the predictability of the
baseline model.


  In Molecular Communications via Diffusion (MCvD), messenger molecules are
emitted by a transmitter and propagate randomly through the fluidic
environment. In biological systems, the environment can be considered a bounded
space, surrounded by various structures such as tissues and organs. The
propagation of molecules is affected by these structures, which reflect the
molecules upon collision. Deriving the channel response of MCvD systems with an
absorbing spherical receiver requires solving the 3-D diffusion equation in the
presence of reflecting and absorbing boundary conditions, which is extremely
challenging. In this paper, the method of images is brought to molecular
communication (MC) realm to find a closed-form solution to the channel response
of a single-input single-output (SISO) system near an infinite reflecting
surface. We showed that a molecular SISO system in a 3-D half-space with an
infinite reflecting surface could be approximated as a molecular single-input
multiple-output (SIMO) system in a 3-D space, which consists of two
symmetrically located, with respect to the reflecting surface, identical
absorbing spherical receivers.


  Classical game theory addresses decision problems in multi-agent environment
where one rational agent's decision affects other agents' payoffs. Game theory
has widespread application in economic, social and biological sciences. In
recent years quantum versions of classical games have been proposed and
studied. In this paper, we consider a quantum version of the classical
Barro-Gordon game which captures the problem of time inconsistency in monetary
economics. Such time inconsistency refers to the temptation of weak policy
maker to implement high inflation when the public expects low inflation. The
inconsistency arises when the public punishes the weak policy maker in the next
cycle. We first present a quantum version of the Barro-Gordon game. Next, we
show that in a particular case of the quantum game, time-consistent Nash
equilibrium could be achieved when public expects low inflation, thus resolving
the game.


  Definition. Let $\kappa$ be an infinite cardinal, let {X(i)} be a (not
necessarily faithfully indexed) set of topological spaces, and let X be the
product of the spaces X(i). The $\kappa$-box product topology on X is the
topology generated by those products of sets U(i) for which
  (a) for each i, U(i) is open in X(i); and
  (b) U(i) = X(i) with fewer than $\kappa$-many exceptions. (Thus, the usual
Tychonoff product topology on X is the $\omega$-box topology.)
  With emphasis on weight, density character, and Souslin number, the authors
study and determine the value of several "cardinal invariants" on the space X
with its $\kappa$-box topology, in terms of the corresponding invariants of the
individual spaces X(i).
  To the authors' knowledge, this work is the first systematic study of its
kind. Some of the results are axiom-sensitive, and some duplicate (and extend,
and make precise) earlier work of Hewitt-Marczewski-Pondiczery, of
Englking-Karlowicz, of Comfort-Negrepontis, and of Cater-Erdos-Galvin.


  We introduce and study a family of operators which act in the span of a Weyl
group $W$ and provide a multi-parameter solution to the quantum Yang-Baxter
equations of the corresponding type. Our operators generalize the "quantum
Bruhat operators" that appear in the explicit description of the multiplicative
structure of the (small) quantum cohomology ring of $G/B$.
  The main combinatorial applications concern the "tilted Bruhat order," a
graded poset whose unique minimal element is an arbitrarily chosen element
$w\in W$. (The ordinary Bruhat order corresponds to the case $w=1$.) Using the
mixed Bruhat operators, we prove that these posets are lexicographically
shellable, and every interval in a tilted Bruhat order is Eulerian. This
generalizes well known results of Verma, Bjorner, Wachs, and Dyer.


  It was recently argued that string theory on ${\rm AdS}_3\times {\rm
S}^3\times \mathbb{T}^4$ with one unit ($k=1$) of NS-NS flux is exactly dual to
the symmetric orbifold CFT ${\rm Sym}^N(\mathbb{T}^4)$. In this paper we show
how to directly relate the $n$-point correlators of the two sides to one
another. In particular, we argue that the correlators of the world-sheet theory
are delta-function-localised in string moduli space to those configurations
that allow for a holomorphic covering map of the $\text{S}^2$-boundary of
$\text{AdS}_3$ by the world-sheet. This striking feature can be seen both from
a careful Ward identity analysis, as well as from semi-classically exact
AdS$_3$ solutions that are pinned to the boundary. The world-sheet correlators
therefore have exactly the same structure as in the Lunin-Mathur construction
of symmetric orbifold CFT correlators in terms of a covering surface -- which
now gets identified with the world-sheet. Together with the results of
arXiv:1803.04423 and arXiv:1812.01007 this essentially demonstrates how the
$k=1$ $\text{AdS}_3$ string theory becomes equivalent to the spacetime orbifold
CFT in the genus expansion.


  We report the detection of a 9.7 $\mu$m silicate dust absorption feature
toward the Cygnus A nucleus. Its optical depth is, however, significantly
smaller than that expected from the dust extinction toward the background
$L$-band emission region ($A_{\rm V}$ $\sim$ 150 mag). We argue that the most
likely explanation for the small optical depth is that the obscuring dust
exists so close to the central engine that a temperature gradient occurs. Our
calculation confirms that the small optical depth and the spectral energy
distribution at 3--30 $\mu$m can be quantitatively reproduced by this
explanation. Combining this picture with the huge AGN luminosity, the emission
properties of Cygnus A are consistent with those of a type 2 quasar, that is, a
highly luminous AGN that is highly obscured ($A_{\rm V}$ $>$ 50 mag) by a dusty
torus with an inner radius of $<$10 pc, and not by $>$ a few 100 pc scale dust
in the host galaxy.


  In this work we analyze the spectroscopic properties of a large number of H
ii regions, \sim2600, located in 38 galaxies. The sample of galaxies has been
assembled from the face-on spirals in the PINGS survey and a sample described
in M\'armol-Queralt\'o (2011, henceforth Paper I). All the galaxies were
observed using Integral Field Spectroscopy with a similar setup, covering their
optical extension up to \sim2.4 effective radii within a wavelength range from
\sim3700 to \sim6900{\AA}. We develop a new automatic procedure to detect H ii
regions, based on the contrast of the H{\alpha} intensity maps. Once detected,
the procedure provides us with the integrated spectra of each individual
segmented region. A well-tested automatic decoupling procedure has been applied
to remove the underlying stellar population, deriving the main proper- ties of
the strongest emission lines in the considered wavelength range (covering from
[O ii] {\lambda}3727 to [S ii] {\lambda}6731). A final catalogue of the
spectroscopic properties of these regions has been created for each galaxy. In
the current study we focused on the understanding of the average properties of
the H ii regions and their radial distributions. We find that the gas-phase
oxygen abundance and the H{\alpha} equivalent width present negative and
positive gradient, respectively. The distribution of slopes is statistically
compatible with a random Gaussian distribution around the mean value, if the
radial distances are measured in units of the respective effective radius. No
difference in the slope is found for galaxies of different morphologies:
barred/non-barred, grand-design/flocculent. Therefore, the effective radius is
a universal scale length for gradients in the evolution of galaxies. Other
properties have a larger variance across each object.


  Let $C$ be a curve in $\mathbb{P}^4$ and $X$ be a hypersurface containing it.
We show how it is possible to construct a matrix factorization on $X$ from the
pair $(C,X)$ and, conversely, how a matrix factorization on $X$ leads to curves
lying on $X$. We use this correspondence to prove the unirationality of the
Hurwitz space $\mathcal{H}_{12,8}$ and the uniruledness of the Brill-Noether
space $\mathcal{W}^1_{13,9}$. Several unirational families of curves of genus
$16 \leq g \leq 20$ in $\mathbb{P}^4$ are also exhibited.


  We use the method of free energy minimization based on the first law of
thermodynamics to derive static meniscus shapes for crystal ribbon growth
systems. To account for the possibility of multivalued curves as solutions to
the minimization problem, we choose a parametric representation of the meniscus
geometry. Using Weierstrass' form of the Euler-Lagrange equation we derive
analytical solutions that provide explicit knowledge on the behaviour of the
meniscus shapes. Young's contact angle and Gibbs pinning conditions are also
analyzed and are shown to be a consequence of the energy minimization problem
with variable end-points. For a given ribbon growth configuration, we find that
there can exist multiple static menisci that satisfy the boundary conditions.
The stability of these solutions is analyzed using second order variations and
are found to exhibit saddle node bifurcations. We show that the arc length is a
natural representation of a meniscus geometry and provides the complete
solution space, not accessible through the classical variational formulation.
We provide a range of operating conditions for hydro-statically feasible
menisci and illustrate the transition from a stable to spill-over configuration
using a simple proof of concept experiment.


  We demonstrate that quantum-critical spin dynamics can be probed in high
magnetic fields using muon-spin relaxation ($\mu^{+}$SR). Our model system is
the strong-leg spin ladder bis(2,3-dimethylpyridinium) tetrabromocuprate
(DIMPY). In the gapless Tomonaga-Luttinger liquid phase we observe
finite-temperature scaling of the $\mu^{+}$SR $1/T_1$ relaxation rate which
allows us to determine the Luttinger parameter $K$. We discuss the benefits and
limitations of local probes compared with inelastic neutron scattering.


  Extremal scalar three-point correlators in the near-NHEK geometry of Kerr
black holes have recently been shown to agree with the result expected from a
holographically dual non-chiral two-dimensional conformal field theory. In this
paper we extend this calculation to extremal three-point functions of scalars
in a general Kerr black hole which need not obey the extremality condition
$M=\sqrt{J}$. It was recently argued that for low frequency scalars in the Kerr
geometry there is a dual conformal field theory description which determines
the interactions in this regime. Our results support this conjecture.
Furthermore, we formulate a recipe for calculating finite-temperature retarded
three-point correlation functions which is applicable to a large class of (even
non-extremal) correlators, and discuss the vanishing of the extremal couplings.


  We consider random walks in a uniformly elliptic, balanced, i.i.d. random
environment in the integer lattice $Z^d$ for $d\geq 2$ and the corresponding
problem of stochastic homogenization of non-divergence form difference
operators. We first derive a quantitative law of large numbers for the
invariant measure, which is nearly optimal. A mixing property of the field of
the invariant measure is then achieved. We next obtain rates of convergence for
the homogenization of the Dirichlet problem for non-divergence form operators,
which are generically optimal for $d\geq 3$ and nearly optimal when $d=2$.
Furthermore, we establish the existence, stationarity and uniqueness properties
of the corrector problem for all dimensions $d\ge 2$. Afterwards, we quantify
the ergodicity of the environmental process for both the continuous-time and
discrete-time random walks, and as a consequence, we get explicit convergence
rates for the quenched central limit theorem of the balanced random walk.


  Protoplanetary discs exhibit a diversity of gaps and rings of dust material,
believed to be a manifestation of pressure maxima commonly associated with an
ongoing planet formation and several other physical processes. Hydrodynamic
disc simulations further suggest that multiple dust ring-like structures may be
ubiquitous in discs. In the recent past, it has been shown that dust rings may
provide a suitable avenue for planet formation. We study how a globally
perturbed disc affects dust evolution and core growth by pebble accretion. We
performed global disc simulations featuring a Gaussian pressure profile, in
tandem with global perturbations of the gas density, mimicking wave-like
structures, and simulated planetary core formation at pressure minima and
maxima. With Gaussian pressure profiles, grains in the inside disc regions were
extremely depleted in the first 0.1 Myrs of disc lifetime. The global pressure
bumps confined dust material for several million years, depending on the
strength of perturbations. A variety of cores formed in bumpy discs, with
massive cores at locations where core growth was not feasible in a smooth disc,
and small cores at locations where massive cores could form in a smooth disc.
We conclude that pressure bumps generated by a planet and/or other physical
phenomena can completely thwart planet formation from the inside parts of the
disc. While inner disc parts are most favourable for pebble accretion in a
smooth disc, multiple wave-like pressure bumps can promote rapid planet
formation by pebble accretion in broad areas of the disc.


  We investigate two greedy strategies for finding an approximation to the
minimum of a convex function $E$ defined on a Hilbert space $H$. We prove
convergence rates for these algorithms under suitable conditions on the
objective function $E$. These conditions involve the behavior of the modulus of
smoothness and the modulus of uniform convexity of $E$.


  The strengths of glasses are intricately linked to their atomic-level
heterogeneity. Atomistic simulations are frequently used to investigate the
statistical physics of this relationship, compensating for the limited
spatiotemporal resolution in experimental studies. However, theoretical
insights are limited by the complexity of glass structures and the accuracy of
the interatomic potentials used in simulations. Here, we investigate the
strengths and fracture mechanisms of 2D silica, with all structural units
accessible to direct experimental observation. We develop a neural network
force field for fracture (NN-F$^{3}$) based on the deep potential-smooth
edition (DeepPot-SE) framework. Representative atomic structures across
crystals, nanocrystalline, paracrystalline, and continuous random network
glasses are studied. We find that the virials or bond lengths control the
initialization of bond-breaking events, creating nanoscale voids in the
vitreous network. However, the voids do not necessarily lead to crack
propagation due to a disorder-trapping effect, which is stronger than the
lattice-trapping effect in a crystalline lattice and occurs over larger length
and time scales. Fracture initiation proceeds with void growth and coalescence,
and advances through a bridging mechanism. The fracture patterns are shaped by
subsequent trapping and cleavage steps, often guided by voids forming ahead of
the crack tip. These heterogeneous processes result in atomically smooth facets
in crystalline regions and rough, amorphous edges in the glassy phase. These
insights into 2D crystals and glasses, both sharing SiO$_{2}$ chemistry,
highlight the pivotal role of atomic-level structures in determining fracture
kinetics and path selection in materials.


  The performance of neural network-based speech enhancement systems is
primarily influenced by the model architecture, whereas training times and
computational resource utilization are primarily affected by training
parameters such as the batch size. Since noisy and reverberant speech mixtures
can have different duration, a batching strategy is required to handle variable
size inputs during training, in particular for state-of-the-art end-to-end
systems. Such strategies usually strive for a compromise between zero-padding
and data randomization, and can be combined with a dynamic batch size for a
more consistent amount of data in each batch. However, the effect of these
strategies on resource utilization and more importantly network performance is
not well documented. This paper systematically investigates the effect of
different batching strategies and batch sizes on the training statistics and
speech enhancement performance of a Conv-TasNet, evaluated in both matched and
mismatched conditions. We find that using a small batch size during training
improves performance in both conditions for all batching strategies. Moreover,
using sorted or bucket batching with a dynamic batch size allows for reduced
training time and GPU memory usage while achieving similar performance compared
to random batching with a fixed batch size.


  The gamma-ray astronomical observatory INTEGRAL, succesfully launched on 17th
October 2002, carries two large gamma-ray telescopes. One of them is the
coded-mask imaging gamma-ray telescope onboard the INTEGRAL satellite (IBIS)
which provides high-resolution (~ 12') sky images of 29deg x 29deg in the
energy range from 15 keV to 10 MeV with typical on-axis sensitivity of ~ 1
mCrab at 100 keV (3 sigma, 10E6 s exposure). We report here the general
description of the IBIS coded-mask imaging system and of the standard IBIS
science data analysis procedures. These procedures reconstruct, clean and
combine IBIS sky images providing at the same time detection, identification
and preliminary analysis of point-like sources present in the field. Spectral
extraction has also been implemented and is based on simultaneous fitting of
source and background shadowgram models to detector images. The procedures are
illustrated using some of the IBIS data collected during the inflight
calibrations and present performance is discussed. The analysis programs
described here have been integrated as instrument specific software in the
Integral Science Data Center (ISDC) analysis software packages currently used
for the Quick Look, Standard and Off-line Scientific Analysis.


  Inflationary and bouncing scenarios are two frameworks that provide the
mechanism to overcome the horizon problem as well as generate the primordial
perturbations. In this work, we investigate the conservation of perturbations
in single-field models of both inflationary and bouncing scenarios, where the
quantity, $z = a \, \rm d \phi/{\rm d}\log a$, with $a$ representing the scale
factor and $\phi$ denoting the scalar field, decreases with time. We observe
that this behaviour occurs during the ultra-slow-roll phase in the context of
inflation and the contracting phase in the context of bounce. We show that the
conjugate momentum associated with the comoving curvature perturbation during
both the ultra-slow-roll phase and the contracting phase of bouncing scenarios
is conserved in the super-Hubble limit. We illustrate that, within the
framework of inflation, this conservation of momentum allows for the evolution
of perturbations across the ultra-slow-roll phase, enabling the calculation of
the power spectrum for modes that exit the Hubble radius before the
ultra-slow-roll phase begins. Similarly, in the context of a bounce, we can
determine the power spectrum after the bounce using this method. We support our
approach with both numerical and analytical arguments.


  Uplift is a particular case of individual treatment effect modeling. Such
models deal with cause-and-effect inference for a specific factor, such as a
marketing intervention. In practice, these models are built on customer data
who purchased products or services to improve product marketing. Uplift is
estimated using either i) conditional mean regression or ii) transformed
outcome regression. Most existing approaches are adaptations of classification
and regression trees for the uplift case. However, in practice, these
conventional approaches are prone to overfitting. Here we propose a new method
using neural networks. This representation allows to jointly optimize the
difference in conditional means and the transformed outcome losses. As a
consequence, the model not only estimates the uplift, but also ensures
consistency in predicting the outcome. We focus on fully randomized
experiments, which is the case of our data. We show our proposed method
improves the state-of-the-art on synthetic and real data.


  Suppose we are given black-box access to a finite ring R, and a list of
generators for an ideal I in R. We show how to find an additive basis
representation for I in poly(log |R|) time. This generalizes a quantum
algorithm of Arvind et al. which finds a basis representation for R itself. We
then show that our algorithm is a useful primitive allowing quantum computers
to rapidly solve a wide variety of problems regarding finite rings. In
particular we show how to test whether two ideals are identical, find their
intersection, find their quotient, prove whether a given ring element belongs
to a given ideal, prove whether a given element is a unit, and if so find its
inverse, find the additive and multiplicative identities, compute the order of
an ideal, solve linear equations over rings, decide whether an ideal is
maximal, find annihilators, and test the injectivity and surjectivity of ring
homomorphisms. These problems appear to be hard classically.


  We investigate effects of strong interactions on the electromagnetic
dissociation of nuclei in heavy ion collisions. We start from the eikonal
approach to the equivalent photon method to describe the electromagnetic
contributions to the cross section of peripheral collisions. We summarize some
results of this approach and characterize recent experiments in "universal
plots". In the second part of this work, we give a straight forward method to
include transitions induced by the strong interactions between the ions. We
introduce different methods to obtain the nuclear transition potential, and
study the behavior of the resulting nuclear contributions.


  Answer Set Planning refers to the use of Answer Set Programming (ASP) to
compute plans, i.e., solutions to planning problems, that transform a given
state of the world to another state. The development of efficient and scalable
answer set solvers has provided a significant boost to the development of
ASP-based planning systems. This paper surveys the progress made during the
last two and a half decades in the area of answer set planning, from its
foundations to its use in challenging planning domains. The survey explores the
advantages and disadvantages of answer set planning. It also discusses typical
applications of answer set planning and presents a set of challenges for future
research.


  Dense clouds of neutrinos and antineutrinos can exhibit fast collective
flavor oscillations. Previously, in Phys. Rev. Lett. 126 (2021) 061302, we
proposed that such flavor oscillations lead to depolarization, i.e., an
irreversible mixing of the flavors, whose extent depends on the initial
momentum distributions of the different flavors. In this paper, we elaborate
and extend this proposal, and compare it with related results in the
literature. We present an accurate analytical estimate for the lower resting
point of the fast flavor pendulum and underline the relaxation mechanisms,
i.e., transverse relaxation, multipole cascade, and mixing of flavor-waves,
that cause it to settle down. We estimate the extent of depolarization, its
dependence on momentum and net lepton asymmetry, and its generalization to
three flavors. Finally, we prescribe approximate analytical recipes for the
depolarized distributions and fluxes that can be used in
supernova/nucleosynthesis simulations and supernova neutrino phenomenology.


  Human activity recognition has drawn considerable attention recently in the
field of computer vision due to the development of commodity depth cameras, by
which the human activity is represented as a sequence of 3D skeleton postures.
Assuming human body 3D joint locations of an activity lie on a manifold, the
problem of recognizing human activity is formulated as the computation of
activity manifold-manifold distance (AMMD). In this paper, we first design an
efficient division method to decompose a manifold into ordered continuous
maximal linear patches (CMLPs) that denote meaningful action snippets of the
action sequence. Then the CMLP is represented by its position (average value of
points) and the first principal component, which specify the major posture and
main evolving direction of an action snippet, respectively. Finally, we compute
the distance between CMLPs by taking both the posture and direction into
consideration. Based on these preparations, an intuitive distance measure that
preserves the local order of action snippets is proposed to compute AMMD. The
performance on two benchmark datasets demonstrates the effectiveness of the
proposed approach.


  Let $X$ be a compact normal complex space of dimension $n$, and $L$ be a
holomorphic line bundle on $X$. Suppose $\Sigma=(\Sigma_1,\ldots,\Sigma_\ell)$
is an $\ell$-tuple of distinct irreducible proper analytic subsets of $X$,
$\tau=(\tau_1,\ldots,\tau_\ell)$ is an $\ell$-tuple of positive real numbers,
and consider the space $H^0_0 (X, L^p)$ of global holomorphic sections of
$L^p:=L^{\otimes p}$ that vanish to order at least $\tau_{j}p$ along
$\Sigma_{j}$, $1\leq j\leq\ell$. We find necessary and sufficient conditions
which ensure that $\dim H^0_0(X,L^p)\sim p^n$, analogous to Ji-Shiffman's
criterion for big line bundles. We give estimates of the partial Bergman
kernel, investigate the convergence of the Fubini-Study currents and their
potentials, and the equilibrium distribution of normalized currents of
integration along zero divisors of random holomorphic sections in $H^0_0 (X,
L^p)$ as $p\to\infty$. Regularity results for the equilibrium envelope are also
included.


  An abstract DNA-type system is defined by a set of nonlinear kinetic
equations with polynomial nonlinearities that admit soliton solutions
associated with helical geometry. The set of equations allows for two different
Lax representations: A von Neumann form and a Darboux-covariant Lax pair. We
explain why non-Kolmogorovian probability models occurring in soliton kinetics
are naturally associated with chemical reactions. The most general known
characterization of soliton kinetic equations is given and a class of explicit
soliton solutions is discussed. Switching between open and closed states is a
generic behaviour of the helices. The effect does not crucially depend on the
order of nonlinearity (i.e. types of reactions), a fact that may explain why
simplified models possess properties occuring in realistic systems. We explain
also why fluctuations based on Darboux transformations will not destroy the
dynamics but only switch between a finite number of helical structures.


  We investigate the structure of the Milky Way by determining how features in
a spatial map correspond to CO features in a velocity map. We examine
structures including logarithmic spiral arms, a ring and a bar. We explore the
available parameter space, including the pitch angle of the spiral arms, radius
of a ring, and rotation curve. We show that surprisingly, a spiral arm provides
a better fit to the observed molecular ring than a true ring feature. This is
because both a spiral arm, and the observed feature known as the molecular
ring, are curved in velocity longitude space. We find that much of the CO
emission in the velocity longitude map can be fitted by a nearly symmetric 2
armed spiral pattern. One of the arms corresponds to the molecular ring, whilst
the opposite arm naturally reproduces the Perseus arm. Multiple arms also
contribute to further emission in the vicinity of the molecular ring and match
other observed spiral arms. Whether the Galactic structure consists primarily
of two, or several spiral arms, the presence of 2 symmetric logarithmic
spirals, which begin in the vicinity of the ends of the bar, suggest a spiral
density wave associated with the bar.


  We prove some uniqueness results for the Riemann zeta-function and the Euler
gamma-function by virtue of shared values using the value distribution theory.


  We present high-resolution, high-sensitivity radio images of the
ultra-luminous infrared galaxy (ULIRG) IRAS 23365+3604. We performed
contemporaneous observations at 1.7 and 5.0 GHz, in three epochs separated by
one year from each other, with the European very long baseline interferometry
Network (EVN). We also present complementary Multi-Element Radio Linked
Interferometry Network (MERLIN) at 1.6 and 5.0 GHz, and archival Very Large
Array (VLA) data, taken at 1.4 and 4.9 GHz. We find that the emission at ~5.0
GHz remains quite compact as seen at different resolutions, whereas at ~1.7
GHz, high resolution imaging reveals some extended structure. The nuclear
region has an approximate linear size of 200 pc and shows the presence of two
main emission components: i) one with a composite spectrum due to ongoing
non-thermal activity (probably due to recently exploded supernovae and AGN
activity), ii) another one with a steep spectrum, likely dominated by an old
population of radio emitters, such as supernova remnants (SNRs). Radiative
losses are important, so re-acceleration or replenishment of new electrons is
necessary. We estimate a magnetic field strength of 18 \mu G at galactic, and
175 \mu G at nuclear scales, which are typical for galaxies in advanced
mergers.


  The aim of this paper is to present basic notions of dense matter physics and
some of its applications to geophysics and astronomy.Topics covered in the
paper include:basic observational data,fun- damental ideas of static high
pressure experiments, notions of theoretical dense matter physics, and finally
some details about theoretical work on dense matter physics and its
astronomical applications in Serbia.


  Recent experimental results have confirmed a possible reduction in the GT$_+$
strengths of pf-shell nuclei. These proton-rich nuclei are of relevance in the
deflagration and explosive burning phases of Type Ia supernovae. While prior GT
strengths result in nucleosynthesis predictions with a lower-than-expected
electron fraction, a reduction in the GT$_+$ strength can result in an slightly
increased electron fraction compared to previous shell model predictions,
though the enhancement is not as large as previous enhancements in going from
rates computed by Fuller, Fowler, and Newman based on an independent particle
model. A shell model parametrization has been developed which more closely
matches experimental GT strengths. The resultant electron-capture rates are
used in nucleosynthesis calculations for carbon deflagration and explosion
phases of Type Ia supernovae, and the final mass fractions are compared to
those obtained using more commonly-used rates.


  The motion of a charged particle in a nonuniform straight magnetic field with
a uniform magnetic-field gradient is solved exactly in terms of elliptic
functions. The connection between this problem and the guiding-center
approximation is discussed. It is shown that, for this problem, the predictions
of guiding-center theory agree very well with the orbit-averaged particle
motion and hold well beyond the standard guiding-center limit $\epsilon \equiv
\rho/L \ll 1$, where $\rho$ is the gyromotion length scale and $L$ is the
magnetic-field gradient length scale.


  We show that, under certain conditions, the micromaser can act as an
effective source of highly correlated atoms. It is possible to create an
extended robust entanglement between two successive, initially unentangled
atoms passing through a cavity filled with with a nonlinear medium taking into
consideration a slight level shift. Information is transfered from the cavity
to the atoms in order to build up entanglement. The scheme has an advantage
over conventional creation of entanglement if the two atoms (qubits) are so far
apart that a direct interaction is difficult to achieve. The interaction of the
atoms with the micromaser occurs under the influence of a two-quantum
transition process. Interesting phenomena are observed, and an extended robust
entangled state is obtained for different values of the system parameters.
Illustrative variational calculations are performed to demonstrate the effect
within an analytically tractable two-qubit model.


  We investigate a perturbative extension of the Standard Model featuring
elementary pseudo-Goldstone Higgs and dark matter particles. These are two of
the five Goldstone bosons parametrising the SU(4)/Sp(4) coset space. They
acquire masses, and therefore become pseudo-Goldstone bosons, due to the
embedding of the Yukawa and the electroweak gauge interactions that do not
preserve the full SU(4) symmetry. At the one-loop order the top corrections
dominate and align the vacuum in the direction where the Higgs is mostly a
pseudo-Goldstone boson. Because of the perturbative and elementary nature of
the theory, the quantum corrections are precisely calculable. The remaining
pseudo-Goldstone boson is identified with the dark matter candidate because it
is neutral with respect to the Standard Model and stable. By a direct
comparison with the Large Hadron Collider experiments, the model is found to be
phenomenologically viable. Furthermore the dark matter particle leads to the
observed thermal relic density while respecting the most stringent current
experimental constraints.


  In \cite{BaDeFePi96} the concept of nondecreasing Dyck paths was introduced.
We continue this research by looking at it from the point of view of words,
rational languages, planted plane trees, and continued fractions.
  We construct a bijection with planted plane trees of height $\le 4$ and
compute various statistics on trees that are the equivalents of nondecreasing
Dyck paths.


  We present new millimeter and radio observations of nine z~6 quasars
discovered in deep optical and near-infrared surveys. We observed the 250 GHz
continuum in eight of the nine objects and detected three of them. New 1.4 GHz
radio continuum data have been obtained for four sources, and one has been
detected. We searched for molecular CO (6-5) line emission in the three 250 GHz
detections and detected two of them. We study the FIR and radio emission and
quasar-host galaxy evolution with a sample of 18 z~6 quasars that are faint at
UV/optical wavelengths (rest-frame 1450A magnitudes of m_1450\ge20.2). The
average FIR-to-AGN UV luminosity ratio of this faint quasar sample is about two
times higher than that of the bright quasars at z~6 (m_1450<20.2). A fit to the
average FIR and AGN bolometric luminosities of both the UV/optically faint and
bright z~6 quasars, and the average luminosities of samples of submillimeter
/millimeter-observed quasars at z~2 to 5, yields a relationship of L_{FIR}
{L_{bol}}^{0.62}. Five of the 18 faint z~6 quasars have been detected at 250
GHz. These 250 GHz detections, as well as most of the millimeter-detected
optically bright z~6 quasars, follow a shallower trend of L_{FIR}
{L_{bol}}^{0.45} defined by the starburst-AGN systems in local and high-z
universe. The millimeter continuum detections in the five objects and molecular
CO detections in three of them reveal a few x10^8 M_sun of FIR-emitting warm
dust and 10^10 M_sun of molecular gas in the quasar host galaxies. All these
results argue for massive star formation in the quasar host galaxies, with
estimated star formation rates of a few hundred M_sun yr^{-1}. Additionally,
the higher FIR-to-AGN luminosity ratio found in these 250 GHz-detected faint
quasars also suggests a higher ratio between star formation rate and
supermassive black hole accretion rate than the UV/optically most luminous
quasars at z~6.


  We propose a road-map to experimental implementation of cytoskeleton-based
computing devices. An overall concept is described in the following.
Collision-based cytoskeleton computers implement logical gates via interactions
between travelling localisation (voltage solitons on AF/MT chains and AF/MT
polymerisation wave fronts). Cytoskeleton networks are grown via programmable
polymerisation. Data are fed into the AF/MT computing networks via electrical
and optical means. Data signals are travelling localisations (solitons,
conformational defects) at the network terminals. The computation is
implemented via collisions between the localisations at structural gates
(branching sites) of the AF/MT network. The results of the computation are
recorded electrically and/or optically at the output terminals of the protein
networks. As additional options, optical I/O elements are envisaged via direct
excitation of the protein network and by coupling to fluorescent molecules.


  We show that the full spurionic symmetry of Galilean-invariant field theories
can be deduced when those theories are the limits of relativistic parents.
Under the limit, the non-relativistic daughter couples to Newton-Cartan
geometry together with all of the symmetries advocated in previous work,
including the recently revived Milne boosts. Our limit is a covariant version
of the usual one, where we start with a gapped relativistic theory with a
conserved charge, turn on a chemical potential equal to the rest mass of the
lightest charged state, and then zoom in to the low energy sector. This
procedure gives a simple physical interpretation for the Milne boosts. Our
methods even apply when there is a magnetic moment, which is known to modify
the non-relativistic symmetry transformations. We focus on two examples, taking
the non-relativistic limits of scalar field theory and hydrodynamics.


  We describe and implement a technique for extracting forces from the
relaxation of an overdamped thermal system with normal modes. At sufficiently
short time intervals, the evolution of a normal mode is well described by a
one-dimensional Smoluchowski equation with constant drift velocity, v, and
diffusion coefficient, D. By virtue of fluctuation-dissipation, these transport
coefficients are simply related to conservative forces, F, acting on the normal
mode: F = k_BT v/D. This relationship implicitly accounts for hydrodynamic
interactions, requires no mechanical calibration, makes no assumptions about
the form of conservative forces, and requires no prior knowledge of material
properties. We apply this method to measure the electrostatic interactions of
polymer microspheres suspended in nonpolar microemulsions.


  We present a method to measure potentials over an extended region using
one-dimensional ion crystals in a radio frequency (RF) ion trap. The
equilibrium spacings of the ions within the crystal allow the determination of
the external forces acting at each point. From this the overall potential, and
also potentials due to specific trap features, are calculated. The method can
be used to probe potentials near proximal objects in real time, and can be
generalized to higher dimensions.


  We use large hybrid (kinetic protons-fluid electrons) simulations to
investigate the transport of energetic particles in self-consistent
electromagnetic configurations of collisionless shocks. In previous papers of
this series, we showed that ion acceleration may be very efficient (up to
$10-20\%$ in energy), and outlined how the streaming of energetic particles
amplifies the upstream magnetic field. Here, we measure particle diffusion
around shocks with different strengths, finding that the mean free path for
pitch-angle scattering of energetic ions is comparable with their gyroradii
calculated in the self-generated turbulence. For moderately-strong shocks,
magnetic field amplification proceeds in the quasi-linear regime, and particles
diffuse according to the self-generated diffusion coefficient, i.e., the
scattering rate depends only on the amount of energy in modes with wavelengths
comparable with the particle gyroradius. For very strong shocks, instead, the
magnetic field is amplified up to non-linear levels, with most of the energy in
modes with wavelengths comparable to the gyroradii of highest-energy ions, and
energetic particles experience Bohm-like diffusion in the amplified field. We
also show how enhanced diffusion facilitates the return of energetic particles
to the shock, thereby determining the maximum energy that can be achieved in a
given time via diffusive shock acceleration. The parametrization of the
diffusion coefficient that we derive can be used to introduce self-consistent
microphysics into large-scale models of cosmic ray acceleration in
astrophysical sources, such as supernova remnants and clusters of galaxies.


  The interaction between substitutional nitrogen atoms in graphene is studied
by performing first principles calculations. The nearest neighbor interaction
between nitrogen dopants is highly repulsive because of the strong
electrostatic repulsion between nitrogen atoms, which prevents the full phase
separation in nitrogen doped graphene. Interestingly, there are two relatively
stable nitrogen-nitrogen pairs due to the anisotropy charge redistribution
induced by nitrogen doping. We reveal two stable semiconducting ordered N doped
graphene structures C3N and C12N through the cluster expansion technique and
particle swarm optimization method. In particular, C12N has a direct band gap
of 0.98 eV. The heterojunctions between C12N and graphene nanoribbons might be
promising organic solar cells.


  Many-body localization was proven under realistic assumptions by constructing
a quasi-local unitary rotation that diagonalizes the Hamiltonian (Imbrie,
2016). A natural generalization is to consider all unitaries that have a
similar structure. We bound entanglement for states generated by such
unitaries, thus providing an independent proof of area law in eigenstates of
many-body localized systems. An error of approximating the unitary by a
finite-depth local circuit is obtained. We connect the defined family of
unitaries to other results about many-body localization (Kim et al, 2014), in
particular Lieb-Robinson bound. Finally we argue that any Hamiltonian can be
diagonalized by such a unitary, given it has a slow enough logarithmic
lightcone in its Lieb-Robinson bound.


  The problem of online change point detection is to detect abrupt changes in
properties of time series, ideally as soon as possible after those changes
occur. Existing work on online change point detection either assumes i.i.d
data, focuses on asymptotic analysis, does not present theoretical guarantees
on the trade-off between detection accuracy and detection delay, or is only
suitable for detecting single change points. In this work, we study the online
change point detection problem for linear dynamical systems with unknown
dynamics, where the data exhibits temporal correlations and the system could
have multiple change points. We develop a data-dependent threshold that can be
used in our test that allows one to achieve a pre-specified upper bound on the
probability of making a false alarm. We further provide a finite-sample-based
bound for the probability of detecting a change point. Our bound demonstrates
how parameters used in our algorithm affect the detection probability and
delay, and provides guidance on the minimum required time between changes to
guarantee detection.


  Methods to detect malignant lesions from screening mammograms are usually
trained with fully annotated datasets, where images are labelled with the
localisation and classification of cancerous lesions. However, real-world
screening mammogram datasets commonly have a subset that is fully annotated and
another subset that is weakly annotated with just the global classification
(i.e., without lesion localisation). Given the large size of such datasets,
researchers usually face a dilemma with the weakly annotated subset: to not use
it or to fully annotate it. The first option will reduce detection accuracy
because it does not use the whole dataset, and the second option is too
expensive given that the annotation needs to be done by expert radiologists. In
this paper, we propose a middle-ground solution for the dilemma, which is to
formulate the training as a weakly- and semi-supervised learning problem that
we refer to as malignant breast lesion detection with incomplete annotations.
To address this problem, our new method comprises two stages, namely: 1)
pre-training a multi-view mammogram classifier with weak supervision from the
whole dataset, and 2) extending the trained classifier to become a multi-view
detector that is trained with semi-supervised student-teacher learning, where
the training set contains fully and weakly-annotated mammograms. We provide
extensive detection results on two real-world screening mammogram datasets
containing incomplete annotations, and show that our proposed approach achieves
state-of-the-art results in the detection of malignant breast lesions with
incomplete annotations.


  We have studied solid hydrogen under pressure at low temperatures. With
increasing pressure we observe changes in the sample, going from transparent,
to black, to a reflective metal, the latter studied at a pressure of 495 GPa.
We have measured the reflectance as a function of wavelength in the visible
spectrum finding values as high as 0.90 from the metallic hydrogen. We have fit
the reflectance using a Drude free electron model to determine the plasma
frequency of 30.1 eV at T= 5.5 K, with a corresponding electron carrier density
of 6.7x1023 particles/cm3, consistent with theoretical estimates. The
properties are those of a metal. Solid metallic hydrogen has been produced in
the laboratory.


  Accelerated proximal gradient methods have recently been developed for
solving quasi-static incremental problems of elastoplastic analysis with some
different yield criteria. It has been demonstrated through numerical
experiments that these methods can outperform conventional optimization-based
approaches in computational plasticity. However, in literature these algorithms
are described individually for specific yield criteria, and hence there exists
no guide for application of the algorithms to other yield criteria. This short
paper presents a general form of algorithm design, independent of specific
forms of yield criteria, that unifies the existing proximal gradient methods.
Clear interpretation is also given to each step of the presented general
algorithm so that each update rule is linked to the underlying physical laws in
terms of mechanical quantities.


  This white paper concerns theoretical and phenomenological aspects relevant
to the physics of future $e^+e^-$ colliders, in particular regarding
initial-state QED radiation. The contributions each contain key technical
aspects, and are formulated in a pedagogical manner so as to render them
accessible also to those who are not directly working on these and
immediately-related topics. This should help both experts and non-experts
understand the theoretical challenges that we shall face at future $e^+e^-$
colliders. Specifically, this paper contains descriptions of the treatment of
initial state radiation from several Monte Carlo collaborations, as well as
contributions that explain a number of more theoretical developments with
promise of future phenomenological impact.


  In this article, we study the topology and bifurcations of the moduli space
$\mathcal{M}_3$ of cubic Newton maps. It's a subspace of the moduli space of
cubic rational maps, carrying the Riemann orbifold structure
$(\mathbb{\widehat{C}}, (2,3,\infty))$. We prove two results: (1). The boundary
of the unique unbounded hyperbolic component is a Jordan arc and the boundaries
of all other hyperbolic components are Jordan curves. (2).The Head's angle map
is surjective and monotone. The fibers of this map are characterized
completely.
  The first result is a moduli space analogue of the first author's dynamical
regularity theorem \cite{Ro08}. The second result confirms a conjecture of Tan
Lei.


  The Large language models (LLMs) have showcased superior capabilities in
sophisticated tasks across various domains, stemming from basic question-answer
(QA), they are nowadays used as decision assistants or explainers for
unfamiliar content. However, they are not always correct due to the data
sparsity in specific domain corpus, or the model's hallucination problems.
Given this, how much should we trust the responses from LLMs? This paper
presents a novel way to evaluate the uncertainty that captures the directional
instability, by constructing a directional graph from entailment probabilities,
and we innovatively conduct Random Walk Laplacian given the asymmetric property
of a constructed directed graph, then the uncertainty is aggregated by the
derived eigenvalues from the Laplacian process. We also provide a way to
incorporate the existing work's semantics uncertainty with our proposed layer.
Besides, this paper identifies the vagueness issues in the raw response set and
proposes an augmentation approach to mitigate such a problem, we conducted
extensive empirical experiments and demonstrated the superiority of our
proposed solutions.


  To every object $X$ of a symmetric tensor category over a field of
characteristic $p>0$ we attach $p$-adic integers $\text{Dim}_+(X)$ and
$\text{Dim}_-(X)$ whose reduction modulo $p$ is the categorical dimension
$\text{dim}(X)$ of $X$, coinciding with the usual dimension when $X$ is a
vector space. We study properties of $\text{Dim}_{\pm}(X)$, and in particular
show that they don't always coincide with each other, and can take any value in
$\mathbb{Z}_p$. We also discuss the connection of $p$-adic dimensions with the
theory of $\lambda$-rings and Brauer characters.


  We employ the Kramers-Henneberger Hamiltonian for time-independent
calculations of multi-photon ionization of atoms with one and two electrons. As
compared to the electromagnetic interaction in the length and velocity gauges,
the presently employed Kramers-Henneberger gauge has an advantage of the dipole
matrix elements for the free-free electron transitions being finite and
well-defined quantities. This circumstance simplifies considerably the
computations and allows to obtain accurate results for the two-photon
ionization of realistic atomic systems.


  On August 17, 2017 the LIGO interferometers detected the gravitational wave
(GW) signal (GW170817) from the coalescence of binary neutron stars. This
signal was also simultaneously seen throughout the electromagnetic (EM)
spectrum from radio waves to gamma-rays. We point out that this simultaneous
detection of GW and EM signals rules out a class of modified gravity theories,
termed ``dark matter emulators,'' which dispense with the need for dark matter
by making ordinary matter couple to a different metric from that of GW. We
discuss other kinds of modified gravity theories which dispense with the need
for dark matter and are still viable. This simultaneous observation also
provides the first observational test of Einstein's Weak Equivalence Principle
(WEP) between gravitons and photons. We estimate the Shapiro time delay due to
the gravitational potential of the total dark matter distribution along the
line of sight (complementary to the calculation in arXiv:1710.05834) to be
about 400 days. Using this estimate for the Shapiro delay and from the time
difference of 1.7 seconds between the GW signal and gamma-rays, we can
constrain violations of WEP using the parameterized post-Newtonian (PPN)
parameter $\gamma$, and is given by $|\gamma_{\rm {GW}}-\gamma_{\rm{EM}}|<9.8
\times 10^{-8}$.


  In this paper we perform an experimental comparison of three different target
based 3D-LIDAR camera calibration algorithms. We briefly elucidate the
mathematical background behind each method and provide insights into practical
aspects like ease of data collection for all of them. We extensively evaluate
these algorithms on a sensor suite which consists multiple cameras and LIDARs
by assessing their robustness to random initialization and by using metrics
like Mean Line Re-projection Error (MLRE) and Factory Stereo Calibration Error.
We also show the effect of noisy sensor on the calibration result from all the
algorithms and conclude with a note on which calibration algorithm should be
used under what circumstances.


  The Wigner distribution function is a quasi-probability distribution. When
properly integrated, it provides the correct charge and current densities, but
it gives negative probabilities in some points and regions of the phase space.
Alternatively, the Husimi distribution function is positive-defined everywhere,
but it does not provide the correct charge and current densities. The origin of
all these difficulties is the attempt to construct a phase space within a
quantum theory that does not allow well-defined (i.e. simultaneous) values of
the position and momentum of an electron. In contrast, within the (de
Broglie-Bohm) Bohmian theory of quantum mechanics, an electron has well-defined
position and momentum. Therefore, such theory provides a natural definition of
the phase space probability distribution and by construction, it is
positive-defined and it exactly reproduces the charge and current densities.
The Bohmian distribution function has many potentialities for quantum problems,
in general, and for quantum transport, in particular, that remains unexplored.


  High momentum hadron suppression is considered to be an excellent probe of
jet-medium interactions in QCD matter created in ultra-relativistic heavy ion
collisions. We previously showed that our dynamical energy loss formalism can
accurately explain suppression measurements at 200 GeV Au+Au collisions at RHIC
and 2.76 TeV Pb+Pb collisions at the LHC. With the upcoming LHC measurements at
notably higher collision energies, there is a question of what differences,
with respect to the current (2.76 TeV) measurements, can be expected. In this
paper we concentrate on heavy flavor suppression at the upcoming 5.1 TeV Pb+Pb
collisions energy at the LHC. Naively, one would expect a notably ($\sim 30\%$)
larger suppression at 5.1 TeV collision energy, due to estimated (significant)
energy loss increase when transitioning from 2.76 to 5.1 TeV. Surprisingly,
more detailed calculations predict nearly the same suppression results at these
two energies. We show that this unexpected result is due to an interplay of the
following two effects, which essentially cancel each other: i) flattening of
the initial distributions with increasing collision energies, and ii)
significantly slower than naively expected increase in the energy loss.
Therefore, the obtained nearly the same suppression provides a clear
(qualitative and quantitative) test of our energy loss formalism.


  We present a stereo-matching method for depth estimation from high-resolution
images using visual hulls as priors, and a memory-efficient technique for the
correlation computation. Our method uses object masks extracted from
supplementary views of the scene to guide the disparity estimation, effectively
reducing the search space for matches. This approach is specifically tailored
to stereo rigs in volumetric capture systems, where an accurate depth plays a
key role in the downstream reconstruction task. To enable training and
regression at high resolutions targeted by recent systems, our approach extends
a sparse correlation computation into a hybrid sparse-dense scheme suitable for
application in leading recurrent network architectures. We evaluate the
performance-efficiency trade-off of our method compared to state-of-the-art
methods, and demonstrate the efficacy of the visual hull guidance. In addition,
we propose a training scheme for a further reduction of memory requirements
during optimization, facilitating training on high-resolution data.


  Astrophysical tests of general relativity belong to two categories: 1)
"internal", i.e. consistency tests within the theory (for example, tests that
astrophysical black holes are indeed described by the Kerr solution and its
perturbations), or 2) "external", i.e. tests of the many proposed extensions of
the theory. I review some ways in which astrophysical black holes can be used
as natural laboratories for both "internal" and "external" tests of general
relativity. The examples provided here (ringdown tests of the black hole
"no-hair" theorem, bosonic superradiant instabilities in rotating black holes
and gravitational-wave tests of massive scalar-tensor theories) are shamelessly
biased towards recent research by myself and my collaborators. Hopefully this
colloquial introduction aimed mainly at astrophysicists will convince skeptics
(if there are any) that space-based detectors will be crucial to study
fundamental physics through gravitational-wave observations.


  ${\cal N} =4$ super Yang-Mills theory admits \cite{Beem:2013sza} a protected
subsector isomorphic to a two-dimensional chiral algebra, obtained by passing
to the cohomology of a certain supercharge. In the large $N$ limit, we expect
this chiral algebra to have a dual description as a subsector of IIB
supergravity on $AdS_5 \times S^5$. This subsector can be carved out by a
version of supersymmetric localization, using the bulk analog of the boundary
supercharge. We illustrate this procedure in a simple model, the theory of an
${\cal N}=4$ vector multiplet in $AdS_5$, for which a convenient off-shell
description is available. This model can be viewed as the simplest truncation
of the full $AdS_5 \times S^5$ supergravity, in which case the vector multiplet
should be taken in the adjoint representation of ${\mathfrak g}_F = \mathfrak
{su}(2)_F$. Localization yields Chern-Simons theory on $AdS_3$ with gauge
algebra ${\mathfrak g}_F$, whose boundary dual is the affine Lie algebra
$\widehat {\mathfrak g}_F$. We comment on the generalization to the full bulk
theory. We propose that the large $N$ limit of the chiral algebra of ${\cal
N}=4$ SYM is again dual to Chern-Simons theory, with gauge algebra a suitable
higher-spin superalgebra.


  A search for R-parity violating supersymmetry in final states characterised
by high jet multiplicity, at least one isolated light lepton and either zero or
at least three $b$-tagged jets is presented. The search uses 139 fb$^{-1}$ of
$\sqrt{s} = 13$ TeV proton-proton collision data collected by the ATLAS
experiment during Run 2 of the Large Hadron Collider. The results are
interpreted in the context of R-parity-violating supersymmetry models that
feature gluino production, top-squark production, or electroweakino production.
The dominant sources of background are estimated using a data-driven model,
based on observables at medium jet multiplicity, to predict the $b$-tagged jet
multiplicity distribution at the higher jet multiplicities used in the search.
Machine learning techniques are used to reach sensitivity to electroweakino
production, extending the data-driven background estimation to the shape of the
machine learning discriminant. No significant excess over the Standard Model
expectation is observed and exclusion limits at the 95% confidence-level are
extracted, reaching as high as 2.4 TeV in gluino mass, 1.35 TeV in top-squark
mass, and 320 (365) GeV in higgsino (wino) mass.


  Recently, single crystalline carbon nitride 2D material with a C3N
stoichiometry has been synthesized. In this investigation, we explored the
mechanical response and thermal transport along pristine, free-standing and
single-layer C3N. To this aim, we conducted extensive first-principles density
functional theory (DFT) calculations as well as molecular dynamics (MD)
simulations. DFT results reveal that C3N nanofilms can yield remarkably high
elastic modulus of 341 GPa.nm and tensile strength of 35 GPa.nm, very close to
those of defect-free graphene. Classical MD simulations performed at a low
temperature, predict accurately the elastic modulus of 2D C3N with less than 3%
difference with the first-principles estimation. The deformation process of C3N
nanosheets was studied both by the DFT and MD simulations. Ab initio molecular
dynamics simulations show that single-layer C3N can withstand high temperatures
like 4000 K. Notably, the phononic thermal conductivity of free-standing C3N
was predicted to be as high as 815 W/mK. Our atomistic modelling results reveal
ultra high stiffness and thermal conductivity of C3N nanomembranes and
therefore propose them as promising candidates for new application such as the
thermal management in nanoelectronics or simultaneously reinforcing the thermal
and mechanical properties of polymeric materials.


  By exploiting Stueckelberg's approach, we obtain a gauge theory for the two
(1+1)-dimensional (2D) Proca theory and demonstrate that this theory is endowed
with, in addition to the usual Becchi-Rouet-Stora-Tyutin (BRST) and anti-BRST
symmetries, the on-shell nilpotent (anti-)co-BRST symmetries, under which the
total gauge-fixing term remains invariant. The anticommutator of the BRST and
co-BRST (as well as anti-BRST and anti-co-BRST) symmetries define a unique
bosonic symmetry in the theory, under which the ghost part of the Lagrangian
density remains invariant. To establish connections of the above symmetries
with the Hodge theory, we invoke a pseudo-scalar field in the theory.
Ultimately, we demonstrate that the full theory provides a field theoretic
example for the Hodge theory where the continuous symmetry transformations
provide a physical realization of the de Rham cohomological operators and
discrete symmetries of the theory lead to the physical realization of the Hodge
duality operation of differential geometry. We also mention the physical
implications and utility of our present investigation.


  We present an application of Hilbert quasi-polynomials to order domains,
allowing the effective check of the second order-domain condition in a direct
way. We also provide an improved algorithm for the computation of the related
Hilbert quasi-polynomials. This allows to identify order domain codes more
easily.


  This paper proposes new tests of conditional independence of two random
variables given a single-index involving an unknown finite-dimensional
parameter. The tests employ Rosenblatt transforms and are shown to be
distribution-free while retaining computational convenience. Some results from
Monte Carlo simulations are presented and discussed.


  We report the first results from a new search for cataclysmic variables (CVs)
using a combined X-ray (ROSAT) / infrared (2MASS) target selection that
discriminates against background AGN. Identification spectra were obtained at
the Isaac Newton Telescope for a total of 174 targets, leading to the discovery
of 12 new CVs. Initially devised to find short-period low-mass-transfer CVs,
this selection scheme has been very successful in identifying new intermediate
polars. Photometric and spectroscopic follow-up observations identify four of
the new CVs as intermediate polars: 1RXSJ063631.9+353537 (Porb~201min,
Pspin=1008.3408s or 930.5829), 1RXSJ070407.9+262501 (Porb~250min,
Pspin=480.708s), 1RXSJ173021.5-055933 (Porb=925.27min, Pspin=128.0s), and
1RXSJ180340.0+401214 (Porb=160.21min, Pspin=1520.51s). RXJ1730, also a
moderately bright hard X-ray source in the INTEGRAL/IBIS Galactic plane survey,
resembles the enigmatic AE Aqr. It is likely that its white dwarf is not
rotating at the spin equilibrium period, and the system may represent a
short-lived phase in CV evolution.


  Let $(A,\m)$ be a local hypersurface with isolated singularity. We show that
Hochster's theta pairing vanishes on elements that are {numerically equivalent
to zero} in the Grothendieck group of $A$ under the mild assumption that $\spec
A$ admits a resolution of singularity. We also prove that when $\dim A =3$, the
Hochster's theta pairing is positive semidefinite. These results combine to
show that the counter-example of Dutta-Hochster-McLaughlin to general vanishing
of Serre's intersection multiplicity exists for any three dimensional isolated
hypersurface singularity that is not a UFD and has a desingularization. Our
method involves showing that theta gives a bivariant class for the morphism
$\spec A/\m \to \spec A$. It also follows that if $A$ is three dimensional
isolated hypersurface singularity that has a desingularization, the divisor
class group of $A$ is finitely generated torsion-free.


  If an appropriate region of Kerr-Newman space-time is removed and suitable
identifications are made, the resulting space-time can be interpreted as an
infinitely thin disk producing the original electromagnetic and gravitational
fields. We choose the shape of the regions removed in such a way that radial
pressures in the disks vanish. Even the very inner parts such as ergoregions
may exist around the disks. The surface energy-momentum tensor of the disks is
checked to satisfy the weak and strong energy conditions. To emphasize the
reality of these sources two models of the disks are presented: (i) rotating
conductive charged rings which are supported against collapse by their internal
pressure, (ii) two counter-rotating streams of charged particles moving along
circular electro-geodesics. All these disk sources form a three-dimensional
parameter space with specific electric charge Q/M, angular momentum a/M and the
size of the excluded region being the parameters.


  Implications of the recent results on neutrino masses and mixing to
underlying new physics are considered. Various approaches to physics behind
neutrino mass are described which include the tri-bimaximal mixing and flavor
symmetries, the quark-lepton complementarity and weak complementarity, the
quark-lepton universality and unification. Some recent results from string
phenomenology are discussed and the issue of model building versus "string
engineering" is outlined.


  We obtain an important generalization of the mechanical solution given by S.
Gueron and R. Tessler w.r. to the weighted Fermat-Torricelli problem which
derives a new structure of solutions which may be called oscillatory
Fermat-Torricelli trees. The weighted Fermat-Torricelli problem in R^2 states
that: Given three points in R^2 and a positive real number (weight) which
correspond to each point , find the point (weighted Fermat-Torricelli point)
such that the sum of the weighted distances to these three points is minimized.
By applying the mechanical device of Pick and Polya the oscillatory tree
solution is a new solution w.r to the weighted Fermat-Torricelli problem for a
given isosceles triangle with corresponding two equal weights at the vertices
of the base segment. it is worth mentioning that after time t the oscillatory
knot of the mechanical system passes from the weighted Fermat-Torricelli point
with non zero velocity. Furthermore, we give a numerical example to verify the
structure of an oscillatory Fermat-Torricelli tree for a given isosceles
triangle with equal weights.