  If spacetime is built out of quantum bits, does the shape of space depend on
how the bits are entangled? The ER=EPR conjecture relates the entanglement
entropy of a collection of black holes to the cross sectional area of
Einstein-Rosen (ER) bridges (or wormholes) connecting them. We show that the
geometrical entropy of classical ER bridges satisfies the subadditivity,
triangle, strong subadditivity, and CLW inequalities. These are nontrivial
properties of entanglement entropy, so this is evidence for ER=EPR. We further
show that the entanglement entropy associated to classical ER bridges has
nonpositive interaction information. This is not a property of entanglement
entropy, in general. For example, the entangled four qubit pure state
|GHZ_4>=(|0000>+|1111>)/\sqrt{2} has positive interaction information, so this
state cannot be described by a classical ER bridge. Large black holes with
massive amounts of entanglement between them can fail to have a classical ER
bridge if they are built out of |GHZ_4> states. States with nonpositive
interaction information are called monogamous. We conclude that classical ER
bridges require monogamous EPR correlations.


  We study the topological $G_2$ and $Spin(7)$ strings at 1-loop. We define new
double complexes for supersymmetric NSNS backgrounds of string theory using
generalised geometry. The 1-loop partition function then has a target-space
interpretation as a particular alternating product of determinants of
Laplacians, which we have dubbed the analytic torsion. In the case without flux
where these backgrounds have special holonomy, we reproduce the worldsheet
calculation of the $G_2$ string and give a new prediction for the $Spin(7)$
string. We also comment on connections with topological strings on Calabi-Yau
and K3 backgrounds.


  Two next-generation high-energy experiments, the Large Hadron Collider (LHC)
and the $e^+e^-$ International Linear Collider (ILC), are highly expected to
unravel the new structure of matter and forces from the electroweak scale to
the TeV scale. In this talk we give a compelling but rather descriptive review
of the complementary role of LHC and ILC in drawing a comprehensive and high
precision picture of the mechanism breaking the electroweak symmetries and
generating mass, the unification of forces and the structure of spacetime.
Supersymmetry is exploited in this description as a prototype scenario of the
physics beyond the Standard Model.


  Symbolic execution is a software verification technique symbolically running
programs and thereby checking for bugs. Ranged symbolic execution performs
symbolic execution on program parts, so called path ranges, in parallel. Due to
the parallelism, verification is accelerated and hence scales to larger
programs.
  In this paper, we discuss a generalization of ranged symbolic execution to
arbitrary program analyses. More specifically, we present a verification
approach that splits programs into path ranges and then runs arbitrary analyses
on the ranges in parallel. Our approach in particular allows to run different
analyses on different program parts. We have implemented this generalization on
top of the tool CPAchecker and evaluated it on programs from the SV-COMP
benchmark. Our evaluation shows that verification can benefit from the
parallelisation of the verification task, but also needs a form of work
stealing (between analyses) as to become efficient


  Relations between neutron star properties that do not depend on the nuclear
equation of state offer insights on neutron star physics and have practical
applications in data analysis. Such relations are obtained by fitting to a
range of phenomenological or nuclear physics equation of state models, each of
which may have varying degrees of accuracy. In this study we revisit
commonly-used relations and re-assess them with a very flexible set of
phenomenological nonparametric equation of state models that are based on
Gaussian Processes. Our models correspond to two sets: equations of state which
mimic hadronic models, and equations of state with rapidly changing behavior
that resemble phase transitions. We quantify the accuracy of relations under
both sets and discuss their applicability with respect to expected upcoming
statistical uncertainties of astrophysical observations. We further propose a
goodness-of-fit metric which provides an estimate for the systematic error
introduced by using the relation to model a certain equation-of-state set.
Overall, the nonparametric distribution is more poorly fit with existing
relations, with the I-Love-Q relations retaining the highest degree of
universality. Fits degrade for relations involving the tidal deformability,
such as the Binary-Love and compactness-Love relations, and when introducing
phase transition phenomenology. For most relations, systematic errors are
comparable to current statistical uncertainties under the nonparametric
equation of state distributions.


  The application of Random Matrix Theory to the Dirac operator of QCD yields
predictions for the probability distributions of the lowest eigenvalues. We
measured Dirac operator spectra using massless overlap fermions in quenched QCD
at topological charge \nu = 0, +- 1 and +- 2, and found agreement with those
predictions - at least for the first non-zero eigenvalue - if the volume
exceeds about (1.2 fm)^4.


  A new technique is proposed for fault-tolerant linear, sesquilinear and
bijective (LSB) operations on $M$ integer data streams ($M\geq3$), such as:
scaling, additions/subtractions, inner or outer vector products, permutations
and convolutions. In the proposed method, the $M$ input integer data streams
are linearly superimposed to form $M$ numerically-entangled integer data
streams that are stored in-place of the original inputs. A series of LSB
operations can then be performed directly using these entangled data streams.
The results are extracted from the $M$ entangled output streams by additions
and arithmetic shifts. Any soft errors affecting any single disentangled output
stream are guaranteed to be detectable via a specific post-computation
reliability check. In addition, when utilizing a separate processor core for
each of the $M$ streams, the proposed approach can recover all outputs after
any single fail-stop failure. Importantly, unlike algorithm-based fault
tolerance (ABFT) methods, the number of operations required for the
entanglement, extraction and validation of the results is linearly related to
the number of the inputs and does not depend on the complexity of the performed
LSB operations. We have validated our proposal in an Intel processor (Haswell
architecture with AVX2 support) via fast Fourier transforms, circular
convolutions, and matrix multiplication operations. Our analysis and
experiments reveal that the proposed approach incurs between $0.03\%$ to $7\%$
reduction in processing throughput for a wide variety of LSB operations. This
overhead is 5 to 1000 times smaller than that of the equivalent ABFT method
that uses a checksum stream. Thus, our proposal can be used in fault-generating
processor hardware or safety-critical applications, where high reliability is
required without the cost of ABFT or modular redundancy.


  Let $A_n$ be the sum of $d$ permutation matrices of size $n\times n$, each
drawn uniformly at random and independently. We prove that the normalized
characteristic polynomial $\frac{1}{\sqrt{d}}\det(I_n - z A_n/\sqrt{d})$
converges when $n\to \infty$ towards a random analytic function on the unit
disk. As an application, we obtain an elementary proof of the spectral gap of
random regular digraphs. Our results are valid both in the regime where $d$ is
fixed and for $d$ slowly growing with $n$.


  Let K be a field of positive characteristic p and KG the group algebra of a
group G. It is known that, if KG is Lie nilpotent, then its upper (or lower)
Lie nilpotency index is at most |G'|+1, where |G'| is the order of the
commutator subgroup. The authors have previously determined the groups G for
which this index is maximal and here they determine the G for which it is
`almost maximal', that is the next highest possible value, namely |G'|-p+2.


  We prove a decomposition theorem for graphs that do not contain a subdivision
of $K_4$ as an induced subgraph where $K_4$ is the complete graph on four
vertices. We obtain also a structure theorem for the class $\cal C$ of graphs
that contain neither a subdivision of $K_4$ nor a wheel as an induced subgraph,
where a wheel is a cycle on at least four vertices together with a vertex that
has at least three neighbors on the cycle. Our structure theorem is used to
prove that every graph in $\cal C$ is 3-colorable and entails a polynomial-time
recognition algorithm for membership in $\cal C$. As an intermediate result, we
prove a structure theorem for the graphs whose cycles are all chordless.


  We present structured domain randomization (SDR), a variant of domain
randomization (DR) that takes into account the structure and context of the
scene. In contrast to DR, which places objects and distractors randomly
according to a uniform probability distribution, SDR places objects and
distractors randomly according to probability distributions that arise from the
specific problem at hand. In this manner, SDR-generated imagery enables the
neural network to take the context around an object into consideration during
detection. We demonstrate the power of SDR for the problem of 2D bounding box
car detection, achieving competitive results on real data after training only
on synthetic data. On the KITTI easy, moderate, and hard tasks, we show that
SDR outperforms other approaches to generating synthetic data (VKITTI, Sim
200k, or DR), as well as real data collected in a different domain (BDD100K).
Moreover, synthetic SDR data combined with real KITTI data outperforms real
KITTI data alone.


  Since its initiation by Connie Smith, the process of Software Performance
Engineering (SPE) is becoming a growing concern. The idea is to bring
performance evaluation into the software design process. This suitable
methodology allows software designers to determine the performance of software
during design. Several approaches have been proposed to provide such
techniques. Some of them propose to derive from a UML (Unified Modeling
Language) model a performance model such as Stochastic Petri Net (SPN) or
Stochastic process Algebra (SPA) models. Our work belongs to the same category.
We propose to derive from a UML model a Stochastic Automata Network (SAN) in
order to obtain performance predictions. Our approach is more flexible due to
the SAN modularity and its high resemblance to UML' state-chart diagram.


  We delve into the first principles of quantum field theory to prove that the
so-called spin-1/2 ''bosons'' and the fermions with mass dimension 1, including
ELKO, cannot represent physical particle states with spin $1/2$. Specifically,
we first demonstrate that both aforementioned fields are not invariant under
rotational symmetry, which implies that the particles created for these fields
are not eigenstates of the spin operator in the
$(\frac{1}{2},0)\oplus(0,\frac{1}{2})$ representation of the Lorentz group, nor
is it possible to construct a Hamiltonian density scalar under the rotational
group from them. Furthermore, following Weinberg's approach to local causal
fields, we prove that regardless of any discrete symmetry or adjoint structure,
the relativistic fields in the $(\frac{1}{2}, 0) \oplus (0,\frac{1}{2})$
representation satisfy the Fermi-Dirac statistics in complete agreement with
the well-established spin-statistics theorem and experimental results.


  This paper presents the first results of a far-infrared search for
protocluster-associated galaxy overdensities using the SPIRE instrument
on-board the {\it Herschel} Space Observatory. Large ($\sim$400 arcmin$^{2}$)
fields surrounding 26 powerful high-redshift radio galaxies ($2.0 < z < 4.1$;
$L_{\rm 500 MHz} > 10^{28.5}$ WHz$^{-1}$) are mapped at 250, 350 and 500\mic to
give a unique wide-field sample.
  On average the fields have a higher than expected, compared to blank fields,
surface density of 500\mic sources within 6 comoving Mpc of the radio galaxy.
The analysis is then restricted to potential protocluster members only, which
are identified using a far-infrared colour selection; this reveals significant
overdensities of galaxies in 2 fields, neither of which are previously known
protoclusters. The probability of finding 2 overdensities of this size by
chance, given the number of fields observed is $5 \times 10^{-4}$.
Overdensities here exist around radio galaxies with $L_{\rm 500 MHz} \gtrsim
10^{29}$ WHz$^{-1}$ and $z < 3$. The radial extent of the average far-infrared
overdensity is found to be $\sim$6 comoving Mpc.
  Comparison with predictions from numerical simulations shows that the
overdensities are consistent with having masses $> 10^{14}$Msolar. However, the
large uncertainty in the redshift estimation means that it is possible that
these far-infrared overdensities consist of several structures across the
redshift range searched.


  With an increasing number of web services, providing an end-to-end Quality of
Service (QoS) guarantee in responding to user queries is becoming an important
concern. Multiple QoS parameters (e.g., response time, latency, throughput,
reliability, availability, success rate) are associated with a service,
thereby, service composition with a large number of candidate services is a
challenging multi-objective optimization problem. In this paper, we study the
multi-constrained multi-objective QoS aware web service composition problem and
propose three different approaches to solve the same, one optimal, based on
Pareto front construction and two other based on heuristically traversing the
solution space. We compare the performance of the heuristics against the
optimal, and show the effectiveness of our proposals over other classical
approaches for the same problem setting, with experiments on WSC-2009 and
ICEBE-2005 datasets.


  We developed the theory of dipolaritons in semiconductor quantum wells
irradiated by an off-resonant electromagnetic wave (dressing field). Solving
the Floquet problem for the dressed dipolaritons, we demonstrated that the
field drastically modifies all dipolaritonic properties. In particular, the
dressing field strongly effects on terahertz emission from the considered
system. The described effect paves the way for optical control of prospective
dipolariton-based terahertz devices.


  In this paper, we consider estimating spot/instantaneous volatility matrices
of high-frequency data collected for a large number of assets. We first combine
classic nonparametric kernel-based smoothing with a generalised shrinkage
technique in the matrix estimation for noise-free data under a uniform sparsity
assumption, a natural extension of the approximate sparsity commonly used in
the literature. The uniform consistency property is derived for the proposed
spot volatility matrix estimator with convergence rates comparable to the
optimal minimax one. For the high-frequency data contaminated by microstructure
noise, we introduce a localised pre-averaging estimation method that reduces
the effective magnitude of the noise. We then use the estimation tool developed
in the noise-free scenario, and derive the uniform convergence rates for the
developed spot volatility matrix estimator. We further combine the kernel
smoothing with the shrinkage technique to estimate the time-varying volatility
matrix of the high-dimensional noise vector. In addition, we consider large
spot volatility matrix estimation in time-varying factor models with observable
risk factors and derive the uniform convergence property. We provide numerical
studies including simulation and empirical application to examine the
performance of the proposed estimation methods in finite samples.


  Applying Reinforcement learning (RL) following maximum likelihood estimation
(MLE) pre-training is a versatile method for enhancing neural machine
translation (NMT) performance. However, recent work has argued that the gains
produced by RL for NMT are mostly due to promoting tokens that have already
received a fairly high probability in pre-training. We hypothesize that the
large action space is a main obstacle to RL's effectiveness in MT, and conduct
two sets of experiments that lend support to our hypothesis. First, we find
that reducing the size of the vocabulary improves RL's effectiveness. Second,
we find that effectively reducing the dimension of the action space without
changing the vocabulary also yields notable improvement as evaluated by BLEU,
semantic similarity, and human evaluation. Indeed, by initializing the
network's final fully connected layer (that maps the network's internal
dimension to the vocabulary dimension), with a layer that generalizes over
similar actions, we obtain a substantial improvement in RL performance: 1.5
BLEU points on average.


  In an earlier paper, we proved that given an asymptotically cylindrical
G_2-manifold M with a Calabi-Yau boundary X, the moduli space of coassociative
deformations of an asymptotically cylindrical coassociative 4-fold C in M with
a fixed special Lagrangian boundary L in X is a smooth manifold of dimension
dim(V_+), where V_+ is the positive subspace of the image of H^2_{cs}(C,R) in
H^2(C,R). In order to prove this we used the powerful tools of Fredholm Theory
for noncompact manifolds which was developed by Lockhart and McOwen, and
independently by Melrose.
  In this paper, we extend our result to the moving boundary case. Let
Upsilon:H^2(L,R)--> H^3_{cs}(C,R) be the natural projection, so that
ker(Upsilon) is a vector subspace of H^2(L,R). Let F be a small open
neighbourhood of 0 in ker(Upsilon) and L_s denote the special Lagrangian
submanifolds of X near L for some s in F and with phase i. Here we prove that
the moduli space of coassociative deformations of an asymptotically cylindrical
coassociative submanifold C asymptotic to L_s x (R,infinity), s in F, is a
smooth manifold of dimension equal to dim V_++dim(ker(Upsilon))=dim V_+
+b^2(L)-b^0(L)+b^3(C)-b^1(C)+b^0(C).


  COVID-19 presents a great threat to public health worldwide and the
infectious agent SARS-CoV-2 is currently the target of much research aiming at
inhibition. The virus' main protease is a dimeric enzyme that has only recently
begun to be thoroughly described, opening the door for virtual screening more
broadly. Here, a PAIN-filtered flavonoid database was screened against four
sites of the protease: a free (normal) conformation of the Substrate Binding
Site (NSBS), an induced-fit state of the SBS (ISBS), a Dimerization Site (DS)
and a Cryptic Site (CS). The mean binding energies of the top five ligands from
each site were -9.52, -11.512, -7.042 and -10.348 kcal/mol for the NSBS, the
ISBS, the DS and the CS, respectively. For the DS and CS, these top five
compounds were selected as candidates to bind their respective site. In the
case of SBS, the top 30 ligands with the lowest binding energies from NSBS and
ISBS were contrasted and the ones present in both lists were selected as the
final candidates. The final list was: Dorsilurin E (FL3FQUNP0001), Euchrenone
a11 (FL2FALNP0014), Kurziflavolactone C (FL2FA9NC0016), Licorice glycoside E
(FL2F1AGSN001) and Taxifolin 3'- (6"-phenyl- acetylglucoside) (FL4DACGS0020)
for the SBS; Sanggenol O (FL2FALNP0020), CHEMBL2171573, Kanzonol E
(FL3F1ANP0001), CHEMBL2171584 and Abyssynoflavanone VI (FL2FACNP0014) for DS
and CHEMBL2171598, CHEMBL2171577, Denticulaflavanol (FL5FAANR0001),
Kurzichalcolactone (FL1CA9NC0001) and CHEMBL2171578 for CS. Virtual screening
integrated several confirmation methods, including cross-docking assays and
positive and negative controls. All 15 compounds are currently subjected to
molecular dynamics so as to theoretically validate their binding to the
protease.


  We present a novel framework that can combine multi-domain learning (MDL),
data imputation (DI) and multi-task learning (MTL) to improve performance for
classification and regression tasks in different domains. The core of our
method is an adversarial autoencoder that can: (1) learn to produce
domain-invariant embeddings to reduce the difference between domains; (2) learn
the data distribution for each domain and correctly perform data imputation on
missing data. For MDL, we use the Maximum Mean Discrepancy (MMD) measure to
align the domain distributions. For DI, we use an adversarial approach where a
generator fill in information for missing data and a discriminator tries to
distinguish between real and imputed values. Finally, using the universal
feature representation in the embeddings, we train a classifier using MTL that
given input from any domain, can predict labels for all domains. We demonstrate
the superior performance of our approach compared to other state-of-art methods
in three distinct settings, DG-DI in image recognition with unstructured data,
MTL-DI in grade estimation with structured data and MDMTL-DI in a selection
process using mixed data.


  The Tur\'{a}n problem asks for the largest number of edges ex$(n,H)$ in an
$n$-vertex graph not containing a fixed forbidden subgraph $H$, which is one of
the most important problems in extremal graph theory. However the order of
magnitude of ex$(n,H)$ for bipartite graphs is known only in a handful of
cases. In particular, giving explicit constructions of extremal graphs is very
challenging in this field. In this paper, we develop a polynomail resultant
approach to algebraic construction of explicit extremal graphs, which can
efficiently decide whether a specified structure exists. A key insight in our
approach is the multipolynomial resultant, which is a fundamental tool of
computational algebraic geometry. Our main results include the matched lowers
bounds for Tur\'{a}n number of $1$-subdivision of $K_{3,t_{1}}$ and linear
Tur\'{a}n number of Berge theta hyerpgraph $\Theta_{3,t_{2}}^{B}$ with
$t_{1}=25$ and $t_{2}=217$. Moreover, the constant $t_{1}$ improves the random
algebraic construction of Bukh and Conlon~[Rational exponents in extremal graph
theory, J. Eur. Math. Soc. 20 (2018), 1747-1757] and makes progress on the
known estimation for the smallest value of $t_{1}$ concerning a problem posed
by Conlon, Janzer and Lee ~[More on the extremal number of subdivisions,
Combinatorica, to appear], while the constant $t_{2}$ improves a result of He
and Tait~[Hypergraphs with few berge paths of fixed length between vertices,
SIAM J. Discrete Math., 33(3), 1472-1481].


  The popularity of neural networks (NNs) spans academia, industry, and popular
culture. In particular, convolutional neural networks (CNNs) have been applied
to many image based machine learning tasks and have yielded strong results. The
availability of hardware/software systems for efficient training and deployment
of large and/or deep CNN models has been, and continues to be, an important
consideration for the field. Early systems for NN computation focused on
leveraging existing dense linear algebra techniques and libraries. Current
approaches use low-level machine specific programming and/or closed-source,
purpose-built vendor libraries. In this work, we present an open source system
that, compared to existing approaches, achieves competitive computational speed
while achieving higher portability. We achieve this by targeting the
vendor-neutral OpenCL platform using a code-generation approach. We argue that
our approach allows for both: (1) the rapid development of new computational
kernels for existing hardware targets, and (2) the rapid tuning of existing
computational kernels for new hardware targets. Results are presented for a
case study of targeting the Qualcomm Snapdragon 820 mobile computing platform
for CNN deployment.


  The deuteration of ammonia by D atoms has been investigated experimentally in
the sub-monolayer regime on realistic analogues of interstellar dust grain
surfaces. About 0.8 monolayer of solid NH3 was deposited on top of an oxidized
graphite surface held at 10 K, partly covered with ASW ice. Ammonia ice is
subsequently exposed to D atoms for different exposure times using a
differentially pumped beam-line. The deuteration experiments of ammonia were
carried out by mass spectroscopy and temperature programmed desorption (TPD)
technique. The experimental results showed the formation of three isotopologue
ammonia species by direct exothermic H-D substitution surface reactions:
NH3+D->NH2D+H, NH2D+D->NHD2+H, and NHD2+D->ND3+H. The formation of the
deuterated isotopologues NH2D, NHD2, and ND3 at low surface temperature (10 K)
is likely to occur through quantum tunneling process on the oxidized graphite
surface. A kinetic model taking into account the diffusion of D atoms on the
surface is developed to estimate the width and the hight of the activation
energy barriers for the successive deuteration reactions of ammonia species by
D atoms. Identical control experiments were performed using CH3OH and D atoms.
The deuteration process of solid methanol is ruled by H abstraction and D
addition mechanism, and is almost five orders of magnitude faster than ammonia
deuteration process.


  Hadron colliders can provide important tests of BFKL `small-x' dynamics. We
discuss two examples of such tests, the inclusive dijet jet cross section at
large rapidity separation and the number of associated `mini-jets' in Higgs
boson production.


  There are only two viable low-energy $E_6$ subgroups: $SU(3)_C \times SU(2)_L
\times U(1)_Y \times U(1)_N$ or $SU(3)_C \times SU(2)_L \times SU(2)'_R \times
U(1)_{Y_L + Y'_R}$, which would not erase any preexisting lepton asymmetry of
the Universe that may have been created by the decay of heavy singlet
(right-handed) neutrinos or any other mechanism. They are also the two most
favored $E_6$ subgroups from a recent analysis of present neutral-current data.
We study details of the leptogenesis, as well as some salient experimental
signatures of the two models.


  The transformation formula of the Berezin integral holds, in the non-compact
case, only up to boundary integrals, which have recently been quantified by
Alldridge-Hilgert-Palzer. We establish divergence theorems in semi-Riemannian
supergeometry by means of the flow of vector fields and these boundary
integrals, and show how superharmonic functions are related to conserved
quantities. An integration over the supersphere was introduced by Coulembier-De
Bie-Sommen as a generalisation of the Pizzetti integral. In this context, a
mean value theorem for harmonic superfunctions was established. We formulate
this integration along the lines of the general theory and give a superior
proof of two mean value theorems based on our divergence theorem.


  It is well known that Lagrangian dynamical systems naturally arise in
describing wave front dynamics in the limit of short waves (which is called
pseudoclassical limit or limit of geometrical optics). Wave fronts are the
surfaces of constant phase, their points move along lines which are called
rays. In non-homogeneous anisotropic media rays are not straight lines. Their
shape is determined by modified Lagrange equations. An important observation is
that for most usual cases propagating wave fronts are perpendicular to rays in
the sense of some Riemannian metric. This happens when Lagrange function is
quadratic with respect to components of velocity vector. The goal of paper is
to study how this property transforms for the case of general (non-quadratic)
Lagrange function.


  We revisit the puzzle of $|V_{us}|$ values obtained from the conventional
implementation of hadronic-$\tau$-decay-based flavor-breaking finite-energy sum
rules lying $>3 \sigma$ below the expectations of three-family unitarity.
Significant unphysical dependences of $|V_{us}|$ on the choice of weight, w,
and upper limit, $s_0$, of the experimental spectral integrals entering the
analysis are confirmed, and a breakdown of assumptions made in estimating
higher dimension, $D>4$, OPE contributions is identified as the main source of
these problems. A combination of continuum and lattice results is shown to
suggest a new implementation of the flavor-breaking sum rule approach in which
not only $|V_{us}|$, but also $D>4$ effective condensates, are fit to data.
Lattice results are also used to clarify how to reliably treat the slowly
converging D=2 OPE series. The new sum rule implementation is shown to cure the
problems of the unphysical w- and $s_0$-dependence of $|V_{us}|$ and to produce
results $\sim 0.0020$ higher than those of the conventional implementation.
With B-factory input, and using, in addition, dispersively constrained results
for the $K\pi$ branching fractions, we find $\vert V_{us}\vert
=0.2231(27)_{exp}(4)_{th}$, in excellent agreement with the result from
$K_{\ell 3}$, and compatible within errors with the expectations of
three-family unitarity, thus resolving the long-standing inclusive $\tau$
$|V_{us}|$ puzzle.


  The binary similarity problem consists in determining if two functions are
similar by only considering their compiled form. Advanced techniques for binary
similarity recently gained momentum as they can be applied in several fields,
such as copyright disputes, malware analysis, vulnerability detection, etc.,
and thus have an immediate practical impact. Current solutions compare
functions by first transforming their binary code in multi-dimensional vector
representations (embeddings), and then comparing vectors through simple and
efficient geometric operations. However, embeddings are usually derived from
binary code using manual feature extraction, that may fail in considering
important function characteristics, or may consider features that are not
important for the binary similarity problem. In this paper we propose SAFE, a
novel architecture for the embedding of functions based on a self-attentive
neural network. SAFE works directly on disassembled binary functions, does not
require manual feature extraction, is computationally more efficient than
existing solutions (i.e., it does not incur in the computational overhead of
building or manipulating control flow graphs), and is more general as it works
on stripped binaries and on multiple architectures. We report the results from
a quantitative and qualitative analysis that show how SAFE provides a
noticeable performance improvement with respect to previous solutions.
Furthermore, we show how clusters of our embedding vectors are closely related
to the semantic of the implemented algorithms, paving the way for further
interesting applications (e.g. semantic-based binary function search).


  Computer vision has advanced significantly that many discriminative
approaches such as object recognition are now widely used in real applications.
We present another exciting development that utilizes generative models for the
mass customization of medical products such as dental crowns. In the dental
industry, it takes a technician years of training to design synthetic crowns
that restore the function and integrity of missing teeth. Each crown must be
customized to individual patients, and it requires human expertise in a
time-consuming and labor-intensive process, even with computer-assisted design
software. We develop a fully automatic approach that learns not only from human
designs of dental crowns, but also from natural spatial profiles between
opposing teeth. The latter is hard to account for by technicians but important
for proper biting and chewing functions. Built upon a Generative Adversar-ial
Network architecture (GAN), our deep learning model predicts the customized
crown-filled depth scan from the crown-missing depth scan and opposing depth
scan. We propose to incorporate additional space constraints and statistical
compatibility into learning. Our automatic designs exceed human technicians'
standards for good morphology and functionality, and our algorithm is being
tested for production use.


  For long, node cooperation has been exploited as a data relaying mechanism.
However, the wireless channel allows for much richer interaction between nodes.
One such scenario is in a multi-channel environment, where transmitter-receiver
pairs may make incorrect decisions (e.g., in selecting channels) but idle
neighbors could help by sharing information to prevent undesirable consequences
(e.g., data collisions). This represents a Distributed Information SHaring
(DISH) mechanism for cooperation and suggests new ways of designing cooperative
protocols. However, what is lacking is a theoretical understanding of this new
notion of cooperation. In this paper, we view cooperation as a network resource
and evaluate the availability of cooperation via a metric, $p_{co}$, the
probability of obtaining cooperation. First, we analytically evaluate $p_{co}$
in the context of multi-channel multi-hop wireless networks. Second, we verify
our analysis via simulations and the results show that our analysis accurately
characterizes the behavior of $p_{co}$ as a function of underlying network
parameters. This step also yields important insights into DISH with respect to
network dynamics. Third, we investigate the correlation between $p_{co}$ and
network performance in terms of collision rate, packet delay, and throughput.
The results indicate a near-linear relationship, which may significantly
simplify performance analysis for cooperative networks and suggests that
$p_{co}$ be used as an appropriate performance indicator itself. Throughout
this work, we utilize, as appropriate, three different DISH contexts ---
model-based DISH, ideal DISH, and real DISH --- to explore $p_{co}$.


  The true level crossing in the asymmetric quantum Rabi model without any
obvious symmetry can be exhibited in the energy spectrum if the qubit bias is a
multiple of the cavity frequency, which should imply the existence of the
hidden symmetry. In this work, within a Bogoliubov operator approach, we can
readily derive the symmetry operators associated with the hidden symmetry
hierarchically for arbitrary multiples. The symmetry operators for small
multiples in the literature can be extremely easily reproduced in our general
scheme. In addition, a general parity operator is defined through the symmetry
operator, which naturally includes the well-known parity operator of the
symmetric model. We believe that the present approach can be straightforwardly
extended to other asymmetric Rabi models to find the relevant symmetry
operators.


  The spin structure of the system of quasifree fermions having total angular
momentum $J=1/2$ is studied in a consistently covariant approach. Within this
model the relations between the spin functions are obtained. Their particular
cases are the sum rules Wanzura - Wilczek, Efremov - Leader - Teryaev,
Burkhardt - Cottingham and also the expression for the Wanzura - Wilczek twist
2 term $g_{2}^{WW}$. With the use of the proton valence quark distributions as
an input, the corresponding spin functions are obtained. The resulting
structure functions $g_{1}$ and $g_{2}$ are well compatible with the
experimental data. Comparison with the basic formulas following from the
standard quark-parton model reveals the importance of the quark intrinsic
motion inside the target for the correct evaluation of the spin structure
functions.


  The vector perturbations induced on the brane by gravitational waves
propagating in the bulk are studied in a cosmological framework. Cosmic
expansion arises from the brane motion in a non-compact five-dimensional
anti-de Sitter spacetime. By solving the vector perturbation equations in the
bulk, for generic initial conditions, we find that they give rise to growing
modes on the brane in the Friedmann-Lema\^{\i}tre era. Among these modes, we
exhibit a class of normalizable perturbations, which are exponentially growing
with respect to conformal time on the brane. The presence of these modes is, at
least, strongly constrained by the current observations of the cosmic microwave
background (CMB). We estimate the anisotropies they induce in the CMB, and
derive quantitative constraints on the allowed amplitude of their primordial
spectrum. Our results provide stringent constraints for all braneworld models
with bulk inflation.


  We prove short time existence for the Ricci flow on open manifolds of
nonnegative complex sectional curvature. We do not require upper curvature
bounds. By considering the doubling of convex sets contained in a
Cheeger-Gromoll convex exhaustion and solving the singular initial value
problem for the Ricci flow on these closed manifolds, we obtain a sequence of
closed solutions of the Ricci flow with nonnegative complex sectional curvature
which subconverge to a solution of the Ricci flow on the open manifold.
Furthermore, we find an optimal volume growth condition which guarantees long
time existence, and we give an analysis of the long time behaviour of the Ricci
flow. Finally, we construct an explicit example of an immortal nonnegatively
curved solution of the Ricci flow with unbounded curvature for all time.


  Li-based phosphates are paradigmatic materials for magnetoelectricity. By
means of first-principles calculations, we elucidate the microscopic origin of
spin anisotropy and of magnetoelectric effects in LiNiPO4. The comparison with
LiCoPO4 reveals that Co-d7 and Ni-d8 electronic clouds show distinct orbital
shapes, which in turn result in an opposite trend of the local spin anisotropy
with respect to the surrounding O6 cages. Due to magnetic anisotropy, the
Ni-based phosphate shows a peculiar "angled-cross" spin ground-state, which is
responsible for magnetoelectricity. In this respect, we show that, under a
magnetic field Hx, an electronic polarization Pz arises, with an estimated
linear magneto-electric coefficient in good agreement with experiments.


  The parton distributions functions (PDFs) derived from the NNLO QCD analysis
of existing light-targets deep-inelastic-scattering data are presented. The NLO
and NNLO PDFs are compared in order to analyze perturbative stability of the
analysis and estimate impact of the higher-order QCD corrections. The main
theoretical uncertainties and experimental uncertainties in PDFs due to all
sources of experimental errors in data are estimated and used to assess
corresponding uncertainties in the cross sections of other hadronic processes.


  In the past years a wealth of observations allowed to unravel the structural
properties of the Dark Matter Halos around spirals. First, their rotation
curves follow an Universal profile (URC) that can be described in terms of an
exponential thin stellar disk and a dark halo with a constant density core,
whose relative importance increases with galaxy luminosity. Careful studies of
individual objects reveal that dark halos have a core, whose size $r_0$
correlates with the central density $\rho_0$.
  These properties are in serious discrepancy with the cuspy density
distribution predicted by N-body simulations in collisionless $\Lambda$CDM
Cosmology.


  The nearby GRB 060216/SN 2006aj was an extremely long, weak and very soft
GRB. It was peculiar in many aspects. We show here that the X-ray,
ultraviolet/optical and radio afterglow of GRB 060218 have to be attributed to
different physical processes arising from different emission regions. From the
several components in this burst's afterglow only the radio afterglow can be
interpreted in terms of the common external shock model. We infer from the
radio that the blast wave's kinetic energy was $\sim 10^{50}$ erg and the
circumburst matter had a constant rather than a wind profile. The lack of a
"jet break" up to 22 days implies that the outflow was wide $\theta_j >1$. Even
though the late X-ray afterglow decays normally it cannot result from an
external shock because of its very steep spectrum. Furthermore, the implied
kinetic energy would have produced far too much radio. We suggest that this
X-ray afterglow could be attributed to a continued activity of the central
engine that within the collapsar scenario could arise from fall-back accretion.
"Central engine afterglow" may be common in under-luminous GRBs where the
kinetic energy of the blast wave is small and the external shock does not
dominate over this component. Such under-luminous GRBs might be very common but
they are rarely recorded because they can be detected only from short
distances.


  We study the response of a Dirac fluid to electric fields and thermal
gradients at finite wave-numbers and frequencies in the hydrodynamic regime. We
find that non-local transport in the hydrodynamic regime is governed by
infinite set of kinetic modes that describe non-collinear scattering events in
different angular harmonic channels. The scattering rates of these modes
$\tau_{m}^{-1}$ increase as $\|m\|$, where $m$ labels the angular harmonics. In
an earlier publication, we pointed out that this dependence leads to anomalous,
L\'evy-flight-like phase space diffusion (Phys. Rev. Lett. 123, 195302 (2019)).
Here, we show how this surprisingly simple, non-analytic dependence allows us
to obtain exact expressions for the non-local charge and electronic thermal
conductivities. The peculiar dependence of the scattering rates on $m$ also
leads to a non-trivial structure of collective excitations: Besides the well
known plasmon, second sound and diffusive modes, we find non-degenerate damped
modes corresponding to excitations of higher angular harmonics. We use these
results to investigate the transport of a Dirac fluid through Poiseuille-type
geometries of different widths, and to study the response to surface acoustic
waves in graphene-piezoelectric devices.


  Many social networks, e.g., Slashdot and Twitter, can be represented as
directed graphs (digraphs) with two types of links between entities: mutual
(bi-directional) and one-way (uni-directional) connections. Social science
theories reveal that mutual connections are more stable than one-way
connections, and one-way connections exhibit various tendencies to become
mutual connections. It is therefore important to take such tendencies into
account when performing clustering of social networks with both mutual and
one-way connections.
  In this paper, we utilize the dyadic methods to analyze social networks, and
develop a generalized mutuality tendency theory to capture the tendencies of
those node pairs which tend to establish mutual connections more frequently
than those occur by chance. Using these results, we develop a
mutuality-tendency-aware spectral clustering algorithm to identify more stable
clusters by maximizing the within-cluster mutuality tendency and minimizing the
cross-cluster mutuality tendency. Extensive simulation results on synthetic
datasets as well as real online social network datasets such as Slashdot,
demonstrate that our proposed mutuality-tendency-aware spectral clustering
algorithm extracts more stable social community structures than traditional
spectral clustering methods.


  In this study, we address the central issue of statistical inference for
Markov jump processes using discrete time observations. The primary problem at
hand is to accurately estimate the infinitesimal generator of a Markov jump
process, a critical task in various applications. To tackle this problem, we
begin by reviewing established methods for generating sample paths from a
Markov jump process conditioned to endpoints, known as Markov bridges.
Additionally, we introduce a novel algorithm grounded in the concept of
time-reversal, which serves as our main contribution. Our proposed method is
then employed to estimate the infinitesimal generator of a Markov jump process.
To achieve this, we use a combination of Markov Chain Monte Carlo techniques
and the Monte Carlo Expectation-Maximization algorithm. The results obtained
from our approach demonstrate its effectiveness in providing accurate parameter
estimates. To assess the efficacy of our proposed method, we conduct a
comprehensive comparative analysis with existing techniques (Bisection,
Uniformization, Direct, Rejection, and Modified Rejection), taking into
consideration both speed and accuracy. Notably, our method stands out as the
fastest among the alternatives while maintaining high levels of precision.


  We present the results of a ~250 square degrees CO mapping (+26d<l<+50d and
-5d<b<+5d) toward the Aquila Rift region at a spatial resolution of ~50" and a
grid spacing of 30". The high dynamic range CO maps with a spectral resolution
of ~0.2km/s display highly structured molecular cloud (MC) morphologies with
valuable velocity information, revealing complex spatial and dynamical features
of the local molecular gas. In combination with the MWISP CO data and the Gaia
DR2, distances of the main MC structures in the local ISM are well determined
toward the Aquila Rift. We find that the total MC mass within 1 kpc is about
>4.1x10^5 Msun in the whole region. In fact, the mass of the molecular gas is
dominated by the W40 giant molecular cloud (GMC) at ~474 pc (~1.4x10^5 Msun)
and the GMC complex G036.0+01.0 at ~560-670 pc (~2.0x10^5 Msun), while the MCs
at ~220-260pc have gas masses of 10^2-10^3 Msun. Interestingly, an ~80pc long
filamentary MC G044.0-02.5 at a distance of ~404 pc shows a systematic velocity
gradient along and perpendicular to the major axis of the filament. The HI gas
with the enhanced emission has the similar spatial morphologies and velocity
features compared to the corresponding CO structure, indicating that the
large-scale converging HI flows are probably responsible for the formation of
the MC. Meanwhile, the long filamentary MC consists of many sub-filaments with
the lengths ranging from ~0.5 pc to several pc, as well as prevalent networks
of filaments in other large-scale local MCs.


  Paul A. Samuelson's (1966) capitulation during the so-called Cambridge
controversy on the re-switching of techniques in capital theory had
implications not only in pointing at supposed internal contradiction of the
marginal theory of production and distribution, but also in preserving vested
interests in the academic and political world. Based on a new non-switching
theorem, the present paper demonstrates that Samuelson's capitulation was
logically groundless from the point of view of the economic theory of
production.


  We propose two Quantum Direct Communication (QDC) protocols with user
authentication. Users can identify each other by checking the correlation of
Greenberger-Horne-Zeilinger (GHZ) states. Alice can directly send a secret
message to Bob using the remaining GHZ states after authentication. Our second
QDC protocol can be used even though there is no quantum link between Alice and
Bob. The security of the transmitted message is guaranteed by properties of
entanglement of GHZ states.


  High resolution peripheral quantitative computed tomography (HR-pQCT) is an
imaging technique capable of imaging trabecular bone in-vivo. HR-pQCT has a
wide range of applications, primarily focused on bone to improve our
understanding of musculoskeletal diseases, assess epidemiological associations,
and evaluate the effects of pharmaceutical interventions. Processing HR-pQCT
images has largely been supported using the scanner manufacturer scripting
language (Image Processing Language, IPL, Scanco Medical). However, by
expanding image processing workflows outside of the scanner manufacturer
software environment, users have the flexibility to apply more advanced
mathematical techniques and leverage modern software packages to improve image
processing. The ORMIR_XCT Python package was developed to reimplement some
existing IPL workflows and provide an open and reproducible package allowing
for the development of advanced HR-pQCT data processing workflows.


  We consider electron states in n-p double quantum dots defined in a
semiconducting carbon nanotube (CNT) by an external potential. We describe
formation of extended single-electron orbitals originating from the conduction
and valence bands confined in a minimum and a maximum of the external
potential, respectively. We solve the problem of a confined electron pair using
an exact diagonalization method within the tight-binding approach, which allows
for a straightforward treatment of the conduction and valence band states,
keeping an exact account for the intervalley scattering mediated by the atomic
defects and the electron-electron interaction. The exchange interaction - which
in the unipolar double dots is nearly independent of the axial magnetic field
(B) and forms singlet-like and triplet-like states - in the n-p system appears
only for selected states and narrow intervals of B. In particular the
ground-state energy level of a n-p double dot is not split by the exchange
interaction and remains four-fold degenerate at zero magnetic field also for a
strong tunnel coupling between the dots.


  In recent years there has been an increased interest in statistical analysis
of data with multiple types of relations among a set of entities. Such
multi-relational data can be represented as multi-layer graphs where the set of
vertices represents the entities and multiple types of edges represent the
different relations among them. For community detection in multi-layer graphs,
we consider two random graph models, the multi-layer stochastic blockmodel
(MLSBM) and a model with a restricted parameter space, the restricted
multi-layer stochastic blockmodel (RMLSBM). We derive consistency results for
community assignments of the maximum likelihood estimators (MLEs) in both
models where MLSBM is assumed to be the true model, and either the number of
nodes or the number of types of edges or both grow. We compare MLEs in the two
models with other baseline approaches, such as separate modeling of layers,
aggregating the layers and majority voting. RMLSBM is shown to have advantage
over MLSBM when either the growth rate of the number of communities is high or
the growth rate of the average degree of the component graphs in the
multi-graph is low. We also derive minimax rates of error and sharp thresholds
for achieving consistency of community detection in both models, which are then
used to compare the multi-layer models with a baseline model, the aggregate
stochastic block model. The simulation studies and real data applications
confirm the superior performance of the multi-layer approaches in comparison to
the baseline procedures.


  A new constraint suppressing formulation of the Einstein evolution equations
is presented, generalizing the five-parameter first-order system due to Kidder,
Scheel and Teukolsky (KST). The auxiliary fields, introduced to make the KST
system first-order, are given modified evolution equations designed to drive
constraint violations toward zero. The algebraic structure of the new system is
investigated, showing that the modifications preserve the hyperbolicity of the
fundamental and constraint evolution equations. The evolution of the
constraints for pertubations of flat spacetime is completely analyzed, and all
finite-wavelength constraint modes are shown to decay exponentially when
certain adjustable parameters satisfy appropriate inequalities. Numerical
simulations of a single Schwarzschild black hole are presented, demonstrating
the effectiveness of the new constraint-damping modifications.


  In this article, we give the exact interval of the cross section of the
Multibrot sets generated by the polynomial $z^p+c$ where $z$ and $c$ are
complex numbers and $p > 2$ is an odd integer. Furthermore, we show that the
same Multibrots defined on the hyperbolic numbers are always squares. Moreover,
we give a generalized 3D version of the hyperbolic Multibrot set and prove that
our generalization is an octahedron for a specific 3D slice of the dynamical
system generated by the tricomplex polynomial $\eta^p+c$ where $p > 2$ is an
odd integer.


  We study the effective field theory (EFT) description of the virtual particle
effects in quasi-single field inflation, which unifies the previous results on
large mass and large mixing cases. By using a horizon crossing approximation
and matching with known limits, approximate expressions for the power spectrum
and the spectral index are obtained. The error of the approximate solution is
within 10% in dominate parts of the parameter space, which corresponds to
less-than-0.1% error in the $n_s$-$r$ diagram. The quasi-single field
corrections on the $n_s$-$r$ diagram are plotted for a few inflation models.
Especially, the quasi-single field correction drives $m^2\phi^2$ inflation to
the best fit region on the $n_s$-$r$ diagram, with an amount of equilateral
non-Gaussianity which can be tested in future experiments.


  This paper introduces the concept of Fractal Frenet equations, a set of
differential equations used to describe the behavior of vectors along fractal
curves. The study explores the analogue of arc length for fractal curves,
providing a measure to quantify their length. It also discusses fundamental
mathematical constructs, such as the analogue of the unit tangent vector, which
indicates the curve's direction at different points, and the analogue of
curvature vector or fractal curvature vector, which characterizes its curvature
at various locations. The concept of torsion, describing the twisting and
turning of fractal curves in three-dimensional space, is also explored.
Specific examples, like the fractal helix and the fractal snowflake, illustrate
the application and significance of the Fractal Frenet equations.


  In this paper, we study a second order variational problem for locally convex
hypersurfaces, which is the affine invariant analogue of the classical Plateau
problem for minimal surfaces. We prove existence, regularity and uniqueness
results for hypersurfaces maximizing affine area under appropriate boundary
conditions.


  We show that the energy required by a turbulent flow to displace a given
amount of fluid through a straight duct in a given time interval can be reduced
by modulating in time the pumping power. The control strategy is hybrid: it is
passive, as it requires neither a control system nor control energy, but it
manipulates how pumping energy is delivered to the system (as in active
techniques) to increase the pumping efficiency. Our control employs a
temporally periodic pumping pattern, where a short and intense acceleration (in
which the pumping system is on) followed by a longer deceleration (in which the
pumping system is off) makes the flow alternately visit a quasi-laminar and a
turbulent state. The computational study is for a plane channel flow, and
employs direct numerical simulations, which present specific computational
challenges, for example the highly varying instantaneous value of the Reynolds
number, and the importance of discretisation effects. Particular care is
devoted to a meaningful definition of drag reduction in the present context.
The ability of the forcing to yield significant savings is demonstrated. Since
only a small portion of the parameter space is investigated, the best
performance of the control technique remains to be assessed.


  We present results from general relativistic calculations of the tidal
disruption of white dwarf stars from near encounters with intermediate mass
black holes. We follow the evolution of 0.2 and $0.6 M_\odot$ stars on
parabolic trajectories that approach $10^3$ - $10^4 M_\odot$ black holes as
close as a few Schwarzschild radii at periapsis, paying particular attention to
the effect tidal disruption has on thermonuclear reactions and the synthesis of
intermediate to heavy ion elements. These encounters create diverse
thermonuclear environments characteristic of Type I supernovae and capable of
producing both intermediate and heavy mass elements in arbitrary ratios,
depending on the strength (or proximity) of the interaction. Nuclear ignition
is triggered in all of our calculations, even at weak tidal strengths $\beta
\sim 2.6$ and large periapsis radius $R_P \sim 28$ Schwarzschild radii. A
strong inverse correlation exists between the mass ratio of calcium to iron
group elements and tidal strength, with $\beta \lesssim 5$ producing
predominately calcium-rich debris. At these moderate to weak interactions,
nucleosynthesis is not especially efficient, limiting the total mass and
outflows of calcium group elements to $< 15$\% of available nuclear fuel. Iron
group elements however continue to be produced in greater quantity and ratio
with increasing tidal strength, peaking at $\sim 60$\% mass conversion
efficiency in our closest encounter cases. These events generate short bursts
of gravitational waves with characteristic frequencies 0.1-0.7 Hz and strain
amplitudes $0.5\times10^{-22}$ - $3.5\times10^{-22}$ at 10 Mpc source distance.


  The Mid-Infrared Instrument (MIRI) on the James Webb Space Telescope (JWST),
has imaging, four coronagraphs and both low and medium resolution spectroscopic
modes . Being able to simulate MIRI observations will help commissioning of the
instrument, as well as get users familiar with representative data. We designed
the MIRI instrument simulator (MIRISim) to mimic the on-orbit performance of
the MIRI imager and spectrometers using the Calibration Data Products (CDPs)
developed by the MIRI instrument team. The software encorporates accurate
representations of the detectors, slicers, distortions, and noise sources along
the light path including the telescope's radiative background and cosmic rays.
The software also includes a module which enables users to create astronomical
scenes to simulate. MIRISim is a publicly available Python package that can be
run at the command line, or from within Python. The outputs of MIRISim are
detector images in the same uncalibrated data format that will be delivered to
MIRI users. These contain the necessary metadata for ingestion by the JWST
calibration pipeline.


  In this article two implementations of a symmetric finite difference
algorithm for a first-order partial differential equation are discussed. The
considered partial differential equation discribes the time evolution of the
crack length distribution of microcracks in brittle materia.


  We study the dipole formation at the surface formed by -CH3 and -CF3
terminated shortchain alkyl-thiolate monolayers on Au(111). In particular, we
monitor the change in work function upon chemisorption using density functional
theory calculations. We separate the surface dipole into two contributions,
resulting from the gold-adsorbate interaction and the intrinsic dipole of the
adsorbate layer, respectively. The two contributions turn out to be
approximately additive. Adsorbate dipoles are defined by calculating dipole
densities of free-standing molecular monolayers. The gold-adsorbate interaction
is to a good degree determined by the Au-S bond only. This bond is nearly
apolar and its contribution to the surface dipole is relatively small. The
surface dipole of the self-assembled monolayer is then dominated by the
intrinsic dipole of the thiolate molecules. Alkyl-thiolates increase the work
function of Au(111), whereas fluorinated alkyl-thiolates decrease it.


  In this paper, we study an energy efficiency maximization problem in uplink
for D2D communications underlaid with cellular networks on multiple bands.
Utilizing stochastic geometry, we derive closed-form expressions for the
average sum rate, successful transmission probability, and energy efficiency of
cellular and D2D users. Then, we formulate an optimization problem to jointly
maximize the energy efficiency of D2D and cellular users and obtain optimum
transmission power of both D2D and cellular users. In the optimization problem,
we guarantee the QoS of users by taking into account the success transmission
probability on each link. To solve the problem, first we convert the problem
into canonical convex form. Afterwards, we solve the problem in two phases,
energy efficiency maximization of devices and energy efficiency maximization of
cellular users. In the first phase, we maximize the energy efficiency of D2D
users and feed the solution to the second phase where we maximize the energy
efficiency of cellular users. Simulation results reveal that significant energy
efficiency can be attained e.g., 10% energy efficiency improvement compared to
fix transmission power in high density scenario.


  Recent direct visual odometry and SLAM algorithms have demonstrated
impressive levels of precision. However, they require a photometric camera
calibration in order to achieve competitive results. Hence, the respective
algorithm cannot be directly applied to an off-the-shelf-camera or to a video
sequence acquired with an unknown camera. In this work we propose a method for
online photometric calibration which enables to process auto exposure videos
with visual odometry precisions that are on par with those of photometrically
calibrated videos. Our algorithm recovers the exposure times of consecutive
frames, the camera response function, and the attenuation factors of the sensor
irradiance due to vignetting. Gain robust KLT feature tracks are used to obtain
scene point correspondences as input to a nonlinear optimization framework. We
show that our approach can reliably calibrate arbitrary video sequences by
evaluating it on datasets for which full photometric ground truth is available.
We further show that our calibration can improve the performance of a
state-of-the-art direct visual odometry method that works solely on pixel
intensities, calibrating for photometric parameters in an online fashion in
realtime.


  Self-supervised learning is a growing paradigm in deep representation
learning, showing great generalization capabilities and competitive performance
in low-labeled data regimes. The SimCLR framework proposes the NT-Xent loss for
contrastive representation learning. The objective of the loss function is to
maximize agreement, similarity, between sampled positive pairs. This short
paper derives and proposes an upper bound for the loss and average similarity.
An analysis of the implications is however not provided, but we strongly
encourage anyone in the field to conduct this.


  In a clinical trial with a survival outcome, an interim analysis is often
performed to allow for early stopping for efficacy. If the interim analysis is
early in the trial, one might conclude that a new treatment is more effective
(compared to e.g.\ a placebo) and stop the trial, whereas the survival curves
in the trial arms are not mature for the research question under investigation,
for example because the curves are still close to 1 at that time. This means
that the decision is based on a small percentage of the events in the long run
only; possibly the events of the more frail patients in the trial who may not
be representative for the whole group of patients. It may not be sensible to
conclude effectiveness based on so little information. Criteria to determine
the moment the interim analysis will be performed, should be chosen with care,
and include the maturity of the data at the time of the interim analysis. Here,
the expected survival rates at the interim analysis play a role. In this paper
we will derive the asymptotic distribution of the Kaplan-Meier curves at the
(random) moment the interim analysis will be performed for a one and two arm
clinical trial. Based on this distribution, an interval in which the Kaplan
Meier curves will fall into (with probability 95\%) is derived and could be
used to plan the moment of the interim analysis in the design stage of the
trial, so before the trial starts.


  We introduce a new approach towards generative quantum machine learning
significantly reducing the number of hyperparameters and report on a
proof-of-principle experiment demonstrating our approach. Our proposal depends
on collaboration between the generators and discriminator, thus, we call it
quantum synergic generative learning. We present numerical evidence that the
synergic approach, in some cases, compares favorably to recently proposed
quantum generative adversarial learning. In addition to the results obtained
with quantum simulators, we also present experimental results obtained with an
actual programmable quantum computer. We investigate how a quantum computer
implementing generative learning algorithm could learn the concept of a Bell
state. After completing the learning process, the network is able both to
recognize and to generate an entangled state. Our approach can be treated as
one possible preliminary step to understanding how the concept of quantum
entanglement can be learned and demonstrated by a quantum computer.


  We present a study of systems of single-molecule magnets using a
semiclassical analysis and catastrophe theory. Separatrices in parameter space
are constructed which are useful to determine the structure of the Hamiltonians
energy levels. In particular the Maxwell set separatrix determines the behavior
of the ground state of the system. We consider an external magnetic field with
two components, one parallel to the easy magnetization axis of the molecule and
the other perpendicular to it. Using the fidelity and heat capacity we were
able to detect the signals of the QPTs as a function of the magnetic field
components.


  Morse matchings capture the essential structural information of discrete
Morse functions. We show that computing optimal Morse matchings is NP-hard and
give an integer programming formulation for the problem. Then we present
polyhedral results for the corresponding polytope and report on computational
results.


  According to the standard picture for binary interactions, the outcome of
binaries surviving the evolution through a common envelope (CE) and spiral-in
phase is determined by the internal structure of the donor star at the onset of
the mass transfer, as well as the poorly-known efficiency parameter, eta_CE},
for the ejection of the H-envelope of the donor. In this Research Note we
discuss the bifurcation point which separates the ejected, unprocessed H-rich
material from the inner core region of the donor (the central part of the star
which will later contract to form a compact object). We demonstrate that the
exact location of this point is very important for evaluating the binding
energy parameter, lambda, which is used to determine the post-CE orbital
separation. Here we compare various methods to define the bifurcation point
(core/envelope boundary) of evolved stars with masses 4, 7, 10 and 20 M_sun. We
consider the specific nuclear energy production rate profile, the change in the
mass-density gradient (Bisscheroux 1998), the inner region containing less than
10% hydrogen, the method suggested by Han et al. (1994) and the entropy
profile. We also calculated effective polytropic index profiles. The entropy
profile method measures the convective boundary (at the onset of flatness in
the specific entropy) which is not equivalent to the core boundary for RGB
stars. Hence, this method is not applicable for RGB stars, unless the actual
bifurcation point of a CE is located at the bottom of the outer convection zone
(resulting in larger values of lambda and larger post-CE orbital separations).
On the AGB, where highly degenerate and condensed cores are formed, we find
good agreement between the various methods, except for massive (20 M_sun)
stars.


  We show that the exponent in the inverse power law of word frequencies for
the monkey-at-the-typewriter model of Zipf's law will tend towards -1 under
broad conditions as the alphabet size increases to infinity and the letter
probabilities are specified as the values from a random division of the unit
interval. This is proved utilizing a strong limit theorem for log-spacings due
to Shao and Hahn.


  We investigate the structure of solutions of boundary value problems for a
one-dimensional nonlinear system of pseudodifferential equations describing the
dynamics (rolling) of p-adic open, closed, and open-closed strings for a scalar
tachyon field using the method of successive approximations. For an open-closed
string, we prove that the method converges for odd values of p of the form
p=4n+1 under the condition that the solution for the closed string is known.
For p=2, we discuss the questions of the existence and the nonexistence of
solutions of boundary value problems and indicate the possibility of
discontinuous solutions appearing.


  The Djokovi\'{c}-Winkler relation $\Theta$ is a binary relation defined on
the edge set of a given graph that is based on the distances of certain
vertices and which plays a prominent role in graph theory. In this paper, we
explore the relatively uncharted ``reflexive complement'' $\overline\Theta$ of
$\Theta$, where $(e,f)\in \overline\Theta$ if and only if $e=f$ or $(e,f)\notin
\Theta$ for edges $e$ and $f$. We establish the relationship between
$\overline\Theta$ and the set $\Delta_{ef}$, comprising the distances between
the vertices of $e$ and $f$ and shed some light on the intricacies of its
transitive closure $\overline\Theta^*$. Notably, we demonstrate that
$\overline\Theta^*$ exhibits multiple equivalence classes only within a
restricted subclass of complete multipartite graphs. In addition, we
characterize non-trivial relations $R$ that coincide with $\overline\Theta$ as
those where the graph representation is disconnected, with each connected
component being the (join of) Cartesian product of complete graphs. The latter
results imply, somewhat surprisingly, that knowledge about the distances
between vertices is not required to determine $\overline\Theta^*$. Moreover,
$\overline\Theta^*$ has either exactly one or three equivalence classes.


  For measure preserving dynamical systems on metric spaces we study the time
needed by a typical orbit to return back close to its starting point. We prove
that when the decay of correlation is super-polynomial the recurrence rates and
the pointwise dimensions are equal. This gives a broad class of systems for
which the recurrence rate equals the Hausdorff dimension of the invariant
measure.


  We analyze experimental data of nuclear structure function ratios
$F_2^A/F_2^D$ for obtaining optimum parton distribution functions (PDFs) in
nuclei. Then, uncertainties of the nuclear PDFs are estimated by the Hessian
method. Parametrization of nuclear parton distribution is investigated in the
leading order of $\alpha_s$. The parton distribution are provided at $Q^2=1
GeV^2$ with a number of parameters, which are determined by a $\chi^2$ analysis
of the data on nuclear structure function. From the analysis, we propose parton
distributions at $Q^2=1 GeV^2$ for nuclei from deuteron to heavy ones with a
mass number $A\sim 208$.


  The Schwarzschild-de Sitter solution in the Einstein theory with a positive
cosmological constant $\Lambda=m^2/\alpha$ becomes an exact solution to the
dRGT non-linear massive gravity theory with the mass parameter $m$ when the
theory parameters $\alpha$ and $\beta$ satisfy the relation $\beta=\alpha^2$.
We study the perturbative behaviour of this black hole solution in the
non-linear dRGT theory with $\beta=\alpha^2$. We find that the linear
perturbation equations become identical to those for the vacuum Einstein theory
when they are expressed in terms of the gauge-invariant variables. This implies
that this black hole is stable in the dRGT theory as far as the spacetime
structure is concerned in contrast to the case of the bi-Schwarzschild solution
in the bi-metric theory. However, we have also found a pathological feature
that the general solution to the perturbation equations contain a single
arbitrary function of spacetime coordinates. This implies a degeneracy of
dynamics in the St\"uckelberg field sector at the linear perturbation level in
this background. Physical significance of this degenercy depends on how the
St\"uckelberg fields couple observable fields.


  We show that, from a topological point of view, 2-tape B\"uchi automata have
the same accepting power than Turing machines equipped with a B\"uchi
acceptance condition. In particular, we show that for every non null recursive
ordinal alpha, there exist some Sigma^0_alpha-complete and some
Pi^0_alpha-complete infinitary rational relations accepted by 2-tape B\"uchi
automata. This very surprising result gives answers to questions of W. Thomas
[Automata and Quantifier Hierarchies, in: Formal Properties of Finite automata
and Applications, Ramatuelle, 1988, LNCS 386, Springer, 1989, p.104-119], of P.
Simonnet [Automates et Th\'eorie Descriptive, Ph. D. Thesis, Universit\'e Paris
7, March 1992], and of H. Lescow and W. Thomas [Logical Specifications of
Infinite Computations, In: "A Decade of Concurrency", LNCS 803, Springer, 1994,
p. 583-621].


  Many people are familiar with the physico-chemical properties of gene
sequences. In this paper I present a mathematical perspective: how do
mathematical principles such as information theory, coding theory, and
combinatorics influence the beginnings of life and the formation of the genetic
codes we observe today? What constraints on possible life forms are imposed by
information-theoretical concepts? Further, I detail how mathematical principles
can help us to analyse the genetic sequences we observe in the world today.


  We study the vibrational spectrum of the protonated water dimer, by means of
a divide-and-conquer semiclassical initial value representation of the quantum
propagator, as a first step in the study of larger protonated water clusters.
We use the potential energy surface from [Huang et al., J. Chem. Phys. 122,
044308 (2005)]. To tackle such an anharmonic and floppy molecule, we employ
fully Cartesian dynamics and carefully reduce the coupling to global rotations
in the definition of normal modes. We apply the time-averaging filter and
obtain clean power spectra relative to suitable reference states, that
highlight the spectral peaks corresponding to the fundamental excitations of
the system. Our trajectory-based approach allows us for physical interpretation
of the very challenging proton transfer modes. We find that it is important,
for such a floppy molecule, to selectively avoid to initially excite lower
energy modes, in order to obtain cleaner spectra. The estimated vibrational
energies display a mean absolute error (MAE) of $\sim29\text{cm}^{-1}$ with
respect to available Multi-Configuration time-dependent Hartree calculations
and $\text{MAE}\sim14\text{cm}^{-1}$ when compared to the optically active
experimental excitations of the Ne-tagged Zundel cation. The reasonable scaling
in the number of trajectories for Monte Carlo convergence is promising for
applications to higher dimensional protonated cluster systems.


  Michael Handel has proved in [Ha] a fixed point theorem for an orientation
preserving homeomorphism of the open unit disk, that turned out to be an
efficient tool in the study of the dynamics of surface homeomorphisms. The
present article fits into a series of articles by the author [LeC2] and by
Juliana Xavier [X1], [X2], where proofs were given, related to the classical
Brouwer Theory, instead of the Homotopical Brouwer Theory used in the original
article. Like in [LeC2], [X1] and [X2], we will use "free brick decompositions"
but will present a more conceptual Morse theoretical argument. It is based on a
new preliminary lemma, that gives a nice "condition at infinity" for our
problem.


  Magnetic response is a fundamental property of superconducting materials,
which helps to distinguish two superconductivity types: the ideally diamagnetic
type I and type II, which can develop the mixed state with Abrikosov vortices.
We demonstrate that multi-band superconductors with one shallow band, that have
recently attracted much attention for their high critical temperatures and
unusual properties, often stay apart of this simple classification. In a wide
range of microscopic parameters such systems fall into the inter-type or
transitional interval in between the standard types and display unconventional
mixed state configurations.


  We provide a criterion for a point satisfying the required disjointness
condition in Sarnak's M\"obius Disjointness Conjecture. As a direct
application, we have that the conjecture holds for any topological model of an
ergodic system with discrete spectrum.


  In this article, the use of channel state information (CSI) for indoor
positioning is studied. In the considered model, a server equipped with several
antennas sends pilot signals to users, while each user uses the received pilot
signals to estimate channel states for user positioning. To this end, we
formulate the positioning problem as an optimization problem aiming to minimize
the gap between the estimated positions and the ground truth positions of
users. To solve this problem, we design a complex-valued neural network (CVNN)
model based federated learning (FL) algorithm. Compared to standard real-valued
centralized machine learning (ML) methods, our proposed algorithm has two main
advantages. First, our proposed algorithm can directly process complex-valued
CSI data without data transformation. Second, our proposed algorithm is a
distributed ML method that does not require users to send their CSI data to the
server. Since the output of our proposed algorithm is complex-valued which
consists of the real and imaginary parts, we study the use of the CVNN to
implement two learning tasks. First, the proposed algorithm directly outputs
the estimated positions of a user. Here, the real and imaginary parts of an
output neuron represent the 2D coordinates of the user. Second, the proposed
method can output two CSI features (i.e., line-of-sight/non-line-of-sight
transmission link classification and time of arrival (TOA) prediction) which
can be used in traditional positioning algorithms. Simulation results
demonstrate that our designed CVNN based FL can reduce the mean positioning
error between the estimated position and the actual position by up to 36%,
compared to a RVNN based FL which requires to transform CSI data into
real-valued data.


  In this paper we present a class of metrics to be considered as new possible
sources for the Kerr metric. These new solutions are generated by applying the
Newman-Janis algorithm (NJA) to any static spherically symmetric (SSS) ``seed''
metric. The continuity conditions for joining any two of these new metrics is
presented. A specific analysis of the joining of interior solutions to the Kerr
exterior is made. The boundary conditions used are those first developed by
Dormois and Israel. We find that the NJA can be used to generate new physically
allowable interior solutions. These new solutions can be matched smoothly to
the Kerr metric. We present a general method for finding such solutions with
oblate spheroidal boundary surfaces. Finally a trial solution is found and
presented.


  In this paper, we point out a novel signature of physics beyond the Standard
Model which could potentially be observed both at the Large Hadron Collider
(LHC) and at future colliders. This signature, which emerges naturally within
many proposed extensions of the Standard Model, results from the multiple
displaced vertices associated with the successive decays of unstable,
long-lived particles along the same decay chain. We call such a sequence of
displaced vertices a "tumbler." We examine the prospects for observing tumblers
at the LHC and assess the extent to which tumbler signatures can be
distinguished from other signatures of new physics which also involve multiple
displaced vertices within the same collider event. As part of this analysis, we
also develop a procedure for reconstructing the masses and lifetimes of the
particles involved in the corresponding decay chains. We find that the
prospects for discovering and distinguishing tumblers can be greatly enhanced
by exploiting precision timing information such as would be provided by the CMS
timing layer at the high-luminosity LHC. Our analysis therefore provides strong
additional motivation for continued efforts to improve the timing capabilities
of collider detectors at the LHC and beyond.


  In this note we consider 2-step nilpotent Lie algebras associated with
graphs. We prove that 2-step nilpotent Lie algebras $\n$ and $\n'$ associated
with graphs $(S, E)$ and $(S', E')$ respectively are isomorphic if and only if
$(S, E)$ and $(S', E')$ are isomorphic.


  Existing Temporal Action Detection (TAD) methods typically take a
pre-processing step in converting an input varying-length video into a
fixed-length snippet representation sequence, before temporal boundary
estimation and action classification. This pre-processing step would temporally
downsample the video, reducing the inference resolution and hampering the
detection performance in the original temporal resolution. In essence, this is
due to a temporal quantization error introduced during the resolution
downsampling and recovery. This could negatively impact the TAD performance,
but is largely ignored by existing methods. To address this problem, in this
work we introduce a novel model-agnostic post-processing method without model
redesign and retraining. Specifically, we model the start and end points of
action instances with a Gaussian distribution for enabling temporal boundary
inference at a sub-snippet level. We further introduce an efficient
Taylor-expansion based approximation, dubbed as Gaussian Approximated
Post-processing (GAP). Extensive experiments demonstrate that our GAP can
consistently improve a wide variety of pre-trained off-the-shelf TAD models on
the challenging ActivityNet (+0.2% -0.7% in average mAP) and THUMOS (+0.2%
-0.5% in average mAP) benchmarks. Such performance gains are already
significant and highly comparable to those achieved by novel model designs.
Also, GAP can be integrated with model training for further performance gain.
Importantly, GAP enables lower temporal resolutions for more efficient
inference, facilitating low-resource applications. The code will be available
in https://github.com/sauradip/GAP


  We consider the existence of \emph{normalized} solutions in $H^1(\R^N) \times
H^1(\R^N)$ for systems of nonlinear Schr\"odinger equations which appear in
models for binary mixtures of ultracold quantum gases. Making a solitary wave
ansatz one is led to coupled systems of elliptic equations of the form \[
\left\{ \begin{aligned} -\De u_1 &= \la_1u_1 + f_1(u_1)+\pa_1F(u_1,u_2),\\ -\De
u_2 &= \la_2u_2 + f_2(u_2)+\pa_2F(u_1,u_2),\\ u_1,u_2&\in H^1(\R^N),\ N\ge2,
\end{aligned} \right. \] and we are looking for solutions satisfying \[
\int_{\R^N}|u_1|^2 = a_1,\quad \int_{\R^N}|u_2|^2 = a_2 \] where $a_1>0$ and
$a_2>0$ are prescribed. In the system $\la_1$ and $\la_2$ are unknown and will
appear as Lagrange multipliers. We treat the case of homogeneous
nonlinearities, i.e.\ $f_i(u_i)=\mu_i|u_i|^{p_i-1}u_i$,
$F(u_1,u_2)=\be|u_1|^{r_1}|u_2|^{r_2}$, with positive constants $\be, \mu_i,
p_i, r_i$. The exponents are Sobolev subcritical but may be
$L^2$-supercritical:
$p_1,p_2,r_1+r_2\in]2,2^*[\,\setminus\left\{2+\frac4N\right\}$.


  In this paper, we study the following quasilinear Schr\"{o}dinger equation of
Choquard type $$ -\triangle u+V(x)u-\triangle (u^{2})u=(I_\alpha
*|u|^p)|u|^{p-2}u, \ \ x \in \mathbb{R}^{N}, $$ where $N\geq 3$,\ $0<\alpha<N$,
$\frac{2(N+\alpha)}{N}\leq p<\frac{2(N+\alpha)}{N-2}$ and $I_\alpha$ is a Riesz
potential. Under appropriate assumptions on $V(x)$, we establish the existence
of positive solutions.


  Magnetic fields are expected to be efficiently amplified during the formation
of the first massive black holes via the small-scale dynamo and in the presence
of strong accretion shocks occurring during gravitational collapse. Here, we
analyze high-resolution cosmological magneto-hydrodynamical simulations of
gravitational collapse in atomic cooling halos, exploring the dynamical role of
magnetic fields, particularly concerning the effect of magnetic braking and
angular momentum transport. We find that after the initial amplification,
magnetic fields contribute to the transport of angular momentum and reduce it
compared to pure hydrodynamical simulations. However, the magnetic and Reynolds
torques do not fully compensate for the inward advection of angular momentum,
which still accumulates over timescales of $\sim1$~Myr. A Jeans analysis
further shows that magnetic pressure strongly contributes to suppressing
fragmentation on scales of $0.1-10$~pc. Overall, the presence of magnetic
fields thus aids in the transport of angular momentum and favors the formation
of massive objects.


  Based on macroscopic quantum electrodynamics in linearly and causally
responding media, we study the local-field corrected van der Waals potentials
and forces for unpolarized ground-state atoms placed within a magnetoelectric
medium of arbitrary size and shape. We start from general expressions for the
van der Waals potentials in terms of the (classical) Green tensor of the
electromagnetic field and the atomic polarizability and incorporate the
local-field correction by means of the real-cavity model. In this context,
special emphasis is given to the decomposition of the Green tensor into a
medium part multiplied by a global local-field correction factor and, in the
single-atom case, a part that only depends on the cavity characteristics. The
result is used to derive general formulas for the local-field corrected van der
Waals potentials and forces. As an application, we calculate the van der Waals
potential between two ground-state atoms placed within magnetoelectric bulk
material.


  A directional random laser mediated by transverse Anderson localization in a
disordered glass optical fiber is reported. Previous demonstrations of random
lasers have found limited applications because of their multi-directionality
and chaotic fluctuations in the laser emission. The random laser presented in
this paper operates in the Anderson localization regime. The disorder induced
localized states form isolated local channels that make the output laser beam
highly directional and stabilize its spectrum. The strong transverse disorder
and longitudinal invariance result in isolated lasing modes with negligible
interaction with their surroundings, traveling back and forth in a Fabry-Perot
cavity formed by the air-fiber interfaces. It is shown that if a localized
input pump is scanned across the disordered fiber input facet, the output laser
signal follows the transverse position of the pump. Moreover, a uniformly
distributed pump across the input facet of the disordered fiber generates a
laser signal with very low spatial coherence that can be of practical
importance in many optical platforms including image transport with fiber
bundles.


  Topological color codes are widely acknowledged as promising candidates for
fault-tolerant quantum computing. Neither a two-dimensional nor a
three-dimensional topology, however, can provide a universal gate set $\{$H, T,
CNOT$\}$, with the T-gate missing in the two-dimensional and the H-gate in the
three-dimensional case. These complementary shortcomings of the isolated
topologies may be overcome in a combined approach, by switching between a two-
and a three-dimensional code while maintaining the logical state. In this work,
we construct resource-optimized deterministic and non-deterministic code
switching protocols for two- and three-dimensional distance-three color codes
using fault-tolerant quantum circuits based on flag-qubits. Deterministic
protocols allow for the fault-tolerant implementation of logical gates on an
encoded quantum state, while non-deterministic protocols may be used for the
fault-tolerant preparation of magic states. Taking the error rates of
state-of-the-art trapped-ion quantum processors as a reference, we find a
logical failure probability of $3\%$ for deterministic logical gates, which
cannot be realized transversally in the respective code. By replacing the
three-dimensional distance-three color code in the protocol for magic state
preparation with the morphed code introduced in [1], we reduce the logical
failure rates by two orders of magnitude, thus rendering it a viable method for
magic state preparation on near-term quantum processors. Our results
demonstrate that code switching enables the fault-tolerant and deterministic
implementation of a universal gate set under realistic conditions, and thereby
provide a practical avenue to advance universal, fault-tolerant quantum
computing and enable quantum algorithms on first, error-corrected logical
qubits.


  We introduce a new class of quantum many-particle entangled states, called
the Dicke squeezed (or DS) states, which can be used to improve the precision
in quantum metrology beyond the standard quantum limit. We show that the
enhancement in measurement precision is characterized by a single
experimentally detectable parameter, called the Dicke squeezing $\xi_{D}$,
which also bounds the entanglement depth for this class of states. The
measurement precision approaches the ultimate Heisenberg limit as $\xi_{D}$
attains the minimum in an ideal Dicke state. Compared with other entangled
states, we show that the Dicke squeezed states are more robust to decoherence
and give better measurement precision under typical experimental noise.


  Named Entity Recognition(NER) is a task of recognizing entities at a token
level in a sentence. This paper focuses on solving NER tasks in a multilingual
setting for complex named entities. Our team, LLM-RM participated in the
recently organized SemEval 2023 task, Task 2: MultiCoNER II,Multilingual
Complex Named Entity Recognition. We approach the problem by leveraging
cross-lingual representation provided by fine-tuning XLM-Roberta base model on
datasets of all of the 12 languages provided -- Bangla, Chinese, English,
Farsi, French, German, Hindi, Italian, Portuguese, Spanish, Swedish and
Ukrainian


  The spin system of the $2d$ Ising model having a hexagonal-lattice is
simulated using non-deterministic Cellular Automata. The method to implement
this program is outlined and our results show a good approximation to the exact
analytic solution. The phase transition in $2d$ Ising model is studied with a
$40\times40$ hexagonal-lattice with five different boundary conditions (bcs)
i.e., adiabatic, periodic, reflexive, fixed $+1$ and fixed $-1$ with random
orientation of spins as initial conditions in the absence of an external
applied magnetic field. The critical temperature below which the spontaneous
magnetization appears as well as other physical quantities such as the
magnetization, energy, specific heat, susceptibility and entropy with each of
the bcs are calculated. The phase transition occurs around $T^H_c$ = 1.5 which
approximates well with the result obtained from exact analytic solution by
Wannier and Houtappel. We compare the behavior of magnetisation per cell for
five different types of bcs by calculating the number of points close to the
line of zero magnetization for $T>T^H_c$. We find that the periodic, adiabatic
and reflexive bcs give closer approximation to the value of $T^H_c$ than fixed
$+1$ and fixed $-1$ bcs with all three initial conditions for lattice size less
than $50\times50$. However, for lattice size between $50\times50$ and
$200\times200$, fixed $+1$ bc and fixed $-1$ bc give closer approximation to
the $T^H_c$ with initial conditions in which all spins are in down
configuration and all spins are in up configuration respectively.


  In this work, we consider the possibility of energy release in pulsar
magnetospheres deformed by gravitational waves from nearby sources. The strong
electromagnetic fields in the magnetospheres may release non-negligible energy
despite the weakness of the gravitational wave. When the background spacetime
is perturbed due to the passage of a gravitational wave, the original
force-free state of the inner magnetosphere will be slightly violated. The
plasma-filled magnetosphere tends to evolve into new force-free states as the
spacetime varies with time. During this process, a small portion of the
electromagnetic energy stored in the magnetosphere will be released to the
acceleration of charged particles along the magnetic field lines. When the
pulsar is close enough to the gravitational wave source (e.g., $\sim10^{-2}$ pc
to the gravitational wave sources observed recently), the resulting energy loss
rate is comparable with the radio luminosity of the pulsar. It is also noticed
that, under very stringent conditions (for magnetars with much shorter distance
to the sources), the released energy can reach the typical energy observed from
fast radio bursts (FRBs).


  We investigate the efficiency of electrical manipulation on two-dimensional
topological insulators by considering a lateral potential superlattice on the
system. The electronic states under various conditions are examined carefully.
It is found that the dispersion of the mini-band and the electron distribution
in the potential well region display an oscillatory behavior as the potential
strength of the lateral superlattice increases. The probability of finding an
electron in the potential well region can be larger or smaller than the average
as the potential strength varies. This indicates that the electric manipulation
efficiency on two-dimensional topological insulators is not as high as
expected, which should be carefully considered in designing a device
application that bases on two-dimensional topological insulators. These
features can be attributed to the coupled multiple-band nature of the
topological insulator model. In addition, it is also found that these behaviors
are not sensitive to the gap parameter of the two-dimensional topological
insulator model.


  A focusing system such as a single lens or a spherical mirror imparts
intrinsic transverse orbital angular momentum (OAM) to spatiotemporal (ST)
coupled fields the ST intensity distribution of which presents ST covariance.
This fact may greatly simplify the experimental setups used to date to impart
transverse OAM. We evaluate analytically the imparted transverse OAM as a
function of the focal length and the covariance. The focused fields with
transverse OAM include elliptical ST vortices and rotating pulses without any
ST phase singularity such as the "lighthouse" pulse. We provide closed-form,
analytical expressions for these fields valid at any propagation distance from
the focusing system, which are of interest in applications such the interaction
of these fields with matter. In general, focusing of ST coupled fields with
intensity covariance generates mixed fields with ST vortices and rotating
pulse-fronts, where one or another feature dominates depending on the input
field.


  We report results of an extensive world-wide observing campaign devoted to a
very active dwarf nova star - IX Draconis. We investigated photometric
behaviour of the system to derive its basic outburst properties and understand
peculiarities of IX Dra as well as other active cataclysmic variables, in
particular dwarf novae of the ER Uma-type. In order to measure fundamental
parameters of the system, we carried out analyses of the light curve, O-C
diagram, and power spectra. During over two months of observations we detected
two superoutbursts and several normal outbursts. The V magnitude of the star
varied in the range 14.6 - 18.2 mag. Superoutbursts occur regularly with the
supercycle length of 58.5+/-0.5 d. When analysing data over the past 20 years,
we found that the supercycle length is increasing at a rate of P_dot = 1.8 *
10^{-3}. Normal outbursts appear to be irregular, with typical occurrence times
in the range 3.1 - 4.1 d. We detected a double-peaked structure of superhumps
during superoutburst, with the secondary maximum becoming dominant near the end
of the superoutburst. The mean superhump period observed during superoutbursts
equals 0.066982(36) d, which is constant over the last two decades of
observations. Based on the power spectrum analysis, the evaluation of the
orbital period was problematic. We found two possible values: the first one,
0.06641(3) d, which is in agreement with previous studies and our O-C analysis
(0.06646(2) d), and the second one, 0.06482(3) d, which is less likely. The
evolutionary status of the object depends dramatically on the choice between
these two values. A spectroscopic determination of the orbital period is
needed. We updated available information on ER UMa-type stars and present a new
set of their basic statistics. Thereby, we provide evidence that this class of
stars is not uniform.


  Hydrodynamics and magnetohydrodynamic simulations of hot accretion flow have
indicated that there is an inward decreasing of mass accretion rate with
decreasing radius. Consequently, we have a flatter density profile ($\rho
\propto r^{-p}$ with $p\propto 1.5-s$ in the case of $\dot{M}\propto r^{s}$, $0
\leq s<1$) compared to the case of a constant accretion rate (($\rho \propto
r^{-\frac{3}{2}}$). In order to describe this behavior two models have been
proposed: inflow-outflow solution and convection-dominated accretion flows. We
have studied the properties of a hot accretion flow in the presence of
convection, large scale magnetic field and outflow. We consider an axisymmetric
viscous flow in the steady state. We used the self-similar solutions to solve
the 1.5 dimensional inflow-outflow equations. We have assumed that the
convection as a free parameter in our model for simplicity. We have considered
two components of magnetic field (toroidal and vertical) in this paper. We have
shown that the strong convection makes the inflow accretes and rotates slower
while it becomes hotter and thicker. We have found that the thickness of the
disc deviates from non-convective solutions obviously. We have represented that
two components of magnetic field have the opposite effects on the thickness of
the disc and similar effects on the radial and angular velocities of the flow.