  We explore the consequences of new observational and theoretical evidence
that long gamma-ray bursts prefer low metallicity environments. Using recently
derived mass-metallicity correlations and the mass function from SDSS studies,
and adopting an average cosmic metallicity evolution from \citet{kewley2005}
and \citet{savaglio2005} we derive expressions for the the relative number of
massive stars formed below a given fraction of solar metallicity, $\epsilon$,
as function of redshift. We demonstrate that about 1/10th of all stars form
with $\epsilon < 0.1$. Therefore, a picture where the majority of GRBs form
with $\epsilon < 0.1$ is not inconsistent with an empirical global SN/GRB ratio
of 1/1000. It implies that (1) GRB's peak at a significantly higher redshift
than supernovae; (2) massive star evolution at low metallicity may be
qualitatively different and; (3) the larger the low-metallicity bias of GRBs
the less likely binary evolution channels can be significant GRB producers.


  We define an action of the symmetric group on the set of domino tableaux, and
prove that the number of domino tableaux of a given weight does not depend on
the permutation of components of the last. A bijective proof of the well-known
result due to J. Stembridge that the number of self-evacuating tableaux of a
given shape is equal to that of domino tableaux of the same shape is given.


  GW170817 has provided valuable constraints on the equations of state of
merging binary neutron stars, which can be considered as the most probable
candidate for the source of gravitational waves. On the other hand, these
natural laboratories of extreme temperature and density may lead to the
estimation of some exotic matter like {deconfined quark matter in their cores}.
In this paper, we investigate the neutron star matter equation of state (EoS)
with the lowest order constrained variational (LOCV) method considering the
excluded volume effect (VLOCV) for nucleons {to} compute the tidal
deformability of binary neutron star mergers (BNSMs). Within this approach, the
size of nucleons makes the EoS {so} stiff that requires a phase transition in
order to avoid causality violation. Therefore, this phase transition {may lead}
to the appearance of the third family of compact stars {including} ``twin
star'' configurations. {Our EoS models are confronted with observations from
GW170817, GW190814, GW190425, and also NICER. We find out that regarding all
these constraints, the EoS models having the {transition}
pressure$\approx$30-100 MeV/fm$^{3}$ and the energy density discontinuity
$\Delta\varepsilon$$\lesssim$300 MeV/fm$^{3}$ are preferable.


  We present a proof that the hyperbolic plane cannot be isometrically immersed
in Euclidean $3$-space by a $C^\infty$ map. Ideas from many topics in
(essentially) undergraduate mathematics are applied; the use of moving frames
and connection forms to express the geometry simplifies the outline of the
proof, compared to, say, using coordinate patches and Christoffel symbols. The
key transition is from expressions in terms of the principal directions on the
immersed surface (which give access to the Gaussian curvature) to expressions
in terms of the asymptotic directions (which yield a coordinate system and give
access to surface area).


  We develop a systematic perturbation theory for the quasiparticle properties
of a single impurity immersed in a Bose-Einstein condensate. Analytical results
are derived for the impurity energy, the effective mass, and residue to third
order in the impurity-boson scattering length. The energy is shown to depend
logarithmically on the scattering length to third order, whereas the residue
and effective mass are given by analytical power series. When the boson-boson
scattering length equals the boson-impurity scattering length, the energy has
the same structure as that of a weakly interacting Bose gas, including terms of
the Lee-Huang-Yang and fourth order logarithmic form. Our results, which cannot
be obtained within the canonical Fr{\"o}hlich model of an impurity interacting
with phonons, provide valuable benchmarks for many-body theories and for
experiments.


  Telesurgical robotic systems provide a well established form of assistance in
the operating theater, with evidence of growing uptake in recent years. Until
now, the da Vinci surgical system (Intuitive Surgical Inc, Sunnyvale,
California) has been the most widely adopted robot of this kind, with more than
6,700 systems in current clinical use worldwide [1]. To accelerate research on
robotic-assisted surgery, the retired first-generation da Vinci robots have
been redeployed for research use as "da Vinci Research Kits" (dVRKs), which
have been distributed to research institutions around the world to support both
training and research in the sector. In the past ten years, a great amount of
research on the dVRK has been carried out across a vast range of research
topics. During this extensive and distributed process, common technical issues
have been identified that are buried deep within the dVRK research and
development architecture, and were found to be common among dVRK user feedback,
regardless of the breadth and disparity of research directions identified. This
paper gathers and analyzes the most significant of these, with a focus on the
technical constraints of the first-generation dVRK, which both existing and
prospective users should be aware of before embarking onto dVRK-related
research. The hope is that this review will aid users in identifying and
addressing common limitations of the systems promptly, thus helping to
accelerate progress in the field.


  We explore the finite temperature phase diagram of the anisotropic XY spin
chain using the Quantum Chernoff Bound metric on thermal states. The analysis
of the metric elements allows to easily identify, in terms of different scaling
with temperature, quasi-classical and quantum-critical regions. These results
extend recent ones obtained using the Bures metric and show that different
information-theoretic notions of distance can carry the same sophisticated
information about the phase diagram of an interacting many-body system
featuring quantum-critical points.


  We give a generalization of the Jordan canonical form theorem for a class of
bounded linear operators on complex separable Hilbert spaces in terms of direct
integrals. Precisely, we study the uniqueness of strongly irreducible
decompositions of the operators on the Hilbert spaces up to similarity.


  We are concerned with the global existence of entropy solutions for the
compressible Euler equations describing the gas flow in a nozzle with general
cross-sectional area, for both isentropic and isothermal fluids. New
viscosities are delicately designed to obtain the uniform bound of approximate
solutions. The vanishing viscosity method and compensated compactness framework
are used to prove the convergence of approximate solutions. Moreover, the
entropy solutions for both cases are uniformly bounded independent of time. No
smallness condition is assumed on initial data. The techniques developed here
can be applied to compressible Euler equations with general source terms.


  The supranova model for gamma-ray bursts (GRBs) has recently gained
popularity. In this scenario the GRB occurs weeks to years after a supernova
explosion, and is located inside a pulsar wind bubble (PWB). High energy
protons from the PWB can interact with photons from the rich radiation field
inside the PWB or collide with cold protons from the supernova remnant,
producing pions which decay into \sim 10-10^3 TeV neutrinos. The predicted
neutrino flux from the PWBs that host the GRBs should be easily detectable by
planned 1 km^2 detectors.


  We investigate the long-range statistical correlations, whereby discuss the
nature of the undermining interacting/ noninteracting domains and associated
phase transitions under variations of the quark mass and the mass scale that
corresponds to renormalized pion masses and the dimensions of an ensemble of
slab sub-volumes of an arbitrary simulated lattice. The purpose of this paper
is to compute the system's stability and its phase structures when it's model
parameters vary infinitesimally. In particular, we focus on the stability
properties and phases of an arbitrary (2+1) flavor QCD configuration under
fluctuations of its parameters. In order to investigate the nature of
statistical and systematic errors, and the presence of noises in the system, we
explore fluctuation theory equivalences of the slab sub-volume method of
computing the topological susceptibility with its low energy ChPT counterpart.
Hereby, we find that the ChPT configurations always correspond to a
non-interacting statistical basis in the space of the quark mass and the mass
scale that corresponds to renormalized pion masses. The second system as an
ensemble of finite slab sub-volumes of a simulated lattice turns out to be
generically interacting under fluctuations of the slab dimensions. However, it
yields an ill-defined degenerate system in the infinitesimal limit of slab
parameters. It is worth mentioning that implications of the intrinsic geometric
analysis are well suited towards the modeling based understanding of the
gluonic topological charge density fluctuations, quark mass dependence and long
auto-correlation of the global topology. Finally, we discuss the stability
properties of sub-volume simulated lattice improvements towards the
understanding of QCD vacua, the behavior of UV divergences, finite-volume
effects, statistical precision, simultaneous measurements, and associated
quantum channel measurements.


  We consider the situation where a spin-induced wavy perturbation is present
on disks of neutron-star low-mass X-ray binaries. By non-linearly coupling with
the perturbation, some modes of disk oscillations resonantly interact with the
disks. We examine the resonant conditions under the assumption that the disks
are vertically isothermal. The results show that when the spin frequency has
some particular values, resonant coupling occurs at some radii. The modes and
frequencies of these resonant oscillations are summarized. Some of these
resonant oscillations seem to explain the frequencies of the observed kHz QPOs
in objects of which the spin frequency is known.


  We consider a holomorphic foliation $\mathcal{F}$ of codimension $k\geq 1$ on
a homogeneous compact K\"ahler manifold $X$ of dimension $n>k$. Assuming that
the singular set $Sing(\mathcal{F})$ of $\mathcal{F}$ is contained in an
absolutely $k$-convex domain $U\subset X$, we prove that the determinant of
normal bundle $\det(N_{\mathcal{F}})$ of $\mathcal{F}$ cannot be an ample line
bundle, provided $[n/k]\geq 2k+3$. Here $[n/k]$ denotes the largest integer
$\leq n/k.$


  The main idea in this paper is that the age associated with reported measles
cases can be used to estimate the number of undetected measles infections.
Somewhat surprisingly, even with age only to the nearest year, estimates of
underreporting can be generated at the much faster, 2 week time-scale
associated with measles transmission. I describe this idea by focusing on the
well-studied, 60 city United Kingdom data set, which covers the transition to
universal healthcare in 1948, and is, as a result, an interesting case study in
infectious disease surveillance. Finally, at the end of the paper, I comment
briefly on how the approach can be modified for application to modern contexts.


  Mehta and Panigrahi (FOCS 2012) introduce the problem of online matching with
stochastic rewards, where edges are associated with success probabilities and a
match succeeds with the probability of the corresponding edge. It is one of the
few online matching problems that have defied the randomized online primal dual
framework by Devanur, Jain, and Kleinberg (SODA 2013) thus far. This paper
unlocks the power of randomized online primal dual in online matching with
stochastic rewards by employing the configuration linear program rather than
the standard matching linear program used in previous works. Our main result is
a 0.572 competitive algorithm for the case of vanishing and unequal
probabilities, improving the best previous bound of 0.534 by Mehta, Waggoner,
and Zadimoghaddam (SODA 2015) and, in fact, is even better than the best
previous bound of 0.567 by Mehta and Panigrahi (FOCS 2012) for the more
restricted case of vanishing and equal probabilities. For vanishing and equal
probabilities, we get a better competitive ratio of 0.576. Our results further
generalize to the vertex-weighted case due to the intrinsic robustness of the
randomized online primal dual analysis.


  In this paper we analyze the rate-distortion function R(D) achievable using
linear codes over GF(q), where q is a prime number.


  We study a model of interacting vector and Kalb-Ramond gauge fields in a
non-trivial Higgs vacuum generated by a charged and a neutral scalar field. The
system admits different vacua for different v.e.v. of the two Higgs fields. Our
primary interest in this paper regards the "mixed phase" where both the photon
and the Kalb-Ramond acquire a mass. In this phase we compute the interaction
potential energy between static test charges. It turns out that the limit in
which the photon becomes massless, while the Kalb-Ramond remains massive, leads
to a Cornell confining potential between test charges.


  Material thermal properties characterization at nanoscales remains a
challenge even if progresses were done in developing specific characterization
techniques like the Scanning Thermal Microscopy (SThM). In the present work, we
propose a detailed procedure based on the combined use of a SThM probe
characterization and its Finite Element Modeling (FEM) to recover in-operando
3omega measurements achieved under high vacuum. This approach is based on a
two-step methodology: (i) a fine description of the probe s electrical and
frequency behaviors in out of contact mode to determine intrinsic parameters of
the SThM tip, (b) a minimization of the free parameter of our model, i.e. the
contact thermal resistance, by comparing 3omega measurements to our simulations
of the probe operating in contact mode. Such an approach allows us to
accurately measure thermal interface resistances of the probe as a function of
the strength applied between the tip and the surface for three different
materials (silicon, silica and gold). In addition, FEM modeling provides
insights about the 3omega-SThM technique sensitivity, as a function of probe /
sample interface resistance to measure material thermal conductivity, paving
the way to quantitative SThM measurements.


  Breast cancer is the most common cancer in women, and hundreds of thousands
of unnecessary biopsies are done around the world at a tremendous cost. It is
crucial to reduce the rate of biopsies that turn out to be benign tissue. In
this study, we build deep neural networks (DNNs) to classify biopsied lesions
as being either malignant or benign, with the goal of using these networks as
second readers serving radiologists to further reduce the number of false
positive findings. We enhance the performance of DNNs that are trained to learn
from small image patches by integrating global context provided in the form of
saliency maps learned from the entire image into their reasoning, similar to
how radiologists consider global context when evaluating areas of interest. Our
experiments are conducted on a dataset of 229,426 screening mammography exams
from 141,473 patients. We achieve an AUC of 0.8 on a test set consisting of 464
benign and 136 malignant lesions.


  Conventional lore from Tremaine and Gunn excludes fermionic dark matter
lighter than a few hundred eV, based on the Pauli exclusion principle. We
highlight a simple way of evading this bound with a large number of species
that leads to numerous non-trivial consequences. In this scenario there are
many distinct species of fermions with quasi-degenerate masses and no couplings
to the standard model. Nonetheless, gravitational interactions lead to
constraints from measurements at the LHC, of cosmic rays, of supernovae, and of
black hole spins and lifetimes. We find that the LHC constrains the number of
distinct species, bosons or fermions lighter than $\sim 500$ GeV, to be $N
\lesssim 10^{62}$. This, in particular, implies that roughly degenerate
fermionic dark matter must be heavier than $\sim 10^{-14}$ eV, which thus
relaxes the Tremaine-Gunn bound by $\sim 16$ orders of magnitude. Slightly
weaker constraints applying to masses up to $\sim100$ TeV exist from cosmic ray
measurements while various constraints on masses $\lesssim10^{-10}$ eV apply
from black hole observations. We consider a variety of phenomenological bounds
on the number of species of particles. Finally, we note that there exist
theoretical considerations regarding quantum gravity which could impose more
severe constraints that may limit the number of physical states to $N\lesssim
10^{32}$.


  The momentum conservation law for general dissipationless reduced-fluid
(e.g., gyrofluid) models is derived by Noether method from a variational
principle. The reduced-fluid momentum density and the reduced-fluid canonical
momentum-stress tensor both exhibit polarization and magnetization effects as
well as an internal torque associated with dynamical reduction. As an
application, we derive an explicit gyrofluid toroidal angular-momentum
conservation law for axisymmetric toroidal magnetized plasmas.


  We study the properties of a modified version of the Bona-Masso family of
hyperbolic slicing conditions. This modified slicing condition has two very
important features: In the first place, it guarantees that if a spacetime is
static or stationary, and one starts the evolution in a coordinate system in
which the metric coefficients are already time independent, then they will
remain time independent during the subsequent evolution, {\em i.e.} the lapse
will not evolve and will therefore not drive the time lines away from the
Killing direction. Second, the modified condition is naturally adapted to the
use of a densitized lapse as a fundamental variable, which in turn makes it a
good candidate for a dynamic slicing condition that can be used in conjunction
with some recently proposed hyperbolic reformulations of the Einstein evolution
equations.


  Recently, it was shown that if multiplicative weights are assigned to the
edges of a Tanner graph used in belief propagation decoding, it is possible to
use deep learning techniques to find values for the weights which improve the
error-correction performance of the decoder. Unfortunately, this approach
requires many multiplications, which are generally expensive operations. In
this paper, we suggest a more hardware-friendly approach in which offset
min-sum decoding is augmented with learnable offset parameters. Our method uses
no multiplications and has a parameter count less than half that of the
multiplicative algorithm. This both speeds up training and provides a feasible
path to hardware architectures. After describing our method, we compare the
performance of the two neural decoding algorithms and show that our method
achieves error-correction performance within 0.1 dB of the multiplicative
approach and as much as 1 dB better than traditional belief propagation for the
codes under consideration.


  Exact large-$N_{f}$ results for the QCD Adler $D$-function and Deep Inelastic
Scattering sum rules are used to resum to all orders the portion of QCD
perturbative coefficients containing the highest power of
$b$=$\frac{1}{6}(11N$--$2N_{f})$, for SU($N$) QCD with $N_{f}$ quark flavours.
These terms correspond to renormalon singularities in the Borel plane and are
expected asymptotically to dominate the coefficients to all orders in the
$1/N_{f}$ expansion. Remarkably, we note that this is already apparent in
comparisons with the exact next-to-leading order (NLO) and next-to-NLO (NNLO)
perturbative coefficients. The ultra-violet ($UV$) and infra-red ($IR$)
renormalon singularities in the Borel transform are isolated and the Borel sum
(principal value regulated for $IR$) performed. Resummed results are also
obtained for the Minkowski quantities related to the $D$-function, the
$e^{+}e^{-}$ $R$-ratio and the analogous $\tau$-lepton decay ratio, $R_{\tau}$.
The renormalization scheme dependence of these partial resummations is
discussed and they are compared with the results from other groups [1--3] and
with exact fixed order perturbation theory at NNLO. Prospects for improving the
resummation by including more exact details of the Borel transform are
considered.


  Oscillations in modified combinants ($C_j$s) have been of interest to
multiparticle production mechanisms since the 1990s. Recently, there has been a
discussion on how these oscillations can be reproduced by compounding a
binomial distribution with a negative binomial distribution. In this work, we
explore a stochastic branching model based on a simple interaction term
$\lambda\overline{\psi}\phi\psi$ for partons and propose a hadronization scheme
to arrive at the final multiplicity distribution. We study the effects that
compounding our model with a binomial distribution has on $C_j$s and explore
its physical implications. We find that there is a significant difference in
the oscillations in $C_j$s between high energy $pp$ and $p\bar{p}$ scattering
that our model can reproduce.


  Can one understand the statistics of wins and losses of baseball teams? Are
their consecutive-game winning and losing streaks self-reinforcing or can they
be described statistically? We apply the Bradley-Terry model, which
incorporates the heterogeneity of team strengths in a minimalist way, to answer
these questions. Excellent agreement is found between the predictions of the
Bradley-Terry model and the rank dependence of the average number team wins and
losses in major-league baseball over the past century when the distribution of
team strengths is taken to be uniformly distributed over a finite range. Using
this uniform strength distribution, we also find very good agreement between
model predictions and the observed distribution of consecutive-game team
winning and losing streaks over the last half-century; however, the agreement
is less good for the previous half-century. The behavior of the last
half-century supports the hypothesis that long streaks are primarily
statistical in origin with little self-reinforcing component. The data further
show that the past half-century of baseball has been more competitive than the
preceding half-century.


  We formalize the way in which one can think about cluster algebras of
infinite rank by showing that every rooted cluster algebra of infinite rank can
be written as a colimit of rooted cluster algebras of finite rank. Relying on
the proof of the posivity conjecture for skew-symmetric cluster algebras (of
finite rank) by Lee and Schiffler, it follows as a direct consequence that the
positivity conjecture holds for cluster algebras of infinite rank. Furthermore,
we give a sufficient and necessary condition for a ring homomorphism between
cluster algebras to give rise to a rooted cluster morphism without
specializations. Assem, Dupont and Schiffler proposed the problem of a
classification of ideal rooted cluster morphisms. We provide a partial solution
by showing that every rooted cluster morphism without specializations is ideal,
but in general rooted cluster morphisms are not ideal.


  The present paper extends the thermodynamic dislocation theory initiated by
Langer, Bouchbinder and Lookman [2010] to non-uniform finite plastic
deformations. The equations of motion are derived from the variational equation
involving the free energy density and the positive definite dissipation
function. We also consider the simplified theory by neglecting the excess
dislocations. For illustration, the problem of finite strain constrained shear
of single crystals with one active slip system is solved within the proposed
theory.


  The measurement-device-independent quantum key distribution (MDI QKD) was
proposed to make BB84 completely free from any side-channel in detectors. Like
in prepare & measure QKD, the use of other protocols in MDI setting would be
advantageous in some practical situations. In this paper, we consider SARG04
protocol in MDI setting. The prepare & measure SARG04 is proven to be able to
generate a key up to two-photon emission events. In MDI setting we show that
the key generation is possible from the event with single or two-photon
emission by a party and single-photon emission by the other party, but the
two-photon emission event by both parties cannot contribute to the key
generation. On the contrary to prepare & measure SARG04 protocol where the
experimental setup is exactly the same as BB84, the measurement setup for
SARG04 in MDI setting cannot be the same as that for BB84 since the measurement
setup for BB84 in MDI setting induces too many bit errors. To overcome this
problem, we propose two alternative experimental setups, and we simulate the
resulting key rate. Our study highlights the requirements that MDI QKD poses on
us regarding with the implementation of a variety of QKD protocols.


  After having developed a method that measures real time evolution of quantum
systems at a finite temperature, we present here the simplest field theory
where this scheme can be applied to, namely the 1+1 Ising model.
  We will compute the probability that if a given spin is up, some other spin
will be up after a time $t$, the whole system being at temperature $T$. We can
thus study spatial correlations and relaxation times at finite $T$. The fixed
points that enable the continuum real time limit can be easily found for this
model.
  The ultimate aim is to get to understand real time evolution in more
complicated field theories, with quantum effects such as tunneling at finite
temperature.


  We review the recent theoretical developments towards understanding the Mott
phases and quantum phase transition of extended Bose-Hubbard models on lattices
in two spatial dimensions . We focuss on the description of these systems using
the dual vortex picture and point out the crucial role played by the geometry
of underlying lattices in determining the nature of both the Mott phases and
the quantum phase transitions. We also briefly compare the results of dual
vortex theory with quantum Monte Carlo results.


  In this work, we discuss the accretion onto static spherical symmetric
regular black holes for specific choices of equation of state parameter. The
underlying regular black holes are charged regular black hole using Fermi-Dirac
Distribution, logistic distribution, nonlinear electrodynamics, respectively
and Kehagias-Sftesos asymptotically flat regular black hole. We obtain the
critical radius, critical speed and squared sound speed during the accretion
process near the regular black holes. We also study the behavior of radial
velocity, energy density and rate of change of mass for each regular black
holes.


  We present ProtoTEx, a novel white-box NLP classification architecture based
on prototype networks. ProtoTEx faithfully explains model decisions based on
prototype tensors that encode latent clusters of training examples. At
inference time, classification decisions are based on the distances between the
input text and the prototype tensors, explained via the training examples most
similar to the most influential prototypes. We also describe a novel
interleaved training algorithm that effectively handles classes characterized
by the absence of indicative features. On a propaganda detection task, ProtoTEx
accuracy matches BART-large and exceeds BERT-large with the added benefit of
providing faithful explanations. A user study also shows that prototype-based
explanations help non-experts to better recognize propaganda in online news.


  We theoretically study the optical properties and the electronic structure of
highly elongated quantum dots (quantum dashes) and show how carrier trapping
due to geometrical fluctuations of the confining potential affects the
excitonic spectrum of the system. We focus on the study of the optical
properties of a single exciton confined in the structure. The dependence of the
absorption and emission intensities on the geometrical properties (depth and
position) of the trapping center of a quantum dash is analyzed and the
dependence of the degree of linear polarization on these geometrical parameters
is studied in detail.


  In this brief report we consider couplings of the dark energy scalar, such as
Quintessence to the neutrinos and discuss its implications in studies on the
neutrino mass limits from Baryogenesis. During the evolution of the dark energy
scalar, the neutrino masses vary, consequently the bounds on the neutrino
masses we have here differ from those obtained before.


  To every double cover ramified in two points of a general trigonal curve of
genus g, one can associate an \'etale double cover of a tetragonal curve of
genus g+1. We show that the corresponding Prym varieties are canonically
isomorphic as principally polarized abelian varieties.


  We present the results of our analysis of the photometric data of globular
clusters in the elliptical galaxy NGC 5128 (Cen A). We show that the integrated
colour U-B can be an effective metallicity indicator for simple stellar
populations. This is because it is sensitive to metallicity via the opacity
effect but relatively insensitive to the effective main sequence turn-off
temperature of the population (and thus to age) when Teff ~ 7000-12000K, that
is, when the Balmer Jump is strong. This flat U-B vs Teff relation is a result
of the fact that the blueing effect of the optical continuum with increasing
temperature is temporarily stopped by the Balmer Jump which becomes greater
with temperature in this range. In this study we use U-B and B-V as metallicity
and age indicators, respectively. We first show that the use of the U-B vs B-V
two-colour diagram roughly yields the metallicities and ages of the Milky Way
globular clusters independently determined, and then apply the technique to the
clusters in NGC 5128. There is a large range in U-B, which corresponds to
[Fe/H] of -2.0 through over +0.3. The large uncertainties from the data and the
models currently prevent us from pinning down their ages and metallicities.
Although a constant age for all these clusters cannot be ruled out, there is a
hint of the metal-rich clusters being younger. Significance of these results
and caveats of the analysis are discussed.


  Optimization results are one method for understanding neural computation from
Nature's perspective and for defining the physical limits on neuron-like
engineering. Earlier work looks at individual properties or performance
criteria and occasionally a combination of two, such as energy and information.
Here we make use of Jaynes' maximum entropy method and combine a larger set of
constraints, possibly dimensionally distinct, each expressible as an
expectation. The method identifies a likelihood-function and a sufficient
statistic arising from each such optimization. This likelihood is a
first-hitting time distribution in the exponential class. Particular constraint
sets are identified that, from an optimal inference perspective, justify
earlier neurocomputational models. Interactions between constraints, mediated
through the inferred likelihood, restrict constraint-set parameterizations,
e.g., the energy-budget limits estimation performance which, in turn, matches
an axonal communication constraint. Such linkages are, for biologists,
experimental predictions of the method. In addition to the related likelihood,
at least one type of constraint set implies marginal distributions, and in this
case, a Shannon bits/joule statement arises.


  We propose an analog quantum simulator that uses ion traps to realize the
many-body electron-electron Coulomb interaction of an electron gas. This
proposal maps a system that is difficult to solve and control to an
experimentally-feasible setup that can be realized with current technologies.
Using a dilatation transform, we show that ion traps can efficiently simulate
electronic Coulomb interactions. No complexity overhead is added if only the
energy spectrum is desired, and only a simple unitary transform is needed on
the initial state otherwise. The runtime of the simulation is found to be much
shorter than the timescale of the corresponding electronic system, minimizing
susceptibility of the proposed quantum simulator to external noise and
decoherence. This proposal works in any number of dimensions, and could be used
to simulate different topological phases of electrons in graphene-like
structures, by using ions trapped in honeycomb lattices.


  Assume that there are multiple data streams (channels, sensors) and in each
stream the process of interest produces generally dependent and non-identically
distributed observations. When the process is in a normal mode (in-control),
the (pre-change) distribution is known, but when the process becomes abnormal
there is a parametric uncertainty, i.e., the post-change (out-of-control)
distribution is known only partially up to a parameter. Both the change point
and the post-change parameter are unknown. Moreover, the change affects an
unknown subset of streams, so that the number of affected streams and their
location are unknown in advance. A good changepoint detection procedure should
detect the change as soon as possible after its occurrence while controlling
for a risk of false alarms. We consider a Bayesian setup with a given prior
distribution of the change point and propose two sequential mixture-based
change detection rules, one mixes a Shiryaev-type statistic over both the
unknown subset of affected streams and the unknown post-change parameter and
another mixes a Shiryaev-Roberts-type statistic. These rules generalize the
mixture detection procedures studied by Tartakovsky (2018) in a single-stream
case. We provide sufficient conditions under which the proposed multistream
change detection procedures are first-order asymptotically optimal with respect
to moments of the delay to detection as the probability of false alarm
approaches zero.


  In large-scale spatial surveys, such as the forthcoming ESA Euclid mission,
images may be undersampled due to the optical sensors sizes. Therefore, one may
consider using a super-resolution (SR) method to recover aliased frequencies,
prior to further analysis. This is particularly relevant for point-source
images, which provide direct measurements of the instrument point-spread
function (PSF). We introduce SPRITE, SParse Recovery of InsTrumental rEsponse,
which is an SR algorithm using a sparse analysis prior. We show that such a
prior provides significant improvements over existing methods, especially on
low SNR PSFs.


  We use an appropriate combination of moments of finite energy sum rules in
QCD in order to compute the B_q-meson decays constants f_B and f_{B_s}.We
perform the calculation using a two-loop computation of the imaginary part of
the pseudoscalar two point function in terms of the running bottom quark mass.
The results are stable with the so called QCD duality threshold and they are in
agreement with the estimates obtained from Borel transform QCD sum rules and
lattice computations.


  Using Henriques' and Kamnitzer's cactus groups, Sch\"utzenberger's promotion
and evacuation operators on standard Young tableaux can be generalised in a
very natural way to operators acting on highest weight words in tensor products
of crystals.
  For the crystals corresponding to the vector representations of the
symplectic groups, we show that Sundaram's map to perfect matchings intertwines
promotion and rotation of the associated chord diagrams, and evacuation and
reversal. We also exhibit a map with similar features for the crystals
corresponding to the adjoint representations of the general linear groups.
  We prove these results by applying van Leeuwen's generalisation of Fomin's
local rules for jeu de taquin, connected to the action of the cactus groups by
Lenart, and variants of Fomin's growth diagrams for the Robinson-Schensted
correspondence.


  In this paper, we introduce a novel Gaussian mixture based evidential
learning solution for robust stereo matching. Diverging from previous
evidential deep learning approaches that rely on a single Gaussian
distribution, our framework posits that individual image data adheres to a
mixture-of-Gaussian distribution in stereo matching. This assumption yields
more precise pixel-level predictions and more accurately mirrors the real-world
image distribution. By further employing the inverse-Gamma distribution as an
intermediary prior for each mixture component, our probabilistic model achieves
improved depth estimation compared to its counterpart with the single Gaussian
and effectively captures the model uncertainty, which enables a strong
cross-domain generation ability. We evaluated our method for stereo matching by
training the model using the Scene Flow dataset and testing it on KITTI 2015
and Middlebury 2014. The experiment results consistently show that our method
brings improvements over the baseline methods in a trustworthy manner. Notably,
our approach achieved new state-of-the-art results on both the in-domain
validated data and the cross-domain datasets, demonstrating its effectiveness
and robustness in stereo matching tasks.


  We describe a system to prove properties of programs. The key feature of this
approach is a method to automatically synthesize inductive invariants of the
loops contained in the program. The method is generic, i.e., it applies to a
large set of programming languages and application domains; and lazy, in the
sense that it only generates invariants that allow one to derive the required
properties. It relies on an existing system called GPiD for abductive reasoning
modulo theories, and on the platform for program verification Why3. Experiments
show evidence of the practical relevance of our approach.


  Understanding the impact of messages on agents' opinions over social networks
is important. However, to our best knowledge, there has been limited
quantitative investigation into this phenomenon in the prior works. To address
this gap, this paper proposes the Message-Enhanced DeGroot model. The Bounded
Brownian Message model provides a quantitative description of the message
evolution, jointly considering temporal continuity, randomness, and
polarization from mass media theory. The Message-Enhanced DeGroot model,
combining the Bounded Brownian Message model with the traditional DeGroot
model, quantitatively describes the evolution of agents' opinions under the
influence of messages. We theoretically study the probability distribution and
statistics of the messages and agents' opinions and quantitatively analyze the
impact of messages on opinions. We also conduct simulations to validate our
analyses.


  Hydronium (H$_3$O$^+$) was first detected in 1986 in interstellar molecular
clouds. It was reported in many galactic diffuse and dense regions, as well as
in extragalactic sources. H$_3$O$^+$ plays a major role both in interstellar
oxygen and water chemistry. However, despite the large number of H$_3$O$^+$
observations, its collisional excitation was investigated only partially. In
the present work we study the state-to-state rotational de-excitation of
$ortho$- and $para$-H$_3$O$^+$ in collisions both with $ortho$- and
$para$-H$_2$. The cross sections are calculated within the close-coupling
formalism using a highly accurate potential energy surface developed for this
system. The rate coefficients are computed up to $300$ K kinetic temperature.
Transitions between the lowest 21 rotation-inversion states were studied for
$para$-H$_3$O$^+$, and the lowest 11 states for $ortho$-H$_3$O$^+$, i.e. all
levels with rotational energies below 430 K ($\sim 300$ cm$^{-1}$) are
considered (up to $j\leq5$). In order to estimate the impact of the new rate
coefficients on the astrophysical models for H$_3$O$^+$, radiative transfer
calculations were also carried out. We have examined how the new collisional
data affect the line intensities with respect to older data previously used for
the interpretation of observations. By analysing all detected transitions we
find that our new, accurate rate coefficients have a significant impact
(typically within a factor of 2) on radiation temperatures, allowing more
accurate estimation of column densities and relative abundances of hydronium,
especially in warm molecular clouds, paving the path towards better
interpretation of interstellar water and oxygen chemistry.


  Diffusion models are the state of the art in text-to-image generation, but
their perceptual variability remains understudied. In this paper, we examine
how prompts affect image variability in black-box diffusion-based models. We
propose W1KP, a human-calibrated measure of variability in a set of images,
bootstrapped from existing image-pair perceptual distances. Current datasets do
not cover recent diffusion models, thus we curate three test sets for
evaluation. Our best perceptual distance outperforms nine baselines by up to 18
points in accuracy, and our calibration matches graded human judgements 78% of
the time. Using W1KP, we study prompt reusability and show that Imagen prompts
can be reused for 10-50 random seeds before new images become too similar to
already generated images, while Stable Diffusion XL and DALL-E 3 can be reused
50-200 times. Lastly, we analyze 56 linguistic features of real prompts,
finding that the prompt's length, CLIP embedding norm, concreteness, and word
senses influence variability most. As far as we are aware, we are the first to
analyze diffusion variability from a visuolinguistic perspective. Our project
page is at http://w1kp.com


  The Kepler-36 system consists of two planets that are spaced unusually close
together, near the 7:6 mean motion resonance. While it is known that mean
motion resonances can easily form by convergent migration, Kepler-36 is an
extreme case due to the close spacing and the relatively high planet masses of
4 and 8 times that of the Earth. In this paper, we investigate whether such a
system can be obtained by interactions with the protoplanetary disc. These
discs are thought to be turbulent and exhibit density fluctuations which might
originate from the magneto-rotational instability. We adopt a realistic
description for stochastic forces due to these density fluctuations and perform
both long term hydrodynamical and N-body simulations. Our results show that
planets in the Kepler-36 mass range can be naturally assembled into a closely
spaced planetary system for a wide range of migration parameters in a turbulent
disc similar to the minimum mass solar nebula. The final orbits of our
formation scenarios tend to be Lagrange stable, even though large parts of the
parameter space are chaotic and unstable.


  The line intensities of the fundamental rotational transitions of H13CN and
HC15N were observed towards two prestellar cores, L183 and L1544, and lead to
molecular isotopic ratios 140 6 14N/15N 6 250 and 140 6 14N/15N 6 360,
respectively. The range of values reflect genuine spatial variations within the
cores. A comprehensive analysis of the available measurements of the nitrogen
isotopic ratio in prestellar cores show that molecules carrying the nitrile
functional group appear to be systematically 15N-enriched com- pared to those
carrying the amine functional group. A chemical origin for the differential
15N-enhance- ment between nitrile- and amine-bearing interstellar molecules is
proposed. This sheds new light on several observations of Solar System objects:
(i) the similar N isotopic fractionation in Jupiter's NH3 and solar wind N+;
(ii) the 15N-enrichments in cometary HCN and CN (that might represent a direct
inter- stellar inheritance); and (iii) 15N-enrichments observed in organics in
primitive cosmomaterials. The large variations in the isotopic composition of
N-bearing molecules in Solar System objects might then simply reflect the
different interstellar N reservoirs from which they are originating.


  The paper studies a relation between fundamental group of the complement to a
plane singular curve and the orbifold pencils containing it. The main tool is
the use of Albanese varieties of cyclic covers ramified along such curves. Our
results give sufficient conditions for a plane singular curve to belong to an
orbifold pencil, i.e. a pencil of plane curves with multiple fibers inducing a
map onto an orbifold curve whose orbifold fundamental group is non trivial. We
construct an example of a cyclic cover of the projective plane which is an
abelian surface isomorphic to the Jacobian of a curve of genus 2 illustrating
the extent to which these conditions are necessary.


  Nitrogen impurities help to stabilize the negatively-charged-state of NV$^-$
in diamond, whereas magnetic fluctuations from nitrogen spins lead to
decoherence of NV$^-$ qubits. It is not known what donor concentration
optimizes these conflicting requirements. Here we used 10-MeV $^{15}$N$^{3+}$
ion implantation to create NV$^-$ in ultrapure diamond. Optically detected
magnetic resonance of single centers revealed a high creation yield of
$40\pm3$% from $^{15}$N$^{3+}$ ions and an additional yield of $56\pm3$% from
$^{14}$N impurities. High-temperature anneal was used to reduce residual
defects, and charge stable NV$^-$, even in a dilute $^{14}$N impurity
concentration of 0.06 ppb were created with long coherence times.


  We propose a novel human-swarm interaction system, allowing the user to
directly control a swarm of drones in a complex environment through trajectory
drawing with a hand gesture interface based on the DNN-based gesture
recognition. The developed CV-based system allows the user to control the swarm
behavior without additional devices through human gestures and motions in
real-time, providing convenient tools to change the swarm's shape and
formation. The two types of interaction were proposed and implemented to adjust
the swarm hierarchy: trajectory drawing and free-form trajectory generation
control. The experimental results revealed a high accuracy of the gesture
recognition system (99.75%), allowing the user to achieve relatively high
precision of the trajectory drawing (mean error of 5.6 cm in comparison to 3.1
cm by mouse drawing) over the three evaluated trajectory patterns. The proposed
system can be potentially applied in complex environment exploration, spray
painting using drones, and interactive drone shows, allowing users to create
their own art objects by drone swarms.


  There are several concepts and definitions that characterize and give
optimality conditions for solutions of a vector optimization problem. One of
the most important is the first-order necessary optimality condition that
generalizes the Karush-Kuhn-Tucker condition. This condition ensures the
existence of an arbitrary neighborhood that contains an local optimal solution.
The present work we introduce an alternative concept to identify the local
optimal solution neighborhood in vector optimization problems. The main aspect
of this contribution is the development of necessary and sufficient Pareto
optimality conditions for the solutions of a particular vector optimization
problem, where each objective function consists of a ratio quadratic functions
and the feasible set is defined by linear inequalities. We show how to
calculate the largest radius of the spherical region centered on a local Pareto
solution in which this solution is optimal. In this process we may conclude
that the solution is also globally optimal. These conditions might be useful to
determine termination criteria in the development of algorithms, including more
general problems in which quadratic approximations are used locally.


  A finite \emph{$k$-net} of order $n$ is an incidence structure consisting of
$k\ge 3$ pairwise disjoint classes of lines, each of size $n$, such that every
point incident with two lines from distinct classes is incident with exactly
one line from each of the $k$ classes. Deleting a line class from a $k$-net,
with $k\ge 4$, gives a \emph{derived} ($k-1$)-net of the same order.
  Finite $k$-nets embedded in a projective plane $PG(2,K)$ coordinatized by a
field $K$ of characteristic $0$ only exist for $k=3,4$, see \cite{knp_k}. In
this paper, we investigate $3$-nets embedded in $PG(2,K)$ whose line classes
are in perspective position with an axis $r$, that is, every point on the line
$r$ incident with a line of the net is incident with exactly one line from each
class. The problem of determining all such $3$-nets remains open whereas we
obtain a complete classification for those coordinatizable by a group. As a
corollary, the (unique) $4$-net of order $3$ embedded in $PG(2,K)$ turns out to
be the only $4$-net embedded in $PG(2,K)$ with a derived $3$-net which can be
coordinatized by a group. Our results hold true in positive characteristic
under the hypothesis that the order of the $k$-net considered is smaller than
the characteristic of $K$.


  Cloud has been a computational and storage solution for many data centric
organizations. The problem today those organizations are facing from the cloud
is in data searching in an efficient manner. A framework is required to
distribute the work of searching and fetching from thousands of computers. The
data in HDFS is scattered and needs lots of time to retrieve. The major idea is
to design a web server in the map phase using the jetty web server which will
give a fast and efficient way of searching data in MapReduce paradigm. For real
time processing on Hadoop, a searchable mechanism is implemented in HDFS by
creating a multilevel index in web server with multi-level index keys. The web
server uses to handle traffic throughput. By web clustering technology we can
improve the application performance. To keep the work down, the load balancer
should automatically be able to distribute load to the newly added nodes in the
server.


  National radio dynamic zone (NRDZs) are intended to be geographically bounded
areas within which controlled experiments can be carried out while protecting
the nearby licensed users of the spectrum. An NRDZ will facilitate research and
development of new spectrum technologies, waveforms, and protocols, in typical
outdoor operational environments of such technologies. In this paper, we
introduce and describe an NRDZ concept that relies on a combination of
autonomous aerial and ground sensor nodes for spectrum sensing and radio
environment monitoring (REM). We elaborate on key characteristics and features
of an NRDZ to enable advanced wireless experimentation while also coexisting
with licensed users. Some preliminary results based on simulation and
experimental evaluations are also provided on out-of-zone leakage monitoring
and real-time REMs.


  We present a novel design for a single-mode, truly sub-wavelength THz disk
laser based on a nano-composite gain medium comprising an array of
metal/ferromagnetic point contacts embedded in a thin dielectric layer.
Stimulated emission of light occurs in the point contacts as a result of
spin-flip relaxation of spin-polarized electrons that are injected from the
ferromagnetic side of the contacts. Ultra-high electrical current densities in
the contacts and a dielectric material with a large refractive index, neither
condition being achievable in conventional semiconductor media, allows the
thresholds of lasing to be overcome for the lowest-order modes of the disk,
hence making single-mode operation possible.


  With the 8 TeV LHC run now concluded, the first consequences of the
experimental results on the supersymmetric parameter space can be drawn. On one
hand, the negative direct searches place more and more stringent bounds on the
mass of supersymmetric particles; on the other hand, the discovery of a 125 GeV
Higgs boson points toward a quite heavy spectrum for the squarks of the third
generation, at least in the minimal supersymmetric model. In this note I will
briefly recap how this constitutes a problem for the naturalness of
supersymmetric models, as well as the current experimental situation. Moreover,
I will point out possible non minimal models in which the naturalness issue can
be at least soften.


  Generalized Donaldson-Thomas invariants corresponding to local D6-D2-D0
configurations are defined applying the formalism of Joyce and Song to ADHM
sheaves on curves. A wallcrossing formula for invariants of D6-rank two is
proven and shown to agree with the wallcrossing formula of Kontsevich and
Soibelman. Using this result, the asymptotic D6-rank two invariants of (-1,-1)
and (0,-2) local rational curves are computed in terms of the D6-rank one
invariants.


  We use numerical simulations of the time evolution of global textures to
investigate the relationship between ordering dynamics and energy density in an
expanding universe. Events in which individual textures become fully wound are
rare. The energy density is dominated by the more numerous partially wound
configurations, with median topological charge alpha ~ 0.44. This verifies the
recent supposition (Borrill et al. 1994) that such partially wound
configurations should dominate the cosmic microwave background.


  In this discussion we demonstrate that fiducial distributions provide a
natural example of an inference paradigm that does not obey Strong Likelihood
Principle while still satisfying the Weak Conditionality Principle.
[arXiv:1302.7021]


  In this article, we present a new method to study relative Cuntz-Krieger
algebras for higher-rank graphs. We only work with edges rather than paths of
arbitrary degrees. We then use this method to simplify the existing results
about relative Cuntz-Krieger algebras. We also give applications to study
ideals and quotients of Toeplitz algebras.


  Accreting black holes (BHs) launch relativistic collimated jets, across many
decades in luminosity and mass, suggesting the jet launching mechanism is
universal, robust and scale-free. Theoretical models and general relativistic
magnetohydrodynamic (GRMHD) simulations indicate that the key jet-making
ingredient is large-scale poloidal magnetic flux. However, its origin is
uncertain, and it is unknown if it can be generated in situ or dragged inward
from the ambient medium. Here, we use the GPU-accelerated GRMHD code H-AMR to
study global 3D BH accretion at unusually high resolutions more typical of
local shearing box simulations. We demonstrate that turbulence in a
radially-extended accretion disc can generate large-scale poloidal magnetic
flux in situ, even when starting from a purely toroidal magnetic field. The
flux accumulates around the BH till it becomes dynamically-important, leads to
a magnetically arrested disc (MAD), and launches relativistic jets that are
more powerful than the accretion flow. The jet power exceeds that of previous
GRMHD toroidal field simulations by a factor of 10,000. The jets do not show
significant kink or pinch instabilities, accelerate to $\gamma \sim 10$ over 3
decades in distance, and follow a collimation profile similar to the observed
M87 jet.


  For a smooth surface $S$, Porta-Sala defined a categorical Hall algebra
generalizing previous work in K-theory of Zhao and Kapranov-Vasserot. We
construct semi-orthogonal decompositions for categorical Hall algebras of
points on $S$. We refine these decompositions in K-theory for a topological
K-theoretic Hall algebra.


  In many concentrated alloys of current interest, the observation of diffuse
superlattice intensities by transmission electron microscopy has been
attributed to chemical short-range order. We briefly review these findings and
comment on the plausibility of widespread interpretations, noting the absence
of expected peaks, conflicts with theoretical predictions, and the possibility
of alternative explanations.


  This is the final one in the series of papers where we introduce and study
the $C^*$-algebras associated with topological graphs. In this paper, we get a
sufficient condition on topological graphs so that the associated
$C^*$-algebras are simple and purely infinite. Using this result, we give one
method to construct all Kirchberg algebras as $C^*$-algebras associated with
topological graphs.


  A new method for finding electronic structure and wavefunctions of electrons
in quasiperiodic potential is introduced. To obtain results it uses slightly
modified Schrodinger equation in spaces of dimensionality higher than physical
space. It enables to get exact results for quasicrystals without expensive
non-exact calculations. New method tested on one-dimensional quasiperiodic
screened Coulomb potential.


  Fragmentation of liquid metal droplets irradiated by linearly and circularly
polarized femtosecond laser pulses is observed in our experiment. The obtained
shadowgraph snapshots demonstrate that a circularly polarized pulse may produce
several randomly-oriented jets effused from the expanding droplets, while a
linearly polarized laser pulse generates strictly the cruciform jets. The
latter orientation is tied with polarization plane, rotation of which causes
rotation of the cruciform jets by the same angle. To shed light on the
experimental data we performed molecular dynamics simulation of droplet
expansion induced by angle-dependent heating.
  Our simulation shows that the jet directions are determined by an oriented
angle-dependent energy distribution within a frontal hemisphere layer of
droplet after absorption of linearly polarized light. As a result, the produced
flow velocity field guided by surface tension forms two high-speed opposite
jets oriented across the electric field vector as in our experiment.
  A shock-wave pulse generated in the frontal layer has angle-dependent
amplitude inherited from the oriented energy deposition. The release part of
shock pulse produces a cavitation zone nearby the droplet center, and thus an
expanding spherical shell is formed from the droplet. The flow velocities
within a rearside hemisphere of the shell, produced after reflection of the
shock wave from the rear side of droplet, generate two low-speed opposite jets
oriented along the electric field vector. Thus we found that the cruciform jets
are originated independently from the frontal and rear sides of droplet, and a
pair of frontal jets is faster than a pair of rearside jets.


  It has been an open question whether the deletion or contraction of an edge
in an intrinsically knotted graph always yields an intrinsically linked graph.
We present a new intrinsically knotted graph that shows the answer to both
questions is no.


  We consider measurement-based quantum computation (MBQC) on thermal states of
the interacting cluster Hamiltonian containing interactions between the cluster
stabilizers that undergoes thermal phase transitions. We show that the
long-range order of the symmetry breaking thermal states below a critical
temperature drastically enhance the robustness of MBQC against thermal
excitations. Specifically, we show the enhancement in two-dimensional cases and
prove that MBQC is topologically protected below the critical temperature in
three-dimensional cases. The interacting cluster Hamiltonian allows us to
perform MBQC even at a temperature an order of magnitude higher than that of
the free cluster Hamiltonian.


  The multiplicity distributions of hadrons produced in central nucleus-nucleus
collisions are studied within the hadron-resonance gas model in the large
volume limit. The microscopic correlator method is used to enforce conservation
of three charges - baryon number, electric charge, and strangeness - in the
canonical ensemble. In addition, in the micro-canonical ensemble energy
conservation is included. An analytical method is used to account for resonance
decays. The multiplicity distributions and the scaled variances for negatively,
positively, and all charged hadrons are calculated along the chemical
freeze-out line of central Pb+Pb (Au+Au) collisions from SIS to LHC energies.
Predictions obtained within different statistical ensembles are compared with
the preliminary NA49 experimental results on central Pb+Pb collisions in the
SPS energy range. The measured fluctuations are significantly narrower than the
Poisson ones and clearly favor expectations for the micro-canonical ensemble.
Thus this is a first observation of the recently predicted suppression of the
multiplicity fluctuations in relativistic gases in the thermodynamical limit
due to conservation laws.


  The random magnetic flux problem on a lattice and in a quasi one-dimensional
(wire) geometry is studied both analytically and numerically. The first two
moments of the conductance are obtained analytically. Numerical simulations for
the average and variance of the conductance agree with the theory. We find that
the center of the band $\epsilon=0$ plays a special role. Away from
$\epsilon=0$, transport properties are those of a disordered quantum wire in
the standard unitary symmetry class. At the band center $\epsilon=0$, the
dependence on the wire length of the conductance departs from the standard
unitary symmetry class and is governed by a new universality class, the chiral
unitary symmetry class. The most remarkable property of this new universality
class is the existence of an even-odd effect in the localized regime:
Exponential decay of the average conductance for an even number of channels is
replaced by algebraic decay for an odd number of channels.


  In the hyperalgebra of the $r$-th Frobenius kernel of a universal Chevalley
group over a field of characteristic $p>0$, we study some subsets and the
subalgebras generated by them and give some results. We are particularly
interested in the case that $p$ is 'very small' and the Dynkin diagram is not
simply-laced.


  This paper shares our experience in a three-session online workshop using a
new web-based data programming environment, Marti. The programming environment
uses a card-based programming strategy in both unplugged and online activities.
Educators can use the physical cards in a board-game style or use the
programming environment's mobile application to scan these cards and render the
final visualization on their phones/tablets. The web environment also uses
visual draggable cards for programming that can manipulate and visualize data.
We used Marti and its offered unplugged activities in three sessions with 12
middle school and 12 high school students, focusing on the data fundamentals,
analysis, and visualization. We assert that integrating unplugged-style
pseudo-code creation and supporting a similar experience using the available
devices have considerable potential for delivering equal and affordable data
programming education for all.


  High-dimensional Bayesian optimization (BO) tasks such as molecular design
often require 10,000 function evaluations before obtaining meaningful results.
While methods like sparse variational Gaussian processes (SVGPs) reduce
computational requirements in these settings, the underlying approximations
result in suboptimal data acquisitions that slow the progress of optimization.
In this paper we modify SVGPs to better align with the goals of BO: targeting
informed data acquisition rather than global posterior fidelity. Using the
framework of utility-calibrated variational inference, we unify GP
approximation and data acquisition into a joint optimization problem, thereby
ensuring optimal decisions under a limited computational budget. Our approach
can be used with any decision-theoretic acquisition function and is compatible
with trust region methods like TuRBO. We derive efficient joint objectives for
the expected improvement and knowledge gradient acquisition functions in both
the standard and batch BO settings. Our approach outperforms standard SVGPs on
high-dimensional benchmark tasks in control and molecular design.


  Scalability in blockchain remains a significant challenge, especially when
prioritizing decentralization and security. The Ethereum community has proposed
comprehensive data-sharding techniques to overcome storage, computational, and
network processing limitations. In this context, the propagation and
availability of large blocks become the subject of research to achieve scalable
data-sharding. This paper provides insights after exploring the usage of a
Kademlia-based DHT to enable Data Availability Sampling (DAS) in Ethereum. It
presents a DAS-DHT simulator to study this problem and validates the results of
the simulator with experiments in a real DHT network, IPFS. Our results help us
understand what parts of DAS can be achieved based on existing Kademlia DHT
solutions and which ones cannot. We discuss the limitations of DHT solutions
and discuss other alternatives.


  We use Monte Carlo simulations and assumptions from evolutionary game theory
in order to study the evolution of words and the population dynamics of a
system comprising two interacting species which initially speak two different
languages. The species are characterized by their identity, vocabulary and have
different initial fitness, i.e. reproduction capability. The questions we want
to answer are: a. Will the different initial fitness lead to a permanent
advantage? b. Will this advantage affect the vocabulary of the species or the
population dynamics? c. How will the spatial distributions of the species be
affected? Does the system exhibit pattern formation or segregation? We show
that an initial fitness advantage, although is very quickly balanced, leads to
better spatial arrangement and enhances survival probabilities of the species.
In most cases the system will arrive at a final state where both languages
coexist. However, in cases where one species greatly outnumbers the other in
population and fitness, then only one species survives with its final language
having a slightly richer vocabulary than its initial language. Thus, our
results offer an explanation for the existence and origin of synonyms in all
currently spoken languages.


  We apply the ultrarelativistic boosting procedure to map the metric of
Schwarzschild-de Sitter spacetime into a metric describing de Sitter spacetime
plus a shock-wave singularity located on a null hypersurface, by exploiting the
picture of the embedding of an hyperboloid in a five-dimensional Minkowski
spacetime. After reverting to the usual four-dimensional formalism, we also
solve the geodesic equation and evaluate the Riemann curvature tensor of the
boosted Schwarzschild-de Sitter metric by means of numerical calculations,
which make it possible to reach the ultrarelativistic regime gradually by
letting the boost velocity approach the speed of light. Eventually, the
analysis of the Kretschmann invariant (and of the geodesic equation) shows the
global structure of space- time, as we demonstrate the presence of a "scalar
curvature singularity" within a 3-sphere and find that it is also possible to
define what we have called "boosted horizon", a sort of elastic wall where all
particles are surprisingly pushed away. This seems to suggest that such
"boosted geometries" are ruled by a sort of "antigravity effect" since all
geodesics seem to refuse entering the "boosted horizon" and are "reflected" by
it, even though their initial conditions are aimed at driving the particles
towards the "boosted horizon" itself.


  An intense terahertz (THz) radiation generated by the beating of two Langmuir
waves, which are excited by the forward Raman scattering, is analyzed
theoretically. The radiation energy per shot can be as high as 0.1 J, with the
duration of 10 pico-second. Appropriate plasma density and the laser
characteristics are examined.


  Learning to coordinate actions among agents is essential in complicated
multi-agent systems. Prior works are constrained mainly by the assumption that
all agents act simultaneously, and asynchronous action coordination between
agents is rarely considered. This paper introduces a bi-level multi-agent
decision hierarchy for coordinated behavior planning. We propose a novel
election mechanism in which we adopt a graph convolutional network to model the
interaction among agents and elect a first-move agent for asynchronous
guidance. We also propose a dynamically weighted mixing network to effectively
reduce the misestimation of the value function during training. This work is
the first to explicitly model the asynchronous multi-agent action coordination,
and this explicitness enables to choose the optimal first-move agent. The
results on Cooperative Navigation and Google Football demonstrate that the
proposed algorithm can achieve superior performance in cooperative
environments. Our code is available at
\url{https://github.com/Amanda-1997/EFA-DWM}.


  The Bayesian methods for linear inverse problems is studied using
hierarchical Gaussian models. The problems are considered with different
discretizations, and we analyze the phenomena which appear when the
discretization becomes finer. A hierarchical solution method for signal
restoration problems is introduced and studied with arbitrarily fine
discretization. We show that the maximum a posteriori estimate converges to a
minimizer of the Mumford--Shah functional, up to a subsequence. A new result
regarding the existence of a minimizer of the Mumford--Shah functional is
proved.
  Moreover, we study the inverse problem under different assumptions on the
asymptotic behavior of the noise as discretization becomes finer. We show that
the maximum a posteriori and conditional mean estimates converge under
different conditions.


  We analyze the microlensing event OGLE-2019-BLG-0304, whose light curve
exhibits two distinctive features: a deviation in the peak region and a second
bump appearing $\sim 61$~days after the main peak. Although a binary-lens model
can explain the overall features, it leaves subtle but noticeable residuals in
the peak region. We find that the residuals can be explained by the presence of
either a planetary companion located close to the primary of the binary lens
(3L1S model) or an additional close companion to the source (2L2S model).
Although the 3L1S model is favored over the 2L2S model, with $\Delta\chi^2\sim
8$, securely resolving the degeneracy between the two models is difficult with
the currently available photometric data. According to the 3L1S interpretation,
the lens is a planetary system, in which a planet with a mass
$0.51^{+0.51}_{-0.23}~M_{\rm J}$ is in an S-type orbit around a binary composed
of stars with masses $0.27^{+0.27}_{-0.12}~M_\odot$ and
$0.10^{+0.10}_{-0.04}~M_\odot$. According to the 2L2S interpretation, on the
other hand, the source is composed of G- and K-type giant stars, and the lens
is composed of a low-mass M dwarf and a brown dwarf with masses
$0.12^{+0.12}_{-0.05}~M_\odot$ and $0.045^{+0.045}_{-.019}~M_\odot$,
respectively. The event illustrates the need for through model testing in the
interpretation of lensing events with complex features in light curves.


  Cactus groups and their pure subgroups appear in various fields of
mathematics and are currently attracting attention from diverse mathematical
communities. They share similarities with both right-angled Coxeter groups and
braid groups. In this article, our goal is to highlight the tools offered by
geometric group theory for the study of these groups. Among the new
contributions made possible thanks to this geometric perspective, we describe
an explicit and efficient solution to the conjugacy problem, and we prove that
cactus groups are virtually cocompact special and acylindrically hyperbolic.


  One of the theories for the origin of life proposes that a significant
fraction of prebiotic material could have arrived to Earth from outer space
between 4.1 and 3.8 billion years ago. This suggests that those prebiotic
compounds could have originated in interstellar space, to be later on
incorporated to small Solar-system bodies and planetesimals. The recent
discovery of prebiotic molecules such as hydroxylamine and ethanolamine in the
interstellar medium, strongly supports this hypothesis. However, some species
such as sugars, key for the synthesis of ribonucleotides and for metabolic
processes, remain to be discovered in space. The unmatched sensitivity of the
Square Kilometer Array (SKA) at centimeter wavelengths will be able to detect
even more complex and heavier prebiotic molecules than existing
instrumentation. In this contribution, we illustrate the potential of the SKA
to detect simple sugars with three and four carbon atoms, using a moderate
investment of observing time.


  Interactions in quantum systems may induce transitions to exotic correlated
phases of matter which can be vulnerable to coupling to an environment. Here,
we study the stability of a Bose-Hubbard chain coupled to a bosonic bath at
zero and non-zero temperature. We show that only above a critical interaction
the chain loses bosons and its properties are significantly affected. The
transition is of a different nature than the superfluid-Mott insulator
transition and occurs at a different critical interaction. We explain such a
stable-unstable transition by the opening of a charge gap. The comparison of
accurate matrix product state simulations to approximative approaches that miss
this transition reveals its many-body origin.


  In this article, we study topological and noninertial effects on the motion
of the two-dimensional Dirac oscillator in the presence of a uniform magnetic
field and the Aharonov-Bohm potential. We obtain the Dirac equation that
describes the model. Expressions for the wave functions and energy spectrum are
derived. The energy spectrum of the oscillator as a function of the various
physical parameters involved in the problem is rigorously studied. Finally, we
present some analogies between our results and others of the condensed matter
physics.


  We study the relationship between tropical and classical Hurwitz moduli
spaces. Following recent work of Abramovich, Caporaso and Payne, we outline a
tropicalization for the moduli space of generalized Hurwitz covers of an
arbitrary genus curve. Our approach is to appeal to the geometry of admissible
covers, which compactify the Hurwitz scheme. We define and construct a moduli
space of tropical admissible covers, and study its relationship with the
skeleton of the Berkovich analytification of the classical space of admissible
covers. We use techniques from non-archimedean geometry to show that the
tropical and classical tautological maps are compatible via tropicalization,
and that the degree of the classical branch map can be recovered from the
tropical side. As a consequence, we obtain a proof, at the level of moduli
spaces, of the equality of classical and tropical Hurwitz numbers.


  In this article we present a brief introduction to the kinematical setup that
underlies the quantization used in loop quantum gravity. This review has been
published as a chapter in the monograph "Loop Quantum Gravity: The First 30
Years", edited by Abhay Ashtekar and Jorge Pullin, that was recently published
in the series "100 Years of General Relativity".


  Robert Denomme and Gordan Savin made a primality test for Fermat numbers
2^(2^k)+1 using elliptic curves. We propose another primality test using
elliptic curves for Fermat numbers and also give primality tests for integers
of the form 2^(2k+1)\pm2^(k+1)+1.


  Active ingredients containing fluorinated organic compounds such as
Fluoroalkylamines or pyrimidine-based molecules are promising in the field of
agriculture (pesticides and herbicides) and pharmacology (antibiotics). The
massive use of these molecules will result in a massive increase in waste
containing this type of molecule. Developed countries have restrictive waste
management policies, which is not the case in developing countries. In the
latter, we are witnessing a proliferation of storage areas and open-air
disposal of waste, sometimes from developed countries. These practices have
enormous consequences on the environment such as air, soil and water pollution
and therefore on human health. One of the solutions already proven on solid
waste would be the use of plasma torches. These torches can reach high
temperatures (5,000 K to 20,000 K). However, the use of these means of
treatment is not without danger since toxic or lethal molecules could be
produced. In order to understand these difficulties, we propose to study the
influence of air on the chemical composition of a plasma based on
fluoroalkylamines (trifluoroethylamine: C2H4F3N, nonafluoropentylamine:
C5H4F9N, etc.), at atmospheric pressure and at atmospheric pressure. local
thermodynamic equilibrium (E.T.L), in a temperature range from 500 K to 20,000
K. In order to obtain the chemical composition of the plasma, we use the Gibbs
free energy minimization method. The results obtained show that dangerous and
toxic gaseous chemical species such as CF2, CO, HCN and HF appear at low
temperatures with high concentration.


  Computer-based tests with randomly generated questions allow a large number
of different tests to be generated. Given a fixed number of alternatives for
each question, the number of tests that need to be generated before all
possible questions have appeared is surprisingly low.


  We present a stacking analysis of EGRET $\gamma$-ray observations at the
positions of luminous and ultraluminous infrared galaxies. The latter were
selected from the recently presented HCN survey, which is thought to contain
the most active star forming regions of the universe. Different sorting
criteria are used and, whereas no positive collective detection of $\gamma$-ray
emission from these objects we determined both collective and individual upper
limits. The upper most excess we find appears in the case of ULIRGs ordered by
redshift, at a value of 1.8$\sigma$.


  Possibilities for observing signals of CPT and Lorentz violation in the
spectroscopy of hydrogen and antihydrogen are considered. We show that
transitions between the c and d hyperfine sublevels in the 1S state can exhibit
theoretically detectable effects that would be unsuppressed by powers of the
fine-structure constant. This transition may therefore offer some advantages
over 1S-2S two-photon spectroscopy.


  In this paper we study constant scalar curvature equation (CSCK), a nonlinear
fourth order elliptic equation, and its weak solutions on K\"ahler manifolds.
We first define a notion of weak solution of CSCK for an $L^\infty$ K\"ahler
metric. The main result is to show that such a weak solution (with uniform
$L^\infty$ bound) is smooth. As an application, this answers in part a
conjecture of Chen regarding the regularity of $K$-energy minimizers. The new
technical ingredient is a $W^{2, 2}$ regularity result for the Laplacian
equation $\Delta_g u=f$ on K\"ahler manifolds, where the metric has only
$L^\infty$ coefficients. It is well-known that such a $W^{2, 2}$ regularity
($W^{2, p}$ regularity for any $p>1$) fails in general (except for dimension
two) for uniform elliptic equations of the form $a^{ij}\partial^2_{ij}u=f$ for
$a^{ij}\in L^\infty$, without certain smallness assumptions on the local
oscillation of $a^{ij}$. We observe that the K\"ahler condition plays an
essential role to obtain a $W^{2, 2}$ regularity for elliptic equations with
only $L^\infty$ elliptic coefficients on compact manifolds.


  The dependence of the magnetic anisotropy of As-capped (Ga,Mn)As epilayers on
the annealing parameters - temperature and time - has been investigated. A
uniaxial magnetic anisotropy is evidenced, whose orientation with respect to
the crystallographic axes changes upon annealing from [-110] for the as-grown
samples to [110] for the annealed samples. Both cubic an uniaxial anisotropies
are tightly linked to the concentration of charge carriers, the magnitude of
which is controlled by the annealing process.


  Source galaxy images are distorted not only by a static gravitational
potential, but also by frame-dragging induced by massive rotating objects like
clusters of galaxies. Such effect is well understood theoretically, it is
therefore of great interest to estimate its detectability for future surveys.
In this work, we analyze the lensing convergence $\kappa$ around rotating dark
matter halos. The rotation of the massive objects generates a gravitomagnetic
potential giving rise to an anisotropic contribution to the lensing potential.
We construct an estimator $\delta \kappa$ to describe the difference between
the symmetric enhancement and reduction of $\kappa$ around the halo rotation
axis, finding that it is well approximated by a function proportional to the
halo velocity dispersion squared times a dimensionless angular momentum
parameter. Using simulation mocks with realistic noise level for a survey like
LSST, we test our estimator, and show that the signal from frame-dragging of
stacked rotating lenses is consistent with zero within $1\sigma$. However, we
find that the most massive cluster in SDSS DR7 spectroscopic selected group
catalog has a line-of-sight rotation velocity of 195.0km/s and velocity
dispersion of 667.8km/s, which is at $1.2\times 10^{-8}$ odds according to the
angular momentum probability distribution inferred from N-body simulations. By
studying SDSS DR7 spectroscopic selected group catalog, we show how rotating
clusters can be identified, and, finding that fast rotating clusters might be
more abundant than in estimates based on simulations, a detection of
gravitomagnetic distortion may be at reach in future surveys


  We perform numerical simulations of magneto-rotational instability in a local
patch of accretion disk in which radiation pressure exceeds gas pressure. Such
conditions may occur in the central regions of disks surrounding compact
objects in active galactic nuclei and Galactic X-ray sources. We assume
axisymmetry, and neglect vertical stratification. The growth rates of the
instability on initially uniform magnetic fields are consistent with the linear
analysis of Blaes & Socrates 2001. As is the case when radiation effects are
neglected, the non-linear development of the instability leads to transitory
turbulence when the initial magnetic field has no net vertical flux. During the
turbulent phase, angular momentum is transported outwards. The Maxwell stress
is a few times the Reynolds stress, and their sum is about four times the mean
pressure in the vertical component of the magnetic field. For magnetic pressure
exceeding gas pressure, turbulent fluctuations in the field produce density
contrasts about equal to the ratio of magnetic to gas pressure. These are many
times larger than in the corresponding gas pressure dominated situation, and
may have profound implications for the steady-state vertical structure of
radiation-dominated disks. Diffusion of radiation from compressed regions damps
turbulent motions, converting kinetic energy into photon energy.


  This paper contributes to modeling and supervision of multi-stage centrifugal
compressors coping with real-gas processes and steady to highly transient
operating conditions. A novel dynamic model is derived, and the incorporation
of the generic Lee-Kesler-Pl\"ocker real-gas equation of state and its
derivatives is presented. The model allows for embedding arbitrarily shaped
performance maps, based on state-of-the-art polytropic change-of-state
compressor characteristics. As the validity of these maps is a key issue for
simulation and model-based monitoring, performance maps are treated as
time-variant, and their shape is to be identified and monitored during
operation. The proposed real-time map estimation scheme comprises an Unscented
Kalman Filter and a newly proposed algorithm, referred to as Recursive Map
Estimation. The combination yields a novel parameter and state estimator, which
is expected to be superior if some parameters are characterized by a distinct
operating point dependency. Two additional time-variant parameters are provided
for monitoring: The first indicates the level of confidence in the local
estimate, and the second points to drastic performance map alterations, which
may be further exploited in fault detection. A modified reference simulation of
a two-stage supercritical carbon dioxide compressor with known state
trajectories, performance maps, and alterations demonstrates the successful
application of the entire monitoring scheme, and serves for a discussion of the
results.


  We study the structure of the accretion flow in the hard state of the
black-hole X-ray binary MAXI~J1820+070 with \nicer data. The power spectra show
broadband variability which can be fit with four Lorentzian components peaking
at different time scales. Extracting power spectra as a function of energy
enables the energy spectra of these different power spectral components to be
reconstructed. We found significant spectral differences among Lorentzians,
with the one corresponding to the shortest variability time scales displaying
the hardest spectrum. Both the variability spectra and the time-averaged
spectrum are well-modelled by a disc blackbody and thermal Comptonization, but
the presence of (at least) two Comptonization zones with different temperatures
and optical depths is required. The disc blackbody component is highly
variable, but only in the variability components peaking at the longest time
scales ($\gsim1$ s). The seed photons for the spectrally harder zone come
predominantly from the softer Comptonization zone. Our results require the
accretion flow in this source to be structured, and cannot be described by a
single Comptonization region upscattering disc blackbody photons, and
reflection from the disc.


  The exact complexity of solving parity games is a major open problem. Several
authors have searched for efficient algorithms over specific classes of graphs.
In particular, Obdr\v{z}\'{a}lek showed that for graphs of bounded tree-width
or clique-width, the problem is in $\mathrm{P}$, which was later improved by
Ganardi, who showed that it is even in $\mathrm{LOGCFL}$ (with an additional
assumption for clique-width case). Here we extend this line of research by
showing that for graphs of bounded tree-depth the problem of solving parity
games is in logspace uniform $\text{AC}^0$. We achieve this by first
considering a parameter that we obtain from a modification of clique-width,
which we call shallow clique-width. We subsequently provide a suitable
reduction.


  This paper considers the motion control of a particle and a spinning disc on
rotating earth. The equations of motion are derived using Lagrangian mechanics.
Trajectory planning is studied as an optimization problem using the method
referred to as Discrete Mechanics and Optimal Control.


  By colliding two Bose-Einstein condensates we have observed strong bosonic
stimulation of the elastic scattering process. When a weak input beam was
applied as a seed, it was amplified by a factor of 20. This large gain atomic
four-wave mixing resulted in the generation of two macroscopically occupied
pair-correlated atomic beams.


  In a recent paper [J. P. M. Pitelli, Phys. Rev. D {\bf 99}, 108701 (2019)],
one of us showed that the vacuum state associated to conformal fields on a
Poicar\'e patch of anti-de Sitter spacetime is not $\text{AdS}$ invariant for
fields satisfying non-trivial boundary conditions (by non-trivial we mean
neither Dirichlet nor Neumann) at the conformal boundary. In this way, two
isometrically related observers in anti-de Sitter space have different notions
of no particle content. Therefore, an observer who is suddenly transported to a
different (but isometrically related) frame will feel a bath of particles. This
process contradicts our intuitive notion based on our experience in Minkowski
spacetime, where the vacuum is Lorentz invariant, and no particle is produced
between boosted frames. We show that the total number of produced particles is
finite, but grows without limit when we approach (via isometric transformation)
Dirichlet or Neumann boundary conditions since in these cases the vacuum is
invariant.


  We study the dynamical Casimir effect using a fully quantum-mechanical
description of both the cavity field and the oscillating mirror. We do not
linearize the dynamics, nor do we adopt any parametric or perturbative
approximation. By numerically diagonalizing the full optomechanical
Hamiltonian, we show that the resonant generation of photons from the vacuum is
determined by a ladder of mirror-field {\em vacuum Rabi splittings}. We find
that vacuum emission can originate from the free evolution of an initial pure
mechanical excited state, in analogy with the spontaneous emission from excited
atoms. By considering a coherent drive of the mirror, using a master-equation
approach to take losses into account, we are able to study the dynamical
Casimir effect for optomechanical coupling strengths ranging from weak to
ultrastrong. We find that a resonant production of photons out of the vacuum
can be observed even for mechanical frequencies lower than the cavity-mode
frequency. Since high mechanical frequencies, which are hard to achieve
experimentally, were thought to be imperative for realizing the dynamical
Casimir effect, this result removes one of the major obstacles for the
observation of this long-sought effect. We also find that the dynamical Casimir
effect can create entanglement between the oscillating mirror and the radiation
produced by its motion in the vacuum field, and that vacuum Casimir-Rabi
oscillations can occur.


  Sky imaging systems use lenses to acquire images concentrating light beams in
a sensor. The light beams received by the sky imager have an elevation angle
with respect to the device normal. Thus, the pixels in the image contain
information from different areas of the sky within the imaging system field of
view. The area of the field of view contained in the pixels increases as the
elevation angle of the incident light beams decreases. When the sky imager is
mounted on a solar tracker, the light beam's angle of incidence in a pixel
varies over time. This investigation formulates and compares two geospatial
reprojections that transform the original euclidean frame of the imager plane
to the geospatial atmosphere cross-section where the sky imager field of view
intersects the cloud layer. One assumes that an object (i.e., cloud) moving in
the troposphere is sufficiently far so the Earth's surface is approximated
\emph{flat}. The other transformation takes into account the curvature of the
Earth in the portion of the atmosphere (i.e., voxel) that is recorded. The
results show that the differences between the dimensions calculated by both
geospatial transformations are in the order of magnitude of kilometers when the
Sun's elevation angle is below $30^\circ$.


  A generalization of the Bethe ansatz equations is studied, where a scalar
two-particle S-matrix has several zeroes and poles in the complex plane, as
opposed to the ordinary single pole/zero case. For the repulsive case (no
complex roots), the main result is the enumeration of all distinct solutions to
the Bethe equations in terms of the Fuss-Catalan numbers. Two new combinatorial
interpretations of the Fuss-Catalan and related numbers are obtained. On the
one hand, they count regular orbits of the permutation group in certain factor
modules over Z^M, and on the other hand, they count integer points in certain
M-dimensional polytopes.


  Transformation optics (TO) has been used to propose various novel optical
devices. With the help of metamaterials, several intriguing designs, such as
invisibility cloaks, have been implemented. However, as the basic units should
be much smaller than the working wavelengths to achieve the effective material
parameters, and the sizes of devices should be much larger than the wavelengths
of illumination to work within the light-ray approximation, it is a big
challenge to implement an experimental system that works simultaneously for
both geometric optics and wave optics. In this letter, by using a
gradient-index micro-structured optical waveguide, we realize a device of
conformal transformation optics (CTO) and demonstrate its self-focusing
property for geometry optics and Talbot effect for wave optics. In addition,
the Talbot effect in such a system has a potential application to transfer
digital information without diffraction. Our findings demonstrate the photon
controlling ability of CTO in a feasible experiment system.


  A family of effective actions in Hamiltonian form is derived for a
self-gravitating sphere of isotropic homogeneous dust. Starting from the
Einstein-Hilbert action for barotropic perfect fluids and making use of the
symmetry and equation of state of the matter distribution we obtain reduced
actions for two canonical variables, namely the radius of the sphere and its
ADM energy, the latter being conserved along trajectories of the former. These
actions differ by the value of the (conserved) geodesic energy of the radius of
the sphere which defines (disconnected) classes of solutions in correspondence
to the inner geometry and proper volume of the sphere. Each class is thus
treated as one constrained dynamical system and the union of all classes covers
the full phase space of the model. Generalization to the (inhomogeneous) Tolman
model is shown to be straightforward. Quantization is also discussed.


  Let $f: \mathbb{C} \to X$ be a transcendental holomorphic curve into a
complex projective manifold $X$. Let $L$ be a very ample line bundle on $X$.
Let $s$ be a very generic holomorphic section of $L$ and $D$ the zero divisor
given by $s$. We prove that the \emph{geometric} defect of $D$ (defect of
truncation $1$) with respect to $f$ is zero. We also prove that $f$ almost
misses general enough analytic subsets on $X$ of codimension $2$.


  We prove that the integral powers of the semicircular distribution are freely
infinitely divisible. As a byproduct we get another proof of the free infnite
divisibility of the classical Gaussian distribution.


  The Relativistic Mean Field (RMF) approach describing the motion of
independent particles in effective meson fields is extended by a microscopic
theory of particle vibrational coupling. It leads to an energy dependence of
the relativistic mass operator in the Dyson equation for the single-particle
propagator. This equation is solved in the shell-model of Dirac states. As a
result of the dynamics of particle-vibrational coupling we observe a noticeable
increase of the level density near the Fermi surface. The shifts of the
single-particle levels in the odd nuclei surrounding 208-Pb and the
corresponding distributions of the single-particle strength are discussed and
compared with experimental data.


  Recently, Shi et al. (Phys. Rev. A, 2015) proposed Quantum Oblivious Set
Member Decision Protocol (QOSMDP) where two legitimate parties, namely Alice
and Bob, play a game. Alice has a secret $k$ and Bob has a set
$\{k_1,k_2,\cdots k_n\}$. The game is designed towards testing if the secret
$k$ is a member of the set possessed by Bob without revealing the identity of
$k$. The output of the game will be either "Yes" (bit $1$) or "No" (bit $0$)
and is generated at Bob's place. Bob does not know the identity of $k$ and
Alice does not know any element of the set. In a subsequent work (Quant. Inf.
Process., 2016), the authors proposed a quantum scheme for Private Set
Intersection (PSI) where the client (Alice) gets the intersected elements with
the help of a server (Bob) and the server knows nothing. In the present draft,
we extended the game to compute the intersection of two computationally
indistinguishable sets $X$ and $Y$ possessed by Alice and Bob respectively. We
consider Alice and Bob as rational players, i.e., they are neither "good" nor
"bad". They participate in the game towards maximizing their utilities. We
prove that in this rational setting, the strategy profile $((cooperate, abort),
(cooperate, abort)$) is a strict Nash equilibrium. If $((cooperate, abort),
(cooperate, abort)$) is strict Nash, then fairness as well as correctness of
the protocol are guaranteed.


  We present a unified scaling description for the dynamics of monomers of a
semiflexible chain under good solvent condition in the free draining limit. We
consider both the cases where the contour length $L$ is comparable to the
persistence length $\ell_p$ and the case $L\gg \ell_p$. Our theory captures the
early time monomer dynamics of a stiff chain characterized by $t^{3/4}$
dependence for the mean square displacement(MSD) of the monomers, but predicts
a first crossover to the Rouse regime of $t^{2\nu/{1+2\nu}}$ for $\tau_1 \sim
\ell_p^3$, and a second crossover to the purely diffusive dynamics for the
entire chain at $\tau_2 \sim L^{5/2}$. We confirm the predictions of this
scaling description by studying monomer dynamics of dilute solution of
semi-flexible chains under good solvent conditions obtained from our Brownian
dynamics (BD) simulation studies for a large choice of chain lengths with
number of monomers per chain N = 16 - 2048 and persistence length $\ell_p = 1 -
500$ Lennard-Jones (LJ) units. These BD simulation results further confirm the
absence of Gaussian regime for a 2d swollen chain from the slope of the plot of
$\langle R_N^2 \rangle/2L \ell_p \sim L/\ell_p$ which around $L/\ell_p \sim 1$
changes suddenly from $\left(L/\ell_p \right) \rightarrow \left(L/\ell_p
\right)^{0.5} $, also manifested in the power law decay for the bond
autocorrelation function disproving the validity of the WLC in 2d. We further
observe that the normalized transverse fluctuations of the semiflexible chains
for different stiffness $\sqrt{\langle l_{\bot}^2\rangle}/L$ as a function of
renormalized contour length $L/\ell_p$ collapse on the same master plot and
exhibits power law scaling $\sqrt{\langle l_{\bot}^2\rangle}/L \sim
(L/\ell_p)^\eta $ at extreme limits, where $\eta = 0.5$ for extremely stiff
chains ($L/\ell_p \gg 1$), and $\eta = -0.25$ for fully flexible chains.


  It is well recognized that looking for new physics at lower energy colliders
is a tendency which is complementary to high energy machines such as LHC. Based
on large database of BESIII, we may have a unique opportunity to do a good job.
In this paper we calculate the branching ratios of semi-leptonic processes
$D^+_s \to K^+ e^-e^+$, $D^+_s \to K^+ e^-\mu^+$ and leptonic processes $D^0
\to e^-e^+$, $D^0 \to e^-\mu^+$ in the frames of $U(1)'$ model, 2HDM and
unparticle separately. It is found that both the $U(1)'$ and 2HDM may influence
the semi-leptonic decay rates, but only the $U(1)'$ offers substantial
contributions to the pure leptonic decays and the resultant branching ratio of
$D^0 \to e^-\mu^+$ can be as large as $10^{-7}\sim10^{-8}$ which might be
observed at the future super $\tau$-charm factory.