  In order to improve the ability of cognitive radar (CR) to adapt to the
environment, the required ambiguity function (AF) can be synthesized by
designing the waveform. The key to this problem is how to minimize the
interference power. Suppressing the interference power is equivalent to
minimize the expectation of slow-time ambiguity function (STAF) over
range-Doppler bins. From a technical point of view, this is actually an
optimization problem of a non-convex quartic function with constant modulus
constraints (CMC). In this paper, we proposed a novel method to design a
waveform to synthesize the STAF based on suppressing the interference power. We
put forward an iterative algorithm within an alternating direction penalty
method (ADPM) framework. In each iteration, this problem is split into two
sub-problems by introducing auxiliary variables. In the first sub-problem, we
solved the convex problem directly with a closed-form solution, then utilized
the Riemannian trust region (RTR) algorithm in the second sub-problem.
Simulation results demonstrate that the proposed algorithm outperforms other
advanced algorithms in the aspects of STAF, range-cut and
signal-to-interference-ratio (SIR) value.


  I review the basic observational properties of accreting millisecond pulsars
that are important for understanding the physics involved in formation of their
pulse profiles. I then discuss main effects responsible for shaping these
profiles. Some analytical results that help to understand the results of
simulations are presented. Constraints on the pulsar geometry and the neutron
star equation of state obtained from the analysis of the pulse profiles are
discussed.


  One of the most challenging problems in enumerative combinatorics is to count
Wilf classes, where you are given a pattern, or set of patterns, and you are
asked to find a "formula", or at least an efficient algorithm, that inputs a
positive integer n and outputs the number of permutations avoiding that
pattern.
  In 1996, John Noonan and Doron Zeilberger initiated the counting of
permutations that have a prescribed, r, say, occurrences of a given pattern.
They gave an ingenious method to generate Functional Equations, alas, with an
unbounded number of "catalytic variables", but then described a clever way,
using multivariable calculus, how to get enumeration schemes. Alas, their
method becomes very complicated for r larger than 1. In the present article we
describe a far simpler way to squeeze the necessary information, in polynomial
time, for increasing patterns of any length, and for any number of occurrences,
r.


  The problem of finding most general form of the classical integrable
relativistic models of many-body interaction of the $BC_{n}$ type is
considered. In the simplest nontrivial case of $n=2$,the extra integral of
motion is presented in explicit form within the ansatz similar to the
nonrelativistic Calogero-Moser models. The resulting Hamiltonian has been found
by solving the set of two functional equations.


  As 5G technology becomes increasingly established, the anticipation for 6G is
growing, which promises to deliver faster and more reliable wireless
connections via cutting-edge radio technologies. However, efficient management
method of the large-scale antenna arrays deployed by those radio technologies
is crucial. Traditional management methods are mainly reactive, usually based
on feedback from users to adapt to the dynamic wireless channel. However, a
more promising approach lies in the prediction of spatial channel state
information (spatial-CSI), which is an all-inclusive channel characterization
and consists of all the feasible line-of-sight (LoS) and non-line-of-sight
(NLoS) paths between the transmitter (Tx) and receiver (Rx), with the
three-dimension (3D) trajectory, attenuation, phase shift, delay, and
polarization of each path. Advances in hardware and neural networks make it
possible to predict such spatial-CSI using precise environmental information,
and further look into the possibility of holographic communication, which
implies complete control over every aspect of the radio waves emitted. Based on
the integration of holographic communication and digital twin, we proposed a
new framework, digital radio twin, which takes advantages from both the digital
world and deterministic control over radio waves, supporting a wide range of
high-level applications. As a preliminary attempt towards this visionary
direction, in this paper, we explore the use of generative artificial
intelligence (AI) to pinpoint the valid paths in a given environment,
demonstrating promising results, and highlighting the potential of this
approach in driving forward the evolution of 6G wireless communication
technologies.


  Recent work in computer vision has yielded impressive results in
automatically describing images with natural language. Most of these systems
generate captions in a sin- gle language, requiring multiple language-specific
models to build a multilingual captioning system. We propose a very simple
technique to build a single unified model across languages, using artificial
tokens to control the language, making the captioning system more compact. We
evaluate our approach on generating English and Japanese captions, and show
that a typical neural captioning architecture is capable of learning a single
model that can switch between two different languages.


  We study remaining Lorentz symmetry, i.e. Lorentz transformations which leave
the noncommutativity parameter $\theta^{\mu\nu}$ invariant, within the approach
of time-ordered perturbation theory (TOPT) to space-time noncommutative
theories. Their violation is shown in a simple scattering process. We argue
that this results from the non-covariant transformation properties of the phase
factors appearing in TOPT.


  This paper examines the performance of a 2x2 Line of Sight (LoS) Multiple
Input Multiple Output (MIMO) channel at three terahertz frequencies-340 GHz,
410 Ghz, and 460 GHz. While theoretical models predict very high channel
capacities, we observe lower capacity which is explained by asymmetric
transmit-to-receive signal strengths as well as due to signal attenuation over
longer distances. Overall, however, we note that at 460 Ghz, channel capacity
of higher than 12 bps/hz is possible even at sub-optimal inter-antenna spacings
(for different distances). An important observation is also that we need to
maintain appropriate receive signal levels at receive antennas in order to
improve capacity.


  The main objective of this chapter is to present an overview of the different
areas of key technologies that will be needed to fly the technically most
challenging of the representative missions identified in chapter 4 (the Pillar
2 Horizon 2061 report). It starts with a description of the future scientific
instruments which will address the key questions of Horizon 2061 described in
chapter 3 (the Pillar 1 Horizon 2061 report) and the new technologies that the
next generations of space instruments will require (section 2). From there, the
chapter follows the line of logical development and implementation of a
planetary mission: section 3 describes some of the novel mission architectures
that will be needed and how they will articulate interplanetary spacecraft and
science platforms; section 4 summarizes the system-level technologies needed:
power, propulsion, navigation, communication, advanced autonomy on board
planetary spacecraft; section 5 describes the diversity of specialized science
platforms that will be needed to survive, operate and return scientific data
from the extreme environments that future missions will target; section 6
describes the new technology developments that will be needed for long-duration
missions and semi-permanent settlements; finally, section 7 attempts to
anticipate on the disruptive technologies that should emerge and progressively
prevail in the decades to come to meet the long-term needs of future planetary
missions.


  We consider the limiting behaviour of the point processes associated with a
branching random walk with supercritical branching mechanism and balanced
regularly varying step size. Assuming that the underlying branching process
satisfies Kesten-Stigum condition, it is shown that the point process sequence
of properly scaled displacements coming from the n-th generation converges
weakly to a Cox cluster process. In particular, we establish that a conjecture
of Brunet and Derrida (2011) remains valid in this setup, investigate various
other issues mentioned in their paper and recover the main result of Durrett
(1983) in our framework.


  The superfluid transition of $^3$He-$^4$He mixture films adsorbed on alumina
powder is studied, with a $^4$He superfluid coverage near one layer. With up to
1.3 layers of $^3$He added, the transition becomes strongly broadened,
indicating a linear increase in the vortex core size for $^3$He coverages below
one layer. Annealing of the sample mixture at 4.2 K is found to be critically
important in ensuring a homogeneous film across the porous substrate.


  To understand the emergence and sustainment of cooperative behavior in
interacting collectives, we perform global convergence analysis for replicator
dynamics of a large, well-mixed population of individuals playing a repeated
snowdrift game with four typical strategies, which are always cooperate (ALLC),
tit-for-tat (TFT), suspicious tit-for-tat (STFT) and always defect (ALLD). The
dynamical model is a three-dimensional ODE system that is parameterized by the
payoffs of the base game. Instead of routine searches for evolutionarily stable
strategies and sets, we expand our analysis to determining the asymptotic
behavior of solution trajectories starting from any initial state, and in
particular show that for the full range of payoffs, every trajectory of the
system converges to an equilibrium point. The convergence results highlight
three findings that are of particular importance for understanding the
cooperation mechanisms among self-interested agents playing repeated snowdrift
games. First, the inclusion of TFT- and STFT-players, the two types of
conditional strategy players in the game, increases the share of cooperators of
the overall population compared to the situation when the population consists
of only ALLC- and ALLD-players. This confirms findings in biology and sociology
that reciprocity may promote cooperation in social collective actions, such as
reducing traffic jams and division of labor, where each individual may gain
more to play the opposite of what her opponent chooses. Second, surprisingly
enough, regardless of the payoffs, there always exists a set of initial
conditions under which ALLC players do not vanish in the long run, which does
not hold for all the other three types of players. So an ALLC-player, although
perceived as the one that can be easily taken advantage of in snowdrift games,
has certain endurance in the long run.


  Inspired by the definition of color-dressed amplitudes in string theory, we
define analogous {\it color-dressed permutations} replacing the color-ordered
string amplitudes by their corresponding permutations. Decomposing the color
traces into symmetrized traces and structure constants, the color-dressed
permutations define {\it BRST-invariant permutations}, which we show are
elements of the inverse Solomon descent algebra and we find a closed formula
for them. We then present evidence that these permutations encode KK-like
relations among the different $\alpha'$ corrections to disk amplitudes refined
by their motivic MZV content. In particular, the number of linearly independent
amplitudes at a given ${\alpha^{\prime}}$ order and motivic MZV content is
given by (sums of) Stirling cycle numbers. In addition, we show how the
superfield expansion of BRST invariants of the pure spinor formalism
corresponding to ${\alpha^{\prime}}^2 f_2$ corrections is encoded in the
descent algebra.


  In the noisy intermediate-scale quantum era, scientists are trying to improve
the entanglement swapping success rate by researching anti-noise technology on
the physical level, thereby obtaining a higher generation rate of long-distance
entanglement. However, we may improve the generation rate from another
perspective, which is studying an efficient entanglement swapping strategy.
This paper analyzes the challenges faced by existing entanglement swapping
strategies, including the node allocation principle, time synchronization, and
processing of entanglement swapping failure. We present Parallel Segment
Entanglement Swapping (PSES) to solve these problems. The core idea of PSES is
to segment the path and perform parallel entanglement swapping between segments
to improve the generation rate of long-distance entanglement. We construct a
tree-like model as the carrier of PSES and propose heuristic algorithms called
Layer Greedy and Segment Greedy to transform the path into a tree-like model.
Moreover, we realize the time synchronization and design the on-demand
retransmission mechanism to process entanglement swapping failure. The
experiments show that PSES performs superiorly to other entanglement swapping
strategies, and the on-demand retransmission mechanism can reduce the average
entanglement swapping time by 80% and the average entanglement consumption by
80%.


  We investigate by means of a variational approach the effective potential of
a 5D U(1) scalar model at finite temperature and compactified on S^1 and
S^1/Z_2 as well as the corresponding 4D model obtained through a trivial
dimensional reduction. We are particularly interested in the behaviour of the
thermal masses of the scalar field with respect to the Wilson line phase and
the results obtained are compared with those coming from a one-loop effective
potential calculation. We also explore the nature of the phase transition.


  The conditions that allow us to consider the vacuum expectation value of the
energy-momentum tensor as a statistical average, at some particular
temperature, are given. When the mean value of created particles is stationary,
a planckian distribution for the field modes is obtained. In the massless
approximation, the temperature dependence is as that corresponding to a
radiation dominated Friedmann-like model.


  We propose a polynomial time $f$-algorithm (a deterministic algorithm which
uses an oracle for factoring univariate polynomials over $\mathbb{F}_q$) for
computing an isomorphism (if there is any) of a finite dimensional
$\mathbb{F}_q(x)$-algebra $A$ given by structure constants with the algebra of
$n$ by $n$ matrices with entries from $\mathbb{F}_q(x)$. The method is based on
computing a finite $\mathbb{F}_q$-subalgebra of $A$ which is the intersection
of a maximal $\mathbb{F}_q[x]$-order and a maximal $R$-order, where $R$ is the
subring of $\mathbb{F}_q(x)$ consisting of fractions of polynomials with
denominator having degree not less than that of the numerator.


  Knowing the band structure of materials is one of the prerequisites to
understand their properties. Therefore, especially in the last decades,
angle-resolved photoemission spectroscopy (ARPES) has become a highly demanded
experimental tool to investigate the band structure. However, especially in
thin film materials with a layered structure and several capping layers, access
to the electronic structure by ARPES is limited. Therefore, several alternative
methods to obtain the required information have been suggested. Here, we
directly invert the results by cyclotron resonance experiments to obtain the
band structure of a two-dimensional (2D) material. This procedure is applied to
the mercury telluride quantum well with critical thickness which is
characterized by a 2D electron gas with linear dispersion relations. The
Dirac-like band structure in this material could be mapped both on the electron
and on the hole side of the band diagram. In this material, purely linear
dispersion of the hole-like carriers is in contrast to detectable quadratic
corrections for the electrons.


  Formal series solutions and the Kovalevskaya exponents of a quasi-homogeneous
polynomial system of differential equations are studied by means of a weighted
projective space and dynamical systems theory. A necessary and sufficient
condition for the series solution to be a convergent Laurent series is given,
which improve the well known Painlev\'{e} test. In particular, if a given
system has the Painlev\'{e} property, an algorithm to construct Okamoto's space
of initial conditions is given. The space of initial conditions is obtained by
weighted blow-ups of the weighted projective space, where the weights for the
blow-ups are determined by the Kovalevskaya exponents. The results are applied
to the first Painlev\'{e} hierarchy ($2m$-th order first Painlev\'{e}
equation).


  An efficient algorithm is developed for quantum spin tubes in the context of
the tensor network representations. It allows to efficiently compute the
ground-state fidelity per lattice site, which in turn enables us to identify
quantum critical points, at which quantum spin tubes undergo quantum phase
transitions. As an illustration, we investigate the isosceles spin 1/2
antiferromagnetic three-leg Heisenberg tube. Our simulation results suggest
that two Kosterlitz-Thouless transitions occur as the degree of asymmetry of
the rung interaction is tuned, thus offering an alternative route towards a
resolution to the conflicting results on this issue arising from the density
matrix renormalization group.


  Recently Taniguchi and Ohyama found that the higher $^{12}$CO to $^{13}$CO
integrated intensity ratios at a transition $J$=1--0, $R =
I(^{12}$CO)$/I(^{13}$CO) $\gtrsim 20$, in a sample of starburst merging
galaxies such as Arp 220 are mainly attributed to the depression of $^{13}$CO
emission with respect to $^{12}$CO. Investigating the same sample of galaxies
analyzed by Taniguchi & Ohyama, we find that there is a tight, almost linear
correlation between the dust mass and $^{13}$CO luminosity. This implies that
dust grains are also depressed in the high-$R$ starburst mergers, leading to
the higher dust temperature ($T_{\rm d}$) in them because of the relative
increase in the radiation density. Nevertheless, the average dust mass ($M_{\rm
d}$) of the high-$R$ starburst mergers is higher significantly than that of
non-high $R$ galaxies. This is naturally understood because the galaxy mergers
could accumulate a lot of dust grains from their progenitor galaxies together
with supply of dust grains formed newly in the star forming regions. Since
$L$(FIR) $\propto M_{\rm d} T_{\rm d}^5$ given the dust emissivity law, $S_\nu
\propto \lambda^{-1}$, the increases in both $M_{\rm d}$ and $T_{\rm d}$
explain well why the starburst mergers are so bright in the FIR. We discuss
that the superwind activity plays an important role in destroying dust grains
as well as dense gas clouds in the central region of mergers.


  This paper develops new mathematical techniques to identify temporal shifts
among a collection of US equities partitioned into a new and more detailed set
of market sectors. Although conceptually related, our three analyses reveal
distinct insights about financial markets, with meaningful implications for
investment managers. First, we explore a variety of methods to identify
nonlinear shifts in market sector structure and describe the mathematical
connection between the measure used and the captured phenomena. Second, we
study network structure with respect to our new market sectors and identify
meaningfully connected sector-to-sector mappings. Finally, we conduct a series
of sampling experiments over different sample spaces and contrast the
distribution of Sharpe ratios produced by long-only, long-short and short-only
investment portfolios. In addition, we examine the sector composition of the
top-performing portfolios for each of these portfolio styles. In practice, the
methods proposed in this paper could be used to identify regime shifts,
optimally structured portfolios, and better communities of equities.


  In our paper [Ann. Phys. (NY) 395, 326 (2018)] we calculate the Casimir
stress on a sphere immersed in a homogeneous background, assuming
dispersionless dielectrics. Our results appear to challenge the conventional
picture of Casimir forces. The paper [arXiv:1909.05721] criticises our approach
without offering an alternative. In particular, the paper [arXiv:1909.05721]
claims that we have made an unjustified mathematical step. This brief comment
clarifies the matter.


  Boundary integral equation formulations of elliptic partial differential
equations lead to dense system matrices when discretized, yet they are
data-sparse. Using the $\mathcal{H}$-matrix format, this sparsity is exploited
to achieve $\mathcal{O}(N\log N)$ complexity for storage and multiplication by
a vector. This is achieved purely algebraically, based on low-rank
approximations of subblocks, and hence the format is also applicable to a wider
range of problems. The $\mathcal{H}^2$-matrix format improves the complexity to
$\mathcal{O}(N)$ by introducing a recursive structure onto subblocks on
multiple levels. However, in practice this comes with a large proportionality
constant, making the $\mathcal{H}^2$-matrix format advantageous mostly for
large problems. In this paper we investigate the usefulness of a matrix format
that lies in between these two: Uniform $\mathcal{H}$-matrices. An algebraic
compression algorithm is introduced to transform a regular $\mathcal{H}$-matrix
into a uniform $\mathcal{H}$-matrix, which maintains the asymptotic complexity.


  We live in a world where data generation is omnipresent. Innovations in
computer hardware in the last few decades coupled with increasingly reliable
connectivity among them have fueled this phenomenon. We are constantly creating
and consuming data across digital devices of varying form factors. Leveraging
huge quantities of data involves making interpretations from it. However,
interpreting data is still a difficult task. We need data analysts to help make
decisions. These experts apply their domain knowledge, understanding of the
problem space and numerical analysis to draw inferences from the data in order
to support decision making. Existing tools and techniques for interference
serve users making decisions with hard constraints. Consumer systems are often
built to support exploratory data analysis in mind rather than sense making.


  In this paper, we prove a criterion for complexity in $g$-ary expansions of a
rational fraction $a/b<1$ with gcd$(a,b)=1$. We prove that for any purely
periodic proper fraction $a/b$ and all $j\geq 1$, each sequence of $j$ digits
occurs in the $g$-ary repetend of $a/b^k$ with a relative frequency that
approaches $1/g^j$ with an increasing $k$. The absolute frequencies can be
calculated by means of a simple transition matrix. Let $(a_k)$ be a sequence of
positive integers relatively prime to $b$. We prove that each sequence of $j$
digits occurs in the $g$-ary repetend of $a_k/b^k$ with a relative frequency
that approaches $1/g^j$ with an increasing $k$, unless all prime factors of $b$
divide the base $g\geq 2$.


  GJ 229B, the first type-T brown dwarf to be discovered, has presented a
tension between comparisons with evolutionary models and the
larger-than-expected mass and radius values derived from spectroscopic and
astrometric observations. We examine the hypothesis that GJ 229B is actually a
binary sub-stellar object by using two grid-based fits using evolutionary
models to explore the range of mass ratios of the possible binary components.
We find that the best-fit component values are most consistent with a roughly
2:1 binary mass ratio and an age range of 2-6 Gyr. The observed temperatures,
masses, and apparent radii match expected values from evolutionary models for a
binary much better than a single-object model, but more detailed observations
and modeling are needed to definitively confirm the binary hypothesis.


  We consider distributed detection problems over adaptive networks, where
dispersed agents learn continually from streaming data by means of local
interactions. The simultaneous requirements of adaptation and cooperation are
achieved by employing diffusion algorithms with constant step-size {\mu}. In
[1], [2] some main features of adaptive distributed detection were revealed. By
resorting to large deviations analysis, it was established that the Type-I and
Type-II error probabilities of all agents vanish exponentially as functions of
1/{\mu}, and that all agents share the same Type-I and Type-II error exponents.
However, numerical evidences presented in [1], [2] showed that the theory of
large deviations does not capture the fundamental impact of network
connectivity on performance, and that additional tools and efforts are required
to obtain accurate predictions for the error probabilities. This work addresses
these open issues and extends the results of [1], [2] in several directions. By
conducting a refined asymptotic analysis based on the mathematical framework of
exact asymptotics, we arrive at a revealing and powerful understanding of the
universal behavior of distributed detection over adaptive networks: as
functions of 1/{\mu}, the error (log-)probability curves corresponding to
different agents stay nearly-parallel to each other (as already discovered in
[1], [2]), however, these curves are ordered following a criterion reflecting
the degree of connectivity of each agent. Depending on the combination weights,
the more connected an agent is, the lower its error probability curve will be.
Interesting and somehow unexpected behaviors emerge, in terms of the interplay
between the network topology, the combination weights, and the inference
performance. The lesson learned is that connectivity matters.


  Two scenarios of possible ion heating due to finite amplitude parallel
propagating Alfv\'en waves in the solar atmosphere are investigated using a 1D
test particle approach. 1. An finite amplitude Alfv\'en wave is instantly
introduced into a plasma (or equivalently, new ions are instantly created). 2.
New ions are constantly created. In both scenarios, ions will be picked up by
the Alfv\'en wave. In case 1, the wave scatters ions in the transverse
direction leading to a randomization (or heating) process. This process is
complete when a phase shift of $\pm \pi$ in the ion gyro-speed is produced
between particles with characteristic parallel thermal speed and particles with
zero parallel speed. This corresponds to $t={\pi \over k v_{th}}$ ($k$ is the
wave number and $v_{th}$ is the ion thermal speed). A ring velocity
distribution can be produced for large wave amplitude. The process yields a
mass-proportional heating in the transverse direction, a temperature anisotropy
and a bulk flow along the background magnetic field. In case 2, continuous ion
creation represents a continuing phase shift in the ion gyro-speed leading to
heating. New particles are picked up by the Alfv\'en wave within one ion
gyroperiod. It is speculated that the mechanism may operate in the chromosphere
and active regions where transient events may generate finite amplitude
Alfv\'en waves.


  An intermediate-scale energy spectrum anisotropy has been found in the
arrival directions of ultra-high energy cosmic rays of energies above
$10^{19.2}$ eV in the northern hemisphere, using 7 years of data from the
Telescope Array surface detector. A relative energy distribution test is done
comparing events inside oversampled spherical caps of equal exposure, to those
outside, using the Poisson likelihood ratio. The center of maximum significance
is at $9^h$$16^m$, $45^{\circ}$. and has a deficit of events with energies
$10^{19.2}$$\leq$$E$$<$$10^{19.75}$ eV and an excess for $E$$\geq$$10^{19.75}$
eV. The post-trial probability of this energy anisotropy, appearing by chance
anywhere on an isotropic sky, is found by Monte Carlo simulation to be
$9$$\times$$10^{-5}$ ($3.74$$\sigma_{global}$).


  In this paper, we address the Ehrenborg's conjecture which proposes that for
any bipartite graph the number of spanning trees does not exceed the product of
the degrees of the vertices divided by the product of the sizes of the graph
components. We show that the conjecture is true for a one-side regular graph
(that is a graph for which all degrees of the vertices of at least one of the
components are equal). We also present a new proof of the fact that the
equality holds for Ferrers graphs.


  Let $K$ be an unramified $p$-adic local field and let $W$ be the ring of
integers of $K$. Let $(X,S)/W$ be a smooth proper scheme together with a normal
crossings divisor. We show that there are only finitely many log crystalline
$\mathbb Z_{p^f}$-local systems over $X_K\setminus S_K$ of given rank and with
geometrically absolutely irreducible residual representation, up to twisting by
a character. The proof uses $p$-adic nonabelian Hodge theory and a finiteness
result due Abe/Lafforgue.


  We investigate numerically models of the static spherically symmetric
boson-fermion stars in the scalar-tensor theory of gravity with massive dilaton
field. The proper mathematical model of such stars is interpreted as a
nonlinear two-parametric eigenvalue problem with unknown internal boundary. To
solve this problem the Continuous Analogue of Newton Method is used.


  The quest for the Standard Model among the huge number of string vacua is
usually based on a set of phenomenological criteria related to the massless
spectrum of string models. In this work we study criteria associated with
interactions in the effective low energy theory and in particular with the
presence of the coupling that provides mass to the top quark. Working in the
context of the Free Fermionic Formulation of the heterotic superstring, we
demonstrate that, in a big class of phenomenologically promising $Z_2\times
Z_2$ compactifications, these criteria can be expressed entirely in terms of
the generalised GSO projection coefficients entering the definition of the
models. They are shown to be very efficient in identifying phenomenologically
viable vacua, especially in the framework of computer-based search, as they are
met by approximately one every $10^4$ models. We apply our results in the
investigation of a class of supersymmetric Pati-Salam vacua, comprising
$10^{16}$ configurations, and show that when combined with other
phenomenological requirements they lead to a relatively small set of about
$10^7$ Standard Model compatible models that can be fully classified.


  We prove a Santal\'{o} and a reverse Santal\'{o} inequality for the polarity
transform, which was recently re-discovered by Artstein-Avidan and Milman, in
the class consisting of (even) log-concave functions attaining their maximal
value 1 at the origin, also called geometric log-cancave functions. The bounds
are sharp up to the optimal universal constants.


  The integrability conditions for the existence of Killing-Yano tensors or,
equivalently, covariantly closed conformal Killing-Yano tensors, in the
presence of torsion are worked out. As an application, all metrics and torsions
compatible with the existence of a Killing-Yano tensor of order n-1 are
obtained. Finally, the issue of defining a maximally symmetric space with
respect to connections with torsion is addressed.


  Nous d\'ecrivons explicitement les paquets d'Arthur des groupes classiques
complexes, ainsi que leur param\'etrisation interne par les caract\`eres du
groupe des composantes connexes du centralisateur de leur param\`etre. Nous
montrons d'abord qu'ils sont obtenus par induction parabolique pr\'eservant
l'irr\'eductibilit\'e \`a partir des paquets unipotents de "bonne parit\'e".
Pour ceux-ci, nous montrons qu'ils co\"incident avec les paquets d\'efinis par
Barbasch-Vogan. Nous utilisons des r\'esultats profonds de Barbasch entrant
dans sa classification du dual unitaire de ces groupes.
  We describe explicitly Arthur packets for complex classical groups, as well
as their internal parametrization by the group of characters of the component
group of the stabilizer of their parameter. We first show that they are
obtained by parabolic induction preserving irreducibility from unipotent
packets of "good parity". For these, we show that they coincide with the
packets defined by Barbasch and Vogan. We use deep results of Barbasch entering
his classification of the unitary dual of these groups.


  Discrete-time queueing system has widespread applications in packet switching
networks, internet protocol, Broadband Integrated Services Digital Network
(B-ISDN), circuit switched time-division multiple access etc. In this paper, we
analyze an infinite-buffer discrete-time group-arrival queue with single and
multiple vacation policy where processing/transmission/service times
dynamically vary with batch-size under service. The bivariate probability
generating function of queue length and server content distribution has been
derived first, and from that we extract the probabilities in terms of roots of
the characteristic equation. We also find the joint distribution at arbitrary
and pre-arrival slot. Discrete phase type distribution plays a noteworthy role
in order to regulate the high transmission error through a particular channel.
In view of this, numerical illustrations include the service time distribution
to follow the discrete phase type distribution.


  We study the envy free pricing problem faced by a seller who wishes to
maximize revenue by setting prices for bundles of items. If there is an
unlimited supply of items and agents are single minded then we show that
finding the revenue maximizing envy free allocation/pricing can be solved in
polynomial time by reducing it to an instance of weighted independent set on a
perfect graph.
  We define an allocation/pricing as \textit{multi envy free} if no agent
wishes to replace her allocation with the union of the allocations of some set
of other agents and her price with the sum of their prices. We show that it is
\textit{coNP}-hard to decide if a given allocation/pricing is multi envy free.
We also show that revenue maximization multi envy free allocation/pricing is
\textit{APX} hard.
  Furthermore, we give efficient algorithms and hardness results for various
variants of the highway problem.


  We demonstrate the separability of the massive vector (Proca) field equation
in general Kerr-NUT-(A)dS black hole spacetimes in any number of dimensions,
filling a long-standing gap in the literature. The obtained separated equations
are studied in more detail for the four-dimensional Kerr geometry and the
corresponding quasinormal modes are calculated. Two of the three independent
polarizations of the Proca field are shown to emerge from the separation ansatz
and the results are found in a perfect agreement with those of the recent
numerical study where the full coupled partial differential equations were
tackled without using the separability property.


  Let $A$ be an $s$-sparse Hermitian matrix, $f(x)$ be a univariate function,
and $i, j$ be two indices. In this work, we investigate the query complexity of
approximating $\bra{i} f(A) \ket{j}$. We show that for any continuous function
$f(x):[-1,1]\rightarrow [-1,1]$, the quantum query complexity of computing
$\bra{i} f(A) \ket{j}\pm \varepsilon/4$ is lower bounded by
$\Omega(\widetilde{\deg}_\varepsilon(f))$. The upper bound is at most quadratic
in $\widetilde{\deg}_\varepsilon(f)$ and is linear in
$\widetilde{\deg}_\varepsilon(f)$ under certain mild assumptions on $A$. Here
the approximate degree $\widetilde{\deg}_\varepsilon(f)$ is the minimum degree
such that there is a polynomial of that degree approximating $f$ up to additive
error $\varepsilon$ in the interval $[-1,1]$. We also show that the classical
query complexity is lower bounded by
$\widetilde{\Omega}((s/2)^{(\widetilde{\deg}_{2\varepsilon}(f)-1)/6})$ for any
$s\geq 4$. Our results show that the quantum and classical separation is
exponential for any continuous function of sparse Hermitian matrices, and also
imply the optimality of implementing smooth functions of sparse Hermitian
matrices by quantum singular value transformation. The main techniques we used
are the dual polynomial method for functions over the reals, linear
semi-infinite programming, and tridiagonal matrices.


  The disagreement between direct late-time measurements of the Hubble constant
from the SH0ES collaboration, and early-universe measurements based on the
$\Lambda$CDM model from the Planck collaboration might, at least in principle,
be explained by new physics in the early universe. Recently, the application of
the Effective Field Theory of Large-Scale Structure to the full shape of the
power spectrum of the SDSS/BOSS data has revealed a new, rather powerful, way
to measure the Hubble constant and the other cosmological parameters from
Large-Scale Structure surveys. In light of this, we analyze two models for
early universe physics, Early Dark Energy and Rock 'n' Roll, that were designed
to significantly ameliorate the Hubble tension. Upon including the information
from the full shape to the Planck, BAO, and Supernovae measurements, we find
that the degeneracies in the cosmological parameters that were introduced by
these models are well broken by the data, so that these two models do not
significantly ameliorate the tension.


  Malicious URL detection is an emerging research area due to continuous
modernization of various systems, for instance, Edge Computing. In this
article, we present a novel malicious URL detection technique, called deepBF
(deep learning and Bloom Filter). deepBF is presented in two-fold. Firstly, we
propose a learned Bloom Filter using 2-dimensional Bloom Filter. We
experimentally decide the best non-cryptography string hash function. Then, we
derive a modified non-cryptography string hash function from the selected hash
function for deepBF by introducing biases in the hashing method and compared
among the string hash functions. The modified string hash function is compared
to other variants of diverse non-cryptography string hash functions. It is also
compared with various filters, particularly, counting Bloom Filter, Kirsch
\textit{et al.}, and Cuckoo Filter using various use cases. The use cases
unearth weakness and strength of the filters. Secondly, we propose a malicious
URL detection mechanism using deepBF. We apply the evolutionary convolutional
neural network to identify the malicious URLs. The evolutionary convolutional
neural network is trained and tested with malicious URL datasets. The output is
tested in deepBF for accuracy. We have achieved many conclusions from our
experimental evaluation and results and are able to reach various conclusive
decisions which are presented in the article.


  Pedestrian detection based on the combination of Convolutional Neural Network
(i.e., CNN) and traditional handcrafted features (i.e., HOG+LUV) has achieved
great success. Generally, HOG+LUV are used to generate the candidate proposals
and then CNN classifies these proposals. Despite its success, there is still
room for improvement. For example, CNN classifies these proposals by the
full-connected layer features while proposal scores and the features in the
inner-layers of CNN are ignored. In this paper, we propose a unifying framework
called Multilayer Channel Features (MCF) to overcome the drawback. It firstly
integrates HOG+LUV with each layer of CNN into a multi-layer image channels.
Based on the multi-layer image channels, a multi-stage cascade AdaBoost is then
learned. The weak classifiers in each stage of the multi-stage cascade is
learned from the image channels of corresponding layer. With more abundant
features, MCF achieves the state-of-the-art on Caltech pedestrian dataset
(i.e., 10.40% miss rate). Using new and accurate annotations, MCF achieves
7.98% miss rate. As many non-pedestrian detection windows can be quickly
rejected by the first few stages, it accelerates detection speed by 1.43 times.
By eliminating the highly overlapped detection windows with lower scores after
the first stage, it's 4.07 times faster with negligible performance loss.


  We study the sensitivity of a pair of Einstein Telescopes (ET)
(hypothetically located at the two sites currently under consideration for ET)
to the anisotropies of the Stochastic Gravitational Wave Background (SGWB). We
focus on the $\ell =0,2,4$ multipoles of an expansion of the SGWB in spherical
harmonics, since the sensitivity to other multipoles is suppressed due to the
fact that this pair of detector operates in a regime for which the product
between the observed frequency and the distance between the two sites is much
smaller than one. In this regime, the interferometer overlap functions for the
anisotropic signal acquire very simple analytic expressions. These expressions
can also be applied to any other pairs of interferometers (each one of
arbitrary opening angle between its two arms) operating in this regime. Once
the measurements at the vertices of the two sites are optimally combined, the
sensitivity to the multipoles of the SGWB depends only on the latitude of the
two sites, on the difference of their longitude, but not on the orientation of
their arms.


  In this paper we discuss the following issue: How do we decide whether a
certain property of language is a competence property or a performance
property? Our claim is that the answer to this question is not given a-priori.
The answer depends on the formal devices (formal grammars and machines)
available to us for describing language. We discuss this issue in the context
of the complexity of processing of center embedding (of relative clauses in
English) and scrambling (in German, for example) from arbitrary depths of
embedding.


  Automatic differentiation (AD) aims to compute derivatives of user-defined
functions, but in Turing-complete languages, this simple specification does not
fully capture AD's behavior: AD sometimes disagrees with the true derivative of
a differentiable program, and when AD is applied to non-differentiable or
effectful programs, it is unclear what guarantees (if any) hold of the
resulting code. We study an expressive differentiable programming language,
with piecewise-analytic primitives, higher-order functions, and general
recursion. Our main result is that even in this general setting, a version of
Lee et al. [2020]'s correctness theorem (originally proven for a first-order
language without partiality or recursion) holds: all programs denote so-called
$\omega$PAP functions, and AD computes correct intensional derivatives of them.
Mazza and Pagani [2021]'s recent theorem, that AD disagrees with the true
derivative of a differentiable recursive program at a measure-zero set of
inputs, can be derived as a straightforward corollary of this fact. We also
apply the framework to study probabilistic programs, and recover a recent
result from Mak et al. [2021] via a novel denotational argument.


  The baryon axial vector current is computed in heavy baryon chiral
perturbation theory in the large-$N_c$ limit, where $N_c$ is the number of
color charges. One-loop nonanalytic corrections of order $m_q \ln m_q$ are
comprised in the analysis, with contributions of both intermediate octet and
decuplet baryon states, to all orders in the $1/N_c$ expansion of the axial
vector current relevant for $N_c=3$. Theoretical expressions are obtained in
the limit of vanishing decuplet-octet mass difference only, which allows one to
carry out a full comparison with conventional heavy baryon chiral perturbation
theory results for three flavors of light quarks and at the physical value
$N_c=3$. Both approaches perfectly agree to all orders considered. Furthermore,
a numerical analysis via a least-squares fit is performed in order to extract
the values of the free parameters of the theory, using the experimental data
available. The predictions of formalism are remarkable.


  The Magnus series is an infinite series which arises in the study of linear
ordinary differential equations. If the series converges, then the matrix
exponential of the sum equals the fundamental solution of the differential
equation. The question considered in this paper is: When does the series
converge? The main result establishes a sufficient condition for convergence,
which improves on several earlier results.


  We show that formation of crossed products and passage to fixed point
algebras by compact group actions with finite Rokhlin dimension preserve the
following regularity properties: finite decomposition rank, finite nuclear
dimension, and tensorial absorption of the Jiang-Su algebra, the latter in the
formulation with commuting towers.


  We introduce a new family of rank metric codes: Low Rank Parity Check codes
(LRPC), for which we propose an efficient probabilistic decoding algorithm.
This family of codes can be seen as the equivalent of classical LDPC codes for
the rank metric. We then use these codes to design cryptosystems \`a la
McEliece: more precisely we propose two schemes for key encapsulation mechanism
(KEM) and public key encryption (PKE). Unlike rank metric codes used in
  previous encryption algorithms -notably Gabidulin codes - LRPC codes have a
very weak algebraic structure. Our cryptosystems can be seen as an equivalent
of the NTRU cryptosystem (and also to the more recent MDPC \cite{MTSB12}
cryptosystem) in a rank metric context. The present paper is an extended
version of the article introducing LRPC codes, with important new
contributions. We have improved the decoder thanks to a new approach which
allows for decoding of errors of higher rank weight, namely up to
$\frac{2}{3}(n-k)$ when the previous decoding algorithm only decodes up to
$\frac{n-k}{2}$ errors. Our codes therefore outperform the classical Gabidulin
code decoder which deals with weights up to $\frac{n-k}{2}$. This comes at the
expense of probabilistic decoding, but the decoding error probability can be
made arbitrarily small. The new approach can also be used to decrease the
decoding error probability of previous schemes, which is especially useful for
cryptography. Finally, we introduce ideal rank codes, which generalize
double-circulant rank codes and allow us to avoid known structural attacks
based on folding. To conclude, we propose different parameter sizes for our
schemes and we obtain a public key of 3337 bits for key exchange and 5893 bits
for public key encryption, both for 128 bits of security.


  In this paper, we will develop a definition of mild solution for impulsive
fractional differential equation of order $\alpha\in (1,2)$ with the help of
solution operator and study the existence results of mild solution for
impulsive fractional differential equations with state dependent delay by using
fixed point theorems. Finally, we present an example of partial fractional
derivative to illustrate the existence and uniqueness result.


  Recent work has shown that models trained to the same objective, and which
achieve similar measures of accuracy on consistent test data, may nonetheless
behave very differently on individual predictions. This inconsistency is
undesirable in high-stakes contexts, such as medical diagnosis and finance. We
show that this inconsistent behavior extends beyond predictions to feature
attributions, which may likewise have negative implications for the
intelligibility of a model, and one's ability to find recourse for subjects. We
then introduce selective ensembles to mitigate such inconsistencies by applying
hypothesis testing to the predictions of a set of models trained using
randomly-selected starting conditions; importantly, selective ensembles can
abstain in cases where a consistent outcome cannot be achieved up to a
specified confidence level. We prove that that prediction disagreement between
selective ensembles is bounded, and empirically demonstrate that selective
ensembles achieve consistent predictions and feature attributions while
maintaining low abstention rates. On several benchmark datasets, selective
ensembles reach zero inconsistently predicted points, with abstention rates as
low 1.5%.


  This paper presents the Crowd Score, a novel method to assess the funniness
of jokes using large language models (LLMs) as AI judges. Our method relies on
inducing different personalities into the LLM and aggregating the votes of the
AI judges into a single score to rate jokes. We validate the votes using an
auditing technique that checks if the explanation for a particular vote is
reasonable using the LLM. We tested our methodology on 52 jokes in a crowd of
four AI voters with different humour types: affiliative, self-enhancing,
aggressive and self-defeating. Our results show that few-shot prompting leads
to better results than zero-shot for the voting question. Personality induction
showed that aggressive and self-defeating voters are significantly more
inclined to find more jokes funny of a set of aggressive/self-defeating jokes
than the affiliative and self-enhancing voters. The Crowd Score follows the
same trend as human judges by assigning higher scores to jokes that are also
considered funnier by human judges. We believe that our methodology could be
applied to other creative domains such as story, poetry, slogans, etc. It could
both help the adoption of a flexible and accurate standard approach to compare
different work in the CC community under a common metric and by minimizing
human participation in assessing creative artefacts, it could accelerate the
prototyping of creative artefacts and reduce the cost of hiring human
participants to rate creative artefacts.


  The paper previously submitted under this title is incorrect in that it
drastically overestimates the cumulative deflection due to a gravitational wave
(GW) background. Avi Loeb gives a simple argument that there can be no
$(D\omega)^{1/2}$ enhancement: since the problem is linear in $h$, one can
decompose the GWs into plane waves and for each of these there is no
enhancement.


  In early phase drug development of combination therapy, the primary objective
is to preliminarily assess whether there is additive activity when a novel
agent combined with an established monotherapy. Due to potential feasibility
issues with a large randomized study, uncontrolled single-arm trials have been
the mainstream approach in cancer clinical trials. However, such trials often
present significant challenges in deciding whether to proceed to the next phase
of development. A hybrid design, leveraging data from a completed historical
clinical study of the monotherapy, offers a valuable option to enhance study
efficiency and improve informed decision-making. Compared to traditional
single-arm designs, the hybrid design may significantly enhance power by
borrowing external information, enabling a more robust assessment of activity.
The primary challenge of hybrid design lies in handling information borrowing.
We introduce a Bayesian dynamic power prior (DPP) framework with three
components of controlling amount of dynamic borrowing. The framework offers
flexible study design options with explicit interpretation of borrowing,
allowing customization according to specific needs. Furthermore, the posterior
distribution in the proposed framework has a closed form, offering significant
advantages in computational efficiency. The proposed framework's utility is
demonstrated through simulations and a case study.


  We use null hypersurface techniques in a new approach to calculate the
retarded waveform from a binary black hole merger in the close approximation.
The process of removing ingoing radiation from the system leads to two notable
features in the shape of the close approximation waveform for a head-on
collision of black holes: (i) an initial quasinormal ringup and (ii) weak
sensitivity to the parameter controlling the collision velocity. Feature (ii)
is unexpected and has the potential importance of enabling the design of an
efficient template for extracting the gravitational wave signal from the noise.


  Consider a scenario where Alice wishes to send a message $m$ to Bob in a
time-slotted wireless network. However, there exists an adversary, Carol, who
aims to prevent the transmission of $m$ by jamming the communication channel.
There is a per-slot cost of $1$ to send, receive or jam $m$ on the channel, and
we are interested in how much Alice and Bob need to spend relative to Carol in
order to guarantee communication.
  Our approach is to design an algorithm in the framework of
resource-competitive analysis where the cost to correct network devices (i.e.,
Alice and Bob) is parameterized by the cost to faulty devices (i.e., Carol). We
present an algorithm that guarantees the successful transmission of $m$ and has
the following property: if Carol incurs a cost of $T$ to jam, then both Alice
and Bob have a cost of $O(T^{\varphi - 1} + 1)=O(T^{.62}+1)$ in expectation,
where $\varphi = (1+ \sqrt{5})/2$ is the golden ratio. In other words, it
possible for Alice and Bob to communicate while incurring asymptotically less
cost than Carol. We generalize to the case where Alice wishes to send $m$ to
$n$ receivers, and we achieve a similar result.
  Our findings hold even if (1) $T$ is unknown to either party; (2) Carol knows
the algorithms of both parties, but not their random bits; (3) Carol can jam
using knowledge of past actions of both parties; and (4) Carol can jam
reactively, so long as there is sufficient network traffic in addition to $m$.


  We characterize the photometric and kinematic properties of simulated
early-type galaxy (ETG) stellar halos, and compare them to observations. We
select a sample of ~1200 ETGs in the TNG100 and TNG50 simulations, spanning a
stellar mass range of $10^{10.3}-10^{12}M_{\odot}$ and within the range of
(g-r) colour and lambda-ellipticity diagram populated by observed ETGs. We
determine photometric parameters, intrinsic shapes, and kinematic observables
in their extended stellar halos. We study the variation in kinematics from
center to halo and connect it to a change in the intrinsic shape of the
galaxies. We find that the simulated galaxy sample reproduces the diversity of
kinematic properties observed in ETG halos. Simulated fast rotators (FRs)
divide almost evenly in one third having flat lambda profiles and high halo
rotational support, a third with gently decreasing profiles, and another third
with low halo rotation. Slow rotators (SRs) tend to have increased rotation in
the outskirts, with half of them exceeding lambda=0.2. For
$M_{*}>10^{11.5}M_{\odot}$ halo rotation is unimportant. A similar variety of
properties is found for the stellar halo intrinsic shapes. Rotational support
and shape are deeply related: the kinematic transition to lower rotational
support is accompanied by a change towards rounder intrinsic shape. Triaxiality
in the halos of FRs increases outwards and with stellar mass. Simulated SRs
have relatively constant triaxiality profiles. Simulated stellar halos show a
large variety of structural properties, with quantitative but no clear
qualitative differences between FRs and SRs. At the same stellar mass, stellar
halo properties show a gradual transition and significant overlap between the
two families, despite the clear bimodality in the central regions. This is in
agreement with observations of extended photometry and kinematics. [abridged]


  What sets A \subset Z^n can be written in the form (K-K) \cap Z^n, where K is
a compact subset of R^n such that K+Z^n=R^n? Such sets A are called achievable,
and it is known that if A is achievable, then < A >=Z^n. This condition
completely characterizes achievable sets for n=1, but not much is known for n
\ge 2. We attempt to characterize achievable sets further by showing that with
any finite, symmetric set A \subset Z^n containing zero, we may associate a
graph G(A). Then if A is achievable, we show the set associated to some
connected component of G(A) is achievable. In two dimensions, we can strengthen
this theorem further. Further generalizations and open questions are discussed.
Throughout, the language and formalism of algebraic topology are useful.


  Food choices are personal and complex and have a significant impact on our
long-term health and quality of life. By helping users to make informed and
satisfying decisions, Recommender Systems (RS) have the potential to support
users in making healthier food choices. Intelligent users-modeling is a key
challenge in achieving this potential. This paper investigates Ensemble Topic
Modelling (EnsTM) based Feature Identification techniques for efficient
user-modeling and recipe recommendation. It builds on findings in EnsTM to
propose a reduced data representation format and a smart user-modeling strategy
that makes capturing user-preference fast, efficient and interactive. This
approach enables personalization, even in a cold-start scenario. This paper
proposes two different EnsTM based and one Hybrid EnsTM based recommenders. We
compared all three EnsTM based variations through a user study with 48
participants, using a large-scale,real-world corpus of 230,876 recipes, and
compare against a conventional Content Based (CB) approach. EnsTM based
recommenders performed significantly better than the CB approach. Besides
acknowledging multi-domain contents such as taste, demographics and cost, our
proposed approach also considers user's nutritional preference and assists them
finding recipes under diverse nutritional categories. Furthermore, it provides
excellent coverage and enables implicit understanding of user's food practices.
Subsequent analysis also exposed correlation between certain features and a
healthier lifestyle.


  We mainly study exceptional configuration for coined quantum walk search. For
searching on a two-dimensional grid by AKR algorithm, we find some new classes
of exceptional configurations that cannot be found by the AKR algorithm
effectively and the known diagonal configuration can be regarded as its special
case. Meanwhile, we give two modified quantum walk models that can improve the
success probability in the exceptional configurations by numerical simulation.
Furthermore, we introduce the concept of generalized exceptional configuration
and consider search by quantum walk on a cycle with Grover coin. We find that
the most natural coin combination model (G,-), where G is a Grover diffusion
transformation, is a generalized exceptional configuration when just searching
one marked vertex on the cycle. In the end, we find generalized exceptional
configuration has a different evolution of quantum coherence from exceptional
configuration. These extend largely the range of exceptional configuration of
quantum walk search in some sense.


  We consider the setting of online linear regression for arbitrary
deterministic sequences, with the square loss. We are interested in the aim set
by Bartlett et al. (2015): obtain regret bounds that hold uniformly over all
competitor vectors. When the feature sequence is known at the beginning of the
game, they provided closed-form regret bounds of $2d B^2 \ln T +
\mathcal{O}_T(1)$, where $T$ is the number of rounds and $B$ is a bound on the
observations. Instead, we derive bounds with an optimal constant of $1$ in
front of the $d B^2 \ln T$ term. In the case of sequentially revealed features,
we also derive an asymptotic regret bound of $d B^2 \ln T$ for any individual
sequence of features and bounded observations. All our algorithms are variants
of the online non-linear ridge regression forecaster, either with a
data-dependent regularization or with almost no regularization.


  We describe generators and defining relations for the commutator subgroup of
topological full groups of minimal subshifts. We show that the word problem in
a topological full group is solvable if and only if the language of the
underlying subshift is recursive.


  In this paper, we study streaming and online algorithms in the context of
randomness in the input. For several problems, a random order of the input
sequence---as opposed to the worst-case order---appears to be a necessary evil
in order to prove satisfying guarantees. However, algorithmic techniques that
work under this assumption tend to be vulnerable to even small changes in the
distribution. For this reason, we propose a new \emph{adversarial injections}
model, in which the input is ordered randomly, but an adversary may inject
misleading elements at arbitrary positions. We believe that studying algorithms
under this much weaker assumption can lead to new insights and, in particular,
more robust algorithms. We investigate two classical combinatorial-optimization
problems in this model: Maximum matching and cardinality constrained monotone
submodular function maximization. Our main technical contribution is a novel
streaming algorithm for the latter that computes a $0.55$-approximation. While
the algorithm itself is clean and simple, an involved analysis shows that it
emulates a subdivision of the input stream which can be used to greatly limit
the power of the adversary.


  Escalator-related injuries threaten public health with the widespread use of
escalators. The existing studies tend to focus on after-the-fact statistics,
reflecting on the original design and use of defects to reduce the impact of
escalator-related injuries, but few attention has been paid to ongoing and
impending injuries. In this study, a multi-module escalator safety monitoring
system based on computer vision is designed and proposed to simultaneously
monitor and deal with three major injury triggers, including losing balance,
not holding on to handrails and carrying large items. The escalator
identification module is utilized to determine the escalator region, namely the
region of interest. The passenger monitoring module is leveraged to estimate
the passengers' pose to recognize unsafe behaviors on the escalator. The
dangerous object detection module detects large items that may enter the
escalator and raises alarms. The processing results of the above three modules
are summarized in the safety assessment module as the basis for the intelligent
decision of the system. The experimental results demonstrate that the proposed
system has good performance and great application potential.


  We propose four finite-length scaling laws to predict the frame error rate
(FER) performance of spatially-coupled low-density parity-check codes under
full belief propagation (BP) decoding with a limit on the number of decoding
iterations and a scaling law for sliding window decoding, also with limited
iterations. The laws for full BP decoding provide a choice between accuracy and
computational complexity; a good balance between them is achieved by the law
that models the number of decoded bits after a certain number of BP iterations
by a time-integrated Ornstein-Uhlenbeck process. This framework is developed
further to model sliding window decoding as a race between the integrated
Ornstein-Uhlenbeck process and an absorbing barrier that corresponds to the
left boundary of the sliding window. The proposed scaling laws yield accurate
FER predictions.


  We demonstrate that graphite phonon dispersions have two Kohn anomalies at
the Gamma-E_2g and K-A'1 modes. The anomalies are revealed by two sharp kinks.
By an exact analytic derivation, we show that the slope of these kinks is
proportional to the square of the electron-phonon coupling (EPC). Thus, we can
directly measure the EPC from the experimental dispersions. The Gamma-E_2g and
K-A'1 EPCs are particularly large, whilst they are negligible for all the other
modes at Gamma and K.


  The eXTP (enhanced X-ray Timing and Polarimetry) mission is a major project
of the Chinese Academy of Sciences (CAS) and China National Space
Administration (CNSA) currently performing an extended phase A study and
proposed for a launch by 2025 in a low-earth orbit. The eXTP scientific payload
envisages a suite of instruments (Spectroscopy Focusing Array, Polarimetry
Focusing Array, Large Area Detector and Wide Field Monitor) offering
unprecedented simultaneous wide-band X-ray timing and polarimetry sensitivity.
A large European consortium is contributing to the eXTP study and it is
expected to provide key hardware elements, including a Wide Field Monitor
(WFM). The WFM instrument for eXTP is based on the design originally proposed
for the LOFT mission within the ESA context. The eXTP/WFM envisages a wide
field X-ray monitor system in the 2-50 keV energy range, achieved through the
technology of the large-area Silicon Drift Detectors. The WFM will consist of 3
pairs of coded mask cameras with a total combined Field of View (FoV) of 90x180
degrees at zero response and a source localization accuracy of ~1 arcmin. In
this paper we provide an overview of the WFM instrument design, including new
elements with respect to the earlier LOFT configuration, and anticipated
performance.


  Introducing interpretability and reasoning into Multiple Instance Learning
(MIL) methods for Whole Slide Image (WSI) analysis is challenging, given the
complexity of gigapixel slides. Traditionally, MIL interpretability is limited
to identifying salient regions deemed pertinent for downstream tasks, offering
little insight to the end-user (pathologist) regarding the rationale behind
these selections. To address this, we propose Self-Interpretable MIL (SI-MIL),
a method intrinsically designed for interpretability from the very outset.
SI-MIL employs a deep MIL framework to guide an interpretable branch grounded
on handcrafted pathological features, facilitating linear predictions. Beyond
identifying salient regions, SI-MIL uniquely provides feature-level
interpretations rooted in pathological insights for WSIs. Notably, SI-MIL, with
its linear prediction constraints, challenges the prevalent myth of an
inevitable trade-off between model interpretability and performance,
demonstrating competitive results compared to state-of-the-art methods on
WSI-level prediction tasks across three cancer types. In addition, we
thoroughly benchmark the local and global-interpretability of SI-MIL in terms
of statistical analysis, a domain expert study, and desiderata of
interpretability, namely, user-friendliness and faithfulness.


  In this paper we give general definitions of non-commutative jets in the
local and global situation using square zero extensions and derivations. We
study the functors Exank(A, I) where A is any k-algebra and I is any left and
right A-module and use this to relate affine non-commutative jets to liftings
of modules. We also study the Kodaira-Spencer class KS(L) and relate it to the
Atiyah class.


  We examine the results of the paper "Precision metrology using weak
measurements", [Zhang, Datta, and Walmsley, arXiv:1310.5302] from a quantum
state discrimination point of view. The Heisenberg scaling of the photon number
for the precision of the interaction parameter between coherent light and a
spin one-half particle (or pseudo-spin) has a simple interpretation in terms of
the interaction rotating the quantum state to an orthogonal one. In order to
achieve this scaling, the information must be extracted from the spin rather
than from the coherent state of light, limiting the applications of the method
to phenomena such as cross-phase modulation. We next investigate the effect of
dephasing noise, and show a rapid degradation of precision, in agreement with
general results in the literature concerning Heisenberg scaling metrology. We
also demonstrate that a von Neumann-type measurement interaction can display a
similar effect.


  We realize the logarithm of the third smallest known Salem number as the
topological entropy of a K3 surface automorphism with a Siegel disk and a
pointwisely fixed curve at the same time. We also show the logarithm of the
Lehmer number, the smallest known Salem number, is not realizable as the
topological entropy of any Enriques surface automorphism. These results are
entirely inspired by McMullen's works and Mathematica programs.


  On the basis of the quasiclassical theory of superconductivity, we obtain a
formula for the local density of states (LDOS) around a vortex core of
superconductors with anisotropic pair-potential and Fermi surface in arbitrary
directions of magnetic fields. Earlier results on the LDOS of d-wave
superconductors and NbSe$_2$ are naturally interpreted within our theory
geometrically; the region with high intensity of the LDOS observed in numerical
calculations turns out to the enveloping curve of the trajectory of Andreev
bound states. We discuss experimental results on YNi$_2$B$_2$C within the
quasiclassical theory of superconductivity.


  Local clustering aims to identify a cluster within a given graph that
includes a designated seed node or a significant portion of a group of seed
nodes. This cluster should be well-characterized, i.e., it has a high number of
internal edges and a low number of external edges. In this work, we propose
SOCIAL, a novel algorithm for local motif clustering which optimizes for motif
conductance based on a local hypergraph model representation of the problem and
an adapted version of the max-flow quotient-cut improvement algorithm (MQI). In
our experiments with the triangle motif, SOCIAL produces local clusters with an
average motif conductance lower than the state-of-the-art, while being up to
multiple orders of magnitude faster.


  We investigate the formation of primordial black holes (PBHs) through delayed
vacuum decay during slow cosmic first-order phase transitions. Two specific
models, the polynomial potential and the real singlet extension of the Standard
Model, are used as illustrative examples. Our findings reveal that models with
zero-temperature scalar potential barriers are conducive to the realization of
this mechanism, as the phase transition duration is extended by the U-shaped
Euclidean action. We find that the resulting PBH density is highly sensitive to
the barrier height, with abundant PBH formation observed for sufficiently high
barriers. Notably, the phase transition needs not to be ultra-supercooled (i.e.
the parameter $\alpha\gg1$), and the commonly used exponential nucleation
approximation $\Gamma(t)\sim e^{\beta t}$ fails to capture the PBH formation
dynamics in such models.


  Graphene nanoribbons (GNRs) are a family of one-dimensional (1D) materials
carved from graphene lattice. GNRs possess high mobility and current carrying
capability, sizable bandgap, and versatile electronic properties tailored by
the orientations and open edge structures. These unique properties make GNRs
promising candidates for prospective electronics applications including
nano-sized field-effect transistors (FETs), spintronic devices, and quantum
information processing. To fully exploit the potential of GNRs, fundamental
understanding of structure-property relationship, precise control of atomic
structures and scalable production are the main challenges. In the last several
years, significant progress has been made toward atomically precise bottom-up
synthesis of GNRs and heterojunctions that provide an ideal platform for
functional molecular devices, as well as successful production of
semiconducting GNR arrays on insulating substrates potentially useful for
large-scale digital circuits. With further development, GNRs can be envisioned
as a competitive candidate material in future quantum information sciences
(QIS). In this Perspective, we review recent progress in GNR research and
identify key challenges and new directions likely to develop in the near
future.


  Large scale numerical simulations are used to study the elastic dynamics of
two-dimensional vortex lattices driven on a disordered medium in the case of
weak disorder. We investigate the so-called elastic depinning transition by
decreasing the driving force from the elastic dynamical regime to the state
pinned by the quenched disorder. Similarly to the plastic depinning transition,
we find results compatible with a second order phase transition, although both
depinning transitions are very different from many viewpoints. We evaluate
three critical exponents of the elastic depinning transition. $\beta = 0.29 \pm
0.03$ is found for the velocity exponent at zero temperature, and from the
velocity-temperature curves we extract the critical exponent $\delta^{-1} =
0.28 \pm 0.05$. Furthermore, in contrast with charge-density waves, a
finite-size scaling analysis suggests the existence of a unique diverging
length at the depinning threshold with an exponent $\nu= 1.04 \pm 0.04$, which
controls the critical force distribution, the finite-size crossover force
distribution and the intrinsic correlation length. Finally, a scaling relation
is found between velocity and temperature with the $\beta$ and $\delta$
critical exponents both independent with regard to pinning strength and
disorder realizations.


  We set up a general framework for enriching a subcategory of the category of
noncommutative sets over a category C using products of the objects of a
non-\Sigma operad P in \C. By viewing the simplicial category as a subcategory
of the category of noncommutative sets in two different ways, we obtain two
generalizations of simplicial objects. For the operad given by the Stasheff
associahedra we obtain a model for the 2-sided bar construction in the first
case and the cyclic bar and cobar construction in the second case. Using either
the associahedra or the cyclohedra in place of the geometric simplices we can
define the geometric realization of these objects.


  Recent work of Jonathan Campbell and Inna Zakharevich has focused on building
machinery for studying scissors congruence problems via algebraic $K$-theory,
and applying these tools to studying the Grothendieck ring of varieties. In
this paper we give a new application of their framework: we construct a
$K$-space that recovers the classical $\mathrm{SK}$ ("schneiden und kleben,"
German for "cut and paste") groups for manifolds on $\pi_0$, and we construct a
derived version of the Euler characteristic.


  One fundamental problem in temporal graph analysis is to count the
occurrences of small connected subgraph patterns (i.e., motifs), which benefits
a broad range of real-world applications, such as anomaly detection, structure
prediction, and network representation learning. However, existing works
focused on exacting temporal motif are not scalable to large-scale temporal
graph data, due to their heavy computational costs or inherent inadequacy of
parallelism. In this work, we propose a scalable parallel framework for exactly
counting temporal motifs in large-scale temporal graphs. We first categorize
the temporal motifs based on their distinct properties, and then design
customized algorithms that offer efficient strategies to exactly count the
motif instances of each category. Moreover, our compact data structures, namely
triple and quadruple counters, enable our algorithms to directly identify the
temporal motif instances of each category, according to edge information and
the relationship between edges, therefore significantly improving the counting
efficiency. Based on the proposed counting algorithms, we design a hierarchical
parallel framework that features both inter- and intra-node parallel
strategies, and fully leverages the multi-threading capacity of modern CPU to
concurrently count all temporal motifs. Extensive experiments on sixteen
real-world temporal graph datasets demonstrate the superiority and capability
of our proposed framework for temporal motif counting, achieving up to 538*
speedup compared to the state-of-the-art methods. The source code of our method
is available at: https://github.com/steven-ccq/FAST-temporal-motif.


  The formation of supermassive black holes through the gravitational collapse
of supermassive objects ($M \ga 10^4 M_\odot$) has been proposed as a source of
cosmological gamma-ray bursts. The major advantage of this model is that such
collapses are far more energetic than stellar-remnant mergers. The major
drawback of this idea is the severe baryon loading problem in one-dimensional
models. We can show that the observed log N - log P (number vs. peak flux)
distribution for gamma-ray bursts in the BATSE database is not inconsistent
with an identification of supermassive object collapse as the origin of the
gamma-ray bursts. This conclusion is valid for a range of plausible
cosmological and gamma-ray burst spectral parameters.


  Active Learning (AL) techniques aim to minimize the training data required to
train a model for a given task. Pool-based AL techniques start with a small
initial labeled pool and then iteratively pick batches of the most informative
samples for labeling. Generally, the initial pool is sampled randomly and
labeled to seed the AL iterations. While recent studies have focused on
evaluating the robustness of various query functions in AL, little to no
attention has been given to the design of the initial labeled pool for deep
active learning. Given the recent successes of learning representations in
self-supervised/unsupervised ways, we study if an intelligently sampled initial
labeled pool can improve deep AL performance. We investigate the effect of
intelligently sampled initial labeled pools, including the use of
self-supervised and unsupervised strategies, on deep AL methods. The setup,
hypotheses, methodology, and implementation details were evaluated by peer
review before experiments were conducted. Experimental results could not
conclusively prove that intelligently sampled initial pools are better for AL
than random initial pools in the long run, although a Variational
Autoencoder-based initial pool sampling strategy showed interesting trends that
merit deeper investigation.


  We present initial results of a project to measure mean longitudinal magnetic
fields in a group of sdB/OB/O stars. The project was inspired by the discovery
of three super-metal-rich sdOB stars, each having metals (e.g. Ti, V) enhanced
by factors of 10^3 to 10^5. Similar behaviour is observed in chemically
peculiar A stars, where strong magnetic fields are responsible for the
enrichment. With this in mind, we obtained circularly polarised spectra of two
of the super-metal-rich sdOBs, two "normal" sdBs and two sdOs using FORS1 on
the ESO/VLT. By examining circular polarisation in the hydrogen Balmer lines
and in helium lines, we have detected magnetic fields with strengths of 1-2 kG
in most of our targets. This suggests that such fields are relatively common in
hot subdwarfs.


  In this article we derive the geodesic equations in the $\text{U(1)}^2$
dyonic rotating black hole spacetime. We present their solutions in terms of
the Kleinian $\sigma$-function and in special cases in terms of the
Weierstra{\ss} $\wp$-, $\sigma$- and $\zeta$-functions. To give a list of all
possible orbits, we analyse the geodesic motion of test particles and light
using parametric diagrams and effective potentials.


  We state and prove a version of Dyson's Lemma for a product of smooth
projective varieties of arbitrary dimension using positivity methods.


  We present our analyses of 15 months of Kepler data on KIC 10139564. We
detected 57 periodicities with a variety of properties not previously observed
all together in one pulsating subdwarf B star. Ten of the periodicities were
found in the low-frequency region, and we associate them with nonradial
g-modes. The other periodicities were found in the high-frequency region, which
are likely p-modes. We discovered that most of the periodicities are components
of multiplets with a common spacing. Assuming that multiplets are caused by
rotation, we derive a rotation period of 25.6(1.8) days. The multiplets also
allow us to identify the pulsations to an unprecedented extent for this class
of pulsator. We also detect l<=2 multiplets, which are sensitive to the
pulsation inclination and can constrain limb darkening via geometric
cancellation factors. While most periodicities are stable, we detected several
regions that show complex patterns. Detailed analyses showed these regions are
complicated by several factors. Two are combination frequencies that originate
in the superNyquist region and were found to be reflected below the Nyquist
frequency. The Fourier peaks are clear in the superNyquist region, but the
orbital motion of Kepler smears the Nyquist frequency in the barycentric
reference frame and this effect is passed on to the subNyquist reflections.
Others are likely multiplets but unstable in amplitudes and/or frequencies. The
density of periodicities also make KIC 10139564 challenging to explain using
published models. This menagerie of properties should provide tight constraints
on structural models, making this subdwarf B star the most promising for
applying asteroseismology.


  In this paper we introduce the notion of weak non-asssociative Doi-Hopf
module and give the Fundamental Theorem of Hopf modules in this setting. Also
we prove that there exists a categorical equivalence that admits as particular
instances the ones constructed in the literature for Hopf algebras, weak Hopf
algebras, Hopf quasigroups, and weak Hopf quasigroups.


  We describe a Hodge theoretic approach to the question: In what ways can a
smooth projective variety degenerate?


  Substreams refer to the streams of each user in a system. Substream
weighting, where the weights determine the prioritization order, can be
important in multiple-input multiple-output interference channels. In this
letter, a distributed algorithm is proposed for the problem of power
minimization subject to weighted SINR constraint. The algorithm is based on two
basic features, the well known distributed power control algorithm by Yates in
1995 and a simple linear search to find feasible SINR targets. The power
control law used in the proposed algorithm is proven to linearly converge to a
unique fixed-point.


  We study the geometry of the cuspidal edge $M$ in $\mathbb R^3$ derived from
its contact with planes and lines (referred to as flat geometry). The contact
of $M$ with planes is measured by the singularities of the height functions on
$M$. We classify submersions on a model of $M$ by diffeomorphisms and recover
the contact of $M$ with planes from that classification. The contact of $M$
with lines is measured by the singularities of orthogonal projections of $M$.
We list the generic singularities of the projections and obtain the generic
deformations of the apparent contour (profile) when the direction of projection
varies locally in $S^2$. We also relate the singularities of the height
functions and of the projections to some geometric invariants of the cuspidal
edge.


  We present an improved calculation of higher-order corrections to the
one-loop self energy of 2P states in hydrogen-like systems with small nuclear
charge Z. The method is based on a division of the integration with respect to
the photon energy into a high- and a low-energy part. The high-energy part is
calculated by an expansion of the electron propagator in powers of the Coulomb
field. The low-energy part is simplified by the application of a
Foldy-Wouthuysen transformation. This transformation leads to a clear
separation of the leading contribution from the relativistic corrections and
removes higher order terms. The method is applied to the 2P_{1/2} and 2P_{3/2}
states in atomic hydrogen. The results lead to new theoretical values for the
Lamb shifts and the fine structure splitting.


  We have been developing the monolithic active pixel detector "XRPIX" onboard
the future X-ray astronomical satellite "FORCE". XRPIX is composed of CMOS
pixel circuits, SiO2 insulator, and Si sensor by utilizing the
silicon-on-insulator (SOI) technology. When the semiconductor detector is
operated in orbit, it suffers from radiation damage due to X-rays emitted from
the celestial objects as well as cosmic rays. From previous studies, positive
charges trapped in the SiO2 insulator are known to cause the degradation of the
detector performance. To improve the radiation hardness, we developed XRPIX
equipped with Double-SOI (D-SOI) structure, introducing an additional silicon
layer in the SiO2 insulator. This structure is aimed at compensating for the
effect of the trapped positive charges. Although the radiation hardness to
cosmic rays of the D-SOI detectors has been evaluated, the radiation effect due
to the X-ray irradiation has not been evaluated. Then, we conduct an X-ray
irradiation experiment using an X-ray generator with a total dose of 10 krad at
the SiO2 insulator, equivalent to 7 years in orbit. As a result of this
experiment, the energy resolution in full-width half maximum for the 5.9 keV
X-ray degrades by 17.8 $\pm$ 2.8% and the dark current increases by 89 $\pm$
13%. We also investigate the physical mechanism of the increase in the dark
current due to X-ray irradiation using TCAD simulation. It is found that the
increase in the dark current can be explained by the increase in the interface
state density at the Si/SiO2 interface.


  This paper is a survey about cylinders in Fano varieties and related
problems.


  Recent findings in neuroscience suggest that the human brain represents
information in a geometric structure (for instance, through conceptual spaces).
In order to communicate, we flatten the complex representation of entities and
their attributes into a single word or a sentence. In this paper we use graph
convolutional networks to support the evolution of language and cooperation in
multi-agent systems. Motivated by an image-based referential game, we propose a
graph referential game with varying degrees of complexity, and we provide
strong baseline models that exhibit desirable properties in terms of language
emergence and cooperation. We show that the emerged communication protocol is
robust, that the agents uncover the true factors of variation in the game, and
that they learn to generalize beyond the samples encountered during training.


  Multi-peaked features appear on the integrated pulse profiles of fast radio
burst observed below 2.5 GHz and the instantaneous spectrum of many bursts
observed between 4 and 8 GHz. The mechanism of pulse or spectrum shaping has
attracted little attention. Here we show that these interference-like pulse
profiles are mostly the instantaneous spectra near the source regions of fast
radio bursts. The corresponding instantaneous spectra are coincident to the
spectrum from a single electron passing through a tapered undulator. The
multi-peaked spectrum observed between 4 and 8 GHz can also be explained
consistently by this type of spectrum. The spectrum is invisible unless the
particles in the radiation beam are bunched. The bunching effect is probably
due to the acceleration of particles in the plasma wakefield.


  Uncontrolled growth of blockchain state can adversely affect client
performance, decentralization and security. Previous attempts to introduce
duration-based state storage pricing or 'storage rent' in Ethereum have
stalled, partly because of complexity. We present a new approach with finer
granularity to "spread" rent payments across peers. Our proposal shifts the
burden of state rent from accounts to transaction senders in a quasi-random
manner. This proposal offers a simple path for initial adoption on Ethereum
Virtual Machine (EVM) compatible chains, and serve as a foundation to address
remaining challenges.


  The COVID-19 pandemic so far has caused huge negative impacts on different
areas all over the world, and the United States (US) is one of the most
affected countries. In this paper, we use methods from the functional data
analysis to look into the COVID-19 data in the US. We explore the modes of
variation of the data through a functional principal component analysis (FPCA),
and study the canonical correlation between confirmed and death cases. In
addition, we run a cluster analysis at the state level so as to investigate the
relation between geographical locations and the clustering structure. Lastly,
we consider a functional time series model fitted to the cumulative confirmed
cases in the US, and make forecasts based on the dynamic FPCA. Both point and
interval forecasts are provided, and the methods for assessing the accuracy of
the forecasts are also included.


  We review basic properties of the Nakayama functor for coalgebras and
introduce a number of applications to tensor categories. We also give
equivalent conditions for a coquasi-bialgebra with preantipode to admit a
non-zero cointegral.


  Emotion Recognition in Conversations (ERC) is an important and active
research area. Recent work has shown the benefits of using multiple modalities
(e.g., text, audio, and video) for the ERC task. In a conversation,
participants tend to maintain a particular emotional state unless some stimuli
evokes a change. There is a continuous ebb and flow of emotions in a
conversation. Inspired by this observation, we propose a multimodal ERC model
and augment it with an emotion-shift component that improves performance. The
proposed emotion-shift component is modular and can be added to any existing
multimodal ERC model (with a few modifications). We experiment with different
variants of the model, and results show that the inclusion of emotion shift
signal helps the model to outperform existing models for ERC on MOSEI and
IEMOCAP datasets.


  The $z$~0.1 type-2 QSO J1430+1339 (the 'Teacup') is a complex galaxy showing
a loop of ionised gas ~10 kpc in diameter, co-spatial radio bubbles, a compact
(~1 kpc) jet, and outflow activity. We used VLT/MUSE optical integral field
spectroscopic observations to characterise the properties and effects of the
galactic ionised outflow from kpc up to tens of kpc scales and compare them
with those of the radio jet. We detect a velocity dispersion enhancement (>300
km/s) elongated over several kpc perpendicular to the radio jet, the AGN
ionisation lobes, and the fast outflow, similar to what is found in other
galaxies hosting compact, low-power jets, indicating that the jet strongly
perturbs the host ISM. The mass outflow rate decreases with distance from the
nucleus, from around 100 $M_\odot$/yr in the inner 1-2 kpc to <0.1 $M_\odot$/yr
at 30 kpc. The ionised mass outflow rate is ~1-8 times higher than the
molecular one, in contrast with what is often quoted in AGN. The driver of the
multi-phase outflow is likely a combination of AGN radiation and the jet. The
outflow mass-loading factor (~5-10) and the molecular gas depletion time
(<10$^8$ yr) indicate that the outflow can significantly affect the star
formation and the gas reservoir in the galaxy. However, the fraction of the
ionised outflow that is able to escape the dark matter halo potential is likely
negligible. We detect blue-coloured continuum emission co-spatial with the
ionised gas loop. Here, stellar populations are younger (<100-150 Myr) than in
the rest of the galaxy (~0.5-1 Gyr). This constitutes possible evidence for
star formation triggered at the edge of the bubble due to the compressing
action of the jet and outflow ('positive feedback'), as predicted by theory.
All in all, the Teacup constitutes a rich system in which AGN feedback from
outflows and jets, in both its negative and positive flavours, co-exist.


  We consider the Neumann problem for the equation $u_{xx}+\lambda f(u)=0$ in
the punctured interval $(-1,1) \setminus \{0\}$, where $\lambda>0$ is a
bifurcation parameter and $f(u)=u-u^3$. At $x=0$, we impose the conditions
$u(-0)+au_x(-0)=u(+0)-au_x(+0)$ and $u_x(-0)=u_x(+0)$ for a constant $a>0$ (the
symbols $+0$ and $-0$ stand for one-sided limits). The problem appears as a
limiting equation for a semilinear elliptic equation in a higher dimensional
domain shrinking to the interval $(-1,1)$. First we prove that odd solutions
and even solutions form families of branches $\{ \mathcal{C}^o_k\}_{k \in
\mathbb{N}}$ and $\{ \mathcal{C}^e_k\}_{k \in \mathbb{N}}$, respectively. Both
$\mathcal{C}^o_k$ and $\mathcal{C}^e_k$ bifurcate from the trivial solution
$u=0$. We then show that $\mathcal{C}^e_k$ contains no other bifurcation point,
while $\mathcal{C}^o_k$ contains two points where secondary bifurcations occur.
Finally we determine the Morse index of solutions on the branches. General
conditions on $f(u)$ for the same assertions to hold are also given.


  We prove comparison results for the Isoperimetric profile function in the
setting of manifolds with integral bounds on the Ricci curvature. We extend
previous work of Ni and Wang and Bayle and Rosales under the usual pointwise
bounds for the Ricci curvature.


  In condensed matter systems, the atoms, electrons or spins can sometimes
arrange themselves in ways that result in unexpected properties but that cannot
be detected by conventional experimental probes. Several historical and
contemporary examples of such hidden orders are known and more are awaiting
discovery, perhaps in the form of more complex composite, entangled or
dynamical hidden orders.


  Quantum information with many-body quantum spin systems has, from time to
time, given intriguing and intuitive outcomes to our understanding of multiport
quantum communications. We identify that in an anisotropic many-body quantum
spin system with two- and three-body interactions, when its two-spin subsystems
are all negative under partial transpose, one can restrict this system for
realizing only the multiport quantum dense coding protocol which has $(N-1)$
senders and a single receiver. All other single and multi channel dense coding
protocols will have quantum dense coding capacities less than that of their
respective classical capacities. We characterize the multiport quantum dense
coding capacity with $(N-1)$ senders and a single receiver for this system with
respect to its system parameters. We also define a magnetic field averaged
dense coding capacity for this system, which allows us to comprehensively
capture the influence of the entire range of external applied magnetic field
and characterize its variation with respect to other system parameters.


  Glassy matter like crystals resists change in shape. Therefore a theory for
their continuous melting should show how the shear elastic constant $\mu$ goes
to zero. Since viscosity is the long wave-length low frequency limit of shear
correlations, the same theory should give phenomena like the Volger-Fulcher
dependence of the viscosity on temperature near the transition. A continuum
model interrupted randomly by asymmetric rigid defects with orientational
degrees of freedom is considered. Such defects are orthogonal to the continuum
excitations, and are required to be imprisoned by rotational motion of the
nearby atoms of the continuum. The defects interact with an angle dependent
$\mu/r^3$ potential. A renormalization group for the elastic constants, and the
fugacity of the defects in 3D is constructed. The principal results are that
there is a scale-invariant reduction of $\mu$ as a function of length at any
temperature $T < T_0$, above which it is 0 macrosopically but has a finite
correlation length $\xi(T)$ which diverges as $T \to T_0$. Viscosity is shown
to be proportional to $\xi^2(T)$ and has the Vogel-Fulcher form. The specific
heat is $\propto \xi^{-3}(T)$. As $T \to T_0$, the Kauzman temperature from
above, the configuration entropy of the liquid is exhausted. The theory also
gives the ``fragility" of glasses in terms of their $T_0/\mu$.


  Louisiana State University Center for Advanced Microstructures and Devices
(CAMD) began a control system upgrade project in early 1997. At the time, the
storage ring was controlled by a VAX/VMS system, primarily using CAMAC for I/O.
The injector Linac was controlled by a separate VME/OS/9 system using custom
I/O components. The storage ring control system has been replaced with a
PC/Linux based system, utilizing the existing CAMAC subsystem [1]. In an effort
to both migrate channels away from CAMAC, and integrate the Linac controls with
the storage ring controls, a design for upgrades utilizing AutomationDirect.com
PLCs was presented [2]. This paper will discuss the detailed design for the
Linac PLC based control system, and discuss the status of PLC upgrades for the
Vacuum system, Kicker controls, 2nd RF system, and utilities monitoring.


  We use infinite dimensional self-dual $\mathrm{CAR}$ $C^{*}$-algebras to
study a $\mathbb{Z}_{2}$-index, which classifies free-fermion systems embedded
on $\mathbb{Z}^{d}$ disordered lattices. Combes-Thomas estimates are pivotal to
show that the $\mathbb{Z}_{2}$-index is uniform with respect to the size of the
system. We additionally deal with the set of ground states to completely
describe the mathematical structure of the underlying system. Furthermore, the
weak$^{*}$-topology of the set of linear functionals is used to analyze paths
connecting different sets of ground states.


  In the paper, we study a class of useful minimax problems on Riemanian
manifolds and propose a class of effective Riemanian gradient-based methods to
solve these minimax problems. Specifically, we propose an effective Riemannian
gradient descent ascent (RGDA) algorithm for the deterministic minimax
optimization. Moreover, we prove that our RGDA has a sample complexity of
$O(\kappa^2\epsilon^{-2})$ for finding an $\epsilon$-stationary solution of the
Geodesically-Nonconvex Strongly-Concave (GNSC) minimax problems, where $\kappa$
denotes the condition number. At the same time, we present an effective
Riemannian stochastic gradient descent ascent (RSGDA) algorithm for the
stochastic minimax optimization, which has a sample complexity of
$O(\kappa^4\epsilon^{-4})$ for finding an $\epsilon$-stationary solution. To
further reduce the sample complexity, we propose an accelerated Riemannian
stochastic gradient descent ascent (Acc-RSGDA) algorithm based on the
momentum-based variance-reduced technique. We prove that our Acc-RSGDA
algorithm achieves a lower sample complexity of
$\tilde{O}(\kappa^{4}\epsilon^{-3})$ in searching for an $\epsilon$-stationary
solution of the GNSC minimax problems. Extensive experimental results on the
robust distributional optimization and robust Deep Neural Networks (DNNs)
training over Stiefel manifold demonstrate efficiency of our algorithms.


  This contribution describes fast time-stamping cameras sensitive to optical
photons and their applications.