  We give a new structural development of harmonic polynomials on Hamming
space, and harmonic weight enumerators of binary linear codes, that parallels
one approach to harmonic polynomials on Euclidean space and weighted theta
functions of Euclidean lattices. Namely, we use the finite-dimensional
representation theory of sl_2 to derive a decomposition theorem for the spaces
of discrete homogeneous polynomials in terms of the spaces of discrete harmonic
polynomials, and prove a generalized MacWilliams identity for harmonic weight
enumerators. We then present several applications of harmonic weight
enumerators, corresponding to some uses of weighted theta functions: an
equivalent characterization of t-designs, the Assmus-Mattson Theorem in the
case of extremal Type II codes, and configuration results for extremal Type II
codes of lengths 8, 24, 32, 48, 56, 72, and 96.


  Open dynamical systems are mathematical models of machines that take input,
change their internal state, and produce output. For example, one may model
anything from neurons to robots in this way. Several open dynamical systems can
be arranged in series, in parallel, and with feedback to form a new dynamical
system---this is called compositionality---and the process can be repeated in a
fractal-like manner to form more complex systems of systems. One issue is that
as larger systems are created, their state space grows exponentially.
  In this paper a technique for calculating the steady states of an
interconnected system of systems, in terms of the steady states of its
component dynamical systems, is provided. These are organized into "steady
state matrices" which generalize bifurcation diagrams. It is shown that the
compositionality structure of dynamical systems fits with the familiar monoidal
structure for the steady state matrices, where serial, parallel, and feedback
composition of matrices correspond to multiplication, Kronecker product, and
partial trace operations. The steady state matrices of dynamical systems
respect this compositionality structure, exponentially reducing the complexity
involved in studying the steady states of composite dynamical systems.


  Incremental Expectation Maximization (EM) algorithms were introduced to
design EM for the large scale learning framework by avoiding the full data set
to be processed at each iteration. Nevertheless, these algorithms all assume
that the conditional expectations of the sufficient statistics are explicit. In
this paper, we propose a novel algorithm named Perturbed Prox-Preconditioned
SPIDER (3P-SPIDER), which builds on the Stochastic Path Integral Differential
EstimatoR EM (SPIDER-EM) algorithm. The 3P-SPIDER algorithm addresses many
intractabilities of the E-step of EM; it also deals with non-smooth
regularization and convex constraint set. Numerical experiments show that
3P-SPIDER outperforms other incremental EM methods and discuss the role of some
design parameters.


  The finite-size effects prominent in zero-range processes exhibiting a
condensation transition are studied by using continuous-time Monte Carlo
simulations. We observe that, well above the thermodynamic critical point, both
static and dynamic properties display fluid-like behavior up to a density
{\rho}c (L), which is the finite-size counterpart of the critical density
{\rho}c = {\rho}c (L \rightarrow \infty). We determine this density from the
cross-over behavior of the average size of the largest cluster. We then show
that several dynamical characteristics undergo a qualitative change at this
density. In particular, the size distribution of the largest cluster at the
moment of relocation, the persistence properties of the largest cluster and
correlations in its motion are studied.


  We develop a formulation of the Baade-Wesselink method which uses the Fourier
coefficients of the observables. We derive an explicit, analytic expression to
determine the mean radius from each Fourier order. The simplicity of this
method allows us to derive the uncertainty in the mean radius due to
measurement errors.
  Using simulations and a recent dataset we demonstrate that the precision of
the radius measurement with optical magnitudes is in most cases limited by the
accuracy of the measurement of the phase difference between the light and the
color index curve. In this case it is advantageous to determine the inverse
radius, because it has normal errors.


  We investigate the problem of network utility maximization in multiple
gateways wireless mesh networks by considering Signal to Interference plus
Noise Ratio (SINR) as the interference model. The aim is a cross layer design
that considers joint rate control, traffic splitting, routing, scheduling, link
rate allocation and power control to formulate the network utility maximization
problem. As this problem is computationally complex, we propose the Joint
dynamic Gateway selection, link Rate allocation and Power control (JGRP)
algorithm based on the differential backlog as a sub-optimal solution. This
algorithm first constructs the initial network topology, and then in each time
slot, determines the generation rate and destination gateway of each traffic
flow, simultaneously. The other main task of this algorithm is joint routing,
scheduling, links rate allocation and node power allocation in each time slot.
Moreover, for improving the fairness, we propose some new parameters instead of
the differential backlog in JGRP algorithm. Simulation results show that using
the proposed parameters in JGRP algorithm improves fairness from throughput and
delay point of views.


  Planetary nebulae (PNe) are strong H$\alpha$ line-emitters and a lot of new
PNe discoveries have been made by the SuperCOSMOS AAO/UKST H$\alpha$ Survey
(SHS) and the Isaac Newton Telescope Photometric H$\alpha$ Survey (IPHAS).
However, the list of auto-generated H$\alpha$-excess candidates from these
surveys as well as any photometric survey, prior to spectroscopic follow-up to
confirm their nature, contains all varieties of H$\alpha$-line emitters like
young stellar objects (YSOs), H II regions, compact PNe and emission line stars
of all kinds. The aim of this work is to find new infrared criteria that can
better distinguish compact PNe from their mimics using a machine learning
approach and the photometric data from the Two-Micron All-Sky Survey and
Wide-field Infrared Survey Explorer. Three classification tree models have been
developed with the following colour criteria: W1-W4$\ge$7.87 and J-H$<$1.10;
H-W2$\ge$2.24 and J-H$<$0.50; and Ks-W3$\ge$6.42 and J-H$<$1.31 providing a
list of candidates, characterized by a high probability to be genuine PNe. The
contamination of this list of candidates from Ha mimics is low but not
negligible. By applying these criteria to the IPHAS list of PN candidates and
the entire IPHAS and VPHAS+ DR2 catalogues, we find 141 sources, from which 92
are known PNe, 39 are new very likely compact PNe (without an available
classification or uncertain) and 10 are classified as H II regions, Wolf-Rayet
stars, AeBe stars and YSOs. The occurrence of false positive identifications in
this technique is between 10 and 15 per cent.


  We describe a procedure of counting all equilateral triangles in the three
dimensional space whose coordinates are allowed only in the set
$\{0,1,...,n\}$. This sequence is denoted here by ET(n) and it has the entry
A102698 in "The On-Line Encyclopedia of Integer Sequences". The procedure is
implemented in Maple and its main idea is based on the results in \cite{eji}.
Using this we calculated the values ET(n) for n=1..55 which are included here.
Some facts and conjectures about this sequence are stated. The main of them is
that $\ds \lim_{n\to \infty} \frac{\ln ET(n)}{\ln n+1}$ exists.


  In this paper, we prove two generalized versions of the Cheeger-Gromoll
splitting theorem via the non-negativity of the Bakry-\'Emery Ricci curavture
on complete Riemannian manifolds.


  Performance of modern trackers degrades substantially on transparent objects
compared to opaque objects. This is largely due to two distinct reasons.
Transparent objects are unique in that their appearance is directly affected by
the background. Furthermore, transparent object scenes often contain many
visually similar objects (distractors), which often lead to tracking failure.
However, development of modern tracking architectures requires large training
sets, which do not exist in transparent object tracking. We present two
contributions addressing the aforementioned issues. We propose the first
transparent object tracking training dataset Trans2k that consists of over 2k
sequences with 104,343 images overall, annotated by bounding boxes and
segmentation masks. Standard trackers trained on this dataset consistently
improve by up to 16%. Our second contribution is a new distractor-aware
transparent object tracker (DiTra) that treats localization accuracy and target
identification as separate tasks and implements them by a novel architecture.
DiTra sets a new state-of-the-art in transparent object tracking and
generalizes well to opaque objects.


  Recently, a new gauging procedure called Sculpting mechanism was proposed to
obtain the M-theory origin of type II gauged Supergravity theories in 9D. We
study this procedurein detail and give a better understanding of the different
deformations and changes in fiber bundles, that are able to generate new
relevant physical gauge symmetries in the theory. We discuss the geometry
involved in the standard approach (Noether-like) and in the new Scultping-like
one and comment on possible new applications.


  When anisotropy is involved, the wave equation becomes simultaneous partial
differential equations that are not easily solved. Moreover, when the
anisotropy occurs due to both permittivity and permeability, these equations
are insolvable without a numerical or an approximate method. The problem is
essentially due to the fact neither $\e$ nor $\m$ can be extracted from the
curl term, when they are in it. The terms $\na\times {\bf E}$ (or ${\bf H})$
and $\na\times \e{\bf E}$ (or $\;\m{\bf H})$ are practically independent
variables, and $\bf E$ and $\bf H$ are coupled to each other. However, if
Maxwell's equations are manipulated in a different way, new wave equations are
obtained. The obtained equations can be applied in anisotropic, as well as
isotropic, cases. In addition, $\bf E$ and $\bf H$ are decoupled in the new
equations, so the equations can be solved analytically by using tensor Green's
functions.


  Causality violations are typically seen as unrealistic and undesirable
features of a physical model. The following points out three reasons why
causality violations, which Bonnor and Steadman identified even in solutions to
the Einstein equation referring to ordinary laboratory situations, are not
necessarily undesirable. First, a space-time in which every causal curve can be
extended into a closed causal curve is singularity free--a necessary property
of a globally applicable physical theory. Second, a causality-violating
space-time exhibits a nontrivial topology--no closed timelike curve (CTC) can
be homotopic among CTCs to a point, or that point would not be causally well
behaved--and nontrivial topology has been explored as a model of particles.
Finally, if every causal curve in a given space-time passes through an event
horizon, a property which can be called "causal censorship", then that
space-time with event horizons excised would still be causally well behaved.


  Despite its common use in quantum theory, the mathematical requirement of
Dirac Hermiticity of a Hamiltonian is sufficient to guarantee the reality of
energy eigenvalues but not necessary. By establishing three theorems, this
paper gives physical conditions that are both necessary and sufficient. First,
it is shown that if the secular equation is real, the Hamiltonian is
necessarily PT symmetric. Second, if a linear operator C that obeys the two
equations [C,H]=0 and C^2=1 is introduced, then the energy eigenvalues of a
PT-symmetric Hamiltonian that is diagonalizable are real only if this C
operator commutes with PT. Third, the energy eigenvalues of PT-symmetric
Hamiltonians having a nondiagonalizable, Jordan-block form are real. These
theorems hold for matrix Hamiltonians of any dimensionality.


  In this work, we leverage the pure skin color patch from the face image as
the additional information to train an auxiliary skin color feature extractor
and face recognition model in parallel to improve performance of
state-of-the-art (SOTA) privacy-preserving face recognition (PPFR) systems. Our
solution is robust against black-box attacking and well-established generative
adversarial network (GAN) based image restoration. We analyze the potential
risk in previous work, where the proposed cosine similarity computation might
directly leak the protected precomputed embedding stored on the server side. We
propose a Function Secret Sharing (FSS) based face embedding comparison
protocol without any intermediate result leakage. In addition, we show in
experiments that the proposed protocol is more efficient compared to the Secret
Sharing (SS) based protocol.


  A number of recent papers have estimated ratios of the partition function
$p(n-j)/p(n)$, which appears in many applications. Here, we prove an
easy-to-use effective bound on these ratios. Using this, we then study second
shifted difference of partitions, $f(j,n):= p(n) -2p(n-j) +p(n-2j)$, and give
another easy-to-use estimate of $f(j,n)$. As applications of these, we prove a
shifted convexity property of $p(n)$, as well as giving new estimates of the
$k$-rank partition function $N_k(m,n)$ and non-$k$-ary partitions along with
their differences.


  The bipartite independence number of a graph $G$, denoted as
$\tilde\alpha(G)$, is the minimal number $k$ such that there exist positive
integers $a$ and $b$ with $a+b=k+1$ with the property that for any two sets
$A,B\subseteq V(G)$ with $|A|=a$ and $|B|=b$, there is an edge between $A$ and
$B$. McDiarmid and Yolov showed that if $\delta(G)\geq\tilde \alpha(G)$ then
$G$ is Hamiltonian, extending the famous theorem of Dirac which states that if
$\delta(G)\geq |G|/2$ then $G$ is Hamiltonian. In 1973, Bondy showed that,
unless $G$ is a complete bipartite graph, Dirac's Hamiltonicity condition also
implies pancyclicity, i.e., existence of cycles of all the lengths from $3$ up
to $n$. In this paper we show that $\delta(G)\geq\tilde \alpha(G)$ implies that
$G$ is pancyclic or that $G=K_{\frac{n}{2},\frac{n}{2}}$, thus extending the
result of McDiarmid and Yolov, and generalizing the classic theorem of Bondy.


  Ultracold atom research presents many avenues to study problems at the
forefront of physics. Due to their unprecedented controllability, these systems
are ideally suited to explore new exotic states of matter, which is one of the
key driving elements of the condensed matter research. One such topic of
considerable importance is topological insulators, materials that are
insulating in the interior but conduct along the edges. Quantum Hall and its
close cousin Quantum Spin Hall states belong to the family of these exotic
states and are the subject of this chapter.


  In recent years several architectures have been proposed to learn embodied
agents complex self-awareness models. In this paper, dynamic incremental
self-awareness (SA) models are proposed that allow experiences done by an agent
to be modeled in a hierarchical fashion, starting from more simple situations
to more structured ones. Each situation is learned from subsets of private
agent perception data as a model capable to predict normal behaviors and detect
abnormalities. Hierarchical SA models have been already proposed using low
dimensional sensorial inputs. In this work, a hierarchical model is introduced
by means of a cross-modal Generative Adversarial Networks (GANs) processing
high dimensional visual data. Different levels of the GANs are detected in a
self-supervised manner using GANs discriminators decision boundaries. Real
experiments on semi-autonomous ground vehicles are presented.


  Systolic arrays and shared-L1-memory manycore clusters are commonly used
architectural paradigms that offer different trade-offs to accelerate parallel
workloads. While the first excel with regular dataflow at the cost of rigid
architectures and complex programming models, the second are versatile and easy
to program but require explicit dataflow management and synchronization. This
work aims at enabling efficient systolic execution on shared-L1-memory manycore
clusters. We devise a flexible architecture where small and energy-efficient
RISC-V cores act as the systolic array's processing elements (PEs) and can form
diverse, reconfigurable systolic topologies through queues mapped in the
cluster's shared memory. We introduce two low-overhead RISC-V ISA extensions
for efficient systolic execution, namely Xqueue and Queue-linked registers
(QLRs), which support queue management in hardware. The Xqueue extension
enables single-instruction access to shared-memory-mapped queues, while QLRs
allow implicit and autonomous access to them, relieving the cores of explicit
communication instructions. We demonstrate Xqueue and QLRs in MemPool, an
open-source shared-memory cluster with 256 PEs, and analyze the hybrid
systolic-shared-memory architecture's trade-offs on several DSP kernels with
diverse arithmetic intensity. For an area increase of just 6%, our hybrid
architecture can double MemPool's compute unit utilization, reaching up to 73%.
In typical conditions (TT/0.80V/25{\deg}C), in a 22 nm FDX technology, our
hybrid architecture runs at 600 MHz with no frequency degradation and is up to
65% more energy efficient than the shared-memory baseline, achieving up to 208
GOPS/W, with up to 63% of power spent in the PEs.


  We describe the application of a novel approach for the reduction of
scattering amplitudes, based on multivariate polynomial division, which we have
recently presented. This technique yields the complete integrand decomposition
for arbitrary amplitudes, regardless of the number of loops. It allows for the
determination of the residue at any multiparticle cut, whose knowledge is a
mandatory prerequisite for applying the integrand-reduction procedure. By using
the division modulo Groebner basis, we can derive a simple integrand recurrence
relation that generates the multiparticle pole decomposition for integrands of
arbitrary multiloop amplitudes. We apply the new reduction algorithm to the
two-loop planar and nonplanar diagrams contributing to the five-point
scattering amplitudes in N=4 super Yang-Mills and N=8 supergravity in four
dimensions, whose numerator functions contain up to rank-two terms in the
integration momenta. We determine all polynomial residues parametrizing the
cuts of the corresponding topologies and subtopologies. We obtain the integral
basis for the decomposition of each diagram from the polynomial form of the
residues. Our approach is well suited for a seminumerical implementation, and
its general mathematical properties provide an effective algorithm for the
generalization of the integrand-reduction method to all orders in perturbation
theory.


  This paper aims to develop the stability theory for singular stochastic
Markov jump systems with state-dependent noise, including both continuous- and
discrete-time cases. The sufficient conditions for the existence and uniqueness
of a solution to the system equation are provided. Some new and fundamental
concepts such as non-impulsiveness and mean square admissibility are
introduced, which are different from those of other existing works. By making
use of the $\mathcal{H}$-representation technique and the pseudo inverse $E^+$
of a singular matrix $E$, sufficient conditions ensuring the system to be mean
square admissible are established in terms of strict linear matrix
inequalities, which can be regarded as extensions of the corresponding results
of deterministic singular systems and normal stochastic systems. Practical
examples are given to demonstrate the effectiveness of the proposed approaches.


  We develop a deep learning model to effectively solve high-dimensional
nonlinear parabolic partial differential equations (PDE). We follow Feynman-Kac
formula to reformulate PDE into the equivalent stochastic control problem
governed by a Backward Stochastic Differential Equation (BSDE) system. The
Markovian property of the BSDE is utilized in designing our neural network
architecture, which is inspired by the Actor-Critic algorithm usually applied
for deep Reinforcement Learning. Compared to the State-of-the-Art model, we
make several improvements including 1) largely reduced trainable parameters, 2)
faster convergence rate and 3) fewer hyperparameters to tune. We demonstrate
those improvements by solving a few well-known classes of PDEs such as
Hamilton-Jacobian-Bellman equation, Allen-Cahn equation and Black-Scholes
equation with dimensions on the order of 100.


  Performing sensitivity analysis for influence diagrams using the decision
circuit framework is particularly convenient, since the partial derivatives
with respect to every parameter are readily available [Bhattacharjya and
Shachter, 2007; 2008]. In this paper we present three non-linear sensitivity
analysis methods that utilize this partial derivative information and therefore
do not require re-evaluating the decision situation multiple times.
Specifically, we show how to efficiently compare strategies in decision
situations, perform sensitivity to risk aversion and compute the value of
perfect hedging [Seyller, 2008].


  We study a forward backward splitting algorithm that solves the variational
inequality \begin{equation*} A x +\nabla \Phi(x)+ N_C (x) \ni 0 \end{equation*}
where $H$ is a real Hilbert space, $A: H\rightrightarrows H$ is a maximal
monotone operator, $\Phi: H\to\mathbb{R}$ is a smooth convex function, and
$N_C$ is the outward normal cone to a closed convex set $C\subset H$. The
constraint set $C$ is represented as the intersection of the sets of minima of
two convex penalization function $\Psi_1:H\to\mathbb{R}$ and $\Psi_2:
H\to\mathbb{R}\cup \{+\infty\}$. The function $\Psi_1$ is smooth, the function
$\Psi_2$ is proper and lower semicontinuous. Given a sequence $(\beta_n)$ of
penalization parameters which tends to infinity, and a sequence of positive
time steps $(\lambda_n)$, the algorithm $$ \left\{\begin{array}{rcl} x_1 & \in
& H,\\ x_{n+1} & = & (I+\lambda_n
A+\lambda_n\beta_n\partial\Psi_2)^{-1}(x_n-\lambda_n\nabla\Phi(x_n)-\lambda_n\beta_n\nabla\Psi_1(x_n)),\
n\geq 1. \end{array}\right. $$ performs forward steps on the smooth parts and
backward steps on the other parts. Under suitable assumptions, we obtain weak
ergodic convergence of the sequence $(x_n)$ to a solution of the variational
inequality. Convergence is strong when either $A$ is strongly monotone or
$\Phi$ is strongly convex. We also obtain weak convergence of the whole
sequence $(x_n)$ when $A$ is the subdifferential of a proper
lower-semicontinuous convex function. This provides a unified setting for
several classical and more recent results, in the line of historical research
on continuous and discrete gradient-like systems.


  Organisms often use cyclic changes in the concentrations of chemicals species
to precisely time biological functions. Underlying these biochemical clocks are
chemical reactions and transport processes, which are inherently stochastic.
Understanding the physical basis for robust biochemical oscillations in the
presence of fluctuations has thus emerged as an important problem. In a
previous paper [C. del Junco and S. Vaikuntanathan, Phys. Rev. E 101, 012410
(2020)], we explored this question using the non-equilibrium statistical
mechanics of single-ring Markov state models of biochemical networks that
support oscillations. Our finding was that they can exploit non-equilibrium
driving to robustly maintain the period and coherence of oscillations in the
presence of randomness in the rates. Here, we extend our work to Markov state
models consisting of a large cycle decorated with multiple small cycles. These
additional cycles are intended to represent alternate pathways that the
oscillator may take as it fluctuates about its average path. Combining a
mapping to single-cycle networks based on first passage time distributions with
our previously developed theory, we are able to make analytical predictions for
the period and coherence of oscillations in these networks. One implication of
our predictions is that a high energy budget can make different network
topologies and arrangements of rates degenerate as far as the period and
coherence of oscillations is concerned. Excellent agreement between analytical
and numerical results confirms that this is the case. Our results suggest that
biochemical oscillators can be more robust to fluctuations in the path of the
oscillator when they have a high energy budget.


  Sequence transformations are important tools for the convergence acceleration
of slowly convergent scalar sequences or series and for the summation of
divergent series. Transformations that depend not only on the sequence elements
or partial sums $s_n$ but also on an auxiliary sequence of so-called remainder
estimates $\omega_n$ are of Levin-type if they are linear in the $s_n$, and
nonlinear in the $\omega_n$. Known Levin-type sequence transformations are
reviewed and put into a common theoretical framework. It is discussed how such
transformations may be constructed by either a model sequence approach or by
iteration of simple transformations. As illustration, two new sequence
transformations are derived. Common properties and results on convergence
acceleration and stability are given. For important special cases, extensions
of the general results are presented. Also, guidelines for the application of
Levin-type sequence transformations are discussed, and a few numerical examples
are given.


  This paper deals with holomorphic self-maps of the complex projective plane
and the algebraic relations among the eigenvalues of the derivatives at the
fixed points. These eigenvalues are constrained by certain index theorems such
as the holomorphic Lefschetz fixed-point theorem. A simple dimensional argument
suggests there must exist even more algebraic relations that the ones currently
known. In this work we analyze the case of quadratic self-maps having an
invariant line and obtain all such relations. We also prove that a generic
quadratic self-map with an invariant line is completely determined, up to
linear equivalence, by the collection of these eigenvalues. Under the natural
correspondence between quadratic rational maps of $\mathbb{P}^2$ and quadratic
homogeneous vector fields on $\mathbb{C}^3$, the algebraic relations among
multipliers translate to algebraic relations among the Kowalevski exponents of
a vector field. As an application of our results, we describe the sets of
integers that appear as the Kowalevski exponents of a class of quadratic
homogeneous vector fields on $\mathbb{C}^3$ having exclusively single-valued
solutions.


  Recent remarkable success in the deep-learning industries has unprecedentedly
increased the need for reliable model deployment. For example, the model should
alert the user if the produced model outputs might not be reliable. Previous
studies have proposed various methods to solve the Out-of-Distribution (OOD)
detection problem, however, they generally require a burden of resources. In
this work, we propose a novel and simple method, Multiple Input Mixup (MIM).
Our method can help improve the OOD detection performance with only single
epoch fine-tuning. Our method does not require training the model from scratch
and can be attached to the classifier simply. Despite its simplicity, our MIM
shows competitive performance. Our method can be suitable for various
environments because our method only utilizes the In-Distribution (ID) samples
to generate the synthesized OOD data. With extensive experiments with CIFAR10
and CIFAR100 benchmarks that have been largely adopted in out-of-distribution
detection fields, we have demonstrated our MIM shows comprehensively superior
performance compared to the SOTA method. Especially, our method does not need
additional computation on the feature vectors compared to the previous studies.
All source codes are publicly available at
https://github.com/ndb796/MultipleInputMixup.


  The parton and hadron cascade model PACIAE based on PYTHIA was utilized to
systematically investigate the strange particle production in pp collisions at
the RHIC and LHC energies. Taking the mechanism of reduction of the strange
quark suppression into account the STAR and ALICE data of strange particle
production in pp collisions are well reproduced. It turned out that the K/{\pi}
ratio as a function of reaction energy in pp collisions shows slightly
increasing from sqrt(s)=0.2 to 0.9 TeV and then turning to saturation.


  Peer review is a laborious, yet essential, part of academic publishing with
crucial impact on the scientific endeavor. The current lack of incentives and
transparency harms the credibility of this process. Researchers are neither
rewarded for superior nor penalized for bad reviews. Additionally, confidential
reports cause a loss of insights and make the review process vulnerable to
scientific misconduct. We propose a community-owned and -governed system that
1) remunerates reviewers for their efforts, 2) publishes the (anonymized)
reports for scrutiny by the community, 3) tracks reputation of reviewers and 4)
provides digital certificates. Automated by transparent smart-contract
blockchain technology, the system aims to increase quality and speed of peer
review while lowering the chance and impact of erroneous judgements.


  Multi-echelon inventory optimization (MEIO) plays a key role in a supply
chain seeking to achieve specified customer service levels with a minimum
capital in inventory. In this work, we propose a generalized MEIO model based
on the Guaranteed Service approach to allocate safety stock levels across the
network at the lowest holding cost. This model integrates several existing and
some novel features that are usually present in pharmaceutical multi-echelon
supply chains into a single model: review periods, manufacturing facilities,
hybrid nodes (nodes with both internal and external demand), minimum order
quantities (MOQ), and different service level performance indicators (fill rate
and cycle service levels). We include a polynomial regression to approximate
fill rates as a possible target measure to set safety stocks. To improve
efficiency, we propose a nonlinear programming model to support decision
making, which can be reformulated as a Quadratically Constrained Program (QCP),
which leads to order of magnitude reductions in computational time. The
performance of the model is evaluated by solving illustrative and real-world
cases, and is validated with simulation.


  Quadratic Poisson tensors of the Dufour-Haraki classification read as a sum
of an $r$-matrix induced structure twisted by a (small) compatible exact
quadratic tensor. An appropriate bigrading of the space of formal Poisson
cochains then leads to a vertically positive double complex. The associated
spectral sequence allows to compute the Poisson-Lichnerowicz cohomology of the
considered tensors. We depict this modus operandi, apply our technique to
concrete examples of twisted Poisson structures, and obtain a complete
description of their cohomology. As richness of Poisson cohomology entails
computation through the whole spectral sequence, we detail an entire model of
this sequence. Finally, the paper provides practical insight into the operating
mode of spectral sequences.


  We report the first arcsecond-resolution observations of the magnetic field
in the mini starburst complex Sgr B2. SMA polarization observations revealed
magnetic field morphology in three dense cores of Sgr B2 N(orth), M(ain), and
S(outh). The total plane-of-sky magnetic field strengths in these cores are
estimated to be 4.3-10.0 mG, 6.2-14.7 mG, and 1.9-4.5 mG derived from the
angular dispersion function method after applying the correction factors of
0.21 and 0.5. Combining with analyses of the parsec-scale polarization data
from SOFIA, we found that a magnetically supercritical condition is present
from the cloud-scale ($\sim$10 pc) to core-scale ($\sim$0.2 pc) in Sgr B2,
which is consistent with the burst of star formation activities in the region
likely resulted from a multi-scale gravitational collapse from the cloud to
dense cores.


  Several applications involving counts present a large proportion of zeros
(excess-of-zeros data). A popular model for such data is the Hurdle model,
which explicitly models the probability of a zero count, while assuming a
sampling distribution on the positive integers. We consider data from multiple
count processes. In this context, it is of interest to study the patterns of
counts and cluster the subjects accordingly. We introduce a novel Bayesian
nonparametric approach to cluster multiple, possibly related, zero-inflated
processes. We propose a joint model for zero-inflated counts, specifying a
Hurdle model for each process with a shifted Negative Binomial sampling
distribution. Conditionally on the model parameters, the different processes
are assumed independent, leading to a substantial reduction in the number of
parameters as compared to traditional multivariate approaches. The
subject-specific probabilities of zero-inflation and the parameters of the
sampling distribution are flexibly modelled via an enriched finite mixture with
random number of components. This induces a two-level clustering of the
subjects based on the zero/non-zero patterns (outer clustering) and on the
sampling distribution (inner clustering). Posterior inference is performed
through tailored MCMC schemes. We demonstrate the proposed approach on an
application involving the use of the messaging service WhatsApp.


  We consider a notion of uniform thinning for a finite sequence of random
variables $(X_1,...,X_n)$ obtained by removing one random variable, uniformly
at random. If a triangular array of random variables $(X_{n,k} : n \in
\mathbb{N}_+, 1 \le k \le n)$ satisfies that the law of $(X_{n,1},...,X_{n,n})$
is obtained by uniformly thinning $(X_{n+1,1},...,X_{n+1,n+1})$, then we call
the array thinning-invariant. We give a representation for the Choquet simplex
of all thinning-invariant triangular arrays of random variables, when all
random variables take values in a compact metric space (with Borel measurable
distributions). We give two applications: to long-ranged, asymmetric classical
spin chains, and long-ranged, asymmetric simple exclusion processes.


  Researchers especially beginning with (Rogers & Graham, 1982) have noticed
important psychophysical and experimental similarities between the
neurologically different motion parallax and stereopsis cues. Their
quantitative analysis relied primarily on the "disparity equivalence"
approximation. In this article we show that retinal motion from lateral
translation satisfies a strong ("asymptotic") approximation to binocular
disparity. This precise mathematical similarity is also practical in the sense
that it applies at normal viewing distances. The approximation is an extension
to peripheral vision of (Cormac & Fox's 1985) well-known non-trig central
vision approximation for binocular disparity. We hope our simple algebraic
formula will be useful in analyzing experiments outside central vision where
less precise approximations have led to a number of quantitative errors in the
vision literature.


  Deep sequencing has enabled the investigation of a wide range of
environmental microbial ecosystems, but the high memory requirements for {\em
de novo} assembly of short-read shotgun sequencing data from these complex
populations are an increasingly large practical barrier. Here we introduce a
memory-efficient graph representation with which we can analyze the k-mer
connectivity of metagenomic samples. The graph representation is based on a
probabilistic data structure, a Bloom filter, that allows us to efficiently
store assembly graphs in as little as 4 bits per k-mer, albeit inexactly. We
show that this data structure accurately represents DNA assembly graphs in low
memory. We apply this data structure to the problem of partitioning assembly
graphs into components as a prelude to assembly, and show that this reduces the
overall memory requirements for {\em de novo} assembly of metagenomes. On one
soil metagenome assembly, this approach achieves a nearly 40-fold decrease in
the maximum memory requirements for assembly. This probabilistic graph
representation is a significant theoretical advance in storing assembly graphs
and also yields immediate leverage on metagenomic assembly.


  The generalized extreme value distribution (GEVD) has been widely used to
model the extreme events in many areas. It is however limited to using only
block maxima, which motivated to model the GEVD dealing with $r$-largest order
statistics (rGEVD). The rGEVD which uses more than one extreme per block can
significantly improves the performance of the GEVD. The four parameter kappa
distribution (K4D) is a generalization of some three-parameter distributions
including the GEVD. It can be useful in fitting data when three parameters in
the GEVD are not sufficient to capture the variability of the extreme
observations. The K4D still uses only block maxima. In this study, we thus
extend the K4D to deal with $r$-largest order statistics as analogy as the GEVD
is extended to the rGEVD. The new distribution is called the $r$-largest four
parameter kappa distribution (rK4D). We derive a joint probability density
function (PDF) of the rK4D, and the marginal and conditional cumulative
distribution functions and PDFs. The maximum likelihood method is considered to
estimate parameters. The usefulness and some practical concerns of the rK4D are
illustrated by applying it to Venice sea-level data. This example study shows
that the rK4D gives better fit but larger variances of the parameter estimates
than the rGEVD. Some new $r$-largest distributions are derived as special cases
of the rK4D, such as the $r$-largest logistic (rLD), generalized logistic
(rGLD), and generalized Gumbel distributions (rGGD).


  Earth-Like is an interactive website and twitter bot that allows users to
explore changes in the average global surface temperature of an Earth-like
planet due to variations in the surface oceans and emerged land coverage, rate
of volcanism (degassing), and the level of the received solar radiation. The
temperature is calculated using a simple carbon-silicate cycle model to change
the level of $\rm CO_2$ in the atmosphere based on the chosen parameters. The
model can achieve a temperature range exceeding $-100^\circ$C to $100^\circ$C
by varying all three parameters, including freeze-thaw cycles for a planet with
our present-day volcanism rate and emerged land fraction situated at the outer
edge of the habitable zone. To increase engagement, the planet is visualised by
using a neural network to render an animated globe, based on the calculated
average surface temperature and chosen values for land fraction and volcanism.
The website and bot can be found at earthlike.world and on twitter as
@earthlikeworld. Initial feedback via a user survey suggested that Earth-Like
is effective at demonstrating that minor changes in planetary properties can
strongly impact the surface environment. The goal of the project is to increase
understanding of the challenges we face in finding another habitable planet due
to the likely diversity of conditions on rocky worlds within our Galaxy.


  Recently, the deep learning method has been used for solving forward-backward
stochastic differential equations (FBSDEs) and parabolic partial differential
equations (PDEs). It has good accuracy and performance for high-dimensional
problems. In this paper, we mainly solve fully coupled FBSDEs through deep
learning and provide three algorithms. Several numerical results show
remarkable performance especially for high-dimensional cases.


  Recently, Iseni (arXiv:1709.03109v1) reported measurements and analysis of
electric field (EF) strengths adjacent to propagating ionization waves (IWs) in
non-thermal atmospheric pressure He plasma jets. We demonstrate that these
measurements are in error due to an improperly aligned electric field probe.


  The discovery of acceleration and dark energy arguably constitutes the most
revolutionary discovery in astrophysics in recent years. Cerro Tololo
Inter-American Observatory (CTIO) played a key role in this amazing discovery
through three systematic supernova surveys organized by staff astronomers: the
"Tololo Supernova Program" (1986-2000), the Calan/Tololo Project (1989-1993),
and the "High-Z Supernova Search Team" (1994-1998). CTIO's state of the art
instruments also were fundamental in the independent discovery of acceleration
by the "Supernova Cosmology Project" (1992-1999). Here I summarize the work on
supernovae carried out from CTIO that led to the discovery of acceleration and
dark energy and provide a brief historical summary on the use of Type Ia
supernovae in cosmology in order to provide context for the CTIO contribution.


  An expert ranking of forestry journals was compared with journal impact
factors and h-indices computed from the ISI Web of Science and internet-based
data. Citations reported by Google Scholar appear to offer the most efficient
way to rank all journals objectively, in a manner consistent with other
indicators. This h-index exhibited a high correlation with the journal impact
factor (r=0.92), but is not confined to journals selected by any particular
commercial provider. A ranking of 180 forestry journals is presented, on the
basis of this index.


  Electron Spin Resonance (ESR) experiments of diluted Nd$^{3+}$ ions in the
claimed topological insulator (TI) YBiPt are reported. Powdered samples with
grain size from $\approx$ 100 $\mu$m to $\approx$ 2,000 $\mu$m were
investigated. At low temperatures, 1.6 K $\lesssim$ \emph{T} $\lesssim$ 20 K,
the X-band ($9.4$ GHz) ESR spectra show a \emph{g}-value of 2.66(4) and a
Dysonian resonance lineshape which shows a remarkably unusual temperature,
concentration, microwave power and particle size dependence. These results
indicate that metallic and insulating behavior coexist within a skin depth of
$\delta \approx$ 15 $\mu$m. Furthermore, the Nd$^{3+}$ spin dynamics in YBiPt
are consistent with the existence of a \emph{phonon-bottleneck process} which
allows the energy absorbed by the Nd$^{3+}$ ions at resonance to reach the
thermal bath via the conduction electrons in the metallic surface states of
YBiPt. These results are discussed in terms of the claimed topological
semi-metal properties of YBiPt.


  We specify the canonical stratifications satisfying respectively Whitney
(a)-regularity, Whitney (b)-regularity, Kuo-Verdier (w)-regularity, and
Mostowski (L)-regularity for the family of surfaces y^a = t^b x^c + x^d, where
a, b, c, d are positive integers, in both the real and complex cases.


  Sturm-Liouville problems are abundant in the numerical treatment of
scientific and engineering problems. In the present contribution, we present an
efficient and highly accurate method for computing eigenvalues of singular
Sturm-Liouville boundary value problems. The proposed method uses the double
exponential formula coupled with Sinc collocation method. This method produces
a symmetric positive-definite generalized eigenvalue system and has exponential
convergence rate. Numerical examples are presented and comparisons with single
exponential Sinc collocation method clearly illustrate the advantage of using
the double exponential formula.


  The elimination of decoherence of a multiphoton two-state quantum system by
using an appropriate external driving field is considered. The multiphoton
process caused by the noise field has a supersymmetric Lie algebraic structure.
The time-evolution equations for the off-diagonal elements of the density
operator of the two-state system are derived in the interaction picture. A
simple explicit formula is given for the time-dependent external driving field
used to eliminate the decoherence of the multiphoton two-state system.


  We show that the modular group has an infinite family of finite index
subgroups, each of which has the same trace set as the modular group itself.
Various congruence subgroups of the modular group, and the Bianchi groups, are
also shown to have this property. In the case of the modular group, we
construct examples of such finite index subgroups.


  We take under consideration Young measures with densities. The notion of
density of a Young measure is introduced and illustrated with examples. It is
proved that the density of a Young measure is weakly sequentially closed set.
In the case when density of a Young measure is a singleton (up to the set of
null measure), it is shown that the strong closedness (in rca(K)) of the set of
such measures, associated with Borel functions with values in the compact set K
? Rl, is equivalent with the strong closedness (in L1(K)) of the set of their
densities, provided the set K is convex. For an m-oscillating function the
notion of a total slope is proposed. It turns out, that if the total slopes of
the elements of the sequence of oscillating functions form monotonic sequence,
then the sequence of the respective (homogeneous) Young measures is weakly
convergent in rca(K). The limit is a homogeneous Young measure with the density
being the weak L1 sequential limit of the densities of the underlying Young
measures.


  We introduce a scale of weighted Carleson norms, which depend on an
integrability parameter p, where p=2 corresponds to the classical Carleson
measure condition. Relations between the weighed BMO norm of a vector-valued
function f:R->X, and the Carleson norm of the sequence of its wavelet
coefficients, are established. These extend the results of
Harboure-Salinas-Viviani, also in the scalar-valued case when p is not 2.


  We report on an indirect method being used to measure luminosity at LHCb. It
involves recording the event rate of elastic diphoton dimuon production.
Preliminary MC studies suggest that with 1 fb^{-1} of data this method could
provide a luminosity measurement with a precision of better than 2%


  In considering alternative higher-order gravity theories, one is liable to be
motivated in pursuing models consistent and inspired by several candidates of a
fundamental theory of quantum gravity. Indeed, motivations from string/M-theory
predict that scalar field couplings with the Gauss-Bonnet invariant, G, are
important in the appearance of non-singular early time cosmologies. In this
work, we discuss the viability of an interesting alternative gravitational
theory, namely, modified Gauss-Bonnet gravity or f(G) gravity. We consider
specific realistic forms of f(G) analyzed in the literature that account for
the late-time cosmic acceleration and that have been found to cure the
finite-time future singularities present in the dark energy models. We present
the general inequalities imposed by the energy conditions and use the recent
estimated values of the Hubble, deceleration, jerk and snap parameters to
examine the viability of the above-mentioned forms of f(G) imposed by the weak
energy condition.


  Pushdown Vector Addition Systems with States (PVASS) consist of finitely many
control states, a pushdown stack, and a set of counters that can be incremented
and decremented, but not tested for zero. Whether the reachability problem is
decidable for PVASS is a long-standing open problem.
  We consider continuous PVASS, which are PVASS with a continuous semantics.
This means, the counter values are rational numbers and whenever a vector is
added to the current counter values, this vector is first scaled with an
arbitrarily chosen rational factor between zero and one. We show that
reachability in continuous PVASS is NEXPTIME-complete. Our result is unusually
robust: Reachability can be decided in NEXPTIME even if all numbers are
specified in binary. On the other hand, NEXPTIME-hardness already holds for
coverability, in fixed dimension, for bounded stack, and even if all numbers
are specified in unary.


  We express the resonant energies of the delta-shell potential in terms of the
Lambert $W$ function, and we calculate their decay widths and decay constants.
The ensuing numerical results strengthen the interpretation of such decay
widths and constants as a way to quantify the coupling between a resonance and
the continuum. We calculate explicitly the decay energy spectrum of the
resonances of the delta-shell potential, and we show numerically that the
lineshape of such spectrum is not the same as, and can be very different from,
the Breit-Wigner (Lorentzian) distribution. We argue that the standard Golden
Rule cannot describe the interference of two resonances, and we show how to
describe such interference by way of the decay energy spectrum of two resonant
states.


  The property of isotonicity of a continuous convex function defined on the
entire space or only on the positive cone is characterized via
subdifferentials. Numerous examples illustrating the obtained results are
included.


  We determine the complete set of generalized spin squeezing inequalities,
given in terms of the collective angular momentum components, for particles
with an arbitrary spin. They can be used for the experimental detection of
entanglement in an ensemble in which the particles cannot be individually
addressed. We also present a large set of criteria involving collective
observables different from the angular momentum coordinates. We show that some
of the inequalities can be used to detect k-particle entanglement and bound
entanglement.


  Many millions of users routinely use their Google accounts to log in to
relying party (RP) websites supporting the Google OpenID Connect service.
OpenID Connect, a newly standardised single-sign-on protocol, builds an
identity layer on top of the OAuth 2.0 protocol, which has itself been widely
adopted to support identity management services. It adds identity management
functionality to the OAuth 2.0 system and allows an RP to obtain assurances
regarding the authenticity of an end user. A number of authors have analysed
the security of the OAuth 2.0 protocol, but whether OpenID Connect is secure in
practice remains an open question. We report on a large-scale practical study
of Google's implementation of OpenID Connect, involving forensic examination of
103 RP websites which support its use for sign-in. Our study reveals serious
vulnerabilities of a number of types, all of which allow an attacker to log in
to an RP website as a victim user. Further examination suggests that these
vulnerabilities are caused by a combination of Google's design of its OpenID
Connect service and RP developers making design decisions which sacrifice
security for simplicity of implementation. We also give practical
recommendations for both RPs and OPs to help improve the security of real world
OpenID Connect systems.


  Lung cancer's high mortality rate can be mitigated by early detection,
increasingly reliant on AI for diagnostic imaging. However, AI model
performance depends on training and validation datasets. This study develops
and validates AI models for both nodule detection and cancer classification
tasks. For detection, two models (DLCSD-mD and LUNA16-mD) were developed using
the Duke Lung Cancer Screening Dataset (DLCSD), with over 2,000 CT scans from
1,613 patients and more than 3,000 annotations. These models were evaluated on
internal (DLCSD) and external datasets, including LUNA16 (601 patients, 1186
nodules) and NLST (969 patients, 1192 nodules), using FROC analysis and AUC
metrics. For classification, five models were developed and tested: a randomly
initialized 3D ResNet50, Genesis, MedNet3D, an enhanced ResNet50 using
Strategic Warm-Start++ (SWS++), and a linear classifier analyzing features from
the Foundation Model for Cancer Biomarkers (FMCB). These models were trained to
distinguish between benign and malignant nodules and evaluated using AUC
analysis on internal (DLCSD) and external datasets, including LUNA16 (433
patients, 677 nodules) and NLST. The DLCSD-mD model achieved an AUC of 0.93
(95% CI: 0.91-0.94) on the internal DLCSD dataset. External validation results
were 0.97 (95% CI: 0.96-0.98) on LUNA16 and 0.75 (95% CI: 0.73-0.76) on NLST.
For classification, the ResNet50-SWS++ model recorded AUCs of 0.71 (95% CI:
0.61-0.81) on DLCSD, 0.90 (95% CI: 0.87-0.93) on LUNA16, and 0.81 (95% CI:
0.79-0.82) on NLST. Other models showed varying performance across datasets,
underscoring the importance of diverse model approaches. This benchmarking
establishes DLCSD as a reliable resource for lung cancer AI research.


  Knowledge graph embedding, which aims to represent entities and relations as
low dimensional vectors (or matrices, tensors, etc.), has been shown to be a
powerful technique for predicting missing links in knowledge graphs. Existing
knowledge graph embedding models mainly focus on modeling relation patterns
such as symmetry/antisymmetry, inversion, and composition. However, many
existing approaches fail to model semantic hierarchies, which are common in
real-world applications. To address this challenge, we propose a novel
knowledge graph embedding model -- namely, Hierarchy-Aware Knowledge Graph
Embedding (HAKE) -- which maps entities into the polar coordinate system. HAKE
is inspired by the fact that concentric circles in the polar coordinate system
can naturally reflect the hierarchy. Specifically, the radial coordinate aims
to model entities at different levels of the hierarchy, and entities with
smaller radii are expected to be at higher levels; the angular coordinate aims
to distinguish entities at the same level of the hierarchy, and these entities
are expected to have roughly the same radii but different angles. Experiments
demonstrate that HAKE can effectively model the semantic hierarchies in
knowledge graphs, and significantly outperforms existing state-of-the-art
methods on benchmark datasets for the link prediction task.


  Functional manipulation of graphene is an important topic in view of both
fundamental researches and practical applications. In this study, we show that
intercalation of 5$d$ transition metals in epitaxial graphene on SiC is a
promising approach to realize topologically nontrivial phases with a finite
band gap in graphene. Using first-principles calculations based on density
functional theory, we show that the Re- and Ta-intercalated graphene become
two-dimensional topological insulators which exhibit linear Dirac cones and
quadratic bands with topological band gaps, respectively. The appearance of the
topological states is attributed to the strong spin-orbit coupling strength of
the intercalants. We find that topological edge states exist within the finite
bulk band gap in accordance with the bulk-boundary correspondence. We also
discuss the spin splitting of the band structure due to the inversion symmetry
breaking and the spin-orbit coupling. Our results demonstrate that
intercalation of graphene is an effective and viable method to manipulate the
band gap and the topological character of graphene. Such intercalated graphene
systems are potentially useful for spintronics and quantum computing
applications.


  The infrared (IR) reflectivity spectra of orthorhombic manganese perovskites
PrMnO$_3$ and CaMnO$_3$ are studied in the frequency range of optical phonon
modes at temperatures varying from 300 to 4 K. The IR phonon spectra of these
two materials are analyzed by a fitting procedure based on a Lorentz model, and
assigned to definite vibrational modes of $Pnma$ structures by comparison with
the results of lattice dynamical calculations. The calculations have been
performed in the framework of a shell model using short range
Born-Mayer-Buckingham and long range Coulomb potentials, whose parameters have
been optimized in order that the calculated Raman and IR active phonon
frequencies, and lattice parameters match with their experimental values. We
find a close correspondence between the values of the IR phonon frequencies of
PrMnO$_3$ and CaMnO$_3$, which shows that the substitution of the Pr$^{3+}$
ions with Ca$^{2+}$ results in a reduction of the frequency of medium- and
high-energy IR phonons, and an increase of the frequency of those of
low-energy. Nevertheless, the experimentally obtained IR phonon amplitudes of
the two materials appear to be unrelated. A comparative study of the
vibrational patterns of these modes reveals that most of them correspond to
complex atomic vibrations significantly different from PrMnO$_3$ to CaMnO$_3$
which cannot be assigned only to a given type of vibration (external, bending,
or stretching modes). In particular, these results confirm that the structure
of CaMnO$_3$ is quite far from the ideal (cubic) perovskite structure.


  Single NV centers in HPHT IIa diamond are fabricated by helium implantation
through lithographic masks. The concentrations of created NV centers in
different growth sectors of HPHT are compared quantitatively. It is shown that
the purest {001} growth sector (GS) of HPHT diamond allows to create groups of
single NV centers in predetermined locations. The {001} GS HPHT diamond is thus
considered a good material for applications that involve single NV centers.


  A simple criterion is given to rule out the existence of closed trapped
surfaces in large open regions inside black holes.


  Adapting Foundation Models (FMs) for downstream tasks through Federated
Learning (FL) emerges a promising strategy for protecting data privacy and
valuable FMs. Existing methods fine-tune FM by allocating sub-FM to clients in
FL, however, leading to suboptimal performance due to insufficient tuning and
inevitable error accumulations of gradients. In this paper, we propose
Federated Proxy Fine-Tuning (FedPFT), a novel method enhancing FMs adaptation
in downstream tasks through FL by two key modules. First, the sub-FM
construction module employs a layer-wise compression approach, facilitating
comprehensive FM fine-tuning across all layers by emphasizing those crucial
neurons. Second, the sub-FM alignment module conducts a two-step
distillations-layer-level and neuron-level-before and during FL fine-tuning
respectively, to reduce error of gradient by accurately aligning sub-FM with FM
under theoretical guarantees. Experimental results on seven commonly used
datasets (i.e., four text and three vision) demonstrate the superiority of
FedPFT.


  We obtain the scaling limits of random graphs drawn uniformly in three
families of intersection graphs: permutation graphs, circle graphs, and unit
interval graphs. The two first families typically generate dense graphs, in
these cases we prove a.s. convergence to an explicit deterministic graphon.
Uniform unit interval graphs are nondense and we prove convergence in the sense
of Gromov-Prokhorov after normalization of the distances: the limiting object
is the interval $[0,1]$ endowed with a random metric defined through a Brownian
excursion. Asymptotic results for the number of cliques of size $k$ ($k$ fixed)
in a uniform random graph in each of these three families are also given.
  In all three cases, an important ingredient of the proof is that, for
indecomposable graphs in each class (where the notion of indecomposability
depends on the class), the combinatorial object defining the graph
(permutation, matching, or intervals) is essentially unique.


  Using existing models for the evolution of clustering we show that the first
sources are likely to be highly biased and thus strongly clustered. We compute
intensity fluctuations for clustered sources in a uniform IGM. The strong
fluctuations imply the universe was reheated and reionized in a highly
inhomogeneous fashion.


  An old conjecture of Erd\H{o}s and R\'enyi, proved by Schinzel, predicted a
bound for the number of terms of a polynomial $g(x) \in \mathbb{C}[x]$ when its
square $g(x)^2$ has a given number of terms. Further conjectures and results
arose, but some fundamental questions remained open.
  In this paper, with methods which appear to be new, we achieve a final result
in this direction for completely general algebraic equations $f(x,g(x))=0$,
where $f(x,y)$ is monic of arbitrary degree in $y$, and has boundedly many
terms in $x$: we prove that the number of terms of such a $g(x)$ is necessarily
bounded. This includes the previous results as extremely special cases.
  We shall interpret polynomials with boundedly many terms as the restrictions
to 1-parameter subgroups or cosets of regular functions of bounded degree on a
given torus $\mathbb{G}_{\mathrm{m}}^l$. Such a viewpoint shall lead to some
best-possible corollaries in the context of finite covers of
$\mathbb{G}_{\mathrm{m}}^l$, concerning the structure of their integral points
over function fields (in the spirit of conjectures of Vojta) and a Bertini-type
irreducibility theorem above algebraic multiplicative cosets. A further natural
reading occurs in non-standard arithmetic, where our result translates into an
algebraic and integral-closedness statement inside the ring of non-standard
polynomials.


  Theory of representations of universal algebra is a natural development of
the theory of universal algebra. In the book, I considered representation of
universal algebra, diagram of representations and examples of representation.
Morphism of the representation is the map that conserve the structure of the
representation. Exploring of morphisms of the representation leads to the
concepts of generating set and basis of representation.


  We determine all the Fourier-Mukai transforms for coherent systems consisting
of a vector bundle over an elliptic curve and a subspace of its global
sections, showing that these transforms are indexed by the positive integers.
We prove that the natural stability condition for coherent systems, which
depends on a parameter, is preserved by these transforms for small and large
values of the parameter. By means of the Fourier-Mukai transforms we prove that
certain moduli spaces of coherent systems corresponding to small and large
values of the parameter are isomorphic. Using these results we draw some
conclusions about the possible birational type of the moduli spaces. We prove
that for a given degree $d$ of the vector bundle and a given dimension of the
subspace of its global sections there are at most $d$ different possible
birational types for the moduli spaces.


  We show that the appropriate vacuum state for the interior of a box with
reflecting walls being lowered adiabatically into a Schwarzschild black hole is
the Boulware state. This is concordant with the results of Unruh and Wald, who
used a different approach to obtain the stress-energy inside the box. Some
comments about an entropy bound for ordinary matter, as first conjectured by
Bekenstein, are presented.


  Large language models (LLM) are perceived to offer promising potentials for
automating security tasks, such as those found in security operation centers
(SOCs). As a first step towards evaluating this perceived potential, we
investigate the use of LLMs in software pentesting, where the main task is to
automatically identify software security vulnerabilities in source code. We
hypothesize that an LLM-based AI agent can be improved over time for a specific
security task as human operators interact with it. Such improvement can be
made, as a first step, by engineering prompts fed to the LLM based on the
responses produced, to include relevant contexts and structures so that the
model provides more accurate results. Such engineering efforts become
sustainable if the prompts that are engineered to produce better results on
current tasks, also produce better results on future unknown tasks. To examine
this hypothesis, we utilize the OWASP Benchmark Project 1.2 which contains
2,740 hand-crafted source code test cases containing various types of
vulnerabilities. We divide the test cases into training and testing data, where
we engineer the prompts based on the training data (only), and evaluate the
final system on the testing data. We compare the AI agent's performance on the
testing data against the performance of the agent without the prompt
engineering. We also compare the AI agent's results against those from
SonarQube, a widely used static code analyzer for security testing. We built
and tested multiple versions of the AI agent using different off-the-shelf LLMs
-- Google's Gemini-pro, as well as OpenAI's GPT-3.5-Turbo and GPT-4-Turbo (with
both chat completion and assistant APIs). The results show that using LLMs is a
viable approach to build an AI agent for software pentesting that can improve
through repeated use and prompt engineering.


  This document is the Technical Design Report covering the two large
spectrometer magnets of the PANDA detector set-up. It shows the conceptual
design of the magnets and their anticipated performance. It precedes the tender
and procurement of the magnets and, hence, is subject to possible modifications
arising during this process.


  The self-consistent Pauli-Poisswell equation for 2-spinors is the first order
in $1/c$ semi-relativistic approximation of the Dirac-Maxwell equation for
4-spinors coupled to the self-consistent electromagnetic fields generated by
the density and current density of a fast moving electric charge. It consists
of a vector-valued magnetic Schr\"odinger equation with an extra term coupling
spin and magnetic field via the Pauli matrices coupled to 1+3 Poisson type
equations as the magnetostatic approximation of Maxwell's equations. The
Pauli-Poisswell equation is a consistent $O(1/c)$ model that keeps both
relativistic effects magnetism and spin which are both absent in the
non-relativistic Schr\"odinger-Poisson equation and inconsistent in the
magnetic Schr\"odinger-Maxwell equation.
  We present the mathematically rigorous semiclassical limit $\hbar \rightarrow
0$ of the Pauli-Poisswell equation towards the magnetic Euler-Poisswell
equation. We use WKB analysis which is valid locally in time only. A key step
is to obtain an a priori energy estimate for which we have to take into account
the Poisson equations for the magnetic potential with the current as source
term. Additionally we obtain the weak convergence of the monokinetic Wigner
transform and strong convergence of the density and the current density. We
also prove local wellposedness of the Euler-Poisswell equation which is global
unless a finite time blow-up occurs.


  The one-variable non-symmetric Wilson polynomials are shown to coincide with
the Bannai-Ito polynomials. The isomorphism between the corresponding
degenerate double affine Hecke algebra of type $(C_1^{\vee}, C_1)$ and the
Bannai-Ito algebra is established. The Bannai-Ito polynomials are seen to
satisfy an orthogonality relation with respect to a positive-definite and
continuous measure on the real line. A non-compact form of the Bannai-Ito
algebra is introduced and a four-parameter family of its infinite-dimensional
and self-adjoint representations is exhibited.


  We generalize Standard Monomial Theory (SMT) to intersections of Schubert
varieties and opposite Schubert varieties; such varieties are called Richardson
varieties. The aim of this article is to get closer to a geometric
interpretation of the standard monomial theory. Our methods show that in order
to develop a SMT for a certain class of subvarieties in G/B (which includes
G/B), it suffices to have the following three ingredients, a basis for the
space of sections of an effective line bundle on G/B, compatibility of such a
basis with the varieties in the class, certain quadratic relations in the
monomials in the basis elements. An important tool will be the construction of
nice filtrations of the vanishing ideal of the boundary of the varieties above.
This provides a direct connection to the equivariant K-theory, where the
combinatorially defined notion of standardness gets a geometric interpretation.


  We study the scaling scenery of Gibbs measures for subshifts of finite type
on self-conformal fractals and applications to Falconer's distance set problem
and dimensions of projections. Our analysis includes hyperbolic Julia sets,
limit sets of Schottky groups and graph-directed self-similar sets.


  The effect of the dipole polarization on the quantum dipole dipole
interaction near an Ag nanosphere (ANS) is investigated. A theoretical
formalism in terms of classical Green function is developed for the transfer
rate and the potential energy of the dipole dipole interaction (DDI) between
two polarized dipoles. It is found that a linear transition dipole can couple
to a left circularly polarized transition dipole much stronger than to a right
circularly polarized transition dipole. This polarization selectivity exists
over a wide frequency range and is robust against the variation of the dipoles'
position or the radius of the ANS. In contrast, a right circularly polarized
transition dipole, can change sharply from coupling strongly to another right
circularly polarized dipole to coupling strongly to a left circularly polarized
dipole with varying frequency. However, if the two dipoles are placed in the
same radial direction of the sphere, the right circularly polarized transition
dipole can only couple to the dipole with the same polarization while not to
the left circularly polarized transition dipole. These findings may be used in
solid-state quantum-information processing based on the DDI.


  We study the far-infrared properties of 498 Lyman Alpha Emitters (LAEs) at
z=2.8, 3.1 and 4.5 in the Extended Chandra Deep Field-South, using 250, 350 and
500 micron data from the Herschel Multi-tiered Extragalactic Survey (HerMES)
and 870 micron data from the LABOCA ECDFS Submillimeter Survey (LESS). None of
the 126, 280 or 92 LAEs at z=2.8, 3.1 and 4.5, respectively, are individually
detected in the far-infrared data. We use stacking to probe the average
emission to deeper flux limits, reaching $1\sigma$ depths of ~0.1 to 0.4 mJy.
The LAEs are also undetected at $\ge3\sigma$ in the stacks, although a
$2.5\sigma$ signal is observed at 870 micron for the z=2.8 sources. We consider
a wide range of far-infrared spectral energy distributions (SEDs), including a
M82 and an Sd galaxy template, to determine upper limits on the far-infrared
luminosities and far-infrared-derived star-formation rates of the LAEs. These
star-formation rates are then combined with those inferred from the Ly$\alpha$
and UV emission to determine lower limits on the LAEs Ly$\alpha$ escape
fraction ($f_{\rm esc}($Ly$\alpha$)). For the Sd SED template, the inferred
LAEs $f_{\rm esc}($Ly$\alpha$) are $\gtrsim30%$ ($1\sigma$) at z=2.8, 3.1 and
4.5, which are all significantly higher than the global $f_{\rm
esc}($Ly$\alpha$) at these redshifts. Thus, if the LAEs $f_{\rm
esc}($Ly$\alpha$) follows the global evolution then they have warmer
far-infrared SEDs than the Sd galaxy template. The average and M82 SEDs produce
lower limits on the LAE $f_{\rm esc}($Ly$\alpha$) of ~10 to 20% ($1\sigma$),
all of which are slightly higher than the global evolution of $f_{\rm
esc}($Ly$\alpha$) but consistent with it at the 2 to 3$\sigma$ level.


  We consider the Schroedinger operator on graphs and study the spectral
statistics of a unitary operator which represents the quantum evolution, or a
quantum map on the graph. This operator is the quantum analogue of the
classical evolution operator of the corresponding classical dynamics on the
same graph. We derive a trace formula, which expresses the spectral density of
the quantum operator in terms of periodic orbits on the graph, and show that
one can reduce the computation of the two-point spectral correlation function
to a well defined combinatorial problem. We illustrate this approach by
considering an ensemble of simple graphs. We prove by a direct computation that
the two-point correlation function coincides with the CUE expression for 2x2
matrices. We derive the same result using the periodic orbit approach in its
combinatorial guise. This involves the use of advanced combinatorial techniques
which we explain.


  In this work, we study the notions of relative comonad and comodule over a
relative comonad, and use these notions to give a terminal coalgebra semantics
for the coinductive type families of streams and of infinite triangular
matrices, respectively, in intensional Martin-L\"of type theory. Our results
are mechanized in the proof assistant Coq.


  While research on the geometry of planar graphs has been active in the past
decades, many properties of planar metrics remain mysterious. This paper
studies a fundamental aspect of the planar graph geometry: covering planar
metrics by a small collection of simpler metrics. Specifically, a \emph{tree
cover} of a metric space $(X, \delta)$ is a collection of trees, so that every
pair of points $u$ and $v$ in $X$ has a low-distortion path in at least one of
the trees.
  The celebrated "Dumbbell Theorem" [ADMSS95] states that any low-dimensional
Euclidean space admits a tree cover with $O(1)$ trees and distortion
$1+\varepsilon$, for any fixed $\varepsilon \in (0,1)$. This result has found
numerous algorithmic applications, and has been generalized to the wider family
of doubling metrics [BFN19]. Does the same result hold for planar metrics? A
positive answer would add another evidence to the well-observed connection
between Euclidean/doubling metrics and planar metrics.
  In this work, we answer this fundamental question affirmatively.
Specifically, we show that for any given fixed $\varepsilon \in (0,1)$, any
planar metric can be covered by $O(1)$ trees with distortion $1+\varepsilon$.
Our result for planar metrics follows from a rather general framework: First we
reduce the problem to constructing tree covers with \emph{additive distortion}.
Then we introduce the notion of \emph{shortcut partition}, and draw connection
between shortcut partition and additive tree cover. Finally we prove the
existence of shortcut partition for any planar metric, using new insights
regarding the grid-like structure of planar graphs. [...]


  We survey a new approach to the duality-invariant systems of nonlinear
electrodynamics, based on introducing auxiliary bi-spinor fields. In this
approach, the entire information about the given self-dual system is encoded in
the U(1) invariant interaction of the auxiliary fields, while the standard
self-dual Lagrangians appear on shell as a result of eliminating auxiliary
fields by their equations of motion. Starting from the simplest U(1) duality,
we show how this approach can be generalized to the U(N) duality (with N
independent Maxwell field strengths), as well as to self-dual systems of {\cal
N}=1 supersymmetric electrodynamics. Also, it works perfectly for self-dual
systems with higher derivatives in the action.


  Revealing a community structure in a network or dataset is a central problem
arising in many scientific areas. The modularity function $Q$ is an established
measure quantifying the quality of a community, being identified as a set of
nodes having high modularity. In our terminology, a set of nodes with positive
modularity is called a \textit{module} and a set that maximizes $Q$ is thus
called \textit{leading module}. Finding a leading module in a network is an
important task, however the dimension of real-world problems makes the
maximization of $Q$ unfeasible. This poses the need of approximation techniques
which are typically based on a linear relaxation of $Q$, induced by the
spectrum of the modularity matrix $M$. In this work we propose a nonlinear
relaxation which is instead based on the spectrum of a nonlinear modularity
operator $\mathcal M$. We show that extremal eigenvalues of $\mathcal M$
provide an exact relaxation of the modularity measure $Q$, however at the price
of being more challenging to be computed than those of $M$. Thus we extend the
work made on nonlinear Laplacians, by proposing a computational scheme, named
\textit{generalized RatioDCA}, to address such extremal eigenvalues. We show
monotonic ascent and convergence of the method. We finally apply the new method
to several synthetic and real-world data sets, showing both effectiveness of
the model and performance of the method.


  New thickness and shape parameters for describing the thermal boundary layer
formed by 2-D fluid flow along a heated (cooled) wall are presented. The
parameters are based on probability distribution function methodology in which
the thermal profile thickness and shape are described by central moments of the
thermal profile. The moment based parameters are simple integrals of the
temperature profile. The usefulness of the new method is demonstrated by
applying the description to laminar and turbulent boundary layer datasets.


  The interaction of edge dislocation with helium-implantation-induced defects
in tungsten is investigated using molecular dynamics. Following prior
investigations, we consider defects with two helium ions in a vacancy with a
self-interstitial bound to it (He2V-SIA). Our observations suggest 3-10
He2V-SIA cluster together, with their pinning strength on glide dislocations
increasing with size. For all cluster sizes, the dislocation bows around the
cluster, until it gets unpinned, carrying the SIAs with it and leaving behind a
helium-vacancy complex and newly created vacancies in its wake. The remnant
helium-vacancy complex has little pinning effect, highlighting the
defect-clearing process. A total solute hardening force for a distribution of
clusters of different sizes, induced by 3000 appm of helium, is found to be
approximately 700 MPa. This is in good agreement with the corresponding value
of 750 MPa estimated in a previously developed crystal plasticity model
simulating the deformation behaviour of the helium-implanted tungsten.


  This thesis presents new applications of Gale duality to the study of
polytopes, point configurations and oriented matroids with extremal
combinatorial properties.
  The first part of the thesis explores construction techniques for neighborly
polytopes and oriented matroids. First, we provide a new interpretation of
Shemer's classical Sewing Construction for neighborly polytopes in terms of
lexicographic extensions of oriented matroids. This allows us to provide a
simplified proof and to generalize it to oriented matroids in two ways: the
Extended Sewing Construction and the Gale Sewing Construction. Estimating the
number of polytopes constructed with the later, we can provide new lower bounds
for the number of combinatorial types of neighborly polytopes that even improve
the current best bounds for the number of polytopes. The combination of both
new techniques also allows us to construct many non-realizable neighborly
oriented matroids.
  The degree of a point configuration is the maximal codimension of its
interior faces. The second part of the thesis presents various results on the
combinatorial structure of point configurations whose degree is small compared
to their dimension; specifically, those whose degree is smaller than [(d+1)/2],
the degree of neighborly polytopes. The study of this problem comes motivated
by Ehrhart theory, where a notion equivalent to the degree - for lattice
polytopes - has been widely studied during the last years. In addition, the
study of the degree is also related to the Generalized Lower Bound Theorem for
simplicial polytopes, with Cayley polytopes and with Tverberg theory. Among
other results, we present a complete combinatorial classification for point
configurations of degree 1. Moreover, we show combinatorial restrictions for
configurations of small degree in terms of the novel concepts of weak Cayley
configurations and codegree decompositions.


  Hydrodynamics and quantum mechanics have many elements in common, as the
density field and velocity fields are common variables that can be constructed
in both descriptions. Starting with the Schroedinger equation and the
Klein-Gordon for a single particle in hydrodynamical form, we examine the basic
assumptions under which a quantum system of particles interacting through their
mean fields can be described by hydrodynamics.


  A frieze on a polygon is a map from the diagonals of the polygon to an
integral domain which respects the Ptolemy relation. Conway and Coxeter
previously studied positive friezes over $\mathbb{Z}$ and showed that they are
in bijection with triangulations of a polygon. We extend their work by studying
friezes over $\mathbb Z[\sqrt{2}]$ and their relationships to dissections of
polygons. We largely focus on the characterization of unitary friezes that
arise from dissecting a polygon into triangles and quadrilaterals. We identify
a family of dissections that give rise to unitary friezes and conjecture that
this gives a complete classification of dissections which admit a unitary
frieze.


  We study model-based offline Reinforcement Learning with general function
approximation without a full coverage assumption on the offline data
distribution. We present an algorithm named Constrained Pessimistic Policy
Optimization (CPPO)which leverages a general function class and uses a
constraint over the model class to encode pessimism. Under the assumption that
the ground truth model belongs to our function class (i.e., realizability in
the function class), CPPO has a PAC guarantee with offline data only providing
partial coverage, i.e., it can learn a policy that competes against any policy
that is covered by the offline data. We then demonstrate that this algorithmic
framework can be applied to many specialized Markov Decision Processes where
additional structural assumptions can further refine the concept of partial
coverage. Two notable examples are: (1) low-rank MDP with representation
learning where the partial coverage condition is defined using a relative
condition number measured by the unknown ground truth feature representation;
(2) factored MDP where the partial coverage condition is defined using density
ratio based concentrability coefficients associated with individual factors.


  The aim of this work is to consider the controllability problem of the linear
system associated to Korteweg-de Vries Burgers equation posed in the whole real
line. We obtain a sort of exact controllability for solutions in
$L^2_{loc}(\R^2)$ by deriving an internal observability inequality and a Global
Carlemann estimate. Following the ideas contained in \cite{rosier2000}, the
problem is reduced to prove an approximate theorem.


  We derive the mass of the white dwarf in the eclipsing recurrent nova U Sco
from the radial velocity semi-amplitudes of the primary and secondary stars.
Our results give a high white dwarf mass of M_1 = 1.55 \pm 0.24M_\odot,
consistent with the thermonuclear runaway model of recurrent nova outbursts. We
confirm that U Sco is the best Type Ia supernova progenitor known, and predict
that the time to explosion is within ~700,000 years.


  Top interactions beyond the Standard Model can be conveniently described in
the framework of gauge-invariant effective operators. We briefly review the
general form of the fermion-fermion-gauge boson and fermion-fermion-Higgs
interactions arising from dimension-6 operators, focusing on the top quark. We
discuss in detail an expansion in powers of 1/Lambda^2, where Lambda is the new
physics scale, to consistently calculate observables in terms of top anomalous
couplings.


  Various procedures for expressing the multipolar expansion of the
electromagnetic field are considered with application to the calculation of the
radiated power. Some results from literature are discussed and perspective of
developing the subject is pointed out.


  In Part I of this work we defined a generalization of the concept of
effective resistance to directed graphs, and we explored some of the properties
of this new definition. Here, we use the theory developed in Part I to compute
effective resistances in some prototypical directed graphs. This exploration
highlights cases where our notion of effective resistance for directed graphs
behaves analogously to our experience from undirected graphs, as well as cases
where it behaves in unexpected ways.


  In cores of supernovae and crusts of neutron stars, nuclei can adopt
interesting shapes, such as rods or slabs, etc., which are referred to as
nuclear "pasta." In recent years, we have studied the pasta phases focusing on
their dynamical aspects with a quantum molecular dynamic (QMD) approach. In
this article, we review these works. We also focus on the treatment of the
Coulomb interaction.


  It is presented a simple algorithm for power network state estimation and
correction (fault detection) employing standard methodology.


  The integrability-based solution of string theories related to
AdS(n)/CFT(n-1) dualities relies on the worldsheet S matrix. Using generalized
unitarity we construct the terms with logarithmic dependence on external
momenta at one- and two-loop order in the worldsheet S matrix for strings in a
general integrable worldsheet theory. We also discuss aspects of calculations
at higher orders. The S-matrix elements are expressed as sums of integrals with
coefficients given in terms of tree-level worldsheet four-point scattering
amplitudes. One-loop rational functions, not determined by two-dimensional
unitarity cuts, are fixed by symmetry considerations. They play an important
role in the determination of the two-loop logarithmic contributions. We
illustrate the general analysis by computing the logarithmic terms in the one-
and two-loop four-particle S-matrix elements in the massive worldsheet sectors
of string theory in AdS_5 x S^5, AdS_4 x CP^3, AdS_3 x S^3 x S^3 x S^1 and
AdS_3 x S^3 x T^4. We explore the structure of the S matrices and provide
explicit evidence for the absence of higher-order logarithms and for the
exponentiation of the one-loop dressing phase.


  We propose a framework for studying optimal market making policies in a limit
order book (LOB). The bid-ask spread of the LOB is modelled by a Markov chain
with finite values, multiple of the tick size, and subordinated by the Poisson
process of the tick-time clock. We consider a small agent who continuously
submits limit buy/sell orders and submits market orders at discrete dates. The
objective of the market maker is to maximize her expected utility from revenue
over a short term horizon by a tradeoff between limit and market orders, while
controlling her inventory position. This is formulated as a mixed regime
switching regular/ impulse control problem that we characterize in terms of
quasi-variational system by dynamic programming methods. In the case of a
mean-variance criterion with martingale reference price or when the asset price
follows a Levy process and with exponential utility criterion, the dynamic
programming system can be reduced to a system of simple equations involving
only the inventory and spread variables. Calibration procedures are derived for
estimating the transition matrix and intensity parameters for the spread and
for Cox processes modelling the execution of limit orders. Several
computational tests are performed both on simulated and real data, and
illustrate the impact and profit when considering execution priority in limit
orders and market orders


  It has recently been proposed that the miscibility of nanoparticles with a
polymer matrix can be controlled by grafting polymer chains to the nanoparticle
surface. As a first step to study this situation, we have used molecular
dynamics simulations on a single nanoparticle of radius R ($4\sigma \le$R$\le
16\sigma$, where $\sigma$ is the diameter of a polymer monomer) grafted with
chains of length 500 in a polymer melt of chains of length 1000. The grafting
density $\Sigma$ was varied between $0.04$-$0.32$ chains/$\sigma^2$. To
facilitate equilibration a Monte Carlo double-bridging algorithm is applied -
new bonds are formed across a pair of chains, creating two new chains each
substantially different from the original. For the long brush chains studied
here, the structure of the brush assumes its large particle limit even for $R$
as small as 8$\sigma$, which is consistent with recent experimental findings.
We study autophobic dewetting of the melt from the brush as a function of
increasing $\Sigma$. Even these long brush and matrix chains of length $6$ and
$12$ $N_e$, respectively, (the entanglement length is $N_e \sim 85$) give
somewhat ambiguous results for the interfacial width, showing that studies of
two or more nanoparticles are necessary to properly understand these
miscibility issues. Entanglement between the brush and melt chains were
identified using the primitive path analysis. We find that the number of
entanglements between the brush and melt chains scale simply with the product
of the local monomer densities of brush and melt chains.


  This addendum shows that a demographic grade gap is best understood using a
course deficit model rather than the more common student deficit model.
Students from a concepts-first class took the same final exam as the three
other classes that were offered at the same time so the grade gaps between
different demographic groups from each class can be compared. It is found that
students identifying as members of a racial/ethnic group underrepresented in
physics had higher final exam grades than their peers from the same concepts
first class rather than the usual case, lower exam grades than their peers,
found in each of the other three classes. After controlling for demonstrated
incoming understanding of calculus and Newtonian mechanics this demographic gap
in the concepts first class is found to differ from that of the other three
classes by over four standard errors. In addition, it's noted that while
students' incoming understandings are useful in explaining within-group
differences they do not explain between-group differences suggesting that a
student deficit model does not explain (between-group) demographic grade gaps.


  With the aim of understanding failure modes in the peeling of silicone-based
adhesive joints and, in particular, the occurrence of adhesive or cohesive
failure, an experimental campaign has been conducted by considering plastic
substrates with different surface roughness. A flexible strip has been bonded
onto such substrates using a silicone adhesive, by controlling its thickness.
Peeling tests with 90{\deg} and 180{\deg} peeling angle configurations have
been performed and the effect of joint parameters, such as surface roughness
and adhesive thickness, onto the adhesion energy and the failure mode are
herein discussed in detail. Experimental results show that the failure mode
varies in each peeling test configuration such that in the case of 180{\deg}
peeling test there is mainly cohesive failure, while for 90{\deg} peeling
angle, a combination of adhesive and cohesive failure occurs. Moreover, due to
the presence of different failure modes in each peeling configuration, the
substrate roughness can increase the adhesion energy only in 90{\deg} peeling
tests.


  While machine learning approaches to visual emotion recognition offer great
promise, current methods consider training and testing models on small scale
datasets covering limited visual emotion concepts. Our analysis identifies an
important but long overlooked issue of existing visual emotion benchmarks in
the form of dataset biases. We design a series of tests to show and measure how
such dataset biases obstruct learning a generalizable emotion recognition
model. Based on our analysis, we propose a webly supervised approach by
leveraging a large quantity of stock image data. Our approach uses a simple yet
effective curriculum guided training strategy for learning discriminative
emotion features. We discover that the models learned using our large scale
stock image dataset exhibit significantly better generalization ability than
the existing datasets without the manual collection of even a single label.
Moreover, visual representation learned using our approach holds a lot of
promise across a variety of tasks on different image and video datasets.


  Neutrino masses may arise from spontaneous breaking of ungauged lepton
number. Due to quantum gravity effects the associated Goldstone boson - the
majoron - will pick up a mass. We determine the lifetime and mass required by
cosmic microwave background observations so that the massive majoron provides
the observed dark matter of the Universe. The majoron DDM scenario fits nicely
in models where neutrino masses arise a la seesaw, and may lead to other
possible cosmological implications.


  A modified Kaluza-Klein theory is proposed in which propagation takes place
only at the speed of light. The propagation can be confined to a small volume,
forming a particle with rest mass. The usual four space-time coordinates locate
the confinement volume, and Kaluza's fifth coordinate is replaced by an
internal degree of freedom. Electromagnetism corresponds to a gauge field on
the phase of the internal motion. Self-gravity might create the confinement, as
in a geon, but the particle would have a Planck mass. This large mass could be
made closer to the masses of observed particles if gravity were allowed to
increase in strength within the confinement volume.


  Unraveling the interplay between connectivity and spatio-temporal dynamics in
neuronal networks is a key step to advance our understanding of neuronal
information processing. Here we investigate how particular features of network
connectivity underpin the propensity of neural networks to generate
slow-switching assembly (SSA) dynamics, i.e., sustained epochs of increased
firing within assemblies of neurons which transition slowly between different
assemblies throughout the network. We show that the emergence of SSA activity
is linked to spectral properties of the asymmetric synaptic weight matrix. In
particular, the leading eigenvalues that dictate the slow dynamics exhibit a
gap with respect to the bulk of the spectrum, and the associated Schur vectors
exhibit a measure of block-localization on groups of neurons, thus resulting in
coherent dynamical activity on those groups. Through simple rate models, we
gain analytical understanding of the origin and importance of the spectral gap,
and use these insights to develop new network topologies with alternative
connectivity paradigms which also display SSA activity. Specifically, SSA
dynamics involving excitatory and inhibitory neurons can be achieved by
modifying the connectivity patterns between both types of neurons. We also show
that SSA activity can occur at multiple timescales reflecting a hierarchy in
the connectivity, and demonstrate the emergence of SSA in small-world like
networks. Our work provides a step towards understanding how network structure
(uncovered through advancements in neuroanatomy and connectomics) can impact on
spatio-temporal neural activity and constrain the resulting dynamics.


  Let $X$ and $Y$ be Banach spaces, $A\in B(X)$, $B\in B(Y)$, $C\in B(Y, X)$,
$M_{C}=({cc}A&C 0&B)$ be the operator matrix acting on the Banach space
$X\oplus Y$. In this paper, we give out 20 kind spectra structure of $M_C$,
decide 18 kind spectra filling-in-hole properties of $M_C$, and present 10
examples to show that some conclusions about the spectra structure or
filling-in-hole properties of $M_C$ are not true.


  We propose a realization of a two-dimensional higher-order topological
insulator with ultracold atoms loaded into orbital angular momentum (OAM)
states of an optical lattice. The symmetries of the OAM states induce relative
phases in the tunneling amplitudes that allow to describe the system in terms
of two decoupled lattice models. Each of these models displays one-dimensional
edge states and zero-dimensional corner states that are correlated with the
topological properties of the bulk. We show that the topologically non-trivial
regime can be explored in a wide range of experimentally feasible values of the
parameters of the physical system. Furthermore, we propose an alternative way
to characterize the second-order topological corner states based on the
computation of the Zak's phases of the bands of first-order edge states.


  Measurements of Deep-Inelastic Neutral and Charged current interactions are
presented in lepton proton scattering at HERA. The measurements are obtained
from taken during 1996 to 1999 and consists of $30 \rm{pb^{-1}}$ of $e^+p$ and
$16 \rm{pb^{-1}}$ of $e^-p$ data. The addition of the new high statistics
electron data with the positron data allows the first extraction of the parity
violating structure function $xF_3$ and tests of high-$Q^2$ electroweak effects
of the heavy bosons $Z^0$ and $W$ are observed and found to be consistent with
the Standard Model expectation.


  With the evergrowing sizes of pre-trained models (PTMs), it has been an
emerging practice to only provide the inference APIs for users, namely
model-as-a-service (MaaS) setting. To adapt PTMs with model parameters frozen,
most current approaches focus on the input side, seeking for powerful prompts
to stimulate models for correct answers. However, we argue that input-side
adaptation could be arduous due to the lack of gradient signals and they
usually require thousands of API queries, resulting in high computation and
time costs. In light of this, we present Decoder Tuning (DecT), which in
contrast optimizes task-specific decoder networks on the output side.
Specifically, DecT first extracts prompt-stimulated output scores for initial
predictions. On top of that, we train an additional decoder network on the
output representations to incorporate posterior data knowledge. By
gradient-based optimization, DecT can be trained within several seconds and
requires only one PTM query per sample. Empirically, we conduct extensive
natural language understanding experiments and show that DecT significantly
outperforms state-of-the-art algorithms with a $200\times$ speed-up.