  Thermodynamic properties are presented for four magnetic impurity models
describing delocalized fermions scattering from a localized orbital at an
energy-dependent rate $\Gamma(\epsilon)$ which vanishes precisely at the Fermi
level, $\epsilon = 0$. Specifically, it is assumed that for small $|\epsilon|$,
$\Gamma(\epsilon)\propto|\epsilon|^r$ with $r>0$. The cases $r=1$ and $r=2$
describe dilute magnetic impurities in unconventional superconductors, ``flux
phases'' of the two-dimensional electron gas, and zero-gap semiconductors. For
the nondegenerate Anderson model, the depression of the low-energy scattering
rate suppresses mixed valence in favor of local-moment behavior, and leads to a
marked reduction in the exchange coupling on entry to the local-moment regime,
with a consequent narrowing of the range of parameters within which the
impurity spin becomes Kondo-screened. The relationship between the Anderson
model and the exactly screened Kondo model with power-law exchange is examined.
The intermediate-coupling fixed point identified in the latter model by Withoff
and Fradkin (WF) has clear signatures in the thermodynamic properties and in
the local magnetic response of the impurity. The underscreened,
impurity-spin-one Kondo model and the overscreened, two-channel Kondo model
both exhibit a conditionally stable intermediate-coupling fixed point in
addition to unstable fixed points of the WF type. In all four models, the
presence or absence of particle-hole symmetry plays a crucial role.


  We give a simple proof of the non-rationality of the Fano threefold defined
by the equations \Sigma x_i = \Sigma x_i^2 = \Sigma x_i^3 = 0 in P^6 .


  First-order resolution has been used for type inference for many years,
including in Hindley- Milner type inference, type-classes, and constrained data
types. Dependent types are a new trend in functional languages. In this paper,
we show that proof-relevant first-order resolution can play an important role
in automating type inference and term synthesis for dependently typed
languages. We propose a calculus that translates type inference and term
synthesis problems in a dependently typed language to a logic program and a
goal in the proof-relevant first-order Horn clause logic. The computed answer
substitution and proof term then provide a solution to the given type inference
and term synthesis problem. We prove the decidability and soundness of our
method. The paper is under consideration for acceptance in TPLP.


  In many applications, it is desired to obtain extreme eigenvalues and
eigenvectors of large Hermitian matrices by efficient and compact algorithms.
In particular, orthogonalization-free methods are preferred for large-scale
problems for finding eigenspaces of extreme eigenvalues without explicitly
computing orthogonal vectors in each iteration. For the top $p$ eigenvalues,
the simplest orthogonalization-free method is to find the best rank-$p$
approximation to a positive semi-definite Hermitian matrix by algorithms
solving the unconstrained Burer-Monteiro formulation. We show that the
nonlinear conjugate gradient method for the unconstrained Burer-Monteiro
formulation is equivalent to a Riemannian conjugate gradient method on a
quotient manifold with the Bures-Wasserstein metric, thus its global
convergence to a stationary point can be proven. Numerical tests suggest that
it is efficient for computing the largest $k$ eigenvalues for large-scale
matrices if the largest $k$ eigenvalues are nearly distributed uniformly.


  The paper proposes a construction of a quantum differentiation operator
defined on the spaces of complex-valued functions of $p$-adic argument, and
taking values in the algebra of bounded operators on a Hilbert space. The
properties of this operator are investigated. In particular, it is proved that
the differentiation operator maps $p$-adic Besov spaces into Schatten-von
Neumann ideals in the algebra of compact operators.


  One century after the discovery of quasi-periodic oscillations in the optical
light curve of Nova GK Per 1901 the cause of the transition phase in a certain
part of the nova population is still unknown. Three years ago we suggested a
solution for this problem and proposed a possible connection between the
transition phase and intermediate polars (IPs). About 10 percent of the
cataclysmic variable population are classified as IPs, which is consistent with
the rarity (about 15 percent) of the transition phase in novae. Recent
observations of three novae seem to support our prediction. The connection is
explained as follows: The nova outburst disrupts the accretion disc only in
IPs. The recovery of the disc, a few weeks-months after the eruption, causes
strong winds that block the radiation from the white dwarf, thus dust is not
destroyed. If the winds are very strong as is probably the case in DQ Her
(perhaps since its spin period is very short) this leads to a dust minimum.


  We study the interplay of collective dynamics and damping in the presence of
correlations and bosonic fluctuations within the framework of a newly proposed
model, which captures the principal transport mechanisms that apply to a
variety of physical systems. We establish close connections to the transport of
lattice and spin polarons, or the dynamics of a particle coupled to a bath. We
analyse the model by exactly calculating the optical conductivity, Drude
weight, spectral functions, groundstate dispersion and particle-boson
correlation functions for a 1D infinite system.


  This article contains a digest of the theory of electromagnetism and a review
of the transformation between inertial frames, especially under low speed
limits. The covariant nature of the Maxwell's equations is explained using the
conventional language. We show that even under low speed limits, the
relativistic effects should not be neglected to get a self-consistent theory of
the electromagnetic fields, unless the intrinsic dynamics of these fields has
been omitted completely. The quasi-static limits, where the relativistic
effects can be partly neglected are also reviewed, to clarify some common
misunderstandings and imprecise use of the theory in presence of moving media
and other related situations. The discussion presented in this paper provide a
clear view of why classical electromagnetic theory is relativistic in its
essence.


  This article unveils a new relation between the Nishimori temperature
parametrizing a distribution P and the Bethe free energy on random Erdos-Renyi
graphs with edge weights distributed according to P. Estimating the Nishimori
temperature being a task of major importance in Bayesian inference problems, as
a practical corollary of this new relation, a numerical method is proposed to
accurately estimate the Nishimori temperature from the eigenvalues of the Bethe
Hessian matrix of the weighted graph. The algorithm, in turn, is used to
propose a new spectral method for node classification in weighted (possibly
sparse) graphs. The superiority of the method over competing state-of-the-art
approaches is demonstrated both through theoretical arguments and real-world
data experiments.


  We construct the five loop anomalous dimensions of the basic fields in
Quantum Chromodynamics in a linear covariant gauge in the modified
Regularization Invariant (RI') scheme. Using these core results we also compute
the four loop Green's function where the quark mass operator and vector current
are separately inserted in a quark 2-point function. These are necessary for
measurements of the same quantities on the lattice. The Green's functions are
provided in both the modified Minimal Subtraction (MSbar) and RI' schemes. All
the results are available for a general Lie group.


  This paper addresses the problem of video object segmentation, where the
initial object mask is given in the first frame of an input video. We propose a
novel spatio-temporal Markov Random Field (MRF) model defined over pixels to
handle this problem. Unlike conventional MRF models, the spatial dependencies
among pixels in our model are encoded by a Convolutional Neural Network (CNN).
Specifically, for a given object, the probability of a labeling to a set of
spatially neighboring pixels can be predicted by a CNN trained for this
specific object. As a result, higher-order, richer dependencies among pixels in
the set can be implicitly modeled by the CNN. With temporal dependencies
established by optical flow, the resulting MRF model combines both spatial and
temporal cues for tackling video object segmentation. However, performing
inference in the MRF model is very difficult due to the very high-order
dependencies. To this end, we propose a novel CNN-embedded algorithm to perform
approximate inference in the MRF. This algorithm proceeds by alternating
between a temporal fusion step and a feed-forward CNN step. When initialized
with an appearance-based one-shot segmentation CNN, our model outperforms the
winning entries of the DAVIS 2017 Challenge, without resorting to model
ensembling or any dedicated detectors.


  Given a knot or link in the form of plat closure of a braid, we describe an
algorithm to obtain a braid representing the same knot or link with the
standard closure, and vice-versa. We analyze the three cases of knots and
links: in \(\mathbb{R}^3\), in handlebodies and in thickened surfaces. We show
that the algorithm is quadratic in the number of crossings and loop generators
of the braid when passing from plat to standard closure, while it is linear
when passing from standard to plat closure.


  The interplay between the torsional potential energy and the scaling of the
1-4 van der Waals and Coulomb interactions determines the stiffness of flexible
molecules. In molecular simulations often ad-hoc values for the scaling factor
(SF) are adopted without adequate justification. In this letter we demonstrate
for the first time that the precise value of the SF has direct consequences on
the critical properties and mechanisms of systems undergoing a phase
transition. By analyzing the melting of n-alkanes (hexane C6, dodecane C12,
tetracosane C24) on graphite, we show that the SF is not a universal feature,
that it monotonically decreases with the molecular length, and that it drives a
cross-over between two distinct mechanisms for melting in such systems.


  Processing-in-memory (PIM) is attractive to overcome the limitations of
modern computing systems. Numerous PIM systems exist, varying by the
technologies and logic techniques used. Successful operation of specific logic
functions is crucial for effective processing-in-memory. Memristive
non-stateful logic techniques are compatible with CMOS logic and can be
integrated into a 1T1R memory array, similar to commercial RRAM products. This
paper analyzes and demonstrates two non-stateful logic techniques: 1T1R logic
and scouting logic. As a first step, the used 1T1R SiO\textsubscript{x} valence
change mechanism memristors are characterized in reference to their feasibility
to perform logic functions. Various logical functions of the two logic
techniques are experimentally demonstrated, showing correct functionality in
all cases. Following the results, the challenges and limitations of the RRAM
characteristics and 1T1R configuration for the application in logical functions
are discussed.


  We have performed high-resolution measurements of the magnetic field (0~T~$
\le B \le 9~$T) and temperature (10 K~$\le T < 140~$K) dependence of the
longitudinal and transverse Hall thermal conductivity of a twinned
YBa$_{2}$Cu$_{3}$O$_{6.95}$ single crystal. We have used and compared two
recently published methods to extract the thermal Hall angle $\theta_H(T,B)$.
Our results indicate that $\cot(\theta_H)$ varies quite accurately as $T^4$ in
the intermediate temperature range $\sim 0.3 < T/T_c$. It shows a well defined
minimum at $T_m \simeq 20~$K which resembles that observed in the $c$-axis
microwave conductivity. The electronic part of the longitudinal and the
transverse thermal conductivity show the scaling behavior for transport
properties predicted for d-wave superconductors in the temperature range $\sim
18~$K~$\le T \le 30~$K.


  HD 106315 and GJ 9827 are two bright, nearby stars that host multiple
super-Earths and sub-Neptunes discovered by K2 that are well suited for
atmospheric characterization. We refined the planets' ephemerides through
Spitzer transits, enabling accurate transit prediction required for future
atmospheric characterization through transmission spectroscopy. Through a
multi-year high-cadence observing campaign with Keck/HIRES and Magellan/PFS, we
improved the planets' mass measurements in anticipation of HST transmission
spectroscopy. For GJ 9827, we modeled activity-induced radial velocity signals
with a Gaussian process informed from the Calcium II H&K lines in order to more
accurately model the effect of stellar noise on our data. We found planet
masses of M$_b$=$4.87\pm 0.37$ M$_\oplus$, M$_c$=$1.92\pm 0.49$ M$_\oplus$, and
M$_d$=$3.42\pm 0.62$ M$_\oplus$. For HD 106315, we found that such
activity-radial velocity decorrelation was not effective due to the reduced
presence of spots and speculate that this may extend to other hot stars as well
(T$_{\rm {eff}}>6200$ K). We found planet masses of M$_b$=$10.5\pm 3.1$
M$_\oplus$ and M$_c$=$12.0\pm 3.8$ M$_\oplus$. We investigated all of the
planets' compositions through comparing their masses and radii to a range of
interior models. GJ 9827 b and GJ 9827 c are both consistent with an Earth-like
rocky composition, GJ 9827 d and HD 106315 b both require additional volatiles
and are consistent with moderate amounts of water or hydrogen/helium, and HD
106315 c is consistent with 10% hydrogen/helium surrounding an Earth-like rock
and iron core.


  This paper focuses on decentralized stochastic optimization in the presence
of Byzantine attacks. During the optimization process, an unknown number of
malfunctioning or malicious workers, termed as Byzantine workers, disobey the
algorithmic protocol and send arbitrarily wrong messages to their neighbors.
Even though various Byzantine-resilient algorithms have been developed for
distributed stochastic optimization with a central server, we show that there
are two major issues in the existing robust aggregation rules when being
applied to the decentralized scenario: disagreement and non-doubly stochastic
virtual mixing matrix. This paper provides comprehensive analysis that
discloses the negative effects of these two issues, and gives guidelines of
designing favorable Byzantine-resilient decentralized stochastic optimization
algorithms. Under these guidelines, we propose iterative outlier scissor (IOS),
an iterative filtering-based robust aggregation rule with provable performance
guarantees. Numerical experiments demonstrate the effectiveness of IOS. The
code of simulation implementation is available at github.com/Zhaoxian-Wu/IOS.


  Consider a periodic tiling of a plane by equal triangles obtained from the
equilateral tiling by a linear transformation. We study a following tiling
billiard: a ball follows straight segments and bounces of the boundaries of the
tiles into neighbouring tiles in such a way that the coefficient of refraction
is equal to -1. We show that almost all the trajectories of such a billiard are
either closed or escape linearly, and for closed trajectories we prove that
their periods belong to the set 4N+2. We also give a precise description of the
exceptional family of trajectories (of zero measure) : these trajectories
escape non-linearly to infinity and approach fractal-like sets. We show that
this exceptional family is parametrized by the famous Rauzy gasket. This proves
several conjectures stated previously on triangle tiling billiards. In this
work, we also give a more precise understanding of fully flipped minimal
exchange transformations on 3 and 4 intervals by proving that they belong to a
special hypersurface. Our proofs are based on the study of Rauzy graphs for
interval exchange transformations with flips.


  One of the major puzzles regarding unconventional superconductivity is how
some of the most interesting superconductors are related to an insulating phase
that lies in close proximity. Here we report scanning tunneling microscopy
studies of the local electronic structure of Cu doped NaFeAs across the
superconductor to insulator transition. We find that in the highly insulating
regime the electronic spectrum develops an energy gap with diminishing density
of state at the Fermi level. The overall lineshape and strong spatial
variations of the spectra are strikingly similar to that of lightly doped
cuprates close to the parent Mott insulator. We propose that the suppression of
itinerant electron state and strong impurity potential induced by Cu dopants
lead to this insulating iron pnictide.


  Characterising the circumstellar dust around nearby main sequence stars is a
necessary step in understanding the planetary formation process and is crucial
for future life-finding space missions such as ESA's Darwin or NASA's
Terrestrial Planet Finder (TPF). Besides paving the technological way to
Darwin/TPF, the space-based infrared interferometers Pegase and FKSI
(Fourier-Kelvin Stellar Interferometer) will be valuable scientific precursors
in that respect. In this paper, we investigate the performance of Pegase and
FKSI for exozodiacal disc detection and compare the results with ground-based
nulling interferometers. Besides their main scientific goal (characterising hot
giant extrasolar planets), Pegase and FKSI are very efficient in assessing
within a few minutes the level of circumstellar dust in the habitable zone
around nearby main sequence stars. They are capable of detecting exozodiacal
discs respectively 5 and 1 time as dense as the solar zodiacal cloud and they
outperform any ground-based instrument. Unlike Pegase, FKSI can achieve this
sensitivity for most targets of the Darwin/TPF catalogue thanks to an
appropriate combination of baseline length and observing wavelength. The
sensitivity of Pegase could, however, be significantly boosted by considering a
shorter interferometric baseline length. These space-based interferometers
would be complementary to Antarctica-based instruments in terms of sky coverage
and would be ideal instruments for preparing future life-finding space
missions.


  We study the initial value problem for the wave equation and the
ultrahyperbolic equation for data posed on initial surface of mixed signature
(both spacelike and timelike). Under a nonlocal constraint, we show that the
Cauchy problem on codimension-one hypersurfaces has global unique solutions in
the Sobolev spaces $H^{m}$, thus it is well-posed. In contrast, we show that
the initial value problem on higher codimension hypersurfaces is ill-posed, at
least when specifying a finite number of derivatives of the data, due to the
failure of uniqueness. This is in contrast to a uniqueness result which Courant
and Hilbert deduce from Asgeirsson's mean value theorem, for which we give an
independent derivation. The proofs use Fourier synthesis and the Holmgren-John
uniqueness theorem.


  This paper considers Schr\"odinger operators, and presents a probabilistic
interpretation of the variation (or shape derivative) of the Dirichlet
groundstate energy when the associated domain is perturbed. This interpretation
relies on the distribution on the boundary of a stopped random process with
Feynman-Kac weights. Practical computations require in addition the explicit
approximation of the normal derivative of the groundstate on the boundary. We
then propose to use this formulation in the case of the so-called fixed node
approximation of fermion groundstates, defined by the bottom eigenelements of
the Schr\"odinger operator of a fermionic system with Dirichlet conditions on
the nodes (the set of zeros) of an initially guessed skew-symmetric function.
We show that the shape derivative of the fixed node energy vanishes if and only
if either (i) the distribution on the nodes of the stopped random process is
symmetric; or (ii) the nodes are exactly the zeros of a skew-symmetric
eigenfunction of the operator. We propose an approximation of the shape
derivative of the fixed node energy that can be computed with a Monte-Carlo
algorithm, which can be referred to as Nodal Monte-Carlo (NMC). The latter
approximation of the shape derivative also vanishes if and only if either (i)
or (ii) holds.


  Quantum communication and clock synchronization protocols can be
significantly enhanced by the careful preparation of the wavepackets of the
produced photons. Following the theoretical proposal published in [Optica, 4,
84 (2017)], we experimentally demonstrate the effect of a remote temporal
wavepacket narrowing of a heralded single photon. It is performed by utilizing
the time-resolved measurement on the heralding photon which is frequency
entangled with the heralded one. We also investigate optimal photon pair source
characteristics that minimize the heralded wavepacket width.


  In this paper we introduce a task-oriented communication design for split
learning (SL) over a communication channel. Our approach involves the
Expressive Neural Network (ENN), a novel neural network featuring adaptive
activation functions (AAF) based on the Discrete Cosine Transform (DCT). This
architecture does not only provide better learning capabilities, but also
facilitates data transmission using the Long Range (LoRa) modulation. The
frequency nature of LoRa is adequate for the communication side of the problem,
while allowing to construct the AAFs at the receiver. Additionally, we propose
orthogonal chirp division multiplexing (OCDM) for multiple access and a
modified modulation aimed at preserving communication bandwidth. Our
experimental results demonstrate the effectiveness of this scheme, achieving
high accuracy in challenging scenarios, including low signal to noise Ratio
(SNR) and absence of channel state information (CSI) for both additive white
Gaussian noise (AWGN) and Rayleigh fading channels.


  This paper presents a method of computing section lift characteristics for a
2-dimensional airfoil with a second 2-dimensional object at a position at or
ahead of the leading edge of the airfoil. Since both objects are 2-dimensional,
the analysis yields a closed form solution to calculation of the airflow over
the airfoil and second object, using conformal mapping of analytically closed
form airflow velocity vector past two circular shaped objects in initial
complex plane, using a standard air flow model for each object individually.
The combined airflow velocity vector is obtained by linear superposition of the
velocity vector for the two objects, computed individually. The lift
characteristics are obtained from the circulation around the airfoil and second
object which is computed from the combined closed form velocity vector and the
geometry along the contour integral for circulation. The illustrative example
considered in this paper shows that the second object which is essentially a
cylinder whose diameter is approximately 9% of the chord length of the airfoil
reduces the section lift coefficient by approximately 6:3% from that of the
airfoil alone. 1.


  Advancing QCD toward astroparticle applications generates new challenges for
perturbation theory, such as the presence of large evolution scales with
sizeable scaling violations involving both the initial and the final state of a
collision. Possible applications in the context of Ultra High Energy Cosmic
Rays (UHECR) of these effects are discussed.


  Compared with model-based control and optimization methods, reinforcement
learning (RL) provides a data-driven, learning-based framework to formulate and
solve sequential decision-making problems. The RL framework has become
promising due to largely improved data availability and computing power in the
aviation industry. Many aviation-based applications can be formulated or
treated as sequential decision-making problems. Some of them are offline
planning problems, while others need to be solved online and are
safety-critical. In this survey paper, we first describe standard RL
formulations and solutions. Then we survey the landscape of existing RL-based
applications in aviation. Finally, we summarize the paper, identify the
technical gaps, and suggest future directions of RL research in aviation.


  CuSiO_3, isotypic to the spin - Peierls compound CuGeO_3, was discovered
recently as a metastable decomposition product of the silicate mineral
dioptase, Cu_6Si_6O_{18}\cdot6H_2O. We investigated the physical properties of
CuSiO_3 using susceptibility, magnetization and specific heat measurements on
powder samples. The magnetic susceptibility \chi(T) is reproduced very well
above T = 8 K by theoretical calculations for an S=1/2 antiferromagnetic
Heisenberg linear chain without frustration (\alpha = 0) and a nearest -
neighbor exchange coupling constant of J/k_{B} = 21 K, much weaker than in
CuGeO_3. Below 8 K the susceptibility exhibits a substantial drop. This feature
is identified as a second - order phase transition at T_{0} = 7.9 K by specific
heat measurements. The influence of magnetic fields on T_{0} is weak, and ac -
magnetization measurements give strong evidence for a spin - flop - phase at
\mu_0H_{SF} ~ 3 T. The origin of the magnetic phase transition at T_{0} = 7.9 K
is discussed in the context of long - range antiferromagnetic order (AF) versus
spin - Peierls(SP)order. Susceptibility and specific heat results support the
AF ordered ground state. Additional temperature dependent ^{63,65}Cu nuclear
quadrupole resonance experiments have been carried out to probe the Cu^{2+}
electronic state and the spin dynamics in CuSiO_3.


  We present the first results of a blind HI survey for galaxies in the
southern Zone of Avoidance with a multibeam receiver on the Parkes telescope.
This survey is eventually expected to catalog several thousand galaxies within
Galactic latitude |b|<5 degrees, mostly unrecognised before due to Galactic
extinction and confusion. We present here results of the first three detections
to have been imaged with the Australia Telescope Compact Array (ATCA). The
galaxies all lie near Galactic longitude 325 degrees and were selected because
of their large angular sizes, up to 1.3 degrees. Linear sizes range from 53 to
108 kpc. The first galaxy is a massive 5.7x10^11 solar mass disk galaxy with a
faint optical counterpart, SGC 1511.1--5249. The second is probably an
interacting group of galaxies straddling the Galactic equator. No optical
identification is possible. The third object appears to be an interacting pair
of low column density galaxies, possibly belonging to an extended Circinus or
Centaurus A galaxy group. No optical counterpart has been seen despite the
predicted extinction (A(B) = 2.7 - 4.4 mag) not being excessive. We discuss the
implications of the results, in particular the low HI column densities (~10^19
atoms/sq.cm) found for two of the three galaxies.


  Spatial resolution of stimulated emission depletion (STED) microscopy varies
with sample labeling techniques and microscope components, e.g., lasers,
lenses, and photo-detectors. Fluctuations in the intensity of the depletion
laser decrease achievable resolution in STED microscopy; the stronger the
fluctuations, the higher the average intensity needed to achieve a given
resolution. This phenomenon is encountered in every STED measurement. However,
a theoretical framework that evaluates the effect of intensity fluctuations on
spatial resolution is lacking. This article presents an analytical formulation
based on a stochastic model that characterizes the impact of the laser
fluctuations and correlation time on the depletion efficiency in the continuous
wave (CW) STED microscopy. We compared analytical results with simulations
using a wide range of intensity noise conditions and found a high degree of
agreement. The stochastic model used considers a colored noise distribution for
the laser intensity fluctuations. Simple analytical expressions were obtained
in the limit of small and large fluctuations correlation time. These
expressions fitted very well the available experimental data. Finally, this
work offers a starting point to model other laser noise effects in various
microscopy implementations.


  Spatio-temporal areal data can be seen as a collection of time series which
are spatially correlated according to a specific neighboring structure.
Incorporating the temporal and spatial dimension into a statistical model poses
challenges regarding the underlying theoretical framework as well as the
implementation of efficient computational methods. We propose to include
spatio-temporal random effects using a conditional autoregressive prior, where
the temporal correlation is modeled through an autoregressive mean
decomposition and the spatial correlation by the precision matrix inheriting
the neighboring structure. Their joint distribution constitutes a Gaussian
Markov random field, whose sparse precision matrix enables the usage of
efficient sampling algorithms. We cluster the areal units using a nonparametric
prior, thereby learning latent partitions of the areal units. The performance
of the model is assessed via an application to study regional unemployment
patterns in Italy. When compared to other spatial and spatio-temporal
competitors, the proposed model shows more precise estimates and the additional
information obtained from the clustering allows for an extended economic
interpretation of the unemployment rates of the Italian provinces.


  We study canonical conformal gravity in four dimensions and construct the
gauge generators and the associated charges. Using slightly generalized
boundary conditions compared to those in \cite{Grumiller:2013mxa} we find that
the charges associated with space-time diffeomorphisms are finite and conserved
in time. They are also shown to agree with the Noether charges found in
\cite{Grumiller:2013mxa}. However, there exists no charge associated with Weyl
transformations. Consequently the asymptotic symmetry algebra is isomorphic to
the Lie algebra of the boundary condition preserving diffeomorphisms. For
illustrative purposes we apply the results to the Mannheim--Kazanas--Riegert
solution of conformal gravity.


  The electronic structure of lanthanide and actinide compounds is often
characterized by orbital ordering of localized $f$-electrons.
Density-functional theory (DFT) studies of such systems using the currently
available LDA+$U$ method are plagued by significant orbital-dependent
self-interaction, leading to erroneous orbital ground states. An alternative
scheme that modifies the exchange, not Hartree, energy is proposed as a remedy.
We show that our LDA+$U$ approach reproduces the expected degeneracy of $f^1$
and $f^2$ states in free ions and the correct ground states in solid PrO$_2$.
We expect our method to be useful in studying compounds of $f$- and heavy-$d$
elements.


  We present Integrated Multimodal Perception (IMP), a simple and scalable
multimodal multi-task training and modeling approach. IMP integrates multimodal
inputs including image, video, text, and audio into a single Transformer
encoder with minimal modality-specific components. IMP makes use of a novel
design that combines Alternating Gradient Descent (AGD) and Mixture-of-Experts
(MoE) for efficient model and task scaling. We conduct extensive empirical
studies and reveal the following key insights: 1) Performing gradient descent
updates by alternating on diverse modalities, loss functions, and tasks, with
varying input resolutions, efficiently improves the model. 2) Sparsification
with MoE on a single modality-agnostic encoder substantially improves the
performance, outperforming dense models that use modality-specific encoders or
additional fusion layers and greatly mitigates the conflicts between
modalities. IMP achieves competitive performance on a wide range of downstream
tasks including video classification, image classification, image-text, and
video-text retrieval. Most notably, we train a sparse IMP-MoE-L variant
focusing on video tasks that achieves new state-of-the-art in zero-shot video
classification: 77.0% on Kinetics-400, 76.8% on Kinetics-600, and 68.3% on
Kinetics-700, improving the previous state-of-the-art by +5%, +6.7%, and +5.8%,
respectively, while using only 15% of their total training computational cost.


  Following a suggestion of A. Connes (see [Co] {\S} I.1), we build up a
(first) simple natural structure of a no finitely generated braided
non-commutative Hopf algebra, suggested by elementary quantum mechanics.


  We explore the role of attention mechanism during inference in
text-conditional diffusion models. Empirical observations suggest that
cross-attention outputs converge to a fixed point after several inference
steps. The convergence time naturally divides the entire inference process into
two phases: an initial phase for planning text-oriented visual semantics, which
are then translated into images in a subsequent fidelity-improving phase.
Cross-attention is essential in the initial phase but almost irrelevant
thereafter. However, self-attention initially plays a minor role but becomes
crucial in the second phase. These findings yield a simple and training-free
method known as temporally gating the attention (TGATE), which efficiently
generates images by caching and reusing attention outputs at scheduled time
steps. Experimental results show when widely applied to various existing
text-conditional diffusion models, TGATE accelerates these models by 10%-50%.
The code of TGATE is available at https://github.com/HaozheLiu-ST/T-GATE.


  Two new QCD sum rules for nucleons in nuclear matter are obtained from a
mixed correlator of spin-1/2 and spin-3/2 interpolating fields. These new sum
rules, which are insensitive to the poorly known four-quark condensates,
provide additional information on the nucleon scalar self-energy. These new sum
rules are analyzed along with previous spin-1/2 interpolator-based sum rules
which are also insensitive to the poorly known four-quark condensates. The
analysis indicates consistency with the expectations of relativistic nuclear
phenomenology at nuclear matter saturation density. However, a weaker density
dependence near saturation is suggested. Using previous estimates of in-medium
condensate uncertainties, we find $M^* = 0.64^{+0.13}_{-0.09}$ GeV and
$\Sigma_v = 0.29^{+0.06}_{-0.10}$ GeV at nuclear matter saturation density.


  Using the near-detailed-balance distribution function obtained in our recent
work, we present a set of covariant gravito-thermal transport equations for
neutral relativistic gases in a generic stationary spacetime. All relevant
tensorial transport coefficients are worked out and are presented using some
particular integration functions in $(\alpha,\zeta)$, where $\alpha =
-\beta\mu$ and $\zeta =\beta m$ is the relativistic coldness, with $\beta$
being the inverse temperature and $\mu$ being the chemical potential. It is
shown that the Onsager reciprocal relation holds in the gravito-thermal
transport phenomena, and that the heat conductivity and the
gravito-conductivity tensors are proportional to each other, with the
coefficient of proportionality given by the product of the so-called Lorenz
number with the temperature, thus proving a gravitational variant of the
Wiedemann-Franz law. It is remarkable that, for strongly degenerate Fermi
gases, the Lorenz number takes a universal constant value $L=\pi^2/3$, which
extends the Wiedemann-Franz law into the Wiedemann-Franz-Lorenz law.


  We call \emph{Alphabet model} a generalization to N types of particles of the
classic ABC model. We have particles of different types stochastically evolving
on a one dimensional lattice with an exchange dynamics. The rates of exchange
are local but under suitable conditions the dynamics is reversible with a
Gibbsian like invariant measure with long range interactions. We discuss
geometrically the conditions of reversibility on a ring that correspond to a
gradient condition on the graph of configurations or equivalently to a
divergence free condition on a graph structure associated to the types of
particles. We show that much of the information on the interactions between
particles can be encoded in associated \emph{Tournaments} that are a special
class of oriented directed graphs. In particular we show that the interactions
of reversible models are corresponding to strongly connected tournaments. The
possible minimizers of the energies are in correspondence with the Hamiltonian
cycles of the tournaments. We can then determine how many and which are the
possible minimizers of the energy looking at the structure of the associated
tournament. As a byproduct we obtain a probabilistic proof of a classic Theorem
of Camion \cite{Camion} on the existence of Hamiltonian cycles for strongly
connected tournaments. Using these results we obtain in the case of an equal
number of k types of particles new representations of the Hamiltonians in terms
of translation invariant $k$-body long range interactions. We show that when
$k=3,4$ the minimizer of the energy is always unique up to translations.
Starting from the case $k=5$ it is possible to have more than one minimizer. In
particular it is possible to have minimizers for which particles of the same
type are not joined together in single clusters.


  We use the avoidance of the trans-Planckian problem of Hawking radiation as a
guiding principle in searching for a compelling scenario for the evaporation of
black holes or black-hole-like objects. We argue that there exist only three
possible scenarios, depending on whether the classical notion of long-lived
horizon is preserved by high-energy physics and on whether the dark and compact
astrophysical objects that we observe have long-lived horizons in the first
place. Along the way, we find that (i) a theory with high-energy superluminal
signalling and a long-lived trapping horizon would be extremely unstable in
astrophysical terms and that (ii) stellar pulsations of objects hovering right
outside but extremely close to their gravitational radius can result in a
mechanism for Hawking-like emission.


  We present a systematic study of the production of the heavy quarkonium,
i.e., $|(c\bar{c})[n] \rangle$ , $|(b\bar{c})[n] \rangle$ (or $|(c\bar{b})[n]
\rangle$), and $|(b\bar{b})[n] \rangle$ quarkonium [$|(Q\bar{Q'})[n]\rangle$
quarkonium for short], through $Z^0$ boson semi-exclusive decays with new
parameters \cite{lx} for the heavy quarkonium under the framework of the NRQCD,
where $[n]$ stands for $n^1S_0$, $n^3S_1$, $n^1P_0$, $n^3P_J$ ($n=1, \cdots,
6$; $J=(0, 1, 2)$). "Improved trace technology" is adopted to derive the
simplified analytic expressions at the amplitude level, which shall be useful
for dealing with these decay channels. If all higher $|(Q\bar{Q'})[n]\rangle$
quarkonium states decay to the ground state $|(Q\bar{Q'})[1^1S_0]\rangle$ with
$100\%$ efficiency via electromagnetic or hadronic interactions, we obtain
$\Gamma{(Z^0\to |(c\bar{c})[1^1S_0]\rangle)}=1476$ KeV, $\Gamma{(Z^0\to
|(b\bar{c})[1^1S_0]\rangle)}=1485$ KeV, $\Gamma{(Z^0\to
|(b\bar{b})[1^1S_0]\rangle)}=127.5$ KeV. At the LHC and ILC with the luminosity
${\cal L}\propto 10^{34}cm^{-2}s^{-1}$, sizable heavy quarkonium events can be
produced through $Z^0$ boson decays, i.e., about $5.9~\times10^{5}$
$(c\bar{c})$, $6.0~\times10^{5}$ $(b\bar{c})$ (or $(c\bar{b})$),
$5.1~\times10^{4}$ $(b\bar{b})$ events per year can be obtained.


  A nonlocal vector calculus was introduced in [2] that has proved useful for
the analysis of the peridynamics model of nonlocal mechanics and nonlocal
diffusion models. A generalization is developed that provides a more general
setting for the nonlocal vector calculus that is independent of particular
nonlocal models. It is shown that general nonlocal calculus operators are
integral operators with specific integral kernels. General nonlocal calculus
properties are developed, including nonlocal integration by parts formula and
Green's identities. The nonlocal vector calculus introduced in [2] is shown to
be recoverable from the general formulation as a special example. This special
nonlocal vector calculus is used to reformulate the peridynamics equation of
motion in terms of the nonlocal gradient operator and its adjoint. A new
example of nonlocal vector calculus operators is introduced, which shows the
potential use of the general formulation for general nonlocal models.


  Android's 3X3 graphical pattern lock scheme is one of the widely used
authentication method on smartphone devices. However, users choose 3X3 patterns
from a small subspace of all possible 389,112 patterns. The two recently
proposed interfaces, SysPal by Cho et al. and TinPal by the authors,
demonstrate that it is possible to influence users 3X3 pattern choices by
making small modifications in the existing interface. While SysPal forces users
to include one, two or three system-assigned random dots in their pattern,
TinPal employs a highlighting mechanism to inform users about the set of
reachable dots from the current selected dot. Both interfaces improved the
security of 3X3 patterns without affecting usability, but no comparison between
SysPal and TinPal was presented.
  To address this gap, we conduct a new user study with 147 participants and
collect patterns on three SysPal interfaces, 1-dot, 2-dot and 3-dot. We also
consider original and TinPal patterns collected in our previous user study
involving 99 participants. We compare patterns created on five different
interfaces, original, TinPal, 1-dot, 2-dot and 3-dot using a range of security
and usability metrics including pattern length, stroke length, guessability,
recall time and login attempts. Our study results show that participants in the
TinPal group created significantly longer and complex patterns than
participants in the other four groups. Consequently, the guessing resistance of
TinPal patterns was the highest among all groups. Further, we did not find any
significant difference in memorability of patterns created in the TinPal group
and the other groups.


  Following Einstein's definition of Lagrangian density and gravitational field
energy density (Einstein, A., Ann. Phys. Lpz., 49, 806 (1916); Einstein, A.,
Phys. Z., 19, 115 (1918); Pauli, W., {\it Theory of Relativity}, B.I.
Publications, Mumbai, 1963, Trans. by G. Field), Tolman derived a general
formula for the total matter plus gravitational field energy ($P_0$) of an
arbitrary system (Tolman, R.C., Phys. Rev., 35(8), 875 (1930); Tolman, R.C.,
{\it Relativity, Thermodynamics & Cosmology}, Clarendon Press, Oxford, 1962));
Xulu, S.S., arXiv:hep-th/0308070 (2003)). For a static isolated system, in
quasi-Cartesian coordinates, this formula leads to the well known result $P_0 =
\int \sqrt{-g} (T_0^0 - T_1^1 -T_2^2 -T_3^3) ~d^3 x$, where $g$ is the
determinant of the metric tensor and $T^a_b$ is the energy momentum tensor of
the {\em matter}. Though in the literature, this is known as "Tolman Mass", it
must be realized that this is essentially "Einstein Mass" because the
underlying pseudo-tensor here is due to Einstein. In fact, Landau -Lifshitz
obtained the same expression for the "inertial mass" of a static isolated
system without using any pseudo-tensor at all and which points to physical
significance and correctness of Einstein Mass (Landau, L.D., and Lifshitz,
E.M., {\it The Classical Theory of Fields}, Pergamon Press, Oxford, 2th ed.,
1962)! For the first time we apply this general formula to find an expression
for $P_0$ for the Friedmann- Robertson -Walker (FRW) metric by using the same
quasi-Cartesian basis. As we analyze this new result, physically, a spatially
flat model having no cosmological constant is suggested. Eventually, it is seen
that conservation of $P_0$ is honoured only in the a static limit.


  The well-established neutrino oscillation phenomenon, which confirms
neutrinos have mass and the charged and neutral leptons are mixed, has been
widely exploited to investigate the physics of this elusive particle. The
complete description of neutrino oscillations, which are dictated by two
mass-squared splittings, three mixing angles, and one Dirac CP-violation phase,
however, has yet to be reached. The ongoing accelerator-based long-baseline
neutrino experiments, T2K and NOvA, are critical in completing this picture.
Using data and analyses accessible by summer 2023, T2K favors a leptonic CP
violation at more than 90\% C.L. while NOvA shows no preference of this
indication. Both experiments weakly opt for the \emph{normal} neutrino mass
ordering and higher octant of the $\theta_{23}$ mixing angle.


  This paper presents a study of two tracking algorithms (SORT~\cite{7533003}
and Tracktor++~\cite{2019}) that were ranked first positions on the MOT
Challenge leaderboard (The MOTChallenge web page: https://motchallenge.net ).
The purpose of this study is to discover the techniques used and to provide
useful insights about these algorithms in the tracking pipeline that could
improve the performance of MOT tracking algorithms. To this end, we adopted the
popular tracking-by-detection approach. We trained our own Pedestrian Detection
model using the MOT17Det dataset (MOT17Det :
https://motchallenge.net/data/MOT17Det/ ). We also used a re-identification
model trained on MOT17 dataset (MOT17 : https://motchallenge.net/data/MOT17/ )
for Tracktor++ to reduce the false re-identification alarms. We then present
experimental results which shows that Tracktor++ is a better multi-person
tracking algorithm than SORT. We also performed ablation studies to discover
the contribution of re-identification(RE-ID) network and motion to the results
of Tracktor++. We finally conclude by providing some recommendations for future
research.


  Graphs and networks play an important role in modeling and analyzing complex
interconnected systems such as transportation networks, integrated circuits,
power grids, citation graphs, and biological and artificial neural networks.
Graph clustering algorithms can be used to detect groups of strongly connected
vertices and to derive coarse-grained models. We define transfer operators such
as the Koopman operator and the Perron-Frobenius operator on graphs, study
their spectral properties, introduce Galerkin projections of these operators,
and illustrate how reduced representations can be estimated from data. In
particular, we show that spectral clustering of undirected graphs can be
interpreted in terms of eigenfunctions of the Koopman operator and propose
novel clustering algorithms for directed graphs based on generalized transfer
operators. We demonstrate the efficacy of the resulting algorithms on several
benchmark problems and provide different interpretations of clusters.


  In this paper we describe the calculation of the process e+e- -> Z/gamma ->
QQbar + X, where Q is a heavy quark, at order alpha_s^2.


  In this paper we analyze a virtual element method for the two dimensional
elasticity spectral problem allowing small edges. Under this approach, and with
the aid of the theory of compact operators, we prove convergence of the
proposed VEM and error estimates, where the influence of the Lam\'e constants
is presented. We present a series of numerical tests to assess the performance
of the method where we analyze the effects of the Poisson ratio on the
computation of the order of convergence, together with the effects of the
stabilization term on the arising of spurious eigenvalues.


  For integer $h\geq2$ and $A\subseteq\mathbb{N}$, we define $hA$ to be all
integers which can be written as a sum of $h$ elements of $A$. The set $A$ is
called an asymptotic basis of order $h$ if $n\in hA$ for all sufficiently large
integers $n$. An asymptotic basis $A$ of order $h$ is minimal if no proper
subset of $A$ is an asymptotic basis of order $h$. For $W\subseteq\mathbb{N}$,
denote by $\mathcal{F}^*(W)$ the set of all finite, nonempty subsets of $W$.
Let $A(W)$ be the set of all numbers of the form $\sum_{f \in F} 2^f$, where $F
\in \mathcal{F}^*(W)$. In this paper, we give some characterizations of the
partitions $\mathbb{N}=W_1\cup\cdots \cup W_h$ with the property that
$A=A(W_1)\cup\cdots \cup A(W_{h})$ is a minimal asymptotic basis of order $h$.
This generalizes a result of Chen and Chen, recent result of Ling and Tang, and
also recent result of Sun.


  We prove the global existence of classical solutions to a class of forced
drift-diffusion equations with $L^2$ initial data and divergence free drift
velocity $\{u^\nu\}_{\nu_\ge0}\subset L^\infty_t BMO^{-1}_x$, and we obtain
strong convergence of solutions as the viscosity $\nu$ vanishes. We then apply
our results to a family of active scalar equations which includes the three
dimensional magneto-geostrophic $\{$MG$^\nu\}_{\nu\ge0}$ equation that has been
proposed by Moffatt in the context of magnetostrophic turbulence in the Earth's
fluid core. We prove the existence of a compact global attractor
$\{\mathcal{A}^\nu\}_{\nu\ge0}$ in $L^2(\mathbb{T}^3)$ for the MG$^\nu$
equations including the critical equation where $\nu=0$. Furthermore, we obtain
the upper semicontinuity of the global attractor as $\nu$ vanishes.


  Via an appropriate field redefinition of the fermions, we find a set of
conditions under which light cone gauge fixed world sheet theories of strings
on two different backgrounds are related by a double Wick rotation. These
conditions take the form of a set of transformation laws for the background
fields, complementing a set of transformation laws for the metric and B field
we found previously with a set for the dilaton and RR fields, and are
compatible with the supergravity equations of motion. Our results prove that at
least to second order in fermions, the AdS_5 x S^5 mirror model which plays an
important role in the field of integrability in AdS/CFT, represents a string on
`mirror AdS_5 x S^5', the background that follows from our transformations. We
discuss analogous solutions for AdS_3 x S^3 x T^4 and AdS_2 x S^2 x T^6. The
main ingredient in our derivation is the light cone gauge fixed action for a
string on an (almost) completely generic background, which we explicitly derive
to second order in fermions.


  This paper considers the classical error correcting problem which is
frequently discussed in coding theory. We wish to recover an input vector $f
\in \R^n$ from corrupted measurements $y = A f + e$. Here, $A$ is an $m$ by $n$
(coding) matrix and $e$ is an arbitrary and unknown vector of errors. Is it
possible to recover $f$ exactly from the data $y$? We prove that under suitable
conditions on the coding matrix $A$, the input $f$ is the unique solution to
the $\ell_1$-minimization problem ($\|x\|_{\ell_1} := \sum_i |x_i|$) $$ \min_{g
\in \R^n} \| y - Ag \|_{\ell_1} $$ provided that the support of the vector of
errors is not too large, $\|e\|_{\ell_0} := |\{i : e_i \neq 0\}| \le \rho \cdot
m$ for some $\rho > 0$. In short, $f$ can be recovered exactly by solving a
simple convex optimization problem (which one can recast as a linear program).
In addition, numerical experiments suggest that this recovery procedure works
unreasonably well; $f$ is recovered exactly even in situations where a
significant fraction of the output is corrupted.


  We provide a theoretical algorithm for checking local optimality and escaping
saddles at nondifferentiable points of empirical risks of two-layer ReLU
networks. Our algorithm receives any parameter value and returns: local
minimum, second-order stationary point, or a strict descent direction. The
presence of $M$ data points on the nondifferentiability of the ReLU divides the
parameter space into at most $2^M$ regions, which makes analysis difficult. By
exploiting polyhedral geometry, we reduce the total computation down to one
convex quadratic program (QP) for each hidden node, $O(M)$ (in)equality tests,
and one (or a few) nonconvex QP. For the last QP, we show that our specific
problem can be solved efficiently, in spite of nonconvexity. In the benign
case, we solve one equality constrained QP, and we prove that projected
gradient descent solves it exponentially fast. In the bad case, we have to
solve a few more inequality constrained QPs, but we prove that the time
complexity is exponential only in the number of inequality constraints. Our
experiments show that either benign case or bad case with very few inequality
constraints occurs, implying that our algorithm is efficient in most cases.


  Here we survey the compactness and geometric stability conjectures formulated
by the participants at the 2018 IAS Emerging Topics Workshop on {\em Scalar
Curvature and Convergence}. We have tried to survey all the progress towards
these conjectures as well as related examples, although it is impossible to
cover everything. We focus primarily on sequences of compact Riemannian
manifolds with nonnegative scalar curvature and their limit spaces. Christina
Sormani is grateful to have had the opportunity to write up our ideas and has
done her best to credit everyone involved within the paper even though she is
the only author listed above. In truth we are a team of over thirty people
working together and apart on these deep questions and we welcome everyone who
is interested in these conjectures to join us.


  We present a new $BF$-type action for complex general relativity with or
without a cosmological constant resembling Plebanski's action, which depends on
an SO(3,$\mathbb{C}$) connection, a set of 2-forms, a symmetric matrix, and a
4-form. However, it differs from the Plebanski formulation in the way that the
symmetric matrix enters into the action. The advantage of this fact is twofold.
First, as compared to Plebanski's action, the symmetric matrix can now be
integrated out, which leads to a pure $BF$-type action principle for general
relativity; the canonical analysis of the new action then shows that it has the
same phase space of the Ashtekar formalism up to a canonical transformation
induced by a topological term. Second, a particular choice of the parameters
involved in the formulation produces a $BF$-type action principle describing
conformally anti-self-dual gravity. Therefore, the new action unifies both
general relativity and anti-self-dual gravity.


  In composite Higgs models the pseudo-Nambu-Goldstone Boson (pNGB) nature of
the Higgs field is an interesting alternative for explaning the smallness of
the electroweak scale with respect to the beyond the Standard Model scale. In
non-minimal models additional pNGB states are present and can be a Dark Matter
(DM) candidate, if there is an approximate symmetry suppressing their decay.
Here we assume that the low energy effective theory (for scales much below the
compositeness scale) corresponds to the Standard Model with a pNGB Higgs
doublet and a pNGB DM multiplet. We derive general effective DM Lagrangians for
several possible DM representations (under the SM gauge group), including the
singlet, doublet and triplet cases. Within this framework we discuss how the DM
observables (relic abundance, direct and indirect detection) constrain the
dimension-6 operators induced by the strong sector assuming that DM behaves as
a Weakly Interacting Particle (WIMP) and that the relic abundance is settled
through the freeze-out mechanism. We also apply our general results to two
specific cosets: $SO(6)/SO(5)$ and $SO(6)/SO(4) \times SO(2)$, which contain a
singlet and doublet DM candidate, respectively. In particular we show that if
compositeness is a solution to the little hierarchy problem, representations
larger than the triplet are strongly disfavored. Furthermore, we find that
composite models can have viable DM candidates with much smaller direct
detection cross-sections than their non-composite counterparts, making DM
detection much more challenging.


  The squashed seven-sphere operator spectrum is completed by deriving the
spectrum of the spin-3/2 operator. The implications of the results for the
$AdS_4$ $\mathcal{N} = 1$ supermultiplets obtained from compactification of
eleven-dimensional supergravity are analysed. The weak $G_2$ holonomy plays an
important role when solving the eigenvalue equations on the squashed sphere.
Here, a novel and more universal algebraic approach to the whole eigenvalue
problem on coset manifolds is provided. Having obtained full control of all the
operator spectra, we can finally determine the irreps $D(E_0, s)$ for all
supermultiplets in the left-squashed vacuum. This includes an analysis of
possible boundary conditions. By performing an orientation flip on the
seven-sphere, we also obtain the full spectrum for the non-supersymmetric
right-squashed compactification which is of interest in the swampland context
and in particular for the $AdS$ swampland conjecture. Here, a number of
boundary condition ambiguities arise making the analysis of dual marginal
operators somewhat involved. This work is a direct continuation of [1] and [2].


  We investigate Maxwell's attempt to justify the mathematical assumptions
behind his 1860 Proposition IV according to which the velocity components of
colliding particles follow the normal distribution. Contrary to the commonly
held view we find that his molecular collision model plays a crucial role in
reaching this conclusion, and that his model assumptions also permit inference
to equalization of mean kinetic energies (temperatures), which is what he
intended to prove in his discredited and widely ignored Proposition VI. If we
take a charitable reading of his own proof of Proposition VI then it was
Maxwell, and not Boltzmann, who gave the first proof of a tendency towards
equilibrium, a sort of H-theorem. We also call attention to a potential
conflation of notions of probabilistic and value independence in relevant prior
works of his contemporaries and of his own, and argue that this conflation
might have impacted his adoption of the suspect independence assumption of
Proposition IV.


We prove a variation of Gronwall's lemma.


  We present a determination of the isovector, $P$-wave $\pi\pi$ scattering
phase shift obtained by extrapolating recent lattice QCD results from the
Hadron Spectrum Collaboration using $m_\pi =236$ MeV. The finite volume spectra
are described using extensions of L\"uscher's method to determine the infinite
volume Unitarized Chiral Perturbation Theory scattering amplitude. We exploit
the pion mass dependence of this effective theory to obtain the scattering
amplitude at $m_\pi= 140$ MeV. The scattering phase shift is found to be in
good agreement with experiment up to center of mass energies of 1.2 GeV. The
analytic continuation of the scattering amplitude to the complex plane yields a
$\rho$-resonance pole at $E_\rho=
\left[755(2)(1)(^{20}_{02})-\frac{i}{2}\,129(3)(1)(^{7}_{1})\right]~{\rm MeV}$.
The techniques presented illustrate a possible pathway towards connecting
lattice QCD observables of few-body, strongly interacting systems to
experimentally accessible quantities.


  In recent years the shperical wave expansion method has been widely applied
to the theory and calculation of electromagnetic fields. But the inner product
exist in reference[1] is defined on the Banach space[2]. Through redefining the
inner product this article limits the wave expansion method to Hibert space[3].
For this reason the mutual energy theorem is introduced.


  AutoAugment has been a powerful algorithm that improves the accuracy of many
vision tasks, yet it is sensitive to the operator space as well as
hyper-parameters, and an improper setting may degenerate network optimization.
This paper delves deep into the working mechanism, and reveals that AutoAugment
may remove part of discriminative information from the training image and so
insisting on the ground-truth label is no longer the best option. To relieve
the inaccuracy of supervision, we make use of knowledge distillation that
refers to the output of a teacher model to guide network training. Experiments
are performed in standard image classification benchmarks, and demonstrate the
effectiveness of our approach in suppressing noise of data augmentation and
stabilizing training. Upon the cooperation of knowledge distillation and
AutoAugment, we claim the new state-of-the-art on ImageNet classification with
a top-1 accuracy of 85.8%.


  This paper is the second part of a trilogy dedicated to the following
problem: given spherically symmetric characteristic initial data for the
Einstein-Maxwell-scalar field system with a cosmological constant $\Lambda$,
with the data on the outgoing initial null hypersurface given by a subextremal
Reissner-Nordstrom black hole event horizon, study the future extendibility of
the corresponding maximal globally hyperbolic development as a "suitably
regular" Lorentzian manifold.
  In the first paper of this sequence, we established well posedness of the
characteristic problem with general initial data.
  In this second paper, we generalize the results of Dafermos on the stability
of the radius function at the Cauchy horizon by including a cosmological
constant. This requires a considerable deviation from the strategy followed by
Dafermos, focusing on the level sets of the radius function instead of the
red-shift and blue-shift regions. We also present new results on the global
structure of the solution when the free data is not identically zero in a
neighborhood of the origin.
  In the third and final paper, we will consider the issue of mass inflation
and extendibility of solutions beyond the Cauchy horizon.


  We identify two orthogonal sources of structural entropy in rattler-free
granular systems - affine, involving structural changes that only deform the
contact network, and topological, corresponding to different topologies of the
contact network. We show that a recently developed connectivity-based granular
statistical mechanics separates the two naturally by identifying the structural
degrees of freedom with spanning trees on the graph of the contact network. We
extend the connectivity-based formalism to include constraints on, and
correlations between, degrees of freedom as interactions between branches of
the spanning tree. We then use the statistical mechanics formalism to calculate
the partition function generally and the different entropies in the
high-angoricity limit. We also calculate the degeneracy of the affine entropy
and a number of expectation values. From the latter, we derive an equipartition
principle and an equation of state relating the macroscopic volume and boundary
stress to the analogue of the temperature, the contactivity.


  We focus on the well-studied problem of distributed overlay network
construction. We consider a synchronous gossip-based communication model where
in each round a node can send a message of small size to another node whose
identifier it knows. The network is assumed to be reconfigurable, i.e., a node
can add new connections (edges) to other nodes whose identifier it knows or
drop existing connections. Each node initially has only knowledge of its own
identifier and the identifiers of its neighbors. The overlay construction
problem is, given an arbitrary (connected) graph, to reconfigure it to obtain a
bounded-degree expander graph as efficiently as possible. The overlay
construction problem is relevant to building real-world peer-to-peer network
topologies that have desirable properties such as low diameter, high
conductance, robustness to adversarial deletions, etc.
  Our main result is that we show that starting from any arbitrary (connected)
graph $G$ on $n$ nodes and $m$ edges, we can construct an overlay network that
is a constant-degree expander in polylog $n$ rounds using only $\tilde{O}(n)$
messages. Our time and message bounds are both essentially optimal (up to
polylogarithmic factors). Our distributed overlay construction protocol is very
lightweight as it uses gossip (each node communicates with only one neighbor in
each round) and also scalable as it uses only $\tilde{O}(n)$ messages, which is
sublinear in $m$ (even when $m$ is moderately dense). To the best of our
knowledge, this is the first result that achieves overlay network construction
in polylog $n$ rounds and $o(m)$ messages. Our protocol uses graph sketches in
a novel way to construct an expander overlay that is both time and
communication efficient. A consequence of our overlay construction protocol is
that distributed computation can be performed very efficiently in this model.


  Models of alpha Cen A & B have been computed using the masses determined by
Pourbaix et al. (2002) and the data derived from the spectroscopic analysis of
Neuforge and Magain (1997). The seismological data obtained by Bouchy and
Carrier (2001, 2002) do help improve our knowledge of the evolutionary status
of the system. All the constraints are satisfied with a model which gives an
age of about 6 Gyr for the binary.


  Condensed matter systems offer the opportunity to maximize the number of
spins, probed in magnetic resonance experiments that search for physics beyond
the standard model. EuCl$_3\cdot 6$H$_2$O is a promising solid-state platform
for such searches. The narrow inhomogeneous linewidth of the Eu optical
$^7\hspace{-0.1em}F_0 \leftrightarrow\,^5\hspace{-0.1em}D_0$ transition in this
material opens the opportunity to optically pump the $^{153}$Eu nuclear spin
ensemble into a single hyperfine sublevel. The closely-spaced opposite-parity
nuclear energy levels, and the low-energy collective octupole mode, or a
possible static octupole deformation, enhance the $^{153}$Eu nuclear Schiff
moment. The optimistic estimate of the effective electric field is
$E^*=10\,$MV/cm. With this estimate, the CASPEr-electric search for the gluon
interaction of axion dark matter can reach QCD axion sensitivity with a 3~cm
sample.


  We survey some results on travel time tomography. The question is whether we
can determine the anisotropic index of refraction of a medium by measuring the
travel times of waves going through the medium. This can be recast as geometry
problems, the boundary rigidity problem and the lens rigidity problem. The
boundary rigidity problem is whether we can determine a Riemannian metric of a
compact Riemannian manifold with boundary by measuring the distance function
between boundary points. The lens rigidity problem problem is to determine a
Riemannian metric of a Riemannian manifold with boundary by measuring for every
point and direction of entrance of a geodesic the point of exit and direction
of exit and its length. The linearization of these two problems is tensor
tomography. The question is whether one can determine a symmetric two-tensor
from its integrals along geodesics. We emphasize recent results on boundary and
lens rigidity and in tensor tomography in the partial data case.


  Molecular para-hydrogen has been proposed theoretically as a possible
candidate for superfluidity, but the eventual superfluid transition is hindered
by its crystallization. In this work, we study a metastable non crystalline
phase of bulk p-H2 by means of the Path Integral Monte Carlo method in order to
investigate at which temperature this system can support superfluidity. By
choosing accurately the initial configuration and using a non commensurate
simulation box, we have been able to frustrate the formation of the crystal in
the simulated system and to calculate the temperature dependence of the
one-body density matrix and of the superfluid fraction. We observe a transition
to a superfluid phase at temperatures around 1 K. The limit of zero temperature
is also studied using the diffusion Monte Carlo method. Results for the energy,
condensate fraction, and structure of the metastable liquid phase at T=0 are
reported and compared with the ones obtained for the stable solid phase.


  We analyze the outage probability of an intelligent reflecting surface
(IRS)-assisted communication network. A tight upper bound on the outage
probability is formulated based on the Chernoff inequality. Furthermore,
through an exact asymptotic (a large number of reflecting elements) analysis
based on a saddlepoint approximation, we derive closed-form expressions of the
outage probability for systems with and without a direct link and obtain the
corresponding diversity orders. Simulation results corroborate our theoretical
analysis and show the inaccuracies inherent in using the central limit theorem
(CLT) to analyze system performance. Our analysis is accurate even for a small
number of IRS elements in the high signal-to-noise ratio (SNR) regime.


  Recently developed methods for rapid continuous volumetric two-photon
microscopy facilitate the observation of neuronal activity in hundreds of
individual neurons and changes in blood flow in adjacent blood vessels across a
large volume of living brain at unprecedented spatio-temporal resolution.
However, the high imaging rate necessitates fully automated image analysis,
whereas tissue turbidity and photo-toxicity limitations lead to extremely
sparse and noisy imagery. In this work, we extend a recently proposed deep
learning volumetric blood vessel segmentation network, such that it supports
temporal analysis. With this technology, we are able to track changes in
cerebral blood volume over time and identify spontaneous arterial dilations
that propagate towards the pial surface. This new capability is a promising
step towards characterizing the hemodynamic response function upon which
functional magnetic resonance imaging (fMRI) is based.


  Light detection and ranging (LIDAR) is critical to many fields in science and
industry. Over the last decade, optical frequency combs were shown to offer
unique advantages in optical ranging, in particular when it comes to fast
distance acquisition with high accuracy. However, current comb-based concepts
are not suited for emerging high-volume applications such as drone navigation
or autonomous driving. These applications critically rely on LIDAR systems that
are not only accurate and fast, but also compact, robust, and amenable to
cost-efficient mass-production. Here we show that integrated dissipative
Kerr-soliton (DKS) comb sources provide a route to chip-scale LIDAR systems
that combine sub-wavelength accuracy and unprecedented acquisition speed with
the opportunity to exploit advanced photonic integration concepts for
wafer-scale mass production. In our experiments, we use a pair of free-running
DKS combs, each providing more than 100 carriers for massively parallel
synthetic-wavelength interferometry. We demonstrate dual-comb distance
measurements with record-low Allan deviations down to 12 nm at averaging times
of 14 $\mu$s as well as ultrafast ranging at unprecedented measurement rates of
up to 100 MHz. We prove the viability of our technique by sampling the
naturally scattering surface of air-gun projectiles flying at 150 m/s (Mach
0.47). Combining integrated dual-comb LIDAR engines with chip-scale
nanophotonic phased arrays, the approach could allow widespread use of compact
ultrafast ranging systems in emerging mass applications.


  How the ground state nature can be dramatically changed by the distinct
underlying spin correlation is a central issue of doped Mott insulators. The
two-leg XXZ ladder provides a prototypical spin background, which can be tuned
from a long-range N\'{e}el order to a short-range ``spin liquid'' via the
superexchange anisotropy, giving rise to a complex phase diagram at finite
doping. By density matrix renormalization group method, we show that although
the charge is always self-localized in the N\'{e}el ordered phase, a second
insulating phase emerges, in which the doped holes become paired but remain
localized while the transverse spin-spin correlation reduces to short-ranged
one to make the N\'{e}el order classical. Only when the N\'{e}el order totally
disappears by further reducing anisotropy, does the pairing become truly
coherent as characterized by a Luther-Emery state. In sharp contrast, the
pairing is totally absent in the in-plane ferromagnetic XXZ regime, where a
direct transition from the charge self-localization in the N\'{e}el ordered
phase to a Fermi-gas-like state in the spin liquid phase is found. A consistent
physical picture is briefly discussed.


  The purpose of this paper is to clarify all of the uniformly relatively Ding
stable toric Fano threefolds and fourfolds as well as unstable ones. The key
player in our classification result is the Mabuchi constants, which can be
calculated by combinatorial data of the associated moment polytopes due to the
work of Yao [33]. In Tables 1-3, we give the list of uniform relative Ding
stability of all toric Fano manifolds in dimension up to four with the values
of the Mabuchi constants.
  As an application of our main theorem (Theorem 1.1), we clarify the
difference between relative $K$-stability and relative Ding stability by
considering some specific toric Fano manifolds (Corollaries 1.6 and 1.9). In
the proof of Corollary 1.9, we used Bott tower structure of relatively Ding
unstable toric Fano manifolds.


  Stem cell-derived organoids are a promising tool to model native human
tissues as they resemble human organs functionally and structurally compared to
traditional monolayer cell-based assays. For instance, colon organoids can
spontaneously develop crypt-like structures similar to those found in the
native colon. While analyzing the structural development of organoids can be a
valuable readout, using traditional image analysis tools makes it challenging
because of the heterogeneities and the abstract nature of organoid
morphologies. To address this limitation, we developed and validated a deep
learning-based image analysis tool, named D-CryptO, for the classification of
organoid morphology. D-CryptO can automatically assess the crypt formation and
opacity of colorectal organoids from brightfield images to determine the extent
of organoid structural maturity. To validate this tool, changes in organoid
morphology were analyzed during organoid passaging and short-term forskolin
stimulation. To further demonstrate the potential of D-CryptO for drug testing,
organoid structures were analyzed following treatments with a panel of
chemotherapeutic drugs. With D-CryptO, subtle variations in how colon organoids
responded to the different chemotherapeutic drugs were detected, which suggest
potentially distinct mechanisms of action. This tool could be expanded to other
organoid types, like intestinal organoids, to facilitate 3D tissue
morphological analysis.


  We study a nonequilibrium Ising model that stochastically evolves under the
simultaneous operation of several spin-flip mechanisms. In other words, the
local magnetic fields change sign randomly with time due to competing kinetics.
This dynamics models a fast and random diffusion of disorder that takes place
in dilute metallic alloys when magnetic ions diffuse. We performe Monte Carlo
simulations on cubic lattices up to L=60. The system exhibits ferromagnetic and
paramagnetic steady states. Our results predict first-order transitions at low
temperatures and large disorder strengths, which correspond to the existence of
a nonequilibrium tricritical point at finite temperature. By means of standard
finite-size scaling equations, we estimate the critical exponents in the
low-field region, for which our simulations uphold continuous phase
transitions.


  We present a novel redirected walking controller based on alignment that
allows the user to explore large and complex virtual environments, while
minimizing the number of collisions with obstacles in the physical environment.
Our alignment-based redirection controller, ARC, steers the user such that
their proximity to obstacles in the physical environment matches the proximity
to obstacles in the virtual environment as closely as possible. To quantify a
controller's performance in complex environments, we introduce a new metric,
Complexity Ratio (CR), to measure the relative environment complexity and
characterize the difference in navigational complexity between the physical and
virtual environments. Through extensive simulation-based experiments, we show
that ARC significantly outperforms current state-of-the-art controllers in its
ability to steer the user on a collision-free path. We also show through
quantitative and qualitative measures of performance that our controller is
robust in complex environments with many obstacles. Our method is applicable to
arbitrary environments and operates without any user input or parameter
tweaking, aside from the layout of the environments. We have implemented our
algorithm on the Oculus Quest head-mounted display and evaluated its
performance in environments with varying complexity. Our project website is
available at https://gamma.umd.edu/arc/.


  In this paper we re-examine the one-dimensional interaction of
electromagnetic and ion acoustic waves in a plasma. Our model is similar to one
solved by Rao et al. (Phys. Fluids, vol. 26, 2488 (1983)) under a number of
analytical approximations. Here we perform a numerical investigation to examine
the stability of the model. We find that for slightly over dense plasmas, the
propagation of stable solitary modes can occur in an adiabatic regime where the
ion acoustic electric field potential is enslaved to the electromagnetic field
of a laser. But if the laser intensity or plasma density increases or the laser
frequency decreases, the adiabatic regime loses stability via a transition to
chaos. New asymptotic states are attained when the adiabatic regime no longer
exists. In these new states, the plasma becomes rarefied, and the laser field
tends to behave like a vacuum field.


  Homological equations of tensor type associated to periodic flows on a
manifold are studied. The Cushman intrinsic formula is generalized to the case
of multivector fields and differential forms. Some applications to normal forms
and the averaging method for perturbed Hamiltonian systems on slow-fast phase
spaces are given.


  Carbon fiber and graphene-based nanostructures such as carbon nanotubes
(CNTs) and defective structures have extraordinary potential as strong and
lightweight materials. A longstanding bottleneck has been lack of understanding
and implementation of atomic-scale engineering to harness the theoretical
limits of modulus and tensile strength, of which only a fraction is routinely
reached today. Here we demonstrate accurate and fast predictions of mechanical
properties for CNTs and arbitrary 3D graphitic assemblies based on a training
set of over 1000 stress-strain curves from cutting-edge reactive MD simulation
and machine learning (ML). Several ML methods are compared and show that our
newly proposed hierarchically structured graph neural networks with spatial
information (HS-GNNs) achieve predictions in modulus and strength for any 3D
nanostructure with only 5-10% error across a wide range of possible values. The
reliability is sufficient for practical applications and a great improvement
over off-the shelf ML methods with up to 50% deviation, as well as over earlier
models for specific chemistry with 20% deviation. The algorithms allow more
than 10 times faster mechanical property predictions than traditional molecular
dynamics simulations, the identification of the role of defects and random 3D
morphology, and high-throughput screening of 3D structures for enhanced
mechanical properties. The algorithms can be scaled to morphologies up to 100
nm in size, expanded for chemically similar compounds, and trained to predict a
broader range of properties.


  High-dimensional quantum entanglement characterizes the entanglement of
quantum systems within a larger Hilbert space, introducing more intricate and
complex correlations among the entangled particles' states. The
high-dimensional Greenberger-Horne-Zeilinger (GHZ) state, symbolic of this type
of entanglement, is of significant importance in various quantum information
processing applications. This study proposes integrating a neutral atom
platform with quantum reservoir engineering to generate a high-dimensional GHZ
state deterministically. Leveraging the advantages of neutral atoms in a
modified unconventional Rydberg pumping mechanism, combined with controlled
dissipation, we achieve a three-dimensional GHZ state with a fidelity
surpassing 99\% through multiple pump and dissipation cycles. This innovative
approach paves the way for experimentally feasible, deterministic preparation
of high-dimensional GHZ states in Rydberg atom systems, thereby advancing the
capabilities of quantum information processing.


  We prove formula between Nekrasov partition functions defined from stable and
co-stable ADHM data for the plane following method by Nakajima-Yoshioka based
on the theory of wall-crossing formula developed by Mochizuki. This formula is
similar to conjectures by Itoh-Maruyoshi-Okuda for $A_{1}$ singularity.


  We demonstrate that the extension of the Zee-Babu model can generate not only
the small neutrino masses but also the baryon number asymmetry in the universe.
In particular, we show that the scale of the singlet scalar responsible for the
leptogenesis can be of order 1 TeV, that can be tested at the LHC and ILC. We
also considered the possible minimal extension of this model to generate the
dark matter.


  In this paper, we consider the problem of estimating multiple graphical
models simultaneously using the fused lasso penalty, which encourages adjacent
graphs to share similar structures. A motivating example is the analysis of
brain networks of Alzheimer's disease using neuroimaging data. Specifically, we
may wish to estimate a brain network for the normal controls (NC), a brain
network for the patients with mild cognitive impairment (MCI), and a brain
network for Alzheimer's patients (AD). We expect the two brain networks for NC
and MCI to share common structures but not to be identical to each other;
similarly for the two brain networks for MCI and AD. The proposed formulation
can be solved using a second-order method. Our key technical contribution is to
establish the necessary and sufficient condition for the graphs to be
decomposable. Based on this key property, a simple screening rule is presented,
which decomposes the large graphs into small subgraphs and allows an efficient
estimation of multiple independent (small) subgraphs, dramatically reducing the
computational cost. We perform experiments on both synthetic and real data; our
results demonstrate the effectiveness and efficiency of the proposed approach.


  In this paper, we present a sharp upper bound for the spectral radius of an
$n$-vertex graph without $F$-minor for sufficient large $n$, where $F$ is
obtained from the complete graph $K_r$ by deleting disjointed paths.
Furthermore, the graphs which achieved the sharp bound are characterized. This
result may be regarded to be an extended revision of the number of edges in an
$n$-vertex graph without $F$-minor.


  A nonassociative generalization of the principal fiber bundles with a smooth
loop mapping on the fiber is presented. Our approach allows us to construct a
new kind of gauge theories that involve higher ''nonassociative'' symmetries.


  This work studies the learning ability of consensus and diffusion distributed
learners from continuous streams of data arising from different but related
statistical distributions. Four distinctive features for diffusion learners are
revealed in relation to other decentralized schemes even under left-stochastic
combination policies. First, closed-form expressions for the evolution of their
excess-risk are derived for strongly-convex risk functions under a diminishing
step-size rule. Second, using these results, it is shown that the diffusion
strategy improves the asymptotic convergence rate of the excess-risk relative
to non-cooperative schemes. Third, it is shown that when the in-network
cooperation rules are designed optimally, the performance of the diffusion
implementation can outperform that of naive centralized processing. Finally,
the arguments further show that diffusion outperforms consensus strategies
asymptotically, and that the asymptotic excess-risk expression is invariant to
the particular network topology. The framework adopted in this work studies
convergence in the stronger mean-square-error sense, rather than in
distribution, and develops tools that enable a close examination of the
differences between distributed strategies in terms of asymptotic behavior, as
well as in terms of convergence rates.


  We construct rotating magnetic solutions to the three-dimensional
Einstein-Maxwell-Chern-Simons-dilaton theory with a Liouville potential. These
include a class of black hole solutions which generalize the warped AdS black
holes. The regular black holes belong to two disjoint sectors. The first sector
includes black holes which have a positive mass and are co-rotating, while the
black holes of the second sector have a negative mass and are counter-rotating.
We also show that a particular, non-black hole, subfamily of our
three-dimensional solutions may be uplifted to new regular non-asymptotically
flat solutions of five-dimensional Einstein-Maxwell-Chern-Simons theory.


  We show that a continuous function on the analytification of a smooth proper
algebraic curve over a non-archimedean field is subharmonic in the sense of
Thuillier if and only if it is psh, i.e. subharmonic in the sense of
Chambert-Loir and Ducros. This equivalence implies that the property psh for
continuous functions is stable under pullback with respect to morphisms of
curves. Furthermore, we prove an analogue of the monotone regularization
theorem on the analytification of the projective line and Mumford curves using
this equivalence.


  It is found that nonlinear interaction of plasma wakefields driven by
counterpropagating laser or particle beams can efficiently generate high-power
electromagnetic radiation at the second harmonic of the plasma frequency. Using
a simple analytical theory and particle-in-cell simulations, we show that this
phenomenon can be attractive for producing high-field ($\sim 10$ MV/cm)
narrowband terahertz pulses with the gigawatt power level and millijoule energy
content.


  In this work we show that homogeneous Neumann boundary conditions inhibit the
Coleman-Weinberg mechanism for spontaneous symmetry breaking in the scalar
electrodynamics if the length of the finite region is small enough ($a =
e^{2}M^{-1}_{\phi}$, where $M_{\phi}$ is the mass of the scalar field generated
by the Coleman-Weinberg mechanism)


  The continuous scaling of semiconductor technology has pushed the footprint
of logic devices below 50 nm. Currently, logic standard cells with one single
fin are being investigated to increase the integration density, although such
options could severely limit the performance of individual devices. In this
letter, we present a novel Trench (T-) FinFET device, composed of a monolayer
two-dimensional (2D) channel material. The device characteristics of a
monolayer WS$_2$-based T-FinFET are studied by combining the first-principles
calculations and quantum transport (QT) simulations. These results serve as
inputs to a predictive analytical model. The latter allows to benchmark the
T-FinFET with strained (s)-Si FinFETs in both quasi-ballistic and diffusive
transport regimes. The circuit-level evaluation highlights that WS$_2$
T-FinFETs exhibit a competitive energy-delay performance compared to s-Si
FinFET and WS$_2$ double-gate transistors, assuming the same mobility and
contact resistivity at small footprints.


  In general, a SAT Solver based on conflict-driven DPLL consists of variable
selection, phase selection, Boolean Constraint Propagation, conflict analysis,
clause learning and its database maintenance. Optimizing any part of these
components can enhance the performance of a solver. This paper focuses on
optimizing phase selection. Although the ACE (Approximation of the Combined
lookahead Evaluation) weight is applied to a lookahead SAT solver such as
March, so far, no conflict-driven SAT solver applies successfully the ACE
weight, since computing the ACE weight is time-consuming. Here we apply the ACE
weight to partial phase selection of conflict-driven SAT solvers. This can be
seen as an improvement of the heuristic proposed by Jeroslow-Wang (1990). We
incorporate the ACE heuristic and the existing phase selection heuristics in
the new solver MPhaseSAT, and select a phase heuristic in a way similar to
portfolio methods. Experimental results show that adding the ACE heuristic can
improve the conflict-driven solvers. Particularly on application instances,
MPhaseSAT with the ACE heuristic is significantly better than MPhaseSAT without
the ACE heuristic, and even can solve a few SAT instances that remain
unsolvable so far.


  Bit threads provide an alternative description of holographic entanglement,
replacing the Ryu-Takayanagi minimal surface with bulk curves connecting pairs
of boundary points. We use bit threads to prove the monogamy of mutual
information (MMI) property of holographic entanglement entropies. This is
accomplished using the concept of a so-called multicommodity flow, adapted from
the network setting, and tools from the theory of convex optimization. Based on
the bit thread picture, we conjecture a general ansatz for a holographic state,
involving only bipartite and perfect-tensor type entanglement, for any
decomposition of the boundary into four regions. We also give new proofs of
analogous theorems on networks.


  Subject to the neutrino experiments, the mixing matrix of ordinary neutrinos
can still have small violation from unitarity. We introduce a quasi-unitary
matrix to interpret this violation and propose a natural scheme to parameterize
it. A quasi-unitary factor $\Delta_{\rm QF}$ is defined to be measured in
neutrino oscillation experiments and our numerical results show that
improvement of experimental precision may help us figure out the secret of
neutrino mixing.


  5D warped extra dimension models with multiple 3-branes can naturally realize
multiple hierarchical mass scales which are ubiquitous in physics beyond the
Standard Model. We discuss cosmological consequences of such multi-brane models
with stabilized radions. It is confirmed that for temperatures below the scale
of the IR brane at the end of the extra dimension, we recover the ordinary
expansion of the Universe, with the Hubble expansion rate determined by sum of
the physical energy densities on all 3-branes where they are localized. In
addition, we explore the cosmology for temperatures above the scales of the
intermediate and IR branes where the Universe is described by a spacetime with
the 3-branes replaced by an event horizon. As the temperature of the Universe
cools down, phase transitions are expected to take place, and the intermediate
and IR branes come out from behind the event horizon. The Goldberger-Wise
mechanism for radion stabilization has a well-known problem of having a
supercooled phase transition, which typically does not get completed in time.
This problem is even more severe when an intermediate brane is introduced,
whose scale is well above TeV, as the corresponding Hubble rate is much larger.
We circumvent the problem by employing an alternative mechanism for radion
stabilization with dark Yang-Mills fields, which prevents a long supercooling
epoch, but still allows the strong first order phase transitions. As a result,
the phase transitions in our multi-brane Universe predict a stochastic
gravitational wave background with a unique multi-peak signature, which is
within the sensitivity reach of future space-based gravitational wave
observers. We also show that there are $N-1$ radions for an $N$ 3-brane set-up,
unlike a recent claim that there exists only one radion.


  We characterize all the pairs of complementary non-homogenous Beatty
sequences $(A_n)_{n\ge 0}$ and $(B_n)_{n\ge 0}$ for which there exists an
invariant game having exactly $\{(A_n,B_n)\mid n\ge 0\}\cup \{(B_n,A_n)\mid
n\ge 0\}$ as set of $\mathcal{P}$-positions. Using the notion of Sturmian word
and tools arising in symbolic dynamics and combinatorics on words, this
characterization can be translated to a decision procedure relying only on a
few algebraic tests about algebraicity or rational independence. Given any four
real numbers defining the two sequences, up to these tests, we can therefore
decide whether or not such an invariant game exists.


  This is the author's PhD thesis, which focuses on the so-called
Landau-Ginzburg/conformal field theory correspondence. This correspondence
dates from the late 80s and early 90s in the physics literature and in
particular, it predicts a relation between defects in Landau-Ginzburg models
and defects in conformal field theories. This relation is supported by
examples, but not understood in general, nor up to date is there a clear
mathematical conjecture of the Landau-Ginzburg/conformal field theory
correspondence. The pursuit of a precise mathematical statement of this
conjecture continues to generate a rich mathematical output, and this PhD
thesis is another contribution towards this end.


  Besides perturbation theory (which clearly requires the knowledge of the
exact unperturbed solution), variational techniques represent the main tool for
any investigation of the eigenvalue problem of some semibounded operator H in
quantum theory. For a reasonable choice of the employed trial subspace of the
domain of H, the lowest eigenvalues of H usually can be located with acceptable
precision whereas the trial-subspace vectors corresponding to these eigenvalues
approximate, in general, the exact eigenstates of H with much less accuracy.
Accordingly, various measures for the accuracy of the approximate eigenstates
derived by variational techniques are scrutinized. In particular, the matrix
elements of the commutator of the operator H and (suitably chosen) different
operators with respect to degenerate approximate eigenstates of H obtained by
variational methods are proposed as new criteria for the accuracy of
variational eigenstates. These considerations are applied to precisely that
Hamiltonian for which the eigenvalue problem defines the well-known spinless
Salpeter equation. This bound-state wave equation may be regarded as (the most
straightforward) relativistic generalization of the usual nonrelativistic
Schroedinger formalism, and is frequently used to describe, e.g., spin-averaged
mass spectra of bound states of quarks.


  In this note we present benchmark scenarios for resonant double Higgs
production at the $13\,$TeV LHC in the 2HDM+S model and the $Z_3$
Next-to-Minimal Supersymmetric Standard Model (NMSSM), which may be accessible
with 300 fb$^{-1}$ of data. The NMSSM Higgs sector can be mapped onto the
2HDM+S. We show benchmark points and relevant parameter planes in the 2HDM+S
for three sets of signatures: ($A\to h_{125} a, ~H\to h_{125} h)$, ($A\to a h,
H\to hh, H\to aa)$, and ($H\to h_{125}h_{125}$). The first two signatures are
optimized in what we call $Z$-Phobic scenarios where $H/A$ decays into final
states with $Z$ bosons are suppressed. The last signature, $h_{125}$ pair
production, is directly proportional to the misalignment of $h_{125}$ with the
interaction state sharing the couplings of a SM Higgs boson, and hence is
presented in the Max Misalignment scenario. We also present two NMSSM benchmark
points for the ($A\to h_{125} a, ~H\to h_{125} h)$ signatures. The benchmark
scenarios presented here are based on Refs. [1,2].


  The reaction $\gamma d\to \pi^+ nn$ is calculated up to order $\chi^{5/2}$ in
chiral perturbation theory, where $\chi$ denotes the ratio of the pion to the
nucleon mass. Special emphasis is put on the role of nucleon--recoil
corrections that are the source of contributions with fractional power in
$\chi$. Using the known near threshold production amplitude for $\gamma p\to
\pi^+ n$ as the only input, the total cross section for $\gamma d\to \pi^+ nn$
is described very well. A conservative estimate suggests that the theoretical
uncertainty for the transition operator amounts to 3 % for the computed
amplitude near threshold.


  We conjecture that if a system S \subseteq {x_i=1, x_i+x_j=x_k, x_i \cdot
x_j=x_k: i,j,k \in {1,...,n}} has only finitely many solutions in integers
x_1,...,x_n, then each such solution (x_1,...,x_n) satisfies |x_1|,...,|x_n|
\leq 2^{2^{n-1}}. By the conjecture, if a Diophantine equation has only
finitely many solutions in integers (non-negative integers, rationals), then
their heights are bounded from above by a computable function of the degree and
the coefficients of the equation. The conjecture implies that the set of
Diophantine equations which have infinitely many solutions in integers
(non-negative integers) is recursively enumerable. The conjecture stated for an
arbitrary computable bound instead of 2^{2^{n-1}} remains in contradiction to
Matiyasevich's conjecture that each recursively enumerable set M \subseteq
{\mathbb N}^n has a finite-fold Diophantine representation.


  We consider a novel question answering (QA) task where the machine needs to
read from large streaming data (long documents or videos) without knowing when
the questions will be given, which is difficult to solve with existing QA
methods due to their lack of scalability. To tackle this problem, we propose a
novel end-to-end deep network model for reading comprehension, which we refer
to as Episodic Memory Reader (EMR) that sequentially reads the input contexts
into an external memory, while replacing memories that are less important for
answering \emph{unseen} questions. Specifically, we train an RL agent to
replace a memory entry when the memory is full, in order to maximize its QA
accuracy at a future timepoint, while encoding the external memory using either
the GRU or the Transformer architecture to learn representations that considers
relative importance between the memory entries. We validate our model on a
synthetic dataset (bAbI) as well as real-world large-scale textual QA
(TriviaQA) and video QA (TVQA) datasets, on which it achieves significant
improvements over rule-based memory scheduling policies or an RL-based baseline
that independently learns the query-specific importance of each memory.


  The \textit{$r$-dynamic choosability} of a graph $G$, written ${\rm
ch}_r(G)$, is the least $k$ such that whenever each vertex is assigned a list
of at least $k$ colors a proper coloring can be chosen from the lists so that
every vertex $v$ has at least $\min\{d_G(v),r\}$ neighbors of distinct colors.
Let ${\rm ch}(G)$ denote the choice number of $G$. In this paper, we prove
${\rm ch}_r(G)\leq (1+o(1)){\rm ch}(G)$ when $\frac{\Delta(G)}{\delta(G)}$ is
bounded. We also show that there exists a constant $C$ such that for the random
graph $G=G(n,p)$ with $\frac{2}{n}<p\leq \frac{1}{2}$, it holds that ${\rm
ch}_2(G)\leq {\rm ch}(G) + C$, asymptotically almost surely. Also if $G$ is
triangle-free regualr graph, then ${\rm ch}_2(G)\leq {\rm ch}(G)+86$ holds.