  Considering that both the entropy-based market information and the Hurst
exponent are useful tools for determining whether the efficient market
hypothesis holds for a given asset, we study the link between the two
approaches. We thus provide a theoretical expression for the market information
when log-prices follow either a fractional Brownian motion or its stationary
extension using the Lamperti transform. In the latter model, we show that a
Hurst exponent close to 1/2 can lead to a very high informativeness of the time
series, because of the stationarity mechanism. In addition, we introduce a
multiscale method to get a deeper interpretation of the entropy and of the
market information, depending on the size of the information set. Applications
to Bitcoin, CAC 40 index, Nikkei 225 index, and EUR/USD FX rate, using daily or
intraday data, illustrate the methodological content.


  The quantum autoencoder is a recent paradigm in the field of quantum machine
learning, which may enable an enhanced use of resources in quantum
technologies. To this end, quantum neural networks with less nodes in the inner
than in the outer layers were considered. Here, we propose a useful connection
between approximate quantum adders and quantum autoencoders. Specifically, this
link allows us to employ optimized approximate quantum adders, obtained with
genetic algorithms, for the implementation of quantum autoencoders for a
variety of initial states. Furthermore, we can also directly optimize the
quantum autoencoders via genetic algorithms. Our approach opens a different
path for the design of quantum autoencoders in controllable quantum platforms.


  This paper introduces a novel theoretical simplification of the Diffusion
Schr\"odinger Bridge (DSB) that facilitates its unification with Score-based
Generative Models (SGMs), addressing the limitations of DSB in complex data
generation and enabling faster convergence and enhanced performance. By
employing SGMs as an initial solution for DSB, our approach capitalizes on the
strengths of both frameworks, ensuring a more efficient training process and
improving the performance of SGM. We also propose a reparameterization
technique that, despite theoretical approximations, practically improves the
network's fitting capabilities. Our extensive experimental evaluations confirm
the effectiveness of the simplified DSB, demonstrating its significant
improvements. We believe the contributions of this work pave the way for
advanced generative modeling. The code is available at
https://github.com/checkcrab/SDSB.


  $f \propto r^{-\alpha} \cdot (r+\gamma)^{-\beta}$ has been empirically shown
more precise than a na\"ive power law $f\propto r^{-\alpha}$ to model the
rank-frequency ($r$-$f$) relation of words in natural languages. This work
shows that the only crucial parameter in the formulation is $\gamma$, which
depicts the resistance to vocabulary growth on a corpus. A method of parameter
estimation by searching an optimal $\gamma$ is proposed, where a ``zeroth
word'' is introduced technically for the calculation. The formulation and
parameters are further discussed with several case studies.


  Thanks to the latest deep learning algorithms, silent speech interfaces (SSI)
are now able to synthesize intelligible speech from articulatory movement data
under certain conditions. However, the resulting models are rather
speaker-specific, making a quick switch between users troublesome. Even for the
same speaker, these models perform poorly cross-session, i.e. after dismounting
and re-mounting the recording equipment. To aid quick speaker and session
adaptation of ultrasound tongue imaging-based SSI models, we extend our deep
networks with a spatial transformer network (STN) module, capable of performing
an affine transformation on the input images. Although the STN part takes up
only about 10% of the network, our experiments show that adapting just the STN
module might allow to reduce MSE by 88% on the average, compared to retraining
the whole network. The improvement is even larger (around 92%) when adapting
the network to different recording sessions from the same speaker.


  Measure structured deformations are introduced to present a unified theory of
deformations of continua. The energy associated with a measure structured
deformation is defined via relaxation departing either from energies associated
with classical deformations or from energies associated with structured
deformations. A concise integral representation of the energy functional is
provided both in the unconstrained case and under Dirichlet conditions on a
part of the boundary.


  Hashtags are semantico-syntactic constructs used across various social
networking and microblogging platforms to enable users to start a topic
specific discussion or classify a post into a desired category. Segmenting and
linking the entities present within the hashtags could therefore help in better
understanding and extraction of information shared across the social media.
However, due to lack of space delimiters in the hashtags (e.g #nsavssnowden),
the segmentation of hashtags into constituent entities ("NSA" and "Edward
Snowden" in this case) is not a trivial task. Most of the current
state-of-the-art social media analytics systems like Sentiment Analysis and
Entity Linking tend to either ignore hashtags, or treat them as a single word.
In this paper, we present a context aware approach to segment and link entities
in the hashtags to a knowledge base (KB) entry, based on the context within the
tweet. Our approach segments and links the entities in hashtags such that the
coherence between hashtag semantics and the tweet is maximized. To the best of
our knowledge, no existing study addresses the issue of linking entities in
hashtags for extracting semantic information. We evaluate our method on two
different datasets, and demonstrate the effectiveness of our technique in
improving the overall entity linking in tweets via additional semantic
information provided by segmenting and linking entities in a hashtag.


  Face Anti-Spoofing (FAS) is significant for the security of face recognition
systems. Convolutional Neural Networks (CNNs) have been introduced to the field
of the FAS and have achieved competitive performance. However, CNN-based
methods are vulnerable to the adversarial attack. Attackers could generate
adversarial-spoofing examples to circumvent a CNN-based face liveness detector.
Studies about the transferability of the adversarial attack reveal that
utilizing handcrafted feature-based methods could improve security in a
system-level. Therefore, handcrafted feature-based methods are worth our
exploration. In this paper, we introduce the deep forest, which is proposed as
an alternative towards CNNs by Zhou et al., in the problem of the FAS. To the
best of our knowledge, this is the first attempt at exploiting the deep forest
in the problem of FAS. Moreover, we propose to re-devise the representation
constructing by using LBP descriptors rather than the Grained-Scanning
Mechanism in the original scheme. Our method achieves competitive results. On
the benchmark database IDIAP REPLAY-ATTACK, 0\% Equal Error Rate (EER) is
achieved. This work provides a competitive option in a fusing scheme for
improving system-level security and offers important ideas to those who want to
explore methods besides CNNs.


  It is shown that the scaling analysis presented in Phys. Rev. Lett. 85, 4988
(2000) (cond-mat/0007141) is valid for finite chains of lengths relevant to
experiments, in contrast to a recent claim made by A. Hanke and R. Metzler in
cond-mat/0108323.


  We introduce the nuclear dimension of a C*-algebra; this is a noncommutative
version of topological covering dimension based on a modification of the
earlier concept of decomposition rank. Our notion behaves well with respect to
inductive limits, tensor products, hereditary subalgebras (hence ideals),
quotients, and even extensions. It can be computed for many examples; in
particular, it is finite for all UCT Kirchberg algebras. In fact, all classes
of nuclear C*-algebras which have so far been successfully classified consist
of examples with finite nuclear dimension, and it turns out that finite nuclear
dimension implies many properties relevant for the classification program.
Surprisingly, the concept is also linked to coarse geometry, since for a
discrete metric space of bounded geometry the nuclear dimension of the
associated uniform Roe algebra is dominated by the asymptotic dimension of the
underlying space.


  The second-order Kuramoto equation describes synchronization of coupled
oscillators with inertia, which occur in power grids for example. Contrary to
the first-order Kuramoto equation it's synchronization transition behavior is
much less known. In case of Gaussian self-frequencies it is discontinuous, in
contrast to the continuous transition for the first-order Kuramoto equation.
Here we investigate this transition on large 2d and 3d lattices and provide
numerical evidence of hybrid phase transitions, that the oscillator phases
$\theta_i$, exhibit a crossover, while the frequency spread a real phase
transition in 3d. Thus a lower critical dimension $d_l^O=2$ is expected for the
frequencies and $d_l^R=4$ for the phases like in the massless case. We provide
numerical estimates for the critical exponents, finding that the frequency
spread decays as $\sim t^{-d/2}$ in case of aligned initial state of the phases
in agreement with the linear approximation. However in 3d, in the case of
initially random distribution of $\theta_i$, we find a faster decay,
characterized by $\sim t^{-1.8(1)}$ as the consequence of enhanced
nonlinearities which appear by the random phase fluctuations.


  We investigate the structure of certain almost split sequences in
$\mathcal{P}(\Lambda)$, i.e., the category of morphisms between projective
modules over an Artin algebra $\Lambda$. The category $\mathcal{P}(\Lambda)$
has very nice properties and is closely related to $\tau$-tilting theory,
$g$-vectors, and Auslander-Reiten theory. We provide explicit constructions of
certain almost split sequences ending at or starting from certain objects.
Applications, such as to $g$-vectors, are given. As a byproduct, we also show
that there exists an injection from Morita equivalence classes of Artin
algebras to equivalence classes of 0-Auslander exact categories.


  In the past several years, observational entropy has been developed as both a
(time-dependent) quantum generalization of Boltzmann entropy, and as a rather
general framework to encompass classical and quantum equilibrium and
non-equilibrium coarse-grained entropy. In this paper we review the
construction, interpretation, most important properties, and some applications
of this framework. The treatment is self-contained and relatively pedagogical,
aimed at a broad class of researchers.


  We derive a lower bound for the subword complexity of the base-$b$ expansion
($b\geq 2$) of all real numbers whose irrationality exponent is equal to 2.
This provides a generalization of a theorem due to Ferenczi and Mauduit. As a
consequence, we obtain the first lower bound for the subword complexity of the
number $e$ and of some other transcendental exponential periods.


  The Nab experiment will measure the ratio of the weak axial-vector and vector
coupling constants $\lambda=g_A/g_V$ with precision
$\delta\lambda/\lambda\sim3\times10^{-4}$ and search for a Fierz term $b_F$ at
a level $\Delta b_F<10^{-3}$. The Nab detection system uses thick, large area,
segmented silicon detectors to very precisely determine the decay proton's time
of flight and the decay electron's energy in coincidence and reconstruct the
correlation between the antineutrino and electron momenta. Excellent
understanding of systematic effects affecting timing and energy reconstruction
using this detection system are required. To explore these effects, a series of
ex situ studies have been undertaken, including a search for a Fierz term at a
less sensitive level of $\Delta b_F<10^{-2}$ in the beta decay of $^{45}$Ca
using the UCNA spectrometer.


  Recently, Adami and coworkers have been able to measure the information
content of digital organisms living in their {\em Avida} artificial life
system. They show that over time, the organisms behave like Maxwell's demon,
accreting information (or complexity) as they evolve. In {\em Avida} the
organisms don't interact with each other, merely reproduce at a particular rate
(their fitness), and attempt to evaluate an externally given arithmetic
function in order win bonus fitness points. Measuring the information content
of a digital organism is essentially a process of counting the number of
genotypes that give rise to the same phenotype.
  Whilst Avidan organisms have a particularly simple phenotype, Tierran
organisms interact with each other, giving rise to an ecology of phenotypes. In
this paper, I discuss techniques for comparing pairs of Tierran organisms to
determine if they are phenotypically equivalent. I then discuss a method for
computing an estimate of the number of phenotypically equivalent genotypes that
is more accurate than the ``hot site'' estimate used by Adami's group. Finally,
I report on an experimental analysis of a Tierra run.


  We compute non--perturbatively the renormalization coefficients of scalar and
pseudoscalar operators, local vector and axial currents, conserved vector and
axial currents, and $O_{LL}^{\Delta S=2}$ over a wide range of energy scales
using a scaling technique that connects the results of simulations at different
values of coupling $\beta$. We use the domain wall fermion formulation in the
quenched approximation at a series of three values of $\beta, 6.0, 6.45, 7.05$
corresponding to lattice spacing scaling by factors of two.


  We use C*-algebra theory to provide a new method of decomposing the eseential
spectra of self-adjoint and non-self-adjoint Schrodinger operators in one or
more space dimensions.


  Our purpose here is to give an overview of known results and open questions
concerning the volume product ${\mathcal P}(K)=\min_{z\in K}{\rm vol}(K){\rm
vol}((K-z)^*)$ of a convex body $K$ in ${\mathbb R}^n$. We present a number of
upper and lower bounds for ${\mathcal P}(K)$, in particular, we discuss the
Mahler's conjecture on the lower bound of ${\mathcal P}(K)$, which is still
open. We also show connections of ${\mathcal P}(K)$ with different parts of
modern mathematics, including Geometric Number Theory, Convex Geometry,
Analysis, Harmonic Analysis as well as Systolic and Symplectic Geometries and
Probability.


  Cross sections were measured for the near-threshold electrodisintegration of
^3He at momentum transfer values of q=2.4, 4.4, and 4.7 fm^{-1}. From these and
prior measurements the transverse and longitudinal response functions R_T and
R_L were deduced. Comparisons are made against previously published and new
non-relativistic A=3 calculations using the best available NN potentials. In
general, for q<2 fm^{-1} these calculations accurately predict the threshold
electrodisintegration of ^3He. Agreement at increasing q demands consideration
of two-body terms, but discrepancies still appear at the highest momentum
transfers probed, perhaps due to the neglect of relativistic dynamics, or to
the underestimation of high-momentum wave-function components.


  We discuss the possibility of existence of entanglement in biological
systems. Our arguments centre on the fact that biological systems are
thermodynamic open driven systems far from equilibrium. In such systems error
correction can occur which may maintain entanglement despite high levels of
de-coherence. We also discuss the possibility of cooling (classical or quantum)
at molecular level.


  We use molecular dynamics simulations to investigate the tracer diffusion in
a sea of polymers with specific binding zones for the tracer. These binding
zones act as traps. Our simulations show that the tracer can undergo normal yet
non-Gaussian diffusion under certain circumstances, e.g, when the polymers with
traps are frozen in space and the volume fraction and the binding strength of
the traps are moderate. In this case, as the tracer moves, it experiences a
heterogeneous environment and exhibits confined continuous time random walk
(CTRW) like motion resulting a non-Gaussian behavior. Also the long time
dynamics becomes subdiffusive as the number or the binding strength of the
traps increases. However, if the polymers are mobile then the tracer dynamics
is Gaussian but could be normal or subdiffusive depending on the number and the
binding strength of the traps. In addition, with increasing binding strength
and the number of the polymer traps, the probability of the tracer being
trapped increases. On the other hand, removing the binding zones does not
result trapping, even at comparatively high crowding. Our simulations also show
that the trapping probability increases with the increasing size of the tracer
and for a bigger tracer with the frozen polymer background the dynamics is only
weakly non-Gaussian but highly subdiffusive. Our observations are in the same
spirit as found in many recent experiments on tracer diffusion in polymeric
materials and questions the validity of Gaussian theory to describe diffusion
in crowded environment in general.


  In this paper we introduce a version of irreducible Laguerre polynomials in
two variables and prove for it a congruence property, which is similar to the
one obtained by Carlitz for the classical Laguerre polynomials in one variable.


  Schauder estimates were a historical stepping stone for establishing
uniqueness and smoothness of solutions for certain classes of partial
differential equations. Since that time, they have remained an essential tool
in the field. Roughly speaking, the estimates state that the H\"older
continuity of the coefficient functions and inhomogeneous term implies the
H\"older continuity of the solution and its derivatives. This document
establishes pointwise Schauder estimates for second order "parabolic" equations
of the form $$\partial_{t}u(x,t)-\sum_{i,j=1}^{m_1}
a_{ij}(x,t)X_iX_ju(x,t)=f(x,t)$$ where $X_{1},\ldots ,X_{m_1}$ generate the
first layer of the Lie algebra stratification for a Carnot group. The Schauder
estimates are shown by means of Campanato spaces. These spaces make the
pointwise nature of the estimates possible by comparing solutions to their
Taylor polynomials. As a prerequisite device, a version of both the mean value
theorem and Taylor inequality are established with the parabolic distance
incorporated.


  High signal-to-noise spectra toward background quasars are crucial for
uncovering weak absorption in the circumgalactic medium (CGM) of intervening
galaxies, such as the diagnostic lines of N V that provide insight to the
ionization process of warm gas but typically have low equivalent widths. We
present a new spectrum from the Hubble Space Telescope with a signal-to-noise
ratio of $\sim20-35$ toward the quasar SDSS J1009+0713 and analyze absorption
systems in the CGM of two $L^\star$ galaxies close to the line of sight. We
identify additional absorption in the CGM of these galaxies that was not
reported by the previous lower signal-to-noise spectrum, as well as Milky Way
absorbers and quasar outflows from J1009+0713. We measure $\log
(N_\mathrm{NV}/N_\mathrm{OVI})\sim-1.1$ for two CGM absorbers, inconsistent
with gas in collisional ionization equilibrium and consistent with a
radiatively cooling bulk flow of $\sim50-150$ km s$^{-1}$, which could be
produced by galactic winds. These column density ratios are also consistent
with those found for other $L^\star$ galaxies and for some gas in the Milky
Way's halo. We place upper limits of $\log (N_\mathrm{NV}/N_\mathrm{OVI})<-1.8$
to $-1.2$ for other O VI absorbers in the same halos, which suggests that O VI
is produced by different processes in different parts of the CGM, even within
the same galactic halo. Together with the kinematically different structure of
high- and low-ionization lines, these results indicate there are many
components to a single galaxy's gaseous halo. We find the redshift number
density of Ly-$\alpha$ forest absorbers and broad Ly-$\alpha$ absorbers are
consistent with expectations at this redshift.


  The nucleus-nucleus impact parameter and collision geometry of a heavy ion
collision are typically characterized by assigning a collision "centrality". In
all present heavy ion experiments centrality is measured indirectly, by
detecting the number of particles or the energy of the particles produced in
the interactions, typically at high rapidity. Centrality parameters are
associated to the measured detector response using the Glauber model. This
approach suffers from systematic uncertainties related to the assumptions about
the particle production mechanism and limitations of the Glauber model. In the
collider based experiments there is a unique possibility to measure centrality
parameters by registering spectator fragments remaining from the collision.
This approach does not require model assumptions and relies on the fact that
spectators and participants are related via the total number of nucleons in the
colliding species. This article describes the concept of the centrality
detector for heavy ion experiment, which measures the total mass number of all
fragments by measuring their deflection in the magnetic field of the collider
elements.


  Early detection of COVID-19 is key in containing the pandemic. Disease
detection and evaluation based on imaging is fast and cheap and therefore plays
an important role in COVID-19 handling. COVID-19 is easier to detect in chest
CT, however, it is expensive, non-portable, and difficult to disinfect, making
it unfit as a point-of-care (POC) modality. On the other hand, chest X-ray
(CXR) and lung ultrasound (LUS) are widely used, yet, COVID-19 findings in
these modalities are not always very clear. Here we train deep neural networks
to significantly enhance the capability to detect, grade and monitor COVID-19
patients using CXRs and LUS. Collaborating with several hospitals in Israel we
collect a large dataset of CXRs and use this dataset to train a neural network
obtaining above 90% detection rate for COVID-19. In addition, in collaboration
with ULTRa (Ultrasound Laboratory Trento, Italy) and hospitals in Italy we
obtained POC ultrasound data with annotations of the severity of disease and
trained a deep network for automatic severity grading.


  The celebrated Foata combinatorial model for Hermite polynomials, and his
seminal and beautiful proof of the Mehler formula, are straightened to deal
with two sexes rather than one, with the exclusion of same-sex relationships
(both marital and non-marital).


  Any solution to the Yang-Baxter equation yields a family of representations
of braid groups. Under certain conditions, identified by Turaev, the
appropriately normalized trace of these representations yields a link
invariant. Any Yang-Baxter solution can be interpreted as a two-qudit quantum
gate. Here we show that if this gate is non-entangling, then the resulting
invariant of knots is trivial. We thus obtain a general connection between
topological entanglement and quantum entanglement, as suggested by Kauffman et
al.


  Applying an interior-point method to the central-path conditions is a widely
used approach for solving quadratic programs. Reformulating these conditions in
the log-domain is a natural variation on this approach that to our knowledge is
previously unstudied. In this paper, we analyze log-domain interior-point
methods and prove their polynomial-time convergence. We also prove that they
are approximated by classical barrier methods in a precise sense and provide
simple computational experiments illustrating their superior performance.


  Various topics at the interface between condensed matter physics and the
physics of ultra-cold fermionic atoms in optical lattices are discussed. The
lectures start with basic considerations on energy scales, and on the regimes
in which a description by an effective Hubbard model is valid. Qualitative
ideas about the Mott transition are then presented, both for bosons and
fermions, as well as mean-field theories of this phenomenon. Antiferromagnetism
of the fermionic Hubbard model at half-filling is briefly reviewed. The
possibility that interaction effects facilitate adiabatic cooling is discussed,
and the importance of using entropy as a thermometer is emphasized. Geometrical
frustration of the lattice, by suppressing spin long-range order, helps
revealing genuine Mott physics and exploring unconventional quantum magnetism.
The importance of measurement techniques to probe quasiparticle excitations in
cold fermionic systems is emphasized, and a recent proposal based on stimulated
Raman scattering briefly reviewed. The unconventional nature of these
excitations in cuprate superconductors is emphasized.


  We design persistent surveillance strategies for the quickest detection of
anomalies taking place in an environment of interest. From a set of predefined
regions in the environment, a team of autonomous vehicles collects noisy
observations, which a control center processes. The overall objective is to
minimize detection delay while maintaining the false alarm rate below a desired
threshold. We present joint (i) anomaly detection algorithms for the control
center and (ii) vehicle routing policies. For the control center, we propose
parallel cumulative sum (CUSUM) algorithms (one for each region) to detect
anomalies from noisy observations. For the vehicles, we propose a stochastic
routing policy, in which the regions to be visited are chosen according to a
probability vector. We study stationary routing policy (the probability vector
is constant) as well as adaptive routing policies (the probability vector
varies in time as a function of the likelihood of regional anomalies). In the
context of stationary policies, we design a performance metric and minimize it
to design an efficient stationary routing policy. Our adaptive policy improves
upon the stationary counterpart by adaptively increasing the selection
probability of regions with high likelihood of anomaly. Finally, we show the
effectiveness of the proposed algorithms through numerical simulations and a
persistent surveillance experiment.


  Making decorated logos requires image editing skills, without sufficient
skills, it could be a time-consuming task. While there are many on-line web
services to make new logos, they have limited designs and duplicates can be
made. We propose using neural style transfer with clip art and text for the
creation of new and genuine logos. We introduce a new loss function based on
distance transform of the input image, which allows the preservation of the
silhouettes of text and objects. The proposed method constrains style transfer
only around the designated area. We demonstrate the characteristics of proposed
method. Finally, we show the results of logo generation with various input
images.


  The transverse momentum spectra for direct photons produced in Pb-Pb
collisions at the LHC, including thermal (hydrodynamics) and prompt (pQCD)
emissions are presented.


  Spin-1 antiferromagnets are abundant in nature, but few theories or results
exist to understand their general properties and behavior, particularly in
situations when geometric frustration is present. Here we study the $S=1$
Kagome compound Na$_2$Ti$_3$Cl$_8$ using a combination of Density Functional
Theory, Exact Diagonalization, and Density Matrix Renormalization Group methods
to achieve a first principles supported explanation of exotic magnetic phases
in this compound. We find that the effective magnetic Hamiltonian includes
essential non-Heisenberg terms that do not stem from spin-orbit coupling, and
both trimerized and spin-nematic magnetic phases are relevant. The
experimentally observed structural transition to a breathing Kagome phase is
driven by spin--lattice coupling, which favors the trimerized magnetic phase
against the quadrupolar one. We thus show that lattice effects can be necessary
to understand the magnetism in frustrated magnetic compounds, and surmise that
Na$_2$Ti$_3$Cl$_8$ is a compound which cannot be understood from only
electronic or only lattice Hamiltonians, very much like VO$_2$.


  Application security traditionally strongly relies upon security of the
underlying operating system. However, operating systems often fall victim to
software attacks, compromising security of applications as well. To overcome
this dependency, Intel introduced SGX, which allows to protect application code
against a subverted or malicious OS by running it in a hardware-protected
enclave. However, SGX lacks support for generic trusted I/O paths to protect
user input and output between enclaves and I/O devices.
  This work presents SGXIO, a generic trusted path architecture for SGX,
allowing user applications to run securely on top of an untrusted OS, while at
the same time supporting trusted paths to generic I/O devices. To achieve this,
SGXIO combines the benefits of SGX's easy programming model with traditional
hypervisor-based trusted path architectures. Moreover, SGXIO can tweak insecure
debug enclaves to behave like secure production enclaves. SGXIO surpasses
traditional use cases in cloud computing and makes SGX technology usable for
protecting user-centric, local applications against kernel-level keyloggers and
likewise. It is compatible to unmodified operating systems and works on a
modern commodity notebook out of the box. Hence, SGXIO is particularly
promising for the broad x86 community to which SGX is readily available.


  We generalize to the relations $(\lambda, \mu) \stackrel{\kappa}{\Rightarrow}
(\lambda', \mu')$ and $\alm (\lambda, \mu) \stackrel{\kappa}{\Rightarrow} \alm
(\lambda', \mu')$ some results obtained in Parts II and IV. We also present a
multi-cardinal version.


  Generating a dissimilarity matrix is typically the first step in big data
analysis. Although numerous methods exist, such as Euclidean distance,
Minkowski distance, Manhattan distance, Bray Curtis dissimilarity, Jaccard
similarity and Dice dissimilarity, it remains unclear which factors drive
dissimilarity between groups. In this paper, we introduce an approach based on
differences in moments and sparsity. We show that this method can delineate the
key factors underlying group differences. For example, in biology, mean
dissimilarity indicates differences driven by up down regulated gene
expressions, standard deviation dissimilarity reflects the heterogeneity of
response to treatment, and sparsity dissimilarity corresponds to differences
prompted by the activation silence of genes. Through extensive reanalysis of
genome, transcriptome, proteome, metabolome, immune profiling, microbiome, and
social science datasets, we demonstrate insights not captured in previous
studies. For instance, it shows that the sparsity dissimilarity is as effective
as the mean dissimilarity in predicting the alleviation effects of a COVID 19
drug, suggesting that sparsity dissimilarity is highly meaningful.


  This paper proposes a hierarchical and multi-scale variational
autoencoder-based non-autoregressive text-to-speech model (HiMuV-TTS) to
generate natural speech with diverse speaking styles. Recent advances in
non-autoregressive TTS (NAR-TTS) models have significantly improved the
inference speed and robustness of synthesized speech. However, the diversity of
speaking styles and naturalness are needed to be improved. To solve this
problem, we propose the HiMuV-TTS model that first determines the global-scale
prosody and then determines the local-scale prosody via conditioning on the
global-scale prosody and the learned text representation. In addition, we
improve the quality of speech by adopting the adversarial training technique.
Experimental results verify that the proposed HiMuV-TTS model can generate more
diverse and natural speech as compared to TTS models with single-scale
variational autoencoders, and can represent different prosody information in
each scale.


  This paper revisits datasets and evaluation criteria for Symbolic Regression
(SR), specifically focused on its potential for scientific discovery. Focused
on a set of formulas used in the existing datasets based on Feynman Lectures on
Physics, we recreate 120 datasets to discuss the performance of symbolic
regression for scientific discovery (SRSD). For each of the 120 SRSD datasets,
we carefully review the properties of the formula and its variables to design
reasonably realistic sampling ranges of values so that our new SRSD datasets
can be used for evaluating the potential of SRSD such as whether or not an SR
method can (re)discover physical laws from such datasets. We also create
another 120 datasets that contain dummy variables to examine whether SR methods
can choose necessary variables only. Besides, we propose to use normalized edit
distances (NED) between a predicted equation and the true equation trees for
addressing a critical issue that existing SR metrics are either binary or
errors between the target values and an SR model's predicted values for a given
input. We conduct benchmark experiments on our new SRSD datasets using various
representative SR methods. The experimental results show that we provide a more
realistic performance evaluation, and our user study shows that the NED
correlates with human judges significantly more than an existing SR metric. We
publish repositories of our code and 240 SRSD datasets.


  Using data from the SAMI Galaxy Survey, we investigate the correlation
between the projected stellar kinematic spin vector of 1397 SAMI galaxies and
the line-of-sight motion of their neighbouring galaxies. We calculate the
luminosity-weighted mean velocity difference between SAMI galaxies and their
neighbours in the direction perpendicular to the SAMI galaxies angular momentum
axes. The luminosity-weighted mean velocity offsets between SAMI and
neighbours, which indicates the signal of coherence between the rotation of the
SAMI galaxies and the motion of neighbours, is 9.0 $\pm$ 5.4 km s$^{-1}$ (1.7
$\sigma$) for neighbours within 1 Mpc. In a large-scale analysis, we find that
the average velocity offsets increase for neighbours out to 2 Mpc. However, the
velocities are consistent with zero or negative for neighbours outside 3 Mpc.
The negative signals for neighbours at distance around 10 Mpc are also
significant at $\sim 2$ $\sigma$ level, which indicate that the positive
signals within 2 Mpc might come from the variance of large-scale structure. We
also calculate average velocities of different subsamples, including galaxies
in different regions of the sky, galaxies with different stellar masses, galaxy
type, $\lambda_{Re}$ and inclination. Although low-mass, high-mass, early-type
and low-spin galaxies subsamples show 2 - 3 $\sigma$ signal of coherence for
the neighbours within 2 Mpc, the results for different inclination subsamples
and large-scale results suggest that the $\sim 2 \sigma$ signals might result
from coincidental scatter or variance of large-scale structure. Overall, the
modest evidence of coherence signals for neighbouring galaxies within 2 Mpc
needs to be confirmed by larger samples of observations and simulation studies.


  We explore the possibility to develop a new axion helioscope type, sensitive
to the higher axion mass region favored by axion models. We propose to use a
low background large volume TPC immersed in an intense magnetic field. Contrary
to traditional tracking helioscopes, this detection technique takes advantage
of the capability to directly detect the photons converted on the buffer gas
which defines the axion mass sensitivity region, and does not require pointing
the magnet to the Sun. The operation flexibility of a TPC to be used with
different gas mixtures (He, Ne, Xe, etc) and pressures (from 10 mbar to 10 bar)
will allow to enhance sensitivity for axion masses from few meV to several eV.
We present different helioscope data taking scenarios, considering detection
efficiency and axion absorption probability, and show the sensitivities
reachable with this technique to be few $\times$ 10$^{-11}\,$GeV$^{-1}$ for a
5$\,$T$\,$m$^3$ scale TPC. We show that a few years program taking data with
such setup would allow to probe the KSVZ axion model for axion masses above 100
meV.


  The standard assumptions that underlie many conceptual and quantitative
frameworks do not hold for many complex physical, biological, and social
systems. Complex systems science clarifies when and why such assumptions fail
and provides alternative frameworks for understanding the properties of complex
systems. This review introduces some of the basic principles of complex systems
science, including complexity profiles, the tradeoff between efficiency and
adaptability, the necessity of matching the complexity of systems to that of
their environments, multi-scale analysis, and evolutionary processes. Our focus
is on the general properties of systems as opposed to the modeling of specific
dynamics; rather than provide a comprehensive review, we pedagogically describe
a conceptual and analytic approach for understanding and interacting with the
complex systems of our world. With the exception of a few footnotes, this paper
assumes only a high school mathematical and scientific background, so that it
may be accessible to academics in all fields, decision-makers in industry,
government, and philanthropy, and anyone who is interested in systems and
society.


  This paper presents a new fuel cycle benchmarking analysis methodology by
coupling Gaussian process regression, a popular technique in Machine Learning,
to dynamic time warping, a mechanism widely used in speech recognition.
Together they generate figures-of-merit that are applicable to any time series
metric that a benchmark may study. The figures-of-merit account for uncertainty
in the metric itself, utilize information across the whole time domain, and do
not require that the simulators use a common time grid. Here, a distance
measure is defined that can be used to compare the performance of each
simulator for a given metric. Additionally, a contribution measure is derived
from the distance measure that can be used to rank order the importance of fuel
cycle metrics. Lastly, this paper warns against using standard signal
processing techniques for error reduction. This is because it is found that
error reduction is better handled by the Gaussian process regression itself.


  The rapid development of diffusion models (DMs) has significantly advanced
image and video applications, making "what you want is what you see" a reality.
Among these, video editing has gained substantial attention and seen a swift
rise in research activity, necessitating a comprehensive and systematic review
of the existing literature. This paper reviews diffusion model-based video
editing techniques, including theoretical foundations and practical
applications. We begin by overviewing the mathematical formulation and image
domain's key methods. Subsequently, we categorize video editing approaches by
the inherent connections of their core technologies, depicting evolutionary
trajectory. This paper also dives into novel applications, including
point-based editing and pose-guided human video editing. Additionally, we
present a comprehensive comparison using our newly introduced V2VBench.
Building on the progress achieved to date, the paper concludes with ongoing
challenges and potential directions for future research.


  We relate the underlying properties of a population of fast radio-emitting
transient events to its expected detection rate in a survey of finite
sensitivity. The distribution of the distances of the detected events is
determined in terms of the population luminosity distribution and survey
parameters, for both extragalactic and Galactic populations. The detection rate
as a function of Galactic position is examined to identify regions that
optimize survey efficiency in a survey whose field of view is limited. The
impact of temporal smearing caused by scattering in the Interstellar Medium has
a large and direction-dependent bearing on the detection of impulsive signals,
and we present a model for the effects of scattering on the detection rate. We
show the detection rate scales as Omega S0^{-3/2 + delta}, where Omega is the
field of view, and S0 is the minimum detectable flux density, and 0 < delta =<
3/2 for a survey of Galactic transients in which interstellar scattering or the
finite volume of the Galaxy is important. We derive formal conditions on the
optimal survey strategy to adopt under different circumstances for fast
transients surveys on next generation large-element, widefield arrays, such as
ASKAP, LOFAR, the MWA and the SKA, and show how interstellar scattering and the
finite spatial extent of a Galactic population modify the choice of optimal
strategy.


  A linearly implicit conservative difference scheme is applied to discretize
the attractive coupled nonlinear Schr\"odinger equations with fractional
Laplacian. Complex symmetric linear systems can be obtained, and the system
matrices are indefinite and Toeplitz-plus-diagonal. Neither efficient
preconditioned iteration method nor fast direct method is available to deal
with these systems. In this paper, we propose a novel matrix splitting
iteration method based on a normal splitting of an equivalent real block form
of the complex linear systems. This new iteration method converges
unconditionally, and the quasi-optimal iteration parameter is deducted. The
corresponding new preconditioner is obtained naturally, which can be
constructed easily and implemented efficiently by fast Fourier transform.
Theoretical analysis indicates that the eigenvalues of the preconditioned
system matrix are tightly clustered. Numerical experiments show that the new
preconditioner can significantly accelerate the convergence rate of the Krylov
subspace iteration methods. Specifically, the convergence behavior of the
related preconditioned GMRES iteration method is spacial mesh-size-independent,
and almost fractional order insensitive. Moreover, the linearly implicit
conservative difference scheme in conjunction with the preconditioned GMRES
iteration method conserves the discrete mass and energy in terms of a given
precision.


  We develop a flexible, relativistically covariant parameterization of dense
nuclear matter equation of state suited for inclusion in computationally
demanding hadronic transport simulations. Within an implementation in the
hadronic transport code SMASH, we show that effects due to bulk thermodynamic
behavior are reproduced in dynamic hadronic systems, demonstrating that
hadronic transport can be used to study critical behavior in dense nuclear
matter, both at and away from equilibrium. We also show that two-particle
correlations calculated from hadronic transport simulation data follow
theoretical expectations based on the second order cumulant ratio, and
constitute a clear signature of crossing the phase diagram above the critical
point.


  Independent and identically distributed (i.i.d.) data is essential to many
data analysis and modeling techniques. In the medical domain, collecting data
from multiple sites or institutions is a common strategy that guarantees
sufficient clinical diversity, determined by the decentralized nature of
medical data. However, data from various sites are easily biased by the local
environment or facilities, thereby violating the i.i.d. rule. A common strategy
is to harmonize the site bias while retaining important biological information.
The ComBat is among the most popular harmonization approaches and has recently
been extended to handle distributed sites. However, when faced with situations
involving newly joined sites in training or evaluating data from unknown/unseen
sites, ComBat lacks compatibility and requires retraining with data from all
the sites. The retraining leads to significant computational and logistic
overhead that is usually prohibitive. In this work, we develop a novel Cluster
ComBat harmonization algorithm, which leverages cluster patterns of the data in
different sites and greatly advances the usability of ComBat harmonization. We
use extensive simulation and real medical imaging data from ADNI to demonstrate
the superiority of the proposed approach. Our codes are provided in
https://github.com/illidanlab/distributed-cluster-harmonization.


  We present cudaclaw, a CUDA-based high performance data-parallel framework
for the solution of multidimensional hyperbolic partial differential equation
(PDE) systems, equations describing wave motion. cudaclaw allows computational
scientists to solve such systems on GPUs without being burdened by the need to
write CUDA code, worry about thread and block details, data layout, and data
movement between the different levels of the memory hierarchy. The user defines
the set of PDEs to be solved via a CUDA- independent serial Riemann solver and
the framework takes care of orchestrating the computations and data transfers
to maximize arithmetic throughput. cudaclaw treats the different spatial
dimensions separately to allow suitable block sizes and dimensions to be used
in the different directions, and includes a number of optimizations to minimize
access to global memory.


  Lecture videos are an increasingly important learning resource for higher
education. However, the challenge of quickly finding the content of interest in
a lecture video is an important limitation of this format. This paper
introduces visual summarization of lecture video segments to enhance
navigation. A lecture video is divided into segments based on the
frame-to-frame similarity of content. The user navigates the lecture video
content by viewing a single frame visual and textual summary of each segment.
The paper presents a novel methodology to generate the visual summary of a
lecture video segment by computing similarities between images extracted from
the segment and employing a graph-based algorithm to identify the subset of
most representative images. The results from this research are integrated into
a real-world lecture video management portal called Videopoints. To collect
ground truth for evaluation, a survey was conducted where multiple users
manually provided visual summaries for 40 lecture video segments. The users
also stated whether any images were not selected for the summary because they
were similar to other selected images. The graph based algorithm for
identifying summary images achieves 78% precision and 72% F1-measure with
frequently selected images as the ground truth, and 94% precision and 72%
F1-measure with the union of all user selected images as the ground truth. For
98% of algorithm selected visual summary images, at least one user also
selected that image for their summary or considered it similar to another image
they selected. Over 65% of automatically generated summaries were rated as good
or very good by the users on a 4-point scale from poor to very good. Overall,
the results establish that the methodology introduced in this paper produces
good quality visual summaries that are practically useful for lecture video
navigation.


  The spectral properties of the post-merger gravitational-wave signal from a
binary of neutron stars encode a variety of information about the features of
the system and of the equation of state describing matter around and above
nuclear saturation density. Characterising the properties of such a signal is
an ``old'' problem, which first emerged when a number of frequencies were shown
to be related to the properties of the binary through ``quasi-universal''
relations. Here we take a new look at this old problem by computing the
properties of the signal in terms of the Weyl scalar $\psi_4$. In this way, and
using a database of more than 100 simulations, we provide the first evidence
for a new instantaneous frequency, $f^{\psi_4}_0$, associated with the instant
of quasi time-symmetry in the postmerger dynamics, and which also follows a
quasi-universal relation. We also derive a new quasi-universal relation for the
merger frequency $f^{h}_{\rm mer}$, which provides a description of the data
that is four times more accurate than previous expressions while requiring
fewer fitting coefficients. Finally, consistently with the findings of numerous
studies before ours, and using an enlarged ensamble of binary systems we point
out that the $\ell=2, m=1$ gravitational-wave mode could become comparable with
the traditional $\ell=2, m=2$ mode on sufficiently long timescales, with strain
amplitudes in a ratio $|h^{21}|/|h^{22}| \sim 0.1-1$ under generic orientations
of the binary, which could be measured by present detectors for signals with
large signal-to-noise ratio or by third-generation detectors for generic
signals should no collapse occur.


  This preliminary study presents a simple modulation scheme to dynamically
create time-averaged optical potentials to trap colloidal particles using
acousto-optical modulation. The method provides access to control
experimentally relevant parameters of a tunable double-well potential. We show
experimental data successfully adjusting the trapping distance in the range
20-2000 nm and discuss situations arising when reconstructing time-averaged
optical potentials from trapped particle data. This is the first step towards
studying colloidal particles in dynamically modulated optical potentials to
explore the stochastic thermodynamics of mesoscopic systems and small-scale
thermo-mechanical machines.


  Extreme ultraviolet (XUV) attosecond pulses, generated by a process known as
laser-induced electron recollision, are a key ingredient for attosecond
metrology, providing a tool to precisely initiate and probe sub-femtosecond
dynamics in the microcosms of atoms, molecules and solids[1]. However, with the
current technology, extending attosecond metrology to scrutinize the dynamics
of the inner-shell electrons is a challenge, that is because of the lower
efficiency in generating the required soft x-ray \hbar\omega>300 eV attosecond
bursts and the lower absorption cross-sections in this spectral range. A way
around this problem is to use the recolliding electron to directly initiate the
desired inner-shell process, instead of using the currently low flux x-ray
attosecond sources.Such an excitation process occurs in a sub-femtosecond
timescale, and may provide the necessary "pump" step in a pump-probe
experiment[2]. Here we used a few cycle infrared \lambda_{0}~1800nm source[3]
and observed direct evidences for inner-shell excitations through the
laser-induced electron recollision process. It is the first step toward
time-resolved core-hole studies in the keV energy range with sub-femtosecond
time resolution.


  We provide a complete classification of the algebraicity of (generalized)
hypergeometric functions with no restriction on the set of their parameters.
Our characterization relies on the interlacing criteria of Christol (1987) and
Beukers-Heckman (1989) for globally bounded and algebraic hypergeometric
functions, however in a more general setting which allows arbitrary complex
parameters with possibly integral differences. We also showcase the adapted
criterion on a variety of different examples.


  The paper has two relatively distinct but connected goals; the first is to
define the notion of Pad\'e\ approximation of Weyl-Stiltjes transforms on an
arbitrary compact Riemann surface of higher genus. The data consists of a
contour in the Riemann surface and a measure on it, together with the
additional datum of a local coordinate near a point and a divisor of degree
$g$. The denominators of the resulting Pad\'e--like approximation also satisfy
an orthogonality relation and are sections of appropriate line bundles. A
Riemann--Hilbert problem for a square matrix of rank two is shown to
characterize these orthogonal sections, in a similar fashion to the ordinary
orthogonal polynomial case.
  The second part extends this idea to explore its connection to integrable
systems. The same data can be used to define a pairing between two sequences of
line bundles. The locus in the deformation space where the pairing becomes
degenerate for fixed degree coincides with the zeros of a "tau" function. We
show how this tau function satisfies the Kadomtsev--Petviashvili hierarchy with
respect to either deformation parameters, and a certain modification of the
2--Toda hierarchy when considering the whole sequence of tau functions. We also
show how this construction is related to the Krichever construction of
algebro--geometric solutions.


  In this paper, we consider a time-slotted cognitive radio (CR) setting with
buffered and energy harvesting primary and CR users. At the beginning of each
time slot, the CR user probabilistically chooses the spectrum sensing duration
from a predefined set. If the primary user (PU) is sensed to be inactive, the
CR user accesses the channel immediately. The CR user optimizes the sensing
duration probabilities in order to maximize its mean data service rate with
constraints on the stability of the primary and cognitive queues. The
optimization problem is split into two subproblems. The first is a
linear-fractional program, and the other is a linear program. Both subproblems
can be solved efficiently.


  The low velocity dynamic of a doubly periodic monopole, also called a
monopole wall or monowall for short, is described by geodesic motion on its
moduli space. This moduli space is hyperkaehler and non-compact. We establish a
relation between the Kaehler potential of this moduli space and the volume of a
region in Euclidean three-space cut out by a plane arrangement associated with
each monowall.


  A "floorplan" is a rectangle subdivided into smaller rectangular sections by
horizontal and vertical line segments. Each section in the floorplan is called
a "block". Two floorplans are considered equivalent if and only if there is a
one-to-one correspondence between the blocks in the two floorplans such that
the relative position relationship of the blocks in one floorplan is the same
as the relative position relationship of the corresponding blocks in another
floorplan. The objects of "Mosaic floorplans" are the same as floorplans, but
an alternative definition of equivalence is used. Two mosaic floorplans are
considered equivalent if and only if they can be converted to each other by
sliding the line segments that divide the blocks.
  Mosaic floorplans are widely used in VLSI circuit design. An important
problem in this area is to find short binary string representations of the set
of n-block mosaic floorplans. The best known representation is the
"Quarter-State Sequence" which uses 4n bits. This paper introduces a simple
binary representation of n-block mosaic floorplan using 3n-3 bits. It has been
shown that any binary representation of n-block mosaic floorplans must use at
least (3n-o(n)) bits. Therefore, the representation presented in this paper is
optimal (up to an additive lower order term).
  "Baxter permutations" are a set of permutations defined by prohibited
subsequences. Baxter permutations have been shown to have one-to-one
correspondences to many interesting objects in the so-called "Baxter
combinatorial family". In particular, there exists a simple one-to-one
correspondence between mosaic floorplans and Baxter permutations. As a result,
the methods introduced in this paper also lead to an optimal binary
representation of Baxter permutations and all objects in the Baxter
combinatorial family.


  Coherent, broadband pulses of extreme ultraviolet (XUV) light provide a new
and exciting tool for exploring attosecond electron dynamics. Using
photoelectron streaking, interferometric spectrograms can be generated that
contain a wealth of information about the phase properties of the
photoionization process. If properly retrieved, this phase information reveals
attosecond dynamics during photoelectron emission such as multielectron
dynamics and resonance processes. However, until now, the full retrieval of the
continuous electron wavepacket phase from isolated attosecond pulses has
remained challenging. Here, after elucidating key approximations and
limitations that hinder one from extracting the coherent electron wavepacket
dynamics using available retrieval algorithms, we present a new method called
Absolute Complex Dipole transmission matrix element reConstruction (ACDC). We
apply the ACDC method to experimental spectrograms to resolve the phase and
group delay difference between photoelectrons emitted from Ne and Ar. Our
results reveal subtle dynamics in this group delay difference of photoelectrons
emitted form Ar. These group delay dynamics were not resolvable with prior
methods that were only able to extract phase information at discrete energy
levels, emphasizing the importance of a complete and continuous phase retrieval
technique such as ACDC. Here we also make this new ACDC retrieval algorithm
available with appropriate citation in return.


  The invariant imbedding evolution equations for the amplitude reflection and
transmission coefficients of a disordered 1D chain are shown to follow from the
continuum limit, for weak disorder, of recursion relations between reflection
(transmission) coefficients of Anderson chains of N and N-1 atoms embedded in
infinite non-disordered chains. We show that various available analytical and
numerical results for reflection phase distributions in the Anderson- and
invariant imbedding models are in good qualitative agreement, as expected from
the above equivalence of these models. We also discuss the distribution of
reflection phases and of reflection delay times for an Anderson model with a
simple distribution of on-site potentials characterizing extreme strong
disorder.


  Among all torus links, we characterise those arising as links of simple plane
curve singularities by the property that their fibre surfaces admit only a
finite number of cutting arcs that preserve fibredness. The same property
allows a characterisation of Coxeter-Dynkin trees (i.e., $A_n$, $D_n$, $E_6$,
$E_7$ and $E_8$) among all positive tree-like Hopf plumbings.


  Stellar and nebular abundance indicators reveal that there exists significant
abundance fluctuations in the interstellar medium (ISM) of gas-rich galaxies.
It is shown that at the present observed solar level of O/H $\sim 6 \times
10^{-4}$, abundance differences of a factor of two, such as existing between
the Sun and the nearby Orion Nebula, are many times larger than expected.
  We examine a variety of hydrodynamical processes operating at scales ranging
from 1 pc to greater than 10 kpc, and show that the ISM should appear better
homogenized chemically than it actually is: $(i)$ on large galactic scales (1
$\geq\ l\ \geq$ 10 kpc), turbulent diffusion of interstellar clouds in the
shear flow of galactic differential rotation is able to wipe out azimuthal O/H
fluctuations in less than $10^9$ yrs; $(ii)$ at the intermediate scale (100
$\geq\ l\ \geq$ 1000 pc), cloud collisions and expanding supershells driven by
evolving associations of massive stars, differential rotation and triggered
star formation will re-distribute and mix gas efficiently in about $10^8$ yrs;
$(iii)$ at small scales (1 $\geq\ l\ \geq$ 100 pc), turbulent diffusion may be
the dominant mechanism in cold clouds, while Rayleigh-Taylor and
Kelvin-Helmhotz instabilities quickly develop in regions of gas ionized by
massive stars, leading to full mixing in


  The onset of frictional sliding between contacting bodies under shear load is
nucleated by the quasi-static growth of localized slip patches. After reaching
a certain critical size, these patches become unstable and continue growing
dynamically, eventually causing the sliding of the entire interface. Two
different theories have been used to compute the nucleation length of such
patches depending on the dominant process driving their growth. If it is only
the yielding of contact asperities (large-scale yielding), a stress criterion
is applied, based on linear stability analysis, whereas if fracture dominates,
an energy criterion is applied, based on fracture mechanics and classical
nucleation theory. Both approaches contain important underlying assumptions
that are well-suited to describe either one situation or the other. However,
what happens in-between is not captured by any of them. In this work, we use
numerical simulations to study what is the dominant underlying process driving
nucleation for different conditions of heterogeneity and what are the
implications for nucleation dynamics and the onset of frictional sliding. We
show that large frictional heterogeneities enable a transition from a
yielding-driven nucleation phase to a fracture-driven one. This transition
occurs only above a certain level of heterogeneity and can either be
quasi-static (stable) or dynamic (unstable), depending on the correlation
length of frictional strength along the interface and the difference in
strength between the strongest and the weakest point (the amplitude). Unstable
transitions generate localized dynamic slip events, whose magnitude increases
with higher correlation length and decreases with larger amplitude. Our work
sheds new light on the role of heterogeneity and fracture in the nucleation of
frictional slip, bridging the gap between the two main governing theories for
nucleation.


  A canonically defined mod 2 linear dependency current is associated to each
collection of m sections of a real rank n vector bundle. This current is
supported on the linear dependency set of the collection of sections. It is
defined whenever the collection satisfies a weak measure theoretic condition
called "atomicity". Essentially any reasonable collection of sections satisfies
this condition, vastly extending the usual general position hypothesis. This
current is a mod 2, closed, locally integrally flat current of degree q= n-m+1
and hence determines a mod 2 cohomology class. This class is shown to be well
defined independent of the collection of sections. Moreover it is the q-th
Stielfel-Whitney class of the vector bundle. More is true if q is odd or q=n.
In this case a linear dependency current which is twisted by the orientation of
the bundle can be associated to the collection. The cohomology class of the
linear dependency current is 2-torsion and is the q-th twisted integral
Stiefel-Whitney class of the bundle. In addition, higher dependency and general
degeneracy currents of bundle maps are studied, together with applications to
singularities of projections and maps. These results rely on a theorem of
Federer which states that the complex of integrally flat currents mod p
computes cohomology mod p. An alternate approach to Federer's theorem is
offered in an appendix. This approach is simpler and is via sheaf theory.


  In this article, we give a representation for compact operators acting
between reflexive Banach spaces, which generalizes the representation given by
Edmunds et al. for compact operators between reflexive Banach spaces with
strictly convex duals. Further, we give a representation for operators on
Banach spaces that are comparable to compact normal operators on Hilbert spaces
and illustrate our result with an example.


  Strong gravitational lensing is a useful probe of both the intrinsic
properties of the lenses and the cosmological parameters of the universe. The
large number of model parameters and small sample of observed lens systems,
however, have made it difficult to obtain useful constraints on more than a few
parameters from lensing statistics. Here we examine how the recent WMAP
measurements help improve the constraining power of statistics from the radio
lensing survey JVAS/CLASS. We find that the absence of theta>3'' lenses in
CLASS places an upper bound of beta<1.25 (1.60) at 68% (95%) CL on the inner
density profile, rho \propto r^{-beta}, of cluster-sized halos. Furthermore,
the favored power spectrum normalization is sigma_8 >= 0.7 (95% CL). We discuss
two possibilities for stronger future constraints: a positive detection of at
least one large-separation system, and next-generation radio surveys such as
LOFAR.


  Objective Semi-supervised video object segmentation refers to segmenting the
object in subsequent frames given the object label in the first frame. Existing
algorithms are mostly based on the objectives of matching and propagation
strategies, which often make use of the previous frame with masking or optical
flow. This paper explores a new propagation method, uses short-term matching
modules to extract the information of the previous frame and apply it in
propagation, and proposes the network of Long-Short-Term similarity matching
for video object segmentation (LSMOVS) Method: By conducting pixel-level
matching and correlation between long-term matching module and short-term
matching module with the first frame and previous frame, global similarity map
and local similarity map are obtained, as well as feature pattern of current
frame and masking of previous frame. After two refine networks, final results
are obtained through segmentation network. Results: According to the
experiments on the two data sets DAVIS 2016 and 2017, the method of this paper
achieves favorable average of region similarity and contour accuracy without
online fine tuning, which achieves 86.5% and 77.4% in terms of single target
and multiple targets. Besides, the count of segmented frames per second reached
21. Conclusion: The short-term matching module proposed in this paper is more
conducive to extracting the information of the previous frame than only the
mask. By combining the long-term matching module with the short-term matching
module, the whole network can achieve efficient video object segmentation
without online fine tuning


  Type Ia supernovae (SNe Ia) are used as distance indicators to infer the
cosmological parameters that specify the expansion history of the universe.
Parameter inference depends on the criteria by which the analysis SN sample is
selected. Only for the simplest selection criteria and population models can
the likelihood be calculated analytically, otherwise it needs to be determined
numerically, a process that inherently has error. Numerical errors in the
likelihood lead to errors in parameter inference. This article presents toy
examples where the distance modulus is inferred given a set of SNe at a single
redshift. Parameter estimators and their uncertainties are calculated using
Monte Carlo techniques. The relationship between the number of Monte Carlo
realizations and numerical errors is presented. The procedure can be applied to
more realistic models and used to determine the computational and data
management requirements of the transient analysis pipeline.


  We describe atoms by a pseudo-relativistic model that has its origin in the
work of Chandrasekhar. We prove that the leading energy correction for heavy
atoms, the Scott correction, exists. It turns out to be lower than in the
non-relativistic description of atoms. Our proof is valid up to and including
the critical coupling constant. It is based on a renormalization of the energy
whose zero level we adjust to be the ground-state energy of the corresponding
non-relativistic problem. This allows us to roll the proof back -- by
relatively simple technical means -- to results for the Schr\"odinger operator.


  Approaches to improving multilingual language understanding often require
multiple languages during the training phase, rely on complicated training
techniques, and -- importantly -- struggle with significant performance gaps
between high-resource and low-resource languages. We hypothesize that the
performance gaps between languages are affected by linguistic gaps between
those languages and provide a novel solution for robust multilingual language
modeling by employing phonemic representations (specifically, using phonemes as
input tokens to LMs rather than subwords). We present quantitative evidence
from three cross-lingual tasks that demonstrate the effectiveness of phonemic
representation, which is further justified by a theoretical analysis of the
cross-lingual performance gap.


  Let $R$ be a noncommutative ring, and let $S$ be an $m$-system of $R$. In
this paper, we give more results on the concept of almost prime (right) ideals,
that were introduced by the first two authors, especially in (right) $S$-unital
rings, local rings, and decomposable rings. In addition, we introduce the
concept of almost right $S$-prime ideals, and we show how some findings
regarding almost prime ideals can be derived as consequences of almost right
$S$-prime ideals. Besides, we show how almost right $S$-prime ideals behave in
related rings such as homomorphic images, quotient rings, and decomposable
rings. Finally, we construct almost right $S$-prime ideals using the Nagata
method of idealization.


  We have analyzed the electronic structure of half-metallic magnets based on
first principles electronic structure calculations of a series of semi-Heusler
alloys. The characteristic feature of the electronic structure of semi-Heusler
systems is a d-d gap in the density of states lying at/close to the Fermi level
depending on the number of valence electrons. We have employed various
indicators of chemical bonding to understand the origin of the gap in these
systems, which is crucial for their half-metallic property. The density of
states of other half-metallic magnets also supports a gap and it is a generic
feature of these systems. We have discussed in some details the origin of
magnetism, in particular, how the presence of the gap is crucial to stabilize
half-metallic ferro and ferri magnetism in these systems. Finally, we have
studied the role of magnetic impurities in semiconducting semi-Heusler systems.
We show with the aid of model supercell calculations that these systems are not
only ferromagnetic but also half-metallic with possibly high Curie temperature.


  We develop efficient group-theoretical approach to the problem of
classification of evolution equations that admit non-local transformation
groups (quasi-local symmetries), i.e., groups involving integrals of the
dependent variable. We classify realizations of two- and three-dimensional Lie
algebras leading to equations admitting quasi-local symmetries. Finally, we
generalize the approach in question for the case of an arbitrary system of
evolution equations with two independent variables.


  This paper investigates a dividend optimization problem with a positive
creeping-associated terminal value at ruin for spectrally negative Levy
processes. We consider an insurance company whose surplus process evolves
according to a spectrally negative Levy process with a Gaussian part and a
finite Levy measure. Its objective function relates to dividend payments until
ruin and a creeping-associated terminal value at ruin. The positive
creeping-associated terminal value represents the salvage value or the creeping
reward when creeping happens. Owing to formulas from fluctuation theory, the
objective considered is represented explicitly. Under certain restrictions on
the terminal value and the surplus process, we show that the threshold strategy
should be the optimal one over an admissible class with bounded dividend rates.


  This report on the topics in the title was written for a lecture series at
the Southwestern Center for Arithmetic Algebraic Geometry at the University of
Arizona.It may serve as an introduction to certain conjectural relations
between number theory and the theory of dynamical systems on foliated spaces.
The material is based on streamlined and updated versions of earlier papers on
this subject.


  Although both theoretical predications and experimental observations
demonstrated that the damping factor is anisotropic at
ferromagnet/semiconductor interface with robust interfacial spin-orbit
coupling, it is not well understood whether non-local Gilbert damping driven by
spin currents in heavy metal/ferromagnetic metal (HM/FM) bilayers is
anisotropic or not. Here, we investigated the in-plane angular- and frequency-
dependence of magnetic relaxation of epitaxial Fe/MgO(001) films with different
capping layers of Pd and Cu. After disentangling the parasitic contributions,
such as two-magnon scattering (TMS), mosaicity, and field-dragging effect, we
unambiguously observed that both local and non-local Gilbert damping are
isotropic in Fe(001) plane, suggesting that the pure spin currents absorption
is independent of Fe magnetization orientation in the epitaxial Pd/Fe
heterostructure. First principles calculation reveals that the effective spin
mixing conductance of Pd/Fe interface is nearly invariant for different
magnetization directions in good agreement with the experimental observations.
These results offer a valuable insight into the transmission and absorption of
pure spin currents, and facilitate us to utilize next-generation spintronic
devices.


  In this paper we explore the possibility of detecting strongly decaying
exotic states. The dibaryon(2.15) $J^P$ = $2^+$ state which decays into d $\pi$
is the example we use in this report.


  Slow swift electrons with low self-inertia interact differently with matter
and light in comparison with their relativistic counterparts: they are easily
recoiled, reflected, and also diffracted form optical gratings and
nanostructures. As a consequence, they can be also better manipulated into the
desired shape. For example, they get bunched quite fast in interaction with
acceleration gratings in presence of an external electromagnetic radiation, a
phenomenon which can be desirable in development of superradiant coherent light
sources. Here, I examine the spatiotemporal behavior of pulsed electron wave
packets at low energies interacting with pulsed light and optical gratings,
using a quantum-mechanical self-consistent numerical toolbox which is
introduced here. It will be shown that electron pulses are accelerated very
fast in interaction with the near-field of the grating, demanding that a
synchronicity condition is met. To prevent the electrons to be transversely
deflected from the grating a symmetric double-grating configuration is
necessary. It is found that even in this configuration, diffraction due to the
interaction of the electron with the standing-wave light inside the gap between
the gratings, is a source of defocusing. Moreover, the longitudinal broadening
of the electron pulse directly affects the final shape of the electron wave
packet due to the occurrence of multiple electron-photon scatterings. These
investigations pave the way towards the design of more efficient
electron-driven photon sources and accelerators.


  Recent searches for leptoquark production in proton-antiproton collisions at
sqrt(s)=1.96TeV are presented using data samples with integrated luminosities
up to 1fb^(-1) recorded with the D0 detector.


  We study the Ricci flow on $\mathbb{R}^{4}$ starting at an
SU(2)-cohomogeneity 1 metric $g_{0}$ whose restriction to any hypersphere is a
Berger metric. We prove that if $g_{0}$ has no necks and is bounded by a
cylinder, then the solution develops a global Type-II singularity and converges
to the Bryant soliton when suitably dilated at the origin. This is the first
example in dimension $n > 3$ of a non-rotationally symmetric Type-II flow
converging to a rotationally symmetric singularity model. Next, we show that if
instead $g_{0}$ has no necks, its curvature decays and the Hopf fibers are not
collapsed, then the solution is immortal. Finally, we prove that if the flow is
Type-I, then there exist minimal 3-spheres for times close to the maximal time.


  This paper introduces the proper notion of variational quasiconvexity
associated to a group of diffeomorphisms. We prove a lower semicontinuity
theorem connected to this notion. In the second part of the paper we apply this
result to a class of functions introduced in [5]. Such functions are
$GL(n,R)^{+}$ quasiconvex, hence they induce lower semicontinuous integrals.


  We study the equilibrium configurations of relativistic Neutron Stars(NS)
with a polytropic model in a $f(R,T)=R+2\lambda T+\xi T^{2}$ gravity.We
investigate the neutron star properties and their dependence on $\lambda$ and
$\xi$ corresponding to different central densities ($\rho_c$) of the NS. For
$\lambda = 0,-1,-3,-5$ with $\xi=0$ and
$\rho_c=1.5\times10^{18}~\rm{kg~m^{-3}}$, we find the maximum mass of the NS as
$M = 1.06 M_\odot$, $1.19 M_\odot$ $1.61 M_\odot$ and $2.47~M_\odot$
corresponding to the radius($R$) $10.409$ km, $10.737$ km, $11.461$ km and
$12.119$ km. This higher value of NS mass can be compared with gravitational
wave data(GW170817). For given $\lambda =-6$ and $\xi = 0$, we find that as
$\rho_c$ increases from $\rho_c=1.1 to 1.6 \times 10^{18}~\rm{kg~m^{-3}}$, the
maximum mass of the NS decreases from $4.19 M_\odot$ to $3.23 M_\odot$ while
it's radius $R$ decreases $13.86 \rm{km}$ to $11.54 \rm{km}$. With the fixed
value of $\xi = 10^{-27}$ and $\lambda = 0,-1,-3,-5$, we find the maximum mass
$M =1.06 M_\odot$,$1.34 M_\odot$,$1.89 M_\odot$ and $3.39~M_\odot$
corresponding to the radius $R = 10.409$ km, $10.843$ km, $11.549$ km and
$11.680$ km. respectively. Taking our observational constraints i.e. GW170817
(BNS Merger) mass - radius data, observed pulsars PSRJ1614-2230, PSRJ0348+0432
maximum mass - radius data; we found that posterior distribution plot of mass
$\&$ radius gives good result and the corner plot of modified gravity
parameters $\lambda$ and $\xi$ are giving very good posterior results. So, for
a range of values of $\lambda$ with $\xi=0 (\neq 0)$, we found that the mass
$M$ and the radius $R$ of the NS lie within the range given by the GW170817
gravitational wave data given by LIGO, Pulsars $\&$ Millisecond Pulsars data
and the NICER (Neutron star Interior Composition ExploreR) mass-radius data
given by NASA.


  Some recent approaches for scalable offline partial evaluation of logic
programs include a size-change analysis for ensuring both so called local and
global termination. In this work|inspired by experimental evaluation|we
introduce several improvements that may increase the accuracy of the analysis
and, thus, the quality of the associated specialized programs. We aim to
achieve this while maintaining the same complexity and scalability of the
recent works.


  This paper quantifies the international spillovers of US interest rates by
explicitly controlling for the "Fed Information Effect". I use multiple
identification strategies that identify two components of monetary policy
surprises around FOMC meetings: a pure US monetary policy shock component and a
"Fed Information Effect" component. On the one hand, a US tightening caused by
a pure US monetary policy component leads to an economic recession, an exchange
rate depreciation and tighter financial conditions. On the other hand, a
tightening of US monetary policy caused by the "Fed Information Effect" leads
to an economic expansion, an exchange rate appreciation and looser financial
conditions. Ignoring the "Fed Information Effect" biases the impact of US
interest rates and may explain recent atypical findings which suggest an
expansionary impact of US monetary policy shocks on the rest of the world.


  The temperature dependence of phonon-induced resistance oscillations has been
investigated in two-dimensional electron system with moderate mobility at large
filling factors at temperature range T = 7.4 - 25.4 K. The amplitude of
phonon-induced oscillations has been found to be governed by quantum relaxation
time which is determined by electron-electron interaction effects. This is in
agreement with results recently obtained in ultra-high mobility two-dimensional
electron system with low electron density [A. T. Hatke et al., Phys. Rev. Lett.
102, 086808 (2009)]. The shift of the main maximum of the magnetophonon
resistance oscillations to higher magnetic fields with increasing temperature
is observed.


  In this paper, we study harmonic Riemannian submersions from 3-dimensional
geometries using the ( generalized) integrability data associated to an
orthonormal frame natural to a Riemannian submersion. We give complete
classifications of harmonic Riemannian submersions from Thurston's
3-dimensional geometries, 3-dimensional BCV spaces and Berger sphere into a
surface. We also give some explicit constructions of these harmonic Riemannian
submersions.


  The proper functioning of some micro-fabricated novel quantum devices, such
as superconducting resonators and qubits, is severely affected by the presence
of parasitic structural material defects known as tunneling two-level-systems
(TLS). Recent experiments have reported unambiguous evidence of the strong
interaction between individual (coherent) TLS using strain-assisted
spectroscopy. This work provides an alternative and simple theoretical insight
that illustrates how to obtain the spectral response of such strongly
interacting defects residing inside the amorphous tunnel barrier of a qubit's
Josephson junction. Moreover, the corresponding spectral signatures obtained
here may serve to quickly and efficiently elucidate the actual state of these
interacting TLS in experiments based on strain- or electric-field spectroscopy.


  To study temperature dependent elastic constants, a new computational method
is proposed by combining continuum elasticity theory and first principles
calculations. A Gibbs free energy function with one variable with respect to
strain at given temperature and pressure was derived, hence the full
minimization of the Gibbs free energy with respect to temperature and lattice
parameters can be put into effective operation by using first principles.
Therefore, with this new theory, anisotropic thermal expansion and temperature
dependent elastic constants can be obtained for crystals with arbitrary
symmetry. In addition, we apply our method to hexagonal beryllium, hexagonal
diamond and cubic diamond to illustrate its general applicability.


  It is the efficient use of resources expected from an exam scheduling
application. There are various criteria for efficient use of resources and for
all tests to be carried out at minimum cost in the shortest possible time. It
is aimed that educational institutions with such criteria successfully carry
out central examination organizations. In the study, a two-stage genetic
algorithm was developed. In the first stage, the assignment of courses to
sessions was carried out. In the second stage, the students who participated in
the test session were assigned to examination rooms. Purposes of the study are
increasing the number of joint students participating in sessions, using the
minimum number of buildings in the same session, and reducing the number of
supervisors using the minimum number of classrooms possible. In this study, a
general purpose exam scheduling solution for educational institutions was
presented. The developed system can be used in different central examinations
to create originality. Given the results of the sample application, it is seen
that the proposed genetic algorithm gives successful results.1


  We use the non-Gaussian fixed points (NGFPs) appearing in the renormalization
group flow of gravity and gravity-matter systems to construct models of
NGFP-driven inflation via a renormalization group improvement scheme. The
cosmological predictions of these models depend sensitively on the
characteristic properties of the NGFPs, including their position and stability
coefficients, which in turn are determined by the field content of the
underlying matter sector. We demonstrate that the NGFPs appearing in
gravity-matter systems where the matter content is close to the one of the
standard model of particle physics are the ones compatible with cosmological
data. Somewhat counterintuitively, the negative fixed point value of the
dimensionless cosmological constant is essential for these findings.


  We show that young pulsars with normal magnetic fields, which are born as
fast rotating neutron stars (NSs) in Type II/Ib supernova explosions, can slow
down quickly by relativistic particles emission along their magnetic axis. When
they slow down sufficiently, they can undergo phase transitions and collapse to
strange stars, quark stars or black holes in explosions that remove a
substantial fraction of their initial angular momentum. The newly born strange
or quark stars continue to cool and spin down very quickly as soft gamma ray
repeaters (SGRs) and anomalous X-ray pulsars (AXPs) to become slowly rotating,
radio-quiet, dim X-ray pulsars or stellar black holes, depending on their
initial mass. It can explain the apparent dearth of young radio pulsars in SNRs
and in the Galaxy.


  The recent realization that atom interferometers (AIs) can be used to test
the gravitational redshift tests has proven to be controversial in some
quarters. Here, we address the issues raised against the interpretation of AIs
as redshift tests, reaffirming the fact that Mueller et al. [Nature 463, 926
(2010)] indeed report a gravitational redshift test.


  Efficient methods to provide sub-optimal solutions to non-convex optimization
problems with knowledge of the solution's sub-optimality would facilitate the
widespread application of nonlinear optimal control algorithms. To that end,
leveraging recent work in risk-aware verification, we provide two algorithms to
(1) probabilistically bound the optimality gaps of solutions reported by novel
percentile optimization techniques, and (2) probabilistically bound the maximum
optimality gap reported by percentile approaches for repetitive applications,
e.g. Model Predictive Control (MPC). Notably, our results work for a large
class of optimization problems. We showcase the efficacy and repeatability of
our results on a few, benchmark non-convex optimization problems and the
utility of our results for controls in a Nonlinear MPC setting.


  We introduce the quantum determinant for the elliptic quantum algebra
$\mathcal{A}_{q,p}(\mathfrak{\widehat{gl}}_N)$ and prove that it generates the
center of this algebra.


  In the framework of the upgrade of the Pierre Auger Observatory, a new high
voltage module is being employed for the power supply of the 1-inch
photomultiplier added to each water-Cherenkov detector of the surface array
with the aim of increasing the dynamic range of the measurements. This module
is located in a dedicated box near the electronics and comprises a low
consumption DC-DC converter hosted inside an aluminum box. All the modules have
undergone specific tests to verify their reliability in the extreme
environmental conditions of the Argentinian pampa. In this paper, we describe
the validation procedure and the facility developed to this aim. The successful
results of the tests on the HVPS modules are presented and discussed.


  We describe the discovery of a satellite in orbit about the dwarf planet
(136472) Makemake. This satellite, provisionally designated S/2015 (136472) 1,
was detected in imaging data collected with the Hubble Space Telescope's Wide
Field Camera 3 on UTC April 27, 2015 at 7.80$\pm$0.04 magnitudes fainter than
Makemake. It likely evaded detection in previous satellite searches due to a
nearly edge-on orbital configuration, placing it deep within the glare of
Makemake during a substantial fraction of its orbital period. This
configuration would place Makemake and its satellite near a mutual event
season. Insufficient orbital motion was detected to make a detailed
characterization of its orbital properties, prohibiting a measurement of the
system mass with the discovery data alone. Preliminary analysis indicates that
if the orbit is circular, its orbital period must be longer than 12.4 days, and
must have a semi-major axis $\gtrsim$21,000 km. We find that the properties of
Makemake's moon suggest that the majority of the dark material detected in the
system by thermal observations may not reside on the surface of Makemake, but
may instead be attributable to S/2015 (136472) 1 having a uniform dark surface.
This "dark moon hypothesis" can be directly tested with future JWST
observations. We discuss the implications of this discovery for the spin state,
figure, and thermal properties of Makemake and the apparent ubiquity of
trans-Neptunian dwarf planet satellites.


  The physical excitations entering the effective Lagrangian for quantum black
holes are related to a Goldstone boson which is present in the Rindler limit
and is due to the spontaneous breaking of the translation symmetry of the
underlying Minkowski space. This physical interpretation, which closely
parallels similar well-known results for the effective stringlike description
of flux tubes in QCD, gives a physical insight into the problem of describing
the quantum degrees of freedom of black holes. It also suggests that the
recently suggested concept of 'black hole complementarity' emerges at the
effective Lagrangian level rather than at the fundamental level.


  Collective cooperation drives the dynamics of many natural, social, and
economic phenomena, making understanding the evolution of cooperation with
evolutionary game theory a central question of modern science. Although human
interactions are best described as complex networks, current explorations are
limited to static networks where interactions represented by network links are
permanent and do not change over time. In reality, human activities often
involve temporal interactions, where links are impermanent, and understanding
the evolution of cooperation on such ubiquitous temporal networks is an open
question. Here, we present a general framework for systematically analyzing how
collective cooperation evolves on any temporal network, which unifies the study
of evolutionary game dynamics with dynamic and static interactions. We show
that the emergence of cooperation is facilitated by a simple rule of thumb:
hubs (individuals with many social ties) should be temporally deprioritized in
interactions. We further provide a quantitative metric capturing the priority
of hubs, which we utilize to orchestrate the ordering of interactions to best
promote cooperation on empirical temporal networks. Our findings unveil the
fundamental advantages conferred by temporal interactions for promoting
collective cooperation, which transcends the specific insights gleaned from
studying traditional static snapshots.


  Dirac's contributions to the discovery of non-relativistic quantum mechanics
and quantum electrodynamics, prior to his discovery of the relativistic wave
equation, are described.


  Let $\mathcal G$ be a family of subsets of an $n$-element set. The family
$\mathcal G$ is called $3$-wise $t$-intersecting if the intersection of any
three subsets in $\mathcal G$ is of size at least $t$. For a real number
$p\in(0,1)$ we define the measure of the family by the sum of
$p^{|G|}(1-p)^{n-|G|}$ over all $G\in\mathcal G$. We prove that if $t\geq 15$
and $p\leq 2/(\sqrt{4t+9}-1)$ then $p^t$ is the maximum measure of $3$-wise
$t$-intersecting families, and the bound for $p$ is sharp. We also present the
corresponding stability result for shifted families.


  By considering negative surgeries on a knot $K$ in $S^3$, we derive a lower
bound to the non-orientable slice genus $\gamma_4(K)$ in terms of the signature
$\sigma(K)$ and the concordance invariants $V_i(\overline{K})$, which
strengthens a previous bound given by Batson, and which coincides with
Ozsv\'ath-Stipsicz-Szab\'o's bound in terms of their $\upsilon$ invariant for
L-space knots and quasi-alternating knots. A curious feature of our bound is
superadditivity, implying, for instance, that the bound on the stable
non-orientable genus is sometimes better than the one on $\gamma_4(K)$.


  CMV matrices are the unitary analog of Jacobi matrices; we review their
general theory.


  In the standard cosmological model, the merger remnant of the Milky Way and
Andromeda (Milkomeda) will be the only galaxy remaining within our event
horizon once the Universe has aged by another factor of ten, ~10^{11} years
after the Big Bang. After that time, the only extragalactic sources of light in
the observable cosmic volume will be hypervelocity stars being ejected
continuously from Milkomeda. Spectroscopic detection of the velocity-distance
relation or the evolution in the Doppler shifts of these stars will allow a
precise measurement of the vacuum mass density as well as the local matter
distribution. Already in the near future, the next generation of large
telescopes will allow photometric detection of individual stars out to the edge
of the Local Group, and may target the ~10^{5+-1} hypervelocity stars that
originated in it as cosmological tracers.


  Weak diameter coloring of graphs recently attracted attention partially due
to its connection to asymptotic dimension of metric spaces. We consider weak
diameter list-coloring of graphs in this paper. Dvo\v{r}\'{a}k and Norin proved
that graphs with bounded Euler genus are 3-choosable with bounded weak
diameter. In this paper, we extend their result by showing that for every graph
$H$, $H$-minor free graphs are 3-choosable with bounded weak diameter. The
upper bound 3 is optimal and it strengthens an earlier result for
non-list-coloring $H$-minor free graphs with bounded weak diameter. As a
corollary, $H$-minor free graphs with bounded maximum degree are 3-choosable
with bounded clustering, strengthening an earlier result for non-list-coloring.
  When $H$ is planar, we prove a much stronger result: for every
2-list-assignment $L$ of an $H$-minor free graph, every precoloring with
bounded weak diameter can be extended to an $L$-coloring with bounded weak
diameter. As a corollary, for any planar graph $H$ and $H$-minor free graph
$G$, there are exponentially many list-colorings of $G$ with bounded weak
diameter (and with bounded clustering if $G$ also has bounded maximum degree);
and every graph with bounded layered tree-width and bounded maximum degree has
exponentially many 3-colorings with bounded clustering.
  We also show that the aforementioned results for list-coloring cannot be
extended to odd minor free graphs by showing that some bipartite graphs with
maximum degree $\Delta$ are $k$-choosable with bounded weak diameter only when
$k=\Omega(\log\Delta/\log\log\Delta)$. On the other hand, we show that odd
$H$-minor graphs are 3-colorable with bounded weak diameter, implying an
earlier result about clustered coloring of odd $H$-minor free graphs with
bounded maximum degree.


  We compute a Chern-Simons term induced by the fermions on noncommutative
torus interacting with two U(1) gauge fields. For rational noncommutativity
\theta \propto P/Q we find a new mixed term in the action which involves only
those fields which are (2\pi)/Q periodic, like the fields in a crystal with Q^2
nodes.


  FIFO is perhaps the simplest scheduling discipline. For single-class FIFO,
its delay guarantee performance has been extensively studied: The well-known
results include a stochastic delay bound for $GI/GI/1$ by Kingman and a
deterministic delay bound for $D/D/1$ by Cruz. However, for multiclass FIFO,
few such results are available. To fill the gap, we prove delay bounds for
multiclass FIFO in this work, considering both deterministic and stochastic
cases. Specifically, delay bounds are presented for multiclass D/D/1, GI/GI/1
and G/G/1. In addition, examples are provided for several basic settings to
demonstrate the obtained bounds in more explicit forms, which are also compared
with simulation results.


  Robot navigation with deep reinforcement learning (RL) achieves higher
performance and performs well under complex environment. Meanwhile, the
interpretation of the decision-making of deep RL models becomes a critical
problem for more safety and reliability of autonomous robots. In this paper, we
propose a visual explanation method based on an attention branch for deep RL
models. We connect attention branch with pre-trained deep RL model and the
attention branch is trained by using the selected action by the trained deep RL
model as a correct label in a supervised learning manner. Because the attention
branch is trained to output the same result as the deep RL model, the obtained
attention maps are corresponding to the agent action with higher
interpretability. Experimental results with robot navigation task show that the
proposed method can generate interpretable attention maps for a visual
explanation.


  $\textbf{This is the conference version of our paper: Spatiotemporal Implicit
Neural Representation as a Generalized Traffic Data Learner}$. Spatiotemporal
Traffic Data (STTD) measures the complex dynamical behaviors of the multiscale
transportation system. Existing methods aim to reconstruct STTD using
low-dimensional models. However, they are limited to data-specific dimensions
or source-dependent patterns, restricting them from unifying representations.
Here, we present a novel paradigm to address the STTD learning problem by
parameterizing STTD as an implicit neural representation. To discern the
underlying dynamics in low-dimensional regimes, coordinate-based neural
networks that can encode high-frequency structures are employed to directly map
coordinates to traffic variables. To unravel the entangled spatial-temporal
interactions, the variability is decomposed into separate processes. We further
enable modeling in irregular spaces such as sensor graphs using spectral
embedding. Through continuous representations, our approach enables the
modeling of a variety of STTD with a unified input, thereby serving as a
generalized learner of the underlying traffic dynamics. It is also shown that
it can learn implicit low-rank priors and smoothness regularization from the
data, making it versatile for learning different dominating data patterns. We
validate its effectiveness through extensive experiments in real-world
scenarios, showcasing applications from corridor to network scales. Empirical
results not only indicate that our model has significant superiority over
conventional low-rank models, but also highlight that the versatility of the
approach. We anticipate that this pioneering modeling perspective could lay the
foundation for universal representation of STTD in various real-world tasks.
$\textbf{The full version can be found at:}$
https://doi.org/10.48550/arXiv.2405.03185.