  This report will explore and answer fundamental questions about taking
Fourier Transforms and tying it with recent advances in AI and neural
architecture. One interpretation of the Fourier Transform is decomposing a
signal into its constituent components by projecting them onto complex
exponentials. Variants exist, such as discrete cosine transform that does not
operate on the complex domain and projects an input signal to only cosine
functions oscillating at different frequencies. However, this is a fundamental
limitation, and it needs to be more suboptimal. The first one is that all
kernels are sinusoidal: What if we could have some kernels adapted or learned
according to the problem? What if we can use neural architectures for this? We
show how one can learn these kernels from scratch for audio signal processing
applications. We find that the neural architecture not only learns sinusoidal
kernel shapes but discovers all kinds of incredible signal-processing
properties. E.g., windowing functions, onset detectors, high pass filters, low
pass filters, modulations, etc. Further, upon analysis of the filters, we find
that the neural architecture has a comb filter-like structure on top of the
learned kernels. Comb filters that allow harmonic frequencies to pass through
are one of the core building blocks/types of filters similar to high-pass,
low-pass, and band-pass filters of various traditional signal processing
algorithms. Further, we can also use the convolution operation with a signal to
be learned from scratch, and we will explore papers in the literature that uses
this with that robust Transformer architectures. Further, we would also explore
making the learned kernel's content adaptive, i.e., learning different kernels
for different inputs.


  We study the relations between some geometric properties of maximal monotone
operators and generic geometric and analytical properties of the functions on
the associate Fitzpatrick family of convex representations. We also investigate
under which conditions a convex function represents a maximal monotone operator
with bounded range and provide an example of a non type (D) operator on this
class.


  When binary systems of neutron stars merge, a very small fraction of their
rest mass is ejected, either dynamically or secularly. This material is
neutron-rich and its nucleosynthesis could provide the astrophysical site for
the production of heavy elements in the universe, together with a kilonova
signal confirming neutron-star mergers as the origin of short gamma-ray bursts.
We perform full general-relativistic simulations of binary neutron-star mergers
employing three different nuclear-physics EOSs, considering both equal- and
unequal-mass configurations, and adopting a leakage scheme to account for
neutrino radiative losses. Using a combination of techniques, we carry out an
extensive and systematic study of the hydrodynamical, thermodynamical, and
geometrical properties of the matter ejected dynamically, employing the WinNet
nuclear-reaction network to recover the relative abundances of heavy elements
produced by each configurations. Among the results obtained, three are
particularly important. First, we find that both the properties of the
dynamical ejecta and the nucleosynthesis yields are robust against variations
of the EOS and masses, and match very well the observed chemical abundances.
Second, using a conservative but robust criterion for unbound matter, we find
that the amount of ejected mass is $\lesssim 10^{-3}\,M_{\odot}$, hence at
least one order of magnitude smaller than what normally assumed in modelling
kilonova signals. Finally, using a simplified and gray-opacity model we assess
the observability of the infrared kilonova emission finding, that for all
binaries the luminosity peaks around $\sim1/2$ day in the $H$-band, reaching a
maximum magnitude of $-13$, and decreasing rapidly after one day. These rather
low luminosities make the prospects for detecting kilonovae less promising than
what assumed so far.


  Use of an optimization algorithm to improve performance of antennas and
electromagnetic structures usually ends up in planar unusual shapes. Using
rectangular conducting elements the proposed structures sometimes have
connections with only one single point in common between two neighboring areas.
The single point connections (point crossing) can affect the electromagnetic
performance of the structure. In this letter, we illustrate the influence of
point crossing on dipole and loop antennas using MoM, FDTD, and FEM solvers.
Current distribution, radiation pattern, and impedance properties for different
junctions are different. These solvers do not agree in the modeling of the
point crossing junctions which is a warning about uncertainty in using such
junctions. However, solvers agree that a negligible change in the junction
would significantly change the antenna performance. We propose that one should
consider both bridging and chamfering of the conflicting cells to find
optimized structures. This reduces the simulation time by 40% using FDTD
modeling, however no significant reduction is obtained using the MoM and FEM
methods.


  The promising application of femtosecond laser filamentation in atmospheric
remote sensing brings imperative demand for diagnosing the spatiotemporal
dynamics of filamentation. Acoustic emission (AE) during filamentation opens a
door to give the insight into the dynamic evolution of filaments in air. In
particular, the frequency features of the acoustic emission provide relevant
information on the conversion of laser energy to acoustic energy. Here, the
acoustic emission of femtosecond laser filament manipulated by energy and the
focal lengths was measured quantitatively by a broadband microphone, and the
acoustic parameters were compared and analyzed. Our results showed that the
acoustic power presents a squared dependence on the laser energy and the
bandwidth of the acoustic spectrum showed a significant positive correlation
with laser energy deposition. It was found that the spectrum of the acoustic
pulse emitted from the middle of the filament has a larger bandwidth compared
to those emitted from the ends of the filament and the spectrum of the acoustic
pulse is also an indicator of the filament intensity distribution. These
findings are helpful for studying the plasma filament properties and complex
dynamic processes through acoustic parameters and allow the optimization of
remote applications.


  We consider the problem of energy-efficient broadcasting on dense ad-hoc
networks. Ad-hoc networks are generally modeled using random geometric graphs
(RGGs). Here, nodes are deployed uniformly in a square area around the origin,
and any two nodes which are within Euclidean distance of $1$ are assumed to be
able to receive each other's broadcast. A source node at the origin encodes $k$
data packets of information into $n\ (>k)$ coded packets and transmits them to
all its one-hop neighbors. The encoding is such that, any node that receives at
least $k$ out of the $n$ coded packets can retrieve the original $k$ data
packets. Every other node in the network follows a probabilistic forwarding
protocol; upon reception of a previously unreceived packet, the node forwards
it with probability $p$ and does nothing with probability $1-p$. We are
interested in the minimum forwarding probability which ensures that a large
fraction of nodes can decode the information from the source. We deem this a
\emph{near-broadcast}. The performance metric of interest is the expected total
number of transmissions at this minimum forwarding probability, where the
expectation is over both the forwarding protocol as well as the realization of
the RGG. In comparison to probabilistic forwarding with no coding, our
treatment of the problem indicates that, with a judicious choice of $n$, it is
possible to reduce the expected total number of transmissions while ensuring a
near-broadcast.


  We study the asymptotic behavior of global solutions to hydrodynamical
systems modeling the nematic liquid crystal flows under kinematic transports
for molecules of different shapes. The coupling system consists of
Navier-Stokes equations and kinematic transport equations for the molecular
orientations. We prove the convergence of global strong solutions to single
steady states as time tends to infinity as well as estimates on the convergence
rate both in 2D for arbitrary regular initial data and in 3D for certain
particular cases.


  In this paper, we study the K0-group of the C?-algebra associated to a
pinwheel tiling. We prove that it is given by the sum of Z + Z^6 with a
cohomological group. The C?-algebra is endowed with a trace that induces a
linear map on its K0-group. We then compute explicitly the image, under this
map, of the summand Z+Z^6, showing that the image of Z is zero and the image of
Z^6 is included in the module of patch frequencies of the pinwheel tiling. We
finally prove that we can apply the measured index theorem due to A. Connes to
relate the image of the last summand of the K0-group to a cohomological formula
which is more computable. This is the first step in the proof of the
gap-labeling conjecture for the pinwheel tiling.


  Ethereum holds multiple billions of U.S. dollars in the form of Ether
cryptocurrency and ERC-20 tokens, with millions of deployed smart contracts
algorithmically operating these funds. Unsurprisingly, the security of Ethereum
smart contracts has been under rigorous scrutiny. In recent years, numerous
defense tools have been developed to detect different types of smart contract
code vulnerabilities. When opportunities for exploiting code vulnerabilities
diminish, the attackers start resorting to social engineering attacks, which
aim to influence humans -- often the weakest link in the system. The only known
class of social engineering attacks in Ethereum are honeypots, which plant
hidden traps for attackers attempting to exploit existing vulnerabilities,
thereby targeting only a small population of potential victims.
  In this work, we explore the possibility and existence of new social
engineering attacks beyond smart contract honeypots. We present two novel
classes of Ethereum social engineering attacks - Address Manipulation and
Homograph - and develop six zero-day social engineering attacks. To show how
the attacks can be used in popular programming patterns, we conduct a case
study of five popular smart contracts with combined market capitalization
exceeding $29 billion, and integrate our attack patterns in their source codes
without altering their existing functionality. Moreover, we show that these
attacks remain dormant during the test phase but activate their malicious logic
only at the final production deployment. We further analyze 85,656 open-source
smart contracts, and discover that 1,027 of them can be used for the proposed
social engineering attacks. We conduct a professional opinion survey with
experts from seven smart contract auditing firms, corroborating that the
exposed social engineering attacks bring a major threat to the smart contract
systems.


  A skew Laurent polynomial ring R[x^{\pm 1};\alpha] is reversible if it has a
reversing automorphism, that is, an automorphism of period two that transposes
x and x^{-1} and restricts to an automorphism of R. We study invariants for
reversing automorphisms and apply our methods to determine the rings of
invariants of reversing automorphisms of two simple skew Laurent polynomial
rings, namely a localization of the enveloping algebra of the two-dimensional
non-abelian solvable Lie algebra and the coordinate ring of the quantum torus.
These two skew Laurent polynomial rings are deformations of Poisson algebras
and we interpret their reversing automorphisms and their invariants as
deformations of Poisson automorphisms and their invariants.


  We present results from spectroscopic observations with the Michigan/Magellan
Fiber System (M2FS) of 182 stellar targets along the line of sight to the
newly-discovered `ultrafaint' object Reticulum 2 (Ret 2). For 38 of these
targets, the spectra are sufficient to provide simultaneous estimates of
line-of-sight velocity ($v_{\rm los}$, median random error $\delta_{v_{\rm
los}}=1.3$ km s$^{-1}$), effective temperature ($T_{\rm eff}$, $\delta_{T_{\rm
eff}}=464$ K), surface gravity ($\log g$, $\delta_{\rm logg}=0.54$ dex) and
iron abundance ([Fe/H], $\delta_{\mathrm{[Fe/H]}}=0.45$ dex). We use these
results to confirm 18 stars as members of Ret 2. From the member sample we
estimate a velocity dispersion of $\sigma_{v_{\rm los}}=3.6_{-0.6}^{+0.9}$ km
s$^{-1}$ about a mean of $\langle v_{\rm los}\rangle =64.8_{-1.0}^{+1.1}$ km
s$^{-1}$ in the solar rest frame ($\sim -90.9$ km s$^{-1}$ in the Galactic rest
frame), and a metallicity dispersion of $\sigma_{\rm
[Fe/H]}=0.50_{-0.13}^{+0.17}$ dex about a mean of $\langle \mathrm{[Fe/H]}
\rangle =-2.67_{-0.34}^{+0.34}$. These estimates marginalize over possible
velocity and metallicity gradients, which are consistent with zero. Our results
place Ret 2 on chemodynamical scaling relations followed by the Milky Way's
dwarf-galactic satellites. Under assumptions of dynamic equilibrium and
negligible contamination from binary stars---both of which must be checked with
deeper imaging and repeat spectroscopic observations---the estimated velocity
dispersion suggests a dynamical mass of $M(R_{\rm h})\approx 5R_{\rm
h}\sigma_{v_{\rm los}}^2/(2G)=2.4_{-0.8}^{+1.3}\times 10^5$ $M_{\odot}$
enclosed within projected halflight radius $R_{\rm h}\sim 32$ pc, with
mass-to-light ratio $\approx 2M(R_{\rm h})/L_{\rm V}=462_{-157}^{+264}$ in
solar units.


  Using a filter in the GROWTH Marshal based on color and the amplitude and the
timescale of variability, we have identified 372 objects as known or candidate
cataclysmic variables (CVs) during the second year of operation of the Zwicky
Transient Facility (ZTF). From the available difference imaging data, we found
that 93 are previously confirmed CVs, and 279 are strong candidates. Spectra of
four of the candidates confirm them as CVs by the presence of Balmer emission
lines, while one of the four has prominent HeII lines indicative of containing
a magnetic white dwarf. Gaia EDR3 parallaxes are available for 154 of these
systems, resulting in distances from 108-2096 pc and absolute magnitudes in the
range of 7.5-15.0, with the largest number of candidates between 10.5-12.5. The
total numbers are 21% higher than from the previous year of the survey with a
greater number of distances available but a smaller percentage of systems close
to the Galactic plane. Comparison of these findings with a machine learning
method of searching all the light curves reveals large differences in each
dataset related to the parameters involved in the search process.


  We present a search for a pentaquark decaying strongly to $pK_S^0$ in $\gamma
N$ collisions at a center-of-mass energy up to 25 GeV/$c^2$. Finding no
evidence for such a state in the mass range of 1470 MeV/$c^2$ to 2200
MeV/$c^2$, we set limits on the yield and on the cross section times branching
ratio relative to $\Sigma^*(1385)^\pm$ and $K^*(892)^+$.


  An inquiry on a possible local origin for the Microwave Background Radiation
is made. Thermal MBR photons are contained in a system called {\it magnetic
bottle} which is due to Earth magnetic field and solar wind particles, mostly
electrons. Observational tests are anticipated.


  Optical Character Recognition (OCR) systems have been widely used in various
applications for extracting semantic information from images. To give the user
more control over their privacy, an on-device solution is needed. The current
state-of-the-art models are too heavy and complex to be deployed on-device. We
develop an efficient lightweight scene text recognition (STR) system, which has
only 0.88M parameters and performs real-time text recognition. Attention
modules tend to boost the accuracy of STR networks but are generally slow and
not optimized for device inference. So, we propose the use of convolution
attention modules to the text recognition networks, which aims to provide
channel and spatial attention information to the LSTM module by adding very
minimal computational cost. It boosts our word accuracy on ICDAR 13 dataset by
almost 2\%. We also introduce a novel orientation classifier module, to support
the simultaneous recognition of both horizontal and vertical text. The proposed
model surpasses on-device metrics of inference time and memory footprint and
achieves comparable accuracy when compared to the leading commercial and other
open-source OCR engines. We deploy the system on-device with an inference speed
of 2.44 ms per word on the Exynos 990 chipset device and achieve an accuracy of
88.4\% on ICDAR-13 dataset.


  We provide accurate upper bounds on the Boolean circuit complexity of the
standard and the Karatsuba methods of integer multiplication


  The photon statistics and bunching of a semiconductor laser with external
optical feedback are investigated experimentally and theoretically. In a
chaotic regime, the photon number distribution is measured and undergoes a
transition from Bose-Einstein distribution to Poisson distribution with
increasing the mean photon number. The second order degree of coherence
decreases gradually from 2 to 1. Based on Hanbury Brown-Twiss scheme,
pronounced photon bunching is observed experimentally for various injection
currents and feedback strengths, which indicates the randomness of the
associated emission light. Near-threshold injection currents and strong
feedback strengths modify exactly the laser performance to be more bunched. The
macroscopic chaotic dynamics is confirmed simultaneously by high-speed analog
detection. The theoretical results qualitatively agree with the experimental
results. It is potentially useful to extract randomness and achieve desired
entropy source for random number generator and imaging science by quantifying
the control parameters.


  Recent advancements in artificial intelligence (AI) and its sub-branch
machine learning (ML) promise machines that go beyond the boundaries of
automation and behave autonomously. Applications of these machines in creative
practices such as art and design entail relationships between users and
machines that have been described as a form of collaboration or co-creation
between computational and human agents. This paper uses examples from art and
design to argue that this frame is incomplete as it fails to acknowledge the
socio-technical nature of AI systems, and the different human agencies involved
in their design, implementation, and operation. Situating applications of
AI-enabled tools in creative practices in a spectrum between automation and
autonomy, this paper distinguishes different kinds of human engagement elicited
by systems deemed automated or autonomous. Reviewing models of artistic
collaboration during the late 20th century, it suggests that collaboration is
at the core of these artistic practices. We build upon the growing literature
of machine learning and art to look for the human agencies inscribed in works
of computational creativity, and expand the co-creation frame to incorporate
emerging forms of human-human collaboration mediated through technical
artifacts such as algorithms and data.


  The Lescure-Meyniel conjecture is the analogue of Hadwiger's conjecture for
the immersion order. It states that every graph $G$ contains the complete graph
$K_{\chi(G)}$ as an immersion, and like its minor-order counterpart it is open
even for graphs with independence number 2. We show that every graph $G$ with
independence number $\alpha(G)\ge 2$ and no hole of length between $4$ and
$2\alpha(G)$ satisfies this conjecture. In particular, every $C_4$-free graph
$G$ with $\alpha(G)= 2$ satisfies the Lescure-Meyniel conjecture. We give
another generalisation of this corollary, as follows. Let $G$ and $H$ be graphs
with independence number at most 2, such that $|V(H)|\le 4$. If $G$ is
$H$-free, then $G$ satisfies the Lescure-Meyniel conjecture.


  We studied the macro evolution of the micro atmospheric glow discharge
generated between a micro argon jet into ambient air and static water. The
micro discharge behaves similarly to a complex ecosystem. Non-linear behaviors
are found for the micro discharge when the water acts as a cathode, different
from the discharge when water behaves as an anode. Groups of snapshots of the
micro discharge formed at different discharge currents are captured by an
intensified charge-coupled device with controlled exposure time, and each group
consisted of 256 images taken in succession. Edge detection methods are used to
identify the water surface and then the total brightness is defined by adding
up the signal counts over the area of the micro discharge. Motions of the water
surface at different discharge currents show that the water surface lowers
increasingly rapidly when the water acts as a cathode. In contrast, the water
surface lowers at a constant speed when the water behaves as an anode. The
light curves are similar to logistic growth curves, suggesting that a
self-inhibition process occurs in the micro discharge. Meanwhile, the total
brightness increases linearly during the same time when the water acts as an
anode. Discharge-water interactions cause the micro discharge to evolve. The
charged particle bomb process is probably responsible for the different
behavior of the micro discharges when the water acts as cathode and anode.


  In this paper, we prove two improved versions of the Finiteness Principle for
nonnegative $ C^2(\mathbb{R}^2) $ interpolation, previously proven by
Fefferman, Israel, and Luli. The first version sharpens the finiteness constant
to $ 64 $, and the second version carries better computational practicality.
Along the way, we also provide detailed construction of nonnegative $ C^2 $
interpolants in one-dimension, and prove the nonexistence of a bounded linear $
C^2 $-extension operator that preserves nonnegativity.


  Cold three flavor quark matter at large (but not asymptotically large)
densities may exist in a crystalline color superconducting phase. These phases
are characterized by a gap parameter $\Delta$ that varies periodically in
space, forming a crystal structure. A Ginzburg-Landau expansion in $\Delta$
shows that two crystal structures based on cubic symmetry are particularly
favorable, and may be the ground state of matter at densities present in
neutron star cores. We derive the effective action for the phonon fields that
describe space- and time-dependent fluctuations of the crystal structure formed
by $\Delta$, and obtain the shear modulus from the coefficients of the spatial
derivative terms. Within a Ginzburg-Landau approximation, we find shear moduli
which are 20 to 1000 times larger than those of neutron star crusts. This phase
of matter is thus more rigid than any known material in the universe, but at
the same time the crystalline color superconducting phase is also superfluid.
These properties raise the possibility that the presence of this phase within
neutron stars may have distinct implications for their phenomenology. For
example, (some) pulsar glitches may originate in crystalline superconducting
neutron star cores.


  We study the amplification of magnetic fields during the formation of
primordial halos. The turbulence generated by gravitational infall motions
during the formation of the first stars and galaxies can amplify magnetic
fields very efficiently and on short timescales up to dynamically significant
values. Using the Kazantsev theory, which describes the so-called small-scale
dynamo - a magnetohydrodynamical process converting kinetic energy from
turbulence into magnetic energy - we can then calculate the growth rate of the
small-scale magnetic field. Our calculations are based on a detailed chemical
network and we include non-ideal magnetohydrodynamical effects such as
ambipolar diffusion and Ohmic dissipation. We follow the evolution of the
magnetic field up to larger scales until saturation occurs on the Jeans scale.
Assuming a weak magnetic seed field generated by the Biermann battery process,
both Burgers and Kolmogorov turbulence lead to saturation within a rather small
density range. Such fields are likely to become relevant after the formation of
a protostellar disk and, thus, could influence the formation of the first stars
and galaxies in the Universe.


  Warped accretion discs of low viscosity are prone to hydrodynamic instability
due to parametric resonance of inertial waves as confirmed by local
simulations. Global simulations of warped discs, using either smoothed particle
hydrodynamics (SPH) or grid-based codes, are ubiquitous but no such instability
has been seen. Here we utilize a hybrid Godunov-type Lagrangian method to study
parametric instability in global simulations of warped Keplerian discs at
unprecedentedly high resolution (up to 120 million particles). In the global
simulations, the propagation of the warp is well described by the linear
bending-wave equations before the instability sets in. The ensuing turbulence,
captured for the first time in a global simulation, damps relative orbital
inclinations and leads to a decrease in the angular momentum deficit. As a
result, the warp undergoes significant damping within one bending-wave crossing
time. Observed protoplanetary disc warps are likely maintained by companions or
aftermath of disc breaking.


  Motivation:Microarray experiments result in large scale data sets that
require extensive mining and refining to extract useful information. We
demonstrate the usefulness of (nonmetric) multidimensional scaling (MDS) method
in analyzing a large number of genes. Applying MDS to the microarray data is
certainly not new, but the existing works are all on small numbers
  (< 100) of points to be analyzed. We have been developing an efficient novel
algorithm for nonmetric multidimensional scaling (nMDS) analysis for very large
data sets as a maximally unsupervised data mining device. We wish to
demonstrate its usefulness in the context of bioinformatics (unraveling
relational patterns among genes from time series data in this paper).
  Results: The Pearson correlation coefficient with its sign flipped is used to
measure the dissimilarity of the gene activities in transcriptional response of
cell-cycle-synchronized human fibroblasts to serum [Iyer {\it et al}., Science
{\bf 283}, 83 (1999)]. These dissimilarity data have been analyzed with our
nMDS algorithm to produce an almost circular relational pattern of the genes.
The obtained pattern expresses a temporal order in the data in this example;
the temporal expression pattern of the genes rotates along this circular
arrangement and is related to the cell cycle. For the data we analyze in this
paper we observe the following. If an appropriate preparation procedure is
applied to the original data set, linear methods such as the principal
component analysis (PCA) could achieve reasonable results, but without data
preprocessing linear methods such as PCA cannot achieve a useful picture.
Furthermore, even with an appropriate data preprocessing, the outcomes of
linear procedures are not as clearcut as those by nMDS without preprocessing.


  The TOTEM Experiment is designed to measure the total proton-proton
cross-section with the luminosity-independent method and to study elastic and
diffractive pp scattering at the LHC. To achieve optimum forward coverage for
charged particles emitted by the pp collisions in the interaction point IP5,
two tracking telescopes, T1 and T2, are installed on each side of the IP in the
pseudorapidity region 3.1 < = |eta | < = 6.5, and special movable beam-pipe
insertions - called Roman Pots (RP) - are placed at distances of +- 147 m and
+- 220 m from IP5. This article describes in detail the working of the TOTEM
detector to produce physics results in the first three years of operation and
data taking at the LHC.


  The phylogenetic network emerged in the 1990s as a new model to represent the
evolution of species in the case where coexisting species transfer genetic
information through hybridization, recombination, lateral gene transfer, etc.
As is true for many rapidly evolving fields, there is considerable
fragmentation and diversity in methodologies, standards and vocabulary in
phylogenetic network research, thus creating the need for an integrated
database of articles, authors, techniques, keywords and software. We describe
such a database, "Who is Who in Phylogenetic Networks", available at
http://phylnet.univ-mlv.fr. "Who is Who in Phylogenetic Networks" comprises
more than 600 publications and 500 authors interlinked with a rich set of more
than 200 keywords related to phylogenetic networks. The database is integrated
with web-based tools to visualize authorship and collaboration networks and
analyze these networks using common graph and social network metrics such as
centrality (betweenness, eigenvector, degree and closeness) and clustering. We
provide downloads of raw information about entries in the database, and a
facility to suggest modifications and contribute new information to the
database. We also present in this article common use cases of the database and
identify trends in the research on phylogenetic networks using the information
in the database and textual analysis.


  Recent methods such as Score Distillation Sampling (SDS) and Variational
Score Distillation (VSD) using 2D diffusion models for text-to-3D generation
have demonstrated impressive generation quality. However, the long generation
time of such algorithms significantly degrades the user experience. To tackle
this problem, we propose DreamPropeller, a drop-in acceleration algorithm that
can be wrapped around any existing text-to-3D generation pipeline based on
score distillation. Our framework generalizes Picard iterations, a classical
algorithm for parallel sampling an ODE path, and can account for non-ODE paths
such as momentum-based gradient updates and changes in dimensions during the
optimization process as in many cases of 3D generation. We show that our
algorithm trades parallel compute for wallclock time and empirically achieves
up to 4.7x speedup with a negligible drop in generation quality for all tested
frameworks.


  Cantor primes are primes p such that 1/p belongs to the middle-third Cantor
set. One way to look at them is as containing the base-3 analogues of the
famous Mersenne primes, which encompass all base-2 repunit primes, i.e., primes
consisting of a contiguous sequence of 1's in base 2 and satisfying an equation
of the form p + 1 = 2^q. The Cantor primes encompass all base-3 repunit primes
satisfying an equation of the form 2p + 1 = 3^q, and I show that in general all
Cantor primes > 3 satisfy a closely related equation of the form 2pK + 1 = 3^q,
with the base-3 repunits being the special case K = 1. I use this to prove that
the Cantor primes > 3 are exactly the prime-valued cyclotomic polynomials of
the form $\Phi_s(3^{s^j}) \equiv 1$ (mod 4). Significant open problems concern
the infinitude of these, making Cantor primes perhaps more interesting than
previously realised.


  We investigate four key issues with using a nonzero weak value of the spatial
projection operator to infer the past path of an individual quantum particle.
First, we note that weak measurements disturb a system, so any approach relying
on such a perturbation to determine the location of a quantum particle
describes the state of a disturbed system, not that of a hypothetical
undisturbed system. Secondly, even assuming no disturbance, there is no reason
to associate the non-zero weak value of an operator containing the spatial
projection operator with the classical idea of `particle presence'. Thirdly,
weak values are only measurable over ensembles, and so to infer properties of
individual particles from values of them is problematic. Finally, weak value
approaches to the path of a particle do not provide information beyond standard
quantum mechanics (and the classical modes supporting the experiment). We know
of no experiment with testable consequences that demonstrates a connection
between particle presence and weak values.


  Sarcasm occurring due to the presence of numerical portions in text has been
quoted as an error made by automatic sarcasm detection approaches in the past.
We present a first study in detecting sarcasm in numbers, as in the case of the
sentence 'Love waking up at 4 am'. We analyze the challenges of the problem,
and present Rule-based, Machine Learning and Deep Learning approaches to detect
sarcasm in numerical portions of text. Our Deep Learning approach outperforms
four past works for sarcasm detection and Rule-based and Machine learning
approaches on a dataset of tweets, obtaining an F1-score of 0.93. This shows
that special attention to text containing numbers may be useful to improve
state-of-the-art in sarcasm detection.


  The problem of $L^p(R^3)\to L^2(S)$ Fourier restriction estimates for smooth
hypersurfaces S of finite type in R^3 is by now very well understood for a
large class of hypersurfaces, including all analytic ones. In this article, we
take up the study of more general $L^p(R^3)\to L^q(S)$ Fourier restriction
estimates, by studying a prototypical class of two-dimensional surfaces with
strongly varying curvature conditions. Our approach is based on an adaptation
of the so-called bilinear method. We discuss several new features arising in
the study of this problem.


  In certain extensions of General Relativity, wormholes generated by
spherically symmetric electric fields can resolve black hole singularities
without necessarily removing curvature divergences. This is shown by studying
geodesic completeness, the behavior of time-like congruences going through the
divergent region, and by means of scattering of waves off the wormhole. This
provides an example of the logical independence between curvature divergences
and space-time singularities, concepts very often identified with each other in
the literature.ns of curvature divergences in the context of space-time
singularities.


  We establish an unconditional effective Chebotarev density theorem that
improves uniformly over the well-known result of Lagarias and Odlyzko. As a
consequence, we give a new asymptotic form of the Chebotarev density theorem
that can count much smaller primes with arbitrary log-power savings, even in
the case where a Landau-Siegel zero is present. Our main theorem interpolates
the strongest unconditional upper bound for the least prime ideal with a given
Artin symbol as well as the Chebotarev analogue of the Brun-Titchmarsh theorem
proved by the authors.
  We also present a new application of our main result that exhibits
considerable gains over earlier versions of the Chebotarev density theorem. If
$f$ is a positive definite primitive binary quadratic form then we count
lattice points $(u,v) \in \mathbb{Z}^2$ such that $f(u,v)$ is prime and $u, v$
have no prime factors $\leq z$ with uniformity in $z$ and the discriminant of
$f$.


  Information of time differentiation is extremely important cue for a motion
representation. We have applied first-order differential velocity from a
positional information, moreover we believe that second-order differential
acceleration is also a significant feature in a motion representation. However,
an acceleration image based on a typical optical flow includes motion noises.
We have not employed the acceleration image because the noises are too strong
to catch an effective motion feature in an image sequence. On one hand, the
recent convolutional neural networks (CNN) are robust against input noises. In
this paper, we employ acceleration-stream in addition to the spatial- and
temporal-stream based on the two-stream CNN. We clearly show the effectiveness
of adding the acceleration stream to the two-stream CNN.


  In this work, we study by means of simulations of hard spheres the
equilibrium between a spherical solid cluster and the fluid. In the NVT
ensemble we observe stable/metastable clusters of the solid phase in
equilibrium with the fluid, representing configurations that are global/local
minima of the Helmholtz free energy. Then, we run NpT simulations of the
equilibrated system at the average pressure of the NVT run and observe that the
clusters are critical because they grow/shrink with a probability of 1/2.
Therefore, a crystal cluster equilibrated in the NVT ensemble corresponds to a
Gibbs free energy maximum where the nucleus is in unstable equilibrium with the
surrounding fluid, in accordance with what has been recently shown for vapor
bubbles in equilibrium with the liquid. Then, within the Seeding framework, we
use Classical Nucleation Theory to obtain both the interfacial free energy
{\gamma} and the nucleation rate. The latter is in very good agreement with
independent estimates using techniques that do not rely on Classical Nucleation
Theory when the mislabeling criterion is used to identify the molecules of the
solid cluster. We therefore argue that the radius obtained from the mislabeling
criterion provides a good approximation for the radius of tension, Rs. We
obtain an estimate of the Tolman length by extrapolating the difference between
Re (the Gibbs dividing surface) and Rs to infinite radius. We show that such
definition of the Tolman length coincides with that obtained by fitting
{\gamma} versus 1/Rs to a straight line as recently applied to hard spheres
[Montero de Hijes et al., J. Chem. Phys. 151, 155401, 2019]


  We compute the total cross-section for $Z$ boson production in bottom-quark
fusion, applying to this case the method we previously used for Higgs
production in bottom fusion. Namely, we match, through the FONLL procedure, the
next-to-next-to-leading-log five-flavor scheme result, in which the $b$~quark
is treated as a massless parton, with the next-to-leading-order
$\order{\alpha_s^3}$ four-flavor scheme computation in which bottom is treated
as a massive final-state particle. Our computation provides a test-case for the
discussion of issues of scale dependence and treatment of heavy quarks, which
we discuss in light of our results.


  Diffusion plays an important role in a wide variety of phenomena, from
bacterial quorum sensing to the dynamics of traffic flow. While it generally
tends to level out gradients and inhomogeneities, diffusion has nonetheless
been shown to promote pattern formation in certain classes of systems.
Formation of stable structures often serves as a key factor in promoting the
emergence and persistence of cooperative behavior in otherwise competitive
environments, however an in-depth analysis on the impact of diffusion on such
systems is lacking. We therefore investigate the effects of diffusion on
cooperative behavior using a cellular automaton (CA) model of the noisy spatial
iterated prisoner's dilemma (IPD), physical extension and stochasticity being
unavoidable characteristics of several natural phenomena. We further derive a
mean-field (MF) model that captures the 3-species predation dynamics from the
CA model and highlight how pattern formation arises in this new model, then
characterize how including diffusion by interchange similarly enables the
emergence of large scale structures in the CA model as well. We investigate how
these emerging patterns favors cooperative behavior for parameter space regions
where IPD error rates classically forbid such dynamics. We thus demonstrate how
the coupling of diffusion with non-linear dynamics can, counter-intuitively,
promote large scale structure formation and in return establish new grounds for
cooperation to take hold in stochastic spatial systems.


  We consider vacuum metrics admitting conformal compactification which is
smooth up to the scri $\mathscr{I^+}$. We write metric in the Bondi-Sachs form
and expand it into power series in the inverse affine distance $1/r$. Like in
the case of the luminosity distance, given the news tensor and initial data for
a part of metric the Einstein equations define coefficients of the series in a
recursive way. This is also true in the stationary case however now the news
tensor vanishes and the role of initial data is taken by multipole moments
which are equivalent to moments of Thorne. We find an approximate form of
metric and show that in the case of vanishing mass the mass dipole may be
different from zero. Then the known result about the Kerr like behaviour of a
stationary metric is violated. Finally we find an approximate (up to the
quadrupole moment) Bondi-Sachs form of the Kerr metric.


  Noninterference offers a rigorous end-to-end guarantee for secure propagation
of information. However, real-world systems almost always involve security
requirements that change during program execution, making noninterference
inapplicable. Prior works alleviate the limitation to some extent, but even for
a veteran in information flow security, understanding the subtleties in the
syntax and semantics of each policy is challenging, largely due to very
different policy specification languages, and more fundamentally, semantic
requirements of each policy.
  We take a top-down approach and present a novel information flow policy,
called Dynamic Release, which allows information flow restrictions to downgrade
and upgrade in arbitrary ways. Dynamic Release is formalized on a novel
framework that, for the first time, allows us to compare and contrast various
dynamic policies in the literature. We show that Dynamic Release generalizes
declassification, erasure, delegation and revocation. Moreover, it is the only
dynamic policy that is both applicable and correct on a benchmark of tests with
dynamic policy.


  Limit cycle oscillations are phenomena arising in nonlinear dynamical systems
and characterized by periodic, locally-stable, and self-sustained state
trajectories. Systems controlled in a closed loop along a periodic trajectory
can also be modelled as systems experiencing limit cycle behavior. The goal of
this work is to identify from data, the local dynamics around the limit cycle
using linear periodically parameter-varying models. Using a coordinate
transformation onto transversal surfaces, the dynamics are decomposed into two
parts: one along the limit cycle, and one on the transversal surfaces. Then,
the model is identified from trajectory data using kernel-based methods with a
periodic kernel design. The kernel-based model is extended to also account for
variations in system parameters associated with different operating conditions.
The performance of the proposed identification method is demonstrated on a
benchmark nonlinear system and on a simplified airborne wind energy model. The
method provides accurate model parameter estimation, compared to the analytical
linearization, and good prediction capability.


  In the drug repurposing approach, the chemically diverse and potentially safe
molecules can be explored as therapeutic potential out of those originally
targeted indications. However, the intellectual property rights, and
competitive over-heating issue from sharing the same drug pipeline information
are drawback of the approach. In current paradigm of drug discovery, despite
approval of new chemical entity, the finding of a new ring system for drug
discovery have stagnated. In addition, there are still rarely used ring systems
from FDA approved drug that can be optimized and used for repurposing purpose.
In the present work, these rarely used drug ring system were re-purposed with
our bidirectional target and ring screening (TR- dual screening) approach
within our defined objectives. The TR-dual screening suggested RARbeta and
cyproheptadine as a pair of target and ring system. The selected ring system
was virtually grown with predefined criterion, ranking of molecular docking and
top score poses made us select test compounds for synthesis and biological
proof. Among the tested compounds, 6c proved RARbeta agonist activity. The
concept of TR dual optimization can contribute to picking either a compound
having acceptable ADMET profile or a target for a selected drug scaffold.


  Taking into account the long-ranged spin interactions due to weak
localization effects in disordered itinerant ferromagnets the scattering of
both electrons and neutrons on critical spin fluctuations near quantum phase
transition is considered. It is shown that for the case of low electron
density, when k_F \xi \ll 1, where k_F is the Fermi momentum and \xi is the
magnetic correlation length, the transport cross section of electrons is
proportional to conventional critical fluctuations in absence of weak
localization effects. However, the intensity of the multiple small-angle
neutron scattering becomes exponentially small as compared with the intensity
of the multiple scattering by conventional critical fluctuations.


  We discuss the Hellmann-Feynman theorem for degenerate states and its
application to the calculation of the derivatives of statistical averages with
respect to external parameters.


  Our recently proposed model of the $\Delta(1600)$ resonance, in which the
dominant component is a quasi-bound state of the $\Delta(1232)$ and the pion,
is confronted with a similar model of the $N^*(1440)$ resonance as its
counterpart in the P11 partial wave. We stress an essentially different
mechanism responsible for generating the two resonances.


  Co lombeau's construction of generalized functions (in its special variant)
is extended to a theory of generalized sections of vector bundles. As
particular cases, generalized tensor analysis and exterior algebra are studied.
A point value characterization for generalized functions on manifolds is
derived, several algebraic characterizations of spaces of generalized sections
are established and consistency properties with respect to linear
distributional geometry are derived. An application to nonsmooth mechanics
indicates the additional flexibility offered by this approach compared to the
purely distributional picture.


  A natural family of potentially 2-torsion elements in the integer homology
cobordism group consists of splices of knots with their mirrors. We show that
such 3-manifolds have locally trivial involutive Floer homology. We show some
related families of splices also have locally trivial involutive Floer
homology. Our arguments show that many gauge theoretic invariants also vanish
on these 3-manifolds.


  Impurities that are present on the surface of a metal often have internal
degrees of freedom. Inelastic scattering due to impurities can be revealed by
observing local features seen in the tunneling current with scanning tunneling
microscope (STM). We consider localized vibrational modes coupled to the
electronic structure of a surface. We argue that vibrational modes of
impurities produce Fermi momentum $k_F$ oscillations in second derivative of
current with respect to voltage $\partial^2I(\br, V)/\partial V^2$. These
oscillations are similar to the well known Friedel oscillations of screening
charge on the surface. We propose to measure inelastic scattering generated by
the presence of the vibrational modes with STM by imaging the
$\partial^2I/\partial V^2$ oscillations on the metal surface.


  Betelgeuse, the bright red supergiant (RSG) in Orion, is a runaway star. Its
supersonic motion through the interstellar medium has resulted in the formation
of a bow shock, a cometary structure pointing in the direction of motion. We
present the first 3D hydrodynamic simulations of the formation and evolution of
Betelgeuse's bow shock. We show that the bow shock morphology depends
substantially on the growth timescale for Rayleigh-Taylor versus
Kelvin-Helmholtz instabilities. We discuss our models in light of the recent
Herschel, GALEX and VLA observations. If the mass in the bow shock shell is low
(~few x 0.001 Msun), as seems to be implied by the AKARI and Herschel
observations, then Betelgeuse's bow shock is very young and is unlikely to have
reached a steady state. The circular, smooth bow shock shell is consistent with
this conclusion. We further discuss the implications of our results, in
particular, the possibility that Betelgeuse may have only recently entered the
RSG phase.


  We introduce a `double-difference' method for the inversion for seismic
wavespeed structure based on adjoint tomography. Differences between seismic
observations and model predictions at individual stations may arise from
factors other than structural heterogeneity, such as errors in the assumed
source-time function, inaccurate timings, and systematic uncertainties. To
alleviate the corresponding nonuniqueness in the inverse problem, we construct
differential measurements between stations, thereby reducing the influence of
the source signature and systematic errors. We minimize the discrepancy between
observations and simulations in terms of the differential measurements made on
station pairs. We show how to implement the double-difference concept in
adjoint tomography, both theoretically and in practice. We compare the
sensitivities of absolute and differential measurements. The former provide
absolute information on structure along the ray paths between stations and
sources, whereas the latter explain relative (and thus higher-resolution)
structural variations in areas close to the stations. Whereas in conventional
tomography a measurement made on a single earthquake-station pair provides very
limited structural information, in double-difference tomography one earthquake
can actually resolve significant details of the structure. The
double-difference methodology can be incorporated into the usual adjoint
tomography workflow by simply pairing up all conventional measurements; the
computational cost of the necessary adjoint simulations is largely unaffected.
Rather than adding to the computational burden, the inversion of
double-difference measurements merely modifies the construction of the adjoint
sources for data assimilation.


  This paper contains a general theory for asymptotic expansions of type (*)
f(x)=a_1 phi_1(x)+...+a_n phi_n(x)+o(phi_n(x)), x tends to x_0, n>=3, where the
asymptotic scale phi_1(x)>>phi_2(x)>>...>>phi_n(x), x tends to x_0, is assumed
to be an extended complete Chebyshev system on a one-sided neighborhood of x_0.
"Factorizational theory" refers to proofs being based on various types of
factorizations of a differential operator associated to (phi_1,...,phi_n),
hence we preliminarly collect various results concerning the concept of
Chebyshev asymptotic scale, associated disconjugate operators and canonical
factorizations. Another guiding thread of our theory is the property of formal
differentiation and we aim at characterizing some n-tuples of asymptotic
expansions formed by (*) and (n-1) expansions obtained by formal applications
of suitable linear differential operators of orders 1,2,...,n-1. Our second
preliminary step will be that of discovering that the class of the operators
naturally associated to "canonical" factorizations seems to be the most
meaningful to be used in a context of formal differentiation. This gives rise
to conjectures whose proofs build an analytic theory of finite asymptotic
expansions in the real domain which, though not elementary, parallels the
familiar results about Taylor's formula. One of the results states that to each
scale of the type under consideration it remains associated an important class
of functions (namely that of generalized convex functions) enjoying the
property that the expansion (*), if valid, is automatically formally
differentiable (n-1) times in two special senses.


  Ground-based measurements of frozen precipitation are heavily influenced by
interactions of surface winds with gauge-shield geometry. The Multi-Angle
Snowflake Camera (MASC), which photographs hydrometeors in free-fall from three
different angles while simultaneously measuring their fall speed, has been used
in the field at multiple mid-latitude and polar locations both with and without
wind shielding. Here we show results of computational fluid dynamics (CFD)
simulations of the airflow and corresponding particle trajectories around the
unshielded MASC and compare these results to Arctic field observations with and
without a Belfort double Alter shield. Simulations in the absence of a wind
shield show a separation of flow at the upstream side of the instrument, with
an upward velocity component just above the aperture, which decreases the mean
particle fall speed by 55%(74%) for a wind speed of 5 m/s(10 m/s).
MASC-measured fall speeds compare well with Ka-band Atmospheric Radiation
Measurement (ARM) Zenith Radar (KAZR) mean Doppler velocities only when winds
are light (<5 m/s) and the MASC is shielded. MASC-measured fall speeds that do
not match KAZR measured velocities tend to fall below a threshold value that
increases approximately linearly with wind speed but is generally <0.5 m/s. For
those events with wind speeds <1.5 m/s, hydrometeors fall with an orientation
angle mode of 12 degrees from the horizontal plane, and large, low-density
aggregates are as much as five times more likely to be observed. We conclude
that accurate MASC observations of the microphysical, orientation, and fall
speed characteristics of snow particles require shielding by a double wind
fence and restriction of analysis to events where winds are light (<5 m/s).
Hydrometeors do not generally fall in still air, so adjustments to these
properties' distributions within natural turbulence remain to be determined.


  Causal soliton formation (e.g. oscillons, Q-balls) in the primordial Universe
is expected to give rise to a universal gravitational wave (GW) background, at
frequencies smaller than scales of nonlinearity. We show that modifications of
the soliton density field, driven by soliton interactions or initial
conditions, can significantly enhance universal GWs. Gravitational clustering
of solitons naturally leads to generation of correlations in the large-scale
soliton density field. As we demonstrate for axion-like particle (ALP)
oscillons, the growing power spectrum amplifies universal GW signals, opening
new avenues for probing the physics of the early Universe with upcoming GW
experiments. Our results are applicable to variety of scenarios, such as
solitons interacting through a long range Yukawa-like fifth force.


  We provide a boundedness criterion for the integral operator $S_{\varphi}$ on
the fractional Fock-Sobolev space $F^{s,2}(\mathbb C^n)$, $s\geq 0$, where
$S_{\varphi}$ (introduced by Kehe Zhu) is given by \begin{eqnarray*}
S_{\varphi}F(z):= \int_{\mathbb{C}^n} F(w) e^{z \cdot\bar{w}} \varphi(z-
\bar{w}) d\lambda(w) \end{eqnarray*} with $\varphi$ in the Fock space
$F^2(\mathbb C^n)$ and $d\lambda(w): = \pi^{-n} e^{-|w|^2} dw$ the Gaussian
measure on the complex space $\mathbb{C}^{n}$. This extends the recent result
in Cao--Li--Shen--Wick--Yan. The main approach is to develop multipliers on the
fractional Hermite-Sobolev space $W_H^{s,2}(\mathbb R^n)$.


  Voice control is a popular way to operate mobile devices, enabling users to
communicate requests to their devices. However, adversaries can leverage voice
control to trick mobile devices into executing commands to leak secrets or to
modify critical information. Contemporary mobile operating systems fail to
prevent such attacks because they do not control access to the speaker at all
and fail to control when untrusted apps may use the microphone, enabling
authorized apps to create exploitable communication channels. In this paper, we
propose a security mechanism that tracks the creation of audio communication
channels explicitly and controls the information flows over these channels to
prevent several types of attacks.We design and implement AuDroid, an extension
to the SELinux reference monitor integrated into the Android operating system
for enforcing lattice security policies over the dynamically changing use of
system audio resources. To enhance flexibility, when information flow errors
are detected, the device owner, system apps and services are given the
opportunity to resolve information flow errors using known methods, enabling
AuDroid to run many configurations safely. We evaluate our approach on 17
widely-used apps that make extensive use of the microphone and speaker, finding
that AuDroid prevents six types of attack scenarios on audio channels while
permitting all 17 apps to run effectively. AuDroid shows that it is possible to
prevent attacks using audio channels without compromising functionality or
introducing significant performance overhead.


  Knowing the state of a robot is critical for many problems, such as feedback
control. For continuum robots, state estimation is an incredible challenge.
First, the motion of a continuum robot involves many kinematic states,
including poses, strains, and velocities. Second, all these states are
infinite-dimensional due to the robot's flexible property. It has remained
unclear whether these infinite-dimensional states are observable at all using
existing sensing techniques. Recently, we presented a solution to this
challenge. It was a mechanics-based dynamic state estimation algorithm, called
a Cosserat theoretic boundary observer, which could recover all the
infinite-dimensional robot states by only measuring the velocity twist of the
tip. In this work, we generalize the algorithm to incorporate tip pose
measurements for more tuning freedom. We also validate this algorithm offline
using experimental data recorded from a tendon-driven continuum robot. We feed
the recorded tendon force and tip measurements into a numerical solver of the
Cosserat rod model based on our robot. It is observed that, even with purposely
deviated initialization, the state estimates by our algorithm quickly converge
to the recorded ground truth states and closely follow the robot's actual
motion.


  The group testing problem is concerned with identifying a small set of $k$
infected individuals in a large population of $n$ people. At our disposal is a
testing scheme that can test groups of individuals. A test comes back positive
if and only if at least one individual is infected. In this note, we lay
groundwork for analysing belief propagation for group testing when $k$ scales
linearly in $n$. To this end, we derive the offspring distribution for
different types of individuals. With these distributions at hand, one can
employ the population dynamics algorithm to simulate the posterior marginal
distribution resulting from belief propagation.


  The class of 2-regular matroids is a natural generalisation of regular and
near-regular matroids. We prove an excluded-minor characterisation for the
class of 2-regular matroids. The class of 3-regular matroids coincides with the
class of matroids representable over the Hydra-5 partial field, and the
3-connected matroids in the class with a $U_{2,5}$- or $U_{3,5}$-minor are
precisely those with six inequivalent representations over GF(5). We also prove
that an excluded minor for this class has at most 15 elements.


  In this paper, we consider the versal deformations of three dimensional Lie
algebras. We classify Lie algebras and study their deformations by using linear
algebra techniques to study the cohomology. We will focus on how the
deformations glue the space of all such structures together. This space is
known as the moduli space. We will give a geometric description of this space,
derived from deformation theory, in order to illustrate general features of
moduli spaces of Lie algebras.


  An interval matrix is a matrix whose entries are intervals in the set of real
numbers. We generalize this concept, which has been broadly studied, to other
fields. Precisely we define a rational interval matrix to be a matrix whose
entries are intervals in the set of the rational numbers. We prove that a
(real) interval matrix with endpoints of all its entries in the set of the
rational numbers contains a rank-one matrix if and only if contains a rational
rank-one matrix and contains a matrix with rank smaller than min{p,q} if and
only if it contains a rational matrix with rank smaller than min{p,q}; from
these results and from the analogous criterions for (real) inerval matrices, we
deduce immediately a criterion to see when a rational interval matrix contains
a rank-one matrix and a criterion to see when it is full-rank, that is, all the
matrices it contains are full-rank. Moreover, given a field K and a matrix a
whose entries are subsets of K, we describe a criterion to find the maximal
rank of a matrix contained in a.


  A vortex in a superfluid gas inside an optical lattice can behave as a
massive particle moving in a periodic potential and exhibiting quantum
properties. In this Letter we discuss these properties and show that the
excitation of vortex motions in a two-dimensional lattice can lead to striking
measurable changes in its dynamic response. It would be possible by means of
Bragg spectroscopy to carry out the first direct measurement of the effective
vortex mass, the pinning to the underlying lattice, and the dissipative
damping.


  To accurately characterize the planets a star may be hosting, stellar
parameters must first be well-determined. $\tau$ Ceti is a nearby solar analog
and often a target for exoplanet searches. Uncertainties in the observed
rotational velocities have made constraining $\tau$ Ceti's inclination
difficult. For planet candidates from radial velocity (RV) observations, this
leads to substantial uncertainties in the planetary masses, as only the minimum
mass ($m \sin i$) can be constrained with RV. In this paper, we used new
long-baseline optical interferometric data from the CHARA Array with the MIRC-X
beam combiner and extreme precision spectroscopic data from the Lowell
Discovery Telescope with EXPRES to improve constraints on the stellar
parameters of $\tau$ Ceti. Additional archival data were obtained from a
Tennessee State University Automatic Photometric Telescope and the Mount Wilson
Observatory HK project. These new and archival data sets led to improved
stellar parameter determinations, including a limb-darkened angular diameter of
$2.019 \pm 0.012$ mas and rotation period of $46 \pm 4$ days. By combining
parameters from our data sets, we obtained an estimate for the stellar
inclination of $7\pm7^\circ$. This nearly-pole-on orientation has implications
for the previously-reported exoplanets. An analysis of the system dynamics
suggests that the planetary architecture described by Feng et al. (2017) may
not retain long-term stability for low orbital inclinations. Additionally, the
inclination of $\tau$ Ceti reveals a misalignment between the inclinations of
the stellar rotation axis and the previously-measured debris disk rotation axis
($i_\mathrm{disk} = 35 \pm 10^\circ$).


  We have developed a theory of the longitudinal $g$ factor of light holes in
semiconductor quantum wells. It is shown that the absolute value of the
light-hole $g$-factor can strongly exceed its value in the bulk and, moreover,
the dependence of the Zeeman splitting on magnetic field becomes non-linear in
relatively low fields. These effects are determined by the proximity of the
ground light-hole subband, $lh1$, to the first excited heavy-hole subband,
$hh2$, in GaAs/AlGaAs-type structures. The particular calculations are
performed in the framework of Luttinger Hamiltonian taking into account both
the magnetic field-induced mixing of $lh1$ and $hh2$ states and the mixing of
these states at heterointerfaces, the latter caused by chemical bonds
anisotropy. A theory of magneto-induced reflection and transmission of light
through the quantum wells for the light-hole-to-electron absorption edge is
also presented.


  Most conventional crowd counting methods utilize a fully-supervised learning
framework to establish a mapping between scene images and crowd density maps.
They usually rely on a large quantity of costly and time-intensive pixel-level
annotations for training supervision. One way to mitigate the intensive
labeling effort and improve counting accuracy is to leverage large amounts of
unlabeled images. This is attributed to the inherent self-structural
information and rank consistency within a single image, offering additional
qualitative relation supervision during training. Contrary to earlier methods
that utilized the rank relations at the original image level, we explore such
rank-consistency relation within the latent feature spaces. This approach
enables the incorporation of numerous pyramid partial orders, strengthening the
model representation capability. A notable advantage is that it can also
increase the utilization ratio of unlabeled samples. Specifically, we propose a
Deep Rank-consistEnt pyrAmid Model (DREAM), which makes full use of rank
consistency across coarse-to-fine pyramid features in latent spaces for
enhanced crowd counting with massive unlabeled images. In addition, we have
collected a new unlabeled crowd counting dataset, FUDAN-UCC, comprising 4,000
images for training purposes. Extensive experiments on four benchmark datasets,
namely UCF-QNRF, ShanghaiTech PartA and PartB, and UCF-CC-50, show the
effectiveness of our method compared with previous semi-supervised methods. The
codes are available at https://github.com/bridgeqiqi/DREAM.


  It is well known that the K\"ahler-Ricci flow on a K\"ahler manifold $X$
admits a long-time solution if and only if $X$ is a minimal model, i.e., the
canonical line bundle $K_X$ is nef. The abundance conjecture in algebraic
geometry predicts that $K_X$ must be semi-ample when $X$ is a projective
minimal model. We prove that if $K_X$ is semi-ample, then the diameter is
uniformly bounded for long-time solutions of the normalized K\"ahler-Ricci
flow. Our diameter estimate combined with the scalar curvature estimate in [34]
for long-time solutions of the K\"ahler-Ricci flow are natural extensions of
Perelman's diameter and scalar curvature estimates for short-time solutions on
Fano manifolds. We further prove that along the normalized K\"ahler-Ricci flow,
the Ricci curvature is uniformly bounded away from singular fibres of $X$ over
its unique algebraic canonical model $X_{can}$ if the Kodaira dimension of $X$
is one. As an application, the normalized K\"ahler-Ricci flow on a minimal
threefold $X$ always converges sequentially in Gromov-Hausdorff topology to a
compact metric space homeomorphic to its canonical model $X_{can}$, with
uniformly bounded Ricci curvature away from the critical set of the
pluricanonical map from $X$ to $X_{can}$.


  Philosophers have recently focused on critical, epistemological challenges
that arise from the opacity of deep neural networks. One might conclude from
this literature that doing good science with opaque models is exceptionally
challenging, if not impossible. Yet, this is hard to square with the recent
boom in optimism for AI in science alongside a flood of recent scientific
breakthroughs driven by AI methods. In this paper, I argue that the disconnect
between philosophical pessimism and scientific optimism is driven by a failure
to examine how AI is actually used in science. I show that, in order to
understand the epistemic justification for AI-powered breakthroughs,
philosophers must examine the role played by deep learning as part of a wider
process of discovery. The philosophical distinction between the 'context of
discovery' and the 'context of justification' is helpful in this regard. I
demonstrate the importance of attending to this distinction with two cases
drawn from the scientific literature, and show that epistemic opacity need not
diminish AI's capacity to lead scientists to significant and justifiable
breakthroughs.


  Current searches for extrasolar planets have concentrated on observing the
reflex Doppler shift of solar-type stars. Little is known, however, about
planetary systems around non-solar-type stars. We suggest a new method to
extend planetary searches to hot white dwarfs. Near a hot white dwarf, the
atmosphere of a Jovian planet will be photoionized and emit hydrogen
recombination lines, which may be detected by high- dispersion spectroscopic
observations. Multi-epoch monitoring can be used to distinguish between non-LTE
stellar emission and planetary emission, and to establish the orbital
parameters of the detected planets. In the future, high-precision astrometric
measurements of the hot white dwarf will allow the masses of the detected
planets to be determined. Searches for Jovian planets around hot white dwarfs
will provide invaluable new insight on the development of planetary systems
around stars more massive than the Sun and on how stellar evolution affects
these systems. We present high-dispersion spectroscopic observations of the
white dwarf Feige 34 to demonstrate the complexity and feasibility of the
search method.


  We give an overview of a model to describe deep-inelastic scattering (DIS)
off the deuteron with a spectator proton, based on the virtual nucleon
approximation (VNA). The model accounts for the final-state interactions (FSI)
of the DIS debris with the spectator proton. Values of the rescattering cross
section are obtained by fits to high-momentum spectator data. By using the
so-called "pole extrapolation method", free neutron structure functions can be
obtained by extrapolating low-momentum spectator proton data to the on-shell
neutron pole. We apply this method to the BONuS data set and find a surprising
Bjorken $x$ dependence, indicating a possible rise of the neutron to proton
structure function ratio at high $x$.


  We study the ground state and low-lying excited states of the
Kitaev-Heisenberg model on a ladder geometry using the density matrix
renormalization group and Lanczos exact diagonalization methods. The Kitaev and
Heisenberg interactions are parametrized as $K=\sin\phi$ and $J=\cos\phi$ with
an angle parameter $\phi$. Based on the results for several types of order
parameters, excitation gaps, and entanglement spectra, the $\phi$-dependent
ground-state phase diagram is determined. Remarkably, the phase diagram is
quite similar to that of the Kitaev-Heisenberg model on a honeycomb lattice,
exhibiting the same long-range ordered states, namely rung-singlet (analog to
N\'eel in 3D), zigzag, ferromagnetic, and stripy; and the presence of Kitaev
spin liquids around the exactly solvable Kitaev points $\phi=\pm\pi/2$. We also
calculate the expectation value of a plaquette operator corresponding to a
$\pi$-flux state in order to establish how the Kitaev spin liquid extends away
from the $\phi=\pm\pi/2$. Furthermore, we determine the dynamical spin
structure factor and discuss the effect of the Kitaev interaction on the
spin-triplet dispersion.


  We present a computer simulation study of glassy and crystalline states using
the standard Lennard-Jones interaction potential that is truncated at a finite
cut-off distance, as is typical of many computer simulations. We demonstrate
that the discontinuity at the cut-off distance in the first derivative of the
potential (corresponding to the interparticle force) leads to the appearance of
cut-off nonlinearities. These cut-off nonlinearities persist into the
very-low-temperature regime thereby affecting low-temperature thermal
vibrations, which leads to a breakdown of the harmonic approximation for many
eigen modes, particularly for low-frequency vibrational modes. Furthermore,
while expansion nonlinearities which are due to higher order terms in the
Taylor expansion of the interaction potential are usually ignored at low
temperatures and show up as the temperature increases, cut-off nonlinearities
can become most significant at the lowest temperatures. Anharmonic effects
readily show up in the elastic moduli which not only depend on the eigen
frequencies, but are crucially sensitive to the eigen vectors of the normal
modes. Whereas, those observables that rely mainly on static structural
information or just the eigen frequencies, such as the vibrational density of
states, total potential energy, and specific heat, show negligible dependence
on the presence of the cut-off. Similar aspects of nonlinear behavior have
recently been reported in model granular materials, where the constituent
particles interact through finite-range, purely-repulsive potentials. These
nonlinearities have been ascribed to the nature of the sudden cut-off at
contact in the force-law, thus we demonstrate that cut-off nonlinearities
emerge as a general feature of ordered and disordered solid state systems
interacting through truncated potentials.


  This thesis discusses the Newtonian limit of General Relativity for static
isolated systems with compactly supported matter. We call these systems
"geometrostatic" to underline their geometric nature. We introduce new
quasi-local notions of mass and center of mass that can be read off locally in
the vicinity of the matter/black holes. We prove that these notions
asymptotically coincide with ADM-mass and the Huisken-Yau CMC-center of mass.
Moreover, we prove that they converge to Newtonian mass and center of mass in
the Newtonian limit. The Newtonian limit is discussed in the language of
Ehlers' frame theory.
  Furthermore, we prove several uniqueness claims in geometrostatics as well as
other geometric and physical properties of these systems. We analyze
equipotential sets, provide a pseudo-Newtonian reformulation of
geometrostatics, and prove uniqueness of static photon spheres.


  Heart Sound (also known as phonocardiogram (PCG)) analysis is a popular way
that detects cardiovascular diseases (CVDs). Most PCG analysis uses supervised
way, which demands both normal and abnormal samples. This paper proposes a
method of unsupervised PCG analysis that uses beta variational auto-encoder
($\beta-\text{VAE}$) to model the normal PCG signals. The best performed model
reaches an AUC (Area Under Curve) value of 0.91 in ROC (Receiver Operating
Characteristic) test for PCG signals collected from the same source. Unlike
majority of $\beta-\text{VAE}$s that are used as generative models, the
best-performed $\beta-\text{VAE}$ has a $\beta$ value smaller than 1. Further
experiments then find that the introduction of a light weighted KL divergence
between distribution of latent space and normal distribution improves the
performance of anomaly PCG detection based on anomaly scores resulted by
reconstruction loss. The fact suggests that anomaly score based on
reconstruction loss may be better than anomaly scores based on latent vectors
of samples


  We study the gauge-fixing approach to the construction of lattice chiral
gauge theories in one-loop weak-coupling perturbation theory. We show how
infrared properties of the gauge degrees of freedom determine the nature of the
continuous phase transition at which we take the continuum limit. The fermion
self-energy and the vacuum polarization are calculated, and confirm that, in
the abelian case, this approach can be used to put chiral gauge theories on the
lattice in four dimensions. We comment on the generalization to the nonabelian
case.


  We use coherence theory to explain why it is necessary to modify the
conventional setup of a Michelson interferometer to obtain Haidinger rings with
an extended source of white light. The modification consists of introducing a
glass slide into one of the two arms of the interferometer. This insertion
circumvents the drastic restriction imposed by the low temporal coherence of
white light, which prevents the observation of interference rings with the
conventional setup. In order to understand this restriction, we developed and
implemented a criterion for observing interference fringes. The modified setup
also makes it possible to perform a spectral interferometry experiment to
analyze the output of the interferometer and determine the refractive index of
the glass slide over the whole visible spectrum. The fit of measured data using
Sellmeier's law gives the extrapolated value of the refractive index to the IR
$n_\mathrm{IR}=1.5307\pm0.0003$ and the value of the characteristic wavelength
$\lambda_0=(164.5\pm0.4)\;\mathrm{nm}$ of the oscillator responsible for the
dispersion.


  It is a common perception that the transport of a spin current in
polycrystalline metal is isotropic and independent of the polarization
direction, even though spin current is a tensorlike quantity and its
polarization direction is a key variable. We demonstrate surprising anisotropic
spin relaxation in mesoscopic polycrystalline Cu channels in nonlocal spin
valves. For directions in the substrate plane, the spin-relaxation length is
longer for spins parallel to the Cu channel than for spins perpendicular to it,
by as much as 9% at 10 K. Spin-orbit effects on the surfaces of Cu channels can
account for this anisotropic spin relaxation. The finding suggests novel
tunability of spin current, not only by its polarization direction but also by
electrostatic gating.


  We study the electronic properties of electrons in flat and curved zigzag
graphene ribbons using a tight-binding model within the Slater Koster
approximation.
  We find that curvature dramatically enhances the action of spin orbit effects
in graphene ribbons and has a strong effect on the spin orientation of the edge
states: whereas spins are normal to the surface in the case of flat ribbons,
this is no longer the case in the case of curved ribbons. We find that for the
edge states, the spin density lies always in the plane perpendicular to the
ribbon axis, and deviate strongly from the normal to the ribbon, even for very
small curvature and the small spin orbit coupling of carbon. We find that
curvature results also in an effective second neighbor hopping that modifies
the electronic properties of zigzag graphene ribbons. We discuss the
implications of our finding in the spin Hall phase of curved graphene Ribbons.


  In this paper, we systematically investigate both the synfire propagation and
firing rate propagation in feedforward neuronal network coupled in an
all-to-all fashion. In contrast to most earlier work, where only reliable
synaptic connections are considered, we mainly examine the effects of
unreliable synapses on both types of neural activity propagation in this work.
We first study networks composed of purely excitatory neurons. Our results show
that both the successful transmission probability and excitatory synaptic
strength largely influence the propagation of these two types of neural
activities, and better tuning of these synaptic parameters makes the considered
network support stable signal propagation. It is also found that noise has
significant but different impacts on these two types of propagation. The
additive Gaussian white noise has the tendency to reduce the precision of the
synfire activity, whereas noise with appropriate intensity can enhance the
performance of firing rate propagation. Further simulations indicate that the
propagation dynamics of the considered neuronal network is not simply
determined by the average amount of received neurotransmitter for each neuron
in a time instant, but also largely influenced by the stochastic effect of
neurotransmitter release. Second, we compare our results with those obtained in
corresponding feedforward neuronal networks connected with reliable synapses
but in a random coupling fashion. We confirm that some differences can be
observed in these two different feedforward neuronal network models. Finally,
we study the signal propagation in feedforward neuronal networks consisting of
both excitatory and inhibitory neurons, and demonstrate that inhibition also
plays an important role in signal propagation in the considered networks.


  Exciting electrons in solids with intense light pulses offers the possibility
of generating new states of matter through nonthermal means and controlling
their macroscopic properties on femto- to picosecond timescales. One way to
manipulate a solid is by altering its lattice structure, which often underlies
the electronic, magnetic and other phases. Here, we review how structures of
solids are affected by photoexcitation and how their ultrafast dynamics are
captured with time-resolved electron diffraction and microscopy. Specifically,
we survey how a strong light pulse has been used to tailor the nonequilibrium
characteristics to yield on-demand properties in various material classes. In
the existing literature, four main routes have been exploited to control
material structures: (i) phase competition, (ii) electronic correlations, (iii)
excitation of coherent modes, and (iv) defect generation. In this review, we
discuss experiments relevant to all four schemes and finish by speculating
about future directions.


  GX 301-2, a bright HMXB with an orbital period of 41.5 days, exhibits stable
periodic orbital intensity modulations with a strong pre-periastron X-ray
flare. Several models have been proposed to explain the accretion at different
orbital phases, invoking accretion via stellar wind, equatorial disk, and
accretion stream from the companion star. We present results from exhaustive
orbital phase resolved spectroscopic measurements of GX 301-2 using data from
the Gas Slit Camera onboard MAXI. Using spectroscopic analysis of the MAXI data
with unprecendented orbital coverage for many orbits continuously, we have
found a strong orbital dependence of the absorption column density and
equivalent width of the iron emission line. A very large equivalent width of
the iron line along with a small value of the column density in the orbital
phase range 0.10-0.30 after the periastron passage indicates presence of high
density absorbing matter behind the neutron star in these orbital phase range.
A low energy excess is also found in the spectrum at orbital phases around the
pre-periastron X-ray flare. The orbital dependence of these parameters are then
used to examine the various models about mode of accretion onto the neutron
star in GX 301-2.


  This is a short review of the physics of single-spin asymmetries caused by
two-photon exchange in elastic scattering of electrons by nucleons and nuclei.


  The MICROSCOPE mission was designed to test the Weak Equivalence Principle
(WEP), stating the equality between the inertial and the gravitational masses,
with a precision of $10^{-15}$ in terms of the E\"otv\"os ratio $\eta$. Its
experimental test consisted of comparing the accelerations undergone by two
collocated test masses of different compositions as they orbited the Earth, by
measuring the electrostatic forces required to keep them in equilibrium. This
was done with ultra-sensitive differential electrostatic accelerometers onboard
a drag-free satellite. The mission lasted two and a half years, cumulating
five-months-worth of science free-fall data, two thirds with a pair of test
masses of different compositions -- Titanium and Platinum alloys -- and the
last third with a reference pair of test masses of the same composition --
Platinum. We summarize the data analysis, with an emphasis on the
characterization of the systematic uncertainties due to thermal instabilities
and on the correction of short-lived events which could mimic a WEP violation
signal. We found no violation of the WEP, with the E\"otv\"os parameter of the
Titanium and Platinum pair constrained to $\eta({\rm Ti, Pt})~=~ [-1.5 \pm
2.3~{\rm (stat)} \pm 1.5~{\rm (syst)}]~\times 10^{-15}$ at $1\sigma$ in
statistical errors.


  Observations of chromospheric and coronal emissions from various solar-type
stars show that the stellar magnetic activity varies with the rotation rates of
the stars. The faster the star rotates, its magnetic activity gets stronger but
activity cycle period does not show a straightforward variation with the
rotation rate. For slowly rotating stars, the cycle period decreases with the
increase of rotation rate, while for the fast rotators dependency of cycle
period on rotation is presently quite complicated. We aim to provide an
explanation of these observational trends of stellar magnetic activity using a
dynamo model. We construct a theoretical dynamo model for stars of mass 1
$M_\odot$ based on the kinematic flux transport dynamo model including radial
pumping near the surface of the stars. The inclusion of this near surface
downward radial pumping is found to be necessary to match the observed surface
magnetic field in case of the Sun. The main ingredients of our dynamo model,
meridional circulation and differential rotation for stars are obtained from a
mean-field hydrodynamic model. Our model shows a decrease of cycle period with
increasing rotation rate in the slowly rotating regime and a slight increase of
cycle period with rotation rate for the rapid rotators. The strength of the
magnetic field is found to be increasing as the rotation rate of the star
increases. We also find that the parity of the stellar magnetic field changes
with rotation. According to our model, the parity flips to quadrupolar from
dipolar if the rotation period of the star is less than 17 days.


  In the origins of complexity theory Booth and Lueker showed that the question
of whether two graphs are isomorphic or not can be reduced to the special case
of chordal graphs. To prove that, they defined a transformation from graphs G
to chordal graphs BL(G). The projective resolutions of the associated edge
ideals is manageable and we investigate to what extent their Betti tables also
tell non-isomorphic graphs apart. It turns out that the coefficients describing
the decompositions of Betti tables into pure diagrams in Boij-Soderberg theory
are much more explicit than the Betti tables themselves, and they are expressed
in terms of classical statistics of the graph G.


  Let M be a hyperk\"ahler manifold. The S^2-family of complex structures
compatible with the hyperk\"ahler metric can be assembled into a single complex
structure on Z=MxS^2; the resulting complex manifold is known as the twistor
space of M. We describe the analogous construction for generalized complex
structures in the sense of Hitchin. Specifically, we exhibit a natural
S^2xS^2-family of generalized complex structures compatible with the
hyperk\"ahler metric, and assemble them into a single generalized complex
structure on X=MxS^2xS^2. We call the resulting generalized complex manifold
the generalized twistor space of M.


  The experimental assessment of the strength ($\alpha_R$) of the Rashba
spin-orbit coupling is rather indirect and involves the measurement of the spin
relaxation length from magnetotransport, together with a model of weak
antilocalization. The analysis of the spin relaxation length in nanowires,
however, clouds the experimental assessment of the $\alpha_R$ and leads to the
prevailing belief that it can be tuned freely with electric field--a central
tenant of spintronics. Here, we report direct theory of $\alpha_R$ leading to
atomistic calculations of the spin band structure of InAs nanowires upon
application of electric field-- a direct method that does not require a theory
of spin relaxation. Surprisingly, we find an {\it upper bound} to the electric
field tunable Rashba spin splitting and the ensuing $\alpha_R$; for InAs
nanowires, $\alpha_R$ is pinned at about 170 meV{\AA} irrespective of the
applied field strength. We find that this pinning is due to the quantum
confined stark effect, that reduces continuously the nanowire band gap with
applied electric field, leading eventually to band gap closure and a
considerable increase in the density of free carriers. This results in turn in
a strong screening that prevents the applied electric field inside the nanowire
from increasing further beyond around 200 kV/cm for InAs nanowires. Therefore,
further increase in the gate voltage will not increase $\alpha_R$. This finding
clarifies the physical trends to be expected in nanowire Rashba SOC and the
roles played by the nano size and electric field.


  The article is devoted to mathematical methods of experimental detection of
interactive phenomena in complex systems and their analysis.


  R-band surface photometry is presented for 171 late-type dwarf and irregular
galaxies. For a subsample of 46 galaxies B-band photometry is presented as
well. We present surface brightness profiles as well as isophotal and
photometric parameters including magnitudes, diameters and central surface
brightnesses. Absolute photometry is accurate to 0.1 mag or better for 77% of
the sample. For over 85% of the galaxies the radial surface brightness profiles
are consistent with published data within the measured photometric uncertainty.
For most of the galaxies in the sample HI data have been obtained with the
Westerbork Synthesis Radio Telescope. The galaxies in our sample are part of
the WHISP project (Westerbork HI Survey of Spiral and Irregular Galaxies),
which aims at mapping about 500 nearby spiral and irregular galaxies in HI. The
availability of HI data makes this data set useful for a wide range of studies
of the structure, dark matter content and kinematics of late-type dwarf
galaxies.


  We construct an example of a purely unrectifiable measure $\mu$ in
$\mathbb{R}^d$ for which the singular integrals associated to the kernels
$\displaystyle{K(x)=\frac{P_{2k+1}(x)}{|x|^{2k+d}}}$, with $k\geq 1$ and
$P_{2k+1}$ a homogeneous harmonic polynomial of degree $2k+1$, are bounded in
$L^2(\mu)$. This contrasts starkly with the results concerning the Riesz kernel
$\displaystyle{\frac{x}{|x|^{d}}}$ in $\mathbb{R}^d$.


  We present an approach to the DFT+U method (Density Functional Theory +
Hubbard model) within which the computational effort for calculation of ground
state energies and forces scales linearly with system size. We employ a
formulation of the Hubbard model using nonorthogonal projector functions to
define the localized subspaces, and apply it to a local-orbital DFT method
including in situ orbital optimization. The resulting approach thus combines
linear-scaling and systematic variational convergence. We demonstrate the
scaling of the method by applying it to nickel oxide nano-clusters with sizes
exceeding 7,000 atoms.


  Entanglement of spin and position variables produced by spatially
inhomogeneous magnetic fields of Stern-Gerlach type acting on spinor
Bose-Einstein condensates may lead to interference effects at the level of
one-boson densities. A model is worked out for these effects which is amenable
to analytical calculation for gaussian shaped condensates. The resulting
interference effects are sensitive to the spin polarization properties of the
condensate.


  The spin angular momentum in an elliptically polarized beam of light plays
several noteworthy roles in optical traps. It contributes to the linear
momentum density in a non-uniform beam, and thus to the radiation pressure
exerted on illuminated objects. It can be converted into orbital angular
momentum, and thus can exert torques even on optically isotropic objects. Its
curl, moreover, contributes to both forces and torques without spin-to-orbit
conversion. We demonstrate these effects experimentally by tracking colloidal
spheres diffusing in elliptically polarized optical tweezers. Clusters of
spheres circulate deterministically about the beam's axis. A single sphere, by
contrast, undergoes stochastic Brownian vortex circulation that maps out the
optical force field.


  Exploring fine-grained relationship between entities(e.g. objects in image or
words in sentence) has great contribution to understand multimedia content
precisely. Previous attention mechanism employed in image-text matching either
takes multiple self attention steps to gather correspondences or uses image
objects (or words) as context to infer image-text similarity. However, they
only take advantage of semantic information without considering that objects'
relative position also contributes to image understanding. To this end, we
introduce a novel position-aware relation module to model both the semantic and
spatial relationship simultaneously for image-text matching in this paper.
Given an image, our method utilizes the location of different objects to
capture spatial relationship innovatively. With the combination of semantic and
spatial relationship, it's easier to understand the content of different
modalities (images and sentences) and capture fine-grained latent
correspondences of image-text pairs. Besides, we employ a two-step aggregated
relation module to capture interpretable alignment of image-text pairs. The
first step, we call it intra-modal relation mechanism, in which we computes
responses between different objects in an image or different words in a
sentence separately; The second step, we call it inter-modal relation
mechanism, in which the query plays a role of textual context to refine the
relationship among object proposals in an image. In this way, our
position-aware aggregated relation network (ParNet) not only knows which
entities are relevant by attending on different objects (words) adaptively, but
also adjust the inter-modal correspondence according to the latent alignments
according to query's content. Our approach achieves the state-of-the-art
results on MS-COCO dataset.


  Let $(\mathcal{G},\Gamma)$ be an abstract graph of finite groups. If $\Gamma$
is finite, we can construct a profinite graph of groups in a natural way
$(\hat{\mathcal{G}},\Gamma)$, where $\hat{\mathcal{G}}(m)$ is the profinite
completion of $\mathcal{G}(m)$ for all $m \in \Gamma$. The main reason for this
is that $\Gamma$ is finite, so it is already profinite. In this paper we deal
with the infinite case, by constructing a profinite graph $\overline{\Gamma}$
where $\Gamma$ is densely embedded and then defining a profinite graph of
groups $(\widehat{\mathcal{G}},\overline{\Gamma})$. We also prove that the
fundamental group $\Pi_1(\widehat{\mathcal{G}},\overline{\Gamma})$ is the
profinite completion of $\Pi_1^{abs}(\mathcal{G},\Gamma)$. This answers Open
Question 6.7.1 of the book Profinite Graphs and Groups, published by Luis Ribes
in 2017. Later we generalise the main theorem of a paper by Luis Ribes and the
second author, proving that if $R$ is a virtually free abstract group and $H$
is a finitely generated subgroup of $R$, then
$\overline{N_{R}(H)}=N_{\hat{R}}(\overline{H})$ answering Open Question
15.11.10 of the book of Ribes. Finally, we generalise the main theorem of a
paper by Sheila Chagas and the second author, showing that every virtually free
group is subgroup conjugacy separable. This answers Open Question 15.11.11 of
the same book of Ribes.


  This paper investigates the one-epoch overfitting phenomenon in Click-Through
Rate (CTR) models, where performance notably declines at the start of the
second epoch. Despite extensive research, the efficacy of multi-epoch training
over the conventional one-epoch approach remains unclear. We identify the
overfitting of the embedding layer, caused by high-dimensional data sparsity,
as the primary issue. To address this, we introduce a novel and simple
Multi-Epoch learning with Data Augmentation (MEDA) framework, suitable for both
non-continual and continual learning scenarios, which can be seamlessly
integrated into existing deep CTR models and may have potential applications to
handle the "forgetting or overfitting" dilemma in the retraining and the
well-known catastrophic forgetting problems. MEDA minimizes overfitting by
reducing the dependency of the embedding layer on subsequent training data or
the Multi-Layer Perceptron (MLP) layers, and achieves data augmentation through
training the MLP with varied embedding spaces. Our findings confirm that
pre-trained MLP layers can adapt to new embedding spaces, enhancing performance
without overfitting. This adaptability underscores the MLP layers' role in
learning a matching function focused on the relative relationships among
embeddings rather than their absolute positions. To our knowledge, MEDA
represents the first multi-epoch training strategy tailored for deep CTR
prediction models. We conduct extensive experiments on several public and
business datasets, and the effectiveness of data augmentation and superiority
over conventional single-epoch training are fully demonstrated. Besides, MEDA
has exhibited significant benefits in a real-world online advertising system.


  We measure the lifetime of the cesium $5^2D_{5/2}$ state using a
time-resolved single-photon-counting method. We excite atoms in a hot vapor
cell via an electric quadrupole transition at a wavelength of
$685\,\mathrm{nm}$ and record the fluorescence of a cascade decay at a
wavelength of $852\,\mathrm{nm}$. We extract a lifetime of
$1353(5)\,\mathrm{ns}$ for the $5^2D_{5/2}$ state, in agreement with a recent
theoretical prediction. In particular, the observed lifetime is consistent with
the literature values of the polarizabilities of the cesium $6P$ states. Our
measurement contributes to resolving a long-standing disagreement between a
number of experimental and theoretical results.


  We study the scattering properties of Schr\"{o}dinger operators with
potentials that have short-range decay along a collection of rays in $\bbR^d$.
This generalizes the classical setting of short-range scattering in which the
potential is assumed to decay along \emph{all} rays. For these operators, we
show that any state decomposes into an asymptotically free piece and a piece
which may interact with the potential for long times. We give a microlocal
characterization of the scattering states in terms of the dynamics and a
corresponding description of their complement. We also show that in certain
cases these characterizations can be purely spatial.


  We discuss a simple model of thermal relic dark matter whose mass can be much
larger than the so-called unitarity limit on the mass of point-like particle
dark matter. The model consists of new strong dynamics with one flavor of
fermions in the fundamental representation which is much heavier than the
dynamical scale of the new strong dynamics. Dark matter is identified with the
lightest baryonic hadron of the new dynamics. The baryonic hadrons annihilate
into the mesonic hadrons of the new strong dynamics when they have large radii.
Resultantly, thermal relic dark matter with a mass in the PeV range is
possible.


  This report contains a tutorial introduction to the method of importance
sampling. The use of this method is illustrated for simulations of the
noise-induced energy jitter of return-to-zero pulses in optical communication
systems.


  A significant bottleneck in training deep networks for part segmentation is
the cost of obtaining detailed annotations. We propose a framework to exploit
coarse labels such as figure-ground masks and keypoint locations that are
readily available for some categories to improve part segmentation models. A
key challenge is that these annotations were collected for different tasks and
with different labeling styles and cannot be readily mapped to the part labels.
To this end, we propose to jointly learn the dependencies between labeling
styles and the part segmentation model, allowing us to utilize supervision from
diverse labels. To evaluate our approach we develop a benchmark on the
Caltech-UCSD birds and OID Aircraft dataset. Our approach outperforms baselines
based on multi-task learning, semi-supervised learning, and competitive methods
relying on loss functions manually designed to exploit sparse-supervision.