  The conditions required for spontaneous parametric down-conversion in a
waveguide with periodic nonlinearity in the presence of an unguided pump field
are established. Control of the periodic nonlinearity and the physical
properties of the waveguide permits the quasi-phase matching equations that
describe counter-propagating guided signal and idler beams to be satisfied. We
compare the tuning curves and spectral properties of such counter-propagating
beams to those for co-propagating beams under typical experimental conditions.
We find that the counter-propagating beams exhibit narrow bandwidth permitting
the generation of quantum states that possess discrete-frequency entanglement.
Such states may be useful for experiments in quantum optics and technologies
that benefit from frequency entanglement.


  Survival probability within a certain time horizon T is a common measure of
population viability. The choice of T implicitly involves a time preference,
similar to economic discounting: Conservation success is evaluated at the time
horizon T, while all effects that occur later than T are not considered.
Despite the obvious relevance of the time horizon, ecological studies seldom
analyze its impact on the evaluation of conservation options. In this paper, we
show that, while the choice of T does not change the ranking of conservation
options for single species under stationary conditions, it may substantially
change conservation decisions for multiple species. We conclude that it is of
crucial importance to investigate the sensitivity of model results to the
choice of the time horizon or other measures of time preference when
prioritizing biodiversity conservation efforts.


  Blockchain-based Vehicular Ad-hoc Network (VANET) is widely considered as
secure communication architecture for a connected transportation system. With
the advent of quantum computing, there are concerns regarding the vulnerability
of this architecture against cyber-attacks. In this study, a potential threat
is investigated in a blockchain-based VANET, and a corresponding quantum
cyber-attack is developed. Specifically, a quantum impersonation attack using
Quantum-Shor algorithm is developed to break the Rivest-Shamir-Adleman (RSA)
encrypted digital signatures of VANET and thus create a threat for the
trust-based blockchain scheme of VANET. A blockchain-based VANET,
vehicle-to-everything (V2X) communication, and vehicular mobility are simulated
using OMNET++, the extended INET library, and vehicles-in-network simulation
(VEINS) along with simulation of urban mobility (SUMO), respectively. A small
key RSA based message encryption is implemented using IBM Qiskit, which is an
open-source quantum software development kit. The findings reveal that the
quantum cyber-attack, example, impersonation attack is able to successfully
break the trust chain of a blockchain-based VANET. This highlights the need for
a quantum secured blockchain.


  The goal of this paper is to propose a new mathematical model for the
combined effect of different treatments and lifestyles on the glucose-insulin
dynamics of Type 2 diabetes (T2D) patients. The model gives the possibility to
take into consideration physical activity, stress, meals, and medications while
evaluating or designing treatment plans for T2D patients. The model is proposed
by combining and modifying some of the available models in the literature.
Simulations were performed for the modifications to show how the model confirm
with literature on T2D patients. Additionally, a discussion is provided to
demonstrate the ability of the model to be used in the assessment of treatment
plans and in the design for robust insulin dose guidance algorithms. An open
source code for the model is additionally provided.


  Recent works have shown that by using large pre-trained models along with
learnable prompts, rehearsal-free methods for class-incremental learning (CIL)
settings can achieve superior performance to prominent rehearsal-based ones.
Rehearsal-free CIL methods struggle with distinguishing classes from different
tasks, as those are not trained together. In this work we propose a
regularization method based on virtual outliers to tighten decision boundaries
of the classifier, such that confusion of classes among different tasks is
mitigated. Recent prompt-based methods often require a pool of task-specific
prompts, in order to prevent overwriting knowledge of previous tasks with that
of the new task, leading to extra computation in querying and composing an
appropriate prompt from the pool. This additional cost can be eliminated,
without sacrificing accuracy, as we reveal in the paper. We illustrate that a
simplified prompt-based method can achieve results comparable to previous
state-of-the-art (SOTA) methods equipped with a prompt pool, using much less
learnable parameters and lower inference cost. Our regularization method has
demonstrated its compatibility with different prompt-based methods, boosting
those previous SOTA rehearsal-free CIL methods' accuracy on the ImageNet-R and
CIFAR-100 benchmarks. Our source code is available at
https://github.com/jpmorganchase/ovor.


  For fixed $t\ge 2$, we consider the class of representations of $1$ as sum of
unit fractions whose denominators are powers of $t$ or equivalently the class
of canonical compact $t$-ary Huffman codes or equivalently rooted $t$-ary plane
"canonical" trees. We study the probabilistic behaviour of the height (limit
distribution is shown to be normal), the number of distinct summands (normal
distribution), the path length (normal distribution), the width (main term of
the expectation and concentration property) and the number of leaves at maximum
distance from the root (discrete distribution).


  We develop a unified model of darkgenesis and baryogenesis involving strongly
interacting dark quarks, utilizing the gravitational anomaly of chiral gauge
theories. In these models, both the visible and dark baryon asymmetries are
generated by the gravitational anomaly induced by the presence of chiral
primordial gravitational waves. We provide a concrete model of an SU(2) gauge
theory with two massless quarks. In this model, the dark quarks condense and
form a dark baryon charge superfluid (DBS), in which the Higgs-mode acts as
cold dark matter. We elucidate the essential features of this dark matter
scenario and discuss its phenomenological prospects.


  We study the problem of extracting accurate correspondences for point cloud
registration. Recent keypoint-free methods have shown great potential through
bypassing the detection of repeatable keypoints which is difficult to do
especially in low-overlap scenarios. They seek correspondences over downsampled
superpoints, which are then propagated to dense points. Superpoints are matched
based on whether their neighboring patches overlap. Such sparse and loose
matching requires contextual features capturing the geometric structure of the
point clouds. We propose Geometric Transformer, or GeoTransformer for short, to
learn geometric feature for robust superpoint matching. It encodes pair-wise
distances and triplet-wise angles, making it invariant to rigid transformation
and robust in low-overlap cases. The simplistic design attains surprisingly
high matching accuracy such that no RANSAC is required in the estimation of
alignment transformation, leading to $100$ times acceleration. Extensive
experiments on rich benchmarks encompassing indoor, outdoor, synthetic,
multiway and non-rigid demonstrate the efficacy of GeoTransformer. Notably, our
method improves the inlier ratio by $18{\sim}31$ percentage points and the
registration recall by over $7$ points on the challenging 3DLoMatch benchmark.
Our code and models are available at
\url{https://github.com/qinzheng93/GeoTransformer}.


  The present paper aims at analyzing the topological content of the complex
trajectories that weeder-autonomous robots follow in operation. We will prove
that the topological descriptors of these trajectories are affected by the
robot environment as well as by the robot state, with respect to maintenance
operations. Topological Data Analysis will be used for extracting the
trajectory descriptors, based on homology persistence. Then, appropriate
metrics will be applied in order to compare that topological representation of
the trajectories, for classifying them or for making efficient pattern
recognition.


  Incentive mechanisms are central to the functionality of permissionless
blockchains: they incentivize participants to run and secure the underlying
consensus protocol. Designing incentive-compatible incentive mechanisms is
notoriously challenging, however. As a result, most public blockchains today
use incentive mechanisms whose security properties are poorly understood and
largely untested. In this work, we propose SquirRL, a framework for using deep
reinforcement learning to analyze attacks on blockchain incentive mechanisms.
We demonstrate SquirRL's power by first recovering known attacks: (1) the
optimal selfish mining attack in Bitcoin [52], and (2) the Nash equilibrium in
block withholding attacks [16]. We also use SquirRL to obtain several novel
empirical results. First, we discover a counterintuitive flaw in the widely
used rushing adversary model when applied to multi-agent Markov games with
incomplete information. Second, we demonstrate that the optimal selfish mining
strategy identified in [52] is actually not a Nash equilibrium in the
multi-agent selfish mining setting. In fact, our results suggest (but do not
prove) that when more than two competing agents engage in selfish mining, there
is no profitable Nash equilibrium. This is consistent with the lack of observed
selfish mining in the wild. Third, we find a novel attack on a simplified
version of Ethereum's finalization mechanism, Casper the Friendly Finality
Gadget (FFG) that allows a strategic agent to amplify her rewards by up to 30%.
Notably, [10] show that honest voting is a Nash equilibrium in Casper FFG: our
attack shows that when Casper FFG is composed with selfish mining, this is no
longer the case. Altogether, our experiments demonstrate SquirRL's flexibility
and promise as a framework for studying attack settings that have thus far
eluded theoretical and empirical understanding.


  We present a review on the progress in the understanding and characterization
of holonomy and topology of a discrete-time quantum walk architecture,
consisting of a unitary step given by a sequence of two non-commuting rotations
in parameter space \cite{Puentesarxiv}. Unlike other similar systems recently
studied in detail in the literature, this system does not present continous 1D
topological boundaries, it only presents a discrete number of Dirac points
where the quasi- energy gap closes. At these discrete points the topological
winding number is not defined. Therefore, such discrete points represent
topological boundaries of dimension zero, and they endow the system with a
non-trivial topology. We illustrate the non-trivial character of the system by
calculating the Zak phase. We also propose a suitable experimental scheme to
implement these ideas, and we present preliminary experimental data.


  DP-coloring (also called correspondence coloring) is a generalization of list
coloring that was introduced by Dvo\v{r}\'{a}k and Postle in 2015. The
chromatic polynomial of a graph is an important notion in algebraic
combinatorics that was introduced by Birkhoff in 1912; denoted $P(G,m)$, it
equals the number of proper $m$-colorings of graph $G$. Counting function
analogues of chromatic polynomials have been introduced for list colorings:
$P_{\ell}$, list color functions (1990); DP colorings: $P_{DP}$, DP color
functions (2019), and $P^*_{DP}$, dual DP color functions (2021). For any graph
$G$ and $m \in \mathbb{N}$, $P_{DP}(G, m) \leq P_\ell(G,m) \leq P(G,m) \leq
P_{DP}^*(G,m)$. In 2022 (improving on older results) Dong and Zhang showed that
for any graph $G$, $P_{\ell}(G,m)=P(G,m)$ whenever $m \geq |E(G)|-1$.
Consequently, the list color function of a graph is a polynomial for
sufficiently large $m$. One of the most important and longstanding open
questions on DP color functions asks: for every graph $G$ is there an $N \in
\mathbb{N}$ and a polynomial $p(m)$ such that $P_{DP}(G,m) = p(m)$ whenever $m
\geq N$? We show that the answer to the analogue of this question for dual DP
color functions is no. Our proof reveals a connection between a dual DP color
function and the balanced chromatic polynomial of a signed graph introduced by
Zaslavsky in 1982.


  In this paper we have investigated enumeration orders of elements of r.e.
sets enumerated by means of Turing machines. We have defined a reducibility
based on enumeration orders named "Enumeration Order Reducibility" on
computable functions and also r.e. sets and studied their properties. Based on
this reducibility we introduce an equivalence relation "Enumeration Order
Equivalency". We have reached some properties of it. In subsequent, we have
introduced another concept named "type-2 Enumeration Order Equivalency" and
studied its properties too.


  Atom and, of late, molecule interferometers find application in both the
crucible of fundamental research and industrial pursuits. A prevalent
methodology in the construction of atom interferometers involves the
utilisation of gratings fashioned from laser beams. While this approach imparts
commendable precision, it is hampered by its incapacity to attain exceedingly
short wavelengths and its dependence on intricate laser systems for operational
efficacy. All applications require the control of matter waves, particularly
the particle's velocity. In this manuscript, we propose a continuous beam
monochromator scheme reaching enormously high velocity purification with speed
ratios in the order of $10^3$ based on atom-surface diffraction. Beyond these
high purifications, the proposed scheme simplifies the application by reducing
the degree of freedom to a single angle, selecting the wanted particle's
velocity.


  We discuss in detail level/rank duality in three-dimensional Chern-Simons
theories and various related dualities in three-dimensional Chern-Simons-matter
theories. We couple the dual Lagrangians to appropriate background fields
(including gauge fields, spin$_c$ connections and the metric). The non-trivial
maps between the currents and the line operators in the dual theories is
accounted for by mixing of these fields. In order for the duality to be valid
we must add finite counterterms depending on these background fields. This
analysis allows us to resolve a number of puzzles with these dualities, to
provide derivations of some of them, and to find new consistency conditions and
relations between them. In addition, we find new level/rank dualities of
topological Chern-Simons theories and new dualities of Chern-Simons-matter
theories, including new boson/boson and fermion/fermion dualities.


  Gaussian periods are certain sums of roots of unity whose study dates back to
Gauss's seminal work in algebra and number theory. Recently, large scale plots
of Gaussian periods have been revealed to exhibit striking visual patterns,
some of which have been explored in the second named author's prior work. In
2020, the first named author produced a new app, \texttt{Gaussian periods},
which allows anyone to create these plots much more efficiently and at a larger
scale than before. In this paper, we introduce Gaussian periods, present
illustrations created with the new app, and summarize how mathematics controls
some visual features, including colorings left unexplained in earlier work.


  From five-dimensional $N=4$ matter-coupled gauged supergravity, smooth
time-dependent cosmological solutions, connecting a $dS_{5-d}\times H^d$ (with
$d=2,3$) spacetime at early times to a $dS_5$ spacetime at late times, are
presented. The solutions are derived from the second-order equations of motion
arising from all the gauged theories that can admit $dS_5$ solutions. There are
eight such theories constructed from gauge groups of the form $SO(1,1)\times
G_{nc}$ and $SO(1,1)^{(n)}_\text{diag}\times G_{nc}$, with $n=2,3$, where
$G_{nc}$ is a non-compact gauge factor whose compact part must be embedded
entirely in the matter symmetry group of 5D matter-coupled supergravity.
Furthermore, we analyze how the cosmological solutions and their corresponding
$dS_5$ vacua cannot arise from the first-order equations that solve the
second-order field equations.


  We demonstrated transferring the stability of one highly stable clock laser
operating at 729 nm to another less stable laser operating at 698 nm. The two
different wavelengths were bridged using an optical frequency comb. The
improved stability of the clock laser at 698 nm enabled us to evaluate the
systematic frequency shifts of the Sr optical lattice clock with shorter
averaging time. We determined the absolute frequency of the clock transition
1S0 - 3P0 in 87Sr to be 429 228 004 229 873.9 (1.4) Hz referenced to the SI
second on the geoid via International Atomic Time (TAI).


  Seagrass meadows, one of the worlds most important and productive coastal
habitats, are threatened by a range of anthropogenic actions. Burial of
seagrass plants due to coastal activities is one important anthropogenic
pressure leading to decline of local populations. In our study, we assessed the
response of eelgrass Zostera marina to sediment burial from physiological,
morphological, and population parameters. In a full factorial field experiment,
burial level (5-20 cm) and burial duration (4-16 weeks) were manipulated.
Negative effects were visible even at the lowest burial level (5 cm) and
shortest duration (4 weeks), with increasing effects over time and burial
level. Buried seagrasses showed higher shoot mortality, delayed growth and
flowering and lower carbohydrate storage. The observed effects will likely have
an impact on next years survival of buried plants. Our results have
implications for the management of this important coastal plant.


  We prove and discuss three results on zero distribution of gaussian analytic
functions: (i) the Edeleman-Kostlan formula for the expectation of the counting
measure; (ii) a variation on the theme of Calabi's rigidity theorem; (iii)
Offord's estimate of exponential decay of the tail probabilities of an anlytic
function having an access or deficiency of zeros in a given region.


  The particle flow approach to calorimetry benefits from highly granular
calorimeters and sophisticated software algorithms in order to reconstruct and
identify individual particles in complex event topologies. The high spatial
granularity, together with analogue energy information, can be further
exploited in software compensation. In this approach, the local energy density
is used to discriminate electromagnetic and purely hadronic sub-showers within
hadron showers in the detector to improve the energy resolution for single
particles by correcting for the intrinsic non-compensation of the calorimeter
system. This improvement in the single particle energy resolution also results
in a better overall jet energy resolution by improving the energy measurement
of identified neutral hadrons and improvements in the pattern recognition stage
by a more accurate matching of calorimeter energies to tracker measurements.
This paper describes the software compensation technique and its implementation
in particle flow reconstruction with the Pandora Particle Flow Algorithm
(PandoraPFA). The impact of software compensation on the choice of optimal
transverse granularity for the analogue hadronic calorimeter option of the
International Large Detector (ILD) concept is also discussed.


  In this paper new characterization equipment for thermal interface materials
is presented. Thermal management of electronic products relies on the
effec-tive dissipation of heat. This can be achieved by the optimization of the
system design with the help of simulation methods. The precision of these
models relies also on the used material data. For the determi-nation of this
data an experimental set-up for a static measurement is presented, which
evaluates thermal conductivity and interface resistance of thermal inter-face
materials (e.g. adhesive, solder, pads, or pastes). A qualitative
structure-property correlation is pro-posed taking into account particle size,
filler content and void formation at the interface based on high resolution FIB
imaging. The paper gives an overview over the set-up and the measurement
technique and discusses experimental and simulation results.


  We obtain extensions of the Poincar\'e and Perron theorems for higher order
recurrence relations and apply them to obtain an inverse type theorem for row
sequences of (type II) Hermite-Pad\'e approximation of a vector of formal power
series.


  We detail how microlensing internal to M31 could be used to test whether a
large fraction of the matter in spiral galaxy haloes is composed of dark
objects with masses comparable to those of stars, and in the process show how
the microlensing matter is distributed in space and as a function of mass. A
survey of small fields in M31 has revealed several such candidate microlensing
events, at roughly the predicted rate. We discuss what efforts have been
required to further verify the microlensing nature of these events. We show how
halo lensing optical depth varies over the face of M31 depending on the shape
of the microlensing halo, and show how this shape could be determined in
representative results from a simulated survey in which roughly one-half square
degree is imaged for six hours every three nights on a two-meter telescope, in
1-arcsec seeing. After two or three seasons of such observation, the flattening
and core radius of the microlensing halo can be measured to an interesting
level of accuracy.


  Cerebral microbleeds detection is an important and challenging task. With the
gaining popularity of the MRI, the ability to detect cerebral microbleeds also
raises. Unfortunately, for radiologists, it is a time-consuming and laborious
procedure. For this reason, various solutions to automate this process have
been proposed for several years, but none of them is currently used in medical
practice. In this context, the need to systematize the existing knowledge and
best practices has been recognized as a factor facilitating the imminent
synthesis of a real CMBs detection system practically applicable in medicine.
To the best of our knowledge, all available publications regarding automatic
cerebral microbleeds detection have been gathered, described, and assessed in
this paper in order to distinguish the current research state and provide a
starting point for future studies.


  Using a new second derivative technique and thermometers which enable us to
determine the local electron temperature in a mesoscopic metallic sample, we
have obtained quantitative measurements of the low temperature field and
temperature dependent thermopower of Andreev interferometers. As in previous
experiments, the thermopower is found to oscillate as a function of magnetic
field. The temperature dependence of the thermopower is nonmonotonic, with a
minimum at a temperature of $\simeq0.5$ K. These results are discussed from the
perspective of Andreev reflection at the normal-metal/superconductor interface.


  Auto-Regressive (AR) models have achieved impressive results in 2D image
generation by modeling joint distributions in the grid space. While this
approach has been extended to the 3D domain for powerful shape generation, it
still has two limitations: expensive computations on volumetric grids and
ambiguous auto-regressive order along grid dimensions. To overcome these
limitations, we propose the Improved Auto-regressive Model (ImAM) for 3D shape
generation, which applies discrete representation learning based on a latent
vector instead of volumetric grids. Our approach not only reduces computational
costs but also preserves essential geometric details by learning the joint
distribution in a more tractable order. Moreover, thanks to the simplicity of
our model architecture, we can naturally extend it from unconditional to
conditional generation by concatenating various conditioning inputs, such as
point clouds, categories, images, and texts. Extensive experiments demonstrate
that ImAM can synthesize diverse and faithful shapes of multiple categories,
achieving state-of-the-art performance.


  High-cycle fatigue is a critical performance metric of structural alloys for
many applications. The high cost, time, and labor involved in experimental
fatigue testing call for efficient and accurate computer models of fatigue
life. We present graph neural networks for polycrystals that, for the first
time, can (i) predict fatigue indicator parameters -- grain-level responses to
cyclic loading well beyond monotonic elastic and inelastic regimes reported in
literature; and (ii) generalize these predictions to large microstructure
volume elements with grain populations well beyond those used in training.
These advances can make significant contributions to statistically rigorous and
computationally efficient modeling of high-cycle fatigue -- a long-standing
challenge in the field.


  We present theoretical formulation and experimental demonstration of a novel
technique for the fast compression-less terahertz imaging based on the
broadband Fourier optics. The technique exploits k-vector/frequency duality in
Fourier optics which allows using a single-pixel detector to perform angular
scan along a circular path, while the broadband spectrum is used to scan along
the radial dimension in Fourier domain. The proposed compression-less image
reconstruction technique (hybrid inverse transform) requires only a small
number of measurements that scales linearly with the image linear size, thus
promising real-time acquisition of high-resolution THz images. Additionally,
our imaging technique handles equally well and on the equal theoretical footing
the amplitude contrast and the phase contrast images, which makes this
technique useful for many practical applications. A detailed analysis of the
novel technique advantages and limitations is presented, as well as its place
among other existing THz imaging techniques is clearly identified


  We introduce a novel approach to obtaining mathematically rigorous results on
the global dynamics of ordinary differential equations. Motivated by models of
regulatory networks, we construct a state transition graph from a piecewise
affine ordinary differential equation. We use efficient graph algorithms to
compute an associated Morse graph that codifies the recurrent and gradient-like
dynamics. We prove that for 2-dimensional systems, the Morse graph defines a
Morse decomposition for the dynamics of any smooth differential equation that
is sufficiently close to the original piecewise affine ordinary differential
equation.


  We propose the possibility of a new phenomenon affecting the settling of dust
grains at the terrestrial region in early protoplanetary disks. Sinking dust
grains evaporate in a hot inner region during the early stage of disk
evolution, and the effects of condensation and evaporation on vertical dust
settling can be significant. A 1-D dust settling model considering both
physical and chemical aspects is presented in this paper. Modeling results show
that dust grains evaporate as they descend into the hotter interior and form a
"condensation front," above which dust-composing major elements, Mg, Si, and
Fe, accumulate, creating a large temperature gradient. Repeated evaporation at
the front inhibits grain growth, and small grain sizes elevate the opacity away
from the mid-plane. Self-consistent calculations including radiative heat
transfer and condensation theory suggest that the mid-disk temperature could be
high enough for silicates to remain evaporated longer than previous estimates.
The formation of a condensation front leads to contrasting settling behaviors
between highly refractory elements, such as Al and Ca, and moderately
refractory elements, such as Mg, Si, and Fe, suggesting that elemental
abundance in planetesimals may not be a simple function of volatility.


  We study the tunneling current through a mesoscopic two-terminal ring with
spin-orbit coupling, which is threaded by a magnetic flux. The
electron-electron interaction in the ring is described in terms of a
Tomonaga-Luttinger model which also allows us to account for a capacitive
coupling between the ring and the gate electrode. In the regime of weak
tunneling, we describe how, at temperatures lower than the mean level spacing,
the peak positions of the conductance depend on magnetic flux, spin-orbit
coupling strength, gate voltage, charging energy, and interaction parameters
(charge and spin velocity and stiffness).


  The relationship between submillimeter (submm) dust emission polarization and
near-infrared (NIR) $H$-band polarization produced by dust dichroic extinction
was studied for the cold starless dense core FeSt 1-457. The distribution of
polarization angles ($90^{\circ}$-rotated for submm) and degrees were found to
be very different between at submm and NIR wavelengths. The mean polarization
angles for FeSt 1-457 at submm and NIR wavelengths are $132.1^{\circ} \pm
22.0^{\circ}$ and $2.7^{\circ} \pm 16.2^{\circ}$, respectively. The correlation
between $P_H$ and $A_V$ was found to be linear from outermost regions to
relatively dense line of sight of $A_V \approx 25$ mag, indicating that NIR
polarization reflects overall polarization (magnetic field) structure of the
core at least in this density range. The flat $P_H/A_V$ versus $A_V$
correlations were confirmed, and the polarization efficiency was found to be
comparable to the observational upper limit (Jones 1989). On the other hand, as
reported by Alves et al., submm polarization degrees show clear linearly
decreasing trend against $A_V$ from $A_V \approx 20$ mag to the densest center
($A_V \approx 41$ mag), appearing as "polarization hole" structure. The power
law index for the $P_{\rm submm}$ versus $A_V$ relationship was obtained to be
$\approx -1$, indicating that the alignment for the submm sensitive dust is
lost. These very different polarization distributions at submm and NIR
wavelengths suggest that (1) there is different radiation environment at these
wavelengths or (2) submm-sensitive dust is localized or the combination of
them.


  In this paper we establish the equivalence of solutions between Schr\"odinger
map into $\mathbb{S}^2$ or $ \mathbb{H}^2$ and their associated gauge invariant
Schr\"odinger equations. We also establish the existence of global weak
solutions into $\mathbb{H}^2$ in two space dimensions. We extend these ideas
for maps into compact hermitian symmetric manifolds with trivial first
cohomology.


  A nonlinear electronic circuit comprising of three nodes with a feedback loop
is analyzed. The system has two stable states, a uniform state and a sinusoidal
oscillating state, and it transitions from one to another by means of a Hopf
bifurcation. The stability of this system is analyzed with nonlinear equations
derived from a repressilator-like transistor circuit. The apparatus is simple
and inexpensive, and the experiment demonstrates aspects of nonlinear dynamical
systems in an advanced undergraduate laboratory setting.


  A simple proof of Thue theorem on Circle Packing is given. The proof is only
based on density analysis of Delaunay triangulation for the set of points that
are centers of circles in a saturated circle configuration.


  We consider the problem of monostatic radar sensing with orthogonal
frequency-division multiplexing (OFDM) joint radar-communications (JRC) systems
in the presence of phase noise (PN) caused by oscillator imperfections. We
begin by providing a rigorous statistical characterization of PN in the radar
receiver over multiple OFDM symbols for free-running oscillators (FROs) and
phase-locked loops (PLLs). Based on the delay-dependent PN covariance matrix,
we derive the hybrid maximum-likelihood (ML)/maximum a-posteriori (MAP)
estimator of the deterministic delay-Doppler parameters and the random PN,
resulting in a challenging high-dimensional nonlinear optimization problem. To
circumvent the nonlinearity of PN, we then develop an iterated small angle
approximation (ISAA) algorithm that progressively refines delay-Doppler-PN
estimates via closed-form updates of PN as a function of delay-Doppler at each
iteration. Moreover, unlike existing approaches where PN is considered to be
purely an impairment that has to be mitigated, we propose to exploit PN for
resolving range ambiguity by capitalizing on its delay-dependent statistics
(i.e., the range correlation effect), through the formulation of a parametric
Toeplitz-block Toeplitz covariance matrix reconstruction problem. Simulation
results indicate quick convergence of ISAA to the hybrid Cram\'{e}r-Rao bound
(CRB), as well as its remarkable performance gains over state-of-the-art
benchmarks, for both FROs and PLLs under various operating conditions, while
showing that the detrimental effect of PN can be turned into an advantage for
sensing.


  The feasibility of performing fast neutron resonance radiography at the PTB
accelerator facility is studied. A neutron beam of a broad spectral
distribution is produced by a pulsed 13 MeV deuterium beam hitting a thick Be
target. The potential of 3 different neutron imaging detectors with time-of
flight capability are investigated. The applied methods comprise wire chambers
with hydrogenous converter layers and a fast plastic scintillator with
different optical readout schemes. We present the neutron facility, the imaging
methods employed and results obtained. in beam experiments where samples of
carbon rods with various length and diameter were imaged to study resolution
and sensitivity of the method.


  A prefix normal word is a binary word with the property that no substring has
more 1s than the prefix of the same length. This class of words is important in
the context of binary jumbled pattern matching. In this paper we present
results about the number $pnw(n)$ of prefix normal words of length $n$, showing
that $pnw(n) =\Omega\left(2^{n - c\sqrt{n\ln n}}\right)$ for some $c$ and
$pnw(n) = O \left(\frac{2^n (\ln n)^2}{n}\right)$. We introduce efficient
algorithms for testing the prefix normal property and a "mechanical algorithm"
for computing prefix normal forms. We also include games which can be played
with prefix normal words. In these games Alice wishes to stay normal but Bob
wants to drive her "abnormal" -- we discuss which parameter settings allow
Alice to succeed.


  We summarize our efforts to date in developing a framework for generating
succinct human-understandable competency self-assessments in terms of machine
self confidence, i.e. a robot's self-trust in its functional abilities to
accomplish assigned tasks. Whereas early work explored machine self-confidence
in ad hoc ways for niche applications, our Factorized Machine Self-Confidence
framework introduces and combines several aspects of probabilistic meta
reasoning for algorithmic planning and decision-making under uncertainty to
arrive at a novel set of generalizable self-confidence factors, which can
support competency assessment for a wide variety of problems.


  We study the conformations of a semiflexible chain, confined in nano-scaled
spherical cavities, under two distinct processes of confinement. Radial
contraction and packaging are employed as two confining procedures. The former
method is performed by gradually decreasing the diameter of a spherical shell
which envelopes a confined chain. The latter procedure is carried out by
injecting the chain inside a spherical shell through a hole on the shell
surface. The chain is modeled with a rigid body molecular dynamics simulation
and its parameters are adjusted to DNA base-pair elasticity. Directional order
parameter is employed to analyze and compare the confined chain and the
conformations of the chain for two different sizes of the spheres are studied
in both procedures. It is shown that for the confined chains in the sphere
sizes of our study, they appear in spiral or tennis-ball structures, and the
tennis-ball structure is more likely to be observed in more compact
confinements. Our results also show that the dynamical procedure of confinement
and the rate of the confinement are influential parameters of the structure of
the chain inside spherical cavities.


  In recent years, distinctive-dictionary construction has gained importance
due to his usefulness in data processing. Usually, one or more dictionaries are
constructed from a training data and then they are used to classify signals
that did not participate in the training process. A new dictionary construction
algorithm is introduced. It is based on a low-rank matrix factorization being
achieved by the application of the randomized LU decomposition to a training
data. This method is fast, scalable, parallelizable, consumes low memory,
outperforms SVD in these categories and works also extremely well on large
sparse matrices. In contrast to existing methods, the randomized LU
decomposition constructs an under-complete dictionary, which simplifies both
the construction and the classification processes of newly arrived signals. The
dictionary construction is generic and general that fits different
applications. We demonstrate the capabilities of this algorithm for file type
identification, which is a fundamental task in digital security arena,
performed nowadays for example by sandboxing mechanism, deep packet inspection,
firewalls and anti-virus systems. We propose a content-based method that
detects file types that neither depend on file extension nor on metadata. Such
approach is harder to deceive and we show that only a few file fragments from a
whole file are needed for a successful classification. Based on the constructed
dictionaries, we show that the proposed method can effectively identify
execution code fragments in PDF files.
  $\textbf{Keywords.}$ Dictionary construction, classification, LU
decomposition, randomized LU decomposition, content-based file detection,
computer security.


  The $2p$-$3s$ lines of Fe XVII in the X-ray spectrum of the O-type star
$\zeta$ Puppis exhibit an anomalous (3G + M2)/(3F) line ratio of $\sim$1.4, in
comparison with $\sim$2.4 for almost all other collisionally excited
astrophysical spectra. Based on the work of Mauche et al. (2001), we
conjectured that the strong UV field of $\zeta$ Puppis produces the observed
ratio by depopulation of metastable $3s$ excited states, and that the ratio can
potentially be used as an independent diagnostic of plasma formation radius. We
used the Flexible Atomic Code (FAC) collisional-radiative model to model the
effect of UV photoexcitation from O stars on the Fe XVII lines. We compared our
model calculations to archival spectra of coronal and hot stars from the
Chandra HETGS and XMM-Newton RGS to benchmark our calculations for various
electron densities and UV field intensities. Our calculations show that UV
photoexcitation does not produce a sufficiently large dynamic range in the
3F/(3F + 3G + M2) fraction to explain the difference in the observed ratio
between coronal stars and $\zeta$ Pup. Thus, this effect likely cannot explain
the observed line ratio of $\zeta$ Pup, and its origin is still unexplained.


  An implementation of GMRES with multiple preconditioners (MPGMRES) is
proposed for solving shifted linear systems with shift-and-invert
preconditioners. With this type of preconditioner, the Krylov subspace can be
built without requiring the matrix-vector product with the shifted matrix.
Furthermore, the multipreconditioned search space is shown to grow only
linearly with the number of preconditioners. This allows for a more efficient
implementation of the algorithm. The proposed implementation is tested on
shifted systems that arise in computational hydrology and the evaluation of
different matrix functions. The numerical results indicate the effectiveness of
the proposed approach.


  A Euro-Asian network of four gravitational-wave (GW) interferometers is
considered, taking into account the plan to create such a detector in
Novosibirsk. The efficiency of the network is assessed by typical numerical
criteria, which also depend on the characteristics of the received signal. In
this work, we calculate the optimal orientation of the Novosibirsk detector for
the problem of detecting GW radiation accompanying the collapse of the
progenitor star with an initial angular momentum. The specificity of the
scenario is the presence of the so-called. bar stage deformation, for which the
shape of the emitted GW signal is known.


  Empirical estimates of the dimensionality of neural population activity are
often much lower than the population size. Similar phenomena are also observed
in trained and designed neural network models. These experimental and
computational results suggest that mapping low-dimensional dynamics to
high-dimensional neural space is a common feature of cortical computation.
Despite the ubiquity of this observation, the constraints arising from such
mapping are poorly understood. Here we consider a specific example of mapping
low-dimensional dynamics to high-dimensional neural activity -- the neural
engineering framework. We analytically solve the framework for the classic ring
model -- a neural network encoding a static or dynamic angular variable. Our
results provide a complete characterization of the success and failure modes
for this model. Based on similarities between this and other frameworks, we
speculate that these results could apply to more general scenarios.


  Let $(X,T)$ be a topological dynamical system and $\mu$ be a invariant
measure, we show that $(X,\mathcal{B},\mu,T)$ is rigid if and only if there
exists some subsequence $A$ of $\mathbb N$ such that $(X,T)$ is
$\mu$-$A$-equicontinuous if and only if there exists some IP-set $A$ such that
$(X,T)$ is $\mu$-$A$-equicontinuous. We show that if there exists a subsequence
$A$ of $\mathbb N$ with positive upper density such that $(X,T)$ is
$\mu$-$A$-mean-equicontinuous, then $(X,\mathcal{B},\mu,T)$ is rigid. We also
give results with respect to functions.


  The multiscale entanglement renormalization ansatz (MERA) provides a
constructive algorithm for realizing wavefunctions that are inherently scale
invariant. Unlike conformally invariant partition functions however, the finite
bond dimension $\chi$ of the MERA provides a cut-off in the fields that can be
realized. In this letter, we demonstrate that this cut-off is equivalent to the
one obtained when approximating a thermal state of a critical Hamiltonian with
a matrix product operator (MPO) of finite bond dimension $\chi$. This is
achieved by constructing an explicit mapping between the isometries of a MERA
and the local tensors of the MPO.


  We present an exact solution of a supersymmetric nonlinear sigma model
describing the crossover between a quantum dot and a disordered quantum wire
with unitary symmetry. The system is coupled ideally to two electron reservoirs
via perfectly conducting leads sustaining an arbitrary number of propagating
channels. We obtain closed expressions for the first three moments of the
conductance, the average shot-noise power and the average density of
transmission eigenvalues. The results are complete in the sense that they are
nonperturbative and are valid in all regimes and length scales. We recover
several known results of the recent literature by taking particular limits.


  In this work, we study probing for the more general problem of computing the
trace of a permutation of $A^{-1}$, say $PA^{-1}$. The motivation comes from
Lattice QCD where we need to construct "disconnected diagrams" to extract
flavor-separated Generalized Parton functions. In Lattice QCD, where the matrix
has a 4D toroidal lattice structure, these non-local operators correspond to a
$PA^{-1}$ where $P$ is the permutation relating to some displacement $\vec{p}$
in one or more dimensions. We focus on a single dimension displacement ($p$)
but our methods are general. We show that probing on $A^k$ or $(PA)^k$ do not
annihilate the largest magnitude elements. To resolve this issue, our
displacement-based probing works on $PA^k$ using a new coloring scheme that
works directly on appropriately displaced neighborhoods on the lattice. We
prove lower bounds on the number of colors needed, and study the effect of this
scheme on variance reduction, both theoretically and experimentally on a
real-world Lattice QCD calculation. We achieve orders of magnitude speedup over
the unprobed or the naively probed methods.


  There has been considerable recent interest in a new class of non-slow roll
inflationary solutions known as \textit{constant roll} inflation. Constant roll
solutions are a generalization of the ultra-slow roll (USR) solution, where the
first Hubble slow roll parameter $\epsilon$ is small, but the second Hubble
slow roll parameter $\eta$ is not. While it is known that the USR solutions
represent dynamical transients, there has been some disagreement in literature
about whether or not large-$\eta$ constant roll solutions are attractors or are
also a class of transient solutions. In this paper we show that the
large-$\eta$ constant roll solutions do in fact represent transient solutions
by performing stability analysis on the exact analytic (large-$\eta$) constant
roll solutions.


  Beliefs are important determinants of an individual's choices and economic
outcomes, so understanding how they comove and differ across individuals is of
considerable interest. Researchers often rely on surveys that report individual
beliefs as qualitative data. We propose using a Bayesian hierarchical latent
class model to analyze the comovements and observed heterogeneity in
categorical survey responses. We show that the statistical model corresponds to
an economic structural model of information acquisition, which guides
interpretation and estimation of the model parameters. An algorithm based on
stochastic optimization is proposed to estimate a model for repeated surveys
when responses follow a dynamic structure and conjugate priors are not
appropriate. Guidance on selecting the number of belief types is also provided.
Two examples are considered. The first shows that there is information in the
Michigan survey responses beyond the consumer sentiment index that is
officially published. The second shows that belief types constructed from
survey responses can be used in a subsequent analysis to estimate heterogeneous
returns to education.


  By Hacon-McKernan-Xu, there is a positive lower bound in each dimension for
the volume of all klt varieties with ample canonical class. We show that these
bounds must go to zero extremely fast as the dimension increases, by
constructing a klt $n$-fold with ample canonical class whose volume is less
than $1/2^{2^n}$. These examples should be close to optimal.
  We also construct a klt Fano variety of each dimension $n$ such that
$H^0(X,-mK_X)=0$ for all $1\leq m < b$ with $b$ roughly $2^{2^n}$. Here again
there is some bound in each dimension, by Birkar's theorem on boundedness of
complements, and we are showing that the bound must increase extremely fast
with the dimension.


  We consider the degenerate Einstein's Brownian motion model for the case when
the time interval ($\tau$) of particle Jumps before collision (free jumps)
reciprocal to the number of particles per unit volume $u(x,t) > 0$ at the point
of observation $x$ at time $t$. The parameter $0 < \tau \leq C < \infty$,
controls characteristic of the fluid "almost decreases" to $ 0 $ when $u
\rightarrow \infty$. This degeneration leads to the localisation of the spread
of particle propagation in the media. In our report we will present a
structural condition of the time interval of free jumps - $\tau$ and the
frequency of these free jumps $\phi$ as functions of $u$ which guarantees the
finite speed of propagation of $u$.


  Controlling the temperature of nano-scale quantum systems is becoming
increasingly important in the efforts to develop thermal devices such as
quantum heat valves, heat engines, and refrigerators, and to explore
fundamental concepts in quantum thermodynamics. In practice, however, it is
challenging to generate arbitrary time-dependent temperatures, similarly to
what has been achieved for electronic voltage pulses. To overcome this problem,
we here propose a fully quantum mechanical scheme to control the time-dependent
environment temperature of an open quantum system. To this end, we consider a
collection of quantum harmonic oscillators that mediate the interactions
between the quantum system and a thermal reservoir, and we show how an
effective time-dependent temperature can be realized by modulating the
oscillator frequencies in time. By doing so, we can apply effective temperature
pulses to the quantum system, and it can be cooled below the temperature of the
environment. Surprisingly, the scheme can be realized using only a few
oscillators, and our proposal thereby paves the way for controlling the
temperature of open quantum systems.


  Abstract. The risks AI presents to society are broadly understood to be
manageable through general calculus, i.e., general frameworks designed to
enable those involved in the development of AI to apprehend and manage risk,
such as AI impact assessments, ethical frameworks, emerging international
standards, and regulations. This paper elaborates how risk is apprehended and
managed by a regulator, developer and cyber-security expert. It reveals that
risk and risk management is dependent on mundane situated practices not
encapsulated in general calculus. Situated practice surfaces iterable
epistopics, revealing how those involved in the development of AI know and
subsequently respond to risk and uncover major challenges in their work. The
ongoing discovery and elaboration of epistopics of risk in AI a) furnishes a
potential program of interdisciplinary inquiry, b) provides AI developers with
a means of apprehending risk, and c) informs the ongoing evolution of general
calculus.


  There is a growing consensus that shear thickening of concentrated
dispersions is driven by the formation of stress-induced frictional contacts.
The Wyart-Cates (WC) model of this phenomenon, in which the microphysics of the
contacts enters solely via the fraction $f$ of contacts that are frictional,
can successfully fit flow curves for suspensions of weakly polydisperse
spheres. However, its validity for "real-life", polydisperse suspensions has
yet to be seriously tested. By performing systematic simulations on bidisperse
mixtures of spheres, we show that the WC model applies only in the monodisperse
limit and fails when substantial bidispersity is introduced. We trace the
failure of the model to its inability to distinguish large-large, large-small
and small-small frictional contacts. By fitting our data using a polydisperse
analogue of $f$ that depends separately on the fraction of each of these
contact types, we show that the WC picture of shear thickening is incomplete.
Systematic experiments on model shear-thickening suspensions corroborate our
findings, but highlight important challenges in rigorously testing the WC model
with real systems. Our results prompt new questions about the microphysics of
thickening for both monodisperse and polydisperse systems.


  Trolling and social bots have been proven as powerful tactics for
manipulating the public opinion and sowing discord among Twitter users. This
effort requires substantial content fabrication and account coordination to
evade Twitter's detection of nefarious platform use. In this paper we explore
an alternative tactic for covert social media interference by inducing
misperceptions about genuine, non-trolling content from verified users. This
tactic uses a malware that covertly manipulates targeted words, hashtags, and
Twitter metrics before the genuine content is presented to a targeted user in a
covert man-in-the-middle fashion. Early tests of the malware found that it is
capable of achieving a similar goal as trolls and social bots, that is,
silencing or provoking social media users to express their opinion in polarized
debates on social media. Following this, we conducted experimental tests in
controlled settings (N=315) where the malware covertly manipulated the
perception in a Twitter debate on the risk of vaccines causing autism. The
empirical results demonstrate that inducing misperception is an effective
tactic to silence users on Twitter when debating polarizing issues like
vaccines. We used the findings to propose a solution for countering the effect
of the malware-induced misperception that could also be used against trolls and
social bots on Twitter.


  In the process of studying a conjecture of Holly M. Green and Martin W.
Liebeck, we obtain two interesting identities by elementary methods, one is a
combinatorial identity, and the other is a number theoretic identity.


  Most recent semi-supervised deep learning (deep SSL) methods used a similar
paradigm: use network predictions to update pseudo-labels and use pseudo-labels
to update network parameters iteratively. However, they lack theoretical
support and cannot explain why predictions are good candidates for
pseudo-labels in the deep learning paradigm. In this paper, we propose a
principled end-to-end framework named deep decipher (D2) for SSL. Within the D2
framework, we prove that pseudo-labels are related to network predictions by an
exponential link function, which gives a theoretical support for using
predictions as pseudo-labels. Furthermore, we demonstrate that updating
pseudo-labels by network predictions will make them uncertain. To mitigate this
problem, we propose a training strategy called repetitive reprediction (R2).
Finally, the proposed R2-D2 method is tested on the large-scale ImageNet
dataset and outperforms state-of-the-art methods by 5 percentage points.


  Self-similarity of systems is very popular and intensively developing field
during last decades. To this field belong so-called stable distributions and
their generalization. In Klebanov and Sl\'amov\'a (2014) there was given an
approach to define additive systems with the property of random self-similarity
- casual stability (c.s.). Here we continue study the notion of casual
stability for additive systems of random variables (r.v.). We also give a
modification of this definition and spread them on multiplicative systems of
r.v. and on the system with operations of taking minimum or maximum of r.v. The
case of systems with a random number of elements is also considered.


  We present a model to describe a generic circuit QED system which consists of
multiple artificial three-level atoms, namely qutrits, strongly coupled to a
cavity mode. When the state transition of the atoms disobey the selection rules
the process that does not conserve the number of excitations can happen
determinatively. Therefore, we can realize coherent exchange interaction among
three or more atoms mediated by the exchange of virtual photons. In addition,
we generalize the one cavity mode mediated interactions to the multi-cavity
situation, providing a method to entangle atoms located in different cavities.
Using experimental feasible parameters, we investigate the dynamics of the
model including three cyclic-transition three-level atoms, for which the two
lowest-energy levels can be treated as qubits. Hence, we have found that two
qubits can jointly exchange excitation with one qubit in a coherent and
reversible way. In the whole process, the population in the third level of
atoms is negligible and the cavity photon number is far smaller than 1. Our
model provides a feasible scheme to couple multiple distant atoms together,
which may find applications in quantum information processing.


  We investigate algebraic and analytic subvarieties of C^n with automorphisms
which can not be extended to the ambient space.


  We investigate the effects of dichotomous noise added to a classical harmonic
oscillator in the form of stochastic time-dependent gain and loss states, whose
durations are sampled from two distinct exponential waiting time distributions.
Despite the stochasticity, stability criteria can be formulated when averaging
over many realizations in the asymptotic time limit and serve to determine the
boundary line in parameter space that separates regions of growing amplitudes
from those of decaying ones. Furthermore, the concept of $\mathcal{PT}$
symmetry remains applicable for such a stochastic oscillator and we use it to
distinguish between an underdamped symmetric phase and an overdamped asymmetric
phase. In the former case, the limit of stability is marked by the same average
duration for the gain and loss states, whilst in the the latter case, a higher
duration of the loss state is necessary to keep the system stable. The
overdamped phase has an ordered structure imposing a position-velocity ratio
locking and is viewed as a phase transition from the underdamped phase, which
instead displays a broad and more disordered, but nevertheless, $\mathcal{PT}$
symmetric structure. We also address the short time limit and the dynamics of
the moments of the position and the velocity with the aim of revealing the
extremely rich dynamics offered by this apparently quite simple mechanical
system. The notions established so far may be extended and applied in the
stabilization of light propagation in metamaterials and optical fibres with
randomly distributed regions of asymmetric active and passive media.


  A model has been proposed in which neutral scalar particles chi, of mass 1-10
MeV, annihilate through the exchange of a light vector boson U, of mass 10-100
MeV, to produce the 511 keV line observed emanating from the center of the
galaxy. The chi interacts weakly with normal matter and is a viable dark matter
candidate. If the U-boson couples to quarks as well as to electrons, it could
enhance the branching ratio for the rare decay pi0 -> e+e-. A recent
measurement by the KTeV Collaboration lies three standard deviations above a
prediction by Dorokhov and Ivanov, and we relate this excess to the couplings
of the U-boson. The values are consistent with other constraints and
considerations. We make some comments on possible improvements in the data.


  Let $X$ be a smooth scheme over a finite field of characteristic $p$.
Consider the coefficient objects of locally constant rank on $X$ in $\ell$-adic
Weil cohomology: these are lisse Weil sheaves in \'etale cohomology when $\ell
\neq p$, and overconvergent $F$-isocrystals in rigid cohomology when $\ell=p$.
Using the Langlands correspondence for global function fields in both the
\'etale and crystalline settings (work of Lafforgue and Abe, respectively), one
sees that on a curve, any coefficient object in one category has "companions"
in the other categories with matching characteristic polynomials of Frobenius
at closed points. A similar statement is expected for general $X$; building on
work of Deligne, Drinfeld showed that any \'etale coefficient object has
\'etale companions. We adapt Drinfeld's method to show that any crystalline
coefficient object has \'etale companions; this has been shown independently by
Abe--Esnault. We also prove some auxiliary results relevant for the
construction of crystalline companions of \'etale coefficient objects; this
subject will be pursued in a subsequent paper.


  Gravitational-wave astronomy of compact binaries relies on theoretical models
of the gravitational-wave signal that is emitted as binaries coalesce. These
models do not only need to be accurate, they also have to be fast to evaluate
in order to be able to compare millions of signals in near real time with the
data of gravitational-wave instruments. A variety of regression and
interpolation techniques have been employed to build efficient waveform models,
but no study has systematically compared the performance of these regression
methods yet. Here we provide such a comparison of various techniques, including
polynomial fits, radial basis functions, Gaussian process regression and
artificial neural networks, specifically for the case of gravitational waveform
modeling. We use all these techniques to regress analytical models of
non-precessing and precessing binary black hole waveforms, and compare the
accuracy as well as computational speed. We find that most regression methods
are reasonably accurate, but efficiency considerations favour in many cases the
most simple approach. We conclude that sophisticated regression methods are not
necessarily needed in standard gravitational-wave modeling applications,
although problems with higher complexity than what is tested here might be more
suitable for machine-learning techniques and more sophisticated methods may
have side benefits.


  We revisit the fundamental problem of liquid-liquid dewetting and perform a
detailed comparison of theoretical predictions based on thin-film models with
experimental measurements obtained by atomic force microscopy (AFM).
Specifically, we consider the dewetting of a liquid polystyrene (PS) layer from
a liquid polymethyl methacrylate (PMMA) layer, where the thicknesses and the
viscosities of PS and PMMA layers are similar. The excellent agreement of
experiment and theory reveals that dewetting rates for such systems follow no
universal power law, in contrast to dewetting scenarios on solid substrates.
Our new energetic approach allows to assess the physical importance of
different contributions to the energy-dissipation mechanism, for which we
analyze the local flow fields and the local dissipation rates.


  In previous work, we developed tools for quantifying the tidal distortion of
a black hole's event horizon due to an orbiting companion. These tools use
techniques which require large mass ratios (companion mass $\mu$ much smaller
than black hole mass $M$), but can be used for arbitrary bound orbits, and for
any black hole spin. We also showed how to visualize these distorted black
holes by embedding their horizons in a global Euclidean 3-space,
${\mathbb{E}}^3$. Such visualizations illustrate interesting and important
information about horizon dynamics. Unfortunately, we could not visualize black
holes with spin parameter $a_* > \sqrt{3}/2 \approx 0.866$: such holes cannot
be globally embedded into ${\mathbb{E}}^3$. In this paper, we overcome this
difficulty by showing how to embed the horizons of tidally distorted Kerr black
holes in a hyperbolic 3-space, ${\mathbb{H}}^3$. We use black hole perturbation
theory to compute the Gaussian curvatures of tidally distorted event horizons,
from which we build a two-dimensional metric of their distorted horizons. We
develop a numerical method for embedding the tidally distorted horizons in
${\mathbb{H}}^3$. As an application, we give a sequence of embeddings into
${\mathbb{H}}^3$ of a tidally interacting black hole with spin $a_*=0.9999$. A
small amplitude, high frequency oscillation seen in previous work shows up
particularly clearly in these embeddings.


  We prove that Axiom A is open and dense in the space of $C^1$ area
contracting orientation-preserving embeddings on compact orientable surfaces
with boundary. This settles the area contracting version of the {\em Smale's
conjecture} \cite{s}.


  The measurement of the biological tissue's electrical impedance is an active
research field that has attracted a lot of attention during the last decades.
Bio-impedances are closely related to a large variety of physiological
conditions; therefore, they are useful for diagnosis and monitoring in many
medical applications. Measuring living tissues, however, is a challenging task
that poses countless technical and practical problems, in particular if the
tissues need to be measured under the skin. This paper presents a bio-impedance
sensor ASIC targeting a battery-free, miniature size, implantable device, which
performs accurate 4-point complex impedance extraction in the frequency range
from 2 kHz to 2 MHz. The ASIC is fabricated in 150 nm CMOS, has a size of 1.22
mm x 1.22 mm and consumes 165 uA from a 1.8 V power supply. The ASIC is
embedded in a prototype which communicates with, and is powered by an external
reader device through inductive coupling. The prototype is validated by
measuring the impedances of different combinations of discrete components,
measuring the electrochemical impedance of physiological solution, and
performing ex vivo measurements on animal organs. The proposed ASIC is able to
extract complex impedances with around 1 Ohm resolution; therefore enabling
accurate wireless tissue measurements.


  A vector lattice model for stresses in granular materials is proposed. A two
dimensional pile built by pouring from a point is constructed numerically
according to this model. Remarkably, the pile violates the Mohr Coulomb
stability criterion for granular matter, probably because of the inherent
anisotropy of such poured piles. The numerical results are also compared to the
earlier continuum FPA model and the (scalar) lattice $q$-model.


  In this paper, we study the possibility of model building of cyclic universe
with Quintom matter in the framework of Loop Quantum Cosmology. After a general
demonstration, we provide two examples, one with double-fluid and another
double-scalar field, to show how such a scenario is obtained. Analytical and
numerical calculations are both presented in the paper.


  The reaction K^+Xe->K^0pX is investigated in a meson-exchange model including
rescattering of the secondary protons with the aim to analyze the evidence for
the Theta^+(1540) resonance reported by the DIANA collaboration. We confirm
that the kinematical cuts introduced by the DIANA collaboration efficiently
suppress the background to the K^+n->K^0p reaction which may contribute to the
Theta^+(1540) production. We find that these kinematical cuts do not produce a
narrow structure in the K^0p effective mass spectra near 1540 MeV. We study the
effect of a narrow Theta^+ resonance of both positive and negative parity in
comparison with the DIANA data. We show that the K^+Xe->K^0pX calculations
without Theta^+ contribution as well as the results obtained with a Theta^+
width of 1 MeV are in comparably good agreement with the DIANA results. More
dedicated experiments are called for to establish this exotic baryon resonance.


  Intense light sources often produce flares in captured images at night, which
deteriorates the visual quality and negatively affects downstream applications.
In order to train an effective flare removal network, a reliable dataset is
essential. The mainstream flare removal datasets are semi-synthetic to reduce
human labour, but these datasets do not cover typical scenarios involving
multiple scattering flares. To tackle this issue, we synthesize a prior-guided
dataset named Flare7K*, which contains multi-flare images where the brightness
of flares adheres to the laws of illumination. Besides, flares tend to occupy
localized regions of the image but existing networks perform flare removal on
the entire image and sometimes modify clean areas incorrectly. Therefore, we
propose a plug-and-play Adaptive Focus Module (AFM) that can adaptively mask
the clean background areas and assist models in focusing on the regions
severely affected by flares. Extensive experiments demonstrate that our data
synthesis method can better simulate real-world scenes and several models
equipped with AFM achieve state-of-the-art performance on the real-world test
dataset.


  Anomaly detection is a classical but worthwhile problem, and many deep
learning-based anomaly detection algorithms have been proposed, which can
usually achieve better detection results than traditional methods. In view of
reconstruct ability of the model and the calculation of anomaly score, this
paper proposes a time series anomaly detection method based on Variational
AutoEncoder model(VAE) with re-Encoder and Latent Constraint network(VELC). In
order to modify reconstruct ability of the model to prevent it from
reconstructing abnormal samples well, we add a constraint network in the latent
space of the VAE to force it generate new latent variables that are similar
with that of training samples. To be able to calculate anomaly score in two
feature spaces, we train a re-encoder to transform the generated data to a new
latent space. For better handling the time series, we use the LSTM as the
encoder and decoder part of the VAE framework. Experimental results of several
benchmarks show that our method outperforms state-of-the-art anomaly detection
methods.


  In this paper we study anisotropic spherical polytropes within the framework
of general relativity. Using the anisotropic Tolman-Oppenheimer-Volkov (TOV)
equations, we explore the relativistic anisotropic Lane-Emden equations. We
find how the anisotropic pressure affects the boundary conditions of these
equations. Also we argue that the behaviour of physical quantities near the
center of star changes in the presence of anisotropy. For constant density, a
class of exact solution is derived with the aid of a new ansatz and its
physical properties are discussed.


  Objective: Modern medicine needs to shift from a wait and react, curative
discipline to a preventative, interdisciplinary science aiming at providing
personalised, systemic and precise treatment plans to patients. The aim of this
work is to present how the integration of machine learning approaches with
mechanistic computational modelling could yield a reliable infrastructure to
run probabilistic simulations where the entire organism is considered as a
whole. Methods: We propose a general framework that composes advanced AI
approaches and integrates mathematical modelling in order to provide a
panoramic view over current and future physiological conditions. The proposed
architecture is based on a graph neural network (GNNs) forecasting clinically
relevant endpoints (such as blood pressure) and a generative adversarial
network (GANs) providing a proof of concept of transcriptomic integrability.
Results: We show the results of the investigation of pathological effects of
overexpression of ACE2 across different signalling pathways in multiple tissues
on cardiovascular functions. We provide a proof of concept of integrating a
large set of composable clinical models using molecular data to drive local and
global clinical parameters and derive future trajectories representing the
evolution of the physiological state of the patient. Significance: We argue
that the graph representation of a computational patient has potential to solve
important technological challenges in integrating multiscale computational
modelling with AI. We believe that this work represents a step forward towards
a healthcare digital twin.


  The finite nuclear-size effect on the leading bound-electron g factor and the
one-loop QED corrections to the bound-electron g factor is investigated for the
ground state of hydrogen-like ions. The calculation is performed to all orders
in the nuclear binding strength parameter Z\alpha\ (where Z is the nuclear
charge and \alpha\ is the fine structure constant) and for the Fermi model of
the nuclear charge distribution. In the result, theoretical predictions for the
isotope shift of the 1s bound-electron g factor are obtained, which can be used
for the determination of the difference of nuclear charge radii from
experimental values of the bound-electron g factors for different isotopes.


  This paper presents cross sections for the production of a W boson in
association with jets, measured in proton--proton collisions at $\sqrt{s}=7$
TeV with the ATLAS experiment at the Large Hadron Collider. With an integrated
luminosity of $4.6 fb^{-1}$, this data set allows for an exploration of a large
kinematic range, including jet production up to a transverse momentum of 1 TeV
and multiplicities up to seven associated jets. The production cross sections
for W bosons are measured in both the electron and muon decay channels.
Differential cross sections for many observables are also presented including
measurements of the jet observables such as the rapidities and the transverse
momenta as well as measurements of event observables such as the scalar sums of
the transverse momenta of the jets. The measurements are compared to numerous
QCD predictions including next-to-leading-order perturbative calculations,
resummation calculations and Monte Carlo generators.


  The current job survey shows that most software employees are planning to
change their job role due to high pay for recent jobs such as data scientists,
business analysts and artificial intelligence fields. The survey also indicated
that work life imbalances, low pay, uneven shifts and many other factors also
make employees think about changing their work life. In this paper, for an
efficient organisation of the company in terms of human resources, the proposed
system designed a model with the help of a random forest algorithm by
considering different employee parameters. This helps the HR department retain
the employee by identifying gaps and helping the organisation to run smoothly
with a good employee retention ratio. This combination of HR and data science
can help the productivity, collaboration and well-being of employees of the
organisation. It also helps to develop strategies that have an impact on the
performance of employees in terms of external and social factors.


  An extensive investigation of low frequency noise in single electron
transistors as a function of gain is presented. Comparing the output noise with
gain for a large number of bias points, it is found that the noise is dominated
by external charge noise. For low gains we find an additional noise
contribution which is compared to a model including resistance fluctuations. We
conclude that this excess noise is not only due to resistance fluctuations. For
one sample, we find a record low minimum charge noise of qn = 9*10^-6
e/sqrt(Hz) in the superconducting state and qn = 9*10^-6 e/sqrt(Hz) in the
normal state at a frequency of 4.4 kHz.


  We consider recurrent solutions of the nonautonomous modified Swift-Hohenberg
equation $$u_t+\Delta^2u+2\Delta u+au+b|\nabla u|^2+u^3=g(t,x).$$ We employ
Conley index theory to show that, if the forcing $g:\mathbb{R}\rightarrow
L^2(\Omega)$ is a recurrent function, then there are at least two recurrent
solutions in $H_0^2(\Omega)$ under appropriate assumptions on the parameters
$a$, $b$ and $g$.


  We consider penalized estimation in hidden Markov models (HMMs) with
multivariate Normal observations. In the moderate-to-large dimensional setting,
estimation for HMMs remains challenging in practice, due to several concerns
arising from the hidden nature of the states. We address these concerns by
$\ell_1$-penalization of state-specific inverse covariance matrices. Penalized
estimation leads to sparse inverse covariance matrices which can be interpreted
as state-specific conditional independence graphs. Penalization is nontrivial
in this latent variable setting; we propose a penalty that automatically adapts
to the number of states $K$ and the state-specific sample sizes and can cope
with scaling issues arising from the unknown states. The methodology is
adaptive and very general, applying in particular to both low- and
high-dimensional settings without requiring hand tuning. Furthermore, our
approach facilitates exploration of the number of states $K$ by coupling
estimation for successive candidate values $K$. Empirical results on simulated
examples demonstrate the effectiveness of the proposed approach. In a
challenging real data example from genome biology, we demonstrate the ability
of our approach to yield gains in predictive power and to deliver richer
estimates than existing methods.


  This paper proposes an algorithm for deciding consistency of systems of
Boolean equations in several variables with co-efficients in the two element
Boolean algebra $B_{0}=\{0,1\}$ and find all satisfying assignments. The
algorithm is based on the application of a well known generalized Boole-Shannon
orthonormal (ON) expansion of Boolean functions. A necessary and sufficient
consistency condition for a special class of functions was developed in
\cite{sule} using such an expansion. Paper \cite{sule} develops a condition for
consistency of the equation $f(X)=0$ for the special classes of Boolean
functions 1) $f$ in $B(\Phi(X))$ for an ON set $\Phi$ of Boolean functions in
$X$ over a general Boolean algebra $B$ and 2) $f$ in $B(X_{2})(\Phi(X_{1}))$.
The present paper addresses the problem of obtaining the consistency conditions
for arbitrary Boolean functions in $B_{0}(X)$. Next, the consistency for a
single equation is shown equivalent to another system of Boolean equations
which involves the ON functions and characterizes all solutions. This result is
then extended for Boolean systems in several variables over the algebra
$B_{0}=\{0,1\}$ which does not convert the system into a single equation. This
condition leads to the algorithm for computing all solutions of the Boolean
system without using analogous resolution and determine satisfiability. For
special systems defined by CNF formulas this algorithm results into an
extension of the DPLL algorithm in which the \emph{splitting rule} is
generalized to several variables in terms of ON terms in the sense that
splitting of CNF set in a single variable $x$ is equivalent to ON terms $x,x'$.


  We show that, for every set of $n$ points in the $d$-dimensional unit cube,
there is an empty axis-parallel box of volume at least $\Omega(d/n)$ as
$n\to\infty$ and $d$ is fixed. In the opposite direction, we give a
construction without an empty axis-parallel box of volume $O(d^2\log d/n)$.
These improve on the previous best bounds of $\Omega(\log d/n)$ and
$O(2^{7d}/n)$ respectively.


  Scanning acoustic microscopy (SAM) has been employed since microscopic images
are widely used for biomedical or materials research. Acoustic imaging is an
important and well-established method used in nondestructive testing (NDT),
bio-medical imaging, and structural health monitoring.The imaging is frequently
carried out with signals of low amplitude, which might result in leading that
are noisy and lacking in details of image information. In this work, we
attempted to analyze SAM images acquired from low amplitude signals and
employed a block matching filter over time domain signals to obtain a denoised
image. We have compared the images with conventional filters applied over time
domain signals, such as the gaussian filter, median filter, wiener filter, and
total variation filter. The noted outcomes are shown in this article.


  This expository note delves into the theory of projective modules parallel to
the one developed for injective modules by Matlis. Given a perfect ring $R$, we
present a characterization of indecomposable projective $R$-modules and
describe a one-to-one correspondence between the projective indecomposable
$R$-modules and the simple $R$-modules.


  Extreme mass ratio bursts (EMRBs) have been proposed as a possible source for
future space-borne gravitational wave detectors, such as the Laser
Interferometer Space Antenna (LISA). These events are characterized by
long-period, nearly-radial orbits of compact objects around a central massive
black hole. The gravitational radiation emitted during such events consists of
a short burst, corresponding to periapse passage, followed by a longer, silent
interval. In this paper we investigate the impact of including relativistic
corrections to the description of the compact object's trajectory via a
geodesic treatment, as well as including higher-order multipole corrections in
the waveform calculation. The degree to which the relativistic corrections are
important depends on the EMRB's orbital parameters. We find that relativistic
EMRBs (v_{max}}/c > 0.25) are not rare and actually account for approximately
half of the events in our astrophysical model. The relativistic corrections
tend to significantly change the waveform amplitude and phase relative to a
Newtonian description, although some of this dephasing could be mimicked by
parameter errors. The dephasing over several bursts could be of particular
importance not only to gravitational wave detection, but also to parameter
estimation, since it is highly correlated to the spin of the massive black
hole. Consequently, we postulate that if a relativistic EMRB is detected, such
dephasing might be used to probe the relativistic character of the massive
black hole and obtain information about its spin.


  In this work and the supporting Parts II [2] and III [3], we provide a rather
detailed analysis of the stability and performance of asynchronous strategies
for solving distributed optimization and adaptation problems over networks. We
examine asynchronous networks that are subject to fairly general sources of
uncertainties, such as changing topologies, random link failures, random data
arrival times, and agents turning on and off randomly. Under this model, agents
in the network may stop updating their solutions or may stop sending or
receiving information in a random manner and without coordination with other
agents. We establish in Part I conditions on the first and second-order moments
of the relevant parameter distributions to ensure mean-square stable behavior.
We derive in Part II expressions that reveal how the various parameters of the
asynchronous behavior influence network performance. We compare in Part III the
performance of asynchronous networks to the performance of both centralized
solutions and synchronous networks. One notable conclusion is that the
mean-square-error performance of asynchronous networks shows a degradation only
of the order of $O(\nu)$, where $\nu$ is a small step-size parameter, while the
convergence rate remains largely unaltered. The results provide a solid
justification for the remarkable resilience of cooperative networks in the face
of random failures at multiple levels: agents, links, data arrivals, and
topology.


  We present a parallel algorithm for the undirected $s,t$-mincut problem with
floating-point valued weights. Our overarching algorithm uses an iteratively
reweighted least squares framework. This generates a sequence of Laplacian
linear systems, which we solve using parallel matrix algorithms. Our overall
implementation is up to 30-times faster than a serial solver when using 128
cores.


  We discuss the feasibility of quantum Hall states of vortices in trapped
low-density two-dimensional Bose gases with large particle interactions. For
interaction strengths larger than a critical dimensionless 2D coupling constant
$g_c \approx 0.6$, upon increasing the rotation frequency, the system is shown
to spatially separate into vortex lattice and melted vortex lattice (vortex
liquid) phases. At a first critical frequency, the lattice melts completely,
and strongly correlated vortex and particle quantum Hall liquids coexist in
inner respectively outer regions of the gas cloud. Finally, at a second
critical frequency, the vortex liquid disappears and the strongly correlated
particle quantum Hall state fills the whole sample.


  We explore constraints on dark energy and modified gravity with forecast 21cm
intensity mapping measurements using the Effective Field Theory approach. We
construct a realistic mock data set forecasting a low redshift 21cm signal
power spectrum $P_{21}(z,k)$ measurement from the MeerKAT radio-telescope. We
compute constraints on cosmological and model parameters through Monte Carlo
Markov chain techniques, testing both the constraining power of $P_{21}(k)$
alone and its effect when combined with the latest Planck 2018 CMB data. We
complement our analysis by testing the effects of tomography from an ideal mock
data set of observations in multiple redshift bins. We conduct our analysis
numerically with the codes EFTCAMB/EFTCosmoMC, which we extend by implementing
a likelihood module fully integrated with original codes. We find that adding
$P_{21}(k)$ to CMB data provides significantly tighter constraints on
$\Omega_ch^2$ and $H_0$, with a reduction of the error with respect to Planck
results at the level of more than $60\%$. For the parameters describing beyond
$\Lambda$CDM theories, we observe a reduction in the error with respect to the
Planck constraints at the level of $\lesssim 10\%$. The improvement increases
up to $\sim 35\%$ when we constrain the parameters using ideal, tomographic
mock observations. We conclude that the power spectrum of the 21cm signal is
sensitive to variations of the parameters describing the examined beyond
$\Lambda$CDM models and, thus, $P_{21}(k)$ observations could help to constrain
dark energy. The constraining power on such theories is improved significantly
by tomography.


  We investigate language interpretations of two extensions of the Lambek
calculus: with additive conjunction and disjunction and with additive
conjunction and the unit constant. For extensions with additive connectives, we
show that conjunction and disjunction behave differently. Adding both of them
leads to incompleteness due to the distributivity law. We show that with
conjunction only no issues with distributivity arise. In contrast, there exists
a corollary of the distributivity law in the language with disjunction only
which is not derivable in the non-distributive system. Moreover, this
difference keeps valid for systems with permutation and/or weakening structural
rules, that is, intuitionistic linear and affine logics and affine
multiplicative-additive Lambek calculus. For the extension of the Lambek with
the unit constant, we present a calculus which reflects natural algebraic
properties of the empty word. We do not claim completeness for this calculus,
but we prove undecidability for the whole range of systems extending this
minimal calculus and sound w.r.t. language models. As a corollary, we show that
in the language with the unit there exissts a sequent that is true if all
variables are interpreted by regular language, but not true in language models
in general.


  We consider a synthetic aperture radar (SAR) system that uses
ultra-narrowband continuous waveforms (CW) as an illumination source. Such a
system has many practical advantages, such as the use of relatively simple,
low-cost and low-power transmitters, and in some cases, using the transmitters
of opportunity, such as TV, radio stations. Additionally, ultra-narrowband CW
signals are suitable for motion estimation due to their ability to acquire high
resolution Doppler information. In this paper, we present a novel synthetic
aperture imaging method for moving targets using a bi-static SAR system
transmitting ultra-narrowband continuous waveforms. Our method exploits the
high Doppler resolution provided by ultra-narrowband CW signals to image both
the scene reflectivity and to determine the velocity of multiple moving
targets. Starting from the first principle, we develop a novel forward model
based on the temporal Doppler induced by the movement of antennas and moving
targets. We form the reflectivity image of the scene and estimate the motion
parameters using a filtered-backprojection technique combined with a contrast
optimization method. Analysis of the point spread function of our image
formation method shows that reflectivity images are focused when the motion
parameters are estimated correctly. We present analysis of the velocity
resolution and the resolution of reconstructed reflectivity images. We analyze
the error between the correct and reconstructed position of targets due to
errors in velocity estimation. Extensive numerical simulations demonstrate the
performance of our method and validate the theoretical results.


  The Rashba$^4$ model is a lattice model of interacting fermions with a
tight-binding dispersion relation that exhibits four Rashba band crossing
points at the same energy. The fermions interact weakly, by an on-site
repulsion and an additional nearest-neighbour two-body interaction, which may
be attractive or repulsive. We study this model when the Fermi energy is at or
close to the band crossings, by a combination of renormalization group flow
equations and mean-field theory. We find that the scattering processes between
different Rashba points drive superconductivity of an unusual triplet type not
found in models with a single Rashba point.


  In the study of stars, the high energy domain occupies a place of choice,
since it is the only one able to directly probe the most violent phenomena:
indeed, young pre-main sequence objects, hot massive stars, or X-ray binaries
are best revealed in X-rays. However, previously available X-ray observatories
often provided only crude information on individual objects in the Magellanic
Clouds. The advent of the highly efficient X-ray facilities XMM-Newton and
Chandra has now dramatically increased the sensitivity and the spatial
resolution available to X-ray astronomers, thus enabling a fairly easy
determination of the properties of individual sources in the LMC.


  This Letter presents the first measurement of event-by-event fluctuations of
the net number (difference between the particle and antiparticle
multiplicities) of multistrange hadrons $\Xi^-$ and $\overline{\Xi}^+$ and its
correlation with the net-kaon number using the data collected by the ALICE
Collaboration in pp, p$-$Pb, and Pb$-$Pb collisions at a center-of-mass energy
per nucleon pair $\sqrt{s_{\mathrm{NN}}}=5.02\ \mathrm{TeV}$. The statistical
hadronization model with a correlation over three units of rapidity between
hadrons having the same and opposite strangeness content successfully describes
the results. On the other hand, string-fragmentation models that mainly
correlate strange hadrons with opposite strange quark content over a small
rapidity range fail to describe the data.


  We show that the set of frequently universal harmonic functions on a tree T
contains a vector space except 0 which is dense in the space of harmonic
functions on T seen as subset of C^T . In order to prove this we replace the
complex plane C by any separable Frechet space E and we repeat all the theory.


  Autonomous driving has garnered significant attention as a key research area
within artificial intelligence. In the context of autonomous driving scenarios,
the varying physical locations of objects correspond to different levels of
danger. However, conventional evaluation criteria for automatic driving object
detection often overlook the crucial aspect of an object's physical location,
leading to evaluation results that may not accurately reflect the genuine
threat posed by the object to the autonomous driving vehicle. To enhance the
safety of autonomous driving, this paper introduces a novel evaluation
criterion based on physical location information, termed PLoc. This criterion
transcends the limitations of traditional criteria by acknowledging that the
physical location of pedestrians in autonomous driving scenarios can provide
valuable safety-related information. Furthermore, this paper presents a newly
re-annotated dataset (ApolloScape-R) derived from ApolloScape. ApolloScape-R
involves the relabeling of pedestrians based on the significance of their
physical location. The dataset is utilized to assess the performance of various
object detection models under the proposed PLoc criterion. Experimental results
demonstrate that the average accuracy of all object detection models in
identifying a person situated in the travel lane of an autonomous vehicle is
lower than that for a person on a sidewalk. The dataset is publicly available
at https://github.com/lnyrlyed/ApolloScape-R.git


  We propose Moebius maps as a tool to model synchronization phenomena in
coupled phase oscillators. Not only does the map provide fast computation of
phase synchronization, it also reflects the underlying group structure of the
sinusoidally coupled continuous phase dynamics. We study map versions of
various known continuous-time collective dynamics, such as the synchronization
transition in the Kuramoto-Sakaguchi model of non-identical oscillators,
chimeras in two coupled populations of identical phase oscillators, and
Kuramoto-Battogtokh chimeras on a ring, and demonstrate similarities and
differences between the iterated map models and their known continuous-time
counterparts.


  In this paper, we investigate Cauchy problem of the two-dimensional full
Maxwell-Navier-Stokes system, and prove the global-in-time existence and
uniqueness of solution in the borderline space which is very close to
$L^2$-energy space by developing the new estimate of $\sup_{j\in\mathbb Z}
2^{2j} \int_0^t \sum_{k\in\mathbb{Z}^2} \big\| \sqrt{\phi_{i,k}} u(\tau)
\big\|^2_{L^2(\mathbb{R}^2)} \text{d}\tau < \infty$. This solves the open
problem in the framework of borderline space purposed by Masmoudi in
\cite{Masmoudi-10}.


  We introduce a framework based on Rockafellar's perturbation theory to
analyze and solve general nonsmooth convex minimization and monotone inclusion
problems involving nonlinearly composed functions as well as linear
compositions. Such problems have been investigated only from a primal
perspective and only for nonlinear compositions of smooth functions in
finite-dimensional spaces in the absence of linear compositions. In the context
of Banach spaces, the proposed perturbation analysis serves as a foundation for
the construction of a dual problem and of a maximally monotone Kuhn--Tucker
operator which is decomposable as the sum of simpler monotone operators. In the
Hilbertian setting, this decomposition leads to a block-iterative primal-dual
algorithm that fully splits all the components of the problem and appears to be
the first proximal splitting algorithm for handling nonlinear composite
problems. Various applications are discussed.


  In this paper we show that the interaction between new light dark matter
mediators and the SM particles can be naturally suppressed if one employs a
single, flat extra dimension (ED). In this setup, the SM fields are localized
in a finite width `fat' brane, similar to models of Universal Extra Dimensions
(UED), while DM, in turn, is confined to a thin brane at the opposite end of
the ED interval. Including brane localized kinetic terms on the fat brane for
the mediator fields, the resulting coupling between the SM and these light
mediators can be several orders of magnitude smaller than the corresponding
ones between the mediators and DM which we assume to be a typical gauge
coupling. We investigate the implications of this scenario for both vector
(i.e., dark photon, DP) and scalar mediator fields in the 5-D bulk. In this
setup kinetic mixing, which is usually employed to suppress light mediator
couplings, is not required. Here we assume that the SM particles couple to the
DP via their $B-L$ charges while the DP couples to the DM via a dark charge.
Both the vector DP couplings and the corresponding Higgs portal couplings with
the SM are shown to be natural small in magnitude with a size dependent on
ratio of the 5-D compactification radius, $R^{-1} \sim 0.1-1$ GeV, and the SM
brane thickness, $L^{-1} \sim 2-10$ TeV, a range chosen to avoid LHC and other
experimental constraints. In this framework one can obtain the observed value
of the DM relic abundance for a wide range of parameter choices, while the
constrains due to direct DM detection and the invisible width of the Higgs do
not impose significant challenges to the model. Finally, this mechanism can
lead to distinct signatures in both present and upcoming experiments as it
combines some common features of UED and DP models in a single ED setup.


  While large language models exhibit remarkable performance in the Question
Answering task, they are susceptible to hallucinations. Challenges arise when
these models grapple with understanding multi-hop relations in complex
questions or lack the necessary knowledge for a comprehensive response. To
address this issue, we introduce the "Decompose-and-Query" framework (D&Q).
This framework guides the model to think and utilize external knowledge similar
to ReAct, while also restricting its thinking to reliable information,
effectively mitigating the risk of hallucinations. Experiments confirm the
effectiveness of D&Q: On our ChitChatQA dataset, D&Q does not lose to ChatGPT
in 67% of cases; on the HotPotQA question-only setting, D&Q achieved an F1
score of 59.6%. Our code is available at
https://github.com/alkaidpku/DQ-ToolQA.


  Source-controlled routing has been proposed as a way to improve flexibility
of future network architectures, as well as simplifying the data plane.
However, if a packet specifies its path, this precludes fast local re-routing
within the network. We propose SlickPackets, a novel solution that allows
packets to slip around failures by specifying alternate paths in their headers,
in the form of compactly-encoded directed acyclic graphs. We show that this can
be accomplished with reasonably small packet headers for real network
topologies, and results in responsiveness to failures that is competitive with
past approaches that require much more state within the network. Our approach
thus enables fast failure response while preserving the benefits of
source-controlled routing.


  Recently, air pollution is one of the most concerns for big cities.
Predicting air quality for any regions and at any time is a critical
requirement of urban citizens. However, air pollution prediction for the whole
city is a challenging problem. The reason is, there are many spatiotemporal
factors affecting air pollution throughout the city. Collecting as many of them
could help us to forecast air pollution better. In this research, we present
many spatiotemporal datasets collected over Seoul city in Korea, which is
currently much suffered by air pollution problem as well. These datasets
include air pollution data, meteorological data, traffic volume, average
driving speed, and air pollution indexes of external areas which are known to
impact Seoul's air pollution. To the best of our knowledge, traffic volume and
average driving speed data are two new datasets in air pollution research. In
addition, recent research in air pollution has tried to build models to
interpolate and predict air pollution in the city. Nevertheless, they mostly
focused on predicting air quality in discrete locations or used hand-crafted
spatial and temporal features. In this paper, we propose the usage of
Convolutional Long Short-Term Memory (ConvLSTM) model \cite{b16}, a combination
of Convolutional Neural Networks and Long Short-Term Memory, which
automatically manipulates both the spatial and temporal features of the data.
Specially, we introduce how to transform the air pollution data into sequences
of images which leverages the using of ConvLSTM model to interpolate and
predict air quality for the entire city at the same time. We prove that our
approach is suitable for spatiotemporal air pollution problems and also
outperforms other related research.