  Needlets have been recognized as state-of-the-art tools to tackle spherical
data, due to their excellent localization properties in both spacial and
frequency domains.
  This paper considers developing kernel methods associated with the needlet
kernel for nonparametric regression problems whose predictor variables are
defined on a sphere. Due to the localization property in the frequency domain,
we prove that the regularization parameter of the kernel ridge regression
associated with the needlet kernel can decrease arbitrarily fast. A natural
consequence is that the regularization term for the kernel ridge regression is
not necessary in the sense of rate optimality. Based on the excellent
localization property in the spacial domain further, we also prove that all the
$l^{q}$ $(01\leq q < \infty)$ kernel regularization estimates associated with
the needlet kernel, including the kernel lasso estimate and the kernel bridge
estimate, possess almost the same generalization capability for a large range
of regularization parameters in the sense of rate optimality.
  This finding tentatively reveals that, if the needlet kernel is utilized,
then the choice of $q$ might not have a strong impact in terms of the
generalization capability in some modeling contexts. From this perspective, $q$
can be arbitrarily specified, or specified merely by other no generalization
criteria like smoothness, computational complexity, sparsity, etc..


  Developing an operating system (OS) for low-end embedded devices requires
continuous adaptation to new hardware architectures and components, while
serviceability of features needs to be assured for each individual platform
under tight resource constraints. It is challenging to design a versatile and
accurate heterogeneous test environment that is agile enough to cover a
continuous evolution of the code base and platforms. This mission is even
morehallenging when organized in an agile open-source community process with
many contributors such as for the RIOT OS. Hardware in the Loop (HiL) testing
and Continuous Integration (CI) are automatable approaches to verify
functionality, prevent regressions, and improve the overall quality at
development speed in large community projects. In this paper, we present PHiLIP
(Primitive Hardware in the Loop Integration Product), an open-source external
reference device together with tools that validate the system software while it
controls hardware and interprets physical signals. Instead of focusing on a
specific test setting, PHiLIP takes the approach of a tool-assisted agile HiL
test process, designed for continuous evolution and deployment cycles. We
explain its design, describe how it supports HiL tests, evaluate performance
metrics, and report on practical experiences of employing PHiLIP in an
automated CI test infrastructure. Our initial deployment comprises 22 unique
platforms, each of which executes 98 peripheral tests every night. PHiLIP
allows for easy extension of low-cost, adaptive testing infrastructures but
serves testing techniques and tools to a much wider range of applications.


  In this note we give a short and elementary proof of a more general version
of Whitney's theorem that 3-connected planar graphs have a unique embedding in
the plane. A consequence of the theorem is that cubic plane graphs cannot be
embedded in a higher genus with a simple dual. The aim of this paper is to
promote a simple and elementary proof, which is especially well suited for
lectures presenting Whitney's theorem.


  We report first-principles calculations of local heating in nanoscale
junctions formed by a single molecule and a gold point contact. Due to a larger
heat dissipation, the single molecule heats up less than the gold point
contact. We also find, at zero temperature, a threshold bias $V_{onset}$ of
about 6 mV and 11 mV for the molecule and the point contact, respectively, is
required to excite the smallest vibrational mode and generate heat. The latter
estimate is in very good agreement with recent experimental results on the same
system. At a given external bias $V$ below $V_{onset}$, heating becomes
noticeable when the background temperature is on the order of $\sim
e(V_{onset}-V)/k_{B}$. Above $V_{onset}$, local heating increases dramatically
with increasing bias but is also considerably suppressed by thermal dissipation
into the electrodes. The results provide a microscopic picture of
current-induced heat generation in atomic-scale structures.


  Some results in QCD_2 at large N are presented using the reduced model on the
lattice. Overlap fermions are used to compute meson propagators.


  We show how the Equation-Free approach for multi-scale computations can be
exploited to systematically study the dynamics of neural interactions on a
random regular connected graph under a pairwise representation perspective.
Using an individual-based microscopic simulator as a black box coarse-grained
timestepper and with the aid of simulated annealing we compute the
coarse-grained equilibrium bifurcation diagram and analyze the stability of the
stationary states sidestepping the necessity of obtaining explicit closures at
the macroscopic level. We also exploit the scheme to perform a rare-events
analysis by estimating an effective Fokker-Planck describing the evolving
probability density function of the corresponding coarse-grained observables.


  We study spacetime estimates for the wave map null form $Q_0$ on $\mathbb{R}
\times \mathbb{S}^3$. By using the Lie group structure of $\mathbb{S}^3$ and
Peter-Weyl theory, combined with the time-periodicity of the conformal wave
equation on $\mathbb{R} \times \mathbb{S}^3$, we extend the classical ideas of
Klainerman and Machedon to estimates on $\mathbb{R} \times \mathbb{S}^3$,
allowing for a range of powers of natural (Laplacian and wave) Fourier
multiplier operators. A key difference in these curved space estimates as
compared to the flat case is a loss of an arbitrarily small amount of
differentiability, attributable to a lack of dispersion of linear waves on
$\mathbb{R} \times \mathbb{S}^3$. This arises in Fourier space from the product
structure of irreducible representations of $\mathrm{SU}(2)$. We further show
that our estimates imply weighted estimates for the null form on Minkowski
space.


  This paper addresses the problem of utility maximization under uncertain
parameters. In contrast with the classical approach, where the parameters of
the model evolve freely within a given range, we constrain them via a penalty
function. We show that this robust optimization process can be interpreted as a
two-player zero-sum stochastic differential game. We prove that the value
function satisfies the Dynamic Programming Principle and that it is the unique
viscosity solution of an associated Hamilton-Jacobi-Bellman-Isaacs equation. We
test this robust algorithm on real market data. The results show that robust
portfolios generally have higher expected utilities and are more stable under
strong market downturns. To solve for the value function, we derive an
analytical solution in the logarithmic utility case and obtain accurate
numerical approximations in the general case by three methods: finite
difference method, Monte Carlo simulation, and Generative Adversarial Networks.


  In this paper, we show some applications to algebraic cycles by using higher
Abel-Jacobi maps which were defined in [the author: Motives and algebraic de
Rham cohomology]. In particular, we prove that the Beilinson conjecture on
algebraic cycles over number fields implies the Bloch conjecture on zero-cycles
on surfaces. Moreover, we construct a zero-cycle on a product of curves whose
Mumford invariant vanishes, but not higher Abel-Jacobi invariant.


  This study introduces a transformative framework for medical education by
integrating semi-structured data with Large Language Models (LLMs), primarily
OpenAIs ChatGPT3.5, to automate the creation of medical simulation scenarios.
Traditionally, developing these scenarios was a time-intensive process with
limited flexibility to meet diverse educational needs. The proposed approach
utilizes AI to efficiently generate detailed, clinically relevant scenarios
that are tailored to specific educational objectives. This innovation has
significantly reduced the time and resources required for scenario development,
allowing for a broader variety of simulations. Preliminary feedback from
educators and learners has shown enhanced engagement and improved knowledge
acquisition, confirming the effectiveness of this AI-enhanced methodology in
simulation-based learning. The integration of structured data with LLMs not
only streamlines the creation process but also offers a scalable, dynamic
solution that could revolutionize medical training, highlighting the critical
role of AI in advancing educational outcomes and patient care standards.


  Reimann and Slaman initiated the study of sequences that are Martin-L\"of
random with respect to a continuous measure, establishing fundamental facts
about NCR, the collection of sequences that are not Martin-L\"of random with
respect to any continuous measure. In the case of sequences that are random
with respect to a computable, continuous measure, the picture is fairly
well-understood: such sequences are truth-table equivalent to a Martin-L\"of
random sequence. However, given a sequence that is random with respect to a
continuous measure but not with respect to any computable measure, we can ask:
how close to effective is the measure with respect to which it is continuously
random?
  In this study, we take up this question by examining various transformations
of 2-random sequences (sequences that are Martin-L\"of random relative to the
halting set $\emptyset'$) to establish several results on sequences that are
continuously random with respect to a measure that is computable in
$\emptyset'$. In particular, we show that (i) every noncomputable sequence that
is computable from a 2-random sequence is Martin-L\"of random with respect to a
continuous, $\emptyset'$-computable measure and (ii) the Turing jump of every
2-random sequence is Martin-L\"of random with respect to a continuous,
$\emptyset'$-computable measure. From these results, we obtain examples of
sequences that are not proper, i.e., not random with respect to any computable
measure, but are random with respect to a continuous, $\emptyset'$-computable
measure. Lastly, we consider the behavior of 2-randomness under a wider class
of effective operators (c.e. operators, pseudojump operators, and operators
defined in terms of pseudojump inversion), showing that these too yield
sequences that are Martin-L\"of random with respect to a continuous,
$\emptyset'$-computable measure.


  We review the physics involved in the production and decay of top quarks in
e^+e^- -> ttbar near threshold, with special emphasis on the recent theoretical
study on the decay process of top quarks in the threshold region. The
energy-angular distribution of l^+ in semileptonic top decays is calculated
including the full O(alpha_s) corrections. Various effects of the final-state
interactions are elucidated. A new observable is defined near threshold, which
depends only on the decay of free polarized top quarks, and thus it can be
calculated without bound-state effects or the final-state interactions.


  Quantum energy transfer in a chain of two-level (spin) units, connected at
its ends to two thermal reservoirs, is analyzed in two limits: (i) In the
off-resonance regime, when the characteristic subsystem excitation energy gaps
are larger than the reservoirs frequencies, or the baths temperatures are low.
(ii) In the resonance regime, when the chain excitation gaps match populated
bath modes. In the latter case the model is studied using a master equation
approach, showing that the dynamics is ballistic for the particular chain model
explored. In the former case we analytically study the system dynamics
utilizing the recently developed Energy-Transfer Born-Oppenheimer formalism
[Phys. Rev. E {\bf 83}, 051114 (2011)], demonstrating that energy transfers
across the chain in a superexchange (bridge assisted tunneling) mechanism, with
the energy current decreasing exponentially with distance. This behavior is
insensitive to the chain details. Since at low temperatures the excitation
spectrum of molecular systems can be truncated to resemble a spin chain model,
we argue that the superexchange behavior obtained here should be observed in
widespread systems satisfying the off-resonance condition.


  By taking the high-energy limit of the two-loop and the three-loop four-point
amplitudes in the maximally supersymmetric N=4 Yang-Mill theory (MSYM), we test
the validity of the loop expansion of the high-energy amplitude, beyond the
next-to-leading-logarithmic (NLL) accuracy. We compute the three-loop Regge
trajectory, and the two-loop and three-loop coefficient functions. These
quantities are relevant for the BFKL evolution beyond NLL, as well as building
MSYM two-loop and three-loop amplitudes with many legs in the high-energy
limit, which in turn may be used as a powerful check of the evaluation of the
corresponding exact amplitudes.


  In this study, a novel physics-data-driven Bayesian method named Heat
Conduction Equation assisted Bayesian Neural Network (HCE-BNN) is proposed. The
HCE-BNN is constructed based on the Bayesian neural network, it is a
physics-informed machine learning strategy. Compared with the existed pure data
driven method, to acquire physical consistency and better performance of the
data-driven model, the heat conduction equation is embedded into the loss
function of the HCE-BNN as a regularization term. Hence, the proposed method
can build a more reliable model by physical constraints with less data. The
HCE-BNN can handle the forward and inverse problems consistently, that is, to
infer unknown responses from known partial responses, or to identify boundary
conditions or material parameters from known responses. Compared with the exact
results, the test results demonstrate that the proposed method can be applied
to both heat conduction forward and inverse problems successfully. In addition,
the proposed method can be implemented with the noisy data and gives the
corresponding uncertainty quantification for the solutions.


  Padberg introduced a geometric notion of ranks for (mixed) integer rational
polyhedrons and conjectured that the geometric rank of the matching polytope is
one. In this work, we prove that this conjecture is true.


  Controlling the quantum properties of individual fluorescent defects in
silicon is a key challenge towards advanced quantum photonic devices prone to
scalability. Research efforts have so far focused on extrinsic defects based on
impurities incorporated inside the silicon lattice. Here we demonstrate the
detection of single intrinsic defects in silicon, which are linked to a
tri-interstitial complex called W-center, with a zero-phonon line at
1.218${\mu}$m. Investigating their single-photon emission properties reveals
new information about this common radiation damage center, such as its dipolar
orientation and its photophysics. We also identify its microscopic structure
and show that although this defect does not feature electronic states in the
bandgap, Coulomb interactions lead to excitonic radiative recombination below
the silicon bandgap. These results could set the stage for numerous quantum
perspectives based on intrinsic luminescent defects in silicon, such as quantum
integrated photonics, quantum communications and quantum sensing.


  The origin of phosphorus, one of the essential elements for life on Earth, is
currently unknown. Prevalent models of Galactic chemical evolution (GCE)
underestimate the amount of P compared to observations. The recently discovered
P-rich ([P/Fe] > 1 dex) and metal-poor giants further challenge current
theories on stellar nucleosynthesis. Since the observed stars are low-mass
giants, our primary goal is to find clues on their progenitor. By increasing
the number of known P-rich stars, we aim to narrow down a reliable chemical
abundance pattern and to place robust constraints on the responsible
nucleosynthetic mechanism. In the long term, identifying the progenitor of the
P-rich stars may contribute to the search for the source of P in our Galaxy. We
performed a detailed chemical abundance analysis based on the H-band spectra
from APOGEE-2 (DR17). Employing the BACCHUS code, we measured the abundances of
13 elements in the sample, which is mainly composed of a recent collection of
Si-enhanced giants. We also analyzed the orbital motions and compared the
abundance results to possible nucleosynthetic formation scenarios, and also to
detailed GCE models. We enlarged the sample of confirmed P-rich stars from 16
to 78 giants, which represents the largest sample of P-rich stars to date.
Significant enhancements in O, Al, Si and Ce, as well as systematic
correlations among the elements, unveil the chemical fingerprint of the P-rich
stars. The high Mg and C+N found in some of the P-rich stars with respect to
P-normal stars is not confirmed over the full sample. Strikingly, the strong
over-abundance in the $\alpha$-element Si is accompanied by normal Ca and S
abundances. Our analysis of the orbital motion showed that the P-rich stars do
not belong to a specific sub-population. In addition, we confirm that the
majority of the sample stars are not part of binary systems.


  A small scale bipolar transistor with polysilicon emitter will, depending on
the emitter window size, display suppression of the hole tramsport due to
single electron effects. In this paper the resulting base current suppression
is computed in terms of the orthodox theory of single electron tunneling and a
recombination time approximation. The possible application of the transistor as
readout system for Coulomb blockade device circuits is discussed.


  We consider a random variable expressed as the Euclidean distance between an
arbitrary point and a random variable uniformly distributed in a closed and
bounded set of a three-dimensional Euclidean space. Four cases are considered
for this set: a union of disjoint disks, a union of disjoint balls, a union of
disjoint line segments, and the boundary of a polyhedron. In the first three
cases, we provide closed-form expressions of the cumulative distribution
function and the density. In the last case, we propose an algorithm with
complexity O(n ln n), n being the number of edges of the polyhedron, that
computes exactly the cumulative distribution function. An application of these
results to probabilistic seismic hazard analysis and extensions are discussed.


  A major prerequisite for the application of machine learning models in
clinical decision making is trust and interpretability. Current explainability
studies in the neuroimaging community have mostly focused on explaining
individual decisions of trained models, e.g. obtained by a convolutional neural
network (CNN). Using attribution methods such as layer-wise relevance
propagation or SHAP heatmaps can be created that highlight which regions of an
input are more relevant for the decision than others. While this allows the
detection of potential data set biases and can be used as a guide for a human
expert, it does not allow an understanding of the underlying principles the
model has learned. In this study, we instead show, to the best of our
knowledge, for the first time results using feature visualization of
neuroimaging CNNs. Particularly, we have trained CNNs for different tasks
including sex classification and artificial lesion classification based on
structural magnetic resonance imaging (MRI) data. We have then iteratively
generated images that maximally activate specific neurons, in order to
visualize the patterns they respond to. To improve the visualizations we
compared several regularization strategies. The resulting images reveal the
learned concepts of the artificial lesions, including their shapes, but remain
hard to interpret for abstract features in the sex classification task.


  Multi-robot coverage is crucial in numerous applications, including
environmental monitoring, search and rescue operations, and precision
agriculture. In modern applications, a multi-robot team must collaboratively
explore unknown spatial fields in GPS-denied and extreme environments where
global localization is unavailable. Coverage algorithms typically assume that
the robot positions and the coverage environment are defined in a global
reference frame. However, coordinating robot motion and ensuring coverage of
the shared convex workspace without global localization is challenging. This
paper proposes a novel anchor-oriented coverage (AOC) approach to generate
dynamic localized Voronoi partitions based around a common anchor position. We
further propose a consensus-based coordination algorithm that achieves
agreement on the coverage workspace around the anchor in the robots' relative
frames of reference. Through extensive simulations and real-world experiments,
we demonstrate that the proposed anchor-oriented approach using localized
Voronoi partitioning performs as well as the state-of-the-art coverage
controller using GPS.


  We present first calculations of the fluctuating gluon distribution in a
proton as a function of impact parameter and rapidity employing the functional
Langevin form of the JIMWLK renormalization group equation. We demonstrate that
when including effects of confinement by screening the long range Coulomb field
of the color charges, the evolution is unitary. The large-x structure of the
proton, characterized by the position of three valence quarks, retains an
effect on the proton shape down to very small values of x. We determine the
dipole scattering amplitude as a function of impact parameter and dipole size
and extract the rapidity evolution of the saturation scale and the proton
radius.


  We provide a theoretical explanation of the results on the intensity
distributions and correlation functions obtained from a random beam speckle
field in nonlinear bulk waveguides reported in the recent publication Y.
Bromberg et.al., Nat. Photonics \textbf{4}, 721 (2010). We study both focusing
and defocusing case and in the limit of small speckle size (short correlated
disordered beam) provide analytical asymptotes for the intensity probability
distributions at the output facet. Additionally we provide a simple relation
between the speckle sizes at the input and output of a focusing nonlinear
waveguide. The results are of practical significance for the nonlinear Hanbury
Brown and Twiss interferometry both in optical waveguides and Bose-Einstein
condensates.


  Quadratic unconstrained binary optimization (QUBO) is the mathematical
formalism for phrasing and solving a class of optimization problems that are
combinatorial in nature. Due to their natural equivalence with the two
dimensional Ising model for ferromagnetism in statistical mechanics, problems
from the QUBO class can be solved on quantum annealing hardware. In this paper,
we report a QUBO formatting of the problem of optimal control of time-dependent
traffic signals on an artificial grid-structured road network so as to ease the
flow of traffic, and the use of D-Wave Systems' quantum annealer to solve it.
Since current-generation D-Wave annealers have a limited number of qubits and
limited inter-qubit connectivity, we adopt a hybrid (classical/quantum)
approach to this problem. As traffic flow is a continuous and evolving
phenomenon, we address this time-dependent problem by adopting a workflow to
generate and solve multiple problem instances periodically.


  At MOVES 2019, Barry Cipra casually introduced a new "Sol Lewitt" puzzle to
fellow conference goers. Several brainstorming sessions ensued with Barry,
Peter Winkler , Donna Dietz, and other attendees. This paper is to document the
puzzle and some insights so others can enjoy and build on this lovely puzzle.
(Look for it in an upcoming book by Peter!)


  We generalize two integral representation formulae of Nevanlinna to functions
of several variables. We show that for a large class of analytic functions that
have non-negative imaginary part on the upper polyhalfplane there are
representation formulae in terms of densely defined self-adjoint operators on a
Hilbert space. We introduce three types of structured resolvent of a
self-adjoint operator and identify four different types of representation in
terms of these resolvents. We relate the types of representation that a
function admits to its growth at infinity.


  The Griffiths phase in systems with quenched disorder occurs below the
ordering transition of the pure system down to the ordering transition of the
actual disordered system. While it does not exhibit long-range order, large
fluctuations in the disorder degrees of freedom result in exponentially rare,
long-range ordered states and hence the occurrence of broad distributions in
response functions. Inside the Griffiths phase of the two-dimensional
bond-diluted Ising model the distribution of the magnetic susceptibility is
expected to have such a broad, exponential tail. A large-deviations Monte Carlo
algorithm is used to sample this distribution and the exponential tail is
extracted over a wide range of the support down to very small probabilities of
the order of $10^{-300}$. We study the behavior of the susceptibility
distribution across the full phase diagram, from the paramagnetic state through
the Griffiths phase to the ferromagnetically ordered system and down to the
zero-temperature point. We extract the rate function of large-deviation theory
as well as its finite-size scaling behavior and we reveal interesting
differences and similarities between the cases. A connection between the
fraction of ferromagnetic bonds in a given disorder sample and the size of the
magnetic susceptibility is demonstrated numerically.


  In this paper we study a class of distribution dependent stochastic
differential equations driven by fractional Brownian motions with Hurst
parameter H\in(1/2,1). We prove the well-posedness of this type equations, and
then establish a general result on the Bismut formula for the Lions derivative
by using Malliavin calculus. As applications, we provide the Bismut formulas of
this kind for both non-degenerate and degenerate cases, and obtain the
estimates of the Lions derivative and the total variation distance between the
laws of two solutions.


  Within the framework of two-flavor covariant baryon chiral perturbation
theory we have expressed the Chernyak-Zhitnitsky, Ioffe and Dosch currents in
terms of chiral fields to provide leading one-loop extrapolation formulae for
the leading and next-to-leading twist normalization constants $f_N$,
$\lambda_1$ and $\lambda_2$. Finite volume effects due to pion loops have been
taken into account. The occurring low energy constants are fitted to data
obtained from recent lattice QCD simulations in order to extract the values at
the physical point.


  We reconsider the general constraints on the perturbative anomalous
dimensions in conformal invariant QFT and in particular in N=4 SYM with gauge
group SU(N_c). We show that all the perturbative corrections to the anomalous
dimension of a renormalized gauge invariant local operator can be written as
polynomials in its one loop anomalous dimension. In the N=4 SYM theory the
coefficients of these polynomials are rational functions of the number of
colours N_c.


  Road user trajectory prediction in dynamic environments is a challenging but
crucial task for various applications, such as autonomous driving. One of the
main challenges in this domain is the multimodal nature of future trajectories
stemming from the unknown yet diverse intentions of the agents. Diffusion
models have shown to be very effective in capturing such stochasticity in
prediction tasks. However, these models involve many computationally expensive
denoising steps and sampling operations that make them a less desirable option
for real-time safety-critical applications. To this end, we present a novel
framework that leverages diffusion models for predicting future trajectories in
a computationally efficient manner. To minimize the computational bottlenecks
in iterative sampling, we employ an efficient sampling mechanism that allows us
to maximize the number of sampled trajectories for improved accuracy while
maintaining inference time in real time. Moreover, we propose a scoring
mechanism to select the most plausible trajectories by assigning relative
ranks. We show the effectiveness of our approach by conducting empirical
evaluations on common pedestrian (UCY/ETH) and autonomous driving (nuScenes)
benchmark datasets on which our model achieves state-of-the-art performance on
several subsets and metrics.


  A crucial problem in learning disentangled image representations is
controlling the degree of disentanglement during image editing, while
preserving the identity of objects. In this work, we propose a simple yet
effective model with the encoder-decoder architecture to address this
challenge. To encourage disentanglement, we devise a distance covariance based
decorrelation regularization. Further, for the reconstruction step, our model
leverages a soft target representation combined with the latent image code. By
exploiting the real-valued space of the soft target representations, we are
able to synthesize novel images with the designated properties. We also design
a classification based protocol to quantitatively evaluate the disentanglement
strength of our model. Experimental results show that the proposed model
competently disentangles factors of variation, and is able to manipulate face
images to synthesize the desired attributes.


  Applying the concept of S-convergence, based on averaging in the spirit of
Strong Law of Large Numbers, the vanishing viscosity solutions of the Euler
system are studied. We show how to efficiently compute a viscosity solution of
the Euler system as the S-limit of numerical solutions obtained by the
Viscosity Finite Volume method. Theoretical results are illustrated by
numerical simulations of the Kelvin--Helmholtz instability problem.


  In a variety of settings, limitations of sensing technologies or other
sampling mechanisms result in missing labels, where the likelihood of a missing
label in the training set is an unknown function of the data. For example,
satellites used to detect forest fires cannot sense fires below a certain size
threshold. In such cases, training datasets consist of positive and
pseudo-negative observations where pseudo-negative observations can be either
true negatives or undetected positives with small magnitudes. We develop a new
methodology and non-convex algorithm P(ositive) U(nlabeled) - O(ccurrence)
M(agnitude) M(ixture) which jointly estimates the occurrence and detection
likelihood of positive samples, utilizing prior knowledge of the detection
mechanism. Our approach uses ideas from positive-unlabeled (PU)-learning and
zero-inflated models that jointly estimate the magnitude and occurrence of
events. We provide conditions under which our model is identifiable and prove
that even though our approach leads to a non-convex objective, any local
minimizer has optimal statistical error (up to a log term) and projected
gradient descent has geometric convergence rates. We demonstrate on both
synthetic data and a California wildfire dataset that our method out-performs
existing state-of-the-art approaches.


  In this paper, we study the complex Landsberg spaces and some of their
important subclasses. We introduce and characterize the class of generalized
Berwald and complex Landsberg spaces. The intersection of these spaces gives
the so called $G-$ Landsberg class.


  Recently, there has been an increasing interest in end-to-end speech
recognition that directly transcribes speech to text without any predefined
alignments. One approach is the attention-based encoder-decoder framework that
learns a mapping between variable-length input and output sequences in one step
using a purely data-driven method. The attention model has often been shown to
improve the performance over another end-to-end approach, the Connectionist
Temporal Classification (CTC), mainly because it explicitly uses the history of
the target character without any conditional independence assumptions. However,
we observed that the performance of the attention has shown poor results in
noisy condition and is hard to learn in the initial training stage with long
input sequences. This is because the attention model is too flexible to predict
proper alignments in such cases due to the lack of left-to-right constraints as
used in CTC. This paper presents a novel method for end-to-end speech
recognition to improve robustness and achieve fast convergence by using a joint
CTC-attention model within the multi-task learning framework, thereby
mitigating the alignment issue. An experiment on the WSJ and CHiME-4 tasks
demonstrates its advantages over both the CTC and attention-based
encoder-decoder baselines, showing 5.4-14.6% relative improvements in Character
Error Rate (CER).


  The proposed approach extends the confidence posterior distribution to the
semi-parametric empirical Bayes setting. Whereas the Bayesian posterior is
defined in terms of a prior distribution conditional on the observed data, the
confidence posterior is defined such that the probability that the parameter
value lies in any fixed subset of parameter space, given the observed data, is
equal to the coverage rate of the corresponding confidence interval. A
confidence posterior that has correct frequentist coverage at each fixed
parameter value is combined with the estimated local false discovery rate to
yield a parameter distribution from which interval and point estimates are
derived within the framework of minimizing expected loss. The point estimates
exhibit suitable shrinkage toward the null hypothesis value, making them
practical for automatically ranking features in order of priority. The
corresponding confidence intervals are also shrunken and tend to be much
shorter than their fixed-parameter counterparts, as illustrated with gene
expression data. Further, simulations confirm a theoretical argument that the
shrunken confidence intervals cover the parameter at a higher-than-nominal
frequency.


  We investigate consequences of the effective colour-dielectric formulation of
lattice gauge theory using the light-cone Hamiltonian formalism with a
transverse lattice (hep-ph/9704408). As a quantitative test of this approach,
we have performed extensive analytic and numerical calculations for
2+1-dimensional pure gauge theory in the large $N$ limit. We study the
structure of coupling constant space for our effective potential by comparing
with results available from conventional Euclidean lattice Monte Carlo
simulations of this system. In particular, we calculate and measure the scaling
behaviour of the entire low-lying glueball spectrum, glueball wavefunctions,
string tension, asymptotic density of states, and deconfining temperature.


  Since the global spread of Covid-19 began to overwhelm the attempts of
governments to conduct manual contact-tracing, there has been much interest in
using the power of mobile phones to automate the contact-tracing process
through the development of exposure notification applications. The rough idea
is simple: use Bluetooth or other data-exchange technologies to record contacts
between users, enable users to report positive diagnoses, and alert users who
have been exposed to sick users. Of course, there are many privacy concerns
associated with this idea. Much of the work in this area has been concerned
with designing mechanisms for tracing contacts and alerting users that do not
leak additional information about users beyond the existence of exposure
events. However, although designing practical protocols is of crucial
importance, it is essential to realize that notifying users about exposure
events may itself leak confidential information (e.g. that a particular contact
has been diagnosed). Luckily, while digital contact tracing is a relatively new
task, the generic problem of privacy and data disclosure has been studied for
decades. Indeed, the framework of differential privacy further permits provable
query privacy by adding random noise. In this article, we translate two results
from statistical privacy and social recommendation algorithms to exposure
notification. We thus prove some naive bounds on the degree to which accuracy
must be sacrificed if exposure notification frameworks are to be made more
private through the injection of noise.


  Approximate Nearest neighbor search (ANNS) is fundamental and essential
operation in applications from many domains, such as databases, machine
learning, multimedia, and computer vision. Although many algorithms have been
continuously proposed in the literature in the above domains each year, there
is no comprehensive evaluation and analysis of their performances.
  In this paper, we conduct a comprehensive experimental evaluation of many
state-of-the-art methods for approximate nearest neighbor search. Our study (1)
is cross-disciplinary (i.e., including 16 algorithms in different domains, and
from practitioners) and (2) has evaluated a diverse range of settings,
including 20 datasets, several evaluation metrics, and different query
workloads. The experimental results are carefully reported and analyzed to
understand the performance results. Furthermore, we propose a new method that
achieves both high query efficiency and high recall empirically on majority of
the datasets under a wide range of settings.


  This paper is motivated by the following question in sieve theory. Given a
subset $X\subset [N]$ and $\alpha\in (0,1/2)$. Suppose that $|X\pmod p|\leq
(\alpha+o(1))p$ for every prime $p$. How large can $X$ be? On the one hand, we
have the bound $|X|\ll_{\alpha}N^{\alpha}$ from Gallagher's larger sieve. On
the other hand, we prove, assuming the truth of an inverse sieve conjecture,
that the bound above can be improved (for example, to
$|X|\ll_{\alpha}N^{O(\alpha^{2014})}$ for small $\alpha$). The result follows
from studying the average size of $|X\pmod p|$ as $p$ varies, when
$X=f(\mathbb{Z})\cap [N]$ is the value set of a polynomial
$f(x)\in\mathbb{Z}[x]$.


  A debate has arisen regarding the importance of stationary versus eruptive
mass loss for massive star evolution. The reason is that stellar winds have
been found to be clumped, which results in the reduction of unclumped empirical
mass-loss rates. Most stellar evolution models employ theoretical mass-loss
rates which are already reduced by a moderate factor of ~2-3 compared to
non-corrected empirical rates. A key question is whether these reduced rates
are of the correct order of magnitude, or if they should be reduced even
further, which would mean that the alternative of eruptive mass loss becomes
necessary. Here we introduce the transition mass-loss rate (dM/dt)_trans
between O and Wolf-Rayet (WR) stars. Its novelty is that it is model
independent. All that is required is postulating the spectroscopic transition
point in a given data-set, and determining the stellar luminosity, which is far
less model dependent than the mass-loss rate. The transition mass-loss rate is
subsequently used to calibrate stellar wind strength by its application to the
Of/WNh stars in the Arches cluster. Good agreement is found with two
alternative modelling/theoretical results, suggesting that the rates provided
by current theoretical models are of the right order of magnitude in the
~50Msun mass range. Our results do not confirm the specific need for eruptive
mass loss as Luminous Blue Variables, and current stellar evolution modelling
for Galactic massive stars seems sound. Mass loss through alternative
mechanisms might still become necessary at lower masses, and/or metallicities,
and the quantification of alternative mass loss is desirable.


  We report in this work on a project aimed at determining Ly{\alpha}
luminosity functions from z=3 to z=6. The project is based on the use of very
deep photometry from the SHARDS Survey, in a set of 24 medium band filters in
the GOODS-N field. We present here some preliminary work carried out with four
test images in four consecutive bands. We use the narrow band selection
technique for searching emission line candidates. Eleven candidates have been
detected so far, many of which are strong Ly{\alpha} candidates. In particular,
we have seen a firm candidate to an interacting pair of Ly{\alpha} sources at
z=5.4.


  The article treats the classical problem of stability of steady rotation of a
rigid homogeneous ellipsoid on a rigid smooth plane which rotates about its
vertical axis. The condition for the steady rotation is derived from the
Euler-Poisson equations.


  Let $\Gamma$ be a lattice in $G=\mathrm{SL}(2,\mathbb{C})$. We give an
effective equidistribution result with precise error terms for expanding
translates of pieces of horospherical orbits in $\Gamma\backslash G$. Our
method of proof relies on the theory of unitary representations.


  Identical particles and entanglement are both fundamental components of
quantum mechanics. However, when identical particles are condensed in a single
spatial mode, the standard notions of entanglement, based on clearly
identifiable subsystems, break down. This has led many to conclude that such
systems have limited value for quantum information tasks, compared to
distinguishable particle systems. To the contrary, we show that any
entanglement formally appearing amongst the identical particles, including
entanglement due purely to symmetrization, can be extracted into an entangled
state of independent modes, which can then be applied to any task. In fact, the
entanglement of the mode system is in one-to-one correspondence with the
entanglement between the inaccessible identical particles. This settles the
long-standing debate about the resource capabilities of such states, in
particular spin-squeezed states of Bose-Einstein condensates, while also
revealing a new perspective on how and when entanglement is generated in
passive optical networks. Our results thus reveal new fundamental connections
between entanglement, squeezing, and indistinguishability.


  We consider bosonic string theory on $\text{AdS}_3$ supported by Kalb-Ramond
flux. It is well known that the $\alpha'$ exact worldsheet theory is described
by the $\text{SL(2,R)}$ WZW model. In this note we perform checks of an
$\alpha'$ exact dual description proposed in [arXiv:2104.07233] involving a
winding condensate on a free theory background. We give the explicit map of
vertex operators for normalizable states on both sides of the duality and
demonstrate the equivalence of their two and three point functions by direct
computation. The duality is of strong-weak nature in $\alpha'$.


  The first study of Nernst effect in NbSe$_2$ reveals a large quasi-particle
contribution with a magnitude comparable and a sign opposite to the vortex
signal. Comparing the effect of the Charge Density Wave(CDW) transition on Hall
and Nernst coefficients, we argue that this large Nernst signal originates from
the thermally-induced counterflow of electrons and holes and indicates a
drastic change in the electron scattering rate in the CDW state. The results
provide new input for the debate on the origin of the anomalous Nernst signal
in high-T$_c$ cuprates.


  Dark matter candidates with electromagnetic dipole moments can arise as dark
baryons in gauge-mediated or technicolor models. These dark matter candidates
interact with nuclei in direct detection experiments mainly through magnetic
and/or electric dipole moments. The scattering cross sections depend on the
nuclear magnetic moments and nuclear charge and have an infrared enhancement
compared with typical WIMP constant contact interactions, leading to
distinctive nuclear recoil energy spectra. These characteristics result in an
enhanced signal for the DAMA experiment compared with the CDMS or XENON
experiments. The positive results of DAMA, along with the null results of CDMS
and XENON, are consistent with a dark matter particle with magnetic dipole
moment and a mass around ten GeV. Significant direct detection signals can
arise from dipolar dark matter with mass up to of order tens of TeV.


  There are various methods for extracting iso-surfaces from volumetric data.
Marching cubes or tetrahedra or raytracing methods are mostly used. There are
many specific techniques to increase speed of computation and decrease memory
requirements. Although a precision of iso-surface extraction is very important,
too, it is not mentioned usually. A comparison of the selected methods was made
in different aspects: iso-surface extraction process time, number of triangles
generated and estimation of radius, area and volume errors based on
approximation of a sphere. Surprisingly, experiments proved that there is no
direct relation between precision of extracted and human perception of the
extracted iso-surface


  Accretion disks formed in binary neutron star mergers play a central role in
many astrophysical processes of interest, including the launching of
relativistic jets or the ejection of neutron-rich matter hosting heavy element
nucleosynthesis. In this work we analyze in detail the properties of accretion
disks from 44 ab initio binary neutron star merger simulations for a large set
of nuclear equations of state, binary mass ratios and remnant fates, with the
aim of furnishing reliable initial conditions for disk simulations and a
comprehensive characterization of their properties. We find that the disks have
a significant thermal support, with an aspect ratio decreasing with the mass
ratio of the binary from $\sim 0.7$ to 0.3. Even if the disk sample spans a
broad range in mass and angular momentum, their ratio is independent from the
equation of state and from the mass ratio. This can be traced back to the
rotational profile of the disc, characterized by a constant specific angular
momentum (as opposed to a Keplerian one) of $3-5 \times 10^{16} \rm ~
cm^2~s^{-1}$. The profiles of the entropy per baryon and of the electron
fraction depend on the mass ratio of the binary. For more symmetric binaries,
they follow a sigmoidal distribution as a function of the rest mass density,
for which we provide a detailed description and a fit. The disk properties
discussed in this work can be used as a robust set of initial conditions for
future long-term simulations of accretion disks from binary neutron star
mergers, posing the basis for a progress in the quantitative study of the
outflow properties.


  We describe a version of an algorithm for evolving self-gravitating
collections of particles that should be nearly ideal for parallel
architectures. Our method is derived from the ``self-consistent field'' (SCF)
approach suggested previously by Clutton-Brock and others. Owing to the use of
a global description of the gravitational field, the particles in an SCF
simulation do not interact with one another directly, minimizing communications
overhead between nodes in a parallel implementation. Ideal load-balancing is
achieved since precisely the same number of operations are needed to compute
the acceleration for each particle. Consequently, the SCF technique is
perfectly scalable and the size of feasible applications will grow in simple
proportion to advances in computational hardware. We describe an SCF code
developed for and tested on a Connection Machine 5. Empirical tests demonstrate
the efficient and scalable nature of the algorithm. Depending on the
application, simulations with particle numbers in the range $N\sim 10^7 -
10^{8.5}$ are now possible. Larger platforms should make simulations with
billions of particles feasible in the near future. Specific astrophysical
applications are discussed in the context of collisionless dynamics.


  The depth of maximum for extensive air showers measured by Fly's Eye and
Yakutsk experiments is analysed. The analysis depends on the hadronic
interaction model that determine cascade development. The novel feature found
in the cascading process for nucleus-nucleus collisions at high energies leads
to a fast increase of the inelasticity in heavy nuclei interactions without
changing the hadron-hadron interaction properties. This effects the development
of the extensive air showers initiated by heavy primaries. The detailed
calculations were performed using the recently developed geometrical multichain
model and the CORSIKA simulation code. The agreement with data on average depth
of shower maxima, the falling slope of the maxima distribution, and these
distribution widths are found for the very heavy cosmic ray mass spectrum
(slightly heavier than expected in the diffusion model at about 3*10**17 eV and
similar to the Fly's Eye composition at this energy).


  We introduce random towers to study almost sure rates of correlation decay
for random partially hyperbolic attractors. Using this framework, we obtain
abstract results on almost sure exponential, stretched exponential and
polynomial correlation decay rates. We then apply our results to small random
perturbations of Axiom A attractors, small perturbations of derived from Anosov
partially hyperbolic systems and to solenoidal attractors with random
intermittency.


  Kelly criterion, that maximizes the expectation value of the logarithm of
wealth for bookmaker bets, gives an advantage over different class of
strategies. We use projective symmetries for a explanation of this fact.
Kelly's approach allows for an interesting financial interpretation of the
Boltzmann/Shannon entropy. A "no-go" hypothesis for big investors is suggested.


  When orchestrating Web service workflows, the geographical placement of the
orchestration engine(s) can greatly affect workflow performance. Data may have
to be transferred across long geographical distances, which in turn increases
execution time and degrades the overall performance of a workflow. In this
paper, we present a framework that, given a DAG-based workflow specification,
computes the op- timal Amazon EC2 cloud regions to deploy the orchestration
engines and execute a workflow. The framework incorporates a constraint model
that solves the workflow deployment problem, which is generated using an
automated constraint modelling system. The feasibility of the framework is
evaluated by executing different sample workflows representative of sci-
entific workloads. The experimental results indicate that the framework reduces
the workflow execution time and provides a speed up of 1.3x-2.5x over
centralised approaches.


  We discover new analytic properties of classical partial and false theta
functions and their potential applications to representation theory of
W-algebras and vertex algebras in general. More precisely, motivated by clues
from conformal field theory, first, we are able to determine modular-like
transformation properties of regularized partial and false theta functions.
Then, after suitable identification of regularized partial/false theta
functions with the characters of atypical modules for the singlet vertex
algebra W(2,2p-1), we formulate and prove a Verlinde-type formula for the
fusion rules of irreducible W(2,2p-1)-modules.


  Transcription factor (TF) molecules translocate by facilitated diffusion (a
combination of 3D diffusion around and 1D random walk on the DNA). Despite the
attention this mechanism received in the last 40 years, only a few studies
investigated the influence of the cellular environment on the facilitated
diffusion mechanism and, in particular, the influence of `other' DNA binding
proteins competing with the TF molecules for DNA space. Molecular crowding on
the DNA is likely to influence the association rate of TFs to their target site
and the steady state occupancy of those sites, but it is still not clear how it
influences the search in a genome-wide context, when the model includes
biologically relevant parameters (such as: TF abundance, TF affinity for DNA
and TF dynamics on the DNA). We performed stochastic simulations of TFs
performing the facilitated diffusion mechanism, and considered various
abundances of cognate and non-cognate TFs. We show that, for both obstacles
that move on the DNA and obstacles that are fixed on the DNA, changes in search
time are not statistically significant in case of biologically relevant
crowding levels on the DNA. In the case of non-cognate proteins that slide on
the DNA, molecular crowding on the DNA always leads to statistically
significant lower levels of occupancy, which may confer a general mechanism to
control gene activity levels globally. When the `other' molecules are immobile
on the DNA, we found a completely different behaviour, namely: the occupancy of
the target site is always increased by higher molecular crowding on the DNA.
Finally, we show that crowding on the DNA may increase transcriptional noise
through increased variability of the occupancy time of the target sites.


  We consider inverse curvature flows in the $(n+1)$-dimensional Euclidean
space, $n\geq 2,$ expanding by arbitrary negative powers of a 1-homogeneous,
monotone curvature function $F$ with some concavity properties. We obtain
asymptotical roundness, meaning that circumradius minus inradius of the flow
hypersurfaces decays to zero and that the flow becomes close to a flow of
spheres.


  A deformed Donaldson-Thomas connection for a manifold with a ${\rm
Spin}(7)$-structure, which we call a ${\rm Spin}(7)$-dDT connection, is a
Hermitian connection on a Hermitian line bundle $L$ over a manifold with a
${\rm Spin}(7)$-structure defined by fully nonlinear PDEs. It was first
introduced by Lee and Leung as a mirror object of a Cayley cycle obtained by
the real Fourier-Mukai transform and its alternative definition was suggested
in our other paper. As the name indicates, a ${\rm Spin}(7)$-dDT connection can
also be considered as an analogue of a Donaldson-Thomas connection (${\rm
Spin}(7)$-instanton).
  In this paper, using our definition, we show that the moduli space
$\mathcal{M}_{{\rm Spin}(7)}$ of ${\rm Spin}(7)$-dDT connections has similar
properties to these objects. That is, we show the following for an open subset
$\mathcal{M}'_{{\rm Spin}(7)} \subset \mathcal{M}_{{\rm Spin}(7)}$. (1)
Deformations of elements of $\mathcal{M}'_{{\rm Spin}(7)}$ are controlled by a
subcomplex of the canonical complex introduced by Reyes Carri\'on by
introducing a new ${\rm Spin}(7)$-structure from the initial ${\rm
Spin}(7)$-structure and a ${\rm Spin}(7)$-dDT connection. (2) The expected
dimension of $\mathcal{M}'_{{\rm Spin}(7)}$ is finite. It is $b^1$, the first
Betti number of the base manifold, if the initial ${\rm Spin}(7)$-structure is
torsion-free. (3) Under some mild assumptions, $\mathcal{M}'_{{\rm Spin}(7)}$
is smooth if we perturb the initial ${\rm Spin}(7)$-structure generically. (4)
The space $\mathcal{M}'_{{\rm Spin}(7)}$ admits a canonical orientation if all
deformations are unobstructed.


  The general class of the graded Lie algebras is defined. These algebras could
be constructed using an arbitrary dynamical systems with discrete time and with
invarinat measure. In this papers we consider the case of the central extension
of Lie algebras which corresponds to the ordinary crossed product (as
associative algebra) - series A. The structure of those Lie algebras is similar
to Kac-Moody algebras, and these are a special case of so called algebras with
continuous root system which were introduced by author with M.Saveliev in
90-th. The central extension open a new possibilty in algebraic theory of
dynamical systems. The simpliest example corresponds to rotation of the circle
(sine-algebra="quantum torus") and to adding of unity the additvie group of the
p-adic integers.


  From statistical distinguishability of probability distributions, one can
define distinguishability of quantum states. A corresponding measurement to
perform, optimal in a definite sense, for distinguishing between two given
states rho_A and rho_B, has been derived by Fuchs and Caves. We show that the
Bures-Uhlmann geodesic through the two states singles out this measurement. The
geodesic `bounces' at the boundary of the set of quantum states. Whenever the
geodesic hits the boundary, the state orthogonal to that boundary state is one
of the basis states for the measurement.


  In 1888 Hilbert showed that every nonnegative homogeneous polynomial with
real coefficients of degree $2d$ in $n$ variables is a sum of squares if and
only if $d=1$ (quadratic forms), $n=2$ (binary forms) or $(n,d)=(3,2)$ (ternary
quartics). In these cases, it is interesting to compute canonical expressions
for these decompositions. Starting from Carath\'eodory's Theorem, we compute
the Carath\'eodory number of Hilbert cones of nonnegative quadratic and binary
forms.


  If $R$ is a semiartinian Von Neumann regular ring, then the set $\Prim_{R}$
of primitive ideals of $R$, ordered by inclusion, is an artinian poset in which
all maximal chains have a greatest element. Moreover, if $\Prim_{R}$ has no
infinite antichains, then the lattice $\BL_{2}(R)$ of all ideals of $R$ is
anti-isomorphic to the lattice of all upper subsets of $\Prim_{R}$. Since the
assignment $U\mapsto r_R(U)$ defines a bijection from any set $\Simp_R$ of
representatives of simple right $R$-modules to $\Prim_{R}$, a natural partial
order is induced in $\Simp_R$, under which the maximal elements are precisely
those simple right $R$-modules which are finite dimensional over the respective
endomorphism division rings; these are always $R$-injective. Given any artinian
poset $I$ with at least two elements and having a finite cofinal subset, a
lower subset $I'\sbs I$ and a field $D$, we present a construction which
produces a semiartinian and unit-regular $D$-algebra $D_I$ having the following
features: (a) $\Simp_{D_I}$ is order isomorphic to $I$; (b) the assignment
$H\mapsto\Simp_{D_I/H}$ realizes an anti-isomorphism from the lattice
$\BL_{2}(D_I)$ to the lattice of all upper subsets of $\Simp_{D_I}$; (c) a
non-maximal element of $\Simp_{D_I}$ is injective if and only if it corresponds
to an element of $I'$, thus $D_I$ is a right $V$-ring if and only if $I' = I$;
(d) $D_I$ is a right \emph{and} left $V$-ring if and only if $I$ is an
antichain; (e) if $I$ has finite dual Krull length, then $D_I$ is (right and
left) hereditary; (f) if $I$ is at most countable and $I' = \vu$, then $D_I$ is
a countably dimensional $D$-algebra.


  We suggest graphene and a two-dimensional (2D) Weyl semimetal (WSM) as 2D
materials for the realization of a broadband coherent perfect absorber (CPA)
respecting overall PT-symmetry. We also demonstrate the conditions for mutually
equal amplitudes and phases of the left and right incoming waves to realize a
CPA. 2D materials in our system play the role to enhance the absorption rate of
a CPA once the appropriate parameters are inserted in the system. We show that
a 2D WSM is more effective than graphene in obtaining the optimal conditions.
We display the behavior of each parameter governing the optical system and show
that optimal conditions of these parameters give rise to enhancement and
possible experimental realization of a broadband CPA-laser.


  We extend the mathematical theory of quantum hypothesis testing to the
general $W^*$-algebraic setting and explore its relation with recent
developments in non-equilibrium quantum statistical mechanics. In particular,
we relate the large deviation principle for the full counting statistics of
entropy flow to quantum hypothesis testing of the arrow of time.


  A finitely generated group $\G$ equipped with a word-length is said to
satisfy property RD if there are $C, s\geq 0$ such that, for all non-negative
integers $n$, we have $\|a\|\leq C (1+n)^s \|a\|_2$ whenever $a\in\C\G$ is
supported on elements of length at most $n$.
  We show that, for infinite $\G$, the degree $s$ is at least 1/2.


  We prove that manifolds admitting a Riemannian metric for which products of
harmonic forms are harmonic satisfy strong topological restrictions, some of
which are akin to properties of flat manifolds. Others are more subtle, and are
related to symplectic geometry and Seiberg-Witten theory.
  We also prove that a manifold admits a metric with harmonic forms whose
product is not harmonic if and only if it is not a rational homology sphere.


  Reinforcement learning is a promising method for robotic grasping as it can
learn effective reaching and grasping policies in difficult scenarios. However,
achieving human-like manipulation capabilities with sophisticated robotic hands
is challenging because of the problem's high dimensionality. Although remedies
such as reward shaping or expert demonstrations can be employed to overcome
this issue, they often lead to oversimplified and biased policies. We present
Dext-Gen, a reinforcement learning framework for Dexterous Grasping in sparse
reward ENvironments that is applicable to a variety of grippers and learns
unbiased and intricate policies. Full orientation control of the gripper and
object is achieved through smooth orientation representation. Our approach has
reasonable training durations and provides the option to include desired prior
knowledge. The effectiveness and adaptability of the framework to different
scenarios is demonstrated in simulated experiments.


  Let $f$ be a symmetric norm on ${\mathbb R}^n$ and let ${\mathcal
B}({\mathcal H})$ be the set of all bounded linear operators on a Hilbert space
${\mathcal H}$ of dimension at least $n$. Define a norm on ${\mathcal
B}({\mathcal H})$ by $\|A\|_f = f(s_1(A), \dots, s_n(A))$, where $s_k(A) =
\inf\{\|A-X\|: X\in {\mathcal B}({\mathcal H}) \hbox{ has rank less than } k\}$
is the $k$th singular value of $A$. Basic properties of the norm $\|\cdot\|_f$
are obtained including some norm inequalities and characterization of the
equality case. Geometric properties of the unit ball of the norm are obtained;
the results are used to determine the structure of maps $L$ satisfying
$\|L(A)-L(B)\|_f=\|A - B\|_f$ for any $A, B \in {\mathcal B}({\mathcal H})$.


  We investigate the convergence of hitting times for jump-diffusion processes.
Specifically, we study a sequence of stochastic differential equations with
jumps. Under reasonable assumptions, we establish the convergence of solutions
to the equations and of the moments when the solutions hit certain sets.


  We study the functional dependence of the spin-weighted angular moments of
the two-point correlation function of the three dimensional cosmic shear on the
expansion history of the universe. We first express the redshift dependent
total equation of state parameter in terms of the growing mode of the gauge
invariant metric perturbation in the conformal-Newtonian gauge for the case of
adiabatic perturbations. We then express the redshift dependent angular moments
of the shear two-point correlation function as an integral in terms of the
metric perturbation. We present the final explicit expression for the case of a
Harrison-Zeldovich spectrum of primordial perturbations. Our analysis is
restricted to the linear regime. We use our results to make a preliminary study
of the required sensitivity that will allow cosmic shear observations to add
significant information about the expansion history of the universe.


  We study entanglement activation in a generalized entanglement swapping
process involving two Bell pairs and generalized measurements. The conventional
understanding posits entangled measurements as both necessary and sufficient
for establishing entanglement between distant parties. In this study, we
reassess the role of measurement operators in entanglement generation within a
generalized entanglement swapping process. We focus on maximally entangled
two-qubit initial states and generalized measurements, investigating the
necessity and sufficiency conditions for entangled measurement operators. By
utilizing two Bell pairs, (1, 2) shared between Alice and Bob, and (3, 4)
shared between Bob and Charlie, we demonstrate that while entangled
measurements are sufficient, they are not indispensable for establishing
entanglement between spatially separated observers. Through a sequential
approach, if Bob performs an initial measurement which is not able to establish
entanglement then followed by another measurement after post-processing the
first measurement it is possible to establish entanglement. We identify
specific criteria for different measurement operators that enable the potential
for performing a second measurement to establish entanglement. Our findings
highlight the feasibility of generating entanglement between distant parties
through a combination of measurements, shedding light on entanglement
distribution in quantum networks. Additionally, we showcase through
illustrative examples how successive measurements enhance entanglement compared
to single measurements, underscoring the practical benefits of our approach in
enhancing entanglement. Moreover, our protocol extends beyond bipartite qubit
states to higher-dimensional maximally entangled states, emphasizing its
versatility and applicability.


  For a group $H$ and a non empty subset $\Gamma\subseteq H$, the commuting
graph $G=\mathcal{C}(H,\Gamma)$ is the graph with $\Gamma$ as the node set and
where any $x,y \in \Gamma$ are joined by an edge if $x$ and $y$ commute in $H$.
We prove that any simple graph can be obtained as a commuting graph of a
Coxeter group, solving the realizability problem in this setup. In particular
we can recover every Dynkin diagram of ADE type as a commuting graph. Thanks to
the relation between the ADE classification and finite subgroups of
$\SL(2,\C)$, we are able to rephrase results from the {\em McKay
correspondence} in terms of generators of the corresponding Coxeter groups. We
finish the paper studying commuting graphs $\mathcal{C}(H,\Gamma)$ for every
finite subgroup $H\subset\SL(2,\C)$ for different subsets $\Gamma\subseteq H$,
and investigating metric properties of them when $\Gamma=H$.


  The proton is a composite object with spin one-half, understood to contain
highly relativistic spin one-half quarks exchanging spin-one gluons, each
possibly with significant orbital angular momenta. While their fundamental
interactions are well described by Quantum ChromoDynamics (QCD), our standard
theory of the strong interaction, nonperturbative calculations of the internal
structure of the proton based directly on QCD are beginning to provide reliable
results. Most of our present knowledge of the structure of the proton is based
on experimental measurements interpreted within the rich framework of QCD. An
area presently attracting intense interest, both experimental and theoretical,
is the relationship between the spin of the proton and the spins and orbital
angular momenta of its constituents. While remarkable progress has been made,
especially in the last decade, the discovery and investigation of new concepts
have revealed that much more remains to be learned. This progress is reviewed
and an outlook for the future is offered.


  Recent work by Marino et al. (2020) showed improved performance in sequential
density estimation by combining masked autoregressive flows with hierarchical
latent variable models. We draw a connection between such autoregressive
generative models and the task of lossy video compression. Specifically, we
view recent neural video compression methods (Lu et al., 2019; Yang et al.,
2020b; Agustssonet al., 2020) as instances of a generalized stochastic temporal
autoregressive transform, and propose avenues for enhancement based on this
insight. Comprehensive evaluations on large-scale video data show improved
rate-distortion performance over both state-of-the-art neural and conventional
video compression methods.


  We study axion strings of hyperlight axions coupled to photons. Hyperlight
axions -- axions lighter than Hubble at recombination -- are a generic
prediction of the string axiverse. These axions strings produce a distinct
quantized polarization rotation of CMB photons which is
$\mathcal{O}(\alpha_{\rm em})$. As the CMB light passes many strings, this
polarization rotation converts E-modes to B-modes and adds up like a random
walk. Using numerical simulations we show that the expected size of the final
result is well within the reach of current and future CMB experiments through
the measurement of correlations of CMB B-modes with E- and T-modes. The
quantized polarization rotation angle is topological in nature and can be seen
as a geometric phase. Its value depends only on the anomaly coefficient and is
independent of other details such as the axion decay constant. Measurement of
the anomaly coefficient by measuring this rotation will provide information
about the UV theory, such as the quantization of electric charge and the value
of the fundamental unit of charge. The presence of axion strings in the
universe relies only on a phase transition in the early universe after
inflation, after which the string network rapidly approaches an attractor
scaling solution. If there are additional stable topological objects such as
domain walls, axions as heavy as $10^{-15}$ eV would be accessible. The
existence of these strings could also be probed by measuring the relative
polarization rotation angle between different images in gravitationally lensed
quasar systems.


  We prove uniform estimates for the decay rate of the Fourier transform of
measures supported on real-analytic hypersurfaces in R^3. If the surface
contains the origin and is oriented such that its normal at the origin is in
the direction of the z-axis and if dS denotes the surface measure for this
surface, then the measures under consideration are of the form K(x,y)g(z) dS
where K(x,y)g(z) is supported near the origin and both K(x,y) and g(z) are
allowed to have singularities. The estimates here generalize the previously
known sharp uniform estimates for when K(x,y)g(z) is smooth. The methods used
in this paper involve an explicit two-dimensional resolution of singularities
theorem, iterated twice, coupled with Van der Corput-type lemmas.


  In this paper, we study the inverse scattering of massive charged Dirac
fields in the exterior region of (de Sitter)-Reissner-Nordstr\"om black holes.
First we obtain a precise high-energy asymptotic expansion of the diagonal
elements of the scattering matrix (i.e. of the transmission coefficients) and
we show that the leading terms of this expansion allows to recover uniquely the
mass, the charge and the cosmological constant of the black hole. Second, in
the case of nonzero cosmological constant, we show that the knowledge of the
reflection coefficients of the scattering matrix on any interval of energy also
permits to recover uniquely these parameters.


  Transition metal dichalcogenide materials $MX_2 (M=Mo,W;X=S,Se)$ are being
thoroughly studied due to their novel two-dimensional structure, that is
associated with exceptional optical and transport properties. From a
computational point of view, Density Functional Theory simulations perform very
well in these systems and are an indispensable tool to predict and complement
experimental results. However, due to the time and length scales where even the
most efficient DFT implementations can reach today, this methodology suffers of
stringent limitations to deal with finite temperature simulations or
electron-lattice coupling when studying excitation states: the unit cells
required to study, for instance, systems with thermal fluctuations or large
polarons would require a large computational power. Multi-scale techniques,
like the recently proposed Second Principles Density Functional Theory, can go
beyond these limitations but require the construction of tight-binding models
for the systems under investigation. In this work, we compare two such methods
to construct the bands of WSe$_2$. In particular, we compare the result of (i)
Wannier-based model construction with (ii) the band fitting method of Liu and
co-workers where the top of the valence band and the bottom of the conduction
band are modeled by three bands symmetrized to have mainly Tungsten $d_{z^2}$,
$d_{xy}$ and $d_{x^2-y^2}$ character. Our results emphasize the differences
between these two approaches and how band-fitting model construction leads to
an overestimation of the localization of the real-space basis in a
tight-binding representation.


  Automated mitotic detection in time-lapse phasecontrast microscopy provides
us much information for cell behavior analysis, and thus several mitosis
detection methods have been proposed. However, these methods still have two
problems; 1) they cannot detect multiple mitosis events when there are closely
placed. 2) they do not consider the annotation gaps, which may occur since the
appearances of mitosis cells are very similar before and after the annotated
frame. In this paper, we propose a novel mitosis detection method that can
detect multiple mitosis events in a candidate sequence and mitigate the human
annotation gap via estimating a spatiotemporal likelihood map by 3DCNN. In this
training, the loss gradually decreases with the gap size between ground truth
and estimation. This mitigates the annotation gaps. Our method outperformed the
compared methods in terms of F1- score using a challenging dataset that
contains the data under four different conditions.


  This paper presents an unsupervised transformer-based framework for temporal
activity segmentation which leverages not only frame-level cues but also
segment-level cues. This is in contrast with previous methods which often rely
on frame-level information only. Our approach begins with a frame-level
prediction module which estimates framewise action classes via a transformer
encoder. The frame-level prediction module is trained in an unsupervised manner
via temporal optimal transport. To exploit segment-level information, we
utilize a segment-level prediction module and a frame-to-segment alignment
module. The former includes a transformer decoder for estimating video
transcripts, while the latter matches frame-level features with segment-level
features, yielding permutation-aware segmentation results. Moreover, inspired
by temporal optimal transport, we introduce simple-yet-effective pseudo labels
for unsupervised training of the above modules. Our experiments on four public
datasets, i.e., 50 Salads, YouTube Instructions, Breakfast, and Desktop
Assembly show that our approach achieves comparable or better performance than
previous methods in unsupervised activity segmentation.


  Generative adversarial networks (GANs) have been widely investigated for many
potential applications in medical imaging. DatasetGAN is a recently proposed
framework based on modern GANs that can synthesize high-quality segmented
images while requiring only a small set of annotated training images. The
synthesized annotated images could be potentially employed for many medical
imaging applications, where images with segmentation information are required.
However, to the best of our knowledge, there are no published studies focusing
on its applications to medical imaging. In this work, preliminary studies were
conducted to investigate the utility of DatasetGAN in medical imaging. Three
improvements were proposed to the original DatasetGAN framework, considering
the unique characteristics of medical images. The synthesized segmented images
by DatasetGAN were visually evaluated. The trained DatasetGAN was further
analyzed by evaluating the performance of a pre-defined image segmentation
technique, which was trained by the use of the synthesized datasets. The
effectiveness, concerns, and potential usage of DatasetGAN were discussed.


  Bonding between polymeric interfaces is encountered widely in several
industrial applications. Many of these bonding processes rely on time-consuming
and temperature-dependent classical mechanism of polymer interdiffusion via
reptation in a melt state. Here, for the first time, we report a new
mechanistic pathway for achieving solid-state polymer bonding by triggering
rapid macromolecular acceleration through mechanical deformation. Large-scale
molecular simulations reveal that active plastic deformation in glassy
polymers, at temperatures well-below the bulk (and surface) glass transition
temperatures, is sufficient to cause segmental translations of the polymer
chains that lead to interfacial interpenetrations, and formation of new
entanglements. The underlying mechanistic basis for this new type of bonding is
identified as enhanced molecular-scale dilatations (or densifications) in
conjunction with accelerated molecular mobility during plastic deformation. The
reported mechanistic insights open promising avenues for designing new bonding
technologies or material systems, and transformation of the existing ones to
achieve quick and energetically less intensive bonding.


  In this paper a class of simple, but nonlinear, systems of recursions
involving $2$ dependent variables $x_{j}\left( n\right) $ is identified, such
that the solutions of their initial-values problems -- with arbitrary initial
data $x_{j}\left( 0\right) $ -- may be explicitly obtained.


  The auxiliary function method allows computation of extremal long-time
averages of functions of dynamical variables in autonomous nonlinear ordinary
differential equations via convex optimization. For dynamical systems defined
by autonomous polynomial vector fields, it is operationally realized as a
semidefinite program utilizing sum of squares technology. In this contribution
we review the method and extend it for application to periodically driven
non-autonomous nonlinear vector fields involving trigonometric functions of the
dynamical variables. The damped driven Duffing oscillator and periodically
driven pendulum are presented as examples to illustrate the auxiliary function
method's utility.


  A measurement of mixing and $C\!P$ violation in neutral charm mesons is
performed using data reconstructed in proton-proton collisions collected by the
LHCb experiment from 2016 to 2018, corresponding to an integrated luminosity of
5.4$\textrm{fb}^{-1}$. A total of $30.6$ million $D^{0}\rightarrow
K^{0}_{\mathrm{S}}\pi^{+}\pi^{-}$ decays are analyzed using a method optimized
for the measurement of the mass difference between neutral charm-meson
eigenstates. Allowing for $C\!P$ violation in mixing and in the interference
between mixing and decay, the mass and decay-width differences are measured to
be $x_{C\!P} = \left[3.97\pm0.46\textrm{(stat)}\pm
0.29\textrm{(syst)}\right]\times10^{-3}$ and $y_{C\!P} =
\left[4.59\pm1.20\textrm{(stat)}\pm0.85\textrm{(syst)}\right]\times10^{-3}$,
respectively. The $C\!P$-violating parameters are measured as $\Delta x =
\left[-0.27\pm0.18\textrm{(stat)}\pm0.01\textrm{(syst)}\right]\times10^{-3}$
and $\Delta y =
\left[0.20\pm0.36\textrm{(stat)}\pm0.13\textrm{(syst)}\right]\times10^{-3}$.
This is the first observation of a nonzero mass difference in the $D^0$ meson
system, with a significance exceeding seven standard deviations. The data are
consistent with $C\!P$ symmetry, and improve existing constraints on the
associated parameters.


  Discriminant ideals of noncommutative algebras $A$, which are module finite
over a central sublagebra $C$, are key invariants that carry important
information about $A$, such as the sum of the squares of the dimensions of its
irreducible modules with a given central character. There has been substantial
research on the computation of discriminants, but very little is known about
the computation of discriminant ideals. In this paper we carry out a detailed
investigation of the lowest discriminant ideals of Cayley-Hamilton Hopf
algebras in the sense of De Concini, Reshetikhin, Rosso and Procesi, whose
identity fiber algebras are basic. The lowest discriminant ideals are the most
complicated ones, because they capture the most degenerate behaviour of the
fibers in the exact opposite spectrum of the picture from the Azumaya locus. We
provide a description of the zero sets of the lowest discriminant ideals of
Cayley-Hamilton Hopf algebras in terms of maximally stable modules of Hopf
algebras, irreducible modules that are stable under tensoring with the maximal
possible number of irreducible modules with trivial central character. In
important situations, this is shown to be governed by the actions of the
winding automorphism groups. The results are illustrated with applications to
the group algebras of central extensions of abelian groups, big quantum Borel
subalgebras at roots of unity and quantum coordinate rings at roots of unity.


  Many recent few-shot learning methods concentrate on designing novel model
architectures. In this paper, we instead show that with a simple backbone
convolutional network we can even surpass state-of-the-art classification
accuracy. The essential part that contributes to this superior performance is
an adversarial feature learning strategy that improves the generalization
capability of our model. In this work, adversarial features are those features
that can cause the classifier uncertain about its prediction. In order to
generate adversarial features, we firstly locate adversarial regions based on
the derivative of the entropy with respect to an averaging mask. Then we use
the adversarial region attention to aggregate the feature maps to obtain the
adversarial features. In this way, we can explore and exploit the entire
spatial area of the feature maps to mine more diverse discriminative knowledge.
We perform extensive model evaluations and analyses on miniImageNet and
tieredImageNet datasets demonstrating the effectiveness of the proposed method.


  We investigate the relation between the BPS baby Skyrme model and its vector
meson formulation, where the baby Skyrme term is replaced by a coupling between
the topological current $B_\mu$ and the vector meson field $\omega_\mu$. The
vector model still possesses infinitely many symmetries leading to infinitely
many conserved currents which stand behind its solvability. It turns out that
the similarities and differences of the two models depend strongly on the
specific form of the potential. We find, for instance, that compactons (which
exist in the BPS baby Skyrme model) disappear from the spectrum of solutions of
the vector counterpart. Specifically, for the vector model with the old baby
Skyrme potential we find that it has compacton solutions only provided that a
delta function source term effectively screening the topological charge is
inserted at the compacton boundary. For the old baby Skyrme potential squared
we find that the vector model supports exponentially localized solitons, like
the BPS baby Skyrme model. These solitons, however, saturate a BPS bound which
is a nonlinear function of the topological charge and, as a consequence, higher
solitons are unstable w.r.t. decay into smaller ones, which is at variance with
the more conventional situation (a linear BPS bound and stable solitons) in the
BPS baby Skyrme model.


  We present GeoRocket, a software for the management of very large geospatial
datasets in the cloud. GeoRocket employs a novel way to handle arbitrarily
large datasets by splitting them into chunks that are processed individually.
The software has a modern reactive architecture and makes use of existing
services including Elasticsearch and storage back ends such as MongoDB or
Amazon S3. GeoRocket is schema-agnostic and supports a wide range of
heterogeneous geospatial file formats. It is also format-preserving and does
not alter imported data in any way. The main benefits of GeoRocket are its
performance, scalability, and usability, which make it suitable for a number of
scientific and commercial use cases dealing with very high data volumes,
complex datasets, and high velocity (Big Data). GeoRocket also provides many
opportunities for further research in the area of geospatial data management.


  In this work, we consider a model of two qubits driven by coherent and
incoherent time-dependent controls. The dynamics of the system is governed by a
Gorini-Kossakowski-Sudarshan-Lindblad master equation, where coherent control
enters into the Hamiltonian and incoherent control enters into both the
Hamiltonian (via Lamb shift) and the dissipative superoperator. We consider two
physically different classes of interaction with coherent control and study the
optimal control problem of state preparation formulated as minimization of the
Hilbert-Schmidt distance's square between the final density matrix and a given
target density matrix at some fixed target time. Taking into account that
incoherent control by its physical meaning is a non-negative function of time,
we derive an analytical expression for the gradient of the objective and
develop optimization approaches based on adaptation for this problem of
GRadient Ascent Pulse Engineering (GRAPE). We study evolution of the von
Neumann entropy, purity, and one-qubit reduced density matrices under optimized
controls and observe a significantly different behavior of GRAPE optimization
for the two classes of interaction with coherent control in the Hamiltonian.


  We study the implications of the absence of a direct discovery of a Higgs
boson at LEP. First we exhibit 15 physically different ways in which one or
more Higgs bosons lighter than the LEP limit could still exist. In the minimal
supersymmetric standard model (MSSM) all of these, as well as the cases where
the Higgs mass equals or exceeds 115 GeV, seem fine-tuned. We examine some
interpretations of the fine tuning in high scale theories. The least fine-tuned
MSSM outcome will have a Higgs mass at 115 GeV, while approaches that extend
the MSSM at the weak scale can naturally have larger Higgs masses.


  In this paper it is shown that $C_\beta$-smooth functions can be approximated
by deep neural networks with ReLU activation function and with parameters
$\{0,\pm \frac{1}{2}, \pm 1, 2\}$. The $l_0$ and $l_1$ parameter norms of
considered networks are thus equivalent. The depth, width and the number of
active parameters of the constructed networks have, up to a logarithmic factor,
the same dependence on the approximation error as the networks with parameters
in $[-1,1]$. In particular, this means that the nonparametric regression
estimation with the constructed networks attains the same convergence rate as
with sparse networks with parameters in $[-1,1]$.


  1. Types of electrical noise
  2. Measuring the unit of transferred charge
  3. Quiet electrons
  4. Detecting open transmission channels
  5. Distinguishing particles from waves
  6. Entanglement detector


  Wireless Mesh Network (WMN) is surely one of the prominent networks in the
modern era which is widely used in numerous evolving applications, viz.
broadband home networking (BHN), community and neighbourhood networks (CNN),
coordinated network management (CNM), and intelligent transportation systems
(ITS), etc. It is a wireless network (WN) with multi-hop formed by many fixed
wireless mesh routers (WMR) that are connected wirelessly with a mesh-alike
backbone arrangement. In the IEEE 802.11s network, the node selection,
scalability, stability, density of the nodes, mobility of the nodes,
transmission power, and routing are major issues that WMN suffers. In this
paper, a critical review of MAC protocols and their Quality of Service (QoS)
parameters for WMN is presented to attain a better understanding of MAC
protocols. Furthermore, the critical comparative analysis and recommendation of
MAC procedures for WMN using Multi-objective optimization and statistical
testing framework are performed. This framework is used for the analysis and
recommendation of different protocols available for QoS parameters.


  Helicenes are inherently chiral polyaromatic molecules composed of all-ortho
fused benzene rings possessing a spring-like structure. Here, using a
combination of density functional theory and tight-binding calculations, it is
demonstrated that controlling the length of the helicene molecule by
mechanically stretching or compressing the molecular junction can dramatically
change the electronic properties of the helicene, leading to a tunable
switching behavior of the conductance and thermopower of the junction with
on/off ratios of several orders of magnitude. Furthermore, control over the
helicene length and number of rings is shown to lead to more than an order of
magnitude increase in the thermopower and thermoelectric figure-of-merit over
typical molecular junctions, presenting new possibilities of making efficient
thermoelectric molecular devices. The physical origin of the strong dependence
of the transport properties of the junction is investigated, and found to be
related to a shift in the position of the molecular orbitals.


  We analyze the reversals of the large scale flow in Rayleigh-B\'enard
convection both through particle image velocimetry flow visualization and
direct numerical simulations (DNS) of the underlying Boussinesq equations in a
(quasi) two-dimensional, rectangular geometry of aspect ratio 1. For medium
Prandtl number there is a diagonal large scale convection roll and two smaller
secondary rolls in the two remaining corners diagonally opposing each other.
These corner flow rolls play a crucial role for the large scale wind reversal:
They grow in kinetic energy and thus also in size thanks to plume detachments
from the boundary layers up to the time that they take over the main, large
scale diagonal flow, thus leading to reversal. Based on this mechanism we
identify a typical time scale for the reversals. We map out the Rayleigh number
vs Prandtl number phase space and find that the occurrence of reversals very
sensitively depends on these parameters.


  Motivated by recent experiments of Zajac et al. [arXiv:1708.03530], we
theoretically describe high-fidelity two-qubit gates using the exchange
interaction between the spins in neighboring quantum dots subject to a magnetic
field gradient. We use a combination of analytical calculations and numerical
simulations to provide the optimal pulse sequences and parameter settings for
the gate operation. We present a novel synchronization method which avoids
detrimental spin flips during the gate operation and provide details about
phase mismatches accumulated during the two-qubit gates which occur due to
residual exchange interaction, non-adiabatic pulses, and off-resonant driving.
By adjusting the gate times, synchronizing the resonant and off-resonant
transitions, and compensating these phase mismatches by phase control, the
overall gate fidelity can be increased significantly.


  Let $\mathcal B$ be a sufficiently smooth rigid body (compact set of $\mathbb
R^3$) of arbitrary shape moving in an unbounded Navier-Stokes liquid under the
action of prescribed external force, $\textup{F}$, and torque, $\textup{M}$. We
show that if the data are suitably regular and small, and $\textup{F}$ and
$\textup{M}$ vanish for large times in the $L^2$-sense, there exists at least
one global strong solution to the corresponding initial-boundary value problem.
Moreover, this solution converges to zero as time approaches infinity. This
type of results was known, so far, only when $\mathcal B$ is a ball.


  We prove that if $A$ is a non-separable abelian tracial von Neuman algebra
then its free powers $A^{*n}, 2\leq n \leq \infty$, are mutually non-isomorphic
and with trivial fundamental group, $\mathcal F(A^{*n})=1$, whenever $2\leq
n<\infty$. This settles the non-separable version of the free group factor
problem.


  The mass of a cluster of galaxies can be estimated from its lens
magnification, which can be determined from the variation in number counts of
background galaxies. In order to derive the mass one needs to make assumptions
for the lens shear, which is unknown from the variation in number counts alone.
Furthermore, one needs to go beyond the weak lensing (linear) approximation as
most of the observational data is concentrated in the central parts of
clusters, where the lensing is strong. By studying the lensing properties of a
complete catalogue of galaxy cluster models, one can find reasonable
approximations about the lens shear as a function of the lens convergence. We
show that using these approximations one can fairly well reconstruct the
surface mass distribution from the magnification alone.


  For analysing and/or understanding languages having no word boundaries based
on morphological analysis such as Japanese, Chinese, and Thai, it is desirable
to perform appropriate word segmentation before word embeddings. But it is
inherently difficult in these languages. In recent years, various language
models based on deep learning have made remarkable progress, and some of these
methodologies utilizing character-level features have successfully avoided such
a difficult problem. However, when a model is fed character-level features of
the above languages, it often causes overfitting due to a large number of
character types. In this paper, we propose a CE-CLCNN, character-level
convolutional neural networks using a character encoder to tackle these
problems. The proposed CE-CLCNN is an end-to-end learning model and has an
image-based character encoder, i.e. the CE-CLCNN handles each character in the
target document as an image. Through various experiments, we found and
confirmed that our CE-CLCNN captured closely embedded features for visually and
semantically similar characters and achieves state-of-the-art results on
several open document classification tasks. In this paper we report the
performance of our CE-CLCNN with the Wikipedia title estimation task and
analyse the internal behaviour.


  Thermal dust emission carries information on physical conditions and dust
properties in many astronomical sources. Because observations represent a sum
of emission along the line of sight, their interpretation often requires
radiative transfer modelling.
  We describe a new radiative transfer program SOC for computations of dust
emission and examine its performance in simulations of interstellar clouds with
external and internal heating.
  SOC implements the Monte Carlo radiative transfer method as a parallel
program for shared memory computers. It can be used to study dust extinction,
scattering, and emission. We tested SOC with realistic cloud models and
examined the convergence and noise of the dust temperature estimates and of the
resulting surface brightness maps.
  SOC has been demonstrated to produces accurate estimates for dust scattering
and for thermal dust emission. It performs well with both with CPUs and with
GPUs, the latter providing up to an order of magnitude speed-up. In the test
cases, ALI improved the convergence rates but also was sensitive to Monte Carlo
noise. Run-time refinement of the hierarchical-grid models did not help in
reducing the run times required for a given accuracy of solution. The use of a
reference field, without ALI, works more robustly. It also allows the run time
to be optimised if the number of photon packages is increased only as the
iterations progress.
  The use of GPUs in radiative transfer computations should be investigated
further.


  The recently proposed "generalized min-max" (GMM) kernel can be efficiently
linearized, with direct applications in large-scale statistical learning and
fast near neighbor search. The linearized GMM kernel was extensively compared
in with linearized radial basis function (RBF) kernel. On a large number of
classification tasks, the tuning-free GMM kernel performs (surprisingly) well
compared to the best-tuned RBF kernel. Nevertheless, one would naturally expect
that the GMM kernel ought to be further improved if we introduce tuning
parameters.
  In this paper, we study three simple constructions of tunable GMM kernels:
(i) the exponentiated-GMM (or eGMM) kernel, (ii) the powered-GMM (or pGMM)
kernel, and (iii) the exponentiated-powered-GMM (epGMM) kernel. The pGMM kernel
can still be efficiently linearized by modifying the original hashing procedure
for the GMM kernel. On about 60 publicly available classification datasets, we
verify that the proposed tunable GMM kernels typically improve over the
original GMM kernel. On some datasets, the improvements can be astonishingly
significant.
  For example, on 11 popular datasets which were used for testing deep learning
algorithms and tree methods, our experiments show that the proposed tunable GMM
kernels are strong competitors to trees and deep nets. The previous studies
developed tree methods including "abc-robust-logitboost" and demonstrated the
excellent performance on those 11 datasets (and other datasets), by
establishing the second-order tree-split formula and new derivatives for
multi-class logistic loss. Compared to tree methods like
"abc-robust-logitboost" (which are slow and need substantial model sizes), the
tunable GMM kernels produce largely comparable results.


  We describe an open-source simulator that creates sensor irradiance and
sensor images of typical automotive scenes in urban settings. The purpose of
the system is to support camera design and testing for automotive applications.
The user can specify scene parameters (e.g., scene type, road type, traffic
density, time of day) to assemble a large number of random scenes from graphics
assets stored in a database. The sensor irradiance is generated using
quantitative computer graphics methods, and the sensor images are created using
image systems sensor simulation. The synthetic sensor images have pixel level
annotations; hence, they can be used to train and evaluate neural networks for
imaging tasks, such as object detection and classification. The end-to-end
simulation system supports quantitative assessment, from scene to camera to
network accuracy, for automotive applications.


  In this paper, we study the so-called intermediate disorder regime for a
directed polymer in a random environment with heavy-tail. Consider a simple
symmetric random walk $(S_n)_{n\geq 0}$ on $\mathbb{Z}^d$, with $d\geq 1$, and
modify its law using Gibbs weights in the product form $\prod_{n=1}^{N}
(1+\beta\eta_{n,S_n})$, where $(\eta_{n,x})_{n\ge 0, x\in \mathbb{Z}^d}$ is a
field of i.i.d. random variables whose distribution satisfies
$\mathbb{P}(\eta>z) \sim z^{-\alpha}$ as $z\to\infty$, for some
$\alpha\in(0,2)$. We prove that if $\alpha< \min(1+\frac{2}{d},2)$, when
sending $N$ to infinity and rescaling the disorder intensity by taking
$\beta=\beta_N \sim N^{-\gamma}$ with $\gamma
=\frac{d}{2\alpha}(1+\frac{2}{d}-\alpha)$, the distribution of the trajectory
under diffusive scaling converges in law towards a random limit, which is the
continuum polymer with L\'evy $\alpha$-stable noise constructed in the
companion paper arXiv:2007.06484.