  Spin-waves (magnons) are among the prime candidates for building fast yet
energy-efficient platforms for information transport and computing. We here
demonstrate theoretically and in state-of-the-art micromagnetic simulation the
effects that strategically-injected spin-polarized current can have on
controlling magnonic transport. We reveal analytically that the Zhang-Li
spin-transfer-torque induced by applied current is analogous to the
Dzyaloshinskii-Moriya interaction for scattering the magnons in the linear
regime, to then provide a generalized Snell's law that describes the spin-wave
propagation across regions with different current densities. We validate the
latter in numerical simulations of realistic systems, and exemplify how these
findings may help advance the design of spin-wave logic and neuromorphic
computing devices.


  We determine the limiting distribution and the explicit tail behavior for the
maximal displacement of a branching symmetric stable process with spatially
inhomogeneous branching structure. Here the branching rate is a Kato class
measure with compact support and can be singular with respect to the Lebesgue
measure.


  We study a model of an equal mixture of two species of fermions in a deep
optical lattice at a filling of two fermions per site. At weak inter-species
interaction, the system is a band insulator. When the inter-species interaction
is tuned via a Feshbach resonance to be larger than an energy related to the
energy separation of the first and second Bloch band, atoms populate equally
the two Bloch bands. With weak tunneling between sites of the optical lattice,
the system becomes a Mott insulator with the low energy effective Hamiltonian
of a spin-1 Heisenberg antiferromagnet, because of a Hund's rule like coupling
between the two bands. We discuss experimental signatures of these two types of
insulators.


  We present high-resolution (0".4) mid-infrared (mid-IR) polarimetric images
and spectra of WL 16, a Herbig Ae star at a distance of 125 pc. WL 16 is
surrounded by a protoplanetary disk of $\sim$ 900 AU in diameter, making it one
of the most extended Herbig Ae/Be disks as seen in the mid-IR. The star is
behind, or embedded in, the $\rho$ Ophiuchus molecular cloud, and obscured by
28 magnitudes of extinction at optical wavelengths by the foreground cloud.
Mid-IR polarization of WL 16, mainly arises from aligned elongated dust grains
present along the line of sight, suggesting a uniform morphology of
polarization vectors with an orientation of 33\degr (East from North) and a
polarization fraction of $\sim$ 2.0\%. This orientation is consistent with
previous polarimetric surveys in the optical and near-IR bands to probe
large-scale magnetic fields in the Ophiuchus star formation region, indicating
that the observed mid-IR polarization toward WL 16 is produced by the dichroic
absorption of magnetically aligned foreground dust grains by a uniform magnetic
field. Using polarizations of WL 16 and Elias 29, a nearby polarization
standard star, we constrain the polarization efficiency,
\textit{$p_{10.3}/A_{10.3}$}, for the dust grains in the $\rho$ Ophiuchus
molecular cloud to be $\sim$ 1.0\% mag$^{-1}$. WL 16 has polycyclic aromatic
hydrocarbon (PAH) emission features detected at 8.6, 11.2, 12.0, and 12.7
$\mu$m by our spectroscopic data, and we find an anti-correlation between the
PAH surface brightness and the PAH ionization fraction between the NW and SW
sides of the disk.


  We investigate in detail an apparently unnoticed consequence of special
relativity. It consists in time dilation/contraction and frequency shift for
emitted light affecting accelerated reference frames at astronomical distances
from an inertial observer. The frequency shift is non-cosmological and
non-Doppler in nature. We derive the main formulae and compare their
predictions with the astronomical data available for Proxima Centauri. We found
no correspondence with observations. Since the implications of the new time
dilation/contraction and frequency shift are blatantly paradoxical, we do not
expect to find one. By all indications, we are dealing with a genuine, and not
a merely apparent, relativity paradox.


  Multiplicity fluctuations are one of the most crucial observables in the Beam
Energy Scan program of the Relativistic Heavy Ion Collider. It is understood
that they can be utilized to probe the whereabouts of the critical point on the
phase diagram of the QCD matter. However, a significant portion of these
fluctuations is, apart from that related to the QCD phase transition,
attributed to the other origins, which we refer to as "noncritical" ones. The
present study is dedicated to the noncritical aspects of the multiplicity
fluctuations in heavy-ion collisions. In particular, we focus on those of
dynamical origin, such as the hydrodynamic expansion of the system and the
event-by-event initial fluctuations, in addition to the usual thermal
fluctuations, finite volume corrections, and resonance decay at the freeze-out
surface. The obtained results are compared to those of the hadronic resonance
gas model as well as to the experimental data.


  E.A. Schoene et al., in arXiv:1012.3207 [Phys. Rev.A, 82, 023419 (2010)] give
incorrect interpretation of their experimental results. Really we observe a
temporary capture and additional cooling of atoms in the presence of the
orthogonal laser beam. Any strong potential barriers are absent here. It may be
easily experimentally tested.


  Helium nanodroplets doped with polar molecules are studied by electrostatic
deflection. This broadly applicable method allows even polyatomic molecules to
attain sub-Kelvin temperatures and nearly full orientation in the field. The
resulting intense force from the field gradient strongly deflects even droplets
with tens of thousands of atoms, the most massive neutral systems studied by
beam "deflectometry." We use the deflections to extract droplet size
distributions. Moreover, since each host droplet deflects according to its
mass, spatial filtering of the deflected beam translates into size filtering of
neutral fragile nanodroplets. As an example, we measure the dopant ionization
probability as a function of droplet radius and determine the mean free path
for charge hopping through the helium matrix. The technique will enable
separation of doped and neat nanodroplets and size-dependent spectroscopic
studies.


  In goal-conditioned hierarchical reinforcement learning (HRL), a high-level
policy specifies a subgoal for the low-level policy to reach. Effective HRL
hinges on a suitable subgoal represen tation function, abstracting state space
into latent subgoal space and inducing varied low-level behaviors. Existing
methods adopt a subgoal representation that provides a deterministic mapping
from state space to latent subgoal space. Instead, this paper utilizes Gaussian
Processes (GPs) for the first probabilistic subgoal representation. Our method
employs a GP prior on the latent subgoal space to learn a posterior
distribution over the subgoal representation functions while exploiting the
long-range correlation in the state space through learnable kernels. This
enables an adaptive memory that integrates long-range subgoal information from
prior planning steps allowing to cope with stochastic uncertainties.
Furthermore, we propose a novel learning objective to facilitate the
simultaneous learning of probabilistic subgoal representations and policies
within a unified framework. In experiments, our approach outperforms
state-of-the-art baselines in standard benchmarks but also in environments with
stochastic elements and under diverse reward conditions. Additionally, our
model shows promising capabilities in transferring low-level policies across
different tasks.


  The nature of the vertical thermal structure of hot Jupiter atmospheres is
one of the key questions raised by the characterization of transiting
exoplanets over the last decade. There have been claims that many hot Jupiter's
exhibit vertical profiles with increasing temperature with decreasing pressure
in the infrared photosphere that leads to the reversal of molecular absorption
bands into emission features (an inversion). However, these claims have been
based on broadband photometry rather than the unambiguous identification of
emission features with spectroscopy, and the chemical species that could cause
the thermal inversions by absorbing stellar irradiation at high altitudes have
not been identified despite extensive theoretical and observational effort.
Here we present high precision HST WFC3 observations of the dayside emission
spectrum of the hot Jupiter HD209458b; the first exoplanet suggested to have a
thermal inversion. Our observations resolve a water band in absorption at 6.2
sigma confidence. When combined with Spitzer photometry the data are indicative
of a monotonically decreasing temperature with pressure over the range 1-0.001
bar at 7.7 sigma confidence. We test the robustness of our results by exploring
a variety of model assumptions including the temperature profile
parameterization, presence of a cloud, and choice of Spitzer data reduction. We
also introduce a new analysis method, "chemical retrieval-on-retrieval", to
determine the elemental abundances from the spectrally retrieved mixing ratios
with thermochemical self-consistency and find plausible abundances consistent
with solar metallicity (0.06 - 10 x solar) and carbon-to-oxygen ratios less
than unity. This work suggests that high-precision spectrophotometric results
are required to robustly infer thermal structures and compositions of
extra-solar planet atmospheres.


  In the quantum process of stimulated Raman scattering (SRS), a laser photon
propagating in a resonance medium undergoes multifold conversions into a Stokes
photon and back. The nontrivial ``cooperative'' behavior of the Stokes
component of light transmitted through the medium is proven to be completely
determined by the interference of scattering amplitudes in different
sub-channels of the Stokes channel, which obviously combines all the
sub-channels with an odd number of photon conversions. The theory of
superfluorescence is then derived as the limiting case of the SRS theory.


  We investigate the space complexity of refuting $3$-CNFs in Resolution and
algebraic systems. We prove that every Polynomial Calculus with Resolution
refutation of a random $3$-CNF $\phi$ in $n$ variables requires, with high
probability, $\Omega(n)$ distinct monomials to be kept simultaneously in
memory. The same construction also proves that every Resolution refutation
$\phi$ requires, with high probability, $\Omega(n)$ clauses each of width
$\Omega(n)$ to be kept at the same time in memory. This gives a $\Omega(n^2)$
lower bound for the total space needed in Resolution to refute $\phi$. These
results are best possible (up to a constant factor).
  The main technical innovation is a variant of Hall's Lemma. We show that in
bipartite graphs $G$ with bipartition $(L,R)$ and left-degree at most 3, $L$
can be covered by certain families of disjoint paths, called VW-matchings,
provided that $L$ expands in $R$ by a factor of $(2-\epsilon)$, for $\epsilon <
1/23$.


  This technical report details changes applied to a noise filter to facilitate
its application and improve its results. The filter is applied to denoise
natural sounds recorded in the wild and to generate an acoustic index used in
soundscape analysis.


  In this paper, we study the robust optimal investment and risk control
problem for an insurer who owns the insider information about the financial
market and the insurance market under model uncertainty. Both financial risky
asset process and insurance risk process are assumed to be very general jump
diffusion processes. The insider information is of the most general form rather
than the initial enlargement type. We use the theory of forward integrals to
give the first half characterization of the robust optimal strategy and
transform the anticipating stochastic differential game problem into the
nonanticipative stochastic differential game problem. Then we adopt the
stochastic maximum principle to obtain the total characterization of the robust
strategy. We discuss the two typical situations when the insurer is `small' and
`large' by Malliavin calculus. For the `small' insurer, we obtain the
closed-form solution in the continuous case and the half closed-form solution
in the case with jumps. For the `large' insurer, we reduce the problem to the
quadratic backward stochastic differential equation (BSDE) and obtain the
closed-form solution in the continuous case without model uncertainty. We
discuss some impacts of the model uncertainty, insider information and the
`large' insurer on the optimal strategy.


  In this paper we have obtained two more characterizations of nearly
pseudocompact spaces.


  We review the subject of Kahler anomalies in gauged supergravity, emphasizing
that field equations are inconsistent when the Kahler potential is
non-invariant under gauge transformations or when there are elementary
Fayet-Iliopoulos couplings. Flux vacua solutions of string theory with gauged
U(1) shift symmetries appear to avoid this problem. The covariant Kahler
anomalies involve tensors which are composite functions of the scalars as well
as the gauge field strength and space-time curvature tensors. Anomaly
cancellation conditions will be discussed in a sequel to this paper.


  A semigroup generated by two dimensional $C^{1+\alpha}$ contracting maps is
considered. We call a such semigroup regular if the maximum $K$ of the
conformal dilatations of generators, the maximum $l$ of the norms of the
derivatives of generators and the smoothness $\alpha$ of the generators satisfy
a compatibility condition $K< 1/l^{\alpha}$. We prove that the shape of the
image of the core of a ball under any element of a regular semigroup is good
(bounded geometric distortion like the Koebe $1/4$-lemma \cite{a}). And we use
it to show a lower and a upper bounds of the Hausdorff dimension of the limit
set of a regular semigroup. We also consider a semigroup generated by higher
dimensional maps.


  In this paper we analyse the existence and non-existence of non-negative
solutions to a non-local parabolic equation with a Hardy-Leray type potential.
More precisely, we consider the problem $$ \begin{cases} (w_t-\Delta
w)^s=\frac{\lambda}{|x|^{2s}} w+w^p +f, &\text{ in }\mathbb{R}^N\times
(0,+\infty),\\ w(x,t)=0, &\text{ in }\mathbb{R}^N\times (-\infty,0],
\end{cases} $$ where $N> 2s$, $0<s<1$ and $0<\lambda<\Lambda_{N,s}$, the
optimal constant in the fractional Hardy-Leray inequality. In particular we
show the existence of a critical existence exponent $p_{+}(\lambda, s)$ and of
a Fujita-type exponent $F(\lambda,s)$ such that the following holds:
  - Let $p>p_+(\lambda,s)$. Then there are not any non-negative supersolutions.
  - Let $p<p_+(\lambda,s)$. Then there exist local solutions while concerning
global solutions we need to distinguish two cases:
  - Let $ 1< p\le F(\lambda,s)$. Here we show that a weighted norm of any
positive solution blows up in finite time.
  - Let $F(\lambda,s)<p<p_+(\lambda,s)$. Here we prove the existence of global
solutions under suitable hypotheses.


  Let g be a complex, semisimple Lie algebra, and Y_h(g) and U_q(Lg) the
Yangian and quantum loop algebra of g. Assuming that h is not a rational number
and that q=exp(i \pi h), we construct an equivalence between the
finite-dimensional representations of U_q(Lg) and an explicit subcategory of
those of Y_h(g) defined by choosing a branch of the logarithm. This equivalence
is governed by the monodromy of the abelian additive difference equations
defined by the commuting fields of Y_h(g). Our results are compatible with
q-characters, and apply more generally to a symmetrisable Kac-Moody algebra g,
in particular to affine Yangians and quantum toroidal algebras. In this
generality, they yield an equivalence between the representations of Y_h(g) and
U_q(Lg) whose restriction to g and U_q(g) respectively are integrable and in
category O.


  We consider distributed gradient descent in the presence of stragglers.
Recent work on \em gradient coding \em and \em approximate gradient coding \em
have shown how to add redundancy in distributed gradient descent to guarantee
convergence even if some workers are \em stragglers\em---that is, slow or
non-responsive. In this work we propose an approximate gradient coding scheme
called \em Stochastic Gradient Coding \em (SGC), which works when the
stragglers are random. SGC distributes data points redundantly to workers
according to a pair-wise balanced design, and then simply ignores the
stragglers. We prove that the convergence rate of SGC mirrors that of batched
Stochastic Gradient Descent (SGD) for the $\ell_2$ loss function, and show how
the convergence rate can improve with the redundancy. We also provide bounds
for more general convex loss functions. We show empirically that SGC requires a
small amount of redundancy to handle a large number of stragglers and that it
can outperform existing approximate gradient codes when the number of
stragglers is large.


  The task of Semantic Parsing can be approximated as a transformation of an
utterance into a logical form graph where edges represent semantic roles and
nodes represent word senses. The resulting representation should be capture the
meaning of the utterance and be suitable for reasoning. Word senses and
semantic roles are interdependent, meaning errors in assigning word senses can
cause errors in assigning semantic roles and vice versa. While statistical
approaches to word sense disambiguation outperform logical, rule-based semantic
parsers for raw word sense assignment, these statistical word sense
disambiguation systems do not produce the rich role structure or detailed
semantic representation of the input. In this work, we provide hints from a
statistical WSD system to guide a logical semantic parser to produce better
semantic type assignments while maintaining the soundness of the resulting
logical forms. We observe an improvement of up to 10.5% in F-score, however we
find that this improvement comes at a cost to the structural integrity of the
parse


  We prove that the "Thaddeus flips" of $L$-twisted sheaves constructed by
Matsuki and Wentworth can be obtained via Bridgeland wall-crossing. Similarly,
we realize the change of polarization for moduli spaces of 1-dimensional
Gieseker semistable sheaves on a surface by varying a family of stability
conditions.


  The problem of possible deviations from the Standard Model is considered in
the framework of a variant of dynamical electroweak symmetry breaking. It comes
clear, that the parameters of the theory, being obtained earlier and describing
deviations from SM in Z --> \bar b b decay, are also consistent with the
existence of a nontrivial solution for vertex \bar t (Z,\gamma) c. The
occurrence of this solution leads to a significant enhancement in neutral
flavor changing transition t --> c. The intensity of this transition is
connected with the c-quark mass, that leads to estimates of probabilities of
exotic decays t --> c (Z,\gamma) (few %) and of the cross-section of a single
t-quark production in process e^+e^- --> t \bar c at LEP2 (around 0.03 pb at
\sqrt{s} = 190 GeV). The model is shown to be consistent with the totality of
the existing data; the predictions allow its unambiguous check.


  We compute the center and the Lie algebra of outer derivations of a familiy
of algebras of differential operators associated to hyperplane arrangements of
the affine space A 3. The results are completed for 4-braid arrangements and
for reflection arrangements associated to the wreath product of a cyclic group
with the symmetric group S 3. To achieve this we use tools from homological
algebra and Lie-Rinehart algebras of differential operators.


  The nucleon wave function may contain a significant component of ssbar pairs,
according to several measurements including the pi-nucleon sigma term, charm
production and polarization effects in deep-inelastic scattering. In addition,
there are excesses of phi production in LEAR and other experiments, above
predictions based the naive Okubo-Zweig-Iizuka rule, that may be explained if
the nucleon wave function contains a polarized ssbar component. This model also
reproduces qualitatively data on Lambda polarization in deep-inelastic neutrino
scattering. The strange component of the proton is potentially important for
other physics, such as the search for astrophysical dark matter.


  Quantum mechanics dramatically differs from classical physics, allowing for a
wide range of genuinely quantum phenomena. The goal of quantum information is
to understand information processing from a quantum perspective. In this
mindset, it is thus natural to focus on tasks where quantum resources provide
an advantage over classical ones, and to overlook tasks where quantum mechanics
provides no advantage. But are the latter tasks really useless from a more
general perspective? Here we discuss a simple information-theoretic game called
'guess your neighbour's input', for which classical and quantum players perform
equally well. We will see that this seemingly innocuous game turns out to be
useful in various contexts. From a fundamental point of view, the game provides
a sharp separation between quantum mechanics and other more general physical
theories, hence bringing a deeper understanding of the foundations of quantum
mechanics. The game also finds unexpected applications in quantum foundations
and quantum information theory, related to Gleason's theorem, and to bound
entanglement and unextendible product bases.


  In this paper, a resilient controller is designed for the linear
time-invariant (LTI) systems subject to attacks on the sensors and the
actuators. A novel probabilistic attack model is proposed to capture
vulnerabilities of the communication links from sensors to the controller and
from the controller to actuators. The observer and the controller formulation
under the attack are derived. Thereafter, By leveraging Lyapunov functional
methods, it is shown that exponential mean-square stability of the system under
the output feedback controller is guaranteed if a certain LMI is feasible. The
simulation results show the effectiveness and applicability of the proposed
controller design approach.


  We study the problem of testing and recovering $k$-clique Ferromagnetic mean
shift in the planted Sherrington-Kirkpatrick model (i.e., a type of spin glass
model) with $n$ spins. The planted SK model -- a stylized mixture of an
uncountable number of Ising models -- allows us to study the fundamental limits
of correlation analysis for dependent random variables under misspecification.
Our paper makes three major contributions: (i) We identify the phase diagrams
of the testing problem by providing minimax optimal rates for multiple
different parameter regimes. We also provide minimax optimal rates for exact
recovery in the high/critical and low temperature regimes. (ii) We prove a
universality result implying that all the obtained rates still hold with
non-Gaussian couplings. (iii) To achieve the major results, we also establish a
family of novel concentration bounds and central limiting theorems for the
averaging statistics in the local and global phases of the planted SK model.
These technical results shed new insights into the planted spin glass models.
The pSK model also exhibits close connections with a binary variant of the
single spike Gaussian sparse principle component analysis model by replacing
the background identity precision matrix with a Wigner random matrix.


  We present direct numerical simulations (DNS) study of confined
buoyancy-driven bubbly flows in a Hele-Shaw setup. We investigate the spectral
properties of the flow and make comparisons with experiments. The energy
spectrum obtained from the gap-averaged velocity field shows $E(k) \sim k$ for
$k < k_d$, $E(k) \sim k^{-5}$ for $k > k_d$, and an intermediate scaling range
with $E(k) \sim k^{-3}$ around $k \sim k_d$. We perform an energy budget
analysis to understand the dominant balances and explain the observed scaling
behavior. We also show that the Navier-Stokes equation with a linear drag can
be used to approximate large scale flow properties of bubbly Hele-Shaw flow.


  An empirical $s_cp^3_a$ tight-binding (TB) model is applied to the
investigation of electronic states in semiconductor quantum dots. A basis set
of three $p$-orbitals at the anions and one $s$-orbital at the cations is
chosen. Matrix elements up to the second nearest neighbors and the spin-orbit
coupling are included in our TB-model. The parametrization is chosen so that
the effective masses, the spin-orbit-splitting and the gap energy of the bulk
CdSe and ZnSe are reproduced. Within this reduced $s_cp_a^3$ TB-basis the
valence (p-) bands are excellently reproduced and the conduction (s-) band is
well reproduced close to the $\Gamma$-point, i.e. near to the band gap. In
terms of this model much larger systems can be described than within a (more
realistic) $sp^3s^*$-basis. The quantum dot is modelled by using the (bulk)
TB-parameters for the particular material at those sites occupied by atoms of
this material. Within this TB-model we study pyramidal-shaped CdSe quantum dots
embedded in a ZnSe matrix and free spherical CdSe quantum dots (nanocrystals).
Strain-effects are included by using an appropriate model strain field. Within
the TB-model, the strain-effects can be artifically switched off to investigate
the infuence of strain on the bound electronic states and, in particular, their
spatial orientation. The theoretical results for spherical nanocrystals are
compared with data from tunneling spectroscopy and optical experiments.
Furthermore the influence of the spin-orbit coupling is investigated.


  In this study, we benchmark query strategies for deep actice learning~(DAL).
DAL reduces annotation costs by annotating only high-quality samples selected
by query strategies. Existing research has two main problems, that the
experimental settings are not standardized, making the evaluation of existing
methods is difficult, and that most of experiments were conducted on the CIFAR
or MNIST datasets. Therefore, we develop standardized experimental settings for
DAL and investigate the effectiveness of various query strategies using six
datasets, including those that contain medical and visual inspection images. In
addition, since most current DAL approaches are model-based, we perform
verification experiments using fully-trained models for querying to investigate
the effectiveness of these approaches for the six datasets. Our code is
available at
\href{https://github.com/ia-gu/Benchmarking-of-Query-Strategies-Towards-Future-Deep-Active-Learning}


  Despite impressive state-of-the-art performance on a wide variety of machine
learning tasks, deep learning methods can produce over-confident predictions,
particularly with limited training data. Therefore, quantifying uncertainty is
particularly important in critical applications such as lesion detection and
clinical diagnosis, where a realistic assessment of uncertainty is essential in
determining surgical margins, disease status and appropriate treatment. In this
work, we propose a novel approach that uses quantile regression for quantifying
aleatoric uncertainty in both supervised and unsupervised lesion detection
problems. The resulting confidence intervals can be used for lesion detection
and segmentation. In the unsupervised setting, we combine quantile regression
with the Variational AutoEncoder (VAE). Here we address the problem of
quantifying uncertainty in the images that are reconstructed by the VAE as the
basis for principled outlier or lesion detection. The VAE models the output as
a conditionally independent Gaussian characterized by its mean and variance.
Unfortunately, joint optimization of both mean and variance in the VAE leads to
the well-known problem of shrinkage or underestimation of variance. Here we
describe an alternative Quantile-Regression VAE (QR-VAE) that avoids this
variance shrinkage problem by directly estimating conditional quantiles for the
input image. Using the estimated quantiles, we compute the conditional mean and
variance for the input image from which we then detect outliers by thresholding
at a false-discovery-rate corrected p-value. In the supervised setting, we
develop binary quantile regression (BQR) for the supervised lesion segmentation
task. We show how BQR can be used to capture uncertainty in lesion boundaries
in a manner that characterizes expert disagreement.


  We introduce Private Collection Matching (PCM) problems, in which a client
aims to determine whether a collection of sets owned by a server matches their
interests. Existing privacy-preserving cryptographic primitives cannot solve
PCM problems efficiently without harming privacy. We propose a modular
framework that enables designers to build privacy-preserving PCM systems that
output one bit: whether a collection of server sets matches the client's set.
The communication cost of our protocols scales linearly with the size of the
client's set and is independent of the number of server elements. We
demonstrate the potential of our framework by designing and implementing novel
solutions for two real-world PCM problems: determining whether a dataset has
chemical compounds of interest, and determining whether a document collection
has relevant documents. Our evaluation shows that we offer a privacy gain with
respect to existing works at a reasonable communication and computation cost.


  We study the gradient method under the assumption that an additively inexact
gradient is available for, generally speaking, non-convex problems. The
non-convexity of the objective function, as well as the use of an inexactness
specified gradient at iterations, can lead to various problems. For example,
the trajectory of the gradient method may be far enough away from the starting
point. On the other hand, the unbounded removal of the trajectory of the
gradient method in the presence of noise can lead to the removal of the
trajectory of the method from the desired exact solution. The results of
investigating the behavior of the trajectory of the gradient method are
obtained under the assumption of the inexactness of the gradient and the
condition of gradient dominance. It is well known that such a condition is
valid for many important non-convex problems. Moreover, it leads to good
complexity guarantees for the gradient method. A rule of early stopping of the
gradient method is proposed. Firstly, it guarantees achieving an acceptable
quality of the exit point of the method in terms of the function. Secondly, the
stopping rule ensures a fairly moderate distance of this point from the chosen
initial position. In addition to the gradient method with a constant step, its
variant with adaptive step size is also investigated in detail, which makes it
possible to apply the developed technique in the case of an unknown Lipschitz
constant for the gradient. Some computational experiments have been carried out
which demonstrate effectiveness of the proposed stopping rule for the
investigated gradient methods.


  To render cosmic shear an astronomical tool of high precision, it is
essential to eliminate systematic effects upon its signal, one of the most
significant ones being correlations between the gravitational shear and the
intrinsic ellipticity of source galaxies. Because of the crudeness of current
models of intrinsic alignment, we have developed a model-independent, purely
geometrical method to remove shear-ellipticity correlations. We eliminate the
contributions to a tomographic cosmic shear signal that may be subject to
contamination by shear-ellipticity correlations, making use of the
characteristic dependence of these correlations on redshift. By introducing an
appropriately chosen weight function to the lensing efficiency that nulls
signals stemming from certain distances, new second-order measures of cosmic
shear, free of intrinsic alignment, can be constructed. The loss of information
induced by this nulling technique and the subsequent degradation of constraints
on cosmological parameters is quantified in a likelihood analysis. Concerning
the construction of optimal weight functions, good agreement is achieved
between all approaches considered. For a survey divided into 20 redshift bins
we find that the area of credible regions increases by 20% up to about 50%
after the application of nulling, depending on the cosmological parameters
considered. We demonstrate that due to an optimization of the weight functions
nearly all information is contained in a small subset of the new second-order
measures. The use of a significantly smaller number of redshift bins than 20
for the nulling considerably degrades parameter constraints under conservative
assumptions, emphasizing the need for detailed redshift information.


  Facial analysis is a key technology for enabling human-machine interaction.
In this context, we present a client-server framework, where a client transmits
the signature of a face to be analyzed to the server, and, in return, the
server sends back various information describing the face e.g. is the person
male or female, is she/he bald, does he have a mustache, etc. We assume that a
client can compute one (or a combination) of visual features; from very simple
and efficient features, like Local Binary Patterns, to more complex and
computationally heavy, like Fisher Vectors and CNN based, depending on the
computing resources available. The challenge addressed in this paper is to
design a common universal representation such that a single merged signature is
transmitted to the server, whatever be the type and number of features computed
by the client, ensuring nonetheless an optimal performance. Our solution is
based on learning of a common optimal subspace for aligning the different face
features and merging them into a universal signature. We have validated the
proposed method on the challenging CelebA dataset, on which our method
outperforms existing state-of-the-art methods when rich representation is
available at test time, while giving competitive performance when only simple
signatures (like LBP) are available at test time due to resource constraints on
the client.


  The class $\mathcal{UP}$ of `ultimate polynomial time' problems over $\mathbb
C$ is introduced; it contains the class $\mathcal P$ of polynomial time
problems over $\mathbb C$.
  The $\tau$-Conjecture for polynomials implies that $\mathcal{UP}$ does not
contain the class of non-deterministic polynomial time problems definable
without constants over $\mathbb C$.
  This latest statement implies that $\mathcal P \ne \mathcal{NP}$ over
$\mathbb C$.
  A notion of `ultimate complexity' of a problem is suggested. It provides
lower bounds for the complexity of structured problems.


  Quantum-mechanical analysis shows that the metrics of a centrally symmetric
uncharged gravitational field, which are exact solutions of the general
relativity equations, are physically non-equivalent. The classical
Schwarzschield metric and the Schwarzschild metrics in isotropic and harmonic
coordinates provide for the existence of stationary bound states of Dirac
particles with a real energy spectrum. The Hilbert condition g_{00}>0 is
responsible for zero values of the wave functions under the "event horizon"
that leads to the absence of Hawking radiation. For the Eddington-Finkelstein
and Painleve-Gullstrand metrics, stationary bound states of spin-half particles
cannot exist because Dirac Hamiltonians are non-Hermitian. For these metrics,
the condition g_{00}>0 also leads to the absence of Hawking evaporation. For
the Finkelstein-Lemaitre and Kruskal metrics, Dirac Hamiltonians are explicitly
time-dependent, and stationary bound states of spin-half particles cannot exist
for them. The Hilbert condition for these metrics does not place any
constraints on the domains of the wave functions. Hawking evaporation of black
holes is possible in this case. The results can lead to revisiting some
concepts of the standard cosmological model related to the evolution of the
universe and interaction of collapsars with surrounding matter.


  Main belt comets (MBCs) are a peculiar class of volatile-containing objects
with comet-like morphology and asteroid-like orbits. However, MBCs are
challenging targets to study remotely due to their small sizes and the
relatively large distance they are from the Sun and the Earth. Recently, a
number of weakly active short-period comets have been identified that might
originate in the asteroid main belt. Among all of the known candidates, comet
66P/du Toit has been suggested to have one of the highest probabilities of
coming from the main belt. We obtained medium and high-resolution spectra of
66P from 300-2500 nm with the X-shooter/VLT and the UVES/VLT instruments in
July 2018. We also obtained a series of narrow-band images of 66P to monitor
the gas and dust activity between May and July 2018 with TRAPPIST-South. In
addition, we applied a dust model to characterize the dust coma of 66P and
performed dynamical simulations to study the orbital evolution of 66P. We
derive the OPR of ammonia (NH$_3$) in 66P to be 1.08$\pm$0.06, which
corresponds to a nuclear spin temperature of $\sim$34 K. We computed the
production rates of OH, NH, CN, C$_3,$ and C$_2$ radicals and measured the dust
proxy, Af$\rho$. The dust analysis reveals that the coma can be best-fit with
an anisotropic model and the peak dust production rate is about 55 kg s$^{-1}$
at the perihelion distance of 1.29 au. Dynamical simulations show that 66P is
moderately asteroidal with the capture time, t$_{cap} \sim 10^4$ yr. Our
observations demonstrate that the measured physical properties of 66P are
consistent with other typical short-period comets and differ significantly from
other MBCs. Therefore, 66P is unlikely to have a main belt origin.


  Given a complex affine hypersurface with isolated singularity determined by a
homogeneous polynomial, we identify the noncommutative Hodge structure on the
periodic cyclic homology of its singularity category with the classical Hodge
structure on the primitive cohomology of the associated projective
hypersurface. As a consequence, we show that the Hodge conjecture for the
projective hypersurface is equivalent to a dg-categorical analogue of the Hodge
conjecture for the singularity category.


  We consider the bimodal language, where the first modality is interpreted by
a binary relation in the standard way, and the second is interpreted by the
relation of inequality. It follows from Hughes (1990), that in this language,
non-$k$-colorability of a graph is expressible for every finite $k$. We show
that modal logics of classes of non-$k$-colorable graphs (directed or
non-directed), and some of their extensions, are decidable.


  Nonequilibrium steady states of vibrated inelastic frictionless spheres are
investigated in quasi-two-dimensional confinement via molecular dynamics
simulations. The phase diagram in the density-amplitude plane exhibits a
fluidlike disordered and an ordered phase with threefold symmetry, as well as
phase coexistence between the two. A dynamical mechanism exists that brings
about metastable traveling clusters and at the same time stable clusters with
anisotropic shapes at low vibration amplitude. Moreover, there is a square
bilayer state which is connected to the fluid by BKTHNY-type two-step melting
with an intermediate tetratic phase. The critical behavior of the two
continuous transitions is studied in detail. For the fluid-tetratic transition,
critical exponents of $\tilde{\gamma}=1.73$, $\eta_4 \approx 1/4$, and $z=2.05$
are obtained.


  It was shown before that the NP-hard problem of deterministic finite automata
(DFA) identification can be effectively translated to Boolean satisfiability
(SAT). Modern SAT-solvers can tackle hard DFA identification instances
efficiently. We present a technique to reduce the problem search space by
enforcing an enumeration of DFA states in depth-first search (DFS) or
breadth-first search (BFS) order. We propose symmetry breaking predicates,
which can be added to Boolean formulae representing various DFA identification
problems. We show how to apply this technique to DFA identification from both
noiseless and noisy data. Also we propose a method to identify all automata of
the desired size. The proposed approach outperforms the current
state-of-the-art DFASAT method for DFA identification from noiseless data. A
big advantage of the proposed approach is that it allows to determine exactly
the existence or non-existence of a solution of the noisy DFA identification
problem unlike metaheuristic approaches such as genetic algorithms.


  The problem of univariate mean change point detection and localization based
on a sequence of $n$ independent observations with piecewise constant means has
been intensively studied for more than half century, and serves as a blueprint
for change point problems in more complex settings. We provide a complete
characterization of this classical problem in a general framework in which the
upper bound $\sigma^2$ on the noise variance, the minimal spacing $\Delta$
between two consecutive change points and the minimal magnitude $\kappa$ of the
changes, are allowed to vary with $n$. We first show that consistent
localization of the change points, when the signal-to-noise ratio $\frac{\kappa
\sqrt{\Delta}}{\sigma} < \sqrt{\log(n)}$, is impossible. In contrast, when
$\frac{\kappa \sqrt{\Delta}}{\sigma}$ diverges with $n$ at the rate of at least
$\sqrt{\log(n)}$, we demonstrate that two computationally-efficient change
point estimators, one based on the solution to an $\ell_0$-penalized least
squares problem and the other on the popular wild binary segmentation
algorithm, are both consistent and achieve a localization rate of the order
$\frac{\sigma^2}{\kappa^2} \log(n)$. We further show that such rate is minimax
optimal, up to a $\log(n)$ term.


  When deploying neural networks in real-life situations, the size and
computational effort are often the limiting factors. This is especially true in
environments where big, expensive hardware is not affordable, like in embedded
medical devices, where budgets are often tight. State-of-the-art proposed
multiple different lightweight solutions for such use cases, mostly by changing
the base model architecture, not taking the input and output resolution into
consideration. In this paper, we propose our architecture that takes advantage
of the fact that in hardware-limited environments, we often refrain from using
the highest available input resolutions to guarantee a higher throughput.
Although using lower-resolution input leads to a significant reduction in
computing and memory requirements, it may also incur reduced prediction
quality. Our architecture addresses this problem by exploiting the fact that we
can still utilize high-resolution ground-truths in training. The proposed model
inputs lower-resolution images and high-resolution ground truths, which can
improve the prediction quality by 5.5% while adding less than 200 parameters to
the model. %reducing the frames per second only from 25 to 20. We conduct an
extensive analysis to illustrate that our architecture enhances existing
state-of-the-art frameworks for lightweight semantic segmentation of cancer in
MRI images. We also tested the deployment speed of state-of-the-art lightweight
networks and our architecture on Nvidia's Jetson Nano to emulate deployment in
resource-constrained embedded scenarios.


  Harnessing the full complexity of optical fields requires complete control of
all degrees-of-freedom within a region of space and time -- an open goal for
present-day spatial light modulators (SLMs), active metasurfaces, and optical
phased arrays. Here, we solve this challenge with a programmable photonic
crystal cavity array enabled by four key advances: (i) near-unity vertical
coupling to high-finesse microcavities through inverse design, (ii) scalable
fabrication by optimized, 300 mm full-wafer processing, (iii)
picometer-precision resonance alignment using automated, closed-loop
"holographic trimming", and (iv) out-of-plane cavity control via a high-speed
micro-LED array. Combining each, we demonstrate near-complete spatiotemporal
control of a 64-resonator, two-dimensional SLM with nanosecond- and
femtojoule-order switching. Simultaneously operating wavelength-scale modes
near the space- and time-bandwidth limits, this work opens a new regime of
programmability at the fundamental limits of multimode optical control.


  In the paper the role of conservation laws in evolutionary processes, which
proceed in material systems (in material media) and lead to generation of
physical fields, is shown using skew-symmetric differential forms.
  In present paper the skew-symmetric differential forms on deforming
(nondifferentiable) manifolds were used in addition to exterior forms, which
have differentiable manifolds as a basis. Such skew-symmetric forms (which were
named evolutionary ones since they possess evolutionary properties), as well as
the closed exterior forms, describe the conservation laws. But in contrast to
exterior forms, which describe conservation laws for physical fields, the
evolutionary forms correspond to conservation laws for material systems.
  The evolutionary forms possess an unique peculiarity, namely, the closed
exterior forms are obtained from these forms. It is just this that enables one
to describe the process of generation of physical fields, to disclose
connection between physical fields and material systems and to resolve many
problems of existing field theories.


  We present a Lagrange--Galerkin scheme free from numerical quadrature for the
Navier--Stokes equations. Our idea is to use a locally linearized velocity and
the backward Euler method in finding the position of fluid particle at the
previous time step. Since the scheme can be implemented exactly as it is, the
theoretical stability and convergence results are assured. While the
conventional Lagrange--Galerkin schemes may encounter the instability caused by
numerical quadrature errors, the present scheme is genuinely stable. For the
$\pk 2/\pk 1$- and $\mini$-finite elements optimal error estimates are proved
in $\ell^\infty(H^1)\times \ell^2(L^2)$ norm for the velocity and pressure. We
present some numerical results, which reflect these estimates and also show the
genuine stability of the scheme.


  We calculate spin-independent and spin-dependent direct detection cross
sections of neutralino dark matter at next-to-leading order of QCD. The
numerical effects are comparable in size to the uncertainties in the nuclear
matrix elements. Our results are applicable to bino, wino or higgsino dark
matter and allow for consistent correlations with the relic density in DM@NLO.


  Most social network analysis works at the level of interactions between
users. But the vast growth in size and complexity of social networks enables us
to examine interactions at larger scale. In this work we use a dataset of 76M
submissions to the social network Reddit, which is organized into distinct
sub-communities called subreddits. We measure the similarity between entire
subreddits both in terms of user similarity and topical similarity. Our goal is
to find community pairs with similar userbases, but dissimilar content; we
refer to this type of relationship as a "latent interest." Detection of latent
interests not only provides a perspective on individual users as they shift
between roles (student, sports fan, political activist) but also gives insight
into the dynamics of Reddit as a whole. Latent interest detection also has
potential applications for recommendation systems and for researchers examining
community evolution.


  Two de-modulation algorithms are used to observe free-oscillations of the
earth that are coincident with earthquakes.


  The ever-growing ecosystem of LLMs has posed a challenge in selecting the
most appropriate pre-trained model to fine-tune amidst a sea of options. Given
constrained resources, fine-tuning all models and making selections afterward
is unrealistic. In this work, we formulate this resource-constrained selection
task into predicting fine-tuning performance and illustrate its natural
connection with Scaling Law. Unlike pre-training, we find that the fine-tuning
scaling curve includes not just the well-known "power phase" but also the
previously unobserved "pre-power phase". We also explain why existing Scaling
Law fails to capture this phase transition phenomenon both theoretically and
empirically. To address this, we introduce the concept of "pre-learned data
size" into our Rectified Scaling Law, which overcomes theoretical limitations
and fits experimental results much better. By leveraging our law, we propose a
novel LLM selection algorithm that selects the near-optimal model with hundreds
of times less resource consumption, while other methods may provide negatively
correlated selection. The project page is available at
rectified-scaling-law.github.io.


  I briefly summarize the application of the Dyson-Schwinger/Faddeev approach
to baryon form factors. Recent results for nucleon electromagnetic and axial
form factors as well as N-Delta-Gamma electromagnetic transition form factors
are discussed. The calculation of the current diagrams from the quark-gluon
level enables an analysis of common features, such as the implications of
dynamical chiral symmetry breaking and quark orbital angular momentum, the
timelike structure of the form factors, and their interpretation in terms of
missing pion-cloud effects.


  We construct a sample of low-redshift Ly-alpha emission-line selected sources
from GALEX grism spectroscopy of nine deep fields to study the role of Ly-alpha
emission in galaxy populations with cosmic time. Our final sample consists of
119 (141) sources selected in the redshift interval z=0.195-0.44 (z=0.65-1.25)
from the FUV (NUV) channel. We classify the Ly-alpha sources as AGNs if
high-ionization emission lines are present in their UV spectra and as possible
star-forming galaxies otherwise. We classify additional sources as AGNs using
line widths for our Ly-alpha emitter (LAE) analysis. These classifications are
broadly supported by comparisons with X-ray and optical spectroscopic
observations. Defining the GALEX LAE sample in the same way as high-redshift
LAE samples, we show that LAEs constitute only about 5% of NUV-continuum
selected galaxies at z~0.3. We also show that they are less common at z~0.3
than they are at z~3. We find that the z~0.3 optically-confirmed Ly-alpha
galaxies lie below the metallicity-luminosity relation of the z~0.3
NUV-continuum selected galaxies but have similar H-alpha velocity widths at
similar luminosities, suggesting that they also lie below the metallicity-mass
relation of the NUV-continuum selected galaxies. We show that, on average, the
Ly-alpha galaxies have bluer colors, lower extinctions as measured from the
Balmer line ratios, and more compact morphologies than the NUV-continuum
selected galaxies. Finally, we confirm that the z~2 Lyman break galaxies (LBGs)
have relatively low metallicities for their luminosities, and we find that they
lie in the same metallicity range as the z~0.3 Ly-alpha galaxies.


  Let $c\phi_{k}(n)$ be the number of $k$-colored generalized Frobenius
partitions of $n$. We establish some infinite families of congruences for
$c\phi_{3}(n)$ and $c\phi_{9}(n)$ modulo arbitrary powers of 3, which refine
the results of Kolitsch. For example, for $k\ge 3$ and $n\ge 0$, we prove that
\[c\phi_{3}\Big(3^{2k}n+\frac{7\cdot 3^{2k}+1}{8}\Big) \equiv 0
\pmod{3^{4k+5}}.\] We give two different proofs to the congruences satisfied by
$c\phi_{9}(n)$. One of the proofs uses an relation between $c\phi_{9}(n)$ and
$c\phi_{3}(n)$ due to Kolitsch, for which we provide a new proof in this paper.


  We consider general linear Higgs-sigma models as ultra-violet completions of
the Higgs inflation. We introduce general higher curvature terms beyond
Einstein gravity and recast them into a class of linear Higgs-sigma models in
the scalar-dual formulation where conformal symmetry is manifest. Integrating
out the sigma field in this class of linear sigma models, we obtain the same
Higgs inflation Lagrangian of non-linear sigma model type in the effective
theory. We show that the successful inflation for sigma field singles out the
sigma-field potential derived from the $R^2$ term and the tracker solution for
dark energy at late times can be realized for the $R^{p+1}$ term with $-1<p<0$.
We also discuss the implications of Higgs-sigma interactions for the inflation
and the vacuum stability in the Standard Model.


  I correct an error in my article arXiv:0911.5474, concerning the
non-surjectivity of the Wahl map of nodal curves on K3 surfaces. I prove that a
modification of the Wahl map is indeed non-surjective for nodal curves with a
low number of nodes, on arbitrary K3 surfaces. Along the way, I also obtain a
lower bound of independent interest for the multiple point Seshadri constants
of K3 surfaces with cyclic Picard group.


  We use recent Belle results on $\bar{B}^0\rightarrow D^{*+}l^-\bar{\nu}_l$
decays to extract the CKM element $|V_{cb}|$ with two different but
well-founded parameterizations of the form factors. We show that the CLN and
BGL parameterizations lead to quite different results for $|V_{cb}|$ and
provide a simple explanation of this unexpected behaviour. A long lasting
discrepancy between the inclusive and exclusive determinations of $|V_{cb}|$
may have to be thoroughly reconsidered.


  We introduce in this work a concept of rough driver that somehow provides a
rough path-like analogue of an enriched object associated with time-dependent
vector fields. We use the machinery of approximate flows to build the
integration theory of rough drivers and prove well-posedness results for rough
differential equations on flows and continuity of the solution flow as a
function of the generating rough driver. We show that the theory of
semi-martingale stochastic flows developed in the 80's and early 90's fits
nicely in this framework, and obtain as a consequence some strong approximation
results for general semimartingale flows and provide a fresh look at large
deviation theorems for 'Gaussian' stochastic flows.


  Lattice sum rules are checked using lattice perturbation theory. The action
sum rule gives a relation between the quark-antiquark potential, its
logarithmic derivative with respect to distance and the expectation value of
the action; the energy sum rule expresses the potential as the sum of the
energy in the gluon fields and of an anomalous term. Two different independent
calculations of the quark-antiquark potential are presented, and the
transversality of the gluonic vacuum polarization on the lattice is proven. The
crucial part of the action sum rule is an identity whose explicit check using
perturbation theory provides methods and results which are useful for checking
the energy sum rule. Additionally, the gauge invariance of the expectation
value of the Wilson loop up to next-to-leading order is proven. The possibility
of restricting the expectation value of the action to one fixed time slice is
discussed. The energy sum rule is checked perturbatively up to next-to-leading
order and shown to be satisfied with good numerical accuracy. The various
contributions to the quark-antiquark potential are analyzed, and the
restriction of the expectation value of the sum over all spatial plaquettes
(the energy in the magnetic fields) to one fixed time slice is examined.


  Electromagnetic field of a fast electric charge in nuclear matter with
spatially uniform but random topological charge density is derived. A useful
approximation is developed for the relativistic heavy-ion collisions.


  We use computer simulation to study crystal-forming model proteins equipped
with interactions that are both orientationally specific and nonspecific.
Distinct dynamical pathways of crystal formation can be selected by tuning the
strengths of these interactions. When the nonspecific interaction is strong,
liquidlike clustering can precede crystallization; when it is weak, growth can
proceed via ordered nuclei. Crystal yields are in certain parameter regimes
enhanced by the nonspecific interaction, even though it promotes association
without local crystalline order. Our results suggest that equipping nanoscale
components with weak nonspecific interactions (such as depletion attractions)
can alter both their dynamical pathway of assembly and optimize the yield of
the resulting material.


  We examine models of fermions with infinite-range interactions which realize
non-Fermi liquids with a continuously variable U(1) charge density
$\mathcal{Q}$, and a non-zero entropy density $\mathcal{S}$ at vanishing
temperature. Real time correlators of operators carrying U(1) charge $q$ at a
low temperature $T$ are characterized by a $\mathcal{Q}$-dependent frequency
$\omega_{\mathcal{S}} = (q \, T/\hbar) (\partial
\mathcal{S}/\partial{\mathcal{Q}})$ which determines a spectral asymmetry. We
show that the correlators match precisely with those of the AdS$_2$ horizons of
extremal charged black holes. On the black hole side, the matching employs
$\mathcal{S}$ as the Bekenstein-Hawking entropy density, and the laws of black
hole thermodynamics which relate
$(\partial{\mathcal{S}}/\partial{\mathcal{Q}})/(2 \pi)$ to the electric field
strength in AdS$_2$. The fermion model entropy is computed using the
microscopic degrees of freedom of a UV complete theory without supersymmetry.


  In this paper we show that n-dimensional dual hyperovals cannot exist in all
but one classical polar space of rank n if n is even. This resolves a question
posed by Yoshiara.


  The Ultra Luminous InfraRed Galaxy Mrk 231 reveals up to seven rotational
lines of water (H2O) in emission, including a very high-lying (E_{upper}=640 K)
line detected at a 4sigma level, within the Herschel/SPIRE wavelength range,
whereas PACS observations show one H2O line at 78 microns in absorption, as
found for other H2O lines previously detected by ISO. The absorption/emission
dichotomy is caused by the pumping of the rotational levels by far-infrared
radiation emitted by dust, and subsequent relaxation through lines at longer
wavelengths, which allows us to estimate both the column density of H2O and the
general characteristics of the underlying far-infrared continuum source.
Radiative transfer models including excitation through both absorption of
far-infrared radiation emitted by dust and collisions are used to calculate the
equilibrium level populations of H2O and the corresponding line fluxes. The
highest-lying H2O lines detected in emission, with levels at 300-640 K above
the ground state, indicate that the source of far-infrared radiation
responsible for the pumping is compact (radius=110-180 pc) and warm
(T_{dust}=85-95 K), accounting for at least 45% of the bolometric luminosity.
The high column density, N(H2O)~5x10^{17} cm^{-2}, found in this nuclear
component, is most probably the consequence of shocks/cosmic rays, an XDR
chemistry, and/or an "undepleted chemistry" where grain mantles are evaporated.
A more extended region, presumably the inner region of the 1-kpc disk observed
in other molecular species, could contribute to the flux observed in low-lying
H2O lines through dense hot cores, and/or shocks. The H2O 78 micron line
observed with PACS shows hints of a blue-shifted wing seen in absorption,
possibly indicating the occurrence of H2O in the prominent outflow detected in
OH (Fischer et al., this volume).


  The characteristic features of $<T_{\mu\nu}>$ in the Boulware, Unruh and
Hartle-Hawking states for a conformal massless scalar field propagating in the
Schwarzschild space-time are obtained by means of effective actions deduced by
the trace anomaly. The actions are made local by the introduction of auxiliary
fields and boundary conditions are carefully imposed on them in order to select
the different quantum states.


  The classical Landau-Lifshitz equation with damping term has been derived
from the time evolution of a quantum mechanical wave function under the
assumption of a non-hermitian Hamilton operator. Further, the trajectory of a
classical spin $\mathrm{S}$ has been compared with the expectation value of the
spin operator $\mathrm{\hat{S}}$. A good agreement between classical and
quantum mechanical trajectories can be found for Hamiltonians linear in
$\mathrm{\hat{S}}$ respectively $\mathrm{S}$. Quadratic or higher order terms
in the Hamiltonian result in a disagreement.


  Establishing how one should describe and study natures fundamental degrees of
freedom is a notoriously difficult problem. It is tempting to assume that the
number of bits (or qubits) needed in a given Planckian 3-volume, or perhaps
2-volume, is a fixed finite number, but this ansatz does not make the problem
much easier. We come not even close to solving this problem, but we propose
various ingredients in phrasing the questions, possibilities and limitations
that may serve as starting points.


  Over the past decade, most factories across developed parts of the world
employ a varying amount of the manufacturing technologies including autonomous
robots, RFID (radio frequency identification) technology, NCs (numerically
controlled machines), wireless sensor networks embedded with specialized
computerized softwares for sophisticated product designs, engineering analysis,
and remote control of machinery, etc. The ultimate aim of these all dramatic
developments in manufacturing sector is thus to achieve aspects such as shorter
innovation / product life cycles and raising overall productivity via
efficiently handling complex interactions among the various stages (functions,
departments) of a production line. The notion, Factory of the Future, is an
unpredictable heaven of efficaciousness, wherein, issues such as the flaws and
downtime would be issues of the long forgotten age. This technical note thus
provides an overview of this awesome revolution waiting to be soon realized in
the manufacturing sector.


  At small x, the gluon distribution dominates the nuclear wave function. The
increase needs to be tamed in avoid violating unitarity constraints. The most
efficient way to study this in colliders is through e+A collisions as the
nucleus is an efficient amplifier of the physics of high gluon densities. To
this end, there are proposals to build an e+A machine in the USA which would
operate over a large range of energies and masses. These studies would also
allow an in-depth comparison to A+A collisions where recent results have given
tantalising hints of a new state of matter produced with partonic degrees of
freedom. As gluon interactions are the dominant source of hard probes, they
themselves must be understood before the results are explained quantitatively.


  Intention-oriented object detection aims to detect desired objects based on
specific intentions or requirements. For instance, when we desire to "lie down
and rest", we instinctively seek out a suitable option such as a "bed" or a
"sofa" that can fulfill our needs. Previous work in this area is limited either
by the number of intention descriptions or by the affordance vocabulary
available for intention objects. These limitations make it challenging to
handle intentions in open environments effectively. To facilitate this
research, we construct a comprehensive dataset called Reasoning
Intention-Oriented Objects (RIO). In particular, RIO is specifically designed
to incorporate diverse real-world scenarios and a wide range of object
categories. It offers the following key features: 1) intention descriptions in
RIO are represented as natural sentences rather than a mere word or verb
phrase, making them more practical and meaningful; 2) the intention
descriptions are contextually relevant to the scene, enabling a broader range
of potential functionalities associated with the objects; 3) the dataset
comprises a total of 40,214 images and 130,585 intention-object pairs. With the
proposed RIO, we evaluate the ability of some existing models to reason
intention-oriented objects in open environments.


  We introduce a new framework to analyze shape descriptors that capture the
geometric features of an ensemble of point clouds. At the core of our approach
is the point of view that the data arises as sampled recordings from a metric
space-valued stochastic process, possibly of nonstationary nature, thereby
integrating geometric data analysis into the realm of functional time series
analysis. We focus on the descriptors coming from topological data analysis.
Our framework allows for natural incorporation of spatial-temporal dynamics,
heterogeneous sampling, and the study of convergence rates. Further, we derive
complete invariants for classes of metric space-valued stochastic processes in
the spirit of Gromov, and relate these invariants to so-called ball volume
processes. Under mild dependence conditions, a weak invariance principle in
$D([0,1]\times [0,\mathscr{R}])$ is established for sequential empirical
versions of the latter, assuming the probabilistic structure possibly changes
over time. Finally, we use this result to introduce novel test statistics for
topological change, which are distribution free in the limit under the
hypothesis of stationarity.


  Detection of the global 21 cm signal arising from neutral hydrogen can
revolutionize our understanding of the standard evolution of the universe after
recombination. In addition, it can also be an excellent probe of Dark Matter
(DM). Among all the DM candidates, Primordial Black Holes (PBHs) are one of the
most well-motivated. Hawking emission from low-mass PBHs can have substantial
effect on the thermal and ionization history of the early universe, and that in
turn can have an imprint on the global 21 cm signal. Recently EDGES has claimed
a global 21 cm signal, though SARAS 3 has rejected that claim. In this work, we
investigate the sensitivities on non-spinning and spinning PBHs arising from an
EDGES-like measurement of the global 21 cm signal, and find that the
sensitivities will be competitive with those arising from other astrophysical
observables. We show that the sensitivities can be significantly strengthened
depending on various uncertain astrophysical parameters. Besides, we also
derive projections on the PBH density from the absorption trough expected
during the Dark Ages. Our work shows that the near future unambiguous detection
of the global 21 cm absorption troughs can be an excellent probe of PBH DM.


  Surface-enhanced Raman spectroscopy (SERS) is a powerful tool for vibrational
spectroscopy as it provides several orders of magnitude higher sensitivity than
inherently weak spontaneous Raman scattering by exciting localized surface
plasmon resonance (LSPR) on metal substrates. However, SERS is not very
reliable, especially for use in life sciences, since it sacrifices
reproducibility and biocompatibility due to its strong dependence on "hot
spots" and large photothermal heat generation. Here we report a metal-free
(i.e., LSPR-free), topologically tailored nanostructure composed of porous
carbon nanowires in an array as a SERS substrate that addresses the decades-old
problem. Specifically, it offers not only high signal enhancement due to its
strong broadband charge-transfer resonance, but also extraordinarily high
reproducibility or substrate-to-substrate, spot-to-spot, sample-to-sample, and
time-to-time consistency in SERS spectrum due to the absence of hot spots and
high compatibility to biomolecules due to its fluorescence quenching and
negligible denaturation capabilities. These excellent properties make SERS
suitable for practical use in diverse biomedical applications.


  We discuss integrable aspects of the logarithmic contribution of the
partition function of cosmological critical topologically massive gravity. On
one hand, written in terms of Bell polynomials which describe the statistics of
set partitions, the partition function of the logarithmic fields is a
generating function of the potential Burgers hierarchy. On the other hand, the
polynomial variables are solutions of the Kadomtsev-Petviashvili equation, and
the partition function is a KP $\tau$ function, making more precise the
solitonic nature of the logarithmic fields being counted. We show that the
partition function is a generating function of Hurwitz numbers, and derive its
expression. The fact that the partition function is the generating function of
branched coverings gives insight on the orbifold target space. We show that the
logarithmic field $\psi^{new}_{\mu \nu}$ can be regarded as a branch point
field associated to the branch point $\mu l =1$.


  Building on the one-to-one relationship between generalized FGM copulas and
multivariate Bernoulli distributions, we prove that the class of multivariate
distributions with generalized FGM copulas is a convex polytope. Therefore, we
find sharp bounds in this class for many aggregate risk measures, such as
value-at-risk, expected shortfall, and entropic risk measure, by enumerating
their values on the extremal points of the convex polytope. This is infeasible
in high dimensions. We overcome this limitation by considering the aggregation
of identically distributed risks with generalized FGM copula specified by a
common parameter $p$. In this case, the analogy with the geometrical structure
of the class of Bernoulli distribution allows us to provide sharp analytical
bounds for convex risk measures.


  Interstellar polarization at far-infrared through millimeter wavelengths (0.1
- 1 mm) is primarily due to thermal emission from dust grains aligned with
magnetic fields. This mechanism has led to studies of magnetic fields in a
variety of celestial sources, as well as the physical characteristics of the
dust grains and their interaction with the field. Observations have covered a
diverse array of sources, from entire galaxies to molecular clouds and
proto-stellar disks. Maps have been generated on a wide range of angular
scales, from surveys covering large fractions of the sky, down to those with
arcsecond spatial resolution. Additionally, the increasing availability of
observations at multiple wavelengths in this band allows empirical tests of
models of grain alignment and cloud structure. I review some of the recent work
in this field, emphasizing comparisons of observations on multiple spatial
scales and at multiple wavelengths.


  The Wishart model for real symmetric correlation matrices is defined as
$\mathsf{W}=\mathsf{AA}^{t}$, where matrix $\mathsf{A}$ is usually a
rectangular Gaussian random matrix and $\mathsf{A}^{t}$ is the transpose of
$\mathsf{A}$. Analogously, for nonsymmetric correlation matrices, a model may
be defined for two statistically equivalent but different matrices $\mathsf{A}$
and $\mathsf{B}$ as $\mathsf{AB}^{t}$. The corresponding Wishart model, thus,
is defined as $\mathbf{C}=\mathsf{AB}^{t}\mathsf{BA}^{t}$. We study the
spectral density of $\mathbf{C}$ for the case when $\mathsf{A}$ and
$\mathsf{B}$ are not statistically independent. The ensemble average of such
nonsymmetric matrices, therefore, does not simply vanishes to a null matrix. In
this paper we derive a Pastur self-consistent equation which describes spectral
density of large $\mathbf{C}$. We complement our analytic results with
numerics.


  Recent monitoring campaigns designed to map the accretion regime in AGN show
major discrepancies with models where the optical/ultraviolet (UV) is produced
by X-ray-illuminated, optically thick disc material within a few hundred
gravitational radii. However, these campaigns only monitored X-rays below $10$
keV, whereas the bolometric luminosity for most of these AGN peaks above $50$
keV. We use data from the recent multiwavelength campaign by \cite{E17} on NGC
4151 - the only AGN bright enough to be monitored at higher energies with
\textit{Swift} BAT. We develop a spectral-timing model with a hot corona, warm
Comptonisation, and outer standard disc. This fits the time-averaged spectrum
well, but completely fails to match the UV variability predicted from the X-ray
lightcurve. However, it reveals that NGC 4151 had a bolometric luminosity
around $1.4\%$ of the Eddington luminosity during this campaign, close to the
luminosity at which AGN show a `changing-state' transition, where the broad
optical lines disappear. Stellar mass black holes show a state transition at a
similarly low Eddington fraction, which is broadly interpreted as the inner
disc being replaced by an optically thin flow. We find that the UV lightcurve
can instead be matched by reprocessing of the X-ray flux on size scales of the
broad line region (BLR; $1.5-20$ light-days) and rule out there being optically
thick material inwards of this, as expected if the thin disc is replaced by the
flow below the inner radius of the BLR. These results emphasise the need for
even longer-timescale, multiwavelength monitoring campaigns on variable AGN.


  This paper summarizes a cross-border mobility study, origin-destination
mobility modelling and visualization, conducted in support of the
infrastructure development efforts of local authorities and NGOs on the area
over the Kayanga-Geba River, at the border between Senegal and Guinea Bissau.
It builds on the data collected through participatory mapping for the
elaboration of the Cross-Border Land Management and Development Plans (Plans
PAGET) aiming to harmonize the different national territorial management tools
into a unique transnational tool through the consideration of border areas as a
territorial unity. Despite a small amount of available mobility data, we were
able to build a mobility model for the considered area, and implemented it in
the Traffic Simulation Framework, which was later used to calculate
origin-destination matrices for the studied regions in two cases: with and
without a cross-border mobility. We analyzed the differences in the mobility
patterns and visualized the mobility flows, deliberating on what may be the
potential impacts of building a bridge in the study area. Our methodology is
general and can be applied in similar studies on different areas. However, the
quality of results may depend on the available data.


  Careful exploration of the idea that equation for radial wave function must
be compatible with the full Schrodinger equation shows appearance of the
delta-function while reduction of full Schrodinger equation in spherical
coordinates. Elimination of this extra term produces a boundary condition for
the radial wave function, which is the same both for regular and singular
potentials.


  The motion of binary star systems is re-examined in the presence of
perturbations from the theory of general relativity. The Kepler problem is
regularized and linearized with quaternions. In this way first order
perturbation results are derived.


  The "developmental hourglass" describes a pattern of increasing morphological
divergence towards earlier and later embryonic development, separated by a
period of significant conservation across distant species (the "phylotypic
stage"). Recent studies have found evidence in support of the hourglass effect
at the genomic level. For instance, the phylotypic stage expresses the oldest
and most conserved transcriptomes. However, the regulatory mechanism that
causes the hourglass pattern remains an open question. Here, we use an
evolutionary model of regulatory gene interactions during development to
identify the conditions under which the hourglass effect can emerge in a
general setting. The model focuses on the hierarchical gene regulatory network
that controls the developmental process, and on the evolution of a population
under random perturbations in the structure of that network. The model
predicts, under fairly general assumptions, the emergence of an hourglass
pattern in the structure of a temporal representation of the underlying gene
regulatory network. The evolutionary age of the corresponding genes also
follows an hourglass pattern, with the oldest genes concentrated at the
hourglass waist. The key behind the hourglass effect is that developmental
regulators should have an increasingly specific function as development
progresses. Analysis of developmental gene expression profiles from Drosophila
melanogaster and Arabidopsis thaliana provide consistent results with our
theoretical predictions.


  In this paper, we propose a modified Density Matrix Renormalization Group
(DMRG) algorithm to preferentially select minimum entropy states (minimally
entangled states) in finite systems with asymptotic ground state degeneracy.
The algorithm adds a "quench" process to the conventional DMRG method, which
mimics the decoherence of physical systems, and collapses non-locally entangled
states such as Schr\"odinger cats. We show that the method works for
representative models with ground state degeneracy arising from either
topological order or spontaneous discrete symmetry breaking. In the minimal
entropy states thus obtained, properties associated with thermodynamic limit,
such as topological entanglement entropy and magnetic order parameters, can be
obtained directly and efficiently.


  Multi-task learning (MTL) seeks to learn a single model to accomplish
multiple tasks by leveraging shared information among the tasks. Existing MTL
models, however, have been known to suffer from negative interference among
tasks. Efforts to mitigate task interference have focused on either
loss/gradient balancing or implicit parameter partitioning with partial
overlaps among the tasks. In this paper, we propose ETR-NLP to mitigate task
interference through a synergistic combination of non-learnable primitives
(NLPs) and explicit task routing (ETR). Our key idea is to employ non-learnable
primitives to extract a diverse set of task-agnostic features and recombine
them into a shared branch common to all tasks and explicit task-specific
branches reserved for each task. The non-learnable primitives and the explicit
decoupling of learnable parameters into shared and task-specific ones afford
the flexibility needed for minimizing task interference. We evaluate the
efficacy of ETR-NLP networks for both image-level classification and
pixel-level dense prediction MTL problems. Experimental results indicate that
ETR-NLP significantly outperforms state-of-the-art baselines with fewer
learnable parameters and similar FLOPs across all datasets. Code is available
at this \href{https://github.com/zhichao-lu/etr-nlp-mtl}.


  Firstly, we demonstrate that unusually large outer HI spiral arms observed in
NGC 2915 can form in an extended gas disk embedded in a massive triaxial dark
matter halo with slow figure rotation, through the strong gravitational torque
of the rotating halo. Secondly, we show that the figure rotation of a triaxial
dark matter halo can influence dynamical evolution of disk galaxies by using
fully self-consistent numerical simulations. We particularly describe the
formation processes of ``halo-triggered'' bars in thin galactic disks dominated
by dark matter halos with figure rotation and discuss the origin of stellar
bars in low luminosity, low surface brightness (LSB) disk galaxies. Thirdly, we
provide several implications of the present numerical results in terms of
triggering mechanism of starbursts in galaxies and stellar bar formation in
high redshifts.


  Quantum computer possesses quantum parallelism and offers great computing
power over classical computer \cite{er1,er2}. As is well-know, a moving quantum
object passing through a double-slit exhibits particle wave duality. A quantum
computer is static and lacks this duality property. The recently proposed
duality computer has exploited this particle wave duality property, and it may
offer additional computing power \cite{r1}. Simply put it, a duality computer
is a moving quantum computer passing through a double-slit. A duality computer
offers the capability to perform separate operations on the sub-waves coming
out of the different slits, in the so-called duality parallelism. Here we show
that an $n$-dubit duality computer can be modeled by an $(n+1)$-qubit quantum
computer. In a duality mode, computing operations are not necessarily unitary.
A $n$-qubit quantum computer can be used as an $n$-bit reversible classical
computer and is energy efficient. Our result further enables a $(n+1)$-qubit
quantum computer to run classical algorithms in a $O(2^n)$-bit classical
computer. The duality mode provides a natural link between classical computing
and quantum computing. Here we also propose a recycling computing mode in which
a quantum computer will continue to compute until the result is obtained. These
two modes provide new tool for algorithm design. A search algorithm for the
unsorted database search problem is designed.


  We investigate the possibility of proving upper bounds on Hadwiger's number
of a graph with partial information, mirroring several known upper bounds for
the chromatic number. For each such bound we determine whether the
corresponding bound for Hadwiger's number holds. Our results suggest that the
``locality'' of an inequality accounts for the existence of such an extension.


  We study the problem of optimal trading using general alpha predictors with
linear costs and temporary impact. We do this within the framework of
stochastic optimization with finite horizon using both limit and market orders.
Consistently with other studies, we find that the presence of linear costs
induces a no-trading zone when using market orders, and a corresponding
market-making zone when using limit orders. We show that, when combining both
market and limit orders, the problem is further divided into zones in which we
trade more aggressively using market orders. Even though we do not solve
analytically the full optimization problem, we present explicit and simple
analytical recipes which approximate the full solution and are easy to
implement in practice. We test the algorithms using Monte Carlo simulations and
show how they improve our Profit and Losses.


  In 1944 Zariski discovered that Bertini's theorem on variable singular points
is no longer true when we pass from a field of characteristic zero to a field
of positive characteristic. In other words, he found fibrations by singular
curves, which only exist in positive characteristic. Such fibrations are
connected with many interesting phenomena. For instance, the extension of
Enrique's classification of surfaces to positive characteristic (Bombieri and
Mumford in 1976), the counterexamples of Kodaira vanishing theorem (Mukai in
2013 and Zheng in 2016) and the isolated singularities with infinity Milnor
number (Hefez, Rodrigues and Salom\~ao in 2019). In this work we are going to
show that the smoothing process introduced by Shimada in 1991 can be used to
classify the set of fibrations by genus two singular curves, up to isomorphism
among their generic fibers, such that their smoothing are elliptic fibrations
on rational surfaces. Moreover we will also describe the vector fields that can
be used to recover such fibrations by singular curves via quotient of rational
elliptic surfaces.


  Some examples are easier for humans to classify than others. The same should
be true for deep neural networks (DNNs). We use the term example perplexity to
refer to the level of difficulty of classifying an example. In this paper, we
propose a method to measure the perplexity of an example and investigate what
factors contribute to high example perplexity. The related codes and resources
are available at https://github.com/vaynexie/Example-Perplexity.


  Motivated by \cite{CG10,CZ6}, we prove the global existence of solutions to
the two-dimensional isentropic compressible Navier-Stokes equations with smooth
initial data which are slowly varying in one direction and with initial density
being away from vacuum. In particular, we present examples of initial data
which generate unique global smooth solutions to 2D compressible Navier-Stokes
equations with constant viscosity and with initial data which are neither small
perturbation of some constant equilibrium state nor of small energy.


  A double-exchange mechanism for the emergence of ferromagnetism in cubic
uranium compounds is proposed on the basis of a $j$-$j$ coupling scheme. The
idea is {\it orbital-dependent duality} of $5f$ electrons concerning itinerant
$\Gamma_8^-$ and localized $\Gamma_7^-$ states in the cubic structure. Since
orbital degree of freedom is still active in the ferromagnetic phase,
orbital-related quantum critical phenomenon is expected to appear. In fact,
odd-parity p-wave pairing compatible with ferromagnetism is found in the
vicinity of an orbital ordered phase. Furthermore, even-parity d-wave pairing
with significant odd-frequency components is obtained. A possibility to observe
such exotic superconductivity in manganites is also discussed briefly.


  Similarly as in (Blancas et al. 2018) where nested coalescent processes are
studied, we generalize the definition of partition-valued homogeneous Markov
fragmentation processes to the setting of nested partitions, i.e. pairs of
partitions $(\zeta,\xi)$ where $\zeta$ is finer than $\xi$. As in the classical
univariate setting, under exchangeability and branching assumptions, we
characterize the jump measure of nested fragmentation processes, in terms of
erosion coefficients and dislocation measures. Among the possible jumps of a
nested fragmentation, three forms of erosion and two forms of dislocation are
identified - one of which being specific to the nested setting and relating to
a bivariate paintbox process.


  The magnetization probability density in d=2 and 3 dimensional Ising models
in slab geometry of volume $L_{\parallel}^{d-1} \times L_{\perp}$ is computed
through Monte-Carlo simulation at the critical temperature and zero magnetic
field. The finite-size scaling of this distribution and its dependence on the
system aspect-ratio $\rho=\frac{L_{\perp}}{L_{\parallel}}$ and boundary
conditions is discussed. In the limiting case $\rho \to 0$ of a macroscopically
large slab ($L_{\parallel} \gg L_{\perp}$) the distribution is found to scale
as a Gaussian function for all tested system sizes and boundary conditions.


  We consider the reconstruction of the interface of compact, connected
"clouds" from satellite or airborne light intensity measurements. In a two
dimensional setting, the cloud is modeled by an interface, locally represented
as a graph, and an outgoing radiation intensity that is consistent with a
diffusion model for light propagation in the cloud. Light scattering inside the
cloud and the optical internal parameters of the cloud are not modeled. The
main objective is to understand what can or cannot be reconstructed in such a
setting from intensity measurements in a finite (on the order of 10) number of
directions along the path of a satellite. Numerical simulations illustrate the
theoretical predictions.


  We review the (2+1)-dimensional Ba\u{n}ados-Teitelboim-Zanelli black hole
solution in conformally invariant gravity, uplifted to (3+1)-dimensional
spacetime. As matter content we use a scalar-gauge field. The metric is written
as $g_{\mu\nu}=\omega^2\tilde g_{\mu\nu}$, where the {\it dilaton field}
$\omega$ contains all the scale dependencies and where $\tilde g_{\mu\nu}$
represents the "un-physical" spacetime. A numerical solution is presented and
shows how the dilaton can be treated on equal footing with the scalar field.
The location of the apparent horizon and ergo-surface depends critically on the
parameters and initial values of the model. It is not a hard task to find
suitable initial parameters in order to obtain a regular and {\it singular
free} $g_{\mu\nu}$ out of a BTZ-type solution for $\tilde g_{\mu\nu}$. In the
vacuum situation, an {\it exact} time-dependent solution in the
Eddington-Finkelstein coordinates is found, which is valid for the
(2+1)-dimensional BTZ spacetime as well as for the uplifted (3+1)-dimensional
BTZ spacetime. While $\tilde g_{\mu\nu}$ resembles the standard BTZ solution
with its horizons, $g_{\mu\nu}$ is {\it flat}. The dilaton field becomes an
infinitesimal renormalizable quantum field, which switches on and off Hawking
radiation. This solution can be used to investigate the small distance scale of
the model and the black hole complementarity issues. It can also be used to
describe the problem how to map the quantum states of the outgoing radiation as
seen by a distant observer and the ingoing by a local observer in a one-to-one
way. The two observers will use a different conformal gauge. A possible
connection is made with the antipodal identification and unitarity issues.


  Sense of hearing is crucial for autonomous vehicles (AVs) to better perceive
its surrounding environment. Although visual sensors of an AV, such as camera,
lidar, and radar, help to see its surrounding environment, an AV cannot see
beyond those sensors line of sight. On the other hand, an AV s sense of hearing
cannot be obstructed by line of sight. For example, an AV can identify an
emergency vehicle s siren through audio classification even though the
emergency vehicle is not within the line of sight of the AV. Thus, auditory
perception is complementary to the camera, lidar, and radar-based perception
systems. This paper presents a deep learning-based robust audio classification
framework aiming to achieve improved environmental perception for AVs. The
presented framework leverages a deep Convolution Neural Network (CNN) to
classify different audio classes. UrbanSound8k, an urban environment dataset,
is used to train and test the developed framework. Seven audio classes i.e.,
air conditioner, car horn, children playing, dog bark, engine idling, gunshot,
and siren, are identified from the UrbanSound8k dataset because of their
relevancy related to AVs. Our framework can classify different audio classes
with 97.82% accuracy. Moreover, the audio classification accuracies with all
ten classes are presented, which proves that our framework performed better in
the case of AV-related sounds compared to the existing audio classification
frameworks.


  We find an algorithm to compute the cohomology groups of spherical vector
bundles on complex projective K3 surfaces, in terms of their Mukai vectors. In
many good cases, we give significant simplifications of the algorithm. As an
application, when the Picard rank is one, we show a numerical condition that is
equivalent to weak Brill-Noether for a spherical vector bundle.


  A virtual link diagram is called normal if the associated abstract link
diagram is checkerboard colorable, and a virtual link is normal if it has a
normal diagram as a representative. Normal virtual links have some properties
similar to classical links.In this paper, we introduce a method of converting a
virtual link diagram to a normal virtual link diagram. We show that the normal
virtual link diagrams obtained by this method from two equivalent virtual link
diagrams are equivalent. We discuss the relationship between this method and
some invariants of virtual links.


  This paper presents a novel approach to the problem of almost global attitude
stabilization. The reduced attitude is steered along a geodesic path on the
n-sphere. Meanwhile, the full attitude is stabilized on SO(n). This action,
essentially two maneuvers in sequel, is fused into one smooth motion. Our
algorithm is useful in applications where stabilization of the reduced attitude
takes precedence over stabilization of the full attitude. A two parameter
feedback gain affords further trade-offs between the full and reduced attitude
convergence speed. The closed loop kinematics on SO(3) are solved for the
states as functions of time and the initial conditions, providing precise
knowledge of the transient dynamics. The exact solutions also help us to
characterize the asymptotic behavior of the system such as establishing the
region of attraction by straightforward evaluation of limits. The geometric
flavor of these ideas is illustrated by a numerical example.


  A persistent challenge in Complex Systems (CS) research is the
phenomenological reconstruction of systems from raw data. In order to face the
problem, the use of sound features to reason on the system from data processing
is a key step. In the specific case of complex societal systems, sentiment
analysis allows to mirror (part of) the affective dimension. However it is not
reasonable to think that individual sentiment categorization can encompass the
new affective phenomena in digital social networks.
  The present papers addresses the problem of isolating sentiment concepts
which emerge in social networks. In an analogy to Artificial Intelligent
Singularity, we propose the study and analysis of these new complex sentiment
structures and how they are similar to or diverge from classic conceptual
structures associated to sentiment lexicons. The conjecture is that it is
highly probable that hypercomplex sentiment structures -not explained with
human categorizations- emerge from high dynamic social information networks.
Roughly speaking, new sentiment can emerge from the new global nervous systems
as it occurs in humans.


  We study real rational models of the euclidean plane $\mathbb{R}^2$ up to
isomorphisms and up to birational diffeomorphisms. The analogous study in the
compact case, that is the classification of real rational models of the real
projective plane $\mathbb{R}\mathbb{P}^2$ is well known: up to birational
diffeomorphisms, there is only one model. A fake real plane is a nonsingular
affine surface defined over the reals with homologically trivial complex locus
and real locus diffeomorphic to $\mathbb{R}^2$ but which is not isomorphic to
the real affine plane. We prove that fake planes exist by giving many examples
and we tackle the question: does there exist fake planes whose real locus is
not birationally diffeomorphic to the real affine plane?


  The scarce data systematics and complexity of deuteron interactions demand
the update of both the experimental database and theoretical frame of deuteron
activation cross sections. Various reactions induced by neutrons and protons
following the deuteron breakup (BU) should be also taken into account. On the
other hand, deuteron reaction cross sections recommended recently for
high-priority elements are still based on data fit without predictive power.
Purpose: Accurate new measurements of low-energy deuteron-induced reaction
cross sections for monoisotopic (55Mn) natural manganese target enhance the
related database as well as the opportunity of an unitary and consistent
account of the related reaction mechanisms. Method: Activation cross sections
of 54,56Mn, and 51Cr nuclei by deuterons on $^{55}$Mn were measured at energies
<20 MeV by the stacked-foil technique and high resolution gamma spectrometry at
the U-120M cyclotron of CANAM, NPI CAS. Then all available data for deuterons
on 55Mn up to 50 MeV are analyzed paying particular attention to BU and direct
reaction (DR) mechanisms. Results: Newly measured activation cross sections
strengthen the deuteron database at low energies, at once with a consistent
account for the first time of all available data. Conclusions: Due account of
deuteron-induced reactions on 55Mn, including particularly the new experimental
data at low energies, is provided by a suitable BU and DR assessment.


  A field theoretic renormalization group method is presented which is capable
of dealing with crossover problems associated with a change in the upper
critical dimension. The method leads to flow functions for the parameters and
coupling constants of the model which depend on the set of parameters which
characterize the fixed point landscape of the underlying problem. Similar to
Nelson's trajectory integral method any vertex function can be expressed as a
line integral along a renormalization group trajectory, which in the field
theoretic formulation are given by the characteristics of the corresponding
Callan-Symanzik equation. The field theoretic renormalization automatically
leads to a separation of the regular and singular parts of all crossover
scaling functions.
  The method is exemplified for the crossover problem in magnetic phase
transitions, percolation problems and quantum phase transitions. The broad
applicability of the method is emphasized.


  We study a quasiperiodic structure in the time evolution of the Bloch vector,
whose dynamics is governed by the thermal Jaynes-Cummings model (JCM). Putting
the two-level atom into a certain pure state and the cavity field into a mixed
state in thermal equilibrium at initial time, we let the whole system evolve
according to the JCM Hamiltonian. During this time evolution, motion of the
Bloch vector seems to be in disorder. Because of the thermal photon
distribution, both a norm and a direction of the Bloch vector change hard at
random. In this paper, taking a different viewpoint compared with ones that we
have been used to, we investigate quasiperiodicity of the Bloch vector's
trajectories. Introducing the concept of the quasiperiodic motion, we can
explain the confused behaviour of the system as an intermediate state between
periodic and chaotic motions. More specifically, we discuss the following two
facts: (1) If we adjust the time interval $\Delta t$ properly, figures
consisting of plotted dots at the constant time interval acquire scale
invariance under replacement of $\Delta t$ by $s\Delta t$, where $s(>1)$ is an
arbitrary real but not transcendental number. (2) We can compute values of the
time variable $t$, which let $|S_{z}(t)|$ (the absolute value of the
$z$-component of the Bloch vector) be very small, with the Diophantine
approximation (a rational approximation of an irrational number).


  We predict the existence and study the basic properties of strongly
asymmetric matter wave solitons that form at the interface produced by regions
with different inter-atomic interaction strengths in pancake Bose-Einstein
condensates. We address several types of surface solitons featuring
topologically complex structures, including vortex and dipole-mode solitons. We
found that the soliton become significantly asymmetric for high number of
particles in the condensate. Yet, we reveal that under suitable conditions,
that we elucidate, even such strongly asymmetric dipole and vortex solitons can
be dynamically stable over wide regions of their existence domains.