  We show that, given a certain transversality condition, the set of relative
equilibria $\mcl E$ near $p_e\in\mcl E$ of a Hamiltonian system with symmetry
is locally Whitney-stratified by the conjugacy classes of the isotropy
subgroups (under the product of the coadjoint and adjoint actions) of the
momentum-generator pairs $(\mu,\xi)$ of the relative equilibria. The dimension
of the stratum of the conjugacy class (K) is $\dim G+2\dim Z(K)-\dim K$, where
Z(K) is the center of K, and transverse to this stratum $\mcl E$ is locally
diffeomorphic to the commuting pairs of the Lie algebra of $K/Z(K)$. The
stratum $\mcl E_{(K)}$ is a symplectic submanifold of P near $p_e\in\mcl E$ if
and only if $p_e$ is nondegenerate and K is a maximal torus of G. We also show
that there is a dense subset of G-invariant Hamiltonians on P for which all the
relative equilibria are transversal. Thus, generically, the types of
singularities that can be found in the set of relative equilibria of a
Hamiltonian system with symmetry are those types found amongst the
singularities at zero of the sets of commuting pairs of certain Lie subalgebras
of the symmetry group.


  The asymptotic method of post-Newtonian (PN) expansion for weak gravitational
fields, recently developed, is compared with the standard method of PN
expansion, in the particular case of a massive test particle moving along a
geodesic line of a weak Schwarzschild field. First, the expression of the
active mass in Schwarzschild's solution is given for a barotropic perfect
fluid, both for general relativity (GR) and for an alternative, scalar theory.
The principle of the asymptotic method is then recalled and the PN expansion of
the active mass is derived. The PN correction to the active mass is made of the
Newtonian elastic energy, augmented, for the scalar theory, by a term due to
the self-reinforcement of the gravitational field. Third, two equations, both
correct to first order, are derived for the geodesic motion of a mass particle:
a "standard" one and an "asymptotic" one. Finally, the difference between the
solutions of these two equations is numerically investigated in the case of
Mercury. The asymptotic solution deviates from the standard one like the square
of the time elapsed since the initial time. This is due to a practical
shortcoming of the asymptotic method, which is shown to disappear if one
reinitializes the asymptotic problem often enough. Thus, both methods are
equivalent in the case investigated. In a general case, the asymptotic method
seems more natural.


  A fundamental problem of interest to policy makers, urban planners, and other
stakeholders involved in urban development projects is assessing the impact of
planning and construction activities on mobility flows. This is a challenging
task due to the different spatial, temporal, social, and economic factors
influencing urban mobility flows. These flows, along with the influencing
factors, can be modelled as attributed graphs with both node and edge features
characterising locations in a city and the various types of relationships
between them. In this paper, we address the problem of assessing
origin-destination (OD) car flows between a location of interest and every
other location in a city, given their features and the structural
characteristics of the graph. We propose three neural network architectures,
including graph neural networks (GNN), and conduct a systematic comparison
between the proposed methods and state-of-the-art spatial interaction models,
their modifications, and machine learning approaches. The objective of the
paper is to address the practical problem of estimating potential flow between
an urban development project location and other locations in the city, where
the features of the project location are known in advance. We evaluate the
performance of the models on a regression task using a custom data set of
attributed car OD flows in London. We also visualise the model performance by
showing the spatial distribution of flow residuals across London.


  In a subcritical reactor, each neutron produces only keff < 1 neutron per
generation (asymptotically and on average), and thus the neutron population
decreases exponentially in the absence of external source. The chain reaction
is thus easy to stop, making such reactors inherently stable. Interestingly,
and contrary to common wisdom, there is no relation between keff, the external
source intensity, and the output power of the reactor. In this paper, I present
various possible strategies to exploit this fact, and apply them to the design
of a rudimentary multi-layer system that allows to reach an arbitrarily large
number of fissions per source neutron, while keeping keff < 1 fixed (I used
keff=0.97). The behavior of the amplifier is verified with simple Monte-Carlo
transport simulations. The proposal admittedly brings complications and
subtleties that need to be studied further, but, if developed, could allow to
drive subcritical reactors with faint neutron sources, e.g. radioisotope based.


  We study the effect of two types of degeneration of the Riemannian metric on
the first eigenvalue of the Laplace operator on surfaces. In both cases we
prove that the first eigenvalue of the round sphere is an optimal asymptotic
upper bound. The first type of degeneration is concentration of the density to
a point within a conformal class. The second is degeneration of the conformal
class to the boundary of the moduli space on the torus and on the Klein bottle.
In the latter, we follow the outline proposed by N. Nadirashvili in 1996.


  The arithmetic of Hilbert modular forms has been extensively studied under
the assumption that the forms concerned are "paritious" -- all the components
of the weight are congruent modulo 2. In contrast, non-paritious Hilbert
modular forms have been relatively little studied, both from a theoretical and
a computational standpoint.
  In this article, we aim to redress the balance somewhat by studying the
arithmetic of non-paritious Hilbert modular eigenforms. On the theoretical
side, our starting point is a theorem of Patrikis, which associates projective
l-adic Galois representations to these forms. We show that a general conjecture
of Buzzard and Gee actually predicts that a strengthening of Patrikis' result
should hold, giving Galois representations into certain groups intermediate
between GL(2) and PGL(2), and we verify that the predicted Galois
representations do indeed exist. On the computational side, we give an
algorithm to compute non-paritious Hilbert modular forms using definite
quaternion algebras. To our knowledge, this is the first time such a general
method has been presented. We end the article with a selection of examples.


  The remnants are investigated by fermions' tunnelling from a 4-dimensional
charged dilatonic black hole and a 5-dimensional black string. Based on the
generalized uncertainty principle, effects of quantum gravity are taken into
account. The quantum numbers of the emitted fermions affects the Hawking
temperatures. For the black hole, the quantum gravity correction slows down the
increase of the temperature, which leads to the remnant left in the
evaporation. For the black string, the existence of the remnant is determined
by the quantum gravity correction and effects of the extra compact dimension.


  We summarize the fall-off of electromagnetic and gravitational fields in n>5
dimensional Ricci-flat spacetimes along an asympotically expanding non-singular
geodesic null congruence.


  Graphs are commonly used to model complex networks prevalent in modern social
media and literacy applications. Our research investigates the vulnerability of
these graphs through the application of feature based adversarial attacks,
focusing on both decision time attacks and poisoning attacks. In contrast to
state of the art models like Net Attack and Meta Attack, which target node
attributes and graph structure, our study specifically targets node attributes.
For our analysis, we utilized the text dataset Hellaswag and graph datasets
Cora and CiteSeer, providing a diverse basis for evaluation. Our findings
indicate that decision time attacks using Projected Gradient Descent (PGD) are
more potent compared to poisoning attacks that employ Mean Node Embeddings and
Graph Contrastive Learning strategies. This provides insights for graph data
security, pinpointing where graph-based models are most vulnerable and thereby
informing the development of stronger defense mechanisms against such attacks.


  In this paper we obtain a generalization of Matkowski's fixed point theorem
and Istratescu's fixed point theorem concerning convex contractions in the
framework of b-metric spaces. By providing appropriate examples we show that
the above mentioned two generalizations are effective.


  Aims. We studied the characteristics of planetary nebulae (PNe) that show
both OH maser and radio continuum emission (hereafter OHPNe). These have been
proposed to be very young PNe, and therefore, they could be key objects for
understanding the formation and evolution of PNe. Methods. We consulted the
literature searching for interferometric observations of radio continuum and OH
masers toward evolved stars, including the information from several surveys. We
also processed radio continuum and OH maser observations toward PNe in the Very
Large Array data archive. The high positional accuracy provided by
interferometric observations allow us to confirm or reject the association
between OH maser and radio continuum emission. Results. We found a total of six
PNe that present both OH maser and radio continuum emissions, as confirmed with
radio interferometric observations. These are bona fide OHPNe. The confirmed
OHPNe present a bipolar morphology in resolved images of their ionized emission
at different wavelengths, suggesting that the OH maser emission in PNe is
related to nonspherical mass-loss phenomena. The OH maser spectra in PNe
present a clear asymmetry, tending to show blueshifted emission with respect to
the systemic velocity. Their infrared colors suggest that most of these objects
are very young PNe. OHPNe do not form a homogeneous group, and seem to
represent a variety of different evolutionary stages. We suggest that OH masers
pumped in the AGB phase may disappear during the post-AGB phase, but reappear
once the source becomes a PN and its radio continuum emission is amplified by
the OH molecules. Therefore, OH maser emission could last significantly longer
than the previously assumed 1000 yr after the end of the AGB phase. This maser
lifetime may be longer in PNe with more massive central stars, which ionize a
larger amount of gas in the envelope.


  We explore the relations between size, stellar mass and average stellar
population age (indicated by D$_n4000$ indices) for a sample of $\sim11000$
intermediate-redshift galaxies from the SHELS spectroscopic survey (Geller et
al. 2014) augmented by high-resolution Subaru Telescope Hyper Suprime-Cam
imaging. In the redshift interval $0.1<z<0.6$, star forming galaxies are on
average larger than their quiescent counterparts. The mass-complete sample of
$\sim3500$ $M_*>10^{10}\, M_\odot$ quiescent galaxies shows that the average
size of a $10^{11}\, M_\odot$ quiescent galaxy increases by $\lesssim25\%$ from
$z\sim0.6$ to $z\sim0.1$. This growth rate is a function of stellar mass: the
most massive ($M_*>10^{11}\, M_\odot$) galaxies grow significantly more slowly
in size than an order of magnitude less massive quiescent systems that grow by
70\% in the $0.1\lesssim z\lesssim0.3$ redshift interval. For $M_*<10^{11}\,
M_\odot$ galaxies age and size are anti-correlated at fixed mass; more massive
quiescent systems show no significant trend in size with average stellar
population age. The evolution in absolute and fractional abundances of
quiescent systems at intermediate redshift are also a function of galaxy
stellar mass. The suite of evolutionary trends suggests that galaxies more
massive than $\sim10^{11}\, M_\odot$ have mostly assembled their mass by
$z\sim0.6$. Quiescent galaxies with lower stellar masses show more complex
evolution that is characterized by a combination of individual quiescent galaxy
size growth (through mergers) and an increase in the size of newly quenched
galaxies joining the population at later times (progenitor bias). The
$M_*\sim10^{10}\, M_\odot$ population grows predominantly as a result of
progenitor bias. For $M_*\sim5\times10^{10}\, M_\odot$ quiescent galaxies,
mergers and progenitor bias make more comparable contributions to the size
growth.[abridged]


  The dual of the lattice AKP equation [P.H. van der Kamp et al., J. Phys. A
51, 365202 (2018)] is equivalent to a 14-point equation related to the lattice
BKP equation, found by King and Schief. If one of the parameters vanishes, it
is equivalent to a 12-point equation related to the lattice AKP equation. This
establishes the integrability of the dual AKP equation. Using the equivalence
we prove the existence of the conjectured $N$-soliton solution of the dual AKP
equation, for all values of the parameters.


  Fingerprints are popular among the biometric based systems due to ease of
acquisition, uniqueness and availability. Nowadays it is used in smart phone
security, digital payment and digital locker. The traditional fingerprint
matching methods based on minutiae are mainly applicable for large-area
fingerprint and the accuracy rate would reduce significantly when dealing with
small-area fingerprint from smart phone. There are many attempts to using deep
learning for small-area fingerprint recognition, and there are many successes.
But training deep neural network needs a lot of datasets for training. There is
no well-known dataset for small-area, so we have to make datasets ourselves. In
this paper, we propose a method of data augmentation to train a small-area
fingerprint recognition deep neural network with a normal fingerprint database
(such as FVC2002) and verify it via tests. The experimental results showed the
efficiency of our method.


  We evaluate the statistical significance of the DAMA/LIBRA claims for annual
modulation using three independent model comparison techniques, viz
frequentist, information theory, and Bayesian analysis. We fit the data from
the DAMA/LIBRA experiment to both cosine and a constant model, and carry out
model comparison by choosing the constant model as the null hypothesis. For the
frequentist test, we invoke Wilk's theorem and calculate the significance using
$\Delta \chi^2$ between the two models. For information theoretical tests, we
calculate the difference in Akaike Information Criterion (AIC) and Bayesian
Information criterion (BIC) between the two models. We also compare the two
models in a Bayesian context by calculating the Bayes factor. We also search
for higher harmonics in the DAMA/LIBRA data using generalized Lomb-Scargle
periodogram. We finally test the sensitivity of these model comparison
techniques in discriminating between pure noise and a cosine signal using
synthetic data. This is the first proof of principles application of AIC, BIC
as well as Bayes factor to the DAMA data. All our analysis codes along with the
data used in this work have been made publicly available.


  The dipolar-random field Ising model (DRFIM) recently introduced displays a
behaviour that can be connected to the magnetization of bidimensional magnetic
media. Epitaxial magnetic garnet films seem to be the ideal test material for
such a model. In this work the results of the measurements performed on garnet
samples are presented, as well as the comparisons with simulation results
obtained by the DRFIM. The results prove that a variety of hysteresis loops are
well described by the DRFIM. This capability does not derive from the fine
tuning of a great number of parameters, but by the interplay of exchange and
dipolar interactions.


  The coronavirus SARS-CoV-2 remains an extant threat against public health on
a global scale. Cell infection begins when the spike protein of SARS-CoV-2
binds with the cell receptor, angiotensin-converting enzyme 2 (ACE2). Here, we
address the role of Tetracycline as an inhibitor for the receptor-binding
domain (RBD) of the spike protein. Targeted molecular investigation show that
Tetracycline binds more favorably to the RBD (-9.40 kcal/mol) compared to
Chloroquine (-6.31 kcal/mol) or Doxycycline (-8.08 kcal/mol) and inhibits
attachment to ACE2 to a greater degree (binding efficiency of 2.98
$\frac{\text{kcal}}{\text{mol}\cdot \text{nm}^2}$ for Tetracycline-RBD, 5.59
$\frac{\text{kcal}}{\text{mol}\cdot \text{nm}^2}$ for Chloroquine-RBD, 5.16
$\frac{\text{kcal}}{\text{mol}\cdot \text{nm}^2}$ for Doxycycline-RBD).
Stronger Tetracycline inhibition is verified with nonequilibrium PMF
calculations, for which the Tetracycline-RBD complex exhibits the lowest free
energy profile along the dissociation pathway from ACE2. Tetracycline appears
to target viral residues that are usually involved in significant hydrogen
bonding with ACE2; this inhibition of cellular infection complements the
anti-inflammatory and cytokine suppressing capability of Tetracycline, and may
further reduce the duration of ICU stays and mechanical ventilation induced by
the coronavirus SARS-CoV-2.


  There is a critical need for efficient and reliable active flow control
strategies to reduce drag and noise in aerospace and marine engineering
applications. While traditional full-order models based on the Navier-Stokes
equations are not feasible, advanced model reduction techniques can be
inefficient for active control tasks, especially with strong non-linearity and
convection-dominated phenomena. Using convolutional recurrent autoencoder
network architectures, deep learning-based reduced-order models have been
recently shown to be effective while performing several orders of magnitude
faster than full-order simulations. However, these models encounter significant
challenges outside the training data, limiting their effectiveness for active
control and optimization tasks. In this study, we aim to improve the
extrapolation capability by modifying network architecture and integrating
coupled space-time physics as an implicit bias. Reduced-order models via deep
learning generally employ decoupling in spatial and temporal dimensions, which
can introduce modeling and approximation errors. To alleviate these errors, we
propose a novel technique for learning coupled spatial-temporal correlation
using a 3D convolution network. We assess the proposed technique against a
standard encoder-propagator-decoder model and demonstrate a superior
extrapolation performance. To demonstrate the effectiveness of 3D convolution
network, we consider a benchmark problem of the flow past a circular cylinder
at laminar flow conditions and use the spatio-temporal snapshots from the
full-order simulations. Our proposed 3D convolution architecture accurately
captures the velocity and pressure fields for varying Reynolds numbers.
Compared to the standard encoder-propagator-decoder network, the
spatio-temporal-based 3D convolution network improves the prediction range of
Reynolds numbers outside of the training data.


  Asteroseismic parameters allow us to measure the basic stellar properties of
field giants observed far across the Galaxy. Most of such determinations are,
up to now, based on simple scaling relations involving the large frequency
separation, \Delta\nu, and the frequency of maximum power, \nu$_{max}$. In this
work, we implement \Delta\nu\ and the period spacing, {\Delta}P, computed along
detailed grids of stellar evolutionary tracks, into stellar isochrones and
hence in a Bayesian method of parameter estimation. Tests with synthetic data
reveal that masses and ages can be determined with typical precision of 5 and
19 per cent, respectively, provided precise seismic parameters are available.
Adding independent information on the stellar luminosity, these values can
decrease down to 3 and 10 per cent respectively. The application of these
methods to NGC 6819 giants produces a mean age in agreement with those derived
from isochrone fitting, and no evidence of systematic differences between RGB
and RC stars. The age dispersion of NGC 6819 stars, however, is larger than
expected, with at least part of the spread ascribable to stars that underwent
mass-transfer events.


  We present a self-contained combinatorial approach to Fujita's conjectures in
the toric case. Our main new result is a generalization of Fujita's very
ampleness conjecture for toric varieties with arbitrary singularities. In an
appendix, we use similar methods to give a new proof of an analogous toric
generalization of Fujita's freeness conjecture due to Fujino.


  The focussing optics of NuSTAR have enabled high signal-to-noise spectra to
be obtained from many X-ray bright Active Galactic Nuclei (AGN) and Galactic
Black Hole Binaries (BHB). Spectral modelling then allows robust
characterization of the spectral index and upper energy cutoff of the coronal
power-law continuum, after accounting for reflection and absorption effects.
Spectral-timing studies, such as reverberation and broad iron line fitting, of
these sources yield coronal sizes, often showing them to be small and in the
range of 3 to 10 gravitational radii in size. Our results indicate that coronae
are hot and radiatively compact, lying close to the boundary of the region in
the compactness - temperature diagram which is forbidden due to runaway pair
production. The coincidence suggests that pair production and annihilation are
essential ingredients in the coronae of AGN and BHB and that they control the
shape of the observed spectra.


  Maxwell's demon is a special case of a feedback controlled system, where
information gathered by measurement is utilized by driving a system along a
thermodynamic process that depends on the measurement outcome. The demon
illustrates that with feedback one can design an engine that performs work by
extracting energy from a single thermal bath. Besides the fundamental questions
posed by the demon - the probabilistic nature of the Second Law, the
relationship between entropy and information, etc. - there are other practical
problems related to feedback engines. One of those is the design of optimal
engines, protocols that extract the maximum amount of energy given some amount
of information. A refinement of the second law to feedback systems establishes
a bound to the extracted energy, a bound that is met by optimal feedback
engines. It is also known that optimal engines are characterized by time
reversibility. As a consequence, the optimal protocol given a measurement is
the one that, run in reverse, prepares the system in the post-measurement state
(preparation prescription). In this paper we review these results and analyze
some specific features of the preparation prescription when applied to
non-ergodic systems.


  We present the evaluation of some definite integrals in the classical table
by I. S. Gradshteyn and I. M. Ryzhik where the integrand is a combination of
powers, exponentials and logarithms.


  In the highly competitive area of product marketing, the visibility of brand
logos on packaging plays a crucial role in shaping consumer perception,
directly influencing the success of the product. This paper introduces a
comprehensive framework to measure the brand logo's attention on a packaging
design. The proposed method consists of three steps. The first step leverages
YOLOv8 for precise logo detection across prominent datasets, FoodLogoDet-1500
and LogoDet-3K. The second step involves modeling the user's visual attention
with a novel saliency prediction model tailored for the packaging context. The
proposed saliency model combines the visual elements with text maps employing a
transformers-based architecture to predict user attention maps. In the third
step, by integrating logo detection with a saliency map generation, the
framework provides a comprehensive brand attention score. The effectiveness of
the proposed method is assessed module by module, ensuring a thorough
evaluation of each component. Comparing logo detection and saliency map
prediction with state-of-the-art models shows the superiority of the proposed
methods. To investigate the robustness of the proposed brand attention score,
we collected a unique dataset to examine previous psychophysical hypotheses
related to brand visibility. the results show that the brand attention score is
in line with all previous studies. Also, we introduced seven new hypotheses to
check the impact of position, orientation, presence of person, and other visual
elements on brand attention. This research marks a significant stride in the
intersection of cognitive psychology, computer vision, and marketing, paving
the way for advanced, consumer-centric packaging designs.


  In this contribution we review recent progress with fixed-order QCD
predictions for the production of a vector boson in association with jets at
hadron colliders, using the programs BlackHat and SHERPA. We review general
features of next-to-leading-order (NLO) predictions for the production of a
massive vector boson in association with four jets. We also discuss how precise
descriptions of vector-boson production can be applied to the determination of
backgrounds to new physics signals. Here we focus on data-driven backgrounds to
a missing-energy-plus-jets search performed by CMS. Finally, we review recent
progress in developing theoretical tools for high-multiplicity loop-computation
within the BlackHat-library. In particular, we discuss methods for handling the
color degrees of freedom in multi-jet predictions at NLO.


  We derive generic equations for a vector field driving the evolution of flat
homogeneous isotropic universe and give a comparison with a scalar filed
dynamics in the cosmology. Two exact solutions are shown as examples, which can
serve to describe an inflation and a slow falling down of dynamical
``cosmological constant'' like it is given by the scalar quintessence. An
attractive feature of vector field description is a generation of ``induced
mass'' proportional to a Hubble constant, which results in a dynamical
suppression of actual cosmological constant during the evolution.


  The Cudaca system composed of isolated Cu2+ S=1/2 tetrahedra with
antiferromagnetic exchange should exhibit properties of a frustrated quantum
spin system. ab initio density functional theory calculations for electronic
structure and molecular dynamics computations suggest a complex interplay
between magnetic exchange, electron delocalization and molecular vibrations.
Yet, extensive experimental characterization of Cudaca by means of synchrotron
x-ray diffraction, magnetization, specific heat and inelastic neutron
scattering reveal that properties of the real material can be only partly
explained by proposed theoretical models as the low temperature properties seem
to be governed by a manifold of molecular configurations coexisting at high
temperatures.


  We present a muon spin relaxation study of the Mott transition in BaCoS_2
using two independent control parameters: (i) pressure p to tune the electronic
bandwidth and (ii) Ni-substitution x on the Co site to tune the band filling.
For both tuning parameters, the antiferromagnetic insulating state first
transitions to an antiferromagnetic metal and finally to a paramagnetic metal
without undergoing any structural phase transition. BaCoS_2 under pressure
displays minimal change in the ordered magnetic moment S_ord until it collapses
abruptly upon entering the antiferromagnetic metallic state at p_cr ~ 1.3 GPa.
In contrast, S_ord in the Ni-doped system Ba(Co_{1-x}Ni_{x})S_{2} steadily
decreases with increasing x until the antiferromagnetic metallic region is
reached at x_cr ~ 0.22. In both cases, significant phase separation between
magnetic and nonmagnetic regions develops when approaching p_cr or x_cr, and
the antiferromagnetic metallic state is characterized by weak, random, static
magnetism in a small volume fraction. No dynamical critical behavior is
observed near the transition for either tuning parameter. These results
demonstrate that the quantum evolution of both the bandwidth- and
filling-controlled metal-insulator transition at zero temperature proceeds as a
first-order transition. This behavior is common to magnetic Mott transitions in
RENiO_3 and V_2O_3, which are accompanied by structural transitions without the
formation of an antiferromagnetic metal phase.


  In this paper we consider the equiform motion of a sphere in Euclidean space
$\mathbf{E}^7$. We study and analyze the corresponding kinematic three
dimensional surface under the hypothesis that its scalar curvature $\mathbf{K}$
is constant. Under this assumption, we prove that $|\mathbf{K}|<2$.


  Many studies in heuristic search suggest that the accuracy of the heuristic
used has a positive impact on improving the performance of the search. In
another direction, historical research perceives that the performance of
heuristic search algorithms, such as A* and IDA*, can be improved by requiring
the heuristics to be consistent -- a property satisfied by any perfect
heuristic. However, a few recent studies show that inconsistent heuristics can
also be used to achieve a large improvement in these heuristic search
algorithms. These results leave us a natural question: which property of
heuristics, accuracy or consistency/inconsistency, should we focus on when
building heuristics? While there are studies on the heuristic accuracy with the
assumption of consistency, no studies on both the inconsistency and the
accuracy of heuristics are known to our knowledge.
  In this study, we investigate the relationship between the inconsistency and
the accuracy of heuristics with A* search. Our analytical result reveals a
correlation between these two properties. We then run experiments on the domain
for the Knapsack problem with a family of practical heuristics. Our empirical
results show that in many cases, the more accurate heuristics also have higher
level of inconsistency and result in fewer node expansions by A*.


  The universal expression for the amplitude square |u_f M u_i|^2 for any
matrix of interaction M is derived. It has obvious covariant form. It allows
the avoidance of calculation of products of the Dirac's matrices traces and
allows easy calculation of cross-sections of any different processes with
polarized and unpolarized particles.


  In string-inspired semi-realistic heterotic orbifolds models with an
anomalous $U(1)_X$, a nonzero Kobayashi-Masakawa (KM) phase is shown to arise
generically from the expectation values of complex scalar fields, which appear
in nonrenormalizable quark mass couplings. Modular covariant nonrenormalizable
superpotential couplings are constructed. A toy $Z_3$ orbifold model is
analyzed in some detail. Modular symmetries and orbifold selection rules are
taken into account and do not lead to a cancellation of the KM phase. We also
discuss attempts to obtain the KM phase solely from renormalizable
interactions.


  We derive a comparison principle for a degenerate elliptic partial
differential equation without boundary conditions which arises naturally in
optimal learning strategies. Our argument is direct and exploits the degeneracy
of the differential operator to construct (logarithmically) diverging barriers.


  $M$ is a cpt. Riemannian manifold without boundary,
$f\in\mathrm{Diff}^{1+\beta}(M)$. In [Sarig13], for all $\chi>0$, for every
small enough $\epsilon>0$, Sarig had first constructed a coding
$\widehat{\pi}:\widehat{\Sigma}\rightarrow M$ which covers the set of all
Lyapunov regular $\chi$-hyperbolic points when $\mathrm{dim}M=2$, where
$\widehat{\Sigma}$ is a topological Markov shift over a locally-finite and
countable directed graph. $\widehat{\pi}$ is H\"older continuous, and is
finite-to-one on
$\widehat{\Sigma}^\#:=\{\underline{u}\in\widehat{\Sigma}:\exists v,w\text{ s.t.
}\#\{i\geq0:u_i=v\}=\infty, \#\{i\leq0:u_i=w\}=\infty\}$; and
$\widehat{\pi}[\widehat{\Sigma}^\#]\supseteq \{\text{Lyapunov regular and
temperable }\chi\text{-hyperbolic points}\}$. We later extended Sarig's result
for the case $\mathrm{dim}M\geq2$ in [BO18]. In this work, we offer an improved
construction for [BO18] such that ($\forall\epsilon>0$ small enough) we could
identify canonically the set $\widehat{\pi}[\widehat{\Sigma}^\#]$. We introduce
the notions of $\chi$-summable, and $\epsilon$-weakly temperable points. In
[BCS], the authors show that for each homoclinic class of a periodic hyperbolic
point $p$, there exists a maximal irreducible component
$\widetilde{\Sigma}\subseteq\widehat{\Sigma}$ s.t. all invariant ergodic
probability $\chi$-hyperbolic measures which are carried by the homoclinic
class of $p$ can be lifted to $\widetilde{\Sigma}$. We use their construction
in the context of ergodic homoclinic classes, to show the stronger claim,
$\widehat{\pi}[\widetilde{\Sigma}\cap\widehat{\Sigma}^\#]=H(p)$ modulo all
conservative (possibly infinite) measures ($\mathrm{dim}M\geq2$); where $H(p)$
is the ergodic homoclinic class of $p$, as defined in [RHRHTU11], with the
(canonically identified) recurrently-codable points replacing the Lyapunov
regular points in the definition in [RHRHTU11].


  We give an overview about well-known basic properties of two classes of
q-Fibonacci and q-Lucas polynomials and offer a common generalization.


  Most query optimizers rely on cardinality estimates to determine optimal
execution plans. While traditional databases such as PostgreSQL, Oracle, and
Db2 utilize many types of synopses -- including histograms, samples, and
sketches -- recent main-memory databases like DuckDB and Heavy.AI often operate
with minimal or no estimates, yet their performance does not necessarily
suffer. To the best of our knowledge, no analytical comparison has been
conducted between optimizers with and without cardinality estimates to
understand their performance characteristics in different settings, such as
indexed, non-indexed, and multi-threaded. In this paper, we present a
comparative analysis between optimizers that use cardinality estimates and
those that do not. We use the Join Order Benchmark (JOB) for our evaluation and
true cardinalities as the baseline. Our investigation reveals that cardinality
estimates have marginal impact in non-indexed settings. Meanwhile, when indexes
are available, inaccurate estimates may lead to sub-optimal physical operators
-- even with an optimal join order. Furthermore, the impact of cardinality
estimates is less significant in highly-parallel main-memory databases.


  Most existing imitation learning approaches assume the demonstrations are
drawn from experts who are optimal, but relaxing this assumption enables us to
use a wider range of data. Standard imitation learning may learn a suboptimal
policy from demonstrations with varying optimality. Prior works use confidence
scores or rankings to capture beneficial information from demonstrations with
varying optimality, but they suffer from many limitations, e.g., manually
annotated confidence scores or high average optimality of demonstrations. In
this paper, we propose a general framework to learn from demonstrations with
varying optimality that jointly learns the confidence score and a
well-performing policy. Our approach, Confidence-Aware Imitation Learning
(CAIL) learns a well-performing policy from confidence-reweighted
demonstrations, while using an outer loss to track the performance of our model
and to learn the confidence. We provide theoretical guarantees on the
convergence of CAIL and evaluate its performance in both simulated and real
robot experiments. Our results show that CAIL significantly outperforms other
imitation learning methods from demonstrations with varying optimality. We
further show that even without access to any optimal demonstrations, CAIL can
still learn a successful policy, and outperforms prior work.


  We present a new experimental approach to investigate the magnetic properties
of the anisotropic heavy-fermion system YbRh$_2$Si$_2$ as a function of
crystallographic orientation. Angle-dependent electron spin resonance (ESR)
measurements are performed at a low temperature of 1.6 K and at an ESR
frequency of 4.4 GHz utilizing a superconducting planar microwave resonator in
a $^4$He-cryostat in combination with in-situ sample rotation. The obtained ESR
g-factor of YbRh$_2$Si$_2$ as a function of the crystallographic angle is
consistent with results of previous measurements using conventional ESR
spectrometers at higher frequencies and fields. Perspectives to implement this
experimental approach into a dilution refrigerator and to reach the
magnetically ordered phase of YbRh$_2$Si$_2$ are discussed.


  An explicit solution is found for the most general independent correlation
functions in lattice QCD$_2$ with Wilson action. The large-$N$ limit of these
correlations may be used to reconstruct the eigenvalue distributions of Wilson
loop operators for arbitrary loops. Properties of these spectral densities are
discussed in the region $\beta<\beta_c={1\over 2}$.


  Conformer-based attention models have become the de facto backbone model for
Automatic Speech Recognition tasks. A blank symbol is usually introduced to
align the input and output sequences for CTC or RNN-T models. Unfortunately,
the long input length overloads computational budget and memory consumption
quadratically by attention mechanism. In this work, we propose a
"Skip-and-Recover" Conformer architecture, named Skipformer, to squeeze
sequence input length dynamically and inhomogeneously. Skipformer uses an
intermediate CTC output as criteria to split frames into three groups: crucial,
skipping and ignoring. The crucial group feeds into next conformer blocks and
its output joint with skipping group by original temporal order as the final
encoder output. Experiments show that our model reduces the input sequence
length by 31 times on Aishell-1 and 22 times on Librispeech corpus. Meanwhile,
the model can achieve better recognition accuracy and faster inference speed
than recent baseline models. Our code is open-sourced and available online.


  While textual reviews have become prominent in many recommendation-based
systems, automated frameworks to provide relevant visual cues against text
reviews where pictures are not available is a new form of task confronted by
data mining and machine learning researchers. Suggestions of pictures that are
relevant to the content of a review could significantly benefit the users by
increasing the effectiveness of a review. We propose a deep learning-based
framework to automatically: (1) tag the images available in a review dataset,
(2) generate a caption for each image that does not have one, and (3) enhance
each review by recommending relevant images that might not be uploaded by the
corresponding reviewer. We evaluate the proposed framework using the Yelp
Challenge Dataset. While a subset of the images in this particular dataset are
correctly captioned, the majority of the pictures do not have any associated
text. Moreover, there is no mapping between reviews and images. Each image has
a corresponding business-tag where the picture was taken, though. The overall
data setting and unavailability of crucial pieces required for a mapping make
the problem of recommending images for reviews a major challenge. Qualitative
and quantitative evaluations indicate that our proposed framework provides high
quality enhancements through automatic captioning, tagging, and recommendation
for mapping reviews and images.


  Emerging wireless applications such as 5G cellular, large intelligent
surfaces (LIS), and holographic massive MIMO require antenna array processing
at mm-wave frequencies with large numbers of independent digital transceivers.
This paper summarizes the authors' recent progress on the design and testing of
28 GHz and 60 GHz fully-digital array processing platforms based on wideband
reconfigurable FPGA-based software-defined radios (SDRs). The digital baseband
and microwave interfacing aspects of the SDRs are implemented on single-chip RF
system-on-chip (RF-SoC) processors from Xilinx. Two versions of the RF-SoC
technology (ZCU-111 and ZCU-1275) were used to implement fully-digital
real-time array processors at 28~GHz (realizing 4 parallel beams with 0.8 GHz
bandwidth per beam) and 60~GHz (realizing 4 parallel beams with 1.8~GHz
bandwidth per beam). Dielectric lenslet arrays fed by a digital phased-array
feed (PAF) located on the focal plane are proposed for further increasing
antenna array gain.


  The geometry of optical lattices can be engineered allowing the study of
atomic transport along paths arranged in patterns that are otherwise difficult
to probe in the solid state. A question readily accessible to atomic systems is
related to the speed of propagation of matter-waves as a function of the
lattice geometry. To address this issue, we have investigated theoretically the
quantum transport of non-interacting and weakly-interacting ultracold fermionic
atoms in several 2D optical lattice geometries. We find that the triangular
lattice has a higher propagation velocity compared to the square lattice,
despite supporting longer paths. The body-centered square lattice has even
longer paths, nonetheless the propagation velocity is yet faster. This apparent
paradox arises from the mixing of the momentum states which leads to different
group velocities in quantum systems. Standard band theory provides an
explanation and allows for a systematic way to search and design systems with
controllable matter-wave propagation. Moreover, the presence of a flat band
such as in a two-leg ladder geometry leads to a dynamical density
discontinuity, which contrasts the behavior of mobile and localized atoms in
quantum transport. Our predictions are realizable with present experimental
capability.


  We view the mind-body problem in terms of the two interconnected problems of
phenomenal consciousness and mental causation, namely, how subjective conscious
experience can arise from physical neurological processes and how conscious
mental states can causally act upon the physical world. In order to address
these problems, I develop here a non-physicalist framework that combines two
apparently antithetical views: the materialist view of the mind as a product of
the brain and the metaphysical view of consciousness rooted in an underlying
hidden reality. I discuss how this framework resolves the problem of mental
causation while being simultaneously consistent with fundamental physical
principles. I will elucidate how the framework ties in to the perspective of
meaning that acts as the bridge between physical neurological processes and the
conscious mind. Moreover, we will see how both our awareness of the self and
our representation of the external world are connected to this perspective.


  In this paper, we will show that nonabelian simple classical groups of Lie
type are uniquely determined by the structure of their complex group algebras.


  We study the spin-1/2 Ising-XXZ model on a decorated honeycomb lattice
composed of five spins per unit cell, one Ising spin, and four Heisenberg
spins. This model involving the Heisenberg exchange interaction is one of the
few models that can be exactly solvable through the generalized star-triangle
transformation. The significance of this model is its close relationship to the
fully decorated quantum Heisenberg honeycomb lattice since 4/5 of the particles
are Heisenberg spins. We investigate the phase diagram at zero temperature and
identify a relevant quantum spin frustrated phase resulting from the
contribution of quantum Heisenberg exchange interaction. We obtain an exact
residual entropy for the quantum spin frustrated phase, which coincides with
the residual entropy of the antiferromagnetic spin-1/2 Ising model on a
triangular lattice. We also thoroughly explore its thermodynamic properties,
focusing mainly on the frustrated region such as entropy, specific heat,
spontaneous magnetization, and critical temperature under several conditions.


  We describe a minimally-supervised method for computing a statistical shape
space model of the palate surface. The model is created from a corpus of
volumetric magnetic resonance imaging (MRI) scans collected from 12 speakers.
We extract a 3D mesh of the palate from each speaker, then train the model
using principal component analysis (PCA). The palate model is then tested using
3D MRI from another corpus and evaluated using a high-resolution optical scan.
We find that the error is low even when only a handful of measured coordinates
are available. In both cases, our approach yields promising results. It can be
applied to extract the palate shape from MRI data, and could be useful to other
analysis modalities, such as electromagnetic articulography (EMA) and
ultrasound tongue imaging (UTI).


  In a model of the late-time cosmic acceleration within the framework of
generalized Proca theories, there exists a de Sitter attractor preceded by the
dark energy equation of state $w_{\rm DE}=-1-s$, where $s$ is a positive
constant. We run the Markov-Chain-Monte-Carlo code to confront the model with
the observational data of Cosmic Microwave Background (CMB), baryon acoustic
oscillations, supernovae type Ia, and local measurements of the Hubble
expansion rate for the background cosmological solutions and obtain the bound
$s=0.254^{{}+ 0.118}_{{}-0.097}$ at 95% confidence level (CL). Existence of the
additional parameter $s$ to those in the $\Lambda$-Cold-Dark-Matter
($\Lambda$CDM) model allows to reduce tensions of the Hubble constant $H_0$
between the CMB and the low-redshift measurements. Including the cosmic growth
data of redshift-space distortions in the galaxy power spectrum and taking into
account no-ghost and stability conditions of cosmological perturbations, we
find that the bound on $s$ is shifted to $s=0.16^{+0.08}_{-0.08}$ (95 % CL) and
hence the model with $s>0$ is still favored over the $\Lambda$CDM model. Apart
from the quantities $s, H_0$ and the today's matter density parameter
$\Omega_{m0}$, the constraints on other model parameters associated with
perturbations are less stringent, reflecting the fact that there are different
sets of parameters that give rise to a similar cosmic expansion and growth
history.


  Device activity detection in the emerging cell-free massive multiple-input
multiple-output (MIMO) systems has been recognized as a crucial task in
machine-type communications, in which multiple access points (APs) jointly
identify the active devices from a large number of potential devices based on
the received signals. Most of the existing works addressing this problem rely
on the impractical assumption that different active devices transmit signals
synchronously. However, in practice, synchronization cannot be guaranteed due
to the low-cost oscillators, which brings additional discontinuous and
nonconvex constraints to the detection problem. To address this challenge, this
paper reveals an equivalent reformulation to the asynchronous activity
detection problem, which facilitates the development of a centralized algorithm
and a distributed algorithm that satisfy the highly nonconvex constraints in a
gentle fashion as the iteration number increases, so that the sequence
generated by the proposed algorithms can get around bad stationary points. To
reduce the capacity requirements of the fronthauls, we further design a
communication-efficient accelerated distributed algorithm. Simulation results
demonstrate that the proposed centralized and distributed algorithms outperform
state-of-the-art approaches, and the proposed accelerated distributed algorithm
achieves a close detection performance to that of the centralized algorithm but
with a much smaller number of bits to be transmitted on the fronthaul links.


  A set of traveling wave solution to convection-reaction-diffusion equation is
studied by means of methods of local nonlinear analysis and numerical
simulation. It is shown the existence of compactly supported solutions as well
as solitary waves within this family for wide range of parameter values.


  Anderson localization of Bogoliubov excitations is studied for disordered
lattice Bose gases in planar quasi-one-dimensional geometries. The inverse
localization length is computed as function of energy by a numerical
transfer-matrix scheme, for strips of different widths. These results are
described accurately by analytical formulas based on a weak-disorder expansion
of backscattering mean free paths.


  The quantum effective action yields equations of motion and correlation
functions including all quantum corrections. We discuss here how it encodes
also Noether currents at the full quantum level. Interestingly, the
construction can be generalized beyond the standard symmetry transformations
that leave the action invariant. We also discuss an extended set of
transformations, which change the action by a term that is locally known on the
level of the quantum effective action. Associated to such extended gauge
transformations are currents for which we obtain a divergence-type equation of
motion, but they are not conserved. We call them non-conserved Noether
currents. We discuss in particular symmetries and extended transformations
associated to space-time geometry for relativistic quantum field theories.
These encompass local dilatations or Weyl gauge transformation, local Lorentz
transformations and local shear transformations. Together they constitute the
symmetry group of the frame bundle GL$(d)$. The corresponding non-conserved
Noether currents are the dilatation or Weyl current, the spin current and the
shear current. In particular for the latter we obtain a new divergence-type
equations of motion.


  We report on the engineering of a non-dispersive (flat) energy band in a
geometrically frustrated lattice of micro-pillar optical cavities. By taking
advantage of the non-hermitian nature of our system, we achieve bosonic
condensation of exciton-polaritons into the flat band. Due to the infinite
effective mass in such band, the condensate is highly sensitive to disorder and
fragments into localized modes reflecting the elementary eigenstates produced
by geometric frustration. This realization offers a novel approach to studying
coherent phases of light and matter under the controlled interplay of
frustration, interactions and dissipation.


  We study the spectral dimensions of Krein-Feller operators for arbitrary for
arbitrary finite Borel measures $\nu$ on the $d$-dimensional unit cube
($d\geq2$) via a form approach. We make use of the spectral partition function
of $\nu$ as introduced in [Kesseb\"ohmer and Niemann, Exact asymptotic order
for adaptive approximations. 2023, arXiv:2312.16644] and, assuming that the
lower $\infty$-dimension of $\nu$ exceeds $d-2$, we identify the upper Neumann
spectral dimension as the unique zero of the spectral partition function, thus
revealing the intrinsic connection of these spectral and fractal-geometric
quantities. We show that if the lower $\infty$-dimension of $\nu$ is strictly
less than $d-2$, the form approach breaks down. Examples are given for the
critical case, that is the lower $\infty$-dimension of $\nu$ equals $d-2$. We
provide additional regularity assumptions on the spectral partition function,
guaranteeing that the Neumann spectral dimension exists and coincides with the
Dirichlet spectral dimension. Several prominent examples previously treated in
the literature are provided, namely absolutely continuous measures and more
generally Ahlfors-David regular measures, and examples not previously treated
in the literature, namely self-conformal measures with or without overlaps, for
which we show that both the Dirichlet and Neumann spectral dimensions exist and
how they can be obtained from the $L^{q}$-spectrum of the measures. We
demonstrate how our approach can be used to obtain upper and lower asymptotic
spectral bounds for the case of Ahlfors-David regular measures. Moreover, we
provide sharp bounds for the upper Neumann spectral dimension in terms of the
upper Minkowski dimension of the support of $\nu$ and its lower
$\infty$-dimension. Finally, we give an example for which the spectral
dimension does not exist.


  Historical literature has traced US efforts to bring Latin American countries
over to the side of the Allies in WWII. Following a period of hesitation and
negotiation with the US and Germany, the Brazilian government aligned itself
with the US. What remains virtually unknown is the involvement of scientists in
these diplomatic arrangements. Recently unearthed material has shown that
Arthur Compton's 1941 trip to a scientific conference on cosmic rays in Brazil
was linked to efforts led by the Office for Inter-American Affairs under Nelson
Rockefeller. For the Brazilian physicists, who, under the leadership of Gleb
Wataghin, had excelled in this area of research during the late 1930s, science
was a strong motivation for the visit; it was not, however, devoid of political
connotations and professional interests.


  Logarithmic capacity is shown to be minimal for a planar set having $N$-fold
rotational symmetry ($N \geq 3$), among all conductors obtained from the set by
area-preserving linear transformations. Newtonian and Riesz capacities obey a
similar property in all dimensions, when suitably normalized linear
transformations are applied to a set having irreducible symmetry group. A
corollary is P\'{o}lya and Schiffer's lower bound on capacity in terms of
moment of inertia.


  These are six papers joined by the same title. The main topics are:
  1. algebraic nature of quantization of relativistic fields,
  2. constructive definition of space of states of quantum electromagnetic
field,
  3. structure of space of states of quantum electromagnetic field from
functional analysis standpoint.


  Here we present the colours of individual globular clusters (GCs) around the
massive elliptical galaxy NGC 1407 out to a projected galactocentric radius of
140 kpc or 17 galaxy effective radii (R$_e$). Such data are a proxy for the
halo metallicity. We find steep, and similar, metallicity gradients of ~ -0.4
dex per dex for both the blue (metal-poor) and red (metal-rich) GC
subpopulations within 5-8.5 R_e (40-70 kpc). At larger radii the mean GC
colours (metallicity) are constant. A similar behaviour is seen in a wide-field
study of M87's GC system, and in our own Galaxy. We interpret these radial
metallicity trends to indicate an inner region formed by early in-situ
dissipative processes and an outer halo formed by ongoing accretion of low mass
galaxies and their GCs. These results provide observational support for the
model of galaxy formation whereby massive galaxies form inside-out in two
phases. We have also searched the literature for other massive early-type
galaxies with reported GC metallicity gradients in their inner regions. No
obvious correlation with galaxy mass or environment is found but the sample is
currently small.


  We theoretically investigate the dynamics of two mutually coupled identical
single-mode semi-conductor lasers. For small separation and large coupling
between the lasers, symmetry-broken one-colour states are shown to be stable.
In this case the light output of the lasers have significantly different
intensities while at the same time the lasers are locked to a single common
frequency. For intermediate coupling we observe stable symmetry-broken
two-colour states, where both lasers lase simultaneously at two optical
frequencies which are separated by up to 150~GHz. Using a five dimensional
model we identify the bifurcation structure which is responsible for the
appearance of symmetric and symmetry-broken one-colour and two-colour states.
Several of these states give rise to multi-stabilities and therefore allow for
the design of all-optical memory elements on the basis of two coupled
single-mode lasers. The switching performance of selected designs of optical
memory elements is studied numerically.


  The conventional coherence is defined with respect to a fixed orthonormal
basis, i.e., to a von Neumann measurement. Recently, generalized quantum
coherence with respect to general positive operator-valued measurements (POVMs)
has been presented. Several well-defined coherence measures, such as the
relative entropy of coherence $C_{r}$, the $l_{1}$ norm of coherence
$C_{l_{1}}$ and the coherence $C_{T,\alpha }$ based on Tsallis relative entropy
with respect to general POVMs have been obtained. In this work, we investigate
the properties of $C_{r}$, $l_{1}$ and $C_{T,\alpha }$. We estimate the upper
bounds of $C_{l_{1}}$; we show that the minimal error probability of the least
square measurement state discrimination is given by $C_{T,1/2}$; we derive the
uncertainty relations given by $C_{r}$, and calculate the average values of
$C_{r}$, $C_{T,\alpha }$ and $C_{l_{1}}$ over random pure quantum states. All
these results include the corresponding results of the conventional coherence
as special cases.


  Motivated by the recent successful formation of the MoSi2N4 monolayer [Hong
et al., Sci. 369, 670 (2020)], the structural, electronic and magnetic
properties of MoSi2N4 nanoribbons (NRs) is investigated for the first time .
The band structure calculations showed spin-polarization in zigzag edges and a
non-magnetic semiconducting character in armchair edges. For armchair-edges, we
identify an indirect to direct band gap shift compared to the MoSi2N4
monolayer, and its energy gap increases with increasing NR width. Anisotropic
electrical and magnetic behavior is observed via band structure calculations in
the zigzag and armchair edges, where, surprisingly, for the one type of
zigzag-edges configuration, we identify a Dirac-semimetal character. The
appearance of magnetism and Dirac-semimetal in MoSi2N4 ribbon can give rise to
novel physical properties, which could be useful in applications for
next-generation electronic devices.


  Reproduction data collected through standard bioassays are classically
analyzed by regression in order to fit exposure-response curves and estimate
ECx values (x% Effective Concentration). But regression is often misused on
such data, ignoring statistical issues related to i) the special nature of
reproduction data (count data), ii) a potential inter-replicate variability and
iii) a possible concomitant mortality. This paper offers new insights in
dealing with those issues. Concerning mortality, particular attention was paid
not to waste any valuable data - by dropping all the replicates with mortality
- or to bias ECx values. For that purpose we defined a new covariate summing
the observation periods during which each individual contributes to the
reproduction process. This covariate was then used to quantify reproduction -
for each replicate at each concentration - as a number of offspring per
individual-day. We formulated three exposure-response models differing by their
stochastic part. Those models were fitted to four datasets and compared using a
Bayesian framework. The individual-day unit proved to be a suitable approach to
use all the available data and prevent bias in the estimation of ECx values.
Furthermore, a non-classical negative-binomial model was shown to correctly
describe the inter-replicate variability observed in the studied datasets.


  The eigenfunctions and eigenvalues of the linearized Boltzmann equation for
inelastic hard spheres (d=3) or disks (d=2) corresponding to d+2 hydrodynamic
modes, are calculated in the long wavelength limit for a granular gas. The
transport coefficients are identified and found to agree with those from the
Chapman-Enskog solution. The dominance of hydrodynamic modes at long times and
long wavelengths is studied via an exactly solvable kinetic model. A
collisional continuum is bounded away from the hydrodynamic spectrum, assuring
a hydrodynamic description at long times. The bound is closely related to the
power law decay of the velocity distribution in the reference homogeneous
cooling state.


  We find that dust clouds which eclipse young stars obscure the stellar disc
inhomogeneously. In the particular case of CQ Tau, we find isolated optically
thick structures with sizes $\lesssim0.6R_*$ and derive the typical $A_{V}$
gradient in the plane of the sky, finding it as high as a few magnitudes per
stellar radius. The large extinction gradients and complex structure of the
obscuring clouds lead not only to a noticeable Rossiter--McLaughlin effect, but
also to complex and variable shaping of stellar absorption lines.


  We study $p$-Faulty Search, a variant of the classic cow-path optimization
problem, where a unit speed robot searches the half-line (or $1$-ray) for a
hidden item. The searcher is probabilistically faulty, and detection of the
item with each visitation is an independent Bernoulli trial whose probability
of success $p$ is known. The objective is to minimize the worst case expected
detection time, relative to the distance of the hidden item to the origin. A
variation of the same problem was first proposed by Gal in 1980. Then in 2003,
Alpern and Gal [The Theory of Search Games and Rendezvous] proposed a so-called
monotone solution for searching the line ($2$-rays); that is, a trajectory in
which the newly searched space increases monotonically in each ray and in each
iteration. Moreover, they conjectured that an optimal trajectory for the
$2$-rays problem must be monotone. We disprove this conjecture when the search
domain is the half-line ($1$-ray). We provide a lower bound for all monotone
algorithms, which we also match with an upper bound. Our main contribution is
the design and analysis of a sequence of refined search strategies, outside the
family of monotone algorithms, which we call $t$-sub-monotone algorithms. Such
algorithms induce performance that is strictly decreasing with $t$, and for all
$p \in (0,1)$. The value of $t$ quantifies, in a certain sense, how much our
algorithms deviate from being monotone, demonstrating that monotone algorithms
are sub-optimal when searching the half-line.


  We investigate convergence of Lagrangian Perturbation Theory (LPT) by
analyzing the model problem of a spherical homogeneous top-hat in an
Einstein-deSitter background cosmology. We derive the formal structure of the
LPT series expansion, working to arbitrary order in the initial perturbation
amplitude. The factors that regulate LPT convergence are identified by studying
the exact, analytic solution expanded according to this formal structure. The
key methodology is to complexify the exact solution, demonstrate that it is
analytic and apply well-known convergence criteria for power series expansions
of analytic functions.This analysis fully explains the previously reported
observation that LPT fails to predict the evolution of an underdense, open
region beyond a certain time. It also implies the existence of other examples,
including overdense, closed regions, for which LPT predictions should also
fail. We show that this is indeed the case by numerically computing the LPT
expansion in these problematic cases. The formal limitations to the validity of
LPT expansion are considerably more complicated than simply the first
occurrence of orbit crossings as is often assumed. Evolution to a future time
generically requires re-expanding the solution in overlapping domains that
ultimately link the initial and final times, each domain subject to its own
convergence criterion. We demonstrate that it is possible to handle all the
problematic cases by taking multiple steps (LPT re-expansion). We characterize
how the leading order numerical error for a solution generated by LPT re-
expansion varies with the choice of Lagrangian order and of time step size.
Convergence occurs when the Lagrangian order increases and/or the time step
size decreases in a simple, well-defined manner. We develop a recipe for time
step control for LPT re-expansion based on these results.


  We investigate a superradiating system coupled to external reservoirs. Under
conditions where electrons tunneling at a rate $T$ act like an electron pump,
we predict a novel phenomenon in the form of oscillations with a frequency
$\omega \simeq \sqrt{2\Gamma T}$ that appear in the (photon) emission
intensity, where $\Gamma $ is the spontaneous decay rate of a single two-level
system. The effect, together with a strong enhancement of the superradiant
peak, should be observable in semiconductor quantum wells in strong magnetic
fields, or in quantum dot arrays.


  Indoor localization becomes a raising demand in our daily lives. Due to the
massive deployment in the indoor environment nowadays, WiFi systems have been
applied to high accurate localization recently. Although the traditional model
based localization scheme can achieve sub-meter level accuracy by fusing
multiple channel state information (CSI) observations, the corresponding
computational overhead is significant. To address this issue, the model-free
localization approach using deep learning framework has been proposed and the
classification based technique is applied. In this paper, instead of using
classification based mechanism, we propose to use a logistic regression based
scheme under the deep learning framework, which is able to achieve sub-meter
level accuracy (97.2cm medium distance error) in the standard laboratory
environment and maintain reasonable online prediction overhead under the single
WiFi AP settings. We hope the proposed logistic regression based scheme can
shed some light on the model-free localization technique and pave the way for
the practical deployment of deep learning based WiFi localization systems.


  The celebrated palette sparsification result of [Assadi, Chen, and Khanna
SODA'19] shows that to compute a $\Delta+1$ coloring of the graph, where
$\Delta$ denotes the maximum degree, it suffices if each node limits its color
choice to $O(\log n)$ independently sampled colors in $\{1, 2, \dots,
\Delta+1\}$. They showed that it is possible to color the resulting sparsified
graph -- the spanning subgraph with edges between neighbors that sampled a
common color, which are only $\tilde{O}(n)$ edges -- and obtain a $\Delta+1$
coloring for the original graph. However, to compute the actual coloring, that
information must be gathered at a single location for centralized processing.
We seek instead a local algorithm to compute such a coloring in the sparsified
graph. The question is if this can be achieved in $\operatorname{poly}(\log n)$
distributed rounds with small messages.
  Our main result is an algorithm that computes a $\Delta+1$-coloring after
palette sparsification with $O(\log^2 n)$ random colors per node and runs in
$O(\log^2 \Delta + \log^3 \log n)$ rounds on the sparsified graph, using
$O(\log n)$-bit messages. We show that this is close to the best possible: any
distributed $\Delta+1$-coloring algorithm that runs in the LOCAL model on the
sparsified graph, given by palette sparsification, for any
$\operatorname{poly}(\log n)$ colors per node, requires $\Omega(\log \Delta /
\log\log n)$ rounds. This distributed palette sparsification result leads to
the first $\operatorname{poly}(\log n)$-round algorithms for
$\Delta+1$-coloring in two previously studied distributed models: the Node
Capacitated Clique, and the cluster graph model.


  A lot of recent work has focused on sparse learned indexes that use deep
neural architectures to significantly improve retrieval quality while keeping
the efficiency benefits of the inverted index. While such sparse learned
structures achieve effectiveness far beyond those of traditional inverted
index-based rankers, there is still a gap in effectiveness to the best dense
retrievers, or even to sparse methods that leverage more expensive
optimizations such as query expansion and query term weighting.
  We focus on narrowing this gap by revisiting and optimizing DeepImpact, a
sparse retrieval approach that uses DocT5Query for document expansion followed
by a BERT language model to learn impact scores for document terms. We first
reinvestigate the expansion process and find that the recently proposed
Doc2Query -- query filtration does not enhance retrieval quality when used with
DeepImpact. Instead, substituting T5 with a fine-tuned Llama 2 model for query
prediction results in a considerable improvement. Subsequently, we study
training strategies that have proven effective for other models, in particular
the use of hard negatives, distillation, and pre-trained CoCondenser model
initialization. Our results substantially narrow the effectiveness gap with the
most effective versions of SPLADE.


  We present a new probabilistic algorithm to find a finite set of points
intersecting the closure of each connected component of the realization of
every sign condition over a family of real polynomials defining regular
hypersurfaces that intersect transversally. This enables us to show a
probabilistic procedure to list all feasible sign conditions over the
polynomials. In addition, we extend these results to the case of closed sign
conditions over an arbitrary family of real multivariate polynomials. The
complexity bounds for these procedures improve the known ones.


  We present results of shell model calculations for the proton drip line
nucleus $^{106}$Sb. The shell model calculations were performed based on an
effective interaction for the $2s1d0g_{7/2}0h11_{11/2}$ shells employing modern
models for the nucleon-nucleon interaction. The results are compared with the
recently proposed experimental yrast states. A good agreement with experiment
is found lending support to the experimental spin assignements.


  Scalar-tensor theories of gravity are known to allow significant deviations
from general relativity through various astrophysical phenomena. In this paper,
we formulate a scalar-connection gravity by setting up scalars and connection
configurations instead of metric. Since the matter sector is not
straightforward to conceive without a metric, we invoke cosmological fluids in
terms of their one-form velocity in the volume element of the invariant action.
This leads to gravitational equations with a perfect fluid source and a
generated metric, which are expected to produce reasonable deviations from
general relativity in the strong-field regime. As a relevant application, we
study spontaneous scalarization mechanism and show that the
Damour-Esposito-Far\`{e}se model arises in a certain class of scalar-connection
gravity. Furthermore, we investigate a general study in which the present
framework becomes distinguishable from the famed scalar-tensor theories.


  Semiconductor nanowires are promising material systems for coming of age
nanotechnology. The usage of the vapor solid solid (VSS) route, where the
catalyst used for promoting axial growth of nanowire is a solid, offers certain
advantages compared to the common vapor liquid solid (VLS) route (using liquid
catalyst). The VSS growth of group-IV elemental nanowires have been
investigated by other groups in situ during growth in a transmission electron
microscope (TEM). Though it is known that compound nanowire growth has
different dynamics compared to monoatomic semiconductors, the dynamics of VSS
growth of compound nanowires has not been understood. Here we investigate VSS
growth of compound nanowires by in situ microscopy, using Au-seeded GaAs as a
model system. The growth kinetics and dynamics at the wire-catalyst interface
by ledge-flow is studied and compared for liquid and solid catalysts at similar
growth conditions. Here the temperature and thermal history of the system is
manipulated to control the catalyst phase. In the first experiment discussed
here we reduce the growth temperature in steps to solidify the initially liquid
catalyst, and compare the dynamics between VLS and VSS growth observed at
slightly different temperatures. In the second experiment we exploit thermal
hysteresis of the system to obtain both VLS and VSS at the same temperature.
The VSS growth rate is comparable or slightly slower than VLS growth. Unlike in
the VLS case, during VSS growth we see several occasions where a new layer
starts before the previous layer is completely grown, i.e. multilayer growth.
Understanding the VSS growth mode enables better control of nanowire properties
by widening the range of usable nanowire growth parameters.


  We show that optical moire lattices enable the existence of vortex solitons
of different types in self-focusing Kerr media. We address the properties of
such states both in lattices having commensurate and incommensurate geometries
(i.e., constructed with Pythagorean and non-Pythagorean twist angles,
respectively), in the different regimes that occur below and above the
localization-delocalization transition. We find that the threshold power
required for the formation of vortex solitons strongly depends on the twist
angle and, also, that the families of solitons exhibit intervals where their
power is a nearly linear function of the propagation constant and they exhibit
strong stability. Also, in the incommensurate phase above the
localization-delocalization transition, we found stable embedded vortex
solitons whose propagation constants belong to the linear spectral domain of
the system.


  We study the non-equilibrium relaxational dynamics of a probe particle
linearly coupled to a thermally fluctuating scalar field and subject to a
harmonic potential, which provides a cartoon for an optically trapped colloid
immersed in a fluid close to its bulk critical point. The average position of
the particle initially displaced from the position of mechanical equilibrium is
shown to feature long-time algebraic tails as the critical point of the field
is approached, the universal exponents of which are determined in arbitrary
spatial dimensions. As expected, this behavior cannot be captured by adiabatic
approaches which assume fast field relaxation. The predictions of the analytic,
perturbative approach are qualitatively confirmed by numerical simulations.


  In this letter, we propose a novel computationally efficient coupled
dictionary learning method that enforces pairwise correlation between the atoms
of dictionaries learned to represent the underlying feature spaces of two
different representations of the same signals, e.g., representations in
different modalities or representations of the same signals measured with
different qualities. The jointly learned correlated feature spaces represented
by coupled dictionaries are used in sparse representation based classification,
recognition and reconstruction tasks. The presented experimental results show
that the proposed coupled dictionary learning method has a significantly lower
computational cost. Moreover, the visual presentation of jointly learned
dictionaries shows that the pairwise correlations between the corresponding
atoms are ensured.


  I demonstrate how chiral fermions with an exact gauge symmetry can appear on
the d-dimensional boundary of a finite volume (d+1)-dimensional manifold,
without any light mirror partners. The condition for the d-dimensional boundary
theory to be local is that gauge anomalies cancel and that the volume be large.
This can likely be achieved on a lattice and provides a new paradigm for the
lattice regularization of chiral gauge theories.


  We introduce the novel phenomena of CP-violating inflation in the frameworks
of a 3-Higgs doublet model where the inflaton doublets have a non-minimal
coupling to gravity. We allow for this coupling to be complex, thereby
introducing CP-violation - a necessary source of the baryon asymmetry - in the
inflaton couplings. We investigate the inflationary dynamics of such a
framework and the inflaton decay in the reheating phase. We discuss how the
CP-violation of the model is imprinted on the particle asymmetries.


  Folding kinetics of a lattice model of protein is studied. It uses the Random
Energy Model for the intrachain couplings and a temperature dependent free
energy of solvation derived from a realistic hydration model of apolar solutes.
The folding times are computed using Monte Carlo simulations in the region of
the phase diagram where the chain occurs in the native structure. These folding
times are roughly equals for the temperatures of cold and warm denaturation for
a large range of solvent quality. Between these temperatures, the folding times
reach maxima and thus, at low temperatures, the kinetics of the chain always
speeds up as the temperature is decreased. The study of the conformational
space as function of the temperature permits to elucidate this phenomenon. At
low temperature, it shows that the activation barriers of the system decrease
faster than the temperature as the temperature is decreased. At high
temperature, the rate of the barriers over the temperature decreases as the
temperature is increased because the height of the barrier is almost constant.


  In this paper we investigate the radiation emitted by a charged particle
moving along a helical orbit around a dielectric cylinder immersed into a
homogeneous medium. Formulae are derived for the electromagnetic potentials,
electric and magnetic fields, and for the spectral-angular distribution of the
radiation in the exterior medium. It is shown that under the Cherenkov
condition for dielectric permittivity of the cylinder and the velocity of the
particle image on the cylinder surface, strong narrow peaks appear in the
angular distribution for the number of quanta radiated on a given harmonic. At
these peaks the radiated energy exceeds the corresponding quantity for a
homogeneous medium by several dozens of times. Simple analytic estimates are
given for the heights and widths of these peaks. The results of numerical
calculations for the angular distribution of the radiated quanta are presented
and they are compared with the corresponding quantities for the radiation from
a charge moving along a helical trajectory inside a dielectric cylinder.


  Some features of hot and dense gas of quarks which are considered as the
quasi-particles of the model Hamiltonian with four-fermion interaction are
studied. Being adapted to the Nambu-Jona-Lasinio model this approach allows us
to accommodate a phase transition similar to the nuclear liquid-gas one at the
proper scale. It allows us to argue an existence of the mixed phase of vacuum
and baryonic matter (even at zero temperature) as a plausible scenario of
chiral symmetry (partial) restoration.


  A new scheme is proposed for dealing with the problem of singularities in
General Relativity. The proposal is, however, much more general than this. It
can be used to deal with manifolds of any dimension which are endowed with
nothing more than an affine connection, and requires a family \calc\ of curves
satisfying a {\em bounded parameter property} to be specified at the outset.
All affinely parametrised geodesics are usually included in this family, but
different choices of family \calc\ will in general lead to different
singularity structures. Our key notion is the {\em abstract boundary\/} or {\em
$a$-boundary\/} of a manifold, which is defined for any manifold \calm\ and is
independent of both the affine connection and the chosen family \calc\ of
curves. The $a$-boundary is made up of equivalence classes of boundary points
of \calm\ in all possible open embeddings. It is shown that for a
pseudo-Riemannian manifold $(\calm,g)$ with a specified family \calc\ of
curves, the abstract boundary points can then be split up into four main
categories---regular, points at infinity, unapproachable points and
singularities. Precise definitions are also provided for the notions of a {\em
removable singularity} and a {\em directional singularity}. The
pseudo-Riemannian manifold will be said to be singularity-free if its abstract
boundary contains no singularities. The scheme passes a number of tests
required of any theory of singularities. For instance, it is shown that all
compact manifolds are singularity-free, irrespective of the metric and chosen
family \calc.


  Methods for solving PDEs using neural networks have recently become a very
important topic. We provide an a priori error analysis for such methods which
is based on the $\mathcal{K}_1(\mathbb{D})$-norm of the solution. We show that
the resulting constrained optimization problem can be efficiently solved using
a greedy algorithm, which replaces stochastic gradient descent. Following this,
we show that the error arising from discretizing the energy integrals is
bounded both in the deterministic case, i.e. when using numerical quadrature,
and also in the stochastic case, i.e. when sampling points to approximate the
integrals. In the later case, we use a Rademacher complexity analysis, and in
the former we use standard numerical quadrature bounds. This extends existing
results to methods which use a general dictionary of functions to learn
solutions to PDEs and importantly gives a consistent analysis which
incorporates the optimization, approximation, and generalization aspects of the
problem. In addition, the Rademacher complexity analysis is simplified and
generalized, which enables application to a wide range of problems.


  Zero rest-mass fields of spin 1 (the electromagnetic field) and spin 2
propagating on flat space and their corresponding Newman-Penrose (NP) constants
are studied near spatial infinity. The aim of this analysis is to clarify the
correspondence between data for these fields on a spacelike hypersurface and
the value of their corresponding NP constants at future and past null infinity.
To do so, Friedrich's framework of the cylinder at spatial infinity is employed
to show that, expanding the initial data in terms spherical harmonics and
powers of the geodesic spatial distance $\rho$ to spatial infinity, the NP
constants correspond to the data for the second highest possible spherical
harmonic at fixed order in $\rho$. In addition, it is shown that for generic
initial data within the class considered in this article, there is no natural
correspondence between the NP constants at future and past null infinity ---for
both the Maxwell and spin-2 field. However, if the initial data is
time-symmetric then the NP constants at future and past null infinity have the
same information.


  Depth completion, aiming to predict dense depth maps from sparse depth
measurements, plays a crucial role in many computer vision related
applications. Deep learning approaches have demonstrated overwhelming success
in this task. However, high-precision depth completion without relying on the
ground-truth data, which are usually costly, still remains challenging. The
reason lies on the ignorance of 3D structural information in most previous
unsupervised solutions, causing inaccurate spatial propagation and mixed-depth
problems. To alleviate the above challenges, this paper explores the
utilization of 3D perceptual features and multi-view geometry consistency to
devise a high-precision self-supervised depth completion method. Firstly, a 3D
perceptual spatial propagation algorithm is constructed with a point cloud
representation and an attention weighting mechanism to capture more reasonable
and favorable neighboring features during the iterative depth propagation
process. Secondly, the multi-view geometric constraints between adjacent views
are explicitly incorporated to guide the optimization of the whole depth
completion model in a self-supervised manner. Extensive experiments on
benchmark datasets of NYU-Depthv2 and VOID demonstrate that the proposed model
achieves the state-of-the-art depth completion performance compared with other
unsupervised methods, and competitive performance compared with previous
supervised methods.


  The field-particle correlation technique utilizes single-point measurements
to uncover signatures of various particle energization mechanisms in turbulent
space plasmas. The signature of Landau damping by electrons has been found in
both simulations and observations from Earth's magnetosheath using this
technique, but instrumental limitations of spacecraft sampling rates present a
challenge to discovering the full extent of the presence of Landau damping in
the solar wind. Theory predicts that field-particle correlations can recover
velocity-space energization signatures even from data that is undersampled with
respect to the characteristic frequencies at which the wave damping occurs. To
test this hypothesis, we perform a high-resoluation gyrokinetic simulation of
space plasma turbulence, confirm that it contains signatures of electron Landau
damping, and then systematically reduce the time resolution of the data to
identify the point at which the signatures become impossible to recover. We
find results in support of our theoretical prediction and look for a rule of
thumb that can be compared with the measurement capabilities of spacecraft
missions to inform the process of applying field-particle correlations to low
time resolution data.


  Stationary, axisymmetric, dust sourced solutions of Einstein's equations have
been proposed as fully general relativistic models for disc galaxies. These
models introduce a novel physical element, i.e., a non-negligible dragging
vortex emerging from a full consideration of the essential self-interaction of
matter and geometry in general relativity, which might demand a profound
recalibration of the inferred amount of dark matter in disc galaxies. Within
this framework, we identify the correct observables for redshift-inferred
rotation curves of distant galaxies, correcting previously overlooked mistakes
in the literature. We find that the presence of the dragging vortex introduces
non-negligible corrective terms for the matter density required to maintain a
stable physical system. We present the first estimate of the dragging speed
which is required to explain a non-negligible fraction of dark matter in disc
galaxies. In particular, we show that a sub-relativistic dragging velocity of
tens of kilometers per second in the neighbourhood of the Sun is sufficient to
reduce the need of dark matter by 50% in the Milky Way. Finally, we find that
the presence of such a dragging vortex also returns a net contribution to the
strong gravitational lensing generated by the galaxy. Thus, we show that the
considered class of general relativistic galaxy models, is not only physically
viable, but suggests the need for recalibration of the estimated dark matter
content in disc galaxies, with far reaching consequences for astrophysics and
cosmology.


  We consider Calabi-Yau compactifications with one K\"ahler modulus. Following
the method of Candelas et al. we use the mirror hypothesis to solve the quantum
theory exactly in dependence of this modulus by performing the calculation for
the corresponding complex structure deformation on the mirror manifold. Here
the information is accessible by techniques of classical geometry. It is
encoded in the Picard-Fuchs differential equation which has to be supplemented
by requirements on the global properties of its solutions.


  We describe a construction of fuzzy spaces which approximate projective toric
varieties. The construction uses the canonical embedding of such varieties into
a complex projective space: The algebra of fuzzy functions on a toric variety
is obtained by a restriction of the fuzzy algebra of functions on the complex
projective space appearing in the embedding. We give several explicit examples
for this construction; in particular, we present fuzzy weighted projective
spaces as well as fuzzy Hirzebruch and del Pezzo surfaces. As our construction
is actually suited for arbitrary subvarieties of complex projective spaces, one
can easily obtain large classes of fuzzy Calabi-Yau manifolds and we comment on
fuzzy K3 surfaces and fuzzy quintic three-folds. Besides enlarging the number
of available fuzzy spaces significantly, we show that the fuzzification of a
projective toric variety amounts to a quantization of its toric base.


  The first terms of the general solution for an asymptotically flat stationary
axisymmetric vacuum spacetime endowed with an equatorial symmetry plane are
calculated from the corresponding Ernst potential up to seventh order in the
radial pseudospherical coordinate. The metric is used to determine the
influence of high order multipoles in the perihelion precession of an
equatorial orbit and in the node line precession of a non-equatorial orbit with
respect to a geodesic circle. Both results are written in terms of invariant
quantities such as the Geroch-Hansen multipoles and the energy and angular
momentum of the orbit.


  We investigate the formation and decay of oscillons during the
post-inflationary reheating epoch from inflaton oscillations around
asymptotically flat potentials $V(\varphi)$ in the presence of an external
coupling of the form $\frac{1}{2}\, g^2 \, \varphi^2 \, \chi^2$. It is
well-known that in the absence of such an external coupling, the attractive
self-interaction term in the potential leads to the formation of copious
amounts of long-lived oscillons both for symmetric and asymmetric plateau
potentials. We perform a detailed numerical analysis to study the formation of
oscillons in the $\alpha$-attractor E- and T-model potentials using the
publicly available lattice simulation code ${\cal C}$osmo${\cal L}$attice. We
observe the formation of nonlinear oscillon-like structures with the average
equation of state $\langle w_\varphi\rangle \simeq 0$ for a range of values of
the inflaton self-coupling $\lambda$ and the external coupling $g^2$. Our
results demonstrate that oscillons form even in the presence of an external
coupling and we determine the upper bound on $g^2$ which facilitates oscillon
formation. We also find that eventually, these oscillons decay into the scalar
inflaton radiation as well as into the quanta of the offspring field $\chi$.
Thus, we establish the possibility that reheating could have proceeded through
the channel of oscillon decay, along with the usual decay of the oscillating
inflaton condensate into $\chi$ particles. For a given value of the
self-coupling $\lambda$, we notice that the lifetime of a population of
oscillons decreases with an increase in the strength of the external coupling,
following an (approximately) inverse power-law dependence on $g^2$.


  We give a direct construction of a specific idempotent in the endomorphism
algebra of a finite lattice $T$. This idempotent is associated with all
possible sublattices of $T$ which are total orders.


  Zero-shot voice conversion (VC) converts source speech into the voice of any
desired speaker using only one utterance of the speaker without requiring
additional model updates. Typical methods use a speaker representation from a
pre-trained speaker verification (SV) model or learn speaker representation
during VC training to achieve zero-shot VC. However, existing speaker modeling
methods overlook the variation of speaker information richness in temporal and
frequency channel dimensions of speech. This insufficient speaker modeling
hampers the ability of the VC model to accurately represent unseen speakers who
are not in the training dataset. In this study, we present a robust zero-shot
VC model with multi-level temporal-channel retrieval, referred to as MTCR-VC.
Specifically, to flexibly adapt to the dynamic-variant speaker characteristic
in the temporal and channel axis of the speech, we propose a novel fine-grained
speaker modeling method, called temporal-channel retrieval (TCR), to find out
when and where speaker information appears in speech. It retrieves
variable-length speaker representation from both temporal and channel
dimensions under the guidance of a pre-trained SV model. Besides, inspired by
the hierarchical process of human speech production, the MTCR speaker module
stacks several TCR blocks to extract speaker representations from
multi-granularity levels. Furthermore, to achieve better speech disentanglement
and reconstruction, we introduce a cycle-based training strategy to simulate
zero-shot inference recurrently. We adopt perpetual constraints on three
aspects, including content, style, and speaker, to drive this process.
Experiments demonstrate that MTCR-VC is superior to the previous zero-shot VC
methods in modeling speaker timbre while maintaining good speech naturalness.


  We quantize the abelian Chern-Simons theory coupled to non-relativistic
matter field on a torus without invoking the flux quantization. Through a
series of canonical transformations which is equivalent to solving the Gauss
constraint, we obtain an effective hamiltonian density with periodic matter
field. We also obtain the many-anyon Schr\"odinger equation with periodic
Aharonov-Bohm potentials and analyze the periodic property of the wavefunction.
Some comments are given on the different features of our approach from the
previous ones.


  We introduce a quotient of the affine Temperley-Lieb category that encodes
all weight-preserving linear maps between finite-dimensional
sl(2)-representations. We study the diagrammatic idempotents that correspond to
projections onto extremal weight spaces and find that they satisfy similar
properties as Jones-Wenzl projectors, and that they categorify the Chebyshev
polynomials of the first kind. This gives a categorification of the Kauffman
bracket skein algebra of the annulus, which is well adapted to the task of
categorifying the multiplication on the Kauffman bracket skein module of the
torus.


  We present a simple model for the electron-phonon interactions between the
energy subbands in polyacene field-effect transistors and the vibrations of the
crystal. We introduce a generalized Su-Schrieffer-Heeger model, arguing that
the strongest electron-phonon interactions in these systems originate from the
dependence of inter-molecule hopping amplitudes on collective molecular motion.
We compute the electron-phonon spectral function $\alpha^2F(\omega)$ as a
function of two-dimensional hole density and the coupling strength constant.
Our results are in agreement with the sharp onset of superconductivity near
half-filling discovered in recent experiments by Sch\"on {\it et al.} [Batlogg]
and predict an increase of $T_c$ with pressure. We further speculate on the
implications that the observation of the quantum Hall effect in these systems
has on the effective band mass in the low carrier density regime.


  We take a closer look at some theoretical challenges of Machine Learning as a
function approximation, gradient descent as the default optimization algorithm,
limitations of fixed length and width networks and a different approach to RNNs
from a mathematical perspective.


  We exhibit a relationship between motivic homotopy theory and spectral
algebraic geometry, based on the motivic $\tau$-deformation picture of
Gheorghe, Isaksen, Wang, Xu. More precisely, we identify cellular motivic
spectra over $\mathbf C$ with ind-coherent sheaves (in a slightly non-standard
sense) on a certain spectral stack $\tau_{\ge 0}(\mathcal
M_\mathrm{FG}^\mathrm{or})$. The latter is the connective cover of the
non-connective spectral stack $\mathcal M_\mathrm{FG}^\mathrm{or}$, the moduli
stack of oriented formal groups, which we have introduced previously and
studied in connection with chromatic homotopy theory. We also provide a
geometric origin on the level of stacks for the observed $\tau$-deformation
behavior on the level of sheaves, based on a notion of extended effective
Cartier divisors in spectral algebraic geometry.


  This article considers the initial boundary value problem for the heat
equation with the time-dependent Sturm-Liouville operator with singular
potentials. To obtain a solution by the method of separation of variables, the
problem is reduced to the problem of eigenvalues of the Sturm-Liouville
operator. Further on, the solution to the initial boundary value problem is
constructed in the form of a Fourier series expansion. A heterogeneous case is
also considered. Finally, we establish the well-posedness of the equation in
the case when the potential and initial data are distributions, also for
singular time-dependent coefficients.


  After a quick tour through the present status of the Standard Model, an
attempt is made to set up a framework to discuss some presently available
exotica, including $R_b$ and the CDF $ee\gamma\gamma+E_T\hskip-13pt/\ $
``event." Supersymmetry seems to be a key player in establishing a paradigm
shift beyond the Standard Model. (XI Topical Workshop on Proton-antiproton
Collider Physics, Abano Terme (Padua), Italy, 26 May-1 June, 1996.)


  A Higgs boson lighter than 2 m_W that decays mostly into invisible channels
(e.g., dark matter particles) is theoretically well-motivated. We study the
prospects for discovery of such an invisible Higgs, h_inv, at the LHC and the
Tevatron in three production modes: (1) in association with a Z, (2) through
Weak Boson Fusion (WBF), and (3) accompanied by a jet. In the Z+h_inv channel,
we show that the LHC can yield a discovery signal above 5 sigma with 10 fb-1 of
integrated luminosity for a Higgs mass of 120 GeV. With 30 fb-1 the discovery
reach extends up to a Higgs mass of 160 GeV. We also study the extraction of
the h_inv mass from production cross sections at the LHC, and find that
combining WBF and Z+h_inv allows a relatively model-independent determination
of the h_inv mass with an uncertainty of 35-50 GeV (15-20 GeV) with 10 (100)
fb-1. At the Tevatron, a 3 sigma observation of a 120 GeV h_inv in any single
channel is not possible with less than 12 fb-1 per detector. However, we show
that combining the signal from WBF with the previously-studied Z+h_inv channel
allows a 3 sigma observation of h_inv with 7 fb-1 per detector. Because of
overwhelming irreducible backgrounds, h_inv+j is not a useful search channel at
either the Tevatron or the LHC, despite the larger production rate.