  Understanding the generalization properties of heavy-tailed stochastic
optimization algorithms has attracted increasing attention over the past years.
While illuminating interesting aspects of stochastic optimizers by using
heavy-tailed stochastic differential equations as proxies, prior works either
provided expected generalization bounds, or introduced non-computable
information theoretic terms. Addressing these drawbacks, in this work, we prove
high-probability generalization bounds for heavy-tailed SDEs which do not
contain any nontrivial information theoretic terms. To achieve this goal, we
develop new proof techniques based on estimating the entropy flows associated
with the so-called fractional Fokker-Planck equation (a partial differential
equation that governs the evolution of the distribution of the corresponding
heavy-tailed SDE). In addition to obtaining high-probability bounds, we show
that our bounds have a better dependence on the dimension of parameters as
compared to prior art. Our results further identify a phase transition
phenomenon, which suggests that heavy tails can be either beneficial or harmful
depending on the problem structure. We support our theory with experiments
conducted in a variety of settings.


  Detection of (ultra-) high-energy cosmic rays with the use of radio frequency
emission from extensive air showers has been proven as complimentary to
existing ground array detection techniques. Great progress has been made in the
understanding of the emission processes and in their Monte Carlo modelling.
These have led to experimental results, notably also at the Auger Engineering
Radio Array, on energy, angular and mass composition resolution of the primary
cosmic rays. Recent results are reported. The measured resolutions turn out to
be competitive with existing techniques and they have independent
uncertainties. Implications for cross-calibration with existing techniques and
for future large-scale applications of radio detection of ultra-high-energy
cosmic rays are discussed.


  It has been recently recognized that in addition to the conventional
longitudinal angular momentum, structured (inhomogeneous) optical fields
exhibit helicity-independent transverse spin angular momentum (SAM) and an
unusual spin (circular polarization)- dependent transverse momentum, the
so-called Belinfante's spin momentum. Such highly nontrivial structure of the
momentum and the spin densities in the structured optical fields (e.g.,
evanescent fields) has led to a number of fundamentally interesting and
intricate phenomena, e.g., the quantum spin Hall effect of light and the
optical spin-momentum locking in surface optical modes similar to that observed
for electrons in topological insulators. In this review, we introduce the basic
concepts and look into the genesis of transverse SAM and transverse spin
momentum in structured light. We then discuss few illustrative examples of
micro and nano optical systems where these illusive entities can be observed.
The studied systems include planar and spherical micro and nano structures. We
also investigate the ways and means of enhancing the elusive extraordinary
spin. In particular, we show that dispersion management leading to avoided
crossing along with perfect absorption mediated by recently discovered coherent
perfect absorption can positively influence the resonant enhancement of the
transverse spin and spin momentum. The role of mode mixing and interference of
neighboring TE and TM scattering modes of diverse micro and nano optical
systems are illustrated with the selected examples. The results demonstrate
possibilities for the enhancement of not only the magnitudes but also the
spatial extent of transverse SAM and the transverse momentum components, which
opens up interesting avenues for experimental detection of these illusive
fundamental entities and may enhance the ensuing spin-based photonic
applications.


  We applied the ab initio spin-polarized Correlation Matrix Renormalization
Theory (CMRT) to the ferromagnetic state of the bulk BCC iron. We showed that
it was capable of reproducing the equilibrium physical properties and the
pressure-volume curve in good comparison with experiments. We then focused on
the analysis of its local electronic correlations. By exploiting different
local fluctuation-related physical quantities as measures of electronic
correlation within target orbits, we elucidated the different roles of $t_{2g}$
and $e_g$ states in both spin channels and presented compelling evidence to
showcase this distinction in their electronic correlation.


  Let K be a field and S a polynomial ring in a finite number of variables over
K. Let F be a finitely generated graded free S-module. We examine some classes
of squarefree monomial submodules of F. Hence, we focalize our attention on the
Betti table of such classes in order to analyze the behavior of their extremal
Betti numbers.


  Assuming that dark energy may be treated as a fluid with a well defined
temperature, close to equilibrium, we argue that if nowadays there is a
transfer of energy between dark energy and dark matter, it must be such that
the latter gains energy from the former and not the other way around.


  In this paper we study the automorphism group of the procongruence mapping
class group through its action on the associated procongruence curve and pants
complexes. Our main result is a rigidity theorem for the procongruence
completion of the pants complex. As an application we prove that moduli stacks
of smooth algebraic curves satisfy a weak anabelian property in the
procongruence setting.


  In this paper we consider the class of truth-functional many-valued logics
with a finite set of truth-values. The main result of this paper is the
development of a new \emph{binary} sequent calculi (each sequent is a pair of
formulae) for many valued logic with a finite set of truth values, and of
Kripke-like semantics for it that is both sound and complete. We did not use
the logic entailment based on matrix with a strict subset of designated truth
values, but a different new kind of semantics based on the generalization of
the classic 2-valued truth-invariance entailment. In order to define this
non-matrix based sequent calculi, we transform many-valued logic into positive
2-valued multi-modal logic with classic conjunction, disjunction and finite set
of modal connectives. In this algebraic framework we define an uniquely
determined axiom system, by extending the classic 2-valued distributive lattice
logic (DLL) by a new set of sequent axioms for many-valued logic connectives.
Dually, in an autoreferential Kripke-style framework we obtain a uniquely
determined frame, where each possible world is an equivalence class of
Lindenbaum algebra for a many-valued logic as well, represented by a truth
value.


  Accelerating the deep learning inference is very important for real-time
applications. In this paper, we propose a novel method to fuse the layers of
convolutional neural networks (CNNs) on Graphics Processing Units (GPUs), which
applies data reuse analysis and access optimization in different levels of the
memory hierarchy. To achieve the balance between computation and memory access,
we explore the fusion opportunities in the CNN computation graph and propose
three fusion modes of convolutional neural networks: straight, merge and split.
Then, an approach for generating efficient fused code is designed, which goes
deeper in multi-level memory usage for cross-layer data reuse. The
effectiveness of our method is evaluated with the network layers from
state-of-the-art CNNs on two different GPU platforms, NVIDIA TITAN Xp and Tesla
P4. The experiments show that the average speedup is 2.02x on representative
structures of CNNs, and 1.57x on end-to-end inference of SqueezeNet.


  Many real-world networks, such as transportation or trade networks, are
dynamic in the sense that the edge set may change over time, but these changes
are known in advance. This behavior is captured by the temporal graphs model,
which has recently become a trending topic in theoretical computer science. A
core open problem in the field is to prove the existence of linear-size
temporal spanners in temporal cliques, i.e., sparse subgraphs of complete
temporal graphs that ensure all-pairs reachability via temporal paths. So far,
the best known result is the existence of temporal spanners with
$\mathcal{O}(n\log n)$ many edges. We present significant progress towards
proving that linear-size temporal spanners exist in all temporal cliques.
  We adapt techniques used in previous works and heavily expand and generalize
them to provide a simpler and more intuitive proof of the $\mathcal{O}(n\log
n)$ bound. Moreover, we use our novel approach to show that a large class of
temporal cliques, called edge-pivot graphs, admit linear-size temporal
spanners. To contrast this, we investigate other classes of temporal cliques
that do not belong to the class of edge-pivot graphs. We introduce two such
graph classes and we develop novel techniques for establishing the existence of
linear temporal spanners in these graph classes as well.


  We compute the structure function scaling of the integrated intensity images
of two J=1-0 13CO maps of Taurus and Perseus. The scaling exponents of the
structure functions follow the velocity scaling of supersonic turbulence,
suggesting that turbulence plays an important role in the fragmentation of cold
interstellar clouds. The data also allows to verify the validity of the two
basic assumptions of the hierarchical symmetry model, originally proposed for
the derivation of the velocity structure function scaling. This shows that the
same hierarchical symmetry holds for the projected density field of cold
interstellar clouds.


  Continuing a previous analysis originally motivated by physics, we consider
representable states on quasi-local quasi *-algebras, starting with examining
the possibility for a {\em compatible} family of {\em local} states to give
rise to a {\em global} state. Some properties of {\em local modifications} of
representable states and some aspects of their asymptotic behavior are also
considered.


  We study the transport of Brownian particles through a corrugated channel
caused by a force field containing curl-free (scalar potential) and
divergence-free (vector potential) parts. We develop a generalized Fick-Jacobs
approach leading to an effective one-dimensional description involving the
potential of mean force. As an application, the interplay of a pressure-driven
flow and an oppositely oriented constant bias is considered. We show that for
certain parameters, the particle diffusion is significantly suppressed via the
property of hyrodynamically enforced entropic particle trapping.


  We study the origin of the Born probability rule rho = |psi|^2 in the de
Broglie-Bohm pilot-wave formulation of quantum theory. It is argued that
quantum probabilities arise dynamically, and have a status similar to thermal
probabilities in ordinary statistical mechanics. This is illustrated by
numerical simulations for a two-dimensional system. We show that a simple
initial ensemble with a non-standard distribution rho not= |psi|^2 of particle
positions evolves towards the quantum distribution to high accuracy. The
relaxation process rho --> |psi|^2 is quantified in terms of a coarse-grained
H-function (equal to minus the relative entropy of rho with respect to
|psi|^2), which is found to decrease approximately exponentially over time,
with a time constant that accords with a simple theoretical estimate.


  Monocular depth estimation is a challenging task that aims to predict a
corresponding depth map from a given single RGB image. Recent deep learning
models have been proposed to predict the depth from the image by learning the
alignment of deep features between the RGB image and the depth domains. In this
paper, we present a novel approach, named Structure-Attentioned Memory Network,
to more effectively transfer domain features for monocular depth estimation by
taking into account the common structure regularities (e.g., repetitive
structure patterns, planar surfaces, symmetries) in domain adaptation. To this
end, we introduce a new Structure-Oriented Memory (SOM) module to learn and
memorize the structure-specific information between RGB image domain and the
depth domain. More specifically, in the SOM module, we develop a Memorable Bank
of Filters (MBF) unit to learn a set of filters that memorize the
structure-aware image-depth residual pattern, and also an Attention Guided
Controller (AGC) unit to control the filter selection in the MBF given image
features queries. Given the query image feature, the trained SOM module is able
to adaptively select the best customized filters for cross-domain feature
transferring with an optimal structural disparity between image and depth. In
summary, we focus on addressing this structure-specific domain adaption
challenge by proposing a novel end-to-end multi-scale memorable network for
monocular depth estimation. The experiments show that our proposed model
demonstrates the superior performance compared to the existing supervised
monocular depth estimation approaches on the challenging KITTI and NYU Depth V2
benchmarks.


  This paper reports the effort of deducing the initial strategy distributions
of agents in mix-game model which is used to predict a real financial time
series generated from a target financial market. Using mix-game to predict
Shanghai Index, we find the time series of prediction accurate rates is
sensitive to the initial strategy distributions of agents in group 2 who play
minority game, but less sensitive to the initial strategy distributions of
agents in group 1 who play majority game. And agents in group 2 tend to cluster
in full strategy space (FSS) if the real financial time series has obvious
tendency (upward or downward), otherwise they tend to scatter in FSS. We also
find that the initial strategy distributions and the number of agents in group
1 influence the level of prediction accurate rates. Finally, this paper gives
suggestion about further research.


  Fermion compositeness, and other types of new physics that can be described
by the exchange of very massive particles, can manifest themselves as the
result of an effective four-fermion contact interaction. In the case of the
processes $e^+e^-\to \mu^+\mu^-,\tau^+\tau^-,\bar{b}b$ and $\bar{c}c$ at future
$e^+e^-$ colliders with $\sqrt{s}=0.5-1$ TeV, we examine the sensitivity to
four-fermion contact interactions of two new integrated observables, $\sigma_+$
and $\sigma_-$, conveniently defined for such kind of analysis. We find that,
if longitudinal polarization of the electron beam were available, these
observables would offer the opportunity to separate the helicity cross sections
and, in this way, to derive model-independent bounds on the relevant
parameters.


  We introduce Appearance-MAT (AMAT), a generalization of the medial axis
transform for natural images, that is framed as a weighted geometric set cover
problem. We make the following contributions: i) we extend previous medial
point detection methods for color images, by associating each medial point with
a local scale; ii) inspired by the invertibility property of the binary MAT, we
also associate each medial point with a local encoding that allows us to invert
the AMAT, reconstructing the input image; iii) we describe a clustering scheme
that takes advantage of the additional scale and appearance information to
group individual points into medial branches, providing a shape decomposition
of the underlying image regions. In our experiments, we show state-of-the-art
performance in medial point detection on Berkeley Medial AXes (BMAX500), a new
dataset of medial axes based on the BSDS500 database, and good generalization
on the SK506 and WH-SYMMAX datasets. We also measure the quality of
reconstructed images from BMAX500, obtained by inverting their computed AMAT.
Our approach delivers significantly better reconstruction quality with respect
to three baselines, using just 10% of the image pixels. Our code and
annotations are available at https://github.com/tsogkas/amat .


  At a 14 TeV proton-proton collider, the Large Hadron Collider (LHC), we show
that top quark pair production is dominated at low invariant mass by the fusion
of two like-helicity gluons, producing top quark pairs in the left-left or
right-right helicity configurations. Whereas, at higher invariant mass the
production is dominated by the fusion of unlike-helicity gluons, producing top
quark pairs in the up-down or down-up off-diagonal configurations, identical to
top quark pair production via quark-antiquark annihilation. We study in detail
the low invariant mass region, and show that the spin correlations can be
easily observed in this region by looking at the distribution of the difference
in the azimuthal angles, Delta-phi, of the dileptons decay products of the top
quarks in the laboratory frame. Due to the large cross section for top pair
production at the LHC, even with a cut requiring that the invariant mass of the
top quark pair be less than 400 GeV, the approximate yield would be 10^4
di-lepton (e, mu) events per fb^{-1} before detector efficiencies are applied.
Therefore, there is ample statistics to form the Delta-phi distribution of the
dilepton events, even with the invariant mass restriction. We also discuss
possibilities for observing these spin correlations in the lepton plus jets
channel.


  The ability to engineer nonlinear optical processes in all-dielectric
nanostructures is both of fundamental interest and highly desirable for
high-performance, robust, and miniaturized nonlinear optical devices. Herein,
we propose a novel paradigm for the efficient tuning of second-harmonic
generation (SHG) process in dielectric nanoantennas by integrating with
chalcogenide phase change material. In a design with Ge$_{2}$Sb$_{2}$Te$_{5}$
(GST) film sandwiched between the AlGaAs nanoantennas and AlO$_{x}$ substrate,
the nonlinear SHG signal from the AlGaAs nanoantennas can be boosted via the
resonantly localized field induced by the optically-induced Mie-type
resonances, and further modulated by exploiting the GST
amorphous-to-crystalline phase change in a non-volatile, multi-level manner.
The tuning strategy originates from the modulation of resonant conditions by
changes in the refractive index of GST. With a thorough examination of tuning
performances for different nanoantenna radii, a maximum modulation depth as
high as 540$\%$ is numerically demonstrated. This work not only reveals out the
potential of GST in optical nonlinearity control, but also provides promising
strategy in smart designing tunable and reconfigurable nonlinear optical
devices, e.g., light emitters, modulators, and sensors.


  In 2003.5 Eta Carinae was expected to undergo an X-ray eclipse (Damineli et
al., 2000). In the framework of an international campaign to obtain
multi-wavelength observations of this event, we have obtained optical CCD
images of Eta Carinae. Here, we present the B, V, R, I, data of Eta Car
obtained before and during the X-ray eclipse.


  We investigate the photometric variability of magnetized stars, particularly
neutron stars, accreting through a magnetic Rayleigh-Taylor-type instability at
the disk-magnetosphere interface, and compare it with the variability during
stable accretion, with the goal of looking for possible quasi-periodic
oscillations. The lightcurves during stable accretion show periodicity at the
star's frequency and sometimes twice that, due to the presence of two funnel
streams that produce antipodal hotspots near the magnetic poles. On the other
hand, lightcurves during unstable accretion through tongues penetrating the
magnetosphere are more chaotic due to the stochastic behaviour of the tongues,
and produce noisier power spectra. However, the power spectra do show some
signs of quasi-periodic variability. Most importantly, the rotation frequency
of the tongues and the resulting hotspots is close to the inner-disk orbital
frequency, except in the most strongly unstable cases. There is therefore a
high probability of observing QPOs at that frequency in longer simulations. In
addition, the lightcurves in the unstable regime show periodicity at the star's
rotation frequency in many of the cases investigated here, again except in the
most strongly unstable cases which lack funnel flows and the resulting
antipodal hotspots. The noisier power spectra result in the fractional rms
amplitudes of the Fourier peaks being smaller.
  We also study in detail the effect of the misalignment angle between the
rotation and magnetic axes of the star on the variability, and find that at
misalignment angles $\gtrsim 25^\circ$, the star's period always appears in the
lightcurves.


  This work studies the problem of predicting the sequence of future actions
for surround vehicles in real-world driving scenarios. To this aim, we make
three main contributions. The first contribution is an automatic method to
convert the trajectories recorded in real-world driving scenarios to action
sequences with the help of HD maps. The method enables automatic dataset
creation for this task from large-scale driving data. Our second contribution
lies in applying the method to the well-known traffic agent tracking and
prediction dataset Argoverse, resulting in 228,000 action sequences.
Additionally, 2,245 action sequences were manually annotated for testing. The
third contribution is to propose a novel action sequence prediction method by
integrating past positions and velocities of the traffic agents, map
information and social context into a single end-to-end trainable neural
network. Our experiments prove the merit of the data creation method and the
value of the created dataset - prediction performance improves consistently
with the size of the dataset and shows that our action prediction method
outperforms comparing models.


  This paper studies the share-of-choice product line design problem, where
decision-makers aim to maximize the market share, i.e., the percentage of the
consumers to whom at least one product delivers a non-negative utility. Because
the customers' utilities are not directly observable, the input utilities of
the existing models need to be estimated from some primitive data. The conjoint
analysis, which asks respondents to evaluate a set of products, is the main
source of such data. However, with the limited survey questions, the utilities
cannot be precisely estimated, and therefore, the models that plugin the
estimated utilities cannot identify the optimal solution and corresponding
market share. In this study, by applying the polyhedral method in utility
calibration and robust optimization techniques, we propose a novel end-to-end
model inputting the survey data and outputting the data-driven design.
Importantly, we provide guarantees of the market share of the returned product
line design. For a general product line design problem, we provide the
guarantees related to the size of the set containing all possible utilities
consistent with the survey data. For a single product design special case, our
model can identify the optimal design within an explored set of all the linear
combinations of the delivered questions and guarantee the market share even if
the uncertainty sets are unbounded. We further develop an adaptive conjoint
analysis where new questions better align with the proposed model are added
based on its solution. The proposed adaptive conjoint analysis is proven to
recover the customer utilities within finite rounds. Through extensive
numerical experiments, we show that the proposed model significantly
outperforms the "estimate-then-optimize" model and the proposed adaptive
conjoint analysis can generate more efficient questions to fit the proposed
model.


  A theoretical study of interacting bosons in a periodic optical lattice is
presented. Instead of the commonly used tight-binding approach (applicable near
the Mott insulating regime of the phase diagram), the present work starts from
the exact single-particle states of bosons in a cubic optical lattice,
satisfying the Mathieu equation, an approach that can be particularly useful at
large boson fillings. The effects of short-range interactions are incorporated
using a self-consistent Hartree-Fock approximation, and predictions for
experimental observables such as the superfluid transition temperature,
condensate fraction, and boson momentum distribution are presented.


  Classical novae are important producers of radioactive nuclei, such as be7,
n13, f18, na22 and al26. The disintegration of these nuclei produces positrons
(except for be7) that through annihilation with electrons produce photons of
energies 511 keV and below. Furthermore, be7 and na22 decay producing photons
with energies of 478 keV and 1275 keV, respectively, well in the gamma-ray
domain. Therefore, novae are potential sources of gamma-ray emission. The
properties of gamma-ray spectra and gamma-ray light curves (for the continuum
and for the lines at 511, 478 and 1275 keV) have been analyzed, with a special
emphasis on the difference between carbon-oxygen and oxygen-neon novae.
Predictions of detectability of individual novae by the future SPI spectrometer
on board the INTEGRAL satellite are made.


  Only seven transits of Venus have been observed and studied up to now since
the first astronomical observations with the telescope: 1639, 1761-69, 1874-82
and 2004-12. The measurement of the Astronomical Unit has been one of the main
goal of the study of this rare phenomenon, as well as the identification of the
planetary atmosphere and its properties, the understanding of the black drop
phenomenon and the measurement of the solar diameter. The transit of 1639
observed by J. Horrocks is presented in more detail.


  For every positive integer $n$ greater than $4$ there is a set of Latin
squares of order $n$ such that every permutation of the numbers $1,\ldots,n$
appears exactly once as a row, a column, a reverse row or a reverse column of
one of the given Latin squares. If $n$ is greater than $4$ and not of the form
$p$ or $2p$ for some prime number $p$ congruent to $3$ modulo $4$, then there
always exists a Latin square of order $n$ in which the rows, columns, reverse
rows and reverse columns are all distinct permutations of $1,\ldots,n$, and
which constitute a permutation group of order $4n$. If $n$ is prime congruent
to $1$ modulo $4$, then a set of $(n-1)/4$ mutually orthogonal Latin squares of
order $n$ can also be constructed by a classical method of linear algebra in
such a way, that the rows, columns, reverse rows and reverse columns are all
distinct and constitute a permutation group of order $n(n-1)$.


  The use of balanced crossover operators in Genetic Algorithms (GA) ensures
that the binary strings generated as offsprings have the same Hamming weight of
the parents, a constraint which is sought in certain discrete optimization
problems. Although this method reduces the size of the search space, the
resulting fitness landscape often becomes more difficult for the GA to explore
and to discover optimal solutions. This issue has been studied in this paper by
applying an adaptive bias strategy to a counter-based crossover operator that
introduces unbalancedness in the offspring with a certain probability, which is
decreased throughout the evolutionary process. Experiments show that improving
the exploration of the search space with this adaptive bias strategy is
beneficial for the GA performances in terms of the number of optimal solutions
found for the balanced nonlinear Boolean functions problem.


  Let $A$ be an Artinian local ring with algebraically closed residue field
$k$, and let $\mathbf{G}$ be an affine smooth group scheme over $A$. The
Greenberg functor $\mathcal{F}$ associates to $\mathbf{G}$ a linear algebraic
group $G:=(\mathcal{F}\mathbf{G})(k)$ over $k$, such that
$G\cong\mathbf{G}(A)$. We prove that if $\mathbf{G}$ is a reductive group
scheme over $A$, and $\mathbf{T}$ is a maximal torus of $\mathbf{G}$, then $T$
is a Cartan subgroup of $G$, and every Cartan subgroup of $G$ is obtained
uniquely in this way. The proof is based on establishing a Nullstellensatz
analogue for smooth affine schemes with reduced fibre over $A$, and that the
Greenberg functor preserves certain normaliser group schemes over $A$.
Moreover, we prove that if $\mathbf{G}$ is reductive and $\mathbf{P}$ is a
parabolic subgroup of $\mathbf{G}$, then $P$ is a self-normalising subgroup of
$G$, and if $\mathbf{B}$ and $\mathbf{B}'$ are two Borel subgroups of
$\mathbf{G}$, then the corresponding subgroups $B$ and $B'$ are conjugate in
$G$.


  The thermoelectric properties of in plane heterostructures made of Graphene
and hexagonal Boron Nitride (BN) have been investigated by means of atomistic
simulation. The heterostructures consist in armchair graphene nanoribbons to
the sides of which BN flakes are periodically attached. This arrangement
generates a strong mismatch of phonon modes between the different sections of
the ribbons, which leads to a very small phonon conductance, while the electron
transmission is weakly affected. In combination with the large Seebeck
coefficient resulting from the BN-induced bandgap opening or broadening, it is
shown that large thermoelectric figure of merit ZT > 0.8 can be reached in
perfect structures at relatively low Fermi energy, depending on the graphene
nanoribbon width. The high value ZT = 1.48 may even be achieved by introducing
appropriately vacancies in the channel, as a consequence of further degradation
of the phonon conductance.


  We consider conditions necessary for a successful implementation of so-called
assisted inflation. We generalize the applicability of assisted inflation
beyond exponential potentials as originally proposed to include standard
chaotic (\lambda \phi^4 or m^2 \phi^2) models as well. We also demonstrate that
in a purely 4-dimensional theory, unless the assisted sector is in fact
decoupled, the additional fields of the assisted sector actually impede
inflation. As a specific example of an assisted sector, we consider a
5-dimensional KK model for which the extra dimension may be somewhat or much
larger than the inverse Planck scale. In this case, the assisted sector (coming
from a KK compactification) eliminates the need for a fine-tuned quartic
coupling to drive chaotic inflation. This is a general result of models with
one or more "large" extra dimensions.


  We previously studied the inner crust and the pasta mantle of a neutron star
within the 4th-order extended Thomas-Fermi (ETF) approach with consistent
proton shell corrections added perturbatively via the Strutinsky integral (SI)
theorem together with the contribution due to pairing. To speed up the
computations and avoid numerical problems, we adopted parametrized nucleon
density distributions. However, the errors incurred by the choice of the
parametrization are expected to become more significant as the mean baryon
number density is increased, especially in the pasta mantle where the
differences in the energy per nucleon of the different phases are very small,
typically a few keV. To improve the description of these exotic structures, we
discuss the important features that a nuclear profile should fulfill and
introduce two new parametrizations. Performing calculations using the BSk24
functional, we find that these parametrizations lead to lower ETF energy
solutions for all pasta phases than the parametrization we adopted before and
more accurately reproduce the exact equilibrium nucleon density distributions
obtained from unconstrained variational calculations. Within the ETFSI method,
all parametrizations predict the same composition in the region with
quasi-spherical clusters. However, the two new parametrizations lead to a
different mantle structure at mean baryon densities above about 0.07 fm^-3, at
which point lasagna is energetically favored. Interestingly, spherical clusters
reappear in the pasta region. The inverted pasta phases such as bucatini and
Swiss cheese are still found in the densest region above the core in all cases.


  Orbital Kondo effect in a system of two single-level quantum dots attached to
external electron reservoirs is considered theoretically. The dots are coupled
via direct hoping term and Coulomb interaction. The Kondo temperature is
evaluated from the scaling approach and slave boson technique. The later method
is also used to calculate linear conductance of the system. Nonlinear
conductance, in turn, is calculated in terms of the nonequilibrium Green
function formalism.


  One of the main uncertainties in evolutionary calculations of massive stars
is the efficiency of internal mixing. It changes the chemical profile inside
the star and can therefore affect the structure and further evolution.
  We demonstrate that eclipsing binaries, in which the tides synchronize the
rotation period of the stars and the orbital period, constitute a potentially
strong test for the efficiency of rotational mixing. We present detailed
stellar evolutionary models of massive binaries assuming the composition of the
Small Magellanic Cloud. In these models we find enhancements in the surface
nitrogen abundance of up to 0.6 dex.


  The most recent searches for long-lived particles at CMS are presented.
Searches for displaced jets, displaced leptons, displaced stops, and heavy
stable charged particles are among those discussed. A variety of models are
constrained by these searches, ranging from hidden valleys to split
supersymmetry.


  We study the linear problem associated with modified affine Toda field
equation for the Langlands dual $\hat{\mathfrak{g}}^\vee$, where
$\hat{\mathfrak{g}}$ is an untwisted affine Lie algebra. The connection
coefficients for the asymptotic solutions of the linear problem are found to
correspond to the $Q$-functions for $\mathfrak{g}$-type quantum integrable
models. The $\psi$-system for the solutions associated with the fundamental
representations of $\mathfrak{g}$ leads to Bethe ansatz equations associated
with the affine Lie algebra $\hat{\mathfrak{g}}$. We also study the
$A^{(2)}_{2r}$ affine Toda field equation in massless limit in detail and find
its Bethe ansatz equations as well as T-Q relations.


  Upgrading the SuperKEKB electron-positron collider with polarized electron
beams opens a new program of precision physics at a center-of-mass energy of
10.58 GeV. This white paper describes the physics potential of this `Chiral
Belle' program. It includes projections for precision measurements of
$\sin^2\theta_W$ that can be obtained from independent left-right asymmetry
measurements of $e^+e^-$ transitions to pairs of electrons, muons, taus, charm
and b-quarks. The $\sin^2\theta_W$ precision obtainable at SuperKEKB will match
that of the LEP/SLC world average, but at the centre-of-mass energy of 10.58
GeV. Measurements of the couplings for muons, charm, and $b$-quarks will be
substantially improved and the existing $3\sigma$ discrepancy between the SLC
$A_{LR}$ and LEP $A_{FB}^b$ measurements will be addressed. Precision
measurements of neutral current universality will be more than an order of
magnitude more precise than currently available. As the energy scale is well
away from the $Z^0$-pole, the precision measurements will have sensitivity to
the presence of a parity-violating dark sector gauge boson, $Z_{\rm dark}$. The
program also enables the measurement of the anomalous magnetic moment $g-2$
form factor of the $\tau$ to be made at an unprecedented level of precision. A
precision of $10^{-5}$ level is accessible with 40~ab$^{-1}$ and with more data
it would start to approach the $10^{-6}$ level. This technique would provide
the most precise information from the third generation about potential new
physics explanations of the muon $g-2$ $4\sigma$ anomaly. Additional $\tau$ and
QCD physics programs enabled or enhanced with having polarized electron beams
are also discussed in this White Paper. This paper includes a summary of the
path forward in R&D and next steps required to implement this upgrade and
access its exciting discovery potential.


  We study the complexity of deciding the equality of infinite objects
specified by systems of equations, and of infinite objects specified by
lambda-terms. For equational specifications there are several natural notions
of equality: equality in all models, equality of the sets of solutions, and
equality of normal forms for productive specifications. For lambda-terms we
investigate Boehm-tree equality and various notions of observational equality.
We pinpoint the complexity of each of these notions in the arithmetical or
analytical hierarchy. We show that the complexity of deciding equality in all
models subsumes the entire analytical hierarchy. This holds already for the
most simple infinite objects, viz. streams over {0,1}, and stands in sharp
contrast to the low arithmetical Pi^0_2-completeness of equality of
equationally specified streams derived in [Rosu 2006] employing a different
notion of equality.


  We discuss microscopic aspects of odd-parity triplet pair in orbital
degenerate systems. From the concept of off-diagonal long-range order, a pair
state is unambiguously defined as the eigenstate with the maximum eigenvalue of
pair correlation function. Performing this scheme by a numerical technique, we
clarify that the odd-parity triplet pair occurs as an out-of-phase combination
of local triplets induced by Hund's rule coupling for the lattice including two
sites in the unit cell.


  We introduce a mechanism in which coupling between fluctuating spin magnetic
dipole moments and polar optical phonons leads to a non-zero ferroic ordering
of quasi-static magnetoelectric multipoles. Using first-principles calculations
within the LSDA$+U$ method of density functional theory, we calculate the
magnitude of the effect for the prototypical cuprate superconductor,
HgBa$_2$CuO$_4$. We show that our proposed mechanism is consistent, to our
knowledge, with all experimental data for the onset of the pseudo-gap phase and
therefore propose the quasi-static magnetoelectric multipole as a possible
pseudo-gap order parameter. Finally, we show that our mechanism embraces some
key aspects of previous theoretical models, in particular the description of
the pseudo-gap phase in terms of orbital currents.


  We study the computational complexity of identifying dense substructures,
namely $r/2$-shallow topological minors and $r$-subdivisions. Of particular
interest is the case when $r=1$, when these substructures correspond to very
localized relaxations of subgraphs. Since Densest Subgraph can be solved in
polynomial time, we ask whether these slight relaxations also admit efficient
algorithms.
  In the following, we provide a negative answer: Dense $r/2$-Shallow
Topological Minor and Dense $r$-Subdivsion are already NP-hard for $r = 1$ in
very sparse graphs. Further, they do not admit algorithms with running time
$2^{o(\mathbf{tw}^2)} n^{O(1)}$ when parameterized by the treewidth of the
input graph for $r \geq 2$ unless ETH fails.


  We study the evolution of dense neutral clumps located in the outer parts of
planetary nebulae. These clumps will be photo-ionized by the ionizing radiation
from the central star and change their structure in the process. The main
effect of the ionization process is the setting up of a photo-evaporation flow
and a shock running through the clump. Once this shock has moved through the
entire clump it starts to accelerate because of the `rocket effect'. This
continues until the entire clump has been photo-ionized. We present an analytic
model for the shock and accelerating phases and also the results of numerical
simulations which include detailed microphysics. We find a good match between
the analytic description and the numerical results and use the numerical
results to produce some of the clump's observational characteristics at
different phases of its evolution. We compare the results with the properties
of the fast moving low ionization knots (ansae or FLIERs) seen in a number of
planetary nebulae. We find that the models match many of the kinematic and
emission properties of FLIERs.


  We consider the Grothendieck--Teichm\"uller group under a new aspect. Using
real algebraic geometry and web theory we show that it preserves dihedral
symmetry relations, present in the fundamental groupoids of configuration
spaces of marked points on $\mathbb{C}$. The motivation of this paper is to be
understood in the light of Grothendieck's initial philosophy stating that
throughout hidden symmetries of the moduli spaces of curves one can shed some
light on the absolute Galois group. This appears as a new development of the
construction of the avatar of the Grothendieck--Teichm\"uller group and
prepares as well the ground for studying further relations to the motivic
Galois group.


  The space of Sobolev connections, as it has been introduced for studying the
variation of Yang-Mills Lagrangian in the critical dimension $4$, happens not
to be weakly sequentially complete in dimension larger than $4$. This is a
major obstruction for studying the variations of this important Lagrangian in
high dimensions. The present paper generalizes the previous result of the
authors from 'The resolution of the Yang-Mills Plateau problem in
super-critical dimensions', Adv. Math. 316 (arxiv:1306.2010), valid in $5$
dimensions to arbitrary dimension and introduces a space of so called 'weak
connections' for which we prove the weak sequential closure under Yang-Mills
energy control. We also establish a strong approximation property of any weak
connection by smooth connections away from codimension $5$ polyhedral sets.
This last property is used in a subsequent work in preparation for establishing
the partial regularity property for general stationary Yang-Mills weak
connections.


  $\ell_0$ constrained optimization is prevalent in machine learning,
particularly for high-dimensional problems, because it is a fundamental
approach to achieve sparse learning. Hard-thresholding gradient descent is a
dominant technique to solve this problem. However, first-order gradients of the
objective function may be either unavailable or expensive to calculate in a lot
of real-world problems, where zeroth-order (ZO) gradients could be a good
surrogate. Unfortunately, whether ZO gradients can work with the
hard-thresholding operator is still an unsolved problem. To solve this puzzle,
in this paper, we focus on the $\ell_0$ constrained black-box stochastic
optimization problems, and propose a new stochastic zeroth-order gradient
hard-thresholding (SZOHT) algorithm with a general ZO gradient estimator
powered by a novel random support sampling. We provide the convergence analysis
of SZOHT under standard assumptions. Importantly, we reveal a conflict between
the deviation of ZO estimators and the expansivity of the hard-thresholding
operator, and provide a theoretical minimal value of the number of random
directions in ZO gradients. In addition, we find that the query complexity of
SZOHT is independent or weakly dependent on the dimensionality under different
settings. Finally, we illustrate the utility of our method on a portfolio
optimization problem as well as black-box adversarial attacks.


  Associating sound and its producer in complex audiovisual scene is a
challenging task, especially when we are lack of annotated training data. In
this paper, we present a flexible audiovisual model that introduces a
soft-clustering module as the audio and visual content detector, and regards
the pervasive property of audiovisual concurrency as the latent supervision for
inferring the correlation among detected contents. To ease the difficulty of
audiovisual learning, we propose a novel curriculum learning strategy that
trains the model from simple to complex scene. We show that such ordered
learning procedure rewards the model the merits of easy training and fast
convergence. Meanwhile, our audiovisual model can also provide effective
unimodal representation and cross-modal alignment performance. We further
deploy the well-trained model into practical audiovisual sound localization and
separation task. We show that our localization model significantly outperforms
existing methods, based on which we show comparable performance in sound
separation without referring external visual supervision. Our video demo can be
found at https://youtu.be/kuClfGG0cFU.


  We discuss a detection scheme that reveals the existence of vortex states in
a cylindrically symmetric condensate trap. It relies on the measurement of the
second-order correlation function of the Schr\"odinger field, and yields
directly the topological charge of the vortex state.


  Quantum random number generators are becoming mandatory in a demanding
technology world of high performing learning algorithms and security
guidelines. Our implementation based on principles of quantum mechanics enable
us to achieve the required randomness. We have generated high-quality quantum
random numbers from a weak coherent source at telecommunication wavelength. The
entropy is based on time of arrival of quantum states within a predefined time
interval. The detection of photons by the InGaAs single-photon detectors and
high precision time measurement of 5 ps enables us to generate 16 random bits
per arrival time which is the highest reported to date. We have presented the
theoretical analysis and experimental verification of the random number
generation methodology. The method eliminates the requirement of any randomness
extractor to be applied thereby, leveraging the principles of quantum physics
to generate random numbers. The output data rate is on an average of 2.4 Mbps.
The raw quantum random numbers are compared with NIST prescribed Blum-Blum-Shub
pseudo random number generator and an in-house built hardware random number
generator from FPGA, on the ENT and NIST Platform.


  Space missions to NEOs are being planned at all major space agencies, and
recently a manned mission to an NEO was announced as a NASA goal. Efforts to
find and select suitable targets (plus backup targets) are severely hampered by
our lack of knowledge of the physical properties of dynamically favorable NEOs.
In particular, current mission scenarios tend to favor primitive low-albedo
objects. For the vast majority of NEOs the albedo is unknown.
  Here we report new constraints on the size and albedo of 65 NEOs with
rendezvous deltaV < 7 km/s. Our results are based on thermal-IR flux data
obtained in the framework of our ongoing (2009--2011) ExploreNEOs survey
(Trilling et al. 2010) using NASA's "Warm Spitzer" space telescope. As of 2010
July 14, we have results for 293 objects in hand (including the 65 low-deltaV
NEOs presented here); before the end of 2011 we expect to have measured the
size and albedo of ~ 700 NEOs (including probably ~ 160 low-deltaV NEOs).
  While there are reasons to believe that primitive volatile-rich materials are
universally low in albedo, the converse need not be true: the orbital evolution
of some dark objects likely has caused them to lose their volatiles by coming
too close to the Sun. For all our targets, we give the closest perihelion
distance they are likely to have reached (using orbital integrations from
Marchi et al. 2009) and corresponding upper limits on the past surface
temperature. Low-deltaV objects for which both albedo and thermal history may
suggest a primitive composition include (162998) 2001 SK162, (68372) 2001 PM9,
and (100085) 1992 UY4.


  We define the direct and reverse secret-key capacities of a memoryless
quantum channel as the optimal rates that entanglement-based quantum key
distribution protocols can reach by using a single forward classical
communication (direct reconciliation) or a single feedback classical
communication (reverse reconciliation). In particular, the reverse secret-key
capacity can be positive for antidegradable channels, where no forward strategy
is known to be secure. This property is explicitly shown in the continuous
variable framework by considering arbitrary one-mode Gaussian channels.


  Depending on the type and arrangement of metastable vacua in the theory,
initial conditions in a de Sitter vacuum with arbitrarily large entropy can be
compatible with the observed arrow of time, if the causal patch or related
measures are used to regulate divergences. An important condition, however, is
that the initial vacuum cannot produce observers from rare fluctuations
(Boltzmann brains). Here we consider more general initial conditions where
multiple vacua have nonzero initial probability. We examine whether the
prediction of an arrow of time is destroyed by a small initial admixture of
vacua that can produce Boltzmann brains. We identify general criteria and apply
them to two nontrivial examples of such initial probability distributions. The
Hartle-Hawking state is superexponentially dominated by the vacuum with
smallest positive cosmological constant, so one might expect that other initial
vacua can be neglected; but in fact, their inclusion drastically narrows the
range of theory parameters for which an arrow of time is predicted. The
dominant eigenvector of the global rate equation of eternal inflation is
dominated by the longest-lived metastable vacuum. If an arrow of time emerges
in the single-initial-vacuum approximation, then we find that this conclusion
survives the admixture of other initial vacua. By global-local measure duality,
this result amounts to a successful consistency test of certain global cutoffs,
including light-cone time and scale-factor time.


  Cosmological implications of asymmetry between particles and antiparticles
are reviewed. Three possible mechanisms of CP-violation in cosmology are
described. General features of kinetics of generation of cosmological charge
asymmetry are discussed in detail. In particular, the cyclic balance condition,
which plays the same role in time non-invariant theory as detailed balance does
in T-invariant case, is derived. Several scenarios of baryogenesis are
described with an emphasis on CP-violation mechanisms. Production of cosmic
antimatter and a possibility of its ``living'' in our neighborhood is
discussed.


  At some point in the history of most nations, one or more events of illegal
electronic surveillance by those in power or law enforcement has occurred that
has the effect of setting State against Citizen. The media sensationalise these
incidents for profit, however they more often correctly express the concern
felt by the general public. At these times politicians rise, either into fame
or infamy, by proposing new legislation which the public is told will protect
them by from future incidents of illegal and unwarranted invasion by officers
of the state. Two things have occurred since these protective laws were
enacted; technological advancement that is claimed has frustrated legitimate
investigation, and changes in the law that are ostensibly presented as
intending to facilitate the prosecution or prevention of a publicly decried
offence, like child pornography, but which in context deliver expanded powers
to the State, effectively weakening the protections previously enacted.
  This report looks at human rights legislation in three jurisdictions,
starting from a position of comparing and contrasting the protections that are
available from illegal search and seizure. By identifying legislative changes
related to several forms of electronic surveillance and technology, and the
situations that led to them, we can locate the effective peak of protection and
discuss the processes that have led to a gradual yet pervasive weakening of
those laws in all three nations.
  We are regularly diverted by those in power towards disregarding the paranoia
of the outliers who have been warning us with their purple prose that big
brother is watching. But if we focus on the effect of recent legislative
changes in the area of electronic surveillance we can clearly see that the
Orwellian dystopia is already here, and we are living it.


  Time-dependent resistive magnetohydrodynamic simulations are carried out to
study a flux rope eruption caused by magnetic reconnection with implication in
coexistent flare-CME (coronal mass ejection) events. An early result obtained
in a recent analysis of double catastrophe of a flux rope system is used as the
initial condition, in which an isolated flux rope coexists with two current
sheets: a vertical one below and a transverse one above the flux rope. The flux
rope erupts when reconnection takes place in the current sheets, and the flux
rope dynamics depends on the reconnection sequence in the two current sheets.
Three cases are discussed: reconnection occurs (1) simultaneously in the two
current sheets, (2) first in the transverse one and then in the vertical, and
(3) in an order opposite to case 2. Such a two-current-sheet reconnection
exhibits characteristics of both magnetic breakout for CME initiation and
standard flare model. We argue that both breakout-like and tether-cutting
reconnections may be important for CME eruptions and associated surface
activities.


  Lossy image compression is one of the most commonly used operators for
digital images. Most recently proposed deep-learning-based image compression
methods leverage the auto-encoder structure, and reach a series of promising
results in this field. The images are encoded into low dimensional latent
features first, and entropy coded subsequently by exploiting the statistical
redundancy. However, the information lost during encoding is unfortunately
inevitable, which poses a significant challenge to the decoder to reconstruct
the original images. In this work, we propose a novel invertible framework
called Invertible Lossy Compression (ILC) to largely mitigate the information
loss problem. Specifically, ILC introduces an invertible encoding module to
replace the encoder-decoder structure to produce the low dimensional
informative latent representation, meanwhile, transform the lost information
into an auxiliary latent variable that won't be further coded or stored. The
latent representation is quantized and encoded into bit-stream, and the latent
variable is forced to follow a specified distribution, i.e. isotropic Gaussian
distribution. In this way, recovering the original image is made tractable by
easily drawing a surrogate latent variable and applying the inverse pass of the
module with the sampled variable and decoded latent features. Experimental
results demonstrate that with a new component replacing the auto-encoder in
image compression methods, ILC can significantly outperform the baseline method
on extensive benchmark datasets by combining with the existing compression
algorithms.


  In the integer quantum Hall (IQH) regime, an antidot provides a finite,
controllable `edge' of quantum Hall fluid that is an ideal laboratory for
investigating the collective dynamics of large numbers of interacting
electrons. Transport measurements of single antidots probe the excitation
spectra of the antidot edge, and gate-defined antidot devices offer the
flexibility to vary both the antidot's dimensions and its couplings to extended
IQH edge modes which serve as leads. We also use the spin-selectivity of the
IQH edge modes to perform spin-resolved transport measurements, from which we
can infer the antidot spin-structure. This thesis describes a combination of
such transport experiments and related computational models designed to
investigate the effects of electron-electron interactions in quantum antidots,
with general implications for the physics of spin and charge in IQH systems.


  Invisibility cloaking imposes strict conditions on the refractive index
profiles of cloaking media that must be satisfied to successfully hide an
object. The first experimental demonstrations of cloaking used artificial
metamaterials to respond to this challenge. In this work we show how a much
simpler technique of electromagnetically induced transparency can be used to
achieve a partial, {\it carpet} cloaking at optical frequencies in atomic
vapours or solids. To generate a desired combination of low absorption with
strong modifications of the refractive index, we use chiral media with an
induced magneto-electrical cross-coupling. We demonstrate that high-contrast
positive refractive indices can be attained by fine tuning the material with a
gradient magnetic field and calculate the parameters required to construct a
carpet cloak.


  The local field correction to the spontanous dacay rate of an impurity source
atom imbedded in a disordered dielectric is calculated to second order in the
dielectric density. The result is found to differ from predictions associated
with both "virtual" and "real" cavity models of this decay process. However, if
the contributions from two dielectric atoms at the same position are included,
the virtual cavity result is reproduced.


  In this work, we employed \textit{ab initio} methods combined with
evolutionary algorithms for searching stable structures for fluorine in the
terapascal (TPa) regime. We performed several structural searches using the
USPEX code, at pressures that spanned from 1 to 5 TPa and considered up to 16
atoms per cell for selected pressures. Our findings partially support recent
studies by validating the transformation of fluorine from a molecular form,
$Cmca$, into an intermediate polymeric form before its eventual dissociation.
In fact, the enthalpy comparisons between candidate structures of fluorine at
high pressure show a direct transition from the molecular phase $Cmca$ into a
$Pm\bar{3}n$ extended structure at 2.7 TPa, the later consisting of linear
chains and independent atoms, which disagrees with previous conflicting reports
that proposed other intermediate phases to also exist as stable crystalline
forms close to 3 TPa.


  Given two metastable states A and B of a biomolecular system, the problem is
to calculate the likely paths of the transition from A to B. Such a calculation
is more informative and more manageable if done for a reduced set of collective
variables chosen so that paths cluster in collective variable space. The
computational task becomes that of computing the "center" of such a cluster. A
good way to define the center employs the concept of a committor, whose value
at a point in collective variable space is the probability that a trajectory at
that point will reach B before A. The committor "foliates" the transition
region into a set of isocommittors. The maximum flux transition path is defined
as a path that crosses each isocommittor at a point which (locally) has the
highest crossing rate of distinct reactive trajectories. (This path is
different from that of the MaxFlux method of Huo and Straub.) It is argued that
such a path is nearer to an ideal path than others that have been proposed with
the possible exception of the finite-temperature string method path. To make
the calculation tractable, three approximations are introduced, yielding a path
that is the solution of a nonsingular two-point boundary-value problem. For
such a problem, one can construct a simple and robust algorithm. One such
algorithm and its performance is discussed.


  We study the purely leptonic $W$ decays $W^+ \to e^+ \mu^- e^+ \nu_e$ and
$W^+ \to e^+ e^+ \mu^- \bar \nu_\mu$ (or their charge conjugates) produced at
the LHC, induced by sterile neutrinos with mass below $M_W$ in the intermediate
state. While the first mode is induced by both Dirac or Majorana neutrinos, the
second mode is induced only by Majorana neutrinos, as it violates lepton
number. We find that, even when the final (anti-)neutrino goes undetected, one
could distinguish between these two processes, thus distinguishing the Dirac or
Majorana character of the sterile neutrinos, by studying the muon spectrum in
the decays.


  In this work we consider a recent proposal in which gravitational
interactions are mediated via classical information and apply it to a
relativistic context. We study a toy model of a quantized
Friedman-Robertson-Walker (FRW) universe with the assumption that any test
particles must feel a classical metric. We show that such a model results in
decoherence in the FRW state that manifests itself as a dark energy fluid that
fills the spacetime. Analysis of the resulting fluid, shows the equation of
state asymptotically oscillates around the value $w=-1/3$, regardless of the
spatial curvature, which provides the bound between accelerating and
decelerating expanding FRW cosmologies. Motivated by quantum-classical
interactions this model is yet another example of theories with violation of
energy-momentum conservation whose signature could have significant
consequences for the observable universe.


  It has been known since Ehrhard and Regnier's seminal work on the Taylor
expansion of $\lambda$-terms that this operation commutes with normalization:
the expansion of a $\lambda$-term is always normalizable and its normal form is
the expansion of the B\"ohm tree of the term. We generalize this result to the
non-uniform setting of the algebraic $\lambda$-calculus, i.e.
$\lambda$-calculus extended with linear combinations of terms. This requires us
to tackle two difficulties: foremost is the fact that Ehrhard and Regnier's
techniques rely heavily on the uniform, deterministic nature of the ordinary
$\lambda$-calculus, and thus cannot be adapted; second is the absence of any
satisfactory generic extension of the notion of B\"ohm tree in presence of
quantitative non-determinism, which is reflected by the fact that the Taylor
expansion of an algebraic $\lambda$-term is not always normalizable. Our
solution is to provide a fine grained study of the dynamics of
$\beta$-reduction under Taylor expansion, by introducing a notion of reduction
on resource vectors, i.e. infinite linear combinations of resource
$\lambda$-terms. The latter form the multilinear fragment of the differential
$\lambda$-calculus, and resource vectors are the target of the Taylor expansion
of $\lambda$-terms. We show the reduction of resource vectors contains the
image of any $\beta$-reduction step, from which we deduce that Taylor expansion
and normalization commute on the nose. We moreover identify a class of
algebraic $\lambda$-terms, encompassing both normalizable algebraic
$\lambda$-terms and arbitrary ordinary $\lambda$-terms: the expansion of these
is always normalizable, which guides the definition of a generalization of
B\"ohm trees to this setting.


  Recent work introduced loss functions which measure the error of a prediction
based on multiple simultaneous observations or outcomes. In this paper, we
explore the theoretical and practical questions that arise when using such
multi-observation losses for regression on data sets of $(x,y)$ pairs. When a
loss depends on only one observation, the average empirical loss decomposes by
applying the loss to each pair, but for the multi-observation case, empirical
loss is not even well-defined, and the possibility of statistical guarantees is
unclear without several $(x,y)$ pairs with exactly the same $x$ value. We
propose four algorithms formalizing the concept of empirical risk minimization
for this problem, two of which have statistical guarantees in settings allowing
both slow and fast convergence rates, but which are out-performed empirically
by the other two. Empirical results demonstrate practicality of these
algorithms in low-dimensional settings, while lower bounds demonstrate
intrinsic difficulty in higher dimensions. Finally, we demonstrate the
potential benefit of the algorithms over natural baselines that use traditional
single-observation losses via both lower bounds and simulations.


  Autonomous exploration requires robots to generate informative trajectories
iteratively. Although sampling-based methods are highly efficient in unmanned
aerial vehicle exploration, many of these methods do not effectively utilize
the sampled information from the previous planning iterations, leading to
redundant computation and longer exploration time. Also, few have explicitly
shown their exploration ability in dynamic environments even though they can
run real-time. To overcome these limitations, we propose a novel dynamic
exploration planner (DEP) for exploring unknown environments using incremental
sampling and Probabilistic Roadmap (PRM). In our sampling strategy, nodes are
added incrementally and distributed evenly in the explored region, yielding the
best viewpoints. To further shortening exploration time and ensuring safety,
our planner optimizes paths locally and refine them based on the Euclidean
Signed Distance Function (ESDF) map. Meanwhile, as the multi-query planner, PRM
allows the proposed planner to quickly search alternative paths to avoid
dynamic obstacles for safe exploration. Simulation experiments show that our
method safely explores dynamic environments and outperforms the benchmark
planners in terms of exploration time, path length, and computational time.


  We study the three-dimensional (3D) attractive Hubbard model by means of the
Determinant Quantum Monte Carlo method. This model is a prototype for the
description of the smooth crossover between BCS superconductivity and
Bose-Einstein condensation. By detailed finite-size scaling we extract the
finite-temperature phase diagram of the model. In particular, we interpret the
observed behavior according to a scenario of two fundamental temperature
scales; T* associated with Cooper pair formation and Tc with condensation
(giving rise to long-range superconducting order). Our results also indicate
the presence of a recently conjectured phase transition hidden by the
superconducting state. A comparison with the 2D case is briefly discussed,
given its relevance for the physics of high-Tc cuprate superconductors.


  We propose a novel approach to tackle integrability problem for evolutionary
differential-difference equations (D$\Delta$Es) on free associative algebras,
also referred to as nonabelian D$\Delta$Es. This approach enables us to derive
necessary integrability conditions, determine the integrability of a given
equation, and make progress in the classification of integrable nonabelian
D$\Delta$Es. This work involves establishing symbolic representations for the
nonabelian difference algebra, difference operators, and formal series, as well
as introducing a novel quasi-local extension for the algebra of formal series
within the context of symbolic representations. Applying this formalism, we
solve the classification problem of integrable skew-symmetric quasi-linear
nonabelian equations of orders $(-1,1)$, $(-2,2)$, and $(-3,3)$, consequently
revealing some new equations in the process.


  In the last decade, the effects of interruptions through mobile notifications
have been extensively researched in the field of Human-Computer Interaction.
Breakpoints in tasks and activities, cognitive load, and personality traits
have all been shown to correlate with individuals' interruptibility. However,
concepts that explain interruptibility in a broader sense are needed to provide
a holistic understanding of its characteristics. In this paper, we build upon
the theory of social roles to conceptualize and investigate the correlation
between individuals' private and work-related smartphone usage and their
interruptibility. Through our preliminary study with four participants over 11
weeks, we found that application sequences on smartphones correlate with
individuals' private and work roles. We observed that participants engaged in
these roles tend to follow specific interruptibility strategies - integrating,
combining, or segmenting private and work-related engagements. Understanding
these strategies breaks new ground for attention and interruption management
systems in ubiquitous computing.


  We present a three-dimensional model, based on cohesive spherical particles,
of rain-induced landslides. The rainwater infiltration into the soil follow the
either the fractional or the fractal diffusion equations. We solve analytically
the fractal diffusion partial differential equation (PDE) with particular
boundary conditions to simulate a rainfall event. Then, for the PDE, we
developed a numerical integration scheme that we integrate with MD (Molecular
Dynamics) algorithm for the triggering and propagation of the simulated
landslide. Therefore we test the numerical integration scheme of fractal
diffusion equation with the analytical solution. We adopt the fractal diffusion
equation in term of gravimetric water content that we use as input of
triggering scheme based on Mohr-Coulomb limit-equilibrium criterion, adapted to
particle level. Moreover, taking into account an interacting force
Lennard-Jones inspired, we use a standard MD algorithm to update particle
positions and velocities. Then we present results for homogeneous and
heterogeneous systems (i.e. composed by particles with same or different radius
respectively). Interestingly, in the heterogeneous case, we observe segregation
effects due to the different volume of the particles. Finally we show the
parameter sensibility analysis both for triggering and propagation phase. Our
simulations confirm the results of our previous two-dimensional model and
therefore the feasible applicability to real cases.


  The aim of this study is to explore the suitability of chromospheric images
for magnetic modeling of active regions. We use high-resolution images (0.1")
from the Interferometric Bidimensional Spectrometer (IBIS) in the Ca II 8542 A
line, the Rapid Oscillations in the Solar Atmosphere (ROSA) instrument in the
H-alpha 6563 A line, the Interface Region Imaging Spectrograph (IRIS) in the
2796 A line, and compare non-potential magnetic field models obtained from
those chromospheric images with those obtained from images of the Atmospheric
Imaging Assembly (AIA) in coronal (171 A, etc.) and in chromospheric (304 A)
wavelengths. Curvi-linear structures are automatically traced in those images
with the OCCULT-2 code, to which we forward-fitted magnetic field lines
computed with the Vertical-Current Approximation Non-Linear Force Free Field
(VCA-NLFFF) code. We find that the chromospheric images: (1) reveal crisp
curvi-linear structures (fibrils, loop segments, spicules) that are extremely
well-suited for constraining magnetic modeling; (2) that these curvi-linear
structures are field-aligned with the best-fit solution by a median
misalignment angle of ~4-7 deg; (3) the free energy computed from coronal data
may underestimate that obtained from cromospheric data by a factor of ~ 2-4,
(4) the height range of chromospheric features is confined to h ~ 4000$ km,
while coronal features are detected up to h ~ 35,000$ km; and (5) the
plasma-beta parameter is beta ~ 10^(-5)-10^(-1) for all traced features. We
conclude that chromospheric images reveal important magnetic structures that
are complementary to coronal images and need to be included in comprehensive
magnetic field models, a quest that is not accomodated in standard NLFFF codes.


  We develop a two stage renormalization group which connects the continuum
Hamiltonian for twisted bilayer graphene at length scales shorter than the
moire superlattice period to the Hamiltonian for the active narrow bands only
which is valid at distances much longer than the moire period. In the first
stage, the Coulomb interaction renormalizes the Fermi velocity and the
interlayer tunnelings in such a way as to suppress the ratio of the same
sublattice to opposite sublatice tunneling, hence approaching the so-called
chiral limit. In the second stage, the interlayer tunneling is treated
non-perturbatively. Via a progressive numerical elimination of remote bands the
relative strength of the one-particle-like dispersion and the interactions
within the active narrow band Hamiltonian is determined, thus quantifying the
residual correlations and justifying the strong coupling approach in the final
step. We also calculate exactly the exciton energy spectrum from the Coulomb
interactions projected onto the renormalized narrow bands. The resulting
softening of the collective modes marks the propinquity of the enlarged
("hidden") $U(4)\times U(4)$ symmetry in the magic angle twisted bilayer
graphene.


  We study the behaviour of one-dimensional strongly dissipative systems
subject to a quasi-periodic force. In particular we are interested in the
existence of response solutions, that is quasi-periodic solutions having the
same frequency vector as the forcing term. Earlier results available in the
literature show that, when the dissipation is large enough and a suitable
function involving the forcing has a simple zero, response solutions can be
proved to exist and to be attractive provided some Diophantine condition is
assumed on the frequency vector. In this paper we show that the results extend
to the case of arbitrary frequency vectors.


  Semitopologies model consensus in distributed system by equating the notion
of a quorum -- a set of participants sufficient to make local progress -- with
that of an open set. This yields a topology-like theory of consensus, but
semitopologies generalise topologies, since the intersection of two quorums
need not necessarily be a quorum. The semitopological model of consensus is
naturally heterogeneous and local, just like topologies can be heterogenous and
local, and for the same reasons: points may have different quorums and there is
no restriction that open sets / quorums be uniformly generated (e.g. open sets
can be something other than two-thirds majorities of the points in the space).
  Semiframes are an algebraic abstraction of semitopologies. They are to
semitopologies as frames are to topologies. We give a notion of semifilter,
which plays a role analogous to filters, and show how to build a semiframe out
of the open sets of a semitopology, and a semitopology out of the semifilters
of a semiframe.
  We define suitable notions of category and morphism and prove a categorical
duality between (sober) semiframes and (spatial) semitopologies, and
investigate well-behavedness properties on semitopologies and semiframes across
the duality. Surprisingly, the structure of semiframes is not what one might
initially expect just from looking at semitopologies, and the canonical
structure required for the duality result -- a compatibility relation *,
generalising sets intersection -- is also canonical for expressing
well-behavedness properties.
  Overall, we deliver a new categorical, algebraic, abstract framework within
which to study consensus on distributed systems, and which is also simply
interesting to consider as a mathematical theory in its own right.


  The discovery of topological quantum materials represents a striking
innovation in modern condensed matter physics with remarkable fundamental and
technological implications. Their classification has been recently extended to
topological Weyl semimetals, i.e., solid state systems which exhibit the
elusive Weyl fermions as low-energy excitations. Here we show that the Nernst
effect can be exploited as a sensitive probe for determining key parameters of
the Weyl physics, applying it to the non-collinear antiferromagnet Mn$_3$Ge.
This compound exhibits anomalous thermoelectric transport due to enhanced Berry
curvature from Weyl points located extremely close to the Fermi level. We
establish from our data a direct measure of the Berry curvature at the Fermi
level and, using a minimal model of a Weyl semimetal, extract for the first
time the Weyl point energy and their distance in momentum-space.


  We present a classification of the massless chiral matter representations
that can arise locally in M-theory on G(2) through geometrically engineered
singularities. We will find that several of the more exceptional singularities
could have applications for model building.


  We provide a class of bound entangled states that have positive distillable
secure key rate. The smallest state of this kind is $4 \otimes 4$, which shows
that peculiar security contained in bound entangled states does not need high
dimensional systems. We show, that for these states a positive key rate can be
obtained by {\it one-way} Devetak-Winter protocol. Subsequently the volume of
bound entangled key-distillable states in arbitrary dimension is shown to be
nonzero. We provide a scheme of verification of cryptographic quality of
experimentally prepared state in terms of local observables. Proposed set of 7
collective settings is proven to be optimal in number of settings.


  A spatial quantum model of spontaneous parametric down-conversion in
nonlinear layered structures is developed expanding the interacting vectorial
fields into monochromatic plane waves. A two-photon spectral amplitude
depending on the signal- and idler-field frequencies and propagation directions
is used to derive transverse profiles of the emitted fields as well as their
spatial correlations. Intensity spatial profiles and their spatial correlations
are mainly determined by the positions of transmission peaks formed in these
structures with photonic bands. A method for geometry optimization of the
structures with respect to efficiency of the nonlinear process is suggested.
Several structures composed of GaN/AlN layers are analyzed as typical examples.
They allow the generation of photon pairs correlated in several emission
directions. Photon-pair generation rates increasing better than the second
power of the number of layers can be reached. Also structures efficiently
generated photon pairs showing anti-bunching and anti-coalescence can be
obtained. Three reasons for splitting the correlated area in photonic-band-gap
structures are revealed: zig-zag movement of photons inside the structure,
spatial symmetry and polarization-dependent properties. Also spectral splitting
can be observed in these structures.


  In this letter we investigate some consequences of considering our 4D
observable universe as locally and isometrically embeded into a 5D spacetime,
where gravity is described by a Brans-Dicke theory in vacuum. Once we impose
the embeding conditions we obtain that gravity on the 4D spacetime is governed
by the Einstein field equations modified by an extra term that can play the
role of a dynamical cosmological constant. Two examples were studied. In the
first we derive a cosmological model of a universe filled only with a
cosmological constant. In the second we obtain a cosmological solution
describing a universe filled with matter, radiation and a dynamical
cosmological constant, in agree with observational data. Due to the 5D
geometrical origin for the dynamical cosmological constant we interpret that
the acceleration in the expansion is explained without the introduction of a
dark energy component. Moreover, all 4D matter sources are geometrically
induced in the same manner as it is usually done in the Wesson's induced matter
theory.


  Theory of electronic and optical properties of exciton and bi-exciton
complexes confined in CdSe spherical nanocrystals is presented. The electron
and hole states are computed using atomistic $sp^3d^5s^*$ tight binding
Hamiltonian including an effective crystal field splitting, spin-orbit
interactions, and model surface passivation. The optically excited states are
expanded in electron-hole configurations and the many-body spectrum is computed
in the configuration-interaction approach. Results demonstrate that the
low-energy electron spectrum is organized in shells ($s$, $p$, ...), whilst the
valence hole spectrum is composed of four low-lying, doubly degenerate states
separated from the rest by a gap. As a result, the bi-exciton and exciton
spectrum is composed of a manifold of closely lying states, resulting in a fine
structure of exciton and bi-exciton spectra. The quasi-degenerate nature of the
hole spectrum results in a correlated bi-exciton state, which makes it slowly
convergent with basis size. We carry out a systematic study of the exciton and
bi-exciton emission spectra as a function of the nanocrystal diameter and find
that the interplay of repulsion between constituent excitons and correlation
effects results in a change of the sign of bi-exciton binding energy from
negative to positive at a critical nanocrystal size.


  Let $G$ be a finite group and let $H$ be a proper subgroup of $G$ of minimal
index. By applying an old result of Y. Berkovich, we provide a polynomial
algorithm for computing $|G : H|$ for a permutation group $G$. Moreover, we
find $H$ explicitly if $G$ is given by a Cayley table. As a corollary, we get
an algorithm for testing whether a finite permutation group acts on a tree or
not.


  We compute the next-to-leading order QCD corrections to spectator effects in
the lifetime ratios of beauty hadrons. With respect to previous calculations,
we take into account the non vanishing value of the charm quark mass. We obtain
the predictions tau(B+)/tau(Bd) = 1.06 +- 0.02, tau(Bs)/tau(Bd)= 1.00 +- 0.01
and tau(Lambdab)/tau(Bd) = 0.90 +- 0.05, in good agreement with the
experimental results. In the case of tau(Bs)/tau(Bd) and tau(Lambdab)/tau(Bd),
however, some contributions, which either vanish in the vacuum insertion
approximation or represent a pure NLO corrections, have not been determined
yet.


  In this paper, we present a novel cache design based on Multi-Level Cell
Spin-Transfer Torque RAM (MLC STTRAM) that can dynamically adapt the set
capacity and associativity to use efficiently the full potential of MLC STTRAM.
We exploit the asymmetric nature of the MLC storage scheme to build cache lines
featuring heterogeneous performances, that is, half of the cache lines are
read-friendly, while the other is write-friendly. Furthermore, we propose to
opportunistically deactivate ways in underutilized sets to convert MLC to
Single-Level Cell (SLC) mode, which features overall better performance and
lifetime. Our ultimate goal is to build a cache architecture that combines the
capacity advantages of MLC and performance/energy advantages of SLC. Our
experiments show an improvement of 43% in total numbers of conflict misses, 27%
in memory access latency, 12% in system performance, and 26% in LLC access
energy, with a slight degradation in cache lifetime (about 7%) compared to an
SLC cache.


  The electronic and magneto transport properties of reduced anatase TiO2
epitaxial thin films are analyzed considering various polaronic effects.
Unexpectedly, with increasing carrier concentration, the mobility increases,
which rarely happens in common metallic systems. We find that the screening of
the electron-phonon (e-ph) coupling by excess carriers is necessary to explain
this unusual dependence. We also find that the magnetoresistance (MR) could be
decomposed into a linear and a quadratic component, separately characterizing
the transport and trap behavior of carriers as a function of temperature. The
various transport behaviors could be organized into a single phase diagram
which clarifies the nature of large polaron in this material.


  Let $P\in \Bbb Q_p[x,y]$, $s\in \Bbb C$ with sufficiently large real part,
and consider the integral operator $
(A_{P,s}f)(y):=\frac{1}{1-p^{-1}}\int_{\Bbb Z_p}|P(x,y)|^sf(x) |dx| $ on
$L^2(\Bbb Z_p)$. We show that if $P$ is homogeneous then for each character
$\chi$ of $\Bbb Z_p^\times$ the characteristic function $\det(1-uA_{P,s,\chi})$
of the restriction $A_{P,s,\chi}$ of $A_{P,s}$ to the eigenspace $L^2(\Bbb
Z_p)_\chi$ is the $q$-Wronskian of a set of solutions of a (possibly confluent)
$q$-hypergeometric equation. In particular, the nonzero eigenvalues of
$A_{P,s,\chi}$ are the reciprocals of the zeros of such $q$-Wronskian.


  For several transition disks (TDs), dark regions interpreted as shadows have
been observed in scattered light imaging and are hypothesized to originate from
misalignments between distinct disk regions. We aim to investigate the presence
of misalignments in TDs. We study the inner disk geometries of 20 well-known
transition disks with VLTI/GRAVITY observations and use complementary $^{12}$CO
and $^{13}$CO molecular line data from ALMA to derive the orientation of the
outer disk regions. We fit simple models to the GRAVITY data to derive the
inner disks inclination and position angles. The outer disk geometries were
derived from Keplerian fits to the ALMA velocity maps and compared to the inner
disk constraints. We also predicted the locations of shadows for significantly
misaligned systems. Our analysis reveals six disks to exhibit significant
misalignments between their inner and outer disks. The predicted shadow
positions agree well with the scattered light images of HD100453 and HD142527,
and we find supporting evidence for a shadow in the disk around CQ Tau. In the
other three targets for which we infer significantly misaligned disks, V1247
Ori, V1366 Ori, and RY Lup, we do not see any evident sign of shadows in the
scattered light images. The scattered light shadows observed in DoAr44,
HD135344B, and HD139614 are consistent with our observations, yet the
underlying morphology is likely too complex to be described by our models and
the accuracy achieved by our observations. Whereas we can derive precise
constraints on the potential shadow positions for well-resolved inner disks
around HAeBe stars, the statistical uncertainties for the marginally resolved
inner disks around the TTS of our sample make it difficult to extract
conclusive constraints for the presence of shadows in these systems.


  The LHC results on particle and transverse energy production and
Bose-Einstein correlations show that the system produced in Pb-Pb collisions at
psNN = 2:76TeV is significantly larger, lives longer and is hotter and denser
than at RHIC energies. The particle spectra and soft particle correlations
allow a more detailed study of the properties of the produced system and its
initial conditions. This contribution highlights some of the first soft physics
results from the LHC.


  We compute the sub-leading terms in the Tian-Yau-Zelditch asymptotic
expansion of the partition function for dual giant gravitons on AdS5 $\times$
L5 and provide a bulk interpretation in terms of curvature invariants. We
accomplish this by relating the partition function of dual giant gravitons to
the Hilbert series for mesonic operators in the CFT. The coefficients of the
subleading terms encode integrated curvature invariants of L5. In the same
spirit of Martelli, Sparks and Yau, we are able to compute these integrated
curvature invariants without explicit knowledge of the Sasaki-Einstein metric
on L5. These curvature invariants contribute to the 1/N^2 corrections of the
difference of the 4D anomaly coefficients a and c recently found by Liu and
Minasian, which we now have a purely field theoretic method of calculating.


  Using the bases of principal subspaces for twisted affine Lie algebras except
$A_{2l}^{(2)}$ by Butorac and Sadowski, we construct bases of the highest
weight modules of highest weight $k\Lambda_0$ and parafermionic spases for the
same affine Lie algebras. As a result, we obtain their character formulas
conjectured in arXiv:math/0102113.


  Fulton's universal Schubert polynomials give cohomology formulas for a class
of degeneracy loci, which generalize Schubert varieties. The K-theoretic quiver
formula of Buch expresses the structure sheaves of these loci as integral
linear combinations of products of stable Grothendieck polynomials. We prove an
explicit combinatorial formula for the coefficients, which shows that they have
alternating signs. Our result is applied to obtain new expansions for the
Grothendieck polynomials of Lascoux and Sch\"utzenberger.


  In this paper we present calculations of thermodynamic functions within
Zhang's SO(5) quantum rotor theory of high-Tc superconductivity. Using the
spherical approach for the three-dimensional quantum rotors we derieved
explicit analytical formulas for entropy and specific heat related to the
lattice version of the SO(5) nonlinear quantum-sigma model. We present the
temperature dependence of these quantities for various settings of relevant
control parameters (quantum fluctuations, chemical potential). We find our
results in overal qualitative agreement with basic thermodynamics of high-Tc
cuprates.


  It is difficult to train a personalized task-oriented dialogue system because
the data collected from each individual is often insufficient. Personalized
dialogue systems trained on a small dataset can overfit and make it difficult
to adapt to different user needs. One way to solve this problem is to consider
a collection of multiple users' data as a source domain and an individual
user's data as a target domain, and to perform a transfer learning from the
source to the target domain. By following this idea, we propose
"PETAL"(PErsonalized Task-oriented diALogue), a transfer-learning framework
based on POMDP to learn a personalized dialogue system. The system first learns
common dialogue knowledge from the source domain and then adapts this knowledge
to the target user. This framework can avoid the negative transfer problem by
considering differences between source and target users. The policy in the
personalized POMDP can learn to choose different actions appropriately for
different users. Experimental results on a real-world coffee-shopping data and
simulation data show that our personalized dialogue system can choose different
optimal actions for different users, and thus effectively improve the dialogue
quality under the personalized setting.


  Flavescence dor\'ee (FD) is a disease of grapevine transmitted by an insect
vector, $Scaphoideus$ $titanus$ Ball. At present, no prophylaxis exists, so
mandatory control procedures (e.g. removal of infected plants, and insecticidal
sprays to avoid transmission) are in place in Italy and other European
countries. We propose a model of the epidemiology of FD by taking into account
the different aspects involved into the transmission process (acquisition of
the disease, latency and expression of symptoms, recovery rate, removal and
replacement of infected plants, insecticidal treatments, and the effect of
hotbeds). The model was constructed as a system of first order nonlinear ODEs
in four compartment variables. We perform a bifurcation analysis of the
equilibria of the model using the severity of the hotbeds as the control
parameter. Depending on the non-dimensional grapevine density of the vineyard
we find either a single family of equilibria in which the health of the
vineyard gradually deteriorates for progressively more severe hotbeds, or
multiple equilibria that give rise to sudden transitions from a nearly healthy
vineyard to a severely deteriorated one when the severity of the hotbeds
crosses a critical value. These results suggest some lines of intervention for
limiting the spread of the disease.


  The aim of this paper is to study the singular solutions to fractional
elliptic equations with absorption $$ \left\{\arraycolsep=1pt
\begin{array}{lll} (-\Delta)^\alpha u+|u|^{p-1}u=0,\quad &
\rm{in}\quad\Omega\setminus\{0\},\\[2mm] u=0,\quad & \rm{in}\quad
\R^N\setminus\Omega,\\[2mm] \lim_{x\to 0}u(x)=+\infty, \end{array} \right. $$
where $p>0$, $\Omega$ is an open, bounded and smooth domain of $\R^N\ (N\ge2)$
with $0\in\Omega$. We analyze the existence, nonexistence, uniqueness and
asymptotic behavior of the solutions.


  We define an abstract regular polytope to be internally self-dual if its
self-duality can be realized as one of its symmetries. This property has many
interesting implications on the structure of the polytope, which we present
here. Then, we construct many examples of internally self-dual polytopes. In
particular, we show that there are internally self-dual regular polyhedra of
each type $\{p, p\}$ for $p \geq 3$ and that there are both infinitely many
internally self-dual and infinitely many externally self-dual polyhedra of type
$\{p, p\}$ for $p$ even. We also show that there are internally self-dual
polytopes in each rank, including a new family of polytopes that we construct
here.


  When using Neural Networks as trial functions to numerically solve PDEs, a
key choice to be made is the loss function to be minimised, which should
ideally correspond to a norm of the error. In multiple problems, this error
norm coincides with--or is equivalent to--the $H^{-1}$-norm of the residual;
however, it is often difficult to accurately compute it. This work assumes
rectangular domains and proposes the use of a Discrete Sine/Cosine Transform to
accurately and efficiently compute the $H^{-1}$ norm. The resulting Deep
Fourier-based Residual (DFR) method efficiently and accurately approximate
solutions to PDEs. This is particularly useful when solutions lack $H^{2}$
regularity and methods involving strong formulations of the PDE fail. We
observe that the $H^1$-error is highly correlated with the discretised loss
during training, which permits accurate error estimation via the loss.


  Plant electrical signals often contains low frequency drifts with or without
the application of external stimuli. Quantification of the randomness in plant
signals in a stimulus-specific way is hindered because the knowledge of vital
frequency information in the actual biological response is not known yet. Here
we design an optimum Infinite Impulse Response (IIR) filter which removes the
low frequency drifts and preserves the frequency spectrum corresponding to the
random component of the unstimulated plant signals by bringing the bias due to
unknown artifacts and drifts to a minimum. We use energy criteria of wavelet
packet transform (WPT) for optimization based tuning of the IIR filter
parameters. Such an optimum filter enforces that the energy distribution of the
pre-stimulus parts in different experiments are almost overlapped but under
different stimuli the distributions of the energy get changed. The reported
research may popularize plant signal processing, as a separate field, besides
other conventional bioelectrical signal processing paradigms.


  In this paper we address the following question arising from the work of P.
Etingof, D. Kazhdan and A. Polishchuk (math.AG/0003009): given a homogeneous
complex polynomial, when the rational map defined by its partials is of degree
1? We answer this question for reduced polynomials in three variables and also
for reduced polynomials in four variables which factor into the product of
linear polynomials.


  The temporal answering grounding in the video (TAGV) is a new task naturally
derived from temporal sentence grounding in the video (TSGV). Given an
untrimmed video and a text question, this task aims at locating the matching
span from the video that can semantically answer the question. Existing methods
tend to formulate the TAGV task with a visual span-based question answering
(QA) approach by matching the visual frame span queried by the text question.
However, due to the weak correlations and huge gaps of the semantic features
between the textual question and visual answer, existing methods adopting
visual span predictor perform poorly in the TAGV task. To bridge these gaps, we
propose a visual-prompt text span localizing (VPTSL) method, which introduces
the timestamped subtitles as a passage to perform the text span localization
for the input text question, and prompts the visual highlight features into the
pre-trained language model (PLM) for enhancing the joint semantic
representations. Specifically, the context query attention is utilized to
perform cross-modal interaction between the extracted textual and visual
features. Then, the highlight features are obtained through the video-text
highlighting for the visual prompt. To alleviate semantic differences between
textual and visual features, we design the text span predictor by encoding the
question, the subtitles, and the prompted visual highlight features with the
PLM. As a result, the TAGV task is formulated to predict the span of subtitles
matching the visual answer. Extensive experiments on the medical instructional
dataset, namely MedVidQA, show that the proposed VPTSL outperforms the
state-of-the-art (SOTA) method by 28.36% in terms of mIOU with a large margin,
which demonstrates the effectiveness of the proposed visual prompt and the text
span predictor.


  We consider an ideal Bose gas contained in a cylinder in three spatial
dimensions, subjected to a uniform gravitational field. It has been claimed by
some authors that there is discrepancy between the semi-classical and quantum
calculations in the thermal properties of such a system. To check this claim,
we calculate the heat capacity and isothermal compressibility of this system
semi-classically as well as from the quantum spectrum of the density of states.
The quantum calculation is done for a finite number of particles. We find good
agreement between the two calculations when the number of particles are taken
to be large. We also find that this system has the same thermal properties as
an ideal five dimensional Bose gas.


  We present a new integral equation for solving the Maxwell scattering problem
against a perfect conductor. The very same algorithm also applies to sound-soft
as well as sound-hard Helmholtz scattering, and in fact the latter two can be
solved in parallel in three dimensions. Our integral equation does not break
down at interior spurious resonances, and uses spaces of functions without any
algebraic or differential constraints. The operator to invert at the boundary
involves a singular integral operator closely related to the three dimensional
Cauchy singular integral, and is bounded on natural function spaces and depend
analytically on the wave number. Our operators act on functions with pairs of
complex two by two matrices as values, using a spin representation of the
fields.


  A subgroup $A$ of a group~$G$ is said to be {\sl NS-supplemented} in $G$, if
there exists a subgroup~$B$ of $G$ such that $G=AB$ and whenever $X$~is a
normal subgroup of~$A$ and $p\in \pi(B)$, there exists a Sylow
$p$-subgroup~$B_p$ of~$B$ such that $XB_p=B_pX$. In this paper, we proved the
supersolubility of a group with NS-supplemented non-cyclic Sylow subgroups. The
solubility of a group with NS-supplemented maximal subgroups is obtained.