  We apply Projected Hartree-Fock theory (PHF) for approximating ground states
of Heisenberg spin clusters. Spin-rotational, point-group and
complex-conjugation symmetry are variationally restored from a broken-symmetry
mean-field reference, where the latter corresponds to a product of local spin
states. A fermionic formulation of the Heisenberg model furnishes a conceptual
connection to PHF applications in quantum chemistry and detailed equations for
a self-consistent field optimization of the reference state are provided.
Different PHF variants are benchmarked for ground-state energies and spin-pair
correlation functions of antiferromagnetic spin rings and three different
polyhedra, with various values of the local spin-quantum number s. The low
computational cost and the compact wave-function representation make PHF a
promising complement to existing approaches for ground states of molecular spin
clusters, particularly for large s and moderately large N. The present work may
also motivate future explorations of more accurate post-PHF methods for
Heisenberg spin clusters.


  In this paper, we establish the links between the Lehmer and H\"older mean
families and maximum weighted likelihood estimator. Considering the regular
one-parameter exponential family of probability density functions, we show that
the maximum weighted likelihood of the parameter is a generalized weighted mean
family from which Lehmer and H\"older mean families are derived. Some of the
outcomes obtained provide a probabilistic interpretation of these mean families
and could therefore broaden their uses in various applications.


  We present the results of a new search for bright star-forming galaxies at z
~ 7 within the UltraVISTA DR2 and UKIDSS UDS DR10 data, which together provide
1.65 sq deg of near-infrared imaging with overlapping optical and Spitzer data.
Using a full photo-z analysis to identify high-z galaxies and reject
contaminants, we have selected a sample of 34 luminous (-22.7 < M_UV < -21.2)
galaxies with 6.5 < z < 7.5. Crucially, the deeper imaging provided by
UltraVISTA DR2 confirms all of the robust objects previously uncovered by
Bowler et al. (2012), validating our selection technique. Our sample includes
the most massive galaxies known at z ~ 7, with M_* ~ 10^{10} M_sun, and the
majority are resolved, consistent with larger sizes (r_{1/2} ~ 1 - 1.5 kpc)
than displayed by less massive galaxies. From our final sample, we determine
the form of the bright end of the rest-frame UV galaxy luminosity function (LF)
at z ~ 7, providing strong evidence that the bright end of the z = 7 LF does
not decline as steeply as predicted by the Schechter function fitted to fainter
data. We consider carefully, and exclude the possibility that this is due to
either gravitational lensing, or significant contamination of our galaxy sample
by AGN. Rather, our results favour a double power-law form for the galaxy LF at
high z, or, more interestingly, a LF which simply follows the form of the
dark-matter halo mass function at bright magnitudes. This suggests that the
physical mechanism which inhibits star-formation activity in massive galaxies
(i.e. AGN feedback or some other form of `mass quenching') has yet to impact on
the observable galaxy LF at z ~ 7, a conclusion supported by the estimated
masses of our brightest galaxies which have only just reached a mass comparable
to the critical `quenching mass' of M_* = 10 ^{10.2} M_sun derived from studies
of the mass function of star-forming galaxies at lower z.


  We present results from experiments with granular packings in three
dimensions in microgravity as realized on parabolic flights. Two different
techniques are employed to monitor the inside of the packings during
compaction: (1) X-ray radiography is used to measure in transmission the
integrated fluctuations of particle positions. (2) Stress-birefringence in
three dimensions is applied to visualize the stresses inside the packing. The
particle motions below the transition into an arrested packing are found to
produce a well agitated state. At the transition, the particles lose their
energy quite rapidly and form a stress network. With both methods, non-arrested
particles (rattlers) can be identified. In particular, it is found that
rattlers inside the arrested packing can be excited to appreciable dynamics by
the rest-accelerations (g-jitter) during a parabolic flight without destroying
the packings. At low rates of compaction, a regime of slow granular cooling is
identified. The slow cooling extends over several seconds, is described well by
a linear law, and terminates in a rapid final collapse of dynamics before
complete arrest of the packing.


  Farr-Gao algorithm is a state-of-the-art algorithm for reduced Gr\"{o}bner
bases of vanishing ideals of finite points, which has been implemented in
Maple$^\circledR$ as a build-in command. In this paper, we present a
two-dimensional improvement for it that employs a preprocessing strategy for
computing reduced Gr\"{o}bner bases associated with tower subsets of given
point sets. Experimental results show that the preprocessed Farr-Gao algorithm
is more efficient than the classical one.


  Although deep learning models for abnormality classification can perform well
in screening mammography, the demographic, imaging, and clinical
characteristics associated with increased risk of model failure remain unclear.
This retrospective study uses the Emory BrEast Imaging Dataset(EMBED)
containing mammograms from 115931 patients imaged at Emory Healthcare between
2013-2020, with BI-RADS assessment, region of interest coordinates for
abnormalities, imaging features, pathologic outcomes, and patient demographics.
Multiple deep learning models were trained to distinguish between abnormal
tissue patches and randomly selected normal tissue patches from screening
mammograms. We assessed model performance by subgroups defined by age, race,
pathologic outcome, tissue density, and imaging characteristics and
investigated their associations with false negatives (FN) and false positives
(FP). We also performed multivariate logistic regression to control for
confounding between subgroups. The top-performing model, ResNet152V2, achieved
accuracy of 92.6%(95%CI=92.0-93.2%), and AUC 0.975(95%CI=0.972-0.978). Before
controlling for confounding, nearly all subgroups showed statistically
significant differences in model performance. However, after controlling for
confounding, we found lower FN risk associates with Other
race(RR=0.828;p=.050), biopsy-proven benign lesions(RR=0.927;p=.011), and
mass(RR=0.921;p=.010) or asymmetry(RR=0.854;p=.040); higher FN risk associates
with architectural distortion (RR=1.037;p<.001). Higher FP risk associates to
BI-RADS density C(RR=1.891;p<.001) and D(RR=2.486;p<.001). Our results
demonstrate subgroup analysis is important in mammogram classifier performance
evaluation, and controlling for confounding between subgroups elucidates the
true associations between variables and model failure. These results can help
guide developing future breast cancer detection models.


  We prove extensions of Halman's discrete Helly theorem for axis-parallel
boxes in $\mathbb{R}^d$. Halman's theorem says that, given a set $S$ in
$\mathbb{R}^d$, if $F$ is a finite family of axis-parallel boxes such that the
intersection of any $2d$ contains a point of $S$, then the intersection of $F$
contains a point of $S$. We prove colorful, fractional, and quantitative
versions of Halman's theorem. For the fractional versions, it is enough to
check that many $(d+1)$-tuples of the family contain points of $S$. Among the
colorful versions we include variants where the coloring condition is replaced
by an arbitrary matroid. Our results generalize beyond axis-parallel boxes to
$H$-convex sets.


  The mother machine is a popular microfluidic device that allows long-term
time-lapse imaging of thousands of cells in parallel by microscopy. It has
become a valuable tool for single-cell level quantitative analysis and
characterization of many cellular processes such as gene expression and
regulation, mutagenesis or response to antibiotics. The automated and
quantitative analysis of the massive amount of data generated by such
experiments is now the limiting step. In particular the segmentation and
tracking of bacteria cells imaged in phase-contrast microscopy---with error
rates compatible with high-throughput data---is a challenging problem.
  In this work, we describe a novel formulation of the multi-object tracking
problem, in which tracking is performed by a regression of the bacteria's
displacement, allowing simultaneous tracking of multiple bacteria, despite
their growth and division over time. Our method performs jointly segmentation
and tracking, leveraging sequential information to increase segmentation
accuracy.
  We introduce a Deep Neural Network architecture taking advantage of a
self-attention mechanism which yields extremely low tracking error rate and
segmentation error rate. We demonstrate superior performance and speed compared
to state-of-the-art methods. Our method is named DiSTNet which stands for
DISTance+DISplacement Segmentation and Tracking Network.
  While this method is particularly well suited for mother machine microscopy
data, its general joint tracking and segmentation formulation could be applied
to many other problems with different geometries.


  The trilinear gauge boson couplings in the SU(3)_C X SU(3)_L X U(1)_N (3 - 3
- 1) models are presented. We find that new $Z_2$ does not interact with the
usual (in the standard model) gauge bosons $Z, W^\pm$. Based on these results,
production of new heavy gauge bosons at high energy colliders such as e^+ e^-
is calculated. We show that the cross sections obtained in the 3 - 3 - 1 model
with right-handed neutrinos can be one order bigger than the same in the
minimal 3 - 3 - 1 model.


  We apply a recently proposed theoretical concept and numerical approach to
obtain time delays in extreme ultraviolet (XUV) photoionization of an electron
in a short- or long-range potential. The results of our numerical simulations
on a space-time grid are compared to those for the well-known Wigner-Smith time
delay and different methods to obtain the latter time delay are reviewed. We
further use our numerical method to analyze the effect of a near-infrared
streaking field on the time delay obtained in the numerical simulations.


  In this paper we follow the general approach, proposed earlier by the first
author, which is derived from the invariant theory field and provides a way of
obtaining of the polynomial identities for any arbitrary polynomial family. We
introduce the notion of Chebyshev derivations of the first and second kinds,
which is based on the polynomial algebra, and corresponding specific
differential operators. We derive the elements of their kernels and prove that
any element of the kernel of the derivations defines a polynomial identity
satisfied by the Chebyshev polynomials of the first and second kinds. Combining
elementary methods and combinatorial techniques, we obtain several new
polynomial identities involving the Chebyshev polynomials of the both kinds and
a special case of the Jacobi polynomials. Using the properties of the
generalised hypergeometric function, we specify the Chebyshev polynomials of
the first and second kinds via the generalised hypergeometric function and, as
a consequence, derive the corresponding identities involving the generalised
hypergeometric function and the Chebyshev polynomials of the first and second
kinds.


  New expansions for some functions related to the Zeta function in terms of
the Pochhammer's polynomials are given (coefficients b(k), d(k), d_(k) and
d__(k). In some formal limit our expansion b(k) obtained via the alternating
series gives the regularized expansion of Maslanka for the Zeta function. The
real and the imaginary part of the function on the critical line is obtained
with a good accuracy up to Im(s) = t < 35.
  Then, we give the expansion (coefficient d_(k)) for the derivative of
ln((s-1)\zeta(s)). The critical function of the derivative, whose bounded
values for Re(s) > 1/2 at large values of k should ensure the truth of the
Riemann Hypothesis (RH), is obtained either by means of the primes or by means
of the zeros (trivial and non-trivial) of the Zeta function. In a numerical
experiment performed up to high values of k i.e. up to k = 10^13 we obtain a
very good agreement between the two functions, with the emergence of twelve
oscillations with stable amplitude.
  For a special case of values of the two parameters entering in the general
Pochhammer's expansion it is argued that the bound on the critical function
should be given by the Euler constant gamma.


  The smallest fullerene, dodecahedral C20, is studied using a one band Hubbard
model parameterized by U/t. Results are obtained using exact diagonalization of
matrices with linear dimensions as large as 5.7 x 10^9, supplemented by quantum
Monte Carlo. We report the magnetic and spectral properties of C20 as a
function of U/t and investigate electronic pair binding. Solid forms of C20 are
studied using cluster perturbation theory and evidence is found for a
metal-insulator transition at U ~ 4t. We also investigate the relevance of
strong correlations to the Jahn-Teller effect in C20.


  We propose a generalization of small world networks, in which the
reconnection of links is governed by a function that depends on the distance
between the elements to be linked. An adequate choice of this function lets us
control the clusterization of the system. Control of the clusterization, in
turn, allows the generation of a wide variety of topologies.


  We study the problem of rapid change of the interaction parameter (quench) in
many-body low-dimensional system. It is shown that, measuring correlation
functions after the quench the information about a spectrum of collective
excitations in a system can be obtained. This observation is supported by
analysis of several integrable models and we argue that it is valid for
non-integrable models as well. Our conclusions are supplemented by performing
exact numerical simulations on finite systems. We propose that measuring power
spectrum in dynamically split 1D Bose-Einsten condensate into two coupled
condensates can be used as experimental test of our predictions.


  Most observations of polluted white dwarf atmospheres are consistent with
accretion of water depleted planetary material. Among tens of known cases,
merely two cases involve accretion of objects that contain a considerable mass
fraction of water. The purpose of this study is to investigate the relative
scarcity of these detections. Based on a new and highly detailed model, we
evaluate the retention of water inside icy minor planets during the high
luminosity stellar evolution that follows the main sequence. Our model fully
considers the thermal, physical, and chemical evolution of icy bodies,
following their internal differentiation as well as water depletion, from the
moment of their birth and through all stellar evolution phases preceding the
formation of the white dwarf. We also account for different initial
compositions and formation times. Our results show that previous studies have
either underestimated or overestimated water retention. We also reaffirm that
water can survive in a variety of circumstances and in great quantities, and
therefore other possibilities are discussed in order to explain the infrequency
of water detections. We find that the most likely explanation is that water
does not survive the dissociation of tidally disrupted minor planets, and
instead a direct impact onto the white dwarf is required. We show that this
possibility is statistically plausible, and predict that if this hypothesis is
correct, future observations of extremely water rich atmospheres will involve
only helium dominated DB white dwarfs.


  Social determinants of health (SDoH) have an important impact on patient
outcomes but are incompletely collected from the electronic health records
(EHR). This study researched the ability of large language models to extract
SDoH from free text in EHRs, where they are most commonly documented, and
explored the role of synthetic clinical text for improving the extraction of
these scarcely documented, yet extremely valuable, clinical data. 800 patient
notes were annotated for SDoH categories, and several transformer-based models
were evaluated. The study also experimented with synthetic data generation and
assessed for algorithmic bias. Our best-performing models were fine-tuned
Flan-T5 XL (macro-F1 0.71) for any SDoH, and Flan-T5 XXL (macro-F1 0.70). The
benefit of augmenting fine-tuning with synthetic data varied across model
architecture and size, with smaller Flan-T5 models (base and large) showing the
greatest improvements in performance (delta F1 +0.12 to +0.23). Model
performance was similar on the in-hospital system dataset but worse on the
MIMIC-III dataset. Our best-performing fine-tuned models outperformed zero- and
few-shot performance of ChatGPT-family models for both tasks. These fine-tuned
models were less likely than ChatGPT to change their prediction when
race/ethnicity and gender descriptors were added to the text, suggesting less
algorithmic bias (p<0.05). At the patient-level, our models identified 93.8% of
patients with adverse SDoH, while ICD-10 codes captured 2.0%. Our method can
effectively extracted SDoH information from clinic notes, performing better
compare to GPT zero- and few-shot settings. These models could enhance
real-world evidence on SDoH and aid in identifying patients needing social
support.


  We present a novel technique to obtain relativistic corrections to the
central force problem in the Lagrangian formulation, using a generalized
potential energy function. We derive a general expression for a generalized
potential energy function for all powers of the velocity, which when made a
part of the regular classical Lagrangian can reproduce the correct
(relativistic) force equation. We then go on to derive the Hamiltonian and
estimate the corrections to the total energy of the system up to the fourth
power in $|\vec{v}|/c$. We found that our work is able to provide a more
comprehensive understanding of relativistic corrections to the central force
results and provides corrections to both the kinetic and potential energy of
the system. We employ our methodology to calculate relativistic corrections to
the circular orbit under the gravitational force and also the first-order
corrections to the ground state energy of the hydrogen atom using a
semi-classical approach. Our predictions in both problems give reasonable
agreement with the known results. Thus we feel that this work has pedagogical
value and can be used by undergraduate students to better understand the
central force and the relativistic corrections to it.


  Deep learning on the point cloud is increasingly developing. Grouping the
point with its neighbors and conducting convolution-like operation on them can
learn the local feature of the point cloud, but this method is weak to extract
the long-distance global feature. Performing the attention-based transformer on
the whole point cloud can effectively learn the global feature of it, but this
method is hardly to extract the local detailed feature. In this paper, we
propose a novel module that can simultaneously extract and fuse local and
global features, which is named as CT-block. The CT-block is composed of two
branches, where the letter C represents the convolution-branch and the letter T
represents the transformer-branch. The convolution-branch performs convolution
on the grouped neighbor points to extract the local feature. Meanwhile, the
transformer-branch performs offset-attention process on the whole point cloud
to extract the global feature. Through the bridge constructed by the feature
transmission element in the CT-block, the local and global features guide each
other during learning and are fused effectively. We apply the CT-block to
construct point cloud classification and segmentation networks, and evaluate
the performance of them by several public datasets. The experimental results
show that, because the features learned by CT-block are much expressive, the
performance of the networks constructed by the CT-block on the point cloud
classification and segmentation tasks achieve state of the art.


  In this letter, we reconsider a popular simplified received signal power
model with single stream beamforming employed by the transmitter and the
receiver in the regime when the beams have high gain and narrow beamwidth. We
define the correction factor as the ratio of the average actual received signal
power divided by the average received signal power using the popular simplified
model. We analytically quantify this factor for LOS and NLOS service and
interfering links under some assumptions. The analysis along with simulations
using a 3GPP compliant new radio (NR) channel model confirm the importance of
incorporating the correction factor in coverage analysis of wireless networks
that utilize the popular simplified received power model.


  ASAS, MACHO, OGLE and SAAO JHKL light curves of 13 stars, that have at some
time been classified as D-type symbiotics, are analysed. Most of the near-IR
light-curves that have been monitored over many years show long-term changes
due to variable dust obscuration, in addition to the stellar pulsation. The
distances to these objects are derived from the period-luminosity relation and
estimates of the mass-loss rates made from the Ko-[12] colour.
  We reclassify AS 245 as an S-type symbiotic, with a semi-regular cool
component with a pulsation period of about one year. The periods of the large
amplitude pulsations of SS73 38 (463 days), AS 210 (423 days) and H2-38 (395
days) are estimated for the first time, confirming that they are symbiotic
Miras.
  A comparison of the symbiotic Miras with normal Miras of similar pulsation
period shows that the symbiotic stars have on average higher values of Ko-[12].
This may indicate that they have higher mass-loss rates, or more likely that
the dust which is being lost by the Mira is trapped within the binary system.


  We study the ensemble optical variability of 276 FSRQs and 86 BL Lacs in the
Palomar-QUEST Survey with the goal of searching for common fluctuation
properties, examining the range of behavior across the sample, and
characterizing the appearance of blazars in such a survey so that future work
can more easily identify such objects. The survey, which covers 15,000 square
degrees multiple times over 3.5 years, allows for the first ensemble blazar
study of this scale. Variability amplitude distributions are shown for the FSRQ
and BL Lac samples for numerous time lags, and also studied through structure
function analyses. Individual blazars show a wide range of variability
amplitudes, timescales, and duty cycles. Of the best sampled objects, 35% are
seen to vary by more than 0.4 magnitudes; for these, the fraction of
measurements contributing to the high amplitude variability ranges constantly
from about 5% to 80%. Blazar variability has some similarities to that of type
I quasars but includes larger amplitude fluctuations on all timescales. FSRQ
variability amplitudes are particularly similar to those of QSOs on timescales
of several months, suggesting significant contributions from the accretion disk
to the variable flux at these timescales. Optical variability amplitudes are
correlated with the maximum apparent velocities of the radio jet for the subset
of FSRQs with MOJAVE VLBA measurements, implying that the optically variable
flux's strength is typically related to that of the radio emission. We also
study CRATES radio-selected FSRQ candidates, which show similar variability
characteristics to known FSRQs; this suggests a high purity for the CRATES
sample.


  We present EucliDreamer, a simple and effective method to generate textures
for 3D models given text prompts and meshes. The texture is parametrized as an
implicit function on the 3D surface, which is optimized with the Score
Distillation Sampling (SDS) process and differentiable rendering. To generate
high-quality textures, we leverage a depth-conditioned Stable Diffusion model
guided by the depth image rendered from the mesh. We test our approach on 3D
models in Objaverse and conducted a user study, which shows its superior
quality compared to existing texturing methods like Text2Tex. In addition, our
method converges 2 times faster than DreamFusion. Through text prompting,
textures of diverse art styles can be produced. We hope Euclidreamer proides a
viable solution to automate a labor-intensive stage in 3D content creation.


  Contact angle is an important parameter in characterizing the wetting
properties of fluids. The most common methods for measuring the contact angle
is to measure it directly from the profile curve of a sessile drop, a method
with certain inherent drawbacks. Here we describe an alternative method that
uses the height and volume of a sessile drop as constraints to construct its
profile by numerical integration of its two governing differential equations.
The integration yields, self consistently, the average value of the contact
angle along the entire contact line as well as the footprint radius of the drop
and its crown radius of curvature. As a test case, the new method is used to
obtain the contact angle of pure water on two different substrates, Teflon and
Lucite. For each substrate, four drops ranging in volume from 10 {\mu}l to 40
{\mu}l are used. The computed contact angles are consistent across the four
different drop sizes for each substrate and are in agreement with typical
literature values.


  Let $N$ be a point of an orbit closure $\bar{O_M}$ in a module variety such
that its orbit $O_N$ has codimension two in $\bar{O_M}$. We show that under
some additional conditions the pointed variety $(\bar{O_M},N)$ is smoothly
equivalent to a cone over a rational normal curve.


  We predict from a survey of equations of state and observations of X-ray
pulsations from SAX J1808.4-3658, that the upper limit of the mass of the
compact star is 2.27 solar mass. The corresponding upper limit of the radius
comes out to be 9.73 km. We also do a study to estimate the lower limit of the
mass of the compact star. Such a limit is very useful to put constraints on
equations of state. We also discuss the implications of the upper mass limit
for the detection of the source in radio frequencies. We point out that the
possible observation of radio-eclipse may be able to rule out several soft
equation of state models, by setting a moderately high value for the lower
limit of inclination angle.


  We present a supervised hyperspectral image segmentation algorithm based on a
convex formulation of a marginal maximum a posteriori segmentation with hidden
fields and structure tensor regularization: Segmentation via the Constraint
Split Augmented Lagrangian Shrinkage by Structure Tensor Regularization
(SegSALSA-STR). This formulation avoids the generally discrete nature of
segmentation problems and the inherent NP-hardness of the integer optimization
associated.
  We extend the Segmentation via the Constraint Split Augmented Lagrangian
Shrinkage (SegSALSA) algorithm by generalizing the vectorial total variation
prior using a structure tensor prior constructed from a patch-based Jacobian.
The resulting algorithm is convex, time-efficient and highly parallelizable.
This shows the potential of combining hidden fields with convex optimization
through the inclusion of different regularizers. The SegSALSA-STR algorithm is
validated in the segmentation of real hyperspectral images.


  We develop a perturbative model to treat the off-diagonal components in the
Hartree-Fock-Bogoliubov (HFB) transformation matrix, which are neglected in the
BCS approximation. Applying the perturbative model to a weakly bound nucleus
$^{84}$Ni, it is shown that the perturbative approach reproduces well the
solutions of the HFB method both for the quasi-particle energies and the radial
dependence of quasi-particle wave functions. We find that the non-resonant part
of the continuum single-particle state can acquire an appreciable occupation
probability when there exists a weakly bound state close to the Fermi surface.
This result originates from the strong coupling between the continuum particle
state and the weakly bound state, and is absent in the BCS approximation. The
limitation of the BCS approximation is pointed out in comparison with the HFB
and the present perturbative model.


  We present a unified direct calculation of the triple-pomeron coupling
$A_{3\Pom}(Q^{2})$ for diffractive real photoproduction ($Q^{2}=0$) and deep
inelastic scattering at large $Q^{2}$ in the framework of the dipole approach
to the generalized BFKL pomeron. The small phenomenological value of
$A_{3\Pom}(0)\approx 0.16$\,GeV$^{2}$, which was a mystery, is related to the
small correlation radius $R_{c}\approx 0.3$\,fm for the perturbative gluons. We
confirm the early expectations of weak $Q^{2}$ dependence of the dimensionfull
coupling $A_{3\Pom}(Q^{2})$ and predict that it rises by the factor $\sim 1.6$
from real photoproduction to deep inelastic scattering.


  Although at temperatures $T\gg \Lambda_{QCD}$ the quark-gluon plasma (QGP) is
a gas of weakly interacting quasiparticles (modulo long-range magnetism), it is
strongly interacting in the regime $T=(1-3) T_c$. As both heavy ion experiments
and lattice simulations are now showing, in this region the QGP displays rather
strong interactions between the constituents. In this paper we investigate the
relationship between four (previously disconnected) lattice results: {\bf i.}
spectral densities from MEM analysis of correlators; {\bf ii.} static quark
free energies $F(R)$; {\bf iii.} quasiparticle masses; {\bf iv.} bulk
thermodynamics $p(T)$. We show a high degree of consistency among them not
known before. The potentials $V(R)$ derived from $F(R)$ lead to large number of
binary bound states, mostly colored, in $gq, qq, gg$, on top of the usual $\bar
q q$ mesons. Using the Klein-Gordon equation and ({\bf ii-iii}) we evaluate
their binding energies and locate the zero binding endpoints on the phase
diagram, which happen to agree with ({\bf i}). We then estimate the
contribution of all states to the bulk thermodynamics in agreement with ({\bf
iv}). We also address a number of theoreticall issues related with to the role
of the quark/gluon spin in binding at large $\alpha_s$, although we do not yet
include those in our estimates. Also the issue of the transport properties
(viscosity, color conductivity) in this novel description of the QGP will be
addressed elsewhere.


  The extended nonlinear Schr\"{o}dinger (ENLS) equation with third-order term
and fourth-order term which describes the wave propagation in the optical
fibers is more accurate than the NLS equation. A study of high-order soliton
matrix is presented for an ENLS equation in the framework of the
Riemann-Hilbert problem (RHP). Through a standard dressing procedure and the
generalized Darboux transformation (gDT), soliton matrix for simple zeros and
elementary high-order zeros in the RHP for the ENLS equation are constructed.
Then the N-soliton solutions and high-order soliton solutions for the ENLS
equation can be determined. Moreover, collision dynamics along with the
asymptotic behavior for the two-solitons and long-time asymptotic estimations
for the high-order one-soliton are concretely analyzed. For the given spectral
parameters, we can control the propagation direction, velocity, width and other
physical quantities of solitons by adjusting the free parameters of ENLS
equation.


  Metal/two-dimensional carbon junctions are characterized by using a nanoprobe
in an ultrahigh vacuum environment. Significant differences were found in bias
voltage (V) dependence of differential conductance (dI/dV) between edge- and
side-contact; the former exhibits a clear linear relationship (i.e., dI/dV
\propto V), whereas the latter is characterized by a nonlinear dependence,
dI/dV \propto V3/2. Theoretical calculations confirm the experimental results,
which are due to the robust two-dimensional nature of the carbon materials
under study. Our work demonstrates the importance of contact geometry in
graphene-based electronic devices.


  We discuss the use of saddlepoint methods in the analysis of portfolios, with
particular reference to credit portfolios. The objective is to proceed from a
model of the loss distribution, given through probabilities, correlations and
the like, to an analytical approximation of the distribution. Once this is done
we show how to derive the so-called risk contributions which are the
derivatives of risk measures, such as a given quantile (VaR) or expected
shortfall, to the allocations in the underlying assets. These show, informally,
where the risk is coming from, and also indicate how to go about optimising the
portfolio.


  We have studied the origin of the broad and skewed feature at 4.5-7.5 keV in
the energy spectra of NGC4151 using the ASCA and RXTE data. The feature
consists of a narrow peak at 6.4 keV and a broad wing extended between 4.5-7.5
keV. An analysis of the long-term variations revealed that the feature became
variable only on a time scale longer than 1.5x10^6 s. Through a comparison with
the continuum variabilities, we found that the emission region of the excess
flux at 4.5-7.5 keV has an extent of 10^17 cm. The broad and skewed feature at
4.5-7.5 keV may be explained by the so-called ``disk-line'' model. If so, the
size of the line-emitting region, 10^17 cm, should be equal to several or
ten-times the Schwarzschild radius of the central black hole. This results in a
black hole mass of 10^11 solar mass, which may be too large for NGC4151. We
propose an alternative explanation for the broad and skewed feature, i.e. a
``reflection'' model, which can also reproduce the overall energy spectra very
well. In this model, cold matter with a sufficiently large column density is
irradiated by X-rays to produce a reflected continuum, which constitutes the
broad wing of the feature, and narrow fluorescent lines. The equivalent width
of the iron fluorescent line (~2 keV) and the upper limit of its width (sigma <
92 eV) are also consistent with this model. From these results and
considerations, we conclude that the ``disk-line'' model has difficulty to
explain the spectral variations of NGC4151, and the reflection model is more
plausible.


  Within the linearized three-dimensional theory of polymer gels, we consider a
sequence of problems formulated on a family of cylindrical domains whose height
tends to zero. We assume that the fluid pressure is controlled at the top and
bottom faces of the cylinder, and we consider two different scaling regimes for
the diffusivity tensor. Through asymptotic-analysis techniques we obtain two
plate models where the transverse displacement is governed by a plate equation
with an extra contribution from the fluid pressure. In the limit obtained
within the first scaling regime the fluid pressure is affine across the
thickness and hence it is determined by its instantaneous trace on the top and
bottom faces. In the second model, instead, the value of the fluid pressure is
governed by a three-dimensional diffusion equation.


  We investigate a flavored washout effect due to the decay of the lightest
right-handed neutrino, assuming that there is non-vanishing initial lepton
asymmetry and the decay of the lightest right-handed neutrinos gives negligible
contribution to the asymmetry. We figure out general features of the washout
effect. It is shown that there is a novel parameter region where an effect that
is negligible in most cases plays a critical role and a sizable lepton
asymmetry can survive against the washout process even in a strong washout
region.


  Assume that a Hamiltonian system is monotone. In this paper, we give several
characterizations on when such a system is Anosov. Assuming that a monotone
Hamiltonian system has no conjugate point, we show that there are two
distributions which are invariant under the Hamiltonian flow. We show that a
monotone Hamiltonian flow without conjugate point is Anosov if and only if
these distributions are transversal. We also show that if the reduced curvature
of the Hamiltonian system is non-positive, then the flow is Anosov if and only
if the reduced curvature is negative somewhere along each trajectory.


  The collaborative sensing of multiple Integrated sensing and communication
(ISAC) base stations is one of the important technologies to achieve
intelligent transportation. Interference elimination between ISAC base stations
is the prerequisite for realizing collaborative sensing. In this paper, we
focus on the mutual interference elimination problem in collaborative sensing
of multiple ISAC base stations that can communicate and radar sense
simultaneously by transmitting ISAC signals. We establish a mutual interference
model of multiple ISAC base stations, which consists of communication and radar
sensing related interference. Moreover, we propose a joint optimization
algorithm (JOA) to solve the collaborative precoding problem with total power
constraint (TPC) and perantenna power constraint (PPC). The optimal precoding
design can be obtained by using JOA to set appropriate tradeoff coefficient
between sensing and communication performance. The proposed collaborative
precoding design algorithm is evaluated by considering sensing and
communication performance via numerical results. The complexity of JOA for
collaborative precoding under TPC and PPC is also compared and simulated in
this paper.


  Deep convolutional neural networks have been proven successful in multiple
benchmark challenges in recent years. However, the performance improvements are
heavily reliant on increasingly complex network architecture and a high number
of parameters, which require ever increasing amounts of storage and memory
capacity. Depthwise separable convolution (DSConv) can effectively reduce the
number of required parameters through decoupling standard convolution into
spatial and cross-channel convolution steps. However, the method causes a
degradation of accuracy. To address this problem, we present depthwise
multiception convolution, termed Multiception, which introduces layer-wise
multiscale kernels to learn multiscale representations of all individual input
channels simultaneously. We have carried out the experiment on four benchmark
datasets, i.e. Cifar-10, Cifar-100, STL-10 and ImageNet32x32, using five
popular CNN models, Multiception achieved accuracy promotion in all models and
demonstrated higher accuracy performance compared to related works. Meanwhile,
Multiception significantly reduces the number of parameters of standard
convolution-based models by 32.48% on average while still preserving accuracy.


  Issued from Optimal Transport, the Wasserstein distance has gained importance
in Machine Learning due to its appealing geometrical properties and the
increasing availability of efficient approximations. In this work, we consider
the problem of estimating the Wasserstein distance between two probability
distributions when observations are polluted by outliers. To that end, we
investigate how to leverage Medians of Means (MoM) estimators to robustify the
estimation of Wasserstein distance. Exploiting the dual Kantorovitch
formulation of Wasserstein distance, we introduce and discuss novel MoM-based
robust estimators whose consistency is studied under a data contamination model
and for which convergence rates are provided. These MoM estimators enable to
make Wasserstein Generative Adversarial Network (WGAN) robust to outliers, as
witnessed by an empirical study on two benchmarks CIFAR10 and Fashion MNIST.
Eventually, we discuss how to combine MoM with the entropy-regularized
approximation of the Wasserstein distance and propose a simple MoM-based
re-weighting scheme that could be used in conjunction with the Sinkhorn
algorithm.


  The problem presented involves the development of a new analytical model for
the general fluid-solid temperature jump. To the best of our knowledge, there
are no analytical models that provide the accurate predictions of the
temperature jump for both gas and liquid systems. In this paper, a unified
model for the fluid-solid temperature jump has been developed based on our
adsorption model of the interfacial interactions. Results obtained from this
model are validated with available results from the literature.


  We present a weighted approach to compute a maximum cardinality matching in
an arbitrary bipartite graph. Our main result is a new algorithm that takes as
input a weighted bipartite graph $G(A\cup B,E)$ with edge weights of $0$ or
$1$. Let $w \leq n$ be an upper bound on the weight of any matching in $G$.
Consider the subgraph induced by all the edges of $G$ with a weight $0$.
Suppose every connected component in this subgraph has $\mathcal{O}(r)$
vertices and $\mathcal{O}(mr/n)$ edges. We present an algorithm to compute a
maximum cardinality matching in $G$ in $\tilde{\mathcal{O}}( m(\sqrt{w}+
\sqrt{r}+\frac{wr}{n}))$ time.
  When all the edge weights are $1$ (symmetrically when all weights are $0$),
our algorithm will be identical to the well-known Hopcroft-Karp (HK) algorithm,
which runs in $\mathcal{O}(m\sqrt{n})$ time. However, if we can carefully
assign weights of $0$ and $1$ on its edges such that both $w$ and $r$ are
sub-linear in $n$ and $wr=\mathcal{O}(n^{\gamma})$ for $\gamma < 3/2$, then we
can compute maximum cardinality matching in $G$ in $o(m\sqrt{n})$ time. Using
our algorithm, we obtain a new $\tilde{\mathcal{O}}(n^{4/3}/\varepsilon^4)$
time algorithm to compute an $\varepsilon$-approximate bottleneck matching of
$A,B\subset\mathbb{R}^2$ and an
$\frac{1}{\varepsilon^{\mathcal{O}(d)}}n^{1+\frac{d-1}{2d-1}}\mathrm{poly}\log
n$ time algorithm for computing $\varepsilon$-approximate bottleneck matching
in $d$-dimensions. All previous algorithms take $\Omega(n^{3/2})$ time. Given
any graph $G(A \cup B,E)$ that has an easily computable balanced vertex
separator for every subgraph $G'(V',E')$ of size $|V'|^{\delta}$, for
$\delta\in [1/2,1)$, we can apply our algorithm to compute a maximum matching
in $\tilde{\mathcal{O}}(mn^{\frac{\delta}{1+\delta}})$ time improving upon the
$\mathcal{O}(m\sqrt{n})$ time taken by the HK-Algorithm.


  We present the first direct constraints on a Degenerate Higher Order Scalar
Tensor (DHOST) inflation model using the Planck 2018 Cosmic Microwave
Background (CMB) results on non-Gaussianities. We identify that the bispectrum
consists of a fixed contribution following from the power spectrum and a linear
combination of terms depending on five free parameters defining the cubic
perturbations to the DHOST model. The former peaks in the squeezed limit, while
the latter is maximised in the equilateral limit. We directly confront the
model predictions to the CMB bispectrum statistics via the public code CMB-BEST
and marginalize over the free parameters. We explicitly show that there are
viable DHOST inflationary models satisfying both power spectrum and bispectrum
constraints from Planck. However, rather surprisingly, the constraints exclude
certain models at the $6\sigma$-level even though they pass the conventional
fudge factor tests. In this case and despite having a handful of free
parameters, the model's large squeezed bispectrum cannot be cancelled out
without introducing a large bispectrum in other limits which are strongly
constrained by Planck's non-detection of primordial non-Gaussianity. We
emphasize that first-order approximations such as fudge factors, albeit
commonly used in the literature, may be misleading and provide weaker
constraints. A proper analysis of the constraints from Planck requires a more
robust approach, such as the one provided by the CMB-BEST code.


  Let X=(x,y). Previously we have found all rational solutions of the
2-dimensional projective translation equation, or PrTE,
(1-z)f(X)=f(f(Xz)(1-z)/z); here f(X)=(u(x,y),v(x,y)) is a pair of two (real or
complex) functions. Solutions of this functional equation are called projective
flows. A vector field of a rational flow is a pair of 2-homogenic rational
functions. On the other hand, only special pairs of 2-homogenic rational
functions give rise to rational flows. In this paper we are interested in all
non-singular (satisfying the boundary condition) and unramified (without
branching points, i.e. single-valued functions in C^2\{union of curves})
projective flows whose vector field is still rational. We prove that, up to
conjugation with 1-homogenic birational plane transformation, these are of 6
types: 1) the identity flow; 2) one flow for each non-negative integer N -
these flows are rational of level N; 3) the level 1 exponential flow, which is
also conjugate to the level 1 tangent flow; 4) the level 3 flow expressable in
terms of Dixonian (equianharmonic) elliptic functions; 5) the level 4 flow
expressable in terms of lemniscatic elliptic functions; 6) the level 6 flow
expressable in terms of Dixonian elliptic functions again. This reveals another
aspect of the PrTE: in the latter four cases this equation is equivalent and
provides a uniform framework to addition formulas for exponential, tangent, or
special elliptic functions (also addition formulas for polynomials and the
logarithm, though the latter appears only in branched flows). Moreover, the
PrTE turns out to have a connection with Polya-Eggenberger urn models. Another
purpose of this study is expository, and we provide the list of open problems
and directions in the theory of PrTE; for example, we define the notion of
quasi-rational projective flows which includes curves of arbitrary genus.


  Here we prove that for a smooth projective variety $X$ of arbitrary dimension
and for a vector bundle $E$ over $X$, the Harder-Narasimhan filtration of a
Frobenius pull back of $E$ is a refinement of the Frobenius pull-back of the
Harder-Narasimhan filtration of $E$, provided there is a lower bound on the
characteristic $p$ (in terms of rank of $E$ and the slope of the destabilising
sheaf of the cotangent bundle of $X$). We also recall some examples, due to
Raynaud and Monsky,to show that some lower bound on $p$ is necessary. We
further prove an analogue of this result for principal $G$-bundles over $X$. We
also give a bound on the instability degree of the Frobenius pull back of $E$
in terms of the instability degree of $E$ and well defined invariants ot $X$
and $E$.


  Conversational recommender systems (CRS) aim to recommend high-quality items
to users through interactive conversations. Although several efforts have been
made for CRS, two major issues still remain to be solved. First, the
conversation data itself lacks of sufficient contextual information for
accurately understanding users' preference. Second, there is a semantic gap
between natural language expression and item-level user preference. To address
these issues, we incorporate both word-oriented and entity-oriented knowledge
graphs (KG) to enhance the data representations in CRSs, and adopt Mutual
Information Maximization to align the word-level and entity-level semantic
spaces. Based on the aligned semantic representations, we further develop a
KG-enhanced recommender component for making accurate recommendations, and a
KG-enhanced dialog component that can generate informative keywords or entities
in the response text. Extensive experiments have demonstrated the effectiveness
of our approach in yielding better performance on both recommendation and
conversation tasks.


  Owing to its unique geometry, the kagome lattice hosts various many-body
quantum states including frustrated magnetism, superconductivity, and
charge-density waves (CDWs), with intense efforts focused on kagome metals
exhibiting $2\times2$ CDWs associated with the nesting of van Hove saddle
points. Recently, a $\sqrt{3}\times\sqrt{3}$ CDW was discovered in the kagome
metal ScV$_6$Sn$_6$ below $T_{\rm CDW}\approx91$~K, whose underlying mechanism
and formation process remain unclear. Using inelastic X-ray scattering, we
discover a short-range $\sqrt{3}\times\sqrt{3}\times2$ CDW that is dominant in
ScV$_6$Sn$_6$ well above $T_{\rm CDW}$, distinct from the
$\sqrt{3}\times\sqrt{3}\times3$ CDW below $T_{\rm CDW}$. The short-range CDW
grows upon cooling, and is accompanied by the softening of phonons, indicative
of its dynamic nature. As the $\sqrt{3}\times\sqrt{3}\times3$ CDW appears, the
short-range CDW becomes suppressed, revealing a competition between these CDW
instabilities. Our first-principles calculations indicate that the
$\sqrt{3}\times\sqrt{3}\times2$ CDW is energetically favored, consistent with
experimental observations at high temperatures. However, the
$\sqrt{3}\times\sqrt{3}\times3$ CDW is selected as the ground state likely due
to a large wavevector-dependent electron-phonon coupling, which also accounts
for the enhanced electron scattering above $T_{\rm CDW}$. The competing CDW
instabilities in ScV$_6$Sn$_6$ lead to an unusual CDW formation process, with
the most pronounced phonon softening and the static CDW occurring at different
wavevectors.


  Photolithography is a process in the production of integrated circuits in
which a mask is used to create an exposed pattern with a desired geometric
shape. In the inverse problem of photolithography, a desired pattern is given
and the mask that produces an exposed pattern which is close to the desired one
is sought. We propose a variational approach formulation of this shape design
problem and introduce a regularization strategy. The main novelty in this work
is the regularization term that makes the thresholding operation involved in
photolithography stable. The potential of the method is demonstrated in
numerical experiments.


  We report first configuration interaction calculations of hyperfine constants
A_\parallel and the effective electric field W_d acting on the electric dipole
moment of the electron, in two excited electronic states of ^{207}PbO. The
obtained hyperfine constants, A_\parallel = -3826 MHz for the a(1) state and
A_\parallel = 4887 MHz for the B(1) state, are in very good agreement with the
experimental data, -4113 MHz and 5000 \pm 200 MHz, respectively. We find W_d =
-(6.1 ^{+1.8}_{-0.6}) 10^{24} Hz/(e cm) for a(1), and W_d = (8.0 \pm 1.6)
10^{24} Hz/(e cm) for B(1). The obtained values are analyzed and compared to
recent relativistic coupled cluster results and a semiempirical estimate of W_d
for the a(1) state.


  We discuss how seesaw neutrino models can be graphically represented in
lepton flavour space. We examine various popular models and show how this
representation helps understanding their properties and connection with
experimental data showing in particular how certain texture zero models are
ruled out. We also introduce a new matrix, the bridging matrix, that brings
from the light to the heavy neutrino mass flavour basis, showing how this is
related to the orthogonal matrix and how different quantities are easily
expressed through it. We then show how one can randomly generate orthogonal and
leptonic mixing matrices uniformly covering all flavour space in an unbiased
way (Haar-distributed matrices). Using the isomorphism between the group of
complex rotations and the Lorentz group, we also introduce the conceptof
Lorentz boost in flavour space for a seesaw model and how this has an
insightful physical interpretation. Finally, as a significant application, we
consider $N_2$-leptogenesis. Using current experimental values of low energy
neutrino parameters, we show that the probability that at least one flavoured
decay parameter of the lightest right-handed neutrino is smaller than unity is
about $49\%$ (to be compared with the tiny probability that the total decay
parameter is smaller than unity, $P(K_{\rm I}< 1)\sim 0.1 \%$, confirming the
crucial role played by flavour effects). On the other hand when $m_1 \gtrsim
0.1\,{\rm eV}$ this probability reduces to less than $5\%$, showing how also
$N_2$-leptogenesis disfavours degenerate light neutrinos.


  The main purpose of this paper is to show that a normalized non-steady
gradient Ricci soliton (M,g,f,{\lambda}) of dimension n is trivial if and only
if its scalar curvature S satisfies the equality S={\lambda}(f+(n/2)).


  With the epochal first detection of gravitational waves from a binary neutron
star (NS) merger with the GW170817 event, and its direct confirmation that
NS-NS mergers are significant sources of the of the r-process nucleosynthesis
of heavy elements, an immense new arena for prompt EM (X-rays through IR and
radio) studies of fundamental physics has been opened. Over the next decade, GW
observatories will expand in scale and sensitivity so the need for facilities
that can provide prompt, high sensitivity, broad-band EM followup becomes more
urgent. NS-NS or NS-black hole (BH) mergers will be instantly recognized (and
announced) by the LIGO-international collaboration. LSST will be a prime
resource for rapid tiling of what will usually be large (~10-100 degree
squared) error boxes. X-ray through IR Telescopes in space with (nearly)
full-sky access that can rapidly image and tile are crucial for providing the
earliest imaging and spectroscopic studies of the kilonova emission immediately
following NS-NS mergers. The Time-domain Spectroscopic Observatory (TSO) is a
proposed Probe-class 1.3 m telescope at L2, with imaging and spectroscopy (R =
200, 1800) in 4 bands (0.3 - 5 micron) and rapid slew capability to 90% of sky.
TSO nUV-mid-IR spectra will enable new constraints on NS structure and
nucleosynthesis.


  In this work, we present a robust and efficient solution for counting and
identifying train wagons using computer vision and deep learning. The proposed
solution is cost-effective and can easily replace solutions based on
radiofrequency identification (RFID), which are known to have high installation
and maintenance costs. According to our experiments, our two-stage methodology
achieves impressive results on real-world scenarios, i.e., 100% accuracy in the
counting stage and 99.7% recognition rate in the identification one. Moreover,
the system is able to automatically reject some of the train wagons
successfully counted, as they have damaged identification codes. The results
achieved were surprising considering that the proposed system requires low
processing power (i.e., it can run in low-end setups) and that we used a
relatively small number of images to train our Convolutional Neural Network
(CNN) for character recognition. The proposed method is registered, under
number BR512020000808-9, with the National Institute of Industrial Property
(Brazil).


  Recent works have demonstrated a surprisingly small variation of the
dust-to-metals ratio in different environments and a correlation between dust
extinction and the density of stars. Naively, one would interpret these
findings as strong evidence of cosmic dust being produced mainly by stars. But
other observational evidence suggest there is a significant variation of the
dust-to-metals ratio with metallicity. As we demonstrate in this paper, a
simple star-dust scenario is problematic also in the sense that it requires
that destruction of dust in the interstellar medium (e.g., due to passage of
supernova shocks) must be highly inefficient. We suggest a model where stellar
dust production is indeed efficient, but where interstellar dust growth is
equally important and acts as a replenishment mechanism which can counteract
the effects of dust destruction. This model appears to resolve the seemingly
contradictive observations, given that the ratio of the effective (stellar)
dust and metal yields is not universal and thus may change from one environment
to another, depending on metallicity.


  We determine the distribution of the $p$-torsion of Jacobian groups of metric
matroids, which are regular matroids that extend the notion of metric graphs.
We show that the Jacobian groups with nontrivial $p$-torsion correspond to
$\mathbb{F}_p$-rational points on configuration hypersurfaces. As a result, we
establish a connection between the distribution of their $p$-torsion and the
number of $\mathbb{F}_p$-rational points on these hypersurfaces. By counting
points over finite fields, we prove that this distribution is asymptotically
equivalent to $1/p$.


  I give a brief introduction to particle interactions based on representations
of Poincare Lie algebra. This is later generalized to interactions based on
representations of the supersymmetry Lie algebra. Globally supersymmetric
models with internal symmetry and locally supersymmetric models leading to
supergravity theories are presented. I also discuss higher dimensional
supergravity theories and some of their applications.


  In the standard Lambda cold dark matter paradigm, pure dark matter
simulations predict dwarf galaxies should inhabit dark matter haloes with a
centrally diverging density `cusp'. This is in conflict with observations that
typically favour a constant density `core'. We investigate this `cusp-core
problem' in `ultra-faint' dwarf galaxies simulated as part of the `Engineering
Dwarfs at Galaxy formation's Edge' (EDGE) project. We find, similarly to
previous work, that gravitational potential fluctuations within the central
region of the simulated dwarfs kinematically heat the dark matter particles,
lowering the dwarfs' central dark matter density. However, these fluctuations
are not exclusively caused by gas inflow/outflow, but also by impulsive heating
from minor mergers. We use the genetic modification approach on one of our
dwarf's initial conditions to show how a delayed assembly history leads to more
late minor mergers and, correspondingly, more dark matter heating. This
provides a mechanism by which even ultra-faint dwarfs ($M_* <
10^5\,\text{M}_{\odot}$), in which star formation was fully quenched at high
redshift, can have their central dark matter density lowered over time. In
contrast, we find that late major mergers can regenerate a central dark matter
cusp, if the merging galaxy had sufficiently little star formation. The
combination of these effects leads us to predict significant stochasticity in
the central dark matter density slopes of the smallest dwarfs, driven by their
unique star formation and mass assembly histories.


  We discuss a progress in calculation of Feynman integrals which has been done
with help of the Differential Equation Method and demonstrate the results for a
class of two-point two-loop diagrams.


  We theoretically demonstrate that earthquake shield made of seismic crystal
can damp down surface waves, which are the most destructive type for
constructions. In the paper, seismic crystal is introduced in aspect of band
gaps (Stop band) and some design concepts for earthquake and tsunami shielding
were discussed in theoretical manner. We observed in our FDTD based 2D elastic
wave simulations that proposed earthquake shield could provide about 0.5
reductions in magnitude of surface wave on the Richter scale. This reduction
rate in magnitude can considerably reduce destructions in the case of
earthquake.


  Let E be an operator algebra on a Hilbert space with finite-dimensional
generated C*-algebra. A classification is given of the locally finite algebras
and the operator algebras obtained as limits of direct sums of matrix algebras
over E with respect to star-extendible homomorphisms. The invariants in the
algebraic case consist of an additive semigroup, with scale, which is a right
module for the semiring $V_E = Hom_u(E \otimes \sK, E \otimes \sK)$ of unitary
equivalence classes of star-extendible homomorphisms. This semigroup is
referred to as the dimension module invariant. In the operator algebra case the
invariants consist of a metrized additive semigroup with scale and a
contractive right module $V_E$-action. Subcategories of algebras determined by
restricted classes of embeddings, such as 1-decomposable embeddings between
digraph algebras, are also classified in terms of simplified dimension module
invariants.


  Despite billions of hours of play and copious discussion online, mouse
sensitivity recommendations for first-person targeting tasks vary by a factor
of 10x or more and remain an active topic of debate in both competitive and
recreational gaming communities. Inspired by previous academic literature in
pointer-based gain optimization, we conduct the first user study of mouse
sensitivity in first person targeting tasks, reporting a statistically
significant range of optimal values in both task completion time and
throughput. Due to inherent incompatibility (i.e., lack of convert-ability)
between sensitivity metrics adopted for prior pointer-based gain literature and
those describing first-person targeting, we provide the first analytically
demonstrated, statistically significant optimal sensitivity range useful for
first-person camera controls. Furthermore, we demonstrate that this optimal
sensitivity range arises (at least in part) from a speed-precision trade-off
impacted by spatial task difficulty, similar to results reported in
pointer-based sensitivity literature previously.


  The calculated rate of events in some of the existing solar neutrino
detectors is directly proportional to the rate of the $^7$Be($p,\gamma)^8$B
reaction measured in the laboratory at low energies. However, the low-energy
cross sections of this reaction are quite uncertain as various measurements
differ from each other by 30-40 %. The Coulomb dissociation process which
reverses the radiative capture by the dissociation of $^8$B in the Coulomb
field of a target, provides an alternate way of accessing this reaction. While
this method has several advantages (like large breakup cross sections and
flexibility in the kinematics), the difficulties arise from the possible
interference by the nuclear interactions, uncertainties in the contributions of
the various multipoles and the higher order effects, which should be considered
carefully. We review the progress made so far in the experimental measurements
and theoretical analysis of the breakup of $^8$B and discuss the current status
of the low-energy cross sections (or the astrophysical $S$-factor) of the
$^7$Be($p,\gamma)^8$B reaction extracted therefrom. The future directions of
the experimental and theoretical investigations are also suggested.


  Matrix languages, including MATLAB and Octave, are established standards for
applications in science and engineering. They provide interactive programming
environments that are easy to use due to their scripting languages with matrix
data types. Current implementations of matrix languages do not fully utilise
high-performance, special-purpose chip architectures such as the IBM PowerXCell
processor (Cell), which is currently used in the fastest computer in the world.
  We present a new framework that extends Octave to harness the computational
power of the Cell. With this framework the programmer is relieved of the burden
of introducing explicit notions of parallelism. Instead the programmer uses a
new matrix data-type to execute matrix operations in parallel on the
synergistic processing elements (SPEs) of the Cell. We employ lazy evaluation
semantics for our new matrix data-type to obtain execution traces of matrix
operations. Traces are converted to data dependence graphs; operations in the
data dependence graph are lowered (split into sub-matrices), scheduled and
executed on the SPEs. Thereby we exploit (1) data parallelism, (2) instruction
level parallelism, (3) pipeline parallelism and (4) task parallelism of matrix
language programs. We conducted extensive experiments to show the validity of
our approach. Our Cell-based implementation achieves speedups of up to a factor
of 12 over code run on recent Intel Core2 Quad processors.


  This paper describes our contributions to the Shared Task of the 9th Workshop
on Argument Mining (2022). Our approach uses Large Language Models for the task
of Argument Quality Prediction. We perform prompt engineering using GPT-3, and
also investigate the training paradigms multi-task learning, contrastive
learning, and intermediate-task training. We find that a mixed prediction setup
outperforms single models. Prompting GPT-3 works best for predicting argument
validity, and argument novelty is best estimated by a model trained using all
three training paradigms.


  We study aspects of the enumeration of permutation classes, sets of
permutations closed downwards under the subpermutation order.
  First, we consider monotone grid classes of permutations. We present
procedures for calculating the generating function of any class whose matrix
has dimensions $m \times 1$ for some $m$, and of acyclic and unicyclic classes
of gridded permutations. We show that almost all large permutations in a grid
class have the same shape, and determine this limit shape.
  We prove that the growth rate of a grid class is given by the square of the
spectral radius of an associated graph and deduce some facts relating to the
set of grid class growth rates. In the process, we establish a new result
concerning tours on graphs. We also prove a similar result relating the growth
rate of a geometric grid class to the matching polynomial of a graph, and
determine the effect of edge subdivision on the matching polynomial. We
characterise the growth rates of geometric grid classes in terms of the
spectral radii of trees.
  We then investigate the set of growth rates of permutation classes and
establish a new upper bound on the value above which every real number is the
growth rate of some permutation class. In the process, we prove new results
concerning expansions of real numbers in non-integer bases in which the digits
are drawn from sets of allowed values.
  Finally, we introduce a new enumeration technique, based on associating a
graph with each permutation, and determine the generating functions for some
previously unenumerated classes. We conclude by using this approach to provide
an improved lower bound on the growth rate of the class of permutations
avoiding the pattern $1324$. In the process, we prove that, asymptotically,
patterns in {\L}ukasiewicz paths exhibit a concentrated Gaussian distribution.


  An open superstring field theory action has been proposed which does not
suffer from contact term divergences. In this paper, we compute the on-shell
four-point tree amplitude from this action using the Giddings map. After
including contributions from the quartic term in the action, the resulting
amplitude agrees with the first-quantized prescription.


  We introduce a new model of algorithmic tile self-assembly called
size-dependent assembly. In previous models, supertiles are stable when the
total strength of the bonds between any two halves exceeds some constant
temperature. In this model, this constant temperature requirement is replaced
by an nondecreasing temperature function $\tau : \mathbb{N} \rightarrow
\mathbb{N}$ that depends on the size of the smaller of the two halves. This
generalization allows supertiles to become unstable and break apart, and
captures the increased forces that large structures may place on the bonds
holding them together.
  We demonstrate the power of this model in two ways. First, we give fixed tile
sets that assemble constant-height rectangles and squares of arbitrary input
size given an appropriate temperature function. Second, we prove that deciding
whether a supertile is stable is coNP-complete. Both results contrast with
known results for fixed temperature.


  We carry out a completely first-principles study of the ferroelectric phase
transitions in BaTiO$_3$. Our approach takes advantage of two features of these
transitions: the structural changes are small, and only low-energy distortions
are important. Based on these observations, we make systematically improvable
approximations which enable the parameterization of the complicated energy
surface. The parameters are determined from first-principles total-energy
calculations using ultra-soft pseudopotentials and a preconditioned
conjugate-gradient scheme. The resulting effective Hamiltonian is then solved
by Monte Carlo simulation. The calculated phase sequence, transition
temperatures, latent heats, and spontaneous polarizations are all in good
agreement with experiment. We find the transitions to be intermediate between
order-disorder and displacive character. We find all three phase transitions to
be of first order. The roles of different interactions are discussed.


  We present Herschel/PACS observations of L1448-MM, a Class 0 protostar with a
prominent outflow. Numerous emission lines are detected at 55 < lambda < 210
micrometer including CO, OH, H2O, and [O I]. We investigate the spatial
distribution of each transition to find that lines from low energy levels tend
to distribute along the outflow direction while lines from high energy levels
peak at the central spatial pixel. Spatial maps reveal that OH emission lines
are formed in a relatively small area, while [O I] emission is extended.
According to the rotational diagram analysis, the CO emission can be fitted by
two (warm and hot) temperature components. For H2O, the ortho-to-para ratio is
close to 3. The non-LTE LVG calculations suggest that CO and H2O lines could
instead be formed in a high kinetic temperature (T > 1000 K) environment,
indicative of a shock origin. For OH, IR-pumping processes play an important
role in the level population. The molecular emission in L1448-MM is better
explained with a C-shock model, but the atomic emission of PACS [O I] and
Spitzer/IRS [Si II] emission is not consistent with C-shocks, suggesting
multiple shocks in this region. Water is the major line coolant of L1448-MM in
the PACS wavelength range, and the best-fit LVG models predict that H2O and CO
emit (50-80)% of their line luminosity in the PACS wavelength range.


  We present SCUBA-2 450{\mu}m and 850{\mu}m observations of the W40 complex in
the Serpens-Aquila region as part of the James Clerk Maxwell Telescope (JCMT)
Gould Belt Survey (GBS) of nearby star-forming regions. We investigate
radiative heating by constructing temperature maps from the ratio of SCUBA-2
fluxes using a fixed dust opacity spectral index, {\beta} = 1.8, and a beam
convolution kernel to achieve a common 14.8" resolution. We identify 82 clumps
ranging between 10 and 36K with a mean temperature of 20{\pm}3K. Clump
temperature is strongly correlated with proximity to the external OB
association and there is no evidence that the embedded protostars significantly
heat the dust. We identify 31 clumps that have cores with densities greater
than 105cm{^{-3}}. Thirteen of these cores contain embedded Class 0/I
protostars. Many cores are associated with bright-rimmed clouds seen in
Herschel 70 {\mu}m images. From JCMT HARP observations of the 12CO 3-2 line, we
find contamination of the 850{\mu}m band of up to 20 per cent. We investigate
the free-free contribution to SCUBA-2 bands from large-scale and ultracompact H
ii regions using archival VLA data and find the contribution is limited to
individual stars, accounting for 9 per cent of flux per beam at 450 {\mu}m or
12 per cent at 850 {\mu}m in these cases. We conclude that radiative heating
has potentially influenced the formation of stars in the Dust Arc sub-region,
favouring Jeans stable clouds in the warm east and fragmentation in the cool
west.


  Zero-knowledge proofs (zk-Proofs) are communication protocols by which a
prover can demonstrate to a verifier that it possesses a solution to a given
public problem without revealing the content of the solution. Arbitrary
computations can be transformed into an interactive zk-Proof so anyone is
convinced that it was executed correctly without knowing what was executed on,
having huge implications for digital currency. Despite this, interactive proofs
are not suited for blockchain applications but novel protocols such as
zk-SNARKs have made zero-knowledge ledgers like Zcash possible. This project
builds upon Wolfram's ZeroKnowledgeProofs paclet and implements a zk-SNARK
compiler based on Pinocchio protocol.


  This paper introduces the stochastic Fej\'{e}r-monotone hybrid steepest
descent method (S-FM-HSDM) to solve affinely constrained and composite convex
minimization tasks. The minimization task is not known exactly; noise
contaminates the information about the composite loss function and the affine
constraints. S-FM-HSDM generates sequences of random variables that, under
certain conditions and with respect to a probability space, converge point-wise
to solutions of the noiseless minimization task. S-FM-HSDM enjoys desirable
attributes of optimization techniques such as splitting of variables and
constant step size (learning rate). Furthermore, it provides a novel way of
exploiting the information about the affine constraints via fixed-point sets of
appropriate nonexpansive mappings. Among the offsprings of S-FM-HSDM, the
hierarchical recursive least squares (HRLS) takes advantage of S-FM-HSDM's
versatility toward affine constraints and offers a novel twist to LS by
generating sequences of estimates that converge to solutions of a hierarchical
optimization task: Minimize a convex loss over the set of minimizers of the
ensemble LS loss. Numerical tests on a sparsity-aware LS task show that HRLS
compares favorably to several state-of-the-art convex, as well as non-convex,
stochastic-approximation and online-learning counterparts.


  Given dense image feature correspondences of a non-rigidly moving object
across multiple frames, this paper proposes an algorithm to estimate its 3D
shape for each frame. To solve this problem accurately, the recent
state-of-the-art algorithm reduces this task to set of local linear subspace
reconstruction and clustering problem using Grassmann manifold representation
\cite{kumar2018scalable}. Unfortunately, their method missed on some of the
critical issues associated with the modeling of surface deformations, for e.g.,
the dependence of a local surface deformation on its neighbors. Furthermore,
their representation to group high dimensional data points inevitably introduce
the drawbacks of categorizing samples on the high-dimensional Grassmann
manifold \cite{huang2015projection, harandi2014manifold}. Hence, to deal with
such limitations with \cite{kumar2018scalable}, we propose an algorithm that
jointly exploits the benefit of high-dimensional Grassmann manifold to perform
reconstruction, and its equivalent lower-dimensional representation to infer
suitable clusters. To accomplish this, we project each Grassmannians onto a
lower-dimensional Grassmann manifold which preserves and respects the
deformation of the structure w.r.t its neighbors. These Grassmann points in the
lower-dimension then act as a representative for the selection of
high-dimensional Grassmann samples to perform each local reconstruction. In
practice, our algorithm provides a geometrically efficient way to solve dense
NRSfM by switching between manifolds based on its benefit and usage.
Experimental results show that the proposed algorithm is very effective in
handling noise with reconstruction accuracy as good as or better than the
competing methods.


  Using continuum extrapolated lattice data we trace a family of running
couplings in three-flavour QCD over a large range of scales from about 4 to 128
GeV. The scale is set by the finite space time volume so that recursive finite
size techniques can be applied, and Schr\"odinger functional (SF) boundary
conditions enable direct simulations in the chiral limit. Compared to earlier
studies we have improved on both statistical and systematic errors. Using the
SF coupling to implicitly define a reference scale $1/L_0\approx 4$ GeV through
$\bar{g}^2(L_0) =2.012$, we quote $L_0 \Lambda^{N_{\rm f}=3}_{\overline{\rm
MS}} =0.0791(21)$. This error is dominated by statistics; in particular, the
remnant perturbative uncertainty is negligible and very well controlled, by
connecting to infinite renormalization scale from different scales $2^n/L_0$
for $n=0,1,\ldots,5$. An intermediate step in this connection may involve any
member of a one-parameter family of SF couplings. This provides an excellent
opportunity for tests of perturbation theory some of which have been published
in a letter [1]. The results indicate that for our target precision of 3 per
cent in $L_0 \Lambda^{N_{\rm f}=3}_{\overline{\rm MS}}$, a reliable estimate of
the truncation error requires non-perturbative data for a sufficiently large
range of values of $\alpha_s=\bar{g}^2/(4\pi)$. In the present work we reach
this precision by studying scales that vary by a factor $2^5= 32$, reaching
down to $\alpha_s\approx 0.1$. We here provide the details of our analysis and
an extended discussion.


  By exploiting the modular RISC-V ISA this paper presents the customization of
instruction set with posit\textsuperscript{\texttrademark} arithmetic
instructions to provide improved numerical accuracy, well-defined behavior and
increased range of representable numbers while keeping the flexibility and
benefits of open-source ISA, like no licensing and royalty fee and community
development. In this work we present the design, implementation and integration
into the low-power Ibex RISC-V core of a full posit processing unit capable to
directly implement in hardware the four arithmetic operations (add, sub, mul,
div and fma), the inversion, the float-to-posit and posit-to-float conversions.
We evaluate speed, power and area of this unit (that we have called Full Posit
Processing Unit). The FPPU has been prototyped on Alveo and Kintex FPGAs, and
its impact on the metrics of the full-RISC-V core have been evaluated, showing
that we can provide real number processing capabilities to the mentioned core
with an increase in area limited to $7\%$ for 8-bit posits and to $15\%$ for
16-bit posits. Finally we present tests one the use of posits for deep neural
networks with different network models and datasets, showing minimal drop in
accuracy when using 16-bit posits instead of 32-bit IEEE floats.


  Given a quasi-median graph $X$, the crossing graph $\Delta X$ and the contact
graph $\Gamma X$ are natural hyperbolic models of $X$. In this article, we show
that the asymptotic translation length in $\Delta X$ or $\Gamma X$ of an
isometry of $X$ is always rational. Moreover, if $X$ is hyperbolic, these
rational numbers can be written with denominators bounded above uniformly; this
is not true in full generality. Finally, we show that, if the quasi-median
graph $X$ is constructible in some sense, then there exists an algorithm
computing the translation length of every computable isometry. Our results
encompass contact graphs in CAT(0) cube complexes and extension graphs of
right-angled Artin groups.


  We have conducted a comprehensive search for optical phase variations of all
planet candidates with tight orbits in fifteen quarters of data from the Kepler
space telescope. After correcting for systematics, we found eight systems that
appear to show secondary eclipses as well as phase variations. Of these, five
(Kepler-5, Kepler-6, Kepler-8, KOI-64 and KOI-2133) are new and three (TrES-2,
HAT-P-7 and KOI-13) have previously published phase curves, albeit with many
fewer observations. We model the full phase curve of each planet candidate,
including the primary and secondary transits, and derive their albedos, day-
and night-side temperatures, ellipsoidal variations and Doppler beaming. We
find that KOI-64 and KOI-2133 have night-side temperatures well above their
equilibrium values (while KOI-2133 also has an albedo >1), so we conclude that
they are likely to be self-luminous objects rather than planets. The
characteristics of the six other candidates are consistent with their being
planets with low geometric albedos (<0.3). For TrES-2 and KOI-13, the Kepler
bandpass appears to probe atmospheric layers hotter than the planet's
equilibrium temperature. For KOI-13, we detect a never-before-seen third cosine
harmonic with an amplitude of 6.7+/-0.3 ppm and a phase shift of -1.1+/-0.1
radians in the phase curve residual, which could be due to its spin-orbit
misalignment. We report derived planetary parameters for all six planets,
including masses from ellipsoidal variations and Doppler beaming, and compare
our results to published values when available. Our results nearly double the
number of Kepler exoplanets with measured phase curve variations, thus
providing valuable new constraints on the properties of close-in hot Jupiters.


  Let \Gamma be a finitely presentable pro-p group with a nontrivial finitely
generated closed normal subgroup N of infinite index. Then def(\Gamma)\leq 1,
and if def(\Gamma)=1 then \Gamma is a pro-p duality group of dimension 2, N is
a free pro-p group and \Gamma/N is virtually free. In particular, if the centre
of \Gamma is nontrivial and def(\Gamma)\geq 1, then def(\Gamma)=1, cd G \leq 2
and \Gamma is virtually a direct product F \times Z_p, with F a finitely
generated free pro-p group.


  Robot arms with lighter weight can reduce unnecessary energy consumption
which is desirable in robotic industry. However, lightweight arms undergo
undesirable elastic deformation. In this paper, the planar motion of a
lightweight flexible arm is investigated. In order to obtain a precise
mathematical model, the axial displacement and nonlinear curvature of flexible
arm arising from large bending deformation is taken into consideration. An
in-extensional condition, the axial displacement is related to transverse
displacement of the flexible beam, is applied. This leads to a robotic model
with three rigid modes and one elastic mode. The elastic mode depends on time
and position. An Assume Mode Method is used to remove the spatial dependence.
The governing equations is derived using Lagrange Method. The effects of
nonlinear terms due to the large deformation, gravity, and tip-mass are
considered. Control inputs include forces and moment exerted at the joint
between slider and arm (see Fig. 1). The conventional computed torque control
laws cannot stabilize the system, since there are not as many control inputs as
states of the system. A Particle Swarm Optimization (PSO) technique is then
used to obtain a suitable trajectory with the aim of minimizing excitations of
the elastic mode. Two methods are considered for generating a trajectory
function, either to use a three-layer Artificial Neural Network (ANN) or to use
spline interpolation. A sliding mode control strategy is proposed in which the
sliding surfaces include elastic mode in order to guarantee robustness. The
simulations show that the three-layer ANN technique provides arbitrary small
settling time, and also the optimization algorithm converges faster and
generates smooth trajectories unlike spline function technique.


  This paper concerns regular connections on trivial algebraic G-principal
fiber bundles over the infinitesimal punctured disc, where G is a connected
reductive linear algebraic group over an algebraically closed field of
characteristic zero. We show that the pull-back of every regular connection to
an appropriate covering of the infinitesimal punctured disc is gauge equivalent
to a connection of the form X z^{-1}dz for some X in the Lie algebra of G. We
may even arrange that the only rational eigenvalue of ad X is zero. Our results
allow a classification of regular SL_n-connections up to gauge equivalence.


  Two-pion interferometry measurements in $d$$+$Au and Au$+$Au collisions at
$\sqrt{s_{{NN}}}=200$ GeV are used to extract and compare the Gaussian source
radii R$_{{\rm out}}$, R$_{{\rm side}}$, and R$_{{\rm long}}$, which
characterize the space-time extent of the emission sources. The comparisons,
which are performed as a function of collision centrality and the mean
transverse momentum for pion pairs, indicate strikingly similar patterns for
the $d$$+$Au and Au$+$Au systems. They also indicate a linear dependence of
R$_{{\rm side}}$ on the initial transverse geometric size $\bar{R}$, as well as
a smaller freeze-out size for the $d$$+$Au system. These patterns point to the
important role of final-state rescattering effects in the reaction dynamics of
$d$$+$Au collisions.


  We present Spitzer Space Telescope and Chandra X-ray Observatory observations
of the composite Galactic supernova remnant Kes 75 (G29.7-0.3). We use the
detected flux at 24 microns and hot gas parameters from fitting spectra from
new, deep X-ray observations to constrain models of dust emission, obtaining a
dust-to-gas mass ratio M_dust/M_gas ~0.001. We find that a two-component
thermal model, nominally representing shocked swept-up interstellar or
circumstellar material and reverse-shocked ejecta, adequately fits the X-ray
spectrum, albeit with somewhat high implied densities for both components. We
surmise that this model implies a Wolf-Rayet progenitor for the remnant. We
also present infrared flux upper limits for the central pulsar wind nebula.


  A moving medium drags light along with it as measured by Fizeau and explained
by Einstein's theory of special relativity. Here we show that the same effect
can be obtained in a situation where there is no physical motion of the medium.
Modulations of both the permittivity and permeability, phased in space and time
in the form of travelling waves, are the basis of our model. Space-time
metamaterials are represented by effective bianisotropic parameters, which can
in turn be mapped to a moving homogeneous medium. Hence these metamaterials
mimic a relativistic effect without the need for any actual material motion. We
discuss how both the permittivity and permeability need to be modulated in
order to achieve these effects, and we present an equivalent transmission line
model.


  The CAST (CERN Axion Solar Telescope) experiment is searching for solar
axions by their conversion into photons inside the magnet pipe of an LHC
dipole. The analysis of the data recorded during the first phase of the
experiment with vacuum in the magnet pipes has resulted in the most restrictive
experimental limit on the coupling constant of axions to photons. In the second
phase, CAST is operating with a buffer gas inside the magnet pipes in order to
extent the sensitivity of the experiment to higher axion masses. We will
present the first results on the $^{4}{\rm He}$ data taking as well as the
system upgrades that have been operated in the last year in order to adapt the
experiment for the $^{3}{\rm He}$ data taking. Expected sensitivities on the
coupling constant of axions to photons will be given for the recent $^{3}{\rm
He}$ run just started in March 2008.


  We have investigated the electronic structure of polycrystalline
Ca$_2$FeReO$_6$ using photoemission spectroscopy and band-structure
calculations within the local-density approximation+$U$ (LDA+$U$) scheme. In
valence-band photoemission spectra, a double-peak structure which is
characteristic of the metallic double perovskite series has been observed near
the Fermi level ($E_{\rm F}$), although it is less distinct compared to the
Sr$_2$FeMoO$_6$ case. The leading near-$E_{\rm F}$ structure has a very weak
spectral weight at $E_{\rm F}$ above the metal-insulator transition (MIT)
temperature $T_{\rm MI}$ of $\sim$140 K, and it loses the $E_{\rm F}$ weight
below $T_{\rm MI}$, forming a small energy gap.
  To reproduce this small energy gap in the calculation, we require a very
large effective $U$ ($U_{\rm eff}$) for Re (4 eV) in addition to a relatively
large $U_{\rm eff}$ for Fe (4 eV). Although the most of the experimental
features can be interpreted with the help of the band theory, the overall
agreement between the theory and the experiment was not satisfactory. We
demonstrate that the effective transfer integral between Fe and Re is actually
smaller than that between Fe and Mo in Ca$_2$FeMoO$_6$, which can explain both
MIT and very high ferrimagnetic transition temperature.


  Adiabatic approximations are a powerful tool for simplifying nonlinear
quantum dynamics, and are applicable whenever a system exhibits a hierarchy of
time scales. Current interest in small nonlinear quantum systems, such as
few-mode Bose-Hubbard models, warrants further development of adiabatic methods
in the particular context of these models. Here we extend our recent work on a
simple four-mode Bose-Hubbard model with two distinct dynamical time scales, in
which we showed that among the perturbations around excited stationary states
of the system is a slow collective excitation that is not present in the
Bogoliubov spectrum. We characterized this mode as a resonant energy exchange
with its frequency shifted by nonlinear effects, and referred to it as a second
Josephson oscillation, in analogy with the second sound mode of liquid helium
II. We now generalize our previous theory beyond the mean field regime, and
construct a general Bogoliubov free quasiparticle theory that explicitly
respects the system's adiabatic invariant as well the exact conservation of
particles. We compare this theory to the numerically exact quantum energy
spectrum with up to forty particles, and find good agreement over a significant
range of parameter space.


  In the Correlation Clustering problem, we are given a set of objects with
pairwise similarity information. Our aim is to partition these objects into
clusters that match this information as closely as possible. More specifically,
the pairwise information is given as a weighted graph $G$ with its edges
labelled as ``similar" or ``dissimilar" by a binary classifier. The goal is to
produce a clustering that minimizes the weight of ``disagreements": the sum of
the weights of similar edges across clusters and dissimilar edges within
clusters. In this exposition we focus on the case when $G$ is complete and
unweighted. We explore four approximation algorithms for the Correlation
Clustering problem under this assumption. In particular, we describe the
following algorithms: (i) the $17429-$approximation algorithm by Bansal, Blum,
and Chawla, (ii) the $4-$approximation algorithm by Charikar, Guruswami, and
Wirth (iii) the $3-$approximation algorithm by Ailon, Charikar, and Newman (iv)
the $2.06-$approximation algorithm by Chawla, Makarychev, Schramm, and
Yaroslavtsev.


  We study the $p$-rank stratification of the moduli space of cyclic degree
$\ell$ covers of the projective line in characteristic $p$ for distinct primes
$p$ and $\ell$. The main result is about the intersection of the $p$-rank $0$
stratum with the boundary of the moduli space of curves. When $\ell=3$ and $p
\equiv 2 \bmod 3$ is an odd prime, we prove that there exists a smooth
trielliptic curve in characteristic $p$, with every genus $g$, signature type
$(r,s)$ and $p$-rank $f$ satisfying the clear necessary conditions.


  We consider a sequence of sums of powers of the the roots of the cubic
equation characterizing the Tribonacci sequences and derive its relationship
with a particular Tribonacci sequence. Then we make a conjecture on the
possible generalization.


  In the present paper construction of the modified function of Green equation
for internal gravity waves in the stratum of the stratified medium at presence
of constant average flows is considered, properties of the corresponding
spectral problems, the modified eigenfunctions and eigenvalues are
investigated. Usage of the modified function of Green equation can give in some
physically interesting events more friendly representations of the solutions
for the fields of the internal gravity waves, including the wave fields
disturbed by the non-local disturbing bodies.


  We introduce the $(j,k)$-Kemeny rule -- a generalization of Kemeny's voting
rule that aggregates $j$-chotomous weak orders into a $k$-chotomous weak order.
Special cases of $(j,k)$-Kemeny include approval voting, the mean rule and
Borda mean rule, as well as the Borda count and plurality voting. Why, then, is
the winner problem computationally tractable for each of these other rules, but
intractable for Kemeny? We show that intractability of winner determination for
the $(j,k)$-Kemeny rule first appears at the $j=3$, $k=3$ level. The proof
rests on a reduction of max cut to a related problem on weighted tournaments,
and reveals that computational complexity arises from the cyclic part in the
fundamental decomposition of a weighted tournament into cyclic and cocyclic
components. Thus the existence of majority cycles -- the engine driving both
Arrow's impossibility theorem and the Gibbard-Satterthwaite theorem -- also
serves as a source of computational complexity in social choice.


  The one-dimensional ($1D$) Galerkin-truncated Burgers equation, with both
dissipation and noise terms included, is studied using spectral methods. When
the truncation-scale Reynolds number $R_{\rm min}$ is varied, from very small
values to order $1$ values, the scale-dependent correlation time $\tau(k)$ is
shown to follow the expected crossover from the short-distance $\tau(k) \sim
k^{-2}$ Edwards-Wilkinson scaling to the universal long-distance
Kardar-Parisi-Zhang scaling $\tau(k) \sim k^{-3/2}$. In the inviscid limit:
$R_{\rm min}\to \infty$, we show that the system displays {\it another}
crossover to the Galerkin-truncated inviscid-Burgers regime that admits
thermalised solutions with $\tau(k) \sim k^{-1}$. The scaling form of the
time-correlation functions are shown to follow the known analytical laws and
the skewness and excess kurtosis of the interface increments distributions are
characterised.


  We argue that standard tools of holography can be used to describe fully
non-perturbative microscopic models of cosmology in which a period of
accelerated expansion may result from the positive potential energy of
time-dependent scalar fields evolving towards a region with negative potential.
In these models, the fundamental cosmological constant is negative, and the
universe eventually recollapses in a time-reversal symmetric way. The
microscopic description naturally selects a special state for the cosmology. In
this framework, physics in the cosmological spacetime is dual to the vacuum
physics in a static planar asymptotically AdS Lorentzian wormhole spacetime, in
the sense that the background spacetimes and observables are related by
analytic continuation. The dual spacetime is weakly curved everywhere, so any
cosmological observables can be computed in the dual picture via effective
field theory without detailed knowledge of the UV completion or the physics
near the big bang. In particular, while inflation may explain the origin of
perturbations in the cosmology picture, the perturbations can be deduced from
the dual picture without any knowledge of the inflationary potential.


  We investigate a system of harmonically coupled identical nonlinear
constituents subject to noise in different spatial arrangements. For global
coupling we find for infinitely many constituents the coexistence of several
ergodic components and a bifurcation behaviour like in first order phase
transitions. These results are compared with simulations for finite systems
both for global coupling and for nearest neighbour coupling on two- and
three-dimensional cubic lattices. The mean-field type results for global
coupling provide a better understanding of the more complex behaviour in the
latter case.


  In this research, we compare malware detection techniques based on static,
dynamic, and hybrid analysis. Specifically, we train Hidden Markov Models (HMMs
) on both static and dynamic feature sets and compare the resulting detection
rates over a substantial number of malware families. We also consider hybrid
cases, where dynamic analysis is used in the training phase, with static
techniques used in the detection phase, and vice versa. In our experiments, a
fully dynamic approach generally yields the best detection rates. We discuss
the implications of this research for malware detection based on hybrid
techniques.


  The drag force and diffusion coefficients for a D meson are calculated in hot
dense matter composed of light mesons and baryons, such as it is formed in
heavy-ion collisions. We use a unitarized approach based on effective models
for the interaction of a D meson with hadrons, which are compatible with chiral
and heavy quark symmetries. We study the propagation of the D meson in the
hadron matter in two distinct cases. On the one hand, we analyze the
propagation of D mesons in matter at vanishing baryochemical potential, which
is relevant for high-energetic collisions at LHC or RHIC. On the other hand, we
show the propagation of D mesons in the hadronic medium following isentropic
trajectories, appropiate at FAIR and NICA heavy-ion experiments. We find a
negligible baryon contribution to the transport coefficients at vanishing
chemical potential. However at finite baryochemical potential we obtain a large
correction to the transport coefficients with the inclusion of nucleons and
Delta baryons. The relaxation time for D mesons is reduced a factor 2-3 in the
later case, producing a more thermalized D meson-spectrum for FAIR physics than
for the typical LHC energies. We finally present results for the spatial
diffusion coefficient of a D meson in hadronic matter and the possible
existence of a minimum near the phase transition to the quark-gluon plasma at
zero and finite baryochemical potential.


  The extraordinary success of the Standard Model asks for a more rigorous
control beyond the perturbative approach, which is affected by mathematical
problems (interaction picture and canonical quantization, non-convergence of
the perturbative series, trivialy results for the $\ph^4$ model and related
models etc.). We shall briefly discuss sone non-perturbative results concerning
the crucial role and realization of symmetry breakings in the Standard Model.


  Parametric imaging is a compartmental approach that processes nuclear imaging
data to estimate the spatial distribution of the kinetic parameters governing
tracer flow. The present paper proposes a novel and efficient computational
method for parametric imaging which is potentially applicable to several
compartmental models of diverse complexity and which is effective in the
determination of the parametric maps of all kinetic coefficients. We consider
applications to [{18}F]-fluorodeoxyglucose Positron Emission Tomography
(FDG-PET) data and analyze the two-compartment catenary model describing the
standard FDG metabolization by an homogeneous tissue and the three-compartment
non-catenary model representing the renal physiology. We show uniqueness
theorems for both models. The proposed imaging method starts from the
reconstructed FDG-PET images of tracer concentration and preliminarily applies
image processing algorithms for noise reduction and image segmentation. The
optimization procedure solves pixelwise the non-linear inverse problem of
determining the kinetic parameters from dynamic concentration data through a
regularized Gauss-Newton iterative algorithm. The reliability of the method is
validated against synthetic data, for the two-compartment system, and
experimental real data of murine models, for the renal three-compartment
system.