  In this paper we use an exact method to impose unitarity on moduli of
neutrino PMNS matrix recently determined, and show how one could obtain
information on CP nonconservation from a limited experimental information. One
suggests a novel type of global fit by expressing all theoretical quantities in
terms of convention independent parameters: the Jarlskog invariant $J$ and the
moduli $|U_{\alpha i}|$, able to resolve the positivity problem of $|U_{e 3}|$.
In this way the fit will directly provide a value for $J$, and if it is
different from zero it will prove the existence of CP violation in the
available experimental data. If the best fit result, $|U_{e3}|^2<0$, from M.
Maltoni {\em et al}, [New J.Phys. {\bf 6} (2004) 122] is confirmed, it will
imply a new physics in the leptonic sector.


  We propose an interesting BPS/CFT correspondence playground: the correlation
function of two intersecting half-BPS surface defects in four-dimensional
$\mathcal{N}=2$ supersymmetric $SU(N)$ gauge theory with $2N$ fundamental
hypermultiplets. We show it satisfies a difference equation, the fractional
quantum T-Q relation. Its Fourier transform is the $5$-point conformal block of
the $\widehat{\mathfrak{sl}}_N$ current algebra with one of the vertex
operators corresponding to the $N$-dimensional $\mathfrak{sl}_N$
representation, which we demonstrate with the help of the
Knizhnik-Zamolodchikov equation. We also identify the correlator with a state
of the $XXX_{\mathfrak{sl}_2}$ spin chain of $N$ Heisenberg-Weyl modules over
$Y(\mathfrak{sl}_2)$. We discuss the associated quantum Lax operators, and
connections to isomonodromic deformations.


  This paper investigates the secure resource allocation for a downlink
integrated sensing and communication system with multiple legal users and
potential eavesdroppers. In the considered model, the base station (BS)
simultaneously transmits sensing and communication signals through beamforming
design, where the sensing signals can be viewed as artificial noise to enhance
the security of communication signals. To further enhance the security in the
semantic layer, the semantic information is extracted from the original
information before transmission. The user side can only successfully recover
the received information with the help of the knowledge base shared with the
BS, which is stored in advance. Our aim is to maximize the sum semantic secrecy
rate of all users while maintaining the minimum quality of service for each
user and guaranteeing overall sensing performance. To solve this sum semantic
secrecy rate maximization problem, an iterative algorithm is proposed using the
alternating optimization method. The simulation results demonstrate the
superiority of the proposed algorithm in terms of secure semantic communication
and reliable detection.


  We study optical activity induced by curvature. The optical activity model we
present has two phenomenological gyration parameters, within which we analyze
three model cases, namely, an exactly integrable model, the Landau-Lifshitz
model and the Fedorov model, these latter two are solved in the short
wavelength approximation. The model background is a gravitational pp-wave. The
solutions show that the optical activity induced by curvature leads to Faraday
rotation.


  Organizations are collecting increasingly large amounts of data for data
driven decision making. These data are often dumped into a centralized
repository, e.g., a data lake, consisting of thousands of structured and
unstructured datasets. Perversely, such mixture of datasets makes the problem
of discovering elements (e.g., tables or documents) that are relevant to a
user's query or an analytical task very challenging. Despite the recent efforts
in data discovery, the problem remains widely open especially in the two fronts
of (1) discovering relationships and relatedness across structured and
unstructured datasets where existing techniques suffer from either scalability,
being customized for a specific problem type (e.g., entity matching or data
integration), or demolishing the structural properties on its way, and (2)
developing a holistic system for integrating various similarity measurements
and sketches in an effective way to boost the discovery accuracy. In this
paper, we propose a new data discovery system, named CMDL, for addressing these
two limitations. CMDL supports the data discovery process over both structured
and unstructured data while retaining the structural properties of tables.


  We investigate integer and fractional quantum Hall states in quantum point
contacts (QPCs) of different geometries, defined in AlGaAs/GaAs
heterostructures employing different doping and screening techniques. We find
that, even in the highest mobility samples, interference and localization
strongly influence the transport properties. We propose microscopic models for
these effects, based on single- and many-electron physics. For integer quantum
Hall states, transport is modulated due to the self-consistent formation of
compressible regions of enhanced or reduced density in the incompressible
region of the constriction. In the fractional quantum Hall regime, we observe
the localization of fractionally charged quasi-particles in the constriction
and an interplay of single- and many-electron physics. At low electron
densities and in comparatively weak magnetic fields, single-electron
interference dominates transport. Utilizing optimized growth and gating
techniques, the $\nu$=5/2 state can be observed in a QPC, conserving the bulk
properties in an unprecedented quality. Our results might improve the
understanding of the influence of localization on the transmission properties
of QPCs, which is necessary for the interpretation of interference experiments
employing QPCs, especially at $\nu$=5/2.


  The outbreak of novel coronavirus disease (COVID- 19) has claimed millions of
lives and has affected all aspects of human life. This paper focuses on the
application of deep learning (DL) models to medical imaging and drug discovery
for managing COVID-19 disease. In this article, we detail various medical
imaging-based studies such as X-rays and computed tomography (CT) images along
with DL methods for classifying COVID-19 affected versus pneumonia. The
applications of DL techniques to medical images are further described in terms
of image localization, segmentation, registration, and classification leading
to COVID-19 detection. The reviews of recent papers indicate that the highest
classification accuracy of 99.80% is obtained when InstaCovNet-19 DL method is
applied to an X-ray dataset of 361 COVID-19 patients, 362 pneumonia patients
and 365 normal people. Furthermore, it can be seen that the best classification
accuracy of 99.054% can be achieved when EDL_COVID DL method is applied to a CT
image dataset of 7500 samples where COVID-19 patients, lung tumor patients and
normal people are equal in number. Moreover, we illustrate the potential DL
techniques in drug or vaccine discovery in combating the coronavirus. Finally,
we address a number of problems, concerns and future research directions
relevant to DL applications for COVID-19.


  Uncovering human mobility patterns is of fundamental importance to the
understanding of epidemic spreading, urban transportation and other
socioeconomic dynamics embodying spatiality and human travel. According to the
direct travel diaries of volunteers, we show the absence of scaling properties
in the displacement distribution at the individual level,while the aggregated
displacement distribution follows a power law with an exponential cutoff. Given
the constraint on total travelling cost, this aggregated scaling law can be
analytically predicted by the mixture nature of human travel under the
principle of maximum entropy. A direct corollary of such theory is that the
displacement distribution of a single mode of transportation should follow an
exponential law, which also gets supportive evidences in known data. We thus
conclude that the travelling cost shapes the displacement distribution at the
aggregated level.


  We derive an expression for the capacity of massive multiple-input
multiple-output Millimeter wave (mmWave) channel where the receiver is equipped
with a variable-resolution Analog to Digital Converter (ADC) and a hybrid
combiner. The capacity is shown to be a function of Cramer-Rao Lower Bound
(CRLB) for a given bit-allocation matrix and hybrid combiner. The condition for
optimal ADC bit-allocation under a receiver power constraint is derived. This
is derived based on the maximization of capacity with respect to bit-allocation
matrix for a given channel, hybrid precoder, and hybrid combiner. It is shown
that this condition coincides with that obtained using the CRLB minimization
proposed by Ahmed et al. Monte-carlo simulations show that the capacity
calculated using the proposed condition matches very closely with the capacity
obtained using the Exhaustive Search bit allocation.


  We study two versions of quasicrystal model, both subcases of Jacobi
matrices. For Off-diagonal model, we show an upper bound of dynamical exponent
and the norm of the transfer matrix. We apply this result to the Off-diagonal
Fibonacci Hamiltonian and obtain a sub-ballistic bound for coupling large
enough. In diagonal case, we improve previous lower bounds on the fractal
box-counting dimension of the spectrum.


  We study the costs and benefits of different quantum approaches to finding
approximate solutions of constrained combinatorial optimization problems with a
focus on Maximum Independent Set. In the Lagrange multiplier approach we
analyze the dependence of the output on graph density and circuit depth. The
Quantum Alternating Ansatz Approach is then analyzed and we examine the
dependence on different choices of initial states. The Quantum Alternating
Ansatz Approach, although powerful, is expensive in terms of quantum resources.
A new algorithm based on a "Dynamic Quantum Variational Ansatz" (DQVA) is
proposed that dynamically changes to ensure the maximum utilization of a fixed
allocation of quantum resources. Our analysis and the new proposed algorithm
can also be generalized to other related constrained combinatorial optimization
problems.


  We have investigated the growth of Escherichia coli E.coli, a mesophilic
bacterium, as a function of pressure $P$ and temperature $T$. E.coli can grow
and divide in a wide range of pressure (1-400atm) and temperature
($23-40^{\circ}$C). For $T>30^{\circ}$ C, the division time of E.coli increases
exponentially with pressure and exhibit a departure from exponential behavior
at pressures between 250-400 atm for all the temperatures studied in our
experiments. For $T<30^{\circ}$ C, the division time shows an anomalous
dependence on pressure -- first decreases with increasing pressure and then
increases upon further increase of pressure. The sharp change in division time
is followed by a sharp change in phenotypic transition of E. Coli at high
pressures where bacterial cells switch to an elongating cell type. We propose a
model that this phenotypic changes in bacteria at high pressures is an
irreversible stochastic process whereas the switching probability to elongating
cell type increases with increasing pressure. The model fits well the
experimental data. We discuss our experimental results in the light of
structural and thus functional changes in proteins and membranes.


  We solve the following problem. Given a continuous complex-valued potential
q_1 defined on a segment [-a,a] and let q_2 be the potential of a Darboux
transformed Schr\"odinger operator. Suppose a transmutation operator T_1 for
the potential q_1 is known such that the corresponding Schr\"odinger operator
is transmuted into the operator of second derivative. Find an analogous
transmutation operator T_2 for the potential q_2.
  It is well known that the transmutation operators can be realized in the form
of Volterra integral operators with continuously differentiable kernels. Given
a kernel K_1 of the transmutation operator T_1 we find the kernel K_2 of T_2 in
a closed form in terms of K_1. As a corollary interesting commutation relations
between T_1 and T_2 are obtained which then are used in order to construct the
transmutation operator for the one-dimensional Dirac system with a scalar
potential.


  Existing proactive caching policies are designed by assuming that all users
request contents with identical activity level at uniformly-distributed or
known locations, among which most of the policies are optimized by assuming
that user preference is identical to content popularity. However, these
assumptions are not true based on recent data analysis. In this paper, we
investigate what happens without these assumptions. To this end, we establish a
framework to optimize caching policy for base stations exploiting heterogeneous
user preference, activity level, and spatial locality. We derive success
probability and average rate of each user as utility function, respectively,
and obtain the optimal caching policy maximizing a weighted sum of average
utility (reflecting network performance) and minimal utility of users
(reflecting user fairness). To investigate the intertwined impact of individual
user request behavior on caching, we provide an algorithm to synthesize user
preference from given content popularity and activity level with controlled
preference similarity, and validate the algorithm with real datasets. Analysis
and simulation results show that exploiting individual user behavior can
improve both network performance and user fairness, and the gain increases with
the skewness of spatial locality, and the heterogeneity of user preference and
activity level.


  We utilize the hydrodynamic and N-body code {\small GIZMO} coupled with our
newly developed sub-grid Population~III (Pop~III) Legacy model, designed
specifically for cosmological volume simulations, to study the baseline metal
enrichment from Pop~III star formation at $z>7$. In this idealized numerical
experiment, we only consider Pop~III star formation. We find that our model
Pop~III star formation rate density (SFRD), which peaks at $\sim 10^{-3}\ {\rm
M_\odot yr^{-1} Mpc^{-1}}$ near $z\sim10$, agrees well with previous numerical
studies and is consistent with the observed estimates for Pop~II SFRDs. The
mean Pop~III metallicity rises smoothly from $z=25-7$, but does not reach the
critical metallicity value, $Z_{\rm crit}=10^{-4}\ Z_\odot$, required for the
Pop~III to Pop~II transition in star formation mode until $z\simeq7$. This
suggests that, while individual halos can suppress in-situ Pop~III star
formation, the external enrichment is insufficient to globally terminate
Pop~III star formation. The maximum enrichment from Pop~III star formation in
star forming dark matter halos is $Z\sim10^{-2}\ Z_\odot$, whereas the minimum
found in externally enriched haloes is $Z\gtrsim10^{-7}\ Z_\odot$. Finally,
mock observations of our simulated IGM enriched with Pop~III metals produce
equivalent widths similar to observations of an extremely metal poor damped
Lyman alpha (DLA) system at $z=7.04$, which is thought to be enriched by
Pop~III star formation only.


  Let $H$ be a group, $m$ be a positive integer, $Ext_m H$ be the set of all
isomorphic in $G$ classes of group monomorphisms $\varphi: H \rightarrow G$
such that index of $\varphi(H)$ in $G$ is $m$. The main goal of this paper is
to describe the elements of $Ext_m H$ in terms of a new concept of hypergroups
over the group. The obtained result is a very broad generalization of the
Schreier theorem (1926). As an application, a series of intermediate
generalizations is obtained; particularly, a description of the set $Ext (H,
Q)$ of isomorphic classes of all extensions of a noncommutative group $H$ by
$Q$.


  We investigate the collider signatures of the three benchmark points in the
singlet fermionic dark matter model. The benchmark points, which were
introduced previously to explain the Fermi gamma-ray excess by dark matter (DM)
pair annihilation at the Galactic center, have definite predictions for future
collider experiments such as the International Linear Collider and the
High-Luminosity LHC. We consider four collider observables: (1) Higgs signal
strength (essentially $hZZ$ coupling), (2) triple Higgs coupling, (3) exotic
Higgs decay, and (4) direct production of a new scalar particle. The benchmark
points are classified by the final states of the DM annihilation process: a
pair of $b$ quarks, SM-like Higgs bosons, and new scalar particles. Each
benchmark scenario has detectable new physics signals for the above collider
observables that can be well tested in the future lepton and hadron colliders.


  Pairs of Planck-mass-scale drops of superfluid helium coated by electrons
(i.e., "Millikan oil drops"), when levitated in the presence of strong magnetic
fields and at low temperatures, can be efficient quantum transducers between
electromagnetic (EM) and gravitational (GR) radiation. A Hertz-like experiment,
in which EM waves are converted at the source into GR waves, and then
back-converted at the receiver from GR waves back into EM waves, should be
practical to perform. This would open up observations of the gravity-wave
analog of the Cosmic Microwave Background from the extremely early Big Bang,
and also communications directly through the interior of the Earth.


  In this paper, we introduce symmetric diagram matrices $A_{s+r,s}$ of size
${_{(s+r)}}C_s$ whose entries are $\{x_i\}_{min\{s,r\}}$. We compute the
eigenvalues of symmetric diagram matrices using elementary row and column
operations inductively. As a byproduct, we obtain the eigenvalues of Gram
matrices of a larger class of diagram algebras like the signed partition
algebras, algebra of $\mathbb{Z}_2$ relations and partition algebras.


  We consider two families of D1-D5-P states and find their gravity duals. In
each case the geometries are found to `cap off' smoothly near r=0; thus there
are no horizons or closed timelike curves. These constructions support the
general conjecture that the interior of black holes is nontrivial all the way
up to the horizon.


  A lower bound on the chromatic number of a graph is derived by majorization
of spectra of weighted adjacency matrices. These matrices are given by Hadamard
products of the adjacency matrix and arbitrary Hermitian matrices.


  The classical Helmholtz problem is applied for modelling the axisymmetric
inviscid cusp-ended separated flow around a sphere. Two coordinate systems are
employed: polar for initial calculations and parabolic the latter being more
suitable for investigation of infinitely-long stagnation zones. Scaled
coordinates are introduced and difference schemes for the free-stream equation
and the Bernoulli integral are devised. The separation point is not initially
prescribed and is defined iteratively. A separated flow with vanishing drag
coefficient is obtained.


  In this paper, we investigate how network densification influences the
performance of downlink cellular network in terms of coverage probability (CP)
and area spectral efficiency (ASE). Instead of the simplified unbounded
pathloss model (UPM), we apply a more realistic bounded pathloss model (BPM) to
model the decay of signal power caused by pathloss. It is shown that network
densification indeed degrades CP when the base station (BS) density $\lambda$
is sufficiently large. This is inconsistent with the result derived using UPM
that CP is independent of $\lambda$. Moreover, we shed light on the impact of
ultra-dense deployment of BSs on the ASE scaling law. Specifically, it is
proved that the cellular network ASE scales with rate $\lambda
e^{-\kappa\lambda}$, i.e., first increases with $\lambda$ and then diminishes
to be zero as $\lambda$ goes to infinity.


  The ultracold mixture of \Na and \Rb atoms has become an important system for
investigating physics in Bose-Bose atomic mixtures and for forming ultracold
ground-state polar molecules. In this work, we provide an improved
characterization of the most commonly used Feshbach resonance near 347.64 G
between \Na and \Rb in their absolute ground states. We form Feshbach molecules
using this resonance and measure their binding energies by dissociating them
via magnetic field modulation. We use the binding energies to refine the
singlet and triplet potential energy curves, using coupled-channel bound-state
calculations. We then use coupled-channel scattering calculations on the
resulting potentials to produce a high-precision mapping between magnetic field
and scattering length. We also observe 10 additional $s$-wave Feshbach
resonances for \Na and \Rb in different combinations of Zeeman sublevels of the
$F = 1$ hyperfine states. Some of the resonances show 2-body inelastic decay
due to spin exchange. We compare the resonance properties with coupled-channel
scattering calculations that full take account of inelastic properties.


  In this paper we engage in a general study of the asymptotic expansion of the
Witten-Reshetikhin-Turaev invariants of mapping tori of surface mapping class
group elements. We use the geometric construction of the
Witten-Reshetikhin-Turaev TQFT via the geometric quantization of moduli spaces
of flat connections on surfaces. We identify assumptions on the mapping class
group elements that allow us to provide a full asymptotic expansion. In
particular, we show that our results apply to all pseudo-Anosov mapping classes
on a punctured torus and show by example that our assumptions on the mapping
class group elements are strictly weaker than hitherto successfully considered
assumptions in this context. The proof of our main theorem relies on our new
results regarding asymptotic expansions of oscillatory integrals, which allows
us to go significantly beyond the standard transversely cut out assumption on
the fixed point set. This makes use of Picard-Lefschetz theory for Laplace
integrals.


  The Fermi Gamma-Ray Space Telescope has discovered many gamma-ray pulsars,
both as radio-loud objects and radio-quiet or radio-weak pulsars that have been
identified through blind period searches. The latter presumably have gamma-ray
beams originating from high altitudes in the magnetosphere, resulting in little
or no overlap with the radio beam. The exponential cut-off of the emission at
high energy also points to a medium- or high-altitude origin of the gamma rays.
Population synthesis offers means to study two complementary aspects of the
gamma-ray pulsar population: energetics and light curve morphology. The latter
(peak multiplicity, position, separation, asymmetries, ...) can be used to
constrain the beam(s) geometry (their origin within the open magnetosphere,
evolution of the radiating region with pulsar power and age, ...). It can also
be used to constrain the obliquity and orientation of a pulsar in the framework
of a given accelerator model. We present preliminary results from new
simulations and light-curve analysis that indicate that the sample of Fermi
pulsars retains much of the geometrical information of the parent gamma-ray
pulsar population.


  Among the reductions of the resonant three-wave interaction system to
six-dimensional differential systems, one of them has been specifically
mentioned as being linked to the generic sixth Painleve' equation P6. We derive
this link explicitly, and we establish the connection to a three-degree of
freedom Hamiltonian previously considered for P6.


  The integration of large language models (LLMs) into robotics significantly
enhances the capabilities of embodied agents in understanding and executing
complex natural language instructions. However, the unmitigated deployment of
LLM-based embodied systems in real-world environments may pose potential
physical risks, such as property damage and personal injury. Existing security
benchmarks for LLMs overlook risk awareness for LLM-based embodied agents. To
address this gap, we propose RiskAwareBench, an automated framework designed to
assess physical risks awareness in LLM-based embodied agents. RiskAwareBench
consists of four modules: safety tips generation, risky scene generation, plan
generation, and evaluation, enabling comprehensive risk assessment with minimal
manual intervention. Utilizing this framework, we compile the PhysicalRisk
dataset, encompassing diverse scenarios with associated safety tips,
observations, and instructions. Extensive experiments reveal that most LLMs
exhibit insufficient physical risk awareness, and baseline risk mitigation
strategies yield limited enhancement, which emphasizes the urgency and
cruciality of improving risk awareness in LLM-based embodied agents in the
future.


  The method of brackets is an procedure to evaluate definite integrals. It is
based on a small number of operational rules. The flexibility of this method is
illustrated with the evaluation of an integral involving the Bessel K0 function
and the exponential integral. Several proofs are presented.


  The most ambitious project within the DREsden Sodium facility for DYNamo and
thermohydraulic studies (DRESDYN) at Helmholtz-Zentrum Dresden-Rossendorf
(HZDR) is the set-up of a precession-driven dynamo experiment. After discussing
the scientific background and some results of water pre-experiments and
numerical predictions, we focus on the numerous structural and design problems
of the machine. We also outline the progress of the building's construction,
and the status of some other experiments that are planned in the framework of
DRESDYN.


  We present a study of the effect of wind-driven advection on the chemical
composition of hot Jupiter atmospheres using a fully-consistent 3D
hydrodynamics, chemistry and radiative transfer code, the Met Office Unified
Model (UM). Chemical modelling of exoplanet atmospheres has primarily been
restricted to 1D models that cannot account for 3D dynamical processes. In this
work we couple a chemical relaxation scheme to the UM to account for the
chemical interconversion of methane and carbon monoxide. This is done
consistently with the radiative transfer meaning that departures from chemical
equilibrium are included in the heating rates (and emission) and hence complete
the feedback between the dynamics, thermal structure and chemical composition.
In this letter we simulate the well studied atmosphere of HD~209458b. We find
that the combined effect of horizontal and vertical advection leads to an
increase in the methane abundance by several orders of magnitude; directly
opposite to the trend found in previous works. Our results demonstrate the need
to include 3D effects when considering the chemistry of hot Jupiter
atmospheres. We calculate transmission and emission spectra, as well as the
emission phase curve, from our simulations. We conclude that gas-phase
non-equilibrium chemistry is unlikely to explain the model-observation
discrepancy in the 4.5\,{\textmu m} {\it Spitzer}/IRAC channel. However, we
highlight other spectral regions, observable with the James Webb Space
Telescope, where signatures of wind-driven chemistry are more prominant.


  We present an analytic description of the $r$-mode instability in newly-born
neutron stars, using the approximation of uniform density. Our computation is
consistently accurate to second order in the angular velocity of the star. We
obtain formulae for the growth-time of the instability due to
gravitational-wave emission, for both current and mass multipole radiation and
for the damping timescale, due to viscosity. The $l=m=2$ current-multipole
radiation dominates the timescale of the instability. We estimate the deviation
of the second order accurate results from the lowest order approximation and
show that the uncertainty in the equation of state has only a small effect on
the onset of the $r$-mode instability. The viscosity coefficients and the
cooling process in newly-born neutron stars are, at present, uncertain and our
analytic formaulae enables a quick check of such effects on the development of
the instability.


  In this paper, we consider downlink low Earth orbit (LEO) satellite
communication systems where multiple LEO satellites are uniformly distributed
over a sphere at a certain altitude according to a homogeneous binomial point
process (BPP). Based on the characteristics of the BPP, we analyze the distance
distributions and the distribution cases for the serving satellite. We
analytically derive the exact outage probability, and its approximated
expression is obtained using the Poisson limit theorem. With these derived
expressions, the system throughput maximization problem is formulated under the
satellite-visibility and outage constraints. To solve this problem, we
reformulate it with bounded feasible sets and propose an iterative algorithm to
obtain near-optimal solutions. Simulation results perfectly match the derived
exact expressions for the outage probability and system throughput. The
analytical results of the approximated expressions are fairly close to those of
the exact ones. It is also shown that the proposed algorithm for the throughput
maximization is very close to the optimal performance obtained by a
two-dimensional exhaustive search.


  Understanding of video creativity and content often varies among individuals,
with differences in focal points and cognitive levels across different ages,
experiences, and genders. There is currently a lack of research in this area,
and most existing benchmarks suffer from several drawbacks: 1) a limited number
of modalities and answers with restrictive length; 2) the content and scenarios
within the videos are excessively monotonous, transmitting allegories and
emotions that are overly simplistic. To bridge the gap to real-world
applications, we introduce a large-scale Subjective Response Indicators for
Advertisement Videos dataset, namely SRI-ADV. Specifically, we collected real
changes in Electroencephalographic (EEG) and eye-tracking regions from
different demographics while they viewed identical video content. Utilizing
this multi-modal dataset, we developed tasks and protocols to analyze and
evaluate the extent of cognitive understanding of video content among different
users. Along with the dataset, we designed a Hypergraph Multi-modal Large
Language Model (HMLLM) to explore the associations among different
demographics, video elements, EEG, and eye-tracking indicators. HMLLM could
bridge semantic gaps across rich modalities and integrate information beyond
different modalities to perform logical reasoning. Extensive experimental
evaluations on SRI-ADV and other additional video-based generative performance
benchmarks demonstrate the effectiveness of our method. The codes and dataset
will be released at https://github.com/suay1113/HMLLM.


  We assume that, in equilibrium, nuclear matter at reduced density and
moderate finite temperature, breaks up into many fragments. A strong support to
this assumption is provided by date accumulated from intermediate energy heavy
ion collisions. The break-up of hot and expanded nuclear matter according to
rules of equilibrium statistical mechanics is the multifragmentation model. The
model gives a first order phase transition. This is studied in detail here.
Phase-equilibrium lines for different degrees of asymmetry are computed.


  We study topology of configuration spaces of planar linkages having one leg
of variable length. Such telescopic legs are common in modern robotics where
they are used for shock absorbtion and serve a variety of other purposes. Using
a Morse theoretic technique, we compute explicitly, in terms of the metric
data, the Betti numbers of configuration spaces of these mechanisms.


  We have investigated the classical stability of charged black $D3$-branes in
type IIB supergravity under small perturbations. For s-wave perturbations it
turns out that black $D3$-branes are unstable when they have small charge
density. As the charge density increases for given mass density, however, the
instability decreases down to zero at a certain finite value of the charge
density, and then black $D3$-branes become stable all the way down to the
extremal point. It has also been shown that such critical value at which its
stability behavior changes agrees very well with the predicted one by the
thermodynamic stability behavior of the corresponding black hole system through
the Gubser-Mitra conjecture. Unstable mode solutions we found involve
non-vanishing fluctuations of the self-dual five-form field strength. Some
implications of our results are also discussed.


  Coherent states (CS) for non-Hermitian systems are introduced as eigenstates
of pseudo-Hermitian boson annihilation operators. The set of these CS includes
two subsets which form bi-normalized and bi-overcomplete system of states. The
subsets consist of eigenstates of two complementary lowering pseudo-Hermitian
boson operators. Explicit constructions are provided on the example of
one-parameter family of pseudo-boson ladder operators. The wave functions of
the eigenstates of the two complementary number operators, which form a
bi-orthonormal system of Fock states, are found to be proportional to new
polynomials, that are bi-orthogonal and can be regarded as a generalization of
standard Hermite polynomials.


  We construct an exotic one-parameter semigroup of endomorphims of a symmetric
cone $C$, whose generator is not the sum of a Lie group generator and an
endomorphism of $C$. The question is motivated by the theory of affine
processes on symmetric cones, which plays an important role in mathematical
finance. On the other hand, theoretical question that we solve in this paper
seems to have been implicitly open even much longer then this motivation
suggests.


  We review the main properties of solar metallicity massive stars in the range
11-120 Msun. The influence of the mass loss on the hydrostatic burning stages
as well as the final explosion is discussed in some detail. We find that the
minimum masses that enter the WNL, WNE and WC stages are 30 Msun, 35 Msun and
40 Msun respectively; the limiting mass between stars exploding as SNII and
SNIb/c is between 30 and 35 Msun; the limiting mass between stars forming
neutron stars and black holes after the explosion is between 25-30 Msun. We
also discuss the properties of the chemical yields integrated over a Salpeter
IMF and we find that stars with M>=35 Msun contribute for ~60% to the
production of C, N and for ~40% to the production Sc and s-process elements up
to Zr, while they do not produce any intermediate mass element because of the
large remnant masses


  We investigate the properties of pure derived categories of module
categories, and show that pure derived categories share many nice properties of
classical derived categories. In particular, we show that bounded pure derived
categories can be realized as certain homotopy categories. We introduce the
pure projective (resp. injective) dimension of complexes in pure derived
categories, and give some criteria for computing these dimensions in terms of
the properties of pure projective (resp. injective) resolutions and pure
derived functors. As a consequence, we get some equivalent characterizations
for the finiteness of the pure global dimension of rings. Finally, pure
projective (resp. injective) resolutions of unbounded complexes are considered.


  In this paper we determine the full character table of a certain split
extension $H_1(q)\rtimes Sp(2,q)$ of the Heisenberg group $H_1$ by the
odd-characteristic symplectic group $Sp(2,q)$.


  Contrastive learning has gained popularity as an effective self-supervised
representation learning technique. Several research directions improve
traditional contrastive approaches, e.g., prototypical contrastive methods
better capture the semantic similarity among instances and reduce the
computational burden by considering cluster prototypes or cluster assignments,
while adversarial instance-wise contrastive methods improve robustness against
a variety of attacks. To the best of our knowledge, no prior work jointly
considers robustness, cluster-wise semantic similarity and computational
efficiency. In this work, we propose SwARo, an adversarial contrastive
framework that incorporates cluster assignment permutations to generate
representative adversarial samples. We evaluate SwARo on multiple benchmark
datasets and against various white-box and black-box attacks, obtaining
consistent improvements over state-of-the-art baselines.


  We generalize a forward light-by-light scattering sum rule to the case of
heavy quarkonium radiative transitions. We apply such sum rule to the
bottomonium states, and use available data on radiative transitions in its
evaluation. For the transitions that are not known experimentally, we provide
theoretical estimates within a potential model, and consider the spread between
similar approaches in the literature as an estimate for the model error. For
the $\Upsilon(1S)$, $\Upsilon(2S)$, and $\Upsilon(3S)$ states we observe that,
due to a cancellation between transitions involving $\chi_{b0}, \chi_{b1}$, and
$\chi_{b2}$ states, the sum rule is satisfied within experimental and
theoretical error estimates. Having tested this sum rule for the low-lying
bottomonium states, it may be used as a tool to investigate the nature of
exotic states in the charmonium and bottomonium spectrum through the
corresponding radiative transitions.


  The results of two searches for pair production of vector-like T or B quarks
in fully hadronic final states are presented, using data from the CMS
experiment at a center-of-mass energy of 13 TeV. The data were collected at the
LHC during 2016 and correspond to an integrated luminosity of 35.9 fb$^{-1}$. A
cut-based analysis specifically targets the bW decay mode of the T quark and
allows for the reconstruction of the T quark candidates. In a second analysis,
a multiclassification algorithm, the "boosted event shape tagger," is deployed
to label candidate jets as originating from top quarks, and W, Z, and H.
Candidate events are categorized according to the multiplicities of identified
jets, and the scalar sum of all observed jet momenta is used to discriminate
signal events from the quantum chromodynamics multijet background. Both
analyses probe all possible branching fraction combinations of the T and B
quarks and set limits at 95% confidence level on their masses, ranging from 740
to 1370 GeV. These results represent a significant improvement relative to
existing searches in the fully hadronic final state.


  The loss of mass from protostars, in the form of a jet or outflow, is a
necessary counterpart to protostellar mass accretion. Outflow ejection events
probably vary in their velocity and/or in the rate of mass loss. Such
`episodic' ejection events have been observed during the Class 0 protostellar
phase (the early accretion stage), and continue during the subsequent class I
phase that marks the first one million years of star formation. Previously
observed episodic-ejection sources were relatively isolated; however, the most
common sites of star formation are clusters. Outflows link protostars with
their environment and provide a viable source of turbulence that is necessary
for regulating star formation in clusters, but it is not known how an
accretion-driven jet or outflow in a clustered environment manifests itself in
its earliest stage. This early stage is important in establishing the initial
conditions for momentum and energy transfer to the environment as the protostar
and cluster evolve. Here we report that an outflow from a very young class 0
protostar, at the hub of the very active and filamentary Serpens South
protostellar cluster, shows unambiguous episodic events. The $^{12}$CO (J=2-1)
emission from the protostar reveals 22 distinct features of outflow ejecta, the
most recent having the highest velocity. The outflow forms bipolar lobes ---
one of the first detectable signs of star formation --- which originate from
the peak of 1-mm continuum emission. Emission from the surrounding C$^{18}$O
envelope shows kinematics consistent with rotation and an infall of material
onto the protostar. The data suggest that episodic accretion-driven outflow
begins in the earliest phase of protostellar evolution, and that the outflow
remains intact in a very clustered environment, probably providing efficient
momentum transfer for driving turbulence.


  One of the main challenges in developing autonomous transport systems based
on connected and automated vehicles is the comprehension and understanding of
the environment around each vehicle. In many situations, the understanding is
limited to the information gathered by the sensors mounted on the ego-vehicle,
and it might be severely affected by occlusion caused by other vehicles or
fixed obstacles along the road. Situational awareness is the ability to
perceive and comprehend a traffic situation and to predict the intent of
vehicles and road users in the surrounding of the ego-vehicle. The main
objective of this paper is to propose a framework for how to automatically
increase the situational awareness for an automatic bus in a realistic scenario
when a pedestrian behind a parked truck might decide to walk across the road.
Depending on the ego-vehicle's ability to fuse information from sensors in
other vehicles or in the infrastructure, shared situational awareness is
developed using a set-based estimation technique that provides robust
guarantees for the location of the pedestrian. A two-level information fusion
architecture is adopted, where sensor measurements are fused locally, and then
the corresponding estimates are shared between vehicles and units in the
infrastructure. Thanks to the provided safety guarantees, it is possible to
appropriately adjust the ego-vehicle speed to maintain a proper safety margin.
It is also argued that the framework is suitable for handling sensor failures
and false detections in a systematic way. Three scenarios of growing
information complexity are considered throughout the study. Simulations show
how the increased situational awareness allows the ego-vehicle to maintain a
reasonable speed without sacrificing safety.


  Let $r(G,H)$ be the smallest integer $N$ such that for any $2$-coloring (say,
red and blue) of the edges of $K\_n$, $n\geqslant N$, there is either a red
copy of $G$ or a blue copy of $H$. Let $K\_n-K\_{1,s}$ be the complete graph on
$n$ vertices from which the edges of $K\_{1,s}$ are dropped. In this note we
present exact values for $r(K\_m-K\_{1,1},K\_n-K\_{1,s})$ and new upper bounds
for $r(K\_m,K\_n-K\_{1,s})$ in numerous cases. We also present some results for
the Ramsey number of Wheels versus $K\_n-K\_{1,s}$.


  Quasi-universal relations connecting the tidal deformability and the
quadrupole moment of individual neutron stars are predicted by theoretical
computations, but have not been measured experimentally. However, such
relations are employed during the interpretation of gravitational waves and,
therefore, have a direct impact on the interpretation of real data. In this
work, we study how quasi-universal relations can be tested and measured from
gravitational wave signals connected to binary neutron star coalescences. We
study a population of $120$ binary neutron star systems and find that Advanced
LIGO and Advanced Virgo at design sensitivity could find possible deviations of
predicted relations if the observed neutron stars are highly spinning. In the
future, a network of third generation (3G) detectors will be able to even allow
a measurement of quasi-universal relations. Thus, the outlined approach
provides a new test of general relativity and nuclear physics predictions.


  The ubiquitous Lanczos method can approximate $f(A)x$ for any symmetric $n
\times n$ matrix $A$, vector $x$, and function $f$. In exact arithmetic, the
method's error after $k$ iterations is bounded by the error of the best
degree-$k$ polynomial uniformly approximating $f(x)$ on the range
$[\lambda_{min}(A), \lambda_{max}(A)]$. However, despite decades of work, it
has been unclear if this powerful guarantee holds in finite precision.
  We resolve this problem, proving that when $\max_{x \in [\lambda_{min},
\lambda_{max}]}|f(x)| \le C$, Lanczos essentially matches the exact arithmetic
guarantee if computations use roughly $\log(nC\|A\|)$ bits of precision. Our
proof extends work of Druskin and Knizhnerman [DK91], leveraging the stability
of the classic Chebyshev recurrence to bound the stability of any polynomial
approximating $f(x)$.
  We also study the special case of $f(A) = A^{-1}$, where stronger guarantees
hold. In exact arithmetic Lanczos performs as well as the best polynomial
approximating $1/x$ at each of $A$'s eigenvalues, rather than on the full
eigenvalue range. In seminal work, Greenbaum gives an approach to extending
this bound to finite precision: she proves that finite precision Lanczos and
the related CG method match any polynomial approximating $1/x$ in a tiny range
around each eigenvalue [Gre89].
  For $A^{-1}$, this bound appears stronger than ours. However, we exhibit
matrices with condition number $\kappa$ where exact arithmetic Lanczos
converges in $polylog(\kappa)$ iterations, but Greenbaum's bound predicts
$\Omega(\kappa^{1/5})$ iterations. It thus cannot offer significant improvement
over the $O(\kappa^{1/2})$ bound achievable via our result. Our analysis raises
the question of if convergence in less than $poly(\kappa)$ iterations can be
expected in finite precision, even for matrices with clustered, skewed, or
otherwise favorable eigenvalue distributions.


  The interest of quadratic algebras for position-dependent mass Schr\"odinger
equations is highlighted by constructing spectrum generating algebras for a
class of d-dimensional radial harmonic oscillators with $d \ge 2$ and a
specific mass choice depending on some positive parameter $\alpha$. Via some
minor changes, the one-dimensional oscillator on the line with the same kind of
mass is included in this class. The existence of a single unitary irreducible
representation belonging to the positive-discrete series type for $d \ge 2$ and
of two of them for d=1 is proved. The transition to the constant-mass limit
$\alpha \to 0$ is studied and deformed su(1,1) generators are constructed.
These operators are finally used to generate all the bound-state wavefunctions
by an algebraic procedure.


  In this paper we study a certain class of central extensions of preprojective
algebras of quivers under the name quiver Heisenberg algebras (QHA). There are
several classes of algebras introduced before by different researchers from
different view points, which have the QHA as a special case. While these have
mainly been studied in characteristic zero, we also study the case of positive
characteristic. Our results show that the QHA is closely related to the
representation theory of the corresponding path algebra in a similar way to the
preprojective algebra.
  Among other things, one of our main results is that the QHA provides an exact
sequence of bimodules over the path algebra of a quiver, which can be called
the universal Auslander-Reiten sequence. Moreover, we show that the QHA
provides minimal left and right approximations with respect to the powers of
the radical functor. Consequently, we obtain a description of the QHA as a
module over the path algebra, which in the Dynkin case, gives a
categorification (as well as a generalization to the positive characteristic
case) of the dimension formula by Etingof-Rains.


  While symplectic manifolds have no local invariants, they do admit many
global numerical invariants. Prominent among them are the so-called symplectic
capacities.
  Different capacities are defined in different ways, and so relations between
capacities often lead to surprising relations between different aspects of
symplectic geometry and Hamiltonian dynamics. In this paper we present an
attempt to better understand the space of all symplectic capacities, and
discuss some further general properties of symplectic capacities.
  We also describe several new relations between certain symplectic capacities
on ellipsoids and polydiscs. Throughout the discussion we mention many open
problems.


  We develop a method for measuring and localizing homology classes. This
involves two problems. First, we define relevant notions of size for both a
homology class and a homology group basis, using ideas from relative homology.
Second, we propose an algorithm to compute the optimal homology basis, using
techniques from persistent homology and finite field algebra. Classes of the
computed optimal basis are localized with cycles conveying their sizes. The
algorithm runs in $O(\beta^4 n^3 \log^2 n)$ time, where $n$ is the size of the
simplicial complex and $\beta$ is the Betti number of the homology group.


  We compute the anharmonic shift of the phonon frequencies in MgB2, using
density functional theory. We explicitly take into account the scattering
between different phonon modes at different q-points in the Brillouin zone. The
shift of the E2g mode at the Gamma point is +5 % of the harmonic frequency.
This result comes from the cancellation between the contributions of the four-
and three-phonon scattering, respectively +10 % and -5 %. A similar shift is
predicted at the A point, in agreement with inelastic X-ray scattering
phonon-dispersion measurements. A smaller shift is observed at the M point.


  We study the neutralino decay in the supersymmetric extra U(1) models which
can solve the $\mu$-problem. In these models the neutralino sector is extended
at least into six components by an extra U(1) gaugino and a superpartner of a
singlet Higgs. Focussing on its two lower mass eigenstates $\tilde\chi_2^0$ and
$\tilde\chi_1^0$, decay processes such as a tree level three body decay
$\tilde\chi_2^0\to \tilde\chi_1^0 f\bar f$ and a one-loop radiative decay
$\tilde\chi_2^0\to \tilde\chi_1^0\gamma$ are estimated. We investigate the
condition under which the radiative decay becomes the dominant mode and also
numerically search for such parameter regions. In this analysis we take account
of the abelian gaugino kinetic term mixing. We suggest that the gaugino mass
relation $M_W\sim M_Y$ may not be necessary for the radiative decay dominance
in the extra U(1) models.


  We study compactifications of Einstein gravity on product spaces in vacuum
and their acceleration phases. Scalar potentials for the dimensionally reduced
effective theory are found to be of exponential form and exact solutions are
obtained for a class of product spaces. The inflation in our solutions is not
sufficient for the early universe. We comment on the possibility of obtaining
sufficient inflation by compactification in general.


  This paper concerns the elastic structures which exhibit non-zero strain at
free equilibria. Many growing tissues (leaves, flowers or marine invertebrates)
attain complicated configurations during their free growth. Our study departs
from the 3d incompatible elasticity theory, conjectured to explain the
mechanism for the spontaneous formation of non-Euclidean metrics.
  Recall that a smooth Riemannian metric on a simply connected domain can be
realized as the pull-back metric of an orientation preserving deformation if
and only if the associated Riemann curvature tensor vanishes identically. When
this condition fails, one seeks a deformation yielding the closest metric
realization. We set up a variational formulation of this problem by introducing
the non-Euclidean version of the nonlinear elasticity functional, and establish
its $\Gamma$-convergence under the proper scaling. As a corollary, we obtain
new necessary and sufficient conditions for existence of a $W^{2,2}$ isometric
immersion of a given 2d metric into $\mathbb R^3$.


  The Witten index counts the difference in the number of bosonic and fermionic
states of a quantum mechanical system. The Schur index, which can be defined
for theories with at least $\mathcal{N}=2$ supersymmetry in four dimensions is
a particular refinement of the index, dependent on one parameter $q$ serving as
the fugacity for a particular set of charges which commute with the hamiltonian
and some supersymmetry generators. This index has a known expression for all
Lagrangian and some non-Lagrangian theories as a finite dimensional integral or
a complicated infinite sum. In the case of $\mathcal{N}=4$ SYM with gauge group
$U(N)$ we rewrite this as the partition function of a gas of $N$ non
interacting and translationally invariant fermions on a circle. This allows us
to perform the integrals and write down explicit expressions for fixed $N$ as
well as the exact all orders large $N$ expansion.


  Dangerous damage to mitochondrial DNA (mtDNA) can be ameliorated during
mammalian development through a highly debated mechanism called the mtDNA
bottleneck. Uncertainty surrounding this process limits our ability to address
inherited mtDNA diseases. We produce a new, physically motivated, generalisable
theoretical model for mtDNA populations during development, allowing the first
statistical comparison of proposed bottleneck mechanisms. Using approximate
Bayesian computation and mouse data, we find most statistical support for a
combination of binomial partitioning of mtDNAs at cell divisions and random
mtDNA turnover, meaning that the debated exact magnitude of mtDNA copy number
depletion is flexible. New experimental measurements from a wild-derived mtDNA
pairing in mice confirm the theoretical predictions of this model. We
analytically solve a mathematical description of this mechanism, computing
probabilities of mtDNA disease onset, efficacy of clinical sampling strategies,
and effects of potential dynamic interventions, thus developing a quantitative
and experimentally-supported stochastic theory of the bottleneck.


  A theoretical attempt to identify the physical process responsible for the
afterglow emission of Gamma-Ray Bursts (GRBs) is presented, leading to the
occurrence of thermal emission in the comoving frame of the shock wave giving
rise to the bursts. The determination of the luminosities and spectra involves
integration over an infinite number of Planckian spectra, weighted by
appropriate relativistic transformations, each one corresponding to a different
viewing angle in the past light cone of the observer. The relativistic
transformations have been computed using the equations of motion of GRBs within
our theory, giving special attention to the determination of the equitemporal
surfaces. The only free parameter of the present theory is the ``effective
emitting area'' in the shock wave front. A self consistent model for the
observed hard-to-soft transition in GRBs is also presented. When applied to GRB
991216 a precise fit $(\chi^2\simeq 1.078)$ of the observed luminosity in the
2--10 keV band is obtained. Similarly, detailed estimates of the observed
luminosity in the 50--300 keV and in the 10--50 keV bands are obtained.


  Lagrangian Particle Tracking (LPT) enables practitioners to study various
concepts in turbulence by measuring particle positions in flows of interest.
This data is subject to measurement errors, and filtering techniques are
applied to mitigate these errors and improve the accuracy of analyses utilizing
the data. We develop a new type of position filter through use of maximum
likelihood estimation by considering both measurement errors and stochastic
process physics. The maximum likelihood estimation scheme we develop is general
and can accommodate many different stochastic process models, enabling it to be
applied to many different turbulent flows. In this work, we propose a process
model similar to existing, complimentary work in the development of B-splines.
We compare our filtering scheme to existing schemes and find that our filter
out performs the scheme proposed by Mordant et al. (2004) considerably, and
produces similar performance to spline filters, proposed by Gesemann (2018). In
comparing to the latter, we note that the maximum likelihood treatment provides
a general framework which is capable of producing different filters based on
the physics of interest, whereas the spline filters are built on less specific
filtering theory and are therefore more difficult to adapt across diverse use
cases in fluids. We quantify the performance of each of the filtering methods
using error metrics which consider both noise reduction as well as signal
degradation, and together these are used to define a concept of filter
efficiency. The maximum likelihood filter developed in this work is shown to be
the most efficient among all the methods examined when applied to simulated
isotropic turbulence data from the Johns Hopkins Database.


  We develop minimax optimal risk bounds for the general learning task
consisting in predicting as well as the best function in a reference set G up
to the smallest possible additive term, called the convergence rate. When the
reference set is finite and when n denotes the size of the training data, we
provide minimax convergence rates of the form C ([log |G|]/n)^v with tight
evaluation of the positive constant C and with exact v in ]0;1], the latter
value depending on the convexity of the loss function and on the level of noise
in the output distribution. The risk upper bounds are based on a sequential
randomized algorithm, which at each step concentrates on functions having both
low risk and low variance with respect to the previous step prediction
function. Our analysis puts forward the links between the probabilistic and
worst-case viewpoints, and allows to obtain risk bounds unachievable with the
standard statistical learning approach. One of the key idea of this work is to
use probabilistic inequalities with respect to appropriate (Gibbs)
distributions on the prediction function space instead of using them with
respect to the distribution generating the data. The risk lower bounds are
based on refinements of the Assouad's lemma taking particularly into account
the properties of the loss function. Our key example to illustrate the upper
and lower bounds is to consider the L_q-regression setting for which an
exhaustive analysis of the convergence rates is given while q describes
[1;+infinity[.


  We have presented 309 new white-dwarf (WD) + main-sequence (MS) star binaries
identified from the Sloan Digital Sky Survey (SDSS) Tenth Data Release (DR10).
The majority of them consist of a white dwarf and a low-mass secondary
(typically M dwarf) companion. The SDSS spectra of the newly found WDMS
binaries with a DA/DB white dwarf and an M/late-K dwarf companion are analyzed
based on a spectral decomposition/fitting method. White dwarf effective
temperatures, surface gravities and masses together with the secondary star
spectral types are obtained, and the stellar parameters of DA WDs with $T_{\rm
eff}\la 14,000$ K are revised to the results in the case of 3D model
atmosphere. Two independent distance estimates are derived from the
flux-scaling factors between the WDMS SDSS spectra and the white dwarf and
M-dwarf model spectra. It is found that about more than 20 per cent of the
newly found WDMS binaries show a significant discrepancy between the two
distance estimates. This might be caused by the effects of M-dwarf stellar
activity or irradiation of the M dwarf companions by the white dwarf. The
stellar parameter distributions are used to investigate the global properties
of newly found WDMS binaries, the results shown in this work are consistent
with those derived by previous investigators. Some WDMS binaries have been
observed more than one ($2-4$) times by SDSS, it is found that four of them
exhibit not only Hydrogen emission in all observable Balmer series lines in
addition to He I line Balmer lines but also the rapid variation in the radial
velocities of the components in these binaries. This suggests that they should
be the post common envelope binaries (PCEBs) with a short orbital period. These
young PCEBs are very important for limiting the results of common envelope
phase of the binary evolution.


  By viewing a velocity gradient in a fluid as an internal disturbance and
treating it as a constraint on the wave function of a system, a linear
evolution equation for the wave function is obtained from the Lagrange
multiplier method. It allows us to define the microscopic response to a
velocity gradient in a pure state. Taking a spatial coarse-graining average
over this microscopic response and averaging it over admissible initial states,
we achieve the observed macroscopic response and transport coefficient. In this
scheme, temporal coarse-graining is not needed. The dissipation caused by a
velocity gradient depends on the square of initial occupation probability,
whereas the dissipation caused by a mechanical perturbation depends on the
initial occupation probability itself. We apply the method of variation of
constants to solve the time-dependent Schrodinger equation with constraints.
The various time scales appearing in the momentum transport are estimated. The
relation\ between the present work and previous theories is discussed.


  Cosmological hysteresis, has interesting and vivid implications in the
scenario of a cyclic bouncy universe. This, purely thermodynamical in nature,
is caused by the asymmetry in the equation of state parameter during expansion
and contraction phase of the universe, due to the presence of a single scalar
field. When applied to variants of modified gravity models this phenomenon
leads to the increase in amplitude of the consecutive cycles of the universe,
provided we have physical mechanisms to make the universe bounce and
turnaround. This also shows that the conditions which creates a universe with
an ever increasing expansion, depend on the signature of $\oint pdV$ and on
model parameters.


  The blazar zone in quasars is commonly assumed to be located inside the
broad-line region at some hundreds of Schwartzschild radii from the central
black hole. Now, the simultaneous Fermi/LAT and MAGIC observations of a strong
flare in the FSRQ PKS 1222+21 (4C 21.35, z=0.432) on 2010 June 17 challenge
this picture. The spectrum can be described by a single power law with photon
index 2.72+/-0.34 between 3 GeV and 400 GeV, and this is consistent with
emission from a single component in the jet. The absence of a spectral cutoff
constrains the gamma-ray emission region to lie outside of the broad-line
region, which would otherwise absorb the VHE gamma-rays. On the other hand, the
MAGIC measurement of a doubling time of about 10 minutes indicates an extremely
compact emission region, in conflict with the "far dissipation" scenario. This
could be a hint for the importance of jet sub-structures, such as filaments,
reconnection zones or shear layers for the occurrence of blazar flares.


  The interplay between band topology and magnetic order plays a key role in
quantum states of matter. MnBi2Te4, a van der Waals magnet, has recently
emerged as an exciting platform for exploring Chern insulator physics. Its
layered antiferromagnetic order was predicted to enable even-odd layer-number
dependent topological states, supported by promising edge transport
measurements. Furthermore, it becomes a Chern insulator when all spins are
aligned by an applied magnetic field. However, the evolution of the bulk
electronic structure as the magnetic state is continuously tuned and its
dependence on layer number remains unexplored. Here, employing multimodal
probes, we establish one-to-one correspondence between bulk electronic
structure, magnetic state, topological order, and layer thickness in atomically
thin MnBi2Te4 devices. As the magnetic state is tuned through the canted
magnetic phase, we observe a band crossing, i.e., the closing and reopening of
the bulk bandgap, corresponding to the concurrent topological phase transition.
Surprisingly, we find that the even- and odd-layer number devices exhibit a
similar topological phase transition coupled to magnetic states, distinct from
recent theoretical and experimental reports. Our findings shed new light on the
interplay between band topology and magnetic order in this newly discovered
topological magnet and validate the band crossing with concurrent measurements
of topological invariant in a continuously tuned topological phase transition.


  The paper presents a theoretical analysis on the interaction between the
Earth's magnetic field of a compass needle and the magnetic field of a straight
infinite current-carrying wire. Implementation of a planar horizontal coil of
wires has been shown as a sinus galvanometer. The magnetic field over the
planar coil of wires has been examined by experiment. The coil could be used as
a model for straight infinite current wire in demonstration set-ups or could be
given as an assignment in Physics laboratory workshops.


  It is proposed the modification of the Jacobi polynomial expansion method
(MJEM) which is based on the application of the truncated moments instead of
the full ones. This allows to reconstruct with a high precision the local quark
helicity distributions even for the narrow accessible for measurement Bjorken
$x$ region using as an input only four first moments extracted from the data in
NLO QCD. It is also proposed the variational (extrapolation) procedure allowing
to reconstruct the distributions outside the accessible Bjorken $x$ region
using the distributions obtained with MJEM in the accessible region. The
numerical calculations encourage one that the proposed variational
(extrapolation) procedure could be applied to estimate the full first
(especially important) quark moments.


  We build homogeneous quasi-morphisms on the universal cover of the
contactomorphism group for certain prequantizations of monotone symplectic
toric manifolds. This is done using Givental's nonlinear Maslov index and a
contact reduction technique for quasi-morphisms. We show how these
quasi-morphisms lead to a hierarchy of rigid subsets of contact manifolds. We
also show that the nonlinear Maslov index has a vanishing property, which plays
a key role in our proofs. Finally we present applications to orderability of
contact manifolds and Sandon-type metrics on contactomorphism groups.


  It is shown by particle-in-cell simulation that intense circularly polarized
(CP) laser light can be contained in the cavity of a solid-density circular
Al-plasma shell for hundreds of light-wave periods before it is dissipated by
laser-plasma interaction. A right-hand CP laser pulse can propagate almost
without reflection into the cavity through a highly magnetized overdense
H-plasma slab filling the entrance hole. The entrapped laser light is then
multiply reflected at the inner surfaces of the slab and shell plasmas,
gradually losing energy to the latter. Compared to that of the incident laser,
the frequency is only slightly broadened and the wave vector slightly modified
by appearance of weak nearly isotropic and homogeneous higher harmonics.


  This paper studies the Cauchy problem for variable coefficient weakly
hyperbolic first order systems of partial differential operators. The
hyperbolicity assumption is that for each $t, x$ the principal symbol is
hyperbolic. No hypothesis is imposed on lower order terms. For coefficients and
Cauchy data sufficiently Gevrey regular the Cauchy problem has a unique
sufficiently Gevrey regular solution. We prove stability and error estimates
for the spectral Crank-Nicholson scheme. Approximate solutions can be computed
with accuracy $epsilon$ in the supremum norm with cost growing at most
polynomially in $epsilon^{-1}$. The proofs use the symmetrizers from [2].


  We explain how the calculations of arXiv:1704.08648, which provided the first
evidence for non-trivial structures of Gaussian correlators in tensor models,
are efficiently performed with the help of the (Hurwitz) character calculus.
This emphasizes a close similarity between technical methods in matrix and
tensor models and supports a hope to understand the emerging structures in very
similar terms. We claim that the $2m$-fold Gaussian correlators of rank $r$
tensors are given by $r$-linear combinations of dimensions with the Young
diagrams of size $m$. The coefficients are made from the characters of the
symmetric group $S_m$ and their exact form depends on the symmetries of the
model. As the simplest application of this new knowledge, we provide simple
expressions for correlators in the Aristotelian tensor model as tri-linear
combinations of dimensions.


  Fuzzy Dark Matter (FDM) has recently gained attention as a motivated
candidate for the dark matter (DM) content of the Universe, as opposed to the
commonly assumed cold DM (CDM), since the soliton profile intrinsic to FDM
models was found to be particularly well suited to reproduce observed galaxy
mass profiles. While FDM as a single DM component has been strongly constrained
by multiple probes, there remained a mass window between
$10^{-25}\,\mathrm{eV}$ and $10^{-24}\,\mathrm{eV}$ in which it can comprise a
large portion ($\gtrsim\mathcal{O}(10\%)$) of the total DM. In this work, we
consider gravitational lensing measurements in the strong lensing regime, which
are one of the only means to directly constrain the distribution and profile of
DM in astronomical bodies. Using a simple model that combines a soliton FDM
component with a Navarro-Frenk-White (NFW) profile, we explore under what
conditions DM halos with this hybrid profile are able to reproduce the observed
Einstein radii of several known lenses. We find that FDM with a particle mass
of $\lesssim 10^{-24}\,{\rm eV}$ cannot explain the observations if it makes up
more than $\sim10\%$ of the total DM, effectively closing the lingering FDM
mass window.


  We consider analysis targets at the International Linear Collider in which
only a single photon can be observed. For such processes, we have developed a
method which uses likelihood distributions using the full event information
(photon energy and angle). The method was applied to a search for neutralino
pair production with a photon from initial state radiation (ISR) in the case of
supergravity in which the neutralino is the lightest supersymmetric particle.
We determine the cross section required to observe the neutralino pair
production with ISR as a function of the neutralino mass in the range of 100 to
250 GeV.


  Reported here are theoretical calculations on the triflic acid and water,
establishing molecular scale information necessary to modeling of the
structure, thermodynamics, and ionic transport of Nafion membranes. To
characterize side chain flexibility and accessibility of the acid proton, free
energies for rotation of both carbon-sulfur and sulfur-oxygen (hydroxyl) bonds
are presented. The energetic barrier to rotation of the acid proton away from
the sulfonic acid oxygen plane is substantially flattened, with barrier less
than one kcal/mol, by electrostatic solvation. The activation free energy for
acid-water proton interchange is about 4.7 kcal/mol.


  Relational data representations have become an increasingly important topic
due to the recent proliferation of network datasets (e.g., social, biological,
information networks) and a corresponding increase in the application of
statistical relational learning (SRL) algorithms to these domains. In this
article, we examine a range of representation issues for graph-based relational
data. Since the choice of relational data representation for the nodes, links,
and features can dramatically affect the capabilities of SRL algorithms, we
survey approaches and opportunities for relational representation
transformation designed to improve the performance of these algorithms. This
leads us to introduce an intuitive taxonomy for data representation
transformations in relational domains that incorporates link transformation and
node transformation as symmetric representation tasks. In particular, the
transformation tasks for both nodes and links include (i) predicting their
existence, (ii) predicting their label or type, (iii) estimating their weight
or importance, and (iv) systematically constructing their relevant features. We
motivate our taxonomy through detailed examples and use it to survey and
compare competing approaches for each of these tasks. We also discuss general
conditions for transforming links, nodes, and features. Finally, we highlight
challenges that remain to be addressed.


  In studying the interstellar medium (ISM) and Galactic cosmic rays (CRs),
uncertainty of the interstellar gas density has always been an issue. To
overcome this difficulty, we used a component decomposition of the 21-cm HI
line emission and used the resulting gas maps in an analysis of $\gamma$-ray
data obtained by the Fermi Large Area Telescope (LAT) for the MBM~53, 54, and
55 molecular clouds and the Pegasus loop. We decomposed the ISM gas into
intermediate-velocity clouds, narrow-line and optically thick HI, broad-line
and optically thin HI, CO-bright H2, and CO-dark H2 using detailed correlations
with the HI line profiles from the HI4PI survey, the Planck dust-emission
model, and the Fermi-LAT $\gamma$-ray data. We found the fractions of optical
depth correction to the HI column density and CO-dark H2 to be nearly equal. We
fitted the CR spectra directly measured at/near the Earth and the measured
$\gamma$-ray emissivity spectrum simultaneously. We obtained a spectral break
in the interstellar proton spectrum at ${\sim}$7~GeV, and found the
$\gamma$-ray emissivity normalization agrees with the AMS-02 proton spectrum
within 10\%, relaxing the tension with the CR spectra previously claimed.


  A sequence $S$ is potentially $K_{p,1,1}$ graphical if it has a realization
containing a $K_{p,1,1}$ as a subgraph, where $K_{p,1,1}$ is a complete
3-partite graph with partition sizes $p,1,1$. Let $\sigma(K_{p,1,1}, n)$ denote
the smallest degree sum such that every $n$-term graphical sequence $S$ with
$\sigma(S)\geq \sigma(K_{p,1,1}, n)$ is potentially $K_{p,1,1}$ graphical. In
this paper, we prove that $\sigma (K_{p,1,1}, n)\geq 2[((p+1)(n-1)+2)/2]$ for
$n \geq p+2.$ We conjecture that equality holds for $n \geq 2p+4.$ We prove
that this conjecture is true for $p=3$.


  For the model of a compressible barotropic fluid on a two dimensional
rotating Riemmanian manifold we discuss a special class of smooth solutions
having a form of a steady non-singular vortex moving with a bearing field. The
model can be obtained from the system of primitive equations governing the
motion of air over the Earth surface after averaging over the height and
therefore the solution obtained can be interpreted as a tropical cyclone which
is known as a long time existing stable vortex. We consider approximations of
$l$- plane and $\beta$ - plane used in geophysics for modeling of middle scale
processes and equations on the whole sphere as well. We show that the solutions
of the mentioned form satisfy the equations of the model either exactly or with
a discrepancy which is small in a neighborhood of the trajectory of the center
of vortex. We perform a numeric study of the change of the shape of the vortex
affected by the neglecting the discrepancy term.


  We consider a particular k-essence scalar field model for the late-time
cosmic acceleration in which the sound speed, parametrized as $c_s$ is
constant. We compute the relevant background and perturbation quantities
corresponding to the observables like cosmic microwave background, type Ia
supernova, cosmic chronometers, baryon acoustic oscillations, and the
$f\sigma_8$. We put constraints on the $c_s^2$ parameter from these
observations along with other parameters. We find lower values of $c_s^2$ which
are close to zero are tightly constrained. Particularly, we find mean value of
$\log_{\rm 10} (c_s^2)$ to be $-0.61$ and $c_s^2 \leq 10^{-3}$ is more than
3$\sigma$ away from this mean value. This means these observations favor a
homogeneous dark energy component compared to the clustering one.


  We formulate and test a hybrid fluid-Monte Carlo scheme for the treatment of
elastic collisions in gases and plasmas. While our primary focus and
demonstrations of applicability are for moderately collisional plasmas, as
described by the Landau-Fokker-Planck equation, the method is expected to be
applicable also to collision processes described by the Boltzmann equation.
This scheme is similar to the previously discussed velocity-based scheme [R.
Caflisch, et. al, Multiscale Modeling & Simulation 7, 865, (2008)] and the
scattering-angle-based scheme [A.M. Dimits, et. al, Bull. APS 55, no. 15 (2010,
Abstract: XP9.00006)], but with a firmer theoretical basis and without the
inherent limitation to the Landau-Fokker-Planck case. It gives a significant
performance improvement (e.g., error for a given computational effort) over the
velocity-based scheme. These features are achieved by assigning passive scalars
to each simulated particle and tracking their evolution through collisions. The
method permits a detailed error analysis that is confirmed by numerical
results. The tests performed are for the evolution from anisotropic Maxwellian
and a bump-on-tail distribution.


  In 1933, Fritz Zwicky's famous investigations of the mass of the Coma cluster
led him to infer the existence of dark matter \cite{1933AcHPh...6..110Z}. His
fundamental discoveries have proven to be foundational to modern cosmology; as
we now know such dark matter makes up 85\% of the matter and 25\% of the
mass-energy content in the universe. Galaxy clusters like Coma are massive,
complex systems of dark matter in addition to hot ionized gas and thousands of
galaxies, and serve as excellent probes of the dark matter distribution.
However, empirical studies show that the total mass of such systems remains
elusive and difficult to precisely constrain. Here, we present new estimates
for the dynamical mass of the Coma cluster based on Bayesian deep learning
methodologies developed in recent years. Using our novel data-driven approach,
we predict Coma's $\mthc$ mass to be $10^{15.10 \pm 0.15}\ \hmsun$ within a
radius of $1.78 \pm 0.03\ h^{-1}\mathrm{Mpc}$ of its center. We show that our
predictions are rigorous across multiple training datasets and statistically
consistent with historical estimates of Coma's mass. This measurement
reinforces our understanding of the dynamical state of the Coma cluster and
advances rigorous analyses and verification methods for empirical applications
of machine learning in astronomy.


  We show that every cubic form with coefficients in an imaginary quadratic
number field $K/\mathbb{Q}$ in at least $14$ variables represents zero
non-trivially. This builds on the corresponding seminal result by Heath-Brown
for rational cubic forms. As an application we deduce that a pair of rational
cubic forms has a non-trivial rational solution provided that $s \geq 627$.
Furthermore, we show that every rational cubic hypersurface in at least $33$
variables contains a rational line, and that every rational cubic form in at
least $33$ variables has "almost-prime" solutions.


  Point-contact Andreev-reflection measurements were performed in
SmFeAsO_{0.8}F_{0.2} polycrystals with T_c \simeq 53 K. The experimental
conductance curves reproducibly exhibit peaks around \pm 6 mV and shoulders at
V \sim 16-20 mV, indicating the presence of two nodeless superconducting gaps.
While the single-band Blonder-Tinkham-Klapwijk fit can only reproduce a small
central portion of the conductance curve, the two-gap one accounts remarkably
well for the shape of the whole experimental dI/dV. The fits of the normalized
curves give Delta_1(0) = 6.15 \pm 0.45 meV and Delta_2(0) = 18 \pm 3 meV. Both
gaps close at the same temperature and follow a BCS-like behavior.


  We examine the violation of the majorization relations between the
eigenvalues of the full and reduced density operators of entangled states of
composite systems and its detection using generalized entropic forms based on
arbitrary concave functions. It is shown that the violation of these relations
may not always be detected by the conditional von Neumann and Tsallis entropies
(for any $q>0$). Families of smooth entropic forms which are always able to
detect such violations are, however, provided. These features are then examined
for particular sets of mixed states in a two-qudit system, which for $d\geq 3$
may exhibit different types of violation of the majorization relations.
Comparison with the Peres criterion for separability is also shown.


  Lasell and Ramachandran show that the existence of rational curves of
positive self-intersection on a smooth projective surface $X$ implies that all
the finite dimensional linear representations of the fundamental group
$\pi_1(X)$ are finite. In this article, we generalize Lasell and Ramachandran's
result to the case of $\pi_1$-small divisors on quasiprojective varieties. We
also study $\pi_1$-small curves and hyperbolicity properties of smooth
projective surfaces of general type with infinite fundamental groups.


  Fast radio bursts (FRBs) are millisecond-duration pulses of radio emission
originating from extragalactic distances. Radio dispersion on each burst is
imparted by intervening plasma mostly located in the intergalactic medium. We
observe a burst, FRB 20220610A, in a morphologically complex host galaxy system
at redshift $z=1.016 \pm 0.002$. The burst redshift and dispersion are
consistent with passage through a substantial column of material from the
intergalactic medium. The burst shows evidence for passage through additional
turbulent magnetized plasma, potentially associated with the host galaxy. We
use the burst energy of $2 \times 10^{42}$ erg, to revise the maximum energy of
an FRB.


  This paper introduces two matrix analogues for set partitions. A composition
matrix on a finite set X is an upper triangular matrix whose entries partition
X, and for which there are no rows or columns containing only empty sets. A
partition matrix is a composition matrix in which an order is placed on where
entries may appear relative to one-another. We show that partition matrices are
in one-to-one correspondence with inversion tables. Non-decreasing inversion
tables are shown to correspond to partition matrices with a row ordering
relation. Partition matrices which are s-diagonal are classified in terms of
inversion tables. Bidiagonal partition matrices are enumerated using the
transfer-matrix method and are equinumerous with permutations which are
sortable by two pop-stacks in parallel. We show that composition matrices on X
are in one-to-one correspondence with (2+2)-free posets on X. Also, composition
matrices whose rows satisfy a column-ordering relation are shown to be in
one-to-one correspondence with parking functions. Finally, we show that pairs
of ascent sequences and permutations are in one-to-one correspondence with
(2+2)-free posets whose elements are the cycles of a permutation, and use this
relation to give an expression for the number of (2+2)-free posets on
{1,...,n}.


  We present a method for early detection of lymphatic fluid accumulation in
lymphedema patients based on microwave imaging of the limb volume across an air
gap. The proposed algorithm uses contour information of the imaged limb surface
to approximate the wave propagation velocity locally to solve the eikonal
equation for implementing the adjoint imaging operator. This modified
backprojection algorithm results in focused imagery close to the limb surface
where lymphatic fluid accumulation presents itself. Next, a deep neural network
based on U-Net architecture is employed to identify the location and extent of
the lymphatic fluid. Simulation studies with various upper and lower arm
profiles compare the focusing performance of the proposed contour assisted
backprojection imaging with the baseline imaging approach that assumes
homogeneous media. The empirical results of the simulation experiments show
that the proposed imaging method significantly improves the ability of the
deepnet model to identify the location and the volume of the excess fluid in
the limb.


  Lecture given Friday 7 April 1995 at the Santa Fe Institute, Santa Fe, New
Mexico. The lecture was videotaped; this is an edited transcript.


  Let a measurement consist of a linear combination of damped complex
exponential modes, plus noise. The problem is to estimate the parameters of
these modes, as in line spectrum estimation, vibration analysis, speech
processing, system identification, and direction of arrival estimation. Our
results differ from standard results of modal analysis to the extent that we
consider sparse and co-prime samplings in space, or equivalently sparse and
co-prime samplings in time. Our main result is a characterization of the
orthogonal subspace. This is the subspace that is orthogonal to the signal
subspace spanned by the columns of the generalized Vandermonde matrix of modes
in sparse or co-prime arrays. This characterization is derived in a form that
allows us to adapt modern methods of linear prediction and approximate least
squares, such as iterative quadratic maximum likelihood (IQML), for estimating
mode parameters. Several numerical examples are presented to demonstrate the
validity of the proposed modal estimation methods, and to compare the fidelity
of modal estimation with sparse and co-prime arrays, versus SNR. Our
calculations of Cram\'{e}r-Rao bounds allow us to analyze the loss in
performance sustained by sparse and co-prime arrays that are compressions of
uniform linear arrays.


  In the recent paper [Jin, Kolda & Ward, arXiv:1909.04801], it is proved that
the Kronecker fast Johnson-Lindenstrauss transform (KFJLT) is, in fact, a
Johnson-Lindenstrauss transform, which had previously only been conjectured. In
this paper, we provide an alternative proof of this, for when the KFJLT is
applied to Kronecker vectors, using a coherence and sampling argument. Our
proof yields a different bound on the embedding dimension, which can be
combined with the bound in the paper by Jin et al. to get a better bound
overall. As a stepping stone to proving our result, we also show that the KFJLT
is a subspace embedding for matrices with columns that have Kronecker product
structure. Lastly, we compare the KFJLT to four other sketch techniques in
numerical experiments on both synthetic and real-world data.


  Human exhibit rich gender cues in both appearance and behavior. In computer
vision domain, gender recognition from facial appearance have been extensively
studied, while facial behavior based gender recognition studies remain rare. In
this work, we first demonstrate that facial expressions influence the gender
patterns presented in 3D face, and gender recognition performance increases
when training and testing within the same expression. In further, we design
experiments which directly extract the morphological changes resulted from
facial expressions as features, for expression-based gender recognition.
Experimental results demonstrate that gender can be recognized with
considerable accuracy in Happy and Disgust expressions, while Surprise and Sad
expressions do not convey much gender related information. This is the first
work in the literature which investigates expression-based gender
classification with 3D faces, and reveals the strength of gender patterns
incorporated in different types of expressions, namely the Happy, the Disgust,
the Surprise and the Sad expressions.


  The main aim of this paper is to introduce some examples of non-compact
locally compact quantum groups to a non-specialized audience. The major
importance of these examples is their simplicity. Other examples as the quantum
E(2) group of Woronowicz are much more difficult to construct. We will make use
of the bicrossed product construction to obtain our examples. This construction
dates back to Kac, Takeuchi and Majid. It was also considered by Baaj &
Skandalis.


  Surface densities of gas, dust and stars provide a window into the physics of
star-formation that, until the advent of high-resolution
far-infrared/sub-millimeter observations, has been historically difficult to
assess amongst dusty galaxies. To study the link between infrared (IR) surface
densities and dust properties, we leverage the Atacama Large
Millimetre/Submillimetre Array (ALMA) archive to measure the extent of cold
dust emission in 15 $z\sim2$ IR selected galaxies selected on the basis of
having available mid-IR spectroscopy from Spitzer. We use the mid-IR spectra to
constrain the relative balance between dust heating from star-formation and
active galactic nuclei (AGN), and to measure emission from Polycylic Aromatic
Hydrocarbons (PAHs) -- small dust grains that play a key role in the
photoelectric heating of gas. In general, we find that dust-obscured
star-formation at high IR surface densities exhibits similar properties at low-
and high-redshift, namely: local luminous IR galaxies have comparable PAH
luminosity to total dust mass ratios as high-$z$ galaxies, and star-formation
at $z\sim0-2$ is more efficient at high IR surface densities despite the fact
that our sample of high$-z$ galaxies are closer to the main-sequence than local
luminous IR galaxies. High star-formation efficiencies are coincident with a
decline in the PAH/IR luminosity ratio reminiscent of the deficit observed in
far-infrared fine-structure lines. Changes in the gas and dust conditions
arising from high star-formation surface densities might help drive the
star-formation efficiency up. This could help explain high efficiencies needed
to reconcile star-formation and gas volume densities in dusty galaxies at
cosmic noon.


  The $s_{i}={1/2}$ nearest neighbor antiferromagnetic Heisenberg model is
considered for spins sitting on the vertices of clusters with the connectivity
of fullerene molecules and a number of sites $n$ ranging from 24 to 32. Using
the permutational and spin inversion symmetries of the Hamiltonian the low
energy spectrum is calculated for all the irreducible representations of the
symmetry group of each cluster. Frustration and connectivity result in
non-trivial low energy properties, with the lowest excited states being
singlets except for $n=28$. Same hexagon and same pentagon correlations are the
most effective in the minimization of the energy, with the $n=32-D_{3h}$
symmetry cluster having an unusually strong singlet intra-pentagon correlation.
The magnetization in a field shows no discontinuities unlike the icosahedral
$I_h$ fullerene clusters, but only plateaux with the most pronounced for
$n=28$. The spatial symmetry as well as the connectivity of the clusters appear
to be important for the determination of their magnetic properties.


  In this article, we investigate large prime factors of Fourier coefficients
of non-CM normalized cuspidal Hecke eigenforms in short intervals. One of the
new ingredients involves deriving an explicit version of Chebotarev density
theorem in an interval of length $\frac{x}{(\log x)^A}$ for any $A>0$,
modifying an earlier work of Balog and Ono. Furthermore, we need to strengthen
a work of Rouse-Thorner to derive a lower bound for the largest prime factor of
Fourier coefficients in an interval of length $x^{1/2 + \epsilon}$ for any
$\epsilon >0$.


  In this paper we study the worst-case complexity of an inexact Augmented
Lagrangian method for nonconvex constrained problems. Assuming that the penalty
parameters are bounded, we prove a complexity bound of
$\mathcal{O}(|\log(\epsilon)|)$ outer iterations for the referred algorithm to
generate an $\epsilon$-approximate KKT point, for $\epsilon\in (0,1)$. When the
penalty parameters are unbounded, we prove an outer iteration complexity bound
of $\mathcal{O}\left(\epsilon^{-2/(\alpha-1)}\right)$, where $\alpha>1$
controls the rate of increase of the penalty parameters. For linearly
constrained problems, these bounds yield to evaluation complexity bounds of
$\mathcal{O}(|\log(\epsilon)|^{2}\epsilon^{-2})$ and
$\mathcal{O}\left(\epsilon^{-\left(\frac{2(2+\alpha)}{\alpha-1}+2\right)}\right)$,
respectively, when appropriate first-order methods ($p=1$) are used to
approximately solve the unconstrained subproblems at each iteration. In the
case of problems having only linear equality constraints, the latter bounds are
improved to $\mathcal{O}(|\log(\epsilon)|^{2}\epsilon^{-(p+1)/p})$ and
$\mathcal{O}\left(\epsilon^{-\left(\frac{4}{\alpha-1}+\frac{p+1}{p}\right)}\right)$,
respectively, when appropriate $p$-order methods ($p\geq 2$) are used as inner
solvers.


  A system composed of an ideal gas of N fermions interacting with an impurity
particle in two space dimensions is considered. The interaction between
impurity and fermions is given in terms of two-body point interactions whose
strength is determined by the two-body binding energy, which is a free
parameter of the model. If the mass of the impurity is 1.225 times larger than
the mass of a fermion, it is shown that the energy is bounded below uniformly
in the number N of fermions. This result improves previous, N-dependent lower
bounds and it complements a recent, similar bound for the Fermi polaron in
three space dimensions.


  Biological molecular machines are bifunctional enzymes that catalyze two
processes: one donating free energy and the other accepting it. Recent studies
show that most protein enzymes have rich stochastic dynamics of transitions
between the multitude of conformation substates that make up their native
state. This dynamics often manifests itself in fluctuating rates of the
catalyzed processes and the presence of short-term memory. For such stochastic
dynamics, after dividing the free energy into operational and organizational
energy, we proved the generalized fluctuation theorem, which leads to the
extension of the second law of thermodynamics to include two competing
functions of process: dissipation and information. Computer simulation of the
course of catalyzed processes taking place on the model network of substates,
expressed in jumps of unit values at random moments of time, indicates the
possibility of negative dissipation of the organizational free energy at the
expense of information temporarily stored in memory, i.e. the behavior like
Maxwell's demon. Because similar courses can be registered in observation of
real systems, all theses of the paper are open to experimental verification.


  Aims. We investigate the degree of improvement in dark energy constraints
that can be achieved by extending Type Ia Supernova (SN Ia) samples to
redshifts z > 1.5 with the Hubble Space Telescope (HST), particularly in the
ongoing CANDELS and CLASH multi-cycle treasury programs.
  Methods. Using the popular CPL parametrization of the dark energy, w = w0
+wa(1-a), we generate mock SN Ia samples that can be projected out to higher
redshifts. The synthetic datasets thus generated are fitted to the CPL model,
and we evaluate the improvement that a high-z sample can add in terms of
ameliorating the statistical and systematic uncertainties on cosmological
parameters.
  Results. In an optimistic but still very achievable scenario, we find that
extending the HST sample beyond CANDELS+CLASH to reach a total of 28 SN Ia at z
> 1.0 could improve the uncertainty in the wa parameter by up to 21%. The
corresponding improvement in the figure of merit (FoM) would be as high as 28%.
Finally, we consider the use of high-redshift SN Ia samples to detect
non-cosmological evolution in SN Ia luminosities with redshift, finding that
such tests could be undertaken by future spacebased infrared surveys using the
James Webb Space Telescope (JWST).


  This article proposes a new method to estimate an existing mutual information
based dependence measure using histogram density estimates. Finding a suitable
bin length for histogram is an open problem. We propose a new way of computing
the bin length for histogram using a function of maximum separation between
points. The chosen bin length leads to consistent density estimates for
histogram method. The values of density thus obtained are used to calculate an
estimate of an existing dependence measure. The proposed estimate is named as
Mutual Information Based Dependence Index (MIDI). Some important properties of
MIDI have also been stated. The performance of the proposed method has been
compared to generally accepted measures like Distance Correlation (dcor),
Maximal Information Coefficient (MINE) in terms of accuracy and computational
complexity with the help of several artificial data sets with different amounts
of noise. The proposed method is able to detect many types of relationships
between variables, without making any assumption about the functional form of
the relationship. The power statistics of proposed method illustrate their
effectiveness in detecting non linear relationship. Thus, it is able to achieve
generality without a high rate of false positive cases. MIDI is found to work
better on a real life data set than competing methods. The proposed method is
found to overcome some of the limitations which occur with dcor and MINE.
Computationally, MIDI is found to be better than dcor and MINE, in terms of
time and memory, making it suitable for large data sets.


  Creativity is an indispensable part of human cognition and also an inherent
part of how we make sense of the world. Metaphorical abstraction is fundamental
in communicating creative ideas through nuanced relationships between abstract
concepts such as feelings. While computer vision benchmarks and approaches
predominantly focus on understanding and generating literal interpretations of
images, metaphorical comprehension of images remains relatively unexplored.
Towards this goal, we introduce MetaCLUE, a set of vision tasks on visual
metaphor. We also collect high-quality and rich metaphor annotations (abstract
objects, concepts, relationships along with their corresponding object boxes)
as there do not exist any datasets that facilitate the evaluation of these
tasks. We perform a comprehensive analysis of state-of-the-art models in vision
and language based on our annotations, highlighting strengths and weaknesses of
current approaches in visual metaphor Classification, Localization,
Understanding (retrieval, question answering, captioning) and gEneration
(text-to-image synthesis) tasks. We hope this work provides a concrete step
towards developing AI systems with human-like creative capabilities.


  We develop an approach to risk classification based on quantile contours and
allometric modelling of multivariate anthropometric measurements. We propose
the definition of allometric direction tangent to the directional quantile
envelope, which divides ratios of measurements into half-spaces. This in turn
provides an operational definition of directional quantile that can be used as
cutoff for risk assessment. We show the application of the proposed approach
using a large dataset from the Vermont Oxford Network containing observations
of birthweight (BW) and head circumference (HC) for more than 150,000 preterm
infants. Our analysis suggests that disproportionately growth-restricted
infants with a larger HC-to-BW ratio are at increased mortality risk as
compared to proportionately growth-restricted infants. The role of maternal
hypertension is also investigated.