  Linear [Q/H]-[O/H] relations, Q = Na, Mg, Si, Ca, Ti, Cr, Fe, Ni, are
inferred from a sample (N=67) of recently studied FGK-type dwarf stars in the
solar neighbourhood including different populations. Regression line slope and
intercept estimators and related variance estimators are determined. With
regard to the straight line, [Q/H] = aQ [O/H] + bQ, sample stars display along
a "main sequence", [Q,O] = [aQ,bQ, Delta bQ], leaving aside the two OL stars
which, in most cases (e.g., Na), lie outside. A unit slope, aQ = 1, implies Q
is a primary element synthesised via SNII progenitors in presence of universal
stellar initial mass function (defined as simple primary element). To this
respect, Mg, Si, Ti, show aQ = 1 within 2 sigma(aQ); Cr, Fe, Ni, within 3
sigma(aQ); Na, Ca, exceeding 3 sigma(aQ). The empirical, differential element
abundance distributions are inferred from different subsamples, where related
regression lines represent their theoretical counterparts within the framework
of simple MCBR (multistage closed box + reservoir) chemical evolution models.
Hence the fractional yields are determined and (as an example) a comparison is
shown with their theoretical counterparts inferred from SNII progenitor
nucleosynthesis under the assumption of a power-law stellar initial mass
function. The generalized fractional yields are determined regardless from the
chemical evolution model. The ratio of outflow to star formation rate is
compared for different populations, in the framework of simple MCBR models. The
opposite situation of element abundance variation entirely due to cosmic
scatter is also considered under reasonable assumptions. The related
differential element abundance distribution fits to the data as well as its
counterpart inferred in the opposite limit of instantaneous mixing in presence
of chemical evolution.


  Transformations achievable by linear optical components allow to generate the
whole unitary group only when restricted to the one-photon subspace of a
multimode Fock space. In this paper, we address the more general problem of
encoding quantum information by multiphoton states, and elaborating it via
ancillary extensions, linear optical passive devices and photodetection. Our
scheme stems in a natural way from the mathematical structures underlying the
physics of linear optical passive devices. In particular, we analyze an
economical procedure for mapping a fiducial 2-photon 2-mode state into an
arbitrary 2-photon 2-mode state using ancillary resources and linear optical
passive N-ports assisted by post-selection. We found that adding a single
ancilla mode is enough to generate any desired target state. The effect of
imperfect photodetection in post-selection is considered and a simple trade-off
between success probability and fidelity is derived.


  Software engineering of network-centric Artificial Intelligence (AI) and
Internet of Things (IoT) enabled Cyber-Physical Systems (CPS) and services,
involves complex design and validation challenges. In this paper, we propose a
novel approach, based on the model-driven software engineering paradigm, in
particular the domain-specific modeling methodology. We focus on a
sub-discipline of AI, namely Machine Learning (ML) and propose the delegation
of data analytics and ML to the IoT edge. This way, we may increase the service
quality of ML, for example, its availability and performance, regardless of the
network conditions, as well as maintaining the privacy, security and
sustainability. We let practitioners assign ML tasks to heterogeneous edge
devices, including highly resource-constrained embedded microcontrollers with
main memories in the order of Kilobytes, and energy consumption in the order of
milliwatts. This is known as TinyML. Furthermore, we show how software models
with different levels of abstraction, namely platform-independent and
platform-specific models can be used in the software development process.
Finally, we validate the proposed approach using a case study addressing the
predictive maintenance of a hydraulics system with various networked sensors
and actuators.


  We study the impact of resonantly scattered X-ray line emission on the
observability of the hot circumgalactic medium (CGM) of galaxies. We apply a
Monte Carlo radiative transfer post-processing analysis to the high-resolution
TNG50 cosmological magnetohydrodynamical galaxy formation simulation. This
allows us to model the resonant scattering of OVII(r) X-ray photons within the
complex, multi-phase, multi-scale CGM. The resonant transition of the OVII
He-like triplet is one of the brightest, and most promising, X-ray emission
lines for detecting the hot CGM and measuring its physical properties. We focus
on galaxies with stellar masses 10 < log(M*/Msun) < 11 at z ~ 0. After
constructing a model for OVII(r) emission from the central galaxy as well as
from CGM gas, we forward model these intrinsic photons to derive observable
surface brightness maps. We find that scattering significantly boosts the
observable OVII(r) surface brightness of the extended and diffuse CGM. This
enhancement can be large -- an order of magnitude on average at a distance of
200 projected kpc for high-mass M* = 10^10.7 Msun galaxies. The enhancement is
larger for lower mass galaxies, and can even reach a factor of 100, across the
extended CGM. Galaxies with higher star formation rates, AGN luminosities, and
central OVII(r) luminosities all have larger scattering enhancements, at fixed
stellar mass. Our results suggest that next-generation X-ray spectroscopic
missions including XRISM, LEM, ATHENA, and HUBS -- which aim to detect the hot
CGM in emission -- could specifically target halos with significant
enhancements due to resonant scattering.


  In the present work we analyse the dynamics of indirect connections between
insurance companies that result from market price channels. In our analysis we
assume that the stock quotations of insurance companies reflect market
sentiments which constitute a very important systemic risk factor.
Interlinkages between insurers and their dynamics have a direct impact on
systemic risk contagion in the insurance sector. We propose herein a new hybrid
approach to the analysis of interlinkages dynamics based on combining the
copula-DCC-GARCH model and Minimum Spanning Trees (MST). Using the
copula-DCC-GARCH model we determine the tail dependence coefficients. Then, for
each analysed period we construct MST based on these coefficients. The dynamics
is analysed by means of time series of selected topological indicators of the
MSTs in the years 2005-2019. Our empirical results show the usefulness of the
proposed approach to the analysis of systemic risk in the insurance sector. The
times series obtained from the proposed hybrid approach reflect the phenomena
occurring on the market. The analysed MST topological indicators can be
considered as systemic risk predictors.


  A novel way of filling high aspect ratio vertical interconnection (microvias)
with an aspect ratio of >2:1 is presented. High frequency acoustic streaming at
megasonic frequencies enables the decrease of the Nernst-diffusion layer down
to the sub-micron range, allowing thereby conformal electrodeposition in deep
grooves. Higher throughput and better control over the deposition properties
are possible for the manufacturing of interconnections and metal-based MEMS.


  In this work, we have studied the peregrine rogue wave dynamics, with a
solitons on finite background (SFB) ansatz, in the recently proposed (Phys.
Rev. Lett. 110 (2013) 064105) continuous nonlinear Schrodinger system with
parity-time symmetric Kerr nonlinearity. We have found that the continuous
nonlinear Schrodinger system with PT-symmetric nonlinearity also admits
Peregrine Soliton solution. Motivated by the fact that Peregrine solitons are
regarded as prototypical solutions of rogue waves, we have studied Peregrine
rogue wave dynamics in the c-PTNLSE model. Upon numerical computation, we
observe the appearance of low-intense Kuznetsov-Ma (KM) soliton trains in the
absence of transverse shift (unbroken PT-symmetry) and well-localized
high-intense Peregrine Rogue waves in the presence of transverse shift (broken
PT-symmetry) in a definite parametric regime.


  There are indications that $\gamma$-ray dark objects such as supernovae (SNe)
with choked jets, and the cores of active galactic nuclei may contribute to the
diffuse flux of astrophysical neutrinos measured by the IceCube observatory. In
particular, stripped-envelope SNe have received much attention since they are
capable of producing relativistic jets and could explain the diversity in
observations of collapsar explosions (e.g., gamma-ray bursts (GRBs),
low-luminosity GRBs, and Type Ibc SNe). We use an unbinned maximum likelihood
method to search for spatial and temporal coincidences between Type Ibc
core-collapse SNe, which may harbor a choked jet, and muon neutrinos from a
sample of IceCube up-going track-like events measured from May 2011-May 2012.
In this stacking analysis, we find no significant deviation from a
background-only hypothesis using one year of data, and are able to place upper
limits on the total amount of isotropic equivalent energy that choked jet
core-collapse SNe deposit in cosmic rays ${\mathcal E}_{\rm cr}$ and the
fraction of core-collapse SNe which have a jet pointed towards Earth $f_{\rm
jet}$. This analysis can be extended with yet to be made public IceCube data,
and the increased amount of optically detected core-collapse SNe discovered by
wide field-of-view surveys such as the Palomar Transient Factory and All-Sky
Automated Survey for Supernovae. The choked jet SNe/high-energy cosmic neutrino
connection can be more tightly constrained in the near future.


  The partition function on the three-sphere of many supersymmetric
Chern-Simons-matter theories reduces, by localization, to a matrix model. We
develop a new method to study these models in the M-theory limit, but at all
orders in the 1/N expansion. The method is based on reformulating the matrix
model as the partition function of an ideal Fermi gas with a non-trivial,
one-particle quantum Hamiltonian. This new approach leads to a completely
elementary derivation of the N^{3/2} behavior for ABJM theory and N=3 quiver
Chern-Simons-matter theories. In addition, the full series of 1/N corrections
to the original matrix integral can be simply determined by a next-to-leading
calculation in the WKB or semiclassical expansion of the quantum gas, and we
show that, for several quiver Chern-Simons-matter theories, it is given by an
Airy function. This generalizes a recent result of Fuji, Hirano and Moriyama
for ABJM theory. It turns out that the semiclassical expansion of the Fermi gas
corresponds to a strong coupling expansion in type IIA theory, and it is dual
to the genus expansion. This allows us to calculate explicitly non-perturbative
effects due to D2-brane instantons in the AdS background.


  The hot carrier dynamics and its effect on the device performance of GaAs
solar cell and InAs/GaAs quantum dot solar cell (QDSC) was investigated. At
first, the fundamental operation feature of conventional hot carrier solar cell
was simulated based on the detailed balance thermodynamic model. Then we
investigated the hot carrier dynamics in the normal junction based solar cell
using hydrodynamic/energy Boltzmann transportation model (HETM) where the two
temperature (carrier temperature and lattice temperature are treated
separately. For the first time, we report an inherent quasi-equivalence between
the detailed balance model and HETM model. The inter-link revealed here
addresses the energy conservation law used in the detailed balance model from
different angle and it paves a way toward an alternative approach to curtail
the selective contact constraints used in the conventional hot carrier solar
cell. In simulation, a specially designed InAs/GaAs quantum dot solar cell was
used in the simulation. By varying the hot carrier energy relaxation time , an
increase in the open circuit voltage was clearly found with the increase of .
Detailed analysis was presented regarding the spatial distribution of hot
carrier temperature and its interplay with electric field and three hot carrier
recombination processes (Auger, SRH and radiative)


  The recent state-of-the-art natural language understanding (NLU) systems
often behave unpredictably, failing on simpler reasoning examples. Despite
this, there has been limited focus on quantifying progress towards systems with
more predictable behavior. We think that reasoning capability-wise behavioral
summary is a step towards bridging this gap. We create a CheckList test-suite
(184K examples) for the Natural Language Inference (NLI) task, a representative
NLU task. We benchmark state-of-the-art NLI systems on this test-suite, which
reveals fine-grained insights into the reasoning abilities of BERT and RoBERTa.
Our analysis further reveals inconsistencies of the models on examples derived
from the same template or distinct templates but pertaining to same reasoning
capability, indicating that generalizing the models' behavior through
observations made on a CheckList is non-trivial. Through an user-study, we find
that users were able to utilize behavioral information to generalize much
better for examples predicted from RoBERTa, compared to that of BERT.


  We report the first measurement of the absolute branching fraction of the
inclusive decay $\Lambda_c^+ \to K_S^0X$. The analysis is performed using an
$e^+e^-$ collision data sample corresponding to an integrated luminosity of 567
pb$^{-1}$ taken at $\sqrt{s}$ = 4.6 GeV with the BESIII detector. Using eleven
Cabibbo-favored $\bar{\Lambda}_c^-$ decay modes and the double-tag technique,
this absolute branching fraction is measured to be $\mathcal{B}(\Lambda_c^+ \to
K_S^0X)=(9.9\pm0.6\pm0.4)\%$, where the first uncertainty is statistical and
the second systematic. The relative deviation between the branching fractions
for the inclusive decay and the observed exclusive decays is $(18.7\pm8.3)\%$,
which indicates that there may be some unobserved decay modes with a neutron or
excited baryons in the final state.


  Cellular phone is one of the most developing technological artifacts today.
The evolution occurs through random innovation. Our effort is trying to view
the evolution of this artifact from memetics. By constructing a phylomemetic
tree based on cellular phone memes to infer or estimate the evolutionary
history and relationship among cellular phone. We adopt several methods, which
are commonly used in constructing phylogenetic tree, they are UPGMA algorithm
and Parsimony Maximum algorithm to construct cellphone phylomemetic tree.
Therefore we compare with the innovation tree, which is based on serial number
and their appearance time. From phylomemetic tree, we then analyze the process
of a cellular phone innovation through looking out on the cellular phone type
lies in the same cluster. The comparison of the simulation tree result shows a
generally different branching pattern, giving a presumption that innovation in
cellular phone is not really relating with their serial number, but occurs
merely because of random mutation of allomeme design and competes with its
technological development.


  The Integrated Nested Laplace Approximation (INLA) has established itself as
a widely used method for approximate inference on Bayesian hierarchical models
which can be represented as a latent Gaussian model (LGM). INLA is based on
producing an accurate approximation to the posterior marginal distributions of
the parameters in the model and some other quantities of interest by using
repeated approximations to intermediate distributions and integrals that appear
in the computation of the posterior marginals.
  INLA focuses on models whose latent effects are a Gaussian Markov random
field (GMRF). For this reason, we have explored alternative ways of expanding
the number of possible models that can be fitted using the INLA methodology. In
this paper, we present a novel approach that combines INLA and Markov chain
Monte Carlo (MCMC). The aim is to consider a wider range of models that cannot
be fitted with INLA unless some of the parameters of the model have been fixed.
Hence, conditioning on these parameters the model could be fitted with the
R-INLA package. We show how new values of these parameters can be drawn from
their posterior by using conditional models fitted with INLA and standard MCMC
algorithms, such as Metropolis-Hastings. Hence, this will extend the use of
INLA to fit models that can be expressed as a conditional LGM. Also, this new
approach can be used to build simpler MCMC samplers for complex models as it
allows sampling only on a limited number parameters in the model.
  We will demonstrate how our approach can extend the class of models that
could benefit from INLA, and how the R-INLA package will ease its
implementation. We will go through simple examples of this new approach before
we discuss more advanced problems with datasets taken from relevant literature.


  We give arguments in the support of a relation between M-atrix theory and
Maldacena's conjecture. M-atrix theory conjecture implies the equivalence of
11-D light-cone supergravity and strongly-coupled (0+1)-D SYM. Maldacena's
SUGRA/SYM duality conjecture implies, in the one dimensional SYM case, the
equivalence between strongly-coupled (0+1)-D SYM and 11-D supergravity
compactified on a spatial circle in the formal Seiberg-Sen limit. Using the
classical equivalence between 11-D supergravity on a light-like circle and on a
spatial circle in the formal Seiberg-Sen limit, we argue that in the (0+1)-D
SYM case, the large-N M-atrix theory in the supergravity regime is equivalent
to SUGRA/SYM duality.


  Employing theory and numerical simulations, we demonstrate discontinuous
force thinning due to the motion of an external probe in a host medium, which
we approximate as structureless. When the driving of the probe exceeds a
critical force, the microviscosity of the medium drops abruptly by about an
order of magnitude. This phenomenon occurs for strong attractive interactions
between probe and a sufficiently dense host medium.


  Given a slightly degenerate fusion category $\mathcal{C}$, we explain how it
naturally gives rise to a Z-modular data. We do not restrict to spherical
categories and work with pivotal categories instead. Finally, we give an
interpretation in this framework of the Bonnaf\'e-Rouquier categorification of
the $\mathbb{Z}$-modular datum associated to non trivial family of the cyclic
complex reflection group.


  Neural Radiance Fields (NeRF) has recently gained popularity for its
impressive novel view synthesis ability. This paper studies the problem of
hallucinated NeRF: i.e., recovering a realistic NeRF at a different time of day
from a group of tourism images. Existing solutions adopt NeRF with a
controllable appearance embedding to render novel views under various
conditions, but they cannot render view-consistent images with an unseen
appearance. To solve this problem, we present an end-to-end framework for
constructing a hallucinated NeRF, dubbed as Ha-NeRF. Specifically, we propose
an appearance hallucination module to handle time-varying appearances and
transfer them to novel views. Considering the complex occlusions of tourism
images, we introduce an anti-occlusion module to decompose the static subjects
for visibility accurately. Experimental results on synthetic data and real
tourism photo collections demonstrate that our method can hallucinate the
desired appearances and render occlusion-free images from different views. The
project and supplementary materials are available at
https://rover-xingyu.github.io/Ha-NeRF/.


  A tuning-free procedure is proposed to estimate the covariate-adjusted
Gaussian graphical model. For each finite subgraph, this estimator is
asymptotically normal and efficient. As a consequence, a confidence interval
can be obtained for each edge. The procedure enjoys easy implementation and
efficient computation through parallel estimation on subgraphs or edges. We
further apply the asymptotic normality result to perform support recovery
through edge-wise adaptive thresholding. This support recovery procedure is
called ANTAC, standing for Asymptotically Normal estimation with Thresholding
after Adjusting Covariates. ANTAC outperforms other methodologies in the
literature in a range of simulation studies. We apply ANTAC to identify
gene-gene interactions using an eQTL dataset. Our result achieves better
interpretability and accuracy in comparison with CAMPE.


  Economic-wise, a common goal for companies conducting marketing is to
maximize the return revenue/profit by utilizing the various effective marketing
strategies. Consumer behavior is crucially important in economy and targeted
marketing, in which behavioral economics can provide valuable insights to
identify the biases and profit from customers. Finding credible and reliable
information on products' profitability is, however, quite difficult since most
products tends to peak at certain times w.r.t. seasonal sales cycle in a year.
On-Shelf Availability (OSA) plays a key factor for performance evaluation.
Besides, staying ahead of hot product trends means we can increase marketing
efforts without selling out the inventory. To fulfill this gap, in this paper,
we first propose a general profit-oriented framework to address the problem of
revenue maximization based on economic behavior, and compute the 0n-shelf
Popular and most Profitable Products (OPPPs) for the targeted marketing. To
tackle the revenue maximization problem, we model the k-satisfiable product
concept and propose an algorithmic framework for searching OPPP and its
variants. Extensive experiments are conducted on several real-world datasets to
evaluate the effectiveness and efficiency of the proposed algorithm.


  Consider a finite Blaschke product $f$ with $f(0) = 0$ which is not a
rotation and denote by $f^n$ its $n$-th iterate. Given a sequence $\{a_n\}$ of
complex numbers, consider the series $F(z) = \sum_n a_n f^n(z).$ We show that
for any $w \in \mathbb{C},$ if $\{a_n\}$ tends to zero but $\sum_n |a_n| =
\infty,$ then the set of points $\xi$ in the unit circle for which the series
$F$ converges to $w$ has Hausdorff dimension $1.$ Moreover, we prove that this
result is optimal in the sense that the conclusion does not hold in general if
one considers Hausdorff measures given by any measure function more restrictive
than the power functions $t^\delta,$ $0 < \delta < 1.$


  We reformulate Heegaard Floer homology in terms of holomorphic curves in the
cylindrical manifold Sigma x [0,1] x R, where Sigma is the Heegaard surface,
instead of Sym^g(Sigma). We then show that the entire invariance proof can be
carried out in our setting. In the process, we derive a new formula for the
index of the dbar-operator in Heegaard Floer homology, and shorten several
proofs. After proving invariance, we show that our construction is equivalent
to the original construction of Ozsvath-Szabo. We conclude with a discussion of
elaborations of Heegaard Floer homology suggested by our construction, as well
as a brief discussion of the relation with a program of C Taubes.


  We consider the problem of estimating the probability of an observed string
drawn i.i.d. from an unknown distribution. The key feature of our study is that
the length of the observed string is assumed to be of the same order as the
size of the underlying alphabet. In this setting, many letters are unseen and
the empirical distribution tends to overestimate the probability of the
observed letters. To overcome this problem, the traditional approach to
probability estimation is to use the classical Good-Turing estimator. We
introduce a natural scaling model and use it to show that the Good-Turing
sequence probability estimator is not consistent. We then introduce a novel
sequence probability estimator that is indeed consistent under the natural
scaling model.


  In a previous paper, we studied two statistical methods used to analyse the
variability of active galactic nuclei (AGNs): the C and F statistics. Applying
them to observed differential light-curves of 39 AGNs, we found that, even
though the C criterion cannot be considered as an actual statistical test, it
could still be a useful parameter to detect variability, whereas F is a good
detector of non-variability. In order to test these results under controlled
input conditions, so that the different error sources could be individually
evaluated, we generated a series of synthetic differential light curves
simulating astronomical images with different atmospheric conditions, such as
cloud cover, seeing or sky brightness, as well as several types of intrinsic
variability of the AGN, all with a specific instrumental configuration. Having
obtained light curves for each case, we applied both statistics to them in
order to test their reliability. We found that a weight factor should always be
used with these indices. The F test has a tendency to classify noisy
non-variable curves as variable (i.e. false positives), although it is reliable
and robust to correctly classify non-variable curves. On the contrary, although
the C index tends to give false negatives, we found that whenever the C index
indicates a source to be variable, it effectively is. Finally, light curves
with low amplitude variabilities are more likely to be affected by changes in
atmospheric conditions.


  We review the energy spectrum and transport properties of several types of
one- dimensional superlattices (SLs) on single-layer and bilayer graphene. In
single-layer graphene, for certain SL parameters an electron beam incident on a
SL is highly collimated. On the other hand there are extra Dirac points
generated for other SL parameters. Using rectangular barriers allows us to find
analytic expressions for the location of new Dirac points in the spectrum and
for the renormalization of the electron velocities. The influence of these
extra Dirac points on the conductivity is investigated. In the limit of
{\delta}-function barriers, the transmission T through, conductance G of a
finite number of barriers as well as the energy spectra of SLs are periodic
functions of the dimensionless strength P of the barriers, P{\delta}(x) ~ V
(x). For a Kronig-Penney SL with alternating sign of the height of the barriers
the Dirac point becomes a Dirac line for P = {\pi}/2 + n{\pi} with n an
integer. In bilayer graphene, with an appropriate bias applied to the barriers
and wells, we show that several new types of SLs are produced and two of them
are similar to type I and type II semiconductor SLs. Similar as in single-layer
graphene extra "Dirac" points are found. Non-ballistic transport is also
considered.


  Denote by $\mathcal{W}_1$ the set of complex valued functions of the form
$a(z)=\sum_{i=-\infty}^{+\infty}a_iz^i$ which are continuous on the unit
circle, and such that $\sum_{i=-\infty}^{+\infty}|ia_i|<\infty$. We call CQT
matrix a quasi-Toeplitz matrix $A$, associated with a continuous symbol
$a(z)\in\mathcal W_1$, of the form $A=T(a)+E$, where
$T(a)=(t_{i,j})_{i,j\in\mathbb{Z}^+}$ is the semi-infinite Toeplitz matrix such
that $t_{i,j}=a_{j-i}$, for $i,j\in\mathbb Z^+$, and
$E=(e_{i,j})_{i,j\in\mathbb{Z}^+}$ is a semi-infinite matrix such that
$\sum_{i,j=1}^{+\infty}|e_{i,j}|$ is finite. We prove that the class of CQT
matrices is a Banach algebra with a suitable sub-multiplicative matrix norm
$\|\cdot\|$. We introduce a finite representation of CQT matrices together with
algorithms which implement elementary matrix operations. An application to
solving quadratic matrix equations of the kind $AX^2+BX+C=0$, encountered in
the solution of Quasi-Birth and Death (QBD) stochastic processes with a
denumerable set of phases, is presented where $A,B,C$ are CQT matrices.


  This paper contributes a new State Of The Art (SOTA) for Semantic Textual
Similarity (STS). We compare and combine a number of recently proposed sentence
embedding methods for STS, and propose a novel and simple ensemble knowledge
distillation scheme that improves on previous approaches. Our experiments
demonstrate that a model trained to learn the average embedding space from
multiple ensemble students outperforms all the other individual models with
high robustness. Utilizing our distillation method in combination with previous
methods, we significantly improve on the SOTA unsupervised STS, and by proper
hyperparameter tuning of previous methods we improve the supervised SOTA
scores.


  Galaxy systems with large magnitude gaps - defined as the difference in
magnitude between the central galaxy and the brightest satellite in the central
region - have been claimed to have earlier formation histories. In this study
we measure the mass concentration, as an indicator of early formation, of
ensembles of galaxy systems divided by redshift and magnitude gaps in the $r$
band. We use cross-correlation weak lensing measurements with NFW parametric
mass profiles to measure masses and concentrations of these ensembles from a
catalogue of systems built from the SDSS Coadd by the redMaPPer algorithm. The
lensing shear data come from the CFHT Stripe 82 (CS82) survey, and consists of
$i$-band images of the SDSS Stripe 82 region. We find that the stack made up of
systems with larger magnitude gaps has a high probability of being more
concentrated on average, in the lowest redshift slice ($0.2<z<0.4$), both when
dividing in quartiles ($P=0.98$) and terciles ($P=0.85$). These results lend
credibility to the claim that the magnitude gap is an indicator of earlier
formed systems.


  The drag anisotropy of slender filaments is a critical physical property
allowing swimming in low-Reynolds number flows, and without it linear
translation is impossible. Here we show that, in contrast, net rotation can
occur under isotropic drag. We first demonstrate this result formally by
considering the consequences of the force- and torque-free conditions on
swimming bodies and we then illustrate it with two examples (a simple swimmers
made of three rods and a model bacterium with two helical flagellar filaments).
Our results highlight the different role of hydrodynamic forces in generating
translational vs.~rotational propulsion.


  The unit cost model is both convenient and largely realistic for describing
integer decision algorithms over (+,*). Additional operations like division
with remainder or bitwise conjunction, although equally supported by computing
hardware, may lead to a considerable drop in complexity. We show a variety of
concrete problems to benefit from such NON-arithmetic primitives by presenting
and analyzing corresponding fast algorithms.


  Mobile manipulators consist of a mobile platform equipped with one or more
robot arms and are of interest for a wide array of challenging tasks because of
their extended workspace and dexterity. Typically, mobile manipulators are
deployed in slow-motion collaborative robot scenarios. In this paper, we
consider scenarios where accurate high-speed motions are required. We introduce
a framework for this regime of tasks including two main components: (i) a
bi-level motion optimization algorithm for real-time trajectory generation,
which relies on Sequential Quadratic Programming (SQP) and Quadratic
Programming (QP), respectively; and (ii) a learning-based controller optimized
for precise tracking of high-speed motions via a learned inverse dynamics
model. We evaluate our framework with a mobile manipulator platform through
numerous high-speed ball catching experiments, where we show a success rate of
85.33%. To the best of our knowledge, this success rate exceeds the reported
performance of existing related systems and sets a new state of the art.


  Managing the inherent variability of solar generation is a critical challenge
for utility grid operators, particularly as the distribution grid-integrated
solar generation is making fast inroads in power systems. This paper proposes
to leverage Battery Swapping Station (BSS) as an energy storage for mitigating
solar photovoltaic (PV) output fluctuations. Using mixed-integer programming, a
model for the BSS optimal scheduling is proposed to capture solar generation
variability. The proposed model aims at minimizing the BSS total operation
cost, which represents the accumulated cost of exchanging power with the
utility grid. The model is subject to four sets of constraints associated with
the utility grid, the BSS system, individual batteries, and solar variability.
Numerical simulations on a test BSS demonstrate the effectiveness of the
proposed model and show its viability in helping the utility grids host a
higher penetration of solar generation.


  We construct a periodic cyclic cocycle on the symbol algebra of Boutet de
Monvel operators and use it to interpret the index formula for elliptic
pseudodifferential boundary value problems due to Fedosov as the Chern--Connes
pairing of the classes in $K$-theory of elliptic symbols with this cyclic
cocycle. We also consider the equivariant case. Namely, we construct a periodic
cyclic cocycle on the crossed product of the algebra of symbols with a group
acting on this algebra by automorphisms. Such crossed products arize in index
theory of nonlocal boundary value problems with shift operators.


  Studying caricature recognition is fundamentally important to understanding
of face perception. However, little research has been conducted in the computer
vision community, largely due to the shortage of suitable datasets. In this
paper, a new caricature dataset is built, with the objective to facilitate
research in caricature recognition. All the caricatures and face images were
collected from the Web. Compared with two existing datasets, this dataset is
much more challenging, with a much greater number of available images, artistic
styles and larger intra-personal variations. Evaluation protocols are also
offered together with their baseline performances on the dataset to allow fair
comparisons. Besides, a framework for caricature face recognition is presented
to make a thorough analyze of the challenges of caricature recognition. By
analyzing the challenges, the goal is to show problems that worth to be further
investigated. Additionally, based on the evaluation protocols and the
framework, baseline performances of various state-of-the-art algorithms are
provided. A conclusion is that there is still a large space for performance
improvement and the analyzed problems still need further investigation.


  We report extensive numerical simulations of different models of 2D polymer
rings with internal elasticity. We monitor the dynamical behavior of the rings
as a function of the packing fraction, to address the effects of particle
deformation on the collective response of the system. In particular, we compare
three different models: (i) a recently investigated model [Gnan \& Zaccarelli,
Nat. Phys. 15, 683 (2019)], where an inner hertzian field providing the
internal elasticity acts on the monomers of the ring, (ii) the same model where
the effect of such a field on the center of mass is balanced by opposite forces
and (iii) a semi-flexible model where an angular potential between adjacent
monomers induces strong particle deformations. By analyzing the dynamics of the
three models, we find that, in all cases, there exists a direct link between
the system fragility and particle asphericity. Among the three, only the first
model displays anomalous dynamics in the form of a super-diffusive behavior of
the mean squared displacement and of a compressed exponential relaxation of the
density auto-correlation function. We show that this is due to the combination
of internal elasticity and the out-of-equilibrium force self-generated by each
ring, both of which are necessary ingredients to induce such peculiar behavior
often observed in experiments of colloidal gels. These findings reinforce the
role of particle deformation, connected to internal elasticity, in driving the
dynamical response of dense soft particles.


  A method for solving model nonlinear equations describing plasma oscillations
in the presence of viscosity and resistivity is given. By first going to the
Lagrangian variables and then transforming the space variable conveniently, the
solution in parametric form is obtained. It involves simple elementary
functions. Our solution includes all known exact solutions for an ideal cold
plasma and a large class of new ones for a more realistic plasma. A new
nonlinear effect is found of splitting of the largest density maximum, with a
saddle point between the peaks so obtained. The method may sometimes be useful
where Inverse Scattering fails.


  Biochemical clocks are essential for virtually all living systems. A
biochemical clock that is isolated from an external periodic signal and
subjected to fluctuations can oscillate coherently only for a finite number of
oscillations. Furthermore, such an autonomous clock can oscillate only if it
consumes free energy. What is the minimum amount of free energy consumption
required for a certain number of coherent oscillations? We conjecture a
universal bound that answers this question. A system that oscillates coherently
for $\mathcal{N}$ oscillations has a minimal free energy cost per oscillation
of $4\pi^2\mathcal{N} k_B T$. Our bound is valid for general finite Markov
processes, is conjectured based on extensive numerical evidence, is illustrated
with numerical simulations of a known model for a biochemical oscillator, and
applies to existing experimental data.


  We study the long-time behaviour and the spatial correlations of a simple
ferromagnetic spin system whose kinetics is governed by a thermal bath with a
time-dependent temperature which is characterized by a given external
relaxation time tau. Exact results are obtained in the framework of the
spherical model in d dimensions. In the paramagnetic phase, the long-time
kinetics is shown to depend crucially on the ratio between tau and the internal
equilibration time tau_eq.
  If tau is less than tau_eq, the model relaxes rapidly towards an equilibrium
state but there appear transient and spatially oscillating contributions in the
spin-spin correlation function. On the other hand, if tau is much greater than
tau_eq the system is clamped and its time evolution is delayed with respect to
the one of the heat bath. For waiting times s such that tau << s << tau_eq, a
quasi-stationary state is found where the fluctuation-dissipation theorem does
not hold.


  Based on the Euler-Lagrange cohomology groups $H_{EL}^{(2k-1)}({\cal M}^{2n})
(1 \leqslant k\leqslant n)$ on symplectic manifold $({\cal M}^{2n}, \omega)$,
their properties and a kind of classification of vector fields on the manifold,
we generalize Liouville's theorem in classical mechanics to two sequences, the
symplectic(-like) and the Hamiltonian-(like) Liouville's theorems. This also
generalizes Noether's theorem, since the sequence of symplectic(-like)
Liouville's theorems link to the cohomology directly.


  This paper develops and analyzes some continuous interior penalty finite
element methods (CIP-FEMs) using piecewise linear polynomials for the Helmholtz
equation with the first order absorbing boundary condition in two and three
dimensions. The novelty of the proposed methods is to use complex penalty
parameters with positive imaginary parts. It is proved that, if the penalty
parameter is a pure imaginary number $\i\ga$ with $0<\ga\le C$, then the
proposed CIP-FEM is stable (hence well-posed) without any mesh constraint.
Moreover the method satisfies the error estimates $C_1kh+C_2k^3h^2$ in the
$H^1$-norm when $k^3h^2\le C_0$ and $C_1kh+\frac{C_2}{\ga}$ when $k^3h^2> C_0$
and $kh$ is bounded, where $k$ is the wave number, $h$ is the mesh size, and
the $C$'s are positive constants independent of $k$, $h$, and $\ga$. Optimal
order $L^2$ error estimates are also derived. The analysis is also applied if
the penalty parameter is a complex number with positive imaginary part. By
taking $\ga\to 0+$, the above estimates are extended to the linear finite
element method under the condition $k^3h^2\le C_0$. Numerical results are
provided to verify the theoretical findings. It is shown that the penalty
parameters may be tuned to greatly reduce the pollution errors.


  This paper addresses the challenge of 3D human pose estimation from a single
color image. Despite the general success of the end-to-end learning paradigm,
top performing approaches employ a two-step solution consisting of a
Convolutional Network (ConvNet) for 2D joint localization and a subsequent
optimization step to recover 3D pose. In this paper, we identify the
representation of 3D pose as a critical issue with current ConvNet approaches
and make two important contributions towards validating the value of end-to-end
learning for this task. First, we propose a fine discretization of the 3D space
around the subject and train a ConvNet to predict per voxel likelihoods for
each joint. This creates a natural representation for 3D pose and greatly
improves performance over the direct regression of joint coordinates. Second,
to further improve upon initial estimates, we employ a coarse-to-fine
prediction scheme. This step addresses the large dimensionality increase and
enables iterative refinement and repeated processing of the image features. The
proposed approach outperforms all state-of-the-art methods on standard
benchmarks achieving a relative error reduction greater than 30% on average.
Additionally, we investigate using our volumetric representation in a related
architecture which is suboptimal compared to our end-to-end approach, but is of
practical interest, since it enables training when no image with corresponding
3D groundtruth is available, and allows us to present compelling results for
in-the-wild images.


  This paper presents a study of generic elements in full isometry groups of
Polish ultrametric spaces. We obtain a complete characterization of Polish
ultrametric spaces X whose isometry group Iso(X) contains an open subgroup H
with ample generics. It also gives a characterization of the existence of an
open subgroup in Iso(X) with a comeager conjugacy class.
  We also study the transfinite sequence defined by the projection of a Polish
ultrametric space X on the ultrametric space of orbits of X under the action of
Iso(X).


  Self-dual codes over $\Z_2\times\Z_4$ are subgroups of $\Z_2^\alpha
\times\Z_4^\beta$ that are equal to their orthogonal under an inner-product
that relates to the binary Hamming scheme. Three types of self-dual codes are
defined. For each type, the possible values $\alpha,\beta$ such that there
exist a code $\C\subseteq \Z_2^\alpha \times\Z_4^\beta$ are established.
Moreover, the construction of a $\add$-linear code for each type and possible
pair $(\alpha,\beta)$ is given. Finally, the standard techniques of invariant
theory are applied to describe the weight enumerators for each type.


  We introduce a framework where the announcements of a clearinghouse about the
allocation process are opaque in the sense that there can be more than one
outcome compatible with a realization of type reports. We ask whether desirable
properties can be ensured under opacity in a robust sense. A property can be
guaranteed under an opaque announcement if every mechanism compatible with it
satisfies the property. We find an impossibility result: strategy-proofness
cannot be guaranteed under any level of opacity. In contrast, in some
environments, weak Maskin monotonicity and non-bossiness can be guaranteed
under opacity.


  The t-J model is studied using a novel and rigorous mapping of the Gutzwiller
projected electrons, in terms of canonical electrons. The mapping has
considerable similarity to the Dyson-Maleev transformation relating spin
operators to canonical Bosons. This representation gives rise to a non
Hermitean quantum theory, characterized by minimal redundancies. A path
integral representation of the canonical theory is given. Using it, the salient
results of the extremely correlated Fermi liquid (ECFL) theory, including the
previously found Schwinger equations of motion, are easily rederived. Further a
transparent physical interpretation of the previously introduced auxiliary
Greens functions and the caparison factor is obtained.
  The low energy electron spectral function in this theory with a strong
intrinsic asymmetry, is summarized in terms of a few expansion coefficients.
These include an important emergent energy scale $\Delta_0$ that shrinks to
zero on approaching the insulating state, thereby making it difficult to access
the underlying low energy Fermi liquid behavior. The scaled low frequency ECFL
spectral function is related simply to the Fano line shape. The resulting
energy dispersion (EDC or MDC) is a hybrid of a massive and a massless Dirac
spectrum $ E^*_Q\sim \gamma\, Q- \sqrt{\Gamma_0^2 + Q^2} $, where the vanishing
of $Q$, a momentum like variable, locates the kink. Therefore the quasiparticle
velocity interpolates between $(\gamma \mp 1)$ over a width $\Gamma_0$ on the
two sides of $Q=0$. The resulting kink strongly resembles a prominent low
energy feature seen in angle resolved photoemission spectra (ARPES) of cuprate
materials. We also propose novel ways of analyzing the ARPES data to isolate
the predicted asymmetry between particle and hole excitations.


  Layered materials span a very broad range of solids ranging from van der
Waals materials to highly complex crystal structures such as clays. They are
commonly believed to have highly anisotropic properties, which is essentially
attributed to weak interlayer interactions. The layered Mg3Sb2 structure is
currently being intensely scrutinized due to its outstanding thermoelectric
properties. Based on quantitative chemical bonding analysis we unravel that
Mg3Sb2 exhibits a nearly isotropic three-dimensional (3D) bonding network with
the interlayer and intralayer bonds being surprisingly similar, and these
unique chemical bonding features are the origin of the nearly isotropic
structural and thermal properties. The isotropic 3D bonding network is found to
be broadly applicable to many Mg-containing compounds with the layered
CaAl2Si2-type structure. Intriguingly, a parameter based on the electron
density can be used as an indicator measuring the anisotropy of lattice thermal
conductivity in layered structures. This work extends our understanding of
structure and properties based on chemical bonding analysis, and it will guide
the search for, and design of, layered materials with tailored anisotropic
properties.


  We report a method for estimating people's achievement based on their fame.
Earlier we discovered (cond-mat/0310049) that fame of fighter pilot aces
(measured as number of Google hits) grows exponentially with their achievement
(number of victories). We hypothesize that the same functional relation between
achievement and fame holds for other professions. This allows us to estimate
achievement for professions where an unquestionable and universally accepted
measure of achievement does not exist. We apply the method to Nobel Prize
winners in Physics. For example, we obtain that Paul Dirac, who is hundred
times less famous than Einstein contributed to physics only two times less. We
compare our results with Landau's ranking.


  We theoretically explore the advantages rendered by non-Gaussian operations
in phase estimation using a parity-detection-based Mach-Zehnder interferometer,
with one input being a coherent state and the other being a non-Gaussian
squeezed vacuum state (SVS). We consider a realistic model to perform three
different non-Gaussian operations, namely photon subtraction, photon addition,
and photon catalysis on a single-mode SVS. We start by deriving the Wigner
function of the non-Gaussian SVSs, which is then utilized to derive the
expression for the phase sensitivity. The analysis of the phase sensitivity
reveals that all three different non-Gaussian operations can enhance the phase
sensitivity under suitable choices of parameters. We also consider the
probabilistic nature of these non-Gaussian operations, the results of which
reveal the single photon addition to be the optimal operation. Further, our
analysis also enables us to identify the optimal squeezing of the SVS and the
transmissivity of the beam splitter involved in the implementation of the
non-Gaussian operations.


  This paper introduces a new approach to finding knots and links with hidden
symmetries using "hidden extensions", a class of hidden symmetries defined
here. We exhibit a family of tangle complements in the ball whose boundaries
have symmetries with hidden extensions, then we further extend these to hidden
symmetries of some hyperbolic link complements.


  Change detection, which aims to detect spatial changes from a pair of
multi-temporal images due to natural or man-made causes, has been widely
applied in remote sensing, disaster management, urban management, etc. Most
existing change detection approaches, however, are fully supervised and require
labor-intensive pixel-level labels. To address this, we develop a novel weakly
supervised change detection technique via Knowledge Distillation and Multiscale
Sigmoid Inference (KD-MSI) that leverages image-level labels. In our approach,
the Class Activation Maps (CAM) are utilized not only to derive a change
probability map but also to serve as a foundation for the knowledge
distillation process. This is done through a joint training strategy of the
teacher and student networks, enabling the student network to highlight
potential change areas more accurately than teacher network based on
image-level labels. Moreover, we designed a Multiscale Sigmoid Inference (MSI)
module as a post processing step to further refine the change probability map
from the trained student network. Empirical results on three public datasets,
i.e., WHU-CD, DSIFN-CD, and LEVIR-CD, demonstrate that our proposed technique,
with its integrated training strategy, significantly outperforms the
state-of-the-art.


  Primordial magnetic fields (PMFs) can enhance matter power spectrum on small
scales ($\lesssim$ Mpc) and still agree with bounds from cosmic microwave
background (CMB) and Faraday rotation measurements. As modes on scales smaller
than Mpc have already become non-linear today, exploring PMFs' impact on
small-scale structures requires dedicated cosmological simulations. Here, for
the first time, we perform a suite of hydrodynamical simulations that take into
account the different impacts of PMFs on baryons and dark matter. Specifically,
in the initial conditions we displace particles according to the Lorentz force
from PMFs. We also highlight the large theoretical uncertainty in the peak
enhancement of the matter power spectrum due to PMFs, which was not considered
in previous studies. We present halo mass functions and show that they can be
accurately reproduced using Sheth-Torman formalism. Moreover, we show that PMFs
can generate galaxies with baryon fraction several times larger than the cosmic
average at high redshifts. This is simply a consequence of the fact that PMFs
enhance baryon perturbations, causing them to be larger than dark matter
perturbations. We argue that this scenario could be tested soon by obtaining
accurate estimates of the baryon fraction in high redshift galaxies.


  We expose the Schr\"odinger quantum mechanics with traditional applications
to Hydrogen atom. We discuss carefully the experimental and theoretical
background for the introduction of the Schr\"odinger, Pauli and Dirac
equations, as well as for the Maxwell equations. We explain in detail all basic
theoretical concepts. We explain all details of the calculations and
mathematical tools: Lagrangian and Hamiltonian formalism for the systems with
finite degree of freedom and for fields, Geometric Optics, the Hamilton-Jacobi
equation and WKB approximation, Noether theory of invariants including the
theorem on currents, four conservation laws (energy, momentum, angular momentum
and charge), Lie algebra of angular momentum and spherical functions,
scattering theory (limiting amplitude principle and limiting absorption
principle), the Lienard-Wiechert formulas, Lorentz group and Lorentz formulas,
Pauli theorem and relativistic covariance of the Dirac equation, etc. We give a
detailed oveview of the conceptual development of the quantum mechanics, and
expose main achievements of the ``old quantum mechanics'' in the form of
exercises.
  One of our basic aim in writing this book, is an open and concrete discussion
of the problem of a mathematical description of the following two fundamental
quantum phenomena: i) Bohr's quantum transitions and ii) de Broglie's
wave-particle duality. Both phenomena cannot be described by autonomous linear
dynamical equations, and we give them a new mathematical treatment related with
recent progress in the theory of global attractors of nonlinear hyperbolic
PDEs.


  We present an open-set logo detection (OSLD) system, which can detect
(localize and recognize) any number of unseen logo classes without re-training;
it only requires a small set of canonical logo images for each logo class. We
achieve this using a two-stage approach: (1) Generic logo detection to detect
candidate logo regions in an image. (2) Logo matching for matching the detected
logo regions to a set of canonical logo images to recognize them.
  We constructed an open-set logo detection dataset with 12.1k logo classes and
released it for research purposes.We demonstrate the effectiveness of OSLD on
our dataset and on the standard Flickr-32 logo dataset, outperforming the
state-of-the-art open-set and closed-set logo detection methods by a large
margin. OSLD is scalable to millions of logo classes.


  A multi-scale model for the evolution of the velocity gradient tensor in
fully developed turbulence is proposed. The model is based on a coupling
between a ``Restricted Euler'' dynamics [{\it P. Vieillefosse, Physica A, {\bf
14}, 150 (1984)}] which describes gradient self-stretching, and a deterministic
cascade model which allows for energy exchange between different scales. We
show that inclusion of the cascade process is sufficient to regularize the
well-known finite time singularity of the Restricted Euler dynamics. At the
same time, the model retains topological and geometrical features of real
turbulent flows: these include the alignment between vorticity and the
intermediate eigenvector of the strain-rate tensor and the typical teardrop
shape of the joint probability density between the two invariants, $R-Q$, of
the gradient tensor. The model also possesses skewed, non-Gaussian longitudinal
gradient fluctuations and the correct scaling of energy dissipation as a
function of Reynolds number. Derivative flatness coefficients are in good
agreement with experimental data.


  We classify the $Q$-multiplicity-free skew Schur $Q$-functions. Towards this
result, we also provide new relations between the shifted Littlewood-Richardson
coefficients.


  Tangent Spaces of V^r_d(L), Specific subschemes of C_d arising from various
line bundles on C, are described. Then we proceed to prove Martense Theorem for
these schemes, by which we determine curves C, which for some very ample line
bundle L on C and some integers r and d with d\leq h^{0}(L)-2, the subscheme
V^r_d(L) might attain its maximum dimension.


  We propose a new simple and natural algorithm for learning the optimal
Q-value function of a discounted-cost Markov Decision Process (MDP) when the
transition kernels are unknown. Unlike the classical learning algorithms for
MDPs, such as Q-learning and actor-critic algorithms, this algorithm doesn't
depend on a stochastic approximation-based method. We show that our algorithm,
which we call the empirical Q-value iteration (EQVI) algorithm, converges to
the optimal Q-value function. We also give a rate of convergence or a
non-asymptotic sample complexity bound, and also show that an asynchronous (or
online) version of the algorithm will also work. Preliminary experimental
results suggest a faster rate of convergence to a ball park estimate for our
algorithm compared to stochastic approximation-based algorithms.


  We report $^{75}$As nuclear magnetic resonance measurements on single
crystals of RbFe$_{2}$As$_{2}$ and CsFe$_{2}$As$_{2}$. Taking previously
reported results for KFe$_{2}$As$_{2}$ into account, we find that the
anisotropic electronic correlations evolve towards a magnetic instability in
the $A$Fe$_{2}$As$_{2}$ series (with $A$ = K, Rb, Cs). Upon isovalent
substitution with larger alkali ions, a drastic enhancement of the anisotropic
nuclear spin-lattice relaxation rate and decreasing Knight shift reveal the
formation of pronounced spin fluctuations with stripe-type modulation.
Furthermore, a decreasing power-law exponent of the nuclear spin-lattice
relaxation rate $(1/T_{1})_{H\parallel{ab}}$, probing the in-plane spin
fluctuations, evidences an emergent deviation from Fermi-liquid behavior. All
these findings clearly indicate that the expansion of the lattice in the
$A$Fe$_{2}$As$_{2}$ series tunes the electronic correlations towards a quantum
critical point at the transition to a yet unobserved, ordered phase.


  The deepest arithmetic invariants attached to an algebraic variety defined
over a number field $F$ are conjecturally captured by the integral part of its
motivic cohomology. There are essentially two ways of defining it when $X$ is a
smooth projective variety: one is via the $K$-theory of a regular model, the
other is through its $\ell$-adic realization. Both approaches are conjectured
to coincide. This paper initiates the study of motivic cohomology for global
fields of positive characteristic, hereafter named $A$-motivic cohomology,
where classical mixed motives are replaced by mixed Anderson $A$-motives. Our
main objective is to set the definitions of the model version and the
$\ell$-adic version of the integral part of $A$-motivic cohomology, using
Gardeyn's notion of maximal models of $A$-motives as the analogue of regular
models of varieties. Our main result states that the model version is contained
in the $\ell$-adic version. As opposed to what is expected in the number field
setting, we show that the two approaches do not match in general. We conclude
this work by introducing the submodule of regulated extensions of mixed
Anderson $A$-motives, for which we expect the two approaches to match, and
solve some particular cases of this expectation.


  The field of computational pathology has witnessed remarkable progress in the
development of both task-specific predictive models and task-agnostic
self-supervised vision encoders. However, despite the explosive growth of
generative artificial intelligence (AI), there has been limited study on
building general purpose, multimodal AI assistants tailored to pathology. Here
we present PathChat, a vision-language generalist AI assistant for human
pathology using an in-house developed foundational vision encoder pretrained on
100 million histology images from over 100,000 patient cases and 1.18 million
pathology image-caption pairs. The vision encoder is then combined with a
pretrained large language model and the whole system is finetuned on over
250,000 diverse disease agnostic visual language instructions. We compare
PathChat against several multimodal vision language AI assistants as well as
GPT4V, which powers the commercially available multimodal general purpose AI
assistant ChatGPT-4. When relevant clinical context is provided with the
histology image, PathChat achieved a diagnostic accuracy of 87% on
multiple-choice questions based on publicly available cases of diverse tissue
origins and disease models. Additionally, using open-ended questions and human
expert evaluation, we found that overall PathChat produced more accurate and
pathologist-preferable responses to diverse queries related to pathology. As an
interactive and general vision language AI assistant that can flexibly handle
both visual and natural language inputs, PathChat can potentially find
impactful applications in pathology education, research, and human-in-the-loop
clinical decision making.


  The recent observation of non-classical electron transport regimes in
two-dimensional materials has called for new high-resolution non-invasive
techniques to locally probe electronic properties. We introduce a novel hybrid
scanning probe technique to map the local resistance and electrochemical
potential with nm- and $\mu$V resolution, and we apply it to study epigraphene
nanoribbons grown on the sidewalls of SiC substrate steps. Remarkably, the
potential drop is non uniform along the ribbons, and $\mu$m-long segments show
no potential variation with distance. The potential maps are in excellent
agreement with measurements of the local resistance. This reveals ballistic
transport in ambient condition, compatible with micrometer-long
room-temperature electronic mean free paths.


  Generic cosmological models in non-critical string theory have a
time-dependent dilaton background at a late epoch. The cosmological
deceleration parameter Q_0 is given by the square of the string coupling,
g_s^2, up to a negative sign. Hence the expansion of the Universe must
accelerate eventually, and the observed value of Q_0 coresponds to g_s^2 ~ 0.6.
In this scenario, the string coupling is asymptotically free at large times,
but its present rate of change is imperceptibly small.


  COVID 19 is an acute disease that started spreading throughout the world,
beginning in December 2019. It has spread worldwide and has affected more than
7 million people, and 200 thousand people have died due to this infection as of
Oct 2020. In this paper, we have forecasted the number of deaths and the
confirmed cases in Los Angeles and New York of the United States using the
traditional and Big Data platforms based on the Times Series: ARIMA and ETS. We
also implemented a more sophisticated time-series forecast model using Facebook
Prophet API. Furthermore, we developed the classification models: Logistic
Regression and Random Forest regression to show that the Weather does not
affect the number of the confirmed cases. The models are built and run in
legacy systems (Azure ML Studio) and Big Data systems (Oracle Cloud and
Databricks). Besides, we present the accuracy of the models.


  We present results of a systematic study of the capture process through the
barrier penetration model. The nucleus-nucleus interaction potential is
calculated using the double-folding model (DFM) with the M3Y Paris NN forces.
The nucleon densities entering the model are generated from the experimental
three-parameter Fermi charge densities. The DFM has been extended to the case
of deformed target nuclei. It is shown that the density-dependent M3Y NN forces
with the finite range exchange part can be mimicked successfully by the
zero-range density-independent forces. The latter option significantly reduces
the required computer time. For the nucleon densities and target nuclei
deformations we employ the values from the commonly used data bases. Thus, we
do not vary any parameters to reach a better agreement with the data. The
resulting cross-sections are compared with data for 20 reactions with the
product of the charge numbers Z_P*Z_T ranging from 216 up to 2576. We discuss
the opinion met in the literature that the M3Y NN forces provide a poorer
description of the capture cross-sections in heavy-ion collisions in comparison
to the NN forces coming from the relativistic mean-field approach. Our
calculations show that the M3Y NN forces give an agreement with the data which
is not perfect yet is not worse than the one resulting from the RMF NN forces.


  We have studied free higher spin gauge fields through an investigation of
their Hamiltonian dynamics. Over a flat space-time, their Hamiltonian
constraints were identified and solved through the introduction of
prepotentials, enjoying both linearized generalized diffeomorphism and
linearized generalized Weyl rescaling gauge invariance, motivating our study of
conformal invariants for higher spins. We built these with the Cotton tensor,
whose properties (tracelessness, symmetry, divergencelessness; completeness,
invariance) we established. With these geometric tools, a first order action
was written down in terms of the prepotentials. It is manifestly invariant
under electric-magnetic duality which, with the gauge freedom of the
prepotentials, completely fixes the action. This action is associated to
twisted self-duality conditions.
  With an interest in supersymmetric extensions, we began to extend this study
to fermions, similarly analyzing the spin $5/2$ massless free field, whose
prepotential also enjoys conformal gauge invariance. The spin $2$-spin $5/2$
supermultiplet was considered, and a rigid symmetry of its action (a
chirality-duality rotation) was built to commute with supersymmetry. We also
investigated the properties of a mixed symmetry field on a flat six-dimensional
space-time, the so-called chiral $(2,2)$-form: Hamiltonian analysis,
prepotentials, and a first order action associated to self-duality conditions.
  Finally, we studied both fermionic and bosonic higher spin surface charges
over a constantly curved background space-time. The Hamitonian constraints are
the generators of gauge transformations. Plugging into them appropriate values
of the gauge parameters (imposing a physical variation of the fields), their
finite and non-vanishing on-shell values were computed and recognized as
conserved charges of the theory. Their algebra was checked to be abelian.


  We report the discovery of 14 quasars in the vicinity of HE2347-4342, one of
the two quasars whose intergalactic HeII forest has been resolved with FUSE. By
analysing the HI and the HeII opacity variations separately, no transverse
proximity effect is detected near three foreground quasars of HE2347-4342:
QSOJ23503-4328 (z=2.282, $\vartheta=3.59$ arcmin), QSOJ23500-4319 (z=2.302,
$\vartheta=8.77$ arcmin) and QSOJ23495-4338 (z=2.690, $\vartheta=16.28$
arcmin). This is primarily due to line contamination and overdensities probably
created by large-scale structure. By comparing the HI absorption and the
corresponding HeII absorption, we estimated the fluctuating spectral shape of
the extragalactic UV radiation field along this line of sight. We find that the
UV spectral shape near HE2347-4342 and in the projected vicinity of the three
foreground quasars is statistically harder than expected from UV background
models dominated by quasars. In addition, we find three highly ionised metal
line systems near the quasars. However, they do not yield further constraints
on the shape of the ionising field. We conclude that the foreground quasars
show a transverse proximity effect that is detectable as a local hardening of
the UV radiation field, although the evidence is strongest for QSOJ23495-4338.
Thus, the relative spectral hardness traces the proximity effect also in
overdense regions prohibiting the traditional detection in the HI forest.
Furthermore, we emphasise that softening of quasar radiation by radiative
transfer in the intergalactic medium is important to understand the observed
spectral shape variations. From the transverse proximity effect of
QSOJ23495-4338 we obtain a lower limit on the quasar lifetime of ~25 Myr.


  It is widely accepted that the notion of an inertial frame is central to
Newtonian mechanics and that the correct space-time structure underlying
$\text{Newton's}$ methods in $\textit{Principia}$ is neo-Newtonian or Galilean
space-time. I argue to the contrary that inertial frames are not needed in
$\text{Newton's}$ theory of motion, and that the right space-time structure for
$\text{Newton's}$ $\textit{Principia}$ requires the notion of parallelism of
spatial directions at different times and nothing more.


  We present a comprehensive study of Majorana dark matter in a $U(1)_{B-L}$
gauge extension of the standard model, where three exotic fermions with $B-L$
charges as $-4, -4, +5$ are added to make the model free from the triangle
gauge anomalies. The enriched scalar sector and the new heavy gauge boson
$Z^{\prime},$ associated with the $U(1)_{B-L}$ symmetry make the model
advantageous to be explored in dual portal scenarios for the search of dark
matter signal. Diagonalizing the exotic fermion mass matrix, we obtain the
Majorana mass eigenstates, of which the lightest one plays the role of dark
matter. Analyzing the effect of two mediators separately, the scalar portal
channels give a viable parameter space consistent with relic density from
PLANCK data and the direct detection limits from various experiments such as
LUX, XENON1T and PandaX. While the $Z^{\prime}$ mediated channels are
constrained from relic abundance and LHC searches for $Z^{\prime}$ in the
dilepton channel. A massless physical Goldstone boson plays a key role in the
scalar portal relic density. Finally, we briefly discuss the neutrino mass
generation at one-loop level.


  When an NS5-brane crosses a D6-brane, a D4-brane is created stretching
between them by the Hanany-Witten effect. However, the T-dual situation
involves a Kaluza-Klein monopole crossing a D5-brane and should not result in
brane creation. Thus, the newly created D4-brane disappears when T-duality is
applied. The T-duality is in a direction transverse to the D4-brane so that one
would naively have expected the creation of a D5-brane in the T-dual picture.
This situation is investigated via the corresponding supergravity solutions and
the tension with the naive result is resolved. Along the way, a differential
form version of the supergravity T-duality relations is developed and some
comments are made concerning the flux-expulsion properties of D6-branes.


  We study some general properties of accretion disc variability in the context
of stationary random processes. In particular, we are interested in
mathematical constraints that can be imposed on the functional form of the
Fourier power-spectrum density (PSD) that exhibits a multiply broken shape and
several local maxima. We develop a methodology for determining the regions of
the model parameter space that can in principle reproduce a PSD shape with a
given number and position of local peaks and breaks of the PSD slope. Given the
vast space of possible parameters, it is an important requirement that the
method is fast in estimating the PSD shape for a given parameter set of the
model. We generated and discuss the theoretical PSD profiles of a
shot-noise-type random process with exponentially decaying flares. Then we
determined conditions under which one, two, or more breaks or local maxima
occur in the PSD. We calculated positions of these features and determined the
changing slope of the model PSD. Furthermore, we considered the influence of
the modulation by the orbital motion for a variability pattern assumed to
result from an orbiting-spot model. We suggest that our general methodology can
be useful in for describing non-monotonic PSD profiles (such as the trend seen,
on different scales, in exemplary cases of the high-mass X-ray binary Cygnus
X-1 and the narrow-line Seyfert galaxy Ark 564). We adopt a model where these
power spectra are reproduced as a superposition of several Lorentzians with
varying amplitudes in the X-ray-band light curve. Our general approach can help
in constraining the model parameters and in determining which parts of the
parameter space are accessible under various circumstances.


  Out-of-distribution (OoD) detection techniques for deep neural networks
(DNNs) become crucial thanks to their filtering of abnormal inputs, especially
when DNNs are used in safety-critical applications and interact with an open
and dynamic environment. Nevertheless, integrating OoD detection into
state-of-the-art (SOTA) object detection DNNs poses significant challenges,
partly due to the complexity introduced by the SOTA OoD construction methods,
which require the modification of DNN architecture and the introduction of
complex loss functions. This paper proposes a simple, yet surprisingly
effective, method that requires neither retraining nor architectural change in
object detection DNN, called Box Abstraction-based Monitors (BAM). The novelty
of BAM stems from using a finite union of convex box abstractions to capture
the learned features of objects for in-distribution (ID) data, and an important
observation that features from OoD data are more likely to fall outside of
these boxes. The union of convex regions within the feature space allows the
formation of non-convex and interpretable decision boundaries, overcoming the
limitations of VOS-like detectors without sacrificing real-time performance.
Experiments integrating BAM into Faster R-CNN-based object detection DNNs
demonstrate a considerably improved performance against SOTA OoD detection
techniques.


  We prove the Lukacs-Olkin-Rubin theorem without invariance of the
distribution of the "quotient", which was the key assumption in the original
proof of [Olkin--Rubin, Ann. Math. Stat. 33 (1962), 1272--1280]. Instead we
assume existence of strictly positive continuous densities of respective random
variables. We consider the (cone variate) "quotient" for any division algorithm
satisfying some natural conditions. For that purpose, the new proof of the
Olkin--Baker functional equation on symmetric cones is given.


  The internal structure of adhesive tapes determines the effective mechanical
properties. This holds true especially for blended systems, here consisting of
acrylate and rubber phases. In this note, we propose a lattice-based model to
study numerically the formation of internal morphologies within a
four-component mixture (of discrete particles) where the solvent components
evaporate. Mimicking numerically the interaction between rubber, acrylate, and
two different types of solvents, relevant for the technology of adhesive tapes,
we aim to obtain realistic distributions of rubber ball-shaped morphologies --
they play a key role in the overall functionality of those special adhesives.
Our model incorporates the evaporation of both solvents and allows for tuning
the strength of two essentially different solvent-solute interactions and of
the temperature of the system.


  We give the definition of a duality that is applicable to arbitrary
$k$-forms. The operator that defines the duality depends on a fixed form
$\Omega$. Our definition extends in a very natural way the Hodge duality of
$n$-forms in $2n$ dimensional spaces and the generalized duality of two-forms.
We discuss the properties of the duality in the case where $\Omega$ is
invariant with respect to a subalgebra of $\mathfrak{so}(V)$. Furthermore, we
give examples for the invariant case as well as for the case of discrete
symmetry.


  We introduce a technique based on infrared thermal emission, termed depth
thermography, that can remotely measure the temperature distribution beneath
the surface of certain objects. Depth thermography utilizes the
thermal-emission spectrum in the semitransparent spectral region of the target
object to extract its temperature as a function of depth, in contrast with
conventional thermography, which uses the spectrally integrated thermally
emitted power to measure the surface temperature. Coupled with two-dimensional
imaging, e.g., using an infrared hyperspectral camera or scanning a
single-pixel spectrometer, this technique can yield volumetric temperature
distributions. We carried out a proof-of-concept experiment on an
asymmetrically heated fused-silica window, extracting the temperature
distribution throughout the sample. Depth thermography may enable noncontact
volumetric temperature measurements of microscopic objects such as multilayer
electronic devices or macroscopic volumes of liquids and gasses as well as
simultaneous all-optical measurements of optical and thermal properties.


  We predict the possibility to generate a finite stationary spin current by
applying an unbiased ac driving to a quasi-one-dimensional asymmetric periodic
structure with Rashba spin-orbit interaction and strong dissipation. We show
that under a finite coupling strength between the orbital degrees of freedom
the electron dynamics at low temperatures exhibits a pure spin ratchet
behavior, {\it i.e.} a finite spin current and the absence of charge transport
in spatially asymmetric structures. It is also found that the equilibrium spin
currents are not destroyed by the presence of strong dissipation.


  We study different dimensional fluids inspired by noncommutative geometry
which admit conformal Killing vectors. The solutions of the Einstein field
equations examined specifically for five different set of spacetime. We
calculate the active gravitational mass and impose stability conditions of the
fluid sphere. The analysis thus carried out immediately indicates that at
$4$-dimension only one can get a stable configuration for any spherically
symmetric stellar system and any other dimensions, lower or higher, becomes
untenable as far as the stability of a system is concerned.


  We study the elastic deformations that appear due to tidal and centrifugal
forces acting on an elastic sphere in helical motion in a spherically symmetric
gravitational field, where gravity is considered to be given by either a
Newtonian or a Schwarzschild background. We review an existence/uniqueness
theorem based on the implicit function theorem for the nonrelativistic case and
give explicit solutions to the linearized elastostatic equations in both cases.


  In recent years, many papers have been published showing relationships
between rough sets and some lattice theoretical structures. We present here
some strong relations between rough sets and three-valued {\L}ukasiewicz
algebras.


  The Goeritz group of the standard genus-g Heegaard splitting of the three
sphere, $G_g$, acts on the space of isotopy classes of reducing spheres for
this Heegaard splitting. Scharlemann MR2199366 (2007c:57020) uses this action
to prove that $G_2$ is finitely generated. In this article, we give an
algorithm to construct any reducing sphere from a standard reducing sphere for
a genus-2 Heegaard splitting of the $S^3$. Using this we give an alternate
proof of the finite generation of $G_2$ assuming the finite generation of the
stabilizer of the standard reducing sphere.


  An instance of Max CSP is a finite collection of constraints on a set of
variables, and the goal is to assign values to the variables that maximises the
number of satisfied constraints. Max CSP captures many well-known problems
(such as Max k-SAT and Max Cut) and is consequently NP-hard. Thus, it is
natural to study how restrictions on the allowed constraint types (or
constraint languages) affect the complexity and approximability of Max CSP. The
PCP theorem is equivalent to the existence of a constraint language for which
Max CSP has a hard gap at location 1, i.e. it is NP-hard to distinguish between
satisfiable instances and instances where at most some constant fraction of the
constraints are satisfiable. All constraint languages, for which the CSP
problem (i.e., the problem of deciding whether all constraints can be
satisfied) is currently known to be NP-hard, have a certain algebraic property.
We prove that any constraint language with this algebraic property makes Max
CSP have a hard gap at location 1 which, in particular, implies that such
problems cannot have a PTAS unless P = NP. We then apply this result to Max CSP
restricted to a single constraint type; this class of problems contains, for
instance, Max Cut and Max DiCut. Assuming P $\neq$ NP, we show that such
problems do not admit PTAS except in some trivial cases. Our results hold even
if the number of occurrences of each variable is bounded by a constant. We use
these results to partially answer open questions and strengthen results by
Engebretsen et al. [Theor. Comput. Sci., 312 (2004), pp. 17--45], Feder et al.
[Discrete Math., 307 (2007), pp. 386--392], Krokhin and Larose [Proc.
Principles and Practice of Constraint Programming (2005), pp. 388--402], and
Jonsson and Krokhin [J. Comput. System Sci., 73 (2007), pp. 691--702]


  We analyzed ground-based low frequency ($<$100\,MHz) radio spectral and
imaging data of the solar corona obtained with the facilities in the
Gauribidanur observatory during the same time as the very weak soft X-ray
flares (sub A-class, flux $\rm {<}10^{-7}\,Wm^{-2}$ in the 1\,-\,8\,$\rm {\AA}$
wavelength range) from the `quiet' Sun observed with the X-ray Solar Monitor
(XSM) onboard Chandrayaan-2 during the recent solar minimum. Non-thermal type I
radio burst activity were noticed in close temporal association with the X-ray
events. The estimated brightness temperature ($T_{b}$) of the bursts at a
typical frequency like 80\,MHz is ${\approx}3{\times}10^{5}$\,K.
Extreme-ultraviolet (EUV) observations at 94{\AA} with the Atmospheric Imaging
Assembly (AIA) onboard the Solar Dynamics Observatory (SDO) revealed a
brightening close to the same location and time as the type I radio bursts. As
far as we know reports of simultaneous observations of X-ray and/or EUV
counterpart to weak transient radio emission at low frequencies from the
`quiet' Sun in particular are rare. Considering this and the fact that low
frequency radio observations are sensitive to weak energy releases in the solar
atmosphere, the results indicate that coordinated observations of similar
events would be useful to understand transient activities in the `quiet' Sun.


  End-to-end speech synthesis models directly convert the input characters into
an audio representation (e.g., spectrograms). Despite their impressive
performance, such models have difficulty disambiguating the pronunciations of
identically spelled words. To mitigate this issue, a separate
Grapheme-to-Phoneme (G2P) model can be employed to convert the characters into
phonemes before synthesizing the audio. This paper proposes SoundChoice, a
novel G2P architecture that processes entire sentences rather than operating at
the word level. The proposed architecture takes advantage of a weighted
homograph loss (that improves disambiguation), exploits curriculum learning
(that gradually switches from word-level to sentence-level G2P), and integrates
word embeddings from BERT (for further performance improvement). Moreover, the
model inherits the best practices in speech recognition, including multi-task
learning with Connectionist Temporal Classification (CTC) and beam search with
an embedded language model. As a result, SoundChoice achieves a Phoneme Error
Rate (PER) of 2.65% on whole-sentence transcription using data from LibriSpeech
and Wikipedia. Index Terms grapheme-to-phoneme, speech synthesis,
text-tospeech, phonetics, pronunciation, disambiguation.


  Feigin-Stoyanovsky's type subspaces for affine Lie algebras of type
$C_\ell^{(1)}$ have monomial bases with a nice combinatorial description. We
describe bases of whole standard modules in terms of semi-infinite monomials
obtained as "a limit of translations" of bases for Feigin-Stoyanovsky's type
subspaces.


  Constraining dynamo theories of magnetic field origin by observation is
indispensable but challenging, in part because the basic quantities measured by
observers and predicted by modelers are different. We clarify these differences
and sketch out ways to bridge the divide. Based on archival and previously
unpublished data, we then compile various important properties of galactic
magnetic fields for nearby spiral galaxies. We consistently compute strengths
of total, ordered, and regular fields, pitch angles of ordered and regular
fields, and we summarize the present knowledge on azimuthal modes, field
parities, and the properties of non-axisymmetric spiral features called
magnetic arms. We review related aspects of dynamo theory, with a focus on
mean-field models and their predictions for large-scale magnetic fields in
galactic discs and halos. Further, we measure the velocity dispersion of HI gas
in arm and inter-arm regions in three galaxies, M 51, M 74, and NGC 6496, since
spiral modulation of the root-mean-square turbulent speed has been proposed as
a driver of non-axisymmetry in large-scale dynamos. We find no evidence for
such a modulation and place upper limits on its strength, helping to narrow
down the list of mechanisms to explain magnetic arms. Successes and remaining
challenges of dynamo models with respect to explaining observations are briefly
summarized, and possible strategies are suggested. With new instruments like
the Square Kilometre Array (SKA), large data sets of magnetic and non-magnetic
properties from thousands of galaxies will become available, to be compared
with theory.


  Recent large language models (LLMs) are promising for making decisions in
grounded environments. However, LLMs frequently fail in complex decision-making
tasks due to the misalignment between the pre-trained knowledge in LLMs and the
actual rules in the environment. Existing methods require either costly
gradient computation or lengthy in-context demonstrations. In this paper, we
propose AutoPlan, an approach to guide LLM-based agents to accomplish
interactive decision-making tasks. AutoPlan augments the LLM prompt with a
task-solving plan and optimizes it through iterative experience collection and
reflection. Our experiments show that AutoPlan, though using no in-context
demonstrations, achieves success rates on par with the baselines using
human-written demonstrations on ALFWorld and even outperforms them by 8% on
HotpotQA. The code is available at https://github.com/owaski/AutoPlan.


  Multimodal machine learning models that combine visual and textual data are
increasingly being deployed in critical applications, raising significant
safety and security concerns due to their vulnerability to adversarial attacks.
This paper presents an effective strategy to enhance the robustness of
multimodal image captioning models against such attacks. By leveraging the Fast
Gradient Sign Method (FGSM) to generate adversarial examples and incorporating
adversarial training techniques, we demonstrate improved model robustness on
two benchmark datasets: Flickr8k and COCO. Our findings indicate that
selectively training only the text decoder of the multimodal architecture shows
performance comparable to full adversarial training while offering increased
computational efficiency. This targeted approach suggests a balance between
robustness and training costs, facilitating the ethical deployment of
multimodal AI systems across various domains.


  Epitaxial trilayer structures consisting of two antifferomagnetic
charge/orbital order insulators Pr0.5Ca0.5MnO3 (PCMO) and La0.5Ca0.5MnO3 (LCMO)
are grown on (001)-oriented SrTiO3 and LaAlO3 substrates. In this trilayer
series, a thin film of LCMO with various thicknesses is sandwiched between the
two fixed thicknesses of PCMO. These samples show a Curie temperature with a
hysteretic field dependent magnetization at 10 K, although the individual
compounds are antiferromagnetic. The zero field electronic transport of all
samples on LAO shows thermally activated behavior, while the thermally
activated behavior is suppressed and a metal-like transport is appearing for
the samples on STO as the LCMO layer thickness increases above 10 unit cell. We
have discussed these magnetic and transport properties of the trilayer
structures on STO and LAO by the interfacial effect due to the stabilized CO
state and the vibration mode of Jahn-Teller distortion.


  We study the behavior of $h$-vectors associated to matroid complexes under
weak maps, or inclusions of matroid polytopes. Specifically, we show that the
$h$-vector of the order complex of the lattice of flats of a matroid is
component-wise non-increasing under a weak map. This result extends to the flag
$h$-vector. We note that the analogous result also holds for independence
complexes and rank-preserving weak maps.


  We apply the convolutional neural networks (CNNs) to the mock 21cm maps from
the post-reionization epoch to show that the $\Lambda$ cold dark matter and
warm dark matter (WDM) model can be distinguished for WDM particle masses
$m_{FD}<3$\,keV, under the assumption of thermal production of WDM following
the Fermi-Dirac (FD) distribution. We demonstrate that the CNN is a potent tool
in distinguishing the dark matter masses, highlighting its sensitivity to the
subtle differences in the 21cm maps produced by varying dark matter masses.
Furthermore, we extend our analysis to encompass different WDM production
mechanisms, recognizing that the dark matter production mechanism in the early
Universe is among the sources of the most significant uncertainty for the dark
matter model building.
  In this work, given the mass of the dark matter, we discuss the feasibility
of discriminating four different WDM models: Fermi-Dirac (FD) distribution
model, neutrino minimal Standard Model ($\nu$MSM), Dodelson-Widrow (DW), and
Shi-Fuller (SF) model. For instance, when the WDM mass is 2\,keV, we show that
one can differentiate between CDM, FD, $\nu$MSM, and DW models while discerning
between the DW and SF models turns out to be challenging. Our results reinforce
the viability of the CNN as a robust analysis for 21cm maps and shed light on
its potential to unravel the features associated with different dark matter
production mechanisms.


  The present volume is a Festschrift for Mike Keane, on the occasion of his
65th birthday on January 2, 2005. It contains 29 contributions by Mike's
closest colleagues and friends, covering a broad range of topics in Dynamics
and Stochastics. To celebrate Mike's scientific achievements, a conference
entitled ``Dynamical Systems, Probability Theory and Statistical Mechanics''
was organized in Eindhoven, The Netherlands, during the week of January 3--7,
2005. This conference was hosted jointly by EURANDOM and by Philips Research.
It drew over 80 participants from 5 continents, which is a sign of the warm
affection and high esteem for Mike felt by the international mathematics
community.


  Elastic production of vector mesons $\gamma^{*} N\to V N$ is the
pomeron-exchange dominated diffractive reaction with much potential of probing
the BFKL pomeron. The BFKL pomeron can conveniently be described in terms of
the dipole cross section which is a solution of the generalized BFKL equation.
In this paper we discuss, how the energy and $Q^{2}$ dependence of elastic
production of vector mesons at HERA will allow scanning the dipole cross
section as a function of dipole size $r$. We show that determinaton of the
intercept of the BFKL pomeron requires measuring the $\rho^{0}$ and $J/\Psi$
production at $Q^{2} \sim (100-200)GeV^2$ and/or the quasireal photoproduction
of the $\Upsilon$. We present predictions for the effective intercept in the
kinematic range of the forthcoming HERA experiments, which can shed much light
on the nonperturbative component of the pomeron.


  A formidable perspective in understanding quantum criticality of a given
many-body system is through its entanglement contents. Until now, most progress
are only limited to the disorder-free case. Here, we develop an efficient
scheme to compute the entanglement entropy of $(2+1)$-dimensional quantum
critical points with randomness, from a conceptually novel angle where the
quenched disorder can be considered as dimensionally reducible interactions. As
a concrete example, we reveal novel entanglement signatures of
$(2+1)$-dimensional Dirac fermion exposed to a random magnetic field, which
hosts a class of emergent disordered quantum critical points. We demonstrate
that the entanglement entropy satisfies the area-law scaling, and observe a
modification of the area-law coefficient that points to the emergent disordered
quantum criticality. Moreover, we also obtain the sub-leading correction to the
entanglement entropy due to a finite correlation length. This sub-leading
correction is found to be a universal function of the correlation length and
disorder strength. We discuss its connection to the renormalization group flows
of underlying theories.


  The congruence orbit of a matrix has a natural connection with the linear
complementarity problem on simplicial cones formulated for the matrix. In terms
of the two approaches -- the congruence orbit and the family of all simplicial
cones -- we give equivalent classification of matrices from the point of view
of the complementarity theory.


  Hubble Space Telescope (HST) imaging of four rich, X-ray luminous, galaxy
clusters (0.33<z<0.83) is used to produce quantitative morphological
measurements for galaxies in their fields. Catalogs of these measurements are
presented for 1642 galaxies brighter than F814W(AB)=23.0 . Galaxy luminosity
profiles are fitted with three models: exponential disk, de Vaucouleurs bulge,
and a disk-plus-bulge hybrid model. The best fit is selected and produces a
quantitative assessment of the morphology of each galaxy: the principal
parameters derived being B/T, the ratio of bulge to total luminosity, the scale
lengths and half-light radii, axial ratios, position angles and surface
brightnesses of each component. Cluster membership is determined using a
statistical correction for field galaxy contamination, and a mass normalization
factor (mass within boundaries of the observed fields) is derived for each
cluster. In the present paper, this catalog of measurements is used to
investigate the luminosity evolution of disk galaxies in the rich-cluster
environment. Examination of the relations between disk scale-length and central
surface brightness suggests, under the assumption that these clusters represent
a family who share a common evolutionary history and are simply observed at
different ages, that there is a dramatic change in the properties of the small
disks (h < 2 kpc). This change is best characterized as a change in surface
brightness by about 1.5 magnitude between z=0.3 and z=0.8 with brighter disks
at higher redshifts.


  I present the analysis of data of astrophysical polarimetric observations
that gives the signature of the fundamental extra dimension Planck scale
magnitude essentially higher than $~1TeV$. Magnetic conversion of photons into
the fundamental particles (scalars, gravitons) is the probable mechanism that
can produce noticeable amount of polarization of optical radiation of
astrophysical objects, especially, of distant extragalactic sources. The
results of magnetic conversion process of optical light of extragalactic
sources are presented for a number of situations including: (a) intergalactic
magnetic field, (b) galaxy cluster magnetic field, (c) magnetic conversion in
the typical galaxy magnetic field, (d) magnetic conversion of CMB radiation.


  The state of chromatin in individual cells is directly related to the state
of the whole organism and may be used for assessment of the state of the whole
organism. Many hereditary diseases are connected with chromatin rearrangements.
Chromatin distribution in cell nucleus is an important characteristic which may
be applied for determination of disease gravity. The method of determination of
the quantity of heterochromatin granules in buccal epithelium cells may be
applied in the assessment of the state of human organism during sportive
trainings and medical treatment.


  Given a finite set $A$ and a group homomorphism $\phi : H \to G$, a
$\phi$-cellular automaton is a function $\mathcal{T} : A^G \to A^H$ that is
continuous with respect to the prodiscrete topologies and $\phi$-equivariant in
the sense that $h \cdot \mathcal{T}(x) = \mathcal{T}( \phi(h) \cdot x)$, for
all $x \in A^G, h \in H$, where $\cdot$ denotes the shift actions of $G$ and
$H$ on $A^G$ and $A^H$, respectively. When $G=H$ and $\phi = \text{id}$, the
definition of $\text{id}$-cellular automata coincides with the classical
definition of cellular automata. The purpose of this paper is to expand the
theory of $\phi$-cellular automata by focusing on the differences and
similarities with their classical counterparts. After discussing some basic
results, we introduce the following definition: a $\phi$-cellular automaton
$\mathcal{T} : A^G \to A^H$ has the unique homomorphism property (UHP) if
$\mathcal{T}$ is not $\psi$-equivariant for any group homomorphism $\psi : H
\to G$, $\psi \neq \phi$. We show that if the difference set $\Delta(\phi,
\psi)$ is infinite, then $\mathcal{T}$ is not $\psi$-equivariant; it follows
that when $G$ is torsion-free abelian, every non-constant $\mathcal{T}$ has the
UHP. Furthermore, inspired by the theory of classical cellular automata, we
study $\phi$-cellular automata over quotient groups, as well as their
restriction and induction to subgroups and supergroups, respectively.


  This paper describes work carried out on a model for the evolution of graph
classes in complex objects. By defining evolution rules and propagation
strategies on graph classes, we aim to define a user-definable means to manage
data evolution model which tackles the complex nature of the classes managed,
using the concepts defined in object systems. So, depending on their needs and
on those of the targeted application, designers can choose the evolution
mechanism they consider to suit them best. They can either create new
evolutions or reuse predefined ones to respond to a given need.


  Utilizing an exhaustive set of simplified models, we revisit dark matter
scenarios potentially capable of generating the observed Galactic Center
gamma-ray excess, updating constraints from the LUX and PandaX-II experiments,
as well as from the LHC and other colliders. We identify a variety of
pseudoscalar mediated models that remain consistent with all constraints. In
contrast, dark matter candidates which annihilate through a spin-1 mediator are
ruled out by direct detection constraints unless the mass of the mediator is
near an annihilation resonance, or the mediator has a purely vector coupling to
the dark matter and a purely axial coupling to Standard Model fermions. All
scenarios in which the dark matter annihilates through $t$-channel processes
are now ruled out by a combination of the constraints from LUX/PandaX-II and
the LHC.


  We consider a generalization of the Cheeger problem in a bounded, open set
$\Omega$ by replacing the perimeter functional with a Finsler-type surface
energy and the volume with suitable powers of a weighted volume. We show that
any connected minimizer $A$ of this weighted Cheeger problem such that
$H^{n-1}(A^{(1)} \cap \partial A)=0$ satisfies a relative isoperimetric
inequality. If $\Omega$ itself is a connected minimizer such that
$H^{n-1}(\Omega^{(1)} \cap \partial \Omega)=0$, then it allows the classical
Sobolev and $BV$ embeddings and the classical $BV$ trace theorem. The same
result holds for any connected minimizer whenever the weights grant the
regularity of perimeter-minimizer sets and $\Omega$ is such that $|\partial
\Omega|=0$ and $H^{n-1}(\Omega^{(1)} \cap \partial \Omega)=0$.