  The goal of this article is to display a $Q$-polynomial structure for the
Attenuated Space poset $\mathcal A_q(N,M)$. The poset $\mathcal A_q(N,M)$ is
briefly described as follows. Start with an $(N+M)$-dimensional vector space
$H$ over a finite field with $q$ elements. Fix an $M$-dimensional subspace $h$
of $H$. The vertex set $X$ of $\mathcal A_q(N,M)$ consists of the subspaces of
$H$ that have zero intersection with $h$. The partial order on $X$ is the
inclusion relation. The $Q$-polynomial structure involves two matrices $A, A^*
\in {\rm Mat}_X(\mathbb C)$ with the following entries. For $y, z \in X$ the
matrix $A$ has $(y,z)$-entry $1$ (if $y$ covers $z$); $q^{{\rm dim}\,y}$ (if
$z$ covers $y$); and 0 (if neither of $y,z$ covers the other). The matrix $A^*$
is diagonal, with $(y,y)$-entry $q^{-{\rm dim}\,y}$ for all $y\in X$. By
construction, $A^*$ has $N+1$ eigenspaces. By construction, $A$ acts on these
eigenspaces in a (block) tridiagonal fashion. We show that $A$ is
diagonalizable, with $2N+1$ eigenspaces. We show that $A^*$ acts on these
eigenspaces in a (block) tridiagonal fashion. Using this action, we show that
$A$ is $Q$-polynomial. We show that $A, A^*$ satisfy a pair of relations called
the tridiagonal relations. We consider the subalgebra $T$ of ${\rm
Mat}_X(\mathbb C)$ generated by $A, A^*$.
  We show that $A,A^*$ act on each irreducible $T$-module as a Leonard pair.


  We present and discuss a conjectured criterion for determining whether a 4d
quantum field theory is IR free, or flows to an interacting conformal field
theory in the infrared: ``the correct infrared phase is that with the larger
conformal anomaly $a$". A stronger conjecture is that ``an operator can become
IR free only if that results in a larger conformal anomaly $a$". We test these
conjectures in the context of N=1 supersymmetric theories. They are verified to
indeed predict the correct IR phase in every tested case, for a plethora of
examples for which the infrared phase could already be determined on other
grounds. When applied to the still unsettled case of SU(2) with a chiral
superfield in the isospin 3/2 representation, the conjecture suggest that the
IR phase is conformal rather than confining.


  This paper studies the problem of determining the optimal cut-off for pairs
trading rules. We consider two correlated assets whose spread is modelled by a
mean-reverting process with stochastic volatility, and the optimal pair trading
rule is formulated as an optimal switching problem between three regimes: flat
position (no holding stocks), long one short the other and short one long the
other. A fixed commission cost is charged with each transaction. We use a
viscosity solutions approach to prove the existence and the explicit
characterization of cut-off points via the resolution of quasi-algebraic
equations. We illustrate our results by numerical simulations.


  The envelopes of stars near the Eddington limit are prone to various
instabilities. A high Eddington factor in connection with the Fe opacity peak
leads to convective instability, and a corresponding envelope inflation may
induce pulsational instability. Here, we investigate the occurrence and
consequences of both instabilities in models of Wolf-Rayet stars. We determine
the convective velocities in the sub-surface convective zones to estimate the
amplitude of the turbulent velocity at the base of the wind that potentially
leads to the formation of small-scale wind structures, as observed in several
WR stars. We also investigate the effect of mass loss on the pulsations of our
models. We approximated solar metallicity WR stars by models of mass-losing
helium stars, and we characterized the properties of convection in the envelope
adopting the standard MLT. Our results show the occurrence of sub-surface
convective regions in all studied models. Small surface velocity amplitudes are
predicted for models with masses below 10Msun. For models with M>10Msun, the
surface velocity amplitudes are of the order of 10km/s. Moreover we find the
occurrence of pulsations for stars in the mass range 9-14Msun, while mass loss
appears to stabilize the more massive WR stars. We confront our results with
observationally derived line variabilities of 17 WN stars. The data suggest
variability to occur for stars above 10Msun, which is increasing linearly with
mass above this value, in agreement with our results. We further find some of
our models to be unstable to radial pulsations, and predict local magnetic
fields of the order of hundreds of Gauss in WR stars more massive than 10Msun.
Our study relates the surface velocity fluctuations induced by sub-surface
convection to the formation of clumping in the inner part of the wind. From
this mechanism, we expect a stronger variability in more massive WR stars.


  We present a general framework for studying regularized estimators; such
estimators are pervasive in estimation problems wherein "plug-in" type
estimators are either ill-defined or ill-behaved. Within this framework, we
derive, under primitive conditions, consistency and a generalization of the
asymptotic linearity property. We also provide data-driven methods for choosing
tuning parameters that, under some conditions, achieve the aforementioned
properties. We illustrate the scope of our approach by presenting a wide range
of applications.


  Geometric frustration and the ice rule are two concepts that are intimately
connected and widespread across condensed matter. The first refers to the
inability of a system to satisfy competing interactions in the presence of
spatial constraints. The second, in its more general sense, represents a
prescription for the minimization of the topological charges in a constrained
system. Both can lead to manifolds of high susceptibility and non-trivial,
constrained disorder where exotic behaviors can appear and even be designed
deliberately. In this Colloquium, we describe the emergence of geometric
frustration and the ice rule in soft condensed matter. This Review excludes the
extensive developments of mathematical physics within the field of geometric
frustration, but rather focuses on systems of confined micro- or mesoscopic
particles that emerge as a novel paradigm exhibiting spin degrees of freedom.
In such systems, geometric frustration can be engineered artificially by
controlling the spatial topology and geometry of the lattice, the position of
the individual particle units, or their relative filling fraction. These
capabilities enable the creation of novel and exotic phases of matter, and also
potentially lead towards technological applications related to memory and logic
devices that are based on the motion of topological defects. We review the
rapid progress in theory and experiments and discuss the intimate physical
connections with other frustrated systems at different length scales.


  Analog quantum simulations offer rich opportunities for exploring complex
quantum systems and phenomena through the use of specially engineered,
well-controlled quantum systems. A critical element, increasing the scope and
flexibility of such experimental platforms, is the ability to access and tune
in situ different interaction regimes. Here, we present a superconducting
circuit building block of two highly coherent transmons featuring in situ
tuneable photon hopping and nonlinear cross-Kerr couplings. The interactions
are mediated via a nonlinear coupler, consisting of a large capacitor in
parallel with a tuneable superconducting quantum interference device (SQUID).
We demonstrate the working principle by experimentally characterising the
system in the single- and two-excitation manifolds, and derive a full
theoretical model that accurately describes our measurements. Both qubits have
high coherence properties, with typical relaxation times in the range of 15 to
40 microseconds at all bias points of the coupler. Our device could be used as
a scalable building block in analog quantum simulators of extended Bose-Hubbard
and Heisenberg XXZ models, and may also have applications in quantum computing
such as realising fast two-qubit gates and perfect state transfer protocols.


  Data augmentation is a key element for training accurate models by reducing
overfitting and improving generalization. For image classification, the most
popular data augmentation techniques range from simple photometric and
geometrical transformations, to more complex methods that use visual saliency
to craft new training examples. As augmentation methods get more complex, their
ability to increase the test accuracy improves, yet, such methods become
cumbersome, inefficient and lead to poor out-of-domain generalization, as we
show in this paper. This motivates a new augmentation technique that allows for
high accuracy gains while being simple, efficient (i.e., minimal computation
overhead) and generalizable. To this end, we introduce Saliency-Guided Mixup
with Optimal Rearrangements (SAGE), which creates new training examples by
rearranging and mixing image pairs using visual saliency as guidance. By
explicitly leveraging saliency, SAGE promotes discriminative foreground objects
and produces informative new images useful for training. We demonstrate on
CIFAR-10 and CIFAR-100 that SAGE achieves better or comparable performance to
the state of the art while being more efficient. Additionally, evaluations in
the out-of-distribution setting, and few-shot learning on mini-ImageNet, show
that SAGE achieves improved generalization performance without trading off
robustness.


  The singlet majoron model of seesaw neutrino mass is appended by one dark
Majorana fermion singlet $\chi$ with $L=2$ and one dark complex scalar singlet
$\zeta$ with $L=1$. This simple setup allows $\chi$ to obtain a small radiative
mass anchored by the same heavy right-handed neutrinos, whereas the one-loop
decay of the standard-model Higgs boson to $\chi \chi + \bar{\chi} \bar{\chi}$
provides the freeze-in mechanism for $\chi$ to be the light dark matter of the
Universe.


  We argue that magnetic flux-conservation in turbulent plasmas at high
magnetic Reynolds numbers neither holds in the conventional sense nor is
entirely broken, but instead is valid in a novel statistical sense associated
to the "spontaneous stochasticity" of Lagrangian particle tra jectories. The
latter phenomenon is due to the explosive separation of particles undergoing
turbulent Richardson diffusion, which leads to a breakdown of Laplacian
determinism for classical dynamics. We discuss empirical evidence for
spontaneous stochasticity, including our own new numerical results. We then use
a Lagrangian path-integral approach to establish stochastic flux-freezing for
resistive hydromagnetic equations and to argue, based on the properties of
Richardson diffusion, that flux-conservation must remain stochastic at infinite
magnetic Reynolds number. As an important application of these results we
consider the kinematic, fluctuation dynamo in non-helical, incompressible
turbulence at unit magnetic Prandtl number. We present results on the
Lagrangian dynamo mechanisms by a stochastic particle method which demonstrate
a strong similarity between the Pr = 1 and Pr = 0 dynamos. Stochasticity of
field-line motion is an essential ingredient of both. We finally consider
briefly some consequences for nonlinear MHD turbulence, dynamo and reconnection


  Using the isospin dependent quantum molecular dynamics model, we study the
effect of charge asymmetry and isospin dependent cross-section on
$\frac{dN}{d(<Cos2\phi>)}$ and $\frac{dN}{p_tdp_t}$. Simulations have been
carried out for the reactions of $^{124}X_{m}+^{124}X_{m}$, where m = (47, 50
and 59) and $^{40}S_{16}+^{40}S_{16}$. Our study shows that these parameters
depend strongly on the isospin of cross-section and charge asymmetry. The
distribution of nucleons and fragments is not symmetric around the beam axis.


  Measuring the purity in the metal powder is critical for preserving the
quality of additive manufacturing products. Contamination is one of the most
headache problems which can be caused by multiple reasons and lead to the
as-built components cracking and malfunctions. Existing methods for
metallurgical condition assessment are mostly time-consuming and mainly focus
on the physical integrity of structure rather than material composition.
Through capturing spectral data from a wide frequency range along with the
spatial information, hyperspectral imaging (HSI) can detect minor differences
in terms of temperature, moisture and chemical composition. Therefore, HSI can
provide a unique way to tackle this challenge. In this paper, with the use of a
near-infrared HSI camera, applications of HSI for the non-destructive
inspection of metal powders are introduced. Technical assumptions and solutions
on three step-by-step case studies are presented in detail, including powder
characterization, contamination detection, and band selection analysis.
Experimental results have fully demonstrated the great potential of HSI and
related AI techniques for NDT of powder metallurgy, especially the potential to
satisfy the industrial manufacturing environment.


  The cluster complex on one hand, parking functions on the other hand, are two
combinatorial (po)sets that can be associated to a finite real reflection
group. Cluster parking functions are obtained by taking an appropriate fiber
product (over noncrossing partitions). There is a natural structure of
simplicial complex on these objects, and our main goal is to show that it has
the homotopy type of a (pure) wedge of spheres. The unique nonzero homology
group (as a representation of the underlying reflection group) is a
sign-twisted parking representation, which is the same as Gordon's quotient of
diagonal coinvariants. Along the way, we prove some properties of the poset of
parking functions. We also provide a long list of remaining open problems.


  In this paper, high frequency wind time series measured at different heights
from the ground (from 5.5 to 25.5 meters) in an urban area were investigated.
The spectrum of each series is characterized by a power-law behaviour at low
frequency range, with a mean spectral exponent of about 1.5, which is rather
consistent with the Kolmogorov spectrum of atmospheric turbulence. The
detrended fluctuation analysis was applied on the magnitude and sign series of
the increments of wind speed, in order to get information about the linear and
nonlinear dynamics of the time series. Both the sign series and magnitude
series are characterized by two timescale ranges; in particular the scaling
exponent of the magnitude series in the high timescale range seems to be
related with the height of the sensor. This study aims to understand better
high frequency wind speed in urban areas and to disclose the underlying
mechanism governing the wind fluctuations at different heights.


  The structural and electronic properties of the metallic hcp phase of Zn in
the bulk, monolayer, bilayer, and quantum dot limits have been studied by using
total energy calculations. From our calculated density of states and electronic
band structure, in agreement with previous work, bulk hybridization of the
Zn--$4s$, $3p$, and $3d$ orbitals is obtained. Furthermore, we found that this
orbital hybridization is also obtained for the monolayer, bilayer, and quantum
dot systems. At the same time, we found that the Zn monolayer and bilayer
systems show electronic properties characteristic of lamellar systems, while
the quantum dot system shows the behavior predicted for a 0D system.


  This paper presents a fast computational method, the Expectation Maximization
algorithm, for Maximum Likelihood (ML) estimation in diffusion tensor imaging
under the Rice noise model. We further extend the ML framework to the maximum a
posterior (MAP) estimation and describe the numerical similarities of both ML
and MAP estimators. This novel method is implemented and applied using both
synthetic and real data in a wide range of b amplitudes. The comparison with
other popular methods are made in accuracy, methodology and computation.


  In this note we give a positive answer to a question of Dimca and Greuel
about the quotient between the Milnor and Tjurina numbers of an isolated plane
curve singularity in the cases of one Puiseux pair and semi-quasi-homogeneous
singularities.


  The stationary state solutions of the Ising-type thin films with different
layers in the presence of an external oscillatory field have been examined
within the effective field theory. The exhibition focuses on understanding of
the external field frequency and amplitude effect on the overall behavior of
system for several powerful treatments. The particular attention has been paid
on the dynamical parametric evolution of the special point at which the
critical temperature of the three-dimensional infinite bulk system, where the
surface and the modified exchange parameter are of no importance. Important
characteristics of the films, such as surface enhancement phenomenon, effect of
thickness on the dynamic process etc. have been introduced together with well
known other characteristics. An attempt has been made to explain the relations
between the competing time scales (intrinsic microscopic relaxation time of the
system and the time period of the external oscillatory field) and frequency
dispersion of the critical temperature coordinate of the special point.


  We describe a new model of massless thermal bosons which predicts an
hyperbolic fluctuation spectrum at low frequencies. It is found that the
partition function per mode is the Euler generating function for unrestricted
partitions $p(n)$. Thermodynamical quantities carry a strong arithmetical
structure: they are given by series with Fourier coefficients equal to
summatory functions $\sigma_k(n)$ of the power of divisors, with $k=-1$ for the
free energy, $k=0$ for the number of particles and $k=1$ for the internal
energy. Low frequency contributions are calculated using Mellin transform
methods. In particular the internal energy per mode diverges as
$\frac{\tilde{E}}{kT}=\frac{\pi^2}{6 x}$ with $x=\frac{h \nu}{kT}$ in contrast
to the Planck energy $\tilde{E}=kT$. The theory is applied to calculate
corrections in black body radiation and in the Debye solid. Fractional energy
fluctuations are found to show a $1/\nu$ power spectrum in the low frequency
range. A satisfactory model of frequency fluctuations in a quartz crystal
resonator follows. A sketch of the whole Ramanujan--Rademacher theory of
partitions is reminded as well.


  We discuss multi-$Z'$ signatures coming from decays of Higgs bosons in models
with a spontaneously broken $U(1)'$ symmetry, which can be observed as "lepton
jets" or multi-lepton final states depending on the mass range of new bosons.
We consider anomaly-free $U(1)'$ models without introducing new fermions except
for right-handed neutrinos, in which the Higgs sector is composed of an isospin
doublet and a singlet fields with zero and non-zero $U(1)'$ charges,
respectively. The multi-$Z'$ signatures can then be obtained via the decays of
the discovered (extra) Higgs boson $h$ ($\phi$), i.e., $h\to Z'Z'$, $\phi \to
Z'Z'$ and/or $h \to \phi\phi \to 4Z'$ as far as kinematically allowed. We give
the upper limit on the branching ratios of $h$ into $Z'Z'$ and $4Z'$ from the
current experimental data in each model. We also show the deviation in the
$hhh$ coupling from the standard model prediction at one-loop level, and find
that its amount is typically smaller than 1\%.


  Modular covariance of torus one-point functions constrains the three point
function coefficients of a two dimensional CFT. This leads to an asymptotic
formula for the average value of light-heavy-heavy three point coefficients,
generalizing Cardy's formula for the high energy density of states. The
derivation uses certain asymptotic properties of one-point conformal blocks on
the torus. Our asymptotic formula matches a dual AdS_3 computation of one point
functions in a black hole background. This is evidence that the BTZ black hole
geometry emerges upon course-graining over a suitable family of heavy
microstates.


  We study how universal properties of quantum quenches across critical points
are modified by a weak coupling to thermal dissipation, focusing on the
paradigmatic case of the transverse field Ising model. Beyond the standard
quench-induced Kibble-Zurek defect production in the absence of the bath, the
bath contributes extra thermal defects. We show that spatial correlations in
the noise produced by the bath can play a crucial role: one obtains
quantitatively different scaling regimes depending on whether the correlation
length of the noise is smaller or larger than the Kibble-Zurek length
associated with the quench speed, and the thermal length set by temperature.
For the case of spatially-correlated bath noise, additional thermal defect
generation is restricted to a window that is both quantum critical and excluded
from the non-equilibrium regime surrounding the critical point. We map the
dissipative quench problem to a set of effectively independent dissipative
Landau-Zener problems. Using this mapping along with both analytic and
numerical calculations allows us to find the scaling of the excess defect
density produced in the quench, and suggests a generic picture for such
dissipative quenches.


  Information retrieval (IR) is essential in search engines and dialogue
systems as well as natural language processing tasks such as open-domain
question answering. IR serve an important function in the biomedical domain,
where content and sources of scientific knowledge may evolve rapidly. Although
neural retrievers have surpassed traditional IR approaches such as TF-IDF and
BM25 in standard open-domain question answering tasks, they are still found
lacking in the biomedical domain. In this paper, we seek to improve information
retrieval (IR) using neural retrievers (NR) in the biomedical domain, and
achieve this goal using a three-pronged approach. First, to tackle the relative
lack of data in the biomedical domain, we propose a template-based question
generation method that can be leveraged to train neural retriever models.
Second, we develop two novel pre-training tasks that are closely aligned to the
downstream task of information retrieval. Third, we introduce the ``Poly-DPR''
model which encodes each context into multiple context vectors. Extensive
experiments and analysis on the BioASQ challenge suggest that our proposed
method leads to large gains over existing neural approaches and beats BM25 in
the small-corpus setting. We show that BM25 and our method can complement each
other, and a simple hybrid model leads to further gains in the large corpus
setting.


  In this paper we consider the problem of computing the likelihood of the
profile of a discrete distribution, i.e., the probability of observing the
multiset of element frequencies, and computing a profile maximum likelihood
(PML) distribution, i.e., a distribution with the maximum profile likelihood.
For each problem we provide polynomial time algorithms that given $n$ i.i.d.\
samples from a discrete distribution, achieve an approximation factor of
$\exp\left(-O(\sqrt{n} \log n) \right)$, improving upon the previous best-known
bound achievable in polynomial time of $\exp(-O(n^{2/3} \log n))$ (Charikar,
Shiragur and Sidford, 2019). Through the work of Acharya, Das, Orlitsky and
Suresh (2016), this implies a polynomial time universal estimator for symmetric
properties of discrete distributions in a broader range of error parameter.
  We achieve these results by providing new bounds on the quality of
approximation of the Bethe and Sinkhorn permanents (Vontobel, 2012 and 2014).
We show that each of these are $\exp(O(k \log(N/k)))$ approximations to the
permanent of $N \times N$ matrices with non-negative rank at most $k$,
improving upon the previous known bounds of $\exp(O(N))$. To obtain our results
on PML, we exploit the fact that the PML objective is proportional to the
permanent of a certain Vandermonde matrix with $\sqrt{n}$ distinct columns,
i.e. with non-negative rank at most $\sqrt{n}$. As a by-product of our work we
establish a surprising connection between the convex relaxation in prior work
(CSS19) and the well-studied Bethe and Sinkhorn approximations.


  Many of the "counterintuitive" features of relativistic quantum field theory
have their formal root in the Reeh-Schlieder theorem, which in particular
entails that local operations applied to the vacuum state can produce any state
of the entire field. It is of great interest, then, that I.E. Segal and, more
recently, G. Fleming (in a paper entitled "Reeh-Schlieder Meets Newton-Wigner")
have proposed an alternative "Newton-Wigner" localization scheme that avoids
the Reeh-Schlieder theorem. In this paper, I reconstruct the Newton-Wigner
localization scheme and clarify the limited extent to which it avoids the
counterintuitive consequences of the Reeh-Schlieder theorem. I also argue that
neither Segal nor Fleming has provided a coherent account of the physical
meaning of Newton-Wigner localization.


  In data exchange, data are materialised from a source schema to a target
schema, according to suitable source-to-target constraints. Constraints are
also expressed on the target schema to represent the domain of interest. A
schema mapping is the union of the source-to-target and of the target
constraints.
  In this paper, we address the problem of containment of schema mappings for
data exchange, which has been recently proposed in this framework as a step
towards the optimization of data exchange settings. We refer to a natural
notion of containment that relies on the behaviour of schema mappings with
respect to conjunctive query answering, in the presence of so-called LAV TGDs
as target constraints. Our contribution is a practical technique for testing
the containment based on the existence of a homomorphism between special
"dummy" instances, which can be easily built from schema mappings.
  We argue that containment of schema mappings is decidable for most practical
cases, and we set the basis for further investigations in the topic. This paper
extends our preliminary results.


  Massive stars play a major role not only in stellar evolution but also
galactic evolution theory. This is because of their dynamical interaction with
binary companions, and because their strong winds and explosive deaths as
supernovae provide chemical, radiative and kinematic feedback to their
environments. Yet this feedback strongly depends on the physics of the
supernova progenitor star. It is only in recent decades that asteroseismology -
the study of stellar pulsations - has developed the necessary tools to a high
level of sophistication to become a prime method at the forefront of
astronomical research for constraining the physical processes at work within
stellar interiors. For example, precise and accurate asteroseismic constraints
on interior rotation, magnetic field strength and geometry, mixing and angular
momentum transport processes of massive stars are becoming increasingly
available across a wide range of masses. Moreover, ongoing large-scale
time-series photometric surveys with space telescopes have revealed a large
diversity in the variability of massive stars, including widespread coherent
pulsations across a large range in mass and age, and the discovery of
ubiquitous stochastic low-frequency (SLF) variability in their light curves. In
this invited review, I discuss the progress made in understanding the physical
processes at work within massive star interiors thanks to modern asteroseismic
techniques, and conclude with a future outlook.


  We report optical absorption imaging of ultracold neutral plasmas.Images are
used to measure the ion absorption spectrum, which is Doppler-broadened.
Through the spectral width, we monitor ion equilibration in the first 250ns
after plasma formation. The equilibration leaves ions on the border between the
weakly coupled gaseous and strongly coupled liquid states. On a longer
timescale of microseconds, we observe radial acceleration of ions resulting
from pressure exerted by the trapped electron gas.


  In this paper, we present a mathematical approach in estimating transition
energy of type-I core-shell quantum dots (CSQDs) in strong and weak confinement
of charge carriers within the core materials. We will do this by using
effective-mass approximation together with a single-band model. The effects of
potential step of conduction band and valence band on confinement strength will
be discussed. It can be seen at the end of this paper that for a same size
CSQDs, CSQDs with bigger potential steps will have stronger carriers
confinement and with more localized excitons.


  We prove new borderline regularity results for solutions to fully nonlinear
elliptic equations together with pointwise gradient potential estimates.


  A Locally Lorentz-covariant theory of gravity which is equivalent to general
relativity in weak gravitational field is present. The space-time standard in
local gravitational field is modified in terms of equivalence principle to keep
consistent with that of inertial frame. The static metric in our theory agrees
with Schwarzschild metric at first order approximation. The gravitational
vector potential produced by a moving body is obtained by applying local
Lorentz transformations in gravitational field. On the other hand, we still
regard inertial frame, i.e. center of mass of the system, as the preferred
frame of reference. This is because Newton's laws of motion hold only for
inertial frames. The apsidal motion of binary system and the expansion of the
universe can be explained reasonably when observed from inertial frame. Black
holes and singularities do not exist in our theory.


  This paper proposes a novel reinforcement learning (RL) framework for credit
underwriting that tackles ungeneralizable contextual challenges. We adapt RL
principles for credit scoring, incorporating action space renewal and
multi-choice actions. Our work demonstrates that the traditional underwriting
approach aligns with the RL greedy strategy. We introduce two new RL-based
credit underwriting algorithms to enable more informed decision-making.
Simulations show these new approaches outperform the traditional method in
scenarios where the data aligns with the model. However, complex situations
highlight model limitations, emphasizing the importance of powerful machine
learning models for optimal performance. Future research directions include
exploring more sophisticated models alongside efficient exploration mechanisms.


  Understanding the dynamics behind black hole state transitions and the
changes they reflect in outbursts has become long-standing problem. The X-ray
reflection spectrum describes the interaction between the hard X-ray source
(the power-law continuum) and the cool accretion disc it illuminates, and thus
permits an indirect view of how the two evolve. We present a systematic
analysis of the reflection spectrum throughout three outbursts (500+
observations) of the black hole binary GX 339-4, representing the largest study
applying a self-consistent treatment of reflection to date. Particular
attention is payed to the coincident evolution of the power-law and reflection,
which can be used to determine the accretion geometry. The hard state is found
to be distinctly reflection weak, however the ratio of reflection to power-law
gradually increases as the source luminosity rises. In contrast the reflection
is found dominate the power-law throughout most of the soft state, with
increasing supremacy as the source decays. We discuss potential dynamics
driving this, favouring inner disc truncation and decreasing coronal height for
the hard and soft states respectively. Evolution of the ionisation parameter,
power-law slope and high-energy cut-off also agree with this interpretation.


  A locally irregular graph is a graph in which the end-vertices of every edge
have distinct degrees. A locally irregular edge coloring of a graph G is any
edge coloring of G such that each of the colors induces a locally irregular
subgraph of G. A graph G is colorable if it admits a locally irregular edge
coloring. The locally irregular chromatic index of a colorable graph G, denoted
by CHI'irr(G), is the smallest number of colors used by a locally irregular
edge coloring of G. The Local Irregularity Conjecture claims that all graphs,
except odd length path, odd length cycle and a certain class of cacti, are
colorable by 3 colors. As the conjecture is valid for graphs with large minimum
degree and all non-colorable graphs are vertex disjoint cacti, we take
direction to study rather sparse graphs. In this paper, we give a cactus graph
B which contradicts this conjecture, i.e. CHI'irr(B) = 4. Nevertheless, we show
that the conjecture holds for unicyclic graphs and cacti with vertex disjoint
cycles.


  Eclipse timing variation analysis has become a powerful method to discover
planets around binary systems. We applied this technique to investigate the
eclipse times of GK Vir. This system is a post-common envelope binary with an
orbital period of 8.26 h. Here, we present 10 new eclipse times obtained
between 2013 and 2020. We calculated the O-C diagram using a linear ephemeris
and verified a clear orbital period variation (OPV) with a cyclic behavior. We
investigated if this variation could be explained by the Applegate mechanism,
the apsidal motion, or the light travel time (LTT) effect. We found that the
Applegate mechanism would hardly explain the OPV with its current theoretical
description. We obtained using different approaches that the apsidal motion is
a less likely explanation than the LTT effect. We showed that the LTT effect
with one circumbinary body is the most likely cause for the OPV, which was
reinforced by the orbital stability of the third body. The LTT best solution
provided an orbital period of ~24 yr for the outer body. Under the assumption
of coplanarity between the external body and the inner binary, we obtained a
Jupiter-like planet around the GK Vir. In this scenario, the planet has one of
the longest orbital periods, with a full observational baseline, discovered so
far. However, as the observational baseline of GK Vir is smaller than twice the
period found in the O-C diagram, the LTT solution must be taken as preliminary.


  For complex parameters a,c, we consider the Henon mapping H_{a,c}: C^2 -> C^2
given by (x,y) -> (x^2 +c -ay, x), and its Julia set, J. In this paper, we
describe a rigorous computer program for attempting to construct a cone field
in the tangent bundle over J, which is preserved by DH, and a continuous norm
in which DH (and DH^{-1}) uniformly expands the cones (and their complements).
We show a consequence of a successful construction is a proof that H is
hyperbolic on J. We give several new examples of hyperbolic maps, produced with
our computer program, Hypatia, which implements our methods.


  When accelerated by a constant force in the lab frame, a classical charge
experiences no self force. In this case, the particle radiates without
dissipating its kinetic and potential energy. But what happens when the
particle enters another region with equal and opposite acceleration? Does the
oscillating charge lose its mechanical energy similar to a radiating dipole,
even though it seems to lose no mechanical energy within each region of
constant acceleration? In this paper, I will show how mechanical energy is
transferred to radiation energy via the Schott energy when the particle crosses
the boundary between the two regions. In particular, I will show how
preacceleration, which is usually regarded as an unphysical effect of the
Lorentz-Abraham-Dirac self force, is essential for the energy transfer.
Moreover, I will show that the commonly adopted Landau-Lifshitz approximation,
which removes preacceleration, introduces second-order secular energy error. On
a more fundamental level, the validity of classical electrodynamics is in fact
questionable because quantum effects are likely important. The classical
prediction can be tested experimentally by observing frequency chirping of
radiation, whereby micro physics leaves signatures on macroscopic scales. The
required experimental accuracy is estimated. Trap experiment of this type is
complementary to collider experiments that endeavor to observe radiation
reaction for elementary particles.


  The scattering of Dirac fermions on the sine-Gordon kink is studied both
analytically and numerically. To achieve invariance with respect to a discrete
symmetry, the sine-Gordon model is treated as a nonlinear $\sigma$-model with a
circular target space that interacts with fermionic isodublets through the
Yukawa interaction. It is shown that the diagonal and antidiagonal parts of the
fermionic wave function interact independently with the external field of the
sine-Gordon kink. The wave functions of the fermionic scattering states are
expressed in terms of the Heun functions. General expressions for the
transmission and reflection coefficients are derived, and their dependences on
the fermion momentum and mass are studied numerically. The existence condition
is found for two fermionic zero modes, and their analytical expressions are
obtained. It is shown that the zero modes do not lead to fragmentation of the
fermionic charge, but can lead to polarization of the fermionic vacuum. The
scattering of the diagonal and antidiagonal fermionic states is found to be
significantly different; this difference is shown to be due to the different
dependences of the energy levels of these bound states on the fermion mass, and
is in accordance with Levinson's theorem.


  Let $\mathcal{M}$ be a smooth $d$-dimensional submanifold of $\mathbb{R}^N$
with boundary that's equipped with the Euclidean (chordal) metric, and choose
$m \leq N$. In this paper we consider the probability that a random matrix $A
\in \mathbb{R}^{m \times N}$ will serve as a bi-Lipschitz function $A:
\mathcal{M} \rightarrow \mathbb{R}^m$ with bi-Lipschitz constants close to one
for three different types of distributions on the $m \times N$ matrices $A$,
including two whose realizations are guaranteed to have fast matrix-vector
multiplies. In doing so we generalize prior randomized metric space embedding
results of this type for submanifolds of $\mathbb{R}^N$ by allowing for the
presence of boundary while also retaining, and in some cases improving, prior
lower bounds on the achievable embedding dimensions $m$ for which one can
expect small distortion with high probability. In particular, motivated by
recent modewise embedding constructions for tensor data, herein we present a
new class of highly structured distributions on matrices which outperform prior
structured matrix distributions for embedding sufficiently low-dimensional
submanifolds of $\mathbb{R}^N$ (with $d \lesssim \sqrt{N}$) with respect to
both achievable embedding dimension, and computationally efficient
realizations. As a consequence we are able to present, for example, a general
new class of Johnson-Lindenstrauss embedding matrices for $\mathcal{O}(\log^c
N)$-dimensional submanifolds of $\mathbb{R}^N$ which enjoy $\mathcal{O}(N \log
(\log N))$-time matrix vector multiplications.


  We prove an inequality that generalizes the Fan-Taussky-Todd discrete analog
of the Wirtinger inequality. It is equivalent to an estimate on the spectral
gap of a weighted discrete Laplacian on the circle. The proof uses a geometric
construction related to the discrete isoperimetric problem on the surface of a
cone.
  In higher dimensions, the mixed volumes theory leads to similar results,
which allows us to associate a discrete Laplace operator to every geodesic
triangulation of the sphere and, by analogy, to every triangulated spherical
cone-metric. For a cone-metric with positive singular curvatures, we conjecture
an estimate on the spectral gap similar to the Lichnerowicz-Obata theorem.


  Comment on the paper by K. E. Nagaev, S. V. Remizov, D. S. Shapiro, Noise in
the helical edge channel anisotropically coupled to a local spin, JETP Lett.
108, 664 (2018).


  The Telescope Array is the largest experiment studying ultra-high energy
cosmic rays in the northern hemisphere. The detection area of the experiment
consists of an array of 507 surface detectors, and a fluorescence detector
divided into three sites at the periphery. The viewing directions of the 38
fluorescence telescopes point over the air space above the surface array. In
this paper, we describe a technique that we have developed for simulating the
response of the array of surface detectors of the Telescope Array experiment.
The two primary components of this method are (a) the generation of a detailed
CORSIKA Monte Carlo simulation with all known characteristics of the data, and
(b) the validation of the simulation by a direct comparison with the Telescope
Array surface detector data. This technique allows us to make a very accurate
calculation of the acceptance of the array. We also describe a study of
systematic uncertainties in this acceptance calculation.


  Classical multiscale analysis based on wavelets has a number of successful
applications, e.g. in data compression, fast algorithms, and noise removal.
Wavelets, however, are adapted to point singularities, and many phenomena in
several variables exhibit intermediate-dimensional singularities, such as
edges, filaments, and sheets. This suggests that in higher dimensions, wavelets
ought to be replaced in certain applications by multiscale analysis adapted to
intermediate-dimensional singularities.
  My lecture described various initial attempts in this direction. In
particular, I discussed two approaches to geometric multiscale analysis
originally arising in the work of Harmonic Analysts Hart Smith and Peter Jones
(and others): (a) a directional wavelet transform based on parabolic dilations;
and (b) analysis via anistropic strips. Perhaps surprisingly, these tools have
potential applications in data compression, inverse problems, noise removal,
and signal detection; applied mathematicians, statisticians, and engineers are
eagerly pursuing these leads.


  We investigate the pair production of a vector-like quark triplet with
hypercharge 5/3 decaying into top quark and a complex scalar triplet with
hypercharge 1 at the LHC. This novel scenario, featuring particles with exotic
charges - two quarks with charge 8/3 and 5/3 and a scalar with charge 2 -
serves as a unique window to models based on the framework of partial
compositeness, where these particles naturally emerge as bound states around
the TeV scale. Leveraging on the LHC data we establish exclusion limits on the
masses of the vector-like quark and the scalar triplet. Subsequently, we design
an analysis strategy aimed at improving sensitivity in the region which is
still allowed. Our analysis focuses on two specific regions in the parameter
space: the first entails a large mass gap between the vector-like quarks and
the scalars, so that the vector-like quarks can decay into the scalars; the
second involves a small mass gap, such that this decay is forbidden. To
simplify the parameter space, both vector-like quarks and scalars are assumed
to be degenerate or almost degenerate within the triplets, such that chain
decays between fermions and scalars are suppressed. As a result, we found that
final states characterized by a same-sign lepton pair, multiple jets, and high
net transverse momentum (i.e. effective mass) will play a pivotal role to
unveil this model and, more in general, models characterised by multiple
vector-like quarks around the same mass scale during the high luminosity LHC
phase.


  The spectral density operator $\hat{\rho}(\omega)=\delta(\omega-\hat{H})$
plays a central role in linear response theory as its expectation value, the
dynamical response function, can be used to compute scattering cross-sections.
In this work, we describe a near optimal quantum algorithm providing an
approximation to the spectral density with energy resolution $\Delta$ and error
$\epsilon$ using
$\mathcal{O}\left(\sqrt{\log\left(1/\epsilon\right)\left(\log\left(1/\Delta\right)+\log\left(1/\epsilon\right)\right)}/\Delta\right)$
operations. This is achieved without using expensive approximations to the
time-evolution operator but exploiting instead qubitization to implement an
approximate Gaussian Integral Transform (GIT) of the spectral density. We also
describe appropriate error metrics to assess the quality of spectral function
approximations more generally.


  Using Herschel PACS and SPIRE observations of Lockman Hole-North and GOODS-N
as part of the HerMES project, we explore the far-IR properties of a sample of
mid-IR selected starburst dominated ultra-luminous infrared galaxies (ULIRGs)
at z ~ 2. The selection of the sample is based on the detection of the stellar
bump that appears in the SED of star-forming galaxies at 1.6um. We derive
robust estimates of infrared luminosities (L_IR) and dust temperatures (T_d) of
the population and find that while the luminosities in our sample span less
than an order of magnitude (12.24< log(L_IR/Lo) < 12.94), they cover a wide
range of dust temperatures (25< T_d < 62 K). Galaxies in our sample range from
those that are as cold as high-z sub-millimeter galaxies (SMGs) to those that
are as warm as optically faint radio galaxies (OFRGs) and local ULIRGs.
Nevertheless, our sample has median T_d=42.3 K, filling the gap between SMGs
and OFRGs, bridging the two populations. We demonstrate that a significant
fraction of our sample would be missed from ground based (sub)mm surveys
(850-1200um) showing that the latter introduce a bias towards the detection of
colder sources. We conclude that Herschel} observations, confirm the existence
of high-z ULIRGs warmer than SMGs, show that the mid-IR selection of high-z
ULIRGs is not T_d-dependent, reveal a large dispersion in T_d of high-z ULIRGs,
and provide the means to characterize the bulk of the ULIRG population, free
from selection biases introduced by ground based (sub)mm surveys.


  In this paper we study subspaces which are invariant under squares and cubes
(separately as well as jointly) of unicellular backward weighted shift
operators on a separable Hilbert space. The finite-dimensional subspaces are
characterized for all weights and the infinite-dimensional subspaces are
characterized for two classes of weights.


  Using the classical Susceptible-Infected-Recovered epidemiological model, an
analytical formula is derived for the number of beds occupied by Covid-19
patients. The analytical curve is fitted to data in Belgium, France, New York
City and Switzerland, with a correlation coefficient exceeding 98.8%,
suggesting that finer models are unnecessary with such macroscopic data. The
fitting is used to extract estimates of the doubling time in the ascending
phase of the epidemic, the mean recovery time and, for those who require
medical intervention, the mean hospitalization time. Large variations can be
observed among different outbreaks.


  We examine the cosmological effects of the Hagedorn phase in models where the
observable universe is pictured as a D-brane. It is shown that, even in the
absence of a cosmological constant, winding modes cause a negative `pressure'
that can drive brane inflation of various types including both power law and
exponential. We also find regimes in which the cosmology is stable but
oscillating (a bouncing universe) with the Hagedorn phase softening the
singular behavior associated with the collapse.


  We present a novel unsupervised domain adaptation method for small bowel
segmentation based on feature disentanglement. To make the domain adaptation
more controllable, we disentangle intensity and non-intensity features within a
unique two-stream auto-encoding architecture, and selectively adapt the
non-intensity features that are believed to be more transferable across
domains. The segmentation prediction is performed by aggregating the
disentangled features. We evaluated our method using intravenous
contrast-enhanced abdominal CT scans with and without oral contrast, which are
used as source and target domains, respectively. The proposed method showed
clear improvements in terms of three different metrics compared to other domain
adaptation methods that are without the feature disentanglement. The method
brings small bowel segmentation closer to clinical application.


  The optical absorption of nanoscale thickness semiconductor films on top of
light-trapping structures based on optical interference effects combined with
spectrum-splitting structures is theoretically investigated. Nearly perfect
absorption over a broad spectrum range can be achieved in $<100$ nm thick films
on top of one-dimensional photonic crystal or metal films. This phenomenon can
be attributed to interference induced photonic localization, which enhances the
absorption and reduces the reflection of the films. Perfect solar absorption
and low carrier thermalization loss can be achieved when the light-trapping
structures with wedge-shaped spacer layer or semiconductor films are combined
with spectrum-splitting structures.


  Symmetric positive semidefinite (SPSD) matrix approximation is an important
problem with applications in kernel methods. However, existing SPSD matrix
approximation methods such as the Nystr\"om method only have weak error bounds.
In this paper we conduct in-depth studies of an SPSD matrix approximation model
and establish strong relative-error bounds. We call it the prototype model for
it has more efficient and effective extensions, and some of its extensions have
high scalability. Though the prototype model itself is not suitable for
large-scale data, it is still useful to study its properties, on which the
analysis of its extensions relies.
  This paper offers novel theoretical analysis, efficient algorithms, and a
highly accurate extension. First, we establish a lower error bound for the
prototype model and improve the error bound of an existing column selection
algorithm to match the lower bound. In this way, we obtain the first optimal
column selection algorithm for the prototype model. We also prove that the
prototype model is exact under certain conditions. Second, we develop a simple
column selection algorithm with a provable error bound. Third, we propose a
so-called spectral shifting model to make the approximation more accurate when
the eigenvalues of the matrix decay slowly, and the improvement is
theoretically quantified. The spectral shifting method can also be applied to
improve other SPSD matrix approximation models.


  Here, we present first principle study of structural, electronic, and optical
properties of pristine and janus tellurene allotropes using density functional
theory (DFT). The $\alpha$, $\beta$, $\delta$, and $\eta$ allotrope of pristine
tellurene exhibit indirect band gap while $\gamma$ and $\sigma$ allotropes are
metallic. The bandgap shows tunability in janus tellurene compared to pristine
tellurene. A metallic to semiconductor transition occurs in janus $\gamma$,
$\sigma$ and its allotropes. Dirac cone-like interesting feature has been
observed for pristine $\sigma$ tellurene which remains preserved with the
opening in energy gap for janus allotrope. In optical properties, imaginary
part dielectric function and electron energy loss spectra show a blue shift in
janus tellurene as compared to pristine form. Static dielectric constant is
tunable in janus tellurene. All allotropes of tellurene are optically active in
UV-Vis region with optical anisotropy in all three directions. We believe that
our findings will provide useful pointers in the experimental fabrication of
devices based on janus tellurene.


  We show that the kinematics underlying Poincare's elongated ellipse,
immediately deduced from Lorentz Transformation (LT), is not the same as
Einstein's kinematics. The two main differences are : On one hand the
relationship of Lorentz contraction with LT, and on the other hand, the
relationship of Doppler formula with wave four-vector. Einstein's wave
four-vector (quantum theory of light, photon, transverse gauge) is not the same
as Poincare's wave four-vector (classical theory of light, electromagnetic
wave, Lorenz gauge) and therefore the Doppler formulas are not the same.
Poincare's Doppler formula is not independent of the metric of space-time. We
show that Poincare's metrics of space-time is based on a cosmological
definition of distance and predicts an expansion of space for remote objects
(Hubble), directly connected with Poincare's Doppler formula.


  Developed structural scheme implementation of an integrated security and
formulated principles for the creation and development of an effective system
of information security.


  Model driven architecture (MDA) concentrates on the use of models during
software development. An approach using models as the central development
artifact is more abstract, more compact and thus more effective and probably
also less error prone. Although the ideas of MDA exist already for years, there
is still much to improve in the development process as well as the underlying
techniques and tools. Therefore, this paper is a follow up on, reexamining und
updating the statements made there. Here two major and strongly related
techniques are identified and discussed: Test case modeling and an evolutionary
approach to model transformation.


  In 1971 J. Serrin proved that, given a smooth bounded domain $\Omega \subset
\mathbb{R}^N$ and $u$ a positive solution of the problem:
  \begin{equation*}
  \begin{array}{ll}
  -\Delta u = f(u) &\mbox{in $\Omega$, }
  u =0 &\mbox{on $\partial\Omega$, }
  \partial_{\nu} u =\mbox{constant} &\mbox{on $\partial\Omega$, }
  \end{array} \end{equation*} then $\Omega$ is necessarily a ball and $u$ is
radially symmetric. In this paper we prove that the positivity of $u$ is
necessary in that symmetry result. In fact we find a sign-changing solution to
that problem for a $C^2$ function $f(u)$ in a bounded domain $\Omega$ different
from a ball. The proof uses a local bifurcation argument, based on the study of
the associated linearized operator.


  In this thesis, we consider the thin-film equation with nonlinear surface
tension term in one space dimension. Relying on the corresponding energy and
entropy estimates, we prove existence of weak solutions as well as
nonnegativity results.


  A Glasma flux-tube model has been proposed to explain strong elongation on
pseudorapidity $\eta$ of the same-side 2D peak in minimum-bias angular
correlations from $\sqrt{s_{NN}} = 200$ GeV \auau collisions. The same-side
peak or "soft ridge" is said to arise from coupling of flux tubes to radial
flow. Gluons radiated transversely from flux tubes are boosted by radial flow
to form a narrow structure or ridge on azimuth. In this study we test the
conjecture by comparing predictions for particle production, spectra and
correlations from the Glasma model and conventional fragmentation processes
with measurements. We conclude that the Glasma model is contradicted by
measured hadron yields, spectra and correlations, whereas a two-component model
of hadron production, including minimum-bias parton fragmentation, provides a
quantitative description of most data, although $\eta$ elongation remains
unexplained.


  Despite the notable advancements of existing prompting methods, such as
In-Context Learning and Chain-of-Thought for Large Language Models (LLMs), they
still face challenges related to various biases. Traditional debiasing methods
primarily focus on the model training stage, including approaches based on data
augmentation and reweighting, yet they struggle with the complex biases
inherent in LLMs. To address such limitations, the causal relationship behind
the prompting methods is uncovered using a structural causal model, and a novel
causal prompting method based on front-door adjustment is proposed to
effectively mitigate LLMs biases. In specific, causal intervention is achieved
by designing the prompts without accessing the parameters and logits of LLMs.
The chain-of-thought generated by LLM is employed as the mediator variable and
the causal effect between input prompts and output answers is calculated
through front-door adjustment to mitigate model biases. Moreover, to accurately
represent the chain-of-thoughts and estimate the causal effects, contrastive
learning is used to fine-tune the encoder of chain-of-thought by aligning its
space with that of the LLM. Experimental results show that the proposed causal
prompting approach achieves excellent performance across seven natural language
processing datasets on both open-source and closed-source LLMs.


  Grain boundaries (GBs) and interfaces in polycrystalline materials are
significant research subjects in the field of materials science. Despite a more
than 50-year history of their study, there are still many open questions. The
main challenge in studying interfacial structures is the extreme complexity of
their experimental and theoretical observation and description. The presence of
phase-like states at grain boundaries called complexions requires even more
effort in their study. Here, we demonstrate the effect of grain boundaries on
the properties of polycrystalline minerals on the example of the
$\Sigma$5[310](001) grain boundary in periclase (MgO). Using the combination of
extended evolutionary algorithm USPEX and modern machine-learning interatomic
potentials, we explore the configuration space of the specified grain boundary
and predict its possible phase-like states. In addition to the widely studied
CSL-type structure, we found several stable GB complexions with various atomic
densities at the boundary plane. Analysis of grain boundary excess volume of
the structures revealed the successive stages of GB failure under the tensile
applied in the normal direction of the boundary plane. Our results demonstrate
that interfacial chemistry and structural diversity can be surprisingly rich
even in seemingly simple and thoroughly investigated materials. The phenomena
we observe here are not specific to MgO and should be general.


  Quantitative description of charge transport across tunneling and
break-junction devices with novel superconductors encounters some problems not
present, or not as severe for traditional superconducting materials. In this
work, we explain unexpected features in related transport characteristics as an
effect of a degraded nano-scaled sheath at the superconductor surface. Model
capturing main aspects of the ballistic charge transport across hybrid
superconducting structures with normally-conducting nm-thick interlayers is
proposed. The calculations are based on a scattering formalism taking into
account Andreev electron-into-hole (and inverse) reflections at normal
metal-superconductor interfaces as well as transmission and backscattering
events in insulating barriers between the electrodes. Current-voltage
characteristics of such devices exhibit a rich diversity of anomalous (from the
viewpoint of the standard theory) features, in particular, shift of
differential-conductance maximums at gap voltages to lower positions and
appearance of well-defined dips instead expected coherence peaks. We compare
our results with related experimental data.


  Using seven semiconductors/insulators with band gaps covering the range from
1 eV to 10 eV we systematically explore the performance of two different
variants of self-consistency associated with famous Hedin's system of
equations: the full self-consistency and the so called quasi-particle
approximation to it. The pros and cons of these two variants of
self-consistency are sufficiently well documented in literature for the
simplest GW approximation to the Hedin's equations. Our study, therefore, aims
primarily at the level of theory beyond GW approximation, i.e. at the level of
theory which includes vertex corrections. Whereas quasi-particle
self-consistency has certain advantages at GW level (well known fact), the
situation becomes quite different when vertex corrections are included. In the
variant with full self-consistency, vertex corrections (both for polarizability
and for self energy) systematically reduce the calculated band gaps making them
closer to the experimental values. In the variant with quasi-particle
self-consistency, however, an inclusion of the same diagrams has considerably
larger effect and calculated band gaps become severely underestimated.
Different effect of vertex corrections in two variants of self-consistency can
be related to the Z-factor cancellation which plays positive role in
quasi-particle self-consistency at GW level of theory but appears to be
destructive for the quasi-particle approximation when higher order diagrams are
included. Second result of our study is that we were able to reproduce the
results obtained with the Questaal code using our FlapwMBPT code when the same
variant of self-consistency (quasi-particle) and the same level of vertex
corrections (for polarizability only, static approximation for screened
interaction, and Tamm-Dancoff approximation for the Bethe-Salpeter equation)
are used.


  In this paper we deal with the cubic Schr\"odinger system $ -\Delta u_i =
\sum_{j=1}^n \beta_{ij}u_j^2 u_i$, $u_1,\dots,u_n \geq 0$ in $\mathbb{R}^N
(N\leq 3)$, where $\beta=(\beta_{i,j})_{ij}$ is a symmetric matrix with real
coefficients and $\beta_{ii}\geq 0$ for every $i=1,\ldots,n$. We analyse the
existence and nonexistence of nontrivial solutions in connection with the
properties of the matrix $\beta$, and provide a complete characterization in
dimensions $N=1,2$. Extensions to more general power-type nonlinearities are
given.


  In this paper we analyze the kinematics, chemistry, and physical properties
of a sample of the most metal-poor damped Lyman-alpha systems (DLAs), to
uncover their links to modern-day galaxies. We present evidence that the DLA
population as a whole exhibits a `knee' in the relative abundances of the
alpha-capture and Fe-peak elements when the metallicity is [Fe/H] ~ -2.0,
assuming that Zn traces the build-up of Fe-peak elements. In this respect, the
chemical evolution of DLAs is clearly different from that experienced by Milky
Way halo stars, but resembles that of dwarf spheroidal galaxies in the Local
Group. We also find a close correspondence between the kinematics of Local
Group dwarf galaxies and of high redshift metal-poor DLAs, which further
strengthens this connection. On the basis of such similarities, we propose that
the most metal-poor DLAs provide us with a unique opportunity to directly study
the dwarf galaxy population more than ten billion years in the past, at a time
when many dwarf galaxies were forming the bulk of their stars. To this end, we
have measured some of the key physical properties of the DLA gas, including
their neutral gas mass, size, kinetic temperature, density, and turbulence. We
find that metal-poor DLAs contain a warm neutral medium with T_gas ~ 9600 K
predominantly held up by thermal pressure. Furthermore, all of the DLAs in our
sample exhibit a subsonic turbulent Mach number, implying that the gas
distribution is largely smooth. These results are among the first empirical
descriptions of the environments where the first few generations of stars may
have formed in the Universe.


  An explicitly covariant formulation is presented of a modified DGP scenario
proposed recently [1], to avoid the instability of the self-accelerating
branch. It is based on the introduction of a bulk scalar field with appropriate
non-minimal coupling to the bulk Einstein-Hilbert term. The method is general
and may be applied to other models as well.


  We study the following generalized matrix rank estimation problem: given an
$n \times n$ matrix and a constant $c \geq 0$, estimate the number of
eigenvalues that are greater than $c$. In the distributed setting, the matrix
of interest is the sum of $m$ matrices held by separate machines. We show that
any deterministic algorithm solving this problem must communicate $\Omega(n^2)$
bits, which is order-equivalent to transmitting the whole matrix. In contrast,
we propose a randomized algorithm that communicates only $\widetilde O(n)$
bits. The upper bound is matched by an $\Omega(n)$ lower bound on the
randomized communication complexity. We demonstrate the practical effectiveness
of the proposed algorithm with some numerical experiments.


  An alternative scenario for the glass transition based on the cooperative
nature of nucleation processes and the role of entropic effects is presented.
The new ingredient is to relate the dissipation during the relaxation process
to the release of strain energy driven by the nucleation of progressively
larger cooperative spatial regions. Using an equiprobability hypothesis for the
transition between different metastable configurations, we obtain a relation
between the free energy dissipation rate and the size of the largest
cooperative regions. Th is leads to a new phenomenological relation between the
largest relaxation time in the supercooled liquid phase and the effective
temperature. This differs from the classical Adam-Gibbs relation in that
predicts no divergence of the primary relaxation time at the Kauzmann
temperature but a crossover from fragile to strong behavior.


  Due to major shifts in European energy supply, a structural change can be
observed in Austrian electricity spot price data starting from the second
quarter of the year 2021 onward. In this work we study the performance of two
different factor models for the electricity spot price in three different time
periods. To this end, we consider three samples of EEX data for the Austrian
base load electricity spot price, one from the pre-crises from 2018 to 2021,
the second from the time of the crisis from 2021 to 2023 and the whole data
from 2018 to 2023. For each of these samples, we investigate the fit of a
classical 3-factor model with a Gaussian base signal and one positive and one
negative jump signal and compare it with a 4-factor model to assess the effect
of adding a second Gaussian base signal to the model. For the calibration of
the models we develop a tailor-made Markov Chain Monte Carlo method based on
Gibbs sampling. To evaluate the model adequacy, we provide simulations of the
spot price as well as a posterior predictive check for the 3- and the 4-factor
model. We find that the 4-factor model outperforms the 3-factor model in times
of non-crises. In times of crises, the second Gaussian base signal does not
lead to a better fit of the model. To the best of our knowledge, this is the
first study regarding stochastic electricity spot price models in this new
market environment. Hence, it serves as a solid base for future research.


  We survey the recent developments in the area that grew out of attempts to
extend an analog of Hilbert's Tenth Problem to the field of rational numbers
and rings of integers of number fields. The paper is based on a plenary talk
the author gave at the North American Annual ASL meeting at the University of
Notre Dame in May of 2009.


  The 1/N expansion of the two-particle irreducible (2PI) effective action is
employed to compute universal properties at the second-order phase transition
of an O(N)-symmetric N-vector model directly in three dimensions. At
next-to-leading order the approach cures the spurious small-N divergence of the
standard (1PI) 1/N expansion for a computation of the critical anomalous
dimension eta(N), and leads to improved estimates already for moderate values
of N.


  According to evolutionary game theory, cooperation in public goods games is
eliminated by free-riders, yet in nature, cooperation is ubiquitous. Artificial
models resolve this contradiction via the mechanism of network reciprocity.
However, existing research only addresses pre-existing networks and does not
specifically consider their origins. Further, much work has focused on
scale-free networks and so pre-supposes attachment mechanisms which may not
exist in nature. We present a coevolutionary model of public goods games in
networks, growing by random attachment, from small founding populations of
simple agents. The model demonstrates the emergence of cooperation in
moderately heterogeneous networks, regardless of original founders' behaviour,
and absent higher cognitive abilities such as recognition or memory. It may
thus illustrate a more general mechanism for the evolution of cooperation, from
early origins, in minimally cognitive organisms. It is the first example of a
model explaining cooperation in public goods games on growing networks.


  A compressible flow characterized by a velocity field $u_x(x,t)=ax/(1+at)$ is
analyzed by means of the Boltzmann equation and the Bhatnagar-Gross-Krook
kinetic model. The sign of the control parameter (the longitudinal deformation
rate $a$) distinguishes between an expansion ($a>0$) and a condensation ($a<0$)
phenomenon. The temperature is a decreasing function of time in the former
case, while it is an increasing function in the latter. The non-Newtonian
behavior of the gas is described by a dimensionless nonlinear viscosity
$\eta^*(a^*)$, that depends on the dimensionless longitudinal rate $a^*$. The
Chapman-Enskog expansion of $\eta^*$ in powers of $a^*$ is seen to be only
asymptotic (except in the case of Maxwell molecules). The velocity distribution
function is also studied. At any value of $a^*$, it exhibits an algebraic
high-velocity tail that is responsible for the divergence of velocity moments.
For sufficiently negative $a^*$, moments of degree four and higher may diverge,
while for positive $a^*$ the divergence occurs in moments of degree equal to or
larger than eight.


  The complicated dynamics of the contact line of a moving droplet on a solid
substrate often hamper the efficient modeling of microfluidic systems. In
particular, the selection of the effective boundary conditions, specifying the
contact line motion, is a controversial issue since the microscopic physics
that gives rise to this displacement is still unknown. Here, a sharp interface,
continuum-level, novel modeling approach, accounting for liquid/solid
micro-scale interactions assembled in a disjoining pressure term, is presented.
By following a unified conception (the model applies both to the liquid/solid
and the liquid/ambient interfaces), the friction forces at the contact line, as
well as the dynamic contact angle are derived implicitly as a result of the
disjoining pressure and viscous effects interplay in the vicinity of the
substrate's intrinsic roughness. Previous hydrodynamic model limitations, of
imposing the contact line boundary condition to an unknown number and
reconfigurable contact lines, when modeling the spreading dynamics on textured
substrates, are now overcome. The validity of our approach is tested against
experimental data of a droplet impacting on a horizontal solid surface. The
study of the early spreading stage on hierarchically structured and chemically
patterned solid substrates reveal an inertial regime where the contact radius
grows according to a universal power law, perfectly agreeing with recently
published experimental findings.


  Multimodal and multi-domain stylization are two important problems in the
field of image style transfer. Currently, there are few methods that can
perform both multimodal and multi-domain stylization simultaneously. In this
paper, we propose a unified framework for multimodal and multi-domain style
transfer with the support of both exemplar-based reference and randomly sampled
guidance. The key component of our method is a novel style distribution
alignment module that eliminates the explicit distribution gaps between various
style domains and reduces the risk of mode collapse. The multimodal diversity
is ensured by either guidance from multiple images or random style code, while
the multi-domain controllability is directly achieved by using a domain label.
We validate our proposed framework on painting style transfer with a variety of
different artistic styles and genres. Qualitative and quantitative comparisons
with state-of-the-art methods demonstrate that our method can generate
high-quality results of multi-domain styles and multimodal instances with
reference style guidance or random sampled style.


  Financial markets are prominent examples for highly non-stationary systems.
Sample averaged observables such as variances and correlation coefficients
strongly depend on the time window in which they are evaluated. This implies
severe limitations for approaches in the spirit of standard equilibrium
statistical mechanics and thermodynamics. Nevertheless, we show that there are
similar generic features which we uncover in the empirical return distributions
for whole markets. We explain our findings by setting up a random matrix model.


  The direct detection of dark matter particles requires ultra-low background
conditions at energies below a few tens of keV. Radioactive isotopes are
produced via cosmogenic activation in detectors and other materials and those
isotopes constitute a background source which has to be under control. In
particular, tritium is specially relevant due to its decay properties (very low
endpoint energy and long half-life) when induced in the detector medium, and
because it can be generated in any material as a spallation product.
Quantification of cosmogenic production of tritium is not straightforward,
neither experimentally nor by calculations. In this work, a method for the
calculation of production rates at sea level has been developed and applied to
some of the materials typically used as targets in dark matter detectors
(germanium, sodium iodide, argon and neon); it is based on a selected
description of tritium production cross sections over the entire energy range
of cosmic nucleons. Results have been compared to available data in the
literature, either based on other calculations or from measurements. The
obtained tritium production rates, ranging from a few tens to a few hundreds of
nuclei per kg and per day at sea level, point to a significant contribution to
the background in dark matter experiments, requiring the application of
specific protocols for target material purification, material storing
underground and limiting the time the detector is on surface during the
building process in order to minimize the exposure to the most dangerous cosmic
ray components.


  The James Webb Space Telescope will have the power to characterize
high-redshift quasars at z>6 with an unprecedented depth and spatial
resolution. While the brightest quasars at such redshift (i.e., with bolometric
luminosity L_bol> 10^46 erg/s) provide us with key information on the most
extreme objects in the Universe, measuring the black hole (BH) mass and
Eddington ratios of fainter quasars with L_bol= 10^45-10^46 erg/s opens a path
to understand the build-up of more normal BHs at z>6. In this paper, we show
that the Illustris, TNG100, TNG300, Horizon-AGN, EAGLE, and SIMBA large-scale
cosmological simulations do not agree on whether BHs at z>4 are overmassive or
undermassive at fixed galaxy stellar mass with respect to the M_BH-M_star
scaling relation at z=0 (BH mass offsets). Our conclusions are unchanged when
using the local scaling relation produced by each simulation or empirical
relations. We find that the BH mass offsets of the simulated faint quasar
population at z>4, unlike those of bright quasars, represent the BH mass
offsets of the entire BH population, for all the simulations. Thus, a
population of faint quasars with L_bol= 10^45-10^46 erg/s observed by JWST can
provide key constraints on the assembly of BHs at high redshift. Moreover, this
will help constraining the high-redshift regime of cosmological simulations,
including BH seeding, early growth, and co-evolution with the host galaxies.
Our results also motivate the need for simulations of larger cosmological
volumes down to z=6, with the same diversity of sub-grid physics, in order to
gain statistics on the most extreme objects at high redshift.


  We introduce a new combinatorial structure: the metasylvester lattice on
decreasing trees. It appears in the context of the $m$-Tamari lattices and
other related $m$-generalizations. The metasylvester congruence has been
recently introduced by Novelli and Thibon. We show that it defines a sublattice
of the $m$-permutations where elements can be represented by decreasing
labelled trees: the metasylvester lattice. We study the combinatorial
properties of this new structure. In particular, we give different realizations
of the lattice. The $m$-Tamari lattice is by definition a sublattice of our
newly defined metasylvester lattice. It leads us to a new realization of the
$m$-Tamari lattice, using certain chains of the classical Tamari lattice.


  Dallard, Milani\v{c}, and \v{S}torgel [arXiv '22] ask if for every class
excluding a fixed planar graph $H$ as an induced minor, Maximum Independent Set
can be solved in polynomial time, and show that this is indeed the case when
$H$ is any planar complete bipartite graph, or the 5-vertex clique minus one
edge, or minus two disjoint edges. A positive answer would constitute a
far-reaching generalization of the state-of-the-art, when we currently do not
know if a polynomial-time algorithm exists when $H$ is the 7-vertex path.
Relaxing tractability to the existence of a quasipolynomial-time algorithm, we
know substantially more. Indeed, quasipolynomial-time algorithms were recently
obtained for the $t$-vertex cycle, $C_t$ [Gartland et al., STOC '21] and the
disjoint union of $t$ triangles, $tC_3$ [Bonamy et al., SODA '23].
  We give, for every integer $t$, a polynomial-time algorithm running in
$n^{O(t^5)}$ when $H$ is the friendship graph $K_1 + tK_2$ ($t$ disjoint edges
plus a vertex fully adjacent to them), and a quasipolynomial-time algorithm
running in $n^{O(t^2 \log n)+t^{O(1)}}$ when $H$ is $tC_3 \uplus C_4$ (the
disjoint union of $t$ triangles and a 4-vertex cycle). The former extends a
classical result on graphs excluding $tK_2$ as an induced subgraph [Alekseev,
DAM '07], while the latter extends Bonamy et al.'s result.


  A recursive method is given for finding generating functions which enumerate
rooted hypermaps by number of vertices, edges and faces for any given number of
darts. It makes use of matrix-integral expressions arising from the study of
bipartite quantum systems. Direct evaluation of these generating functions is
then demonstrated through the enumeration of all rooted hypermaps with up to 13
darts.


  We consider a classical test particle subject to electromagnetic and
gravitational fields, described by a Lagrangian depending on the acceleration
and on a fundamental length. We associate to the particle a moving local
reference frame and we study its trajectory in the principal fibre bundle of
all the Lorentz frames. We discuss in this framework the general form of the
Lagrange equations and the connection between symmetries and conservation laws
(Noether theorem). We apply these results to a model, already discussed by
other authors, which implies an upper bound to the proper acceleration and to
another new model in which a similar quantity, called ``pseudo-acceleration'',
is bounded. With some simple choices of the fields, we illustrate some other
interesting properties of the models and we show that unwanted features may
appear, as unstable run-away solutions and unphysical values of the
energy-momentum or of the velocity.


  Computer vision techniques have attracted a great interest in precision
agriculture, recently. The common goal of all computer vision-based precision
agriculture tasks is to detect the objects of interest (e.g., crop, weed) and
discriminating them from the background. The Weeds are unwanted plants growing
among crops competing for nutrients, water, and sunlight, causing losses to
crop yields. Weed detection and mapping is critical for site-specific weed
management to reduce the cost of labor and impact of herbicides. This paper
investigates the use of color and texture features for discrimination of
Soybean crops and weeds. Feature extraction methods including two color spaces
(RGB, HSV), gray level Co-occurrence matrix (GLCM), and Local Binary Pattern
(LBP) are used to train the Support Vector Machine (SVM) classifier. The
experiment was carried out on image dataset of soybean crop, obtained from an
unmanned aerial vehicle (UAV), which is publicly available. The results from
the experiment showed that the highest accuracy (above 96%) was obtained from
the combination of color and LBP features.


  We derive the modified L\"uscher equation in the presence of the long-range
force caused by the exchange of a light particle. It is shown that the use of
this equation enables one to circumvent the problems related to the strong
partial-wave mixing and the t-channel sub-threshold singularities. It is also
demonstrated that the present method is intrinsically linked to the so-called
modified effective-range expansion (MERE) in the infinite volume. A detailed
comparison with the two recently proposed alternative approaches is provided.


  We have designed and developed a new experimental setup, based on the 3-omega
method, to measure thermal conductivity, heat capacity and electrical
resistivity of a variety of samples in a broad temperature range (2-550 K) and
under magnetic fields up to 9 T. The validity of this method is tested by
measuring various types of metallic (copper, platinum, and constantan) and
insulating (SiO_2) materials, which have a wide range of thermal conductivity
values (1-400 Wm-1K-1). We have successfully employed this technique for
measuring the thermal conductivity of two actinide single crystals, uranium
dioxide, and uranium nitride. This new experimental approach for studying
nuclear materials will help to advance reactor fuel development and
understanding. We have also shown that this experimental setup can be adapted
to the Physical Property Measurement System (Quantum Design) environment and/or
other cryocooler systems.


  On the framework of the Linear Farmer's Model, we approach the indeterminacy
of agents' behaviour by associating with each agent an unconditional
probability for her to be active at each time step.
  We show that Pareto tailed returns can appear even if value investors are the
only strategies on the market and give a procedure for the determination of the
tail exponent.
  Numerical results indicate that the returns' distribution is heavy tailed and
volatility is clustered if trading occurs at the zero Lyapunov (critical)
point.


  A sorting network is a shortest path from 12...n to n...21 in the Cayley
graph of S_n generated by nearest-neighbour swaps. We prove that for a uniform
random sorting network, as n->infinity the space-time process of swaps
converges to the product of semicircle law and Lebesgue measure. We conjecture
that the trajectories of individual particles converge to random sine curves,
while the permutation matrix at half-time converges to the projected surface
measure of the 2-sphere. We prove that, in the limit, the trajectories are
Holder-1/2 continuous, while the support of the permutation matrix lies within
a certain octagon. A key tool is a connection with random Young tableaux.


  Harnessing data to discover the underlying governing laws or equations that
describe the behavior of complex physical systems can significantly advance our
modeling, simulation and understanding of such systems in various science and
engineering disciplines. This work introduces a novel physics-informed deep
learning framework to discover governing partial differential equations (PDEs)
from scarce and noisy data for nonlinear spatiotemporal systems. In particular,
this approach seamlessly integrates the strengths of deep neural networks for
rich representation learning, physics embedding, automatic differentiation and
sparse regression to (1) approximate the solution of system variables, (2)
compute essential derivatives, as well as (3) identify the key derivative terms
and parameters that form the structure and explicit expression of the PDEs. The
efficacy and robustness of this method are demonstrated, both numerically and
experimentally, on discovering a variety of PDE systems with different levels
of data scarcity and noise accounting for different initial/boundary
conditions. The resulting computational framework shows the potential for
closed-form model discovery in practical applications where large and accurate
datasets are intractable to capture.


  We introduce a new random group model called the square model: we quotient a
free group on $n$ generators by a random set of relations, each of which is a
reduced word of length four. We prove, as in the Gromov density model, that for
densities $> \frac{1}{2}$ a random group in the square model is trivial with
overwhelming probability and for densities $<\frac{1}{2}$ a random group is
with overwhelming probability hyperbolic. Moreover we show that for densities
$\frac{1}{4} < d < \frac{1}{3}$ a random group in the square model does not
have Property (T). Inspired by the results for the triangular model we prove
that for densities $<\frac{1}{4}$ in the square model, a random group is free
with overwhelming probability. We also introduce abstract diagrams with fixed
edges and prove a generalization of the isoperimetric inequality.


  The dispersion laws of two-dimensional plasmons in narrow-gap HgTe/CdHgTe
quantum wells are calculated taking into account the spatial dispersion of the
electron susceptibility. At the energy scale of the band gap the dependence of
plasmon frequencies on the wave vector is shown to be close to linear that
changes significantly the critical concentration of noneqilibrium electron-hole
gas corresponding to "switching-on" the carrier recombination with plasmon
emission. The recombination rates with the plasmon emission have been
calculated.


  We discuss various aspects of the inner structure formation in virialized
dark matter (DM) halos that form as primordial density inhomogeneities evolve
in the cosmological standard model. The main focus is on the study of central
cusps/cores and of the profiles of DM halo rotation curves, problems that
reveal disagreements among the theory, numerical simulations, and observations.
A method that was developed by the authors to describe equilibrium DM systems
is presented, which allows investigating these complex nonlinear structures
analytically and relating density distribution profiles within a halo both to
the parameters of the initial small-scale inhomogeneity field and to the
nonlinear relaxation characteristics of gravitationally compressed matter. It
is shown that cosmological random motions of matter `heat up' the DM particles
in collapsing halos, suppressing cusp-like density profiles within developing
halos, facilitating the formation of DM cores in galaxies, and providing an
explanation for the difference between observed and simulated galactic rotation
curves. The analytic conclusions obtained within this approach can be confirmed
by the N-body model simulation once improved spatial resolution is achieved for
central halo regions.


  Unsupervised video-based object-centric learning is a promising avenue to
learn structured representations from large, unlabeled video collections, but
previous approaches have only managed to scale to real-world datasets in
restricted domains. Recently, it was shown that the reconstruction of
pre-trained self-supervised features leads to object-centric representations on
unconstrained real-world image datasets. Building on this approach, we propose
a novel way to use such pre-trained features in the form of a temporal feature
similarity loss. This loss encodes semantic and temporal correlations between
image patches and is a natural way to introduce a motion bias for object
discovery. We demonstrate that this loss leads to state-of-the-art performance
on the challenging synthetic MOVi datasets. When used in combination with the
feature reconstruction loss, our model is the first object-centric video model
that scales to unconstrained video datasets such as YouTube-VIS.


  We define the entropic bounds, i.e minimal uncertainty for pairs of unitary
testers in distinguishing between unitary transformations not unlike the well
known entropic bounds for observables. We show that in the case of specific
sets of testers which pairwise saturate the trivial zero bound, the testers are
all equivalent in the sense their statistics are the same. On the other hand,
when maximal bounds are saturated by such sets of testers, the unitary
operators would form unitary bases which are mutually unbiased. This resembles
very much the role of mutually unbiased bases in maximizing the entropic bounds
for observables. We show how such a bound can be useful in certain quantum
cryptographic protocols.


  We prove the Murgnaghan--Nakayama rule for $k$-Schur functions of Lapointe
and Morse, that is, we give an explicit formula for the expansion of the
product of a power sum symmetric function and a $k$-Schur function in terms of
$k$-Schur functions. This is proved using the noncommutative $k$-Schur
functions in terms of the nilCoxeter algebra introduced by Lam and the affine
analogue of noncommutative symmetric functions of Fomin and Greene.


  For immersive applications, the generation of binaural sound that matches its
visual counterpart is crucial to bring meaningful experiences to people in a
virtual environment. Recent studies have shown the possibility of using neural
networks for synthesizing binaural audio from mono audio by using 2D visual
information as guidance. Extending this approach by guiding the audio with 3D
visual information and operating in the waveform domain may allow for a more
accurate auralization of a virtual audio scene. We propose Points2Sound, a
multi-modal deep learning model which generates a binaural version from mono
audio using 3D point cloud scenes. Specifically, Points2Sound consists of a
vision network and an audio network. The vision network uses 3D sparse
convolutions to extract a visual feature from the point cloud scene. Then, the
visual feature conditions the audio network, which operates in the waveform
domain, to synthesize the binaural version. Results show that 3D visual
information can successfully guide multi-modal deep learning models for the
task of binaural synthesis. We also investigate how 3D point cloud attributes,
learning objectives, different reverberant conditions, and several types of
mono mixture signals affect the binaural audio synthesis performance of
Points2Sound for the different numbers of sound sources present in the scene.


  Contact processes describe the transmission of distinct properties of nodes
via the links of a network. They provide a simple framework for many phenomena,
such as epidemic spreading and opinion formation. Combining contact processes
with rules for topological evolution yields an adaptive network in which the
states of the nodes can interact dynamically with the topological degrees of
freedom. By moment-closure approximation it is possible to derive
low-dimensional systems of ordinary differential equations that describe the
dynamics of the adaptive network on a coarse-grained level. In this chapter we
discuss the approximation technique itself as well as its applications to
adaptive networks. Thus, it can serve both as a tutorial as well as a review of
recent results.


  We explore the potential of polarimetry as a tool for detecting and
characterizing exorings. For that purpose, we have improved the publicly
available photometric code Pryngles by adding the results of radiative transfer
calculations that fully include polarization and scattering by irregularly
shaped particles. With this improved code, we compute the total and polarized
fluxes and the degree of polarization of a ringed gas giant along its orbit. We
vary key model parameters such as the orbit inclination, ring size and
orientation, particle albedo and optical thickness, and demonstrate the
versatility of our code by predicting the total and polarized fluxes of the
"puffed-up" planet HIP41378f assuming this planet has an opaque dusty ring. We
find that spatially unresolved dusty rings can significantly modify the flux
and polarization signals of the light that is reflected. Rings are expected to
have a low polarization signal and will generally decrease the degree of
polarization as the ring casts a shadow on the planet and/or blocks part of the
light the planet reflects. During ring-plane crossings, when the thin ring is
illuminated edge-on, a ringed exoplanet's flux and degree of polarization are
close to those of a ring-less planet and generally appear as sharp changes in
the flux and polarization curves. Ringed planets in edge-on orbits tend to be
difficult to distinguish from ring-less planets in reflected flux and degree of
polarization. We show that if HIP41378f is surrounded by a ring, its reflected
flux (compared to the star) will be of the order of $10^{-9}$, and the ring
would decrease the degree of polarization in a detectable way. The improved
version of the photometric code Pryngles that we present here shows that dusty
rings may produce distinct polarimetric features in light curves across a wide
range of orbital configurations, orientations and ring optical properties.


  The atmospheres of highly irradiated exoplanets are observed to undergo
hydrodynamic escape. However, due to strong pressures, stellar winds can
confine planetary atmospheres, reducing their escape. Here, we investigate
under which conditions atmospheric escape of close-in giants could be confined
by the large pressure of their host star's winds. For that, we simulate escape
in planets at a range of orbital distances ([0.04, 0.14] au), planetary
gravities ([36%, 87%] of Jupiter's gravity), and ages ([1, 6.9] Gyr). For each
of these simulations, we calculate the ram pressure of these escaping
atmospheres and compare them to the expected stellar wind external pressure to
determine whether a given atmosphere is confined or not. We show that, although
younger close-in giants should experience higher levels of atmospheric escape,
due to higher stellar irradiation, stellar winds are also stronger at young
ages, potentially reducing escape of young exoplanets. Regardless of the age,
we also find that there is always a region in our parameter space where
atmospheric escape is confined, preferably occurring at higher planetary
gravities and orbital distances. We investigate confinement of some known
exoplanets and find that the atmosphere of several of them, including pi Men c,
should be confined by the winds of their host stars, thus potentially
preventing escape in highly irradiated planets. Thus, the lack of hydrogen
escape recently reported for pi Men c could be caused by the stellar wind.


  In this paper I first address the question of whether the seat of the power
radiated by an antenna made of conducting members is distributed over the
``arms'' of the antenna according to -J . E, where J is the specified current
density and E is the electric field produced by that source. Poynting's theorem
permits only a global identification of the total input power, usually from a
localized generator, with the total power radiated to infinity, not a local
correspondence of -J . E dv with some specific radiated power, r^2 S . n dO. I
then describe a model antenna consisting of two perfectly conducting
hemispheres of radius a separated by a small equatorial gap across which occurs
the driving oscillatory electric field. The fields and surface current are
determined by solution of the boundary value problem. In contrast to the first
approach (not a boundary value problem), the tangential electric field vanishes
on the metallic surface. There is no radial Poynting vector normal to the
surface. Numerical examples are shown to illustrate how the energy flows from
the input region of the gap and is guided near the antenna by its ``arms''
until it is launched at larger r/a into the radiation pattern determined by the
value of ka.


  The objective of this review article is to present recent results on the
mathematical analysis of the Accelerated Dynamics algorithms introduced by A.F.
Voter in collaboration with D. Perez and M. Sorensen. Using the notion of
quasi-stationary distribution, one is able to rigorously justify the fact that
the exit event from a metastable state for the Langevin or overdamped Langevin
dynamics can be modeled by a kinetic Monte Carlo model. Moreover, under some
geometric assumptions, one can prove that this kinetic Monte Carlo model can be
parameterized using Eyring-Kramers formulas. These are the building blocks
required to analyze the Accelerated Dynamics algorithms, to understand their
efficiency and their accuracy, and to improve and generalize these techniques
beyond their original scope.


  Tumblr is one of the largest and most popular microblogging website on the
Internet. Studies shows that due to high reachability among viewers, low
publication barriers and social networking connectivity, microblogging websites
are being misused as a platform to post hateful speech and recruiting new
members by existing extremist groups. Manual identification of such posts and
communities is overwhelmingly impractical due to large amount of posts and
blogs being published every day. We propose a topic based web crawler primarily
consisting of multiple phases: training a text classifier model consisting
examples of only hate promoting users, extracting posts of an unknown tumblr
micro-blogger, classifying hate promoting bloggers based on their activity
feeds, crawling through the external links to other bloggers and performing a
social network analysis on connected extremist bloggers. To investigate the
effectiveness of our approach, we conduct experiments on large real world
dataset. Experimental results reveals that the proposed approach is an
effective method and has an F-score of 0.80. We apply social network analysis
based techniques and identify influential and core bloggers in a community.


  The interaction of an obliquely incident laser pulse with a flat TNSA target
is known to enhance the cut-off energy of protons/ions as compared to a
normally incident laser pulse, mostly owing to Brunnel absorption. However, it
is not well understood how the oblique incidence of the laser pulse would
affect the protons/ion spectra in the case of a micro-structured target. Using
two-dimensional particle-in-cell simulations, we show here that the
protons/ions cut-off energies are rather reduced in the case of oblique
incidence of the laser pulse if the target has a micron-sized groove on its
front surface. This is also found to be true for a periodically grooved target.


  We study the spin polarization of tunneling holes injected from ferromagnetic
GaMnAs into a p-doped semiconductor through a tunneling barrier. We obtain an
upper limit to the spin injection rate. We find that spin-orbit interaction
interaction in the barrier and in the drain limits severely spin injection.
Spin depolarization is stronger when the magnetization is parallel to the
current than when is perpendicular to it.