  We study representations of wreath product analogues of categories of finite
sets. This includes the category of finite sets and injections (studied by
Church, Ellenberg, and Farb) and the opposite of the category of finite sets
and surjections (studied by the authors in previous work). We prove noetherian
properties for the injective version when the group in question is
polycyclic-by-finite and use it to deduce general twisted homological stability
results for such wreath products and indicate some applications to
representation stability. We introduce a new class of formal languages
(quasi-ordered languages) and use them to deduce strong rationality properties
of Hilbert series of representations for the surjective version when the group
is finite.


  Models for the origin of the hard X-ray background have suggested that
sources with the most accretion activity lie hidden in highly obscured AGN. We
report on our study of hard, serendipitous sources in the fields of Chandra
clusters with fluxes close to the turn-over in the source-counts. These include
two Type II quasars with measured X-ray luminosities >10^{45} ergs per second
and column-densities >10^{23} cm^{-2}, one possibly being Compton-thick. Both
show indications of redshifted Fe K\alpha line emission. Radiative transfer
modelling of the broad-band spectrum of a highly-magnified source with deep
ISOCAM detections implies the presence of warm-to-hot dust obscuring a quasar
with L_{UV}>10^{45} ergs per second. Multi-wavelength spectroscopic and
photometric follow-up of the optically-faint sources suggests that these
objects are found in the centres of massive evolved galaxies at a range of
redshifts, with red optical / near-infrared colours dominated by the host
galaxy. Detailed source identification is difficult due to the paucity of
strong emission features, especially in the infrared. We present the main
results from a sample of near-infrared spectra of optically-faint sources
obtained with 4 m and 8 m telescopes. Through the study of the harder and
brighter X-ray background source population, we are likely to be viewing the
most intense phase of the growth of supermassive black holes.


  The theory of multi-norms was developed by H.\ G.\ Dales and M.\ E.\ Polyakov
in a memoir that was published in \emph{Dissertationes Mathematicae}. In that
memoir, the notion of `equivalence' of multi-norms was defined. In the present
memoir, we make a systematic study of when various pairs of multi-norms are
mutually equivalent.


  For a nonlinear partial differential equation for (pseudo)scalars in the bulk
of Euclidean AdS_4, arising from a truncation of 11-dimensional supergravity
over AdS_4 x S^7/Z_k, we use math tools and in particular Adomian Decomposition
Method, with initial data from near the boundary behavior of a special or
general solution, although we focus on normalizable modes and Dirichlet
boundary condition, to get perturbative series solutions (of the equation valid
in probe approximation) for three special modes of m^2=4, 0, -9/4. Meantime, we
remind that for the skew-whiffed M2-branes background, there are Higgs-like
(pseudo)scalars that make the equation homogeneous and provide spontaneous
symmetry breaking. Then, with the setups and solutions in the bulk, where all
supersymmetries and parity are broken, we swap the three fundamental
representations of SO(8) for gravitino, deform the ABJM-like three-dimensional
boundary actions with various corresponding SU(4) x U(1)-singlet operators made
of fermions, scalars and SU(N) gauge fields, find new SO(4)-invariant
instantons, and finally adjust the bulk and boundary solutions and confirm
state-operator AdS_4/CFT_3 correspondence.


  This paper relates comparative belief structures and a general view of belief
management in the setting of deductively closed logical representations of
accepted beliefs. We show that the range of compatibility between the classical
deductive closure and uncertain reasoning covers precisely the nonmonotonic
'preferential' inference system of Kraus, Lehmann and Magidor and nothing else.
In terms of uncertain reasoning any possibility or necessity measure gives
birth to a structure of accepted beliefs. The classes of probability functions
and of Shafer's belief functions which yield belief sets prove to be very
special ones.


  Neutron-diffraction experiments have been carried out on U(Pt1-xPdx)3 single
crystals (x<= 0.05). The small-moment antiferromagnetic order (SMAF) reported
for pure UPt3 is robust upon doping and persists till at least x= 0.005. The
ordered moment grows from 0.018(2) mB/U-atom for pure UPt3 to 0.048(8)
mB/U-atom for x= 0.005. The Neel temperature, TN, is approximately 6 K and does
not vary with Pd contents. The order parameter for the SMAF has an unusual
quasi-linear temperature variation. For x>= 0.01 a large moment
antiferromagnetic phase (LMAF) is found. For this phase at optimum doping (x=
0.05) TN attains a maximum value of 5.8 K and the ordered moment equals 0.63(5)
mB/U-atom. TN(x) for the LMAF follows a Doniach-type phase diagram. We infer
that the antiferromagnetic instability in U(Pt1-xPdx)3 is located in the range
0.5-1 at.% Pd.


  As no heat effect and mechanical work are observed, we have a simple
experimental resolution of the Gibbs paradox: both the thermodynamic entropy of
mixing and the Gibbs free energy change are zero during the formation of any
ideal mixtures. Information loss is the driving force of these spontaneous
processes. Information is defined as the amount of the compressed data.
Information losses due to dynamic motion and static symmetric structure
formation are defined as two kinds of entropies - dynamic entropy and static
entropy, respectively. There are three laws of information theory, where the
first and the second laws are analogs of the two thermodynamic laws. However,
the third law of information theory is different: for a solid structure of
perfect symmetry (e.g., a perfect crystal), the entropy (static entropy for
solid state) S is the maximum. More generally, a similarity principle is set
up: if all the other conditions remain constant, the higher the similarity
among the components is, the higher the value of entropy of the mixture (for
fluid phases) or the assemblage (for a static structure or a system of
condensed phases) or any other structure (such as quantum states in quantum
mechanics) will be, the more stable the mixture or the assemblage will be, and
the more spontaneous the process leading to such a mixture or an assemblage or
a chemical bond will be.


  We present data for the scaling behavior of lattice QCD with two flavors of
light Wilson fermions. This is done by matching $\pi$ n and $\rho$ masses at
the two lattice sizes of $16^3\times32 $ and $8^3\times16$. We find that at
$\beta=6/g^2\equiv5.3$ the matching does not occur over a range extending down
to $\beta=3.5$. For $\beta=5.5$ matching may be achieved at $\beta=4.8-4.9$,
leading to a $\Delta \beta =0.6-0.7$ which is higher than the perturbative
2-loop value of 0.45. In both cases we conclude that the simulations are very
far from the perturbative scaling region.


  Session-based recommendation aims to predict users' based on anonymous
sessions. Previous work mainly focuses on the transition relationship between
items during an ongoing session. They generally fail to pay enough attention to
the importance of the items in terms of their relevance to user's main intent.
In this paper, we propose a Session-based Recommendation approach with an
Importance Extraction Module, i.e., SR-IEM, that considers both a user's
long-term and recent behavior in an ongoing session. We employ a modified
self-attention mechanism to estimate item importance in a session, which is
then used to predict user's long-term preference. Item recommendations are
produced by combining the user's long-term preference and current interest as
conveyed by the last interacted item. Experiments conducted on two benchmark
datasets validate that SR-IEM outperforms the start-of-the-art in terms of
Recall and MRR and has a reduced computational complexity.


  While space-charge-limited current measurements are often used to
characterize charge-transport in relatively intrinsic, low-mobility
semiconductors, it is currently difficult to characterize lightly or heavily
doped semiconductors with this method. By combining the theories describing
ohmic and space-charge-limited conduction, we derive a general analytical
approach to extract the charge-carrier density, the conduction-band edge and
the drift components of the current density-voltage curves of a single-carrier
device when the semiconductor is either undoped, lightly doped or heavily
doped. The presented model covers the entire voltage range, i.e., both the
low-voltage regime and the Mott-Gurney regime. We demonstrate that there is an
upper limit to how doped a device must be before the current density-voltage
curves are significantly affected, and we show that the background
charge-carrier density must be considered to accurately model the drift
component in the low-voltage regime, regardless of whether the device is doped
or not. We expect that the final analytical expressions presented herein to be
directly useful to experimentalists studying charge transport in novel
materials and devices.


  We report the influence of 6 MeV Zr$^{4+}$ irradiation and post-irradiation
annealing (200 {\deg}C) in the in-field dependences of the critical current
densities J$_c$ of 1.3 $\mu$m thick GdBa$_2$Cu$_3$O$_{7-d}$ coated conductors
grown by co-evaporation. Samples were irradiated with 6 MeV Zr$^{4+}$ and
fluences between 2.3x10$^{11}$ cm$^{-2}$ and 3x10$^{12}$ cm$^{-2}$. The
correlation between the superconducting critical temperature T$_c$ and in-field
dependences of critical current densities J$_c$ has been analyzed. In addition,
random disorder introduced by irradiation was reduced by thermal annealed at
200 {\deg}C. The analysis of our experimental findings indicates that the
optimal irradiation (reducing random disorder by annealing) results in the
suppression of the self-field J$_c$ of $\simeq$ 10 $\%$ and in-field J$_c$
enhancements nearly doubled at about 5 T. A clear correlation between T$_c$,
disorder and self-field J$_c$ is observed. Additional random disorder and
nanoclusters suppress systematically T$_c$ and increase the flux creep
relaxation at intermediate temperatures (reducing the characteristic glassy
$\mu$ value).


  We provide a simple mechanism for going from Lee-Yang type theorems to
analyticity of correlation functions by exploiting under appreciated
inequalities of Newman. We also describe a Lee-Yang approach that recovers the
consequences of a low density cluster expansion for spin S models without any
combinatorics.


  We consider Gibbs' definition of chemical equilibrium and connect it with
dynamic equilibrium, in terms of no substance formed. We determine the activity
coefficient as a function of temperature and pressure, in reactions with or
without interaction of a solvent, incorporating the error terms from Raoult's
Law and Henry's Law, if necessary. We compute the maximal reaction paths and
apply the results to electrochemistry, using the Nernst equation.


  We examine the stability of steady-state galileon accretion for the case of a
Schwarzshild black hole. Considering the galileon action up to the cubic term
in a static and spherically symmetric background we obtain the general solution
for the equation of motion which is divided in two branches. By perturbing this
solution we define an effective metric which determines the propagation of
fluctuations. In this general picture we establish the position of the sonic
horizon together with the matching condition of the two branches on it.
Restricting to the case of a Schwarzschild background, we show, via the
analysis of the energy of the perturbations and its time derivative, that the
accreting field is linearly stable.


  We develop a general stochastic thermodynamics of RLC electrical networks
built on top of a graph-theoretical representation of the dynamics commonly
used by engineers. The network is: open, as it contains resistors and current
and voltage sources, nonisothermal as resistors may be at different
temperatures, and driven, as circuit elements may be subjected to external
parametric driving. The proper description of the heat dissipated in each
resistor requires care within the white noise idealization as it depends on the
network topology. Our theory provides the basis to design circuits-based
thermal machines, as we illustrate by designing a refrigerator using a simple
driven circuit. We also derive exact results for the low temperature regime in
which the quantum nature of the electrical noise must be taken into account. We
do so using a semiclassical approach which can be shown to coincide with a
fully quantum treatment of linear circuits for which canonical quantization is
possible. We use it to generalize the Landauer-Buttiker formula for energy
currents to arbitrary time-dependent driving protocols.


  The symmetry energy and the isoscaling properties of the fragments produced
in the multifragmentation of $^{40}$Ar, $^{40}$Ca + $^{58}$Fe, $^{58}$Ni
reactions at 25 - 53 MeV/nucleon were investigated within the framework of
statistical multifragmentation model. The isoscaling parameters $\alpha$, from
the primary (hot) and secondary (cold) fragment yield distributions, were
studied as a function of excitation energy, isospin (neutron-to-proton
asymmetry) and fragment symmetry energy. It is observed that the isoscaling
parameter $\alpha$ decreases with increasing excitation energy and decreasing
symmetry energy. The parameter $\alpha$ is also observed to increase with
increasing difference in the isospin of the fragmenting system. The sequential
decay of the primary fragments into secondary fragments, when studied as a
function of excitation energy and isospin of the fragmenting system, show very
little influence on the isoscaling parameter. The symmetry energy however, has
a strong influence on the isospin properties of the hot fragments. The
experimentally observed scaling parameters can be explained by symmetry energy
that is significantly lower than that for the ground state nuclei near
saturation density. The results indicate that the properties of hot nuclei at
excitation energies, densities and isospin away from the normal ground state
nuclei could be significantly different.


  Let $X$ and $Y$ be smooth and projective varieties over a field $k$ finitely
generated over $\mathbb Q$, and let $\ov X$ and $\ov Y$ be the varieties over
an algebraic closure of $k$ obtained from $X$ and $Y$, respectively, by
extension of the ground field. We show that the Galois invariant subgroup of
$\Br(\ov X)\oplus \Br(\ov Y)$ has finite index in the Galois invariant subgroup
of $\Br(\ov X\times\ov Y)$. This implies that the cokernel of the natural map
$\Br(X)\oplus\Br(Y)\to\Br(X\times Y)$ is finite when $k$ is a number field. In
this case we prove that the Brauer-Manin set of the product of varieties is the
product of their Brauer-Manin sets.


  The extragalactic distance scale is perhaps the most important application of
stellar distance indicators. Among these, classical Cepheids are high-accuracy
standard candles that support a $1.4\%$ measurement of Hubble's constant,
$H_0$. The accuracy of Cepheid distances is thus directly relevant for
understanding the implications of the Hubble tension, the $>5\sigma$ discord
among direct, late-Universe $H_0$ measurements and $H_0$ values inferred from
the early Universe observations assuming $\Lambda$CDM cosmology. This invited
review aims to provide an accessible overview of the state of the art distance
ladder that has established the Hubble tension, with a focus on Cepheids, their
absolute calibration using trigonometric parallaxes from the ESA mission Gaia,
and other Cepheid-related systematics. New observational facilities such as
JWST and upcoming large surveys will provide exciting avenues to further
improve distance estimates based on Cepheids.


  This paper aims to make up for the lack of documented baselines for Hungarian
language modeling. Various approaches are evaluated on three publicly available
Hungarian corpora. Perplexity values comparable to models of similar-sized
English corpora are reported. A new, freely downloadable Hungar- ian benchmark
corpus is introduced.


  In standard communication information is carried by particles or waves.
Counterintuitively, in counterfactual communication particles and information
can travel in opposite directions. The quantum Zeno effect allows Bob to
transmit a message to Alice by encoding information in particles he never
interacts with. The first suggested protocol not only required thousands of
ideal optical components, but also resulted in a so-called "weak trace" of the
particles having travelled from Bob to Alice, calling the scalability and
counterfactuality of previous proposals and experiments into question. Here we
overcome these challenges, implementing a new protocol in a programmable
nanophotonic processor, based on reconfigurable silicon-on-insulator waveguides
that operate at telecom wavelengths. This, together with our telecom
single-photon source and highly-efficient superconducting nanowire
single-photon detectors, provides a versatile and stable platform for a
high-fidelity implementation of genuinely trace-free counterfactual
communication, allowing us to actively tune the number of steps in the Zeno
measurement, and achieve a bit error probability below 1%, with neither
post-selection nor a weak trace. Our demonstration shows how our programmable
nanophotonic processor could be applied to more complex counterfactual tasks
and quantum information protocols.


  Automated variable selection is widely applied in statistical model
development. Algorithms like forward, backward or stepwise selection are
available in statistical software packages like R and SAS. Many researchers
have criticized the use of these algorithms because the models resulting from
automated selection algorithms are not based on theory and tend to be unstable.
Furthermore, simulation studies have shown that they often select incorrect
variables due to random effects which makes these model building strategies
unreliable. In this article, a comprehensive stepwise selection algorithm
tailored to logistic regression is proposed. It uses multiple criteria in
variable selection instead of relying on one single measure only, like a
$p$-value or Akaike's information criterion, which ensures robustness and
soundness of the final outcome. The result of the selection process might not
be unambiguous. It might select multiple models that could be considered as
statistically equivalent. A simulation study demonstrates the superiority of
the proposed variable selection method over available alternatives.


  This thesis presents a study of the decays $\tau\rightarrow
e\nu\overline{\nu}$ identified after a selection of $\tau^+\tau^-$ events
produced in $e^+e^-$ collisions at LEP. These collisions, predominantly
mediated by a $Z^0$ boson, offer a good laboratory for the study of weak
current parameters. Moreover, the decays of the tau lepton, which proceed via a
$W$ boson, increase the possibilities of our study. The experimental
observables, which imply an indirect knowledge of the coupling constants,
include the polarization asymmetry and the forward-backward polarization
asymmetry. The branching ratio of the electronic decay of the $\tau$ lepton
($18.24\pm0.28\pm0.32)\%$) derives a measurement of the strong coupling
constant $\alpha_s$ at the scale of the $Z^0$ boson mass
($0.118^{+0.004}_{-0.006}\pm0.006$) and a test of lepton universality in weak
currents ($\frac{g_{\tau}}{g_{\mu}}=1.000\pm0.014$). The spectra of momenta and
electromagnetic energy depositions used as estimates of the energy of the
electron allow to measure the polarization asymmetries
($P_{\tau}=-0.16\pm0.09\pm0.05$ and $A^{FB}_{pol}=-0.19\pm0.09\pm0.01$) giving
subsequent values for the effective $sin^2\theta_W$ ($0.230\pm0.013$ and
$0.218\pm0.015$).


  During software evolution, it is advocated that test code should co-evolve
with production code. In real development scenarios, test updating may lag
behind production code changing, which may cause the project to fail to compile
or bring other troubles. Existing techniques based on pre-trained language
models can be adopted to repair obsolete tests caused by such unsynchronized
code changes, especially syntactic-related ones. However, the lack of
target-oriented contextual information affects repair accuracy on large-scale
projects. Starting from an obsoleted test, the key challenging task is
precisely identifying and constructing Test-Repair-Oriented Contexts (TROCtx)
from the whole repository within a limited token size.
  In this paper, we propose SynBCIATR (Syntactic-Breaking-Change-Induced
Automated Test Repair), a novel approach to automatically repair obsolete test
cases via precise and concise TROCtx construction. Inspired by developers'
programming practices of the task, we design three types of TROCtx: class
contexts, usage contexts, and environment contexts. For every type of TROCtx,
SynBCIATR automatically collects the changed-token-related code information
through static analysis techniques. Then it generates reranking queries to
identify the most relevant TROCtxs, which will be taken as the repair-required
key context and be input to the Large Language Model for the final test repair.
  To evaluate the effectiveness of SynBCIATR, we construct a benchmark dataset
that contains diverse syntactic breaking changes. The experimental results show
that SynBCIATR outperforms baseline approaches both on textual- and
intent-matching metrics. With the augmentation of TROCtx constructed by
SynBCIATR, hallucinations are reduced by 57.1%.


  According to the Bloch-Beilinson conjectures, an automorphism of a K3 surface
X that acts as the identity on the transcendental lattice should act trivially
on CH^2(X). We discuss this conjecture for symplectic involutions and prove it
in one third of all cases. The main point is to use special elliptic K3
surfaces and stable maps to produce covering families of elliptic curves on the
generic K3 surface that are invariant under the involution.


  We investigate the properties of the Lieb lattice, i.e a face-centered square
lattice, subjected to external gauge fields. We show that an Abelian gauge
field leads to a peculiar quantum Hall effect, which is a consequence of the
single Dirac cone and the flat band characterizing the energy spectrum. Then we
explore the effects of an intrinsic spin-orbit term - a non-Abelian gauge field
- and demonstrate the occurrence of the quantum spin Hall effect in this model.
Besides, we obtain the relativistic Hamiltonian describing the Lieb lattice at
low energy and derive the Landau levels in the presence of external Abelian and
non-Abelian gauge fields. Finally, we describe concrete schemes for realizing
these gauge fields with cold fermionic atoms trapped in an optical Lieb
lattice. In particular, we provide a very efficient method to reproduce the
intrinsic (Kane-Mele) spin-orbit term with assisted-tunneling schemes.
Consequently, our model could be implemented in order to produce a variety of
topological states with cold-atoms.


  The Billera-Holmes-Vogtmann (BHV) space of weighted trees can be embedded in
Euclidean space, but the extrinsic Euclidean mean often lies outside of
treespace. Sturm showed that the intrinsic Frechet mean exists and is unique in
treespace. This Frechet mean can be approximated with an iterative algorithm,
but bounds on the convergence of the algorithm are not known, and there is no
other known polynomial algorithm for computing the Frechet mean nor even the
edges present in the mean. We give the first necessary and sufficient
conditions for an edge to be in the Frechet mean. The conditions are in the
form of inequalities on the weights of the edges. These conditions provide a
pre-processing step for finding the treespace orthant containing the Frechet
mean. This work generalizes to orthant spaces.


  We show that the distribution of the maximum of the fractional Brownian
motion $B^H$ with Hurst parameter $H\to 0$ over an $n$-point set $\tau \subset
[0,1]$ can be approximated by the normal law with mean $\sqrt{\ln n}$ and
variance $1/2$ provided that $n\to \infty$ slowly enough and the points in
$\tau$ are not too close to each other.


  We consider a family of discrete coagulation-fragmentation equations closely
related to the one-dimensional forest-fire model of statistical mechanics: each
pair of particles with masses $i,j \in \nn$ merge together at rate 2 to produce
a single particle with mass $i+j$, and each particle with mass $i$ breaks into
$i$ particles with mass 1 at rate $(i-1)/n$. The (large) parameter $n$ controls
the rate of ignition and there is also an acceleration factor (depending on the
total number of particles) in front of the coagulation term.
  We prove that for each $n\in \nn$, such a model has a unique equilibrium
state and study in details the asymptotics of this equilibrium as $n\to
\infty$: (I) the distribution of the mass of a typical particle goes to the law
of the number of leaves of a critical binary Galton-Watson tree, (II) the
distribution of the mass of a typical size-biased particle converges, after
rescaling, to a limit profile, which we write explicitly in terms of the zeroes
of the Airy function and its derivative.
  We also indicate how to simulate perfectly a typical particle and a
size-biased typical particle, which allows us to give some probabilistic
interpretations of the above results in terms of pruned Galton-Watson trees and
pruned continuum random trees.


  In this paper we consider parallel implementations of approximate
multiplication of large matrices with exponential decay of elements. Such
matrices arise in computations related to electronic structure calculations and
some other fields of computational science. Commonly, sparsity is introduced by
dropping out small entries (truncation) of input matrices. Another approach,
the sparse approximate multiplication algorithm [M. Challacombe and N. Bock,
arXiv preprint 1011.3534, 2010] performs truncation of sub-matrix products. We
consider these two methods and their combination, i.e. truncation of both input
matrices and sub-matrix products. Implementations done using the Chunks and
Tasks programming model and library [E. H. Rubensson and E. Rudberg, Parallel
Comput., 40:328-343, 2014] are presented and discussed. We show that the
absolute error in the Frobenius norm behaves as $O\left(n^{1/2} \right), n
\longrightarrow \infty $ and $O\left(\tau^{p/2} \right), \tau \longrightarrow
0,\,\, \forall p < 2$ for all three methods, where $n$ is the matrix size and
$\tau$ is the truncation threshold. We compare the methods on a model problem
and show that the combined method outperforms the original two. The methods are
also applied to matrices coming from large chemical systems with $\sim 10^6$
atoms. We show that the combination of the two methods achieves better weak
scaling by reducing the amount of communication by a factor of $\approx 2$.


  Let $G$ be a group acting on a finite set $\Omega$. Then $G$ acts on
$\Omega\times \Omega$ by its entry-wise action and its orbits form the basis
relations of a coherent configuration (or shortly scheme). Our concern is to
consider what follows from the assumption that the number of orbits of $G$ on
$\Omega_i\times \Omega_j$ is constant whenever $\Omega_i$ and $\Omega_j$ are
orbits of $G$ on $\Omega$. One can conclude from the assumption that the
actions of $G$ on ${\Omega_i}$'s have the same permutation character and are
not necessarily equivalent. From this viewpoint one may ask how many
inequivalent actions of a given group with the same permutation character there
exist. In this article we will approach to this question by a purely
combinatorial method in terms of schemes and investigate the following topics:
  (i) balanced schemes and their central primitive idempotents, (ii)
characterization of reduced balanced schemes.


  Clifford indices for semistable vector bundles on a smooth projective curve
of genus at least 4 were defined in a previous paper of the authors. The
present paper studies bundles which compute these Clifford indices. We show
that under certain conditions on the curve all such bundles and their Serre
duals are generated.


  For single-antenna Gaussian interference channels, we re-formulate the
problem of determining the Generalized Degrees of Freedom (GDoF) region
achievable by treating interference as Gaussian noise (TIN) derived in [3] from
a combinatorial perspective. We show that the TIN power control problem can be
cast into an assignment problem, such that the globally optimal power
allocation variables can be obtained by well-known polynomial time algorithms.
Furthermore, the expression of the TIN-Achievable GDoF region (TINA region) can
be substantially simplified with the aid of maximum weighted matchings. We also
provide conditions under which the TINA region is a convex polytope that relax
those in [3]. For these new conditions, together with a channel connectivity
(i.e., interference topology) condition, we show TIN optimality for a new class
of interference networks that is not included, nor includes, the class found in
[3].
  Building on the above insights, we consider the problem of joint link
scheduling and power control in wireless networks, which has been widely
studied as a basic physical layer mechanism for device-to-device (D2D)
communications. Inspired by the relaxed TIN channel strength condition as well
as the assignment-based power allocation, we propose a low-complexity
GDoF-based distributed link scheduling and power control mechanism (ITLinQ+)
that improves upon the ITLinQ scheme proposed in [4] and further improves over
the heuristic approach known as FlashLinQ. It is demonstrated by simulation
that ITLinQ+ provides significant average network throughput gains over both
ITLinQ and FlashLinQ, and yet still maintains the same level of implementation
complexity. More notably, the energy efficiency of the newly proposed ITLinQ+
is substantially larger than that of ITLinQ and FlashLinQ, which is desirable
for D2D networks formed by battery-powered devices.


  We consider the self-localization of neutral impurity atoms in a
Bose-Einstein condensate in a 1D model. Within the strong coupling approach, we
show that the self-localized state exhibits parametric soliton behavior. The
corresponding stationary states are analogous to the solitons of non-linear
optics and to the solitonic solutions of the Schroedinger-Newton equation
(which appears in models that consider the connection between quantum mechanics
and gravitation). In addition, we present a Bogoliubov-de-Gennes formalism to
describe the quantum fluctuations around the product state of the strong
coupling description. Our fluctuation calculations yield the excitation
spectrum and reveal considerable corrections to the strong coupling
description. The knowledge of the spectrum allows a spectroscopic detection of
the impurity self-localization phenomenon.


  In this paper, we propose a one-pass algorithm on MapReduce for penalized
linear regression
  \[f_\lambda(\alpha, \beta) = \|Y - \alpha\mathbf{1} - X\beta\|_2^2 +
p_{\lambda}(\beta)\] where $\alpha$ is the intercept which can be omitted
depending on application; $\beta$ is the coefficients and $p_{\lambda}$ is the
penalized function with penalizing parameter $\lambda$. $f_\lambda(\alpha,
\beta)$ includes interesting classes such as Lasso, Ridge regression and
Elastic-net. Compared to latest iterative distributed algorithms requiring
multiple MapReduce jobs, our algorithm achieves huge performance improvement;
moreover, our algorithm is exact compared to the approximate algorithms such as
parallel stochastic gradient decent. Moreover, what our algorithm distinguishes
with others is that it trains the model with cross validation to choose optimal
$\lambda$ instead of user specified one.
  Key words: penalized linear regression, lasso, elastic-net, ridge, MapReduce


  In the present paper, we introduce a multibasic extension of the Ehrhart
theory. We give a multibasic extension of Ehrhart polynomials and Ehrhart
series. We also show that an analogue of Ehrhart reciprocity holds for
multibasic Ehrhart polynomials.


  We present the results of magnetic properties and entanglement for kagome
lattice using Heisenberg model with two-, and three-site exchange interactions
in strong magnetic field. Kagome lattice correspond to the third layer of fluid
3He absorbed on the surface of graphite. The magnetic properties and
concurrence as a measure of pairwise thermal entanglement are studied by means
of variational mean-field like treatment based on Gibbs-Bogoliubov inequality.
The system exhibits different magnetic behaviors, depending on the values of
the exchange parameters (J2, J3). We have obtained the magnetization plateaus
at low temperatures. The central theme of the paper is the comparing the
entanglement and magnetic behavior for kagome lattice. We have found that in
the antiferromagnetic region behaviour of the concurrence coincides with the
magnetization one.


  In this study we aim for a deeper understanding of the power law slope,
$\alpha$, of waiting time distributions. Statistically independent events with
linear behavior can be characterized by binomial, Gaussian, exponential, or
Poissonian size distribution functions. In contrast, physical processes with
nonlinear behavior exhibit spatio-temporal coherence (or memory) and "fat
tails" in their size distributions that fit power law-like functions, as a
consequence of the time variability of the mean event rate, as demonstrated by
means of Bayesian block decomposition in the work of Wheatland et al.~(1998).
  In this study we conduct numerical simulations of waiting time distributions
$N(\tau)$ in a large parameter space for various (polynomial, sinusoidal,
Gaussian) event rate functions $\lambda(t)$, parameterized with an exponent $p$
that expresses the degree of the polynomial function $\lambda(t) \propto t^p$.
We derive an analytical exact solution of the waiting time distribution
function in terms of the incomplete gamma function, which is similar to a
Pareto type-II function and has a power law slope of $\alpha = 2 + 1/p$, in the
asymptotic limit of large waiting times. Numerically simulated random
distributions reproduce this theoretical prediction accurately. Numerical
simulations in the nonlinear regime ($p \ge 2$) predict power law slopes in the
range of $2.0 \le \alpha \le 2.5$. The self-organized criticality model yields
a prediction of $\alpha=2$. Observations of solar flares and coronal mass
ejections (over at least a half solar cycle) are found in the range of
$\alpha_{obs} \approx 2.1-2.4$. Deviations from strict power law functions are
expected due to the variability of the flare event rate $\lambda(t)$, and
deviations from theoretically predicted slope values $\alpha$ occur due to the
Poissonian weighting bias of power law fits.


  We derive a Hamiltonian control theory which can be applied to a 4D
symplectic map that models a ring particle accelerator composed of elements
with sextupole nonlinearity. The controlled system is designed to exhibit a
more regular orbital behavior than the uncontrolled one. Using the Smaller
Alignement Index (SALI) chaos indicator, we are able to show that the
controlled system has a dynamical aperture up to 1.7 times larger than the
original mode


  Two coarse-grained models for polymer chains in dense glass-forming polymer
melts are studied by computer simulation: the bond-fluctuation model on a
simple cubic lattice, where a bond-length potential favors long bonds, is
treated by dynamic Monte Carlo methods, and a bead-spring model in the
continuum with a Lennard-Jones potential between the beads is treated by
Molecular Dynamics. While the dynamics of both models differ for short length
scales and associated time scales, on mesoscopic spatial and temporal scales
both models behave similarly. In particular, the mode coupling theory of the
glass transition can be used to interpret the slowing down of the undercooled
polymer melt. For the off-lattice model, the approach to the critical point of
mode coupling is both studied for constant pressure and for constant volume.
The lattice model allows a test of the Gibbs-Di Marzio entropy theory of the
glass transition, and our finding is that although the entropy does decrease
significantly, there is no ``entropy catastrophe'', where the fluid entropy
would turn negative. Finally, an outlook on confinement effects on the glass
transition in thin film geometry is given.


  We demonstrate that the confinement of half-quantized vortices (HQVs) in
coherently coupled Bose-Einstein condensates (BECs) simulates certain aspects
of the confinement in $SU(2)$ quantum chromodynamics (QCD) in 2+1 space-time
dimensions. By identifying the circulation of superfluid velocity as the baryon
number and the relative phase between two components as a dual gluon, we
identify HQVs in a single component as electrically charged particles with a
half baryon number. Further, we show that only singlet states of the relative
phase of two components can stably exist as bound states of vortices, that is,
a pair of vortices in each component (a baryon) and a pair of a vortex and an
antivortex in the same component (a meson). We then study the dynamics of a
baryon and meson; baryon is static at the equilibrium and rotates once it
deviates from the equilibrium, while a meson moves with constant velocity. For
both baryon and meson we verify a linear confinement and determine that they
are broken, thus creating other baryons or mesons in the middle when two
constituent vortices are separated by more than some critical distance,
resembling QCD.


  We prove that if the Hausdorff dimension of $E\subset\mathbb{R}^d$, $d\geq 2$
is greater than $\frac{d}{2}+\frac{1}{3}$, the set of gaps of $2$-chains inside
$E$, $$\Delta_2(E)=\{(|x-y|, |y-z|): x, y, z\in E \}\subset\mathbb{R}^2$$ has
positive Lebesgue measure. It generalizes Wolff-Erdogan's result on distances
and improves a result of Bennett, Iosevich and Taylor on finite chains.
  We also consider the similarity class of $2$-chains,
$$S_2(E)=\left\{\frac{t_1}{t_2}:(t_1,t_2)\in\Delta_2(E)\right\}=\left\{\frac{|x-y|}{|y-z|}:
x, y, z\in E \right\}\subset\mathbb{R},$$ and show that $|S_2(E)|>0$ whenever
$\dim_{\mathcal{H}}(E)>\frac{d}{2}+\frac{1}{7}$.


  We extend the recently developed treatment of baryon resonances in large N_c
QCD to describe resonance multiplets collected according to the SU(3) flavor
symmetry that includes strange quarks. As an illustration we enumerate the
SU(3) partners of a hypothetical J^P = 1/2^{+/-} resonance in the SU(3)
representation that reduces to 10-bar when N_c = 3, and reproduce results
hitherto obtained only in the context of a large N_c quark picture. While these
specific quantum numbers represent one favored set for the possible pentaquark
state Theta^+ (1540), the method is applicable to baryon resonances with any
quantum numbers.


  We study orthogonal polynomials with weight $\exp[-NV(x)]$, where
$V(x)=\sum_{k=1}^{d}a_{2k}x^{2k}/2k$ is a polynomial of order 2d. We derive the
generalised Freud's equations for $d=3$, 4 and 5 and using this obtain
$R_{\mu}=h_{\mu}/h_{\mu -1}$, where $h_{\mu}$ is the normalization constant for
the corresponding orthogonal polynomials. Moments of the density functions,
expressed in terms of $R_{\mu}$, are obtained using Freud's equation and using
this, explicit results of level densities as $N\rightarrow\infty$ are derived.


  With an apparent cluster diameter of 1.5{\deg} and an age of ~4 Myr, Trumpler
37 is an ideal target for photometric monitoring of young stars as well as for
the search of planetary transits, eclipsing binaries and other sources of
variability. The YETI consortium has monitored Trumpler 37 throughout 2010 and
2011 to obtain a comprehensive view of variable phenomena in this region. In
this first paper we present the cluster properties and membership determination
as derived from an extensive investigation of the literature. We also compared
the coordinate list to some YETI images. For 1872 stars we found literature
data. Among them 774 have high probability of being member and 125 a medium
probability. Based on infrared data we re-calculate a cluster extinction of
0.9-1.2 mag. We can confirm the age and distance to be 3-5 Myr and ~870 pc.
Stellar masses are determined from theoretical models and the mass function is
fitted with a power-law index of alpha=1.90 (0.1-0.4 M_sun) and alpha=1.12
(1-10 M_sun).


  This article is an introduction for the nonpractitioner to the ideas and
issues of LISA data analysis, as reflected in the explorations and experiments
of the participants in the Mock LISA Data Challenges. In particular, I discuss
the methods and codes that have been developed for the detection and parameter
estimation of supermassive black-hole binaries, extreme mass-ratio inspirals,
and Galactic binaries.


  We investigate the collective dynamics of bursting neurons on clustered
network. The clustered network is composed of subnetworks each presenting a
small-world property, and in a given subnetwork each neuron has a probability
to be connected to the other subnetworks. We give bounds for the critical
coupling strength to obtain global burst synchronization in terms of the
network structure, i.e., intracluster and intercluster probabilities
connections. As the heterogeneity in the network is reduced the network global
synchronization is improved. We show that the transitions to global synchrony
may be abrupt or smooth depending on the intercluster probability.


  We have used second order relativistic hydrodynamics equipped with equation
of state which includes the critical point to study the propagation of
perturbation in a relativistic QCD fluid. Dispersion relation for the sound
wave has been derived to ascertain the fate of the perturbation in the fluid
near the QCD critical end point (CEP). We observe that the threshold value of
the wavelength of the sound in the fluid diverges at the CEP, implying that all
the modes of the perturbations are dissipated at this point. Some consequences
of the suppression of sound near the critical point have been discussed.


  In this paper we study the asymptotics (as $n\to \infty$) of the sequences of
Laguerre polynomials with varying complex parameters $\alpha$ depending on the
degree $n$. More precisely, we assume that $\alpha_n = n A_n, $ and $ \lim_n
A_n=A \in \mathbb{C}$. This study has been carried out previously only for
$\alpha_n\in \mathbb{R}$, but complex values of $A$ introduce an asymmetry that
makes the problem more difficult.
  The main ingredient of the asymptotic analysis is the right choice of the
contour of orthogonality, which requires the analysis of the global structure
of trajectories of an associated quadratic differential on the complex plane,
which may have an independent interest.
  While the weak asymptotics is obtained by reduction to the theorem of
Gonchar--Rakhmanov--Stahl, the strong asymptotic results are derived via the
non-commutative steepest descent analysis based on the Riemann-Hilbert
characterization of the Laguerre polynomials.


  A modular tensor category is a non-degenerate ribbon finite tensor category.
And a ribbon factorizable Hopf algebra is exactly the Hopf algebra whose
finite-dimensional representations form a modular tensor category. The goal of
this paper is to construct both semisimple and non-semisimple modular
categories with Hopf algebras. In particular, we study central extensions of
Hopf algebras and characterize some conditions for a quotient Hopf algebra to
be a factorizable one. Then we give a special way to obtain ribbon elements. As
a result, we apply to some finite dimensional pointed Hopf algebras introduced
by Andruskiewitsch etc and obtain two families of ribbon factorizable Hopf
algebras. With little restrictions to their parameters, we prove that their
representation categories are prime modular tensor categories which are not
tensor equivalent to representation categories of small quantum groups. Lastly,
we construct a family of semisimple ribbon factorizable Hopf algebas A(p,q),
where p,q are prime numbers satisfying some conditions. And we decompose
Rep(A(p,q)) into prime modular tensor categories and prove that A(p,q) can't be
obtained by some obvious ways, i.e. it's not tensor product of trivial Hopf
algebras (group algebras or their dual) and Drinfeld doubles.


  Interest in many strongly spin-orbit coupled 5d-transition metal oxide
insulators stems from mapping their electronic structures to a J=1/2 Mott
phase. One of the hopes is to establish their Mott parent states and explore
these systems' potential of realizing novel electronic states upon carrier
doping. However, once doped, little is understood regarding the role of their
reduced Coulomb interaction U relative to their strongly correlated 3d-electron
cousins. Here we show that, upon hole-doping a candidate J=1/2 Mott insulator,
carriers remain localized within a nanoscale phase separated ground state. A
percolative metal-insulator transition occurs with interplay between localized
and itinerant regions, stabilizing an antiferromagnetic metallic phase beyond
the critical region. Our results demonstrate a surprising parallel between
doped 5d- and 3d-electron Mott systems and suggest either through the near
degeneracy of nearby electronic phases or direct carrier localization that U is
essential to the carrier response of this doped spin-orbit Mott insulator.


  Existing attention mechanisms are trained to attend to individual items in a
collection (the memory) with a predefined, fixed granularity, e.g., a word
token or an image grid. We propose area attention: a way to attend to areas in
the memory, where each area contains a group of items that are structurally
adjacent, e.g., spatially for a 2D memory such as images, or temporally for a
1D memory such as natural language sentences. Importantly, the shape and the
size of an area are dynamically determined via learning, which enables a model
to attend to information with varying granularity. Area attention can easily
work with existing model architectures such as multi-head attention for
simultaneously attending to multiple areas in the memory. We evaluate area
attention on two tasks: neural machine translation (both character and
token-level) and image captioning, and improve upon strong (state-of-the-art)
baselines in all the cases. These improvements are obtainable with a basic form
of area attention that is parameter free.


  Cognitive radio networks (CRNs) have emerged as an essential technology to
enable dynamic and opportunistic spectrum access which aims to exploit
underutilized licensed channels to solve the spectrum scarcity problem. Despite
the great benefits that CRNs offer in terms of their ability to improve
spectrum utilization efficiency, they suffer from user location privacy issues.
Knowing that their whereabouts may be exposed can discourage users from joining
and participating in the CRNs, thereby potentially hindering the adoption and
deployment of this technology in future generation networks. The location
information leakage issue in the CRN context has recently started to gain
attention from the research community due to its importance, and several
research efforts have been made to tackle it. However, to the best of our
knowledge, none of these works have tried to identify the vulnerabilities that
are behind this issue or discuss the approaches that could be deployed to
prevent it. In this paper, we try to fill this gap by providing a comprehensive
survey that investigates the various location privacy risks and threats that
may arise from the different components of this CRN technology, and explores
the different privacy attacks and countermeasure solutions that have been
proposed in the literature to cope with this location privacy issue. We also
discuss some open research problems, related to this issue, that need to be
overcome by the research community to take advantage of the benefits of this
key CRN technology without having to sacrifice the users' privacy.


  Smectic liquid crystals are materials formed by stacking deformable, fluid
layers. Though smectics prefer to have flat, uniformly-spaced layers, boundary
conditions can impose curvature on the layers. Since the layer spacing and
curvature are intertwined, the problem of finding minimal configurations for
the layers becomes highly nontrivial. We discuss various topological and
geometrical aspects of these materials and present recent progress on finding
some exact layer configurations. We also exhibit connections to the study of
certain embedded minimal surfaces and briefly summarize some important open
problems.


  The von Neumann entropy for an electron in periodic, disorder and
quasiperiodic quantum small-world networks(QSWNs) are studied numerically. For
the disorder QSWNs, the derivative of the spectrum averaged von Neumann entropy
is maximal at a certain density of shortcut links p*, which can be as a
signature of the localization delocalization transition of electron states. The
transition point p* is agreement with that obtained by the level statistics
method. For the quasiperiodic QSWNs, it is found that there are two regions of
the potential parameter. The behaviors of electron states in different regions
are similar to that of periodic and disorder QSWNs, respectively.


  We review the concept of dynamical ensembles in nonequilibrium statistical
mechanics as specified from an action functional or Lagrangian on spacetime.
There, under local detailed balance, the breaking of time-reversal invariance
is quantified via the entropy flux, and we revisit some of the consequences for
fluctuation and response theory. Frenesy is the time-symmetric part of the
path-space action with respect to a reference process. It collects the variable
quiescence and dynamical activity as function of the system's trajectory, and
as has been introduced under different forms in studies of nonequilibria. We
discuss its various realizations for physically inspired Markov jump and
diffusion processes and why it matters a good deal for nonequilibrium physics.
This review then serves also as an introduction to the exploration of frenetic
contributions in nonequilibrium phenomena.


  Main topic of the paper is a study of properties of massless fields of spin
3/2 in its Euclidean version. A lot of information is available already for
massless fields in dimension 4. Here, we concentrate on dimension 6 and we are
using the fact that the group SL(4,C) is isomorphic with the group Spin(6,C).
It makes it possible to use tensor formalism for massless fields. Main problems
treated in the paper are a description of fields which need to be considered in
the spin 3/2 case, a suitable choice of equations they should satisfy,
irreducibility of homogeneous solutions of massless field equations, the
Fischer decomposition and the Howe duality for such fields.


  We report three manifestly Lorentz-invariant Hamiltonian formulations of
minimally and nonminimally coupled fermion fields to the Holst action. These
formulations are achieved by making a suitable parametrization of both the
tetrad and the Lorentz connection, which allows us to integrate out some
auxiliary fields without spoiling the local Lorentz symmetry. They have the
peculiarity that their noncanonical symplectic structures as well as the
phase-space variables for the gravitational sector are real. Moreover, two of
these Hamiltonian formulations involve half-densitized fermion fields. We also
impose the time gauge on these formulations, which leads to real connections
for the gravitational configuration variables. Finally, we perform a
symplectomorphism in one of the manifestly Lorentz-invariant Hamiltonian
formulations and analyze the resulting formulation, which becomes the
Hamiltonian formulation of fermion fields minimally coupled to the Palatini
action for particular values of the coupling parameters.


  Recent advancements in deep learning-based modeling of molecules promise to
accelerate in silico drug discovery. A plethora of generative models is
available, building molecules either atom-by-atom and bond-by-bond or
fragment-by-fragment. However, many drug discovery projects require a fixed
scaffold to be present in the generated molecule, and incorporating that
constraint has only recently been explored. Here, we propose MoLeR, a
graph-based model that naturally supports scaffolds as initial seed of the
generative procedure, which is possible because it is not conditioned on the
generation history. Our experiments show that MoLeR performs comparably to
state-of-the-art methods on unconstrained molecular optimization tasks, and
outperforms them on scaffold-based tasks, while being an order of magnitude
faster to train and sample from than existing approaches. Furthermore, we show
the influence of a number of seemingly minor design choices on the overall
performance.


  Let $\fa$ be an ideal of a local ring $(R,\fm)$ and $M$ a finitely generated
$R$-module. We investigate the structure of the formal local cohomology modules
${\vpl}_nH^i_{\fm}(M/\fa^n M)$, $i\geq 0$. We prove several results concerning
finiteness properties of formal local cohomology modules which indicate that
these modules behave very similar to local cohomology modules. Among other
things, we prove that if $\dim R\leq 2$ or either $\fa$ is principal or $\dim
R/\fa\leq 1$, then $\Tor_j^R(R/\fa,{\vpl}_nH^i_{\fm}(M/\fa^n M))$ is Artinian
for all $i$ and $j$. Also, we examine the notion $\fgrade(\fa,M)$, the formal
grade of $M$ with respect to $\fa$ (i.e. the least integer $i$ such that
${\vpl}_nH^i_{\fm}(M/\fa^n M) \neq 0$). As applications, we establish a
criterion for Cohen-Macaulayness of $M$, and also we provide an upper bound for
cohomological dimension of $M$ with respect to $\fa$.


  Contributions by the MAGIC collaboration to ICRC 2005, Pune, India, Part 2:
Future Plans and Developments (9 contributions)


  A near perfect, storage time-extended photon echo-based quantum memory
protocol has been analyzed by solving the Maxwell-Bloch equations for a
backward scheme in a three-level system. The backward photon echo scheme is
combined with a controlled coherence conversion process via control Rabi
flopping to a third state, where the control Rabi flopping collectively shifts
the phase of the ensemble coherence. The propagation direction of photon echoes
is coherently determined by the phase matching condition between the data
(quantum) and the control (classical) pulses. Herein we discuss the classical
controllability of a quantum state for both phase and propagation direction by
manipulating the control pulses in both single and double rephasing photon echo
schemes of a three-level system. Compared with their well-understood use for
two-level photon echoes, the Maxwell-Bloch equations to a three-level system
have a critical limitation regarding the phase change when interacted with an
arbitrary control pulse area.


  Invertible neural networks are a recent technique in machine learning
promising neural network architectures that can be run in forward and reverse
mode. In this paper, we will be introducing invertible surrogate models that
approximate complex forward simulation of the physics involved in laser plasma
accelerators: iLWFA. The bijective design of the surrogate model also provides
all means for reconstruction of experimentally acquired diagnostics. The
quality of our invertible laser wakefield acceleration network will be verified
on a large set of numerical LWFA simulations.


  An external magnetic field can induce a transition in $\alpha$-RuCl$_3$ from
an ordered zigzag state to a disordered state that is possibly related to the
Kitaev quantum spin liquid. Here we present new field dependent inelastic
neutron scattering and magnetocaloric effect measurements implying the
existence of an additional transition out of the quantum spin liquid phase at
an upper field limit $B_u$. The neutron scattering shows three distinct regimes
of magnetic response. In the low field ordered state the response shows magnon
peaks; the intermediate field regime shows only continuum scattering, and above
$B_u$ the response shows sharp magnon peaks at the lower bound of a strong
continuum. Measurable dispersion of magnon modes along the $(0,0,L)$ direction
implies non-negligible inter-plane interactions. Combining the magnetocaloric
effect measurements with other data a $T-B$ phase diagram is constructed. The
results constrain the range where one might expect to observe quantum spin
liquid behavior in $\alpha$-RuCl$_3$.


  We consider probabilistic amplitude shaping (PAS) as a means of increasing
the spectral efficiency of fiber-optic communication systems. In contrast to
previous works in the literature, we consider probabilistic shaping with hard
decision decoding (HDD). In particular, we apply the PAS recently introduced by
B\"ocherer \emph{et al.} to a coded modulation (CM) scheme with bit-wise HDD
that uses a staircase code as the forward error correction code. We show that
the CM scheme with PAS and staircase codes yields significant gains in spectral
efficiency with respect to the baseline scheme using a staircase code and a
standard constellation with uniformly distributed signal points. Using a single
staircase code, the proposed scheme achieves performance within $0.57$--$1.44$
dB of the corresponding achievable information rate for a wide range of
spectral efficiencies.


  We study the vacuum (i.e., zero-temperature) Casimir energy for a system of
neutral conductors which are isolated, as opposed to grounded. The former is
meant to describe a situation where the total charge on each conductor, as well
as all of its fluctuations, vanishes, while the latter describes a situation
where the conductors are connected to a charge reservoir. We compute the
difference between the vacuum energies for a given system of conductors, but
subjected to the two different conditions stated above. The results can be
written in terms of a generalized, frequency-dependent capacitance matrix of
the system. Using a multipolar expansion, we show that the grounded Casimir
energy includes a monopole-monopole interaction term that is absent in the
isolated case in the large distance limit


  We show that a regression of unsmoothed peculiar velocity measurements
against peculiar velocities predicted from a smoothed galaxy density field
leads to a biased estimate of the cosmological density parameter Omega, even
when galaxies trace the underlying mass distribution and galaxy positions and
velocities are known perfectly. The bias arises because the errors in the
predicted velocities are correlated with the predicted velocities themselves.
We investigate this bias using cosmological N-body simulations and analytic
arguments. In linear perturbation theory, for cold dark matter power spectra
and Gaussian or top hat smoothing filters, the bias in Omega is always
positive, and its magnitude increases with increasing smoothing scale. This
linear calculation reproduces the N-body results for Gaussian smoothing radii
R_s > 10 Mpc/h, while non-linear effects lower the bias on smaller smoothing
scales, and for R_s < 3 Mpc/h Omega is underestimated rather than
overestimated. The net bias in Omega for a given smoothing filter depends on
the underlying cosmological model. The effect on current estimates of Omega
from velocity-velocity comparisons is probably small relative to other
uncertainties, but taking full advantage of the statistical precision of future
peculiar velocity data sets will require either equal smoothing of the
predicted and measured velocity fields or careful accounting for the biases
discussed here.


  This note shows how to use the framework of Euler characteristic formulae to
study Selmer groups of abelian varieties in certain dihedral or anticyclotomic
extensions of CM fields via Iwasawa main conjectures, and in particular how to
verify the p-part of the refined Birch and Swinnerton-Dyer conjecture in this
setting. When the Selmer group is cotorsion with respect to the associated
Iwasawa algebra, we obtain the p-part of formula predicted by the refined Birch
and Swinnerton-Dyer conjecture. When the Selmer group is not cotorsion with
respect to the associated Iwasawa algebra, we give a conjectural description of
the Euler characteristic of the cotorsion submodule, and explain how to deduce
inequalities from the associated main conjecture divisibilities of Perrin-Riou
and Howard.


  We present faster high-accuracy algorithms for computing $\ell_p$-norm
minimizing flows. On a graph with $m$ edges, our algorithm can compute a
$(1+1/\text{poly}(m))$-approximate unweighted $\ell_p$-norm minimizing flow
with $pm^{1+\frac{1}{p-1}+o(1)}$ operations, for any $p \ge 2,$ giving the best
bound for all $p\gtrsim 5.24.$ Combined with the algorithm from the work of
Adil et al. (SODA '19), we can now compute such flows for any $2\le p\le
m^{o(1)}$ in time at most $O(m^{1.24}).$ In comparison, the previous best
running time was $\Omega(m^{1.33})$ for large constant $p.$ For
$p\sim\delta^{-1}\log m,$ our algorithm computes a $(1+\delta)$-approximate
maximum flow on undirected graphs using $m^{1+o(1)}\delta^{-1}$ operations,
matching the current best bound, albeit only for unit-capacity graphs.
  We also give an algorithm for solving general $\ell_{p}$-norm regression
problems for large $p.$ Our algorithm makes
$pm^{\frac{1}{3}+o(1)}\log^2(1/\varepsilon)$ calls to a linear solver. This
gives the first high-accuracy algorithm for computing weighted $\ell_{p}$-norm
minimizing flows that runs in time $o(m^{1.5})$ for some $p=m^{\Omega(1)}.$ Our
key technical contribution is to show that smoothed $\ell_p$-norm problems
introduced by Adil et al., are interreducible for different values of $p.$ No
such reduction is known for standard $\ell_p$-norm problems.


  For $\mathcal{O}$ a bounded domain in $\mathbb{R}^d$ and a given smooth
function $g:\mathcal{O}\to\mathbb{R}$, we consider the statistical nonlinear
inverse problem of recovering the conductivity $f>0$ in the divergence form
equation $$
  \nabla\cdot(f\nabla u)=g\ \textrm{on}\ \mathcal{O}, \quad
  u=0\ \textrm{on}\ \partial\mathcal{O}, $$ from $N$ discrete noisy point
evaluations of the solution $u=u_f$ on $\mathcal O$. We study the statistical
performance of Bayesian nonparametric procedures based on a flexible class of
Gaussian (or hierarchical Gaussian) process priors, whose implementation is
feasible by MCMC methods. We show that, as the number $N$ of measurements
increases, the resulting posterior distributions concentrate around the true
parameter generating the data, and derive a convergence rate $N^{-\lambda},
\lambda>0,$ for the reconstruction error of the associated posterior means, in
$L^2(\mathcal{O})$-distance.


  The propagation of matter waves in curved geometry is relevant for electrons
in nano-wires, solid-state physics structures and atomtronics. Curvature
effects are usually addressed within the adiabatic limit and treated via an
effective potential acting on the manifold to which the particles are strongly
confined. However, the strength of the confinements that can be achieved
experimentally are in practice limited, and the adiabatic approximation
framework often appears too restrictive for the realistic design of relevant
propagation structures. Here, we explore the design of 2D sharply bent
wave-guides for the propagation of matter waves beyond the adiabatic regime.
The bend design, which enables the connection of guide components rotated by an
arbitrary angle and of arbitrary curvatures, rests on an exact
inverse-engineering technique. The resolution of the full 2D Schr\"odinger
equation in curved geometry shows that our method yields reflectionless guides
with a transverse stability improved by several orders of magnitude when
compared to circular guides of similar size.


  In this paper we develop a method to solve evolution equations on Gelfand
triples with time-fractional derivative based on monotonicity techniques.
Applications include deterministic and stochastic quasi-linear partial
differential equations with time-fractional derivatives, including
time-fractional (stochastic) porous media equations (including the case where
the Laplace operator is also fractional) and $p$-Laplace equations as special
cases.


  We investigate the effects of strain on a crystal surface close to the bulk
melting temperature T_m, where surface melting usually sets in. Strain lowers
the bulk melting point, so that at a fixed temperature below but close to T_m
the thickness of the quasi-liquid film is expected to grow with strain,
irrespective of sign. In addition, a strain-induced solid surface free energy
increase/decrease takes place, favoring/disfavoring surface melting depending
on the sign of strain relative to surface stress. In the latter case one can
produce a strain-induced prewetting transition, where for increasing
temperature the liquid film suddenly jumps from zero to a finite thickness.
This phenomenology is illustrated by a realistic molecular dynamics simulation
of strained Al(110).


  Let $p$ a large enough prime number. When $A$ is a subset of
$\mathbb{F}_p\smallsetminus\{0\}$ of cardinality $|A|> (p+1)/3$, then an
application of Cauchy-Davenport Theorem gives
$\mathbb{F}_p\smallsetminus\{0\}\subset A(A+A)$. In this note, we improve on
this and we show that if $|A|\ge 0.3051 p$ implies
$A(A+A)\supseteq\mathbb{F}_p\smallsetminus\{0\}$. In the opposite direction we
show that there exists a set $A$ such that $|A| > (1/8+o(1))p$ and
$\mathbb{F}_p\smallsetminus\{0\}\not\subseteq A(A+A)$.


  We use an effective field theory (EFT) approach to calculate the next to
leading order (NLO) gravitational spin-orbit interaction between two spinning
compact objects. The NLO spin-orbit interaction provides the most
computationally complex sector of the NLO spin effects, previously derived
within the EFT approach. In particular, it requires the inclusion of
non-stationary cubic self-gravitational interaction, as well as the
implementation of a spin supplementary condition (SSC) at higher orders. The
EFT calculation is carried out in terms of the non-relativistic gravitational
field parametrization, making the calculation more efficient with no need to
rely on automated computations, and illustrating the coupling hierarchy of the
different gravitational field components to the spin and mass sources. Finally,
we show explicitly how to relate the EFT derived spin results to the canonical
results obtained with the ADM Hamiltonian formalism. This is done using
non-canonical transformations, required due to the implementation of covariant
SSC, as well as canonical transformations at the level of the Hamiltonian, with
no need to resort to the equations of motion or the Dirac brackets.


  We formulate and validate a finite element approach to the propagation of a
slowly decaying electromagnetic wave, called surface plasmon-polariton, excited
along a conducting sheet, e.g., a single-layer graphene sheet, by an electric
Hertzian dipole. By using a suitably rescaled form of time-harmonic Maxwell's
equations, we derive a variational formulation that enables a direct numerical
treatment of the associated class of boundary value problems by appropriate
curl-conforming finite elements. The conducting sheet is modeled as an
idealized hypersurface with an effective electric conductivity. The requisite
weak discontinuity for the tangential magnetic field across the hypersurface
can be incorporated naturally into the variational formulation. We carry out
numerical simulations for an infinite sheet with constant isotropic
conductivity embedded in two spatial dimensions; and validate our numerics
against the closed-form exact solution obtained by the Fourier transform in the
tangential coordinate. Numerical aspects of our treatment such as an absorbing
perfectly matched layer, as well as local refinement and a-posteriori error
control are discussed.


  We present a linearized shear-transformation-zone (STZ) theory of glassy
dynamics in which the internal STZ transition rates are characterized by a
broad distribution of activation barriers. For slowly aging or fully aged
systems, the main features of the barrier-height distribution are determined by
the effective temperature and other near-equilibrium properties of the
configurational degrees of freedom. Our theory accounts for the wide range of
relaxation rates observed in both structural glasses and soft glassy materials
such as colloidal suspensions. We find that the frequency dependent loss
modulus is not just a superposition of Maxwell modes. Rather, it exhibits an
$\alpha$ peak that rises near the viscous relaxation rate and, for nearly
jammed, glassy systems, extends to much higher frequencies in accord with
experimental observations. We also use this theory to compute strain recovery
following a period of large, persistent deformation and then abrupt unloading.
We find that strain recovery is determined in part by the initial
barrier-height distribution, but that true structural aging also occurs during
this process and determines the system's response to subsequent perturbations.
In particular, we find by comparison with experimental data that the initial
deformation produces a highly disordered state with a large population of low
activation barriers, and that this state relaxes quickly toward one in which
the distribution is dominated by the high barriers predicted by the
near-equilibrium analysis. The nonequilibrium dynamics of the barrier-height
distribution is the most important of the issues raised and left unresolved in
this paper.


  This paper aims at demystifying a single motion-blurred image with events and
revealing temporally continuous scene dynamics encrypted behind motion blurs.
To achieve this end, an Implicit Video Function (IVF) is learned to represent a
single motion blurred image with concurrent events, enabling the latent sharp
image restoration of arbitrary timestamps in the range of imaging exposures.
Specifically, a dual attention transformer is proposed to efficiently leverage
merits from both modalities, i.e., the high temporal resolution of event
features and the smoothness of image features, alleviating temporal ambiguities
while suppressing the event noise. The proposed network is trained only with
the supervision of ground-truth images of limited referenced timestamps.
Motion- and texture-guided supervisions are employed simultaneously to enhance
restorations of the non-referenced timestamps and improve the overall
sharpness. Experiments on synthetic, semi-synthetic, and real-world datasets
demonstrate that our proposed method outperforms state-of-the-art methods by a
large margin in terms of both objective PSNR and SSIM measurements and
subjective evaluations.


  In social dilemmas under weak selection, the capacity for a player to exhibit
updating passivity or interact with its own strategy can lead to conflicting
outcomes. The central question is which effect is stronger and how their
simultaneous presence influences the evolution of cooperation. We introduce a
model that considers both effects using different weight factors. We derive
theoretical solutions for the conditions of cooperation success and the
cooperation level under weak selection, scanning the complete parameter space.
When the weight factors are equally strong, the promoting effect of
self-interaction to cooperation surpasses the inhibitory effect of updating
passivity. Intriguingly, however, we identify non-monotonous
cooperation-supporting effects when the weight of updating passivity increases
more rapidly. Our findings are corroborated by Monte Carlo simulations and
demonstrate robustness across various game types, including the prisoner's
dilemma, stag-hunt, and snowdrift games.


  We find asymptotically anti de Sitter solutions in N=8 supergravity which
have negative total energy. This is possible since the boundary conditions
required for the positive energy theorem are stronger than those required for
finite mass (and allowed by string theory). But stability of the anti de Sitter
vacuum is still ensured by the positivity of a modified energy, which includes
an extra surface term. Some of the negative energy solutions describe classical
evolution of nonsingular initial data to naked singularities. Since there is an
open set of such solutions, cosmic censorship is violated generically in
supergravity. Using the dual field theory description, we argue that these
naked singularities will be resolved in the full string theory.


  This paper studies the poset of eigenspaces of elements of an imprimitive
unitary reflection group, for a fixed eigenvalue, ordered by the reverse of
inclusion. The study of this poset is suggested by the eigenspace theory of
Springer and Lehrer. The posets are shown to be isomorphic to certain subposets
of Dowling lattices (the `d-divisible, k-evenly coloured Dowling lattices').
This enables us to prove that these posets are Cohen-Macaulay, and to determine
the dimension of their top homology.


  The projector onto the Minkowski sum of closed convex sets is generally not
equal to the sum of individual projectors. In this work, we provide a complete
answer to the question of characterizing the instances where such an equality
holds. Our results unify and extend the case of linear subspaces and
Zarantonello's results for projectors onto cones. A detailed analysis in the
case of convex combinations is also carried out. We establish the partial sum
property for projectors onto convex cones, and we also present various examples
as well as a detailed analysis in the univariate case.


  The period-luminosity (P-L) relation for Cepheid variables is important in
modern astrophysics. In this work, we present the multi-band P-L relations
derived from the Large Magellanic Cloud (LMC) and Small Magellanic Cloud (SMC)
Cepheids, based on the latest release of OGLE-III catalogs. In addition to the
V I band mean magnitudes adopted from OGLE-III catalogs, we also cross-matched
the LMC and SMC Cepheids to the 2MASS point source catalogs and publicly
available Spitzer catalogs from SAGE program. Mean magnitudes for these
Cepheids were corrected for extinction using available extinction maps. When
comparing the P-L slopes, we found that the P-L slopes in these two galaxies
are consistent with each others within ~2.5sigma level.


  Massive stars have a strong impact on their surroundings, in particular when
they produce a core-collapse supernova at the end of their evolution. In these
proceedings, we review the general evolution of massive stars and their
properties at collapse as well as the transition between massive and
intermediate-mass stars. We also summarise the effects of metallicity and
rotation. We then discuss some of the major uncertainties in the modelling of
massive stars, with a particular emphasis on the treatment of convection in 1D
stellar evolution codes. Finally, we present new 3D hydrodynamic simulations of
convection in carbon burning and list key points to take from 3D hydrodynamic
studies for the development of new prescriptions for convective boundary mixing
in 1D stellar evolution codes.


  Introducing a notion of the weighted mean sigma-r curvature and using the
weighted Newton transformations we derive in this paper some integral formulae
on weighted manifolds. These formulae generalize the flux formula and some of
its examples of applications obtained by Alias, de Lira and Malacarne [3].


  On hypothesis of self-scaling co-flows in tapered rectanglar PMMA
micro-channels for producing mono-dispersed liquid cells, universal scalings
through all liquid detaching regimes are found under a self-similarity frame.
Pan-dripping and Pan-jetting regimes are calculated clearly to border at the
Weber number approximately $1$ and the capillary number approximately $0.28$ by
machine learning classification. The sizes, as well as detaching frequencies,
of liquid cells in different flow regimes behave at the same manner and submit
to the same law, and such highly consistent behaviors breaking through physical
barriers among flow regimes have never been reported.


  The dynamics of the tilted axisymmetric Bianchi IX cosmological models are
explored allowing energy flux in the source fluid. The Einstein equations and
the continuity equation are presented treating the equation of state $w$ and
the tilt angle of the fluid $\lambda$ as time dependent functions, but when
analysing the phase space $w$ and $\lambda$ are considered free parameters and
the shear, the vorticity and the curvature of the spacetime span a
three-dimensional phase space that contains seven fixed points. One of them is
an attractor that inflates the universe anisotropically, thus providing a
counter example to the cosmic no-hair conjecture. Also, examples of a realistic
though fine-tuned cosmologies are presented wherein the rotation can grow
significant towards the present epoch but the shear stays within the
observational bounds. The examples suggest that the model used here can explain
the parity-violating anomalies of the cosmic microwave background. The result
significantly differs from an earlier study, where a non-axisymmetric Bianchi
IX type with a tilted perfect dust source was found to induce too much shear
for observationally significant vorticity.


  Existing domain adaptation methods aim at learning features that can be
generalized among domains. These methods commonly require to update source
classifier to adapt to the target domain and do not properly handle the trade
off between the source domain and the target domain. In this work, instead of
training a classifier to adapt to the target domain, we use a separable
component called data calibrator to help the fixed source classifier recover
discrimination power in the target domain, while preserving the source domain's
performance. When the difference between two domains is small, the source
classifier's representation is sufficient to perform well in the target domain
and outperforms GAN-based methods in digits. Otherwise, the proposed method can
leverage synthetic images generated by GANs to boost performance and achieve
state-of-the-art performance in digits datasets and driving scene semantic
segmentation. Our method empirically reveals that certain intriguing hints,
which can be mitigated by adversarial attack to domain discriminators, are one
of the sources for performance degradation under the domain shift.


  We consider the design of regenerating codes for distributed storage systems
at the minimum bandwidth regeneration (MBR) point. The codes allow for a repair
process that is exact and uncoded, but table-based. These codes were introduced
in prior work and consist of an outer MDS code followed by an inner fractional
repetition (FR) code where copies of the coded symbols are placed on the
storage nodes. The main challenge in this domain is the design of the inner FR
code.
  In our work, we consider generalizations of FR codes, by establishing their
connection with a family of combinatorial structures known as resolvable
designs. Our constructions based on affine geometries, Hadamard designs and
mutually orthogonal Latin squares allow the design of systems where a new node
can be exactly regenerated by downloading $\beta \geq 1$ packets from a subset
of the surviving nodes (prior work only considered the case of $\beta = 1$).
Our techniques allow the design of systems over a large range of parameters.
Specifically, the repetition degree of a symbol, which dictates the resilience
of the system can be varied over a large range in a simple manner. Moreover,
the actual table needed for the repair can also be implemented in a rather
straightforward way. Furthermore, we answer an open question posed in prior
work by demonstrating the existence of codes with parameters that are not
covered by Steiner systems.


  Let X be a projective hypersurface in P_k^n of degree d <= n. In this paper
we study the relation between the class [X] in K_0(Var_k) and the existence of
k-rational points. Using elementary geometric methods we show, for some
particular X, that X(k) is nonempty if and only if [X] is equivalent to 1
modulo the class of the affine line in K_0(Var_k). More precisely we consider
the following cases: a union of hyperplanes, a quadric, a cubic hypersurface
with a singular k-rational point, and a quartic which is a union of two
quadrics one of which being smooth.


  To extract accurate speaker information for text-independent speaker
verification, temporal dynamic CNNs (TDY-CNNs) adapting kernels to each time
bin was proposed. However, model size of TDY-CNN is too large and the adaptive
kernel's degree of freedom is limited. To address these limitations, we propose
decomposed temporal dynamic CNNs (DTDY-CNNs) which forms time-adaptive kernel
by combining static kernel with dynamic residual based on matrix decomposition.
Proposed DTDY-ResNet-34(x0.50) using attentive statistical pooling without data
augmentation shows EER of 0.96%, which is better than other state-of-the-art
methods. DTDY-CNNs are successful upgrade of TDY-CNNs, reducing the model size
by 64% and enhancing the performance. We showed that DTDY-CNNs extract more
accurate frame-level speaker embeddings as well compared to TDY-CNNs. Detailed
behaviors of DTDY-ResNet-34(x0.50) on extraction of speaker information were
analyzed using speaker activation map (SAM) produced by modified
gradient-weighted class activation mapping (Grad-CAM) for speaker verification.
DTDY-ResNet-34(x0.50) effectively extracts speaker information from not only
formant frequencies but also high frequency information of unvoiced phonemes,
thus explaining its outstanding performance on text-independent speaker
verification.


  We study Tully-Fisher relations for a sample that combines extremely faint
(M_B > -14.0) galaxies along with bright (i.e. L_*) galaxies. Accurate (~ 10%)
distances, I band photometry, and B-V colors are known for the majority of the
galaxies in our sample. The faint galaxies are drawn from the Faint Irregular
Galaxy GMRT survey (FIGGS), and we have HI rotation velocities derived from
aperture synthesis observations for all of them. For the faint galaxies, we
find that even though the median HI and stellar masses are comparable, the HI
mass correlates significantly better with the circular velocity indicators than
the stellar mass. We also find that W$_{20}$ correlates better with mass than
the rotation velocity, although the difference is not statistically
significant. The faint galaxies lie systematically below the I band TF relation
defined by bright galaxies, and also show significantly more intrinsic scatter.
This implies that the integrated star formation in these galaxies has been both
less efficient and also less regulated than in large galaxies. We find that
while the faint end deviation is greatly reduced in Baryonic Tully-Fisher (BTF)
relations, the existence of a break at the faint end of the BTF is subject to
systematics such as the assumed stellar mass to light ratio. If we assume that
there is an intrinsic BTF and try to determine the baryonic mass by searching
for prescriptions that lead to the tightest BTF, we find that scaling the HI
mass leads to a much more significant tightening than scaling the stellar mass
to light ratio. The most significant tightening that we find however, is if we
scale the entire baryonic mass of the faint (but not the bright) galaxies. Such
a scenario would be consistent with models where dwarf (but not large) galaxies
have a large fraction of dark or ``missing'' baryons (Slightly abridged)


  Determining the mathematical dynamics and associated parameter values that
should be used to accurately reflect tumor growth continues to be of interest
to mathematical modelers, experimentalists and practitioners. However, while
there are several competing canonical tumor growth models that are often
implemented, how to determine which of the models should be used for which
tumor types remains an open question. In this work, we determine the best fit
growth dynamics and associated parameter ranges for ten different tumor types
by fitting growth functions to at least five sets of published experimental
growth data per type of tumor. These time-series tumor growth data are used to
determine which of the five most common tumor growth models (exponential, power
law, logistic, Gompertz, or von Bertalanffy) provides the best fit for each
type of tumor.


  We propose a method for transforming probability distributions so that
parameters of interest are forced into a specified distribution. We prove that
this approach is the maximum entropy choice, and provide a motivating example
applicable to neutrino hierarchy inference.


  The cosmological constant is an unexplained until now phenomena of nature
that requires an explanation through string effects. The apparent discrepancy
between theory and experiment is enourmous and has already been explained
several times by the author including mechanisms. In this work the string
theory theory of abolished string modes is documented and given perturbatively
to all loop orders. The holographic underpinning is also exposed. The matching
with the data of the LIGO and D0 experiments is also explained to the first
three or more moments in the cosmological expansion.


  Specialized worker profiles of crowdsourcing platforms may contain a large
amount of identifying and possibly sensitive personal information (e.g.,
personal preferences, skills, available slots, available devices) raising
strong privacy concerns. This led to the design of privacy-preserving
crowdsourcing platforms, that aim at enabling efficient crowd-sourcing
processes while providing strong privacy guarantees even when the platform is
not fully trusted. In this paper, we propose two contributions. First, we
propose the PKD algorithm with the goal of supporting a large variety of
aggregate usages of worker profiles within a privacy-preserving crowdsourcing
platform. The PKD algorithm combines together homomorphic encryption and
differential privacy for computing (perturbed) partitions of the
multi-dimensional space of skills of the actual population of workers and a
(perturbed) COUNT of workers per partition. Second, we propose to benefit from
recent progresses in Private Information Retrieval techniques in order to
design a solution to task assignment that is both private and affordable. We
perform an in-depth study of the problem of using PIR techniques for proposing
tasks to workers, show that it is NP-Hard, and come up with the PKD PIR Packing
heuristic that groups tasks together according to the partitioning output by
the PKD algorithm. In a nutshell, we design the PKD algorithm and the PKD PIR
Packing heuristic, we prove formally their security against honest-but-curious
workers and/or platform, we analyze their complexities, and we demonstrate
their quality and affordability in real-life scenarios through an extensive
experimental evaluation performed over both synthetic and realistic datasets.


  Steve Gull, in unpublished work available on his Cambridge University
homepage, has outlined a proof of Bell's theorem using Fourier theory. Gull's
philosophy is that Bell's theorem (or perhaps a key lemma in its proof) can be
seen as a no-go theorem for a project in distributed computing with classical,
not quantum, computers. We present his argument, correcting misprints and
filling gaps. In his argument, there were two completely separated computers in
the network. We need three in order to fill all the gaps in his proof: a third
computer supplies a stream of random numbers to the two computers representing
the two measurement stations in Bell's work. One could also imagine that
computer replaced by a cloned, virtual computer, generating the same
pseudo-random numbers within each of Alice and Bob's computers. Either way, we
need an assumption of the presence of shared i.i.d. randomness in the form of a
synchronised sequence of realisations of i.i.d. hidden variables underlying the
otherwise deterministic physics of the sequence of trials. Gull's proof then
just needs a third step: rewriting an expectation as the expectation of a
conditional expectation given the hidden variables.


  In our previous paper, "A Unified Approach to Systemic Risk Measures via
Acceptance Set" (\textit{Mathematical Finance, 2018}), we have introduced a
general class of systemic risk measures that allow for random allocations to
individual banks before aggregation of their risks. In the present paper, we
prove the dual representation of a particular subclass of such systemic risk
measures and the existence and uniqueness of the optimal allocation related to
them. We also introduce an associated utility maximization problem which has
the same optimal solution as the systemic risk measure. In addition, the
optimizer in the dual formulation provides a \textit{risk allocation} which is
fair from the point of view of the individual financial institutions. The case
with exponential utilities which allows for explicit computation is treated in
details.


  Fix 2<n<\omega. Let L_n denote first order logic restricted to the first n
variables. CA_n denotes the class of cylindric algebras of dimension n and for
m>n, Nr_n\CA_m(\subseteq CA_n) denotes the class of n-neat reducts of CA_m's.
The existence of certain finite relation algebras and finite CA_n's lacking
relativized complete representations is shown to imply that the omitting types
theorem (OTT) fails for L_n with respect to clique guarded semantics (which is
an equivalent formalism of its packed fragments), and for the multi-dimensional
modal logic S5^n. Several such relation and cylindric algebras are explicitly
exhibited using rainbow constructions and Monk-like algebras. Certain CA_n
constructed to show non-atom canonicity of the variety S\Nr_n\CA_{n+3} are used
to show that Vaught's theorem (VT) for L_{\omega, \omega}, looked upon as a
special case of OTT for L_{\omega, \omega}, fails almost everywhere (a notion
to be defined below) when restricted to L_n. That VT fails everywhere for L_n,
which is stronger than failing almost everywhere as the name suggests, is
reduced to the existence, for each n<m<\omega, of a finite relation algebra R_m
having a so-called m-1 strong blur, but R_m has no m-dimensional relational
basis. VT for other modal fragments and expansions of L_n, like its guarded
fragments, n-products of uni-modal logics like K^n, and first order definable
expansions, is approached. It is shown that any multi-modal canonical logic L,
such that $K^n\subseteq L\subseteq S5^n$, L cannot be axiomatized by canonical
equations. In particular, L is not Sahlqvist. Elementary generation and
di-completeness for L_n and its clique guarded fragments are proved. Positive
omitting types theorems are proved for L_n with respect to standard semantics.


  We apply the objective method of Aldous to the problem of finding the
minimum-cost edge cover of the complete graph with random independent and
identically distributed edge costs. The limit, as the number of vertices goes
to infinity, of the expected minimum cost for this problem is known via a
combinatorial approach of Hessler and W\"{a}stlund. We provide a proof of this
result using the machinery of the objective method and local weak convergence,
which was used to prove the $\zeta(2)$ limit of the random assignment problem.
A proof via the objective method is useful because it provides us with more
information on the nature of the edge's incident on a typical root in the
minimum-cost edge cover. We further show that a belief propagation algorithm
converges asymptotically to the optimal solution. This can be applied in a
computational linguistics problem of semantic projection. The belief
propagation algorithm yields a near optimal solution with lesser complexity
than the known best algorithms designed for optimality in worst-case settings.


  The tensor terms of the Skyrme effective interaction are included in the
self-consistent Hartree-Fock plus Random Phase Approximation (HF+RPA) model.
The Gamow-Teller (GT) strength function of 90Zr and 208Pb are calculated with
and without the tensor terms. The main peaks are moved downwards by about 2 MeV
when including the tensor contribution. About 10% of the non-energy weighted
sum rule is shifted to the excitation energy region above 30 MeV by the RPA
tensor correlations. The contribution of the tensor terms to the energy
weighted sum rule is given analytically, and compared to the outcome of RPA.


  Deep convolutional neural networks (CNNs) trained for object classification
have a number of striking similarities with the primate ventral visual stream.
In particular, activity in early, intermediate, and late layers is closely
related to activity in V1, V4, and the inferotemporal cortex (IT). This study
further compares activity in late layers of object-classification CNNs to
activity patterns reported in the IT electrophysiology literature. There are a
number of close similarities, including the distributions of population
response sparseness across stimuli, and the distribution of size tuning
bandwidth. Statisics of scale invariance, responses to clutter and occlusion,
and orientation tuning are less similar. Statistics of object selectivity are
quite different. These results agree with recent studies that highlight strong
parallels between object-categorization CNNs and the ventral stream, and also
highlight differences that could perhaps be reduced in future CNNs.


  The limits of linear electrodynamics are reviewed, and possible directions of
nonlinear extension are explored. The central theme is that the qualitative
character of the empirical successes of quantum electrodynamics must be used as
a guide for understanding the nature of the nonlinearity of electrodynamics at
the subatomic level. Some established theories of nonlinear electrodynamics,
namely, those of Mie, Born, and Infeld are presented in the language of the
modern geometrical and topological methods of mathematical physics. The manner
by which spacetime curvature and topology can affect electromagnetism is also
reviewed. Finally, the phenomena of nonlinear optics are discussed as a
possible guide to building one's intuition regarding the process of extending
electrodynamics into nonlinearity in a manner that is consistent with the
qualitative and empirical results of quantum electrodynamics.


  For a prime $p,$ let $\mathbb{F}_q$ be a finite extension of $\mathbb{F}_p$
and $\mathcal{G}=\text{GL}_2(\mathbb{F}_q).$ Then the irreducible
representations of $\mathcal{G}$ are classified as twists of
Sym$^{\vec{r}}(\overline{\mathbb F}_p^2).$ The restriction of irreducibles of
$\mathcal{G}$ to its subgroup $G=\text{GL}_2(\mathbb{F}_p)$ is same as
investigating the behavior of the tensor product of irreducible representations
of $G.$ In this paper, we study the restriction of some of these
representations of $\mathcal{G}$ to $G,$ for $2$ and $3$ degree extensions of
$\mathbb{F}_p.$


  Robotic research encounters a significant hurdle when it comes to the
intricate task of grasping objects that come in various shapes, materials, and
textures. Unlike many prior investigations that heavily leaned on specialized
point-cloud cameras or abundant RGB visual data to gather 3D insights for
object-grasping missions, this paper introduces a pioneering approach called
RGBGrasp. This method depends on a limited set of RGB views to perceive the 3D
surroundings containing transparent and specular objects and achieve accurate
grasping. Our method utilizes pre-trained depth prediction models to establish
geometry constraints, enabling precise 3D structure estimation, even under
limited view conditions. Finally, we integrate hash encoding and a proposal
sampler strategy to significantly accelerate the 3D reconstruction process.
These innovations significantly enhance the adaptability and effectiveness of
our algorithm in real-world scenarios. Through comprehensive experimental
validations, we demonstrate that RGBGrasp achieves remarkable success across a
wide spectrum of object-grasping scenarios, establishing it as a promising
solution for real-world robotic manipulation tasks. The demonstrations of our
method can be found on: https://sites.google.com/view/rgbgrasp


  In this paper, we solve an optimal control problem governed by a system of
mean-field stochastic differential equations with multiple defaults (MMFSDEs).
We transform the global optimal control problem into several optimal control
subproblems governed by a system of mean-field stochastic differential
equations with single default (SMFSDEs) and derive both the sufficient and
necessary maximum principles for these subproblems. We also give the existence
and uniqueness of solutions to the MMFSDEs and the mean-field backward
stochastic differential equations with multiple defaults (MMFBSDEs),
respectively. Finally, as an example, our results are applied to obtain the
explicit solution for an optimal control problem whose cost function is
considered as a recursive utility process with multiple defaults.


  In this work the pure spinor formulation of the superstring is used to study
quantum corrections to the left current OPE algebra of the coset $PSU(2,
2|4)/SO(4, 1) \times SO(5)$ sigma model, which describes the superstring
dynamics in the $AdS_5 \times S^5$ background. In particular, the one loop
corrections to the simple poles of the bosonic currents are computed. Unlike
the case of the double poles, we show that the simple poles suffer corrections,
which are important since the simple poles contribute to the four point
amplitudes. We show that the only contribution to the simple poles comes from
the pure spinor Lorentz currents.