  We present a new optimization-based structure-preserving model order
reduction (MOR) method for port-Hamiltonian descriptor systems (pH-DAEs) with
differentiation index two. Our method is based on a novel parameterization that
allows us to represent any linear time-invariant pH-DAE with a minimal number
of parameters, which makes it well-suited to model reduction. We propose two
algorithms which directly optimize the parameters of a reduced model to
approximate a given large-scale model with respect to either the H-infinity or
the H-2 norm. This approach has several benefits. Our parameterization ensures
that the reduced model is again a pH-DAE system and enables a compact
representation of the algebraic part of the large-scale model, which in
projection-based methods often requires a more involved treatment. The direct
optimization is entirely based on transfer function evaluations of the
large-scale model and is therefore independent of the system matrices'
structure. Numerical experiments are conducted to illustrate the high accuracy
and small reduced model orders in comparison to other structure-preserving MOR
methods.


  We propose new continuous-time formulations for first-order stochastic
optimization algorithms such as mini-batch gradient descent and
variance-reduced methods. We exploit these continuous-time models, together
with simple Lyapunov analysis as well as tools from stochastic calculus, in
order to derive convergence bounds for various types of non-convex functions.
Guided by such analysis, we show that the same Lyapunov arguments hold in
discrete-time, leading to matching rates. In addition, we use these models and
Ito calculus to infer novel insights on the dynamics of SGD, proving that a
decreasing learning rate acts as time warping or, equivalently, as landscape
stretching.


  Motivated by the recent use of certain consistent truncations of M-theory to
study condensed matter physics using holographic techniques, we study the
SU(3)-invariant sector of four-dimensional, N=8 gauged supergravity and compute
the complete scalar spectrum at each of the five non-trivial critical points.
We demonstrate that the smaller SU(4)^- sector is equivalent to a consistent
truncation studied recently by various authors and find that the critical point
in this sector, which has been proposed as the ground state of a holographic
superconductor, is unstable due to a family of scalars that violate the
Breitenlohner-Freedman bound. We also derive the origin of this instability in
eleven dimensions and comment on the generalization to other embeddings of this
critical point which involve arbitrary Sasaki-Einstein seven manifolds. In the
spirit of a resurging interest in consistent truncations, we present a formal
treatment of the SU(3)-invariant sector as a U(1)xU(1) gauged N=2 supergravity
theory coupled to one hypermultiplet.


  The NOvA project is a long-baseline neutrino experiment. It utilizes the NuMI
neutrino beam at Fermilab and consists of two functionally-identical liquid
scintillator filled detectors. The detectors are placed 14 milliradians
off-axis from the beam and 810 km apart. A 209 ton prototype detector, the Near
Detector On the Surface (NDOS), was built and began taking initial neutrino
data in December 2010. NDOS is 110 milliradians off-axis from the NuMI beam and
also records neutrinos from the Booster Neutrino Beam. As NDOS is in the
commissioning phase, metrics are being developed to improve understanding of
the detector as well as monitor the quality of data. Performance of the
prototype detector will be presented.


  AMBER was installed in March 2004 in the VLTI focal lab of the VLT
observatory in Cerro Paranal run by ESO. Since then, there have been 4
commissioning runs and additional VLTI infrastructure installed (IRIS, FINITO
and ATs,...), but AMBER is not yet fulfilling all its initial specifications
and some important primary science objectives cannot be achieved. At the
consortium level, an action plan has been decided in Oct 2007 that created an
AMBER Task Force (ATF) to understand and possibly cure the eventual technical
issues. The objectives of the February 2008 run was mainly to bring AMBER into
contractual specifications the accuracy of the absolute visibility, of the
differential and of the closure phase through a fundamental analysis of the
instrument status and limitations. This report is the official report of the
AMBER Task Force.


  Consider an energy-harvesting receiver that uses the same received signal
both for decoding information and for harvesting energy, which is employed to
power its circuitry. In the scenario where the receiver has limited battery
size, a signal with bursty energy content may cause power outage at the
receiver since the battery will drain during intervals with low signal energy.
In this paper, we consider a discrete memoryless channel and characterize
achievable information rates when the energy content in each codeword is
regularized by ensuring that sufficient energy is carried within every subblock
duration. In particular, we study constant subblock-composition codes (CSCCs)
where all subblocks in every codeword have the same fixed composition, and this
subblock-composition is chosen to maximize the rate of information transfer
while meeting the energy requirement. Compared to constant composition codes
(CCCs), we show that CSCCs incur a rate loss and that the error exponent for
CSCCs is also related to the error exponent for CCCs by the same rate loss
term. We show that CSCC capacity can be improved by allowing different
subblocks to have different composition while still meeting the subblock energy
constraint. We provide numerical examples highlighting the tradeoff between
delivery of sufficient energy to the receiver and achieving high information
transfer rates. It is observed that the ability to use energy in real-time
imposes less of penalty than the ability to use information in real-time.


  Given a unitary representation of a finite group on a finite-dimensional
Hilbert space, we show how to find a state whose translates under the group are
distinguishable with the highest probability. We apply this to several quantum
oracle problems, including the GROUP MULTIPLICATION problem, in which the
product of an ordered $n$-tuple of group elements is to be determined by
querying elements of the tuple. For any finite group $G$, we give an algorithm
to find the product of two elements of $G$ with a single quantum query with
probability $2/|G|$. This generalizes Deutsch's Algorithm from $Z_2$ to an
arbitrary finite group. We further prove that this algorithm is optimal. We
also introduce the HIDDEN CONJUGATING ELEMENT PROBLEM, in which the oracle acts
by conjugating by an unknown element of the group. We show that for many
groups, including dihedral and symmetric groups, the unknown element can be
determined with probability $1$ using a single quantum query.


  Let F be a local non-archimedean field and let G be the group of F-valued
points of a reductive algebraic group over F. In this paper we compute the
Ext-groups of generalized Steinberg representations in the category of smooth
G-representations with coefficients in a certain self-injective ring.


  The so-called Whitham equation arises in the modeling of free surface water
waves, and combines a generic nonlinear quadratic term with the exact linear
dispersion relation for gravity waves on the free surface of a fluid with
finite depth.
  In this work, the effect of incorporating capillarity into the Whitham
equation is in focus. The capillary Whitham equation is a nonlocal equation
similar to the usual Whitham equation, but containing an additional term with a
coefficient depending on the Bond number T which measures the relative strength
of capillary and gravity effects on the wave motion.
  A spectral collocation scheme for computing approximations to periodic
traveling waves for the capillary Whitham equation is put forward. Numerical
approximations of periodic traveling waves are computed using a bifurcation
approach, and a number of bifurcation curves are found. Our analysis uncovers a
rich structure of bifurcation patterns, including subharmonic bifurcations, as
well as connecting and crossing branches. Indeed, for some values of the Bond
number T, the bifurcation diagram features distinct branches of solutions which
intersect at a secondary bifurcation point. The same branches may also cross
without connecting, and some bifurcation curves feature self-crossings without
self-connections.


  Let $\gamma'_s(G)$ be the signed edge domination number of G. In 2006, Xu
conjectured that: for any $2$-connected graph G of order $ n (n \geq 2),$
$\gamma'_s(G)\geq 1$. In this article we show that this conjecture is not true.
More precisely, we show that for any positive integer $m$, there exists an
$m$-connected graph $G$ such that $ \gamma'_s(G)\leq -\frac{m}{6}|V(G)|.$ Also
for every two natural numbers $m$ and $n$, we determine $\gamma'_s(K_{m,n})$,
where $K_{m,n}$ is the complete bipartite graph with part sizes $m$ and $n$.


  A variation of Rosenstock's trapping model in which $N$ independent random
walkers are all initially placed upon a site of a one-dimensional lattice in
the presence of a {\em one-sided} random distribution (with probability $c$) of
absorbing traps is investigated. The probability (survival probability)
$\Phi_N(t)$ that no random walker is trapped by time $t$ for $N \gg 1$ is
calculated by using the extended Rosenstock approximation. This requires the
evaluation of the moments of the number $S_N(t)$ of distinct sites visited in a
{\em given} direction up to time $t$ by $N$ independent random walkers. The
Rosenstock approximation improves when $N$ increases, working well in the range
$Dt\ln^2(1-c) \ll \ln N$, $D$ being the diffusion constant. The moments of the
time (lifetime) before any trapping event occurs are calculated asymptotically,
too. The agreement with numerical results is excellent.


  In these lectures I discuss the impact of soft hadronic physics on
predictions for B decays. Unfortunately our tools for calculating these effects
are limited; even after the use of the best available tools the resulting
theoretical uncertainties are difficult to delimit, and can obscure tests for
the presence of beyond-Standard-Model physics. The first lecture reviews what
tools are available, the second reviews in more detail two examples of how
these tools can be used.


  Over the past decade there has been a significant growth in bioinformatics
databases, tools and resources. Although, bioinformatics is becoming more
specific, increasing the number of bioinformatics-wares has made it difficult
for researchers to find the most appropriate databases, tools or methods which
match their needs. Our coordinated effort has been planned to establish a
reference website in Bioinformatics as a public repository of tools, databases,
directories and resources annotated with contextual information and organized
by functional relevance. Within the first phase of BioInfoBase development, 22
experts in different fields of molecular biology contributed and more than 2500
records were registered, which are increasing daily. For each record submitted
to the database of website almost all related data (40 features) has been
extracted. These include information from the biological category and
subcategory to the scientific article and developer information. Searching the
query keyword(s) returns links containing the entered keyword(s) found within
the different features of the records with more weights on the title, abstract
and application fields. The search results simply provide the users with the
most informative features of the records to select the most suitable ones. The
usefulness of the returned results is ranked according to the matching score
based on the Term Frequency-Inverse Document Frequency (TF-IDF) methods.
Therefore, this search engine will screen a comprehensive index of
bioinformatics tools, databases and resources and provide the best suited
records (links) to the researchers need. The BioInfoBase resource is available
at www.bioinfobase.info.


  Based on a talk given at the Pomeranchuk memorial conference at ITEP in June
2013, we review the vacuum dynamics in 3d supersymmetric
Yang-Mills-Chern-Simons theories with and without extra matter multiplets. By
analyzing the effective Born-Oppenheimer Hamiltonian in a small spatial box, we
calculate the number of vacuum states (Witten index) and examine their
structure for these theories. The results are identical to those obtained by
other methods.


  The evolutionary significance of hybridization and subsequent introgression
has long been appreciated, but evaluation of the genome-wide effects of these
phenomena has only recently become possible. Crop-wild study systems represent
ideal opportunities to examine evolution through hybridization. For example,
maize and the conspecific wild teosinte Zea mays ssp. mexicana, (hereafter,
mexicana) are known to hybridize in the fields of highland Mexico. Despite
widespread evidence of gene flow, maize and mexicana maintain distinct
morphologies and have done so in sympatry for thousands of years. Neither the
genomic extent nor the evolutionary importance of introgression between these
taxa is understood. In this study we assessed patterns of genome-wide
introgression based on 39,029 single nucleotide polymorphisms genotyped in 189
individuals from nine sympatric maize-mexicana populations and reference
allopatric populations. While portions of the maize and mexicana genomes were
particularly resistant to introgression (notably near known
cross-incompatibility and domestication loci), we detected widespread evidence
for introgression in both directions of gene flow. Through further
characterization of these regions and preliminary growth chamber experiments,
we found evidence suggestive of the incorporation of adaptive mexicana alleles
into maize during its expansion to the highlands of central Mexico. In
contrast, very little evidence was found for adaptive introgression from maize
to mexicana. The methods we have applied here can be replicated widely, and
such analyses have the potential to greatly informing our understanding of
evolution through introgressive hybridization. Crop species, due to their
exceptional genomic resources and frequent histories of spread into sympatry
with relatives, should be particularly influential in these studies.


  In this paper, we propose a general framework for distribution-free
nonparametric testing in multi-dimensions, based on a notion of multivariate
ranks defined using the theory of measure transportation. Unlike other existing
proposals in the literature, these multivariate ranks share a number of useful
properties with the usual one-dimensional ranks; most importantly, these ranks
are distribution-free. This crucial observation allows us to design
nonparametric tests that are exactly distribution-free under the null
hypothesis. We demonstrate the applicability of this approach by constructing
exact distribution-free tests for two classical nonparametric problems: (i)
testing for mutual independence between random vectors, and (ii) testing for
the equality of multivariate distributions. In particular, we propose
(multivariate) rank versions of distance covariance (Sz\'ekely et al., 2007)
and energy statistic (Sz\'ekely and Rizzo, 2013) for testing scenarios (i) and
(ii) respectively. In both these problems, we derive the asymptotic null
distribution of the proposed test statistics. We further show that our tests
are consistent against all fixed alternatives. Moreover, the proposed tests are
tuning-free, computationally feasible and are well-defined under minimal
assumptions on the underlying distributions (e.g., they do not need any moment
assumptions). We also demonstrate the efficacy of these procedures via
extensive simulations. In the process of analyzing the theoretical properties
of our procedures, we end up proving some new results in the theory of measure
transportation and in the limit theory of permutation statistics using Stein's
method for exchangeable pairs, which may be of independent interest.


  Big data is no more "all just hype" but widely applied in nearly all aspects
of our business, governments, and organizations with the technology stack of
AI. Its influences are far beyond a simple technique innovation but involves
all rears in the world. This chapter will first have historical review of big
data; followed by discussion of characteristics of big data, i.e. from the 3V's
to up 10V's of big data. The chapter then introduces technology stacks for an
or-ganization to build a big data application, from
infrastruc-ture/platform/ecosystem to constructional units and components.
Finally, we provide some big data online resources for reference.


  In this article we present the post-Newtonian (pN) coefficients of the energy
flux (and angular momentum flux) at infinity and event horizon for a particle
in circular, equatorial orbits about a Kerr black hole (of mass $M$ and
spin-parameter $a$) up to 20-pN order. When a pN term is not a polynomial in
$a/M$ and includes irrational functions (like polygamma functions), it is
written as a power series of $a/M$. This is achieved by calculating the fluxes
numerically with an accuracy greater than 1 part in $10^{600}$. Such high
accuracy allows us to extract analytical values of pN coefficients that are
linear combinations of transcendentals like the Euler constant, logarithms of
prime numbers and powers of $\pi$. We also present the 22-pN expansion
(spin-independent pN expansion) of the ingoing energy flux at the event horizon
for a particle in circular orbit about a Schwarzschild black hole.


  After the prediction that strong enough optical activity may result in
negative refraction and negative reflection, more and more artificial chiral
metamaterials were designed and fabricated at difference frequency ranges from
microwaves to optical waves. Therefore, a simple and robust method to retrieve
the effective constitutive parameters for chiral metamaterials is urgently
needed. Here, we analyze the wave propagation in chiral metamaterials and
follow the regular retrieval procedure for ordinary metamaterials and apply it
in chiral metamaterial slabs. Then based on the transfer matrix technique, the
parameter retrieval is extended to treat samples with not only the substrate
but also the top layers. After the parameter retrieval procedure, we take two
examples to check our method and study how the substrate influences on the thin
chiral metamaterials slabs. We find that the substrate may cause the
homogeneous slab to be inhomogeneous, i.e. the reflections in forward and
backward directions are different. However, the chiral metamaterial where the
resonance element is embedded far away from the substrate is insensitive to the
substrate.


  Statistical evaluations of the economic mobility of a society are more
difficult than measurements of the income distribution, because they require to
follow the evolution of the individuals' income for at least one or two
generations. In micro-to-macro theoretical models of economic exchanges based
on kinetic equations, the income distribution depends only on the asymptotic
equilibrium solutions, while mobility estimates also involve the detailed
structure of the transition probabilities of the model, and are thus an
important tool for assessing its validity. Empirical data show a remarkably
general negative correlation between economic inequality and mobility, whose
explanation is still unclear. It is therefore particularly interesting to study
this correlation in analytical models. In previous work we investigated the
behavior of the Gini inequality index in kinetic models in dependence on
several parameters which define the binary interactions and the taxation and
redistribution processes: saving propensity, taxation rates gap, tax evasion
rate, welfare means-testing etc. Here, we check the correlation of mobility
with inequality by analyzing the mobility dependence from the same parameters.
According to several numerical solutions, the correlation is confirmed to be
negative.


  A search for anomalous single-top production, ep -> etX, t -> Wb, has been
made with the ZEUS detector at HERA using an integrated luminosity of 130
pb^-1. No evidence for top-quark production was found in either the leptonic or
the hadronic decay channel of the W boson. The resulting constraints on
single-top production via quark-flavour changing neutral current (FCNC)
transitions exclude a substantial region in the FCNC t-u-gamma coupling not
ruled out by other experiments.


  The Spallation Neutron Source (SNS) is being designed, constructed, installed
and commissioned by the staff of six national laboratories, Argonne National
Laboratory, Brookhaven National Laboratory, Jefferson National Accelerator
Laboratory, Lawrence Berkeley National Laboratory, Los Alamos National
Laboratory, and Oak Ridge National Laboratory. The accelerator systems are
designed to deliver a 695 ns proton-pulse onto a mercury target at a 60-Hz
repetition rate and an average power of 2-MW. Neutron moderators that will
convert the spallation neutrons into slow neutrons for material science
research will surround the target. The Front-End systems are designed to
generate an H- beam of minipulses, 68% beam on, 32% beam off every 965 ns, at
2.5 MeV for 1 ms, 60 times a second. The Front-End systems include a RF driven,
volume-production ion source, beam chopping system, RFQ, and beam transport.
The ion source will have to achieve about 65 mA to deliver 52 mA at the input
to the linac. The linac consists of a drift tube linac up to 86.8 MeV, a
coupled-cell linac to 185 MeV, and a superconducting RF linac to the nominal
energy of 1 GeV. The design of the superconducting section includes 11
cryomodules with three, 0.61-beta cavities per cryomodule and 17 cryomodules
with four, 0.81-beta cavities per cryomodule, with space to install four more
0.81-beta cryomodules. The accumulator ring is designed for charge exchange
injection at full energy. The peak charge per bunch at the end of the
accumulation cycle will reach 2.08x10**14 for 2-MW operation. The goal is to
control beam losses to less than 1x10**-4.


  Let $S(a,b)=12s(a,b)$, where $s(a,b)$ denotes the classical Dedekind sum. In
a recent note E. Tsukerman gave a necessary and sufficient condition for
$S(a_1,b)-S(a_2,b)\in 8\mathbb Z$. In the present paper we show that this
condition is equivalent to $S(a_1,b)-S(a_2,b)\in 24\mathbb Z$, provided that
$9\nmid b$. Tsukerman also obtained a congruence mod 8 for $bT(a,b)$, where
$T(a,b)$ is the alternating sum of the partial quotients of the continued
fraction expansion of $a/b$. We show that the respective congruence holds mod
$24$ if $3\nmid b$ and mod $72$ if $3\mid b$.


  We train embodied agents to play Visual Hide and Seek where a prey must
navigate in a simulated environment in order to avoid capture from a predator.
We place a variety of obstacles in the environment for the prey to hide behind,
and we only give the agents partial observations of their environment using an
egocentric perspective. Although we train the model to play this game from
scratch, experiments and visualizations suggest that the agent learns to
predict its own visibility in the environment. Furthermore, we quantitatively
analyze how agent weaknesses, such as slower speed, effect the learned policy.
Our results suggest that, although agent weaknesses make the learning problem
more challenging, they also cause more useful features to be learned. Our
project website is available at: http://www.cs.columbia.edu/
~bchen/visualhideseek/.


  The experimental thermal neutron cross sections of the twenty proteinogenic
amino acids have been measured over the incident-neutron energy range spanning
from 1 meV to 10 keV and data have been interpreted using the multi-phonon
expansion based on first-principles calculations. The scattering cross section,
dominated by the incoherent inelastic contribution from the hydrogen atoms, can
be rationalised in terms of the average contributions of different functional
groups, thus neglecting their correlation. These results can be used for
modelling the total neutron cross sections of complex organic systems like
proteins, muscles, or human tissues from a limited number of starting input
functions. This simplification is of crucial importance for fine-tuning of
transport simulations used in medical applications, including boron neutron
capture therapy as well as secondary neutrons-emission induced during proton
therapy. Moreover, the parametrized neutron cross sections allow a better
treatment of neutron scattering experiments, providing detailed sample
self-attenuation corrections for a variety of biological and soft-matter
systems.


  We study the azimuthal asymmetries in proton-proton Drell-Yan processes with
one incident proton being transversely or longitudinally polarized. We consider
particularly the asymmetries contributed by the leading-twist chiral-odd quark
distributions. We analyze the asymmetries with $\sin(2\phi+\phi_S)$ and
$\sin(2\phi-\phi_S)$ modulations in transverse single polarized $p^\uparrow p$
Drell-Yan and $\sin2\phi$ asymmetries in longitudinal single polarized
$p^\rightarrow p$ Drell-Yan at RHIC, J-PARC, E906 (Fermi Lab) and NICA (JINR).
We show that the measurements of the asymmetries in those facilities can
provide valuable information of the chiral-odd structure of the nucleon both in
the valence and sea regions.


  The program Ortocartan for algebraic calculations in relativity has just been
implemented in the Codemist Standard Lisp and can now be used under the Windows
98 and Linux operating systems. The paper describes the new facilities and
subprograms that have been implemented since the previous release in 1992.
These are: the possibility to write the output as Latex input code and as
Ortocartan's input code, the calculation of the Ellis evolution equations for
the kinematic tensors of flow, the calculation of the curvature tensors from
given (torsion-free) connection coefficients in a manifold of arbitrary
dimension, the calculation of the lagrangian from a given metric by the
Landau-Lifshitz method, the calculation of the Euler-Lagrange equations from a
given lagrangian (only for sets of ordinary differential equations) and the
calculation of first integrals of sets of ordinary differential equations of
second order (the first integrals are assumed to be polynomials of second
degree in the first derivatives of the functions).


  The dynamics of induced fission of $^{226}$Th is investigated in a
theoretical framework based on the finite-temperature time-dependent generator
coordinate method (TDGCM) in the Gaussian overlap approximation (GOA). The
thermodynamical collective potential and inertia tensor at temperatures in the
interval $T=0 - 1.25$ MeV are calculated using the self-consistent
multidimensionally constrained relativistic mean field (MDC-RMF) model, based
on the energy density functional DD-PC1. Pairing correlations are treated in
the BCS approximation with a separable pairing force of finite range.
Constrained RMF+BCS calculations are carried out in the collective space of
axially symmetric quadrupole and octupole deformations for the asymmetric
fissioning nucleus $^{226}$Th. The collective Hamiltonian is determined by the
temperature-dependent free energy surface and perturbative cranking inertia
tensor, and the TDGCM+GOA is used to propagate the initial collective state in
time. The resulting charge and mass fragment distributions are analyzed as
functions of the internal excitation energy. The model can qualitatively
reproduce the empirical triple-humped structure of the fission charge and mass
distributions already at $T=0$, but the precise experimental position of the
asymmetric peaks and the symmetric-fission yield can only be accurately
reproduced when the potential and inertia tensor of the collective Hamiltonian
are determined at finite temperature, in this particular case between $T=0.75$
MeV and $T=1$ MeV.


  Motivated by recent experiments on colloidal suspensions, we study
analytically and numerically a microscopic model for self-propelled particles
lacking alignment interactions. In this model, even for purely repulsive
interactions, a dynamical instability leading to phase separation has been
reported. Starting from the many-body Smoluchowski equation, we develop a
mean-field description based on a novel closure scheme and derive the effective
hydrodynamic equations. We demonstrate that the microscopic origin of the
instability is a force imbalance due to an anisotropic pair distribution
leading to self-trapping. The phase diagram can be understood in terms of two
quantities: a minimal drive and the force imbalance. At sufficiently high
propulsion speeds there is a reentrance into the disordered fluid.


  J. Beck has shown that if two players alternately select previously unchosen
points from the plane, Player 1 can always build a congruent copy of any given
finite goal set G, in spite of Player 2's efforts to stop him. We give a finite
goal set G (it has 5 points) which Player 1 cannot construct before Player 2 in
this achievement game played in the plane.


  Combining first-principles calculations and spin- and angle-resolved
photoemission spectroscopy measurements, we identify the helical spin textures
for three different Dirac cone states in the interfaced systems of a 2D
topological insulator (TI) of Bi(111) bilayer and a 3D TI Bi2Se3 or Bi2Te3. The
spin texture is found to be the same for the intrinsic Dirac cone of Bi2Se3 or
Bi2Te3 surface state, the extrinsic Dirac cone of Bi bilayer state induced by
Rashba effect, and the hybridized Dirac cone between the former two states.
Further orbit- and atom-resolved analysis shows that s and pz orbits have a
clockwise (counterclockwise) spin rotation tangent to the iso-energy contour of
upper (lower) Dirac cone, while px and py orbits have an additional radial spin
component. The Dirac cone states may reside on different atomic layers, but
have the same spin texture. Our results suggest that the unique spin texture of
Dirac cone states is a signature property of spin-orbit coupling, independent
of topology.


  In the continuum, the single flavor massless Schwinger model has an exact
global axial $U(1)$ symmetry in the sector of perturbative gauge fields. This
symmetry is explicitly broken by gauge fields with nonzero topological charge
inducing a nonzero expectation value for the bilinear $\bar\psi\psi$. We show
that a lattice formulation of this model, using the overlap formalism to treat
the massless fermions, explicitly exhibits this phenomenon. A Monte Carlo
simulation of the complete system yields the correct value of the fermion
condensate and shows unambiguously that it originates from the sector of
topological charge equal to unity.


  We address a problem which is mathematically reminiscent of the one of
Anderson localization, although it is related to a strongly dissipative
dynamics. Specifically, we study thermal convection in a horizontal porous
layer heated from below in the presence of a parametric disorder; physical
parameters of the layer are time-independent and randomly inhomogeneous in one
of the horizontal directions. Under such a frozen parametric disorder,
spatially localized flow patterns appear. We focus our study on their
localization properties and the effect of an imposed advection along the layer
on these properties. Our interpretation of the results of the linear theory is
underpinned by numerical simulation for the nonlinear problem. Weak advection
is found to lead to an upstream delocalization of localized current patterns.
Due to this delocalization, the transition from a set of localized patterns to
an almost everywhere intense "global" flow can be observed under conditions
where the disorder-free system would be not far below the instability
threshold. The results presented are derived for a physical system which is
mathematically described by a modified Kuramoto-Sivashinsky equation and
therefore they are expected to be relevant for a broad variety of dissipative
media where pattern selection occurs.


  We have implemented the Memento MediaWiki Extension Version 2.0, which brings
the Memento Protocol to MediaWiki, used by Wikipedia and the Wikimedia
Foundation. Test results show that the extension has a negligible impact on
performance. Two 302 status code datetime negotiation patterns, as defined by
Memento, have been examined for the extension: Pattern 1.1, which requires 2
requests, versus Pattern 2.1, which requires 3 requests. Our test results and
mathematical review find that, contrary to intuition, Pattern 2.1 performs
better than Pattern 1.1 due to idiosyncrasies in MediaWiki. In addition to
implementing Memento, Version 2.0 allows administrators to choose the optional
200-style datetime negotiation Pattern 1.2 instead of Pattern 2.1. It also
permits administrators the ability to have the Memento MediaWiki Extension
return full HTTP 400 and 500 status codes rather than using standard MediaWiki
error pages. Finally, version 2.0 permits administrators to turn off
recommended Memento headers if desired. Seeing as much of our work focuses on
producing the correct revision of a wiki page in response to a user's datetime
input, we also examine the problem of finding the correct revisions of the
embedded resources, including images, stylesheets, and JavaScript; identifying
the issues and discussing whether or not MediaWiki must be changed to support
this functionality.


  With advances in emerging technologies, options for operating public transit
services have broadened from conventional fixed-route service through
semi-flexible service to on-demand microtransit. Nevertheless, guidelines for
deciding between these services remain limited in the real implementation. An
open-source simulation sandbox is developed that can compare
state-of-the-practice methods for evaluating between the different types of
public transit operations. For the case of the semi-flexible service, the
Mobility Allowance Shuttle Transit (MAST) system is extended to include
passenger deviations. A case study demonstrates the sandbox to evaluate and
existing B63 bus route in Brooklyn, NY and compares its performance with the
four other system designs spanning across the three service types for three
different demand scenarios.


  We provide conjectural necessary and (separately) sufficient conditions for
the Hilbert scheme of points of a given length to have the maximum dimension
tangent space at a point. The sufficient condition is claimed for 3D and
reduces the original problem to a problem in convex geometry. Proving either of
the two conjectural statements will in particular resolve a long-standing
conjecture by Brian\c{c}on and Iarrobino back in the '70s for the case of the
powers of the maximal ideal. Furthermore, for specific classes of lengths, we
conjecturally classify points satisfying the conjectural sufficient conditions.
This in particular (conjecturally) provides many new explicit families of
examples of maximum dimension tangent space at a point of the Hilbert schemes
of points of lengths strictly between two consecutive tetrahedral numbers ${3+k
\choose 3}$.


  The Schmidt decomposition is an important tool in the study of quantum
systems especially for the quantification of the entanglement of pure states.
However, the Schmidt decomposition is only unique for bipartite pure states,
and some multipartite pure states. Here a generalized Schmidt decomposition is
given for states which are equivalent to depolarized pure states. Experimental
methods for the identification of this class of mixed states are provided and
some examples are discussed which show the utility of this description. A
particularly interesting example provides, for the first time, an
interpretation of the number of negative eigenvalues of the density matrix.


  Spatial heterogeneity in the elastic properties of soft random solids is
investigated via a two-pronged approach. First, a nonlocal phenomenological
model for the elastic free energy is examined. This features a quenched random
kernel, which induces randomness in the residual stress and Lame coefficients.
Second, a semi-microscopic model network is explored using replica statistical
mechanics. The Goldstone fluctuations of the semi-microscopic model are shown
to reproduce the phenomenological model, and via this correspondence the
statistical properties of the residual stress and Lame coefficients are
inferred. Correlations involving the residual stress are found to be
long-ranged and governed by a universal parameter that also gives the mean
shear modulus.


  We present new results of fully general relativistic magnetohydrodynamic
simulations of binary neutron star (BNS) mergers performed with the Whisky
code. All the models use a piecewise polytropic approximation of the APR4
equation of state for cold matter, together with a 'hybrid' part to incorporate
thermal effects during the evolution. We consider both equal and unequal-mass
models, with total masses such that either a supramassive NS or a black hole is
formed after merger. Each model is evolved with and without a magnetic field
initially confined to the stellar interior. We present the different
gravitational wave (GW) signals as well as a detailed description of the matter
dynamics (magnetic field evolution, ejected mass, post-merger remnant/disk
properties). Our simulations provide new insights into BNS mergers, the
associated GW emission and the possible connection with the engine of short
gamma-ray bursts (both in the 'standard' and in the 'time-reversal' scenarios)
and other electromagnetic counterparts.


  It is often desirable to be able to recognize when inputs to a recognition
function learned in a supervised manner correspond to classes unseen at
training time. With this ability, new class labels could be assigned to these
inputs by a human operator, allowing them to be incorporated into the
recognition function --- ideally under an efficient incremental update
mechanism. While good algorithms that assume inputs from a fixed set of classes
exist, e.g., artificial neural networks and kernel machines, it is not
immediately obvious how to extend them to perform incremental learning in the
presence of unknown query classes. Existing algorithms take little to no
distributional information into account when learning recognition functions and
lack a strong theoretical foundation. We address this gap by formulating a
novel, theoretically sound classifier --- the Extreme Value Machine (EVM). The
EVM has a well-grounded interpretation derived from statistical Extreme Value
Theory (EVT), and is the first classifier to be able to perform nonlinear
kernel-free variable bandwidth incremental learning. Compared to other
classifiers in the same deep network derived feature space, the EVM is accurate
and efficient on an established benchmark partition of the ImageNet dataset.


  When $G(z)$ is a power series in $z$, many authors now write `$[z^n] G(z)$'
for the coefficient of $z^n$ in $G(z)$, using a notation introduced by Goulden
and Jackson in [\GJ, p. 1]. More controversial, however, is the proposal of the
same authors [\GJ, p. 160] to let `$[z^n/n!] G(z)$' denote the coefficient of
$z^n/n!$, i.e., $n!$ times the coefficient of $z^n$. An alternative
generalization of $[z^n] G(z)$, in which we define $[F(z)] G(z)$ to be a linear
function of both $F$ and $G$, seems to be more useful because it facilitates
algebraic manipulations. The purpose of this paper is to explore some of the
properties of such a definition. The remarks are dedicated to Tony Hoare
because of his lifelong interest in the improvement of notations that
facilitate manipulation.


  Motivated by recent physical interpretation on quasinormal modes presented by
Maggiore, the adiabatic quantity method given by Kunstatter is used to
calculate the spectrums of a non-extremal Schwarzschild de Sitter black hole in
this paper, as well as electrically charged case. According to highly damped
Konoplya and Zhidenko's numerical observational results for high overtone
modes\cite{Konoplya}, we found that the asymptotic non-flat spacetime structure
leads two interesting facts as followings: (i) near inner event horizon, the
area and entropy spectrums, which are given by $A_{en} = 8 n_1 \pi \hbar$,
$S_{en} = 2\pi n_1\hbar$, are equally spaced accurately. (ii) However, near
outer cosmological horizon the spectrums, which are in the form of $A_{cn} = 16
n_2 \pi \hbar - \sqrt{\frac{48\pi}{\Lambda}A_{cn} - 3 A_{cn}^2}$, $S_{cn} = 4
\pi n_2 \hbar - \sqrt{\frac{3\pi}{\Lambda}A_{cn} - 3/16 A_{cn}^2}$, are not
markedly equidistant. Finally, we also discuss the electrically charged case
and find the black holes in de Sitter spacetime have similar quantization
behavior no matter with or without charge.


  We investigate the peculiar velocities predicted for galaxy clusters by
theories in the cold dark matter family. A widely used hypothesis identifies
rich clusters with high peaks of a suitably smoothed version of the linear
density fluctuation field. Their peculiar velocities are then obtained by
extrapolating the similarly smoothed linear peculiar velocities at the
positions of these peaks. We test these ideas using large high resolution
N-body simulations carried out within the Virgo supercomputing consortium. We
find that at early times the barycentre of the material which ends up in a rich
cluster is generally very close to a high peak of the initial density field.
Furthermore the mean peculiar velocity of this material agrees well with the
linear value at the peak. The late-time growth of peculiar velocities is,
however, systematically underestimated by linear theory. At the time clusters
are identified we find their rms peculiar velocity to be about 40% larger than
predicted. Nonlinear effects are particularly important in superclusters. These
systematics must be borne in mind when using cluster peculiar velocities to
estimate the parameter combination $\sigma_8\Omega^{0.6}$.


  A new result in convex analysis on the calculation of proximity operators in
certain scaled norms is derived. We describe efficient implementations of the
proximity calculation for a useful class of functions; the implementations
exploit the piece-wise linear nature of the dual problem. The second part of
the paper applies the previous result to acceleration of convex minimization
problems, and leads to an elegant quasi-Newton method. The optimization method
compares favorably against state-of-the-art alternatives. The algorithm has
extensive applications including signal processing, sparse recovery and machine
learning and classification.


  We prove that an interesting result concerning generalized Hyers-Ulam-Rassias
stability of a linear functional equation obtained in 2014 by S.M. Jung, D.
Popa and M.T. Rassias in Journal of Global Optimization is a particular case of
a fixed point theorem given by us in 2012. Moreover, we give a characterization
of functions that can be approximated with a given error, by the solution of
the previously mention linear equation.


  In today's digital age, online communities have become an integral part of
our lives, fostering collaboration, knowledge sharing, and community
engagement. Higher education institutions, in particular, can greatly benefit
from dedicated platforms that facilitate academic discussions and provide
incentives for active participation. This research paper presents a
comprehensive study and implementation of a decentralized application (DApp)
leveraging the blockchain technology to address these needs specifically for
E-JUST (Egypt-Japan University of Science and Technology) students and academic
staff.


  The Main Injector Neutrino Oscillation search (MINOS) uses two detectors
separated by 735km to measure a beam of neutrinos created by the Neutrinos at
the Main Injector (NuMI) facility at Fermi National Accelerator Laboratory. The
experiment has recently reported an observation of muon-neutrino disappearance
consistent with neutrino oscillations. We describe the manner in which the
experiment's results depend on the correct understanding and modeling of
hadronic systems.


  The risk of a financial position shines through by means of the fluctuation
of its market price. The factors affecting the price of a financial position
include not only market internal factors, but also other various market
external factors. The latter can be understood as sorts of environments to
which financial positions have to expose. Motivated by this observation, this
paper aims to design a novel axiomatic approach to risk measures in random
environments. We construct a new distortion-type risk measure, which can
appropriately evaluate the risk of financial positions in the presence of
environments. After having studied its fundamental properties, we also
axiomatically characterize it by proposing a novel set of axioms. Furthermore,
its coherence and dual representation are investigated. The new class of risk
measures in random environments is rich enough, for example, it not only can
recover some known risk measures such as the common weighted value at risk and
range value at risk, but also can induce other new specific risk measures such
as risk measures in the presence of background risk. Examples are given to
illustrate the new framework of risk measures. This paper gives some
theoretical results about risk measures in random environments, helping one to
have an insight look at the potential impact of environments on risk measures
of positions.


  The forward scattering amplitude of a small dipole at high energies is given
in the mean field approximation by the Balitsky-Kovchegov (BK) evolution
equation. It requires an initial condition $N(r; x_0)$ describing the
scattering of a dipole with size $r$ off the target that is probed at momentum
fraction $x_0$. Rather than using ad hoc parameterizations tuned to high-energy
data at $x\ll x_0$, here we attempt to construct an initial scattering
amplitude that is consistent with low-energy, large-$x$ properties of the
proton. We start from a non-perturbative three quark light-cone model wave
function from the literature. We add ${\cal O}(g)$ corrections due to the
emission of a gluon, and ${\cal O}(g^2)$ virtual corrections due to the
exchange of a gluon, computed in light-cone perturbation theory with exact
kinematics. We provide numerical data as well as analytic parameterizations of
the resulting $N(r; x_0)$ for $x_0=0.01 - 0.05$. Solving the BK equation in the
leading logarithmic (LL) approximation towards lower $x$, we obtain a fair
description of the charm cross section in deeply inelastic scattering measured
at HERA by fitting one parameter, the coupling constant $\alpha_s\simeq 0.2$.
However, without the option to tune the initial amplitude at $x_0$, the fit of
the high precision data results in $\chi^2/N_\text{dof} = 2.3$ at $N_\text{dof}
=38$, providing clear statistical evidence for the need of systematic
improvement e.g. of the photon wave function, evolution equation, and initial
condition.


  The measurement of the pion form factor and, more generally, of the cross
section for electron--positron annihilation into hadrons through the radiative
return has become an important task for high luminosity colliders such as the
$\Phi$- or $B$-meson factories. This quantity is crucial for predictions of the
hadronic contributions to $(g-2)_\mu$, the anomalous magnetic moment of the
muon, and to the running of the electromagnetic coupling. But the radiative
return opens also the possibility of many other physical applications. The
physics potential of this method at high luminosity meson factories is
discussed and recent results are reviewed.


  Multi-field inflation models include a variety of scenarios for how inflation
proceeds and ends. Models with the same potential but different kinetic terms
are common in the literature. We compare spiral inflation and Dante's
inferno-type models, which differ only in their field-space metric. We justify
a single-field effective description in these models and relate the
single-field description to a mass-matrix formalism. We note the effects of the
nontrivial field-space metric on inflationary observables, and consequently on
the viability of these models. We also note a duality between spiral inflation
and Dante's inferno models with different potentials.


  We construct a new version of the effective average action together with its
flow equation. The construction entails in particular the consistency of
fluctuation field and background field equations of motion, even for finite
renormalization group scales. Here we focus on the quantum gravity application,
while the generalization of this idea to gauge theories is obvious. Our
approach has immediate impact on the background field approximation, which is
the most prominent approximation scheme within the asymptotic safety scenario.
We outline the calculation of quantum gravity observables from first principles
using the new effective average action.


  We discuss a duel-type game in which Player I uses his resource continuously
and Player II distributes it by discrete portions. Each player knows how much
resources he and his opponent have at every moment of time. The solution of the
game is given in an explicit form.
  Keywords: noisy duel, payoff, strategy, the value of a game, consumption of
resource.


  Ozel, in a recent reanalysis of EXO 0748-676 observational data
(astro-ph/0605106), concluded that quark matter probably does not exist in the
center of compact stars. We show that the data is actually consistent with the
presence of quark matter in compact stars.


  Generalized linear statistics are an unifying class that contains
U-statistics, U-quantiles, L-statistics as well as trimmed and winsorized
U-statistics. For example, many commonly used estimators of scale fall into
this class. GL-statistics only have been studied under independence; in this
paper, we develop an asymptotic theory for GL-statistics of sequences which are
strongly mixing or L^1 near epoch dependent on an absolutely regular process.
For this purpose, we prove an almost sure approximation of the empirical
U-process by a Gaussian process. With the help of a generalized Bahadur
representation, it follows that such a strong invariance principle also holds
for the empirical U-quantile process and consequently for GL-statistics. We
obtain central limit theorems and laws of the iterated logarithm for
U-processes, U-quantile processes and GL-statistics as straightforward
corollaries.


  We highlight recent progresses in the study of the Weil-Petersson (WP)
geometry of finite dimensional Teichm\"{u}ller spaces. For recent progress on
and the understanding of infinite dimensional Teichm\"{u}ller spaces the reader
is directed to the recent work of Teo-Takhtajan. As part of the highlight, we
also present possible directions for future investigations.


  Since graphene, a single sheet of graphite, has all of its carbon atoms on
the surface, its property is very sensitive to materials contacting the
surface. Herein, we report novel Raman peaks ob-served in annealed graphene and
elucidate their chemical origins by Raman spectroscopy and atomic force
microscopy (AFM). Graphene annealed in oxygen-free atmosphere revealed very
broad additional Raman peaks overlapping the D, G and 2D peaks of graphene
itself. Based on the topographic confirmation by AFM, the new Raman peaks were
attributed to amorphous carbon formed on the surface of graphene by
carbonization of environmental hydrocarbons. While the carbonaceous layers were
formed for a wide range of annealing temperature and time, they could be
effectively removed by prolonged annealing in vacuum. This study underlines
that spectral features of graphene and presumably other 2-dimensional
ma-terials are highly vulnerable to interference by foreign materials of
molecular thickness.


  Jumping of coalescing condensate droplets from superhydrophobic surfaces is
an interesting phenomenon which yields marked heat transfer enhancement over
the more explored gravity-driven droplet removal mode in surface condensation,
a phase change process of central interest to applications ranging from energy
to water harvesting. However, when condensate microdroplets coalesce, they can
also spontaneously propel themselves omnidirectionally on the surface
independent of gravity and grow by feeding from droplets they sweep along the
way. Here we observe and explain the physics behind this phenomenon of roaming
of coalescing condensate microdroplets on solely nanostructured
superhydrophobic surfaces, where the microdroplets are orders of magnitude
larger than the underlaying surface nanotexture. We quantify and show that it
is the inherent asymmetries in droplet adhesion during condensation, arising
from the stochastic nature of nucleation within the nanostructures, that
generates the tangential momentum driving the roaming motion. Subsequent
dewetting during this conversion initiates a vivid roaming and successive
coalescence process, preventing condensate flooding of the surface, and
enhancing surface renewal. Finally, we show that the more efficient conversion
process of roaming from excess surface energy to kinetic energy results in
significantly improved heat transfer efficiency over condensate droplet
jumping, the mechanism currently understood as maximum.


  Quantitative formulations of Fefferman's counterexample for the ball
multiplier are naturally linked to square function and vector-valued estimates
for directional singular integrals. The latter are usually referred to as
Meyer-type lemmas and are traditionally attacked by combining weighted
inequalities with sharp estimates for maximal directional averaging operators.
This classical approach fails to give sharp bounds. In this article we develop
a novel framework for square function estimates, based on directional Carleson
embedding theorems and multi-parameter time-frequency analysis, which overcomes
the limitations of weighted theory. In particular we prove the sharp form of
Meyer's lemma, namely a sharp operator norm bound for vector-valued directional
singular integrals, in both one and two parameters, in terms of the cardinality
of the given set of directions. Our sharp Meyer lemma implies an improved
quantification of the reverse square function estimate for tangential
$\delta\times \delta^2$-caps on $\mathbb S^1$. We also prove sharp square
function estimates for conical and radial multipliers. A suitable combination
of these estimates yields a new and currently best known bound for the Fourier
restriction to a $N$-gon, improving on previous results of A. C\'ordoba.


  The binary-forking model is a parallel computation model, formally defined by
Blelloch et al. very recently, in which a thread can fork a concurrent child
thread, recursively and asynchronously. The model incurs a cost of $\Theta(\log
n)$ to spawn or synchronize $n$ tasks or threads. The binary-forking model
realistically captures the performance of parallel algorithms implemented using
modern multithreaded programming languages on multicore shared-memory machines.
In contrast, the widely studied theoretical PRAM model does not consider the
cost of spawning and synchronizing threads, and as a result, algorithms
achieving optimal performance bounds in the PRAM model may not be optimal in
the binary-forking model. Often, algorithms need to be redesigned to achieve
optimal performance bounds in the binary-forking model and the non-constant
synchronization cost makes the task challenging.
  Though the binary-forking model allows the use of atomic {\em test-and-set}
(TS) instructions to reduce some synchronization overhead, assuming the
availability of such instructions puts a stronger requirement on the hardware
and may limit the portability of the algorithms using them. In this paper, we
avoid the use of locks and atomic instructions in our algorithms except
possibly inside the join operation which is implemented by the runtime system.
  In this paper, we design efficient parallel algorithms in the binary-forking
model without atomics for three fundamental problems: Strassen's (and
Strassen-like) matrix multiplication (MM), comparison-based sorting, and the
Fast Fourier Transform (FFT). All our results improve over known results for
the corresponding problem in the binary-forking model both with and without
atomics.


  Principal components computed via PCA (principal component analysis) are
traditionally used to reduce dimensionality in genomic data or to correct for
population stratification. In this paper, we explore the penalized eigenvalue
problem (PEP) which reformulates the computation of the first eigenvector as an
optimization problem and adds an L1 penalty constraint. The contribution of our
article is threefold. First, we extend PEP by applying Nesterov smoothing to
the original LASSO-type L1 penalty. This allows one to compute analytical
gradients which enable faster and more efficient minimization of the objective
function associated with the optimization problem. Second, we demonstrate how
higher order eigenvectors can be calculated with PEP using established results
from singular value decomposition (SVD). Third, using data from the 1000 Genome
Project dataset, we empirically demonstrate that our proposed smoothed PEP
allows one to increase numerical stability and obtain meaningful eigenvectors.
We further investigate the utility of the penalized eigenvector approach over
traditional PCA.


  We prove the existence of an exact triangle for the Pin(2)-monopole Floer
homology groups of three manifolds related by specific Dehn surgeries on a
given knot. Unlike the counterpart in usual monopole Floer homology, only two
of the three maps are those induced by the corresponding elementary cobordism.
We use this triangle to describe the invariants associated to homology spheres
obtained by (\pm1)-surgery on alternating knots.


  We theoretically investigate photoinduced phenomena induced by time-periodic
driving fields in two-dimensional electron gases under perpendicular magnetic
fields with Rashba spin-orbit coupling. Using perturbation theory, we provide
analytical results for the Floquet-Landau energy spectrum appearing due to THz
radiation. By employing the resulting photo-modulated states, we compute the
dynamical evolution of the spin polarization function for an initially prepared
coherent state. We find that the interplay of the magnetic field, Rashba
spin-orbit interaction and THz radiation can lead to inversion of the spin
polarization. The dynamics also induces fractional revivals and non-trivial
beating patterns in the autocorrelation function due to interference of the
photo-modulated quantum states. We also calculate the transverse photo-assisted
conductivity in the linear response regime using Kubo formalism and analyze the
impact of the radiation field and Rashba spin-orbit interaction. In the static
limit, we find that our results reduce to well-known expressions of the
conductivity in non-relativistic and quasi-relativistic (topological insulator
surfaces) two-dimensional electron gas thoroughly described in the literature.
We discuss the possible experimental detection of our theoretical prediction
and their relevance for spin-orbit physics at high magnetic fields.


  We show that complementary series representations of SO(n,1) contain
discretely complementary series of SO(m,1) provided the continuous parameter is
sufficiently close to the first point of reducibility and the representation of
the compact part of the Levi is a sufficiently small fundamental
representation.
  We prove as a consequence that cohomological representations of SO(n,1) of
degree $i$ less than m/2 contain discretely, cohomogical representations of
SO(m,1).


  Using a CO$_2$ laser to directly heat the crystals from the back side,
SrTiO$_3$ substrates may be thermally prepared in situ for epitaxy without the
need for ex-situ etching and annealing. We find that the formation of large
terraces with straight steps at 900-1100 {\deg}C is independent from the
formation of the ideal surface reconstruction for epitaxy, which requires
temperatures in excess of 1200 {\deg}C to complete. The process may be
universal, at least for perovskite oxide surfaces, as it also works, at
different temperatures, for LaAlO$_3$ and NdGaO$_3$, two other widely used
oxide substrate materials.


  We introduce Algorithm MGB (Multi Grid Barrier) for solving highly nonlinear
convex Euler-Lagrange equations. This class of problems includes many highly
nonlinear partial differential equations, such as $p$-Laplacians. We prove
that, if certain regularity hypotheses are satisfied, then our algorithm
converges in $\tilde{O}(1)$ damped Newton iterations, or $\tilde{O}(n)$ FLOPS,
where the tilde indicates that we neglect some polylogarithmic terms. This the
first algorithm whose running time is proven optimal in the big-$\tilde{O}$
sense. Previous algorithms for the $p$-Laplacian required $\tilde{O}(\sqrt{n})$
damped Newton iterations or more.


  We study the general relation between the power spectrum and the squeezed
limit of the bispectrum of the comoving curvature perturbation produced during
single-field slow-roll inflation when the initial state is a general vacuum.
Assuming the scale invariance of the power spectrum, we derive a formula for
the squeezed limit of the bispectrum, represented by the parameter fNL, which
is not slow-roll suppressed and is found to contain a single free parameter for
a given amplitude of the power spectrum. Then we derive the conditions for
achieving a scale-invariant fNL, and discuss a few examples.


  We describe a novel adaptive ray tracing scheme to solve the equation of
radiative transfer around point sources in hydrodynamical simulations. The
angular resolution adapts to the local hydrodynamical resolution and hence is
of use for adaptive meshes as well as adaptive smooth particle hydrodynamical
simulations. Recursive creation of rays ensures ease of implementation. The
multiple radial integrations needed to solve the time dependent radiative
transfer are sped up significantly using a quad-tree once the rays are cast.
Simplifications advantageous for methods with one radiation source are briefly
discussed. The suggested method is easily generalized to speed up Monte Carlo
radiative transfer techniques. In summary a nearly optimal use of long
characteristics is presented and aspects of its implementation and comparison
to other methods are given.


  The GRAPH MOTIF problem asks whether a given multiset of colors appears on a
connected subgraph of a vertex-colored graph. The fastest known parameterized
algorithm for this problem is based on a reduction to the $k$-Multilinear
Detection (k-MlD) problem: the detection of multilinear terms of total degree k
in polynomials presented as circuits. We revisit k-MLD and define k-CMLD, a
constrained version of it which reflects GRAPH MOTIF more faithfully. We then
give a fast algorithm for k-CMLD. As a result we obtain faster parameterized
algorithms for GRAPH MOTIF and variants of it.


  We construct magnetized stars composed of a fluid stably stratified by
entropy gradients in the framework of general relativity, assuming ideal
magnetohydrodynamics and employing a barotropic equation of state. We first
revisit basic equations for describing stably-stratified stationary
axisymmetric stars containing both poloidal and toroidal magnetic fields. As
sample models, the magnetized stars considered by Ioka and Sasaki (2004),
inside which the magnetic fields are confined, are modified to the ones stably
stratified. The magnetized stars newly constructed in this study are believed
to be more stable than the existing relativistic models because they have both
poloidal and toroidal magnetic fields with comparable strength, and magnetic
buoyancy instabilities near the surface of the star, which can be stabilized by
the stratification, are suppressed.


  In this article we construct a cochain complex of a complex Clifford algebra
with coefficients in itself in a combinatorial fashion and we call the
corresponding cohomology by {\it Clifford cohomology.} We show that {\it
Clifford cohomology} controls the deformation of a complex Clifford algebra and
can classify them up to Morita equivalence. We also study Hochschild cohomology
groups and formal deformations of the algebra of smooth sections of a complex
Clifford algebra bundle over an even dimensional orientable Riemannian manifold
\(M\) which admits a \(Spin^{c}\) structure.


  It is noted that the internal space-time symmetries of relativistic particles
are dictated by Wigner's little groups. The symmetry of massive particles is
like the three-dimensional rotation group, while the symmetry of massless
particles is locally isomorphic to the two-dimensional Euclidean group. It is
noted also that, while the rotational degree of freedom for a massless particle
leads to its helicity, the two translational degrees of freedom correspond to
its gauge degrees of freedom. It is shown that the E(2)-like symmetry of of
massless particles can be obtained as an infinite-momentum and/or zero-mass
limit of the O(3)-like symmetry of massive particles. This mechanism is
illustrated in terms of a sphere elongating into a cylinder. In this way, the
helicity degree of freedom remains invariant under the Lorentz boost, but the
transverse rotational degrees of freedom become contracted into the gauge
degree of freedom.


  I discuss the recent progress in bypassing the KPZ barrier for the existence
of nonperturbative bosonic strings in $1<d<25$. I consider string anomalies
which emerge from higher terms of the DeWitt-Seeley expansion as $\varepsilon
\times \varepsilon^{-1}$ with $\varepsilon$ being a UV cutoff. I show they give
a nonvanishing contribution to the central charge and to the string
susceptibility, telling the Nambu-Goto and Polyakov strings apart. I describe
an exact solution of the emerging four-derivative two-dimensional conformal
theory and its relation to minimal models.
  Talk at "Gravity, Strings and Fields: A Conference in Honour of Gordon
Semenoff", Montreal July 24-28, 2023.


  In semi-supervised medical image segmentation, there exist empirical mismatch
problems between labeled and unlabeled data distribution. The knowledge learned
from the labeled data may be largely discarded if treating labeled and
unlabeled data separately or in an inconsistent manner. We propose a
straightforward method for alleviating the problem - copy-pasting labeled and
unlabeled data bidirectionally, in a simple Mean Teacher architecture. The
method encourages unlabeled data to learn comprehensive common semantics from
the labeled data in both inward and outward directions. More importantly, the
consistent learning procedure for labeled and unlabeled data can largely reduce
the empirical distribution gap. In detail, we copy-paste a random crop from a
labeled image (foreground) onto an unlabeled image (background) and an
unlabeled image (foreground) onto a labeled image (background), respectively.
The two mixed images are fed into a Student network and supervised by the mixed
supervisory signals of pseudo-labels and ground-truth. We reveal that the
simple mechanism of copy-pasting bidirectionally between labeled and unlabeled
data is good enough and the experiments show solid gains (e.g., over 21% Dice
improvement on ACDC dataset with 5% labeled data) compared with other
state-of-the-arts on various semi-supervised medical image segmentation
datasets. Code is available at https://github.com/DeepMed-Lab-ECNU/BCP}.


  Several radio-wave scintillation phenomena exhibit properties which are
difficult to accommodate within the standard propagation model based on
distributed Kolmogorov turbulence in the ionised ISM; here we discuss one such
phenomenon, namely Extreme Scattering Events. By analysis of the data we
demonstrate that these events are caused by ionised gas associated with
self-gravitating, AU-sized gas clouds. The data also show that the ionised gas
is confined by ram pressure, with the clouds moving at hundreds of km/s
relative to the diffuse ISM and causing strong shocks. These conclusions are
supported by a quantitative model in which heat from the shocked ISM evaporates
gas from the surface of a cold cloud; this model readily explains the physical
conditions which are required for Extreme Scattering and yields passable
reproductions of the light-curves. The magnetotail of the cloud provides a site
in which two other ``anomalous'' radio-wave propagation phenomena -- IntraDay
Variability of quasars, and pulsar parabolic arcs -- can plausibly arise, thus
linking three anomalous propagation phenomena in a single physical model.
Locally there must be thousands of these neutral clouds per cubic parsec and by
mass they are the primary constituent of interstellar matter.


  We consider the symplectic vortex equations for a linear Hamiltonian torus
action. We show that the associated genus zero moduli space itself is homotopic
(in the sense of a homotopy of regular G-moduli problems) to a toric manifold
with combinatorial data directly obtained from the original torus action. This
allows to view the wall crossing formula of Cieliebak and Salamon for the
computation of vortex invariants as a consequence of a generalized
Jeffrey-Kirwan localization formula for integrals over symplectic quotients.


  Electron and photon triggers covering transverse energies from 5 GeV to
several TeV are essential for the ATLAS experiment to record signals for a wide
variety of physics: from Standard Model processes to searches for new phenomena
in both proton-proton and heavy-ion collisions. To cope with a fourfold
increase of peak LHC luminosity from 2015 to 2018 (Run 2), to
2.1$\times$10$^{34}$cm$^{-2}$s$^{-1}$, and a similar increase in the number of
interactions per beam-crossing to about 60, trigger algorithms and selections
were optimised to control the rates while retaining a high efficiency for
physics analyses. For proton-proton collisions, the single-electron trigger
efficiency relative to a single-electron offline selection is at least 75% for
an offline electron of 31 GeV, and rises to 96% at 60 GeV; the trigger
efficiency of a 25 GeV leg of the primary diphoton trigger relative to a tight
offline photon selection is more than 96% for an offline photon of 30 GeV. For
heavy-ion collisions, the primary electron and photon trigger efficiencies
relative to the corresponding standard offline selections are at least 84% and
95%, respectively, at 5 GeV above the corresponding trigger threshold.


  Proton therapy is nowadays becoming a wide spread clinical practice in cancer
therapy and sophisticated treatment planning systems are routinely used to
exploit at best the ballistic properties of charged particles. The information
on the quality of the beams and the range of the protons is a key issue for the
optimization of the treatment. For this purpose, proton radiography can be used
in proton therapy to obtain direct information on the range of the protons, on
the average density of the tissues for treatment planning optimization and to
perform imaging with negligible dose to the patient. We propose an innovative
method based on nuclear emulsion film detectors for proton radiography, a
technique in which images are obtained by measuring the position and the
residual range of protons passing through the patient's body. Nuclear emulsion
films interleaved with tissue equivalent absorbers can be fruitfully used to
reconstruct proton tracks with very high precision. The first prototype of a
nuclear emulsion based detector has been conceived, constructed and tested with
a therapeutic proton beam at PSI. The scanning of the emulsions has been
performed at LHEP in Bern, where a fully automated microscopic scanning
technology has been developed for the OPERA experiment on neutrino
oscillations. After track reconstruction, the first promising experimental
results have been obtained by imaging a simple phantom made of PMMA with a step
of 1 cm. A second phantom with five 5 x 5 mm^2 section aluminum rods located at
different distances and embedded in a PMMA structure has been also imaged.
Further investigations are in progress to improve the resolution and to image
more sophisticated phantoms.


  Due to Girard's (sometimes called Waring's) formula the sum of the $r-$th
power of the zeros of every one variable polynomial of degree $N$, $P_{N}(x)$,
can be given explicitly in terms of the coefficients of the monic ${\tilde
P}_{N}(x)$ polynomial. This formula is closely related to a known \par
\noindent $N-1$ variable generalization of Chebyshev's polynomials of the first
kind, $T_{r}^{(N-1)}$. The generating function of these power sums (or moments)
is known to involve the logarithmic derivative of the considered polynomial.
This entails a simple formula for the Stieltjes transform of the distribution
of zeros. Perron-Stieltjes inversion can be used to find this distribution,
{\it e.g.} for $N\to \infty$.\par Classical orthogonal polynomials are taken as
examples. The results for ordinary Chebyshev $T_{N}(x)$ and $U_{N}(x)$
polynomials are presented in detail. This will correct a statement about power
sums of zeros of Chebyshev's $T-$polynomials found in the literature. For the
various cases (Jacobi, Laguerre, Hermite) these moment generating functions
provide solutions to certain Riccati equations.


  The level moduli space $A_g^{4,8}$ is mapped to the projective space by means
of gradients of odd Theta functions, such a map turning out no to be injective
in the genus 2 case. In this work a congruence subgroup $\Gamma$ is located
between $\Gamma_2(4,8)$ and $\Gamma_2(2,4)$ in such a way the map factors on
the related level moduli space $A_{\Gamma}$, the new map being injective on
$A_{\Gamma}$. Satake's compactification $\text{Proj}A(\Gamma)$ and the
desingularization $\text{Proj}S(\Gamma)$ are also due to be investigated, since
the map does not extend to the boundary of the compactification; to aim at
this, an algebraic description is provided, by proving a structure theorem both
for the ring of modular forms $A(\Gamma)$ and the ideal of cusp forms
$S(\Gamma)$


  In the previous paper, we adopted the method using quantum mutual entropy to
measure the degree of entanglement in the time development of the
Jaynes-Cummings model. In this paper, we formulate the entanglement in the time
development of the Jaynes-Cummings model with squeezed states, and then show
that the entanglement can be controlled by means of squeezing.


  We give a definition of noncommutative finite-dimensional Euclidean spaces
$\mathbb R^n$. We then remind our definition of noncommutative products of
Euclidean spaces $\mathbb R^{N_1}$ and $\mathbb R^{N_2}$ which produces
noncommutative Euclidean spaces $\mathbb R^{N_1+N_2}$. We solve completely the
conditions defining the noncommutative products of the Euclidean spaces
$\mathbb R^{N_1}$ and $\mathbb R^{N_2}$ and prove that the corresponding
noncommutative unit spheres $S^{N_1+N_2-1}$ are noncommutative spherical
manifolds. We then apply these concepts to define "noncommutative" quaternionic
planes and noncommutative quaternionic tori on which acts the classical
quaternionic torus $T^2_{\mathbb H}=U_1(\mathbb H)\times U_1(\mathbb H)$


  In this talk, I describe a class of electroweak (EW) scale dark matter (DM)
models where its stability or longevity are the results of underlying dark
gauge symmetries: stable due to unbroken local dark gauge symmetry or topology,
or long-lived due to the accidental global symmetry of dark gauge theories.
Compared with the usual phenomenological dark matter models (including DM EFT
or simplified DM models), DM models with local dark gauge symmetries include
dark gauge bosons, dark Higgs bosons and sometimes excited dark matter. And
dynamics among these fields are completely fixed by local gauge principle. The
idea of singlet portals including the Higgs portal can thermalize these hidden
sector dark matter very efficiently, so that these DM could be easily thermal
DM. I also discuss the limitation of the usual DM effective field theory or
simplified DM models without the full SM gauge symmetry, and emphasize the
importance of the full SM gauge symmetry and renormalizability especially for
collider searches for DM.


  Given a real algebraic curve in the projective 3-space, its hyperbolicity
locus is the set of lines with respect to which the curve is hyperbolic. We
give an example of a smooth irreducible curve whose hyperbolicity locus is
disconnected but the connected components are not distinguished by the linking
numbers with the connected components of the curve.


  Facial Micro-Expressions (MEs) are spontaneous, involuntary facial movements
when a person experiences an emotion but deliberately or unconsciously attempts
to conceal his or her genuine emotions. Recently, ME recognition has attracted
increasing attention due to its potential applications such as clinical
diagnosis, business negotiation, interrogations, and security. However, it is
expensive to build large scale ME datasets, mainly due to the difficulty of
inducing spontaneous MEs. This limits the application of deep learning
techniques which require lots of training data. In this paper, we propose a
simple, efficient yet robust descriptor called Extended Local Binary Patterns
on Three Orthogonal Planes (ELBPTOP) for ME recognition. ELBPTOP consists of
three complementary binary descriptors: LBPTOP and two novel ones Radial
Difference LBPTOP (RDLBPTOP) and Angular Difference LBPTOP (ADLBPTOP), which
explore the local second order information along the radial and angular
directions contained in ME video sequences. ELBPTOP is a novel ME descriptor
inspired by unique and subtle facial movements. It is computationally efficient
and only marginally increases the cost of computing LBPTOP, yet is extremely
effective for ME recognition. In addition, by firstly introducing Whitened
Principal Component Analysis (WPCA) to ME recognition, we can further obtain
more compact and discriminative feature representations, then achieve
significantly computational savings. Extensive experimental evaluation on three
popular spontaneous ME datasets SMIC, CASME II and SAMM show that our proposed
ELBPTOP approach significantly outperforms the previous state-of-the-art on all
three single evaluated datasets and achieves promising results on
cross-database recognition.Our code will be made available.


  The annihilation cross section of TeV scale dark matter particles $\chi^0$
with electroweak charges into photons is affected by large quantum corrections
due to Sudakov logarithms and the Sommerfeld effect. We calculate the
semi-inclusive photon energy spectrum in $\chi^0\chi^0\to \gamma+X$ in the
vicinity of the maximal photon energy $E_\gamma = m_\chi$ with NLL' accuracy in
an all-order summation of the electroweak perturbative expansion adopting the
pure wino model. This results in the most precise theoretical prediction of the
annihilation rate for $\gamma$-ray telescopes with photon energy resolution of
parametric order $m_W^2/m_\chi$ for photons with TeV energies.


  We establish spectral, linear, and nonlinear stability of the vanishing and
slow-moving travelling waves that arise as time asymptotic solutions to the
Fisher-Stefan equation. Nonlinear stability is in terms of the limiting
equations that the asymptotic waves satisfy.


  Pulsed spin-torque switching has been studied using single-shot time-resolved
electrical measurements in perpendicularly magnetized magnetic tunnel junctions
as a function of pulse amplitude and junction size in 50 to 100 nm diameter
circular junctions. The mean switching time depends inversely on pulse
amplitude for all junctions studied. However, the switching dynamics is found
to be strongly dependent on junction size and pulse amplitude. In 50 nm
diameter junctions the switching onset is stochastic but the switching once
started, is fast; after being initiated it takes less than 2 ns to switch. In
larger diameter junctions the time needed for complete switching is strongly
dependent on the pulse amplitude, reaching times less than 2 ns at large pulse
amplitudes. Anomalies in the switching rate versus pulse amplitude are shown to
be associated with the long lived (> 2 ns) intermediate junction resistance
states.


  The perception module of self-driving vehicles relies on a multi-sensor
system to understand its environment. Recent advancements in deep learning have
led to the rapid development of approaches that integrate multi-sensory
measurements to enhance perception capabilities. This paper surveys the latest
deep learning integration techniques applied to the perception module in
autonomous driving systems, categorizing integration approaches based on "what,
how, and when to integrate". A new taxonomy of integration is proposed, based
on three dimensions: multi-view, multi-modality, and multi-frame. The
integration operations and their pros and cons are summarized, providing new
insights into the properties of an "ideal" data integration approach that can
alleviate the limitations of existing methods. After reviewing hundreds of
relevant papers, this survey concludes with a discussion of the key features of
an optimal data integration approach.


  Currently ALS is undergoing an upgrade to ALSU to produce 100 times brighter
soft X-ray light. The LLRF system for Accumulator Ring (AR) is composed of two
identical LLRF stations, for driving RF amplifiers. The closed loop RF
amplitude and phase stability is measured as $< 0.1\%$ and $< 0.1^\circ$
respectively, using the non-IQ digital down conversion together with analog
up/down conversion, under a system-on-chip architecture. Realtime interlock
system is implemented with $< 2 \mu$s latency, for machine protection against
arc flash and unexpected RF power. Control interfaces are developed to enable
PLC-FPGA-EPICS communication to support operation, timing, cavity tuning, and
interlock systems. The LLRF system handles alignment of buckets to swap beams
between AR and Storage Ring by synchronous phase loop ramping between the two
cavities. The system also includes an optimization routine to characterize the
loop dynamics and determine optimal operating point using a built-in network
analyzer feature. A cavity emulator of 31 kHz bandwidth is integrated with the
LLRF system to validate the performance of the overall system being developed.


  We describe the asymptotic behavior of minimal area submanifolds in product
spacetimes of an asymptotically hyperbolic space times a compact internal
manifold. In particular, we find that unlike the case of a minimal area
submanifold just in an asymptotically hyperbolic space, the internal part of
the boundary submanifold is constrained to be itself a minimal area
submanifold. For applications to holography, this tells us what are the allowed
"flavor branes" that can be added to a holographic field theory. We also give a
compact geometric expression for the spectrum of operator dimensions associated
with the slipping modes of the submanifold in the internal space. We illustrate
our results with several examples, including some that haven't appeared in the
literature before.


  Recent development on Ge$_{1-x}$Sn$_x$ nanowires with high Sn content, beyond
its solid solubility limit, make them attractive for all group-IV Si-integrated
infrared photonics at nanoscale. Herein, we report a chemical vapour
deposition-grown high Sn-content Ge-Ge$_{0.92}$Sn$_{0.08}$ core-shell based
single nanowire photodetector operating at the optical communication wavelength
of 1.55 $\mu$m. The atomic concentration of Sn in nanowires has been studied
using X-ray photoelectron and Raman spectroscopy data. A
metal-semiconductor-metal based single nanowire photodetector, fabricated via
electron beam lithography process, exhibits significant room-temperature
photoresponse even at zero bias. In addition to the high-crystalline quality
and identical shell composition of the nanowire, the efficient collection of
photogenerated carriers under an external electric field result in the superior
responsivity and photoconductive gain as high as ~70.8 A/W and ~57,
respectively at an applied bias of -1.0 V. The extra-ordinary performance of
the fabricated photodetector demonstrates the potential of GeSn nanowires for
future Si CMOS compatible on-chip optical communication device applications.


  Transformer architectures have become the model of choice in natural language
processing and are now being introduced into computer vision tasks such as
image classification, object detection, and semantic segmentation. However, in
the field of human pose estimation, convolutional architectures still remain
dominant. In this work, we present PoseFormer, a purely transformer-based
approach for 3D human pose estimation in videos without convolutional
architectures involved. Inspired by recent developments in vision transformers,
we design a spatial-temporal transformer structure to comprehensively model the
human joint relations within each frame as well as the temporal correlations
across frames, then output an accurate 3D human pose of the center frame. We
quantitatively and qualitatively evaluate our method on two popular and
standard benchmark datasets: Human3.6M and MPI-INF-3DHP. Extensive experiments
show that PoseFormer achieves state-of-the-art performance on both datasets.
Code is available at \url{https://github.com/zczcwh/PoseFormer}


  We show a collection of scripts, called $G$-strongly positive scripts, which
is used to recognize critical configurations of a chip firing game (CFG) on a
multi-digraph with a global sink. To decrease the time of the process of
recognition caused by the stabilization we present an algorithm to find the
minimum G-strongly positive script. From that we prove the non-stability of
configurations obtained from a critical configuration by firing inversely any
non-empty multi-subset of vertices. This result is a generalization of a very
recent one by Aval \emph{et.al} which is applied for CFG on undirected graphs.
Last, we give a combinatorial proof for the duality between critical and
super-stable configurations.


  Current-induced motion of non-axisymmetric skyrmions within angular phases of
polar helimagnetis with the easy plane anisotropy is studied by micromagnetic
simulations.Such non-axisymmetric skyrmions consist of a circular core and a
crescent-shaped domain-wall region formed with respect to the tilted
surrounding state. A current-driven motion of non-axisymmetric skyrmions
exhibits two distinct time regimes: initially the skyrmions rotate towards the
current flow direction and subsequently move along the current with the
skyrmionic crescent first. According to the Thiele equation, the asymmetric
distribution of the topological charge and the dissipative force tensor play an
important role for giving the different velocities for the circular and the
crescent-shaped constituent parts of the skyrmion what underlies such a
shuttlecock-like movement. Moreover, the current-velocity relation depends on
the tilt angle of the surrounding angular phase what makes in particular the
transverse velocity of skyrmions sensitive to their field-driven
configurational transformation.


  We provide a new lower bound on the minimum distance of a family of quantum
LDPC codes based on Cayley graphs proposed by MacKay, Mitchison and
Shokrollahi. Our bound is exponential, improving on the quadratic bound of
Couvreur, Delfosse and Z\'emor. This result is obtained by examining a family
of subsets of the hypercube which locally satisfy some parity conditions.


  We present time-dependent 1D simulations of multifluid magnetic shocks with
chemistry resolved down to the mean free path. They are obtained with an
adaptive moving grid implemented with an implicit scheme. We examine a broad
range of parameters relevant to conditions in dense molecular clouds, with
preshock densities between 10^3 and 10^5 cm-3, velocities between 10 and 40
km/s, and three different scalings for the transverse magnetic field: B=0,0.1,1
\mu G \sqrt{n.cm3}. We first use this study to validate the results of
Chi\`eze, Pineau des For\^ets & Flower (1998), in particular the long delays
necessary to obtain steady C-type shocks, and we provide evolutionary
time-scales for a much greater range of parameters. We also present the first
time-dependent models of dissociative shocks with a magnetic precursor,
including the first models of stationary CJ shocks in molecular conditions. We
find that the maximum speed for steady C-type shocks is reached before the
occurrence of a sonic point in the neutral fluid, unlike previously thought. As
a result, the maximum speed for C-shocks is lower than previously believed.
Finally, we find a large amplitude bouncing instability in J-type fronts near
the H2 dissociation limit (u ~ 25-30 km/s), driven by H2
dissociation/reformation. At higher speeds, we find an oscillatory behaviour of
short period and small amplitude linked to collisional ionisation of H. Both
instabilities are suppressed after some time when a magnetic field is present.
In a companion paper, we use the present simulations to validate a new
semi-analytical construction method for young low-velocity magnetic shocks
based on truncated steady-state models.


  This paper is a survey of results proved in recent years that pertain to
classifying cobounded hyperbolic actions of any group $G$. In other words, we
discuss results that allow us to describe the partially ordered set
$\mathcal{H}(G)$, first introduced in by Abbott-Balasubramanya-Osin. In certain
cases, a complete classification of the poset is possible. In cases where this
seems out of reach, we provide descriptions of large subsets of the poset. This
covers a wide range of groups, including acylindrically hyperbolic groups,
nilpotent groups, many solvable groups and ``Thompson-like" groups. We also
cover the range of strategies utilized to obtain these classification results.
As a result, we produce some new examples of groups with interesting
$\mathcal{H}(G)$ structure.


  The non-mesonic weak decay of polarized Lambda-hypernuclei is studied for the
first time by taking into account, with a Monte Carlo intranuclear cascade
code, the nucleon final state interactions. A one-meson-exchange model is
employed to describe the Lambda N-> n N processes in a finite nucleus
framework. The relationship between the intrinsic Lambda asymmetry parameter
a_\Lambda and the asymmetry a^M_\Lambda accessible in experiments is discussed.
A strong dependence of a^M_\Lambda on nucleon final state interactions and
detection threshold is obtained. Our results for a^M_\Lambda are consistent
with ^{11}_\Lambda B and ^{12}_\Lambda C data but disagree with observations in
^5_\Lambda He.


  The free multiplicative Brownian motion $b_{t}$ is the large-$N$ limit of
Brownian motion $B_t^N$ on the general linear group
$\mathrm{GL}(N;\mathbb{C})$. We prove that the Brown measure for
$b_{t}$---which is an analog of the empirical eigenvalue distribution for
matrices---is supported on the closure of a certain domain $\Sigma_{t}$ in the
plane. The domain $\Sigma_t$ was introduced by Biane in the context of the
large-$N$ limit of the Segal--Bargmann transform associated to
$\mathrm{GL}(N;\mathbb{C})$.
  We also consider a two-parameter version, $b_{s,t}$: the large-$N$ limit of a
related family of diffusion processes on $\mathrm{GL}(N;\mathbb{C})$ introduced
by the second author. We show that the Brown measure of $b_{s,t}$ is supported
on the closure of a certain planar domain $\Sigma_{s,t}$, generalizing
$\Sigma_t$, introduced by Ho.
  In the process, we introduce a new family of spectral domains related to any
operator in a tracial von Neumann algebra: the {\em $L^p_n$-spectrum} for
$n\in\mathbb{N}$ and $p\ge 1$, a subset of the ordinary spectrum defined
relative to potentially-unbounded inverses. We show that, in general, the
support of the Brown measure of an operator is contained in its
$L_2^2$-spectrum.


  In this work, we prove a novel one-shot multi-sender decoupling theorem
generalising Dupuis result. We start off with a multipartite quantum state, say
on A1 A2 R, where A1, A2 are treated as the two sender systems and R is the
reference system. We apply independent Haar random unitaries in tensor product
on A1 and A2 and then send the resulting systems through a quantum channel. We
want the channel output B to be almost in tensor with the untouched reference
R. Our main result shows that this is indeed the case if suitable entropic
conditions are met. An immediate application of our main result is to obtain a
one-shot simultaneous decoder for sending quantum information over a k-sender
entanglement unassisted quantum multiple access channel (QMAC). The rate region
achieved by this decoder is the natural one-shot quantum analogue of the
pentagonal classical rate region. Assuming a simultaneous smoothing conjecture,
this one-shot rate region approaches the optimal rate region of Yard, Dein the
asymptotic iid limit. Our work is the first one to obtain a non-trivial
simultaneous decoder for the QMAC with limited entanglement assistance in both
one-shot and asymptotic iid settings; previous works used unlimited
entanglement assistance.


  We consider a straight one-dimensional potential step created across a
graphene flake. Charge and spin transport through such a potential step are
studied in the presence of both intrinsic and extrinsic (Rashba) spin-orbit
coupling (SOC). At normal incidence electrons are completely reflected when the
Rashba interaction (with strength $\lambda_R$) is dominant whereas they are
perfectly transmitted if the two types of SOC are exactly balanced. At normal
incidence, the transmission probability of the step is thus controlled
continuously from 0 to 1 by tuning the ratio of the two types of SOC. Besides
the transport of charge in the direction normal to the barrier, we show the
existence of a spin transport along the barrier. The magnitude of the spin Hall
current is determined by a subtle interplay between the height of the potential
step and the position of Fermi energy. It is demonstrated that contributions
from inter-band matrix elements and evanescent modes are dominant in spin
transport. Moreover, in the case of vanishing extrinsic SOC ($\lambda_R =0$),
each channel carries a conserved spin current, in contrast to the general case
of a finite $\lambda_R$, in which only integrated spin current is a conserved
quantity. Finally, we provide a quasi-classical picture of the charge and spin
transport by imaging flow lines over the entire sample and Veselago lensing
(negative refraction) in the case of a $p-n$ junction.


  We give a selection of results on spectrum and decay constants of light and
heavy-light hadrons. Effective field theories relevant for their lattice
calculation, namely non-relativistic QCD (NRQCD) for heavy quarks on the
lattice and Chiral Perturbation Theory for light quarks, are briefly discussed.


  The magnetic field is believed to play a critical role in the bulk
acceleration and propagation of jets produced in active galactic nuclei (AGN).
Polarization observations of AGN jets provide valuable information about their
magnetic fields. As a result of radiative transfer, jet structure, and
stratification, among other factors, it is not always straightforward to
determine the magnetic field structures from observed polarization. We review
these effects and their impact on polarization emission at a variety of
wavelengths, including radio, optical, and ultraviolet wavelengths in this
paper. It is also possible to study the magnetic field in the launching and
acceleration regions of AGN jets by using very long baseline interferometry
(VLBI), which occurs on a small physical scale. Due to the weak polarization of
the jets in these regions, probing the magnetic field is generally difficult.
However, recent VLBI observations have detected significant polarization and
Faraday rotation in some nearby sources. We present the results of these
observations as well as prospects for future observations. Additionally, we
briefly discuss recently developed polarization calibration and imaging
techniques for VLBI data, which enable more in-depth analysis of the magnetic
field structure around supermassive black holes and in AGN jets.


  We numerically investigate the area statistics of the outer boundary of
planar random loops, on the square and triangular lattices. Our Monte Carlo
simulations suggest that the underlying limit distribution is the Airy
distribution, which was recently found to appear also as area distribution in
the model of self-avoiding loops.


  We study chiral models in one spatial dimension, both static and periodically
driven. We demonstrate that their topological properties may be read out
through the long time limit of a bulk observable, the mean chiral displacement.
The derivation of this result is done in terms of spectral projectors, allowing
for a detailed understanding of the physics. We show that the proposed
detection converges rapidly and it can be implemented in a wide class of chiral
systems. Furthermore, it can measure arbitrary winding numbers and topological
boundaries, it applies to all non-interacting systems, independently of their
quantum statistics, and it requires no additional elements, such as external
fields, nor filled bands.


  In the spirit of recent work of Harada-Kaveh and Nishinou-Nohara-Ueda, we
study the symplectic geometry of Popov's horospherical degenerations of complex
algebraic varieties with the action of a complex linearly reductive group. We
formulate an intrinsic symplectic contraction of a Hamiltonian space, which is
a surjective, continuous map onto a new Hamiltonian space that is a
symplectomorphism on an explicitly defined dense open subspace. This map is
given by a precise formula, using techniques from the theory of symplectic
reduction and symplectic implosion. We then show, using the Vinberg monoid,
that the gradient-Hamiltonian flow for a horospherical degeneration of an
algebraic variety gives rise to this contraction from a general fiber to the
special fiber. We apply this construction to branching problems in
representation theory, and finally we show how the Gel'fand-Tsetlin integrable
system can be understood to arise this way.


  We demonstrate efficient generation of mid-infrared frequency combs based on
continuous-wave-seeded femtosecond optical parametric generation in nonlinear
waveguides. Conversion of the near-infrared pump to signal and idler light
takes place with very high efficiency (74 %) and the threshold (25 pJ) is over
300 times lower than in bulk analogs. Relative intensity noise of the
mid-infrared comb is exceptionally low, below 5*10-5 (detector-limited,
integrated from 10 Hz to 2 MHz). Furthermore, the mid-infrared bandwidth can be
increased by driving the process with broadband pump obtained via
supercontinuum generation.