  Quantifying entanglement of multiple subsystems is a challenging open problem
in interacting quantum systems. Here, we focus on two subsystems of length
$\ell$ separated by a distance $r=\alpha\ell$ and quantify their entanglement
negativity (${\cal E}$) and mutual information (${\cal I}$) in critical random
Ising chains. Both the disorder averaged ${\cal E}$ and ${\cal I}$ are found to
be scale-invariant and universal, i.e. independent of the form of disorder. We
find a constant ${\cal E}(\alpha)$ and ${\cal I}(\alpha)$ over any distances,
using the asymptotically exact strong disorder renormalization group method.
Our results are qualitatively different from both those in the clean Ising
model and random spin chains of a singlet ground state, like the
spin-$\frac{1}{2}$ random Heisenberg chain and the random XX chain. While for
random singlet states ${\cal I}(\alpha)/{\cal E}(\alpha)=2$, in the random
Ising chain this universal ratio is strongly $\alpha$-dependent. This deviation
between systems contrasts with the behavior of the entanglement entropy of a
single subsystem, for which the various random critical chains and clean models
give the same qualitative behavior. Therefore, studying multipartite
entanglement provides additional universal information in random quantum
systems, beyond what we can learn from a single subsystem.


  A manifestly relativistic-invariant Lellouch-L\"uscher formalism for the
three-particle decays is proposed. Similarly to ref.[1], the formalism is based
on the use of the non-relativistic effective Lagrangians. Manifest Lorentz
invariance is guaranteed, as in ref.[2], by choosing the quantization axis
along the total four-momentum of the three-particle system. A systematic
inclusion of the higher-order derivative couplings, as well as higher partial
waves is addressed.


  The maximally supersymmetric Yang-Mills theory in four-dimensional Minkowski
space is an exceptional model of mathematical physics. Even more so in the
planar limit, where the theory is believed to be integrable. In particular, the
tree-level scattering amplitudes were shown to be invariant under the Yangian
of the superconformal algebra psu(2,2|4). This infinite-dimensional symmetry is
a hallmark of integrability. In this dissertation we explore connections
between these amplitudes and integrable models. Our aim is to lay foundations
for an efficient integrability-based computation of amplitudes. To this end, we
characterize Yangian invariants within the quantum inverse scattering method,
which is an extensive toolbox for integrable spin chains. Making use of this
setup, we develop methods for the construction of Yangian invariants. We show
that the algebraic Bethe ansatz can be specialized to yield Yangian invariants
for u(2). Our approach also allows to interpret these Yangian invariants as
partition functions of vertex models. What is more, we establish a unitary
Gra{\ss}mannian matrix model for the construction of u(p,q|m) Yangian
invariants with oscillator representations. In a special case our formula
reduces to the Brezin-Gross-Witten model. We apply an integral transformation
due to Bargmann to our unitary Gra{\ss}mannian matrix model, which turns the
oscillators into spinor helicity-like variables. Thereby we are led to a
refined version of the Gra{\ss}mannian integral formula for certain amplitudes.
The most decisive differences are that we work in Minkowski signature and that
the integration contour is fixed to be a unitary group manifold. We compare
Yangian invariants defined by our integral to amplitudes and recently
introduced deformations thereof.


  We demonstrate that the onset of complex spin orders in ACr$_2$O$_4$ spinels
with magnetic A$=$Co, Fe and Cu ions lowers the lattice symmetry. This is
clearly indicated by the emergence of anisotropic lattice dynamics -- as
evidenced by the pronounced phonon splittings -- even when experiments probing
static distortions fail. We show that the crystal symmetry in the magnetic
phase is reduced from tetragonal to orthorhombic for FeCr$_2$O$_4$ and
CuCr$_2$O$_4$ with Jahn-Teller active A-site ions. The conical spin structure
in FeCr$_2$O$_4$ is also manifested in the phonon frequencies. In contrast, the
multiferroic CoCr$_2$O$_4$ with no orbital degrees of freedom remains nearly
cubic in its ground state.


  We introduce ($\alpha,\beta,\gamma$) weighted Wigner-Yanase-Dyson
(($\alpha,\beta,\gamma$) WWYD) skew information and ($\alpha,\beta,\gamma$)
modified weighted Wigner-Yanase-Dyson (($\alpha,\beta,\gamma$) MWWYD) skew
information. We explore the sum uncertainty relations for arbitrary $N$
mutually noncommutative observables based on ($\alpha,\beta,\gamma$) WWYD skew
information. A series of uncertainty inequalities are derived. We show by
detailed example that our results cover and improve the previous ones based on
the original Wigner-Yanase (WY) skew information. Finally, we establish new sum
uncertainty relations in terms of the ($\alpha,\beta,\gamma$) MWWYD skew
information for arbitrary $N$ quantum channels.


  We perform computational studies of static packings of a variety of
nonspherical particles including circulo-lines, circulo-polygons, ellipses,
asymmetric dimers, and dumbbells to determine which shapes form hypostatic
versus isostatic packings and to understand why hypostatic packings of
nonspherical particles can be mechanically stable despite having fewer contacts
than that predicted from na\"ive constraint counting. To generate highly
accurate force- and torque-balanced packings of circulo-lines and -polygons, we
developed an interparticle potential that gives continuous forces and torques
as a function of the particle coordinates. We show that the packing fraction
and coordination number at jamming onset obey a master-like form for all of the
nonspherical particle packings we studied when plotted versus the particle
asphericity ${\cal A}$, which is proportional to the ratio of the squared
perimeter to the area of the particle. Further, the eigenvalue spectra of the
dynamical matrix for packings of different particle shapes collapse when
plotted at the same ${\cal A}$. For hypostatic packings of nonspherical
particles, we verify that the number of "quartic" modes along which the
potential energy increases as the fourth power of the perturbation amplitude
matches the number of missing contacts relative to the isostatic value. In
addition, we calculate the principal curvatures of the inequality constraints
for each contact in circulo-line packings and identify specific types of
contacts with inequality constraints that possess convex curvature. These
contacts can constrain multiple degrees of freedom and allow hypostatic
packings of nonspherical particles to be mechanically stable.


  The General Curve Lemma is a tool of Infinite-Dimensional Analysis, which
enables refined studies of differentiability properties of mappings between
real locally convex spaces. In this article, we generalize the General Curve
Lemma in two ways: First, we remove the condition of local convexity in the
real case. Second, we adapt the lemma to the case of curves in topological
vector spaces over ultrametric fields.


  The paper is devoted to the construction of a probabilistic particle
algorithm. This is related to nonlin-ear forward Feynman-Kac type equation,
which represents the solution of a nonconservative semilinear parabolic Partial
Differential Equations (PDE). Illustrations of the efficiency of the algorithm
are provided by numerical experiments.


  The explosion of scientific publications overloads researchers with
information. This is even more dramatic for interdisciplinary studies, where
several fields need to be explored. A tool to help researchers overcome this is
Natural Language Processing (NLP): a machine-learning (ML) technique that
allows scientists to automatically synthesize information from many articles.
As a practical example, we have used NLP to conduct an interdisciplinary search
for compounds that could be carriers for Diffuse Interstellar Bands (DIBs), a
long-standing open question in astrophysics. We have trained a NLP model on a
corpus of 1.5 million cross-domain articles in open access, and fine-tuned this
model with a corpus of astrophysical publications about DIBs. Our analysis
points us toward several molecules, studied primarily in biology, having
transitions at the wavelengths of several DIBs and composed of abundant
interstellar atoms. Several of these molecules contain chromophores, small
molecular groups responsible for the molecule's colour, that could be promising
candidate carriers. Identifying viable carriers demonstrates the value of using
NLP to tackle open scientific questions, in an interdisciplinary manner.


  Of concern are lump solutions for the fractional Kadomtsev--Petviashvili
(fKP) equation. As in the classical Kadomtsev--Petviashvili equation, the fKP
equation comes in two versions: fKP-I (strong surface tension case) and fKP-II
(weak surface tension case). We prove the existence of nontrivial lump
solutions for the fKP-I equation in the energy subcritical case
$\alpha>\frac{4}{5}$ by means of variational methods. It is already known that
there exist neither nontrivial lump solutions belonging to the energy space for
the fKP-II equation nor for the fKP-I when $\alpha \leq \frac{4}{5}$.
Furthermore, we show that for any $\alpha>\frac{4}{5}$ lump solutions for the
fKP-I equation are smooth and decay quadratically at infinity. Numerical
experiments are performed for the existence of lump solutions and their decay.
Moreover, numerically, we observe cross-sectional symmetry of lump solutions
for the fKP-I equation.


  Entanglement can modify the interference patterns of multi-particle systems.
We analyse, using the path integral formalism, a novel example of
multi-particle interference and some unexplored aspects of this phenomenon by
considering the two-slit arrangement with two distinguishable particles in a
superposition state. The two components of entanglement, multiplicity of
multi-particle terms and their coherence, can be studied separately by
comparing the patterns of product, mixed and superposition states. This
suggests a scheme to detect multi-particle superposition in some favourable
cases. Moreover, the dependence of the effect on the entanglement degree,
measured by the Schmidt number, is not a monotone.


  We examine an infinite, linear system of ordinary differential equations that
models the evolution of fragmenting clusters, where each cluster is assumed to
be composed of identical units. In contrast to previous investigations into
such discrete-size fragmentation models, we allow the fragmentation
coefficients to vary with time. By formulating the initial-value problem for
the system as a non-autonomous abstract Cauchy problem, posed in an
appropriately weighted $\ell^1$ space, and then applying results from the
theory of evolution families, we prove the existence and uniqueness of
physically relevant, classical solutions for suitably constrained coefficients.


  For proper minimizers of parabolic variational integrals with linear growth
with respect to $|Du|$, we establish a necessary and sufficient condition for
$u$ to be continuous at a point $(x_o,t_o)$, in terms of a sufficient fast
decay of the total variation of $u$ about $(x_o,t_o)$ (see (1.4) below). These
minimizers arise also as {proper} solutions to the parabolic $1$-laplacian
equation. Hence, the continuity condition continues to hold for such solutions
(\S\ 3).


  Functional data clustering is to identify heterogeneous morphological
patterns in the continuous functions underlying the discrete
measurements/observations. Application of functional data clustering has
appeared in many publications across various fields of sciences, including but
not limited to biology, (bio)chemistry, engineering, environmental science,
medical science, psychology, social science, etc. The phenomenal growth of the
application of functional data clustering indicates the urgent need for a
systematic approach to develop efficient clustering methods and scalable
algorithmic implementations. On the other hand, there is abundant literature on
the cluster analysis of time series, trajectory data, spatio-temporal data,
etc., which are all related to functional data. Therefore, an overarching
structure of existing functional data clustering methods will enable the
cross-pollination of ideas across various research fields. We here conduct a
comprehensive review of original clustering methods for functional data. We
propose a systematic taxonomy that explores the connections and differences
among the existing functional data clustering methods and relates them to the
conventional multivariate clustering methods. The structure of the taxonomy is
built on three main attributes of a functional data clustering method and
therefore is more reliable than existing categorizations. The review aims to
bridge the gap between the functional data analysis community and the
clustering community and to generate new principles for functional data
clustering.


  Theoretical and experimental resonance strengths for KLL dielectronic
recombination (DR) into He-, Li-, Be-, and B-like mercury ions are presented,
based on state-resolved DR x-ray spectra recorded at the Heidelberg electron
beam ion trap. The DR resonance strengths were experimentally extracted by
normalizing them to simultaneously recorded radiative recombination signals.
The results are compared to state-of-the-art atomic calculations that include
relativistic electron-electron correlation and configuration mixing effects.
Combining the present data with other existing ones, we derive an improved
semi-empirical $Z$-scaling law for DR resonance strength as a function of the
atomic number, taking into account higher-order relativistic corrections, which
are especially relevant for heavy highly charged ions.


  We present a novel solution to the camera pose estimation problem, where
rotation and translation of a camera between two views are estimated from
matched feature points in the images. The camera pose estimation problem is
traditionally solved via algorithms that are based on the essential matrix or
the Euclidean homography. With six or more feature points in general positions
in the space, essential matrix based algorithms can recover a unique solution.
However, such algorithms fail when points are on critical surfaces (e.g.,
coplanar points) and homography should be used instead. By formulating the
problem in quaternions and decoupling the rotation and translation estimation,
our proposed algorithm works for all point configurations. Using both simulated
and real world images, we compare the estimation accuracy of our algorithm with
some of the most commonly used algorithms. Our method is shown to be more
robust to noise and outliers. For the benefit of community, we have made the
implementation of our algorithm available online and free.


  In 1970 Smith classified all connected graphs with the spectral radius at
most $2$. Here the spectral radius of a graph is the largest eigenvalue of its
adjacency matrix. Recently, the definition of spectral radius has been extended
to $r$-uniform hypergraphs. In this paper, we generalize the Smith's theorem to
$r$-uniform hypergraphs. We show that the smallest limit point of the spectral
radii of connected $r$-uniform hypergraphs is $\rho_r=(r-1)!\sqrt[r]{4}$. We
discovered a novel method for computing the spectral radius of hypergraphs, and
classified all connected $r$-uniform hypergraphs with spectral radius at most
$\rho_r$.


  Network resource allocation shows revived popularity in the era of data
deluge and information explosion. Existing stochastic optimization approaches
fall short in attaining a desirable cost-delay tradeoff. Recognizing the
central role of Lagrange multipliers in network resource allocation, a novel
learn-and-adapt stochastic dual gradient (LA-SDG) method is developed in this
paper to learn the sample-optimal Lagrange multiplier from historical data, and
accordingly adapt the upcoming resource allocation strategy. Remarkably, LA-SDG
only requires just an extra sample (gradient) evaluation relative to the
celebrated stochastic dual gradient (SDG) method. LA-SDG can be interpreted as
a foresighted learning scheme with an eye on the future, or, a modified
heavy-ball iteration from an optimization viewpoint. It is established - both
theoretically and empirically - that LA-SDG markedly improves the cost-delay
tradeoff over state-of-the-art allocation schemes.


  I. P. Goulden, S. Litsyn, and V. Shevelev [On a sequence arising in algebraic
geometry, J. Integer Sequences 8 (2005), 05.4.7] conjectured that certain
Laurent polynomials associated with the solution of a functional equation have
only odd negative powers. We prove their conjecture and generalize it.


  The physical mechanisms for damage formation in graphite films induced by
femtosecond laser pulses are analyzed using a microscopic electronic theory. We
describe the nonequilibrium dynamics of electrons and lattice by performing
molecular dynamics simulations on time-dependent potential energy surfaces. We
show that graphite has the unique property of exhibiting two distinct laser
induced structural instabilities. For high absorbed energies (> 3.3 eV/atom) we
find nonequilibrium melting followed by fast evaporation. For low intensities
above the damage threshold (> 2.0 eV/atom) ablation occurs via removal of
intact graphite sheets.


  An exposition of the basic geometry of twistor integrals, intended for
mathematicians.


  The excitation spectrum of the nucleon with the spin 1/2 is examined by using
the Friedberg-Lee model containing the constituent quark and the scalar meson.
  An appropriate way of quantization for the non-linear meson field is employed
by taking account of the non-topological soliton existed in the classical
level.
  Our model space for the nucleon resonances includes the three-quark plus
one-meson state in addition to the pure three-quark state.
  The excitation spectrum in this model space shows that the positive parity
state appears as the first excited state associated with the 0s-excitation of
the scalar meson.
  The meson excitation also generates the additional negative parity state
apart from the well-known 0p-excitation of the quark.


  We report on the Zeeman deceleration of ground-state NH radicals, using a
decelerator that consists of 100 pulsed solenoids and 100 permanent hexapoles.
Packets of state-selected NH ($X\,^3\Sigma^-$, N=0, J=1) radicals are produced
with final velocities ranging between 510 m/s and 150 m/s. The velocity
distributions of the packets of NH exiting the Zeeman decelerator are probed
using velocity map imaging detection. We present a new 1+2' resonance-enhanced
multiphoton ionization scheme for NH, that allows for velocity map imaging
detection under ion recoil-free conditions. The packets of Zeeman-decelerated
NH radicals, in combination with the new detection scheme, offer interesting
prospects for the use of this important radical in high-resolution crossed-beam
scattering experiments.


  We perform a complete next to leading order evaluation of inclusive neutral
pion production from hadronic colliders which is based on the knowledge of the
pion fragmentation functions at next to leading order. This problem has been
tackled for the first time using different approaches. Predictions at LHC are
given with the estimate of the theoretical uncertainty.


  We consider free rotation of a body whose parts move slowly with respect to
each other under the action of internal forces. This problem can be considered
as a perturbation of the Euler-Poinsot problem. The dynamics has an approximate
conservation law - an adiabatic invariant. This allows to describe the
evolution of rotation in the adiabatic approximation. The evolution leads to an
overturn in the rotation of the body: the vector of angular velocity crosses
the separatrix of the Euler-Poinsot problem. This crossing leads to a
quasi-random scattering in body's dynamics. We obtain formulas for
probabilities of capture into different domains in the phase space at
separatrix crossings.


  Dark compact objects ("clumps") transiting the Solar System exert
accelerations on the test masses (TM) in a gravitational-wave (GW) detector. We
reexamine the detectability of these clump transits in a variety of current and
future GW detectors, operating over a broad range of frequencies. TM
accelerations induced by clump transits through the inner Solar System have
frequency content around $f \sim \mu$Hz. Some of us [arXiv:2112.11431] recently
proposed a GW detection concept with $\mu$Hz sensitivity, based on
asteroid-to-asteroid ranging. From the detailed sensitivity projection for this
concept, we find both analytically and in simulation that purely gravitational
clump-matter interactions would yield one detectable transit every $\sim 20$
yrs, if clumps with mass $m_{\text{cl}} \sim 10^{14} \text{kg}$ saturate the
dark-matter (DM) density. Other (proposed) GW detectors using local TMs and
operating in higher frequency bands are sensitive to smaller clump masses and
have smaller rates of discoverable signals. We also consider the case of clumps
endowed with an additional attractive long-range clump-matter fifth force
significantly stronger than gravity (but evading known fifth-force
constraints). For the $\mu$Hz detector concept, we use simulations to show
that, for example, a clump-matter fifth-force $\sim 10^3$ times stronger than
gravity with a range of $\sim\text{AU}$ would boost the rate of detectable
transits to a few per year for clumps in the mass range $10^{11} \text{kg}
\lesssim m_{\text{cl}} \lesssim 10^{14} \text{kg}$, even if they are a $\sim
1$% sub-component of the DM. The ability of $\mu$Hz GW detectors to probe
asteroid-mass-scale dark objects that may otherwise be undetectable bolsters
the science case for their development.


  We formulate the Bethe Ansatz equations for the open super spin chain based
on the super Yangian of osp(M|2n) and with diagonal boundary conditions. We
then study the bulk and boundary scattering of the osp(1|2n) open spin chain.


  The building of mathematical and computer models of cities has a long
history. The core elements are models of flows (spatial interaction) and the
dynamics of structural evolution. In this article, we develop a stochastic
model of urban structure to formally account for uncertainty arising from less
predictable events. Standard practice has been to calibrate the spatial
interaction models independently and to explore the dynamics through
simulation. We present two significant results that will be transformative for
both elements. First, we represent the structural variables through a single
potential function and develop stochastic differential equations (SDEs) to
model the evolution. Secondly, we show that the parameters of the spatial
interaction model can be estimated from the structure alone, independently of
flow data, using the Bayesian inferential framework. The posterior distribution
is doubly intractable and poses significant computational challenges that we
overcome using Markov chain Monte Carlo (MCMC) methods. We demonstrate our
methodology with a case study on the London retail system.


  Recently, very large language models (LLMs) have shown exceptional
performance on several English NLP tasks with just in-context learning (ICL),
but their utility in other languages is still underexplored. We investigate
their effectiveness for NLP tasks in low-resource languages (LRLs), especially
in the setting of zero-labelled cross-lingual transfer (0-CLT), where no
labelled training data for the target language is available -- however training
data from one or more related medium-resource languages (MRLs) is utilized,
alongside the available unlabeled test data for a target language. We introduce
Self-Supervised Prompting (SSP), a novel ICL approach tailored for the 0-CLT
setting.
  SSP is based on the key observation that LLMs output more accurate labels if
in-context exemplars are from the target language (even if their labels are
slightly noisy). To operationalize this, since target language training data is
not available in 0-CLT, SSP operates in two stages. In Stage I, using source
MRL training data, target language's test data is noisily labeled. In Stage II,
these noisy test data points are used as exemplars in ICL for further improved
labelling. Additionally, our implementation of SSP uses a novel Integer Linear
Programming (ILP)-based exemplar selection that balances similarity, prediction
confidence (when available) and label coverage. Experiments on three tasks and
eleven LRLs (from three regions) demonstrate that SSP strongly outperforms
existing SOTA fine-tuned and prompting-based baselines in 0-CLT setup.


  This paper gives a construction of braid group actions on the derived
category of coherent sheaves on a variety $X$. The motivation for this is
Kontsevich's homological mirror conjecture, together with the occurrence of
certain braid group actions in symplectic geometry. One of the main results is
that when $\dim X \geq 2$, our braid group actions are always faithful.
  We describe conjectural mirror symmetries between smoothings and resolutions
of singularities that lead us to find examples of braid group actions arising
from crepant resolutions of various singularities. Relations with the McKay
correspondence and with exceptional sheaves on Fano manifolds are given.
Moreover, the case of an elliptic curve is worked out in some detail.


  Quantum low-density parity-check (QLDPC) codes have emerged as a promising
technique for quantum error correction. A variety of decoders have been
proposed for QLDPC codes and many of them utilize belief propagation (BP)
decoding in some fashion. However, the use of BP decoding for degenerate QLDPC
codes is known to have issues with convergence. These issues are typically
attributed to short cycles in the Tanner graph and code degeneracy (i.e.
multiple error patterns with the same syndrome). Although various methods have
been proposed to mitigate the non-convergence issue, such as BP with ordered
statistics decoding (BP-OSD) and BP with stabilizer inactivation (BP-SI),
achieving better performance with lower complexity remains an active area of
research.
  In this work, we propose a decoder for QLDPC codes based on BP guided
decimation (BPGD), which has been previously studied for constraint
satisfaction and lossy compression problems. The decimation process is
applicable to both binary and quaternary BP and it involves sequentially fixing
the value of the most reliable qubits to encourage BP convergence. Despite its
simplicity, We find that BPGD significantly reduces the BP failure rate due to
non-convergence, achieving performance on par with BP with ordered statistics
decoding and BP with stabilizer inactivation, without the need to solve systems
of linear equations.


  We curate a comprehensive dataset of 4,550 questions and solutions from
problem sets, midterm exams, and final exams across all MIT Mathematics and
Electrical Engineering and Computer Science (EECS) courses required for
obtaining a degree. We evaluate the ability of large language models to fulfill
the graduation requirements for any MIT major in Mathematics and EECS. Our
results demonstrate that GPT-3.5 successfully solves a third of the entire MIT
curriculum, while GPT-4, with prompt engineering, achieves a perfect solve rate
on a test set excluding questions based on images. We fine-tune an open-source
large language model on this dataset. We employ GPT-4 to automatically grade
model responses, providing a detailed performance breakdown by course,
question, and answer type. By embedding questions in a low-dimensional space,
we explore the relationships between questions, topics, and classes and
discover which questions and classes are required for solving other questions
and classes through few-shot learning. Our analysis offers valuable insights
into course prerequisites and curriculum design, highlighting language models'
potential for learning and improving Mathematics and EECS education.


  The present paper deals with the estimate of the differences of certain
positive linear operators and their derivatives. Our approach involves
operators defined on bounded intervals, as Bernstein operators, Kantorovich
operators, genuine Bernstein-Durrmeyer operators, Durrmeyer operators with
Jacobi weights. The estimates in quantitative form are given in terms of first
modulus of continuity. In order to analyze the theoretical results in the last
section we consider some numerical examples.


  In this paper, we settle the sampling complexity of solving discounted
two-player turn-based zero-sum stochastic games up to polylogarithmic factors.
Given a stochastic game with discount factor $\gamma\in(0,1)$ we provide an
algorithm that computes an $\epsilon$-optimal strategy with high-probability
given $\tilde{O}((1 - \gamma)^{-3} \epsilon^{-2})$ samples from the transition
function for each state-action-pair. Our algorithm runs in time nearly linear
in the number of samples and uses space nearly linear in the number of
state-action pairs. As stochastic games generalize Markov decision processes
(MDPs) our runtime and sample complexities are optimal due to Azar et al
(2013). We achieve our results by showing how to generalize a near-optimal
Q-learning based algorithms for MDP, in particular Sidford et al (2018), to
two-player strategy computation algorithms. This overcomes limitations of
standard Q-learning and strategy iteration or alternating minimization based
approaches and we hope will pave the way for future reinforcement learning
results by facilitating the extension of MDP results to multi-agent settings
with little loss.


  Many previous studies have demonstrated that work statistics can exhibit
certain singular behaviors in the quantum critical regimes of many-body systems
at zero or very low temperatures. However, as the temperature increases, it is
commonly believed that such singularities will vanish. Contrary to this common
recognition, we report a nonanalytic behavior of the averaged work done, which
occurs at finite temperature, in the Dicke model as well as the
Lipkin-Meshkov-Glick model subjected to the sudden quenches of their work
parameters. It is revealed that work statistics can be viewed as a signature of
the thermal phase transition when the quenched parameters are tuned across the
critical line that separates two different thermal phases.


  We demonstrate a two-player communication problem that can be solved in the
one-way quantum model by a 0-error protocol of cost O (log n) but requires
exponentially more communication in the classical interactive (bounded error)
model.


  For bounded right linear operators, in a right quaternionic Hilbert space
with a left multiplication defined on it, we study the approximate $S$-point
spectrum. In the same Hilbert space, then we study the Fredholm operators and
the Fredholm index. In particular, we prove the invariance of the Fredholm
index under small norm operator and compact operator perturbations. Finally, in
association with Fredholm operators, we develop the theory of essential
S-spectrum. We also characterize the $S$-spectrum in terms of the essential
S-spectrum and Fredholm operators. In the sequel we study left and right
S-spectrums as needed for the development of the theory presented in this note.


  Rydberg atoms provide a wide range of possibilities to tailor interactions in
a quantum gas. Here we report on Rydberg excitation of Bose-Einstein condensed
87Rb atoms. The Rydberg fraction was investigated for various excitation times
and temperatures above and below the condensation temperature. The excitation
is locally blocked by the van der Waals interaction between Rydberg atoms to a
density-dependent limit. Therefore the abrupt change of the thermal atomic
density distribution to the characteristic bimodal distribution upon
condensation could be observed in the Rydberg fraction. The observed features
are reproduced by a simulation based on local collective Rydberg excitations.


  We study the Higgs inflation model realized in the supersymmetric SU(5) grand
unified theory (GUT), focusing on its multifield dynamics and prediction of
cosmological observables. The requirement for GUT symmetry breaking during
inflation imposes tight constraints on the model parameters. We find,
nevertheless, with an appropriately chosen noncanonical Kahler potential the
model is in excellent agreement with the present cosmological observation. The
effects from multifield dynamics is found to be minor and thus, unlike other
similar supersymmetric implementation of nonminimally coupled Higgs inflation,
the prediction of this model is robust against multifield ambiguities.


  The large scale geometry of the late Universe can be decomposed as R$\times
{\Sigma}_3$, where R stands for cosmic time and ${\Sigma}_3$ is the three
dimensional spatial manifold. We conjecture that the spatial geometry of the
Universe's spatial section ${\Sigma}_3$ conforms with the Thurston-Perelman
theorem, according to which the geometry of $\Sigma_3$ is either one of the
eight geometries from the Thurston geometrization conjecture, or a combination
of Thurston geometries smoothly sewn together. We assume that topology of
individual geometries plays no observational role, i.e. the size of individual
geometries is much larger than the Hubble radius today. We investigate the
dynamics of each of the individual geometries by making use of the simplifying
assumption that our local Hubble patch consists of only one such geometry,
which is approximately homogeneous on very large scales, but spatial isotropy
is generally violated. Spatial anisotropies grow in time in decelerating
universes, but they decay in accelerating universes. The thus-created
anisotropy problem can be solved by a period of primordial inflation, akin to
how the flatness problem is solved. Therefore, as regards Universe's large
scale geometry, any of the Thurston's geometries should be considered on a par
with Friedmann's geometries. We consider two observational methods that can be
used to test our conjecture: one based on luminosity distance and one on
angular diameter distance measurements, but leave for the future their detailed
forecasting implementations.


  This survey focuses on the current problems in Earth systems science where
machine learning algorithms can be applied. It provides an overview of previous
work, ongoing work at the Ministry of Earth Sciences, Gov. of India, and future
applications of ML algorithms to some significant earth science problems. We
provide a comparison of previous work with this survey, a mind map of
multidimensional areas related to machine learning and a Gartner's hype cycle
for machine learning in Earth system science (ESS). We mainly focus on the
critical components in Earth Sciences, including atmospheric, Ocean,
Seismology, and biosphere, and cover AI/ML applications to statistical
downscaling and forecasting problems.


  We introduce a variant of the watchman route problem, which we call the
quickest pair-visibility problem. Given two persons standing at points $s$ and
$t$ in a simple polygon $P$ with no holes, we want to minimize the distance
they travel in order to see each other in $P$. We solve two variants of this
problem, one minimizing the longer distance the two persons travel (min-max)
and one minimizing the total travel distance (min-sum), optimally in linear
time. We also consider a query version of this problem for the min-max variant.
We can preprocess a simple $n$-gon in linear time so that the minimum of the
longer distance the two persons travel can be computed in $O(\log^2 n)$ time
for any two query positions $s,t$ where the two persons start.


  Large-scale vision-language models (VLMs) pre-trained on billion-level data
have learned general visual representations and broad visual concepts. In
principle, the well-learned knowledge structure of the VLMs should be inherited
appropriately when being transferred to downstream tasks with limited data.
However, most existing efficient transfer learning (ETL) approaches for VLMs
either damage or are excessively biased towards the prior knowledge, e.g.,
prompt tuning (PT) discards the pre-trained text-based classifier and builds a
new one while adapter-style tuning (AT) fully relies on the pre-trained
features. To address this, we propose a new efficient tuning approach for VLMs
named Task Residual Tuning (TaskRes), which performs directly on the text-based
classifier and explicitly decouples the prior knowledge of the pre-trained
models and new knowledge regarding a target task. Specifically, TaskRes keeps
the original classifier weights from the VLMs frozen and obtains a new
classifier for the target task by tuning a set of prior-independent parameters
as a residual to the original one, which enables reliable prior knowledge
preservation and flexible task-specific knowledge exploration. The proposed
TaskRes is simple yet effective, which significantly outperforms previous ETL
methods (e.g., PT and AT) on 11 benchmark datasets while requiring minimal
effort for the implementation. Our code is available at
https://github.com/geekyutao/TaskRes.


  We provide a sufficient condition for a measure on the real line to satisfy a
modified logarithmic Sobolev inequality, thus extending the criterion of Bobkov
and G\"{o}tze. Under mild assumptions the condition is also necessary.
Concentration inequalities are derived. This completes the picture given in
recent contributions by Gentil, Guillin and Miclo.


  Large wildfires pose a major environmental concern, and precise maps of fire
risk can improve disaster relief planning. Fosberg Fire Weather Index (FFWI) is
often used to measure wildfire risk; FFWI exhibits non-Gaussian marginal
distributions as well as strong spatiotemporal extremal dependence and thus,
modeling FFWI using geostatistical models like Gaussian processes is
questionable. Extreme value theory (EVT)-driven models like max-stable
processes are theoretically appealing but are computationally demanding and
applicable only for threshold exceedances or block maxima. Disaster management
policies often consider moderate-to-extreme quantiles of climate parameters and
hence, joint modeling of the bulk and the tail of the data is required. In this
paper, we consider a Dirichlet process mixture of spatial skew-t processes that
can flexibly model the bulk as well as the tail. The proposed model has
nonstationary mean and covariance structure, and also nonzero spatiotemporal
extremal dependence. A simulation study demonstrates that the proposed model
has better spatial prediction performance compared to some competing models. We
develop spatial maps of FFWI medians and extremes, and discuss the wildfire
risk throughout the Santa Ana region of California.


  The classical attenuation regulation of gene expression in bacteria is
considered. We propose to represent the secondary RNA structure in the leader
region of a gene or an operon by a term, and we give a probabilistic term
rewriting system modeling the whole process of such a regulation.


  By a result of Gerstenhaber and Schack the simplicial cohomology ring
$H^*(\mathcal{C};k)$ of a poset $\mathcal{C}$ is isomorphic to the Hochschild
cohomology ring $HH^*(k\mathcal{C})$ of the category algebra $k\mathcal{C}$,
where the poset is viewed as a category and $k$ is a field. Extending results
of Mishchenko [6], under certain assumptions on a category $\mathcal{C}$, we
construct a category $\mathcal{D}$ and a graded $k$-linear isomorphism
$HH^*(k\mathcal{C})\cong H^*(\mathcal{D}; k)$. Interpreting the degree one
cohomology, we also show how the $k$-space of derivations on $k\mathcal{C}$,
graded by some semigroup, corresponds to the $k$-space of characters on
$\mathcal{D}$.


  Neural ordinary differential equations (NODE) have been recently proposed as
a promising approach for nonlinear system identification tasks. In this work,
we systematically compare their predictive performance with current
state-of-the-art nonlinear and classical linear methods. In particular, we
present a quantitative study comparing NODE's performance against neural
state-space models and classical linear system identification methods. We
evaluate the inference speed and prediction performance of each method on
open-loop errors across eight different dynamical systems. The experiments show
that NODEs can consistently improve the prediction accuracy by an order of
magnitude compared to benchmark methods. Besides improved accuracy, we also
observed that NODEs are less sensitive to hyperparameters compared to neural
state-space models. On the other hand, these performance gains come with a
slight increase of computation at the inference time.


  Machine learning techniques are utilised in several areas of astrophysical
research today. This dissertation addresses the application of ML techniques to
two classes of problems in astrophysics, namely, the analysis of individual
astronomical phenomena over time and the automated, simultaneous analysis of
thousands of objects in large optical sky surveys. Specifically investigated
are (1) techniques to approximate the precise orbits of the satellites of
Jupiter and Saturn given Earth-based observations as well as (2) techniques to
quickly estimate the distances of quasars observed in the Sloan Digital Sky
Survey. Learning methods considered include genetic algorithms, particle swarm
optimisation, artificial neural networks, and radial basis function networks.
  The first part of this dissertation demonstrates that GAs and PSO can both be
efficiently used to model functions that are highly non-linear in several
dimensions. It is subsequently demonstrated in the second part that ANNs and
RBFNs can be used as effective predictors of spectroscopic redshift given
accurate photometry, especially in combination with other learning-based
approaches described in the literature. Careful application of these and other
ML techniques to problems in astronomy and astrophysics will contribute to a
better understanding of stellar evolution, binary star systems, cosmology, and
the large-scale structure of the universe.


  The step bunching instability is studied in three models of step motion
defined in terms of ordinary differential equations (ODE). The source of
instability in these models is step-step attraction, it is opposed by step-step
repulsion and the developing surface patterns reflect the balance between the
two. The first model, TE2, is a generalization of the seminal model of Tersoff
et al. (1995). The second one, LW2, is obtained from the model of Liu and Weeks
(1998) using the repulsions term to construct the attractions one with retained
possibility to change the parameters in the two independently. The third model,
MM2, is a minimal one constructed ad hoc and in this article it plays a central
role. New scheme for scaling the ODE in vicinal studies is applied towards
deciphering the pre-factors in the time-scaling relations. In all these models
the patterned surface is self-similar - only one length scale is necessary to
describe its evolution (hence B1-type). The bunches form finite angles with the
terraces. Integrating numerically the equations for step motion and changing
systematically the parameters we obtain the overall dependence of time-scaling
exponent \b{eta} on the power of step-step attractions p as \b{eta} = 1/(3+p)
for MM2 and hypothesize based on restricted set of data that it is \b{eta} =
1/(5+p) for LW2 and TE2.


  In recent years, China has witnessed the proliferation and success of the
online food delivery industry, an emerging type of the gig economy. Online food
deliverers who deliver the food from restaurants to customers play a critical
role in enabling this industry. Mediated by algorithms and coupled with
interactions with multiple stakeholders, this emerging kind of labor has been
taken by millions of people. In this paper, we present a mixed-methods analysis
to investigate this labor of online food deliverers and uncover how the
mediation of algorithms shapes it. Combining large-scale quantitative
data-driven investigations of 100,000 deliverers' behavioral data with in-depth
qualitative interviews with 15 online food deliverers, we demonstrate their
working activities, identify how algorithms mediate their delivery procedures,
and reveal how they perceive their relationships with different stakeholders as
a result of their algorithm-mediated labor. Our findings provide important
implications for enabling better experiences and more humanized labor of
deliverers as well as workers in gig economies of similar kinds.


  We investigate low-energy properties of a generalized spin ladder model with
both of the spin alternation and the bond alternation, which allows us to
systematically study not only ladder systems but also alternating spin chains.
By exploiting non-linear $\sigma$ model techniques we study the model with
particular emphasis on the competition between gapful and gapless states. Our
approach turns out to provide a more consistent semi-classical description of
alternating spin chains than that in the previous work. We also study a closely
related model, i.e., a spin chain with plaquette structure, and show that
frustration causes little effect on its low-energy properties so far as the
strength of frustration is weaker than a certain critical value.


  We study a perturbative scheme for normalization problems involving
resonances of the unperturbed situation, and therefore the necessity of a
non-trivial normal form, in the general framework of Banach scale Lie algebras
(this notion is defined in the article). This situation covers the case of
classical and quantum normal forms in a unified way which allows a direct
comparison. In particular we prove a precise estimate for the difference
between quantum and classical normal forms, proven to be of order of the square
of the Planck constant. Our method uses mould calculus (recalled in the
article) and properties of the solution of a universal mould equation studied
in a preceding paper.


  Using holographic duality, we investigate the impact of finite temperature on
the instability and splitting patterns of quadruply quantized vortices,
providing the first-ever analysis in this context. Through linear stability
analysis, we reveal the occurrence of two consecutive dynamical transitions. At
a specific low temperature, the dominant unstable mode transitions from the
$2$-fold rotational symmetry mode to the $3$-fold one, followed by a transition
from the $3$-fold one to the $4$-fold one at a higher temperature. As the
temperature is increased, we also observe the $5$ and $6$-fold rotational
symmetry unstable modes get excited successively. Employing the full non-linear
numerical simulations, we further demonstrate that these two novel dynamical
transitions, along with the temperature-induced instabilities for the $5$ and
$6$-fold rotational symmetry modes, can be identified by examining the
resulting distinct splitting patterns, which offers a promising route for the
experimental verification in the cold atom gases.


  The theory of Dvorak, Kral, and Thomas (2015) shows that a 4-critical
triangle-free graph embedded in the torus has only a bounded number of faces of
length greater than 4 and that the size of these faces is also bounded. We
study the natural reduction in such embedded graphs - identification of
opposite vertices in 4-faces. We give a computer-assisted argument showing that
there are exactly four 4-critical triangle-free irreducible toroidal graphs in
which this reduction cannot be applied without creating a triangle. Using this
result, we show that every 4-critical triangle-free graph embedded in the torus
has at most four 5-faces, or a 6-face and two 5-faces, or a 7-face and a
5-face, in addition to at least seven 4-faces. This result serves as a basis
for the exact description of $4$-critical triangle-free toroidal graphs, which
we present in a followup paper.


  We have studied the laser induced ultrafast quenching of Gd 4f magnetic order
in ferrimagnetic Co100-xGdx alloys to highlight the role of the inter-atomic
exchange coupling. We have taken advantage of the ultrashort soft X-ray pulses
deliver by the femtoslicing beamline at the BESSY II synchrotron radiation
source at the Helmholtz-Zentrum Berlin to perform element- and time-resolved
X-ray Magnetic Circular Dichroism spectroscopy.Our results show that the laser
induced quenching of Gd 4f magnetic order occurs on very different time-scales
for the Co72Gd28, the Co77Gd23 and the Co79Gd21 alloys. Most of the magnetic
moment losses occur within the first picosecond (ps) while the electron
distribution is strongly out of equilibrium. After the equilibration of the
electrons and lattice temperatures (t > 1 ps), the magnetic losses occur on
slower rates that depend on the alloy composition: increasing the Co
composition speeds up the demagnetization of Gd 4f sublattice. The strength of
the inter-atomic exchange coupling which depends on composition, determines the
efficiency of the angular momentum flow from the Gd 4f spin towards the
lattice. Our results are in qualitative agreements with the predictions of the
microscopic three temperatures model for ferrimagnetic alloys.


  In this paper, we prove sharp estimates for the average cost of the optimal
matching problem on the flat 2-torus, using quantitative linearization and the
method of trajectories.


  It is shown by Barchini, Kable, and Zierau that conformally invariant systems
of differential operators yield explicit homomorphisms between certain
generalized Verma modules. In this paper we determine whether or not the
homomorphisms arising from such systems of first and second order differential
operators associated to maximal parabolic subalgebras of quasi-Heisenberg type
are standard.


  Materials containing non-Kramers magnetic ions can show unusual quantum
excitations because of the exact mapping of the two-singlet crystal-field
ground state to a quantum model of Ising spins in a transverse magnetic field.
Here, we model the magnetic excitation spectrum of garnet-structured Ho3Ga5O12,
which has a two-singlet crystal-field ground state. We use a reaction-field
approximation to explain published inelastic neutron-scattering data [Zhou et
al., Phys. Rev. B 78, 140406(R) (2008)] using a three-parameter model
containing the magnetic dipolar interaction, the two-singlet crystal-field
splitting, and the nuclear hyperfine coupling. Our study clarifies the magnetic
Hamiltonian of Ho3Ga5O12, reveals that the nuclear hyperfine interaction drives
magnetic ordering in this system, and provides a framework for quantitative
analysis of magnetic excitation spectra of materials with singlet crystal-field
ground states.


  This paper introduces techniques for computing a variety of numerical
invariants associated to a Legendrian knot in a contact manifold presented by
an open book with a Morse structure. Such a Legendrian knot admits a front
projection to the boundary of a regular neighborhood of the binding. From this
front projection, we compute the rotation number for any null-homologous
Legendrian knot as a count of oriented cusps and linking or intersection
numbers; in the case that the manifold has non-trivial second homology, we can
recover the rotation number with respect to a Seifert surface in any homology
class. We also provide explicit formulas for computing the necessary
intersection numbers from the front projection, and we compute the Euler class
of the contact structure supported by the open book. Finally, we introduce a
notion of Lagrangian projection and compute the classical invariants of a
null-homologous Legendrian knot from its projection to a fixed page.


  Two approaches (micro- and macro- investigations) are used to determine the
dimension dependences of the optical parameters of the nanometer-scale layers
of materials. It is shown that both an index of refraction and coefficient of
absorption depend strongly on the thickness of the layer. In this region of
thicknesses, the dimension resonance occurs, where an index of refraction has a
maximum and a coefficient of absorption has a minimum. The numerical
calculation of the optical parameters of some materials (Ag, Al, Fe, Ge, Si,
Se, Te) have been carried out with the use of the experimental data of
reflection and transparency of thin layers, obtained in a series of works, and
with our formulas for the wave amplitudes and the laws of refractions. The
analogues of the Fresnel formulas and the Snell law have been derived from the
Maxwell boundary conditions where the absorption and conductivity of media were
taken into account. The use of our formulas for the wave amplitudes leads to
the fulfillment of the conservation law of energy both for the TE- and TM-
polarizations of light. The reemission of light is possible for the
thicknesses, which is equal to the wavelength of light in a medium, divisible
by integer:
$\frac{2{\pi}d_{res}}{2}={\lambda}_m{\cdot}m=\frac{{\lambda}_0}{n}{\cdot}m$,
where m=1,2,3... The visible luminescence of the porous silicon, silicon
whiskers and other nanometer-scale structures can be explained by their
emission in the case of dimension resonance because in this region of
thicknesses, layers have a big negative coefficient of absorption and little -
of a damping. It is also shown that in the case of the TM-polarization, in a
material with a high conductivity, light refracts in a "wrong" direction (at
all positive optical parameters) due to a surface current. In the case of the
TE-polarization, light refracts only in a "right" direction.


  The concentration of primary radiation induced defects has been previously
estimated considering both the explicit mechanisms of the primary interaction
between the incoming particle and the nuclei of the semiconductor lattice, and
the recoil energy partition between ionisation and displacements, in the frame
of the Lindhard theory. The primary displacement defects are vacancies and
interstitials, that are essentially unstable in silicon. They interact via
migration, recombination, annihilation or produce other defects. In the present
work, the time evolution of the concentration of defects induced by pions in
medium and high resistivity silicon for detectors is modelled, after
irradiation. In some approximations, the differential equations representing
the time evolution processes could be decoupled. The theoretical equations so
obtained are solved analytically in some particular cases, with one free
parameter, for a wide range of particle fluences and/or for a wide energy range
of the incident particles, for different temperatures; the corresponding
stationary solutions are also presented.


  In this paper, we present a covariant approach that utilizes Noether's second
theorem to derive a symmetric stress tensor from the grand thermodynamic
potential functional. We focus on the practical case where the density of the
grand thermodynamic potential is dependent on the first and second coordinate
derivatives of the scalar order parameters. Our approach is applied to several
models of inhomogeneous ionic liquids that consider electrostatic correlations
of ions or short-range correlations related to packing effects. Specifically,
we derive analytical expressions for the symmetric stress tensors of the
Cahn-Hilliard-like model, Bazant-Storey-Kornyshev model, and
Maggs-Podgornik-Blossey model. All of these expressions are found to be
consistent with respective self-consistent field equations.


  Instead of Lorentz invariance, gravitational degrees of freedom may obey
Lifshitz scaling at high energies, as it happens in Ho\v{r}ava's proposal for
quantum gravity. We study consequences of this proposal for the spectra of
primordial perturbations generated at inflation. Breaking of 4D diffeomorphism
(Diff) invariance down to the foliation-preserving Diff in Ho\v{r}ava-Lifshitz
(HL) gravity leads to appearance of a scalar degree of freedom in the gravity
sector, khronon, which describes dynamics of the time foliation. One can
naively expect that mixing between inflaton and khronon will jeopardize
conservation of adiabatic perturbations at super Hubble scales. This indeed
happens in the projectable version of the theory. By contrast, we find that in
the non-projectable version of HL gravity, khronon acquires an effective mass
which is much larger than the Hubble scale well before the Hubble crossing time
and decouples from the adiabatic curvature perturbation $\zeta$ sourced by the
inflaton fluctuations. As a result, at super Hubble scales the adiabatic
perturbation $\zeta$ behaves as in an effectively single field system and its
spectrum is conserved in time. Lifshitz scaling is imprinted in the power
spectrum of $\zeta$ through the modified dispersion relation of the inflaton.
We point out violation of the consistency relation between the tensor-to-scalar
ratio and the spectral tilt of primordial gravitational waves and suggest that
it can provide a signal of Lorentz violation in inflationary era.


  Semi-annihilation is a generic feature of dark matter theories with
symmetries larger than Z2. We investigate two examples with multi-component
dark sectors comprised of an SU(2)L singlet or triplet fermion besides a scalar
singlet. These are respectively the minimal fermionic semi-annihilating model,
and the minimal case for a gauge-charged fermion. We study the relevant dark
matter phenomenology, including the interplay of semi-annihilation and the
Sommerfeld effect. We demonstrate that semi-annihilation in the singlet model
can explain the gamma ray excess from the galactic center. For the triplet
model we scan the parameter space, and explore how signals and constraints are
modified by semi-annihilation. We find that the entire region where the model
comprises all the observed dark matter is accessible to current and planned
direct and indirect searches.


  Maximum cardinality matching in bipartite graphs is an important and
well-studied problem. The fully dynamic version, in which edges are inserted
and deleted over time has also been the subject of much attention. Existing
algorithms for dynamic matching (in general graphs) seem to fall into two
groups: there are fast (mostly randomized) algorithms that do not achieve a
better than 2-approximation, and there slow algorithms with $\O(\sqrt{m})$
update time that achieve a better-than-2 approximation. Thus the obvious
question is whether we can design an algorithm -- deterministic or randomized
-- that achieves a tradeoff between these two: a $o(\sqrt{m})$ approximation
and a better-than-2 approximation simultaneously. We answer this question in
the affirmative for bipartite graphs.
  Our main result is a fully dynamic algorithm that maintains a $3/2 + \eps$
approximation in worst-case update time $O(m^{1/4}\eps^{/2.5})$. We also give
stronger results for graphs whose arboricity is at most $\al$, achieving a $(1+
\eps)$ approximation in worst-case time $O(\al (\al + \log n))$ for constant
$\eps$. When the arboricity is constant, this bound is $O(\log n)$ and when the
arboricity is polylogarithmic the update time is also polylogarithmic.
  The most important technical developement is the use of an intermediate graph
we call an edge degree constrained subgraph (EDCS). This graph places
constraints on the sum of the degrees of the endpoints of each edge: upper
bounds for matched edges and lower bounds for unmatched edges. The main
technical content of our paper involves showing both how to maintain an EDCS
dynamically and that and EDCS always contains a sufficiently large matching. We
also make use of graph orientations to help bound the amount of work done
during each update.


  We present the detection of He II sources in the Im galaxy NGC 1569 from HST
WFPC2 imagery. Out of the fifteen detections, seven were Wolf-Rayet stars, five
were stellar clusters with associated He II emission, and three were sources of
unknown origin. The detected Wolf-Rayet stars' colors and magnitudes are
similar to Large Magellanic Cloud late-type WN stars. The physical origin of
the other He II sources are discussed. We conclude that the equivalent of
51+/-19 WNL stars have been detected in NGC 1569, and we have estimated the
total Wolf-Rayet population in NGC 1569 as 78+/-51. These numbers are compared
with the Wolf-Rayet stellar populations in the SMC, LMC, Milky Way, and other
starburst galaxies relative to their luminosities, dynamical masses, and
ionized gas masses. Previous to this study, Wolf-Rayet stars in NGC 1569 were
not detected using ground-based imagery, but were only indicated through
longslit spectroscopy. This is the first time the exact locations of the
Wolf-Rayet stars in this nearby, well-studied, "post-starburst" galaxy have
been determined.


  Given a manifold $\mathbb{M}$ admitting a maximally supersymmetric consistent
truncation, we show how to formulate new consistent truncations by restricting
to a set of Kaluza-Klein modes on $\mathbb{M}$ invariant under some subgroup of
the group of isometries of $\mathbb{M}$. These truncations may involve either
finite or infinite sets of modes. We provide their global description using
exceptional generalised geometry to construct a `deformed' generalised
parallelisation starting with that on $\mathbb{M}$. This allows us to
explicitly embed known consistent truncations directly into exceptional
generalised geometry/exceptional field theory, and to obtain the equations
governing situations where the consistent truncation retains an infinite tower
of modes.


  In this first part of a study of ordered operator spaces, we develop the
basic theory of `ordered C*-bimodules'. A crucial role is played by `open
central tripotents', a JB*-triple variant of Akemann's notion of open
projection.


  We present a combinatorial method for a calculation of knot Floer homology
with Z-coefficient of (1,1)-knots, and then demonstrate it for non-alternating
(1,1)-knots with ten crossings and the pretzel knots of type (-2,m,n). Our
calculations determine the unknotting numbers and 4-genera of the pretzel knots
of this type.


  3-dimensional (3D) reconstruction is an emerging field in image processing
and computer vision that aims to create 3D visualizations/ models of objects/
scenes from image sets. However, its commercial applications and benefits are
yet to be fully explored. In this paper, we describe ongoing work towards
assessing the value of 3D reconstruction in the building construction domain.
We present preliminary results from a user study, where our objective is to
understand the use of visual information in building construction in order to
determine problems with the use of visual information and identify potential
benefits and scenarios for the use of 3D reconstruction.


  In an efficient stock market, the log-returns and their time-dependent
variances are often jointly modelled by stochastic volatility models (SVMs).
Many SVMs assume that errors in log-return and latent volatility process are
uncorrelated, which is unrealistic. It turns out that if a non-zero correlation
is included in the SVM (e.g., Shephard (2005)), then the expected log-return at
time t conditional on the past returns is non-zero, which is not a desirable
feature of an efficient stock market. In this paper, we propose a
mean-correction for such an SVM for discrete-time returns with non-zero
correlation. We also find closed form analytical expressions for higher moments
of log-return and its lead-lag correlations with the volatility process. We
compare the performance of the proposed and classical SVMs on S&P 500 index
returns obtained from NYSE.


  In the present paper, we investigate the collapsed phase of the interacting
partially-directed self-avoiding walk (IPDSAW) that was introduced in Zwanzig
and Lauritzen (1968). We provide sharp asymptotics of the partition function
inside the collapsed phase, proving rigorously a conjecture formulated in
Guttmann (2015) and Owczarek et al. (1993). As a by-product of our result, we
obtain that, inside the collapsed phase, a typical IPDSAW trajectory is made of
a unique macroscopic bead, consisting of a concatenation of long vertical
stretches of alternating signs, outside which only finitely many monomers are
lying.


  A traditional paper-based passport contains a Machine- Readable Zone (MRZ)
and a Visual Inspection Zone (VIZ). The MRZ has two lines of the holder's
personal data, some document data, and verification characters encoded using
the Optical Character Recognition font B (OCRB). The encoded data includes the
holder's name, date of birth, and other identifying information for the holder
or the document. The VIZ contains the holder's photo and signature, usually on
the data page. However, the MRZ and VIZ can be easily duplicated with normal
document reproduction technology to produce a fake passport which can pass
traditional verification. Neither of these features actively verify the
holder's identity; nor do they bind the holder's identity to the document. A
passport also contains pages for stamps of visas and of country entry and exit
dates, which can be easily altered to produce fake permissions and travel
records. The electronic passport, supporting authentication using secure
credentials on a tamper-resistant chip, is an attempt to improve on the
security of the paper-based passport at minimum cost. This paper surveys the
security mechanisms built into the firstgeneration of authentication mechanisms
and compares them with second-generation passports. It analyzes and describes
the cryptographic protocols used in Basic Access Control (BAC) and Extended
Access Control (EAC).


  In this paper, we investigate the extent to which knowledge compilation can
be used to improve inference from propositional weighted bases. We present a
general notion of compilation of a weighted base that is parametrized by any
equivalence--preserving compilation function. Both negative and positive
results are presented. On the one hand, complexity results are identified,
showing that the inference problem from a compiled weighted base is as
difficult as in the general case, when the prime implicates, Horn cover or
renamable Horn cover classes are targeted. On the other hand, we show that the
inference problem becomes tractable whenever DNNF-compilations are used and
clausal queries are considered. Moreover, we show that the set of all preferred
models of a DNNF-compilation of a weighted base can be computed in time
polynomial in the output size. Finally, we sketch how our results can be used
in model-based diagnosis in order to compute the most probable diagnoses of a
system.


  This letter presents wide-field optical and and NIR UBVRI,Halpha,K' images of
the galaxy M74 which were taken between 0.6-8.3 years before the discovery of
the Type Ic SN2002ap. We have located the position of the SN on these images
with an accuracy of 0.3''. We find no sign of a progenitor object on any of the
images. The deepest of these images is the B-band exposure which has a
sensitivity limit corresponding to an absolute magnitude of M_B <= -6.3. From
our observed limits, we rule out as the progenitor all evolved states of single
stars with initial masses greater than 20Msol unless the WR phase has been
entered. Two popular theories for the origin of Type Ic SNe are the core
collapse of massive stars when they are in the WR phase, or the core collapse
of a massive star in an interacting binary which has had its envelope stripped
through mass transfer. Our prediscovery images are sensitive only to the most
luminous ~30% of WR stars, leaving a substantial fraction of typical WR stars
as viable progenitors. The energetics measured from modelling the spectral
evolution of SN 2002ap suggest an explosion of a 5Msol C+O core. While WR stars
generally have measured final masses greater than this, the uncertainties
associated with the explosion model, stellar evolutionary calculations and mass
measurements suggest we cannot definitively rule out a WR star progenitor. The
alternative scenario is that the progenitor was a star of initial mass
20-25Msol which was part of an interacting binary. We discuss future
observations which will provide further constraints on the nature of the
progenitor.


  Non-stationarity appears in many online applications such as web search and
advertising. In this paper, we study the online learning to rank problem in a
non-stationary environment where user preferences change abruptly at an unknown
moment in time. We consider the problem of identifying the K most attractive
items and propose cascading non-stationary bandits, an online learning variant
of the cascading model, where a user browses a ranked list from top to bottom
and clicks on the first attractive item. We propose two algorithms for solving
this non-stationary problem: CascadeDUCB and CascadeSWUCB. We analyze their
performance and derive gap-dependent upper bounds on the n-step regret of these
algorithms. We also establish a lower bound on the regret for cascading
non-stationary bandits and show that both algorithms match the lower bound up
to a logarithmic factor. Finally, we evaluate their performance on a real-world
web search click dataset.


  Let $G$ be an arbitrary (not necessarily isomorphic to a closed subgroup of
$\mathrm{GL}(r,\mathbb{C})$) complex Lie group, $U$ a complex manifold and
$p:P\to U$ a $\mathcal{C}^\infty$ principal $G$-bundle on $U$. We introduce and
study the space $\mathcal{J}^\kappa_P$ of bundle almost complex structures of
H{\"o}lder class $\mathcal{C}^\kappa$ on $P$. To any $J\in
\mathcal{J}^\kappa_P$ we associate an $\mathrm{Ad}(P)$-valued form
$\mathfrak{f}_J$ of type (0,2) on $U$ which should be interpreted as the
obstruction to the integrability of $J$. For $\kappa\geq 1$ we have
$\mathfrak{f}_J\in\mathcal{C}^{\kappa-1}(U,\bigwedge\hspace{-3.5pt}^{0,2}_{\,\,U}\otimes\mathrm{Ad}(P))$
whereas, for $\kappa\in[0,1)$, $\mathfrak{f}_J$ is a form with distribution
coefficients. Let $J\in \mathcal{J}^\kappa_P$ with $\kappa\in
(0,+\infty]\setminus\mathbb{N}$. We prove that $J$ admits locally
$J$-pseudo-holomorphic sections of class $\mathcal{C}^{\kappa+1}$ if and only
if $\mathfrak{f}_J=0$. If this is the case, $J$ defines a holomorphic reduction
of the underlying $\mathcal{C}^{\kappa+1}$-bundle of $P$ in the sense of the
theory of principal bundles on complex manifolds. The proof is based on
classical regularity results for the $\bar\partial$-Neumann operator on
compact, strictly pseudo-convex complex manifolds with boundary.The result will
be used in forthcoming articles dedicated to moduli spaces of holomorphic
bundles (on a compact complex manifold $X$) framed along a real hypersurface
$S\subset X$.


  Privacy and security are often intertwined. For example, identity theft is
rampant because we have become accustomed to authentication by identification.
To obtain some service, we provide enough information about our identity for an
unscrupulous person to steal it (for example, we give our credit card number to
Amazon.com). One of the consequences is that many people avoid e-commerce
entirely due to privacy and security concerns. The solution is to perform
authentication without identification. In fact, all on-line actions should be
as anonymous as possible, for this is the only way to guarantee security for
the overall system. A credential system is a system in which users can obtain
credentials from organizations and demonstrate possession of these credentials.
Such a system is anonymous when transactions carried out by the same user
cannot be linked. An anonymous credential system is of significant practical
relevance because it is the best means of providing privacy for users.


  The goal of program synthesis is to automatically generate programs in a
particular language from corresponding specifications, e.g. input-output
behavior. Many current approaches achieve impressive results after training on
randomly generated I/O examples in limited domain-specific languages (DSLs), as
with string transformations in RobustFill. However, we empirically discover
that applying test input generation techniques for languages with control flow
and rich input space causes deep networks to generalize poorly to certain data
distributions; to correct this, we propose a new methodology for controlling
and evaluating the bias of synthetic data distributions over both programs and
specifications. We demonstrate, using the Karel DSL and a small Calculator DSL,
that training deep networks on these distributions leads to improved
cross-distribution generalization performance.


  This article describes a formal proof of the Kepler conjecture on dense
sphere packings in a combination of the HOL Light and Isabelle proof
assistants. This paper constitutes the official published account of the now
completed Flyspeck project.


  We construct marginal operators of the orbifold SCFT corresponding to all
twenty near-horizon moduli in supergravity, including operators involving twist
fields which correspond to the blowing up modes. We identify the operators with
the supergravity moduli in a 1-1 fashion by inventing a global SO(4) algebra in
the SCFT. We analyze the gauge dynamics of the D1/D5 system relevant to the
splitting $(Q_1,Q_5)\to (Q'_1,Q'_5)+ (Q''_1,Q''_5)$ with the help of a linear
sigma model. We show in supergravity as well as in SCFT that the absorption
cross-section for minimal scalars is the same all over the near-horizon moduli
space.


  Dealing with datasets of very high dimension is a major challenge in machine
learning. In this paper, we consider the problem of feature selection in
applications where the memory is not large enough to contain all features. In
this setting, we propose a novel tree-based feature selection approach that
builds a sequence of randomized trees on small subsamples of variables mixing
both variables already identified as relevant by previous models and variables
randomly selected among the other variables. As our main contribution, we
provide an in-depth theoretical analysis of this method in infinite sample
setting. In particular, we study its soundness with respect to common
definitions of feature relevance and its convergence speed under various
variable dependance scenarios. We also provide some preliminary empirical
results highlighting the potential of the approach.


  We study the strong unique continuation property backwards in time for the
nonlocal equation in $\mathbb{R}^{n} \times \mathbb{R}$
\begin{equation}\label{one} (\partial_t - \Delta)^{s} u = V(x,t)u
  \end{equation} for $s \in (0,1)$. Our main result Theorem 1.2 can be thought
of as the nonlocal counterpart of the result obtained by Poon for the case when
$s=1$. In order to prove Theorem 1.2 we develop the regularity theory of the
extension problem for the equation above. With such theory in hands we
establish:
  i) a basic monotonicity result for an adjusted frequency function which plays
a central role in this paper, see Theorem 1.3;
  ii) an extensive blowup analysis of the so-called Almgren rescalings
associated with the extension problem.
  We feel that our work will also be of interest e.g. in the study of certain
basic open questions in free boundary problems, as well as in nonlocal
segregation problems.


  We run numerical simulations of the disruption of satellite galaxies in a
Galactic potential to build up the entire stellar halo, in order to investigate
what the next generation of astrometric satellites will reveal by observing the
halo of the Milky Way. We generate artificial DIVA, FAME and GAIA halo
catalogues, in which we look for the signatures left by the accreted
satellites. We develop a method based on the standard Friends-of-Friends
algorithm applied to the space of integrals of motion. We find this simple
method can recover about 50% of the different accretion events, when the
observational uncertainties expected for GAIA are taken into account, even when
the exact form of the Galactic potential is unknown. The recovery rate for DIVA
and FAME is much smaller, but these missions, like GAIA, should be able to test
the hierarchical formation paradigm on our Galaxy by measuring the amount of
halo substructure in the form of nearby kinematically cold streams with for
example, a two-point correlation function in velocity space.


  This work aims to study a scalable state-space model (SSM), Mamba, for the
speech enhancement (SE) task. We exploit a Mamba-based regression model to
characterize speech signals and build an SE system upon Mamba, termed SEMamba.
We explore the properties of Mamba by integrating it as the core model in both
basic and advanced SE systems, along with utilizing signal-level distances as
well as metric-oriented loss functions. SEMamba demonstrates promising results
and attains a PESQ score of 3.55 on the VoiceBank-DEMAND dataset. When combined
with the perceptual contrast stretching technique, the proposed SEMamba yields
a new state-of-the-art PESQ score of 3.69.


  We compare the dynamics of a Bose-Einstein condensate in two coupled
potential wells with atoms diffracting from a standing light wave. The
corresponding Hamiltonians have an identical appearance, but with a different
set of commutation rules. Well-known diffraction phenomena as Pendellosung
oscillations between opposite momenta in the case of Bragg diffraction, and
adiabatic transitions between momentum states are shown to have analogies in
the two-well case. They represent the collective exchange of a fixed number of
atoms between the wells.


  The dynamics of quantum Fisher information (QFI) of the phase parameter in a
driven two-state system is studied within the framework of non-Markovian
dissipative process. The influences of memory effects, classical driving and
detunings on the parameter-estimation precision are demonstrated by exactly
solving the Hamiltonian under rotating-wave approximation. In sharp contrast
with the results obtained in the presence of Markovian dissipation, we find
that classical driving can drastically enhance the QFI, namely, the precision
of parameter estimation in the non-Markovian regime. Moreover, the
parameter-estimation precision may even be preserved from the influence of
surrounding non-Markovian dissipation with the assistance of classical driving.
Remarkably, we reveal that the enhancement and preservation of QFI highly
depend on the combination of classical driving and non-Markovian effects.
Finally, a phenomenological explanation of the underlying mechanism is
presented in detail via the quasimode theory


  In the quest to find quantum spin liquids, layered cobalt oxides Na2Co2TeO6
and Na3Co2SbO6 have been proposed as promising candidates for approximating the
Kitaev honeycomb model. Yet, their suitability has been thrown into question
due to observed long-range magnetic order at low temperatures and indications
of easy-plane, rather than Kitaev-type, spin anisotropy. Here we use muon spin
relaxation to reveal an unexpected picture: contrary to the anticipated static
nature of the long-range order, the systems show prevalent spin dynamics with
spatially uneven distribution and varied correlation times. This underlines
that the magnetic ground states cannot be solely described by the long-range
order, suggesting a significant role of quantum fluctuations. Our findings not
only shed new light on the complex physics of these systems but also underscore
the need for a refined approach in the search for realizable quantum spin
liquids.


  This is the write-up of a talk given in RIMS conference ``Analytic and
arithmetic aspects of automorphic representations", where I outlined two kinds
of different results related to the D4 lattice, obtained in a joint work with
Hirao and Nozaki. In general, from the design theoretical viewpoints, we are
interested in determining the harmonic strength of finite subsets on the unit
sphere. When considering the shells of a lattice, this problem shifts to the
non-vanishing problem of the Fourier coefficients of elliptic cusp forms.
Various instances, mostly from root lattices, are listed in this note.


  We study a Heisenberg chain with nearest-neighbor (NN) J1 and next-NN J2
exchange interactions with anisotropies Delta_1 and Delta_2 respectively. We
investigate by analytical and numerical methods the region of parameters for
which there is a jump in the magnetization M as a function of magnetic field B.
Some materials with edge sharing CuO polihedra are candidates to show an abrupt
change in M(B).


  We define a higher level version of the affine Hecke algebra and prove that,
after completion, this algebra is isomorphic to a completion of Webster's
tensor product algebra of type A. We then introduce a higher level version of
the affine Schur algebra and establish, again after completion, an isomorphism
with the quiver Schur algebra. An important observation is that the higher
level affine Schur algebra surjects to the Dipper-James-Mathas cyclotomic
q-Schur algebra. Moreover, we give nice diagrammatic presentations for all the
algebras introduced in this paper.


  This paper presents a novel systematic methodology to obtain new simple and
tight approximations, lower bounds, and upper bounds for the Gaussian
Q-function, and functions thereof, in the form of a weighted sum of exponential
functions. They are based on minimizing the maximum absolute or relative error,
resulting in globally uniform error functions with equalized extrema. In
particular, we construct sets of equations that describe the behaviour of the
targeted error functions and solve them numerically in order to find the
optimized sets of coefficients for the sum of exponentials. This also allows
for establishing a trade-off between absolute and relative error by controlling
weights assigned to the error functions' extrema. We further extend the
proposed procedure to derive approximations and bounds for any polynomial of
the Q-function, which in turn allows approximating and bounding many functions
of the Q-function that meet the Taylor series conditions, and consider the
integer powers of the Q-function as a special case. In the numerical results,
other known approximations of the same and different forms as well as those
obtained directly from quadrature rules are compared with the proposed
approximations and bounds to demonstrate that they achieve increasingly better
accuracy in terms of the global error, thus requiring significantly lower
number of sum terms to achieve the same level of accuracy than any reference
approach of the same form.


  This paper presents three results on F-singularities. First, we give a new
proof of Eisenstein's restriction theorem for adjoint ideal sheaves, using the
theory of F-singularities. Second, we show that a conjecture of Musta\c{t}\u{a}
and Srinivas implies a conjectural correspondence of F-purity and log
canonicity. Finally, we prove this correspondence when the defining equations
of the variety are very general.


  Kalman and H-infinity filters, the most popular paradigms for linear state
estimation, are designed for very specific specific noise and disturbance
patterns, which may not appear in practice. State observers based on the
minimization of regret measures are a promising alternative, as they aim to
adapt to recognizable patterns in the estimation error. In this paper, we show
that the regret minimization problem for finite horizon estimation can be cast
into a simple convex optimization problem. For this purpose, we first rewrite
linear time-varying system dynamics using a novel system level synthesis
parametrization for state estimation, capable of handling both disturbance and
measurement noise. We then provide a tractable formulation for the minimization
of regret based on semi-definite programming. Both contributions make the
minimal regret observer design easily implementable in practice. Finally,
numerical experiments show that the computed observer can significantly
outperform both H-2 and H-infinity filters.


  Machine learning is advancing towards a data-science approach, implying a
necessity to a line of investigation to divulge the knowledge learnt by deep
neuronal networks. Limiting the comparison among networks merely to a
predefined intelligent ability, according to ground truth, does not suffice, it
should be associated with innate similarity of these artificial entities. Here,
we analysed multiple instances of an identical architecture trained to classify
objects in static images (CIFAR and ImageNet data sets). We evaluated the
performance of the networks under various distortions and compared it to the
intrinsic similarity between their constituent kernels. While we expected a
close correspondence between these two measures, we observed a puzzling
phenomenon. Pairs of networks whose kernels' weights are over 99.9% correlated
can exhibit significantly different performances, yet other pairs with no
correlation can reach quite compatible levels of performance. We show
implications of this for transfer learning, and argue its importance in our
general understanding of what intelligence is, whether natural or artificial.


  We study how rotation affects observable amplitudes of high-order g- and
mixed r/g-modes and examine prospects for their detection and identification.
Our formalism, which is described in some detail, relies on a nonadiabatic
generalization of the traditional approximation. Numerical results are
presented for a number of unstable modes in a model of SPB star, at rotation
rates up to 250 km/s. It is shown that rotation has a large effect on mode
visibility in light and in mean radial velocity variations. In most cases, fast
rotation impairs mode detectability of g-modes in light variation, as Townsend
(2003b) has already noted, but it helps detection in radial velocity variation.
The mixed modes, which exist only at sufficiently fast rotation, are also more
easily seen in radial velocity. The amplitude ratios and phase differences are
strongly dependent on the aspect, the rotational velocity and on the mode. The
latter dependence is essential for mode identification.


  We present broad band optical afterglow observations of a long duration GRB
060124 using the 1.04-m Sampurnanand Telescope at ARIES, Nainital and the
2.01-m HCT at IAO, Hanle, including the earliest ground based observations in R
band for this GRB. We determine the decay slope of the light curve at different
bands and examine the reality of a proposed jet break. We use data from our
observations as well as others reported in the literature to construct light
curves in different bands and make power law fits to them. The spectral slope
of the afterglow emission in the optical band is estimated. Our first R-band
observations were taken $\sim 0.038$~d after burst. We find that all available
optical data after this epoch are well fit by a single power law, with a
temporal flux decay index $\alpha\sim 0.94$. We do not find any evidence of a
jet break within our data, which extend till $\sim 2$~d after the burst. The
X-ray light curve, however, shows a distinct break around 0.6 day. We attribute
this break to a steepening of the electron energy spectrum at high energies. We
conclude that the above measurements are consistent with the picture of a
standard fireball evolution with no jet break within $t\sim 2$~days after the
burst. This sets a lower limit of $3\times 10^{50}$~erg to the total energy
released in the explosion.


  In their third observing run, the LIGO-Virgo-KAGRA gravitational-wave (GW)
observatory was sensitive to binary black hole (BBH) mergers out to redshifts
$z_\mathrm{merge}\approx1$. Because GWs are inefficient at shrinking the binary
orbit, some of these BBH systems likely experienced long delay times $\tau$
between the formation of their progenitor stars at $z_\mathrm{form}$ and their
GW merger at $z_\mathrm{merge}$. In fact, the distribution of delay times
predicted by isolated binary evolution resembles a power law
$p(\tau)\propto\tau^{\alpha_\tau}$ with slope
$-1\lesssim\alpha_\tau\lesssim-0.35$ and a minimum delay time of
$\tau_\mathrm{min}=10$ Myr. We use these predicted delay time distributions to
infer the formation redshifts of the $\sim70$ BBH events reported in the third
GW transient catalog GWTC-3 and the formation rate of BBH progenitors. For our
default $\alpha_\tau=-1$ delay time distribution, we find that GWTC-3 contains
at least one system (with 90\% credibility) that formed earlier than
$z_\mathrm{form}>4.4$. Comparing our inferred BBH progenitor formation rate to
the star formation rate (SFR), we find that at $z_\mathrm{form}=4$, the number
of BBH progenitor systems formed per stellar mass was
$6.4^{+9.4}_{-5.5}\times10^{-6}\,M_\odot^{-1}$ and this yield dropped to
$0.134^{+1.6}_{-0.127}\times10^{-6}\,M_\odot^{-1}$ by $z_\mathrm{form}=0$. We
discuss implications of this measurement for the cosmic metallicity evolution,
finding that for typical assumptions about the metallicity-dependence of the
BBH yield, the average metallicity at $z_\mathrm{form}=4$ was
$\langle\log_{10}(Z/Z_\odot)\rangle=-0.3^{+0.3}_{-0.4}$, although the inferred
metallicity can vary by a factor of $\approx3$ for different assumptions about
the BBH yield. Our results highlight the promise of current GW observatories to
probe high-redshift star formation.


  Although various image-based domain adaptation (DA) techniques have been
proposed in recent years, domain shift in videos is still not well-explored.
Most previous works only evaluate performance on small-scale datasets which are
saturated. Therefore, we first propose two large-scale video DA datasets with
much larger domain discrepancy: UCF-HMDB_full and Kinetics-Gameplay. Second, we
investigate different DA integration methods for videos, and show that
simultaneously aligning and learning temporal dynamics achieves effective
alignment even without sophisticated DA methods. Finally, we propose Temporal
Attentive Adversarial Adaptation Network (TA3N), which explicitly attends to
the temporal dynamics using domain discrepancy for more effective domain
alignment, achieving state-of-the-art performance on four video DA datasets
(e.g. 7.9% accuracy gain over "Source only" from 73.9% to 81.8% on "HMDB -->
UCF", and 10.3% gain on "Kinetics --> Gameplay"). The code and data are
released at http://github.com/cmhungsteve/TA3N.


  We study entanglement dynamics of the three-qubit system which is initially
prepared in pure Greenberger-Horne- Zeilinger (GHZ) or W state and transmitted
through one of the Pauli channels $\sigma_z, \, \sigma_x, \, \sigma_y$ or the
depolarizing channel. With the help of the lower bound for three-qubit
concurrence we show that the W state preserves more entanglement than the GHZ
state in transmission through the Pauli channel $\sigma_z$. For the Pauli
channels $\sigma_x, \, \sigma_y$ and the depolarizing channel, however, the
entanglement of the GHZ state is more resistant against decoherence than the
W-type entanglement. We also briefly discuss how the accuracy of the lower
bound approximation depends on the rank of the density matrix under
consideration.


  Most stars host convection zones in which heat is transported directly by
fluid motion, but the behavior of convective boundaries is not well understood.
Here we present 3D numerical simulations which exhibit penetration zones:
regions where the entire luminosity \emph{could} be carried by radiation, but
where the temperature gradient is approximately adiabatic and convection is
present. To parameterize this effect, we define the "penetration parameter"
$\mathcal{P}$ which compares how far the radiative gradient deviates from the
adiabatic gradient on either side of the Schwarzschild convective boundary.
Following Roxburgh (1989) and Zahn (1991), we construct an energy-based
theoretical model in which $\mathcal{P}$ controls the extent of penetration. We
test this theory using 3D numerical simulations which employ a simplified
Boussinesq model of stellar convection. The convection is driven by internal
heating and we use a height-dependent radiative conductivity; this allows us to
separately specify $\mathcal{P}$ and the stiffness $\mathcal{S}$ of the
radiative-convective boundary. We find significant convective penetration in
all simulations. Our simple theory describes the simulations well. Penetration
zones can take thousands of overturn times to develop, so long simulations or
accelerated evolutionary techniques are required. In stars, we expect
$\mathcal{P} \approx 1$ and in this regime our results suggest that convection
zones may extend beyond the Schwarzschild boundary by up to $\sim$20-30% of a
mixing length. We present a MESA stellar model of the Sun which employs our
parameterization of convective penetration as a proof of concept. We discuss
prospects for extending these results to more realistic stellar contexts.


  Meetings are typically considered to be the fuel of an organization's
productivity -- a place where employees discuss ideas and make collective
decisions. However, it is no secret that meetings are also often perceived as
wasteful vacuums, depleting employee morale and productivity, likely due to the
fact that current technologies fall short in fully supporting physical or
virtual meeting experience. In this position paper, we discuss the three key
elements that make a meeting successful (i.e., execution, psychological safety,
and physical comfort), and present new tools for hybrid meetings that
incorporate those elements. As past research has focused on supporting meeting
execution (the first element), we set the roadmap for future research on the
two other elements: on psychological safety by articulating how new
technologies could make meeting useful for all participants, ensure all
participants give and receive appropriate levels of attention, and enable all
participants to feel and make others feel comfortable; and on physical comfort
by dwelling on how new technologies could make the meeting experience
comfortable by integrating all human senses. We also discuss the potential
danger of these technologies inadvertently becoming surveillance tools.


  We demonstrate Rabi flopping at MHz rates between ground hyperfine states of
neutral $^{87}$Rb atoms that are trapped in two micron sized optical traps.
Using tightly focused laser beams we demonstrate high fidelity, site specific
Rabi rotations with crosstalk on neighboring sites separated by $8 \mu\rm m$ at
the level of $10^{-3}$. Ramsey spectroscopy is used to measure a dephasing time
of $870 \mu\rm s$ which is $\approx$ 5000 times longer than the time for a
$\pi/2$ pulse.


  A toy model of particles packings is presented, which consists in arranging
hexagons on a triangular lattice according to local stability rules. The number
of stable packings is analytically computed and found to grow exponentially
with the size of the lattice, which illustrates the concept of packing entropy
first proposed by Edwards and collaborators. The analysis is carried out for
both the monodispersed case and the more interesting, i.e. more disordered,
bidispersed case.


  In this paper, we study expected utility maximization under ratchet and
drawdown constraints on consumption in a general incomplete semimartingale
market using duality methods. The optimization is considered with respect to
two parameters: the initial wealth and the essential lower bound on consumption
process. In order to state the problem and define the primal domains, we
introduce a natural extension of the notion of running maximum to arbitrary
non-negative optional processes and study its properties. The dual domains for
optimization are characterized in terms of solidity with respect to an ordering
that is introduced on the set of non-negative optional processes. The abstract
duality result we obtain for the optimization problem is used in order to
derive a more detailed characterization of solutions in the complete market
case.


  We investigate the divergences appearing in the two-particle irreducible
vertex functions of many-fermion systems with attractive on-site interactions.
By means of dynamical mean-field theory calculations, we determine the location
of singularity lines in the phase diagram of the attractive Hubbard model at
half-filling, where the local Bethe-Salpeter equations are non invertible. We
find that divergences appear both in the magnetic and in the density scattering
channels. The former affect a sector of suppressed fluctuations and comply with
the mapping of the physical susceptibilities of the repulsive case. At the same
time, the appearance of singularities in the density channel of the attractive
model demonstrates that vertex divergences can also plague the dominant
scattering sectors associated with enhanced local susceptibilities. This
constitutes a counterexample to previously proposed interpretations.
Eventually, by exploiting the underlying physical symmetries and a spectral
representation of the susceptibilities, we clarify the relation between vertex
divergences and the local response of the system in different channels.


  CN-Stream is a library for the computation of nonlinear regular ocean waves.
The library is developed in order to be easily integrated with wave generation
models in CFD solvers. It is based on the stream function theory and provides
significant improvements regarding the applicability of the method for waves
close to breaking (in deep or shallow water) compared to the classical
implementation of Rienecker and Fenton [26]. The complete description of the
wave field is available, including the free-surface evolution and the wave
kinematics in the fluid domain. It is released as open-source, developed and
distributed under the terms of GPL v3.


  Very recently, Mehadi et al [M. Asadi, E. Karap{\i}nar, and P. Salimi, New
extension of partial metric spaces with some fixed-point results on $M-$metric
spaces] extended the partial metric spaces to the notion of $M-$metric spaces.
In this article, we study some relations between partial metric spaces and
$M-$metric spaces. Also, we generalize Caristi Kirki's Theorem from partial
metric spaces to $M-$metric spaces, where we corrected some gaps in the proof
of the main Theorem in E. Karap\i nar [E. Karap\i nar, Generalizations of
Caristi Kirk's Theorem on Partial Metric Spaces, Fixed Point Theory Appl. 2011:
4, (2011)].
  We close our contribution by introducing some examples to validate and verify
our extension results.