  Based on the author's previous work on the Jacobi identity for twisted
relative vertex operator algebras and modules and on the generating function
identities for affine Lie algebras, we interpret the second difference sequence
of the sequence of the number of integer partitions with distinct parts (the
strict partitions) as the sequence of the strict partitions of n with at least
three parts, the three largest parts consecutive, and the smallest part at
least two. The name butterfly describes both the sequence's interpretation and
the underlying bijection between the set of strict partitions of positive
integers m with the two largest parts consecutive, and a subset of the same
kind of strict partitions of m+1. Using the cyclotomic polynomials 1-x and
1+x+x^2, we compute generating function identities o the butterfly sequence and
related sequences both as infinite products and as series filtered by the
number of parts of the corresponding partitions, and we see that the number of
partitions of positive integers n with odd parts greater than or equal to 5 is
the sum of three consecutive terms of the butterfly sequence. We also determine
a subtler merging and splitting construction of the butterfly sequence as a
sequence of some of the partitions with odd parts larger or equal to 3, and we
offer a related detailed interpretation of the butterfly sequence as a sequence
of what we define as generalized pentagonal, pentagonal with domino, and
non-pentagonal butterfly partitions. Finally, Euler's Pentagonal Number Theorem
and a slightly different specialization of the Jacobi triple product lead to
recursive algorithms to compute the butterfly sequence and related sequences
using pentagonal number sequences and the series of triangular powers.


  Cluster multipole orderings composed of atomic high-rank multipole moments
are theoretically investigated with a 5$d$-electron compound
Ca$_5$Ir$_3$O$_{12}$ in mind. Ca$_5$Ir$_3$O$_{12}$ exhibits two hidden orders:
One is an intermediate-temperature phase with time-reversal symmetry and the
other is a low-temperature phase without time-reversal symmetry. By performing
the symmetry and augmented multipole analyses for a $d$-orbital model under the
hexagonal point group $D_{\rm 3h}$, we find that the 120$^{\circ}$-type
ordering of the electric quadrupole corresponds to cluster electric toroidal
dipole ordering with the electric ferroaxial moment, which can become the
microscopic origin of the intermediate-temperature phase in
Ca$_5$Ir$_3$O$_{12}$. Furthermore, based on ${}^{193}$Ir
synchrotron-radiation-based M\"{o}ssbauer spectroscopy, we propose that the
low-temperature phase in Ca$_5$Ir$_3$O$_{12}$ is regarded as a coexisting state
with cluster electric toroidal dipole and cluster magnetic toroidal quadrupole,
the latter of which is formed by the 120$^{\circ}$-type ordering of the
magnetic octupole and accompanies a small uniform magnetization as a secondary
effect. Our results provide a clue to two hidden phases in
Ca$_5$Ir$_3$O$_{12}$.


  Image rasterization is a mature technique in computer graphics, while image
vectorization, the reverse path of rasterization, remains a major challenge.
Recent advanced deep learning-based models achieve vectorization and semantic
interpolation of vector graphs and demonstrate a better topology of generating
new figures. However, deep models cannot be easily generalized to out-of-domain
testing data. The generated SVGs also contain complex and redundant shapes that
are not quite convenient for further editing. Specifically, the crucial
layer-wise topology and fundamental semantics in images are still not well
understood and thus not fully explored. In this work, we propose Layer-wise
Image Vectorization, namely LIVE, to convert raster images to SVGs and
simultaneously maintain its image topology. LIVE can generate compact SVG forms
with layer-wise structures that are semantically consistent with human
perspective. We progressively add new bezier paths and optimize these paths
with the layer-wise framework, newly designed loss functions, and
component-wise path initialization technique. Our experiments demonstrate that
LIVE presents more plausible vectorized forms than prior works and can be
generalized to new images. With the help of this newly learned topology, LIVE
initiates human editable SVGs for both designers and other downstream
applications. Codes are made available at
https://github.com/Picsart-AI-Research/LIVE-Layerwise-Image-Vectorization.


  We present a general derivation of the arbitrage-free pricing framework for
multiple-currency collateralized products. We include the impact on option
pricing of the policy adopted to fund in foreign currency, so that we are able
to price contracts with cash flows and/or collateral accounts expressed in
foreign currencies inclusive of funding costs originating from dislocations in
the FX market. Then, we apply these results to price cross-currency swaps under
different market situations, to understand how to implement a feasible curve
bootstrap procedure. We present the main practical problems arising from the
way the market is quoting liquid instruments: uncertainties about collateral
currencies and renotioning features. We discuss the theoretical requirements to
implement curve bootstrapping and the approximations usually taken to
practically implement the procedure. We also provide numerical examples based
on real market data.


  We prove a conjecture of Pappas and Rapoport for all Shimura varieties of
abelian type with parahoric level structure when $p>3$ by showing that the
Kisin-Pappas-Zhou integral models of Shimura varieties of abelian type are
canonical. In particular, this shows that these models of are independent of
the choices made during their construction, and that they satisfy functoriality
with respect to morphisms of Shimura data.


  We present an integral framework for training sketch simplification networks
that convert challenging rough sketches into clean line drawings. Our approach
augments a simplification network with a discriminator network, training both
networks jointly so that the discriminator network discerns whether a line
drawing is a real training data or the output of the simplification network,
which in turn tries to fool it. This approach has two major advantages. First,
because the discriminator network learns the structure in line drawings, it
encourages the output sketches of the simplification network to be more similar
in appearance to the training sketches. Second, we can also train the
simplification network with additional unsupervised data, using the
discriminator network as a substitute teacher. Thus, by adding only rough
sketches without simplified line drawings, or only line drawings without the
original rough sketches, we can improve the quality of the sketch
simplification. We show how our framework can be used to train models that
significantly outperform the state of the art in the sketch simplification
task, despite using the same architecture for inference. We additionally
present an approach to optimize for a single image, which improves accuracy at
the cost of additional computation time. Finally, we show that, using the same
framework, it is possible to train the network to perform the inverse problem,
i.e., convert simple line sketches into pencil drawings, which is not possible
using the standard mean squared error loss. We validate our framework with two
user tests, where our approach is preferred to the state of the art in sketch
simplification 92.3% of the time and obtains 1.2 more points on a scale of 1 to
5.


  We use a combination of X-ray diffraction, total scattering and quantum
mechanical calculations to determine the mechanism responsible for
hydration-driven contraction in ZrW$_2$O$_8$. Inclusion of H$_2$O molecules
within the ZrW$_2$O$_8$ network drives the concerted formation of new W--O
bonds to give one-dimensional (--W--O--)$_n$ strings. The topology of the
ZrW$_2$O$_8$ network is such that there is no unique choice for the string
trajectories: the same local changes in coordination can propagate with a large
number of different periodicities. Consequently, ZrW$_2$O$_8$ is heavily
disordered, with each configuration of strings forming a dense aperiodic
`spaghetti'. This new connectivity contracts the unit cell \emph{via} large
shifts in the Zr and W atom positions. Fluctuations of the undistorted parent
structure towards this spaghetti phase emerge as the key NTE phonon modes in
ZrW$_2$O$_8$ itself. The large relative density of NTE phonon modes in
ZrW$_2$O$_8$ actually reflect the degeneracy of volume-contracting spaghetti
excitations, itself a function of the particular topology of this remarkable
material.


  Current studies on heavy hadrons in nuclear medium are reviewed with a
summary of the basic theoretical concepts of QCD, namely chiral symmetry, heavy
quark spin symmetry, and the effective Lagrangian approach. The nuclear matter
is an interesting place to study the properties of heavy hadrons from many
different points of view. We emphasize the importance of the following topics:
(i) charm/bottom hadron-nucleon interaction, (ii) structure of charm/bottom
nuclei, and (iii) QCD vacuum properties and hadron modifications in nuclear
medium. We pick up three different groups of heavy hadrons, quarkonia
($J/\psi$, $\Upsilon$), heavy-light mesons ($D$/$\bar{D}$, $\bar{B}$/$B$) and
heavy baryons ($\Lambda_{c}$, $\Lambda_{b}$). The modifications of those
hadrons in nuclear matter provide us with important information to investigate
the essential properties of heavy hadrons. We also give the discussions about
the heavy hadrons, not only in nuclear matter with infinite volume, but also in
atomic nuclei with finite baryon numbers, to serve future experiments.


  By performing new, long and numerically accurate general-relativistic
simulations of magnetized, equal-mass neutron-star binaries, we investigate the
role that realistic magnetic fields may have in the evolution of these systems.
In particular, we study the evolution of the magnetic fields and show that they
can influence the survival of the hypermassive-neutron star produced at the
merger by accelerating its collapse to a black hole. We also provide evidence
that even if purely poloidal initially, the magnetic fields produced in the
tori surrounding the black hole have toroidal and poloidal components of
equivalent strength. When estimating the possibility that magnetic fields could
have an impact on the gravitational-wave signals emitted by these systems
either during the inspiral or after the merger we conclude that for realistic
magnetic-field strengths B<~1e12 G such effects could be detected, but only
marginally, by detectors such as advanced LIGO or advanced Virgo. However,
magnetically induced modifications could become detectable in the case of
small-mass binaries and with the development of gravitational-wave detectors,
such as the Einstein Telescope, with much higher sensitivities at frequencies
larger than ~2 kHz.


  In an inhomogeneously illuminated photoacoustic image, important information
like vascular geometry is not readily available when only the initial pressure
is reconstructed. To obtain the desired information, algorithms for image
segmentation are often applied as a post-processing step. In this work, we
propose to jointly acquire the photoacoustic reconstruction and segmentation,
by modifying a recently developed partially learned algorithm based on a
convolutional neural network. We investigate the stability of the algorithm
against changes in initial pressures and photoacoustic system settings. These
insights are used to develop an algorithm that is robust to input and system
settings. Our approach can easily be applied to other imaging modalities and
can be modified to perform other high-level tasks different from segmentation.
The method is validated on challenging synthetic and experimental photoacoustic
tomography data in limited angle and limited view scenarios. It is
computationally less expensive than classical iterative methods and enables
higher quality reconstructions and segmentations than state-of-the-art learned
and non-learned methods.


  Clozel, Harris and Taylor proposed conjectural generalizations of the
classical Ihara's lemma for $\mathrm{GL}_2$, to higher dimensional similitude
groups. We prove these conjectures in the so called limit case, which after
base change is the essential one, under any hypothesis allowing level raising
as for example in the work of Gee.


  The magneto-conductance of an open carbon nanotube (CNT)-quantum wire was
measured in pulsed magnetic fields. At low temperatures we find a peculiar
split magneto-conductance peak close to the charge neutrality point. Our
analysis of the data reveals that this splitting is intimately connected to the
spin-orbit interaction and the tube chirality. Band structure calculations
suggest that the current in the peak regions is highly spin-polarized, which
calls for application in future CNT-based spintronic devices.


  We show that matrix $Q\times Q$ Self-dual type $S$-integrable Partial
Differential
  Equations (PDEs) possess a family of lower-dimensional reductions represented
by the matrix $ Q \times n_0 Q$ quasilinear first order PDEs solved in
\cite{SZ1} by the method of characteristics. In turn, these PDEs admit two
types of available particular solutions: (a) explicit solutions and (b)
solutions described implicitly by a system of non-differential equations. The
later solutions, in particular, exhibit the wave profile breaking. Only first
type of solutions is available for (1+1)-dimensional nonlinear $S$-integrable
PDEs. (1+1)-dimensional $N$-wave equation, (2+1)- and (3+1)-dimensional
Pohlmeyer equations are represented as examples. We also represent a new
version of the dressing method which supplies both classical solutions and
solutions with wave profile breaking to the above $S$-integrable PDEs.


  Exploiting the known structure of soliton solutions, obtained through the
Hirota transformation, a quantized representation of the Kadomtsev-Petviashvili
(KP) equation on the soliton sector is constructed over a Fock space of
particles, which may be either bosons or fermions. The classical solution is
mapped into an operator, which also obeys the KP equation. The operator is
constructed in terms of the particle-number operators. Classical soliton
solutions are the expectation values of this operator in multi-particle states
in the Fock space. The operator is equation-specific and the state in the Fock
space is in one-to-one correspondence with the particular soliton solution.


  We investigate differences in the molecular abundances between magnetically
super- and sub-critical prestellar cores, performing three-dimensional
non-ideal magnetohydrodynamical (MHD) simulations with varying densities and
magnetic field strengths, and post-processing the results with a time-dependent
gas-grain chemical code. Most molecular species show significantly more central
depletion in subcritical models, due to the longer duration of collapse.
However, the directly observable quantities - the molecule to hydrogen column
density ratios - are generally too similar for observational data to
discriminate between models. The profiles of N$_2$H$^+$ and HCO$^+$ show
qualitative differences between supercritical and subcritical models on scales
of $0.01 \, {\rm pc}$, which may allow the two cases to be distinguished.
However, this requires knowledge of the hydrogen column density, which is not
directly measureable, and predicted line intensity profiles from radiative
transfer modelling are similar for these molecules. Other commonly observed
species, such as HCN and CH$_3$OH, have line intensity profiles which differ
more strongly between models, and so are more promising as tracers of the
mechanism of cloud collapse.


  Understanding the physics of glass formation remains one of the major
unsolved challenges of condensed matter science. As a material solidifies into
a glass, it exhibits a spectacular slowdown of the dynamics upon cooling or
compression, but at the same time undergoes only minute structural changes.
Among the numerous theories put forward to rationalize this complex behavior,
Mode-Coupling Theory (MCT) stands out as the only framework that provides a
fully first-principles-based description of glass phenomenology. This review
outlines the key physical ingredients of MCT, its predictions, successes, and
failures, as well as recent improvements of the theory. We also discuss the
extension and application of MCT to the emerging field of non-equilibrium
active soft matter


  In this article, we generalize the theory of discrete Lagrangian mechanics
and variational integrators in two principal directions. First, we show that
Lagrangian submanifolds of symplectic groupoids give rise to discrete dynamical
systems, and we study the properties of these systems, including their
regularity and reversibility, from the perspective of symplectic and Poisson
geometry. Next, we use this framework -- along with a generalized notion of
generating function due to Sniatycki and Tulczyjew -- to develop a theory of
discrete constrained Lagrangian mechanics. This allows for systems with
arbitrary constraints, including those which are non-integrable (in an
appropriate discrete, variational sense). In addition to characterizing the
dynamics of these constrained systems, we also develop a theory of reduction
and Noether symmetries, and study the relationship between the dynamics and
variational principles. Finally, we apply this theory to discretize several
concrete examples of constrained systems in mechanics and optimal control.


  The core of planetary nebula NGC 6302 is filled with high-excitation
photoionised gas at low expansion velocities. It represents a unique
astrophysical situation in which to search for hyperfine structure (HFS) in
coronal emission lines from highly ionised species. HFS is otherwise blended by
thermal or velocity broadening. Spectra containing [AlVI]~3.66um 3P2-3P1,
obtained with Phoenix on Gemini-South at resolving powers of up to 75000,
resolve the line into five hyperfine components separated by 20 to 60km/s due
to the coupling of the I=5/2 nuclear spin of 27Al with the total electronic
angular momentum J. 26Al has a different nuclear spin of I=5, and a different
HFS, which allows us to place a 3sigma upper limit on the 26Al/27Al abundance
ratio of 1/33. We measure the HFS magnetic-dipole coupling constants for
[AlVI], and provide the first estimates of the electric-quadrupole HFS coupling
constants obtained through astronomical observations of an atomic transition.


  Making causal inferences from observational studies can be challenging when
confounders are missing not at random. In such cases, identifying causal
effects is often not guaranteed. Motivated by a real example, we consider a
treatment-independent missingness assumption under which we establish the
identification of causal effects when confounders are missing not at random. We
propose a weighted estimating equation (WEE) approach for estimating model
parameters and introduce three estimators for the average causal effect, based
on regression, propensity score weighting, and doubly robust estimation. We
evaluate the performance of these estimators through simulations, and provide a
real data analysis to illustrate our proposed method.


  A new solution to the Fermi Paradox is presented: probes or visits from
putative alien civilizations have a very low probability until a civilization
reaches a certain age (called the Contact Era) after the onset of radio
communications. If biotic planets are common, putative advanced civilizations
may preferentially send probes to planets with technosignatures, such as radio
broadcastings. The contact probability is defined as the chance to find a
nearby civilization located close enough so that it could have detected the
earliest radio emissions (the radiosphere) and sent a probe that would reach
the Solar System at present. It is found that the current contact probability
for Earth is very low unless civilizations are extremely abundant. Since the
radiosphere expands with time, so does the contact probability. The Contact Era
is defined as the time (since the onset of radio transmissions) at which the
contact probability becomes of order unity. At that time alien probes (or
messages) become more likely. Unless civilizations are highly abundant, the
Contact Era is shown to be of the order of a few hundred to a few thousand
years and may be applied not only to physical probes but also to transmissions
(i.e. SETI). Consequently, it is shown that civilizations are unlikely to be
able to inter-communicate unless their communicative lifetime is at least a few
thousand years.


  We extend study of the Jaynes-Cummings model involving a pair of identical
two-level atoms (or qubits) interacting with a single mode quantized field. We
investigate the effects of replacing the radiation field mode with a composite
spin, comprising $N$ qubits, or spin-1/2 particles. This model is relevant for
physical implementations in superconducting circuit QED, ion trap and molecular
systems. For the case of the composite spin prepared in a spin coherent state,
we demonstrate the similarities of this set-up to the qubits-field model in
terms of the time evolution, attractor states and in particular the collapse
and revival of the entanglement between the two qubits. We extend our analysis
by taking into account an effect due to qubit imperfections. We consider a
difference (or `mismatch') in the dipole interaction strengths of the two
qubits, for both the field mode and composite spin cases. To address
decoherence due to this mismatch, we then average over this coupling strength
difference with distributions of varying width. We demonstrate in both the
field mode and the composite spin scenarios that increasing the width of the
`error' distribution increases suppression of the coherent dynamics of the
coupled system, including the collapse and revival of the entanglement between
the qubits.


  Fluctuations in the redshifted 21 centimeter emission from neutral hydrogen
probe the epoch of reionization. We examine the observability of this signal
and the impact of extragalactic foreground radio sources. We use cosmological
simulations to predict the angular correlation functions of intensity
fluctuations due to unresolved radio galaxies, cluster radio halos and relics
and free-free emission from the interstellar and intergalactic medium at the
frequencies and angular scales relevant for the proposed 21cm tomography. In
accord with previous findings, the brightness temperature fluctuations due to
foreground sources are much larger than those from the primary 21cm signal at
all scales. In particular, diffuse cluster radio emission, which has been
previously neglected, provides the most significant foreground contamination.
However, we show that the contribution to the angular fluctuations at scales
\theta > 1' is dominated by the spatial clustering of bright foreground
sources. This excess can be removed if sources above flux levels S > 0.1 mJy
are detected and removed. Hence, efficient source removal may be sufficient to
allow the detection of angular fluctuations in the 21cm emission free of
extragalactic foregrounds at \theta > 1 arcmin. In addition, the removal of
sources above S=0.1 mJy also reduces the foreground fluctuations to roughly the
same level as the 21cm signal at scales \theta < 1 arcmin. This should allow
the substraction of the foreground components in frequency space, making it
possible to observe in detail the topology and history of reionization.


  We give circularly symmetric solutions for null fluid collapse in
2+1-dimensional Einstein gravity with a cosmological constant. The fluid
pressure $P$ and energy density $\rho$ are related by $P=k\rho$ $(k\le 1)$. The
long time limit of the solutions are black holes whose horizon structures
depend on the value of $k$. The $k=1$ solution is the
Banados-Teitelboim-Zanelli black hole metric in the long time static limit,
while the $k<1$ solutions give other, `hairy' black hole metrics in this limit.


  We present preliminary observational results of the multi-site STEPHI
campaign on the cluster NGC 1817. The three observatories involved are San
Pedro Martir (Mexico), Xing Long (China) and the Observatorio del Teide (Spain)
- giving an ideal combination to maximise the duty cycle. The cluster has 12
known delta Scuti stars and at least two detached eclipsing binary systems.
This combination of characteristics is ideal for extracting information about
global parameters of the targets, which will in turn impose strict constraints
on the stellar models. From an initial comparison with stellar models using the
known fundamental parameters, and just the observed pulsation frequencies and
measured effective temperatures, it appears that a lower value of initial
helium mass fraction will most likely explain the observations of these stars.


  Robot design is often a slow and difficult process requiring the iterative
construction and testing of prototypes, with the goal of sequentially
optimizing the design. For most robots, this process is further complicated by
the need, when validating the capabilities of the hardware to solve the desired
task, to already have an appropriate controller, which is in turn designed and
tuned for the specific hardware. In this paper, we propose a novel approach,
HPC-BBO, to efficiently and automatically design hardware configurations, and
evaluate them by also automatically tuning the corresponding controller.
HPC-BBO is based on a hierarchical Bayesian optimization process which
iteratively optimizes morphology configurations (based on the performance of
the previous designs during the controller learning process) and subsequently
learns the corresponding controllers (exploiting the knowledge collected from
optimizing for previous morphologies). Moreover, HPC-BBO can select a "batch"
of multiple morphology designs at once, thus parallelizing hardware validation
and reducing the number of time-consuming production cycles. We validate
HPC-BBO on the design of the morphology and controller for a simulated 6-legged
microrobot. Experimental results show that HPC-BBO outperforms multiple
competitive baselines, and yields a $360\%$ reduction in production cycles over
standard Bayesian optimization, thus reducing the hypothetical manufacturing
time of our microrobot from 21 to 4 months.


  A finite Blaschke product is a product of finitely many automorphisms of the
unit disk. This brief survey covers some of the main topics in the area,
including characterizations of finite Blaschke products, approximation
theorems, derivatives and residues of finite Blaschke products, geometric
localization of zeros, and selected other topics.


  We present a fuzzy version of the Group Identification Problem ("Who is a
J?") introduced by Kasher and Rubinstein (1997). We consider a class $N =
\{1,2,\ldots,n\}$ of agents, each one with an opinion about the membership to a
group J of the members of the society, consisting in a function $\pi : N \to
[0; 1]$, indicating for each agent, including herself, the degree of membership
to J. We consider the problem of aggregating those functions, satisfying
different sets of axioms and characterizing different aggregators. While some
results are analogous to those of the originally crisp model, the fuzzy version
is able to overcome some of the main impossibility results of Kasher and
Rubinstein.


  Recent work of M. Yoshinaga shows that in some instances certain higher
homotopy groups of arrangements map onto non-resonant homology. This is in
contrast to the usual Hurewicz map to untwisted homology, which is always the
zero homomorphism in degree greater than one. In this work we examine this
dichotomy, generalizing both results.


  In 1972, K. Kenmotsu studied a class of almost contact Riemannian manifolds.
Later, such a manifold was called a Kenmotsu manifold. This paper, we studied
Kenmotsu manifolds with $(2n+s)$-dimensional $s-$contact metric manifold and
this manifold, we have called generalized Kenmotsu manifolds. Necessary and
sufficient condition is given for an almost $s-$contact metric manifold to be a
generalized Kenmotsu manifold.We show that a generalized Kenmotsu manifold is a
locally warped product space. In addition, we study some curvature properties
of generalized Kenmotsu manifolds. Moreover, we show that the $\varphi $%
-sectional curvature of any semi-symmetric and projective semi-symmetric $%
(2n+s)$-dimensional generalized Kenmotsu manifold is $-s$.


  This paper describes the fortran program rhad which performs a numerical
evaluation of the photon-induced hadronic R-ratio, R(s), related to the cross
section for electron-positron annihilation, for a given center-of-mass energy
\sqrt{s}. In rhad the state-of-the-art perturbative corrections to R(s) are
implemented and the running and decoupling of the strong coupling constant and
the quark masses is automatically treated consistently. Several options allow
for a flexible use of the program.


  In this paper, firstly, we define the Generalized Tribonacci-Lucas numbers.
In addition, by also defining circulant matrices C_{n}(G) and C_{n}(S) whose
entries are Generalized Tribonacci and Generalized Tribonacci-Lucas numbers, we
compute spectral norms and determinants of these matrices.


  Nematicity is ubiquitous in electronic phases of high-$T_c$ superconductors,
particularly in the Fe-based systems. While several experiments have probed
nematic fluctuations, they have been restricted to uniform or momentum averaged
fluctuations. Here, we investigate the behavior of finite-momentum nematic
fluctuations by utilizing the anomalous softening of acoustic phonon modes in
optimally doped Ba(Fe$_{0.94}$Co$_{0.06}$)$_2$As$_2$. We determine the nematic
correlation length and find that it sharply changes its $T$-dependence at
$T_c$, revealing a strong connection between nematicity and superconductivity.


  The EDELWEISS collaboration reports on the search for Dark Matter (DM)
particle interactions via Migdal effect with masses between $32$
MeV$\cdot$c$^{-2}$ to $2$ GeV$\cdot$c$^{-2}$ using a $200$ g cryogenic Ge
detector sensitive to simultaneously heat and ionization signals and operated
underground at the Laboratoire Souterrain de Modane in France. The phonon
signal was read out using a Transition Edge Sensor made of a NbSi thin film.
The detector was biased at $66$ V in order to benefit from the
Neganov-Trofimov-Luke amplification and resulting in a resolution on the energy
of electron recoils of $4.46$ eV$_{ee}$ (RMS) and an analysis threshold of $30$
eV$_{ee}$. The sensitivity is limited by a dominant background not associated
to charge creation in the detector. The search constrains a new region of
parameter space for cross-sections down to $10^{-29}$ cm$^2$ and masses between
$32$ and $100$ MeV$\cdot$c$^{-2}$. The achieved low threshold with the NbSi
sensor shows the relevance of its use for athermal-phonon sensitive devices for
low-mass DM searches.


  We study the motion of the hypersurface $(\gamma_t)_{t\geq 0}$ evolving
according to the mean curvature perturbed by $\dot{w}^Q$, the formal time
derivative of the $Q$-Wiener process ${w}^Q$, in a two dimensional bounded
domain. Namely, we consider the equation describing the evolution of $\gamma_t$
as a stochastic partial differential equation (SPDE) with a multiplicative
noise in the Stratonovich sense, whose inward velocity $V$ is determined by
$V=\kappa\,+\,G \circ \dot{w}^Q$, where $\kappa$ is the mean curvature and $G$
is a function determined from $\gamma_t$. Already known results in which the
noise depends on only time variable is not applicable to our equation. To
construct a local solution of the equation describing $\gamma_t$, we will
derive a certain second order quasilinear SPDE with respect to the signed
distance function determined from $\gamma_0$. Then we construct the local
solution making use of probabilistic tools and the classical Banach fixed-point
theorem on suitable Sobolev spaces.


  We study the Generalized Uncertainty Principle (GUP) modified time evolution
for the width of wave-packets for a scalar potential. Free particle case is
solved exactly where the wave-packet broadening is modified by a coupling
between the GUP parameter and higher order moments in the probability
distribution in momentum space. We consider two popular forms of deformations
widely used in the literature - one of which modifies the commutator with a
quadratic term in momentum, while the other modifies it with terms both linear
and quadratic in momentum. Unlike the standard case, satisfying Heisenberg
uncertainty, here the GUP modified broadening rates, for both deformations, not
only depend on the initial size (both in position and momentum space) of the
wave-packet, but also on the initial probability distribution and momentum of
the particle. The new rates of wave-packet broadening, for both situations, are
modified by a handful of new terms - such as the skewness and kurtosis
coefficients, as well as the (constant) momentum of the particle. Comparisons
with the standard Heisenberg Uncertainty Principle (HUP)-based results show
potentially measurable differences in the rates of free wave-packet broadening
for physical systems such as the $C_{60}$ and $C_{176}$ molecules, and more so
for large organic molecular wave-packets. In doing so, we open a path to scan
the GUP parameter space by several orders of magnitude inside the best existing
upper bounds for both forms of GUP.


  In a previous work, we have shown that, like BPS Dp branes, bulk gravity gets
decoupled from the brane even for the non-susy Dp branes of type II string
theories indicating a possible extension of AdS/CFT correspondence for the
non-supersymmetric case. In that work, the decoupling of gravity on the
non-susy Dp branes has been shown numerically for the general case as well as
analytically for some special case. Here we discuss the decoupling limit and
the throat geometry of the non-susy D3 brane when the charge associated with
the brane is very large. We show that in the decoupling limit the throat
geometry of the non-susy D3 brane, under appropriate coordinate change, reduces
to the Constable-Myers solution and thus confirming that this solution is
indeed the holographic dual of a (non-gravitational) gauge theory discussed
there. We also show that when one of the parameters of the solution takes a
specific value, it reduces, under another coordinate change, to the
five-dimensional solution obtained by Csaki and Reece, again confirming its
gauge theory interpretation.


  There is nowhere else in emerging technology, but in Quantum-dot Cellular
Automata, one can find high speed, low power operation, and high packaging
density, which deals with electrostatic interaction between electrons within a
cell. Literature survey lacks in hazards free design of QCA circuit. Hazards
create ambiguous and unpredictable output, which can be avoided. This work
considers both hazards and hazards-free asynchronous sequential circuits; both
are compared in terms of kink energy, and a better one has been proposed. The
circuit simulation has been verified in the QCADesigner tool.


  The magneto-structural correlations of superexchange-coupled doubly
hydroxo-bridged Cu(II)-dimers have been investigated. To this end, an
analytical approach has been applied to [Cu2(OH)2F4]2- model complexes. This
approach supplies an analytical scheme, based on orbital interactions, for
calculating the transfer integral, HAB, which is shown to play the key role in
the magnetic coupling constant J for understanding magneto-structural
correlations. The single contributions to the transfer integral are calculated
and described explicitly. Therefore, this approach supplies a detailed insight
into the magnetic behavior and the interaction mechanisms of the
hydroxo-bridged Cu-dimers. All analytical results are compared with
experimental and numerical data.


  Polymer 3D printing is a broad set of manufacturing methods that permit the
fabrication of complex architectures, and, as a result, numerous efforts focus
on formulating processible chemistries that produce desirable material behavior
in printed parts. However, current resin chemistries typically result in a
single fixed set of properties once fully polymerized, a fact that poses
significant engineering challenges to obtaining multimaterial devices. As an
alternative to single-property materials, we introduce a ternary sequential
reaction scheme that exhibits diverse multimaterial properties by profoundly
altering the polymer microstructure from within a single resin composition. In
this system, the photodosage during 3D printing sets both the shape and extent
of conversion for each subsequent reaction. This different polymerization
mechanisms of the subsequent stages yield disparate crosslink densities and
viscoelastic properties. As a result, our materials possess Young's Moduli
spanning over three orders of magnitude (400 kPa < E < 1.6 GPa) with smooth
transitions between soft and stiff regions. We successfully pattern a 500x
change in modulus in under a millimeter while the sequential assembly of our
polymer networks ensures robust interfaces and enhances toughness by 10x
compared to the single property materials. Most importantly, the final objects
remain stable to UV and thermal aging, a key limitation to applications of
previous multimaterial chemistries. We demonstrate the ability to 3D print
intricate multimaterial architectures by fabricating a soft, wearable braille
display.


  In this article we prove new results regarding the existence of Bernstein
processes associated with the Cauchy problem of certain forward-backward
systems of decoupled linear deterministic parabolic equations defined in
Euclidean space of arbitrary dimension N, whose initial and final conditions
are positive measures. We concentrate primarily on the case where the elliptic
part of the parabolic operator is related to the Hamiltonian of an isotropic
system of quantum harmonic oscillators. In this situation there are many
Gaussian processes of interest whose existence follows from our analysis,
including N-dimensional stationary and non-stationary Ornstein-Uhlenbeck
processes, as well as a Bernstein bridge which may be interpreted as a
Markovian loop in a particular case. We also introduce a new class of
stationary non-Markovian processes which we eventually relate to the
N-dimensional periodic Ornstein-Uhlenbeck process, and which is generated by a
one-parameter family of non-Markovian probability measures. In this case our
construction requires an infinite hierarchy of pairs of forward-backward heat
equations associated with the pure point spectrum of the elliptic part, rather
than just one pair in the Markovian case. We finally stress the potential
relevance of these new processes to statistical mechanics, the random evolution
of loops and general pattern theory.


  We have observed the Galactic Center (GC) region at 0.154 and 0.255 GHz with
the GMRT. A total of 62 compact likely extragalactic sources are detected.
Their scattering sizes go down linearly with increasing angular distance from
the GC up to about 1 deg. The apparent scattering sizes of sources are more
than an order of magnitude down than predicted earlier by the NE2001 model of
Galactic electron distribution within 359.5 deg < l < 0.5 deg and -0.5 deg <b
<0.5 deg (Hyperstrong scattering region) of the Galaxy. High free-free optical
depths are observed towards most of the extended nonthermal sources within 0.6
deg from the GC. Significant variation of optical depth indicate the absorbing
medium is patchy at an angular scale of 10' and electron density is ~10 per cc
that matches with the NE2001 model. This model predicts the extragalactic (EG)
sources to be resolved out from 1.4 GHz interferometric surveys. However, 8
likely EG sources out of 10 expected in the region are present in 1.4 GHz
catalog. Ionized interfaces of dense molecular clouds to the ambient medium are
most likely responsible for strong scattering and low radio frequency
absorption. However, dense GC clouds traced by CS $J=1-0$ emission are found to
have a narrow distribution of ~0.2 deg across the Galactic plane. Angular
distribution of most of the EG sources seen through the so called Hyperstrong
scattering region are random in $b$, and typically ~7 out of 10 sources will
not be seen through to the dense molecular clouds, and it explains why most of
them are not scatter broadened at 1.4 GHz.


  Current CoVID-19 pandemic is spreading rapidly worldwide, and it may become
one of the largest pandemic events in modern history if out of control. It
appears most of the SARS-CoV2 virus infection resulted deaths are mainly due to
dysfunctions or failures of the lung or multiple organs that could be
attributed to hosts immunodysfunctions particularly hyperinflammatory type
disorders. In this brief review and study, a math model is proposed to
correlate the Pathogen Infection Recovery Probability (PIRP) versus
Proinflammatory Anti-Pathogen Species (PIAPS) levels within a host unit, where
a maximum PIRP is exhibited when the PIAPS levels are equal to or around PIAPS
equilibrium levels at the pathogen elimination or clearance onset. Based on
this model, rational or effective therapeutic strategies at right stages or
timing, with right type of agents (immuno-stimulators or immuno-suppressors),
and right dosages, may be designed and implemented that are expected to
effectively achieve maximum PIRP or reduce the mortality.


  In a triangulated category equipped with a $t$-structure, we investigate a
relation between ICE-closed (=Image-Cokernel-Extension-closed) subcategories of
the heart of the $t$-structure and aisles in the triangulated categories. We
introduce an ICE sequence, a sequence of ICE-closed subcategories satisfying a
certain condition, and establish a bijection between ICE sequences and
homology-determined preaisles. Moreover we give a sufficient condition that an
ICE sequence induces a $t$-structure via the bijection. In the case of the
bounded derived category $D^b({\mathsf{mod}}\Lambda)$ of a $\tau$-tilting
finite algebra $\Lambda$, we give a description of ICE sequences in
${\mathsf{mod}}\Lambda$ which induce bounded $t$-structures on
$D^b({\mathsf{mod}}\Lambda)$ from the viewpoint of a lattice consisting of
torsion classes in ${\mathsf{mod}}\Lambda$.


  We present an all-optical protocol for detecting population in a selected
Rydberg state of alkali atoms. The detection scheme is based on the interaction
of an ensemble of ultracold atoms with two laser pulses: one weak probe pulse
which is resonant with the transition between the ground state and the first
excited state, and a pulse with high intensity which couples the first excited
state to the selected Rydberg state. We show that by monitoring the absorption
signal of the probe laser over time, one can deduce the initial population of
the Rydberg state. Furthermore, it is shown that - for suitable experimental
conditions - the dynamical absorption curve contains information on the initial
coherence between the ground state and the selected Rydberg state. We present
the results of a proof-of-principle measurement performed on a cold gas of
$^{87}$Rb atoms. The method is expected to find application in quantum
computing protocols based on Rydberg atoms.


  We study and discuss rejuvenation and memory (numerical) experiments in Ising
and Heisenberg three and four dimensional spin glasses. We introduce a
quantitative procedure to analyze the results of temperature cycling
experiments. We also run, compare and discuss ``twin'' couples of experiments.
We find that in our systems aging is always cumulative in nature, and
rejuvenation and memory effects are also cumulative: they are very different
from the ones observed in experiments on spin glass materials.


  In this paper we present the equations of motion of a moving screw
dislocation in the framework of the translation gauge theory of dislocations.
In the gauge field theoretical formulation, a dislocation is a massive gauge
field. We calculate the gauge field theoretical solutions of a uniformly moving
screw dislocation. We give the subsonic and supersonic solutions. Thus,
supersonic dislocations are not forbidden from the field theoretical point of
view. We show that the elastic divergences at the dislocation core are removed.
We also discuss the Mach cones produced by supersonic screw dislocations.


  Black holes in core-collapse of massive stars are expected to surge in mass
and angular momentum by hyper-accretion immediately following their formation.
We here describe a general framework of extended emission in gravitational
waves from non-axisymmetric accretion flows from fallback matter of the
progenitor envelope. It shows (a) a maximum efficiency in conversion of
accretion energy into gravitational waves at hyper-accretion rates exceeding a
critical value set by the ratio of the quadrupole mass inhomogeneity and
viscosity with (b) a peak characteristic strain amplitude at the frequency
$f_b=\Omega_b/\pi$, where $\Omega_b$ is the Keplerian angular velocity at which
viscous torques equal angular momentum loss in gravitational radiation, with
$h_{char}\propto f^{1/6}$ at $f<f_b$ and $h_{char}\propto f^{-1/6}$ at $f>f_b$.
Upcoming gravitational wave observations may probe this scaling by extracting
broadband spectra using time-sliced matched filtering with chirp templates,
recently developed for identifying turbulence in noisy time series.


  Co4Nb2O9 (CNO) having {\alpha}-Al2O3 crystal structure with Co chains along
c-direction shows gigantic magnetoelelctric coupling below antiferromagnetic
ordering temperature of 27 K but above a spin flop field of 1.6 T. We have
investigated structural, magnetic and magnetoelectric properties of Fe
substituted (10% and 20%) samples and compared with the parent one. In fact
magnetic and specific heat measurements have revealed an additional magnetic
transition below 10 K and presence of short range magnetic ordering above ~ 50
K in parent as well as in Fe substituted samples. Linear magnetoelelctric and
ferroelectric behaviours are evidenced in the Fe substituted samples where an
electric field of 5 kV/m is sufficient to align the dipoles and the
magnetoelelctric coupling is ensured for magnetic fields as low as 0.25 T, far
below the spin flop field.


  We construct steady states of the Euler-Poisson system with a barotropic
equation of state as minimizers of a suitably defined energy functional. Their
minimizing property implies the non-linear stability of such states against
general, i.e., not necessarily spherically symmetric perturbations. The
mathematical approach is based on previous stability results for the
Vlasov-Poisson system by Y. Guo and the author, exploiting the energy-Casimir
technique. The analysis is conditional in the sense that it assumes the
existence of solutions to the initial value problem for the Euler-Poisson
system which preserve mass and energy. The relation between the Euler-Poisson
and the Vlasov-Poisson system in this context is also explored.


  We have studied experimentally the generation of vortex flow by gravity waves
with a frequency of 2.34 Hz excited on the water surface at an angle $2 \theta
= arctan(3/4) \approx 36\deg$ to each other. The resulting horizontal surface
flow has a stripe-like spatial structure. The width of the stripes L =
$\pi$/(2ksin$\theta$) is determined by the wave vector k of the surface waves
and the angle between them, and the length of the stripes is limited by the
system size. It was found that the vertical vorticity $\Omega$ of the current
on the fluid surface is proportional to the product of wave amplitudes, but its
value is much higher than the value corresponding to the Stokes drift and it
continues to grow with time even after the wave motion reaches a stationary
regime. We demonstrate that the measured dependence $\Omega$(t) can be
described within the recently developed model that takes into account the
Eulerian contribution to the generated vortex flow and the effect of surface
contamination. This model contains a free parameter that describes the elastic
properties of the contaminated surface, and we also show that the found value
of this parameter is in reasonable agreement with the measured decay rate of
surface waves.


  Nowadays, electrochemical reduction of CO$_2$ has been considered as an
effective method to solve the problem of global warming. The primary challenge
in studying the mechanism is to determine the adsorption states of CO$_2$,
since complicated metal surfaces often result in many different adsorption
sites. Based on the density functional theory (DFT) calculations, we performed
a theoretical study on the adsorption of CO$_2$ on the Ag electrode surface.
The results show that the adsorption populations of CO$_2$ are extremely
sensitive to the adsorption sites. Importantly, we found that the preferable
adsorption positions are the terrace sites, rather than the previous reported
step sites. The adsorption populations were found with the order of (211) >
(110) > (111) > (100). Subsequently, the adsorption characteristics were
correlated with the d-band theory and the charge transfers between Ag surfaces
and CO$_2$.


  We propose a new approach to construct the eigenvalue expansion in a weighted
Hilbert space of the solution to the Cauchy problem associated to
Gauss-Laguerre invariant Markov semigroups that we introduce. Their generators
turn out to be natural non-self-adjoint and non-local generalizations of the
Laguerre differential operator. Our methods rely on intertwining relations that
we establish between these semigroups and the classical Laguerre semigroup and
combine with techniques based on non-harmonic analysis. As a by-product we also
provide regularity properties for the semigroups as well as for their heat
kernels. The biorthogonal sequences that appear in their eigenvalue expansion
can be expressed in terms of sequences of polynomials, and they generalize the
Laguerre polynomials. By means of a delicate saddle point method, we derive
uniform asymptotic bounds that allow us to get an upper bound for their norms
in weighted Hilbert spaces. We believe that this work opens a way to construct
spectral expansions for more general non-self-adjoint Markov semigroups.


  We give a higher-algebraic interpretation of complex orientations of ring
spectra as "$\mathbb{E}_2$ strictifications" of the identity element. We show
that higher strictifications do not exist for most ring spectra of interest in
chromatic homotopy theory.


  Precise and fast static type analysis for dynamically typed language is very
difficult. This is mainly because the lack of static type information makes it
difficult to approximate all possible values of a variable. Actually, the
existing static type analysis methods are imprecise or slow. In this paper, we
propose a novel method to improve the precision of static type analysis for
Python code, where a backward analysis is used to obtain the path-sensitivity.
By doing so, our method aims to obtain more precise static type information,
which contributes to the overall improvement of static analysis. To show the
effectiveness of our method, we conducted a preliminary experiment to compare
our method implementation and the existing analysis tool with respect to
precision and time efficiency. The result shows our method provides more
precise type analysis with fewer false positives than the existing static type
analysis tool. Also it shows our proposed method increases the analysis time,
but it is still within the range of practical use.


  We present a method giving a spinorial characterization of an immersion in a
product of spaces of constant curvature. As a first application we obtain a
proof using spinors of the fundamental theorem of immersion theory in that
spaces. We also study special cases: we recover previously known results
concerning immersions in $\mathbb{S}^2\times\mathbb{R}$ and we obtain new
spinorial characterizations of immersions in $\mathbb{S}^2\times\mathbb{R}^2$
and in $\mathbb{H}^2\times\mathbb{R}.$ We then study the theory of $H=1/2$
surfaces in $\mathbb{H}^2\times\mathbb{R}$ using this spinorial approach,
obtain new proofs of some of its fundamental results and give a direct relation
with the theory of $H=1/2$ surfaces in $\mathbb{R}^{1,2}.$


  The recently-discovered polar codes are widely seen as a major breakthrough
in coding theory. These codes achieve the capacity of many important channels
under successive cancellation decoding. Motivated by the rapid progress in the
theory of polar codes, we propose a family of architectures for efficient
hardware implementation of successive cancellation decoders. We show that such
decoders can be implemented with O(n) processing elements and O(n) memory
elements, while providing constant throughput. We also propose a technique for
overlapping the decoding of several consecutive codewords, thereby achieving a
significant speed-up factor. We furthermore show that successive cancellation
decoding can be implemented in the logarithmic domain, thereby eliminating the
multiplication and division operations and greatly reducing the complexity of
each processing element.


  The BBCRS scheme is a variant of the McEliece public-key encryption scheme
where the hiding phase is performed by taking the inverse of a matrix which is
of the form $\mathbf{T} +\mathbf{R}$ where $\mathbf{T}$ is a sparse matrix with
average row/column weight equal to a very small quantity $m$, usually $m < 2$,
and $\mathbf{R}$ is a matrix of small rank $z\geqslant 1$. The rationale of
this new transformation is the reintroduction of families of codes, like
generalized Reed-Solomon codes, that are famously known for representing
insecure choices. We present a key-recovery attack when $z = 1$ and $m$ is
chosen between $1$ and $1 + R + O( \frac{1}{\sqrt{n}} )$ where $R$ denotes the
code rate. This attack has complexity $O(n^6)$ and breaks all the parameters
suggested in the literature.


  We compute the entropy of antiferromagnetic quantum spin-s chains in an
external magnetic field using exact diagonalization and Quantum Monte Carlo
simulations. The magnetocaloric effect, i.e., temperature variations during
adiabatic field changes, can be derived from the isentropes. First, we focus on
the example of the spin-s=1 chain and show that one can cool by closing the
Haldane gap with a magnetic field. We then move to quantum spin-s chains and
demonstrate linear scaling with $s$ close to the saturation field. In passing,
we propose a new method to compute many low-lying excited states using the
Lanczos recursion.


  A new equilibrium pressure profile extending the Rigid-Rotor (RR) model with
a simple unified expression $P=P(\psi;\beta_{s},\alpha, \sigma)$ for both
inside and outside the separatrix is proposed, in which the radial normalized
field-reversed configuration (FRC) equilibrium profiles for pressure, magnetic
field, and current can be determined by only two dimensionless parameters
$\beta_s\equiv P_s/2\mu_0B_e^2$ and $\delta_s\equiv L_{ps}/R_s$, where $P_s$ is
the thermal pressure at the separatrix, $B_e$ is the external magnetic field
strength, $L_{ps}$ is the pressure profile scale length at the separatrix, and
$R_s$ is the separatrix radius. This modified rigid rotor (MRR) model has
sufficient flexibility to accommodate the narrow scrape of layer (SOL) width
and hollow current density profiles, and can be used to fit experimental
measurements satisfactorily. Detailed one-dimensional (1D) characteristics of
the new MRR model are investigated analytically and numerically, and the
results are also confirmed in two-dimensional (2D) numerical equilibrium
solutions.


  Producing a usable semiconducting form of graphene has plagued the
development of graphene electronics for nearly two decades. Now that new
preparation methods have become available, graphene's intrinsic properties can
be measured and the search for semiconducting graphene has begun to produce
results. This is the case of the first graphene "buffer" layer grown on
SiC(0001) presented in this work. We show, contrary to assumptions of the last
forty years, that the buffer graphene layer is not commensurate with SiC. The
new modulated structure we've found resolves a long standing contradiction
where ab initio calculations expect a metallic buffer, while experimentally it
is found to be a semiconductor. Model calculations using the new incommensurate
structure show that the semiconducting $\pi$-band character of the buffer comes
from partially hybridized graphene incommensurate boundaries surrounding
unperturbed graphene islands.


  A contact projective structure is a contact path geometry the paths of which
are among the geodesics of some affine connection. In the manner of T.Y. Thomas
there is associated to each contact projective structure an ambient affine
connection on a symplectic manifold with one-dimensional fibers over the
contact manifold and using this the local equivalence problem for contact
projective structures is solved by the construction of a canonical regular
Cartan connection. This Cartan connection is normal if and only if an invariant
contact torsion vanishes. Every contact projective structure determines
canonical paths transverse to the contact structure which fill out the contact
projective structure to give a full projective structure, and the vanishing of
the contact torsion implies the contact projective ambient connection agrees
with the Thomas ambient connection of the corresponding projective structure.
An analogue of the classical Beltrami theorem is proved for pseudo-hermitian
manifolds with transverse symmetry.


  In this paper we present a general scheme for how to relate differential
equations for the recurrence coefficients of semi-classical orthogonal
polynomials to the Painlev\'e equations using the geometric framework of the
Okamoto Space of Initial Conditions. We demonstrate this procedure in two
examples. For semi-classical Laguerre polynomials appearing in \cite{HC17}, we
show how the recurrence coefficients are connected to the fourth Painlev\'e
equation. For discrete orthogonal polynomials associated with the
hypergeometric weight appearing in \cite{FVA18} we discuss the relation of the
recurrence coefficients to the sixth Painlev\'e equation, extending the results
of \cite{DFS19}, where a similar approach was used for a discrete system for
the same recurrence coefficients. Though the discrete and differential systems
here share the same geometry, the construction of the space of initial
conditions from the differential system is different and reveals extra
considerations that must be made. We also discuss a number of related topics in
the context of the geometric approach, such as Hamiltonian forms of the
differential equations for the recurrence coefficients, Riccati solutions for
special parameter values, and associated discrete Painlev\'e equations.


  The aim of the project is to characterise both components of the nearest
brown dwarf sytem to the Sun, WISE J104915.57-531906.1 (=Luhman16AB) at optical
and near-infrared wavelengths. We obtained high signal-to-noise
intermediate-resolution (R~6000-11000) optical (600-1000 nm) and near-infrared
(1000-2480nm) spectra of each component of Luhman16AB, the closest brown dwarf
binary to the Sun, with the X-Shooter instrument on the Very Large Telescope.
We classify the primary and secondary of the Luhman16 system as L6-L7.5 and
T0+/-1, respectively, in agreement with previous measurements published in the
literature. We present measurements of the lithium pseudo-equivalent widths,
which appears of similar strength on both components (8.2+/-1.0 Angstroms and
8.4+/-1.5 Angstroms for the L and T components, respectively). The presence of
lithium (Lithium 7) in both components imply masses below 0.06 Msun while
comparison with models suggests lower limits of 0.04 Msun. The detection of
lithium in the T component is the first of its kind. Similarly, we assess the
strength of other alkali lines (e.g. pseudo-equivalent widths of 6-7 Angstroms
for RbI and 4-7 Angstroms for CsI) present in the optical and near-infrared
regions and compare with estimates for L and T dwarfs. We also derive effective
temperatures and luminosities of each component of the binary: -4.66+/-0.08 dex
and 1305(+180)(-135) for the L dwarf and -4.68+/-0.13 dex and 1320(+185)(-135)
for the T dwarf, respectively. Using our radial velocity determinations, the
binary does not appear to belong to any of the well-known moving group. Our
preliminary theoretical analysis of the optical and J-band spectra indicates
that the L- and T-type spectra can be reproduced with a single temperature and
gravity but different relative chemical abundances which impact strongly the
spectral energy distribution of L/T transition objects.


  We present three tiers of Bayesian consistency tests for the general case of
$correlated$ datasets. Building on duplicates of the model parameters assigned
to each dataset, these tests range from Bayesian evidence ratios as a global
summary statistic, to posterior distributions of model parameter differences,
to consistency tests in the data domain derived from posterior predictive
distributions. For each test we motivate meaningful threshold criteria for the
internal consistency of datasets. Without loss of generality we focus on
mutually exclusive, correlated subsets of the same dataset in this work. As an
application, we revisit the consistency analysis of the two-point weak lensing
shear correlation functions measured from KiDS-450 data. We split this dataset
according to large vs. small angular scales, tomographic redshift bin
combinations, and estimator type. We do not find any evidence for significant
internal tension in the KiDS-450 data, with significances below $3\, \sigma$ in
all cases. Software and data used in this analysis can be found at
http://kids.strw.leidenuniv.nl/sciencedata.php


  The quantum Cram\'er-Rao bound sets a fundamental limit on the accuracy of
unbiased parameter estimation in quantum systems, relating the uncertainty in
determining a parameter to the inverse of the quantum Fisher information. We
experimentally demonstrate near saturation of the quantum Cram\'er-Rao bound in
the phase estimation of a solid-state spin system, provided by a
nitrogen-vacancy center in diamond. This is achieved by comparing the
experimental uncertainty in phase estimation with an independent measurement of
the related quantum Fisher information. The latter is independently extracted
from coherent dynamical responses of the system under weak parametric
modulations, without performing any quantum-state tomography. While optimal
parameter estimation has already been observed for quantum devices involving a
limited number of degrees of freedom, our method offers a versatile and
powerful experimental tool to explore the Cram\'er-Rao bound and the quantum
Fisher information in systems of higher complexity, as relevant for quantum
technologies.


  Explaining and reasoning about processes which underlie observed black-box
phenomena enables the discovery of causal mechanisms, derivation of suitable
abstract representations and the formulation of more robust predictions. We
propose to learn high level functional programs in order to represent abstract
models which capture the invariant structure in the observed data. We introduce
the $\pi$-machine (program-induction machine) -- an architecture able to induce
interpretable LISP-like programs from observed data traces. We propose an
optimisation procedure for program learning based on backpropagation, gradient
descent and A* search. We apply the proposed method to two problems: system
identification of dynamical systems and explaining the behaviour of a DQN
agent. Our results show that the $\pi$-machine can efficiently induce
interpretable programs from individual data traces.


  We discuss a variety of developments in the study of large time behavior of
the positive minimal heat kernel of a time independent (not necessarily
symmetric) second-order parabolic operator defined on a domain M in $R^d$, or
more generally, on a noncompact Riemannian manifold M. Our attention is mainly
focused on general results in general settings.


  Dual Connectivity (DC) is an important lower-layer feature accelerating the
transition from 4G to 5G that also is expected to play an important role in
standalone 5G radio networks. However, even though the packet reordering
introduced by DC can significantly impact the performance of upper-layer
protocols, no prior work has studied the impact of DC on QUIC. In this paper,
we present the first such performance study. Using a series of throughput and
fairness experiments, we show how QUIC is affected by different DC parameters,
network conditions, and whether the DC implementation aims to improve
throughput or reliability. Results for two QUIC implementations (aioquic,
ngtcp2) and two congestion control algorithms (NewReno, CUBIC) are presented
under both static and highly time-varying network conditions. Our findings
provide network operators with insights and understanding into the impacts of
splitting QUIC traffic in a DC environment. With reasonably selected DC
parameters and increased UDP receive buffers, QUIC over DC performs similarly
to TCP over DC and achieves optimal fairness under symmetric link conditions
when DC is not used for packet duplication. The insights can help network
operators provide modern users with better end-to-end service when deploying
DC.


  Uncertainty Quantification of closure relationships integrated into
thermal-hydraulic system codes is a critical prerequisite in applying the
Best-Estimate Plus Uncertainty (BEPU) methodology for nuclear safety and
licensing processes.The purpose of the CIRCE method is to estimate the
(log)-Gaussian probability distribution of a multiplicative factor applied to a
reference closure relationship in order to assess its uncertainty. Even though
this method has been implemented with success in numerous physical scenarios,
it can still suffer from substantial limitations such as the linearity
assumption and the difficulty of properly taking into account the inherent
statistical uncertainty. In the paper, we will extend the CIRCE method in two
aspects. On the one hand, we adopt the Bayesian setting putting prior
probability distributions on the parameters of the (log)-Gaussian distribution.
The posterior distribution of the parameters is then computed with respect to
an experimental database by means of Markov Chain Monte Carlo (MCMC)
algorithms. On the other hand, we tackle the more general setting where the
simulations do not move linearly against the multiplicative factor(s). MCMC
algorithms then become time-prohibitive when the thermal-hydraulic simulations
exceed a few minutes. This handicap is overcome by using Gaussian process (GP)
emulators which can yield both reliable and fast predictions of the
simulations. The GP-based MCMC algorithms will be applied to quantify the
uncertainty of two condensation closure relationships at a safety injection
with respect to a database of experimental tests. The thermal-hydraulic
simulations will be run with the CATHARE 2 computer code.


  When electrons are confined in two dimensions and subjected to strong
magnetic fields, the Coulomb interactions between them become dominant and can
lead to novel states of matter such as fractional quantum Hall liquids. In
these liquids electrons linked to magnetic flux quanta form complex composite
quasipartices, which are manifested in the quantization of the Hall
conductivity as rational fractions of the conductance quantum. The recent
experimental discovery of an anomalous integer quantum Hall effect in graphene
has opened up a new avenue in the study of correlated 2D electronic systems, in
which the interacting electron wavefunctions are those of massless chiral
fermions. However, due to the prevailing disorder, graphene has thus far
exhibited only weak signatures of correlated electron phenomena, despite
concerted experimental efforts and intense theoretical interest. Here, we
report the observation of the fractional quantum Hall effect in ultraclean
suspended graphene, supporting the existence of strongly correlated electron
states in the presence of a magnetic field. In addition, at low carrier density
graphene becomes an insulator with an energy gap tunable by magnetic field.
These newly discovered quantum states offer the opportunity to study a new
state of matter of strongly correlated Dirac fermions in the presence of large
magnetic fields.


  India has twenty-two official languages. Serving such a diverse language base
is a challenge for survey statisticians, call center operators, software
developers, and other such service providers. To help provide better services
to different language communities via better localization, we introduce a new
machine learning model that predicts the language(s) that the user can speak
from their name. Using nearly 438M records spanning 33 Indian states and 1.13M
unique last names from the Indian Electoral Rolls Corpus (?), we build a
character-level transformer-based machine-learning model that predicts the
state of residence based on the last name. The model has a top-3 accuracy of
85.3% on unseen names. We map the states to languages using the Indian census
to infer languages understood by the respondent. We provide open-source
software that implements the method discussed in the paper.


  This report presents the systems developed and submitted by Fortemedia
Singapore (FMSG) and Joint Laboratory of Environmental Sound Sensing (JLESS)
for DCASE 2024 Task 4. The task focuses on recognizing event classes and their
time boundaries, given that multiple events can be present and may overlap in
an audio recording. The novelty this year is a dataset with two sources, making
it challenging to achieve good performance without knowing the source of the
audio clips during evaluation. To address this, we propose a sound event
detection method using domain generalization. Our approach integrates features
from bidirectional encoder representations from audio transformers and a
convolutional recurrent neural network. We focus on three main strategies to
improve our method. First, we apply mixstyle to the frequency dimension to
adapt the mel-spectrograms from different domains. Second, we consider training
loss of our model specific to each datasets for their corresponding classes.
This independent learning framework helps the model extract domain-specific
features effectively. Lastly, we use the sound event bounding boxes method for
post-processing. Our proposed method shows superior macro-average pAUC and
polyphonic SED score performance on the DCASE 2024 Challenge Task 4 validation
dataset and public evaluation dataset.


  The detailed study of the low-energy spectrum for a mobile impurity in the
one-dimensional bosonic enviroment is performed. Particularly we have
considered only two analytically accessible limits, namely, the case of an
impurity immersed in a dilute Bose gas, where one can use many-body
perturbation techniques for low-dimensional bosonic systemsm and the case of
the Tonks-Girardeau gas, for which the usual fermionic diagrammatic expansion
up to the second order is applied.


  This paper concerns inverse problems for strongly coupled Schr\"odinger
equations. The purpose of this inverse problem is to retrieve a stationary
potential in the strongly coupled Schr\"odinger equations from either boundary
or internal measurements. Two stability results are derived from a new Carleman
estimate for the strongly coupled Schr\"odinger equations.


  In connection with recent discussion of topological order and topological
phase transitions in quantum systems, we reexamine circumstances that lead to
the appearance of a topological glass in certain classical lattice spin models.
Local bonding enforces constraints on low energy states which organize
themselves into topologically distinct classes that break ergodicity but not
any apparent symmetry as in the usual Landau theory of phase transitions.
Various properties of such a topological glass are demonstrated using two
classical Ising-like models.


  By using a result from the numerical algebraic geometry package Bertini we
show that (up to high numerical accuracy) a specific set of degree 6 and degree
9 polynomials cut out the secant variety $\sigma_{4}(\mathbb{P}^{2}\times
\mathbb{P} ^{2} \times \mathbb{P} ^{3})$. This, combined with an argument
provided by Landsberg and Manivel (whose proof was corrected by Friedland),
implies set-theoretic defining equations in degrees 5, 6 and 9 for a much
larger set of secant varieties, including $\sigma_{4}(\mathbb{P}^{3}\times
\mathbb{P} ^{3} \times \mathbb{P} ^{3})$ which is of particular interest in
light of the salmon prize offered by E. Allman for the ideal-theoretic defining
equations.


  Given a hermitian line bundle $L\to M$ on a closed Riemannian manifold
$(M^n,g)$, the self-dual Yang-Mills-Higgs energies are a natural family of
functionals \begin{align*}
  &E_\epsilon(u,\nabla):=\int_M\Big(|\nabla
u|^2+\epsilon^2|F_\nabla|^2+\frac{(1-|u|^2)^2}{4\epsilon^2}\Big) \end{align*}
defined for couples $(u,\nabla)$ consisting of a section $u\in\Gamma(L)$ and a
hermitian connection $\nabla$ with curvature $F_\nabla$. While the critical
points of these functionals have been well-studied in dimension two by the
gauge theory community, it was shown in previous work of the second- and
third-named authors that critical points in higher dimension converge as
$\epsilon\to 0$ (in an appropriate sense) to minimal submanifolds of
codimension two, with strong parallels to the correspondence between the
Allen-Cahn equations and minimal hypersurfaces.
  In this paper, we complement this idea by showing the $\Gamma$-convergence of
$E_\epsilon$ to ($2\pi$ times) the codimension two area: more precisely, given
a family of couples $(u_\epsilon,\nabla_\epsilon)$ with $\sup_\epsilon
E_\epsilon(u_\epsilon,\nabla_\epsilon)<\infty$, we prove that a suitable gauge
invariant Jacobian $J(u_\epsilon,\nabla_\epsilon)$ converges to an integral
$(n-2)$-cycle $\Gamma$, in the homology class dual to the Euler class $c_1(L)$,
with mass $2 \pi \mathbb{M}(\Gamma)\le\liminf_{\epsilon \rightarrow
0}E_\epsilon(u_\epsilon,\nabla_\epsilon)$. We also obtain a recovery sequence
for any integral cycle in this homology class.
  Finally, we apply these techniques to compare min-max values for the
$(n-2)$-area from the Almgren-Pitts theory with those obtained from the
Yang-Mills-Higgs framework, showing that the former values always provide a
lower bound for the latter. As an ingredient, we also establish a Huisken-type
monotonicity result along the gradient flow of $E_{\epsilon}$.


  We analyze BPS black hole attractors in 4d gauged supergravity in the
presence of higher derivative supersymmetric terms, including a
Weyl-squared-type action, and determine the resulting corrections to the
Bekenstein-Hawking entropy. The near-horizon geometry AdS$_2 \times$S$^2$ (or
other Riemann surface) preserves half of the supercharges in $N=2$ supergravity
with Fayet-Iliopoulos gauging. We derive a relation between the entropy and the
black hole charges that suggests via AdS/CFT how subleading corrections
contribute to the supersymmetric index in the dual microscopic picture.
  Depending on the model, the attractors are part of full black hole solutions
with different asymptotics, such as Minkowski, AdS$_4$, and hvLif$_4$. We give
explicit examples for each of the asymptotic cases and comment on the
implications. Among other results, we find that the Weyl-squared terms spoil
the exact two-derivative relation to non-BPS asymptotically flat black holes in
ungauged supergravity.


  Truth based entailments are not sufficient for a good comprehension of NL. In
fact, it can not deduce implicit information necessary to understand a text. On
the other hand, norm based entailments are able to reach this goal. This idea
was behind the development of Frames (Minsky 75) and Scripts (Schank 77, Schank
79) in the 70's. But these theories are not formalized enough and their
adaptation to new situations is far from being obvious. In this paper, we
present a reasoning system which uses norms in a causal reasoning process in
order to find the cause of an accident from a text describing it.


  It is well known that any sufficiently regular one-dimensional payoff
function has an explicit static hedge by bonds, forward contracts and lots of
vanilla options. We show that the natural extension of the corresponding
representation leads to a static hedge based on the same instruments along with
traffic light options, which have recently been introduced in the market. One
big advantage of these replication strategies is the easy structure of the
hedge. Hence, traffic light options are particularly powerful building blocks
for more complicated bivariate options. While it is well known that the second
strike derivative of non-discounted prices of vanilla options are related to
the risk-neutral density of the underlying asset price in the corresponding
absolutely continuous settings, similar statements hold for traffic light
options in sufficiently regular bivariate settings.


  This paper studies the feedback stabilization problem of the motion of a tank
that contains an incompressible, Newtonian, viscous liquid. The control input
is the force applied on the tank and the overall system consists of two
nonlinear Partial Differential Equations and two Ordinary Differential
Equations. Moreover, a spill-free condition is required to hold. By applying
the Control Lyapunov Functional methodology, a set of initial conditions (state
space) is determined for which spill-free motion of the liquid is possible by
applying an appropriate control input. Semi-global stabilization of the liquid
and the tank by means of a simple feedback law is achieved, in the sense that
for every closed subset of the state space, it is possible to find appropriate
controller gains, so that every solution of the closed-loop system initiated
from the given closed subset satisfies specific stability estimates. The
closed-loop system exhibits an exponential convergence rate to the desired
equilibrium point. The proposed stabilizing feedback law does not require
measurement of the liquid level and velocity profiles inside the tank and
simply requires measurements of: (i) the tank position error and tank velocity,
(ii) the total momentum of the liquid, and (iii) the liquid levels at the tank
walls. The obtained results allow an algorithmic solution of the problem of the
spill-free movement and slosh-free settlement of a liquid in a vessel of
limited height (such as water in a glass) by a robot to a pre-specified
position, no matter how full the vessel is.


  In tropical geometry, given a curve in a toric variety, one defines a
corresponding graph embedded in Euclidean space. We study the problem of
reversing this process for curves of genus zero and one. Our methods focus on
describing curves by parameterizations, not by their defining equations; we
give parameterizations by rational functions in the genus zero case and by
non-archimedean elliptic functions in the genus one case. For genus zero
curves, those graphs which can be lifted can be characterized in a completely
combinatorial manner. For genus one curves, show that certain conditions
identified by Mikhalkin are sufficient and we also identify a new necessary
condition.


  A central problem in many-body quantum physics is the determination of the
ground state of a thermodynamically large physical system. We construct a
cluster expansion for ground states of local Hamiltonians, which naturally
incorporates physical requirements inherited by locality as conditions on its
cluster amplitudes. Applying a diagrammatic technique we derive the relation of
these amplitudes to thermodynamic quantities and local observables. Moreover we
derive a set of functional equations that determine the cluster amplitudes for
a general Hamiltonian, verify the consistency with perturbation theory and
discuss non-perturbative approaches. Lastly we verify the persistence of
locality features of the cluster expansion under unitary evolution with a local
Hamiltonian and provide applications to out-of-equilibrium problems: a
simplified proof of equilibration to the GGE and a cumulant expansion for the
statistics of work, for an interacting-to-free quench.


  Electroweak (EW) corrections can be enhanced at high energies due to the soft
or collinear radiation of virtual and real $W$ and $Z$ bosons that result in
Sudakov-like corrections of the form $\alpha_W^l\log^n(Q^2/M_{W,Z}^2)$, where
$\alpha_W =\alpha/(4\pi\sin^2\theta_W)$ and $n\le 2l-1$. The inclusion of EW
corrections in predictions for hadron colliders is therefore especially
important when searching for signals of possible new physics in distributions
probing the kinematic regime $Q^2 \gg M_V^2$. Next-to-leading order (NLO) EW
corrections should also be taken into account when their size
($\mathcal{O}(\alpha)$) is comparable to that of QCD corrections at
next-to-next-to-leading order (NNLO) ($\mathcal{O}(\alpha_s^2)$). To this end
we have implemented the NLO weak corrections to the Neutral-Current Drell-Yan
process, top-quark pair production and di-jet production in the parton-level
Monte-Carlo program MCFM. This enables a combined study with the corresponding
QCD corrections at NLO and NNLO. We provide both the full NLO weak corrections
and their Sudakov approximation since the latter is often used for a fast
evaluation of weak effects at high energies and can be extended to higher
orders. With both the exact and approximate results at hand, the validity of
the Sudakov approximation can be readily quantified


  It is proved that there exists a local-in-time solution $u\in
C([0,T),bmo(\mathbb{R}^d)^d)$ of the Navier-Stokes equations such that every
$u(t)$ has an analytic extension on a complex domain whose size only depends on
$t$ (and increases with $t$) and the external force $f$, assuming only that the
initial velocity $u_0$ is a local $BMO$ function. Our method for proving is a
combination and refinement of the work by Gruji\'c and Kukavica [13],
Guberovi\'c [15] and Kozono et al. [18]. One challenging step is the estimation
of the heat and Stokes semigroups from $BMO$-type spaces to $L^\infty$; a
result itself of independent interest. We also apply the idea to the
analyticity of vorticity with the assistance of Calder\'on-Zygmund theory.


  Partition functions $Z(x)$ of statistical mechanics are generally
approximated by integrals. The approximation fails in small cavities or at very
low temperature, when the ratio $x$ between the energy quantum and thermal
energy is larger or equal to unity. In addition, the exact calculation, which
is based on number theoretical concepts, shows excess low frequency noise in
thermodynamical quantities, that the continuous approximation fails to predict.
It is first shown that Riemann zeta function is essentially the Mellin
transform of the partition function $Z(x)$ of the non degenerate (one
dimensional) perfect gas. Inverting the transform leads to the conventional
perfect gas law. The degeneracy has two aspects. One is related to the wave
nature of particles: this is accounted for from quantum statistics, when the de
Broglie wavelength exceeds the mean distance between particles. We emphasize
here the second aspect which is related to the degeneracy of energy levels. It
is given by the number of solutions $r_3(p)$ of the three squares diophantine
equation, a highly discontinuous arithmetical function. In the conventional
approach the density of states is proportional to the square root of energy,
that is $r_3(p)\simeq 2 \pi p^{1/2}$. We found that the exact density of states
relates to the class number in the quadratic field $Q(\sqrt{-p})$. One finds
$1/f$ noise around the mean value.


  Observations of caustic-crossing galaxies at redshift $0.7<z<1$ show a wealth
of transient events. Most of them are believed to be microlensing events of
highly magnified stars. Earlier work predicted such events should be common
near the critical curves (CCs) of galaxy clusters, but some are found
relatively far away from these CCs. We consider the possibility that
substructure on milliarcsecond scales (few parsecs in the lens plane) is
boosting the microlensing signal. We study the combined magnification from the
macrolens, millilenses, and microlenses (3M-lensing). After considering
realistic populations of millilenses and microlenses, we conclude that the
enhanced microlensing rate around millilenses is not sufficient to explain the
high fraction of observed events in the far region. Instead we find a that the
shape of the luminosity function (LF) of the lensed stars combined with the
amount of substructure in the lens plane determines the number of mcirolensing
events found near and far from the CC. By measuring $\beta$ (the exponent of
the LF), and the number density of microlensing events at each location, one
can create a pseudoimage of the underlying distribution of mass on small
scales. We identify two regimes: (i) positive imaging regime where $\beta>2$
and the number density of events is greater around substructureand the number
density of events is greater around substructures, and (ii) negative imaging
regime where $\beta<2$. We study the particular case of seven microlensing
events found by HST in the Dragon arc (at z=0.725). We find that a population
of supergiant stars with a steep LF with $\beta=2.55$ fits the distribution of
these events. We identify a small region of high density of microlensing
events, and interpret it as evidence of a possible invisible substructure, for
which we derive a mass of $\sim 1.3 \times 10^8\,\Msun$ (within its Einstein
radius).


  We study a one-component quaternionic wave equation which is relativistically
covariant. Bi-linear forms include a conserved 4-current and an antisymmetric
second rank tensor. Waves propagate within the light-cone and there is a
conserved quantity which looks like helicity. The principle of superposition is
retained in a slightly altered manner. External potentials can be introduced in
a way that allows for gauge invariance. There are some results for scattering
theory and for two-particle wavefunctions as well as the beginnings of second
quantization. However, we are unable to find a suitable Lagrangian or an
energy-momentum tensor.


  We explore the origin of Majorana masses within the majoron model and how
this can lead to the generation of a distinguishable primordial stochastic
background of gravitational waves. We first show how in the simplest majoron
model only a contribution from cosmic string can be within the reach of planned
experiments. We then consider extensions containing multiple complex scalars,
demonstrating how in this case a spectrum comprising contributions from both a
strong first order phase transition and cosmic strings can naturally emerge. We
show that the interplay between multiple scalar fields can amplify the phase
transition signal, potentially leading to double peaks over the wideband sloped
spectrum from cosmic strings. We also underscore the possibility of observing
such a gravitational wave background to provide insights into the reheating
temperature of the universe. We conclude highlighting how the model can be
naturally combined with scenarios addressing the origin of matter of the
universe, where baryogenesis occurs via leptogenesis and a right-handed
neutrino plays the role of dark matter.


  In this paper we consider the problem of testing whether a graph has bounded
arboricity. The family of graphs with bounded arboricity includes, among
others, bounded-degree graphs, all minor-closed graph classes (e.g. planar
graphs, graphs with bounded treewidth) and randomly generated preferential
attachment graphs. Graphs with bounded arboricity have been studied extensively
in the past, in particular since for many problems they allow for much more
efficient algorithms and/or better approximation ratios.
  We present a tolerant tester in the sparse-graphs model. The sparse-graphs
model allows access to degree queries and neighbor queries, and the distance is
defined with respect to the actual number of edges. More specifically, our
algorithm distinguishes between graphs that are $\epsilon$-close to having
arboricity $\alpha$ and graphs that $c \cdot \epsilon$-far from having
arboricity $3\alpha$, where $c$ is an absolute small constant. The query
complexity and running time of the algorithm are
$\tilde{O}\left(\frac{n}{\sqrt{m}}\cdot \frac{\log(1/\epsilon)}{\epsilon} +
\frac{n\cdot \alpha}{m} \cdot
\left(\frac{1}{\epsilon}\right)^{O(\log(1/\epsilon))}\right)$ where $n$ denotes
the number of vertices and $m$ denotes the number of edges. In terms of the
dependence on $n$ and $m$ this bound is optimal up to poly-logarithmic factors
since $\Omega(n/\sqrt{m})$ queries are necessary (and $\alpha = O(\sqrt{m}))$.
  We leave it as an open question whether the dependence on $1/\epsilon$ can be
improved from quasi-polynomial to polynomial. Our techniques include an
efficient local simulation for approximating the outcome of a global (almost)
forest-decomposition algorithm as well as a tailored procedure of edge
sampling.


  Autonomous cyber-physical agents and systems play an increasingly large role
in our lives. To ensure that agents behave in ways aligned with the values of
the societies in which they operate, we must develop techniques that allow
these agents to not only maximize their reward in an environment, but also to
learn and follow the implicit constraints of society. These constraints and
norms can come from any number of sources including regulations, business
process guidelines, laws, ethical principles, social norms, and moral values.
We detail a novel approach that uses inverse reinforcement learning to learn a
set of unspecified constraints from demonstrations of the task, and
reinforcement learning to learn to maximize the environment rewards. More
precisely, we assume that an agent can observe traces of behavior of members of
the society but has no access to the explicit set of constraints that give rise
to the observed behavior. Inverse reinforcement learning is used to learn such
constraints, that are then combined with a possibly orthogonal value function
through the use of a contextual bandit-based orchestrator that picks a
contextually-appropriate choice between the two policies (constraint-based and
environment reward-based) when taking actions. The contextual bandit
orchestrator allows the agent to mix policies in novel ways, taking the best
actions from either a reward maximizing or constrained policy. In addition, the
orchestrator is transparent on which policy is being employed at each time
step. We test our algorithms using a Pac-Man domain and show that the agent is
able to learn to act optimally, act within the demonstrated constraints, and
mix these two functions in complex ways.


  Using the AdS/CFT correspondence, we calculate the vacuum decay rate for the
Schwinger effect in confining large $N_{c}$ gauge theories. The instability is
induced by the quark antiquark pair creation triggered by strong
electromagnetic fields. The decay rate is obtained as the imaginary part of the
Euler-Heisenberg effective Lagrangian evaluated from the D-brane action with a
constant electromagnetic field in holographic QCD models such as the
Sakai-Sugimoto model and the deformed Sakai-Sugimoto model. The decay rate is
found to increase with the magnetic field parallel to the electric field, while
it decreases with the magnetic field perpendicular to the electric field. We
discuss generic features of a critical electric field as a function of the
magnetic field and the QCD string tension in the Sakai-Sugimoto model.


  Development of multimodal models has marked a significant step forward in how
machines understand videos. These models have shown promise in analyzing short
video clips. However, when it comes to longer formats like movies, they often
fall short. The main hurdles are the lack of high-quality, diverse video data
and the intensive work required to collect or annotate such data. In face of
these challenges, we propose MovieLLM, a novel framework designed to synthesize
consistent and high-quality video data for instruction tuning. The pipeline is
carefully designed to control the style of videos by improving textual
inversion technique with powerful text generation capability of GPT-4. As the
first framework to do such thing, our approach stands out for its flexibility
and scalability, empowering users to create customized movies with only one
description. This makes it a superior alternative to traditional data
collection methods. Our extensive experiments validate that the data produced
by MovieLLM significantly improves the performance of multimodal models in
understanding complex video narratives, overcoming the limitations of existing
datasets regarding scarcity and bias.


  Protective applications require energy-absorbing materials that are soft and
compressible enough to absorb kinetic energy from impacts, yet stiff enough to
bear crushing loads. Achieving this balance requires careful consideration of
both mechanical properties and geometric design. Conventional shock-absorbing
pads are made of very thick foams that exhibit a plateau of constant stress in
their stress-strain response. Contrary to this belief, we report that foams
with a nonlinear stress-strain response can be useful to achieve simultaneously
thin and lightweight protective pads. We introduce a new framework for the
thickness or volume-constrained design of compact and lightweight protective
foams while ensuring the desired structural integrity and mechanical
performance. Our streamlined dimensional analysis approach provides geometric
constraints on the dimensionless thickness and cross-sectional area of a
protective foam with a given stress-strain response to limit the acceleration
and compressive strain within desired critical limits. We also identify optimal
mechanical properties that will result in the most compact and lightest
protective foam layer for absorbing a given kinetic energy of impact. Guided by
this design framework, we achieve optimal protective properties in
hierarchically architected vertically aligned carbon nanotube (VACNT) foams,
enabling next generation protective applications in extreme environments.


  We present an efficient and stable numerical ansatz for solving a class of
integro-differential equations. We define the class as integro-differential
equations with increasingly smooth memory kernels. The resulting algorithm
reduces the computational cost from the usual T^2 to T*C(T), where T is the
total simulation time and C(T) is some function. For instance, C(T) is equal to
lnT for polynomially decaying memory kernels. Due to the common occurrence of
increasingly smooth memory kernels in physical, chemical, and biological
systems, the algorithm can be applied in quite a wide variety of situations. We
demonstrate the performance of the algorithm by examining two cases. First, we
compare the algorithm to a typical numerical procedure for a simple
integro-differential equation. Second, we solve the NIBA equations for the
spin-boson model in real time.


  We investigate neural models' ability to capture lexicosyntactic inferences:
inferences triggered by the interaction of lexical and syntactic information.
We take the task of event factuality prediction as a case study and build a
factuality judgment dataset for all English clause-embedding verbs in various
syntactic contexts. We use this dataset, which we make publicly available, to
probe the behavior of current state-of-the-art neural systems, showing that
these systems make certain systematic errors that are clearly visible through
the lens of factuality prediction.


  This paper is devoted to the construction of finite elements on grids that
consist of general quadrilaterals not limited in parallelograms. Two finite
elements defined as Ciarlet's triple are established for the $H^1$ and $H(\rm
rot)$ elliptic problems, respectively. An $\mathcal{O}(h)$ order convergence
rate in energy norm for both of them and an $\mathcal{O}(h^2)$ order
convergence in $L^2$ norm for the $H^1$ scheme are proved under the
asymptotic-parallelogram assumption on the grids. Further, the two finite
element spaces on general quadrilateral grids, together with the space of
piecewise constant functions, formulate a discretized de Rham complex.
  The finite element spaces consist of piecewise polynomial functions, and,
thus, are nonconforming on general quadrilateral grids. Indeed, a rigorous
analysis is given in this paper that it is impossible to construct a
practically useful finite element defined as Ciarlet's triple that can
formulate a finite element space which consists of continuous piecewise
polynomial functions on a grid that may include arbitrary quadrilaterals.


  Origami has recently emerged as a platform for building functional
engineering systems with versatile characteristics that targeted niche
applications. One widely utilized origami-based structure is known as the
Kresling origami spring (KOS), which inspired, among many other things, the
design of vibration isolators, fluidic muscles, and mechanical bit memory
switches. Previous demonstrations of such concepts were carried out using
paper-based KOSs, which are suitable for conceptual illustrations but not for
implementation in a real environment. In addition to the very low durability
resulting from the high plastic deformations at the paper folds; lack of
repeatability, and high variation of performance among similar samples are also
inevitable. To circumvent these issues, this paper presents a novel approach
for the design of a non-paper based KOS, which mimics the qualitative behavior
of the paper-based KOS without compromising on durability, repeatability, and
functionality. In the new design, each fundamental triangle in the paper-based
KOS is replaced by an inner central rigid core and an outer flexible
rubber-like frame, which are fabricated out of different visco-elastic
materials using advanced 3-D printing technologies. The quasi-static behavior
of the fabricated springs was assessed under both compressive and tensile
loads. It is shown that KOSs with linear, softening, hardening, mono- and
bi-stable restoring force behavior can be fabricated using the proposed design
by simple changes to the geometric design parameters, further pointing to the
vast range of potential applications of such springs.