  We present optical photometry and spectroscopy of SN 2016iet, an
unprecedented Type I supernova (SN) at $z=0.0676$ with no obvious analog in the
existing literature. The peculiar light curve has two roughly equal brightness
peaks ($\approx -19$ mag) separated by 100 days, and a subsequent slow decline
by 5 mag in 650 rest-frame days. The spectra are dominated by emission lines of
calcium and oxygen, with a width of only $3400$ km s$^{-1}$, superposed on a
strong blue continuum in the first year, and with a large ratio of $L_{\rm
[Ca\,II]}/L_{\rm [O\,I]}\approx 4$ at late times. There is no clear evidence
for hydrogen or helium associated with the SN at any phase. We model the light
curves with several potential energy sources: radioactive decay, central
engine, and circumstellar medium (CSM) interaction. Regardless of the model,
the inferred progenitor mass near the end of its life (i.e., CO core mass) is
$\gtrsim 55$ M$_\odot$ and up to $120$ M$_\odot$, placing the event in the
regime of pulsational pair instability supernovae (PPISNe) or pair instability
supernovae (PISNe). The models of CSM interaction provide the most consistent
explanation for the light curves and spectra, and require a CSM mass of
$\approx 35$ M$_\odot$ ejected in the final decade before explosion. We further
find that SN 2016iet is located at an unusually large offset ($16.5$ kpc) from
its low metallicity dwarf host galaxy ($Z\approx 0.1$ Z$_\odot$, $M\approx
10^{8.5}$ M$_\odot$), supporting the PPISN/PISN interpretation. In the final
spectrum, we detect narrow H$\alpha$ emission at the SN location, likely due to
a dim underlying galaxy host or an H II region. Despite the overall consistency
of the SN and its unusual environment with PPISNe and PISNe, we find that the
inferred properties of SN\,2016iet challenge existing models of such events.


  One of the factors which may limit the intensity in the Fermilab Recycler is
a fast transverse instability. It develops within a hundred turns and, in
certain conditions, may lead to a beam loss. The high rate of the instability
suggest that its cause is electron cloud. We studied the phenomena by observing
the dynamics of stable and unstable beam, simulating numerically the build-up
of the electron cloud, and developed an analytical model of an electron cloud
driven instability with the electrons trapped in combined function di-poles. We
found that beam motion can be stabilized by a clearing bunch, which confirms
the electron cloud nature of the instability. The clearing suggest electron
cloud trapping in Recycler combined function mag-nets. Numerical simulations
show that up to 1% of the particles can be trapped by the magnetic field. Since
the process of electron cloud build-up is exponential, once trapped this amount
of electrons significantly increases the density of the cloud on the next
revolution. In a Recycler combined function dipole this multi-turn accumulation
allows the electron cloud reaching final intensities orders of magnitude
greater than in a pure dipole. The estimated resulting instability growth rate
of about 30 revolutions and the mode fre-quency of 0.4 MHz are consistent with
experimental observations and agree with the simulation in the PEI code. The
created instability model allows investigating the beam stability for the
future intensity upgrades.


  Large language models (LLMs) achieved great success in multiple application
domains and attracted huge attention from different research communities
recently. Unfortunately, even for the best LLM, there still exist many faults
that LLM cannot correctly predict. Such faults will harm the usability of LLMs.
How to quickly reveal them in LLMs is important, but challenging. The reasons
are twofold, 1) the heavy labeling effort for preparing the test data, and 2)
accessing closed-source LLMs such as GPT4 is money-required. To handle this
problem, in the traditional deep learning testing field, test selection methods
have been proposed for efficiently testing deep learning models by prioritizing
faults. However, the usefulness of these methods on LLMs is unclear and under
exploration. In this paper, we first study the effectiveness of existing fault
detection methods for LLMs. Experimental results on four different
tasks~(including both code tasks and natural language processing tasks) and
four LLMs (e.g., LLaMA and GPT4) demonstrated that existing fault detection
methods cannot perform well on LLMs (e.g., seven out of eight methods perform
worse than random selection on LLaMA). To enhance existing fault detection
methods, we propose MuCS, a prompt Mutation-based prediction Confidence
Smoothing method for LLMs. Concretely, we mutate the prompts and compute the
average prediction confidence of all mutants as the input of fault detection
methods. The results show that our proposed solution significantly enhances
existing methods with the improvement of test relative coverage by up to
97.64%.


  xloops is a program package that calculates Feynman diagrams by using
computer algebra systems. In this paper it is shown which problems to be solved
by computer algebra arise during such calculations, and how this problems are
handled in the framework of xloops.


  Continual learning, the ability of a model to learn over time without
forgetting previous knowledge and, therefore, be adaptive to new data, is
paramount in dynamic fields such as disease outbreak prediction. Deep neural
networks, i.e., LSTM, are prone to error due to catastrophic forgetting. This
study introduces a novel CEL model for continual learning by leveraging domain
adaptation via Elastic Weight Consolidation (EWC). This model aims to mitigate
the catastrophic forgetting phenomenon in a domain incremental setting. The
Fisher Information Matrix (FIM) is constructed with EWC to develop a
regularization term that penalizes changes to important parameters, namely, the
important previous knowledge. CEL's performance is evaluated on three distinct
diseases, Influenza, Mpox, and Measles, with different metrics. The high
R-squared values during evaluation and reevaluation outperform the other
state-of-the-art models in several contexts, indicating that CEL adapts to
incremental data well. CEL's robustness and reliability are underscored by its
minimal 65% forgetting rate and 18% higher memory stability compared to
existing benchmark studies. This study highlights CEL's versatility in disease
outbreak prediction, addressing evolving data with temporal patterns. It offers
a valuable model for proactive disease control with accurate, timely
predictions.


  We prove that for any positive integer $k$, the edges of any graph whose
fractional arboricity is at most $k + 1/(3k+2)$ can be decomposed into $k$
forests and a matching.


  We demonstrate sub-wavelength imaging of excitons confined to single CdTe
quantum dots. By combining slit-confocal microscopy with a hemispherical solid
immersion lens we simultaneously map the emission of thousands of single
quantum dots with a spatial resolution of 400 nm. By analyzing the linear
polarization of the quantum dot emissions at B=0T, we find that the
distribution of the exchange splitting is centered at zero with a standard
deviation of 0.34 meV. Similar experiments performed at B=3T give an average
value of the exciton effective g factor of 3.1. This experimental approach
provides an effective means to gain statistical information about the quantum
dot exciton fine structure in the ensemble.


  In this paper, we prove a generalization of Orlov's projectivization formula
for the derived category $D^b_{\rm coh} (\mathbb{P}(\mathscr{E}))$, where
$\mathscr{E}$ does not need to be a vector bundle; Instead, $\mathscr{E}$ is a
coherent sheaf which locally admits two-step resolutions. As a special case,
this also gives Orlov's generalized universal hyperplane section formula. As
applications, (i) we obtain a blowup formula for blowup along codimension two
Cohen-Macaulay subschemes, (ii) we obtain new "flop-flop=twist" results for a
large class of flops obtained by crepant resolutions of degeneracy loci. As
another consequence, this gives a perverse Schober on C. (iii) we give
applications of the above results to symmetric powers of curves and
$\Theta$-flops, following Toda.


  Graphene on hexagonal boron-nitride (h-BN) is an atomically flat conducting
system that is ideally suited for probing the effect of Zeeman splitting on
electron transport. We demonstrate by magneto-transport measurements that a
parallel magnetic field up to 30 Tesla does not affect the transport properties
of graphene on h-BN even at charge neutrality where such an effect is expected
to be maximal. The only magnetoresistance detected at low carrier
concentrations is shown to be associated with a small perpendicular component
of the field which cannot be fully eliminated in the experiment. Despite the
high mobility of charge carries at low temperatures, we argue that the effects
of Zeeman splitting are fully masked by electrostatic potential fluctuations at
charge neutrality.


  This paper creates and analyses a new quantum algorithm called the Amplified
Quantum Fourier Transform (Amplified-QFT) for solving the following problem:
The Local Period Problem: Let L = {0,1...N-1} be a set of N labels and let A be
a subset of M labels of period P, i.e. a subset of the form A = {j : j = s +
rP; r = 0,1...M-1} where P < sqrt(N) and M << N, and where M is assumed known.
Given an oracle f : L->{0,1} which is 1 on A and 0 elsewhere, find the local
period P. A separate algorithm finds the offset s. The first part of the paper
defines the Amplified-QFT algorithm. The second part of the paper summarizes
the main results and compares the Amplified-QFT algorithm against the Quantum
Fourier Transform (QFT) and Quantum Hidden Subgroup (QHS) algorithms when
solving the local period problem. It is shown that the Amplified-QFT is, on
average, quadratically faster than both the QFT and QHS algorithms. The third
part of the paper provides the detailed proofs of the main results, describes
the method of recovering P from an observation y and describes the method for
recovering the offset s.


  The general non-split scalar coset of supergravity theories is discussed.The
symmetric space sigma model is studied in two equivalent formulations and for
different coset parametrizations.The dualisation and the local first order
formulation is performed for the non-split scalar coset G/K when the rigid
symmetry group G is a real form of a non-compact semisimple Lie group (not
necessarily split) and the local symmetry group K is G's maximal compact
subgroup.A comparison with the scalar cosets arising in the
T^{10-D}-compactification of the heterotic string theory in ten dimensions is
also mentioned.


  Previous observations of Phobos and Deimos, the moons of Mars, have improved
our understanding of these small bodies. However, their formation and
composition remain poorly constrained. Physical and spectral properties suggest
that Phobos may be a weakly thermal-altered captured asteroid but the dynamical
properties of the martian system suggest a formation by giant collision similar
to the Earth moon. In 2027, the JAXA's MMX mission aims to address these
outstanding questions. We undertook measurements with a new simulant called
OPPS (Observatory of Paris Phobos Simulant) which closely matches Phobos
spectra in the visible to the mid-infrared range. The simulant was synthesized
using a mixture of olivine, saponite, anthracite, and coal. Since observation
geometry is a crucial aspect of planetary surface remote sensing exploration,
we evaluated the parameters obtained by modeling the phase curves -- obtained
through laboratory measurements -- of two different Phobos simulants (UTPS-TB
and OPPS) using Hapke IMSA model. Our results show that the photometric
properties of Phobos simulants are not fully consistent with those of Tagish
Lake, Allende, or the NWA 4766 shergottite. We also investigated the detection
of volatiles/organic compounds and hydrated minerals, as the presence of such
components is expected on Phobos in the hypothesis of a captured primitive
asteroid. The results indicate that a significant amount of organic compounds
is required for the detection of C-H bands at 3.4 $\mu$m. In contrast, the 2.7
$\mu$m absorption band, due to hydrated minerals, is much deeper and easier to
detect than C-H organic features at the same concentration levels. Posing
limits on detectability of some possible key components of Phobos surface will
be pivotal to prepare and interpret future observations of the MIRS
spectrometer onboard MMX mission.


  We prove that to each almost periodic (in the sense of distributions) divisor
in a tube one can assign a first Chern class of a special line bundle over
Bohr's compact set generated by the divisor such that the trivial cohomology
class represents divisors of all almost periodic holomorphic functions on a
tube. This description yields various geometric conditions for an almost
periodic divisor to be the divisor of a holomorphic almost periodic function.
We also give a complete description for the divisors of homogeneous coordinates
for holomorphic almost periodic curves; in particular, we obtain a description
for the divisors of meromorphic almost periodic functions.


  In 2011, the first author introduced (relative) Riemann-Zariski spaces
corresponding to a morphism of schemes and established their basic properties.
In this paper we clarify that theory and extend it to morphisms between
algebraic spaces. As an application, a new proof of Nagata's compactification
theorem for algebraic spaces is obtained.


  The transition form factors of $\bar B_s^0\to D_{s}^+(2317)$ and $\bar
B_s^0\to D_s^+(1968)$ at large recoil region are investigated in the light cone
sum rules approach, where the heavy quark effective theory is adopted to
describe the form factors at small recoil region. With the form factors
obtained, we carry out a detailed analysis on both the semileptonic decays
$\bar B_s^0\to D_s^+(1968,2317) l \bar{\nu}_l$ and nonleptonic decays $B_s \to
D_s^+(1968,2317) M$ with $M$ being a light meson or a charmed meson under the
factorization approach. Our results show that the branching fraction of $\bar
B_s^0\to D_s^+(2317) \mu \bar{\nu}_\mu$ is around $2.3 \times 10^{-3}$, which
should be detectable with ease at the Tevatron and LHC. It is also found that
the branching fractions of $\bar B_s^0\to D_s^+(1968) l \bar{\nu}_l$ are almost
one order larger than those of the corresponding $B_s^0\to D_s^+(2317) l
\bar{\nu}_l$ decays. The consistency of predictions for $B_s \to
D_s^+(1968,2317) L$ ($L$ denotes a light meson) in the factorization assumption
and $k_T$ factorization also supports the success of color transparency
mechanism in the color allowed decay modes. Most two-charmed meson decays of
$B_s$ meson possess quite large branching ratios that are accessible in the
experiments. These channels are of great importance to explore the hadronic
structure of charmed mesons as well as the nonperturbative dynamics of QCD.


  We estimate gamma-ray fluxes due to the decay of nuclei beyond Bi209 from a
supernova or a supernova remnant assuming that the r-process occurs in
supernovae. We find that a detector with a sensitivity of about 10**(-7)
photons/cm**2/s at energies of 40 keV to 3 MeV may detect fluxes due to the
decay of Ra226, Th229, Am241, Am243, Cf249, and Cf251 in the newly discovered
supernova remnant near Vela. In addition, such a detector may detect fluxes due
to the decay of Ac227 and Ra228 produced in a future supernova at a distance of
about 1 kpc. As nuclei with mass numbers A > 209 are produced solely by the
r-process, such detections are the best proof for a supernova r-process site.
Further, they provide the most direct information on yields of progenitor
nuclei with A > 209 at r-process freeze-out. Finally, detection of fluxes due
to the decay of r-process nuclei over a range of masses from a supernova or a
supernova remnant provides the opportunity to compare yields in a single
supernova event with the solar r-process abundance pattern.


  Algorithm, based on explicit representations for analytic continuation of the
T-matrix Faddeev components on unphysical sheets, is worked out for
calculations of resonances in the three-body quantum problem. According to the
representations, poles of T-matrix, scattering matrix and Green function on
unphysical sheets, interpreted as resonances, coincide with those complex
energy values where appropriate truncations of the scattering matrix have zero
as eigenvalue. Scattering amplitudes on the physical sheet, necessary to
construct scattering matrix, are calculated on the basis of the Faddeev
differential equations. The algorithm developed is applied to search for the
resonances in the $nnp$ system and in a model three-boson system.


  We present several algorithms for computing the visibility polygon of a
simple polygon $P$ from a viewpoint inside the polygon, when the polygon
resides in read-only memory and only few working variables can be used. The
first algorithm uses a constant number of variables, and outputs the vertices
of the visibility polygon in $O(n\Rout)$ time, where $\Rout$ denotes the number
of reflex vertices of $P$ that are part of the output. The next two algorithms
use $O(\log \Rin)$ variables, and output the visibility polygon in $O(n\log
\Rin)$ randomized expected time or $O(n\log^2 \Rin)$ deterministic time, where
$\Rin$ is the number of reflex vertices of $P$.


  We present a global magnetohydrodynamic (MHD) three dimensional simulation of
a nonradiative accretion flow originating in a pressure supported torus. The
evolution is controlled by the magnetorotational instability which produces
turbulence. The flow forms a nearly Keplerian disk. The total pressure scale
height in this disk is comparable to the vertical size of the initial torus.
Gas pressure dominates only near the equator; magnetic pressure is more
important in the surrounding atmosphere. A magnetically dominated bound outflow
is driven from the disk. The accretion rate through the disk exceeds the final
rate into the hole, and a hot torus forms inside 10 r_g. Hot gas, pushed up
against the centrifugal barrier and confined by magnetic pressure, is ejected
in a narrow, unbound, conical outflow. The dynamics are controlled by magnetic
turbulence, not thermal convection, and a hydrodynamic alpha model is
inadequate to describe the flow. The limitations of two dimensional MHD
simulations are also discussed.


  Chromatin organization and dynamics is studied in this work at scales ranging
from single nucleosome to nucleosomal array by using a unique combination of
biochemical assays, single molecule imaging technique and numerical modeling.
We demonstrate that a subtle modification in the nucleosome structure induced
by the histone variant H2A.Bbd drastically modifies the higher order
organization of the nucleosomal arrays. Importantly, as directly visualized by
AFM, conventional H2A nucleosomal arrays exhibit specific local organization,
in contrast to H2A.Bbd arrays, which show "beads on a string" structure. The
combination of systematic image analysis and theoretical modeling allows a
quantitative description relating the observed gross structural changes of the
arrays to their local organization. Our results strongly suggest that
higher-order organization of H1-free nucleosomal arrays is mainly determined by
the fluctuation properties of individual nucleosomes. Moreover, numerical
simulations suggest the existence of attractive interactions between
nucleosomes to provide the degree of compaction observed for conventional
chromatin fibers.


  Calculations of eta->pi^0 pi^0 gamma gamma decay in Generalized chiral
perturbation theory are presented. Tree level and next-to-leading corrections
are involved. Sensitivity to the violation of the standard counting is
discussed.


  Starting from the earlier notions of stationary action principles, we show
how Schwinger's Quantum Action Principle descended from Dirac's formulation,
which independently led Feynman to his path-integral formulation of quantum
mechanics. The connection between the two is brought out, and applications are
discussed. The Keldysh-Schwinger time-cycle method of extracting matrix
elements is described. Part II will discuss the variational formulation of
quantum electrodynamics and the development of source theory.


  The Brieskorn manifolds $B(p,q,r)$ are the $r$-fold cyclic coverings of the
3-sphere $S^{3}$ branched over the torus knot $T(p,q)$. The generalised
Sieradski groups $S(m,p,q)$ are groups with $m$-cyclic pre\-sen\-tation
$G_{m}(w)$, where defining word $w$ has a special form, depending of $p$ and
$q$. In particular, $S(m,3,2) = G_{m}(w)$ is the group with $m$ generators
$x_{1}, \ldots, x_{m}$ and $m$ defining relations $w(x_{i}, x_{i+1},
x_{i+2})=1$, where $w(x_{i}, x_{i+1}, x_{i+2}) = x_{i} x_{i+2} x_{i+1}^{-1}$.
Presentations of $S(2n,3,2)$ in a certain form $G_{n}(w)$ were investigated by
Howie and Williams. They proved that the $n$-cyclic presentations are
geometric, i.e., correspond to the spines of closed orientable 3-manifolds. We
establish an analogous result for the groups $S(2n,5,2)$. It is shown that in
both cases the manifolds are $n$-fold cyclic branched coverings of lens spaces.
To classify some of constructed manifolds we used the Matveev's computer
program "Recognizer".


  In this paper, we explore the field propagator with a structure that is
general enough to encompass both the case of newly-defined mass-dimension $1$
fermions and spin-$1/2$ bosons. The method we employ is to define a map between
spinors of different Lounesto classes, and then write the propagator in terms
of the corresponding dual structures.


  In this paper we consider the simplified form that a recently introduced
general operator description of the Hubbard model on the square lattice with
$N_a^2\gg 1$ sites, effective transfer integral $t$, and onsite repulsion $U$
has in a suitable one- and two-electron subspace. Such an operator description
is that consistent with the model exact global symmetry recently extended to
$SO(3)\times SO(3)\times U(1)$. There is a large consensus that in the
thermodynamic limit $N_a^2\rightarrow\infty$ long-range antiferromagnetic order
occurs in the spin-density $m=0$ ground state of the half-filled Hubbard model
on the square lattice. Here we find that the corresponding spontaneous symmetry
breaking lowers the symmetry of such a state from $SO(3)\times SO(3)\times
U(1)$ for $N_a^2\gg 1$ large but finite to $[U(2)\times U(1)]/Z_2^2 \equiv
[SO(3)\times U(1)\times U(1)]/Z_2$ for $N_a^2\rightarrow\infty$. Moreover, we
argue that the spin effective lattice being identical to the original lattice
is a necessary condition for the occurrence of ground-state long-range
antiferromagnetic order in the limit $N_a^2\rightarrow\infty$. Consistently,
strong evidence is provided that for very small hole concentration $0<x\ll1$
the ground state has a short-range incommensurate-spiral spin order. Our
results are of interest both for condensed-matter systems and ultra-cold
fermionic atoms on an optical square lattice.


  We show that, for many holomorphic function spaces on the unit disk, a
continuous endomorphism that sends inner functions to inner functions is
necessarily a weighted composition operator.


  We analyse a system of partial differential equations describing the
behaviour of an elastic plate with periodic moduli in the two planar
directions, in the asymptotic regime when the period and the plate thickness
are of the same order of smallness. Assuming that the displacement gradients of
the points of the plate are small enough for the equations of linearised
elasticity to be a suitable approximation of the material response, such as the
case in e.g. acoustic wave propagation, we derive a class of "hybrid",
homogenisation dimension-reduction, norm-resolvent estimates for the plate,
under different energy scalings with respect to the plate thickness.


  Self-exciting spatio-temporal point process models predict the rate of events
as a function of space, time, and the previous history of events. These models
naturally capture triggering and clustering behavior, and have been widely used
in fields where spatio-temporal clustering of events is observed, such as
earthquake modeling, infectious disease, and crime. In the past several
decades, advances have been made in estimation, inference, simulation, and
diagnostic tools for self-exciting point process models. In this review, I
describe the basic theory, survey related estimation and inference techniques
from each field, highlight several key applications, and suggest directions for
future research.


  Convolutional neural networks and vision transformers have achieved
outstanding performance in machine perception, particularly for image
classification. Although these image classifiers excel at predicting
image-level class labels, they may not discriminate missing or shifted parts
within an object. As a result, they may fail to detect corrupted images that
involve missing or disarrayed semantic information in the object composition.
On the contrary, human perception easily distinguishes such corruptions. To
mitigate this gap, we introduce the concept of "image grammar", consisting of
"image semantics" and "image syntax", to denote the semantics of parts or
patches of an image and the order in which these parts are arranged to create a
meaningful object. To learn the image grammar relative to a class of visual
objects/scenes, we propose a weakly supervised two-stage approach. In the first
stage, we use a deep clustering framework that relies on iterative clustering
and feature refinement to produce part-semantic segmentation. In the second
stage, we incorporate a recurrent bi-LSTM module to process a sequence of
semantic segmentation patches to capture the image syntax. Our framework is
trained to reason over patch semantics and detect faulty syntax. We benchmark
the performance of several grammar learning models in detecting patch
corruptions. Finally, we verify the capabilities of our framework in Celeb and
SUNRGBD datasets and demonstrate that it can achieve a grammar validation
accuracy of 70 to 90% in a wide variety of semantic and syntactical corruption
scenarios.


  We present a Generative Adversarial Network (GAN) based room impulse response
generator (IR-GAN) for generating realistic synthetic room impulse responses
(RIRs). IR-GAN extracts acoustic parameters from captured real-world RIRs and
uses these parameters to generate new synthetic RIRs. We use these generated
synthetic RIRs to improve far-field automatic speech recognition in new
environments that are different from the ones used in training datasets. In
particular, we augment the far-field speech training set by convolving our
synthesized RIRs with a clean LibriSpeech dataset. We evaluate the quality of
our synthetic RIRs on the real-world LibriSpeech test set created using
real-world RIRs from the BUT ReverbDB and AIR datasets. Our IR-GAN reports up
to an 8.95% lower error rate than Geometric Acoustic Simulator (GAS) in
far-field speech recognition benchmarks. We further improve the performance
when we combine our synthetic RIRs with synthetic impulse responses generated
using GAS. This combination can reduce the word error rate by up to 14.3% in
far-field speech recognition benchmarks.


  Current models for event causality identification (ECI) mainly adopt a
supervised framework, which heavily rely on labeled data for training.
Unfortunately, the scale of current annotated datasets is relatively limited,
which cannot provide sufficient support for models to capture useful indicators
from causal statements, especially for handing those new, unseen cases. To
alleviate this problem, we propose a novel approach, shortly named CauSeRL,
which leverages external causal statements for event causality identification.
First of all, we design a self-supervised framework to learn context-specific
causal patterns from external causal statements. Then, we adopt a contrastive
transfer strategy to incorporate the learned context-specific causal patterns
into the target ECI model. Experimental results show that our method
significantly outperforms previous methods on EventStoryLine and
Causal-TimeBank (+2.0 and +3.4 points on F1 value respectively).


  We study reinforcement learning with linear function approximation, unknown
transition, and adversarial losses in the bandit feedback setting.
Specifically, we focus on linear mixture MDPs whose transition kernel is a
linear mixture model. We propose a new algorithm that attains an
$\widetilde{O}(d\sqrt{HS^3K} + \sqrt{HSAK})$ regret with high probability,
where $d$ is the dimension of feature mappings, $S$ is the size of state space,
$A$ is the size of action space, $H$ is the episode length and $K$ is the
number of episodes. Our result strictly improves the previous best-known
$\widetilde{O}(dS^2 \sqrt{K} + \sqrt{HSAK})$ result in Zhao et al. (2023a)
since $H \leq S$ holds by the layered MDP structure. Our advancements are
primarily attributed to (i) a new least square estimator for the transition
parameter that leverages the visit information of all states, as opposed to
only one state in prior work, and (ii) a new self-normalized concentration
tailored specifically to handle non-independent noises, originally proposed in
the dynamic assortment area and firstly applied in reinforcement learning to
handle correlations between different states.


  In this work, our goal is to extend the existing search and rescue paradigm
by allowing teams of autonomous unmanned aerial vehicles (UAVs) to collaborate
effectively with human searchers on the ground. We derive a framework that
includes a simulated lost person behavior model, as well as a human searcher
behavior model that is informed by data collected from past search tasks. These
models are used together to create a probabilistic heatmap of the lost person's
position and anticipated searcher trajectories. We then use Gaussian processes
with a Gibbs' kernel to accurately model a limited field-of-view (FOV) sensor,
e.g., thermal cameras, from which we derive a risk metric that drives UAV path
optimization. Our framework finally computes a set of search paths for a team
of UAVs to autonomously complement human searchers' efforts.


  This paper proposes an adversarial learning based training approach for brain
tumor segmentation task. In this concept, the 3D segmentation network learns
from dual reciprocal adversarial learning approaches. To enhance the
generalization across the segmentation predictions and to make the segmentation
network robust, we adhere to the Virtual Adversarial Training approach by
generating more adversarial examples via adding some noise on original patient
data. By incorporating a critic that acts as a quantitative subjective referee,
the segmentation network learns from the uncertainty information associated
with segmentation results. We trained and evaluated network architecture on the
RSNA-ASNR-MICCAI BraTS 2021 dataset. Our performance on the online validation
dataset is as follows: Dice Similarity Score of 81.38%, 90.77% and 85.39%;
Hausdorff Distance (95\%) of 21.83 mm, 5.37 mm, 8.56 mm for the enhancing
tumor, whole tumor and tumor core, respectively. Similarly, our approach
achieved a Dice Similarity Score of 84.55%, 90.46% and 85.30%, as well as
Hausdorff Distance (95\%) of 13.48 mm, 6.32 mm and 16.98 mm on the final test
dataset. Overall, our proposed approach yielded better performance in
segmentation accuracy for each tumor sub-region. Our code implementation is
publicly available at https://github.com/himashi92/vizviva_brats_2021


  We consider the simple random walk on random graphs generated by discrete
point processes. This random graph has a random subset of a cubic lattice as
the vertices and lines between any consecutive vertices on lines parallel to
each coordinate axis as the edges. Under the assumption that discrete point
processes are finitely dependent and stationary, we prove that the quenched
invariance principle holds, that is, for almost every configuration of a point
process, the path distribution of the walk converges weakly to that of a
Brownian motion.


  Suppose we have n keys, n access probabilities for the keys, and n+1 access
probabilities for the gaps between the keys. Let h_min(n) be the minimal height
of a binary search tree for n keys. We consider the problem to construct an
optimal binary search tree with near minimal height, i.e.\ with height h <=
h_min(n) + Delta for some fixed Delta. It is shown, that for any fixed Delta
optimal binary search trees with near minimal height can be constructed in time
O(n^2). This is as fast as in the unrestricted case.
  So far, the best known algorithms for the construction of height-restricted
optimal binary search trees have running time O(L n^2), whereby L is the
maximal permitted height. Compared to these algorithms our algorithm is at
least faster by a factor of log n, because L is lower bounded by log n.


  We present initial results from a Hubble Space Telescope snapshot imaging
survey of the host galaxies of Swift-BAT active galactic nuclei (AGN) at z<0.1.
The hard X-ray selection makes this sample sample relatively unbiased in terms
of obscuration compared to optical AGN selection methods. The high-resolution
images of 154 target AGN enable us to investigate the detailed photometric
structure of the host galaxies, such as the Hubble type and merging features.
We find that 48% and 44% of the sample is hosted by early-type and late-type
galaxies, respectively. The host galaxies of the remaining 8% of the sample are
classified as peculiar galaxies because they are heavily disturbed. Only a
minor fraction of host galaxies (18%-25%) exhibit merging features (e.g., tidal
tails, shells, or major disturbance). The merging fraction increases strongly
as a function of bolometric AGN luminosity, revealing that merging plays an
important role in triggering luminous AGN in this sample. However, the merging
fraction is weakly correlated with the Eddington ratio, suggesting that merging
does not necessarily lead to an enhanced Eddington ratio. Type 1 and type 2 AGN
are almost indistinguishable in terms of their Hubble type distribution and
merging fraction. However, the merging fraction of type 2 AGN peaks at a lower
bolometric luminosity compared with those of type 1 AGN. This result may imply
that the triggering mechanism and evolutionary stages of type 1 and type 2 AGN
are not identical.


  Referring video segmentation relies on natural language expressions to
identify and segment objects, often emphasizing motion clues. Previous works
treat a sentence as a whole and directly perform identification at the
video-level, mixing up static image-level cues with temporal motion cues.
However, image-level features cannot well comprehend motion cues in sentences,
and static cues are not crucial for temporal perception. In fact, static cues
can sometimes interfere with temporal perception by overshadowing motion cues.
In this work, we propose to decouple video-level referring expression
understanding into static and motion perception, with a specific emphasis on
enhancing temporal comprehension. Firstly, we introduce an
expression-decoupling module to make static cues and motion cues perform their
distinct role, alleviating the issue of sentence embeddings overlooking motion
cues. Secondly, we propose a hierarchical motion perception module to capture
temporal information effectively across varying timescales. Furthermore, we
employ contrastive learning to distinguish the motions of visually similar
objects. These contributions yield state-of-the-art performance across five
datasets, including a remarkable $\textbf{9.2%}$ $\mathcal{J\&F}$ improvement
on the challenging $\textbf{MeViS}$ dataset. Code is available at
https://github.com/heshuting555/DsHmp.


  Modern autonomous underwater vehicles (AUVs) have advanced sensing
capabilities including sonar, cameras, acoustic communication, and diverse
bio-sensors. Instead of just sensing its environment and storing the data for
post-Mission inspection, an AUV could use the collected information to gain an
understanding of its environment, and based on this understanding autonomously
adapt its behavior to enhance the overall effectiveness of its mission. Many
such tasks are highly computation intensive. This paper presents the results of
a case study that illustrates the effectiveness of an energy-aware, many-core
computing architecture to perform on-board path planning within a
batteryoperated AUV. A previously published path planning algorithm was ported
onto the SCC, an experimental 48 core single-chip system developed by Intel.
The performance, power, and energy consumption of the application were measured
for different numbers of cores and other system parameters. This case study
shows that computation intensive tasks can be executed within an AUV that
relies mainly on battery power. Future plans include the deployment and testing
of an SCC system within a Teledyne Webb Research Slocum glider.


  When developing technologies for the Metaverse, it is important to understand
the needs and requirements of end users. Relatively little is known about the
specific perspectives on the use of the Metaverse by the youngest audience:
children ten and under. This paper explores the Metaverse from the perspective
of a young gamer. It examines their understanding of the Metaverse in relation
to the physical world and other technologies they may be familiar with, looks
at some of their expectations of the Metaverse, and then relates these to the
specific multimedia signal processing (MMSP) research challenges. The
perspectives presented in the paper may be useful for planning more detailed
subjective experiments involving young gamers, as well as informing the
research on MMSP technologies targeted at these users.


  Recent works on localized charge transport along DNA, based on a
three--dimensional, tight--binding model (Eur. Phys. J. B 30:211, 2002; Phys. D
180:256, 2003), suggest that charge transport is mediated by the coupling of
the radial and electron variables. However, these works are based on a linear
approximation of the distances among nucleotides, which forces for consistency
the assumption that the parameter $\alpha$, that describes the coupling between
the transfer integral and the distance between nucleotides is fairly small. In
the present letter we perform an improvement of the model which allows larger
values of $\alpha$, showing that there exist two very different regimes.
Particulary, for large $\alpha$, the conclusions of the previous works are
reversed and charge transport can be produced only by the coupling with the
twisting modes.


  As the use of black-box models becomes ubiquitous in high stake
decision-making systems, demands for fair and interpretable models are
increasing. While it has been shown that interpretable models can be as
accurate as black-box models in several critical domains, existing fair
classification techniques that are interpretable by design often display poor
accuracy/fairness tradeoffs in comparison with their non-interpretable
counterparts. In this paper, we propose FairCORELS, a fair classification
technique interpretable by design, whose objective is to learn fair rule lists.
Our solution is a multi-objective variant of CORELS, a branch-and-bound
algorithm to learn rule lists, that supports several statistical notions of
fairness. Examples of such measures include statistical parity, equal
opportunity and equalized odds. The empirical evaluation of FairCORELS on
real-world datasets demonstrates that it outperforms state-of-the-art fair
classification techniques that are interpretable by design while being
competitive with non-interpretable ones.


  The simple derivation of the string equation of motion adopted in the
nonrelativistic case is presented, paying the special attention to the effects
of finite masses of bosonic fields of an Abelian Higgs model. The role of the
finite mass effects in the evaluation of various topological characteristics of
the closed strings is discussed. The rate of the dissipationless helicity
change is calculated. It is demonstrated how the conservation of the sum of the
twisting and writhing numbers of the string is recovered despite the changing
helicity.


  For inviscid, rotational accretion flows driven by a general pseudo-Newtonian
potential on to a Schwarzschild black hole, the only possible fixed points are
saddle points and centre-type points. For the specific choice of the Newtonian
potential, the flow has only two critical points, of which the outer one is a
saddle point while the inner one is a centre-type point. A restrictive upper
bound is imposed on the admissible range of values of the angular momentum of
sub-Keplerian flows through a saddle point. These flows are very unstable to
any deviation from a necessarily precise boundary condition. The difficulties
against the physical realisability of a solution passing through the saddle
point have been addressed through a temporal evolution of the flow, which gives
a non-perturbative mechanism for selecting a transonic solution passing through
the saddle point. An equation of motion for a real-time perturbation about the
stationary flows reveals a very close correspondence with the metric of an
acoustic black hole, which is also an indication of the primacy of
transonicity.


  Speech synthesis is one of the challenging tasks to automate by deep
learning, also being a low-resource language there are very few attempts at
Bangla speech synthesis. Most of the existing works can't work with anything
other than simple Bangla characters script, very short sentences, etc. This
work attempts to solve these problems by introducing Byakta, the first-ever
open-source deep learning-based bilingual (Bangla and English) text to a speech
synthesis system. A speech recognition model-based automated scoring metric was
also proposed to evaluate the performance of a TTS model. We also introduce a
test benchmark dataset for Bangla speech synthesis models for evaluating speech
quality. The TTS is available at https://github.com/zabir-nabil/bangla-tts


  We consider a single-interface model for the description of Barkhausen noise
in soft ferromagnetic materials. Previously, the model had been used only in
the adiabatic regime of infinitely slow field ramping. We introduce finite
driving rates and analyze the scaling of event sizes and durations for
different regimes of the driving rate. Coexistence of intermittency, with
non-trivial scaling laws, and finite-velocity interface motion is observed for
high enough driving rates. Power spectra show a decay $\sim \omega^{-t}$, with
$t<2$ for finite driving rates, revealing the influence of the internal
structure of avalanches.


  We study the Wold decomposition for representations of a self-similar
semigroup $P$ action on a directed graph $E$. We then apply this decomposition
to the case where $P=\mathbb{N}$ to study the C*-envelope of the associated
universal non-selfadjoint operator algebra $\mathcal{A}_{\mathbb{N}, E}$ by
carefully constructing explicit non-trivial dilations for non-boundary
representations. In particular, it is shown that the C*-envelope of
$\mathcal{A}_{\mathbb{N}, E}$ coincides with the self-similar C*-algebra
$\mathcal{O}_{\mathbb{Z}, E}$.


  One of the most dramatic discoveries made with the Rossi X-Ray Timing
Explorer is that many accreting neutron stars in low-mass binary systems
produce strong, remarkably coherent, high-frequency X-ray brightness
oscillations. The 325-1200 Hz quasi-periodic oscillations (QPOs) observed in
the accretion-powered emission are thought to be produced by gas orbiting very
close to the neutron star, whereas the 360-600 Hz brightness oscillations seen
during thermonuclear X-ray bursts are produced by one or two hot spots rotating
with the star and have frequencies equal to the stellar spin frequency or its
first overtone. The oscillations constrain the masses and radii of these
neutron stars, which are thought to be the progenitors of the millisecond
pulsars. Modeling indicates that the stars have spin frequencies 250-350 Hz and
magnetic fields 1e7-5e9 G.


  We define the periodic Full Kostant-Toda on every simple Lie algebra, and
show its Liouville integrability. More precisely we show that this lattice is
given by a Hamiltonian vector field, associated to a Poisson bracket which
results from an R-matrix. We construct a large family of constant of motion
which we use to prove the Liouville integrability of the system with the help
of several results on simple Lie algebras, R-matrix, invariant functions and
root systems.


  Close inspection of the pre-edge in oxygen near-edge x-ray absorption fine
structure spectra of single step, gas phase synthesized titanium oxynitride
photocatalysts with 20 nm particle size reveals an additional eg resonance in
the VB that went unnoticed in previous TiO2 anion doping studies. The relative
spectral weight of this Ti(3d)-O(2p) hybridized state with respect to and
located between the readily established t2g and eg resonances scales
qualitatively with the photocatalytic decomposition power, suggesting that this
extra resonance bears co-responsibility for the photocatalytic performance of
titanium oxynitrides at visible light wavelengths.


  The emerging Web of Data utilizes the web infrastructure to represent and
interrelate data. The foundational standards of the Web of Data include the
Uniform Resource Identifier (URI) and the Resource Description Framework (RDF).
URIs are used to identify resources and RDF is used to relate resources. While
RDF has been posited as a logic language designed specifically for knowledge
representation and reasoning, it is more generally useful if it can
conveniently support other models of computing. In order to realize the Web of
Data as a general-purpose medium for storing and processing the world's data,
it is necessary to separate RDF from its logic language legacy and frame it
simply as a data model. Moreover, there is significant advantage in seeing the
Semantic Web as a particular interpretation of the Web of Data that is focused
specifically on knowledge representation and reasoning. By doing so, other
interpretations of the Web of Data are exposed that realize RDF in different
capacities and in support of different computing models.


  The paper is devoted to an analytical study of the "master-worker" framework
scalability on multiprocessors with distributed memory. A new model of parallel
computations called BSF is proposed. The BSF model is based on BSP and SPMD
models. The scope of BSF model is the compute-intensive applications. The
architecture of BSF-computer is defined. The structure of BSF-program is
described. The Using this metric, the upper scalability bounds of BSF programs
on distributed memory multiprocessors are evaluated. The formulas for
estimating the parallel efficiency of BSF programs also proposed.


  Gauss's law in integral form states that closed surface integral of electric
field is proportional to net charge present within the volume bounded by this
closed surface. Gauss's law in differential form states that divergence of
electric field is proportional to charge's volume density. From Gauss's law it
is concluded that in vacuum, where no electric charges are present, divergence
of electric field and closed surface integral of electric field are zero. In
this paper we make an attempt to theoretically prove that for time-varying
electric fields Gauss's law is not valid. In other words, for time-varying
electric field even in vacuum divergence of electric field and closed surface
integral of electric field are non-zero. We do this by considering simple
sinusoidal motion of the charge and then by calculating closed surface integral
at specific time of time-varying electric field due to charge motion. Results
show that for charges at still and at motion with constant velocity Gauss's law
is valid. However for charges moving with acceleration, Gauss's law is no
longer valid.


  We study Ramsey expansions of certain homogeneous 3-hypertournaments. We show
that they exhibit an interesting behaviour and, in one case, they seem not to
submit to current gold-standard methods for obtaining Ramsey expansions. This
makes these examples very interesting from the point of view of structural
Ramsey theory as there is a large demand for novel examples.


  We consider a closed Friedmann-Robertson-Walker Universe driven by the back
reaction from a massless, non-conformally coupled quantum scalar field. We show
that the back-reaction of the quantum field is able to drive the cosmological
scale factor over the barrier of the classical potential so that if the
universe starts near zero scale factor (initial singularity) it can make the
transition to an exponentially expanding de Sitter phase, with a probability
comparable to that from quantum tunneling processes. The emphasis throughout is
on the stochastic nature of back reaction, which comes from the quantum
fluctuations of the fundamental fields.


  Education is a right of all, however, every individual is different than
others. Teachers in post-communism era discover inherent individualism to
equally train all towards job market of fourth industrial revolution. We can
consider scenario of ethnic minority education in academic practices. Ethnic
minority group has grown in their own culture and would prefer to be taught in
their native way. We have formulated such linguistic anthropology(how people
learn)based engagement as semi-supervised problem. Then, we have developed an
conditional deep generative adversarial network algorithm namely LA-GAN to
classify linguistic ethnographic features in student engagement. Theoretical
justification proves the objective, regularization and loss function of our
semi-supervised adversarial model. Survey questions are prepared to reach some
form of assumptions about z-generation and ethnic minority group, whose
learning style, learning approach and preference are our main area of interest.


  In this paper we study viscosity solutions of semilinear parabolic equations
in the Heisenberg group. We show uniqueness of viscosity solutions with
exponential growth at space infinity. We also study Lipschitz and horizontal
convexity preserving properties under appropriate assumptions. Counterexamples
show that in general such properties that are well-known for semilinear and
fully nonlinear parabolic equations in the Euclidean spaces do not hold in the
Heisenberg group.


  We investigate the orderability properties of fundamental groups of
3-dimensional manifolds. Many 3-manifold groups support left-invariant
orderings, including all compact P^2-irreducible manifolds with positive first
Betti number. For seven of the eight geometries (excluding hyperbolic) we are
able to characterize which manifolds' groups support a left-invariant or
bi-invariant ordering. We also show that manifolds modelled on these geometries
have virtually bi-orderable groups. The question of virtual orderability of
3-manifold groups in general, and even hyperbolic manifolds, remains open, and
is closely related to conjectures of Waldhausen and others.


  Detecting scene types in a movie can be very useful for application such as
video editing, ratings assignment, and personalization. We propose a system for
detecting kissing scenes in a movie. This system consists of two components.
The first component is a binary classifier that predicts a binary label (i.e.
kissing or not) given a features exctracted from both the still frames and
audio waves of a one-second segment. The second component aggregates the binary
labels for contiguous non-overlapping segments into a set of kissing scenes. We
experimented with a variety of 2D and 3D convolutional architectures such as
ResNet, DesnseNet, and VGGish and developed a highly accurate kissing detector
that achieves a validation F1 score of 0.95 on a diverse database of Hollywood
films ranging many genres and spanning multiple decades. The code for this
project is available at http://github.com/amirziai/kissing-detector.


  Yurinskii's coupling is a popular theoretical tool for non-asymptotic
distributional analysis in mathematical statistics and applied probability,
offering a Gaussian strong approximation with an explicit error bound under
easily verified conditions. Originally stated in $\ell^2$-norm for sums of
independent random vectors, it has recently been extended both to the
$\ell^p$-norm, for $1 \leq p \leq \infty$, and to vector-valued martingales in
$\ell^2$-norm, under some strong conditions. We present as our main result a
Yurinskii coupling for approximate martingales in $\ell^p$-norm, under
substantially weaker conditions than those previously imposed. Our formulation
further allows for the coupling variable to follow a more general Gaussian
mixture distribution, and we provide a novel third-order coupling method which
gives tighter approximations in certain settings. We specialize our main result
to mixingales, martingales, and independent data, and derive uniform Gaussian
mixture strong approximations for martingale empirical processes. Applications
to nonparametric partitioning-based and local polynomial regression procedures
are provided.


  Spectral flow in two-dimensional field theories is known to correspond to
geometrical twisting between two circles in the gravity dual. We generalize
this operation to the geometries which have SO(k+1) x SO(k+1) isometries with
k>1 and perform various non-abelian T-dualities of the resulting twisted
backgrounds. Combination of non-abelian twists and dualities leads to a new
solution generating technique in supergravity, and we apply it to the
geometries dual to supersymmetric states in N=4 super-Yang-Mills theory.


  We study time-dependent perturbations to a family of five-dimensional black
hole spacetimes constructed as a holographic model of the QCD phase diagram. We
use the results to calculate two transport coefficients, the bulk viscosity and
conductivity, as well as the associated baryon diffusion constant, throughout
the phase diagram. Near the critical point in the T-mu plane, the transport
coefficients remain finite, although their derivatives diverge, and the
diffusion goes to zero. This provides further evidence that large-N_c gauge
theories suppress convective transport. We also find a divergence in the
low-temperature bulk viscosity, outside the region expected to match QCD, and
compare the results to the transport behavior of known R-charged black holes.


  A special conformal transformation which carries a vacuum gravitational wave
into another vacuum one is built by using M\"obius-redefined time. It can
either transform a globally defined vacuum wave into a vacuum sandwich wave, or
carry the gravitational wave into itself. The first type, illustrated by
linearly and circularly polarized vacuum plane gravitational waves, permutes
the symmetries and the geodesics. Our pp waves with conformal O(2,1) symmetry
of the second type, which seem to ahve escaped attention so far, are
anisotropic generalizations of the familiar inverse-square profile. An example
inspired by molecular physics, for which the particle can escape, or perform
periodic motion, or fall into the singularity is studied in detail.


  TeV-range cosmic ray electrons and positrons (CREs) have been directly
measured in the search for new physics or unknown astrophysical sources. CREs
can inverse-Compton scatter solar photons and boost their energies into gamma
ray bands. Any potential CRE excess would enhance the resultant inverse Compton
emission spectrum in the relevant energy range, offering a new window to verify
the measured CRE spectrum. In this paper, we show that an excess in the TeV
range of the CRE spectrum, such as the one indicated by the DAMPE experiment,
can induce a characteristic solar gamma ray signal. Accounting for
contamination from extragalactic gamma ray backgrounds (EGB), we forecast the
DAMPE feature is testable ($\gtrsim 4 \sigma$) with a $\sim
10^{5}\,\mathrm{m}^2\,{\rm yr}$ exposure in the off-disk direction. This can be
achieved by long-exposure observations of water Cherenkov telescopes, such as
LHAASO (7.2 years) and HAWC (25.9 years).


  Few-shot learning (FSL) is an emergent paradigm of learning that attempts to
learn to reason with low sample complexity to mimic the way humans learn,
generalise and extrapolate from only a few seen examples. While FSL attempts to
mimic these human characteristics, fundamentally, the task of FSL as
conventionally formulated using meta-learning with episodic-based training does
not in actuality align with how humans acquire and reason with knowledge. FSL
with episodic training, while only requires $K$ instances of each test class,
still requires a large number of labelled training instances from disjoint
classes. In this paper, we introduce the novel task of constrained few-shot
learning (CFSL), a special case of FSL where $M$, the number of instances of
each training class is constrained such that $M \leq K$ thus applying a similar
restriction during FSL training and test. We propose a method for CFSL
leveraging Cat2Vec using a novel categorical contrastive loss inspired by
cognitive theories such as fuzzy trace theory and prototype theory.


  We investigate analytical properties of free stable distributions and
discover many connections with their classical counterparts. Our main result is
an explicit formula for the Mellin transform, which leads to explicit series
representations for the characteristic function and for the density of a free
stable distribution. All of these formulas bear close resemblance to the
corresponding expressions for classical stable distributions. As further
applications of our results, we give an alternative proof of the duality law
due to Biane and a new factorization of a classical stable random variable into
an independent (in the classical sense) product of a free stable random
variable and a power of a Gamma(2) random variable.


  One of the most crucial aspects of communication in daily life is speech
recognition. Speech recognition that is based on natural language processing is
one of the essential elements in the conversion of one system to another. In
this paper, we created an interface that transforms speech and other auditory
inputs into text using a digital filter. Contrary to the many methods for this
conversion, it is also possible for linguistic faults to appear occasionally,
gender recognition, speech recognition that is unsuccessful (cannot recognize
voice), and gender recognition to fail. Since technical problems are involved,
we developed a program that acts as a mediator to prevent initiating software
issues in order to eliminate even this little deviation. Its planned MFCC and
HMM are in sync with its AI system. As a result, technical errors have been
avoided.


  Abrupt changes in behavior can often be associated with changes in underlying
behavioral states. When placed off food, the foraging behavior of C. elegans
can be described as a change between an initial local-search behavior
characterized by a high rate of reorientations, followed by a global-search
behavior characterized by sparse reorientations. This is commonly observed in
individual worms, but when numerous worms are characterized, only about half
appear to exhibit this behavior. We propose an alternative model that predicts
both abrupt and continuous changes to reorientation that does not rely on
behavioral states. This model is inspired by molecular dynamics modeling that
defines the foraging reorientation rate as a decaying parameter. By
stochastically sampling from the probability distribution defined by this rate,
both abrupt and gradual changes to reorientation rates can occur, matching
experimentally observed results. Crucially, this model does not depend on
behavioral states or information accumulation. Even though abrupt behavioral
changes do occur, they may not necessarily be indicative of abrupt changes in
behavioral states, especially when abrupt changes are not universally observed
in the population.


  The Kepler and TESS missions delivered high-precision, long-duration
photometric time series for hundreds of main-sequence stars with
gravito-inertial (g) pulsation modes. This high precision allows us to evaluate
increasingly detailed theoretical stellar models. Recent theoretical work
extended the traditional approximation of rotation (TAR), a framework to
evaluate the effect of the Coriolis acceleration on g-modes, to include the
effects of the centrifugal acceleration in the approximation of slightly
deformed stars, which so far had mostly been neglected in asteroseismology.
This extension of the TAR was conceived by rederiving the TAR in a
centrifugally deformed, spheroidal coordinate system. We explore the effect of
the centrifugal acceleration on g modes and assess its detectability in
space-based photometry. We implement the new framework to calculate the
centrifugal deformation of precomputed 1D spherical stellar structure models
and compute the corresponding g-mode frequencies, assuming uniform rotation.
The framework is evaluated for a grid of stellar structure models covering a
relevant parameter space for observed g-mode pulsators. The centrifugal
acceleration modifies the effect of the Coriolis acceleration on g modes,
narrowing the equatorial band in which they are trapped. Furthermore, the
centrifugal acceleration causes the pulsation periods and period spacings of
the most common g modes (prograde dipole modes and r modes) to increase with
values similar to the observational uncertainties in Kepler and TESS data. The
effect of the centrifugal acceleration on g~modes is formally detectable in
modern space photometry. Implementation of the new theoretical framework in
stellar structure and pulsation codes will allow for more precise asteroseismic
modelling of centrifugally deformed stars, to assess its effect on mode
excitation, -trapping and -damping.


  In this paper we study the Hilbert scheme of smooth, linearly normal, special
scrolls under suitable assumptions on degree, genus and speciality.


  Many astrophysical bodies harbor magnetic fields that are thought to be
sustained by a dynamo process. However, it has been argued that the production
of large-scale magnetic fields by mean-field dynamo action is strongly
suppressed at large magnetic Reynolds numbers owing to the conservation of
magnetic helicity. This phenomenon is known as {\it catastrophic quenching}.
Advection of magnetic fields by stellar and galactic winds toward the outer
boundaries and away from the dynamo is expected to alleviate such quenching.
Here we explore the relative roles played by advective and turbulent--diffusive
fluxes of magnetic helicity in the dynamo. In particular, we study how the
dynamo is affected by advection. We do this by performing direct numerical
simulations of a turbulent dynamo of $\alpha^2$ type driven by forced
turbulence in a Cartesian domain in the presence of a flow away from the
equator where helicity changes sign. Our results indicate that in the presence
of advection, the dynamo, otherwise stationary, becomes oscillatory. We confirm
an earlier result for turbulent--diffusive magnetic helicity fluxes that for
small magnetic Reynolds numbers ($\Rm\lesssim 100...200$, based on the
wavenumber of the energy-carrying eddies) the magnetic helicity flux scales
less strongly with magnetic Reynolds number ($\Rm^{-1/2}$) than the term
describing magnetic helicity destruction by resistivity ($\Rm^{-1}$). Our new
results now suggest that for larger $\Rm$ the former becomes approximately
independent of $\Rm$, while the latter falls off more slowly. We show for the
first time that both for weak and stronger winds, the magnetic helicity flux
term becomes comparable to the resistive term for $\Rm\gtrsim 1000$, which is
necessary for alleviating catastrophic quenching.


  The topological complexity of a path-connected space $X,$ denoted $TC(X),$
can be thought of as the minimum number of continuous rules needed to describe
how to move from one point in $X$ to another. The space $X$ is often
interpreted as a configuration space in some real-life context. Here, we
consider the case where $X$ is the space of configurations of $n$ points on a
tree $\Gamma.$ We will be interested in two such configuration spaces. In the,
first, denoted $C^n(\Gamma),$ the points are distinguishable, while in the
second, $UC^n(\Gamma),$ the points are indistinguishable. We determine
$TC(UC^n(\Gamma))$ for any tree $\Gamma$ and many values of $n,$ and
consequently determine $TC(C^n(\Gamma))$ for the same values of $n$ (provided
the configuration spaces are path-connected).


  We investigate the formation of substructure in spiral galaxies using global
MHD simulations, including gas self-gravity. Our models extend previous local
models by Kim and Ostriker (2002) by including the full effects of curvilinear
coordinates, a realistic log-spiral perturbation, self-gravitational
contribution from 5 radial wavelengths of the spiral shock, and variation of
density and epicyclic frequency with radius. We show that with realistic Toomre
Q values, self-gravity and galactic differential rotation produce filamentary
gaseous structures with kpc-scale separations, regardless of the strength -- or
even presence -- of a stellar spiral potential. However, the growth of sheared
features distinctly associated with the spiral arms, described as spurs or
feathers in optical and IR observations of many spiral galaxies, requires a
sufficiently strong spiral potential in self gravitating models. Unlike
independently-growing ''background'' filaments, the orientation of arm spurs
depends on galactic location. Inside corotation, spurs emanate outward, on the
convex side of the arm; outside corotation, spurs grow inward, on the concave
side of the arm. Based on spacing, orientation, and the relation to arm clumps,
it is possible to distinguish ''true spurs'' that originate as instabilities in
the spiral arms from independently growing ''background'' filaments. Our models
also suggest that magnetic fields are important in preserving grand design
spiral structure when gas in the arms fragments via self-gravity into GMCs.


  Bayesian optimization (BO) is a typical approach to solve expensive
optimization problems. In each iteration of BO, a Gaussian process(GP) model is
trained using the previously evaluated solutions; then next candidate solutions
for expensive evaluation are recommended by maximizing a cheaply-evaluated
acquisition function on the trained surrogate model. The acquisition function
plays a crucial role in the optimization process. However, each acquisition
function has its own strengths and weaknesses, and no single acquisition
function can consistently outperform the others on all kinds of problems. To
better leverage the advantages of different acquisition functions, we propose a
new method for batch BO. In each iteration, three acquisition functions are
dynamically selected from a set based on their current and historical
performance to form a multi-objective optimization problem (MOP). Using an
evolutionary multi-objective algorithm to optimize such a MOP, a set of
non-dominated solutions can be obtained. To select batch candidate solutions,
we rank these non-dominated solutions into several layers according to their
relative performance on the three acquisition functions. The empirical results
show that the proposed method is competitive with the state-of-the-art methods
on different problems.


  We study a general model describing a self-detecting single electron
transistor realized by a suspended carbon nanotube actuated by a nearby
antenna. The main features of the device, recently observed in a number of
experiments, are accurately reproduced. When the device is in a low
current-carrying state, a peak in the current signals a mechanical resonance.
On the contrary, a dip in the current is found in high current-carrying states.
In the nonlinear vibration regime of the resonator, we are able to reproduce
quantitatively the characteristic asymmetric shape of the current-frequency
curves. We show that the nonlinear effects coming out at high values of the
antenna amplitude are related to the effective nonlinear force induced by the
electronic flow. The interplay between electronic and mechanical degrees of
freedom is understood in terms of an unifying model including in an intrinsic
way the nonlinear effects driven by the external probe.


  Despite the steady progress in video analysis led by the adoption of
convolutional neural networks (CNNs), the relative improvement has been less
drastic as that in 2D static image classification. Three main challenges exist
including spatial (image) feature representation, temporal information
representation, and model/computation complexity. It was recently shown by
Carreira and Zisserman that 3D CNNs, inflated from 2D networks and pretrained
on ImageNet, could be a promising way for spatial and temporal representation
learning. However, as for model/computation complexity, 3D CNNs are much more
expensive than 2D CNNs and prone to overfit. We seek a balance between speed
and accuracy by building an effective and efficient video classification system
through systematic exploration of critical network design choices. In
particular, we show that it is possible to replace many of the 3D convolutions
by low-cost 2D convolutions. Rather surprisingly, best result (in both speed
and accuracy) is achieved when replacing the 3D convolutions at the bottom of
the network, suggesting that temporal representation learning on high-level
semantic features is more useful. Our conclusion generalizes to datasets with
very different properties. When combined with several other cost-effective
designs including separable spatial/temporal convolution and feature gating,
our system results in an effective video classification system that that
produces very competitive results on several action classification benchmarks
(Kinetics, Something-something, UCF101 and HMDB), as well as two action
detection (localization) benchmarks (JHMDB and UCF101-24).


  This paper deals with existence of a nontrivial positive solution to systems
of equations involving nontrivial nonhomogeneous terms and critical or
subcritical nonlinearities. Via a minimization argument we prove existence of a
positive solution whose energy is negative provided that the nonhomogeneous
terms are small enough in the dual norm.


  We study the double-exchange model at half-filling with competing
superexchange interactions on a triangular lattice, combining exact
diagonalization and Monte-Carlo methods. We find that in between the expected
itinerant ferromagnetic and $120^{\circ}$ Yafet-Kittel phases a robust
scalar-chiral, insulating spin state emerges. At finite temperatures the
ferromagnet - scalar-chiral quantum critical point is characterized by
anomalous bad-metal behavior in charge transport as observed in frustrated
itinerant magnets R$_2$Mo$_{2}$O$_7$.


  Conformational transitions of a single macromolecule of finite size $N$
cannot be described within standard thermodynamic framework. Taking as a basis
a simple model of homopolymer exhibiting a coil-globule transition, we show
that a relevant approach is to describe the thermal equilibrium distribution
$P_N^{(\beta)}(t)$ of some variable $t$ characterizing the conformation.
Although the mean order parameter exhibits a second-order behaviour in the
infinite-size limit, the $\Theta$-point arises from the coexistence of two
distinct populations, associated with two well-separated peaks of
$P_N^{(\beta)}(t)$ and identified respectively with a coil state and a globule
state. Remarkably, this first-order feature increases with the size of the
chain. It allows to describe the transition within a two-state model,
well-suited to analyse experimental data.


  Young neutron stars (NSs) born in core-collapse explosions are promising
candidates for the central engines of fast radio bursts (FRBs), since the first
localized repeating burst FRB 121102 happens in a star forming dwarf galaxy,
which is similar to the host galaxies of superluminous supernovae (SLSNe) and
long gamma-ray bursts (LGRBs). However, FRB 180924 and FRB 190523 are localized
to massive galaxies with low rates of star formation, compared with the host of
FRB 121102. Meanwhile, the offsets between the bursts and host centers are
about 4 kpc and 29 kpc for FRB 180924 and FRB 190523, respectively. These
properties of hosts are similar to short gamma-ray bursts \textbf{(SGRBs)},
which are produced by mergers of binary neutron star (BNS) or neutron
star-black hole (NS-BH). Therefore, the NSs powering FRBs may be formed in BNS
mergers. In this paper, we study the BNS merger rates, merger times, and
predict their most likely merger locations for different types of host galaxies
using population synthesis method. We find that the BNS merger channel is
consistent with the recently reported offsets of FRB 180924 and FRB 190523. The
offset distribution of short GRBs is well reproduced by population synthesis
using galaxy model which is similar to GRB hosts. The event rate of FRBs
(including non-repeating and repeating), is larger than those of BNS merger and
short GRBs, which requires a large fraction of observed FRBs emitting several
bursts. Using curvature radiation by bunches in NS magnetospheres, we also
predict the observational properties of FRBs from BNS mergers, including the
dispersion measure, and rotation measure. At late times ($t\geq1$yr), the
contribution to dispersion measure and rotation measure from BNS merger ejecta
could be neglected.


  We observed a new mechanism for vortex nucleation in Bose-Einstein
condensates (BECs) subject to synthetic magnetic fields. We made use of a
strong synthetic magnetic field initially localized between a pair of merging
BECs to rapidly create vortices in the bulk of the merged condensate. Unlike
previous implementations and in agreement with our Gross-Pitaevskii equation
simulations, our dynamical process rapidly injects vortices into our system's
bulk, and with initial number in excess of the system's equilibrium vortex
number.


  These lectures form a personal, and not necessarily comprehensive, survey of
physics at the Fermilab Tevatron proton-antiproton collider. They cover
detectors, analysis issues, and physics prospects for the current Tevatron run.
(Version 2 has typographic corrections).


  A connected graph is called a multi-block graph if each of its blocks is a
complete multi-partite graph. Building on the work of \cite{Bp3,Hou3}, we
compute the determinant and inverse of the distance matrix for a class of
multi-block graphs.


  Components in many real-world complex systems depend on each other for the
resources required for survival, and may die of a shortage. These patterns of
dependencies often take the form of a complex network whose structure
potentially affects how the resources produced in the system are efficiently
shared among its components, which in turn decides a network's survivability.
Here we present a simple threshold model that provides insight into this
relationship between the network structure and survivability. We show that, as
a combined effect of local sharing and finite lifetime of resources, many
components in a complex system may die of lack of resources even when
sufficient amount is available in the system. We also obtain a surprising
result that although the scale-free networks exhibit a significantly higher
survivability compared to their homogeneous counterparts, a vertex in the later
survives longer on average. Finally, we demonstrate that the system's
survivability can be substantially improved by changing the way vertices
distribute resources among the neighbours. Our work is a step towards
understanding the relationship between intricate resource dependencies present
in many real-world complex systems and their survivability.


  Left-Right symmetric theories solve the strong CP problem and explain the
small Higgs quartic coupling at high energy scales via the Higgs Parity
mechanism, which forces the Higgs quartic coupling to vanish at the Left-Right
symmetry breaking scale. They also predict three right-handed neutrinos; one
may be stable and provide dark matter, and another may decay and explain the
baryon asymmetry of the universe through leptogenesis. For the dark matter
abundance to arise from freeze-out, the required range of the Left-Right
symmetry breaking scale is $10^{10}$-$10^{13}$ GeV, in remarkable agreement
with the energy scale at which the Higgs quartic coupling vanishes. The allowed
parameter space can be probed by the warmness of dark matter, precise
measurements of the top quark mass and QCD coupling constant by future
colliders and lattice computations, and measurement of the neutrino mass
hierarchy.


  We consider the dynamics of $n$ points on a sphere in $\mathbb{R}^d$ ($d \geq
2$) which attract each other according to a function $\varphi$ of their inner
products. When $\varphi$ is linear ($\varphi(t) = t$), the points converge to a
common value (i.e., synchronize) in various connectivity scenarios: this is
part of classical work on Kuramoto oscillator networks. When $\varphi$ is
exponential ($\varphi(t) = e^{\beta t}$), these dynamics correspond to a limit
of how idealized transformers process data, as described by Geshkovski et al.
(2024). Accordingly, they ask whether synchronization occurs for exponential
$\varphi$.
  In the context of consensus for multi-agent control, Markdahl et al. (2018)
show that for $d \geq 3$ (spheres), if the interaction graph is connected and
$\varphi$ is increasing and convex, then the system synchronizes. What is the
situation on circles ($d=2$)? First, we show that $\varphi$ being increasing
and convex is no longer sufficient. Then we identify a new condition (that the
Taylor coefficients of $\varphi'$ are decreasing) under which we do have
synchronization on the circle. In so doing, we provide some answers to the open
problems posed by Geshkovski et al. (2024).


  The general-purpose Compact Muon Solenoid (CMS) detector at the Large Hadron
Collider (LHC) at CERN includes the hadronic calorimeter to register the
energies of the charged and neutral hadrons produced in the proton-proton
collisions at the LHC at a centre of mass energy 13.6 TeV. The calorimeter is
located inside the superconducting solenoid of 6 m in diameter and 12.5 m in
length creating the central magnetic flux density of 3.8 T. For operating
optimally in the high pileup and high radiation environment of the High
Luminosity LHC, the existing CMS endcap calorimeters will be replaced with a
new high granularity calorimeter (HGCal) comprising of an electromagnetic and a
hadronic section in each of the two endcaps. The hadronic section of the HGCAL
will include 44 stainless steel absorber plates with a relative permeability
value well below 1.05. The volume occupied by 22 plates in each endcap is about
21 m$^{3}$. The calculation of the axial electromagnetic forces on the absorber
plates is a crucial element in designing the mechanical construction of the
device. With a three-dimensional computer model of the CMS magnet, the axial
forces on each absorber plate are calculated and the dependence of forces on
the central magnetic flux density value is presented. The method of calculation
and the obtained results are discussed.


  Simultaneous localization and mapping (SLAM) is a critical capability in
autonomous navigation, but in order to scale SLAM to the setting of "lifelong"
SLAM, particularly under memory or computation constraints, a robot must be
able to determine what information should be retained and what can safely be
forgotten. In graph-based SLAM, the number of edges (measurements) in a pose
graph determines both the memory requirements of storing a robot's observations
and the computational expense of algorithms deployed for performing state
estimation using those observations; both of which can grow unbounded during
long-term navigation. To address this, we propose a spectral approach for pose
graph sparsification which maximizes the algebraic connectivity of the
sparsified measurement graphs, a key quantity which has been shown to control
the estimation error of pose graph SLAM solutions. Our algorithm, MAC (for
"maximizing algebraic connectivity"), which is based on convex relaxation, is
simple and computationally inexpensive, and admits formal post hoc performance
guarantees on the quality of the solutions it provides. In experiments on
benchmark pose-graph SLAM datasets, we show that our approach quickly produces
high-quality sparsification results which retain the connectivity of the graph
and, in turn, the quality of corresponding SLAM solutions, as compared to a
baseline approach which does not consider graph connectivity.


  Recent work has explored the potential to adapt a pre-trained vision
transformer (ViT) by updating only a few parameters so as to improve storage
efficiency, called parameter-efficient transfer learning (PETL). Current PETL
methods have shown that by tuning only 0.5% of the parameters, ViT can be
adapted to downstream tasks with even better performance than full fine-tuning.
In this paper, we aim to further promote the efficiency of PETL to meet the
extreme storage constraint in real-world applications. To this end, we propose
a tensorization-decomposition framework to store the weight increments, in
which the weights of each ViT are tensorized into a single 3D tensor, and their
increments are then decomposed into lightweight factors. In the fine-tuning
process, only the factors need to be updated and stored, termed Factor-Tuning
(FacT). On VTAB-1K benchmark, our method performs on par with NOAH, the
state-of-the-art PETL method, while being 5x more parameter-efficient. We also
present a tiny version that only uses 8K (0.01% of ViT's parameters) trainable
parameters but outperforms full fine-tuning and many other PETL methods such as
VPT and BitFit. In few-shot settings, FacT also beats all PETL baselines using
the fewest parameters, demonstrating its strong capability in the low-data
regime.


  The renormalization of a scalar field theory with a quartic self-coupling (a
$\lambda \phi^4$ theory) via adiabatic regularization in a general
Robertson-Walker spacetime is discussed. The adiabatic counterterms are
presented in a way that is most conducive to numerical computations. A
variation of the adiabatic regularization method is presented which leads to
analytic approximations for the energy-momentum tensor of the field and the
quantum contribution to the effective mass of the mean field. Conservation of
the energy-momentum tensor for the field is discussed and it is shown that the
part of the energy-momentum tensor which depends only on the mean field is not
conserved but the full renormalized energy-momentum tensor is conserved as
expected and required by the semiclassical Einstein's equation. It is also
shown that if the analytic approximations are used then the resulting
approximate energy-momentum tensor is conserved. This allows a self-consistent
backreaction calculation to be performed using the analytic approximations. The
usefulness of the approximations is discussed.


  The purpose of this paper is to explore the possibility of a wave-packet
collapse induced by topological disconnectivity, based on the discussions of
the wave-corpuscle duality. Several experimental suggestions are proposed to
test this sort of wave-packet collapse based on quantum interference.


  We introduce here a method which uses etale neighborhoods to extend results
from smooth semi-local rings to arbitrary semi-local rings A by passing to the
henselization of a smooth presentation of A. The technique is used to show that
etale cohomology of A agrees with Galois cohomology, the Merkuriev-Suslin
theorem holds for A, and to describe torsion in K_2(A).


  Copula models are flexible tools to represent complex structures of
dependence for multivariate random variables. According to Sklar's theorem
(Sklar, 1959), any d-dimensional absolutely continuous density can be uniquely
represented as the product of the marginal distributions and a copula function
which captures the dependence structure among the vector components. In real
data applications, the interest of the analyses often lies on specific
functionals of the dependence, which quantify aspects of it in a few numerical
values. A broad literature exists on such functionals, however extensions to
include covariates are still limited. This is mainly due to the lack of
unbiased estimators of the copula function, especially when one does not have
enough information to select the copula model. Recent advances in computational
methodologies and algorithms have allowed inference in the presence of
complicated likelihood functions, especially in the Bayesian approach, whose
methods, despite being computationally intensive, allow us to better evaluate
the uncertainty of the estimates. In this work, we present several Bayesian
methods to approximate the posterior distribution of functionals of the
dependence, using nonparametric models which avoid the selection of the copula
function. These methods are compared in simulation studies and in two realistic
applications, from civil engineering and astrophysics.


  An unsupervised online streaming model is considered where samples arrive in
an online fashion over $T$ slots. There are $M$ classifiers, whose confusion
matrices are unknown a priori. In each slot, at most one sample can be labeled
by any classifier. The accuracy of a sample is a function of the set of labels
obtained for it from various classifiers. The utility of a sample is a scalar
multiple of its accuracy minus the response time (difference of the departure
slot and the arrival slot), where the departure slot is also decided by the
algorithm. Since each classifier can label at most one sample per slot, there
is a tradeoff between obtaining a larger set of labels for a particular sample
to improve its accuracy, and its response time. The problem of maximizing the
sum of the utilities of all samples is considered, where learning the confusion
matrices, sample-classifier matching assignment, and sample departure slot
decisions depend on each other. The proposed algorithm first learns the
confusion matrices, and then uses a greedy algorithm for sample-classifier
matching. A sample departs once its incremental utility turns non-positive. We
show that the competitive ratio of the proposed algorithm is
$\frac{1}{2}-{\mathcal O}\left(\frac{\log T}{T}\right)$.


  I analyse the extension of the Ryu Takayanagi formula from the perspective of
the universal coefficient theorem and cohomology with different coefficients.
Looking at the axioms of cohomology, the so called Eilenberg-Steenrod axioms,
the third axiom states that the cohomology of a point is trivial in all orders.
If this axiom is abandoned the point may have additional structure. This
phenomenon is not unusual in physics, a simple example for that being the spin
structure or even the point particle to string transition. I studied the
transition between different coefficients in cohomology and hence between
different structures of the geometrical point by means of the universal
coefficient theorem. The results may have impact on recent island calculations
of the black hole radiation entropy and the Page curve as well as on a
potential mapping of higher genus diagrams to genus one diagrams in the
topological expansion of string theory.


  By solving the Fokker-Planck equation directly we examine effects of
annihilation, particle escape and injection on the form of a steady-state
positron distribution in thermal hydrogen plasmas with $kT<m_ec^2$. We show
that the escape of positrons in the form of electron-positron pairs and/or pair
plasma has an effect on the positron distribution causing, in some cases, a
strong deviation from a Maxwellian. Additionally, we present accurate formulas
for energy exchange rates, and losses due to Coulomb scattering,
bremsstrahlung, and Compton scattering in the Klein-Nishina regime. Suggesting
that annihilation features observed by SIGMA telescope from Nova Muscae and the
1E 1740.7-2942 are due to the positron/electron slowing down and annihilation
in thermal plasma, the electron number density and the size of the emitting
regions have been estimated. We show that in the case of Nova Muscae the
observed radiation is coming from a pair plasma stream ($n_{e^+}\approx
n_{e^-}$) rather than from a gas cloud. We argue that two models are probably
relevant to the 1E 1740.7-2942 source: annihilation in (hydrogen) plasma
$n_{e^+}\la n_{e^-}$ at rest, and annihilation in the pair plasma stream, which
involves matter from the source environment.


  We investigate the effect of the global charge conservation on the cumulants
of conserved charges in relativistic heavy ion collisions in a finite rapidity
window by studying the time evolution of cumulants in the hadronic medium. It
is argued that the global charge conservation does not affect the experimental
result of the net-electric charge fluctuation observed by ALICE, because of the
finite diffusion distance of charged particles in the hadronic stage.


  Discretizations of differential equations are often studied through their
modified equation. This is a differential equation, usually obtained as a power
series, with solutions that exactly interpolate the discretization. By
comparing the St\"ormer-Verlet discretization of the harmonic oscillator with
its modified equation, we obtain a relatively simple derivation of the
expansion \[ \left( \arcsin \frac{h}{2} \right)^2 = \frac{1}{2}
\sum_{k=1}^\infty \frac{(k-1)!^2}{(2k)!} h^{2k}, \] which can be used to show
that $\zeta(2) = \frac{\pi^2}{6}$.


  Van der Waals materials can be easily combined in lateral and vertical
heterostructures, providing an outstanding platform to engineer elusive quantum
states of matter. However, a critical problem in material science is to
establish tangible links between real materials properties and terms that can
be cooked up on the model Hamiltonian level to realize different exotic
phenomena. Our review aims to do precisely this: we first discuss, in a way
accessible to the materials community, what ingredients need to be included in
the hybrid quantum materials recipe, and second, we elaborate on the specific
materials that would possess the necessary qualities. We will review the
well-established procedures for realizing 2D topological superconductors,
quantum spin-liquids and flat bands systems, emphasizing the connection between
well-known model Hamiltonians and real compounds. We will use the most recent
experimental results to illustrate the power of the designer approach.


  Above lunar crustal magnetic anomalies, large fractions of solar wind
electrons and ions can be scattered and stream back towards the solar wind
flow, leading to a number of interesting effects such as electrostatic
instabilities and waves. These electrostatic structures can also interact with
the background plasma, resulting in electron heating and scattering. We study
the electrostatic waves and electron heating observed over the lunar magnetic
anomalies by analyzing data from the Acceleration, Reconnection, Turbulence,
and Electrodynamics of Moon's Interaction with the Sun (ARTEMIS) spacecraft.
Based on the analysis of two lunar flybys in 2011 and 2013, we find that the
electron two-stream instability (ETSI) and electron cyclotron drift instability
(ECDI) may play an important role in driving the electrostatic waves. We also
find that ECDI, along with the modified two-stream instability (MTSI), may
provide the mechanisms responsible for substantial isotropic electron heating
over the lunar magnetic anomalies.


  We analyze the pump wavelength dependence for the photo-induced enhancement
of interlayer coupling in La1.885Ba0.115CuO4, which is promoted by optical
melting of the stripe order. In the equilibrium superconducting state (T < Tc =
13 K), in which stripes and superconductivity coexist, time-domain THz
spectroscopy reveals a photo-induced blue-shift of the Josephson Plasma
Resonance after excitation with optical pulses polarized perpendicular to the
CuO2 planes. In the striped, non-superconducting state (Tc < T < T_SO = 40 K) a
transient plasma resonance similar to that seen below Tc appears from a
featureless equilibrium reflectivity. Most strikingly, both these effects
become stronger upon tuning of the pump wavelength from the mid-infrared to the
visible, underscoring an unconventional competition between stripe order and
superconductivity, which occurs on energy scales far above the ordering
temperature.


  We analyze the structure and evolution of ribbons from the M7.3
SOL2014-04-18T13 flare using ultraviolet (UV) images from IRIS and SDO/AIA,
magnetic data from SDO/HMI, hard X-ray (HXR) images from RHESSI, and light
curves from Fermi/GBM, in order to infer properties of coronal magnetic
reconnection. As the event progresses, two flare ribbons spread away from the
magnetic polarity inversion line. The width of the newly brightened front along
the extension of the ribbon is highly intermittent in both space and time,
presumably reflecting non-uniformities in the structure and/or dynamics of the
flare current sheet. Furthermore, the ribbon width grows most rapidly in
regions exhibiting concentrated non-thermal HXR emission, with sharp increases
slightly preceding the HXR bursts. The light curve of the ultraviolet emission
matches the HXR light curve at photon energies above 25 keV. In other regions
the ribbon-width evolution and light curves do not temporally correlate with
the HXR emission. This indicates that the production of non-thermal electrons
is highly non-uniform within the flare current sheet. Our results suggest a
strong connection between the production of non-thermal electrons and the
locally enhanced perpendicular extent of flare ribbon fronts, which in turn
reflects inhomogeneous structure and/or reconnection dynamics of the current
sheet. Despite this variability, the ribbon fronts remain nearly continuous,
quasi-one-dimensional features. Thus, although the reconnecting coronal current
sheets are highly structured, they remain quasi-two-dimensional and the
magnetic energy release occurs systematically, rather than stochastically,
through the volume of reconnecting magnetic flux.


  In this paper, we use the technique of Finslerian submersion to deduce a flag
curvature formula for homogeneous Finsler spaces. Based on this formula, we
give a complete classification of even-dimensional smooth coset spaces $G/H$
admitting $G$-invariant Finsler metrics with positive flag curvature. It turns
out that the classification list coincides with that of the even dimensional
homogeneous Riemannian manifolds with positive sectional curvature obtained by
N.R. Wallach. We also find out all the coset spaces admitting invariant
non-Riemannian Finsler metrics with positive flag curvature.


  This paper provides a quantitative version of the recent result of Kn\"upfer
and Muratov ({\it Commun. Pure Appl. Math.} {\bf 66} (2013), 1129--1162)
concerning the solutions of an extension of the classical isoperimetric problem
in which a non-local repulsive term involving Riesz potential is present. There
it was shown that in two space dimensions the minimizer of the considered
problem is either a ball or does not exist, depending on whether or not the
volume constraint lies in an explicit interval around zero, provided that the
Riesz kernel decays sufficiently slowly. Here we give an explicit estimate for
the exponents of the Riesz kernel for which the result holds.


  A measurement of $C\!P$-violating observables in $B^{\pm} \to D^{*} K^{\pm}$
and $B^{\pm} \to D^{*} \pi^{\pm}$ decays is made where the photon or neutral
pion from the $D^{*} \to D\gamma$ or $D^{*} \to D\pi^{0}$ decay is not
reconstructed. The $D$ meson is reconstructed in the self-conjugate decay
modes, $D \to K_{S}^{0} \pi^{+} \pi^{-}$ or $D \to K_{S}^{0} K^{+} K^{-}$. The
distribution of signal yields in the $D$ decay phase space is analysed in a
model-independent way. The measurement uses a data sample collected in
proton-proton collisions at centre-of-mass energies of 7, 8, and 13 TeV,
corresponding to a total integrated luminosity of approximately 9 fb$^{-1}$.
The $B^{\pm} \to D^{*} K^{\pm}$ and $B^{\pm} \to D^{*} \pi^{\pm}$
$C\!P$-violating observables are interpreted in terms of hadronic parameters
and the CKM angle $\gamma$, resulting in a measurement of $\gamma =
(92^{+21}_{-17})^{\circ}$. The total uncertainty includes the statistical and
systematic uncertainties, and the uncertainty due to external strong-phase
inputs.


  We present the first hydrodynamical simulations of structure formation using
the new moving mesh code AREPO and compare the results with GADGET simulations
based on a traditional smoothed particle hydrodynamics (SPH) technique. The two
codes share the same Tree-PM gravity solver and include identical
sub-resolution physics, but employ different methods to solve the equations of
hydrodynamics. This allows us to assess the impact of hydro-solver
uncertainties on the results of cosmological studies of galaxy formation. We
focus on predictions for global baryon statistics, such as the cosmic star
formation rate density, after we introduce our simulation suite and numerical
methods. Properties of individual galaxies and haloes are examined by Keres et
al. (2011), while a third paper by Sijacki et al. (2011) uses idealised
simulations to analyse the differences between the hydrodynamical schemes. We
find that the global baryon statistics differ significantly between the two
simulation approaches. AREPO shows higher star formation rates at late times,
lower mean temperatures, and different gas mass fractions in characteristic
phases of the intergalactic medium, in particular a reduced amount of hot gas.
Although both codes use the same implementation of cooling, more gas cools out
of haloes in AREPO compared with GADGET towards low redshifts. We show that
this is caused by a higher heating rate with SPH in the outer parts of haloes,
owing to viscous dissipation of SPH's inherent sonic velocity noise and SPH's
efficient damping of subsonic turbulence injected in the halo infall region,
and because of a higher efficiency of gas stripping in AREPO. As a result of
such differences, AREPO leads also to more disk-like morphologies compared to
GADGET. Our results indicate that inaccuracies in hydrodynamic solvers can lead
to comparatively large systematic differences.