  This study proposes a deep learning methodology to predict the propagation of
traffic shockwaves. The input to the deep neural network is time-space diagram
of the study segment, and the output of the network is the predicted (future)
propagation of the shockwave on the study segment in the form of time-space
diagram. The main feature of the proposed methodology is the ability to extract
the features embedded in the time-space diagram to predict the propagation of
traffic shockwaves.


  The recent search for non $q \bar{q}$ mesons in $\pi^{-}p$ interactions at
Brookhaven National Laboratory is summarized. Many final states such as $\eta
\pi$, $\eta' \pi^{-}$, $a_{0} \pi$, $f_{1} \pi$, $a_{2} \pi$, $b_{1} \pi$,
which are favored decay modes of exotics, are under investigation.


  In this small note we strengthen the classic result about the regularity time
t* of arbitrary Leray solutions to the (incompressible) Navier-Stokes equations
in Rn (n = 3, 4), which have the form: t* <= K_{3} nu^{-5} || u(.,0)
||_{L2}^{4} if n = 3, and t* <= K_{4} nu^{-3} || u(.,0) ||_{L2}^{2} if n = 4
(in particular, by reducing the current best known values for the constants
K_{3}, K_{4}). Some related results of clear interest are also included
(derived) in our discussion.


  We have calculated the electrostatic interaction between two rod-like charged
objects with arbitrary orientations in three dimensions. we obtained a closed
form formula expressing the interaction energy in terms of the separation
distance between the centers of the two rod-like objects, $r$, their lengths
(denoted by $2l_1$ and $2l_2$), and their relative orientations (indicated by
$\theta$ and $\phi$). When the objects have the same length ($2l_1=2l_2=l$),
for particular values of separations, i.e for $r\leq0.8 l$, two types of
minimum are appeared in the interaction energy with respect to $\theta$. By
employing the closed form formula and introducing a scaled temperature $t$, we
have also studied the thermodynamic properties of a one dimensional system of
rod-like charged objects. For different separation distances, the dependence of
the specific heat of the system to the scaled temperature has been studied. It
is found that for $r<0.8 l$, the specific heat has a maximum.


  Signed directed social networks, in which the relationships between users can
be either positive (indicating relations such as trust) or negative (indicating
relations such as distrust), are increasingly common. Thus the interplay
between positive and negative relationships in such networks has become an
important research topic. Most recent investigations focus upon edge sign
inference using structural balance theory or social status theory. Neither of
these two theories, however, can explain an observed edge sign well when the
two nodes connected by this edge do not share a common neighbor (e.g., common
friend). In this paper we develop a novel approach to handle this situation by
applying a new model for node types. Initially, we analyze the local node
structure in a fully observed signed directed network, inferring underlying
node types. The sign of an edge between two nodes must be consistent with their
types; this explains edge signs well even when there are no common neighbors.
We show, moreover, that our approach can be extended to incorporate directed
triads, when they exist, just as in models based upon structural balance or
social status theory. We compute Bayesian node types within empirical studies
based upon partially observed Wikipedia, Slashdot, and Epinions networks in
which the largest network (Epinions) has 119K nodes and 841K edges. Our
approach yields better performance than state-of-the-art approaches for these
three signed directed networks.


  According to a recent no-go theorem (M. Pusey, J. Barrett and T. Rudolph,
Nature Physics 8, 475 (2012)), models in which quantum states correspond to
probability distributions over the values of some underlying physical variables
must have the following feature: the distributions corresponding to distinct
quantum states do not overlap. This is significant because if the distributions
do not overlap, then the quantum state itself is encoded by the physical
variables. In such a model, it cannot coherently be maintained that the quantum
state merely encodes information about underlying physical variables. The
theorem, however, considers only models in which the physical variables
corresponding to independently prepared systems are independent. This work
considers models that are defined for a single quantum system of dimension $d$,
such that the independence condition does not arise. We prove a result in a
similar spirit to the original no-go theorem, in the form of an upper bound on
the extent to which the probability distributions can overlap, consistently
with reproducing quantum predictions. In particular, models in which the
quantum overlap between pure states is equal to the classical overlap between
the corresponding probability distributions cannot reproduce the quantum
predictions in any dimension $d \geq 3$. The result is noise tolerant, and an
experiment is motivated to distinguish the class of models ruled out from
quantum theory.


  For the Hopfield model with the Hebb connection matrix we investigate the
case of $p$ memorized patterns that are distorted copies of the same {\it
standard}. In other words, we try to simulate that learning always takes place
by means of repeating presentations of one and the same standard, and the
presentations are accompanied by distortions of the standard. We obtain some
rigorous results relating to the dependence of the fixed points on external
parameters of the problem.


  We report on experimental measurements of energy transfer efficiencies in a
GeV-class laser wakefield accelerator. Both the transfer of energy from the
laser to the plasma wakefield, and from the plasma to the accelerated electron
beam were diagnosed by simultaneous measurement of the deceleration of laser
photons and the acceleration of electrons as a function of plasma length. The
extraction efficiency, which we define as the ratio of the energy gained by the
electron beam to the energy lost by the self-guided laser mode, was maximised
at $19\pm3$\% by tuning of the plasma density and length. The additional
information provided by the octave-spanning laser spectrum measurement allows
for independent optimisation of the plasma efficiency terms, which is required
for the key goal of improving the overall efficiency of laser wakefield
accelerators.


  Let $B\rightarrow A$ be a homomorphism of Hopf algebras and let $C$ be an
algebra. We consider the induction from $B$ to $A$ of $C$ in two cases: when
$C$ is a $B$-interior algebra and when $C$ is a $B$-module algebra. Our main
results establish the connection between the two inductions. The inspiration
comes from finite group representation theory, and some constructions work in
even more general contexts.


  Zero-shot learning (ZSL) recognizes the unseen classes by conducting
visual-semantic interactions to transfer semantic knowledge from seen classes
to unseen ones, supported by semantic information (e.g., attributes). However,
existing ZSL methods simply extract visual features using a pre-trained network
backbone (i.e., CNN or ViT), which fail to learn matched visual-semantic
correspondences for representing semantic-related visual features as lacking of
the guidance of semantic information, resulting in undesirable visual-semantic
interactions. To tackle this issue, we propose a progressive semantic-guided
vision transformer for zero-shot learning (dubbed ZSLViT). ZSLViT mainly
considers two properties in the whole network: i) discover the semantic-related
visual representations explicitly, and ii) discard the semantic-unrelated
visual information. Specifically, we first introduce semantic-embedded token
learning to improve the visual-semantic correspondences via semantic
enhancement and discover the semantic-related visual tokens explicitly with
semantic-guided token attention. Then, we fuse low semantic-visual
correspondence visual tokens to discard the semantic-unrelated visual
information for visual enhancement. These two operations are integrated into
various encoders to progressively learn semantic-related visual representations
for accurate visual-semantic interactions in ZSL. The extensive experiments
show that our ZSLViT achieves significant performance gains on three popular
benchmark datasets, i.e., CUB, SUN, and AWA2. Codes are available at:
https://github.com/shiming-chen/ZSLViT .


  The extensive surviving corpus of the ancient scholar Plutarch of Chaeronea
(ca. 45-120 CE) also contains several texts which, according to current
scholarly opinion, did not originate with him and are therefore attributed to
an anonymous author Pseudo-Plutarch. These include, in particular, the work
Placita Philosophorum (Quotations and Opinions of the Ancient Philosophers),
which is extremely important for the history of ancient philosophy. Little is
known about the identity of that anonymous author and its relation to other
authors from the same period. This paper presents a BERT language model for
Ancient Greek. The model discovers previously unknown statistical properties
relevant to these literary, philosophical, and historical problems and can shed
new light on this authorship question. In particular, the Placita
Philosophorum, together with one of the other Pseudo-Plutarch texts, shows
similarities with the texts written by authors from an Alexandrian context
(2nd/3rd century CE).


  This study examines the increasing complexity in the magnetic properties of
small $n$ = 3, 4, 5, 6 spin-1/2 quantum rings. Using an exact diagonalization
of the isotropic Heisenberg Hamiltonian with nearest and next-nearest neighbor
interactions, the energy eigenstates, magnetic specific heat capacity, magnetic
susceptibility, and inelastic neutron scattering structure factors are
determined for variable next-nearest neighbor interactions. Here, it is shown
that the presence of a complex spin-mixing, multiple ground states, and
non-zero ground states greatly complicate the spin Hamiltonian. Overall, the
energy eigenstates and structure factor intensities are presented in closed
form, while the thermodynamic properties detail the effect of a crossing
interaction in the rings. The goal of this work is to provide insight into the
evolution of the magnetic properties and spin excitations within these systems.


  Large-batch stochastic gradient descent (SGD) is widely used for training in
distributed deep learning because of its training-time efficiency, however,
extremely large-batch SGD leads to poor generalization and easily converges to
sharp minima, which prevents naive large-scale data-parallel SGD (DP-SGD) from
converging to good minima. To overcome this difficulty, we propose gradient
noise convolution (GNC), which effectively smooths sharper minima of the loss
function. For DP-SGD, GNC utilizes so-called gradient noise, which is induced
by stochastic gradient variation and convolved to the loss function as a
smoothing effect. GNC computation can be performed by simply computing the
stochastic gradient on each parallel worker and merging them, and is therefore
extremely easy to implement. Due to convolving with the gradient noise, which
tends to spread along a sharper direction of the loss function, GNC can
effectively smooth sharp minima and achieve better generalization, whereas
isotropic random noise cannot. We empirically show this effect by comparing GNC
with isotropic random noise, and show that it achieves state-of-the-art
generalization performance for large-scale deep neural network optimization.


  The periodogram is a widely used tool to analyze second order stationary time
series. An attractive feature of the periodogram is that the expectation of the
periodogram is approximately equal to the underlying spectral density of the
time series. However, this is only an approximation, and it is well known that
the periodogram has a finite sample bias, which can be severe in small samples.
In this paper, we show that the bias arises because of the finite boundary of
observation in one of the discrete Fourier transforms which is used in the
construction of the periodogram. Moreover, we show that by using the best
linear predictors of the time series over the boundary of observation we can
obtain a "complete periodogram" that is an unbiased estimator of the spectral
density. In practice, the "complete periodogram" cannot be evaluated as the
best linear predictors are unknown. We propose a method for estimating the best
linear predictors and prove that the resulting "estimated complete periodogram"
has a smaller bias than the regular periodogram. The estimated complete
periodogram and a tapered version of it are used to estimate parameters, which
can be represented in terms of the integrated spectral density. We prove that
the resulting estimators have a smaller bias than their regular periodogram
counterparts. The proposed method is illustrated with simulations and real
data.


  Future e^+ e^- linear colliders will enable us to determine the top quark
mass with high accuracy from the measurement of the 1S peak position of
(remnant of) toponium. The estimated statistical error in this measurement is
about 50 MeV with integrated luminosity of 30 ${\rm fb^{-1}}$. We calculate
${\cal O}(\alpha_s^5 m)$ corrections to the quarkonium 1S energy spectrum in
the large-$\beta_0$ approximation to reduce theoretical uncertainties below the
corresponding experimental error. We discuss the significance of the ${\cal
O}(\alpha_s^5 m)$ corrections and estimate theoretical uncertainties of our
prediction.


  Conventional strategies of quantum metrology are built upon POVMs, thereby
possessing several general features, including the demolition of the state to
be measured, the need of performing a number of measurements, and the
degradation of performance under decoherence and dissipation. Here, we propose
an innovative measurement scheme, called dissipative adiabatic measurements
(DAMs), based on which, we further develop an approach to estimation of
parameters characterizing dissipative processes. Unlike a POVM, whose outcome
is one of the eigenvalues of an observable, a DAM yields the expectation value
of the observable as its outcome, without collapsing the state to be measured.
By virtue of the very nature of DAMs, our approach is capable of solving the
estimation problem in a state-protective fashion with only $M$ measurements,
where $M$ is the number of parameters to be estimated. More importantly,
contrary to the common wisdom, it embraces decoherence and dissipation as
beneficial effects and offers a Heisenberg-like scaling of precision, thus
outperforming conventional strategies. Our DAM-based approach is direct,
efficient, and expected to be immensely useful in the context of dissipative
quantum information processing.


  We consider linear bounded operators acting in Banach spaces with a basis,
such operators can be represented by an infinite matrix. We prove that for an
invertible operator there exists a sequence of invertible finite-dimensional
operators so that the family of norms of their inverses is uniformly bounded.
It leads to the fact that solutions of finite-dimensional equations converge to
the solution of initial operator equation with infinite-dimensional matrix.


  Anomaly detection is a challenging problem in intelligent video surveillance.
Most existing methods are computation consuming, which cannot satisfy the
real-time requirement. In this paper, we propose a real-time anomaly detection
framework with low computational complexity and high efficiency. A new feature,
named Histogram of Magnitude Optical Flow (HMOF), is proposed to capture the
motion of video patches. Compared with existing feature descriptors, HMOF is
more sensitive to motion magnitude and more efficient to distinguish anomaly
information. The HMOF features are computed for foreground patches, and are
reconstructed by the auto-encoder for better clustering. Then, we use Gaussian
Mixture Model (GMM) Classifiers to distinguish anomalies from normal activities
in videos. Experimental results show that our framework outperforms
state-of-the-art methods, and can reliably detect anomalies in real-time.


  In this paper, some tensor commutation matrices are expressed in termes of
the generalized Pauli matrices by tensor products of the Pauli matrices.


  Pop II stars formed a few hundred million years after the Big Bang were key
drivers of cosmic reionization and building blocks of high redshift galaxies.
How and when these stars formed is a subject of ongoing research. We conduct
cosmological radiation hydrodynamical simulations to investigate the formation
of Pop II star clusters in dark matter halos forming at $z=10-25$ in the
aftermath of a pair instability supernova (PISN). Our simulations model the
formation of Pop III and Pop II stars in a self-consistent manner along with
their radiative, chemical and SN feedback in halos of $\rm 5 \times 10^5- 7
\times 10^7~M_{\odot}$. We find that a PISN evacuates the gas from halos $\rm
\leq 3 \times 10^{6}~M_{\odot}$ and thereafter shuts off in situ star formation
for at-least 30 Myr. Pop II stellar clusters of $\rm 923~M_{\odot}$ and $\rm
6800~M_{\odot}$ form in halos of $\rm 3.5 \times 10^7~M_{\odot}$ and $\rm 7.2
\times 10^7~M_{\odot}$, respectively. The mode of star formation is highly
episodic and mainly regulated by Pop II SN feedback. The average star formation
rates are $\rm 10^{-5}-10^{-4}~M_{\odot}/yr$ and the star formation efficiency
is less than 1\%.


  This festive issue concludes the civilian year 2008 with details on a special
issue of Topology and its Applications dedicated to SPM, and with a quite large
list of research announcements.


  The next-generation, broadband geodetic very long baseline interferometry
system, named VGOS, is developing its global network, and VGOS networks with a
small size of 3--7 stations have already made broadband observations from 2017
to 2019. We made quality assessments for two kinds of observables in the 21
VGOS sessions currently available: group delay and differential total electron
content ($\delta$TEC). Our study reveals that the random measurement noise of
VGOS group delays is at the level of less than 2 ps (1 ps = 10$^{-12}$ s),
while the contributions from systematic error sources, mainly source structure
related, are at the level of 20 ps. Due to the significant improvement in
measurement noise, source structure effects with relatively small magnitudes
that are not overwhelming in the S/X VLBI system, for instance 10 ps, are
clearly visible in VGOS observations. Another critical error source in VGOS
observations is discrete delay jumps, for instance, a systematic offset of
about 310 ps or integer multiples of that. The predominant causative factor is
found to be related to source structure. The measurement noise level of
$\delta$TEC observables is about 0.07 TECU, but the systematic effects are five
times larger than that. A strong correlation between group delay and
$\delta$TEC observables is discovered with a trend of 40 ps/TECU for
observations with large structure effects; there is a second trend in the range
60 ps/TECU to 70 ps/TECU when the measurement noise is dominant.


  We examine the decoupling properties of the N=2 SQCD vacua when the adjoint
mass term is turned on and then the N=1 limit is taken. The BPS domain wall
tension in N=1 MQCD and SQCD is also examined. The correspondence of the MQCD
integrals with the superpotential and the gaugino condensate is shown.


  In this paper, we explore a distributed setting, where a user seeks to
compute a linearly-separable Boolean function of degree $M$ from $N$ servers,
each with a cache size $M$. Exploiting the fundamental concepts of sensitivity
and influences of Boolean functions, we devise a novel approach to capture the
interplay between dataset placement across servers and server transmissions and
to determine the optimal solution for dataset placement that minimizes the
communication cost. In particular, we showcase the achievability of the minimum
average joint sensitivity, $\frac{N}{2^{M-1}}$, as a measure for the
communication cost.


  We show that it is possible for WIMP dark matter to produce a large signal in
indirect dark matter searches without producing signals elsewhere. We
illustrate our point by fitting the Fermi-LAT extended galactic gamma-ray
excess with a simple model of Dirac dark matter that annihilates primarily into
b quarks via a pseudoscalar. Current collider constraints are weak while the 14
TeV LHC run will constrain a limited portion of the parameter space. No signal
is expected in additional indirect searches or at future direct detection
experiments. Our results emphasise the importance of fully understanding
potential indirect signals of dark matter as they may provide the only
information about the dark matter particle.


  We present a new measurement constraining Lorentz and CPT violation of the
proton using a hydrogen maser double resonance technique. A search for hydrogen
Zeeman frequency variations with a period of the sidereal day (23.93 h) sets a
clean limit on violation of Lorentz and CPT symmetry of the proton at the
10^{-27} GeV level.


  Multi-label classification of chest X-ray images is frequently performed
using discriminative approaches, i.e. learning to map an image directly to its
binary labels. Such approaches make it challenging to incorporate auxiliary
information such as annotation uncertainty or a dependency among the labels.
Building towards this, we propose a novel knowledge graph reformulation of
multi-label classification, which not only readily increases predictive
performance of an encoder but also serves as a general framework for
introducing new domain knowledge.
  Specifically, we construct a multi-modal knowledge graph out of the chest
X-ray images and its labels and pose multi-label classification as a link
prediction problem. Incorporating auxiliary information can then simply be
achieved by adding additional nodes and relations among them. When tested on a
publicly-available radiograph dataset (CheXpert), our relational-reformulation
using a naive knowledge graph outperforms the state-of-art by achieving an
area-under-ROC curve of 83.5%, an improvement of "sim 1" over a purely
discriminative approach.


  We consider the creation of polarization entangled light from parametric
down- conversion driven by an intense pulsed pump inside a cavity. The
multi-photon states produced are close approximations to singlet states of two
very large spins. A criterion is derived to quantify the entanglement of such
states. We study the dynamics of the system in the presence of losses and other
imperfections, concluding that the creation of strongly entangled states with
photon numbers up to a million seems achievable.


  We study thermodynamic properties of the doped Hubbard model on the square
lattice in the regime of strong charge and spin fluctuations at low
temperatures near the metal-to-insulator crossover and obtain results with
controlled accuracy using the diagrammatic Monte Carlo method directly in the
thermodynamic limit. The behavior of the entropy reveals a non-Fermi-liquid
state at sufficiently high interactions near half-filling: a maximum in the
entropy at non-zero doping develops as the coupling strength is increased,
along with an inflection point, evidencing a metal to non-Fermi-liquid
crossover. The specific heat exhibits additional distinctive features of a
non-Fermi-liquid state. Measurements of the entropy can therefore be used as a
probe of the state of the system in quantum simulation experiments with
ultracold atoms in optical lattices.


  We define for any 4-tetrahedron (4-simplex) the simplest finite closed
piecewise flat manifold consisting of this 4-tetrahedron and of the one else
4-tetrahedron identical up to reflection to the present one (call it bisimplex
built on the given 4-simplex, or two-sided 4-simplex). We consider arbitrary
piecewise flat manifold. Gravity action for it can be expressed in terms of sum
of the actions for the bisimplices built on the 4-simplices constituting this
manifold. We use representation of each bisimplex action in terms of rotation
matrices (connections) and area tensors. This gives some representation of any
piecewise flat gravity action in terms of connections. The action is a sum of
terms each depending on the connection variables referring to a single
4-tetrahedron. Application of this representation to the path integral
formalism is considered. Integrations over connections in the path integral
reduce to independent integrations over finite sets of connections on separate
4-simplices. One of the consequences is exponential suppression of the result
at large areas or lengths (compared to Plank scale). It is important for the
consistency of the simplicial description of spacetime.


  As a potential consequence of Lorentz invariance violation~(LIV), threshold
anomalies open a window to study LIV. Recently the Large High Altitude Air
Shower Observatory~(LHAASO) reported that more than 5000 photons from GRB
221009A have been observed with energies above 500~GeV and up to
$18~\text{TeV}$. In the literature, it is suggested that this observation may
have tension with the standard model result because extragalactic background
light~(EBL) can prevent photons around 18~TeV from reaching the earth and that
LIV induced threshold anomalies might be able to explain the observation. In
this work we further study this proposal with more detailed numerical
calculation for different LIV scales and redshifts of the sources. We find that
GRB 221009A is a rather unique opportunity to search LIV, and a LIV scale
$E_\text{LIV} \lesssim E_\text{Planck}\approx 1.22\times 10^{19}~\text{GeV}$ is
feasible to the observation of GRB 221009A on 9 October, 2022.


  Because of the strong inherent resonances, the giant optical activity
obtained via chiral metamaterials generally suffers from high dispersion, which
has been a big stumbling block to broadband applications. In this paper, we
propose a type of chiral metamaterial consisting of interconnected metal helix
structures with four-fold symmetry, which exhibits nonresonant Drude-like
response and can therefore avoid the highly dispersive optical activity
resulting from resonances. It shows that the well-designed chiral metamaterial
can achieve nondispersive and pure optical activity with high transmittance in
a broadband frequency range. And the optical activity of multi-layer chiral
metamaterials is proportional to the layer numbers of single-layer chiral
metamaterial. Most remarkably, the broadband behaviors of nondispersive optical
activity and high transmission are insensitive to the incident angles of
electromagnetic waves and permittivity of dielectric substrate, thereby
enabling more flexibility in polarization manipulation.


  We present the status of our analysis on the order of the finite temperature
transition in QCD with two flavors of degenerate fermions. Our new simulations
on large lattices support the hypothesis of the first order nature of the
transition, showing a preliminary two state signal. We will discuss the
implications and the next steps in our analysis.


  Experimental values of SdH and dHvA periods and cyclotron effective masses
found by Rosenman and Doi et al. have been compared with the theoretical
predictions derived in this work for a tetragonal narrow gap semiconductor. By
the least square fit method the values of band parameters were obtained. It has
been established that Cd$_3$As$_2$ has inverted band structure resembling HgTe
under tensile stress.


  Several authors modelled networks ad hoc by oriented or disoriented graphs,
whereby the problem of allowance (allocation) of the frequencies at the level
of the network was transformed into coloring problem of nodes in the graph.
Graph coloring is a tool to characterize the graphs. In our study, we were
interested in particular in the coloring of vertex. In this domain, a large
number of parameters of coloring were defined. A coloring for which two
neighboring summits do not have same color is called proper coloring. We
proposed to evaluate two other parameters vertex coloring maximizing the number
of colors to use: b-chromatic number and especially the number of Grundy. These
studies have focused on two types of graphs, which are the powers graphs and
Cartesian sum of graphs. In the first part, we determined borders among Grundy
for the Cartesian sum of graphs and finally we proposed algorithms for the
coloration of graphs. First of all, we gave some properties and results for
simple graphs (stable, chain, cycle, full, star, bipartisan). Secondly, we
studied the Cartesian sum of two graphs by giving exact values of the number of
Grundy for diverse classes of graphs (sum of a chain and a chain, a chain and a
cycle, a cycle and a cycle) then we estimated borders of this parameter for the
sum of a complete graph and any other graph. In the second part, we presented
the results of the Cartesian sum of several graphs and in the last part; we
also gave an algorithm for generating graphs with a given number of Grundy.
Thereafter, we studied another parameter namely the partial coloring Grundy.
The properties of this parameter are close to those of total Grundy. Finally,
we used parameters of coloring total Grundy and partial Grundy to generate
algorithms of coloring of graphs. We proposed algorithms of coloring basing on
the properties of certain graphs.


  In the feature space, the collapse between features invokes critical problems
in representation learning by remaining the features undistinguished.
Interpolation-based augmentation methods such as mixup have shown their
effectiveness in relieving the collapse problem between different classes,
called inter-class collapse. However, intra-class collapse raised in
coarse-to-fine transfer learning has not been discussed in the augmentation
approach. To address them, we propose a better feature augmentation method,
asymptotic midpoint mixup. The method generates augmented features by
interpolation but gradually moves them toward the midpoint of inter-class
feature pairs. As a result, the method induces two effects: 1) balancing the
margin for all classes and 2) only moderately broadening the margin until it
holds maximal confidence. We empirically analyze the collapse effects by
measuring alignment and uniformity with visualizing representations. Then, we
validate the intra-class collapse effects in coarse-to-fine transfer learning
and the inter-class collapse effects in imbalanced learning on long-tailed
datasets. In both tasks, our method shows better performance than other
augmentation methods.


  Let $G$ be a reductive group acting on an affine scheme $V$. We study the set
of principal $G$-bundles on a smooth projective curve $\mathcal C$ such that
the associated $V$-bundle admits a section sending the generic point of
$\mathcal C$ into the GIT stable locus $V^{\mathrm{s}}(\theta)$. We show that
after fixing the degree of the line bundle induced by the character $\theta$,
the set of such principal $G$-bundles is bounded. The statement of our theorem
is made slightly more general so that we deduce from it the boundedness for
$\epsilon$-stable quasimaps and $\Omega$-stable LG-quasimap.


  The late inspiral, merger, and ringdown of a black hole-neutron star (BHNS)
system can provide information about the neutron-star equation of state (EOS).
Candidate EOSs can be approximated by a parametrized piecewise-polytropic EOS
above nuclear density, matched to a fixed low-density EOS; and we report
results from a large set of BHNS inspiral simulations that systematically vary
two parameters. To within the accuracy of the simulations, we find that, apart
from the neutron-star mass, a single physical parameter Lambda, describing its
deformability, can be extracted from the late inspiral, merger, and ringdown
waveform. This parameter is related to the radius, mass, and l=2 Love number,
k_2, of the neutron star by Lambda = 2k_2 R^5/3M_{NS}^5, and it is the same
parameter that determines the departure from point-particle dynamics during the
early inspiral. Observations of gravitational waves from BHNS inspiral thus
restrict the EOS to a surface of constant Lambda in the parameter space,
thickened by the measurement error. Using various configurations of a single
Advanced LIGO detector, we find that neutron stars are distinguishable from
black holes of the same mass and that Lambda^{1/5} or equivalently R can be
extracted to 10-40% accuracy from single events for mass ratios of Q=2 and 3 at
a distance of 100 Mpc, while with the proposed Einstein Telescope, EOS
parameters can be extracted to accuracy an order of magnitude better.


  We give a method for constructing many examples of automorphisms with
positive entropy on rational complex surfaces. The general idea is to begin
with a quadratic Cremona transformation that fixes a reduced cubic curve and
then use the group structure on the cubic to understand when the indeterminacy
and exceptional behavior of the transformation may be eliminated by repeated
blowing up.


  We report the measurement of electron neutrino elastic scattering from 8B
solar neutrinos with 3 MeV energy threshold by the Borexino detector in Gran
Sasso (Italy). The rate of solar neutrino-induced electron scattering events
above this energy in Borexino is 0.217 +- 0.038 (stat) +- 0.008 (syst) cpd/100
t, which corresponds to the equivalent unoscillated flux of (2.4 +- 0.4 (stat)
+- 0.1 (syst))x10^6 cm^-2 s^-1, in good agreement with measurements from SNO
and SuperKamiokaNDE. Assuming the 8B neutrino flux predicted by the high
metallicity Standard Solar Model, the average 8B neutrino survival probability
above 3 MeV is measured to be 0.29+-0.10. The survival probabilities for 7Be
and 8B neutrinos as measured by Borexino differ by 1.9 sigma. These results are
consistent with the prediction of the MSW-LMA solution of a transition in the
solar electron neutrino survival probability between the low energy
vacuum-driven and the high-energy matter-enhanced solar neutrino oscillation
regimes.


  We determine all possible multiplicities of general singular fibers of a
holomorphic Lagrangian fibration, under the assumption that all components of
the fibers are of Fujiki class. The multiplicities are at most 6 and the
possible values are intricately related to the Kodaira type of the
characteristic cycle.


  We introduce a general method to construct one-dimensional translationally
invariant valence bond solid states with a built-in Lie group $G$ and derive
their matrix product representations. The general strategies to find their
parent Hamiltonians are provided so that the valence bond solid states are
their unique ground states. For quantum integer spin-$S$ chains, we discuss two
topologically distinct classes of valence bond solid states: One consists of
two virtual SU(2) spin-$J$ variables in each site and another is formed by
using two $SO(2S+1)$ spinors. Among them, a new spin-1 fermionic valence bond
solid state, its parent Hamiltonian, and its properties are discussed in
detail. Moreover, two types of valence bond solid states with SO(5) symmetry
are further generalized and their respective properties are analyzed as well.


  We compute generators and relations for the graded rings of paramodular forms
of degree two and levels 5 and 7. The generators are expressed as quotients of
Gritsenko lifts and Borcherds products. The computation is made possible by a
characterization of modular forms on the Humbert surfaces of discriminant 4
that arise from paramodular forms by restriction.


  We explore the effect of antidot size on electronic and magnetic properties
of graphene antidot lattices from first-principles calculations. The
spin-polarized density of states, band gap, formation energy and the total
magnetization of two different equilateral triangular and right triangular
antidots with zigzag and mixed zigzag-armchair edges are studied. We find that
although the values of band gap, formation energy and the total magnetization
of both structures are different, these values may increase when the number of
zigzag edges is increased. The armchair edges have no contribution in the total
magnetization of right triangular antidots. The induced magnetic moments are
mainly localized on the edge atoms with a maximum value at the center of each
side of the triangles. We show that a spin-dependent band gap opens up in
bilayer graphene as a result of antidot pattern in only one layer of the
structure. Such periodic arrays of triangular antidots that cause a
spin-dependent band gap around the Fermi energy can be utilized for turning
graphene from a diamagnetic semimetal into a magnetic semiconductor.


  Track one of CTI competition is on click-through rate (CTR) prediction. The
dataset contains millions of records and each field-wise feature in a record
consists of hashed integers for privacy. For this task, the keys of
network-based methods might be type-wise feature extraction and information
fusion across different fields. Multi-layer perceptrons (MLPs) are able to
extract field feature, but could not efficiently fuse features. Motivated by
the natural fusion characteristic of cross attention and the efficiency of
transformer-based structures, we propose simple plug-in mixers for
field/type-wise feature fusion, and thus construct an field&type-wise ensemble
model, namely EMOFM (Ensemble MLP mOdel with Feature-based Mixers). In the
experiments, the proposed model is evaluated on the dataset, the optimization
process is visualized and ablation studies are explored. It is shown that EMOFM
outperforms compared baselines. In the end, we discuss on future work. WARNING:
The comparison might not be fair enough since the proposed method is designed
for this data in particular while compared methods are not. For example, EMOFM
especially takes different types of interactions into consideration while
others do not. Anyway, we do hope that the ideas inside our method could help
other developers/learners/researchers/thinkers and so on.


  We provide a simple reformulation of the $\epsilon$-$\delta$ limit definition
introduced in undergraduate calculus courses that enhances its pedagogical
value for conceptual understanding and computational skill.


  Program translation is a growing demand in software engineering. Manual
program translation requires programming expertise in source and target
language. One way to automate this process is to make use of the big data of
programs, i.e., Big Code. In particular, one can search for program
translations in Big Code. However, existing code retrieval techniques are not
designed for cross-language code retrieval. Other data-driven approaches
require human efforts in constructing cross-language parallel datasets to train
translation models. In this paper, we present RPT, a novel code translation
retrieval system. We propose a lightweight but informative program
representation, which can be generalized to all imperative PLs. Furthermore, we
present our index structure and hierarchical filtering mechanism for efficient
code retrieval from a Big Code database.


  In this work, we have expounded the communication procedure of quantum
systems by means of process algebra. The main objective of our research effort
is to formally represent the communication between distributed quantum systems.
In this new proposed communication model we have ameliorated the existing rules
of Lalire's quantum process algebra QPAlg. We have brought some important
modification in QPAlg by introducing the concept of formally specifying the
Quantum teleportation protocol. We have further introduced the formal
description of protocol by using programs that best explains its working and
satisfies the specification. Examples have been provided to describe the
working of the improved algebra that formally explain the sending and receiving
of both classical as well as quantum data, keeping in mind the principal
features of quantum mechanics.


  We examine long-term low-dispersion IUE, SWP and LWP spectroscopy of the R
Coronae Borealis (RCB) star V854 Cen, obtained across the deep 1991, 1992-1993
and 1994 declines. We also report the optical light curve for the star in the
interval 1987-1998, including multi-color photometry obtained during 1989-1998.
  Analysis of the UV emission line spectra indicates most lines decay during
the deep declines on characteristic timescales comparable to that reported for
optical features. Fe, Mg and neutral C lines decay on timescales of typically
50-100 d. Other lines, notably ionized C lines, decay on longer timescales (>
200 d) or appear to be unaffected by the declines. The general nature of the UV
emission lines and other UV features during the declines is consistent with the
E1/E2/BL line-region model developed from the behavior of optical spectral
features during declines. However, the detailed line-behavior indicates large
intrinsic variability between decline events inconsistent with the simple
E1/E2/BL model. Limited temporal coverage prevents detailed examination of the
geometry of the emission line region or the obscuring dust. We also report the
first detection of the transition-region line C IV 1550 in the spectrum of an
RCB star.


  Within the framework of the Landau-Ginzburg-Devonshire approach we explore
the impact of elastic anisotropy, electrostriction, flexoelectric couplings,
and mismatch strain on the domain structure morphology in ferroelectric
core-shell nanoparticles of spherical shape. We perform finite element
modelling (FEM) for multiaxial ferroelectric nanoparticle cores covered with an
elastically-isotropic soft or elastically-anisotropic rigid paraelectric shell,
with and without mismatch strains. In the case of a core covered with a soft
shell, the FEM results show that at room temperature a single polarization
vortex with a dipolar kernel can be stable if the electrostriction coupling is
weak. With increasing anisotropic electrostriction coupling, the vortex
disappears and is replaced by complex flux-closure structures, which are formed
in the equatorial plane and transform into an elongated vortex with a central
180-degree domain wall near the core poles. This complex domain morphology
develops in the core due to the anisotropic electrostriction, and the
flexoelectric coupling leads to an additional curvature and twist of the
polarization isosurfaces. In contrast to this, FEM performed for a core covered
with a rigid shell shows that, at room temperature, the anisotropic elastic
properties of the shell can stabilize vortex-like structures with three
flux-closure domains, which gradually cross in the equatorial plane of the core
and transform into 120-degree domains near the core poles. The flexoelectric
coupling leads to a noticeable curling of the flux-closure domain walls. A
mismatch strain compensates the curling of the flux-closure domains in the core
confined by the elastically-anisotropic rigid shell. Our analysis reveals
different types of topological defects, namely Bloch point structures (BPS) and
Ising lines, that form in a ferroelectric core covered with a soft or rigid
shell.


  We design the first polynomial time approximation schemes (PTASs) for the
Minimum Betweenness problem in tournaments and some related higher arity
ranking problems. This settles the approximation status of the Betweenness
problem in tournaments along with other ranking problems which were open for
some time now. The results depend on a new technique of dealing with fragile
ranking constraints and could be of independent interest.


  Given a pair of second order diffusion operators, one on the total space of a
principle bundle $N$ and the other on the base space $M$, intertwined by the
projection $\pi:N\to M$, if the operator ${\mathcal A}$ on the base manifold
has constant rank, we define a semi-connection on the principal bundle which
allows to split the diffusion operator ${\mathcal B}$ on the total space into
the sum of the horizontal lift of ${\mathcal A}$ and the other vertical. This
allow to conclude a disintegration theorem for the law of ${\mathcal B}$. As an
application, a decomposition of stochastic flow is given.


  We consider the inflaton as a scalar field described by a non-minimal
derivative coupling model with a power law potential. We study the slow roll
inflation, the rapid oscillation phase, the radiation dominated and the
recombination eras respectively, and estimate e-folds numbers during these
epochs. Using these results and recent astrophysical data we determine the
reheating temperature in terms of the spectral index and the amplitude of the
power spectrum of scalar perturbations.


  How to learn a better speech representation for end-to-end speech-to-text
translation (ST) with limited labeled data? Existing techniques often attempt
to transfer powerful machine translation (MT) capabilities to ST, but neglect
the representation discrepancy across modalities. In this paper, we propose the
Speech-TExt Manifold Mixup (STEMM) method to calibrate such discrepancy.
Specifically, we mix up the representation sequences of different modalities,
and take both unimodal speech sequences and multimodal mixed sequences as input
to the translation model in parallel, and regularize their output predictions
with a self-learning framework. Experiments on MuST-C speech translation
benchmark and further analysis show that our method effectively alleviates the
cross-modal representation discrepancy, and achieves significant improvements
over a strong baseline on eight translation directions.


  We theoretically investigate electron transport through corrugated graphene
ribbons and show how the ribbon curvature leads to an electronic superlattice
with a period set by the corrugation wave length. Transport through the ribbon
depends sensitively on the superlattice band structure which, in turn, strongly
depends on the geometry of the deformed sheet. In particular, we find that for
ribbon widths where the transverse level separation is comparable to the the
band edge energy, a strong current switching occurs as function of an applied
backgate voltage. Thus, artificially corrugated graphene sheets or ribbons can
be used for the study of Dirac fermions in periodic potentials. Furthermore,
this provides an additional design paradigm for graphene-based electronics.


  We study resonant response of an underdamped nanomechanical resonator with
fluctuating frequency. The fluctuations are due to diffusion of molecules or
microparticles along the resonator. They lead to broadening and change of shape
of the oscillator spectrum. The spectrum is found for the diffusion confined to
a small part of the resonator and where it occurs along the whole nanobeam. The
analysis is based on extending to the continuous limit, and appropriately
modifying, the method of interfering partial spectra. We establish the
conditions of applicability of the fluctuation-dissipation relations between
the susceptibility and the power spectrum. We also find where the effect of
frequency fluctuations can be described by a convolution of the spectra without
these fluctuations and with them as the only source of the spectral broadening.


  An electrically-controllable, solid-state, reversible device for sourcing and
sinking alkali vapor is presented. When placed inside an alkali vapor cell,
both an increase and decrease of the rubidium vapor density by a factor of two
are demonstrated through laser absorption spectroscopy on 10 to 15 s time
scales. The device requires low voltage (5 V), low power (<3.4 mW peak power),
and low energy (<10.7 mJ per 10 s pulse). The absence of oxygen emission during
operation is shown through residual gas analysis, indicating Rb is not lost
through chemical reaction but rather by ion transport through the designed
channel. This device is of interest for atomic physics experiments and, in
particular, for portable cold-atom systems where dynamic control of alkali
vapor density can enable advances in science and technology.


  We show that the number of non-isotopic commutative semifields of odd order
$p^{n}$ is exponential in $n$ when $n = 4t$ and $t$ is not a power of $2$. We
introduce a new family of commutative semifields and a method for proving
isotopy results on commutative semifields that we use to deduce the
aforementioned bound. The previous best bound on the number of non-isotopic
commutative semifields of odd order was quadratic in $n$ and given by Zhou and
Pott [Adv. Math. 234 (2013)]. Similar bounds in the case of even order were
given in Kantor [J. Algebra 270 (2003)] and Kantor and Williams [Trans. Amer.
Math. Soc. 356 (2004)].


  A general framework for the deformation of the single-mode oscillators is
presented and all deformed single-mode oscillators are unified. The extensions
of the Aric-Coon, genon, the para-Bose and the para-Fermi oscillators are
proposed. The generalized harmonic oscillator considered by Brzezinski et al.
is rederived in a simple way.Some remarks on deformation of $SU(1,1)$ and
supersymmetry are made.


  We reanalyze the gravitating monopole and its black hole solutions in the
Einstein-Yang-Mills-Higgs system and we discuss their stabilities from the
point of view of catastrophe theory. Although these non-trivial solutions
exhibit fine and complicated structures, we find that stability is
systematically understood via a swallow tail catastrophe. The
Reissner-Nordstr\"{o}m trivial solution becomes unstable from the point where
the non-trivial monopole black hole appears. We also find that, within a very
small parameter range, the specific heat of a monopole black hole changes its
sign .


  In this paper we study the variations in human brain activity when listening
to real and fake audio. Our preliminary results suggest that the
representations learned by a state-of-the-art deepfake audio detection
algorithm, do not exhibit clear distinct patterns between real and fake audio.
In contrast, human brain activity, as measured by EEG, displays distinct
patterns when individuals are exposed to fake versus real audio. This
preliminary evidence enables future research directions in areas such as
deepfake audio detection.


  Data taken by CRESST in 2000 with a cryogenic detector system based on 262 g
sapphire crystals is used to place limits on WIMP dark matter in the Galactic
Halo. The detector is especially sensitive for low-mass WIMPS with
spin-dependent cross sections and improves on existing limits in this region.
CRESST is now preparing for a second phase, which will use a 10 kg detector
consisting of 300 g CaWO4 crystals with simultaneous detection of phonons and
scintillation light to reduce background.


  I present an overview of the physics of the Josephson effect between Bose
condensed systems, with emphasis on the recently achieved BEC's in trapped
alkali gases. I focus mostly on those physical phenomena that are likely to be
observed only (or more easily) in these novel systems. Thus I omit the
discussion of problems which may be viewed as straightforward applications of
well known Josephson physics. In particular, I review the external and the
internal Josephson effects, and discuss how in the latter case it may be
possible to explore the crossover between collective Josephson behavior and
independent boson Rabi dynamics. I also describe novel macroscopic quantum
phenomena such as self-trapping and interference between separate Bose
condensates.


  In this paper we first note a result of birational automorphisms with bounded
degree of projective varieties related with the Zariski dense orbit conjecture
(ZDO) and the Zariski density of periodic points. Next, we give a reduced
result of ZDO for automorphisms of projective threefolds, and showed ZDO for
automorphisms of projective varieties $X$ with the irregularity $q(X)\ge\dim
X-1$.


  We report our new observations of redshifted carbon monoxide emission from
six z~6 quasars, using the PdBI. CO (6-5) or (5-4) line emission was detected
in all six sources. Together with two other previous CO detections, these
observations provide unique constraints on the molecular gas emission
properties in these quasar systems close to the end of the cosmic reionization.
Complementary results are also presented for low-J CO lines observed at the GBT
and the VLA, and dust continuum from five of these sources with the SHARC-II
bolometer camera at the CSO. We then present a study of the molecular gas
properties in our combined sample of eight CO-detected quasars at z~6. The
detections of high-order CO line emission in these objects indicates the
presence of highly excited molecular gas, with estimated masses on the order of
10^10 M_sun within the quasar host galaxies. No significant difference is found
in the gas mass and CO line width distributions between our z~6 quasars and
samples of CO-detected $1.4\leq z\leq5$ quasars and submillimeter galaxies.
Most of the CO-detected quasars at z~6 follow the far infrared-CO luminosity
relationship defined by actively star-forming galaxies at low and high
redshifts. This suggests that ongoing star formation in their hosts contributes
significantly to the dust heating at FIR wavelengths. The result is consistent
with the picture of galaxy formation co-eval with supermassive black hole
(SMBH) accretion in the earliest quasar-host systems. We investigate the black
hole--bulge relationships of our quasar sample, using the CO dynamics as a
tracer for the dynamical mass of the quasar host. The results place important
constraints on the formation and evolution of the most massive SMBH-spheroidal
host systems at the highest redshift.


  Innovation is slowing greatly in the pharmaceutical sector. It is considered
here how part of the problem is due to overly limiting intellectual property
relations in the sector. On the other hand, computing and software in
particular are characterized by great richness of intellectual property
frameworks. Could the intellectual property ecosystem of computing come to the
aid of the biosciences and life sciences? We look at how the answer might well
be yes, by looking at (i) the extent to which a drug mirrors a software
program, and (ii) what is to be gleaned from trends in research publishing in
the life and biosciences.


  We propose a systematic T-matrix approach to solve few-body problems with
s-wave contact interactions in ultracold atomic gases. The problem is generally
reduced to a matrix equation expanded by a set of orthogonal molecular states,
describing external center-of-mass motions of pairs of interacting particles;
while each matrix element is guaranteed to be finite by a proper
renormalization for internal relative motions. This approach is able to
incorporate various scattering problems and the calculations of related
physical quantities in a single framework, and also provides a physically
transparent way to understand the mechanism of resonance scattering. For
applications, we study two-body effective scattering in 2D-3D mixed dimensions,
where the resonance position and width are determined with high precision from
only a few number of matrix elements. We also study three fermions in a
(rotating) harmonic trap, where exotic scattering properties in terms of mass
ratios and angular momenta are uniquely identified in the framework of
T-matrix.


  We present an idealized, semi-empirical model for the evolution of
gravitationally contracting molecular clouds (MCs) and their star formation
rate (SFR) and efficiency (SFE). The model assumes that the instantaneous SFR
is given by the mass above a certain density threshold divided by its free-fall
time. The instantaneous number of massive stars is computed assuming a Kroupa
IMF. These stars feed back on the cloud through ionizing radiation, eroding it.
The main controlling parameter of the evolution turns out to be the maximum
cloud mass, $\Mmax$. This allows us to compare various properties of the model
clouds against their observational counterparts. A giant molecular cloud (GMC)
model ($\Mmax \sim 10^5 \Msun$) adheres very well to the evolutionary scenario
recently inferred by Kawamura et al. (2009) for GMCs in the Large Magellanic
Cloud. A model cloud with $\Mmax \approx 2000 \Msun$ evolves in the
Kennicutt-Schmidt diagram first passing through the locus of typical low-
to-intermediate mass star-forming clouds, and then moving towards the locus of
high-mass star-forming ones over the course of $\sim 10$ Myr. Also, the stellar
age histograms for this cloud a few Myr before its destruction agree very well
with those observed in the $\rho$-Oph stellar association, whose parent cloud
has a similar mass, and imply that the SFR of the clouds increases with time.
Our model thus agrees well with various observed properties of star-forming
MCs, suggesting that the scenario of gravitationally collapsing MCs, with their
SFR regulated by stellar feedback, is entirely feasible and in agreement with
key observed properties of molecular clouds.


  We use the moment approach of Nolting (exact sum rules) (Z. Physik 255, 25
(1972)) for the attractive Hubbard model in the superconducting phase. Our
diagonal and off - diagonal spectral functions are constructed and evaluated
with the sum rules. They reduce to the $BCS$ limit for weak interaction.
However, the presence of correlations modify the $BCS$ picture dramatically.
For example, due to the presence of correlations we have postulated a three -
pole ansatz for the diagonal Green function, $G(\vec{k},\omega)$, while the off
- diagonal one, $B(\vec{k},\omega)$, is supposed to have two poles. In the
paper we present results for the three spectral weights of the diagonal Green
function, $\alpha_j(\vec{k})$, j = 1,2,3. Our results compare reasonably well
with more elaborated auto - consistent highly non - linear equations (double
fluctuation calculations in the $T-$ Matrix approach of one of the authors).
Then, the physical picture which emerges is that the lower Hubbard band is
split due to the superconducting gap and the upper Hubbard band remains mostly
unmodified.


  We present high-resolution observations of the 880 $\mu$m (rest-frame FIR)
continuum emission in the z$=$4.05 submillimeter galaxy GN20 from the IRAM
Plateau de Bure Interferometer (PdBI). These data resolve the obscured star
formation in this unlensed galaxy on scales of
0.3$^{\prime\prime}$$\times$0.2$^{\prime\prime}$ ($\sim$2.1$\times$1.3 kpc).
The observations reveal a bright (16$\pm$1 mJy) dusty starburst centered on the
cold molecular gas reservoir and showing a bar-like extension along the major
axis. The striking anti-correlation with the HST/WFC3 imaging suggests that the
copious dust surrounding the starburst heavily obscures the rest-frame
UV/optical emission. A comparison with 1.2 mm PdBI continuum data reveals no
evidence for variations in the dust properties across the source within the
uncertainties, consistent with extended star formation, and the peak star
formation rate surface density (119$\pm$8 M$_{\odot}$ yr$^{-1}$ kpc$^{-2}$)
implies that the star formation in GN20 remains sub-Eddington on scales down to
3 kpc$^2$. We find that the star formation efficiency is highest in the central
regions of GN20, leading to a resolved star formation law with a power law
slope of $\Sigma_{\rm SFR}$ $\sim$ $\Sigma_{\rm H_2}^{\rm 2.1\pm1.0}$, and that
GN20 lies above the sequence of normal star-forming disks, implying that the
dispersion in the star formation law is not due solely to morphology or choice
of conversion factor. These data extend previous evidence for a fixed star
formation efficiency per free-fall time to include the star-forming medium on
$\sim$kpc-scales in a galaxy 12 Gyr ago.


  We study the cohomology of the massless BRST complex of the Type IIB pure
spinor superstring in flat space. In particular, we find that the cohomology at
the ghost number three is nontrivial and transforms in the same representation
of the supersymmetry algebra as the solutions of the linearized classical
supergravity equations. Modulo some finite dimensional spaces, the ghost number
three cohomology is the same as the ghost number two cohomology. We also
comment on the difference between the naive and semi-relative cohomology, and
the role of b-ghost.


  We have observed the Crab pulsar with the Deep Space Network (DSN) Goldstone
70 m antenna at 1664 MHz during three observing epochs for a total of 4 hours.
Our data analysis has detected more than 2500 giant pulses, with flux densities
ranging from 0.1 kJy to 150 kJy and pulse widths from 125 ns (limited by our
bandwidth) to as long as 100 microseconds, with median power amplitudes and
widths of 1 kJy and 2 microseconds respectively. The most energetic pulses in
our sample have energy fluxes of approximately 100 kJy-microsecond. We have
used this large sample to investigate a number of giant-pulse emission
properties in the Crab pulsar, including correlations among pulse flux density,
width, energy flux, phase and time of arrival. We present a consistent
accounting of the probability distributions and threshold cuts in order to
reduce pulse-width biases. The excellent sensitivity obtained has allowed us to
probe further into the population of giant pulses. We find that a significant
portion, no less than 50%, of the overall pulsed energy flux at our observing
frequency is emitted in the form of giant pulses.


  We develop nilpotently $p$-localization of knot groups in terms of the
(symplectic) automorphism groups of free nilpotent groups. We show that any map
from the set of conjugacy classes of the outer automorphism groups yields a
knot invariant. We also investigate the automorphism groups and compute the
resulting knot invariants.


  Transformer, composed of self-attention and Feed-Forward Network, has
revolutionized the landscape of network design across various vision tasks. FFN
is a versatile operator seamlessly integrated into nearly all AI models to
effectively harness rich representations. Recent works also show that FFN
functions like key-value memories. Thus, akin to the query-key-value mechanism
within self-attention, FFN can be viewed as a memory network, where the input
serves as query and the two projection weights operate as keys and values,
respectively. We hypothesize that the importance lies in query-key-value
framework itself rather than in self-attention. To verify this, we propose
converting self-attention into a more FFN-like efficient token mixer with only
convolutions while retaining query-key-value framework, namely FFNification.
Specifically, FFNification replaces query-key and attention coefficient-value
interactions with large kernel convolutions and adopts GELU activation function
instead of softmax. The derived token mixer, FFNified attention, serves as
key-value memories for detecting locally distributed spatial patterns, and
operates in the opposite dimension to the ConvNeXt block within each
corresponding sub-operation of the query-key-value framework. Building upon the
above two modules, we present a family of Fast-Forward Networks. Our FFNet
achieves remarkable performance improvements over previous state-of-the-art
methods across a wide range of tasks. The strong and general performance of our
proposed method validates our hypothesis and leads us to introduce MetaMixer, a
general mixer architecture that does not specify sub-operations within the
query-key-value framework. We show that using only simple operations like
convolution and GELU in the MetaMixer can achieve superior performance.


  We show that a neural network with arbitrary depth and non-linearities, with
dropout applied before every weight layer, is mathematically equivalent to an
approximation to a well known Bayesian model. This interpretation might offer
an explanation to some of dropout's key properties, such as its robustness to
over-fitting. Our interpretation allows us to reason about uncertainty in deep
learning, and allows the introduction of the Bayesian machinery into existing
deep learning frameworks in a principled way.
  This document is an appendix for the main paper "Dropout as a Bayesian
Approximation: Representing Model Uncertainty in Deep Learning" by Gal and
Ghahramani, 2015.


  We present high resolution imaging of the low order (J=1 and 2) CO line
emission from the z = 3.93 submillimeter galaxy (SMG) MM18423+5938 using the
Expanded Very Large Array, and optical and near-IR imaging using the
Canada-France-Hawaii Telescope. This SMG with a spectroscopic redshift was
thought to be gravitationally lensed given its enormous apparent brightness. We
find that the CO emission is consistent with a complete Einstein ring with a
major axis diameter of ~ 1.4", indicative of lensing. We have also identified
the lens galaxy as a very red elliptical coincident with the geometric center
of the ring and estimated its photometric redshift z~1.1. A first estimate of
the lens magnification factor is m~12. The luminosity L'_CO(1-0) of the CO(1-0)
emission is 2.71+/-0.38 x10^11/m K km s^-1 pc^2, and, adopting the commonly
used conversion factor for ULIRGs, the molecular gas mass is M(H_2) = 2.2
x10^11/m M_sol, comparable to unlensed SMGs if corrected by m ~ 12. Our revised
estimate of the far-IR luminosity of MM18423+5938 is 2 x10^13/m < L_FIR < 3
x10^14/m L_sol, comparable to that of ULIRGs. Further observations are required
to quantify the star formation rate in MM18423+5938 and to constrain the mass
model of the lens in more detail.


  Bi2Te3 is a member of a new class of materials known as topological
insulators which are supposed to be insulating in the bulk and conducting on
the surface. However experimental verification of the surface states has been
difficult in electrical transport measurements due to a conducting bulk. We
report low temperature magnetotransport measurements on single crystal samples
of Bi2Te3. We observe metallic character in our samples and large and linear
magnetoresistance from 1.5 K to 290 K with prominent Shubnikov-de Haas (SdH)
oscillations whose traces persist upto 20 K. Even though our samples are
metallic we are able to obtain a Berry phase close to the value of {\pi}
expected for Dirac fermions of the topological surface states. This indicates
that we might have obtained evidence for the topological surface states in
metallic single crystals of Bi2Te3. Other physical quantities obtained from the
analysis of the SdH oscillations are also in close agreement with those
reported for the topological surface states. The linear magnetoresistance
observed in our sample, which is considered as a signature of the Dirac
fermions of the surface states, lends further credence to the existence of
topological surface states.


  In each step of the creative writing process, writers must grapple with their
creative goals and individual perspectives. This process affects the writer's
sense of authenticity and their engagement with the written output. Fluent text
generation by AIs risks undermining the reflective loop of rewriting. We
hypothesize that deliberately generating imperfect intermediate text can
encourage rewriting and prompt higher level decision making. Using logs from 27
writing sessions using a text generation AI, we characterize how writers adapt
and rewrite AI suggestions, and show that intermediate suggestions
significantly motivate and increase rewriting. We discuss the implications of
this finding, and future steps for investigating how to leverage intermediate
text in AI writing support tools to support ownership over creative expression.


  The far-field subwavlength imaging is a challenging issue. In this letter we
demonstrate numerically that the far-field subwavelength imaging of weakly
scattering objects can be obtained by processing the data acquired by a single
antenna, which benefits from the use of the strongly disordered medium. A
mathematical model has been proposed for solving such problem based on the idea
of sparse reconstruction. Moreover, this study leads to an important conclusion
that the strongly disordered medium can serves as an efficient apparatus for
the single-antenna compressive measurement, which shifts the complexity of
devising compressive sensing (CS) hardware from the design, fabrication and
electronic control. The proposed method and associated results can find
applications in several imaging disciplines, such as optics, THz, RF or
ultrasound imaging.


  The nondeterministic advice complexity of the P-selective sets is known to be
exactly linear. Regarding the deterministic advice complexity of the
P-selective sets--i.e., the amount of Karp--Lipton advice needed for
polynomial-time machines to recognize them in general--the best current upper
bound is quadratic [Ko, 1983] and the best current lower bound is linear
[Hemaspaandra and Torenvliet, 1996].
  We prove that every associatively P-selective set is commutatively,
associatively P-selective. Using this, we establish an algebraic sufficient
condition for the P-selective sets to have a linear upper bound (which thus
would match the existing lower bound) on their deterministic advice complexity:
If all P-selective sets are associatively P-selective then the deterministic
advice complexity of the P-selective sets is linear. The weakest previously
known sufficient condition was P=NP.
  We also establish related results for algebraic properties of, and advice
complexity of, the nondeterministically selective sets.


  During accretion, terrestrial bodies attain a wide range of thermal and
rotational states, which are accompanied by significant changes in physical
structure (size, shape, pressure and temperature profile, etc.). However,
variations in structure have been neglected in most studies of rocky planet
formation and evolution. Here, we present a new code, HERCULES, that solves for
the equilibrium structure of planets as a series of overlapping
constant-density spheroids. Using HERCULES and a smoothed particle
hydrodynamics code, we show that Earth-like bodies display a dramatic range of
morphologies. For any rotating planetary body, there is a thermal limit beyond
which the rotational velocity at the equator intersects the Keplerian orbital
velocity. Beyond this corotation limit (CoRoL), a hot planetary body forms a
structure, which we name a synestia, with a corotating inner region connected
to a disk-like outer region. By analyzing calculations of giant impacts and
models of planet formation, we show that typical rocky planets are
substantially vaporized multiple times during accretion. For the expected
angular momentum of growing planets, a large fraction of post-impact bodies
will exceed the CoRoL and form synestias. The common occurrence of hot,
rotating states during accretion has major implications for planet formation
and the properties of the final planets. In particular, the structure of
post-impact bodies influences the physical processes that control accretion,
core formation and internal evolution. Synestias also lead to new mechanisms
for satellite formation. Finally, the wide variety of possible structures for
terrestrial bodies also expands the mass-radius range for rocky exoplanets.


  We review some connections between quantum information and statistical
mechanics. We focus on three sets of results for classical spin models. First,
we show that the partition function of all classical spin models (including
models in different dimensions, different types of many-body interactions,
different symmetries, etc) can be mapped to the partition function of a single
model. Second, we give efficient quantum algorithms to estimate the partition
function of various classical spin models, such as the Ising or the Potts
model. The proofs of these two results are based on a mapping from partition
functions to quantum states and to quantum circuits, respectively. Finally, we
show how classical spin models can be used to describe certain fluctuating
lattices appearing in models of discrete quantum gravity.


  Robots with increasing autonomy progress our space exploration capabilities,
particularly for in-situ exploration and sampling to stand in for human
explorers. Currently, humans drive robots to meet scientific objectives, but
depending on the robot's location, the exchange of information and driving
commands between the human operator and robot may cause undue delays in mission
fulfillment. An autonomous robot encoded with a scientific objective and an
exploration strategy incurs no communication delays and can fulfill missions
more quickly. Active learning algorithms offer this capability of intelligent
exploration, but the underlying model structure varies the performance of the
active learning algorithm in accurately forming an understanding of the
environment. In this paper, we investigate the performance differences between
active learning algorithms driven by Gaussian processes or Bayesian neural
networks for exploration strategies encoded on agents that are constrained in
their trajectories, like planetary surface rovers. These two active learning
strategies were tested in a simulation environment against science-blind
strategies to predict the spatial distribution of a variable of interest along
multiple datasets. The performance metrics of interest are model accuracy in
root mean squared (RMS) error, training time, model convergence, total distance
traveled until convergence, and total samples until convergence. Active
learning strategies encoded with Gaussian processes require less computation to
train, converge to an accurate model more quickly, and propose trajectories of
shorter distance, except in a few complex environments in which Bayesian neural
networks achieve a more accurate model in the large data regime due to their
more expressive functional bases. The paper concludes with advice on when and
how to implement either exploration strategy for future space missions.


  The notion of partial fidelities as invented recently by A.Uhlmann for pairs
of finite dimensional density matrices will be extended to the vN-algebraic
context and is considered and thoroughly discussed in detail from a
mathematical point of view. Especially, in the case of semifinite vN-algebras
formulae and estimates for the partial fidelity between the functionals of a
dense cone of inner derived normal positive linear forms are obtained. Also,
some generalities on the notion of fidelity in quantum physics are collected in
an appendix, and another system of mathematical axioms for fidelity over
density operators, which is based on the concept of relative majorization and
which is intimately related to the concept of complete positivity, is proposed.


  We explore the consequences of treating the X(3872) meson as a tetraquark
bound state. As dynamical framework we employ a relativistic constituent quark
model which includes infrared confinement in an effective way. We calculate the
hadronic decay widths of the observed channels. For reasonable values of the
size parameter of the X(3872) we find consistency with the available
experimental data.


  We construct analytic surface symplectomorphisms with unstable elliptic fixed
points; this solves a problem of Birkhoff (1927). More precisely, we construct
analytic symplectomorphisms of the sphere and of the disk which are transitive,
with respectively only 2 and 1 periodic points. This also solves problems of
proposed by Herman (1998), Fayad-Katok (2004) and Fayad-Krikorian (2018). To
establish these results, we introduce a principle that enables to realize, by
an analytic symplectomorphism, properties which are $C^0$-realizable by the
approximation by conjugacy method of Anosov-Katok.


  Let $\{G_n\}_1^{\infty}$ be a sequence of non-trivial finite groups. In this
paper, we study the properties of a random walk on the complete monomial group
$G_n\wr S_n$ generated by the elements of the form
$(\text{e},\dots,\text{e},g;\text{id})$ and
$(\text{e},\dots,\text{e},g^{-1},\text{e},\dots,\text{e},g;(i,n))$ for $g\in
G_n,\;1\leq i< n$. We call this the warp-transpose top with random shuffle on
$G_n\wr S_n$. We find the spectrum of the transition probability matrix for
this shuffle. We prove that the mixing time for this shuffle is $O\left(n\log
n+\frac{1}{2}n\log (|G_n|-1)\right)$. We show that this shuffle exhibits
$\ell^2$-cutoff at $n\log n+\frac{1}{2}n\log (|G_n|-1)$ and total variation
cutoff at $n\log n$.


  We give an estimate of the Gauss curvature for minimal surfaces in ${\mathbb
R}^m$ whose Gauss map omits more than $m(m+1)/2$ hyperplanes in ${\mathbb
P}^{m-1}({\mathbb C})$.


  To bridge the gaps between topology-aware Graph Neural Networks (GNNs) and
inference-efficient Multi-Layer Perceptron (MLPs), GLNN proposes to distill
knowledge from a well-trained teacher GNN into a student MLP. Despite their
great progress, comparatively little work has been done to explore the
reliability of different knowledge points (nodes) in GNNs, especially their
roles played during distillation. In this paper, we first quantify the
knowledge reliability in GNN by measuring the invariance of their information
entropy to noise perturbations, from which we observe that different knowledge
points (1) show different distillation speeds (temporally); (2) are
differentially distributed in the graph (spatially). To achieve reliable
distillation, we propose an effective approach, namely Knowledge-inspired
Reliable Distillation (KRD), that models the probability of each node being an
informative and reliable knowledge point, based on which we sample a set of
additional reliable knowledge points as supervision for training student MLPs.
Extensive experiments show that KRD improves over the vanilla MLPs by 12.62%
and outperforms its corresponding teacher GNNs by 2.16% averaged over 7
datasets and 3 GNN architectures.


  The specific heat of the perovskite manganite La0.78Pb0.22MnO3-d was measured
from 0.5 to 25 K. The results yield values of the electronic density of states,
the Debye temperature, and the spin-wave stiffness constant of the compound.
The magnetic contribution was found to be consistent with the existence of a
gap in the spin-wave spectrum, and a phonon term in T^5 was needed to fit the
data.


  We give a classification result for a certain class of $C^{*}$-algebras
$\mathfrak{A}$ over a finite topological space $X$ in which there exists an
open set $U$ of $X$ such that $U$ separates the finite and infinite
subquotients of $\mathfrak{A}$. We will apply our results to $C^{*}$-algebras
arising from graphs.


  Maybe not. We identify and analyse errors in the popular Massive Multitask
Language Understanding (MMLU) benchmark. Even though MMLU is widely adopted,
our analysis demonstrates numerous ground truth errors that obscure the true
capabilities of LLMs. For example, we find that 57% of the analysed questions
in the Virology subset contain errors. To address this issue, we introduce a
comprehensive framework for identifying dataset errors using a novel error
taxonomy. Then, we create MMLU-Redux, which is a subset of 3,000 manually
re-annotated questions across 30 MMLU subjects. Using MMLU-Redux, we
demonstrate significant discrepancies with the model performance metrics that
were originally reported. Our results strongly advocate for revising MMLU's
error-ridden questions to enhance its future utility and reliability as a
benchmark. Therefore, we open up MMLU-Redux for additional annotation
https://huggingface.co/datasets/edinburgh-dawg/mmlu-redux.


  We study centralizer clones of finite lattices and semilattices. For
semilattices, we give two characterizations of the centralizer and also derive
formulas for the number of operations of a given essential arity in the
centralizer. We also characterize operations in the centralizer clone of a
distributive lattice, and we prove that the essential arity of operations in
the centralizer is bounded for every finite (possibly nondistributive) lattice.
Using these results, we present a simple derivation for the centralizers of
clones of Boolean functions.


  Quantum Hall Effects (QHEs) on the complex Grassmann manifolds
$\mathbf{Gr}_2(\mathbb{C}^N)$ are formulated. We set up the Landau problem in
$\mathbf{Gr}_2(\mathbb{C}^N)$ and solve it using group theoretical techniques
and provide the energy spectrum and the eigenstates in terms of the $SU(N)$
Wigner ${\cal D}$-functions for charged particles on
$\mathbf{Gr}_2(\mathbb{C}^N)$ under the influence of abelian and non-abelian
background magnetic monopoles or a combination of these thereof. In particular,
for the simplest case of $\mathbf{Gr}_2(\mathbb{C}^4)$ we explicitly write down
the $U(1)$ background gauge field as well as the single and many-particle
eigenstates by introducing the Pl\"{u}cker coordinates and show by calculating
the two-point correlation function that the Lowest Landau Level (LLL) at
filling factor $\nu =1$ forms an incompressible fluid. Our results are in
agreement with the previous results in the literature for QHE on ${\mathbb
C}P^N$ and generalize them to all $\mathbf{Gr}_2(\mathbb{C}^N)$ in a suitable
manner. Finally, we heuristically identify a relation between the $U(1)$ Hall
effect on $\mathbf{Gr}_2(\mathbb{C}^4)$ and the Hall effect on the odd sphere
$S^5$, which is yet to be investigated in detail, by appealing to the already
known analogous relations between the Hall effects on ${\mathbb C}P^3$ and
${\mathbb C}P^7$ and those on the spheres $S^4$ and $S^8$, respectively.


  We investigate the electronic properties and electron correlations of the
bipolaron formed by the electron-hole excitations in the presence of
Yukawa-type coupling (between nonrelativistic fermions) in three spatial
dimension. The electron-hole excitation, which is necessary to the formation of
bipolaron, leads to imaginary particle-hole order parameter, and provide finite
boson field mass to the single-polaron dispersion in a broken-symmetry phase.
We found that the bipolaron exhibits fermi-liquid features as long as the
long-range strong interaction is suppressed, and it behave differently compared
to the single-polaron. The bosonic momentum determines the mass of boson field
propagator and the gap function, and it also related to the self-energies and
the single-particle Green's functions. The Thouless criterion is also used
during the calculation of gap equation at critical temperature (which become
lower in weak-coupling regime), which corresponds to the pole (instability) of
the pair propagator in zero center-of-mass freamwork. The mean field term and
the bosonic fluctuation-induced contribution to free energy of bipolaron are
also studied.


  Close encounters of stars to the Sun could affect life on Earth through
gravitational perturbations of comets in the Oort cloud or exposure to ionizing
radiation. By integrating orbits through the Galactic potential, I identify
which of 33 million stars in Gaia DR3 with complete phase space information
come close to the Sun. 61 stars formally approach within 1 pc, although there
is high confidence in only 42 (two thirds) of these, the rest being spurious
measurements or (in) binary systems. Most of the stars will encounter within
the past or future 6 Myr; earlier/later encounters are less common due to the
magnitude limit of the Gaia radial velocities (RVs). Several close encountering
stars are identified for the first time, and the encounter times, distances,
and velocities of previously known close encounters are determined more
precisely on account of the significantly improved precision of Gaia DR3 over
earlier releases. The K7 dwarf Gl 710 remains the closest known encounter, with
an estimated (median) encounter distance of 0.0636 pc (90% confidence interval
0.0595-0.0678 pc) to take place in 1.3 Myr. The new second closest encounter
took place 2.8 Myr ago: this was the G3 dwarf HD 7977, now 76 pc away, which
approached within less than 0.05 pc of the Sun with a probability of one third.
The apparent close encounter of the white dwarf UPM J0812-352 is probably
spurious due to an incorrect RV in Gaia DR3.


  A transformation of the form x to iy; x,y in R, or an equivalent similarity
transformation with a metric operator $\eta$ are shown to transform
non-Hermitian PT-symmetric Hamiltonians into Hermitian partner Hamiltonians in
Hilbert space. Isospectrality and mass signature are discussed.


  Damage assessment after natural disasters is needed to distribute aid and
forces to recovery from damage dealt optimally. This process involves acquiring
satellite imagery for the region of interest, localization of buildings, and
classification of the amount of damage caused by nature or urban factors to
buildings. In case of natural disasters, this means processing many square
kilometers of the area to judge whether a particular building had suffered from
the damaging factors.
  In this work, we develop a computational approach for an automated comparison
of the same region's satellite images before and after the disaster, and
classify different levels of damage in buildings. Our solution is based on
Siamese neural networks with encoder-decoder architecture. We include an
extensive ablation study and compare different encoders, decoders, loss
functions, augmentations, and several methods to combine two images. The
solution achieved one of the best results in the Computer Vision for Building
Damage Assessment competition.


  In this pioneering study, inspired by AutoGPT, the state-of-the-art
open-source application based on the GPT-4 large language model, we develop a
novel tool called AD-AutoGPT which can conduct data collection, processing, and
analysis about complex health narratives of Alzheimer's Disease in an
autonomous manner via users' textual prompts. We collated comprehensive data
from a variety of news sources, including the Alzheimer's Association, BBC,
Mayo Clinic, and the National Institute on Aging since June 2022, leading to
the autonomous execution of robust trend analyses, intertopic distance maps
visualization, and identification of salient terms pertinent to Alzheimer's
Disease. This approach has yielded not only a quantifiable metric of relevant
discourse but also valuable insights into public focus on Alzheimer's Disease.
This application of AD-AutoGPT in public health signifies the transformative
potential of AI in facilitating a data-rich understanding of complex health
narratives like Alzheimer's Disease in an autonomous manner, setting the
groundwork for future AI-driven investigations in global health landscapes.


  Recently WMAP and BOOMERanG experiments have set stringent constraints on the
polarization angle of photons propagating in an expanding universe: $\Delta
\alpha = (-2.4 \pm 1.9)^\circ$. The polarization of the Cosmic Microwave
Background radiation (CMB) is reviewed in the context of nonlinear
electrodynamics (NLED). We compute the polarization angle of photons
propagating in a cosmological background with planar symmetry. For this
purpose, we use the Pagels-Tomboulis (PT) Lagrangian density describing NLED,
which has the form $L\sim (X/\Lambda^4)^{\delta - 1}\; X $, where $X=1/4
F_{\alpha\beta} F^{\alpha \beta}$, and $\delta$ the parameter featuring the
non-Maxwellian character of the PT nonlinear description of the electromagnetic
interaction. After looking at the polarization components in the plane
orthogonal to the ($x$)-direction of propagation of the CMB photons, the
polarization angle is defined in terms of the eccentricity of the universe, a
geometrical property whose evolution on cosmic time (from the last scattering
surface to the present) is constrained by the strength of magnetic fields over
extragalactic distances.


  This paper is intended as an introductory survey of a newly emerging field: a
topological approach to the study of locally finite graphs that crucially
incorporates their ends. Topological arcs and circles, which may pass through
ends, assume the role played in finite graphs by paths and cycles.
  This approach has made it possible to extend to locally finite graphs many
classical theorems of finite graph theory that do not extend verbatim. The
shift of paradigm it proposes is thus as much an answer to old questions as a
source of new ones; many concrete problems of both types are suggested in the
paper.
  This paper attempts to provide an entry point to this field for readers that
have not followed the literature that has emerged in the last 10 years or so.
It takes them on a quick route through what appear to be the most important
lasting results, introduces them to key proof techniques, identifies the most
promising open problems, and offers pointers to the literature for more detail.


  Transmit power control (TPC) is a key mechanism for managing interference,
energy utilization, and connectivity in wireless systems. In this paper, we
propose a simple low-complexity TPC algorithm based on the deep unfolding of
the iterative projected gradient descent (PGD) algorithm into layers of a deep
neural network and learning the step-size parameters. An unsupervised learning
method with either online learning or offline pretraining is applied for
optimizing the weights of the DNN. Performance evaluation in dense
device-to-device (D2D) communication scenarios showed that the proposed method
can achieve better performance than the iterative algorithm with more than a
factor of 2 lower number of iterations.


  It is shown that, under the Wentzel-Kramers-Brillouin approximation
conditions, using the Foldy-Wouthuysen representation allows the problem of
finding a classical limit of relativistic quantum mechanical equations to be
reduced to the replacement of operators in the Hamiltonian and quantum
mechanical equations of motion by the respective classical quantities.


  The influence of vector fields on the origin of a classical space in quantum
cosmologies and on the possible compactification process in multidimensional
gravity is investigated. It is shown that all general features of the
transition between classical and quantum regimes of the evolution can be
obtained within the simplest Bianchi-I model for arbitrary number of
dimensions. It is shown that the classical space appears when the horizon size
reaches the smallest of characteristic scales (the characteristic scale of
inhomogeneity or a scale associated with vector fields). In multidimensional
case the presence of vector fields completely removes the initial stage of the
compactification process which takes place in the case of vacuum models.


  The state price density of a basket, even under uncorrelated Black-Scholes
dynamics, does not allow for a closed from density. (This may be rephrased as
statement on the sum of lognormals and is especially annoying for such are used
most frequently in Financial and Actuarial Mathematics.) In this note we
discuss short time and small volatility expansions, respectively. The method
works for general multi-factor models with correlations and leads to the
analysis of a system of ordinary (Hamiltonian) differential equations.
Surprisingly perhaps, even in two asset Black-Scholes situation (with its flat
geometry), the expansion can degenerate at a critical (basket) strike level; a
phenomena which seems to have gone unnoticed in the literature to date.
Explicit computations relate this to a phase transition from a unique to more
than one "most-likely" paths (along which the diffusion, if suitably
conditioned, concentrates in the afore-mentioned regimes). This also provides a
(quantifiable) understanding of how precisely a presently out-of-money basket
option may still end up in-the-money.


  In view to scrutinize the idea that nonlocal modifications of General
Relativity could dynamically address the dark energy problem, we investigate
the evolution of the Universe at infrared scales as an Infinite Derivative
Gravity model of the Ricci scalar, without introducing the cosmological
constant $\Lambda$ or any scalar field. The accelerated expansion of the late
Universe is shown to be compatible with the emergence of nonlocal gravitational
effects at sufficiently low energies. A technique for circumventing the
mathematical complexity of the nonlocal cosmological equations is developed
and, after drawing a connection with the Starobinsky gravity, verifiable
predictions are considered, like a possible decreasing in the strength of the
effective gravitational constant. In conclusion, the emergence of nonlocal
gravity corrections at given scales could be an efficient mechanism to address
the dark energy problem.


  Foundation models are becoming the dominant deep learning technologies.
Pretraining a foundation model is always time-consumed due to the large scale
of both the model parameter and training dataset. Besides being
computing-intensive, the training process is extremely memory-intensive and
communication-intensive. These features make it necessary to apply 3D
parallelism, which integrates data parallelism, pipeline model parallelism and
tensor model parallelism, to achieve high training efficiency.
  To achieve this goal, some custom software frameworks such as Megatron-LM and
DeepSpeed are developed. However, current 3D parallelism frameworks still meet
two issues: i) they are not transparent to model developers, which need to
manually modify the model to parallelize training. ii) their utilization of
computation, GPU memory and network bandwidth are not sufficient. We propose
Merak, an automated 3D parallelism deep learning training framework with high
resource utilization. Merak automatically deploys with an automatic model
partitioner, which uses a graph sharding algorithm on a proxy representation of
the model. Merak also presents the non-intrusive API for scaling out foundation
model training with minimal code modification. In addition, we design a
high-performance 3D parallel runtime engine in Merak. It uses several
techniques to exploit available training resources, including shifted critical
path pipeline schedule that brings a higher computation utilization,
stage-aware recomputation that makes use of idle worker memory, and
sub-pipelined tensor model parallelism that overlaps communication and
computation. Experiments on 64 GPUs show Merak can speedup the training
performance over the state-of-the-art 3D parallelism frameworks of models with
1.5, 2.5, 8.3, and 20 billion parameters by up to 1.42X, 1.39X, 1.43X, and
1.61X, respectively.


  Emission characteristics of quantum-dot micropillar lasers (QDMLs) are
located at the intersection of nanophotonics and nonlinear dynamics, which
provides an ideal platform for studying the optical interface between classical
and quantum systems. In this work, a noise-induced bimodal QDML with orthogonal
dual-mode outputs is modeled, and nonlinear dynamics, stochastic mode jumping
and quantum statistics with the variation of stochastic noise intensity are
investigated. Noise-induced effects lead to the emergence of two intensity
bifurcation points for the strong and the weak mode, and the maximum output
power of the strong mode becomes larger as the noise intensity increases. The
anti-correlation of the two modes reaches the maximum at the second intensity
bifurcation point. The dual-mode stochastic jumping frequency and effective
bandwidth can exceed 100 GHz and 30 GHz under the noise-induced effect.
Moreover, the noise-induced photon correlations of both modes simultaneously
exhibit super-thermal bunching effects ($g^{(2)}(0)>2$) in the low injection
current region. The $g^{(2)}(0)$-value of the strong mode can reach over 6 in
the high injection current region. Photon bunching ($g^{(2)}(0)>1$) of both
modes is observed over a wide range of noise intensities and injection
currents. In the presence of the noise-induced effect, the photon number
distribution of the strong or the weak mode is a mixture of Bose-Einstein and
Poisson distributions. As the noise intensity increases, the photon number
distribution of the strong mode is dominated by the Bose-Einstein distribution,
and the proportion of the Poisson distribution is increased in the high
injection current region, while that of the weak mode is reduced. Our results
contribute to the development preparation of super-bunching quantum integrated
light sources for improving the spatiotemporal resolution of quantum sensing
measurements.


  The control of electric currents in solids is at the origin of the modern
electronics revolution which has driven our daily life since the second half of
20th century. Surprisingly, to date, there is no thermal analog for a control
of heat flux. Here, we summarize the very last developments carried out in this
direction to control heat exchanges by radiation both in near and far-field in
complex architecture networks.


  Human mobility networks can reveal insights into resilience phenomena, such
as population response to, impacts on, and recovery from crises. The majority
of human mobility network resilience characterizations, however, focus mainly
on macroscopic network properties; little is known about variation in measured
resilience characteristics (i.e., the extent of impact and recovery duration)
across macroscopic, substructure (motif), and microscopic mobility scales. To
address this gap, in this study, we examine the human mobility network in eight
parishes in Louisiana (USA) impacted by the 2021 Hurricane Ida. We constructed
human mobility networks using location-based data and examined three sets of
measures: (1) macroscopic measures, such as network density, giant component
size, and modularity; (2) substructure measures, such motif distribution; and
(3) microscopic mobility measures, such as the radius of gyration and average
travel distance. To determine the extent of impact and duration of recovery,
for each measure, we established the baseline values and examined the
fluctuation of measures during the perturbation caused by Hurricane Ida. The
results reveal the variation of impact extent and recovery duration obtained
from different sets of measures at different scales. Macroscopic measures, such
as giant components, tend to recover more quickly than substructure and
microscopic measures. In fact, microscopic measures tend to recover more slowly
than measures in other scales. These findings suggest that resilience
characteristics in human mobility networks are scale-variant, and thus, a
single measure at a particular scale may not be representative of the
perturbation impacts and recovery duration in the network as a whole. These
results spotlight the need to use measures at different scales to properly
characterize resilience in human mobility networks.