  Let $G$ be a group. We give a categorical definition of the $G$-equivariant
$\alpha$-induction associated with a given $G$-equivariant Frobenius algebra in
a $G$-braided multitensor category, which generalizes the $\alpha$-induction
for $G$-twisted representations of conformal nets. For a given $G$-equivariant
Frobenius algebra in a spherical $G$-braided fusion category, we construct a
$G$-equivariant Frobenius algebra, which we call a $G$-equivariant
$\alpha$-induction Frobenius algebra, in a suitably defined category called
neutral double. This construction generalizes Rehren's construction of
$\alpha$-induction Q-systems. Finally, we define the notion of the
$G$-equivariant full center of a $G$-equivariant Frobenius algebra in a
spherical $G$-braided fusion category and show that it indeed coincides with
the corresponding $G$-equivariant $\alpha$-induction Frobenius algebra, which
generalizes a theorem of Bischoff, Kawahigashi and Longo.


  By balancing the average energy gap with its typical change due to mutations
for protein-like heteropolymers with M residues, we show that native states are
unstable to mutations on a scale M* ~ (lambda/sigma_mu)^(1/zeta_s), where
lambda is the dispersion in the interaction free energies and sigma_mu their
typical change. Theoretical bounds and numerical estimates (based on complete
enumeration on four lattices) of the instability exponent zeta_s are given. Our
analysis suggests that a limiting size of single-domain proteins should exist,
and leads to the prediction that small proteins are insensitive to random
mutations.


  The effective potential of quantized scalar field on fuzzy sphere is
evaluated to the two-loop level. We see that one-loop potential behaves like
that in the commutative sphere and the Coleman-Weinberg mechanism of the
radiatively symmetry breaking could be also shown in the fuzzy sphere system.
In the two-loop level, we use the heavy-mass approximation and the
high-temperature approximation to perform the evaluations. The results show
that both of the planar and nonplanar Feynman diagrams have inclinations to
restore the symmetry breaking in the tree level. However, the contributions
from planar diagrams will dominate over those from nonplanar diagrams by a
factor N^2. Thus, at heavy-mass limit or high-temperature system the quantum
field on the fuzzy sphere will behave like those on the commutative sphere. We
also see that there is a drastic reduction of the degrees of freedom in the
nonplanar diagrams when the particle wavelength is smaller than the
noncommutativity scale.


  The orbital superposition method originally developed by Schwarzschild (1979)
is used to study the dynamics of growth of a black hole and its host galaxy,
and has uncovered new relationships between the galaxy's global
characteristics. Scientists are specifically interested in finding optimal
parameter choices for this model that best match physical measurements along
with quantifying the uncertainty of such procedures. This renders a statistical
calibration problem with multivariate outcomes. In this article, we develop a
Bayesian method for calibration with multivariate outcomes using orthogonal
bias functions thus ensuring parameter identifiability. Our approach is based
on projecting the posterior to an appropriate space which allows the user to
choose any nonparametric prior on the bias function(s) instead of having to
model it (them) with Gaussian processes. We develop a functional projection
approach using the theory of Hilbert spaces. A finite-dimensional analogue of
the projection problem is also considered. We illustrate the proposed approach
using a BART prior and apply it to calibrate the Schwarzschild model
illustrating how a multivariate approach may resolve discrepancies resulting
from a univariate calibration.


  Environment, Social, and Governance (ESG) KPIs assess an organization's
performance on issues such as climate change, greenhouse gas emissions, water
consumption, waste management, human rights, diversity, and policies. ESG
reports convey this valuable quantitative information through tables.
Unfortunately, extracting this information is difficult due to high variability
in the table structure as well as content. We propose Statements, a novel
domain agnostic data structure for extracting quantitative facts and related
information. We propose translating tables to statements as a new supervised
deep-learning universal information extraction task. We introduce SemTabNet - a
dataset of over 100K annotated tables. Investigating a family of T5-based
Statement Extraction Models, our best model generates statements which are 82%
similar to the ground-truth (compared to baseline of 21%). We demonstrate the
advantages of statements by applying our model to over 2700 tables from ESG
reports. The homogeneous nature of statements permits exploratory data analysis
on expansive information found in large collections of ESG reports.


  Finding min $s$-$t$ cuts in graphs is a basic algorithmic tool with
applications in image segmentation, community detection, reinforcement
learning, and data clustering. In this problem, we are given two nodes as
terminals, and the goal is to remove the smallest number of edges from the
graph so that these two terminals are disconnected. We study the complexity of
differential privacy for the min $s$-$t$ cut problem and show nearly tight
lower and upper bounds where we achieve privacy at no cost for running time
efficiency. We also develop a differentially private algorithm for the multiway
$k$-cut problem, in which we are given $k$ nodes as terminals that we would
like to disconnect. As a function of $k$, we obtain privacy guarantees that are
exponentially more efficient than applying the advanced composition theorem to
known algorithms for multiway $k$-cut. Finally, we empirically evaluate the
approximation of our differentially private min $s$-$t$ cut algorithm and show
that it almost matches the quality of the output of non-private ones.


  This paper presents an abstract Isaacs property that involves the Fourier
transform for fusion rings, which may be non-commutative, thus expanding upon
the commutative version described in [12]. A categorical version of this
property was subsequently introduced in [8] for any spherical fusion category,
matching with our abstract version in the pseudo-unitary case. We demonstrate
that the Isaacs property occupies a distinct position, falling between the
integrality of structure constants and the 1-Frobenius properties, in the
commutative case. We show that the Extended Haagerup fusion categories, denoted
as EHi, do not satisfy the Isaacs property. This finding provides a negative
response to [8, Question 5.8], refutes [12, Conjecture 2.5], and recovers that
EH1 lacks a braiding structure.


  The issue of constructing a risk minimizing hedge under an additional
almost-surely type constraint on the shortfall profile is examined. Several
classical risk minimizing problems are adapted to the new setting and solved.
In particular, the bankruptcy threat of optimal strategies appearing in the
classical risk minimizing setting is ruled out. The existence and concrete
forms of optimal strategies in a general semimartingale market model with the
use of conditional statistical tests are proven. The well known quantile
hedging method as well as the classical Neyman-Pearson lemma are generalized.
Optimal hedging strategies with shortfall constraints in the Black-Scholes and
exponential Poisson model are explicitly determined.


  We introduce a new approach for multiscale 3Dsemantic scene completion from
voxelized sparse 3D LiDAR scans. As opposed to the literature, we use a 2D UNet
backbone with comprehensive multiscale skip connections to enhance feature
flow, along with 3D segmentation heads. On the SemanticKITTI benchmark, our
method performs on par on semantic completion and better on occupancy
completion than all other published methods -- while being significantly
lighter and faster. As such it provides a great performance/speed trade-off for
mobile-robotics applications. The ablation studies demonstrate our method is
robust to lower density inputs, and that it enables very high speed semantic
completion at the coarsest level. Our code is available at
https://github.com/cv-rits/LMSCNet.


  Virtual labs allow researchers to design high-throughput and macro-level
experiments that are not feasible in traditional in-person physical lab
settings. Despite the increasing popularity of online research, researchers
still face many technical and logistical barriers when designing and deploying
virtual lab experiments. While several platforms exist to facilitate the
development of virtual lab experiments, they typically present researchers with
a stark trade-off between usability and functionality. We introduce Empirica: a
modular virtual lab that offers a solution to the usability-functionality
trade-off by employing a "flexible defaults" design strategy. This strategy
enables us to maintain complete "build anything" flexibility while offering a
development platform that is accessible to novice programmers. Empirica's
architecture is designed to allow for parameterizable experimental designs,
reusable protocols, and rapid development. These features will increase the
accessibility of virtual lab experiments, remove barriers to innovation in
experiment design, and enable rapid progress in the understanding of
distributed human computation.


  Experimental data bases are typically very large and high dimensional. To
learn from them requires to recognize important features (a pattern), often
present at scales different to that of the recorded data. Following the
experience collected in statistical mechanics and thermodynamics, the process
of recognizing the pattern (the learning process) can be seen as a dissipative
time evolution driven by entropy from a detailed level of description to less
detailed. This is the way thermodynamics enters machine learning. On the other
hand, reversible (typically Hamiltonian) evolution is propagation within the
levels of description, that is also to be recognized. This is how Poisson
geometry enters machine learning. Learning to handle free surface liquids and
damped rigid body rotation serves as an illustration.


  We construct a nerve from double categories into double
$(\infty,1)$-categories and show that it gives a right Quillen and
homotopically fully faithful functor between the model structure for weakly
horizontally invariant double categories and the model structure on
bisimplicial spaces for double $(\infty,1)$-categories seen as double Segal
objects in spaces complete in the horizontal direction. We then restrict the
nerve along a homotopical horizontal embedding of 2-categories into double
categories, and show that it gives a right Quillen and homotopically fully
faithful functor between Lack's model structure for 2-categories and the model
structure for 2-fold complete Segal spaces. We further show that Lack's model
structure is right-induced along this nerve from the model structure for 2-fold
complete Segal spaces.


  Suggestion of modifications of finite-dimensional QED models are proposed for
interpreting chemical reactions in terms of artificial atoms and molecules on
quantum dots placed in optical cavities. Moving both photons and atoms is
possible between the cavities. Super dark states of diatomic systems are
described, in which the motion of atoms between cavities is impossible due
quantum interference. Chemical processes with two level atoms and three level
atoms with lambda spectrum are schematically modeled by solving the single
quantum master equation with the Lindblad operators of photon leakage from the
cavity and influx into it; association and dissociation reactions then differ
only in the initial states. An example is given of the optical interpretation
of the transition of an electron from atom to atom in terms of the multilevel
Tavis-Cummings-Hubbard model with an estimate of the accuracy. Polyatomic
chemical reactions are too complex for accurate modeling. Our method of rough
interpretation helps to obtain their long-term results, for example, the form
of stationary states of reagents, such as dark and super dark states.


  This letter defines a physical bound based array figure of merit that
provides a tool to compare the performance of both single and multi-band array
antennas with respect to return-loss, thickness of the array over the
ground-plane, and scan-range. The result is based on a sum-rule result of
Rozanov-type for linear polarization. For single-band antennas it extends an
existing limit for a given fixed scan-angle to include the whole scan-range of
the array, as well as the unit-cell structure in the bound. The letter ends
with an investigation of the array figure of merit for some wideband and/or
wide-scan antennas with linear polarization. We find arrays with a figure of
merit >0.6 that empirically defines high-performance antennas with respect to
this measure.


  Early dark energy (EDE) is one of the most promising possibilities in order
to resolve the Hubble tension: the discrepancy between early and late-Universe
measurements of the Hubble constant. In this paper we propose a model of a
scalar field which can explain both EDE and late Dark Energy (DE) in a joined
manner without additional fine-tuning. The field features kinetic poles as with
alpha-attractors. Our model provides an injection of EDE near matter-radiation
equality, and redshifts away shortly after via free-fall, later refreezing to
become late-time DE at the present day. Using reasonable estimates of the
current constraints on EDE from the literature, we find that the parameter
space is narrow but viable. As such our model is readily falsifiable. In
contrast to other work in EDE, our model is non-oscillatory, which causes its
decay to be faster than that of the usual oscillatory EDE, thereby achieving
better agreement with observations.


  Loop closure can effectively correct the accumulated error in robot
localization, which plays a critical role in the long-term navigation of the
robot. Traditional appearance-based methods rely on local features and are
prone to failure in ambiguous environments. On the other hand, object
recognition can infer objects' category, pose, and extent. These objects can
serve as stable semantic landmarks for viewpoint-independent and non-ambiguous
loop closure. However, there is a critical object-level data association
problem due to the lack of efficient and robust algorithms.
  We introduce a novel object-level data association algorithm, which
incorporates IoU, instance-level embedding, and detection uncertainty,
formulated as a linear assignment problem. Then, we model the objects as TSDF
volumes and represent the environment as a 3D graph with semantics and
topology. Next, we propose a graph matching-based loop detection based on the
reconstructed 3D semantic graphs and correct the accumulated error by aligning
the matched objects. Finally, we refine the object poses and camera trajectory
in an object-level pose graph optimization.
  Experimental results show that the proposed object-level data association
method significantly outperforms the commonly used nearest-neighbor method in
accuracy. Our graph matching-based loop closure is more robust to environmental
appearance changes than existing appearance-based methods.


  We improve on a method to compute the fermion contribution to the vacuum
polarization energy of string-like configurations in a non-Abelian gauge
theory. We establish the new method by numerically verifying the invariance
under (a subset of) local gauge transformations. This also provides further
support for the use of spectral methods to compute vacuum polarization energies
in general. We confirm that the vacuum energy in the MS-bar renormalization
scheme is tiny as compared to the mass of the fluctuating fermion field.
Numerical results for the physical on-shell scheme are also presented.


  In this paper we present a numerical scheme for the approximation of singular
shock solutions of the Keyfitz-Kranzer model system. Consistence in the sense
of distributions is studied. As long as some numerical properties are verified
when the space step tends to 0, we prove that the scheme provides a numerical
solution that satisfies the equations in the sense of distributions with an
approximation that tends to 0 when h \rightarrow 0. We also show that this
scheme adapts to degenerate systems. This is illustrated by two examples: the
system presenting delta wave solutions originally studied by Korchinski and
another system studied by Keyfitz-Kranzer that models elasticity. Consistence
of the scheme in the sense of distributions is fully proved in the case of the
Korchinski model.


  In this note we study multivariate integration for permutation-invariant
functions from a certain Banach space E_{d,\alpha} of Korobov type in the worst
case setting. We present a lower error bound which particularly implies that in
dimension d every cubature rule which reduces the initial error necessarily
uses at least d+1 function values. Since this holds independently of the number
of permutation-invariant coordinates, this shows that the integration problem
can never be strongly polynomially tractable in this setting. Our assertions
generalize results due to Sloan and Wo\'zniakowski. Moreover, for large
smoothness parameters \alpha our bound can not be improved. Finally, we extend
our results to the case of permutation-invariant functions from Korobov-type
spaces equipped with product weights.
  Keywords: Permutation-invariance, Integration, Information complexity,
Tractability, Lower bounds


  We show that the proportionately spaced emission bands in the dynamic
spectrum of the Crab pulsar (Hankins T. H. & Eilek J. A., 2007, ApJ, 670, 693)
fit the oscillations of the square of a Bessel function whose argument exceeds
its order. This function has already been encountered in the analysis of the
emission from a polarization current with a superluminal distribution pattern:
a current whose distribution pattern rotates (with an angular frequency
$\omega$) and oscillates (with a frequency $\Omega>\omega$ differing from an
integral multiple of $\omega$) at the same time (Ardavan H., Ardavan A. &
Singleton J., 2003, J Opt Soc Am A, 20, 2137). Using the results of our earlier
analysis, we find that the dependence on frequency of the spacing and width of
the observed emission bands can be quantitatively accounted for by an
appropriate choice of the value of the single free parameter $\Omega/\omega$.
In addition, the value of this parameter, thus implied by Hankins & Eilek's
data, places the last peak in the amplitude of the oscillating Bessel function
in question at a frequency ($\sim\Omega^3/\omega^2$) that agrees with the
position of the observed ultraviolet peak in the spectrum of the Crab pulsar.
We also show how the suppression of the emission bands by the interference of
the contributions from differring polarizations can account for the differences
in the time and frequency signatures of the interpulse and the main pulse in
the Crab pulsar. Finally, we put the emission bands in the context of the
observed continuum spectrum of the Crab pulsar by fitting this broadband
spectrum (over 16 orders of magnitude of frequency) with that generated by an
electric current with a superluminally rotating distribution pattern.


  There is considered a connection with skew symmetric torsion on a
quasi-K\"ahler manifold with Norden metric. Some necessary and sufficient
conditions are derived for the corresponding curvature tensor to be
K\"ahlerian. In the case when this tensor is K\"ahlerian, some relations are
obtained between its scalar curvature and the scalar curvature of other
curvature tensors. Conditions are given for the considered manifolds to be
isotropic-K\"ahler.


  The quasi-two-dimensional electronic gas at the (111) SrTiO$_3$-based
heterostructure interfaces is described by a multi-band tight-binding model
providing electronic bands in agreement at low energies with photoemission
experiments. We analyze both the roles of the spin-orbit coupling and of the
trigonal crystal field effects. We point out the presence of a regime with
sizable strain where the band structure exhibits a Dirac cone whose features
are consistent with \textit{ab-initio} approaches. The combined effect of
spin-orbit coupling and trigonal strain gives rise to non-trivial spin and
orbital angular momenta patterns in the Brillouin zone and to quantum spin Hall
effect by opening a gap at the Dirac cone. The system can switch from a
conducting to a topological insulating state \textit{via} modification of
trigonal strain within a parameter range which is estimated to be
experimentally achievable.


  This paper introduces EcoPull, a sustainable Internet of Things (IoT)
framework empowered by tiny machine learning (TinyML) models for fetching
images from wireless visual sensor networks. Two types of learnable TinyML
models are installed in the IoT devices: i) a behavior model and ii) an image
compressor model. The first filters out irrelevant images for the current task,
reducing unnecessary transmission and resource competition among the devices.
The second allows IoT devices to communicate with the receiver via latent
representations of images, reducing communication bandwidth usage. However,
integrating learnable modules into IoT devices comes at the cost of increased
energy consumption due to inference. The numerical results show that the
proposed framework can save > 70% energy compared to the baseline while
maintaining the quality of the retrieved images at the ES.


  Membrane viscosity is known to play a central role in the transient dynamics
of isolated viscoelastic capsules by decreasing their deformation, inducing
shape oscillations and reducing the loading time, that is, the time required to
reach the steady-state deformation. However, for dense suspensions of capsules,
our understanding of the influence of the membrane viscosity is minimal. In
this work, we perform a systematic numerical investigation based on coupled
immersed boundary -- lattice Boltzmann (IB-LB) simulations of viscoelastic
spherical capsule suspensions in the non-inertial regime. We show the effect of
the membrane viscosity on the transient dynamics as a function of volume
fraction and capillary number. Our results indicate that the influence of
membrane viscosity on both deformation and loading time strongly depends on the
volume fraction in a non-trivial manner: dense suspensions with large surface
viscosity are more resistant to deformation but attain loading times that are
characteristic of capsules with no surface viscosity, thus opening the
possibility to obtain richer combinations of mechanical features.


  Let $p$ be a prime and let $G$ be a finite group such that the smallest prime
that divides $|G|$ is $p$. We find sharp bounds, depending on $p$, for the
commuting probability and the average character degree to guarantee that $G$ is
nilpotent or supersolvable.


  Tile \(\mathbb{R}^2\) into disjoint unit squares \(\{S_k\}_{k \geq 0}\) with
the origin being the centre of \(S_0\) and say that \(S_i\) and \(S_j\) are
star adjacent if they share a corner and plus adjacent if they share an edge.
Every square is either vacant or occupied. Star and plus connected components
containing the origin have been previously studied using unicoherence and
interface graphs. In this paper, we use the structure of the outermost
boundaries derived in Ganesan (2015) to alternately obtain duality between star
and plus connected components in the following sense: There is a plus connected
cycle of vacant squares attached to surrounding the finite star connected
component containing the origin. There is a star connected cycle of vacant
squares attached to and surrounding the finite plus connected component
containing the origin.


  We examine the conditions under which binary and multiple stars may form out
of turbulent molecular cloud cores using high resolution 3-D, adaptive mesh
refinement (AMR) hydrodynamics (Truelove et al., 1997, 1998; Klein, 1999). We
argue that previous conclusions on the conditions for cloud fragmentation have
limited applicability, since they did not allow for the nonlinear density and
velocity perturbations that are ubiquitous in molecular cloud cores. Over the
past year, we have begun to simulate the evolution of marginally stable,
turbulent cores. These models have radii, masses, density contrasts, turbulent
linewidths, and projected velocity gradients consistent with observations of
low-mass molecular cloud cores. Our models are evolved in time under
self-gravitational hydrodynamics with AMR using a barotropic equation of state
that models the transition from an isothermal to an adiabatic equation of
state. We examine several properties of the resulting protostellar fragments
and discuss the qualitative nature of the fragmentation process in realistic
cloud cores: the transition from single to binary and multiple stars; the
formation of misaligned binary systems; and the role played by filament
formation in the formation of stars.


  We use cosmological SPH simulations to study the kinematic signatures of cool
gas accretion onto a pair of well-resolved galaxy halos. Cold-flow streams and
gas-rich mergers produce a circum-galactic component of cool gas that generally
orbits with high angular momentum about the galaxy halo before falling in to
build the disk. This signature of cosmological accretion should be observable
using background-object absorption line studies as features that are offset
from the galaxy's systemic velocity by ~100 km/s. Accreted gas typically
co-rotates with the central disk in the form of a warped, extended cold flow
disk, such that the observed velocity offset is in the same direction as galaxy
rotation, appearing in sight lines that avoid the galactic poles. This
prediction provides a means to observationally distinguish accreted gas from
outflow gas: the accreted gas will show large one-sided velocity offsets in
absorption line studies while radial/bi-conical outflows will not (except
possibly in special polar projections). This rotation signature has already
been seen in studies of intermediate redshift galaxy-absorber pairs; we suggest
that these observations may be among the first to provide indirect
observational evidence for cold accretion onto galactic halos. Cold mode halo
gas typically has ~3-5 times more specific angular momentum than the dark
matter. The associated cold mode disk configurations are likely related to
extended HI/XUV disks seen around galaxies in the local universe. The fraction
of galaxies with extended cold flow disks and associated offset absorption-line
gas should decrease around bright galaxies at low redshift, as cold mode
accretion dies out.


  It has been long known that sparsity is an effective inductive bias for
learning efficient representation of data in vectors with fixed dimensionality,
and it has been explored in many areas of representation learning. Of
particular interest to this work is the investigation of the sparsity within
the VAE framework which has been explored a lot in the image domain, but has
been lacking even a basic level of exploration in NLP. Additionally, NLP is
also lagging behind in terms of learning sparse representations of large units
of text e.g., sentences. We use the VAEs that induce sparse latent
representations of large units of text to address the aforementioned
shortcomings. First, we move in this direction by measuring the success of
unsupervised state-of-the-art (SOTA) and other strong VAE-based sparsification
baselines for text and propose a hierarchical sparse VAE model to address the
stability issue of SOTA. Then, we look at the implications of sparsity on text
classification across 3 datasets, and highlight a link between performance of
sparse latent representations on downstream tasks and its ability to encode
task-related information.


  We draw attention on the fact that the Riccati-Pad\'e method developed some
time ago enables the accurate calculation of bound-state eigenvalues as well as
of resonances embedded either in the continuum or in the discrete spectrum. We
apply the approach to several one-dimensional models that exhibit different
kind of spectra. In particular we test a WKB formula for the imaginary part of
the resonance in the discrete spectrum of a three-well potential.


  In this paper, we associate the quantum toroidal algebra $\mathcal{E}_N$ of
type $\mathfrak{gl}_N$ with quantum vertex algebra through equivariant
$\phi$-coordinated quasi modules. More precisely, for every $\ell\in
\mathbb{C}$, by deforming the universal affine vertex algebra of
$\mathfrak{sl}_\infty$, we construct an $\hbar$-adic quantum $\Z$-vertex
algebra $V_{\widehat{\mathfrak{sl}}_{\infty},\hbar}(\ell,0)$. Then we prove
that the category of restricted $\mathcal{E}_N$-modules of level $\ell$ is
canonically isomorphic to that of equivariant $\phi$-coordinated quasi
$V_{\widehat{\mathfrak{sl}}_{\infty},\hbar}(\ell,0)$-modules.


  Pull Request (PR) is the main method for code contributions from the external
contributors in GitHub. PR review is an essential part of open source software
developments to maintain the quality of software. Matching a new PR for an
appropriate integrator will make the PR reviewing more effective. However, PR
and integrator matching are now organized manually in GitHub. To make this
process more efficient, we propose a Topic-based Integrator Matching Algorithm
(TIMA) to predict highly relevant collaborators(the core developers) as the
integrator to incoming PRs . TIMA takes full advantage of the textual semantics
of PRs. To define the relationships between topics and collaborators, TIMA
builds a relation matrix about topic and collaborators. According to the
relevance between topics and collaborators, TIMA matches the suitable
collaborators as the PR integrator.


  We report results from a high resolution numerical study of fluid particles
transported by a fully developed turbulent flow. Single particle trajectories
were followed for a time range spanning more than three decades, from less than
a tenth of the Kolmogorov time-scale up to one large-eddy turnover time. We
present results concerning acceleration statistics and the statistics of
trapping by vortex filaments conditioned to the local values of vorticity and
enstrophy. We distinguish two different behaviors between the joint statistics
of vorticity and centripetal acceleration or vorticity and longitudinal
acceleration.


  The confirmation of a globular cluster (GC) in the recently discovered
ultrafaint galaxy Eridanus II (Eri II) motivated us to examine the question
posed in the title. After estimating the halo mass of Eri II using a published
stellar mass - halo mass relation, the one GC in this galaxy supports extending
the relationship between the number of GCs hosted by a galaxy and the galaxy's
total mass about two orders of magnitude in stellar mass below the previous
limit. For this empirically determined specific frequency of between 0.06 and
0.39 globular clusters per 10$^9$ $M_\odot$ of total mass, the surviving Milky
Way (MW) subhalos with masses smaller than $10^{10} M_\odot$ could host as many
as 5 to 31 GCs, broadly consistent with the actual population of outer halo MW
GCs, although matching the radial distribution in detail remains a challenge.
Using a subhalo mass function from published high resolution numerical
simulations and a Poissonian model for populating those halos with the
aforementioned empirically constrained frequency, we find that about 90$\%$ of
these GCs lie in lower-mass subhalos than that of Eri II. From what we know
about the stellar mass-halo mass function, the subhalo mass function, and the
mass-normalized GC specific frequency, we conclude that some of the MW's outer
halo GCs are likely to be hosted by undetected subhalos with extremely modest
stellar populations.


  The apparently unrelated experimental observations of optical sum rule
violation[1] and of tunneling asymmetry in NIS tunneling[2] find a simple
explanation within the theory of hole superconductivity. In fact, both
phenomena were predicted by the theory long before they were experimentally
observed[3,4]. Other experimental predictions of the theory, in particular a
novel feature expected in photoemission experiments, are discussed.


  The excess radio background detected by ARCADE 2 represents a puzzle within
the standard cosmological model. There is no clear viable astrophysical
solution, and therefore, it might indicate the presence of new physics.
Radiative decays of a relic neutrino $\nu_i$ (either $i=1$, or $i=2$, or $i=3$)
into a sterile neutrino $\nu_{\rm s}$, assumed to be quasi-degenerate, provide
a solution that currently evades all constraints posed by different
cosmological observations and reproduces very well the ARCADE 2 data. We find a
very good fit to the ARCADE 2 data with best fit values $\tau_i = 1.46 \times
10^{21}\,{\rm s}$ and $\Delta m_i = 4.0 \times 10^{-5}\,{\rm eV}$, where
$\tau_i$ is the lifetime and $\Delta m_i$ is the mass difference between the
decaying active neutrino and the sterile neutrino. On the other hand, if relic
neutrino decays do not explain ARCADE 2 data, then these place a stringent
constraint $\Delta m_i^{3/2} \tau_i \gtrsim 2 \times 10^{14}\,{\rm
eV}^{3/2}\,{\rm s}$ in the range $1.4 \times 10^{-5} \, {\rm eV} < \Delta m_i <
2.5 \times 10^{-4}\,{\rm eV}$. The solution also predicts a stronger 21 cm
absorption global signal than the predicted one from the $\Lambda$CDM model,
with a contrast brightness temperature $T_{21} = -238^{+21}_{-20}\,{\rm mK}$
($99\%$ C.L.) at redshift $z\simeq 17$. This is in mild tension with the even
stronger signal found by the EDGES collaboration, $T_{21} = -
500^{+200}_{-500}\,{\rm mK} $, suggesting that this might have been
overestimated, possibly receiving a contribution from some unidentified
foreground source.


  We report experimental results on the dynamics of large bubbles in a
Hele-Shaw cell subject to various inclination angles with respect to gravity.
Low Reynolds number cases are studied by injecting bubbles in an stagnant
water/UCON mixture in three different Hele-Shaw cell geometry. The leading
order rise speed $v_b$ follows the Taylor-Saffman limit which is inversely
proportional to the viscosity $\eta$, but directly proportional to the square
of the cell gap $h$ and the effective gravity, accounting for cell tilt angle
$\theta$. However, when the cell is inclined more and more, the bubble buoyancy
in the cell gap leads to a substantial decrease in the rise speed, as compared
to the Taylor-Saffman speed. Buoyancy pushes the bubble towards the top channel
wall, whereby a difference between the lubrication film thickness on top of and
underneath the rising bubble occurs. We attribute these observations to the
loss of symmetry in the channel gap, due to cell inclination. Nonetheless, the
top lubrication film is observed to follow the Bretherton scaling, namely,
$(\eta v_b/\sigma)^{2/3}$, where $\sigma$ is the liquid surface tension while
the bottom film does not exhibit such a scaling. Finally, we illustrate that a
model incorporating a friction term to the power balance between buoyancy and
viscous dissipation matches well with all experimental data.


  Conventionally, a microscopic particle that performs a reciprocal stroke
cannot move through its environment. This is because at small scales, the
response of simple Newtonian fluids is purely viscous and flows are
time-reversible. We show that by contrast, fluid elasticity enables propulsion
by reciprocal forcing that is otherwise impossible. We present experiments on
rigid objects actuated reciprocally in viscous fluids, demonstrating for the
first time a purely elastic propulsion set by the object's shape and boundary
conditions. We describe two different artificial "swimmers" that experimentally
realize this principle.


  We show that the covariant effective action for M5-brane is a solution to the
Hamilton-Jacobi (H-J) equations of 11-dimensional supergravity. The solution to
the H-J equations reproduces the supergravity solution that represents the
M2-M5 bound states.


  We prove the following middle-dimensional non-squeezing result for analytic
symplectic embeddings of domains in $\mathbb{R}^{2n}$. Let $\varphi: D
\hookrightarrow \mathbb{R}^{2n}$ be an analytic symplectic embedding of a
domain $D \subset \mathbb{R}^{2n}$ and $P$ be a symplectic projector onto a
linear $2k$-dimensional symplectic subspace $V\subset \mathbb{R}^{2n}$. Then
there exists a positive function $r_0:D\rightarrow (0,+ \infty)$, bounded away
from $0$ on compact subsets $K \subset D$, such that the inequality
$Vol_{2k}(P\varphi (B_r(x)),\omega ^k _{0|V})\geq \pi^{k} r^{2k}$ holds for
every $x \in D$ and for every $r < r_0(x)$. This claim will be deduced from an
analytic middle-dimensional non-squeezing result (stated by considering paths
of symplectic embeddings) whose proof will be carried on by taking advantage of
a work by \'{A}lvarez Paiva and Balacheff.


  The origin of the high inclination of Uranus' spin-axis (Uranus' obliquity)
is one of the great unanswered questions about the Solar system. Giant planets
are believed to form with nearly zero obliquity, and it has been shown that the
present behaviour of Uranus' spin is essentially stable. Several attempts were
made in order to solve this problem. Here we report numerical simulations
showing that Uranus' axis can be tilted during the planetary migration, without
the need of a giant impact, provided that the planet had an additional
satellite and a temporary large inclination. This might have happened during
the giant planet instability phase described in the Nice model. In our
scenario, the satellite is ejected after the tilt by a close encounter at the
end of the migration. This model can both explain Uranus' large obliquity and
bring new constraints on the planet orbital evolution.


  In this paper, we present the results of the HSE-NN team in the 4th
competition on Affective Behavior Analysis in-the-wild (ABAW). The novel
multi-task EfficientNet model is trained for simultaneous recognition of facial
expressions and prediction of valence and arousal on static photos. The
resulting MT-EmotiEffNet extracts visual features that are fed into simple
feed-forward neural networks in the multi-task learning challenge. We obtain
performance measure 1.3 on the validation set, which is significantly greater
when compared to either performance of baseline (0.3) or existing models that
are trained only on the s-Aff-Wild2 database. In the learning from synthetic
data challenge, the quality of the original synthetic training set is increased
by using the super-resolution techniques, such as Real-ESRGAN. Next, the
MT-EmotiEffNet is fine-tuned on the new training set. The final prediction is a
simple blending ensemble of pre-trained and fine-tuned MT-EmotiEffNets. Our
average validation F1 score is 18% greater than the baseline convolutional
neural network.


  Let D be a database of N objects where each object has m fields. The objects
are given in m sorted lists (where the ith list is sorted according to the ith
field). Our goal is to find the top k objects according to a monotone
aggregation function t, while minimizing access to the lists. The problem
arises in several contexts. In particular Fagin (JCSS 1999) considered it for
the purpose of aggregating information in a multimedia database system.
  We are interested in instance optimality, i.e. that our algorithm will be as
good as any other (correct) algorithm on any instance. We provide and analyze
several instance optimal algorithms for the task, with various access costs and
models.


  The East Asian summer monsoon (EASM) is important for bringing rainfall to
large areas of China. Historically, variations in the EASM have had major
impacts including flooding and drought. We present an analysis of the impact of
anthropogenic climate change on EASM rainfall in Eastern China using a newly
updated attribution system. Our results suggest that anthropogenic climate
change has led to an overall decrease in total monsoon rainfall over the past
65 years, and an increased number of dry days. However the model also predicts
that anthropogenic forcings have caused the most extreme heavy rainfall events
to become shorter in duration and more intense. With the potential for future
changes in aerosol and greenhouse gas emissions, historical trends in monsoon
rainfall may not be indicative of future changes, although extreme rainfall is
projected to increase over East Asia with continued warming in the region.


  We improve complexity bounds for energy-efficient speed scheduling problems
for both the single processor and multi-processor cases. Energy conservation
has become a major concern, so revisiting traditional scheduling problems to
take into account the energy consumption has been part of the agenda of the
scheduling community for the past few years.
  We consider the energy minimizing speed scaling problem introduced by Yao et
al. where we wish to schedule a set of jobs, each with a release date, deadline
and work volume, on a set of identical processors. The processors may change
speed as a function of time and the energy they consume is the $\alpha$th power
of its speed. The objective is then to find a feasible schedule which minimizes
the total energy used.
  We show that in the setting with an arbitrary number of processors where all
work volumes are equal, there is a $2(1+\varepsilon)(5(1+\varepsilon))^{\alpha
-1}\tilde{B}_{\alpha}=O_{\alpha}(1)$ approximation algorithm, where
$\tilde{B}_{\alpha}$ is the generalized Bell number. This is the first constant
factor algorithm for this problem. This algorithm extends to general unequal
processor-dependent work volumes, up to losing a factor of
$(\frac{(1+r)r}{2})^{\alpha}$ in the approximation, where $r$ is the maximum
ratio between two work volumes. We then show this latter problem is APX-hard,
even in the special case when all release dates and deadlines are equal and $r$
is 4.
  In the single processor case, we introduce a new linear programming
formulation of speed scaling and prove that its integrality gap is at most
$12^{\alpha -1}$. As a corollary, we obtain a $(12(1+\varepsilon))^{\alpha -1}$
approximation algorithm where there is a single processor, improving on the
previous best bound of $2^{\alpha-1}(1+\varepsilon)^{\alpha}\tilde{B}_{\alpha}$
when $\alpha \ge 25$.


  For a three-state Markov system in a stationary state, we discuss whether, on
the basis of data obtained from effective two-state (or on-off) trajectories,
it is possible to discriminate between an equilibrium state and a
non-equilibrium steady state. By calculating the full phase diagram we identify
a large region where such data will be consistent only with non-equilibrium
conditions. This regime is considerably larger than the region with oscillatory
relaxation, which has previously been identified as a sufficient criterion for
non-equilibrium.


  Assortative mixing in networks is the tendency for nodes with the same
attributes, or metadata, to link to each other. It is a property often found in
social networks manifesting as a higher tendency of links occurring between
people with the same age, race, or political belief. Quantifying the level of
assortativity or disassortativity (the preference of linking to nodes with
different attributes) can shed light on the factors involved in the formation
of links and contagion processes in complex networks. It is common practice to
measure the level of assortativity according to the assortativity coefficient,
or modularity in the case of discrete-valued metadata. This global value is the
average level of assortativity across the network and may not be a
representative statistic when mixing patterns are heterogeneous. For example, a
social network spanning the globe may exhibit local differences in mixing
patterns as a consequence of differences in cultural norms. Here, we introduce
an approach to localise this global measure so that we can describe the
assortativity, across multiple scales, at the node level. Consequently we are
able to capture and qualitatively evaluate the distribution of mixing patterns
in the network. We find that for many real-world networks the distribution of
assortativity is skewed, overdispersed and multimodal. Our method provides a
clearer lens through which we can more closely examine mixing patterns in
networks.


  Neural architecture for named entity recognition has achieved great success
in the field of natural language processing. Currently, the dominating
architecture consists of a bi-directional recurrent neural network (RNN) as the
encoder and a conditional random field (CRF) as the decoder. In this paper, we
propose a deformable stacked structure for named entity recognition, in which
the connections between two adjacent layers are dynamically established. We
evaluate the deformable stacked structure by adapting it to different layers.
Our model achieves the state-of-the-art performances on the OntoNotes dataset.


  The cerebellar grey matter morphology is an important feature to study
neurodegenerative diseases such as Alzheimer's disease or Down's syndrome. Its
volume or thickness is commonly used as a surrogate imaging biomarker for such
diseases. Most studies about grey matter thickness estimation focused on the
cortex, and little attention has been drawn on the morphology of the
cerebellum. Using ex vivo high-resolution MRI, it is now possible to visualise
the different cell layers in the mouse cerebellum. In this work, we introduce a
framework to extract the Purkinje layer within the grey matter, enabling the
estimation of the thickness of the cerebellar grey matter, the granular layer
and molecular layer from gadolinium-enhanced ex vivo mouse brain MRI.
Application to mouse model of Down's syndrome found reduced cortical and layer
thicknesses in the transchromosomic group.


  Given a Klein surface Y, there is a unique symmetric Riemann surface X being
the complex double of Y. In this paper we shall show that the situation is not
the same when we work in the category of surfaces with nodes.


  Surface defect inspection is of great importance for industrial manufacture
and production. Though defect inspection methods based on deep learning have
made significant progress, there are still some challenges for these methods,
such as indistinguishable weak defects and defect-like interference in the
background. To address these issues, we propose a transformer network with
multi-stage CNN (Convolutional Neural Network) feature injection for surface
defect segmentation, which is a UNet-like structure named CINFormer. CINFormer
presents a simple yet effective feature integration mechanism that injects the
multi-level CNN features of the input image into different stages of the
transformer network in the encoder. This can maintain the merit of CNN
capturing detailed features and that of transformer depressing noises in the
background, which facilitates accurate defect detection. In addition, CINFormer
presents a Top-K self-attention module to focus on tokens with more important
information about the defects, so as to further reduce the impact of the
redundant background. Extensive experiments conducted on the surface defect
datasets DAGM 2007, Magnetic tile, and NEU show that the proposed CINFormer
achieves state-of-the-art performance in defect detection.


  We present fully formalized proofs of some central theorems from
combinatorics. These are Dilworth's decomposition theorem, Mirsky's theorem,
Hall's marriage theorem and the Erd\H{o}s-Szekeres theorem. Dilworth's
decomposition theorem is the key result among these. It states that in any
finite partially ordered set (poset), the size of a smallest chain cover and a
largest antichain are the same. Mirsky's theorem is a dual of Dilworth's
decomposition theorem, which states that in any finite poset, the size of a
smallest antichain cover and a largest chain are the same. We use Dilworth's
theorem in the proofs of Hall's Marriage theorem and the Erd\H{o}s-Szekeres
theorem. The combinatorial objects involved in these theorems are sets and
sequences. All the proofs are formalized in the Coq proof assistant. We develop
a library of definitions and facts that can be used as a framework for
formalizing other theorems on finite posets.


  A synopsis exemplifying the employment of Dyson-Schwinger equations in the
calculation and explanation of hadron electromagnetic form factors and related
phenomena. In particular the contribution: presents the pion form factor
computed simultaneously at spacelike and timelike momenta; reports aspects of
the evolution of the nucleon and Delta masses with current-quark mass and the
correlation of their mass difference with that between scalar and axial-vector
diquarks; describes an estimate of the s-quark content of a dressed u-quark and
its impact on the nucleon's strangeness magnetic moment; and comments upon the
domain within which a pseudoscalar meson cloud can materially contribute to
hadron form factors.


  Let $M^m$ be an $m$-dimensional, smooth and closed manifold, equipped with a
smooth involution $T\colon M^m \to M^m$ fixing submanifolds $F^n$ and $F^4$ of
dimensions $n$ and $4$, respectively, where $4<n<m$ and $F^n\cup F^4$ does not
bound. We determine the upper bound for $m$, for each $n$. The existence of
these bounds is ensured by the famous Five Halves Theorem of J. Boardman, which
establishes that, under the above hypotheses, $m\leqslant\frac{5}{2}n$.


  Superpositions of coherent light waves typically interfere. We present
superpositions of up to six plane waves which defy this expectation by having a
perfectly homogeneous mean square of the electric field. For many applications
in optics these superpositions can be seen as having a homogeneous intensity.
Our superpositions show interesting one- two- and three dimensional patterns in
their helicity densities, including several that support bright regions of
superchirality. Our superpositions might be used to write chiral patterns in
certain materials and, conversely, such materials might be used as the basis of
an 'optical helicity' camera capable of recording spatial variations in
helicity.


  In this paper, an open-loop two-person non-zero sum stochastic differential
game is considered for forward-backward stochastic systems. More precisely, the
controlled systems are described by a fully coupled nonlinear multi-
dimensional forward-backward stochastic differential equation driven by a
multi-dimensional Brownian motion. one sufficient (a verification theorem) and
one necessary conditions for the existence of open-loop Nash equilibrium points
for the corresponding two-person non-zero sum stochastic differential game are
proved. The control domain need to be convex and the admissible controls for
both players are allowed to appear in both the drift and diffusion of the state
equations.


  There are currently three main classes of high-performance liquid-repellent
surfaces: micro-/nano-structured lotus-effect superhydrophobic surfaces, flat
surfaces grafted with 'liquid-like' polymer brushes, and various lubricated
surfaces. Despite recent progress, the mechanistic understanding of the
differences in droplet behavior on such surfaces is still under debate. We
measured the dissipative force acting on a droplet moving on representatives of
these classes at different velocities U = 0.01-1 mm/s using a cantilever force
sensor with sub-uN accuracy, and correlated it to the contact line dynamics
observed using optical interferometry at high spatial (micron) and temporal (<
0.1s) resolutions. We find that the dissipative force, due to very different
physical mechanisms at the contact line, is independent of velocity on
superhydrophobic surfaces, but depends non-linearly on velocity for flat and
lubricated surfaces. The techniques and insights presented here will inform
future work on liquid-repellent surfaces and enable their rational design.


  Within the framework of a constituent quark model, we investigate the heavy
quark conserving weak decays of $\Xi_c$ and $\Xi_b$. This process involves
elementary transitions of $us\to du$ or $s\to ud \bar u$ with the heavy quark
as a spectator, while for the charmed baryon in the initial state it can also
occur via $cs\to dc$ to conserve the heavy quark flavor in the weak decays. It
shows that the heavy quark symmetry (HQS) plays an essential role in the
processes where the heavy quark acts as a spectator. For the $\Xi_c$ decays,
the dominance of the pole terms in the parity-conserving transitions is
evident. This can naturally explain the sizeable branching ratio for
$\Xi_c^0\to\Lambda_c\pi^-$ as recently reported by LHCb. The same mechanism
predicts a large branching ratio for $\Xi_c^+\to\Lambda_c\pi^0$. In contrast,
the decays of $\Xi_b$ will only go through the parity-violating processes
because of the HQS. In addition, the branching ratios of the $\Xi_c^+\to
\Lambda_c \pi^0$ and $\Xi_b^0\to \Lambda_b \pi^0$ processes are also predicted
for the further experimental measurement.


  For a fixed integer $k$, we define the multiplicative function
\[D_{k,\omega}(n) := \frac{d(n)}{k^{\omega(n)}}, \]where $d(n)$ is the divisor
function and $\omega (n)$ is the number of distinct prime divisors of $n$. The
main purpose of this paper is the study of the mean value of the function
$D_{k,\omega}(n)$ by using elementary methods.


  Relations of simulated annealing and quantum annealing are studied by a
mapping from the transition matrix of classical Markovian dynamics of the Ising
model to a quantum Hamiltonian and vice versa. It is shown that these two
operators, the transition matrix and the Hamiltonian, share the eigenvalue
spectrum. Thus, if simulated annealing with slow temperature change does not
encounter a difficulty caused by an exponentially long relaxation time at a
first-order phase transition, the same is true for the corresponding process of
quantum annealing in the adiabatic limit. One of the important differences
between the classical-to-quantum mapping and the converse quantum-to-classical
mapping is that the Markovian dynamics of a short-range Ising model is mapped
to a short-range quantum system, but the converse mapping from a short-range
quantum system to a classical one results in long-range interactions. This
leads to a difference in efficiencies that simulated annealing can be
efficiently simulated by quantum annealing but the converse is not necessarily
true. We conclude that quantum annealing is easier to implement and is more
flexible than simulated annealing. We also point out that the present mapping
can be extended to accommodate explicit time dependence of temperature, which
is used to justify the quantum-mechanical analysis of simulated annealing by
Somma, Batista, and Ortiz. Additionally, an alternative method to solve the
non-equilibrium dynamics of the one-dimensional Ising model is provided through
the classical-to-quantum mapping.


  We prove a sharp large deviation principle concerning intervals shrinking
with sub-exponential speed for certain models involving the Poincar\'e map
related to a Markov family for an Axiom A flow restricted to a basic set
$\Lambda$ satisfying some additional regularity assumptions.


  Vorticity is ubiquitous in nature however, to date, studies of vorticity in
cosmology and the early universe have been quite rare. In this paper, based on
a talk in session CM1 of the 13th Marcel Grossmann Meeting, we consider
vorticity generation from scalar cosmological perturbations of a perfect fluid
system. We show that, at second order in perturbation theory, vorticity is
sourced by a coupling between energy density and entropy gradients, thus
extending a well-known feature of classical fluid dynamics to a relativistic
cosmological framework. This induced vorticity, sourced by isocurvature
perturbations, may prove useful in the future as an additional discriminator
between inflationary models.


  The purpose of this research is to develop an Information System of Selling
and Services using Microsoft Visual Basic and Microsoft Access for it database.
The benefits of this research is to help CV Computer Plus in selling and
services data processing everyday. To develop this IS is used 5 (five) steps:
1) Planning, 2) Analysis, 3) Design, 4) Implementation, and 5) Evaluation. The
Information System can record the selling and services data, it also prepared
usefull reports. By using this IS, CV Computer Plus can operate their selling
and services efficiency and effectively. In the future it can be upgraded for
network application.


  Quantum state reconstruction is an essential element in quantum information
processing. However, efficient and reliable reconstruction of non-trivial
quantum states in the presence of hardware imperfections can be challenging.
This task is particularly demanding for high-dimensional states encoded in
continuous-variable (CV) systems, as many error-prone measurements are needed
to cover the relevant degrees of freedom of the system in phase space. In this
work, we introduce an efficient and robust technique for optimized
reconstruction based on excitation number sampling (ORENS). We use a standard
bosonic circuit quantum electrodynamics (cQED) setup to experimentally
demonstrate the robustness of ORENS and show that it outperforms the existing
cQED reconstruction techniques such as Wigner and Husimi Q tomography. Our
investigation highlights that ORENS is naturally free of parasitic system
dynamics and resilient to decoherence effects in the hardware. Finally, ORENS
relies only on the ability to accurately measure the excitation number of the
state, making it a versatile and accessible tool for a wide range of CV
platforms and readily scalable to multimode systems. Thus, our work provides a
crucial and valuable primitive for practical quantum information processing
using bosonic modes.


  In this paper, we consider robust joint access point (AP) clustering and
beamforming design with imperfect channel state information (CSI) in cell-free
systems. Specifically, we jointly optimize AP clustering and beamforming with
imperfect CSI to simultaneously maximize the worst-case sum rate and minimize
the number of AP clustering under power constraint and the sparsity constraint
of AP clustering. By transformations, the semi-infinite constraints caused by
the imperfect CSI are converted into more tractable forms for facilitating a
computationally efficient unsupervised deep learning algorithm. In addition, to
further reduce the computational complexity, a computationally effective
unsupervised deep learning algorithm is proposed to implement robust joint AP
clustering and beamforming design with imperfect CSI in cell-free systems.
Numerical results demonstrate that the proposed unsupervised deep learning
algorithm achieves a higher worst-case sum rate under a smaller number of AP
clustering with computational efficiency.


  Given a monoidal category $\mathscr{C}$ with an object $J$, we construct a
monoidal category $\mathscr{C}[J^{\vee}]$ by freely adjoining a right dual
$J^{\vee}$ to $J$. We show that the canonical strong monoidal functor $\Omega :
\mathscr{C}\to \mathscr{C}[J^{\vee}]$ provides the unit for a biadjunction with
the forgetful 2-functor from the 2-category of monoidal categories with a
distinguished dual pair to the 2-category of monoidal categories with a
distinguished object. We show that $\Omega : \mathscr{C}\to
\mathscr{C}[J^{\vee}]$ is fully faithful and provide coend formulas for homs of
the form $\mathscr{C}[J^{\vee}](U,\Omega A)$ and $\mathscr{C}[J^{\vee}](\Omega
A,U)$ for $A\in \mathscr{C}$ and $U\in \mathscr{C}[J^{\vee}]$.
  If $\mathbb{N}$ denotes the free strict monoidal category on a single
generating object $1$ then $\mathbb{N}[1^{\vee}]$ is the free monoidal category
$\mathrm{Dpr}$ containing a dual pair $- \dashv +$ of objects. As we have the
monoidal pseudopushout $\mathscr{C}[J^{\vee}] \simeq \mathrm{Dpr}
+_{\mathbb{N}} \mathscr{C}$, it is of interest to have an explicit model of
$\mathrm{Dpr}$: we provide both geometric and combinatorial models. We show
that the (algebraist's) simplicial category $\Delta$ is a monoidal full
subcategory of $\mathrm{Dpr}$ and explain the relationship with the free
2-category $\mathrm{Adj}$ containing an adjunction. We describe a
generalization of $\mathrm{Dpr}$ which includes, for example, a combinatorial
model $\mathrm{Dseq}$ for the free monoidal category containing a duality
sequence $X_0\dashv X_1\dashv X_2 \dashv \dots$ of objects. Actually,
$\mathrm{Dpr}$ is a monoidal full subcategory of $\mathrm{Dseq}$.


  The temperature effect on the Raman scattering efficiency is investigated in
$\varepsilon$-GaSe and $\gamma$-InSe crystals. We found that varying the
temperature over a broad range from 5 K to 350 K permits to achieve both the
resonant conditions and the antiresonance behaviour in Raman scattering of the
studied materials. The resonant conditions of Raman scattering are observed at
about 270 K under the 1.96 eV excitation for GaSe due to the energy proximity
of the optical band gap. In the case of InSe, the resonant Raman spectra are
apparent at about 50 K and 270 K under correspondingly the 2.41 eV and 2.54 eV
excitations as a result of the energy proximity of the \mbox{so-called} B
transition. Interestingly, the observed resonances for both materials are
followed by an antiresonance behaviour noticeable at higher temperatures than
the detected resonances. The significant variations of phonon-modes intensities
can be explained in terms of electron-phonon coupling and quantum interference
of contributions from different points of the Brillouin zone


  We study the characterization of the non-Hermitian skin effect (NHSE) in
non-Hermitian systems with on-site disorder. We extend the application of
generalized-Brillouin-zone (GBZ) theory to these systems. By proposing a
modified GBZ theory, we give a faithfully description of the NHSE. For
applications, we obtain a unified $\beta$ for system with long-range hopping,
and explain the conventional-GBZ irrelevance of the magnetic suppression of the
NHSE in the previous study.


  We report the first 17-O NMR studies of a triangular-lattice superconductor
Na{1/3}CoO{2}-[4/3]H{2}O and the host material Na{x}CoO{2} (x=0.35 and 0.72).
Knight shift measurements reveal that p-d hybridization induces sizable spin
polarization in the O triangular-lattice layers. Water-intercalation makes
CoO{2} planes homogeneous, and enhances low frequency spin fluctuations near
T{c}=4.5 K at some finite wave-vectors different from both the ferromagnetic
and ``120 degree'' modes.


  We propose NeuronaBox, a flexible, user-friendly, and high-fidelity approach
to emulate DNN training workloads. We argue that to accurately observe
performance, it is possible to execute the training workload on a subset of
real nodes and emulate the networked execution environment along with the
collective communication operations. Initial results from a proof-of-concept
implementation show that NeuronaBox replicates the behavior of actual systems
with high accuracy, with an error margin of less than 1% between the emulated
measurements and the real system.


  A brief recollection is made of the many scientific collaborations of Bologna
with colleagues from Developing Countries. In particular are discussed in
detail the collaborations in some recent Astroparticle Physics experiments.


  We discuss the excess in the hadroproduction of B mesons at the Tevatron. We
show that an accurate use of up-to-date information on the B fragmentation
function reduces the observed excess to an acceptable level. Possible
implications for experimental results reporting bottom quark cross sections,
also showing an excess with respect to next-to-leading order theoretical
predictions, are discussed.


  Astrophysical explosions result from the release of magnetic, gravitational,
or thermonuclear energy on dynamical timescales, typically the sound-crossing
time for the system. These explosions include solar and stellar flares,
eruptive phenomena in accretion disks, thermonuclear combustion on the surfaces
of white dwarfs and neutron stars, violent magnetic reconnection in neutron
stars, thermonuclear and gravitational collapse supernovae and cosmic gamma-ray
bursts, each representing a different type and amount of energy release. This
paper summarizes the properties of these explosions and describes new research
on thermonuclear explosions and explosions in extended circumstellar media.
Parallels are drawn between studies of terrestrial and astrophysical
explosions, especially the physics of the transition from deflagration to
detonation.
  Keywords: neutron stars, black holes, supernovae, gamma-ray bursts,
deflagration, detonation.


  Increasingly powerful Large Language Model (LLM) based chatbots, like ChatGPT
and Bard, are becoming available to users that have the potential to
revolutionize the quality of decision-making achieved by the public. In this
context, we set out to investigate how such systems perform in the personal
finance domain, where financial inclusion has been an overarching stated aim of
banks for decades. We asked 13 questions representing banking products in
personal finance: bank account, credit card, and certificate of deposits and
their inter-product interactions, and decisions related to high-value
purchases, payment of bank dues, and investment advice, and in different
dialects and languages (English, African American Vernacular English, and
Telugu). We find that although the outputs of the chatbots are fluent and
plausible, there are still critical gaps in providing accurate and reliable
financial information using LLM-based chatbots.


  In this paper, we revisit Moggi's celebrated calculus of computational
effects from the perspective of logic of monoidal action (actegory). Our
development takes the following steps. Firstly, we perform proof-theoretic
reconstruction of Moggi's computational metalanguage and obtain a type theory
with a modal type $\rhd$ as a refinement. Through the proposition-as-type
paradigm, its logic can be seen as a decomposition of lax logic via Benton's
adjoint calculus. This calculus models as a programming language a weaker
version of effects, which we call \emph{semi-effects}. Secondly, we give its
semantics using actegories and equivariant functors. Compared to previous
studies of effects and actegories, our approach is more general in that models
are directly given by equivariant functors, which include Freyd categories
(hence strong monads) as a special case. Thirdly, we show that categorical
gluing along equivariant functors is possible and derive logical predicates for
$\rhd$-modality. We also show that this gluing, under a natural assumption,
gives rise to logical predicates that coincide with those derived by
Katsumata's categorical $\top\top$-lifting for Moggi's metalanguage.


  We utilize a discrete version of the notion of degree of freedom to prove a
sharp min-entropy-variance inequality for integer valued log-concave random
variables. More specifically, we show that the geometric distribution minimizes
the min-entropy within the class of log-concave probability sequences with
fixed variance. As an application, we obtain a discrete R\'enyi entropy power
inequality in the log-concave case, which improves a result of Bobkov,
Marsiglietti and Melbourne (2022).


  Normalization layers are essential in a Deep Convolutional Neural Network
(DCNN). Various normalization methods have been proposed. The statistics used
to normalize the feature maps can be computed at batch, channel, or instance
level. However, in most of existing methods, the normalization for each layer
is fixed. Batch-Instance Normalization (BIN) is one of the first proposed
methods that combines two different normalization methods and achieve diverse
normalization for different layers. However, two potential issues exist in BIN:
first, the Clip function is not differentiable at input values of 0 and 1;
second, the combined feature map is not with a normalized distribution which is
harmful for signal propagation in DCNN. In this paper, an Instance-Layer
Normalization (ILN) layer is proposed by using the Sigmoid function for the
feature map combination, and cascading group normalization. The performance of
ILN is validated on image segmentation of the Right Ventricle (RV) and Left
Ventricle (LV) using U-Net as the network architecture. The results show that
the proposed ILN outperforms previous traditional and popular normalization
methods with noticeable accuracy improvements for most validations, supporting
the effectiveness of the proposed ILN.


  This thesis describes an analysis developed for the MicroBooNE experiment to
investigate an anomalous excess of electron-like events observed in the
MiniBooNE detector. The hypothesis investigated here is that the MiniBooNE
anomaly represents appearance of electron neutrinos. Using an amalgam of novel
Deep Learning and standard algorithmic techniques this analysis reconstructs
and identifies a highly pure sample of charged current quasi-elastic muon
neutrino and electron neutrino interactions. This thesis describes the steps in
the analysis chain and provides data-to-simulation comparisons for each step
that establish confidence in the final prediction. When interpreted in the
context of a $\nu e$ appearance like model, this analysis predicts a
3.2$\sigma$ sensitivity to exclude a standard model fluctuation which would
appear as a MiniBooNE like anomaly using $7\times10^{20}$ protons on target of
MicroBooNE Data.


  We present a study of correlations between the elemental abundances and
galaxy morphologies of 91 blue compact galaxies (BCGs) at z=0.20-0.35 with
Sloan Digital Sky Survey (SDSS) DR7 data. We classify the morphologies of the
galaxies as either 'disturbed' or 'undisturbed', by visual inspection of the
SDSS images, and using the Gini coefficient and M_20. We derive oxygen and
nitrogen abundances using the T_e method. We find that a substantial fraction
of BCGs with disturbed morphologies, indicative of merger remnants, show
relatively high N/O and low O/H abundance ratios. The majority of the disturbed
BCGs exhibit higher N/O values at a given O/H value compared to the
morphologically undisturbed galaxies, implying more efficient nitrogen
enrichment in disturbed BCGs. We detect Wolf-Rayet (WR) features in only a
handful of the disturbed BCGs, which appears to contradict the idea that WR
stars are responsible for high nitrogen abundance. Combining these results with
Galaxy Evolution Explorer (GALEX) GR6 ultraviolet (UV) data, we find that the
majority of the disturbed BCGs show systematically lower values of the H alpha
to near-UV star formation rate ratio. The equivalent width of the H beta
emission line is also systematically lower in the disturbed BCGs. Based on
these results, we infer that disturbed BCGs have undergone star formation over
relatively longer time scales, resulting in a more continuous enrichment of
nitrogen. We suggest that this correlation between morphology and chemical
abundances in BCGs is due to a difference in their recent star formation
histories.


  Compressed sensing magnetic resonance imaging (CS-MRI) seeks to recover
visual information from subsampled measurements for diagnostic tasks.
Traditional CS-MRI methods often separately address measurement subsampling,
image reconstruction, and task prediction, resulting in a suboptimal end-to-end
performance. In this work, we propose TACKLE as a unified co-design framework
for jointly optimizing subsampling, reconstruction, and prediction strategies
for the performance on downstream tasks. The na\"ive approach of simply
appending a task prediction module and training with a task-specific loss leads
to suboptimal downstream performance. Instead, we develop a training procedure
where a backbone architecture is first trained for a generic pre-training task
(image reconstruction in our case), and then fine-tuned for different
downstream tasks with a prediction head. Experimental results on multiple
public MRI datasets show that TACKLE achieves an improved performance on
various tasks over traditional CS-MRI methods. We also demonstrate that TACKLE
is robust to distribution shifts by showing that it generalizes to a new
dataset we experimentally collected using different acquisition setups from the
training data. Without additional fine-tuning, TACKLE leads to both numerical
and visual improvements compared to existing baselines. We have further
implemented a learned 4$\times$-accelerated sequence on a Siemens 3T MRI Skyra
scanner. Compared to the fully-sampling scan that takes 335 seconds, our
optimized sequence only takes 84 seconds, achieving a four-fold time reduction
as desired, while maintaining high performance.


  An anticipatory system for guiding plot development in interactive narratives
is described. The executable model is a finite automaton that provides the
implemented system with a look-ahead. The identification of undesirable future
states in the model is used to guide the player, in a transparent manner. In
this way, too radical twists of the plot can be avoided. Since the player
participates in the development of the plot, such guidance can have many forms,
depending on the environment of the player, on the behavior of the other
players, and on the means of player interaction. We present a design method for
interactive narratives which produces designs suitable for the implementation
of anticipatory mechanisms. Use of the method is illustrated by application to
our interactive computer game Kaktus.


  It is possible to eliminate exactly all the auxiliary fields (einbein fields)
appearing in the rotating string Hamiltonian to obtain the classical equations
of motion of the relativistic flux tube model. A clear interpretation can then
be done for the characteristic variables of the rotating string model.


  We study the $E_2$-algebra $\Lambda\mathfrak{M}_{*,1}=\coprod_{g\geqslant
0}\Lambda\mathfrak{M}_{g,1}$ consisting of free loop spaces of moduli spaces of
Riemann surfaces with one parametrised boundary component, and compute the
homotopy type of the group completion $\Omega B\Lambda\mathfrak{M}_{*,1}$: it
is the product of $\Omega^\infty\mathbf{MTSO}(2)$ with a certain free
$\Omega^\infty$-space depending on the family of all boundary-irreducible
mapping classes in all mapping class groups $\Gamma_{g,n}$ with $g\geqslant 0$
and $n\geqslant 1$.


  This note constitutes a corrigendum to the article of Azomahou, JSPI,
139:2581-2597. The aggregation of isotropic four nearest neighbors
autoregressive models on the lattice, with random coefficient, is investigated.
The spectral density of the resulting random field is studied in details for a
large class of law of the AR coefficient. Depending on this law, the aggregated
field may exhibit short memory or isotropic long memory.


  Theories that contain first class constraints possess gauge invariance which
results in the necessity of altering the measure in the associated quantum
mechanical path integral. If the path integral is derived from the canonical
structure of the theory, then the choice of gauge conditions used in
constructing Faddeev's measure cannot be covariant. This shortcoming is
normally overcome either by using the "Faddeev-Popov" quantization procedure,
or by the approach of Batalin-Fradkin-Fradkina-Vilkovisky, and then
demonstrating that these approaches are equivalent to the path integral
constructed from the canonical approach with Faddeev's measure. We propose in
this paper an alternate way of defining the measure for the path integral when
it is constructed using the canonical procedure for theories containing first
class constraints and that this new approach can be used in conjunction with
covariant gauges. This procedure follows the Faddeev-Popov approach, but rather
than working with the form of the gauge transformation in configuration space,
it employs the generator of the gauge transformation in phase space. We
demonstrate this approach to the path integral by applying it to Yang-Mills
theory, a spin-two field and the first order Einstein-Hilbert action in two
dimensions. The problems associated with defining the measure for theories
containing second-class constraints and ones in which there are fewer secondary
first class constraints than primary first class constraints are discussed.


  In this new energy regime, quarkonium provides a unique probe to study the
properties of the high-density, strongly interacting system formed in the early
stages of high-energy heavy-ion collisions. In ALICE, quarkonium states are
reconstructed down to p_T=0 via their mu+mu- decay channel in the muon
spectrometer (2.5<y<4.0) and via their e+e- channel in the central barrel
(|y|<0.9). Measurement of the transverse momentum and rapidity distributions of
inclusive J/psi production cross section in proton-proton collisions at
sqrt{s}=2.76 and 7 TeV will be presented. We will discuss the dependence on
charged particle multiplicity of the inclusive J/psi yield in proton-proton
collisions at sqrt{s}=7 TeV. Finally, the analysis of the inclusive J/psi
production in Pb-Pb collisions at sqrt{s_NN}=2.76 TeV will be described.
Preliminary results on the nuclear modification factor (R_AA) and the central
to peripheral nuclear modification factor (R_CP) will be discussed.


  Self-driving labs (SDLs) leverage combinations of artificial intelligence,
automation, and advanced computing to accelerate scientific discovery. The
promise of this field has given rise to a rich community of passionate
scientists, engineers, and social scientists, as evidenced by the development
of the Acceleration Consortium and recent Accelerate Conference. Despite its
strengths, this rapidly developing field presents numerous opportunities for
growth, challenges to overcome, and potential risks of which to remain aware.
This community perspective builds on a discourse instantiated during the first
Accelerate Conference, and looks to the future of self-driving labs with a
tempered optimism. Incorporating input from academia, government, and industry,
we briefly describe the current status of self-driving labs, then turn our
attention to barriers, opportunities, and a vision for what is possible. Our
field is delivering solutions in technology and infrastructure, artificial
intelligence and knowledge generation, and education and workforce development.
In the spirit of community, we intend for this work to foster discussion and
drive best practices as our field grows.


  In this paper, we present the concept of boosting the resiliency of
optimization-based observers for cyber-physical systems (CPS) using auxiliary
sources of information. Due to the tight coupling of physics, communication and
computation, a malicious agent can exploit multiple inherent vulnerabilities in
order to inject stealthy signals into the measurement process. The problem
setting considers the scenario in which an attacker strategically corrupts
portions of the data in order to force wrong state estimates which could have
catastrophic consequences. The goal of the proposed observer is to compute the
true states in-spite of the adversarial corruption. In the formulation, we use
a measurement prior distribution generated by the auxiliary model to refine the
feasible region of a traditional compressive sensing-based regression problem.
A constrained optimization-based observer is developed using l1-minimization
scheme. Numerical experiments show that the solution of the resulting problem
recovers the true states of the system. The developed algorithm is evaluated
through a numerical simulation example of the IEEE 14-bus system.


  We prove uniform bounds on moments X_a = \sum_{m}{m^a f_m(x,t)} of the
Smoluchowski coagulation equations with diffusion, valid in any dimension. If
the collision propensities \alpha(n,m) of mass n and mass m particles grow more
slowly than (n+m)(d(n) + d(m)), and the diffusion rate d(\cdot) is
non-increasing and satisfies m^{-b_1} \leq d(m) \leq m^{-b_2} for some b_1 and
b_2 satisfying 0 \leq b_2 < b_1 < \infty, then any weak solution satisfies X_a
\in L^{\infty}(\mathbb{R}^d \times [0,T]) \cap L^1(\mathbb{R}^d \times [0,T])
for every a \in \mathbb{N} and T \in (0,\infty), (provided that certain moments
of the initial data are finite). As a consequence, we infer that these
conditions are sufficient to ensure uniqueness of a weak solution and its
conservation of mass.


  Recent research discovered that charge transfer processes in chiral molecules
can be spin selective and named the effect chiral-induced spin selectivity
(CISS). Follow-up work studied hybrid spintronic devices with conventional
electronic materials and chiral (bio)molecules. However, a theoretical
foundation for the CISS effect is still in development and the spintronic
signals were not evaluated quantitatively. We present a circuit-model approach
that can provide quantitative evaluations. Our analysis assumes the scheme of a
recent experiment that used photosystem~I (PSI) as spin injectors, for which we
find that the experimentally observed signals are, under any reasonable
assumptions on relevant PSI time scales, too high to be fully due to the CISS
effect. We also show that the CISS effect can in principle be detected using
the same type of solid-state device, and by replacing silver with graphene, the
signals due to spin generation can be enlarged four orders of magnitude. Our
approach thus provides a generic framework for analyzing this type of
experiments and advancing the understanding of the CISS effect.


  In this paper, we introduce a novel, data-driven approach for solving
high-dimensional Bayesian inverse problems based on partial differential
equations (PDEs), called Weak Neural Variational Inference (WNVI). The method
complements real measurements with virtual observations derived from the
physical model. In particular, weighted residuals are employed as probes to the
governing PDE in order to formulate and solve a Bayesian inverse problem
without ever formulating nor solving a forward model. The formulation treats
the state variables of the physical model as latent variables, inferred using
Stochastic Variational Inference (SVI), along with the usual unknowns. The
approximate posterior employed uses neural networks to approximate the inverse
mapping from state variables to the unknowns. We illustrate the proposed method
in a biomedical setting where we infer spatially varying material properties
from noisy tissue deformation data. We demonstrate that WNVI is not only as
accurate and more efficient than traditional methods that rely on repeatedly
solving the (non)linear forward problem as a black-box, but it can also handle
ill-posed forward problems (e.g., with insufficient boundary conditions).


  The electronic properties of the oxygen molecule, in its singlet and triplet
states, and of many small oxygen-containing radicals and anions have important
roles in different fields of Chemistry, Biology and Atmospheric Science.
Nevertheless, the electronic structure of such species is a challenge for
ab-initio computational approaches because of the difficulties to correctly
describe the statical and dynamical correlation effects in presence of one or
more unpaired electrons. Only the highest-level quantum chemical approaches can
yield reliable characterizations of their molecular properties, such as binding
energies, equilibrium structures, molecular vibrations, charge distribution and
polarizabilities. In this work we use the variational Monte Carlo (VMC) and the
lattice regularized Monte Carlo (LRDMC) methods to investigate the equilibrium
geometries and molecular properties of oxygen and oxygen reactive species.
Quantum Monte Carlo methods are used in combination with the Jastrow
Antisymmetrized Geminal Power (JAGP) wave function ansatz, which has been
recently shown to effectively describe the statical and dynamical correlation
of different molecular systems. In particular we have studied the oxygen
molecule, the superoxide anion, the nitric oxide radical and anion, the
hydroxyl and hydroperoxyl radicals and their corresponding anions, and the
hydrotrioxyl radical. Overall, the methodology was able to correctly describe
the geometrical and electronic properties of these systems, through compact but
fully-optimised basis sets and with a computational cost which scales as
$N^3-N^4$, where $N$ is the number of electrons. This work is therefore opening
the way to the accurate study of the energetics and of the reactivity of large
and complex oxygen species by first principles.


  We propose a scheme to generate a superposition with arbitrary coefficients
on a line in phase space for the center-of-mass vibrational mode of N ions by
means of isolating all other spectator vibrational modes from the
center-of-mass mode. It can be viewed as the generation of previous methods for
preparing motional states of one ion. For large number of ions, we need only
one cyclic operatin to generate such a superposition of many coherent states.


  We use a semi-analytic model of halo formation to study the dynamical history
of giant field galaxies like the Milky Way. We find that in a concordance LCDM
cosmology, most isolated disk galaxies have remained undisturbed for 8-10 Gyr,
such that the age of the Milky Way's thin disk is unremarkable. Many systems
also have older disk components which have been thickened by minor mergers,
consistent with recent observations of nearby field galaxies. We do have a
considerable problem, however, reproducing the morphological mix of nearby
galaxies. In our fiducial model, most systems have disk-to-bulge mass ratios of
order 1, and look like S0s rather than spirals. This result depends mainly on
merger statistics, and is unchanged for most reasonable choices of our model
parameters. We discuss two possible solutions to this morphology problem in
LCDM.


  In this paper we review an approach to estimating the causal effect of a
time-varying treatment on time to some event of interest. This approach is
designed for the situation where the treatment may have been repeatedly adapted
to patient characteristics, which themselves may also be time-dependent. In
this situation the effect of the treatment cannot simply be estimated by
conditioning on the patient characteristics, as these may themselves be
indicators of the treatment effect. This so-called time-dependent confounding
is typical in observational studies. We discuss a new class of failure time
models, structural nested failure time models, which can be used to estimate
the causal effect of a time-varying treatment, and present methods for
estimating and testing the parameters of these models.


  We employ the Noether procedure to derive a general formula for the radially
conserved heat current in AdS planar black holes with certain transverse and
traceless perturbations, for a general class of gravity theories. For Einstein
gravity, the general higher-order Lovelock gravities and also a class of
Horndeski gravities, we derive the boundary stress tensor and show that the
resulting boundary heat current matches precisely the bulk Noether current.


  We used femtosecond optical pump-probe spectroscopy to study the photoinduced
change in reflectivity of thin films of the electron-doped cuprate
La$_{2-x}$Ce$_x$CuO$_4$ (LCCO) with dopings of x$=$0.08 (underdoped) and
x$=$0.11 (optimally doped). Above T$_c$, we observe fluence-dependent
relaxation rates which onset at a similar temperature that transport
measurements first see signatures of antiferromagnetic correlations. Upon
suppressing superconductivity with a magnetic field, it is found that the
fluence and temperature dependence of relaxation rates is consistent with
bimolecular recombination of electrons and holes across a gap (2$\Delta_{AF}$)
originating from antiferromagnetic correlations which comprise the pseudogap in
electron-doped cuprates. This can be used to learn about coupling between
electrons and high-energy ($\omega>2\Delta_{AF}$) excitations in these
compounds and set limits on the timescales on which antiferromagnetic
correlations are static.


  Robotic manipulators navigating cluttered shelves or cabinets may find it
challenging to avoid contact with obstacles. Indeed, rearranging obstacles may
be necessary to access a target. Rather than planning explicit motions that
place obstacles into a desired pose, we suggest allowing incidental contacts to
rearrange obstacles while monitoring contacts for safety. Bypassing object
identification, we present a method for categorizing object motions from
tactile data collected from incidental contacts with a capacitive tactile skin
on an Allegro Hand. We formalize tactile cues associated with categories of
object motion, demonstrating that they can determine with $>90$% accuracy
whether an object is movable and whether a contact is causing the object to
slide stably (safe contact) or tip (unsafe).


  Variation Autoencoder (VAE) has become a powerful tool in modeling the
non-linear generative process of data from a low-dimensional latent space.
Recently, several studies have proposed to use VAE for unsupervised clustering
by using mixture models to capture the multi-modal structure of latent
representations. This strategy, however, is ineffective when there are outlier
data samples whose latent representations are meaningless, yet contaminating
the estimation of key major clusters in the latent space. This exact problem
arises in the context of resting-state fMRI (rs-fMRI) analysis, where
clustering major functional connectivity patterns is often hindered by heavy
noise of rs-fMRI and many minor clusters (rare connectivity patterns) of no
interest to analysis. In this paper we propose a novel generative process, in
which we use a Gaussian-mixture to model a few major clusters in the data, and
use a non-informative uniform distribution to capture the remaining data. We
embed this truncated Gaussian-Mixture model in a Variational AutoEncoder
framework to obtain a general joint clustering and outlier detection approach,
called tGM-VAE. We demonstrated the applicability of tGM-VAE on the MNIST
dataset and further validated it in the context of rs-fMRI connectivity
analysis.


  We study the problem of mapping an unknown mixed quantum state onto a known
pure state without the use of unitary transformations. This is achieved with
the help of sequential measurements of two non-commuting observables only. We
show that the overall success probability is maximized in the case of measuring
two observables whose eigenstates define mutually unbiased bases. We find that
for this optimal case the success probability quickly converges to unity as the
number of measurement processes increases and that it is almost independent of
the initial state. In particular, we show that to guarantee a success
probability close to one the number of consecutive measurements must be larger
than the dimension of the Hilbert space. We connect these results to quantum
copying, quantum deleting and entanglement generation.


  Digital solutions have substantially contributed to the growth and
dissemination of education. The distance education modality has been presented
as an opportunity for worldwide students in many types of courses. However,
projects of digital educational platforms require different expertise including
knowledge areas such as pedagogy, psychology, computing, and digital
technologies associated with education that allow the correct development and
application of these solutions. To support the evolution of such solutions with
satisfactory quality indicators, this research presents a model focused on
quality of online educational solutions grounded in an approach aimed to
continuous process improvement. The model considers of three maturity levels
and six common entities that address the specific practices for planning and
developing digital educational solutions, targeting quality standards that
satisfy their users, such as students, teachers, tutors, and other people
involved in development and use of these kinds of educational solutions.


  The work shows that the associated Einstein like gravity for the Klein-Gordon
field shows the spontaneous emergence of the cosmological pressure tensor
density (CPTD) that in the classical limit leads to the cosmological constant
(CC). Even if the classical cosmological constant is set to zero, the model
shows that exists a residual theory-derived quantum CPTD. The work shows that
the cosmological constant can be considered as a second order
quantum-mechanical correction to the Newtonian gravity. The outputs of the
theory show that the expectation value of the CPTD is independent by the
zero-point vacuum energy density and that it takes contribution only from the
space where the mass is localized (and the space-time is curvilinear) while
tending to zero as the space-time approaches to the flat vacuum. A developed
model of scalar matter universe shows an overall cosmological effect of the
CPTD on the motion of the galaxies that agrees with the astronomical
observations.


  The degrees of freedom (DoF) region is characterized for the $2$-user
multiple input multiple output (MIMO) broadcast channel (BC), where the
transmitter is equipped with $M$ antennas, the two receivers are equipped with
$N_1$ and $N_2$ antennas, and the levels of channel state information at the
transmitter (CSIT) for the two users are parameterized by $\beta_1, \beta_2$,
respectively. The achievability of the DoF region was established by Hao,
Rassouli and Clerckx, but no proof of optimality was heretofore available. The
proof of optimality is provided in this work with the aid of sum-set
inequalities based on the aligned image sets (AIS) approach.


  Development of defenses against physical world attacks such as adversarial
patches is gaining traction within the research community. We contribute to the
field of adversarial patch detection by introducing an uncertainty-based
adversarial patch localizer which localizes adversarial patch on an image,
permitting post-processing patch-avoidance or patch-reconstruction. We quantify
our prediction uncertainties with the development of \textit{\textbf{D}etection
of \textbf{U}ncertainties in the \textbf{E}xceedance of \textbf{T}hreshold}
(DUET) algorithm. This algorithm provides a framework to ascertain confidence
in the adversarial patch localization, which is essential for safety-sensitive
applications such as self-driving cars and medical imaging. We conducted
experiments on localizing adversarial patches and found our proposed DUET model
outperforms baseline models. We then conduct further analyses on our choice of
model priors and the adoption of Bayesian Neural Networks in different layers
within our model architecture. We found that isometric gaussian priors in
Bayesian Neural Networks are suitable for patch localization tasks and the
presence of Bayesian layers in the earlier neural network blocks facilitates
top-end localization performance, while Bayesian layers added in the later
neural network blocks contribute to better model generalization. We then
propose two different well-performing models to tackle different use cases.


  We show that the restriction of the Dehornoy ordering to an appropriate free
subgroup of the three-strand braid group defines a left ordering of the free
group on k generators, k>1, that has no convex subgroups.


  We consider the problem of inferring the mobility map, which is the
distribution of the building occupants at each timestamp, from the temperatures
of the rooms. We also want to explore the effects of noise in the temperature
measurement, room layout, etc. in the reconstruction of the movement of people
within the building. Our proposed algorithm tackles down the aforementioned
challenges leveraging a parameter learner, the modified Least Square Estimator.
In the absence of a complete data set with mobility map, room and ambient
temperatures, and HVAC data in the public domain, we simulate a physics-based
thermal model of the rooms in a building and evaluate the performance of our
inference algorithm on this simulated data. We find an upper bound of the noise
standard deviation (<= 1F) in the input temperature data of our model. Within
this bound, our algorithm can reconstruct the mobility map with a reasonable
reconstruction error. Our work can be used in a wide range of applications, for
example, ensuring the physical security of office buildings, elderly and infant
monitoring, building resources management, emergency building evacuation, and
vulnerability assessment of HVAC data. Our work brings together multiple
research areas, Thermal Modeling and Parameter Estimation, towards achieving a
common goal of inferring the distribution of people within a large office
building.


  The standard recurrent neural network language model (RNNLM) generates
sentences one word at a time and does not work from an explicit global sentence
representation. In this work, we introduce and study an RNN-based variational
autoencoder generative model that incorporates distributed latent
representations of entire sentences. This factorization allows it to explicitly
model holistic properties of sentences such as style, topic, and high-level
syntactic features. Samples from the prior over these sentence representations
remarkably produce diverse and well-formed sentences through simple
deterministic decoding. By examining paths through this latent space, we are
able to generate coherent novel sentences that interpolate between known
sentences. We present techniques for solving the difficult learning problem
presented by this model, demonstrate its effectiveness in imputing missing
words, explore many interesting properties of the model's latent sentence
space, and present negative results on the use of the model in language
modeling.


  We propose a novel type filter for multicolor imaging to improve on the
photometric redshift estimation of galaxies. An extra filter - specific to a
certain photometric system - may be utilized with high efficiency. We present a
case study of the Hubble Space Telescope's Advanced Camera for Surveys and show
that one extra exposure could cut down the mean square error on photometric
redshifts by 34% over the z<1.3 redshift range.


  We show that the model proposed by Esin, McClintock & Narayan (1997) for the
low state, intermediate state and high state of the black hole soft X-ray
transient, Nova Muscae 1991, is consistent with the spectral evolution of the
black hole X-ray binary, Cyg X-1, during the hard-to-soft state transition
observed in 1996. We also apply the model to the outbursts of two other black
hole X-ray transients, GRO J0422+32 and GRO J1719-24.