  With the goal of maximizing the thermoelectric (TE) figure of merit $ZT$,
Mahan and Sofo [Proc. Natl. Acad. Sci. U.S.A. 93, 7436 (1996)] found that the
optimal transport distribution (TD) is a delta function. Materials, however,
have TDs that appear to always be finite and non-diverging. Motivated by this
observation, this study focuses on deriving what is the optimal bounded TD,
which is determined to be a boxcar function for $ZT$ and a Heaviside function
for power factor. From these optimal TDs upper limits on $ZT$ and power factor
are obtained; the maximum $ZT$ scales with $\Sigma_{\rm max} T /\kappa_l$,
where $\Sigma_{\rm max}$ is the TD magnitude and $\kappa_l$ is the lattice
thermal conductivity. These results help establish practical upper limits on
the performance of TE materials and provide target TDs to guide band/scattering
engineering strategies.


  We consider a Bose gas in spatial dimension $n>3$ with a repulsive, radially
symmetric two-body potential $V$. In the limit of low density $\rho$, the
ground state energy per particle in the thermodynamic limit is shown to be
$(n-2)|\mathbb S^{n-1}|a^{n-2}\rho$, where $|\mathbb S^{n-1}|$ denotes the
surface measure of the unit sphere in $\mathbb{R}^n$ and $a$ is the scattering
length of $V$. Furthermore, for smooth and compactly supported two-body
potentials, we derive upper bounds to the ground state energy with a correction
term $(1+C\gamma)8\pi^4a^6\rho^2|\ln(a^4\rho)|$ in dimension $n=4$, where
$\gamma:=\int V(x)|x|^{-2}\, dx$, and a correction term which is
$\mathcal{O}(\rho^2)$ in higher dimensions.


  This paper presents a simple yet efficient ensemble learning framework for
Vietnamese scene text spotting. Leveraging the power of ensemble learning,
which combines multiple models to yield more accurate predictions, our approach
aims to significantly enhance the performance of scene text spotting in
challenging urban settings. Through experimental evaluations on the VinText
dataset, our proposed method achieves a significant improvement in accuracy
compared to existing methods with an impressive accuracy of 5%. These results
unequivocally demonstrate the efficacy of ensemble learning in the context of
Vietnamese scene text spotting in urban environments, highlighting its
potential for real world applications, such as text detection and recognition
in urban signage, advertisements, and various text-rich urban scenes.


  We investigate an XY spin-glass model in which both spins and couplings
evolve in time: the spins change rapidly according to Glauber-type rules,
whereas the couplings evolve slowly with a dynamics involving spin correlations
and Gaussian disorder. For large times the model can be solved using replica
theory. In contrast to the XY-model with static disordered couplings, solving
the present model requires two levels of replicas, one for the spins and one
for the couplings. Relevant order parameters are defined and a phase diagram is
obtained upon making the replica-symmetric Ansatz. The system exhibits two
different spin-glass phases, with distinct de Almeida-Thouless lines, marking
continuous replica-symmetry breaking: one describing freezing of the spins
only, and one describing freezing of both spins and couplings.


  In this work, we propose a unified framework, called Visual Reasoning with
Differ-entiable Physics (VRDP), that can jointly learn visual concepts and
infer physics models of objects and their interactions from videos and
language. This is achieved by seamlessly integrating three components: a visual
perception module, a concept learner, and a differentiable physics engine. The
visual perception module parses each video frame into object-centric
trajectories and represents them as latent scene representations. The concept
learner grounds visual concepts (e.g., color, shape, and material) from these
object-centric representations based on the language, thus providing prior
knowledge for the physics engine. The differentiable physics model, implemented
as an impulse-based differentiable rigid-body simulator, performs
differentiable physical simulation based on the grounded concepts to infer
physical properties, such as mass, restitution, and velocity, by fitting the
simulated trajectories into the video observations. Consequently, these learned
concepts and physical models can explain what we have seen and imagine what is
about to happen in future and counterfactual scenarios. Integrating
differentiable physics into the dynamic reasoning framework offers several
appealing benefits. More accurate dynamics prediction in learned physics models
enables state-of-the-art performance on both synthetic and real-world
benchmarks while still maintaining high transparency and interpretability; most
notably, VRDP improves the accuracy of predictive and counterfactual questions
by 4.5% and 11.5% compared to its best counterpart. VRDP is also highly
data-efficient: physical parameters can be optimized from very few videos, and
even a single video can be sufficient. Finally, with all physical parameters
inferred, VRDP can quickly learn new concepts from a few examples.


  We consider metric versions of the notions of local embeddability and LEF. We
pay special attention to normally finitely generated groups with word metrics.


  We formulate for the first time the economic dispatch problem in an
integrated electrical and gas distribution system as a game equilibrium problem
between distributed prosumers. Specifically, by approximating the non-linear
gas-flow equations either with a mixed-integer second order cone or a
piece-wise affine model and by assuming that electricity and gas prices depend
linearly on the total consumption we obtain a potential mixed-integer game. To
compute an approximate generalized Nash equilibrium, we propose an iterative
two-stage method that exploits a problem convexification and the gas flow
models. We quantify the quality of the computed solution and perform a
numerical study to evaluate the performance of our method.


  Second-order [O(k^2), k=omega/c] nondipole effects in soft-x-ray
photoemission are demonstrated via an experimental and theoretical study of
angular distributions of neon valence photoelectrons in the 100--1200 eV
photon-energy range. A newly derived theoretical expression for nondipolar
angular distributions characterizes the second-order effects using four new
parameters with primary contributions from pure-quadrupole and octupole-dipole
interference terms. Independent-particle calculations of these parameters
account for a significant portion of the existing discrepancy between
experiment and theory for Ne 2p first-order nondipole parameters.


  Modal Transition Systems (MTS) are a well-known formalism that extend
Labelled Transition Systems (LTS) with the possibility of specifying necessary
and permitted behaviour. Modal refinement ($\preceq_m$) of MTS represents a
step of the design process, namely the one in which some optional behaviour is
discarded while other optional behaviour becomes necessary. Whenever two MTS
are not in modal refinement relation, it could still be the case that the set
of implementations of one MTS is included in the set of implementations of the
other.
  The challenge of devising an alternative notion of modal refinement that is
both sound and complete with respect to the set of implementations, without
disregarding valuable implementations, remains open. We introduce a subset of
MTS called Non-reducible Modal Transition Systems (NMTS), together with a novel
refinement relation $\preceq_n$ for NMTS. We illustrate through examples the
additional constraints imposed by NMTS. Furthermore, we discuss a property
holding for NMTS whose implementations are non-deterministic.


  We propose a Deep Operator Network~(DeepONet) framework to learn the dynamic
response of continuous-time nonlinear control systems from data. To this end,
we first construct and train a DeepONet that approximates the control system's
local solution operator. Then, we design a numerical scheme that recursively
uses the trained DeepONet to simulate the control system's long/medium-term
dynamic response for given control inputs and initial conditions. We accompany
the proposed scheme with an estimate for the error bound of the associated
cumulative error. Furthermore, we design a data-driven Runge-Kutta~(RK)
explicit scheme that uses the DeepONet forward pass and automatic
differentiation to better approximate the system's response when the numerical
scheme's step size is sufficiently small. Numerical experiments on the
predator-prey, pendulum, and cart pole systems confirm that our DeepONet
framework learns to approximate the dynamic response of nonlinear control
systems effectively.


  The Apache Accumulo database is an open source relaxed consistency database
that is widely used for government applications. Accumulo is designed to
deliver high performance on unstructured data such as graphs of network data.
This paper tests the performance of Accumulo using data from the Graph500
benchmark. The Dynamic Distributed Dimensional Data Model (D4M) software is
used to implement the benchmark on a 216-node cluster running the MIT
SuperCloud software stack. A peak performance of over 100,000,000 database
inserts per second was achieved which is 100x larger than the highest
previously published value for any other database. The performance scales
linearly with the number of ingest clients, number of database servers, and
data size. The performance was achieved by adapting several supercomputing
techniques to this application: distributed arrays, domain decomposition,
adaptive load balancing, and single-program-multiple-data programming.


  In this paper, we introduce a notion of adjoint ideal sheaves along closed
subvarieties of higher codimension and study its local properties using
characteristic $p$ methods. When $X$ is a normal Gorenstein closed subvariety
of a smooth complex variety $A$, we formulate a restriction property of the
adjoint ideal sheaf $\adj_X(A)$ of $A$ along $X$ involving the l.c.i. ideal
sheaf $\mathcal{D}_X$ of $X$. The proof relies on a modification of generalized
test ideals of Hara and Yoshida.


  Deterministic placement and dynamic manipulation of individual plasmonic
nanoparticles with nanoscale precision feature an important step towards active
nanoplasmonic devices with prescribed levels of performance and functionalities
at optical frequencies. In this Letter, we demonstrate a plasmonic walker
couple system, in which two gold nanorod walkers can independently or
simultaneously perform stepwise walking powered by DNA hybridization along the
same DNA origami track. We utilize optical spectroscopy to resolve such dynamic
walking with nanoscale steps well below the optical diffraction limit. We also
show that the number of walkers and the optical response of the system can be
correlated. Our studies exemplify the power of plasmonics, when integrated with
DNA nanotechnology for realization of advanced artificial nanomachinery with
tailored optical functionalities.


  To achieve the extremely high luminosity for colliding electron-positron
beams at the future International Linear Collider (ILC) an undulator-based
source with about 230 meters helical undulator and a thin titanium-alloy target
rim rotated with tangential velocity of about 100 meters per second are
foreseen. The very high density of heat deposited in the target has to be
analyzed carefully. The energy deposited by the photon beam in the target has
been calculated in FLUKA. The resulting stress in the target material after one
bunch train has been simulated in ANSYS.


  We determine higher-derivative terms in the open superstring effective action
with U(N) gauge group up to and including order alpha'^4 as can be extracted
from 4 boson, 2 boson - 2 fermion and 4 fermion string scattering amplitudes.
This yields corrections to the non-abelian Born-Infeld action involving higher
derivatives as is relevant for studying D-branes beyond the slowly varying
field approximation. While at order alpha'^2 the action has recently been shown
to be a symmetrised trace, this no longer is true at order alpha'^3 or
alpha'^4. We argue that these terms including higher derivatives are as
important in a low-energy expansion as e.g. the much-discussed alpha'^4 F^6
terms. In particular a computation of the fluctuation spectra at order alpha'^4
has to take into account these non-symmetrised trace higher-derivative terms
computed here.


  Superconductivity is significantly enhanced in monolayer FeSe grown on
SrTiO3, but not for multilayer films, in which large strength of nematicity
develops. However, the link between the high-transition temperature
superconductivity in monolayer and the correlation related nematicity in
multilayer FeSe films is not well understood. Here, we use low-temperature
scanning tunneling microscopy to study few-layer FeSe thin films grown by
molecular beam epitaxy. We observe an incommensurate long-range smectic phase,
which solely appears in bilayer FeSe films. The smectic order still locally
exists and gradually fades away with increasing film thickness, while it
suddenly vanishes in monolayer FeSe, indicative of an abrupt smectic phase
transition. Surface alkali-metal doping can suppress the smectic phase and
induce high-Tc superconductivity in bilayer FeSe. Our observations provide
evidence that the monolayer FeSe is in close proximity to the smectic phase,
and its superconductivity is likely enhanced by this electronic instability as
well.


  Coherent conversion of microwave and optical photons in the single-quantum
level can significantly expand our ability to process signals in various
fields. Efficient up-conversion of a feeble signal in the microwave domain to
the optical domain will lead to quantum-noise-limited microwave amplifiers.
Coherent exchange between optical photons and microwave photons will also be a
stepping stone to realize long-distance quantum communication. Here we
demonstrate bidirectional and coherent conversion between microwave and light
using collective spin excitations in a ferromagnet. The converter consists of
two harmonic oscillator modes, a microwave cavity mode and a magnetostatic mode
called Kittel mode, where microwave photons and magnons in the respective modes
are strongly coupled and hybridized. An itinerant microwave field and a
travelling optical field can be coupled through the hybrid system, where the
microwave field is coupled to the hybrid system through the cavity mode, while
the optical field addresses the hybrid system through the Kittel mode via
Faraday and inverse Faraday effects. The conversion efficiency is theoretically
analyzed and experimentally evaluated. The possible schemes for improving the
efficiency are also discussed.


  We reconsider the problem of determining the semiclassical 3-point function
in the Euclidean AdS_3 model. Exploiting the affine symmetry of the model we
use solutions of the classical Knizhnik-Zamolodchikov (KZ) equation to compute
the saddle point of the action in the presence of three vertex operators. This
alternative derivation reproduces the "heavy charge" classical limit of the
quantum 3-point correlator. It is different from the recently proposed
expression obtained by generalised Pohlmeyer reduction in AdS_2


  Lung tumors, especially those located close to or surrounded by soft tissues
like the mediastinum, are difficult to segment due to the low soft tissue
contrast on computed tomography images. Magnetic resonance images contain
superior soft-tissue contrast information that can be leveraged if both
modalities were available for training. Therefore, we developed a
cross-modality educed learning approach where MR information that is educed
from CT is used to hallucinate MRI and improve CT segmentation. Our approach,
called cross-modality educed deep learning segmentation (CMEDL) combines CT and
pseudo MR produced from CT by aligning their features to obtain segmentation on
CT. Features computed in the last two layers of parallelly trained CT and MR
segmentation networks are aligned. We implemented this approach on U-net and
dense fully convolutional networks (dense-FCN). Our networks were trained on
unrelated cohorts from open-source the Cancer Imaging Archive CT images
(N=377), an internal archive T2-weighted MR (N=81), and evaluated using
separate validation (N=304) and testing (N=333) CT-delineated tumors. Our
approach using both networks were significantly more accurate (U-net $P
<0.001$; denseFCN $P <0.001$) than CT-only networks and achieved an accuracy
(Dice similarity coefficient) of 0.71$\pm$0.15 (U-net), 0.74$\pm$0.12
(denseFCN) on validation and 0.72$\pm$0.14 (U-net), 0.73$\pm$0.12 (denseFCN) on
the testing sets. Our novel approach demonstrated that educing cross-modality
information through learned priors enhances CT segmentation performance


  Our low-temperature magneto-Raman scattering measurements performed on
graphene-like locations on the surface of bulk graphite reveal a new series of
magneto-phonon resonances involving both K-point and Gamma-point phonons. In
particular, we observe for the first time the resonant splitting of three
crossing excitation branches. We give a detailed theoretical analysis of these
new resonances. Our results highlight the role of combined excitations and the
importance of multi-phonon processes (from both K and Gamma points) for the
relaxation of hot carriers in graphene.


  We present microscopic Molecular Dynamics simulations including the efficient
Ewald sum procedure to study warm and dense stellar plasmas consisting of
finite-size ion charges immerse in a relativistic neutralizing electron gas.
For densities typical of Supernova matter and crust in a proto-neutron star, we
select a representative single ion composition and obtain the virialized
equation of state (vEoS). We scrutinize the finite-size and screening
corrections to the Coulomb potential appearing in the virial coefficients $B_2,
B_3$ and $B_4$ as a function of temperature. In addition, we study the thermal
heat capacity at constant volume, $C_V$, and the generalized Mayer's relation
i.e. the difference $C_P-C_V$ with $C_P$ being the heat capacity at constant
pressure, obtaining clear features signaling the onset of the liquid-gas phase
transition. Our findings show that microscopic simulations reproduce the
discontinuity in $C_V$, whose value lies between that of idealized gas and
crystallized configurations. We study the pressure isotherms marking the
boundary of the metastable region before the gaseous transition takes place.
The resulting vEoS displays a behaviour where effective virial coefficients
include extra density dependence showing a generalized density-temperature
form. As an application we parametrize pressure as a function of density and
temperature under the form of an artificial neural network showing the
potential of machine learning for future regression analysis in more refined
multicomponent approaches. This is of interest to size the importance of these
corrections in the liquid-gas phase transition in warm and dense plasma phases
contributing to the cooling behaviour of early Supernova phases and
proto-neutron stars.


  We construct an explicit Deligne - Du Bois complex for algebraic varieties
which are locally analytically isomorphic to the spectrum of a toric face ring.


  Feedback control is expected to considerably protect quantum states against
decoherence caused by interaction between the system and environment.
Especially, Markovian feedback scheme developed by Wiseman can modify the
properties of decoherence and eventually recover the purity of the steadystate
of the corresponding master equation. This paper provides a condition for which
the modified master equation has a pure steady state. By applying this
condition to a two-qubit system, we obtain a complete parametrization of the
feedback Hamiltonian such that the steady state becomes a maximally entangled
state.


  HCI and NLP traditionally focus on different evaluation methods. While HCI
involves a small number of people directly and deeply, NLP traditionally relies
on standardized benchmark evaluations that involve a larger number of people
indirectly. We present five methodological proposals at the intersection of HCI
and NLP and situate them in the context of ML-based NLP models. Our goal is to
foster interdisciplinary collaboration and progress in both fields by
emphasizing what the fields can learn from each other.


  In this paper we will define notion homotopy of morphisms of crossed modules
of Lie algebras. Then we construct a groupoid structure of Lie crossed module
morphisms and their homotopies.


  Exploring the topological physics of phonons is fundamentally important for
understanding various practical applications. Here, we present a
density-functional perturbation theory and finite displacement supercell based
Python 3 software package called PH-NODE for efficiently computing phonon nodes
present in real material through a first-principle approach. The present
version of the code is interfaced with the WIEN2k, Elk, and ABINIT packages. In
order to benchmark the code, four different types of materials are considered,
which include (i) FeSi, a well-known double-Weyl point; (ii) LiCaAs, a
half-Heusler single-type-I Weyl topological phonon (TP); and (iii) ScZn,
coexisting nodal-line and nodal-ring TPs; (iv) TiS, six pairs of bulk Weyl
nodes. In FeSi, the node points are found at ${\Gamma}$(0, 0, 0) and R(0.5,
0.5, 0.5) high symmetric points. Also, there are 21 energy values at which the
node points are situated, corresponding to the full Brillouin Zone. For LiCaAs,
the previously reported literature claims that there is a node point along the
W-X high symmetry direction between the highest longitudinal acoustic and the
lowest transverse optical branch, while in our DFT calculations, a gap of 0.17
meV is found. Furthermore, ScZn hosts six nodal-ring TPs phonons at the
boundary planes of the Brillouin Zone in the vicinity of the M high-symmetric
point. In addition to this, straight-line TPs are also found along the
${\Gamma}$-X and ${\Gamma}$-R high symmetric directions. Moreover, for TiS, six
weyl node points (WP1, WP2, WP3, WP4, WP5 and WP6) are found along H-K
high-symmetric direction. The results obtained from the PH-NODE code are in
good agreement with the experimentally and theoretically reported data for each
material.


  We analyze the near-infrared to UV data of 16 quasars with redshifts ranging
from 0.71 $<$ $z$ $<$ 2.13 to investigate dust extinction properties. The
sample presented in this work is obtained from the High $A_V$ Quasar (HAQ)
survey. The quasar candidates were selected from the Sloan Digital Sky Survey
(SDSS) and the UKIRT Infrared Deep Sky Survey (UKIDSS), and follow-up
spectroscopy was carried out at the Nordic Optical Telescope (NOT) and the New
Technology Telescope (NTT). To study dust extinction curves intrinsic to the
quasars, from the HAQ survey we selected 16 cases where the Small Magellanic
Cloud (SMC) law could not provide a good solution to the spectral energy
distributions (SEDs). We derived the extinction curves using Fitzpatrick &
Massa 1986 (FM) law by comparing the observed SEDs to the combined quasar
template from Vanden Berk et al. 2001 and Glikman et al. 2006. The derived
extinction, $A_V$, ranges from 0.2-1.0 mag. All the individual extinction
curves of our quasars are steeper ($R_V=2.2$-2.7) than that of the SMC, with a
weighted mean value of $R_V=2.4$. We derive an `average quasar extinction
curve' for our sample by fitting SEDs simultaneously by using the weighted mean
values of the FM law parameters and a varying $R_V$. The entire sample is well
fit with a single best-fit value of $R_V=2.2\pm0.2$. The `average quasar
extinction curve' deviates from the steepest Milky Way and SMC extinction
curves at a confidence level $\gtrsim95\%$. Such steep extinction curves
suggest a significant population of silicates to produce small dust grains.
Moreover, another possibility could be that the large dust grains may have been
destroyed by the activity of the nearby active galactic nuclei (AGN), resulting
in steep extinction curves.


  A simple model for medium modification of the jet function can be used to
extract the jet energy loss distribution through a parameterized form. We carry
out a comprehensive Bayesian analysis of the world data on single inclusive jet
spectra in heavy-ion collisions at both RHIC and LHC energies. We extract the
average jet energy loss $\langle \Delta E\rangle$ as a function of jet
transverse momentum $p_T$ for each collision system and centrality
independently. Assuming jet energy loss is proportional to the initial parton
density $\rho \sim dN_{\rm ch}/d\eta/\pi R_{\rm eff}^2$ as estimated from the
pseudorapidity density of charged hadron multiplicity $dN_{\rm ch}/d\eta$ and
the effective system size $R_{\rm eff}\sim N_{\rm part}^{1/3}$ given by the
number of participant nucleons $N_{\rm part}$, the scaled average jet energy
loss $\langle \Delta E\rangle/\rho \sim R_{\rm eff}^{0.59} p_T^{0.13}\ln p_T $
for jet cone-size $R=0.4$ is found to have a momentum dependence that is
slightly stronger than a logarithmic form while the system size or length
dependence is slower than a linear one. The fluctuation of jet energy loss is,
however, independent of the initial parton density or the system size.


  In this paper we study the regularity of non-linear parabolic PDEs and
stochastic PDEs on metric measure spaces admitting heat kernels. In particular
we consider mild function solutions to abstract Cauchy problems and show that
the unique solution is H\"older continuous in time with values in a suitable
fractional Sobolev space. As this analysis is done via a-priori estimates, we
can apply this result to stochastic PDEs on metric measure spaces and solve the
equation in a pathwise sense for almost all paths. The main example of noise
term is of fractional Brownian type and the metric measure spaces can be
classical as well as given by various fractal structures. The whole approach is
low dimensional and works for spectral dimensions less than 4.


  Central place systems have been demonstrated to possess self-similar patterns
in both the theoretical and empirical perspectives. A central place fractal can
be treated as a monofractal with a single scaling process. However, in the real
world, a system of human settlements is a complex network with multi-scaling
processes. The simple fractal central place models are not enough to interpret
the spatial patterns and evolutive processes of urban systems. It is necessary
to construct multi-scaling fractal models of urban places. Based on the
postulate of intermittent space filling, two typical multifractal models of
central places are proposed in this paper. One model is put forward to reflect
the process of spatial convergence (aggregation), and the generalized
correlation dimension varies from 0.7306 to 1.3181; the other model is
presented to describe the process of spatial divergence (diffusion), the
generalized correlation dimension ranges from 1.6523 to 1.7118. As a case
study, an analogy is drawn between the theoretical models and a system of
cities and towns of Central Plains, China. A finding is that urban systems take
on multifractal form, and can be modeled with multi-scaling fractals. This is a
preliminary attempt to develop the theory of fractal central places, and the
results are helpful for understanding the similarities and differences between
the geographical process of spatial aggregation and that of spatial diffusion.


  In this dissertation, we study the evolution and properties of the relic (or
cosmic) neutrino distribution from neutrino freeze-out at $T=O(1)$ MeV through
the free-streaming era up to today, focusing on the deviation of the neutrino
spectrum from equilibrium. In particular, we demonstrate the presence of
chemical non-equilibrium that continues to the present day. The work naturally
separates into two parts. The first focuses on aspects of the relic neutrinos
that can be explored using conservation laws. The second part studies the
neutrino distribution using the full general relativistic Boltzmann equation.
  Part one begins with an overview of the history of the Universe, from just
prior to neutrino freeze-out up through the present day, placing the history of
cosmic neutrino evolution in its proper context. Motivated by the Planck CMB
measurements of the effective number of neutrinos, we derive those properties
of neutrino freeze-out that depend only on conservation laws and are
independent of the details of the scattering processes. Part one ends with a
characterization of the present day neutrino spectrum as seen from Earth.
  The second part of this dissertation focuses on the properties of cosmic
neutrinos that depend on the details of the neutrino reactions, as is necessary
for modeling the non-thermal distortions from equilibrium and computing
freeze-out temperatures. We detail a new spectral method for solving the
Boltzmann equation, based on a dynamical basis of orthogonal polynomials, as
well as an improved procedure for analytically simplifying the corresponding
scattering integrals for subsequent numerical computation. We apply these novel
solution methods to solve the Boltzmann equation through the neutrino
freeze-out period and perform parametric studies of the dependence of neutrino
freeze-out on standard model parameters.


  The Schelling model has become a paradigm in social sciences to explain the
emerge of residential spatial segregation even in the presence of high
tolerance to mixed neighborhoods by the side of citizens. In particular, we
consider a noisy constrained version of the Schelling model, in which agents
maximize its satisfaction, related to the composition of the local
neighborhood, by infinite-range movements towards satisfying vacancies. We add
to it an aging effect by making the probability of agents to move inversely
proportional to the time they have been satisfied in their present location.
This mechanism simulates the development of an emotional attachment to a
location where an agent has been satisfied for a while. The introduction of
aging has several major impacts on the model statics and dynamics: the phase
transition between a segregated and a mixed phase of the original model
disappears, and we observe segregated states with high level of agent
satisfaction even for high values of the tolerance. In addition, the new
segregated phase is dynamically characterized by a slow power-law coarsening
process and by a glassy-like dynamics in which the asymptotic time
translational invariance is broken.


  This paper investigates the randomness properties of a function of the
divisor pairs of a natural number. This function, the antecedents of which go
to very ancient times, has randomness properties that can find applications in
cryptography, key distribution, and other problems of computer science. It is
shown that the function is aperiodic and it has excellent autocorrelation
properties.


  This paper presents the first hardware implementation of the Datagram
Transport Layer Security (DTLS) protocol to enable end-to-end security for the
Internet of Things (IoT). A key component of this design is a reconfigurable
prime field elliptic curve cryptography (ECC) accelerator, which is 238x and 9x
more energy-efficient compared to software and state-of-the-art hardware
respectively. Our full hardware implementation of the DTLS 1.3 protocol
provides 438x improvement in energy-efficiency over software, along with code
size and data memory usage as low as 8 KB and 3 KB respectively. The
cryptographic accelerators are coupled with an on-chip low-power RISC-V
processor to benchmark applications beyond DTLS with up to two orders of
magnitude energy savings. The test chip, fabricated in 65 nm CMOS, demonstrates
hardware-accelerated DTLS sessions while consuming 44.08 uJ per handshake, and
0.89 nJ per byte of encrypted data at 16 MHz and 0.8 V.


  In the Next-to-Minimal Supersymmetric Standard Model (NMSSM), it is possible
to have strong mass degeneracies between the new singlet-like scalar and the
heavy doublet-like scalar, as well as between the singlet-like and doublet-like
pseudoscalar Higgs states. When the difference in the masses of such states is
comparable with the sum of their widths, the quantum mechanical interference
between their propagators can become significant. We study these effects by
taking into account the full Higgs boson propagator matrix in the calculation
of the production process of $\tau^+\tau^-$ pairs in gluon fusion at the Large
Hadron Collider (LHC). We find that, while these interference effects are
sizeable, they are not resolvable in terms of the distributions of differential
cross sections, owing to the poor detector resolution of the $\tau^+\tau^-$
invariant mass. They are, however, identifiable via the inclusive cross
sections, which are subject to significant variations with respect to the
standard approaches, wherein the propagating Higgs bosons are treated
independently from one another. We quantify these effects for several
representative benchmark points, extracted from a large set of points, obtained
by numerical scanning of the NMSSM parameter space, that satisfy the most
important experimental constraints currently available.


  The signature of a path is a sequence of tensors which allows to uniquely
reconstruct the path. In this paper we propose a systematic study of basic
properties of signature tensors, starting from their rank, symmetries and
conciseness. We prove a sharp upper bound on the rank of signature tensors of
piecewise linear paths. We show that there are no skew-symmetric signature
tensors of order three or more, and we also prove that specific instances of
partial symmetry can only happen for tensors of order three. Finally, we give a
simple geometric characterization of paths whose signature tensors are not
concise.


  Box-ball system (BBS) is a prominent example of integrable cellular automata
in one dimension connected to quantum groups, Bethe ansatz,
ultradiscretization, tropical geometry and so forth. In this paper we study the
generalized Gibbs ensemble of BBS soliton gas by thermodynamic Bethe ansatz and
generalized hydrodynamics. The results include the solution to the speed
equation for solitons, an intriguing connection of the effective speed with the
period matrix of the tropical Riemann theta function, an explicit description
of the density plateaux that emerge from domain wall initial conditions
including their diffusive corrections.


  Consider the motion of a Brownian particle in two or more dimensions, whose
coordinate processes are standard Brownian motions with zero drift initially,
and then at some random/unobservable time, one of the coordinate processes gets
a (known) non-zero drift permanently. Given that the position of the Brownian
particle is being observed in real time, the problem is to detect the time at
which a coordinate process gets the drift as accurately as possible. We solve
this problem in the most uncertain scenario when the random/unobservable time
is (i) exponentially distributed and (ii) independent from the initial motion
without drift. The solution is expressed in terms of a stopping time that
minimises the probability of a false early detection and the expected delay of
a missed late detection. To our knowledge this is the first time that such a
problem has been solved exactly in the literature.


  In designing an online A/B experiment, it is crucial to select a sample size
and duration that ensure the resulting confidence interval (CI) for the
treatment effect is the right width to detect an effect of meaningful magnitude
with sufficient statistical power without wasting resources. While the
relationship between sample size and CI width is well understood, the effect of
experiment duration on CI width remains less clear. This paper provides an
analytical formula for the width of a CI based on a ratio treatment effect
estimator as a function of both sample size (N) and duration (T). The formula
is derived from a mixed effects model with two variance components. One
component, referred to as the temporal variance, persists over time for
experiments where the same users are kept in the same experiment arm across
different days. The remaining error variance component, by contrast, decays to
zero as T gets large. The formula we derive introduces a key parameter that we
call the user-specific temporal correlation (UTC), which quantifies the
relative sizes of the two variance components and can be estimated from
historical experiments. Higher UTC indicates a slower decay in CI width over
time. On the other hand, when the UTC is 0 -- as for experiments where users
shuffle in and out of the experiment across days -- the CI width decays at the
standard parametric 1/T rate. We also study how access to pre-period data for
the users in the experiment affects the CI width decay. We show our formula
closely explains CI widths on real A/B experiments at YouTube.


  Reinforcement Learning (RL) agents demonstrating proficiency in a training
environment exhibit vulnerability to adversarial perturbations in input
observations during deployment. This underscores the importance of building a
robust agent before its real-world deployment. To alleviate the challenging
point, prior works focus on developing robust training-based procedures,
encompassing efforts to fortify the deep neural network component's robustness
or subject the agent to adversarial training against potent attacks. In this
work, we propose a novel method referred to as Transformed Input-robust RL
(TIRL), which explores another avenue to mitigate the impact of adversaries by
employing input transformation-based defenses. Specifically, we introduce two
principles for applying transformation-based defenses in learning robust RL
agents: (1) autoencoder-styled denoising to reconstruct the original state and
(2) bounded transformations (bit-depth reduction and vector quantization (VQ))
to achieve close transformed inputs. The transformations are applied to the
state before feeding it into the policy network. Extensive experiments on
multiple MuJoCo environments demonstrate that input transformation-based
defenses, i.e., VQ, defend against several adversaries in the state
observations. The official code is available at
https://github.com/tunglm2203/tirl


  We investigate the microscopic description of exciton-polaritons that
involves electrons, holes and photons within a two-dimensional microcavity. We
show that in order to recover the simplified exciton-photon model that is
typically used to describe polaritons, one must correctly define the
exciton-photon detuning and exciton-photon (Rabi) coupling in terms of the bare
microscopic parameters. For the case of unscreened Coulomb interactions, we
find that the exciton-photon detuning is strongly shifted from its bare value
in a manner akin to renormalization in quantum electrodynamics. Within the
renormalized theory, we exactly solve the problem of a single exciton-polariton
for the first time and obtain the full spectral response of the microcavity. In
particular, we find that the electron-hole wave function of the polariton can
be significantly modified by the very strong Rabi couplings achieved in current
experiments. Our microscopic approach furthermore allows us to obtain the
effective interaction between identical polaritons for any light-matter
coupling. Crucially, we show that the standard treatment of polariton-polariton
interactions in the very strong coupling regime is incorrect, since it neglects
the light-induced modification of the exciton size and thus greatly
overestimates the effect of Pauli exclusion on the Rabi coupling, i.e., the
saturation of exciton oscillator strength. Our findings thus provide the
foundations for understanding and characterizing exciton-polariton systems
across the whole range of polariton densities.


  We review recent measurements of the properties of the top quark: the decay
width of the top quark, of spin correlations between the top and the antitop
quarks in $\ttbar$ production, the $W$ boson helicity in top decays, the strong
colour flow in $\ttbar$ events, and the asymmetry of $\ttbar$ production due to
the strong colour charge. The measurements are performed on data samples of up
to 5.4 \fb\ of integrated luminosity acquired by the CDF and D0 collaborations
in Run II of the Fermilab Tevatron $p\bar p$ collider at a centre-of-mass
energy of $\sqrt s=1.96 \TeV$.


  First-order optimization methods for nonconvex functions with Lipschitz
continuous gradients and Hessian have been studied intensively in both machine
learning and optimization. State-of-the-art methods finding an
$\varepsilon$-stationary point within $O(\varepsilon^{-{7/4}})$ or
$\tilde{O}(\varepsilon^{-{7/4}})$ gradient evaluations are based on Nesterov's
accelerated gradient descent (AGD) or Polyak's heavy-ball method. However,
these algorithms employ additional mechanisms, such as restart schemes and
negative curvature exploitation, which complicate the algorithms' behavior and
make it challenging to apply them to more advanced settings (e.g., stochastic
optimization). To realize a simpler algorithm, we investigate the heavy-ball
differential equation, a continuous-time analogy of the AGD and heavy-ball
methods; we prove that the dynamics attains an $\varepsilon$-stationary point
within $O(\varepsilon^{-{7/4}})$ time. We also show that a vanilla heavy-ball
algorithm, obtained by discretizing the dynamics, achieves the complexity of
$O(\varepsilon^{-{7/4}})$ under an additional assumption.


  We exhaustively explore the reprogrammability capabilities and the intrinsic
universality of the Cartesian product $P \times C$ of the space $P$ of all
possible computer programs of increasing size and the space $C$ of all possible
compilers of increasing length such that $p \in P$ emulates $p^\prime \in P$
with $T|p^\prime|=|p|$ under a coarse-graining transformation $T$. Our approach
yields a novel perspective on the complexity, controllability, causality and
(re)programmability discrete dynamical systems. We find evidence that the
density of (qualitatively different) computer programs that can be reprogrammed
grows asymptotically as a function of program and compiler size. To illustrate
these findings we show a series of behavioural boundary crossing results,
including emulations (for all initial conditions) of Wolfram class 2 Elementary
Cellular Automata (ECA) by Class 1 ECA, emulations of Classes 1, 2 and 3 ECA by
Class 2 and 3 ECA, and of Classes 1, 2 and 3 by Class 3 ECA, along with results
of even greater emulability for general CA (neighbourhood $r=3/2$), including
Class 1 CA emulating Classes 2 and 3, and Classes 3 and 4 emulating all other
classes (1, 2, 3 and 4). The emulations occur with only a linear overhead and
can be considered computationally efficient. We also found that there is no
hacking strategy to compress the search space based on compiler profiling in
terms of e.g. similarity or complexity, suggesting that no strategy other than
exhaustive search is viable. We also introduce emulation networks, derive a
topologically-based measure of complexity based upon out- and in-degree
connectivity, and establish bridges to fundamental ideas of complexity,
universality, causality and dynamical systems.


  Double-strand breaks (DSBs) in DNA are naturally occurring destructive events
in all organisms that may lead to genome instability. Cells employ various
repair methods known as non-homologous end joining (NHEJ), microhomology
mediated end joining (MMEJ), and homology-directed recombination (HDR). These
repair processes may lead to DNA sequence variations (e.g., nucleotide
insertions, deletions, and substitutions) at the location of the break.
Studying DNA DSB repair processes often involves the use of high throughput
sequencing assays to precisely quantify the sequence variations near the break
with software tools. Often methods of assessing and visualizing these data have
not taken into account the full complexity of the sequencing data, such as the
frequency, type, and position of the sequence variations in a single
comprehensive representation. Here we present a method that allows
visualization of the overall variation pattern as well as comparison of these
patterns among experimental setups.


  We present a four-dimensional double-black-hole (or dihole) solution in
Kaluza-Klein theory, describing a superposition of an electrically charged and
a magnetically charged black hole. This system can be balanced for
appropriately chosen parameters, and the resulting space-time is completely
regular on and outside the event horizons. This solution was constructed using
the inverse-scattering method in five-dimensional vacuum gravity, in which it
describes a rotating black ring surrounding a static black hole on a Taub-NUT
background space. Various properties of this solution are studied, from both a
four- and five-dimensional perspective.


  One of the main motivations for low energy supersymmetric theories is their
ability to address the hierarchy and naturalness problems in the Higgs sector
of the Standard Model. In these theories, at least two doublets of scalar
fields are required to break the electroweak symmetry and to generate the
masses of the elementary particles, resulting in a rather rich Higgs spectrum.
The search for the Higgs bosons of Supersymmetry and the determination of their
basic properties is one of the major goals of high--energy colliders and, in
particular, the LHC which will soon start operation. We review the salient
features of the Higgs sector of the Minimal Supersymmetric Standard Model and
of some of its extensions and summarize the prospects for probing them at the
LHC and at the future ILC.


  We detail interferometric observations of 44GHz class I methanol masers
detected by MALT-45 (a 7mm unbiased auto-correlated spectral-line
Galactic-plane survey) using the Australia Telescope Compact Array. We detect
238 maser spots across 77 maser sites. Using high-resolution positions, we
compare the class I CH$_3$OH masers to other star formation maser species,
including CS (1-0), SiO $v=0$ and the H53$\alpha$ radio-recombination line.
Comparison between the cross- and auto-correlated data has allowed us to also
identify quasi-thermal emission in the 44GHz class I methanol maser line. We
find that the majority of class I methanol masers have small spatial and
velocity ranges ($<$0.5pc and $<$5 km s$^{-1}$), and closely trace the systemic
velocities of associated clouds. Using 870$\mu$m dust continuum emission from
the ATLASGAL survey, we determine clump masses associated with class I masers,
and find they are generally associated with clumps between 1000 and 3000
$M_\odot$. For each class I methanol maser site, we use the presence of OH
masers and radio recombination lines to identify relatively evolved regions of
high-mass star formation; we find that maser sites without these associations
have lower luminosities and preferentially appear toward dark infrared regions.


  We present a catalogue of Giant Molecular Clouds (GMCs) in M33, extracted
from cold dust continuum emission. Our GMCs are identified by computing
dendrograms. We measure the spatial distribution of these clouds, and
characterise their dust properties. Combining these measured properties with
CO(J=2-1) and 21cm HI data, we calculate the gas-to-dust ratio (GDR) of these
clouds, and from this compute a total cloud mass. In total, we find 165 GMCs
with cloud masses in the range of 10$^4$-10$^7$ M$_\odot$. We find that
radially, $\log_{10}(\mathrm{GDR}) = -0.043(\pm0.038) \,\mathrm{R [kpc]} +
1.88(\pm0.15)$, a much lower GDR than found in the Milky Way, and a
correspondingly higher $\alpha_{\rm CO}$ factor. The mass function of these
clouds follows a slope proportional to M$^{-2.84}$, steeper than many previous
studies of GMCs in local galaxies, implying that M33 is poorer at forming
massive clouds than other nearby spirals. Whilst we can rule out interstellar
pressure as the major contributing factor, we are unable to disentangle the
relative effects of metallicity and HI velocity dispersion. We find a
reasonably featureless number density profile with galactocentric radius, and
weak correlations between galactocentric radius and dust temperature/mass.
These clouds are reasonably consistent with Larson's scaling relationships, and
many of our sources are co-spatial with earlier CO studies. Massive clouds are
identified at large galactocentric radius, unlike in these earlier studies,
perhaps indicating a population of CO-dark gas dominated clouds at these larger
distances.


  In this paper, first a great number of inverse problems which arise in
instrumentation, in computer imaging systems and in computer vision are
presented. Then a common general forward modeling for them is given and the
corresponding inversion problem is presented. Then, after showing the
inadequacy of the classical analytical and least square methods for these ill
posed inverse problems, a Bayesian estimation framework is presented which can
handle, in a coherent way, all these problems. One of the main steps, in
Bayesian inversion framework is the prior modeling of the unknowns. For this
reason, a great number of such models and in particular the compound hidden
Markov models are presented. Then, the main computational tools of the Bayesian
estimation are briefly presented. Finally, some particular cases are studied in
detail and new results are presented.


  An improved procedure is suggested for finding the total photoabsorption
cross section on the neutron from data on the deuteron at energies < 1.5 GeV.
It includes unfolding of smearing effects caused by Fermi motion of nucleons in
the deuteron and also takes into account non-additive contributions to the
deuteron cross section due to final-state interactions of particles in single
and double pion photoproduction. This procedure is applied to analysis of
existing data.


  This article concerns the problems regarding different lattice regularization
techniques for the matter fields of Hamiltonian constraints defined in the
framework of loop quantum gravity. The analysis is formulated in the phase
space-reduced cosmological model of the hypothetical theory of canonical
quantum general relativity. This article explains why a different than
links-related lattice smearing of fields leads to a local violation of general
covariance. This happens by assuming, for instance, the nodes-related smearing.
Therefore, this problem occurs in the case of any polymerlike scalar field
quantization method by breaking the background independence of the
semiclassical predictions. In consequence, the diffeomorphism symmetry that
depends on a links distribution is broken locally at the level of generally
relativistic corrections. Moreover, by using the phase space-reduced gauge
fixing technique to analyze this issue, the results are general and they
concern any coupling with the links-regularized gravitational degrees of
freedom in loop quantum gravity. Therefore, they lead to the following no-go
conclusion. Any lattice smearing of matter, not defined by using the
geometrical distribution specified by the links-fluxes duality, violates the
general principle of relativity.


  What, if any, was Einstein's biggest mistake, the one most affecting our
physics today? There is a perhaps apocryphal story, recounted by George Gamow,
that he counted his cosmological constant as his biggest blunder. We now know
his hypothesized cosmological constant to be correct. His lifelong rejection of
quantum mechanics, an interesting side-story in the evolution of 20th-century
physics, is a candidate. None of these introduced difficulties in how our
physics is done today. It can be argued that his biggest actual mistake, one
that affects many subfields of physics and chemistry and bewilders students
today, occurred in his naming of his A and B coefficients.


  We study the dynamic behavior of frameless ALOHA, both in terms of throughput
and age of information (AoI). In particular, differently from previous studies,
our analysis accounts for the fact that the number of terminals contending the
channel may vary over time, as a function of the duration of the previous
contention period. The stability of the protocol is analyzed via a drift
analysis, which allows us to determine the presence of stable and unstable
equilibrium points. We also provide an exact characterization of the AoI
performance, through which we determine the impact of some key protocol
parameters, such as the maximum length of the contention period, on the average
AoI. Specifically, we show that configurations of parameters that maximize the
throughput may result in a degradation of the AoI performance.


  We give a bijection between the set of self-conjugate partitions and that of
ordinary partitions. Also, we show the relation between hook lengths of self
conjugate partition and corresponding partition via the bijection. As a
corollary, we give new combinatorial interpretations for the Catalan number and
the Motzkin number in terms of self-conjugate simultaneous core partitions.


  Cyclic codes have efficient encoding and decoding algorithms. The decoding
error probability and the undetected error probability are usually bounded by
or given from the weight distributions of the codes. Most researches are about
the determination of the weight distributions of cyclic codes with few
nonzeros, by using quadratic form and exponential sum but limited to low
moments. In this paper, we focus on the application of higher moments of the
exponential sum to determine the weight distributions of a class of ternary
cyclic codes with three nonzeros, combining with not only quadratic form but
also MacWilliams' identities. Another application of this paper is to emphasize
the computer algebra system Magma for the investigation of the higher moments.
In the end, the result is verified by one example using Matlab.


  We present IRAM-30m Telescope $^{12}$CO and $^{13}$CO observations of a
sample of 55 luminous and ultraluminous infrared galaxies (LIRGs and ULIRGs) in
the local universe. This sample is a subset of the Great Observatory All-Sky
LIRG Survey (GOALS), for which we use ancillary multi-wavelength data to better
understand their interstellar medium and star formation properties. Fifty-three
(96%) of the galaxies are detected in $^{12}$CO, and 29 (52%) are also detected
in $^{13}$CO above a 3$\sigma$ level. The median full width at zero intensity
(FWZI) velocity of the CO line emission is 661km s$^{-1}$, and $\sim$54% of the
galaxies show a multi-peak CO profile. Herschel photometric data is used to
construct the far-IR spectral energy distribution of each galaxy, which are fit
with a modified blackbody model that allows us to derive dust temperatures and
masses, and infrared luminosities. We make the assumption that the gas-to-dust
mass ratio of (U)LIRGs is comparable to local spiral galaxies with a similar
stellar mass (i.e., gas/dust of mergers is comparable to their progenitors) to
derive a CO-to-H$_2$ conversion factor of
$\langle\alpha\rangle=1.8^{+1.3}_{-0.8}M_\odot$(K km s$^{-1}$pc$^{2}$)$^{-1}$;
such a value is comparable to that derived for (U)LIRGs based on dynamical mass
arguments. We derive gas depletion times of $400-600$Myr for the (U)LIRGs,
compared to the 1.3Gyr for local spiral galaxies. Finally, we re-examine the
relationship between the $^{12}$CO/$^{13}$CO ratio and dust temperature,
confirming a transition to elevated ratios in warmer systems.


  Bilayer graphene in a magnetic field supports eight zero-energy Landau
levels, which, as a tunable band gap develops, split into two nearly-degenerate
quartets separated by the band gap. A close look is made into the properties of
such an isolated quartet of pseudo-zero-mode levels at half filling in the
presence of an in-plane electric field and the Coulomb interaction, with focus
on revealing further controllable features in bilayer graphene. The half-filled
pseudo-zero-mode levels support, via orbital level mixing, charge carriers with
nonzero electric moment, which would lead to field-induced level splitting and
the current-induced quantum Hall effect. It is shown that the Coulomb
interaction enhances the effect of the in-plane field and their interplay leads
to rich spectra of collective excitations, pseudospin waves, accessible by
microwave experiments; also a duality in the excitation spectra is revealed.


  In this work we study the stability of the Jordan-Brans-Dicke (JBD) static
universe. This is motivated by the possibility that the universe might have
started out in an asymptotically JBD static state, in the context of the so
called emergent universe scenario. We extent our previous results on stability
of JBD static universe by considering spatially homogeneous Bianchi type IX
anisotropic perturbation modes and by including more general perfect fluids.
Contrary to general relativity, we have found that the JBD static universe,
dominated by a standard perfect fluid, could be stable against isotropic and
anisotropic perturbations. The implications of these results for the initial
state of the universe and its pre-inflationary evolution are discussed.


  We study the relation between isolated hypersurface singularities (e.g. ADE)
and the quantum cohomology ring by using spectral invariants, which are
symplectic invariants coming from Floer theory. We prove, under the assumption
that the quantum cohomology ring is semi-simple, that (1) if the smooth Fano
variety (or the symplectic manifold) degenerates to a Fano variety with an
isolated hypersurface singularity, then the singularity has to be an
$A_m$-singularity, (2) if the symplectic manifold contains an
$A_m$-configuration of Lagrangian spheres, then there are consequences on the
Hofer geometry, and that (3) the Dehn twist reduces spectral invariants.


  To create more realistic experiences in human-virtual object interactions,
texture rendering has become a research hotspot in recent years. Different
frequency components of designed vibrations can activate texture-related
sensations due to similar receptors. However, designing specific vibrations for
numerous real-world materials is impractical. Therefore, this study proposes a
human-in-the-loop vibration generation model based on user preferences. To
enable users to easily control the generation of vibration samples with large
parameter spaces, we introduce an optimization model based on Differential
Subspace Search (DSS) and Generative Adversarial Network (GAN). With DSS, users
can use a one-dimensional slider to easily modify the high-dimensional latent
space so that the GAN can generate desired vibrations. We trained the
generative model using a open dataset of tactile vibration data and selected
five types of vibrations as target samples for the generation experiment.
Extensive user experiments were conducted using the generated and real samples.
The results indicate that our system can generate distinguishable samples that
match the target characteristics. Moreover, the results also reveal a
correlation between subjects' ability to distinguish real samples and their
ability to distinguish generated samples.


  In this paper, we introduce a notion of the center and radius of a subset A
of metric space X. In the Euclidean spaces, this notion can be seen as the
extension of the center and radius of open/closed balls. The center and radius
of a finite product of subsets of metric spaces, and a finite union of subsets
of a metric space are also determined. For any subset A of metric space X,
there is a natural question to identify the open balls of X with the largest
radius that are entirely contained in A. To answer this question, we introduce
a notion of quasi-center and quasi-radius of a subset A of metric space X. We
prove that the center of the largest open balls contained in A belongs to the
quasi-center of A, and its radius is equal to the quasi-radius of A. In
particular, for the Euclidean spaces, we see that the center of largest open
balls contained in A belongs to the center of A, and its radius is equal to the
radius of A.


  Denosing diffusion model, as a generative model, has received a lot of
attention in the field of image generation recently, thanks to its powerful
generation capability. However, diffusion models have not yet received
sufficient research in the field of image fusion. In this article, we introduce
diffusion model to the image fusion field, treating the image fusion task as
image-to-image translation and designing two different conditional injection
modulation modules (i.e., style transfer modulation and wavelet modulation) to
inject coarse-grained style information and fine-grained high-frequency and
low-frequency information into the diffusion UNet, thereby generating fused
images. In addition, we also discussed the residual learning and the selection
of training objectives of the diffusion model in the image fusion task.
Extensive experimental results based on quantitative and qualitative
assessments compared with benchmarks demonstrates state-of-the-art results and
good generalization performance in image fusion tasks. Finally, it is hoped
that our method can inspire other works and gain insight into this field to
better apply the diffusion model to image fusion tasks. Code shall be released
for better reproducibility.


  This paper is concerned with programming adaptive linear neural networks
(ALNNs) using chemical reaction networks (CRNs) equipped with mass-action
kinetics. Through individually programming the forward propagation and the
backpropagation of ALNNs, and also utilizing the permeation walls technique, we
construct a powerful CRN possessing the function of ALNNs, especially having
the function of automatic computation. We also provide theoretical analysis and
a case study to support our construction. The results will have potential
implications for the developments of synthetic biology, molecular computer and
artificial intelligence.


  We present a new estimator for the self-energy based on a combination of two
equations of motion and discuss its benefits for numerical renormalization
group (NRG) calculations. In challenging regimes, NRG results from the standard
estimator, a ratio of two correlators, often suffer from artifacts: the
imaginary part of the retarded self-energy is not properly normalized and, at
low energies, overshoots to unphysical values and displays wiggles. We show
that the new estimator resolves the artifacts in these properties as they can
be determined directly from the imaginary parts of auxiliary correlators and do
not involve real parts obtained by Kramers-Kronig transform. Furthermore, we
find that the new estimator yields converged results with reduced numerical
effort (for a lower number of kept states) and thus is highly valuable when
applying NRG to multiorbital systems. Our analysis is targeted at NRG
treatments of quantum impurity models, especially those arising within
dynamical mean-field theory, but most results can be straightforwardly
generalized to other impurity or cluster solvers.


  Model evaluations are central to understanding the safety, risks, and
societal impacts of AI systems. While most real-world AI applications involve
human-AI interaction, most current evaluations (e.g., common benchmarks) of AI
models do not. Instead, they incorporate human factors in limited ways,
assessing the safety of models in isolation, thereby falling short of capturing
the complexity of human-model interactions. In this paper, we discuss and
operationalize a definition of an emerging category of evaluations -- "human
interaction evaluations" (HIEs) -- which focus on the assessment of human-model
interactions or the process and the outcomes of humans using models. First, we
argue that HIEs can be used to increase the validity of safety evaluations,
assess direct human impact and interaction-specific harms, and guide future
assessments of models' societal impact. Second, we propose a safety-focused HIE
design framework -- containing a human-LLM interaction taxonomy -- with three
stages: (1) identifying the risk or harm area, (2) characterizing the use
context, and (3) choosing the evaluation parameters. Third, we apply our
framework to two potential evaluations for overreliance and persuasion risks.
Finally, we conclude with tangible recommendations for addressing concerns over
costs, replicability, and unrepresentativeness of HIEs.


  We discuss the Casimir effect for boundary conditions involving perfect
electromagnetic conductors (PEMCs). Based on the corresponding reciprocal
Green's tensor we construct the Green's tensor for two perfectly reflecting
plates with magnetoelectric coupling (non-reciprocal media) within the
framework of macroscopic quantum electrodynamics. We calculate the Casimir
force between two PEMC plates in terms of the PEMC parameter M and the duality
transformation angle ${\theta}$ resulting in a universal analytic expression
that connects the attractive Casimir force with the repulsive Boyer force. We
relate the results to the duality symmetry of electromagnetism.


  Feature tracking is the building block of many applications such as visual
odometry, augmented reality, and target tracking. Unfortunately, the
state-of-the-art vision-based tracking algorithms fail in surgical images due
to the challenges imposed by the nature of such environments. In this paper, we
proposed a novel and unified deep learning-based approach that can learn how to
track features reliably as well as learn how to detect such reliable features
for tracking purposes. The proposed network dubbed as Deep-PT, consists of a
tracker network which is a convolutional neural network simulating
cross-correlation in terms of deep learning and two fully connected networks
that operate on the output of intermediate layers of the tracker to detect
features and predict trackability of the detected points. The ability to detect
features based on the capabilities of the tracker distinguishes the proposed
method from previous algorithms used in this area and improves the robustness
of the algorithms against dynamics of the scene. The network is trained using
multiple datasets due to the lack of specialized dataset for feature tracking
datasets and extensive comparisons are conducted to compare the accuracy of
Deep-PT against recent pixel tracking algorithms. As the experiments suggest,
the proposed deep architecture deliberately learns what to track and how to
track and outperforms the state-of-the-art methods.


  Video capture is limited by the trade-off between spatial and temporal
resolution: when capturing videos of high temporal resolution, the spatial
resolution decreases due to bandwidth limitations in the capture system.
Achieving both high spatial and temporal resolution is only possible with
highly specialized and very expensive hardware, and even then the same basic
trade-off remains. The recent introduction of compressive sensing and sparse
reconstruction techniques allows for the capture of single-shot high-speed
video, by coding the temporal information in a single frame, and then
reconstructing the full video sequence from this single coded image and a
trained dictionary of image patches. In this paper, we first analyze this
approach, and find insights that help improve the quality of the reconstructed
videos. We then introduce a novel technique, based on convolutional sparse
coding (CSC), and show how it outperforms the state-of-the-art, patch-based
approach in terms of flexibility and efficiency, due to the convolutional
nature of its filter banks. The key idea for CSC high-speed video acquisition
is extending the basic formulation by imposing an additional constraint in the
temporal dimension, which enforces sparsity of the first-order derivatives over
time.


  A new type of dark matter (DM) theories are proposed in the light of the
standard model (SM) singlet scalar $\phi$ which is responsible for the diphoton
excess at the LHC Run 2. In the so-called $\phi$-portal DM models, after taking
into account the LHC constraints and DM direct detection limits, we show that
in the perturbative framework DM as either a SM singlet scalar or Dirac fermion
can be allowed in a wide mass range between 400 GeV and 3 TeV. The DM can be
directly detected in SM multi-jets and missing energy.


  We present a model of a coupled bosonic atom-molecule system, using the
recently developed c-field methods as the basis in our formalism. We derive
expressions for the s-wave scattering length and binding energy within this
formalism, and by relating these to the corresponding experimental parameters,
we can accurately determine the phenomenological parameters in our system.


  Numerous research topics rely on an improved cosmic distance scale (e.g.,
cosmology, gravitational waves), and the NASA/IPAC Extragalactic Database of
Distances (NED-D) supports those efforts by tabulating multiple
redshift-independent distances for 12,000 galaxies (e.g., Large Magellanic
Cloud (LMC) zero-point). Six methods for securing a mean estimate distance
(MED) from the data are presented (e.g., indicator and Decision Tree). All six
MEDs yield surprisingly consistent distances for the cases examined, including
for the key benchmark LMC and M106 galaxies. The results underscore the utility
of the NED-D MEDs in bolstering the cosmic distance scale and facilitating the
identification of systematic trends.


  In this paper we derive ages and masses for 276 clusters in the merger galaxy
NGC 3256. This was achieved by taking accurate photometry in four wavebands
from archival HST images. Photometric measurements are compared to synthetic
stellar population (SSP) models to find the most probable age, mass and
extinction. The cluster population of NGC 3256 reveals an increase in the star
formation rate over the last 100 million years and the initial cluster mass
function (ICMF) is best described by a power law relation with slope $\alpha =
1.85 \pm 0.12$. Using the observed cluster population for NGC 3256 we calculate
the implied mass of clusters younger than 10 million years old, and convert
this to a cluster formation rate over the last 10 million years. Comparison of
this value with the star formation rate (SFR) indicates the fraction of stars
found within bound clusters after the embedded phase of cluster formation,
$\Gamma$, is $22.9% \pm^{7.3}_{9.8} $ for NGC 3256. We carried out an in-depth
analysis into the errors associated with such calculations showing that errors
introduced by the SSP fitting must be taken into account and an unconstrained
metallicity adds to these uncertainties. Observational biases should also be
considered. Using published cluster population data sets we calculate $\Gamma$
for six other galaxies and examine how $\Gamma$ varies with environment. We
show that $\Gamma$ increases with the star formation rate density and can be
described as a power law type relation of the form $\Gamma(%) = (29.0\pm{6.0})
\Sigma_{SFR}^{0.24\pm0.04} (\msol yr^{-1} kpc^{-2})$.


  Machine learning models are shown to face a severe threat from Model
Extraction Attacks, where a well-trained private model owned by a service
provider can be stolen by an attacker pretending as a client. Unfortunately,
prior works focus on the models trained over the Euclidean space, e.g., images
and texts, while how to extract a GNN model that contains a graph structure and
node features is yet to be explored. In this paper, for the first time, we
comprehensively investigate and develop model extraction attacks against GNN
models. We first systematically formalise the threat modelling in the context
of GNN model extraction and classify the adversarial threats into seven
categories by considering different background knowledge of the attacker, e.g.,
attributes and/or neighbour connections of the nodes obtained by the attacker.
Then we present detailed methods which utilise the accessible knowledge in each
threat to implement the attacks. By evaluating over three real-world datasets,
our attacks are shown to extract duplicated models effectively, i.e., 84% - 89%
of the inputs in the target domain have the same output predictions as the
victim model.


  In a perturbed Universe, comoving tracers on a two-dimensional surface of
constant observed redshift are at different proper time since the Big Bang. For
tracers whose age is known independently, one can measure these perturbations
of the proper time. Examples of such sources include cosmic events which only
happen during a short period of cosmic history, as well as evolving standard
candles and standard rulers. In this paper we derive a general gauge-invariant
linear expression for this perturbation in terms of space-time perturbations.
As an example, we show that the observed temperature perturbations of the
cosmic microwave background (CMB) on large scales are exactly given by these
proper time perturbations. Together with the six ruler perturbations derived in
Schmidt and Jeong (2012), this completes the set of independent observables
which can be measured with standard rulers and candles.


  We consider the question of how well points in a quadric hypersurface
$M\subset\mathbb R^d$ can be approximated by rational points of $\mathbb
Q^d\cap M$. This contrasts with the more common setup of approximating points
in a manifold by all rational points in $\mathbb Q^d$. We provide complete
answers to major questions of Diophantine approximation in this context. Of
particular interest are the impact of the real and rational ranks of the
defining quadratic form, quantities whose roles in Diophantine approximation
have never been previously elucidated. Our methods include a correspondence
between the intrinsic Diophantine approximation theory on a rational quadric
hypersurface and the dynamics of the group of projective transformations which
preserve that hypersurface, similar to earlier results in the non-intrinsic
setting due to Dani ('86) and Kleinbock--Margulis ('99).


  We calculate accurate eigenvalues of a bounded oscillator by means of the
Riccati--Pad\'e method that is based on a rational approximation to a
regularized logarithmic derivative of the wavefunction. Sequences of roots of
Hankel determinants approach the model eigenvalues from below with remarkable
convergence rate.


  Evolutionary optimization is a generic population-based metaheuristic that
can be adapted to solve a wide variety of optimization problems and has proven
very effective for combinatorial optimization problems. However, the potential
of this metaheuristic has not been utilized in Distributed Constraint
Optimization Problems (DCOPs), a well-known class of combinatorial optimization
problems prevalent in Multi-Agent Systems. In this paper, we present a novel
population-based algorithm, Anytime Evolutionary DCOP (AED), that uses
evolutionary optimization to solve DCOPs. In AED, the agents cooperatively
construct an initial set of random solutions and gradually improve them through
a new mechanism that considers an optimistic approximation of local benefits.
Moreover, we present a new anytime update mechanism for AED that identifies the
best among a distributed set of candidate solutions and notifies all the agents
when a new best is found. In our theoretical analysis, we prove that AED is
anytime. Finally, we present empirical results indicating AED outperforms the
state-of-the-art DCOP algorithms in terms of solution quality.


  We develop properties of unramified, \'etale and smooth morphisms between
Berkovich spaces over $\mathbb{Z}$. We prove that they satisfy properties
analogous to those of morphisms of schemes and we provide analytification
criteria. Our results hold for any valued field, rings of integers of a number
field and discrete valuation rings. Those cases are treated by a unified way.


  The problem of phase retrieval has many applications in the field of optical
imaging. Motivated by imaging experiments with biological specimens, we
primarily consider the setting of low-dose illumination where Poisson noise
plays the dominant role. In this paper, we discuss gradient descent algorithms
based on different loss functions adapted to data affected by Poisson noise, in
particular in the low-dose regime. Starting from the maximum log-likelihood
function for the Poisson distribution, we investigate different regularizations
and approximations of the problem to design an algorithm that meets the
requirements that are faced in applications. In the course of this, we focus on
low-count measurements. For all suggested loss functions, we study the
convergence of the respective gradient descent algorithms to stationary points
and find constant step sizes that guarantee descent of the loss in each
iteration. Numerical experiments in the low-dose regime are performed to
corroborate the theoretical observations.


  We report the results from observations of 24 gamma ray burst (GRB) fields
from 2005 and 2006 undertaken at the Danish 1.54m telescope at ESO/La Silla.
Photometry and positions for two previously unpublished host galaxy candidates
(GRBs 050915 and 051021) are presented, as well as for eight other detected
objects which are either known GRB hosts or candidate hosts. The candidates are
suitable for spectroscopic follow-up in order to have their redshifts and other
physical characteristics determined. In the cases where no likely host
candidate is detected inside the refined Swift XRT error circle we are still
able to put interesting and rather deep limits on the host magnitude. Based on
our detections and upper limits we have performed simulations which suggest
that the host galaxies are drawn from a fainter sample than previous (i.e.
pre-Swift) studies.


  A critical aspect of crowds' evacuation processes is the dynamism of
individual decision making. Here, we investigate how to favor a coordinated
group dynamic through optimal exit-choice instructions using behavioral
strategy optimization. We propose and evaluate an adaptive guidance system
(Cell-based Crowd Evacuation, CellEVAC) that dynamically allocates colors to
cells in a cell-based pedestrian positioning infrastructure, to provide
efficient exit-choice indications. The operational module of CellEVAC
implements an optimized discrete-choice model that integrates the influential
factors that would make evacuees adapt their exit choice. To optimize the
model, we used a simulation-optimization modeling framework that integrates
microscopic pedestrian simulation based on the classical Social Force Model. We
paid particular attention to safety by using Pedestrian Fundamental Diagrams
that model the dynamics of the exit gates. CellEVAC has been tested in a
simulated real scenario (Madrid Arena) under different external pedestrian flow
patterns that simulate complex pedestrian interactions. Results showed that
CellEVAC outperforms evacuation processes in which the system is not used, with
an exponential improvement as interactions become complex. We compared our
system with an existing approach based on Cartesian Genetic Programming. Our
system exhibited a better overall performance in terms of safety, evacuation
time, and the number of revisions of exit-choice decisions. Further analyses
also revealed that Cartesian Genetic Programming generates less natural
pedestrian reactions and movements than CellEVAC. The fact that the decision
logic module is built upon a behavioral model seems to favor a more natural and
effective response. We also found that our proposal has a positive influence on
evacuations even for a low compliance rate (40%).


  The aim of this article is to establish the existence of big Cohen-Macaulay
algebras in mixed characteristic in some special situation. The main result
follows from the so-called almost purity theorem proved by Davis and Kedlaya.


  The time dependent evolution of the accretion disk around black hole is
computed. The classical description of the $\alpha$-viscosity is adopted so the
evolution is driven by the instability operating in the innermost
radiation-pressure dominated part of the accretion disk. We assume that the
optically thick disk always extends down to the marginally stable orbit so it
is never evacuated completely. We include the effect of the advection, coronal
dissipation and vertical outflow. We show that the presence of the corona
and/or the outflow reduce the amplitude of the outburst. If only about half of
the energy is dissipated in the disk (with the other half dissipated in the
corona and carried away by the outflow) the outburst amplitude and duration are
consistent with observations of the microquasar GRS 1915+105. Viscous evolution
explains in a natural way the lack of direct transitions from the state C to
the state B in color-color diagram of this source. Further reduction of the
fraction of energy dissipated in the optically thick disk switches off the
outbursts which may explain why they are not seen in all high accretion rate
sources being in the Very High State.


  Conformal symmetry is taken as an attribute of theories of massless fields in
manifolds with specific dimensionalities. This paper shows that this is not an
absolute truth; it is a consequence of the mathematical representation used for
the physical interactions. It introduces a new kind of representation where the
propagation of massive (invariant mass) and massless interactions are unifiedly
described by a single conformally symmetric Green's function. Sources and
fields are treated at a same footing, symmetrically, as discrete fields - the
fields in this new representation - fields defined with support on straight
lines embedded in a (3+1)-Minkowski manifold. The discrete field turns out to
be a point in phase space. It is finite everywhere. With a finite number of
degrees of freedom it does not share the well known problems faced by the
standard continuous formalism which can be retrieved from the discrete one by
an integration over a hypersurface. The passage from discrete to continuous
fields illuminates the physical meaning and origins of their properties and
problems. The price for having massive discrete field with conformal symmetry
is of hiding its mass and time-like velocity behind its non-constant
proper-time.


  We aim at constructing a high performance model for defect detection that
detects unknown anomalous patterns of an image without anomalous data. To this
end, we propose a two-stage framework for building anomaly detectors using
normal training data only. We first learn self-supervised deep representations
and then build a generative one-class classifier on learned representations. We
learn representations by classifying normal data from the CutPaste, a simple
data augmentation strategy that cuts an image patch and pastes at a random
location of a large image. Our empirical study on MVTec anomaly detection
dataset demonstrates the proposed algorithm is general to be able to detect
various types of real-world defects. We bring the improvement upon previous
arts by 3.1 AUCs when learning representations from scratch. By transfer
learning on pretrained representations on ImageNet, we achieve a new
state-of-theart 96.6 AUC. Lastly, we extend the framework to learn and extract
representations from patches to allow localizing defective areas without
annotations during training.


  We develop an integrability-based framework to compute structure constants of
two sub-determinant operators and a single-trace non-BPS operator in ABJM
theory in the planar limit. In this first paper, we study them at weak coupling
using a relation to an integrable spin chain. We first develop a nested Bethe
ansatz for an alternating SU(4) spin chain that describes single-trace
operators made out of scalar fields. We then apply it to the computation of the
structure constants and show that they are given by overlaps between a Bethe
eigenstate and a matrix product state. We conjecture that the determinant
operator corresponds to an integrable matrix product state and present a
closed-form expression for the overlap, which resembles the so-called Gaudin
determinant. We also provide evidence for the integrability of general
sub-determinant operators. The techniques developed in this paper can be
applied to other quantities in ABJM theory including three-point functions of
single-trace operators.


  Federated learning (FL) can help promote data privacy by training a shared
model in a de-centralized manner on the physical devices of clients. In the
presence of highly heterogeneous distributions of local data, personalized FL
strategy seeks to mitigate the potential client drift. In this paper, we
present the group personalization approach for applications of FL in which
there exist inherent partitions among clients that are significantly distinct.
In our method, the global FL model is fine-tuned through another FL training
process over each homogeneous group of clients, after which each group-specific
FL model is further adapted and personalized for any client. The proposed
method can be well interpreted from a Bayesian hierarchical modeling
perspective. With experiments on two real-world datasets, we demonstrate this
approach can achieve superior personalization performance than other FL
counterparts.


  We present a new method for the determination of [Fe/H] for globular
clusters. This new method is based on moderate resolution (R~1500) near-IR
spectroscopy in the K-band of 6 to 10 of the brightest giants in a cluster. Our
calibration is derived from spectra of 105 stars in 15 globular clusters. From
measurements of the equivalent widths of three features in these spectra, Na,
Ca, and CO, we are able to reproduce the Zinn & West (1984) abundance scale as
updated by Harris (1996) to better than 0.10 dex for clusters with near solar
[Fe/H] down to an [Fe/H] of -1.8. Three advantages of this method are that it
can be used for metal rich, heavily reddened globulars in crowded fields, it
does not require any knowledge of any other cluster or stellar parameters such
as reddening, distance, or luminosity, and it requires only minimal telescope
time. If stellar (J-K)0 and MK values are available as well, the accuracy of
the [Fe/H] estimate is further improved. Observations of as few as three stars
per cluster still gives an [Fe/H] estimate wich is nearly as reliable as that
based on two to three times as many stars.
  The accuracy of an [Fe/H] value based on observations of CO absorption alone
is significantly less than that which results from the three spectroscopic
indices. However, we predict that space-based observations of this feature in
the integrated light of stellar systems will prove to be of great value for
abundance determinations at distances as far as the Coma cluster of galaxies.


  The nonlinear problem of steady free-surface flow past a submerged source is
considered as a case study for three-dimensional ship wave problems. Of
particular interest is the distinctive wedge-shaped wave pattern that forms on
the surface of the fluid. By reformulating the governing equations with a
standard boundary-integral method, we derive a system of nonlinear algebraic
equations that enforce a singular integro-differential equation at each
midpoint on a two-dimensional mesh. Our contribution is to solve the system of
equations with a Jacobian-free Newton-Krylov method together with a banded
preconditioner that is carefully constructed with entries taken from the
Jacobian of the linearised problem. Further, we are able to utilise graphics
processing unit acceleration to significantly increase the grid refinement and
decrease the run-time of our solutions in comparison to schemes that are
presently employed in the literature. Our approach provides opportunities to
explore the nonlinear features of three-dimensional ship wave patterns, such as
the shape of steep waves close to their limiting configuration, in a manner
that has been possible in the two-dimensional analogue for some time.


  As Artificial Intelligence (AI) technologies continue to gain traction in the
modern-day world, they ultimately pose an immediate threat to current
cybersecurity systems via exploitative methods. Prompt engineering is a
relatively new field that explores various prompt designs that can hijack large
language models (LLMs). If used by an unethical attacker, it can enable an AI
system to offer malicious insights and code to them. In this paper, an enhanced
intrusion detection system (IDS) that utilizes machine learning (ML) and
hyperparameter tuning is explored, which can improve a model's performance in
terms of accuracy and efficacy. Ultimately, this improved system can be used to
combat the attacks made by unethical hackers. A standard IDS is solely
configured with pre-configured rules and patterns; however, with the
utilization of machine learning, implicit and different patterns can be
generated through the models' hyperparameter settings and parameters. In
addition, the IDS will be equipped with multiple datasets so that the accuracy
of the models improves. We evaluate the performance of multiple ML models and
their respective hyperparameter settings through various metrics to compare
their results to other models and past research work. The results of the
proposed multi-dataset integration method yielded an accuracy score of 99.9%
when equipped with the XGBoost and random forest classifiers and
RandomizedSearchCV hyperparameter technique.


  Modeling the underlying pairing mechanism of charge carriers in strongly
correlated electrons, starting from a microscopic theory, is among the central
challenges of condensed-matter physics. Hereby, the key task is to understand
what causes the appearance of superconductivity at comparatively high
temperatures upon hole doping an antiferromagnetic (AFM) Mott insulator.
Recently, it has been proposed that at strong coupling and low doping, the
fundamental one- and two-hole meson-type constituents -- magnetic polarons and
bipolaronic pairs -- likely realize an emergent Feshbach resonance producing
near-resonant $d_{x^2-y^2}$ interactions between charge carriers. Here, we
provide detailed calculations of the proposed scenario by describing the open
and closed meson scattering channels in the $t$-$t'$-$J$ model using a
truncated basis method. After integrating out the closed channel constituted by
bipolaronic pairs, we find $d_{x^2-y^2}$ attractive interactions between open
channel magnetic polarons. The closed form of the derived interactions allows
us analyze the resonant pairing interactions and we find enhanced (suppressed)
attraction for hole (electron) doping in our model. The formalism we introduce
provides a framework to analyze the implications of a possible Feshbach
scenario, e.g. in the context of BEC-BCS crossover, and establishes a
foundation to test quantitative aspects of the proposed Feshbach pairing
mechanisms in doped antiferromagnets.


  The kinetic instabilities of the Weibel-type are presently invoked in a large
variety of astrophysical scenarios because anisotropic plasma structures are
ubiquitous in space. The Weibel instability is driven by a temperature
anisotropy which is commonly modeled by a bi-axis distribution function, such
as a bi-Maxwellian or a generalized bi-Kappa. Previous studies have been
limited to a bi-Kappa distribution and found a suppression of this instability
in the presence of suprathermal tails. In the present paper it is shown that
the Weibel growth rate is rather more sensitive to the shape of the anisotropic
distribution function. In order to illustrate the distinguishing properties of
this instability a \emph{product-bi-Kappa distribution} is introduced, with the
advantage that this distribution function enables the use of different values
of the spectral index in the two directions, $\kappa_{\parallel} \ne
\kappa_{\perp}$. The growth rates and the instability threshold are derived and
contrasted with those for a simple bi-Kappa and a bi-Maxwellian. Thus, while
the maximum growth rates reached at the saturation are found to be higher, the
threshold is drastically reduced making the anisotropic product-bi-Kappa (with
small kappas) highly susceptible to the Weibel instability. This effect could
also rise questions on the temperature or the temperature anisotropy that seems
to be not an exclusive source of free energy for this instability, and
definition of these notions for such Kappa distributions must probably be
reconsidered.


  Inspired by the quantum computing algorithms for Linear Algebra problems
[HHL,TaShma] we study how the simulation on a classical computer of this type
of "Phase Estimation algorithms" performs when we apply it to solve the
Eigen-Problem of Hermitian matrices. The result is a completely new, efficient
and stable, parallel algorithm to compute an approximate spectral decomposition
of any Hermitian matrix. The algorithm can be implemented by Boolean circuits
in $O(\log^2 n)$ parallel time with a total cost of $O(n^{\omega+1})$ Boolean
operations. This Boolean complexity matches the best known rigorous $O(\log^2
n)$ parallel time algorithms, but unlike those algorithms our algorithm is
(logarithmically) stable, so further improvements may lead to practical
implementations.
  All previous efficient and rigorous approaches to solve the Eigen-Problem use
randomization to avoid bad condition as we do too. Our algorithm makes further
use of randomization in a completely new way, taking random powers of a unitary
matrix to randomize the phases of its eigenvalues. Proving that a tiny Gaussian
perturbation and a random polynomial power are sufficient to ensure almost
pairwise independence of the phases $(\mod (2\pi))$ is the main technical
contribution of this work. This randomization enables us, given a Hermitian
matrix with well separated eigenvalues, to sample a random eigenvalue and
produce an approximate eigenvector in $O(\log^2 n)$ parallel time and
$O(n^\omega)$ Boolean complexity. We conjecture that further improvements of
our method can provide a stable solution to the full approximate spectral
decomposition problem with complexity similar to the complexity (up to a
logarithmic factor) of sampling a single eigenvector.


  The emergence of multiview displays has made the need for synthesizing
virtual views more pronounced, since it is not practical to capture all of the
possible views when filming multiview content. View synthesis is performed
using the available views and depth maps. There is a correlation between the
quality of the synthesized views and the quality of depth maps. In this paper
we study the effect of depth map quality on perceptual quality of synthesized
view through subjective and objective analysis. Our evaluation results show
that: 1) 3D video quality depends highly on the depth map quality and 2) the
Visual Information Fidelity index computed between the reference and distorted
depth maps has Pearson correlation ratio of 0.75 and Spearman rank order
correlation coefficient of 0.67 with the subjective 3D video quality.


  This article presents new numerical simulation tools, respectively developed
in Matlab and Blender softwares. Available in open-source under the GPL 3.0
license, it uses a ray-tracing/image-sources hybrid method to calculate the
room acoustics for large meshes. Performances are optimized to solve problems
of significant size (typically more than 100,000 surface elements and about a
million of rays). For this purpose, a Divide and Conquer approach with a
recursive binary tree structure has been implemented to reduce the quadratic
complexity of the ray/element interactions to near-linear. Thus, execution
times are less sensitive to the mesh density, which allows simulations of
complex geometry. After ray propagation, a hybrid method leads to
image-sources, which can be visually analyzed to localize sound map. Finally,
impulse responses are constructed from the image-sources and FIR filters are
proposed natively over 8 octave bands, taking into account material absorption
properties and propagation medium. This algorithm is validated by comparisons
with theoretical test cases. Furthermore, an example on a quite complex case,
namely the ancient theater of Orange is presented.


  The paper is concerned with sharp estimates of constants in Poincare type
inequalities for functions having zero mean value on the boundary of a
Lipschitz domain or on a measurable part of it. These estimates are useful for
various numerical methods, in particular, for a posteriori error estimation
methods for partial differential equations (PDEs). Therefore, we are mainly
focused on domains typical for numerical analysis (simplexes in 2d and 3d) and
suggest easily computable relations that provide sharp bounds of the respective
constants. Also, we investigate numerically the behavior of the constants in
the classical Poincare inequalities and compare these results with known
analytical estimates. In the last section, the estimates are used in order to
obtain new a posteriori estimates for an elliptic boundary value problem.


  In a regime where data are only mildly informative, prior choices can play a
significant role in Bayesian statistical inference, potentially affecting the
inferred physics. We show this is indeed the case for some of the parameters
inferred from current gravitational-wave measurements of binary black hole
coalescences. We reanalyze the first detections performed by the twin LIGO
interferometers using alternative (and astrophysically motivated) prior
assumptions. We find different prior distributions can introduce deviations in
the resulting posteriors that impact the physical interpretation of these
systems. For instance, (i) limits on the $90\%$ credible interval on the
effective black hole spin $\chi_{\rm eff}$ are subject to variations of $\sim
10\%$ if a prior with black hole spins mostly aligned to the binary's angular
momentum is considered instead of the standard choice of isotropic spin
directions, and (ii) under priors motivated by the initial stellar mass
function, we infer tighter constraints on the black hole masses, and in
particular, we find no support for any of the inferred masses within the
putative mass gap $M \lesssim 5 M_\odot$.