  We study the growth of product sets in some finite three-dimensional matrix
groups. In particular, we prove two results about the group of $2\times 2$
upper triangular matrices over arbitrary finite fields: a product set estimate
using techniques from multiplicative combinatorics, and an energy estimate
using incidence geometry. The energy method gives better quantitative results,
but only applies to small sets. We also prove an energy result for the
Heisenberg group.


  We present large sample properties and conditions for asymptotic normality of
linear functionals of powers of the periodogram constructed with the use of
tapered data.


  The local coupling of two photons to the fundamental quark currents of a
hadron gives an energy-independent contribution to the Compton amplitude
proportional to the charge squared of the struck quark, a contribution which
has no analog in hadron scattering reactions. We show that this local
contribution has a real phase and is universal, giving the same contribution
for real or virtual Compton scattering for any photon virtuality and skewness
at fixed momentum transfer squared t. The t-dependence of this J=0 fixed Regge
pole is parameterized by a yet unmeasured even charge-conjugation form factor
of the target nucleon. The t=0 limit gives an important constraint on the
dependence of the nucleon mass on the quark mass through the Weisberger
relation. We discuss how this 1/x form factor can be extracted from high energy
deeply virtual Compton scattering and examine predictions given by models of
the H generalized parton distribution.


  Fine-tuned pre-trained language models can suffer from severe miscalibration
for both in-distribution and out-of-distribution (OOD) data due to
over-parameterization. To mitigate this issue, we propose a regularized
fine-tuning method. Our method introduces two types of regularization for
better calibration: (1) On-manifold regularization, which generates pseudo
on-manifold samples through interpolation within the data manifold. Augmented
training with these pseudo samples imposes a smoothness regularization to
improve in-distribution calibration. (2) Off-manifold regularization, which
encourages the model to output uniform distributions for pseudo off-manifold
samples to address the over-confidence issue for OOD data. Our experiments
demonstrate that the proposed method outperforms existing calibration methods
for text classification in terms of expectation calibration error,
misclassification detection, and OOD detection on six datasets. Our code can be
found at https://github.com/Lingkai-Kong/Calibrated-BERT-Fine-Tuning.


  Like a scientist or a playing child, PowerPlay not only learns new skills to
solve given problems, but also invents new interesting problems by itself. By
design, it continually comes up with the fastest to find, initially novel, but
eventually solvable tasks. It also continually simplifies or compresses or
speeds up solutions to previous tasks. Here we describe first experiments with
PowerPlay. A self-delimiting recurrent neural network SLIM RNN is used as a
general computational problem solving architecture. Its connection weights can
encode arbitrary, self-delimiting, halting or non-halting programs affecting
both environment (through effectors) and internal states encoding abstractions
of event sequences. Our PowerPlay-driven SLIM RNN learns to become an
increasingly general solver of self-invented problems, continually adding new
problem solving procedures to its growing skill repertoire. Extending a recent
conference paper, we identify interesting, emerging, developmental stages of
our open-ended system. We also show how it automatically self-modularizes,
frequently re-using code for previously invented skills, always trying to
invent novel tasks that can be quickly validated because they do not require
too many weight changes affecting too many previous tasks.


  Recent observation of several microwave transitions in H2O2 from the
interstellar medium [Astron. Astrophys., 531, L8 (2011)] raised interest to
this molecule as yet another sensitive probe of the tentative variation of the
electron-to-proton mass ratio mu. We estimate sensitivity coefficients of the
microwave transitions in H2O2 to mu-variation. The largest coefficient for 14.8
GHz transition is equal to 37, which is comparable to highest sensitivities in
methanol and an order of magnitude higher than sensitivity of the tunneling
transition in ammonia.


  The problem of characterizing the optimal rate achievable with analog network
coding (ANC) for a unicast communication over general wireless relay networks
is computationally hard. A relay node performing ANC scales and forwards its
input signals. The source-destination channel in such communication scenarios
is, in general, an intersymbol interference (ISI) channel which leads to the
single-letter characterization of the optimal rate in terms of an optimization
problem with nonconvex, non closed-form objective function and non-convex
constraints. For a special class of such networks, called layered networks, a
few key results and insights are however available.
  To gain insights into the nature of the optimal solution and to construct
low-complexity schemes to characterize the optimal rate for general wireless
relay networks, we need (1) network topologies that are regular enough to be
amenable for analysis, yet general enough to capture essential characteristics
of general wireless relay networks, and (2) schemes to approximate the
objective function in closed-form without significantly compromising the
performance. Towards these two goals, this work proposes (1) nonlinear chain
networks, and (2) two approximation schemes. We show that their combination
allows us to tightly characterize the optimal ANC rate with low computational
complexity for a much larger class of general wireless relay networks than
possible with existing schemes.


  We consider the Schr\"odinger operator with a potential q on a disk and the
map that associates to q the corresponding Dirichlet to Neumann (DtN) map. We
give some numerical and analytical results on the range of this map and its
stability, for the particular class of one-step radial potentials.


  Unconventional superconductivity has long been believed to arise from a
lab-grown correlated electronic system. Here we report compelling evidence of
unconventional nodal superconductivity in a mineral superconductor \rhs. We
investigated the temperature-dependent London penetration depth
$\Delta\lambda(T)$ and disorder evolution of the critical temperature $T_c$ and
upper critical field $H_{c2}(T)$ in synthetic miassite \rhs. We found a
power-law behavior of $\Delta\lambda(T)\sim T^n$ with $n\approx 1.1$ at low
temperatures below $0.3T_c$ ($T_c$ = 5.4 K), which is consistent with the
presence of lines of the node in the superconducting gap of \rhs. The nodal
character of the superconducting state in \rhs~was supported by the observed
pairbreaking effect in $T_c$ and $H_{c2}(T)$ in samples with the controlled
disorder that was introduced by low-temperature electron irradiation. We
propose a nodal sign-changing superconducting gap in the $A_{1g}$ irreducible
representation, which preserves the cubic symmetry of the crystal and is in
excellent agreement with the superfluid density, $\lambda^2(0)/\lambda^2(T)$.


  Moment of inertia ($I$), rotational~(tidal) Love number ($\lambda^{\rm
(rot)}$) and quadrupole moment ($Q$) of slowly rotating massive neutron
star~(NS) with holographic multiquark~(MQ) core are computed in comparison to
pure MQ star. The Chiral Effective Theory~(CET) stiff equation of state~(EoS)
is used in the crust of the neutron star. The dimensionless multipole moments
$\bar{I},\bar{\lambda}^{\rm (rot)}, \bar{Q}$ are found to be independent of the
rotation parameters and determined completely by the zeroth-order star profile.
Universal ``I-Love-Q'' relations found by Yagi and Yunes [1,2] are mostly
preserved even in the presence of the MQ core. Tidal deformation parameter
$\bar{\lambda}^{\rm (tid)}$ is also explored in connection with $\bar{I},
\bar{\lambda}^{\rm (rot)}, \bar{Q}$, two kinds of universal I-Love-Q relations
are verified. However, the unique kink in the plots of multipoles with respect
to mass and compactness of the population of neutron stars can reveal the
existence of massive NS with the MQ core.


  In this paper we attempt to prove Lehmer's conjecture on Ramanujan's tau
function, namely tau(n) is never zero, for each n larger than zero by
investigating the additive group structure attached to tau(n) with the aid of
unique factorization theorem.


  Sterilization is a very popular word used in biomedical testing (like removal
of all microorganisms on surface of an article or in fluid using appropriate
chemical products). Motivated by this biological analogy, we, for the first
time, introduce the concept of sterilization of an image, i.e., removing any
steganographic information embedded in the image. Experimental results show
that our technique succeeded in sterilizing around 76% to 91% of stego pixels
in an image on average, where data is embedded using LSB-based steganography.


  We construct a Banach space $X$ for which the set of norm-attaining
functionals $NA(X,\mathbb{R})$ does not contain any non-trivial cone. Even
more, given two linearly independent norm-attaining functionals on $X$, no
other element of the segment between them attains its norm. Equivalently, the
intersection of $NA(X,\mathbb{R})$ with the unit sphere of a two-dimensional
subspace of $X^*$ contains, at most, four elements. In terms of proximinality,
we show that for every closed subspace $Z$ of $X$ of codimension two, at most
four element of the unit sphere of $X/Z$ has a representative of norm-one. We
further relate this example with an open problem on norm-attaining operators.


  We describe a 3-step filtration on all logarithmic abelian varieties with
constant degeneration. The obstruction to descending this filtration, as a
variegated extension, from logarithmic geometry to algebraic geometry is
encoded in a bilinear pairing valued in the characteristic monoid of the base.
This pairing is realized as the monodromy pairing in p-adic, l-adic, and Betti
cohomolgies, and recovers the Picard-Lefschetz transformation in the case of
Jacobians. The Hodge realization of the filtration is the monodromy weight
filtration on the limit mixed Hodge structure.


  Materials which possess coupling between different degrees of freedom such as
charge, spin, orbital and lattice are of tremendous interest due to their
potential for device applications. It has been recently realized that some of
manganite perovskite oxides show structural and ferroelectric instabilities
which may be tuned by imposing internal or external strain. Among manganite
perovskites, AMnO3 (A = Ca, Sr and Ba) are reported to be good candidates to
show spin-phonon coupling driven multiferroicity. Here, we have probed the
correlation between vibrational and magnetic properties in the 9R-type
hexagonal Ba0.9Sr0.1MnO3 (BSM10). Nine Raman active modes are observed which
are characteristic phonon modes for 9R phase. The frequency ({omega}) of an Eg
(344 cm-1) mode which is related to Mn vibrations shows anomaly with
temperature (T) manifested as a change in slope of {omega} vs T at 260 K. The
temperature-dependent magnetization of BSM10 suggests a possible
antiferromagnetic ordering at ~ 260 K. We, therefore, attribute the phonon
anomaly to spin-phonon coupling arising due to the magnetic ordering.


  We define combinatorial counterparts to the geometric string vertices of
Sen-Zwiebach and Costello-Zwiebach, which are certain closed subsets of the
moduli spaces of curves. Our combinatorial vertices contain the same
information as the geometric ones, are effectively computable, and act on the
Hochschild chains of a cyclic $A_\infty$-algebra.
  This is the first in a series of two papers where we define enumerative
invariants associated to a pair consisting of a cyclic $A_\infty$-algebra and a
splitting of the Hodge filtration on its cyclic homology. These invariants
conjecturally generalize the Gromov-Witten and Fan-Jarvis-Ruan-Witten
invariants from symplectic geometry, and the Bershadsky-Cecotti-Ooguri-Vafa
invariants from holomorphic geometry.


  Sequential data is everywhere, and it can serve as a basis for research that
will lead to improved processes. For example, road infrastructure can be
improved by identifying bottlenecks in GPS data, or early diagnosis can be
improved by analyzing patterns of disease progression in medical data. The main
obstacle is that access and use of such data is usually limited or not
permitted at all due to concerns about violating user privacy, and rightly so.
Anonymizing sequence data is not a simple task, since a user creates an almost
unique signature over time. Existing anonymization methods reduce the quality
of information in order to maintain the level of anonymity required. Damage to
quality may disrupt patterns that appear in the original data and impair the
preservation of various characteristics. Since in many cases the researcher
does not need the data as is and instead is only interested in the patterns
that exist in the data, we propose PrivGen, an innovative method for generating
data that maintains patterns and characteristics of the source data. We
demonstrate that the data generation mechanism significantly limits the risk of
privacy infringement. Evaluating our method with real-world datasets shows that
its generated data preserves many characteristics of the data, including the
sequential model, as trained based on the source data. This suggests that the
data generated by our method could be used in place of actual data for various
types of analysis, maintaining user privacy and the data's integrity at the
same time.


  We present 11 detections of FRB 121102 in ~3 hours of observations during its
'active' period on the 10th of September 2019. The detections were made using
the newly deployed MeerTRAP system and single pulse detection pipeline at the
MeerKAT radio telescope in South Africa. Fortuitously, the Nancay radio
telescope observations on this day overlapped with the last hour of MeerKAT
observations and resulted in 4 simultaneous detections. The observations with
MeerKAT's wide band receiver, which extends down to relatively low frequencies
(900-1670 MHz usable L-band range), have allowed us to get a detailed look at
the complex frequency structure, intensity variations and frequency-dependent
sub-pulse drifting. The drift rates we measure for the full-band and sub-banded
data are consistent with those published between 600-6500 MHz with a slope of
-0.147 +/- 0.014 ms^-1. Two of the detected bursts exhibit fainter 'precursors'
separated from the brighter main pulse by ~28 ms and ~34 ms. A follow-up
multi-telescope campaign on the 6th and 8th October 2019 to better understand
these frequency drifts and structures over a wide and continuous band was
undertaken. No detections resulted, indicating that the source was 'inactive'
over a broad frequency range during this time.


  Phase singularities are locations where light is twisted like a corkscrew,
with positive or negative topological charge depending on the twisting
direction. Among the multitude of singularities arising in random wave fields,
some can be found at the same location, but only when they exhibit opposite
topological charge, which results in their mutual annihilation. New pairs can
be created as well. With near-field experiments supported by theory and
numerical simulations, we study the persistence and pairing statistics of phase
singularities in random optical fields as a function of the excitation
wavelength. We demonstrate how such entities can encrypt fundamental properties
of the random fields in which they arise.


  This article improves on existing methods to estimate the spectral density of
stationary and nonstationary time series assuming a Gaussian process prior. By
optimising an appropriate eigendecomposition using a smoothing spline
covariance structure, our method more appropriately models data with both
simple and complex periodic structure. We further justify the utility of this
optimal eigendecomposition by investigating the performance of alternative
covariance functions other than smoothing splines. We show that the optimal
eigendecomposition provides a material improvement, while the other covariance
functions under examination do not, all performing comparatively well as the
smoothing spline. During our computational investigation, we introduce new
validation metrics for the spectral density estimate, inspired from the
physical sciences. We validate our models in an extensive simulation study and
demonstrate superior performance with real data.


  In this work we study the following class of systems of coupled nonlinear
fractional nonlinear Schr\"odinger equations, \begin{equation*} \left \{
\begin{array}{l} (-\Delta)^s u_1+ \lambda_1 u_1= \mu_1 |u_1|^{2p-2}u_1+\beta
|u_2|^{p} |u_1|^{p-2}u_1 \quad\text{in }\mathbb{R}^N,\\[3pt] (-\Delta)^s u_2 +
\lambda_2 u_2= \mu_2 |u_2|^{2p-2}u_2+\beta |u_1|^{p}|u_2|^{p-2}u_2
\quad\text{in }\mathbb{R}^N, \end{array} \right. \end{equation*} where $ u_1,\,
u_2\in W^{s,2}(\mathbb{R}^N)$, with $ N=1,\, 2,\, 3$; $\lambda_j,\,\mu_j>0$,
$j=1,2$, $\beta\in \mathbb{R}$, $p\geq 2$ and
$\displaystyle\frac{p-1}{2p}N<s<1$. Precisely, we prove the existence of
positive radial bound and ground state solutions provided the parameters
$\beta, p, \lambda_j,\mu_j$, ($j=1,\, 2$) satisfy appropriate conditions. We
also study the previous system with $m$-equations, $$ (-\Delta)^s u_j+
\lambda_j u_j =\mu_j |u_j|^{2p-2}u_j+ \sum_{\substack{k=1\\k\neq
j}}^m\beta_{jk} |u_k|^p|u_j|^{p-2}u_j,\quad u_j\in W^{s,2}(\mathbb{R}^N);\:
j=1,\ldots,m $$ where $\lambda_j,\, \mu_j>0$ for $j=1,\ldots ,m\ge 3$, the
coupling parameters $\beta_{jk}=\beta_{kj}\in \mathbb{R}$ for $j,k=1,\ldots,m$,
$j\neq k$. For this system we prove similar results as for $m=2$, depending on
the values of the parameters $\beta_{jk}, p, \lambda_j,\mu_j$, (for
$j,k=1,\ldots,m$, $j\neq k$).


  There exists a variety of proposals to transform a conventional s-wave
superconductor into a topological superconductor, supporting Majorana fermion
mid-gap states. A necessary ingredient of these proposals is strong spin-orbit
coupling. Here we propose an alternative system consisting of a one-dimensional
chain of magnetic nanoparticles on a superconducting substrate. No spin-orbit
coupling in the superconductor is needed. We calculate the topological quantum
number of a chain of finite length, including the competing effects of disorder
in the orientation of the magnetic moments and in the hopping energies, to
identify the transition into the topologically nontrivial state (with Majorana
fermions at the end points of the chain).


  Quantum catalysis, the ability to enable previously impossible
transformations by using auxiliary systems without degrading them, has emerged
as a powerful tool in various resource theories. Although catalytically enabled
state transformations have been formally characterized by the monotonic
behaviour of entropic quantifiers (e.g., the von Neumann entropy or
non-equilibrium free energy), such characterizations often rely on unphysical
assumptions, namely the ability of using catalysts of infinitely large
dimension. This approach offers very limited insights into the practical
significance of using catalysis for quantum information processing. Here, we
address this problem across a broad class of quantum resource theories.
Leveraging quantum information tools beyond the asymptotic regime, we establish
sufficient conditions for the existence of catalytic transformations with
finite-size catalysts. We further unveil connections between finite-size
catalysis and multi-copy transformations. Notably, we discover a fascinating
phenomenon of catalytic resonance: by carefully tailoring the catalysts's
state, one can drastically reduce the required dimension of the catalyst, thus
enabling efficient catalytic transformations with minimal resources. Finally,
we illustrate our findings with examples from the resource theories of
entanglement and thermodynamics, as well in the context of catalytic unitary
transformations.


  We study some aspects of 2d supersymmetric sigma models on orbifolds. It
turns out that independently of whether the 2d QFT is conformal the operator
products of twist operators are non-singular, suggesting that massive
(non-conformal) orbifolds also `resolve singularities' just as in the conformal
case. Moreover we recover the OPE of twist operators for conformal theories by
considering the UV limit of the massive orbifold correlation functions.
Alternatively, we can use the OPE of twist fields at the conformal point to
derive conditions for the existence of non-singular solutions to special
non-linear differential equations (such as Painleve III).


  In this article we examine the concentration and oscillation effects
developed by high-frequency eigenfunctions of the Laplace operator in a compact
Riemannian manifold. More precisely, we are interested in the structure of the
possible invariant semiclassical measures obtained as limits of Wigner measures
corresponding to eigenfunctions. These measures describe simultaneously the
concentration and oscillation effects developed by a sequence of
eigenfunctions. We present some results showing how to obtain invariant
semiclassical measures from eigenfunctions with prescribed symmetries. As an
application of these results, we give a simple proof of the fact that in a
manifold of constant positive sectional curvature, every measure which is
invariant by the geodesic flow is an invariant semiclassical measure.


  We illustrate the effects of one-loop weak corrections onto the production of
neutral gauge bosons of the Standard Model at RHIC-Spin, Tevatron and LHC, in
presence of quark/gluon radiation from the initial state. We find such effects
to be rather large, up to ${\cal O}(10-20%)$ in typical observables at all such
colliders, where the cross section is measurable, thus advocating their
inclusion in precision analyses


  We investigate entanglement in two-qubit systems using a geometric
representation based on the minimum of essential parameters. The states are
X-shaped and host pairs of identical populations while reducing the number of
coherences involved. A geometric L-measure of entanglement is introduced as the
distance between the points that represent entangled states and the closest
point that defines separable states. Our results give a geometric meaning to
the Hill-Wootters concurrence C since L coincides with C. Furthermore, unlike
C, the measure L distinguishes the rank of states with maximum entanglement. We
construct a time-dependent two-qubit state, traced out over the complementary
components of a pure tetra-partite system, and find that its one-qubit states
share the same entropy. The entanglement measure results bounded from above by
the envelope of the minima of such entropy.


  We study the photoelectric effect on the example of a simplified model of an
atom with a single bound state, coupled to the quantized electromagnetic field.
For this model, we show that Einstein's prediction for the photoelectric effect
is qualitatively and quantitatively correct to leading order in the coupling
parameter. More specifically, considering the ionization of the atom by an
incident photon cloud consisting of $N$ photons, we prove that the total
ionized charge is additive in the $N$ involved photons. Furthermore, if the
photon cloud is approaching the atom from a large distance, the kinetic energy
of the ejected electron is shown to be given by the difference of the photon
energy of each single photon in the photon cloud and the ionization energy.


  Motivated by a zero-intelligence approach, the aim of this paper is to
connect the microscopic (discrete price and volume), mesoscopic (discrete price
and continuous volume) and macroscopic (continuous price and volume) frameworks
for the modelling of limit order books, with a view to providing a natural
probabilistic description of their behaviour in a high to ultra high-frequency
setting. Starting with a microscopic framework, we first examine the limiting
behaviour of the order book process when order arrival and cancellation rates
are sent to infinity and when volumes are considered to be of infinitesimal
size. We then consider the transition between this mesoscopic model and a
macroscopic model for the limit order book, obtained by letting the tick size
tend to zero. The macroscopic limit can then be described using reflected SPDEs
which typically arise in stochastic interface models. We then use financial
data to discuss a possible calibration procedure for the model and illustrate
numerically how it can reproduce observed behaviour of prices. This could then
be used as a market simulator for short-term price prediction or for testing
optimal execution strategies.


  Infectious disease forecasting has been a key focus and proved to be crucial
in controlling epidemic. A recent trend is to develop forecast-ing models based
on graph neural networks (GNNs). However, existing GNN-based methods suffer
from two key limitations: (1) Current models broaden receptive fields by
scaling the depth of GNNs, which is insuffi-cient to preserve the semantics of
long-range connectivity between distant but epidemic related areas. (2)
Previous approaches model epidemics within single spatial scale, while ignoring
the multi-scale epidemic pat-terns derived from different scales. To address
these deficiencies, we devise the Multi-scale Spatio-temporal Graph Neural
Network (MSGNN) based on an innovative multi-scale view. To be specific, in the
proposed MSGNN model, we first devise a novel graph learning module, which
directly captures long-range connectivity from trans-regional epidemic signals
and integrates them into a multi-scale graph. Based on the learned multi-scale
graph, we utilize a newly designed graph convolution module to exploit
multi-scale epidemic patterns. This module allows us to facilitate multi-scale
epidemic modeling by mining both scale-shared and scale-specific pat-terns.
Experimental results on forecasting new cases of COVID-19 in United State
demonstrate the superiority of our method over state-of-arts. Further analyses
and visualization also show that MSGNN offers not only accurate, but also
robust and interpretable forecasting result.


  We give a sufficient condition for the quantum adiabatic approximation, which
is quantitative and can be used to estimate error caused by this approximation.
We also discuss when the traditional condition is sufficient.


  At low energies, the microscopic characteristics and changes of physical
systems as viewed at different distance scales are described by universal scale
invariant properties investigated by the Renormalization Group (RG) apparatus,
an efficient tool used to deal with scaling problems in effective field
theories. We employ an information-theoretic approach in a deep learning setup
by introducing an artificial neural network algorithm to map and identify new
physical degrees of freedom. Using deep learning methods mapped to a genuine
field theory, we develop a mechanism capable to identify relevant degrees of
freedom and induce scale invariance without prior knowledge about a system. We
show that deep learning algorithms that use an RG-like scheme to learn relevant
features from data could help to understand the nature of the holographic
entanglement entropy and the holographic principle in context of the AdS/CFT
correspondence.


  We investigate the quantum phase transitions in the half-filled Hubbard model
on the triangular lattice by means of the path-integral renormalization group
(PIRG) method with a new iteration scheme proposed recently. It is found that
as the Hubbard interaction $U$ increases, the paramagnetic metallic state
undergoes a first-order phase transition to a nonmagnetic insulating (NMI)
state at $U_{c1}\sim 7.7t$, which is followed by another first-order transition
to a $120^\circ$ N\'eel ordered state at $U_{c2}\sim 10t$, where $t$ is the
transfer integral. Our results ensure the existence of the intermediate NMI
phase, and resolve some controversial arguments on the nature of the previously
proposed quantum phase transitions. We find that
$\kappa$-(BEDT-TTF)$_2$Cu$_2$(CN)$_3$ is located in the NMI phase close to the
metal-insulator transition point.


  Much of the physical world around us can be described in terms of harmonic
oscillators in thermodynamic equilibrium. At the same time, the far from
equilibrium behavior of oscillators is important in many aspects of modern
physics. Here, we investigate a resonating system subject to a fundamental
interplay between intrinsic nonlinearities and a combination of several driving
forces. We have constructed a controllable and robust realization of such a
system using a macroscopic doubly clamped string. We experimentally observe a
hitherto unseen double hysteresis in both the amplitude and the phase of the
resonator's response function and present a theoretical model that is in
excellent agreement with the experiment. Our work provides a thorough
understanding of the double-hysteretic response through a symmetry breaking of
parametric phase states that elucidates the selection criteria governing
transitions between stable solutions. Our study motivates applications ranging
from ultrasensitive force detection to low-energy computing memory units.


  In this paper we are concerned with rate of convergence of parabolic systems
with large diffusion. We will exhibit the exact moment that spatial
homogenization occurs and estimate the continuity of attractors by a rate of
convergence. We will show an example where our estimate is optimal.


  The current status of the derivation of kinetic equations from quantum
many-particle dynamics is reviewed.


  This paper presents robust discontinuous Galerkin methods for the
incompressible Navier-Stokes equations on moving meshes. High-order accurate
arbitrary Lagrangian-Eulerian formulations are proposed in a unified framework
for both monolithic as well as projection or splitting-type Navier-Stokes
solvers. The framework is flexible, allows implicit and explicit formulations
of the convective term, and adaptive time-stepping. The Navier-Stokes equations
with ALE transport term are solved on the deformed geometry storing one
instance of the mesh that is updated from one time step to the next.
Discretization in space is applied to the time discrete equations so that all
weak forms and mass matrices are evaluated at the end of the current time step.
This design ensures that the proposed formulations fulfill the geometric
conservation law automatically, as is shown theoretically and demonstrated
numerically by the example of the free-stream preservation test. We discuss the
peculiarities related to the imposition of boundary conditions in intermediate
steps of projection-type methods and the ingredients needed to preserve
high-order accuracy. We show numerically that the formulations proposed in this
work maintain the formal order of accuracy of the Navier-Stokes solvers.
Moreover, we demonstrate robustness and accuracy for under-resolved turbulent
flows.


  We prove that knot Floer homology and Khovanov homology can detect
non-fibered knots, including the knot $5_2$, and that HOMFLY homology detects
infinitely many such knots. This is the first time that a Floer theory or any
of the Khovanov-Rozansky link homology theories has been shown to detect
non-fibered knots, or infinitely many knots. These results rely on our main
theorem, which gives a complete classification of genus-1 knots in $S^3$ whose
knot Floer homology in the top Alexander grading is 2-dimensional.


  We consider the inverse problem of reconstructing an effective model for a
prototypical diffusion process in strongly heterogeneous media based on coarse
measurements. The approach is motivated by quasi-local numerical effective
forward models that are provably reliable beyond periodicity assumptions and
scale separation. The goal of this work is to show that an identification of
the matrix representation related to these effective models is possible. On the
one hand, this provides a reasonable surrogate in cases where a direct
reconstruction is unfeasible due to a mismatch between the coarse data scale
and the microscopic quantities to be reconstructed. On the other hand, the
approach allows us to investigate the requirement for a certain non-locality in
the context of numerical homogenization. Algorithmic aspects of the inversion
procedure and its performance are illustrated in a series of numerical
experiments.


  We study the $b$-matching problem in bipartite graphs $G=(S,R,E)$. Each
vertex $s\in S$ is a server with individual capacity $b_s$. The vertices $r\in
R$ are requests that arrive online and must be assigned instantly to an
eligible server. The goal is to maximize the size of the constructed matching.
We assume that $G$ is a $(k,d)$-graph~\cite{NW}, where $k$ specifies a lower
bound on the degree of each server and $d$ is an upper bound on the degree of
each request. This setting models matching problems in timely applications.
  We present tight upper and lower bounds on the performance of deterministic
online algorithms. In particular, we develop a new online algorithm via a
primal-dual analysis. The optimal competitive ratio tends to~1, for arbitrary
$k\geq d$, as the server capacities increase. Hence, nearly optimal solutions
can be computed online. Our results also hold for the vertex-weighted problem
extension, and thus for AdWords and auction problems in which each bidder
issues individual, equally valued bids.
  Our bounds improve the previous best competitive ratios. The asymptotic
competitiveness of~1 is a significant improvement over the previous factor of
$1-1/e^{k/d}$, for the interesting range where $k/d\geq 1$ is small. Recall
that $1-1/e\approx 0.63$. Matching problems that admit a competitive ratio
arbitrarily close to~1 are rare. Prior results rely on randomization or
probabilistic input models.


  The no-masking theorem says that masking quantum information is impossible in
a bipartite scenario. However, there exist schemes to mask quantum states in
multipartite systems. In this work, we show that, the joint measurement in the
teleportation is really a masking process, when the apparatus is regarded as a
quantum participant in the whole system.Based on the view, we present two
four-partite maskers and a tripartite masker. One of the former provides a
generalization in arbitrary dimension of the four-qubit scheme given by Li and
Wang [Phys. Rev. A 98, 062306 (2018)], and the latter is precisely their
tripartite scheme. The occupation probabilities and coherence of quantum states
are masked in two steps of our schemes. And the information can be extracted
naturally in their reverse processes.


  The yrast line of the N=Z nucleus 48Cr is studied up to high spins by means
of the cranked Hartree-Fock-Bogoliubov method including the T=0 and T=1 isospin
pairing channels. A Skyrme force is used in the mean-field channel together
with a zero-range density-dependent interaction in the pairing channels. The
extensions of the method needed to incorporate the neutron-proton pairing are
summarized. The T=0 pairing correlations are found to play a decisive role for
deformation properties and excitation energies above 16hbar which is the
maximum spin that can be obtained in the f7/2 subshell.


  Several open-source systems, such as Flower and NVIDIA FLARE, have been
developed in recent years while focusing on different aspects of federated
learning (FL). Flower is dedicated to implementing a cohesive approach to FL,
analytics, and evaluation. Over time, Flower has cultivated extensive
strategies and algorithms tailored for FL application development, fostering a
vibrant FL community in research and industry. Conversely, FLARE has
prioritized the creation of an enterprise-ready, resilient runtime environment
explicitly designed for FL applications in production environments. In this
paper, we describe our initial integration of both frameworks and show how they
can work together to supercharge the FL ecosystem as a whole. Through the
seamless integration of Flower and FLARE, applications crafted within the
Flower framework can effortlessly operate within the FLARE runtime environment
without necessitating any modifications. This initial integration streamlines
the process, eliminating complexities and ensuring smooth interoperability
between the two platforms, thus enhancing the overall efficiency and
accessibility of FL applications.


  We describe an approach for modeling fluid concentration profiles in
grid-based microfluidic chips for fluid mixing. This approach provides an
algorithm that predicts fluid concentrations at the chip outlets. Our algorithm
significantly outperforms COMSOL finite element simulations in term of runtime
while still producing results that closely approximate those of COMSOL.


  We explore different ways of incorporating accurate trial wave functions into
free projection auxiliary field quantum Monte Carlo (fp-AFQMC). Trial states
employed include coupled cluster singles and doubles, multi-Slater, and
symmetry projected mean-field wave functions. We adapt a recently proposed fast
multi-Slater local energy evaluation algorithm for fp-AFQMC, making the use of
long expansions from selected configuration interaction methods feasible. We
demonstrate how these trial wave functions serve to mitigate the sign problem
and accelerate convergence in quantum chemical problems, allowing the
application of fp-AFQMC to systems of substantial sizes. Our calculations on
the widely studied $\text{Cu}_2\text{O}_2^{2+}$ model system show that many
previously reported isomerization energies differ substantially from the
near-exact fp-AFQMC value.


  We describe an implementation of the Farfel Fortran AD extensions. These
extensions integrate forward and reverse AD directly into the programming
model, with attendant benefits to flexibility, modularity, and ease of use. The
implementation we describe is a "prepreprocessor" that generates input to
existing Fortran-based AD tools. In essence, blocks of code which are targeted
for AD by Farfel constructs are put into subprograms which capture their
lexical variable context, and these are closure-converted into top-level
subprograms and specialized to eliminate EXTERNAL arguments, rendering them
amenable to existing AD preprocessors, which are then invoked, possibly
repeatedly if the AD is nested.


  The omnipresence of dust particulates in space and astrophysical plasmas has
been attracting numerous researchers to study the collective excitation and
propagation dynamics of different eigen-mode structures in diversifed
astrocosmic circumstances for years. It includes planetary rings,
interplanetary space, cometary tails, asteroid zones, planetary atmospheres,
etc. The ubiquitous charged dust particulates possess collective degrees of
dynamic freedom resulting in the excitation of relatively low-frequency modes,
such as dust-ion-acoustic waves (DIAWs), dust-acoustic waves (DAWs),
dust-Coulomb waves (DCWs), and so forth. An interesting prevalency of dusty
plasma stability research lies in the Jovian magnetosphere (i.e., Jovian
plasmas), embedded inside the supersonic solar wind. A brief review of the
updated research works on dust-acoustic waves and related collective
instability dynamics in the presence of trapped plasma particles is presented
herein. The key aim of the proposed explorative meta-analysis is rooted in
outlining concisely the main up-to-date investigations on such collective
instability processes chronologically. An especial attention is given primarily
to the thermostatistical distribution laws of the constitutive lighter
electrons and ions against the heavier positively charged dust grains
(microspheres). The trapping mechanism of both the lighter species
(electrons+ions) is another additive feature revisited here properly. Finally,
we clearly extrapolate a number of futuristic directions in light of sensible
novelties with a wider scope, both horizontally as well as vertically.


  Changing-look active galactic nuclei (AGNs) present an important laboratory
to understand the origin and physical properties of the broad-line region
(BLR). We investigate follow-up optical spectroscopy spanning $\sim 500$ days
after the outburst of the changing-look AGN 1ES\,1927+654. The emission lines
displayed dramatic, systematic variations in intensity, velocity width,
velocity shift, and symmetry. Analysis of optical spectra and multi-band images
indicate that the host galaxy contains a pseudobulge and a total stellar mass
of $3.56_{-0.35}^{+0.38} \times 10^{9}\, M_\odot$. Enhanced continuum radiation
from the outburst produced an accretion disk wind, which condensed into BLR
clouds in the region above and below the temporary eccentric disk. Broad Balmer
lines emerged $\sim 100$ days after the outburst, together with an unexpected,
additional component of narrow-line emission. The newly formed BLR clouds then
traveled along a similar eccentric orbit ($e \approx 0.6$). The Balmer
decrement of the BLR increased by a factor of $\sim 4-5$ as a result of secular
changes in cloud density. The drop in density at late times allowed the
production of \hei\ and \heii\ emission. The mass of the black hole cannot be
derived from the broad emission lines because the BLR is not virialized.
Instead, we use the stellar properties of the host galaxy to estimate
$M_\mathrm{BH} = 1.38_{-0.66}^{+1.25} \times 10^{6}\, M_\odot$. The nucleus
reached near or above its Eddington limit during the peak of the outburst. We
discuss the nature of the changing-look AGN 1ES\,1927+654 in the context of
other tidal disruption events.


  Motivated from the experimental observation of metal induced gap states
(MIGS) at insulator/metal interfaces by Kiguchi {\it et al.} [Phys. Rev. Lett.
{\bf 90}, 196803 (2003)], we have theoretically investigated the electronic
properties of MIGS at interfaces between various alkali halides and a metal
represented by a jellium with the first-principles density functional method.
We have found that, on top of the usual evanescent state, MIGS generally have a
long tail on halogen sites with a $p_z$-like character, whose penetration depth
($\lambda$) is as large as half the lattice constant of bulk alkali halides.
This implies that $\lambda$, while little dependent on the carrier density in
the jellium, is dominated by the lattice constant (hence by energy gap) of the
alkali halide, where $\lambda_{\rm LiF} < \lambda_{\rm LiCl} < \lambda_{\rm
LiI}$. We also propose a possibility of the MIGS working favorably for the
exciton-mediated superconductivity.


  In this paper, we analytically compute the basic parameters of the p-wave
holographic superconductors with Weyl geometrical corrections using the
matching method. The explicit correspondence between the critical temperature
$T_c$ and the dual charge density $\rho$ has been calculated as
$T_c\propto\rho^{{1}{3}}$ and the dependence of the vacuum expectation value
for the dual condensate operator $\cal{O}$ on the temperature has been found
analytically in the form $<{\cal O}_{+}>\propto
T_c^{{3}{2}}T^{\Delta-{1}{2}}\sqrt{1-({T}{T_c})^3}$. The critical exponent
${1}{2}$ is an universal quantity according to predictions of the mean field
theory and independent from the Weyl coupling $\gamma$. Our analytical results
confirm the numerical results and also agree on computations using by the
variational method.


  The design of neural architectures for structured objects is typically guided
by experimental insights rather than a formal process. In this work, we appeal
to kernels over combinatorial structures, such as sequences and graphs, to
derive appropriate neural operations. We introduce a class of deep recurrent
neural operations and formally characterize their associated kernel spaces. Our
recurrent modules compare the input to virtual reference objects (cf. filters
in CNN) via the kernels. Similar to traditional neural operations, these
reference objects are parameterized and directly optimized in end-to-end
training. We empirically evaluate the proposed class of neural architectures on
standard applications such as language modeling and molecular graph regression,
achieving state-of-the-art results across these applications.


  Cloud environment is very different from traditional computing environment
and therefore tracking the performance of cloud leverages additional
requirements. The movement of data in cloud is very fast. Hence, it requires
that resources and infrastructure available at disposal must be equally
competent. Infrastructure level performance in cloud involves the performance
of servers, network and storage which act as the heart and soul for driving the
entire cloud business. Thus a constant improvement and enhancement of
infrastructure level performance is an important task that needs to be taken
into account. This paper proposes a framework for infrastructure performance
enhancement in a cloud based environment. The framework is broadly divided into
four steps: a) Infrastructure level monitoring of usage pattern and behaviour
of the cloud end users, b) Reporting of the monitoring activities to the cloud
service provider c) Cloud service provider assigns priority according to our
decision matrix based max-min algorithm (DMMM) d) Providing services to cloud
users leading to infrastructure performance enhancement. Our framework is based
on decision matrix and monitoring in cloud using our proposed decision matrix
based max-min algorithm, which draws its inspiration from the original min-min
algorithm. This algorithm makes use of decision matrix to make decisions
regarding distribution of resources among the cloud users.


  We proved the existence of supersymmetric Hermitian metrics with torsion on a
class of non-Kaehler manifolds.


  The popularization of Text-to-Image (T2I) diffusion models enables the
generation of high-quality images from text descriptions. However, generating
diverse customized images with reference visual attributes remains challenging.
This work focuses on personalizing T2I diffusion models at a more abstract
concept or category level, adapting commonalities from a set of reference
images while creating new instances with sufficient variations. We introduce a
solution that allows a pretrained T2I diffusion model to learn a set of soft
prompts, enabling the generation of novel images by sampling prompts from the
learned distribution. These prompts offer text-guided editing capabilities and
additional flexibility in controlling variation and mixing between multiple
distributions. We also show the adaptability of the learned prompt distribution
to other tasks, such as text-to-3D. Finally we demonstrate effectiveness of our
approach through quantitative analysis including automatic evaluation and human
assessment. Project website: https://briannlongzhao.github.io/DreamDistribution


  Gamma-ray bursts are cosmological sources emitting radiation from the
gamma-rays to the radio band. Substantial observational efforts have been
devoted to the study of GRBs during the prompt phase, i.e. the initial burst of
high-energy radiation, and during the longer-lasting afterglows. In spite of
many successes in interpreting these phenomena there are still several open key
questions about the fundamental emission processes, their energetics and the
environment. Moreover, independently of their modeling, GRB spectra are
remarkably simple, being satisfactorily fitted with power-laws, and therefore
offer a very valuable tool to probe the extragalactic background light
distribution affecting all high-energy observations of cosmological sources.
Observations carried out with Cherenkov telescopes, as MAGIC, can be
fundamental for all these scientific topics. GRB080430, being at a rather
moderate redshift, z~0.76, and well-studied in the optical, although observed
only a few hours after the high-energy event, is a good test case to evaluate
the perspective for late-afterglow observations with ground based GeV/TeV
observatories.


  A new scheme of state classification is proposed and applied to analyze
masses of the heavy baryons $\Omega_{Q}$, $\Sigma_{Q}$ and $\Xi_{Q}^{\prime}$
in P-waves. The results confirm all excited $\Omega_{c}$ and $\Omega_{b}$
baryons reported recently by LHCb to be bound states of a P-wave $ss$-diquark
and a respective charm or bottom quark, and thereby predict Regge trajectories
for more excited $\Omega_{c}$ and $\Omega_{b}$ baryons. We suggest one excited
{$J^{P}=5/2^{-}$} $\Omega_{b}$ state to be unseen by LHCb around $6352$ MeV,
and predict P-wave masses of all spin-partners of the odd-parity baryons
$\Sigma_{c}(2800)/\Xi_{c}^{\prime}(2942)$ and
$\Sigma_{b}(6097)$/$\Xi_{b}^{\prime }(6227)$. A computation is further given in
a relativized potential quark models to explain matched values of spin
couplings of all considered baryons, by which a scaling law for these spin
couplings is discussed.


  This paper deals with a new filter algorithm for selecting the smallest
subset of features carrying all the information content of a data set (i.e. for
removing redundant features). It is an advanced version of the fractal
dimension reduction technique, and it relies on the recently introduced
Morisita estimator of Intrinsic Dimension (ID). Here, the ID is used to
quantify dependencies between subsets of features, which allows the effective
processing of highly non-linear data. The proposed algorithm is successfully
tested on simulated and real world case studies. Different levels of sample
size and noise are examined along with the variability of the results. In
addition, a comprehensive procedure based on random forests shows that the data
dimensionality is significantly reduced by the algorithm without loss of
relevant information. And finally, comparisons with benchmark feature selection
techniques demonstrate the promising performance of this new filter.


  We perform a Next-to-Leading order analysis of Delta S=2 processes beyond the
Standard Model. Combining the recently computed NLO anomalous dimensions and
the B parameters of the most general Delta S=2 effective Hamiltonian, we give
an analytic formula for Delta M_K and epsilon_K in terms of the Wilson
coefficients at the high energy scale. This expression can be used for any
extension of the Standard Model with new heavy particles. Using this result, we
consider gluino-mediated contributions to Delta S=2 transitions in general SUSY
models and provide an improved analysis of the constraints on off-diagonal mass
terms between the first two generations of down-type squarks. Finally, we
improve the constraints on R-violating couplings from Delta M_K and epsilon_K.


  We present a numerical study of the \lambda \phi^{4} model in three Euclidean
dimensions, where the two spatial coordinates are non-commutative (NC). We
first show the explicit phase diagram of this model on a lattice. The ordered
regime splits into a phase of uniform order and a ``striped phase''. Then we
discuss the dispersion relation, which allows us to introduce a dimensionful
lattice spacing. Thus we can study a double scaling limit to zero lattice
spacing and infinite volume, which keeps the non-commutativity parameter
constant. The dispersion relation in the disordered phase stabilizes in this
limit, which represents a non-perturbative renormalization. From its shape we
infer that the striped phase persists in the continuum, and we observe UV/IR
mixing as a non-perturbative effect.


  Accurately extracting driving events is the way to maximize computational
efficiency and anomaly detection performance in the tire frictional nose-based
anomaly detection task. This study proposes a concise and highly useful method
for improving the precision of the event extraction that is hindered by extra
noise such as wind noise, which is difficult to characterize clearly due to its
randomness. The core of the proposed method is based on the identification of
the road friction sound corresponding to the frequency of interest and removing
the opposite characteristics with several frequency filters. Our method enables
precision maximization of driving event extraction while improving anomaly
detection performance by an average of 8.506%. Therefore, we conclude our
method is a practical solution suitable for road surface anomaly detection
purposes in outdoor edge computing environments.


  Backdoor attacks are a kind of emergent training-time threat to deep neural
networks (DNNs). They can manipulate the output of DNNs and possess high
insidiousness. In the field of natural language processing, some attack methods
have been proposed and achieve very high attack success rates on multiple
popular models. Nevertheless, there are few studies on defending against
textual backdoor attacks. In this paper, we propose a simple and effective
textual backdoor defense named ONION, which is based on outlier word detection
and, to the best of our knowledge, is the first method that can handle all the
textual backdoor attack situations. Experiments demonstrate the effectiveness
of our model in defending BiLSTM and BERT against five different backdoor
attacks. All the code and data of this paper can be obtained at
https://github.com/thunlp/ONION.


  A serious problem in learning probabilistic models is the presence of hidden
variables. These variables are not observed, yet interact with several of the
observed variables. Detecting hidden variables poses two problems: determining
the relations to other variables in the model and determining the number of
states of the hidden variable. In this paper, we address the latter problem in
the context of Bayesian networks. We describe an approach that utilizes a
score-based agglomerative state-clustering. As we show, this approach allows us
to efficiently evaluate models with a range of cardinalities for the hidden
variable. We show how to extend this procedure to deal with multiple
interacting hidden variables. We demonstrate the effectiveness of this approach
by evaluating it on synthetic and real-life data. We show that our approach
learns models with hidden variables that generalize better and have better
structure than previous approaches.


  We study the geometry of PQKT-connections. We find conditions to the
existence of a PQKT-connection and prove that if it exists it is unique. We
show that PQKT geometry persist in a conformal class of metrics.


  Incremental gradient and incremental proximal methods are a fundamental class
of optimization algorithms used for solving finite sum problems, broadly
studied in the literature. Yet, without strong convexity, their convergence
guarantees have primarily been established for the ergodic (average) iterate.
Motivated by applications in continual learning, we obtain the first
convergence guarantees for the last iterate of both incremental gradient and
incremental proximal methods, in general convex smooth (for both) and convex
Lipschitz (for the proximal variants) settings. Our oracle complexity bounds
for the last iterate nearly match (i.e., match up to a square-root-log or a log
factor) the best known oracle complexity bounds for the average iterate, for
both classes of methods. We further obtain generalizations of our results to
weighted averaging of the iterates with increasing weights and for randomly
permuted ordering of updates. We study incremental proximal methods as a model
of continual learning with generalization and argue that large amount of
regularization is crucial to preventing catastrophic forgetting. Our results
generalize last iterate guarantees for incremental methods compared to state of
the art, as such results were previously known only for overparameterized
linear models, which correspond to convex quadratic problems with infinitely
many solutions.


  Learning-based image quality assessment (IQA) has made remarkable progress in
the past decade, but nearly all consider the two key components -- model and
data -- in isolation. Specifically, model-centric IQA focuses on developing
``better'' objective quality methods on fixed and extensively reused datasets,
with a great danger of overfitting. Data-centric IQA involves conducting
psychophysical experiments to construct ``better'' human-annotated datasets,
which unfortunately ignores current IQA models during dataset creation. In this
paper, we first design a series of experiments to probe computationally that
such isolation of model and data impedes further progress of IQA. We then
describe a computational framework that integrates model-centric and
data-centric IQA. As a specific example, we design computational modules to
quantify the sampling-worthiness of candidate images. Experimental results show
that the proposed sampling-worthiness module successfully spots diverse
failures of the examined blind IQA models, which are indeed worthy samples to
be included in next-generation datasets.


  Deep networks, especially convolutional neural networks (CNNs), have been
successfully applied in various areas of machine learning as well as to
challenging problems in other scientific and engineering fields. This paper
introduces Butterfly-Net, a low-complexity CNN with structured and sparse
cross-channel connections, together with a Butterfly initialization strategy
for a family of networks. Theoretical analysis of the approximation power of
Butterfly-Net to the Fourier representation of input data shows that the error
decays exponentially as the depth increases. Combining Butterfly-Net with a
fully connected neural network, a large class of problems are proved to be well
approximated with network complexity depending on the effective frequency
bandwidth instead of the input dimension. Regular CNN is covered as a special
case in our analysis. Numerical experiments validate the analytical results on
the approximation of Fourier kernels and energy functionals of Poisson's
equations. Moreover, all experiments support that training from Butterfly
initialization outperforms training from random initialization. Also, adding
the remaining cross-channel connections, although significantly increase the
parameter number, does not much improve the post-training accuracy and is more
sensitive to data distribution.


  We prove that there are no effective or anti-effective classes of square -1
or -2 arising from nodal curves on smooth algebraic surfaces by way of
divisibility. This general fact has interesting applications to Enriques and K3
surfaces. The proof relies on specific properties of root lattices and their
duals.


  We have studied the role of virtual excitations of inner shells upon outer
shell photoionization. The calculations were performed in the frames of the
Random Phase Approximation and its generalized version GRPAE that take into
account variation of the atomic field due to electron elimination and the inner
vacancies decay. We employ both analytic approximation and numeric
computations. The results are presented for 3p electrons in Ar and 4d-electrons
in Pd near inner shells thresholds. The effect proved to be noticeable.


  Future lepton colliders such as the FCC-ee, CEPC, ILC, or a muon collider
will collect large data samples that allow precision physics studies with
unprecedented accuracy, especially when the data is collected by innovative
state-of-the-art detectors. An electromagnetic calorimeter based on
scintillating crystals, designed to separately record Cherenkov and
scintillation light, can achieve precision measurements of electrons and
photons without sacrificing jet energy resolution, given adequate light
collection efficiency and separation. This paper presents initial measurements
from a program aimed at developing such a calorimeter system for future
colliders. We focus on using PbF2 crystals to enhance the understanding of
Cherenkov light collection, marking the first step in this endeavor.


  Digital correlated double sampling (DCDS), a readout technique for
charge-coupled devices (CCD), is gaining popularity in astronomical
applications. By using an oversampling ADC and a digital filter, a DCDS system
can achieve a better performance than traditional analogue readout techniques
at the expense of a more complex system analysis. Several attempts to analyse
and optimize a DCDS system have been reported, but most of the work presented
in the literature has been experimental. Some approximate analytical tools have
been presented for independent parameters of the system, but the overall
performance and trade-offs have not been yet modelled. Furthermore, there is
disagreement among experimental results that cannot be explained by the
analytical tools available. In this work, a theoretical analysis of a generic
DCDS readout system is presented, including key aspects such as the signal
conditioning stage, the ADC resolution, the sampling frequency and the digital
filter implementation. By using a time-domain noise model, the effect of the
digital filter is properly modelled as a discrete-time process, thus avoiding
the imprecision of continuous-time approximations that have been used so far.
As a result, an accurate, closed-form expression for the signal-to-noise ratio
at the output of the readout system is reached. This expression can be easily
optimized in order to meet a set of specifications for a given CCD, thus
providing a systematic design methodology for an optimal readout system.
Simulated results are presented to validate the theory, obtained with both
time- and frequency-domain noise generation models for completeness.


  High resolution radio observations of the composite supernova remnant (SNR)
G326.3-1.8 or MSH 15-56 with the Australia Telescope Compact Array show details
of both the shell and the bright plerion which is offset about 1/3 of the
distance from the center of the SNR to the shell. The shell appears to be
composed of thin filaments, typical of older shell SNRs. The central part of
the elongated plerion is composed of a bundle of parallel ridges which bulge
out at the ends and form a distinct ring structure on the northwestern end. The
magnetic field with a strength of order 45 microGauss, is directed along the
axis of the ridges but circles around the northwestern ring. This plerion is
large and bright in the radio but is not detected in x-ray or optical
wavelengths. There is, however, a faint hard x-ray feature closer to the shell
outside the plerion. Perhaps if the supernova explosion left a rapidly moving
magnetar with large energy input but initially rapid decay of both relativistic
particles and magnetic field, the observed differences with wavelength could be
explained.


  We define a corestriction map for equivariant Brauer groups in the sense of
Fr\"ohlich and Wall, which contain as a special case the Brauer-Clifford groups
introduced by Turull. We show that this corestriction map has similar
properties as the corestriction map in group cohomology (especially Galois
cohomology). In particular, composing corestriction and restriction associated
to a subgroup $H\leq G$ amounts to powering with the index $\lvert G:H \rvert$.


  In this paper, we prove the global $C^\infty$ regularity of the Oleinik's
solution for the steady Prandtl equation with favorable pressure.


  A hypercomplex manifold is a manifold equipped with three complex structures
I, J, K satisfying the quaternionic relations. Let M be a 4-dimensional compact
smooth manifold equipped with a hypercomplex structure, and E be a vector
bundle on M. We show that the moduli space of anti-self-dual connections on E
is also hypercomplex, and admits a strong HKT metric. We also study manifolds
with (4,4)-supersymmetry, that is, Riemannian manifolds equipped with a pair of
strong HKT-structures that have opposite torsion. In the language of Hitchin's
and Gualtieri's generalized complex geometry, (4,4)-manifolds are called
``generalized hyperkaehler manifolds''. We show that the moduli space of
anti-self-dual connections on M is a (4,4)-manifold if M is equipped with a
(4,4)-structure.


  Following a brief historical introduction of the notions of chaos in
dynamical systems, we will present recent developments that attempt to profit
from the rich structure and complexity of the chaotic dynamics. In particular,
we will demonstrate the ability to control chaos in realistic complex
environments. Several applications will serve to illustrate the theory and to
highlight its advantages and weaknesses. The presentation will end with a
survey of possible generalizations and extensions of the basic formalism as
well as a discussion of applications outside the field of the physical
sciences. Future research avenues in this rapidly growing field will also be
addressed.


  A good observation of preflare activities is important for us to understand
the origin and triggering mechanism of solar flares, and to predict the
occurrence of solar flares. This work presents the characteristics of microwave
spectral fine structures as preflare activities of four solar flares observed
by Ond\v{r}ejov radio spectrograph in the frequency range of 0.8--2.0 GHz. We
found that these microwave bursts which occurred 1--4 minutes before the onset
of flares have spectral fine structures with relatively weak intensities and
very short timescales. They include microwave quasi-periodic pulsations (QPP)
with very short period of 0.1-0.3 s and dot bursts with millisecond timescales
and narrow frequency bandwidths. Accompanying these microwave bursts, there are
filament motions, plasma ejection or loop brightening on the EUV imaging
observations and non-thermal hard X-ray emission enhancements observed by
RHESSI. These facts may reveal certain independent non-thermal energy releasing
processes and particle acceleration before the onset of solar flares. They may
be conducive to understand the nature of solar flares and predict their
occurrence.


  We present a Reinforcement Learning (RL) solution to the view planning
problem (VPP), which generates a sequence of view points that are capable of
sensing all accessible area of a given object represented as a 3D model. In
doing so, the goal is to minimize the number of view points, making the VPP a
class of set covering optimization problem (SCOP). The SCOP is NP-hard, and the
inapproximability results tell us that the greedy algorithm provides the best
approximation that runs in polynomial time. In order to find a solution that is
better than the greedy algorithm, (i) we introduce a novel score function by
exploiting the geometry of the 3D model, (ii) we model an intuitive human
approach to VPP using this score function, and (iii) we cast VPP as a Markovian
Decision Process (MDP), and solve the MDP in RL framework using well-known RL
algorithms. In particular, we use SARSA, Watkins-Q and TD with function
approximation to solve the MDP. We compare the results of our method with the
baseline greedy algorithm in an extensive set of test objects, and show that we
can out-perform the baseline in almost all cases.


  A dimension allowing in particular to state necessary and sufficient
conditions of the Morse-Sard Theorem for real valued functions is introduced.


  In the presented paper left-invariant pseudo-Riemannian metrics on
four-dimensional Lie groups with zero Schouten-Weyl tensor are investigated.
The complete classification of these metric Lie groups is obtained in terms of
the structure constants of corresponding Lie algebras.


  The effects of interpersonal interactions on individual's agreements result
in a social aggregation process which is reflected in the formation of
collective states, as for instance, groups of individuals with a similar
opinion about a given issue. This field, which has been a longstanding concern
of sociologists and psychologists, has been extended into an area of
experimental social psychology, and even has attracted the attention of
physicists and mathematicians. In this article, we present a novel model of
opinion formation in which agents may either have a strict preference for a
choice, or be undecided. The opinion shift emerges during interpersonal
communications, as a consequence of a cumulative process of conviction for one
of the two extremes opinions through repeated interactions. There are two main
ingredients which play key roles in determining the steady state: the initial
fraction of undecided agents and the conviction's sensitivity in each
interaction. As a function of these two parameters, the model presents a wide
range of possible solutions, as for instance, consensus of each opinion,
bi-polarisation or convergence of undecided individuals. We found that a
minimum fraction of undecided agents is crucial not only for reaching consensus
of a given opinion, but also to determine a dominant opinion in a polarised
situation. In order to gain a deeper comprehension of the dynamics, we also
present the theoretical master equations of the model.


  Despite the level of attention given to rollups there is limited empirical
research about their performance. To address this gap, we conduct a
comprehensive data-driven analysis of the late 2023 transaction boom that is
attributed to inscriptions: a novel approach to record data onto a blockchain
with no outside server needed. Inscriptions were first introduced on the
Bitcoin blockchain to allow for the representation of NFTs or ERC-20-like
tokens without smart contracts, but were later spread to other blockchains.
  This work examines the applications of inscription transactions in Ethereum
and its major EVM-compatible rollups and their impact on blockchain scalability
during periods of sudden transaction surges. We found that on certain days,
inscription-related transactions comprised over 89% on Arbitrum, over 88% on
zkSync Era, and over 53% on Ethereum. Furthermore, 99% of these transactions
were related to the minting of meme coins, followed by limited trading
activity. Unlike L1 blockchains, during periods of transaction surges, zkSync
and Arbitrum experienced lower median gas fees, attributable to the compression
of L2 transactions for a single L1 batch. Additionally, zkSync Era, a ZK
rollup, demonstrated a stronger reduction in fees than optimistic rollups
considered in our study: Arbitrum, Base, and Optimism.


  We define a notion of weak omega-category internal to a model of Martin-L\"of
type theory, and prove that each type bears a canonical weak omega-category
structure obtained from the tower of iterated identity types over that type. We
show that the omega-categories arising in this way are in fact omega-groupoids.


  We give an explicit description of the Mirkovic-Vilonen cycles on the affine
Grassmannian for arbitrary complex reductive groups. We also give a
combinatorial characterization of the MV polytopes. We prove that a polytope is
an MV polytope if and only if it a lattice polytope whose defining hyperplanes
are parallel to those of the Weyl polytopes and whose 2-faces are rank 2 MV
polytopes. As an application, we give a bijection between Lusztig's canonical
basis and the set of MV polytopes.


  In this paper, we study a family of stochastic volatility processes; this
family features a mean reversion term for the volatility and a double CEV-like
exponent that generalizes SABR and Heston's models. We derive approximated
closed form formulas for the digital prices, the local and implied
volatilities. Our formulas are efficient for small maturities.
  Our method is based on differential geometry, especially small time
diffusions on riemanian spaces. This geometrical point of view can be extended
to other processes, and is very accurate to produce variate smiles for small
maturities and small moneyness.


  We discuss distortion in microlensing-induced light curves which are
considered to be curves due to single-point-mass lenses at a first glance. As
factors of the distortion, we consider close binary and planetary systems,
which are the limiting cases of two-point-mass lenses, and the gravitational
potential is regarded as the sum of the single point mass and the corrections.
In order to quantitatively estimate the asymmetric features of such distorted
light curves, we propose a cutoff dependent skewness, and show how to
discriminate the similar light curves with it. We also examine as the
distortion the general relativistic effect of frame dragging, but the effect
coincides with the close binary case in the light curves.


  Advanced ACTPol is an instrument upgrade for the six-meter Atacama Cosmology
Telescope (ACT) designed to measure the cosmic microwave background (CMB)
temperature and polarization with arcminute-scale angular resolution. To
achieve its science goals, Advanced ACTPol utilizes a larger readout
multiplexing factor than any previous CMB experiment to measure detector arrays
with approximately two thousand transition-edge sensor (TES) bolometers in each
150 mm detector wafer. We present the implementation and testing of the
Advanced ACTPol time-division multiplexing readout architecture with a 64-row
multiplexing factor. This includes testing of individual multichroic detector
pixels and superconducting quantum interference device (SQUID) multiplexing
chips as well as testing and optimizing of the integrated readout electronics.
In particular, we describe the new automated multiplexing SQUID tuning
procedure developed to select and optimize the thousands of SQUID parameters
required to readout each Advanced ACTPol array. The multichroic detector pixels
in each array use separate channels for each polarization and each of the two
frequencies, such that four TESes must be read out per pixel. Challenges
addressed include doubling the number of detectors per multiplexed readout
channel compared to ACTPol and optimizing the Nyquist inductance to minimize
detector and SQUID noise aliasing.


  The radio source Sgr A* at the center of our Galaxy is believed to be a 2.6 x
10^6 solar mass black hole which accretes gas from the winds of nearby stars.
We show that limits on the X-ray and infrared emission from the Galactic Center
provide an upper limit of ~ 8 x 10^{-5} solar masses per year on the mass
accretion rate in Sgr A*. The advection-dominated accretion flow (ADAF) model
favors a rate < 10^{-5} solar masses per year. In comparison, the Bondi
accretion rate onto Sgr A*, estimated using the observed spatial distribution
of mass losing stars and assuming non-interacting stellar winds, is ~ 3 x
10^{-5} solar masses per year. There is thus rough agreement between the Bondi,
the ADAF, and the X-ray inferred accretion rates for Sgr A*. We discuss
uncertainties in these estimates, emphasizing the importance of upcoming
observations by the Chandra X-ray observatory (CXO) for tightening the X-ray
derived limits.


  Minimal models of self-propelled particles with short-range volume exclusion
interactions have been shown to exhibit signatures of phase separation. Here I
show that the observed interfacial stability and fluctuations in
motility-induced phase separations (MIPS) can be explained by modeling the
microscopic dynamics of the active particles in the interfacial region. In
addition, I demonstrate the validity of the Gibbs-Thomson relation in MIPS,
which provides a functional relationship between the size of a condensed drop
and its surrounding vapor concentration. As a result, the coarsening dynamics
of MIPS at vanishing supersaturation follows the classic Lifshitz-Slyozov
scaling law at the late stage.


  For totally ergodic Z^2-actions a collection of weak limits provide the set
{2,4, ..., 2 ^ n} of spectral multiplicities for their tensor product. Our
conditions allow to obtain a similar result for mixing actions via some limit
procedure.


  We have developed a highly-tuned software library that accelerates the
calculation of quadrupole terms in the Barnes-Hut tree code by use of a SIMD
instruction set on the x86 architecture, Advanced Vector eXtensions 2 (AVX2).
Our code is implemented as an extension of Phantom-GRAPE software library
(Tanikawa et al. 2012, 2013) that significantly accelerates the calculation of
monopole terms. If the same accuracy is required, the calculation of quadrupole
terms can accelerate the evaluation of forces than that of only monopole terms
because we can approximate gravitational forces from closer particles by
quadrupole moments than by only monopole moments. Our implementation can
calculate gravitational forces about 1.1 times faster in any system than the
combination of the pseudoparticle multipole method and Phantom-GRAPE. Our
implementation allows simulating homogeneous systems up to 2.2 times faster
than that with only monopole terms, however, speed up for clustered systems is
not enough because the increase of approximated interactions is insufficient to
negate the increased calculation cost by computing quadrupole terms. We have
estimated that improvement in performance can be achieved by the use of a new
SIMD instruction set, AVX-512. Our code is expected to be able to accelerate
simulations of clustered systems up to 1.08 times faster on AVX-512 environment
than that with only monopole terms.


  Complex Legendre duality is a generalization of Legendre transformation from
Euclidean spaces to Kahler manifolds, that Berndtsson and collaborators have
recently constructed. It is a local isometry of the space of Kahler potentials.
We show that the fixed point of such a transformation must correspond to a real
analytic Kahler metric.


  Audio CAPTCHAs are supposed to provide a strong defense for online resources;
however, advances in speech-to-text mechanisms have rendered these defenses
ineffective. Audio CAPTCHAs cannot simply be abandoned, as they are
specifically named by the W3C as important enablers of accessibility.
Accordingly, demonstrably more robust audio CAPTCHAs are important to the
future of a secure and accessible Web. We look to recent literature on attacks
on speech-to-text systems for inspiration for the construction of robust,
principle-driven audio defenses. We begin by comparing 20 recent attack papers,
classifying and measuring their suitability to serve as the basis of new
"robust to transcription" but "easy for humans to understand" CAPTCHAs. After
showing that none of these attacks alone are sufficient, we propose a new
mechanism that is both comparatively intelligible (evaluated through a user
study) and hard to automatically transcribe (i.e., $P({\rm transcription}) = 4
\times 10^{-5}$). Finally, we demonstrate that our audio samples have a high
probability of being detected as CAPTCHAs when given to speech-to-text systems
($P({\rm evasion}) = 1.77 \times 10^{-4}$). In so doing, we not only
demonstrate a CAPTCHA that is approximately four orders of magnitude more
difficult to crack, but that such systems can be designed based on the insights
gained from attack papers using the differences between the ways that humans
and computers process audio.


  We propose an integrable model of one-dimensional (1D) interacting electrons
coupled with the local orbitals arrayed periodically in the chain. Since the
local orbitals are introduced in a way that double occupation is forbidden, the
model keeps the main feature of the periodic Anderson model with an interacting
host. For the attractive interaction, it is found that the local orbitals
enhance the effective mass of the Cooper-pair-like singlets and also the pair
correlation in the ground state. However, the persistent current is depressed
in this case. For the repulsive interaction case, the Hamiltonian is
non-Hermitian but allows Cooper pair solutions with small momenta, which are
induced by the hybridization between the extended state and the local orbitals.


  Ferroelectric nanostructures can be formed by local switching of domains
using techniques such as piezo-force microscopy (PFM). Understanding lateral
size effects is important to determine the minimum feature size for writing
ferroelectric nanostructures. To understand these lateral size effects, we use
the time-dependent-Ginzburg-Landau equations to simulate localized switching of
domains for a PFM type and parallel-plate capacitor configurations. Our
investigations indicate that fringing electric fields lead to switching via 90
deg domain wedge nucleation for thicker films while at smaller thicknesses, the
polarization switches directly by 180 deg rotations. The voltage required to
switch the domain increases by decreasing the lateral size and at very small
lateral sizes the coercive voltage becomes so large that it becomes virtually
impossible to switch the domain. In all cases, the width of the switched region
extends beyond the electrodes, due to fringing.


  We use the concept of reproducing pairs to study Gabor systems at critical
density. First, we present a generalization of the Balian-Low theorem to the
reproducing pairs setting. Then, we prove our main result that there exists a
reproducing partner for the Gabor system of integer time-frequency shifts of
the Gaussian. In other words, the coefficients for this Gabor expansion of a
square integrable function can be calculated using inner products with an
unstructured family of vectors in $ L^2(\R)$. This solves the possibly last
open question for this system.


  We propose a Jacobi-style distributed algorithm to solve convex,
quadratically constrained quadratic programs (QCQPs), which arise from a broad
range of applications. While small to medium-sized convex QCQPs can be solved
efficiently by interior-point algorithms, large-scale problems pose significant
challenges to traditional algorithms that are mainly designed to be implemented
on a single computing unit. The exploding volume of data (and hence, the
problem size), however, may overwhelm any such units. In this paper, we propose
a distributed algorithm for general, non-separable, large-scale convex QCQPs,
using a novel idea of predictor-corrector primal-dual update with an adaptive
step size. The algorithm enables distributed storage of data as well as
parallel distributed computing. We establish the conditions for the proposed
algorithm to converge to a global optimum, and implement our algorithm on a
computer cluster with multiple nodes using Message Passing Interface (MPI). The
numerical experiments are conducted on data sets of various scales from
different applications, and the results show that our algorithm exhibits
favorable scalability for solving large-scale problems.


  Eye tracking data collection in the virtual reality context is typically
carried out in laboratory settings, which usually limits the number of
participants or consumes at least several months of research time. In addition,
under laboratory settings, subjects may not behave naturally due to being
recorded in an uncomfortable environment. In this work, we propose a
proof-of-concept eye tracking data collection protocol and its implementation
to collect eye tracking data from remotely located subjects, particularly for
virtual reality using Ethereum blockchain and smart contracts. With the
proposed protocol, data collectors can collect high quality eye tracking data
from a large number of human subjects with heterogeneous socio-demographic
characteristics. The quality and the amount of data can be helpful for various
tasks in data-driven human-computer interaction and artificial intelligence.


  Computer vision enables the development of new approaches to monitor the
behavior, health, and welfare of animals. Instance segmentation is a
high-precision method in computer vision for detecting individual animals of
interest. This method can be used for in-depth analysis of animals, such as
examining their subtle interactive behaviors, from videos and images. However,
existing deep-learning-based instance segmentation methods have been mostly
developed based on public datasets, which largely omit heavy occlusion
problems; therefore, these methods have limitations in real-world applications
involving object occlusions, such as farrowing pen systems used on pig farms in
which the farrowing crates often impede the sow and piglets. In this paper, we
adapt a Center Clustering Network originally designed for counting to achieve
instance segmentation, dubbed as CClusnet-Inseg. Specifically, CClusnet-Inseg
uses each pixel to predict object centers and trace these centers to form masks
based on clustering results, which consists of a network for segmentation and
center offset vector map, Density-Based Spatial Clustering of Applications with
Noise (DBSCAN) algorithm, Centers-to-Mask (C2M), and Remain-Centers-to-Mask
(RC2M) algorithms. In all, 4,600 images were extracted from six videos
collected from three closed and three half-open farrowing crates to train and
validate our method. CClusnet-Inseg achieves a mean average precision (mAP) of
84.1 and outperforms all other methods compared in this study. We conduct
comprehensive ablation studies to demonstrate the advantages and effectiveness
of core modules of our method. In addition, we apply CClusnet-Inseg to
multi-object tracking for animal monitoring, and the predicted object center
that is a conjunct output could serve as an occlusion-resistant representation
of the location of an object.


  Solar cells based on hybrid perovskites have shown high efficiency while
possessing simple processing methods. To gain a fundamental understanding of
their properties on an atomic level, we investigate single crystals of
CH3NH3PbI3 with a narrow transition (~5 K) near 327 K. Temperature dependent
structural measurements reveal a persistent tetragonal structure with smooth
changes in the atomic displacement parameters (ADPs) on crossing T*. We show
that the ADPs for I ions yield extended flat regions in the potential wells
consistent with the measured large thermal expansion parameter. Molecular
dynamics simulations reveal that this material exhibits significant high
asymmetries in the Pb-I pair distribution functions. We also show that the
intrinsically enhanced freedom of motion of the iodine atoms enables large
deformations. This flexibility (softness) of the atomic structure results in
highly localized atomic relaxation about defects and hence accounts for both
the high carrier mobility as well as the structural instability.


  We perform cooling simulations for isolated neutron stars using recently
developed equations of state for their core. The equations of state are
obtained from new parametrizations of the FSU2 relativistic mean-field
functional that reproduce the properties of nuclear matter and finite nuclei,
while fulfilling the restrictions on high-density matter deduced from heavy-ion
collisions, measurements of massive 2$M_{\odot}$ neutron stars, and neutron
star radii below 13 km. We find that two of the models studied, FSU2R (with
nucleons) and in particular FSU2H (with nucleons and hyperons), show very good
agreement with cooling observations, even without including extensive nucleon
pairing. This suggests that the cooling observations are more compatible with
an equation of state that produces a soft nuclear symmetry energy and, hence,
generates small neutron star radii. However, both models favor large stellar
masses, above $1.8 M_{\odot}$, to explain the colder isolated neutron stars
that have been observed, even if nucleon pairing is present.


  V445 Pup was a peculiar nova with no hydrogen spectral lines during the
outburst. The spectrum contained strong emission lines of carbon, oxygen,
calcium, sodium, and iron. We have performed digital processing of photographic
images of the V445 Pup progenitor using astronomical plate archives. The
brightness of the progenitor in the B band was 14.3 mag. It was a periodic
variable star, its most probable period being 0.650654+/-0.000011 day. The
light curve shape suggests that the progenitor was a common-envelope binary
with a spot on the surface and variable surface brightness. The spectral energy
distribution of the progenitor between 0.44 and 2.2 micrometers was similar to
that of an A0V type star. After the explosion in 2001, the dust was formed in
the ejecta, and the star became a strong infrared source. This resulted in the
star's fading below 20 mag in the V band. Our CCD BVR observations acquired
between 2003 and 2009 suggest that the dust absorption minimum finished in
2004, and the remnant reappeared at the level of 18.5 mag V. The dust dispersed
but a star-like object was absent in frames taken in the K band with the VLT
adaptive optics. Only expanding ejecta of the explosion were seen in these
frames till March 2007. No reddened A0V type star reappeared in the spectral
energy distribution. The explosion of V445 Pup in 2000 was a helium flash on
the surface of a CO-type white dwarf. Taking into account the results of modern
dynamic calculations, we discuss the possibility of a white-dwarf core
detonation triggered by the helium flash and the observational evidence for it.
Additionally, the common envelope of the system was lost in the explosion.
Destruction in the system and mass loss from its components exclude the future
SN Ia scenario for V445 Pup.


  We analyze surface codes, the topological quantum error-correcting codes
introduced by Kitaev. In these codes, qubits are arranged in a two-dimensional
array on a surface of nontrivial topology, and encoded quantum operations are
associated with nontrivial homology cycles of the surface. We formulate
protocols for error recovery, and study the efficacy of these protocols. An
order-disorder phase transition occurs in this system at a nonzero critical
value of the error rate; if the error rate is below the critical value (the
accuracy threshold), encoded information can be protected arbitrarily well in
the limit of a large code block. This phase transition can be accurately
modeled by a three-dimensional Z_2 lattice gauge theory with quenched disorder.
We estimate the accuracy threshold, assuming that all quantum gates are local,
that qubits can be measured rapidly, and that polynomial-size classical
computations can be executed instantaneously. We also devise a robust recovery
procedure that does not require measurement or fast classical processing;
however for this procedure the quantum gates are local only if the qubits are
arranged in four or more spatial dimensions. We discuss procedures for
encoding, measurement, and performing fault-tolerant universal quantum
computation with surface codes, and argue that these codes provide a promising
framework for quantum computing architectures.


  Using a new definition of a prime ideal of a skew brace A, on set Spec A of
prime ideals of A we endow a spectral topology (in the sense of Grothendieck).
We characterize irreducible closed subsets of Spec A and prove every
irreducible closed subset of the space has a unique generic point. We give a
sufficient condition for the space to be Noetherian. We study continuous maps
between such spaces, and finally, we prove that Spec(Idl A) is a spectral
space, where Idl A is the set of all ideals of A.


  We extend the semiclassical two-step model [Phys. Rev. A 94, 013415 (2016)]
to include a multielectron polarization-induced dipole potential. Using this
model we investigate the imprints of multielectron effects in the momentum
distributions of photoelectrons ionized by a linearly polarized laser pulse. We
predict narrowing of the longitudinal momentum distributions due to electron
focusing by the induced dipole potential. We show that the polarization of the
core also modifies interference structures in the photoelectron momentum
distributions. Specifically, the number of fanlike interference structures in
the low-energy part of the electron momentum distribution may be altered. We
analyze the mechanisms underlying this interference effect. The account of the
multielectron dipole potential seems to improve the agreement between theory
and experiment.


  In recent years, the use of the automobile as the primary mode of
transportation has been increasing and driving has become an important part of
daily life. Driving is a multi-sensory experience as drivers rely on their
senses to provide them with important information. In a vehicular context human
senses are all too often limited and obstructed. Today, road accidents
constitute the eighth leading cause of death. The escalation of technology has
propelled new ways in which driver's senses may be augmented. The enclosed
aspect of a car, allied with the configuration of the controls and displays
directed towards the driver, offer significant advantages for augmented reality
(AR) systems when considering the amount of immersion it can provide to the
user. In addition, the inherent mobility and virtually unlimited power autonomy
transform cars into perfect mobile computing platforms. However, automobiles
currently present limited network connectivity and thus the created augmented
objects are merely providing information captured by in-vehicle sensors,
cameras and other databases. By combining the new paradigm of Vehicular Ad Hoc
Networking (VANET) with AR human machine interfaces, we show that it is
possible to design novel cooperative Advanced Driver Assistance Systems (ADAS),
that base the creation of AR content on the information collected from
neighbouring vehicles or roadside infrastructures. As such we implement
prototypes of both visual and acoustic AR systems, which can significantly
improve the driving experience. We believe our results contribute to the
formulation of a vision where the vehicle is perceived as an extension of the
body which permeates the human senses to the world outside the vessel, where
the car is used as a better, multi-sensory immersive version of a mobile phone
that integrates touch, vision and sound enhancements, leveraging unique
properties of VANET.


  Low luminosity active galactic nuclei are more abundant and closer to us than
the luminous ones but harder to explore as they are faint. We have selected the
four sources NGC 315, NGC 4261, NGC 1275, and NGC 4486, which have been
detected in gamma rays byFermi-LAT. We have compiled their long-term radio,
optical, X-ray data from different telescopes, analysed XMM-Newton data for NGC
4486, XMM-Newton and Swift data for NGC 315. We have analysed the Fermi-LAT
data collected over the period of 2008 to 2020 for all of them. Electrons are
assumed to be accelerated to relativistic energies in sub-parsec scale jets,
which radiate by synchrotron and synchrotron self-Compton emission covering
radio to gamma-ray energies. This model can fit most of the multi-wavelength
data points of the four sources. However, the gamma-ray data points from NGC
315 and NGC 4261 can be well fitted only up to 1.6 GeV and 0.6 GeV,
respectively in this model. This motivates us to find out the origin of the
higher energy {\gamma}-rays detected from these sources. Kilo-parsec scale jets
have been observed previously from these sources in radio and X-ray
frequencies. If we assume {\gamma}-rays are also produced in kilo-parsec scale
jets of these sources from inverse Compton scattering of starlight photons by
ultra-relativistic electrons, then it is possible to fit the gamma-ray data at
higher energies. Our result also suggests that strong host galaxy emission is
required to produce GeV radiation from kilo-parsec scale jets.


  In this paper, we investigate the quantum correlations and coherence of two
accelerating Unruh-deWitt detectors coupled to a scalar field in 3 + 1
Minkowski space-time. We show that the entanglement is completely destroyed in
the limit of infinite acceleration while the local quantum uncertainty and
l1-norm of coherence remain nonzero. In addition, we also highlight the role of
Unruh temperature and energy spacing of detectors on quantum correlations for
different choices of initial states.


  The gravitating matter is studied within the framework of the non-commutative
geometry. The non-commutative Einstein-Hilbert action on the product of a four
dimensional manifold with a discrete space gives the models of matter fields
coupled to the standard Einstein gravity.The matter multiplet is encoded in the
Dirac operator which yields the representation of the algebra of the universal
forms. The general form of the Dirac operator depends on a choice of the
grading of the corresponding spinor bundle. A choice is given, which leads to
the nonlinear vector sigma-model coupled to the Einstein gravity.


  We study a version of the Ornstein-Uhlenbeck bridge driven by a
spectrally-positive subordinator. Our formulation is based on a
Linear-Quadratic control subject to a singular terminal condition. The
Ornstein-Uhlenbeck bridge, we develop, is written as a limit of the obtained
optimally controlled processes, and is shown to admit an explicit expression.
Its extension with self-excitement is also considered. The terminal condition
is confirmed to be satisfied by the obtained process both analytically and
numerically. The methods are also applied to a streamflow regulation problem
using a real-life dataset.


  Space observatories like the Hubble Space Telescope and Gaia are providing
unprecedented 6D phase space information of satellite galaxies. Such
measurements can shed light on the structure and assembly history of the Local
Group, but improved statistical methods are needed to use them efficiently.
Here we illustrate such a method using analogs of the Local Group's two most
massive satellite galaxies, the Large Magellanic Cloud (LMC) and Triangulum
(M33), from the Illustris dark-matter-only cosmological simulation. We use a
Bayesian inference scheme combining measurements of positions, velocities, and
specific orbital angular momenta ( j ) of the LMC/M33 with importance sampling
of their simulated analogs to compute posterior estimates of the Milky Way (MW)
and Andromeda's (M31) halo masses. We conclude the resulting host halo mass is
more susceptible to bias when using measurements of the current position and
velocity of satellites, especially when satellites are at short-lived phases of
their orbits (i.e. at pericentre). Instead, the j value of a satellite is
well-conserved over time and provides a more reliable constraint on host mass.
The inferred virial mass of the MW (M31) using j of the LMC (M33) is $\rm
M_{vir, MW}=1.02^{+0.77}_{-0.55}\times10^{12}\; M_{\odot}$ ($\rm M_{vir,
M31}=1.37^{+1.39}_{-0.75}\times10^{12}\; M_{\odot}$). Choosing simulated
analogs whose j values are consistent with the conventional picture of a
previous (< 3 Gyr ago), close encounter (< 100 kpc) of M33 about M31 results in
a very low virial mass for M31 ($\rm\sim\!10^{12}\; M_{\odot}$). This supports
the new scenario put forth in Patel et al. (2017), wherein M33 is on its first
passage about M31 or on a long period orbit. We conclude that this Bayesian
inference scheme, utilising satellite j, is a promising method to reduce the
current factor of two spread in the mass range of the MW and M31 moving
forward.