  CP violation from physics beyond the Standard Model (SM) is investigated in
the Cabbibo-suppressed decay $\tau\to K\pi\nu_{\tau}$ with polarized $\tau$
leptons, to which both the ${\rm J}^{P}=1^-$ resonance $K^*$ and the $
J^{P}=0^+$ resonance $K^*_0$ contribute. In addition to the CP-odd rate
asymmetry, $\tau$ polarization enables us to construct three additional CP-odd
polarization asymmetries that can be enhanced due to the interference between
the $K^*$ and $K^*_0$, and whose magnitudes depend crucially on the $K^*_0$
decay constant, $f_{K^*_0}$. Taking a QCD sum rule estimate of $f_{K^*_0}=45$
MeV and the present experimental constraints on the CP-odd parameters into
account, we estimate quantitatively the maximally-allowed values for the CP-odd
rate and polarization asymmetries in the multi-Higgs-doublet (MHD) model and
the scalar-leptoquark (SLQ) models consistent with the SM gauge symmetry where
neutrinos are massless and left-handed as in the SM. We find that the CP-odd
rate and polarization asymmetries are of a similar size for highly-polarized
$\tau$ leptons and, for their maximally-allowed values, CP violation in the MHD
model and two SLQ models may be detected with about $10^6$ and $10^7$ $\tau$'s
at the $1\sigma$ level.


  In natural scenes, objects generally appear together with other objects. Yet,
theoretical studies of neural population coding typically focus on the encoding
of single objects in isolation. Experimental studies suggest that neural
responses to multiple objects are well described by linear or nonlinear
combinations of the responses to constituent objects, a phenomenon we call
stimulus mixing. Here, we present a theoretical analysis of the consequences of
common forms of stimulus mixing observed in cortical responses. We show that
some of these mixing rules can severely compromise the brain's ability to
decode the individual objects. This cost is usually greater than the cost
incurred by even large reductions in the gain or large increases in neural
variability, explaining why the benefits of attention can be understood
primarily in terms of a stimulus selection, or demixing, mechanism rather than
purely as a gain increase or noise reduction mechanism. The cost of stimulus
mixing becomes even higher when the number of encoded objects increases,
suggesting a novel mechanism that might contribute to set size effects observed
in myriad psychophysical tasks. We further show that a specific form of neural
correlation and heterogeneity in stimulus mixing among the neurons can
partially alleviate the harmful effects of stimulus mixing. Finally, we derive
simple conditions that must be satisfied for unharmful mixing of stimuli.


  We study the landscape models of eternal inflation with an arbitrary number
of different vacua states, both recyclable and terminal. We calculate the
abundances of bubbles following different geodesics. We show that the results
obtained from generic time-like geodesics have undesirable dependence on
initial conditions. In contrast, the predictions extracted from ``eternal''
geodesics, which never enter terminal vacua, do not suffer from this problem.
We derive measure equations for ensembles of geodesics and discuss possible
interpretations of initial conditions in eternal inflation.


  A revised version of the semilocal exchange-correlation functional [Phys.
Rev. Lett. 117, 073001 (2016)] (TM) is proposed by incorporating the
modifications to its correlation content obtained from the full high-density
second-order gradient expansion as proposed in the case of revised
Tao-Perdew-Staroverov-Scuseria (revTPSS) [Phys. Rev. Lett. 103, 026403 (2009)]
functional. The present construction improves the performance of TM functional
over a wide range of quantum chemical and solid-state properties
(thermochemistry and structural). More specifically, the cohesive energies,
jellium surface exchange-correlation energies, and real metallic surface
energies are improved by preserving the accuracy of the solid-state lattice
constants and bulk moduli. The present proposition is not only physically
motivated but also enhances the applicability of the TM functional. New
physical insights with proper exemplification of the present modification which
is presented here can further serve for more realistic non-empirical density
functional construction.


  Liv\v{s}ic theorem for flows asserts that a Lipschitz observable that has
zero mean average along every periodic orbit is necessarily a coboundary, that
is the Lie derivative of a Lipschitz function smooth along the flow direction.
The positive Liv\v{s}ic theorem bounds from below the observable by such a
coboundary as soon as the mean average along every periodic orbit is non
negative. Previous proofs give a H\"older coboundary. Assuming that the
dynamics is given by a locally maximal hyperbolic flow, we show that the
coboundary can be Lipschitz. We introduce a new tool: the Lax-Oleinik
semigroup, inspired by Fathi's weak KAM theory.


  This is a theoretical study of the interplay of optical phase-conjugation and
multiple scattering. We calculate the intensity of light reflected by a
phase-conjugating mirror when it is placed behind a disordered medium. We
compare the results of a fully phase-coherent theory with those from the theory
of radiative transfer. Both methods are equivalent if the dwell time
\tau_{dwell} of a photon in the disordered medium is much larger than the
inverse of the frequency shift 2\Delta\omega acquired at the phase-conjugating
mirror. When \tau_{dwell} \Delta\omega < 1, in contrast, phase coherence
drastically affects the reflected intensity. In particular, a minimum in the
dependence of the reflectance on the disorder strength disappears when
\Delta\omega is reduced below 1/\tau_{dwell}. The analogies and differences
with Andreev reflection of electrons at the interface between a normal metal
and a superconductor are discussed.


  In this paper, we derive an effective model for transport processes in
periodically perforated elastic media, taking into account, e.g., cyclic
elastic deformations as they occur in lung tissue due to respiratory movement.
The underlying microscopic problem couples the deformation of the domain with a
diffusion process within a mixed \textit{Lagrangian}/\textit{Eulerian}
formulation. After a transformation of the diffusion problem onto the fixed
domain, we use the formal method of two-scale asymptotic expansion to derive
the upscaled model, which is nonlinearly coupled through effective
coefficients. The effective model is implemented and validated using an
application-inspired model problem. Numerical solutions for both, cell problems
and macroscopic equations, are investigated and interpreted. We use simulations
to qualitatively determine the effect of the deformation on the transport
process.


  A new exponentially fitted version of the Discrete Variational Derivative
method for the efficient solution of oscillatory complex Hamiltonian Partial
Differential Equations is proposed. When applied to the nonlinear Schroedinger
equation, the new scheme has discrete conservation laws of charge and energy.
The new method is compared with other conservative schemes from the literature
on a benchmark problem whose solution is an oscillatory breather wave.


  Earlier studies have shown that stock market distributions can be well
described by distributions derived from Tsallis entropy, which is a
generalization of Shannon entropy to non-extensive systems. In this paper,
Tsallis relative entropy (TRE), which is the generalization of Kullback-Leibler
relative entropy (KLRE) to non-extensive systems, is investigated as a possible
risk measure in constructing risk optimal portfolios whose returns beat market
returns. Portfolios are constructed by binning the risk values and allocating
the stocks to bins according to their risk values. The average return in excess
of market returns for each bin is calculated to get the risk-return patterns of
the portfolios. The results are compared with those from three other risk
measures: 1) the commonly used 'beta' of the Capital Asset Pricing Model
(CAPM), 2) Kullback-Leibler relative entropy, and 3) the relative standard
deviation. Tests carried out for both long (~18 years) and shorter terms (~9
years), which include the dot-com bubble and the 2008 crash periods, show that
a linear fit can be obtained for the risk-excess return profiles of all four
risk measures. However, in all cases, the profiles from Tsallis relative
entropy show a more consistent behavior in terms of both goodness of fit and
the variation of returns with risk, than the other three risk measures.


  We present a new optomechanical device where the motion of a micromechanical
membrane couples to a microwave resonance of a three-dimensional
superconducting cavity. With this architecture, we realize ultrastrong
parametric coupling, where the coupling rate not only exceeds the dissipation
rates in the system but also rivals the mechanical frequency itself. In this
regime, the optomechanical interaction induces a frequency splitting between
the hybridized normal modes that reaches 88% of the bare mechanical frequency,
limited by the fundamental parametric instability. The coupling also exceeds
the mechanical thermal decoherence rate, enabling new applications in ultrafast
quantum state transfer and entanglement generation.


  Large-dimensional factor model has drawn much attention in the big-data era,
in order to reduce the dimensionality and extract underlying features using a
few latent common factors. Conventional methods for estimating the factor model
typically requires finite fourth moment of the data, which ignores the effect
of heavy-tailedness and thus may result in unrobust or even inconsistent
estimation of the factor space and common components. In this paper, we propose
to recover the factor space by performing principal component analysis to the
spatial Kendall's tau matrix instead of the sample covariance matrix. In a
second step, we estimate the factor scores by the ordinary least square (OLS)
regression. Theoretically, we show that under the elliptical distribution
framework the factor loadings and scores as well as the common components can
be estimated consistently without any moment constraint. The convergence rates
of the estimated factor loadings, scores and common components are provided.
The finite sample performance of the proposed procedure is assessed through
thorough simulations. An analysis of a financial data set of asset returns
shows the superiority of the proposed method over the classical PCA method.


  Probabilities of resonant tunneling through a potential barrier are compared
for a rigid molecule and an excited molecule. It is shown that the resonance
spectrum is mainly governed by the transmission resonance spectrum of the rigid
molecule. Analytical expressions for the probability for the tunneling of the
rigid molecule through a barrier allow resonance-spectrum-averaged observables,
including quantum diffusion, to be estimated.


  We prove that the degree of Fano threefolds with terminal Q-factorial
singularities and Picard number one is at most 125/2 and the bound is sharp.


  We present results for a variety of Monte Carlo annealing approaches, both
classical and quantum, benchmarked against one another for the textbook
optimization exercise of a simple one-dimensional double-well. In classical
(thermal) annealing, the dependence upon the move chosen in a Metropolis scheme
is studied and correlated with the spectrum of the associated Markov transition
matrix. In quantum annealing, the Path-Integral Monte Carlo approach is found
to yield non-trivial sampling difficulties associated with the tunneling
between the two wells. The choice of fictitious quantum kinetic energy is also
addressed. We find that a ``relativistic'' kinetic energy form, leading to a
higher probability of long real space jumps, can be considerably more effective
than the standard one.


  Reinforcement learning is a popular method of finding optimal solutions to
complex problems. Algorithms like Q-learning excel at learning to solve
stochastic problems without a model of their environment. However, they take
longer to solve deterministic problems than is necessary. Q-learning can be
improved to better solve deterministic problems by introducing such a
model-based approach. This paper introduces the recursive backwards Q-learning
(RBQL) agent, which explores and builds a model of the environment. After
reaching a terminal state, it recursively propagates its value backwards
through this model. This lets each state be evaluated to its optimal value
without a lengthy learning process. In the example of finding the shortest path
through a maze, this agent greatly outperforms a regular Q-learning agent.


  The orthogonal multi-matching pursuit (OMMP) is a natural extension of
orthogonal matching pursuit (OMP). We denote the OMMP with the parameter $M$ as
OMMP(M) where $M\geq 1$ is an integer. The main difference between OMP and
OMMP(M) is that OMMP(M) selects $M$ atoms per iteration, while OMP only adds
one atom to the optimal atom set. In this paper, we study the performance of
orthogonal multi-matching pursuit (OMMP) under RIP. In particular, we show
that, when the measurement matrix A satisfies $(9s, 1/10)$-RIP, there exists an
absolutely constant $M_0\leq 8$ so that OMMP(M_0) can recover $s$-sparse signal
within $s$ iterations. We furthermore prove that, for slowly-decaying
$s$-sparse signal, OMMP(M) can recover s-sparse signal within $O(\frac{s}{M})$
iterations for a large class of $M$. In particular, for $M=s^a$ with $a\in
[0,1/2]$, OMMP(M) can recover slowly-decaying $s$-sparse signal within
$O(s^{1-a})$ iterations. The result implies that OMMP can reduce the
computational complexity heavily.


  Some emerging 5G and beyond use-cases impose stringent latency constraints,
which necessitates a paradigm shift towards finite blocklength performance
analysis. In contrast to Shannon capacity-achieving codes, the codeword length
in the finite blocklength regime (FBR) is a critical design parameter that
imposes an intricate tradeoff between delay, reliability, and information
coding rate. In this context, this paper presents a novel mathematical analysis
to characterize the performance of large-scale downlink networks using short
codewords. Theoretical achievable rates, outage probability, and reliability
expressions are derived using the finite blocklength coding theory in
conjunction with stochastic geometry, and compared to the performance in the
asymptotic regime (AR). Achievable rates under practical modulation schemes as
well as multilevel polar coded modulation (MLPCM) are investigated. Numerical
results provide theoretical performance benchmarks, highlight the potential of
MLPCM in achieving close to optimal performance with short codewords, and
confirm the discrepancy between the performance in the FBR and that predicted
by analysis in the AR. Finally, the meta distribution of the coding rate is
derived, providing the percentiles of users that achieve a predefined target
rate in a network.


  The dual complex of a singularity is defined, up-to homotopy, using
resolutions of singularities. In many cases, for instance for isolated
singularities, we identify and study a "minimal" representative of the homotopy
class that is well defined up-to piecewise linear homeomorphism. This is
derived from a more global result concerning dual complexes of dlt pairs. As an
application, we also show that the dual complex of a log terminal singularity
as well as the one of a simple normal crossing degeneration of a family of
rationally connected manifolds are contractible.


  We develop a lumped parameter model to describe and predict the mass release
of (absorption from) an arbitrary shaped body of any dimension in a large
environment. Through the one-to-one analogy between diffusion-dominated mass
transfer systems and electrical circuits we provide exact solutions in terms of
averaged concentrations and mass released. An estimate of the release and
characteristic time is also given. The proposed electrical analogue approach
allows the definition of a time constant and lets an easy extension to a
multi-layer and multi-phase cases. The simulation results are compared with
those obtained from the solution of the corresponding analytical and numerical
solutions, showing a good agreement.


  Face recognition has already been well studied under the visible light and
the infrared,in both intra-spectral and cross-spectral cases. However, how to
fuse different light bands, i.e., hyperspectral face recognition, is still an
open research problem, which has the advantages of richer information retaining
and all-weather functionality over single band face recognition. Among the very
few works for hyperspectral face recognition, traditional non-deep learning
techniques are largely used. Thus, we in this paper bring deep learning into
the topic of hyperspectral face recognition, and propose a new fusion model
(termed HyperFaceNet) especially for hyperspectral faces. The proposed fusion
model is characterized by residual dense learning, a feedback style encoder and
a recognition-oriented loss function. During the experiments, our method is
proved to be of higher recognition rates than face recognition using either
visible light or the infrared. Moreover, our fusion model is shown to be
superior to other general-purposed image fusion methods including
state-of-the-arts, in terms of both image quality and recognition performance.


  SgrA$^*$, the supermassive black hole candidate at the center of our Galaxy,
seems to be one of the most promising object to test the Kerr black hole
hypothesis with near future observations. In a few years, it will hopefully be
possible to measure a number of relativistic effects around this body, and the
combination of different observations can be used to constrain possible
deviations from the Kerr solution. In this paper, I discuss the combination of
three promising techniques in the framework of the Cardoso-Pani-Rico
parametrization: the observation of blobs of plasma orbiting near the innermost
stable circular orbit, the detection of the black hole shadow, and timing
observations of a radio pulsar in a compact orbit. The observations of blobs of
plasma and of the shadow can probe the strong gravitational field around
SgrA$^*$, while the radio pulsar would be sensitive to the weak field region at
larger radii. In the case of a fast-rotating object, the combination of the
three measurements could provide strong constraints on the actual nature of
SgrA$^*$. For a non-rotating or slow-rotating object, the bounds would be weak.


  Using the data set of The Three Hundred project, i.e. a suite of 324
hydrodynamical resimulations of cluster-sized haloes, we study galaxy cluster
mergers and their effect on colour and luminosity changes of their brightest
cluster galaxies (BCG). We track the main progenitor of each halo at z=0 and
search for merger situations based on its mass accretion history, defining
mergers as very rapid increases in the halo mass. Based upon the evolution of
the dynamical state of the cluster we define a pre- and post-merger phase. We
create a list of all these events and statistically study their mass ratio and
timescales, with the former verifying that all instances are in fact major
mergers. By comparing to a control sample of clusters without mergers, we study
the effect mergers have on the stellar component of the BCG. Analysing the
mass, age and metallicity of the BCG stellar particles, we find that the
stellar content of BCGs grows significantly during mergers and, even though the
main growth mechanism is the accretion of older stars, there is even a burst in
star formation induced by the merger. In our simulations, BCGs in mergers form
in median around 70 per cent more stars than those normally growing, although
this depends on the radius considered for defining the BCG. Regarding
observable properties, we see an increase in SDSS-u luminosity of 20 per cent
during mergers, accompanied by a slightly slower increase of the galaxy g-r
colour as compared to the control sample.


  We define and study two generalizations of the Krull dimension for rings,
which can assume cardinal number values of arbitrary size. The first, which we
call the "cardinal Krull dimension," is the supremum of the cardinalities of
chains of prime ideals in the ring. The second, which we call the "strong
cardinal Krull dimension," is a slight strengthening of the first. Our main
objective is to address the following question: for which cardinal pairs (K,L)
does there exist a ring of cardinality K and (strong) cardinal Krull dimension
L? Relying on results from the literature, we answer this question completely
in the case where K>L or K=L. We also give several constructions, utilizing
valuation rings, polynomial rings, and Leavitt path algebras, of rings having
cardinality K and (strong) cardinal Krull dimension L>K. The exact values of K
and L that occur in this situation depend on set-theoretic assumptions.


  This work presents for the first time a flexible over-moded resonator (OMR)
based on P(VDF-TrFE) thin films. The devices were manufactured on commercially
available elastic substrate with inkjet-printed electrodes. The sensing
copolymer films used in the devices were polarized by the corona method after
electrode deposition. The main performance parameters of the component were
then determined. The manufactured OMRs on P(VDF-TrFE) exhibited a linear
variation of frequency versus temperature and a very large value of temperature
coefficient of frequency (TCF > 1600 ppm/degrees C). These properties suggest a
great potential for using such components as low-cost and high-precision
temperature sensors. The electromechanical coupling coefficient and the quality
factor of the resonator were also characterized versus temperature.


  The shape memory effect and pseudoelasticity in Cu nanowires is one possible
pair of mechanisms that prevents high aspect ratio nanosized field electron
emitters to be stable at room temperature and permits their growth under high
electric field. By utilizing hybrid electrodynamics molecular dynamics
simulations we show that a global electric field of 1 GV/m or more
significantly increases the stability and critical temperature of spontaneous
reorientation of nanosized <100> Cu field emitters. We also show that in the
studied tips the stabilizing effect of an external applied electric field is an
order of magnitude greater than the destabilization caused by the field
emission current. We detect the critical temperature of spontaneous
reorientation using the tool that spots the changes in crystal structure. The
method is compatible with techniques that consider the change in potential
energy, has a wider range of applicability and allows pinpointing different
stages in the reorientation processes.


  We study the dynamics of a small number of impurity particles coupled to the
ideal Fermi gas in a $d$-dimensional box. The impurities interact with the
fermions via a two-body potential $\lambda v(x)$ where $\lambda$ is a coupling
constant and $v(x)$ for instance a screened Coulomb potential. After taking the
large-volume limit at positive Fermi momentum $k_F$ we consider the regime of
high density of the fermions, that is, $k_F$ large compared to one. For
coupling constants that scale like $\lambda^2 \sim k_F^{(2-d)}$ we show that
the impurity particles effectively decouple from the fermions but evolve with
an attractive pair interaction among each other which is induced by
fluctuations in the Fermi gas.


  The Euclidean version of Yang-Mills theory coupled to a massive dilaton is
investigated. Our analytical and numerical results imply existence of infinite
number of branches of globally regular, spherically symmetric, dyonic type
solutions for any values of dilaton mass $m$. Solutions on different branches
are labelled by the number of nodes of gauge field amplitude $W$. They have
finite reduced action and provide new saddle points in the Euclidean path
integral.


  We lay out an experiment to realize time-reversal invariant topological
insulators in alkali atomic gases. We introduce an original method to
synthesize a gauge field in the near-field of an atom-chip, which effectively
mimics the effects of spin-orbit coupling and produces quantum spin-Hall
states. We also propose a feasible scheme to engineer sharp boundaries where
the hallmark edge states are localized. Our multi-band system has a large
parameter space exhibiting a variety of quantum phase transitions between
topological and normal insulating phases. Due to their remarkable versatility,
cold-atom systems are ideally suited to realize topological states of matter
and drive the development of topological quantum computing.


  Sophisticated thin film growth techniques increasingly rely on the addition
of a plasma component to open or widen a processing window, particularly at low
temperatures. However, the addition of the plasma into the growth environment
also complicates the surface dynamical evolution. Taking advantage of continued
increases in accelerator-based X-ray source brilliance, this real-time study
uses X-ray Photon Correlation Spectroscopy (XPCS) to elucidate the nanoscale
surface dynamics during Plasma-Enhanced Atomic Layer Deposition (PE-ALD) of an
epitaxial indium nitride film. XPCS examines the evolution of the coherent
X-ray scattering speckle pattern, which is a fingerprint of the unique sample
microstructure at each moment in time. In PE-ALD, ultrathin films are
synthesized from repeated cycles of alternating self-limited surface reactions
induced by temporally-separated pulses of material precursor and plasma
reactant, allowing the influence of each on the evolving morphology to be
examined. During the heteroepitaxial 3D growth examined here, sudden changes in
surface structure during initial film growth, consistent with numerous
overlapping stress-relief events, are observed. When the film becomes
continuous, the nanoscale surface morphology abruptly becomes long-lived with
correlation time spanning the period of the experiment. Throughout the growth
experiment, there is a consistent repeating pattern of correlations associated
with the cyclic growth process, which is modeled as transitions between
different surface states. The plasma exposure does not simply freeze in a
structure that is then built upon in subsequent cycles, but rather there is
considerable surface evolution during all phases of the growth cycle.


  A free industry-grade education tool is developed for bulk-power-system
reliability assessment. The software architecture is illustrated using a
high-level flowchart. Three main algorithms of this tool, i.e., sequential
Monte Carlo simulation, unit preventive maintenance schedule, and
optimal-power-flow-based load shedding, are introduced. The input and output
formats are described in detail, including the roles of different data cards
and results categorization. Finally, an example case study is conducted on a
five-area system to demonstrate the effectiveness and efficiency of this tool.


  We present a simple group representation analysis of massive, and
particularly ``partially massless'', fields of arbitrary spin in de Sitter
spaces of any dimension. The method uses bulk to boundary propagators to relate
these fields to Euclidean conformal ones at one dimension lower. These results
are then used to revisit an old question: can a consistent de Sitter
supergravity be constructed, at least within its intrinsic horizon?


  We demonstrate quantum dot (QD) formation in three-dimensional Dirac
semimetal Cd$_{3}$As$_{2}$ nanowires using two electrostatically tuned p$-$n
junctions with a gate and magnetic fields. The linear conductance measured as a
function of gate voltage under high magnetic fields is strongly suppressed at
the Dirac point close to zero conductance, showing strong conductance
oscillations. Remarkably, in this regime, the Cd$_{3}$As$_{2}$ nanowire device
exhibits Coulomb diamond features, indicating that a clean single QD forms in
the Dirac semimetal nanowire. Our results show that a p$-$type QD can be formed
between two n$-$type leads underneath metal contacts in the nanowire by
applying gate voltages under strong magnetic fields. Analysis of the quantum
confinement in the gapless band structure confirms that p$-$n junctions formed
between the p$-$type QD and two neighboring n$-$type leads under high magnetic
fields behave as resistive tunnel barriers due to cyclotron motion, resulting
in the suppression of Klein tunneling. The p$-$type QD with magnetic
field-induced confinement shows a single hole filling. Our results will open up
a route to quantum devices such as QDs or quantum point contacts based on Dirac
and Weyl semimetals.


  In this paper, we showcase the class XNLP as a natural place for many hard
problems parameterized by linear width measures. This strengthens existing
$W[1]$-hardness proofs for these problems, since XNLP-hardness implies
$W[t]$-hardness for all $t$. It also indicates, via a conjecture by Pilipczuk
and Wrochna [ToCT 2018], that any XP algorithm for such problems is likely to
require XP space.
  In particular, we show XNLP-completeness for natural problems parameterized
by pathwidth, linear clique-width, and linear mim-width. The problems we
consider are Independent Set, Dominating Set, Odd Cycle Transversal,
($q$-)Coloring, Max Cut, Maximum Regular Induced Subgraph, Feedback Vertex Set,
Capacitated (Red-Blue) Dominating Set, and Bipartite Bandwidth.


  Reply to `Comment on "Gapless Spin-1 Neutral Collective Mode Branch for
Graphite"' by Peres et al [cond-mat/0312263].


  We present a lightweight, open source Agda framework for manually verifying
effectful programs using predicate transformer semantics. We represent the
abstract syntax trees (AST) of effectful programs with a generalized algebraic
datatype (GADT) AST, whose generality enables even complex operations to be
primitive AST nodes. Users can then assign bespoke predicate transformers to
such operations to aid the proof effort, for example by automatically
decomposing proof obligations for branching code. Our framework codifies and
generalizes a proof engineering methodology used by the authors to reason about
a prototype implementation of LibraBFT, a Byzantine fault tolerant consensus
protocol in which code executed by participants may have effects such as
updating state and sending messages. Successful use of our framework in this
context demonstrates its practical applicability.


  Advances in Artificial Intelligence are challenged by the biases rooted in
the datasets used to train the models. In image geolocation estimation, models
are mostly trained using data from specific geographic regions, notably the
Western world, and as a result, they may struggle to comprehend the
complexities of underrepresented regions. To assess this issue, we apply a
state-of-the-art image geolocation estimation model (ISNs) to a crowd-sourced
dataset of geolocated images from the African continent (SCA100), and then
explore the regional and socioeconomic biases underlying the model's
predictions. Our findings show that the ISNs model tends to over-predict image
locations in high-income countries of the Western world, which is consistent
with the geographic distribution of its training data, i.e., the IM2GPS3k
dataset. Accordingly, when compared to the IM2GPS3k benchmark, the accuracy of
the ISNs model notably decreases at all scales. Additionally, we cluster images
of the SCA100 dataset based on how accurately they are predicted by the ISNs
model and show the model's difficulties in correctly predicting the locations
of images in low income regions, especially in Sub-Saharan Africa. Therefore,
our results suggest that using IM2GPS3k as a training set and benchmark for
image geolocation estimation and other computer vision models overlooks its
potential application in the African context.


  If $T$ is a Kreiss bounded operator on a Banach space, then $\|T^n\|=O(n)$.
Forty years ago Shields conjectured that in Hilbert spaces, $\|T^n\| =
O(\sqrt{n})$. A negative answer to this conjecture was given by Spijker,
Tracogna and Welfert in 2003. We improve their result and show that this
conjecture is not true even for uniformly Kreiss bounded operators. More
precisely, for every $\varepsilon>0$ there exists a uniformly Kreiss bounded
operator $T$ on a Hilbert space such that
  $\|T^n\|\sim (n+1)^{1-\varepsilon}$ for all $n\in \Bbb N$. On the other hand,
any Kreiss bounded operator on Hilbert spaces satisfies
$\|T^n\|=O(\frac{n}{\sqrt{\log n}})$.
  We also prove that the residual spectrum of a Kreiss bounded operator on a
reflexive Banach space is contained in the open unit disc, extending known
results for power bounded operators. As a consequence we obtain examples of
mean ergodic Hilbert space operators which are not Kreiss bounded.


  Building upon score-based learning, new interest in stochastic localization
techniques has recently emerged. In these models, one seeks to noise a sample
from the data distribution through a stochastic process, called observation
process, and progressively learns a denoiser associated to this dynamics. Apart
from specific applications, the use of stochastic localization for the problem
of sampling from an unnormalized target density has not been explored
extensively. This work contributes to fill this gap. We consider a general
stochastic localization framework and introduce an explicit class of
observation processes, associated with flexible denoising schedules. We provide
a complete methodology, $\textit{Stochastic Localization via Iterative
Posterior Sampling}$ (SLIPS), to obtain approximate samples of this dynamics,
and as a by-product, samples from the target distribution. Our scheme is based
on a Markov chain Monte Carlo estimation of the denoiser and comes with
detailed practical guidelines. We illustrate the benefits and applicability of
SLIPS on several benchmarks of multi-modal distributions, including Gaussian
mixtures in increasing dimensions, Bayesian logistic regression and a
high-dimensional field system from statistical-mechanics.


  We develop the foundations of the theory of relatively geometric actions of
relatively hyperbolic groups on CAT(0) cube complexes, a notion introduced in
our previous work [5]. In the relatively geometric setting we prove: full
relatively quasi-convex subgroups are convex compact; an analog of Agol's
Theorem; and a version of Haglund--Wise's Canonical Completion and Retraction.


  Atomic masses of the neutron-rich isotopes $^{76-80}$Zn, $^{78-83}$Ga,
$^{80-85}Ge, $^{81-87}$As and $^{84-89}$Se have been measured with high
precision using the Penning trap mass spectrometer JYFLTRAP at the IGISOL
facility. The masses of $^{82,83}$Ga, $^{83-85}$Ge, $^{84-87}$As and $^{89}$Se
were measured for the first time. These new data represent a major improvement
in the knowledge of the masses in this neutron-rich region. Two-neutron
separation energies provide evidence for the reduction of the N=50 shell gap
energy towards germanium Z=32 and a subsequent increase at gallium (Z=31). The
data are compared with a number of theoretical models. An indication of the
persistent rigidity of the shell gap towards nickel (Z=28) is obtained.


  In reinforcement learning, we encode the potential behaviors of an agent
interacting with an environment into an infinite set of policies, the policy
space, typically represented by a family of parametric functions. Dealing with
such a policy space is a hefty challenge, which often causes sample and
computation inefficiencies. However, we argue that a limited number of policies
are actually relevant when we also account for the structure of the environment
and of the policy parameterization, as many of them would induce very similar
interactions, i.e., state-action distributions. In this paper, we seek for a
reward-free compression of the policy space into a finite set of representative
policies, such that, given any policy $\pi$, the minimum R\'enyi divergence
between the state-action distributions of the representative policies and the
state-action distribution of $\pi$ is bounded. We show that this compression of
the policy space can be formulated as a set cover problem, and it is inherently
NP-hard. Nonetheless, we propose a game-theoretic reformulation for which a
locally optimal solution can be efficiently found by iteratively stretching the
compressed space to cover an adversarial policy. Finally, we provide an
empirical evaluation to illustrate the compression procedure in simple domains,
and its ripple effects in reinforcement learning.


  Previous surveys in the far-infrared have found very few, if any, M-dwarf
debris discs among their samples. It has been questioned whether M-dwarf discs
are simply less common than earlier types, or whether the low detection rate
derives from the wavelengths and sensitivities available to those studies. The
highly sensitive, long wavelength Atacama Large Millimetre/submillimetre Array
can shed light on the problem. This paper presents a survey of M-dwarf stars in
the young and nearby Beta Pictoris Moving Group with ALMA at Band 7
(880\,$\mu$m). From the observational sample we detect two new sub-mm excesses
that likely constitute unresolved debris discs around GJ\,2006\,A and
AT\,Mic\,A and model distributions of the disc fractional luminosities and
temperatures. From the science sample of 36 M-dwarfs including AU\,Mic we find
a disc detection rate of 4/36 or 11.1$^{+7.4}_{-3.3}$\% that rises to
23.1$^{+8.3}_{-5.5}$\% when adjusted for completeness. We conclude that this
detection rate is consistent with the detection rate of discs around G and K
type stars and that the disc properties are also likely consistent with earlier
type stars. We additionally conclude that M-dwarf stars are not less likely to
host debris discs, but instead their detection requires longer wavelength and
higher sensitivity observations than have previously been employed.


  We study amorphous systems with completely random sites and find that,
through constructing and exploring a concrete model Hamiltonian, such a system
can host an exotic phase of topological amorphous metal in three dimensions. In
contrast to the traditional Weyl semimetals, topological amorphous metals break
translational symmetry, and thus cannot be characterized by the first Chern
number defined based on the momentum space band structures. Instead, their
topological properties will manifest in the Bott index and the Hall
conductivity as well as the surface states. By studying the energy band and
quantum transport properties, we find that topological amorphous metals exhibit
a diffusive metal behavior. We further introduce a practical experimental
proposal with electric circuits where the predicted phenomena can be observed
using state-of-the-art technologies. Our results open a door for exploring
topological gapless phenomena in amorphous systems.


  After reviewing the importance of light as a probe for testing the structure
of space-time, we describe the GINGER project. GINGER will be a
three-dimensional array of large size ring-lasers able to measure the de Sitter
and Lense-Thirring effects. The instrument will be located at the underground
laboratory of GranSasso, in Italy. We describe the preliminary actions and
measurements already under way and present the full road map to GINGER. The
intermediate apparatuses GP2 and GINGERino are described. GINGER is expected to
be fully operating in few years.


  We search for a new gauge boson $Z'$ that couples only to heavy leptons and
their corresponding neutrinos in the process $e^{+} e^{-} \rightarrow
Z'(\rightarrow \mu^{+}\mu^{-}) \mu^{+}\mu^{-}$, using a 643 fb$^{-1}$ data
sample collected by the Belle experiment at or near the
$\Upsilon(1S,2S,3S,4S,5S)$ resonances at the KEKB collider. For the first time,
effects due to initial state radiation are used in estimating the detection
efficiency. No signal is observed in the mass range of 0.212 \ -- 10 GeV/${\it
c}^2$ and we set an upper limit on the coupling strengh, $g'$, constraining
$Z'$ as a possible contributor to the anomalous magnetic dipole moment of muon.


  Bounded context switching (BCS) is an under-approximate method for finding
violations to safety properties in shared memory concurrent programs.
Technically, BCS is a reachability problem that is known to be NP-complete. Our
contribution is a parameterized analysis of BCS.
  The first result is an algorithm that solves BCS when parameterized by the
number of context switches (cs) and the size of the memory (m) in
O*(m^(cs)2^(cs)). This is achieved by creating instances of the easier problem
Shuff which we solve via fast subset convolution. We also present a lower bound
for BCS of the form m^o(cs / log(cs)), based on the exponential time
hypothesis. Interestingly, closing the gap means settling a conjecture that has
been open since FOCS'07. Further, we prove that BCS admits no polynomial
kernel.
  Next, we introduce a measure, called scheduling dimension, that captures the
complexity of schedules. We study BCS parameterized by the scheduling dimension
(sdim) and show that it can be solved in O*((2m)^(4sdim)4^t)$, where t is the
number of threads. We consider variants of the problem for which we obtain
(matching) upper and lower bounds.


  We present a new compilation of inferences of the linear 3D matter power
spectrum at redshift $z\,{=}\,0$ from a variety of probes spanning several
orders of magnitude in physical scale and in cosmic history. We develop a new
lower-noise method for performing this inference from the latest Ly$\alpha$
forest 1D power spectrum data. We also include cosmic microwave background
(CMB) temperature and polarization power spectra and lensing reconstruction
data, the cosmic shear two-point correlation function, and the clustering of
luminous red galaxies. We provide a Dockerized Jupyter notebook housing the
fairly complex dependencies for producing the plot of these data, with the hope
that groups in the future can help add to it. Overall, we find qualitative
agreement between the independent measurements considered here and the standard
$\Lambda$CDM cosmological model fit to the {\it Planck} data


  In this paper we present a detailed description of the statistical and
computational techniques that were employed to study a driven
far-from-equilibrium steady-state Rayleigh-B{\'e}nard system in the
non-turbulent regime ($Ra\leq 3500$). In our previous work on the
Rayleigh-B{\'e}nard convection system we try to answer two key open problems
that are of great interest in contemporary physics: (i) how does an
out-of-equilibrium steady-state differ from an equilibrium state and (ii) how
do we explain the spontaneous emergence of stable structures and simultaneously
interpret the physical notion of temperature when out-of-equilibrium. We
believe that this paper will offer a useful repository of the technical details
for a first principles study of similar kind. In addition, we are also hopeful
that our work will spur considerable interest in the community which will lead
to the development of more sophisticated and novel techniques to study
far-from-equilibrium behavior.


  In recent years, reversible logic has emerged as a promising computing
paradigm having its applications in low power computing, quantum computing,
nanotechnology, optical computing and DNA computing. The classical set of gates
such as AND, OR, and EXOR are not reversible. Recently, it has been shown how
to encode information in DNA and use DNA amplification to implement Fredkin
gates. Furthermore, in the past Fredkin gates have been constructed using DNA,
whose outputs are used as inputs for other Fredkin gates. Thus, it can be
concluded that arbitrary circuits of Fredkin gates can be constructed using
DNA. This paper provides the initial threshold to building of more complex
system having reversible sequential circuits and which can execute more
complicated operations. The novelty of the paper is the reversible designs of
sequential circuits using Fredkin gate. Since, Fredkin gate has already been
realized using DNA, it is expected that this work will initiate the building of
complex systems using DNA. The reversible circuits designed here are highly
optimized in terms of number of gates and garbage outputs. The modularization
approach that is synthesizing small circuits and thereafter using them to
construct bigger circuits is used for designing the optimal reversible
sequential circuits.


  Software fault localization is one of the most expensive, tedious, and
time-consuming activities in program debugging. This activity becomes even much
more challenging in Software Product Line (SPL) systems due to the variability
of failures in SPL systems. These unexpected behaviors are caused by
variability faults which can only be exposed under some combinations of system
features. Although localizing bugs in non-configurable code has been
investigated in-depth, variability fault localization in SPL systems still
remains mostly unexplored. To approach this challenge, we propose a benchmark
for variability fault localization with a large set of 1,570 buggy versions of
six SPL systems and baseline variability fault localization performance
results. Our hope is to engage the community to propose new and better
approaches to the problem of variability fault localization in SPL systems.


  We calibrate the effective-one-body (EOB) model to an accurate numerical
simulation of an equal-mass, non-spinning binary black-hole coalescence
produced by the Caltech-Cornell collaboration. Aligning the EOB and numerical
waveforms at low frequency over a time interval of ~1000M, and taking into
account the uncertainties in the numerical simulation, we investigate the
significance and degeneracy of the EOB adjustable parameters during inspiral,
plunge and merger, and determine the minimum number of EOB adjustable
parameters that achieves phase and amplitude agreements on the order of the
numerical error. We find that phase and fractional amplitude differences
between the numerical and EOB values of the dominant gravitational wave mode
h_{22} can be reduced to 0.02 radians and 2%, respectively, until a time 26 M
before merger, and to 0.1 radians and 10%, at a time 16M after merger (during
ringdown), respectively. Using LIGO, Enhanced LIGO and Advanced LIGO noise
curves, we find that the overlap between the EOB and the numerical h_{22},
maximized only over the initial phase and time of arrival, is larger than 0.999
for equal-mass binary black holes with total mass 30-150 Msun. In addition to
the leading gravitational mode (2,2), we compare the dominant subleading modes
(4,4) and (3,2) and find phase and amplitude differences on the order of the
numerical error. We also determine the mass-ratio dependence of one of the EOB
adjustable parameters by fitting to numerical {\it inspiral} waveforms for
black-hole binaries with mass ratios 2:1 and 3:1. These results improve and
extend recent successful attempts aimed at providing gravitational-wave data
analysts the best analytical EOB model capable of interpolating accurate
numerical simulations.


  The recent discoveries about topological insulators have been promoting
theoretical and experimental research. In this dissertation, the basic concepts
of topological insulators and the Quantum Hall Effect are reviewed focusing the
discussion on edge states and their band structure. Lattice models with pierced
magnetism are described and the Hofstadter model is presented for bounded
systems with and without an in-site disorder. An overview of the experimental
procedure based on cold atoms in optical lattices with synthetic dimensions is
given. In order to understand to what extent these small systems of cold atoms
mimic the behaviour of a topological insulator, an analysis of some finite size
effects is provided and a deduction of the gap opening in the band structure is
presented using perturbation theory.


  The long-term (over more than one decade) X-ray emission from two massive
stellar systems known to be particle accelerators is investigated using
XMM-Newton. Their X-ray properties are interpreted taking into account recent
information about their multiplicity and orbital parameters. The two targets,
HD168112 and HD167971 appear to be overluminous in X-rays, lending additional
support to the idea that a significant contribution of the X-ray emission comes
from colliding-wind regions. The variability of the X-ray flux from HD168112 is
interpreted in terms of varying separation expected to follow the 1/D rule for
adiabatic shocked winds. For HD167971, marginal decrease of the X-ray flux in
September 2002 could tentatively be explained by a partial wind eclipse in the
close pair. No long-term variability could be demonstrated despite the
significant difference of separation between 2002 and 2014. This suggests the
colliding-wind region in the wide orbit does not contribute a lot to the total
X-ray emission, with a main contribution coming from the radiative shocked
winds in the eclipsing pair. The later result provides evidence that shocks in
a colliding-wind region may be efficient particle accelerators even in the
absence of bright X-ray emission, suggesting particle acceleration may operate
in a wide range of conditions. Finally, in hierarchical triple O-type systems,
thermal X-rays do not necessarily constitute an efficient tracer to detect the
wind-wind interaction in the long period orbit.


  We present the theory of QED x QCD resummation and its interplay with
shower/matrix element matching in precision LHC physics scenarios. We
illustrate the theory using single heavy gauge boson production at hadron
colliders.


  Over the past five years, there has been considerable growth and established
value in the practice of modeling automotive software requirements. Much of
this growth has been centered on requirements of software associated with the
established functional areas of an automobile, such as those associated with
powertrain, chassis, body, safety and infotainment. This paper makes a case for
modeling four additional attributes that are increasingly important as vehicles
become information conduits: security, privacy, usability, and reliability.
These four attributes are important in creating specifications for embedded
in-vehicle automotive software.


  Light-matter interaction is exploited in spectroscopic techniques to access
information about molecular, atomic or nuclear constituents of the sample of
interest. While scattered light carries both amplitude and phase information of
the electromagnetic field, most of the time the latter is lost in intensity
measurements. However, often the phase information is paramount to reconstruct
the desired information of the target, as it is well known from coherent x-ray
imaging. Here we introduce a new phase retrieval algorithm which allows us to
reconstruct the field phase information from two-dimensional time- and
energy-resolved spectra. We apply this method to the particular case of x-ray
scattering off M\"ossbauer nuclei at a synchrotron radiation source. Knowledge
of the phase allows also for an excellent reconstruction of the energy spectra
from experimental data, which could not be achieved with this resolution
otherwise. Our approach provides an efficient novel data analysis tool which
will benefit x-ray quantum optics and M\"ossbauer spectroscopy with synchrotron
radiation alike.


  Traditional coverage grey-box fuzzers perform a breadth-first search of the
state space of Program Under Test (PUT). This aimlessness wastes a lot of
computing resources. Directed grey-box fuzzing focuses on the target of PUT and
becomes one of the most popular topics of software testing. The early
termination of unreachable test cases is a method to improve directed grey-box
fuzzing. However, existing solutions have two problems: firstly, reachability
analysis needs to introduce extra technologies (e.g., static analysis);
secondly, the performance of reachability analysis and auxiliary technologies
lack versatility.
  We propose FGo, a probabilistic exponential cut-the-loss directed grey-box
fuzzer. FGo terminates unreachable test cases early with exponentially
increasing probability. Compared to other technologies, FGo makes full use of
the unreachable information contained in iCFG and doesn't generate any
additional overhead caused by reachability analysis. Moreover, it is easy to
generalize to all PUT. This strategy based on probability is perfectly adapted
to the randomness of fuzzing.
  The experiment results show that FGo is 106% faster than AFLGo in reproducing
crashes. We compare multiple parameters of probabilistic exponential
cut-the-loss algorithm and analyze them in detail. In addition, for enhancing
the inerpretability of FGo, this paper discusses the difference between the
theoretical performance and the practical performance of probabilistic
exponential cut-the-loss algorithm.


  A panel structure on a topological space is just a locally finite family of
closed subspaces. A space together with a panel structure is called a space
with faces. In this paper, we define the notion of polyhedral product over a
space with faces. This notion provides a unifying viewpoint on the
constructions of polyhedral products and generalized moment-angle complexes in
various settings. We compute the stable decomposition of these spaces and use
it to study their cohomology ring structures by the partial diagonal maps.
Besides, we can compute the equivariant cohomology ring of the moment-angle
complex over a space with faces with respect to the canonical torus action. The
calculation leads to a notion of topological face ring of a space with faces,
which generalizes the classical notion of face ring of a simplicial complex. We
will see that many known results in the study of polyhedral products and
moment-angle complexes can be reinterpreted from our general theorems on the
polyhedral product over a space with faces. Moreover, we can derive some new
results via our approach in some settings.


  This paper establishes a direct, robust and intimate connection between (i)
non classicality tests for various quantum features, e.g., non-Boolean logic,
quantum coherence, nonlocality, quantum entanglement, quantum discord; (ii)
negative probability, and (iii) anomalous weak values. It has been shown
[Adhikary et al. Eur. Phys. J. D, 74(68):68, 2020] that nonexistence of a
classical joint probability scheme gives rise to sufficiency conditions for
nonlocality, a nonclassical feature not restricted to quantum mechanics. The
conditions for nonclassical features of quantum mechanics are obtained by
employing pseudo probabilities, which are expectation values of the parent
pseudo projections. The crux of the paper is that the pseudo-probabilities,
which can take negative values, can be directly measured as anomalous weak
values. We expect that this opens up new avenues for testing nonclassicality
via weak measurements, and also gives deeper insight into negative pseudo
probabilities which become measurable. A quantum game, based on violation of
classical probability rule is also proposed that can be played by employing
weak measurements.


  We investigate reaction mechanisms occurring in heavy ion collisions at low
energy (around 20 MeV/u). In particular, we focus on the competition between
fusion and break-up processes (Deep-Inelastic and fragmentation) in
semi-peripheral collisions, where the formation of excited systems in various
conditions of shape and angular momentum is observed. Adopting a Langevin
treatment for the dynamical evolution of the system configuration, described in
terms of shape observables such as quadrupole and octupole moments, we derive
fusion/fission probabilities, from which one can finally evaluate the
corresponding fusion and break-up cross sections. The dependence of the results
on shape, angular momentum and excitation energy is discussed.


  While most chemical reactions in the interstellar medium take place in the
gas phase, those occurring on the surfaces of dust grains play an essential
role. Chemical models based on rate equations including both gas phase and
grain surface reactions have been used in order to simulate the formation of
chemical complexity in interstellar clouds. For reactions in the gas phase and
on large grains, rate equations, which are highly efficient to simulate, are an
ideal tool. However, for small grains under low flux, the typical number of
atoms or molecules of certain reactive species on a grain may go down to order
one or less. In this case the discrete nature of the opulations of reactive
species as well as the fluctuations become dominant, thus the mean-field
approximation on which the rate equations are based does not apply. Recently, a
master equation approach, that provides a good description of chemical
reactions on interstellar dust grains, was proposed. Here we present a related
approach based on moment equations that can be obtained from the master
equation. These equations describe the time evolution of the moments of the
distribution of the population of the various chemical species on the grain. An
advantage of this approach is the fact that the production rates of molecular
species are expressed directly in terms of these moments. Here we use the
moment equations to calculate the rate of molecular hydrogen formation on small
grains. It is shown that the moment equation approach is efficient in this case
in which only a single reactive specie is involved. The set of equations for
the case of two species is presented and the difficulties in implementing this
approach for complex reaction networks involving multiple species are
discussed.


  The recent flourish of deep learning in various tasks is largely accredited
to the rich and accessible labeled data. Nonetheless, massive supervision
remains a luxury for many real applications, boosting great interest in
label-scarce techniques such as few-shot learning (FSL), which aims to learn
concept of new classes with a few labeled samples. A natural approach to FSL is
data augmentation and many recent works have proved the feasibility by
proposing various data synthesis models. However, these models fail to well
secure the discriminability and diversity of the synthesized data and thus
often produce undesirable results. In this paper, we propose Adversarial
Feature Hallucination Networks (AFHN) which is based on conditional Wasserstein
Generative Adversarial networks (cWGAN) and hallucinates diverse and
discriminative features conditioned on the few labeled samples. Two novel
regularizers, i.e., the classification regularizer and the anti-collapse
regularizer, are incorporated into AFHN to encourage discriminability and
diversity of the synthesized features, respectively. Ablation study verifies
the effectiveness of the proposed cWGAN based feature hallucination framework
and the proposed regularizers. Comparative results on three common benchmark
datasets substantiate the superiority of AFHN to existing data augmentation
based FSL approaches and other state-of-the-art ones.


  The Low Latency Fault Tolerance (LLFT) system provides fault tolerance for
distributed applications, using the leader-follower replication technique. The
LLFT system provides application-transparent replication, with strong replica
consistency, for applications that involve multiple interacting processes or
threads. The LLFT system comprises a Low Latency Messaging Protocol, a
Leader-Determined Membership Protocol, and a Virtual Determinizer Framework.
The Low Latency Messaging Protocol provides reliable, totally ordered message
delivery by employing a direct group-to-group multicast, where the message
ordering is determined by the primary replica in the group. The
Leader-Determined Membership Protocol provides reconfiguration and recovery
when a replica becomes faulty and when a replica joins or leaves a group, where
the membership of the group is determined by the primary replica. The Virtual
Determinizer Framework captures the ordering information at the primary replica
and enforces the same ordering at the backup replicas for major sources of
non-determinism, including multi-threading, time-related operations and socket
communication. The LLFT system achieves low latency message delivery during
normal operation and low latency reconfiguration and recovery when a fault
occurs.


  Recent years have seen fast advances in neural recording circuits and systems
as they offer a promising way to investigate real-time brain monitoring and the
closed-loop modulation of psychological disorders and neurodegenerative
diseases. In this context, this tutorial brief presents a concise overview of
concepts and design methodologies of neural recording, highlighting neural
signal characteristics, system-level specifications and architectures,
circuit-level implementation, and noise reduction techniques. Future trends and
challenges of neural recording are finally discussed.


  We investigate Hopf-Galois structures on a cyclic field extension $L/K$ of
squarefree degree $n$. By a result of Greither and Pareigis, each such
Hopf-Galois structure corresponds to a group of order $n$, whose isomorphism
class we call the type of the Hopf-Galois structure. We show that every group
of order $n$ can occur, and we determine the number of Hopf-Galois structures
of each type. We then express the total number of Hopf-Galois structures on
$L/K$ as a sum over factorisations of $n$ into three parts. As examples, we
give closed expressions for the number of Hopf-Galois structures on a cyclic
extension whose degree is a product of three distinct primes. (There are
several cases, depending on congruence conditions between the primes.) We also
consider one case where the degree is a product of four primes.


  Software container solutions have revolutionized application development
approaches by enabling lightweight platform abstractions within the so-called
"containers." Several solutions are being actively developed in attempts to
bring the benefits of containers to high-performance computing systems with
their stringent security demands on the one hand and fundamental resource
sharing requirements on the other.
  In this paper, we discuss the benefits and short-comings of such solutions
when deployed on real HPC systems and applied to production scientific
applications.We highlight use cases that are either enabled by or significantly
benefit from such solutions. We discuss the efforts by HPC system
administrators and support staff to support users of these type of workloads on
HPC systems not initially designed with these workloads in mind focusing on
NCSA's Blue Waters system.


  The classical Hopf invariant is an invariant of homotopy classes of maps from
$S^{4n-1} $ to $S^{2n}$, and is an important invariant in homotopy theory. The
goal of this paper is to use the Koszul duality theory for $E_n$-operads to
define a generalization of the classical Hopf invariant. One way of defining
the classical Hopf invariant is by defining a pairing between the cohomology of
the associative bar construction on the cochains of a space $X$ and the
homotopy groups of $X$. In this paper we will give a generalization of the
classical Hopf invariant by defining a pairing between the cohomology of the
$E_n$-bar construction on the cochains of $X$ and the homotopy groups of $X$.
This pairing gives us a set of invariants of homotopy classes of maps from
$S^m$ to a simplicial set $X$, this pairing can detect more homotopy classes of
maps than the classical Hopf invariant.
  The second part of the paper is devoted to combining the $E_n$-Hopf
invariants with the Koszul duality theory for $E_n$-operads to get a relation
between the $E_n$-Hopf invariants of a space $X$ and the $E_{n+1}$-Hopf
invariants of the suspension of $X$. This is done by studying the suspension
morphism for the $E_\infty$-operad, which is a morphism from the
$E_{\infty}$-operad to the desuspension of the $E_\infty$-operad. We show that
it induces a functor from $E_\infty$-algebras to $E_\infty$-algebras, which has
the property that it sends an $E_\infty$-model for a simplicial set $X$ to an
$E_\infty$-model for the suspension of $X$.
  We use this result to give a relation between the $E_n$-Hopf invariants of
maps from $S^m$ into $X$ and the $E_{n+1}$-Hopf invariants of maps from
$S^{m+1}$ into the suspension of $X$. One of the main results we show here, is
that this relation can be used to define invariants of stable homotopy classes
of maps.


  In digital quantum simulation of fermionic models with qubits, non-local maps
for encoding are often encountered. Such maps require linear or logarithmic
overhead in circuit depth which could render the simulation useless, for a
given decoherence time. Here we show how one can use a cavity-QED system to
perform digital quantum simulation of fermionic models. In particular, we show
that highly nonlocal Jordan-Wigner or Bravyi-Kitaev transformations can be
efficiently implemented through a hardware approach. The key idea is using
ancilla cavity modes, which are dispersively coupled to a qubit string, to
collectively manipulate and measure qubit states. Our scheme reduces the
circuit depth in each Trotter step of the Jordan-Wigner encoding by a factor of
$N^2$, comparing to the scheme for a device with only local connectivity, where
$N$ is the number of orbitals for a generic two-body Hamiltonian. Additional
analysis for the Fermi-Hubbard model on an $N\times N$ square lattice results
in a similar reduction. We also discuss a detailed implementation of our scheme
with superconducting qubits and cavities.


  The exponential growth of data has driven technology providers to develop new
protocols, such as cache coherent interconnects and memory semantic fabrics, to
help users and facilities leverage advances in memory technologies to satisfy
these growing memory and storage demands. Using these new protocols,
fabric-attached memories (FAM) can be directly attached to a system
interconnect and be easily integrated with a variety of processing elements
(PEs). Moreover, systems that support FAM can be smoothly upgraded and allow
multiple PEs to share the FAM memory pools using well-defined protocols. The
sharing of FAM between PEs allows efficient data sharing, improves memory
utilization, reduces cost by allowing flexible integration of different PEs and
memory modules from several vendors, and makes it easier to upgrade the system.
One promising use-case for FAMs is in High-Performance Compute (HPC) systems,
where the underutilization of memory is a major challenge. However, adopting
FAMs in HPC systems brings new challenges. In addition to cost, flexibility,
and efficiency, one particular problem that requires rethinking is virtual
memory support for security and performance. To address these challenges, this
paper presents decoupled access control and address translation (DeACT), a
novel virtual memory implementation that supports HPC systems equipped with
FAM. Compared to the state-of-the-art two-level translation approach, DeACT
achieves speedup of up to 4.59x (1.8x on average) without compromising
security.


  This paper tackles the task of estimating the topology of road networks from
aerial images. Building on top of a global model that performs a dense
semantical classification of the pixels of the image, we design a Convolutional
Neural Network (CNN) that predicts the local connectivity among the central
pixel of an input patch and its border points. By iterating this local
connectivity we sweep the whole image and infer the global topology of the road
network, inspired by a human delineating a complex network with the tip of
their finger. We perform an extensive and comprehensive qualitative and
quantitative evaluation on the road network estimation task, and show that our
method also generalizes well when moving to networks of retinal vessels.


  We compare the topological Milnor fibration and the motivic Milnor fibre of a
regular complex function with only normal crossing singularities by introducing
their common extension: the complete Milnor fibration. We give two equivalent
constructions: the first one extending the classical Kato-Nakayama log-space,
and the second one, more geometric, based on the real oriented multigraph
construction, a version of the real oriented deformation to the normal cone. As
an application, we recover A'Campo's model of the topological Milnor fibration,
by quotienting the motivic Milnor fibration with suitable powers of
$\mathbb{R}_{>0}$, and show that it determines the classical motivic Milnor
fibre.
  We also give precise formulae expressing how the introduced objects change
under blowings-up. As an application, we show that the motivic Milnor fibre is
well-defined as an element of a suitable Grothendieck ring without requiring
that the Lefschetz motive be invertible.


  We classify primitive, rank 1, omega-categorical structures having
polynomially many types over finite sets. For a fixed number of 4-types, we
show that there are only finitely many such structures and that all are built
out of finitely many linear orders interacting in a restricted number of ways.
As an example of application, we deduce the classification of primitive
structures homogeneous in a language consisting of n linear orders as well as
all reducts of such structures.


  The aim of this paper is to present a new approach to construct constants of
motion associated with scaling symmetries of dynamical systems. Scaling maps
could be symmetries of the equations of motion but not of its associated
Lagrangian action. We have constructed a Noether inspired theorem in a vertical
extended space that can be used to obtain constants of motion for these
symmetries. Noether theorem can be obtained as a particular case of our
construction. To illustrate how the procedure works, we present two interesting
examples, a) the Schwarzian Mechanics based on Schwarzian derivative operator
and b) the Korteweg-de Vries (KdV) non linear partial differential equation in
the context of the asymptotic dynamics of General Relativity on AdS$_3$. We
also study the inverse of Noether theorem for scaling symmetries and show how
we can construct and identify the generator of the scaling transformation, and
how it works for the vertical extended constant of motion that we are able to
construct. We find an interesting contribution to the symmetry associated with
the fact that the scaling symmetry is not a Noether symmetry of the action.
Finally, we have contrasted our results with recent analysis and previous
attempts to find constants of motion associated with these beautiful scaling
laws.


  This paper explores Deep Learning (DL) methods that are used or have the
potential to be used for traffic video analysis, emphasizing driving safety for
both Autonomous Vehicles (AVs) and human-operated vehicles. We present a
typical processing pipeline, which can be used to understand and interpret
traffic videos by extracting operational safety metrics and providing general
hints and guidelines to improve traffic safety. This processing framework
includes several steps, including video enhancement, video stabilization,
semantic and incident segmentation, object detection and classification,
trajectory extraction, speed estimation, event analysis, modeling and anomaly
detection. Our main goal is to guide traffic analysts to develop their own
custom-built processing frameworks by selecting the best choices for each step
and offering new designs for the lacking modules by providing a comparative
analysis of the most successful conventional and DL-based algorithms proposed
for each step. We also review existing open-source tools and public datasets
that can help train DL models. To be more specific, we review exemplary traffic
problems and mentioned requires steps for each problem. Besides, we investigate
connections to the closely related research areas of drivers' cognition
evaluation, Crowd-sourcing-based monitoring systems, Edge Computing in roadside
infrastructures, Automated Driving Systems (ADS)-equipped vehicles, and
highlight the missing gaps. Finally, we review commercial implementations of
traffic monitoring systems, their future outlook, and open problems and
remaining challenges for widespread use of such systems.


  We consider directed graphs where each edge is labeled with an integer weight
and study the fundamental algorithmic question of computing the value of a
cycle with minimum mean weight. Our contributions are twofold: (1) First we
show that the algorithmic question is reducible in O(n^2) time to the problem
of a logarithmic number of min-plus matrix multiplications of n-by-n matrices,
where n is the number of vertices of the graph. (2) Second, when the weights
are nonnegative, we present the first (1 + {\epsilon})-approximation algorithm
for the problem and the running time of our algorithm is \tilde(O)(n^\omega
log^3(nW/{\epsilon}) / {\epsilon}), where O(n^\omega) is the time required for
the classic n-by-n matrix multiplication and W is the maximum value of the
weights.


  A fundamental procedure in the analysis of massive datasets is the
construction of similarity graphs. Such graphs play a key role for many
downstream tasks, including clustering, classification, graph learning, and
nearest neighbor search. For these tasks, it is critical to build graphs which
are sparse yet still representative of the underlying data. The benefits of
sparsity are twofold: firstly, constructing dense graphs is infeasible in
practice for large datasets, and secondly, the runtime of downstream tasks is
directly influenced by the sparsity of the similarity graph. In this work, we
present $\textit{Stars}$: a highly scalable method for building extremely
sparse graphs via two-hop spanners, which are graphs where similar points are
connected by a path of length at most two. Stars can construct two-hop spanners
with significantly fewer similarity comparisons, which are a major bottleneck
for learning based models where comparisons are expensive to evaluate.
Theoretically, we demonstrate that Stars builds a graph in nearly-linear time,
where approximate nearest neighbors are contained within two-hop neighborhoods.
In practice, we have deployed Stars for multiple data sets allowing for graph
building at the $\textit{Tera-Scale}$, i.e., for graphs with tens of trillions
of edges. We evaluate the performance of Stars for clustering and graph
learning, and demonstrate 10~1000-fold improvements in pairwise similarity
comparisons compared to different baselines, and 2~10-fold improvement in
running time without quality loss.


  In this paper we study a model for phase segregation consisting in a sistem
of a partial and an ordinary differential equation. By a careful definition of
maximal solution to the latter equation, this system reduces to an Allen-Cahn
equation with a memory term. Global existence and uniqueness of a smooth
solution are proven and a characterization of the omega-limit set is given.


  The formation mechanism of the enigmatic subclass of radio galaxies, called
'X-shaped radio galaxies' (XRGs), or 'winged' radio galaxies, which account for
$\sim 10\%$ of the radio galaxy population, can be effectively constrained
using the radio spectral-index distribution across their twin pairs of radio
lobes. If indeed, the existing claims of no systematic spectral index
difference between the wing and the associated primary lobe are valid in
general, this would provide impetus to the XRG model attributing their origin
to an unresolved binary of active supermassive black holes within the nucleus
of the host galaxy. To investigate this interesting possibility, we have mapped
spatial variation of spectral index for a well-defined sample of 25 XRGs, by
combining their 1.4 GHz VLA (FIRST survey)/uGMRT maps with their 144 MHz maps
(LoTSS-DR2). This has yielded the best available combination of sensitivity,
angular resolution, frequency range and sample size, for spectral mapping of an
XRG sample. A rich diversity of spectral index patterns is thus revealed in our
XRG sample, but we find at most one case where a secondary lobe (wing) exhibits
a flatter spectrum compared to its associated primary lobe. We conclude that
such a spectral pattern is exceedingly rare and by no means a common trait of
XRGs.


  Quantum memories are a crucial element towards efficient quantum protocols.
In the continuous variables domain, such memories need to have near unity
efficiencies. Moreover, one needs to store complex quantum states exhibiting
negative Wigner functions after storage. We report the implementation of an all
optical quantum memory: the storage of single and two-photon Fock states with
high fidelities has been realized. The Wigner functions of the reconstructed
states shows negativity after $\sim 0.75~\mu s$ and $\sim 0.61~\mu s$
respectively for the single-photon and two-photon Fock states. This is, to our
knowledge, the first demonstration of the storage of non-Gaussian states with
more than one photon, representing a key step towards hybrid quantum protocols.


  Detection and Classification Acoustic Scene and Events Challenge 2021 Task 4
uses a heterogeneous dataset that includes both recorded and synthetic
soundscapes. Until recently only target sound events were considered when
synthesizing the soundscapes. However, recorded soundscapes often contain a
substantial amount of non-target events that may affect the performance. In
this paper, we focus on the impact of these non-target events in the synthetic
soundscapes. Firstly, we investigate to what extent using non-target events
alternatively during the training or validation phase (or none of them) helps
the system to correctly detect target events. Secondly, we analyze to what
extend adjusting the signal-to-noise ratio between target and non-target events
at training improves the sound event detection performance. The results show
that using both target and non-target events for only one of the phases
(validation or training) helps the system to properly detect sound events,
outperforming the baseline (which uses non-target events in both phases). The
paper also reports the results of a preliminary study on evaluating the system
on clips that contain only non-target events. This opens questions for future
work on non-target subset and acoustic similarity between target and non-target
events which might confuse the system.


  We establish a symmetry-operator framework for designing quantum error
correcting~(QEC) codes based on fundamental properties of the underlying system
dynamics. Based on this framework, we propose three hardware-efficient bosonic
QEC codes that are suitable for $\chi^{(2)}$-interaction based quantum
computation: the $\chi^{(2)}$ parity-check code, the $\chi^{(2)}$ embedded
error-correcting code, and the $\chi^{(2)}$ binomial code, all of which detect
photon-loss or photon-gain errors by means of photon-number parity measurements
and then correct them via $\chi^{(2)}$ Hamiltonian evolutions and linear-optics
transformations. Our symmetry-operator framework provides a systematic
procedure for finding QEC codes that are not stabilizer codes. The $\chi^{(2)}$
binomial code is of special interest because, with $m\le N$ identified from
channel monitoring, it can correct $m$-photon loss errors, $m$-photon gain
errors, and $(m-1)$th-order dephasing errors using logical qudits that are
encoded in $O(N)$ photons. In comparison, other bosonic QEC codes require
$O(N^2)$ photons to correct the same degree of bosonic errors. Such improved
photon-efficiency underscores the additional error-correction power that can be
provided by channel monitoring. We develop quantum Hamming bounds for
photon-loss errors in the code subspaces associated with the $\chi^{(2)}$
parity-check code and the $\chi^{(2)}$ embedded error-correcting code, and we
prove that these codes saturate their respective bounds. Our $\chi^{(2)}$ QEC
codes exhibit hardware efficiency in that they address the principal error
mechanisms and exploit the available physical interactions of the underlying
hardware, thus reducing the physical resources required for implementing their
encoding, decoding, and error-correction operations, and their universal
encoded-basis gate sets.


  Modern communication systems organize receivers in blocks in order to
simplify their analysis and design. However, an approach that considers the
receiver design from a wider perspective rather than treating it block-by-block
may take advantage of the impacts of these blocks on each other and provide
better performance. Herein, we can benefit from machine learning and compose a
receiver model implementing supervised learning techniques. With this
motivation, we consider a one-to-one transmission system over a flat fast
fading wireless channel and propose a support vector machines (SVM)-based
receiver that combines the pilot-based channel estimation, data demodulation
and decoding processes in one joint operation. We follow two techniques in the
receiver design. We first design one SVM-based classifier that outputs the
class of the encoding codeword that enters the encoder at the transmitter side.
Then, we put forward a model with one SVM-based classifier per one bit in the
encoding codeword, where each classifier assigns the value of the corresponding
bit in the encoding vector. With the second technique, we simplify the receiver
design especially for longer encoding codewords. We show that the SVM-based
receiver performs very closely to the maximum likelihood decoder, which is
known to be the optimal decoding strategy when the encoding vectors at the
transmitter are equally likely. We further show that the SVM-based receiver
outperforms the conventional receivers that perform channel estimation, data
demodulation and decoding in blocks. Finally, we show that we can train the
SVM-based receiver with 1-bit analog-to-digital converter (ADC) outputs and the
SVM-based receiver can perform very closely to the conventional receivers that
take 32-bit ADC outputs as inputs.


  Privacy-enhancing blocking tools based on filter-list rules tend to break
legitimate functionality. Filter-list maintainers could benefit from automated
breakage detection tools that allow them to proactively fix problematic rules
before deploying them to millions of users. We introduce SINBAD, an automated
breakage detector that improves the accuracy over the state of the art by 20%,
and is the first to detect dynamic breakage and breakage caused by
style-oriented filter rules. The success of SINBAD is rooted in three
innovations: (1) the use of user-reported breakage issues in forums that enable
the creation of a high-quality dataset for training in which only breakage that
users perceive as an issue is included; (2) the use of 'web saliency' to
automatically identify user-relevant regions of a website on which to
prioritize automated interactions aimed at triggering breakage; and (3) the
analysis of webpages via subtrees which enables fine-grained identification of
problematic filter rules.


  The production of eta pi - system at low mass by the pi- beam in the Coulomb
field of Be nuclei was studied. The cross section of the reaction pi- Be -->
eta pi- Be was compared to the experimental data on the decay eta --> pi+ pi-
gamma and to the theoretical predictions.


  In the study on nonlinear wave-wave processes in an ionosphere and a
magnetosphere usually the main attention is paid to investigation of plasma
turbulence at well developed stage, when the wide spectrum of plasma wave is
present. On the other side, it is well known that even if the number of
cooperating waves remains small due to a competition of processes of their
instability and attenuation, the turbulence appears in the result of their
stochastic behavior. The regimes of nonlinear dynamics of low frequency waves
excited due to Farley-Buneman instability in weakly ionized and inhomogeneous
ionospheric plasma in the presence of electric current perpendicular to ambient
magnetic field are considered. The problem is essentially three dimensional and
difficult for full numerical simulation, but the strong collisional damping of
waves allow to assume that in this case a perturbed state of plasma can be
described as finite set of interacting waves, some of which are unstable and
other strongly damping. The proposed nonlinear model allow to make full study
of nonlinear stabilization, conditions of stochasticity and to consider the
different regimes and properties of few mode plasma turbulence.


  We derive an uncertainty relation for two unitary operators which obey a
commutation relation of the form UV=exp[i phi] VU. Its most important
application is to constrain how much a quantum state can be localised
simultaneously in two mutually unbiased bases related by a Discrete Fourier
Transform. It provides an uncertainty relation which smoothly interpolates
between the well known cases of the Pauli operators in 2 dimensions and the
continuous variables position and momentum. This work also provides an
uncertainty relation for modular variables, and could find applications in
signal processing. In the finite dimensional case the minimum uncertainty
states, discrete analogues of coherent and squeezed states, are minimum energy
solutions of Harper's equation, a discrete version of the Harmonic oscillator
equation.


  We study the orbital magnetic quadrupole moment (MQM) in three dimensional
higher-order topological phases. Much like electric quadrupole moment, which is
associated with a charge response on the boundaries of a finite sample, the
diagonal components of the MQM manifest as surface-localized magnetization and
hinge currents. The hinge current is generally not equal to the difference of
surface magnetizations that intersect at the hinge, and we show this mismatch
is precisely quantified by the bulk MQM. We derive a quantum mechanical formula
for the layer-resolved magnetization in slab geometries and use it to define
the MQM of systems with gapped boundaries. Our formalism is then applied to
several higher-order topological phases, and we show that the MQM can
distinguish phases in some intrinsic and boundary-obstructed higher-order
topological insulators. We then show that derivatives of the MQM with respect
to the chemical potential can act as quantized topological invariants, similar
to obtaining the 2D Chern number as a derivative of the magnetization with
respect to the chemical potential. These invariants provide a new way to
characterize 3D time-reversal breaking insulators that have vanishing
magnetization.


  We propose a dynamic sensor selection approach for deep neural networks
(DNNs), which is able to derive an optimal sensor subset selection for each
specific input sample instead of a fixed selection for the entire dataset. This
dynamic selection is jointly learned with the task model in an end-to-end way,
using the Gumbel-Softmax trick to allow the discrete decisions to be learned
through standard backpropagation. We then show how we can use this dynamic
selection to increase the lifetime of a wireless sensor network (WSN) by
imposing constraints on how often each node is allowed to transmit. We further
improve performance by including a dynamic spatial filter that makes the
task-DNN more robust against the fact that it now needs to be able to handle a
multitude of possible node subsets. Finally, we explain how the selection of
the optimal channels can be distributed across the different nodes in a WSN. We
validate this method on a use case in the context of body-sensor networks,
where we use real electroencephalography (EEG) sensor data to emulate an EEG
sensor network. We analyze the resulting trade-offs between transmission load
and task accuracy.


  Active nematics are the nonequilibrium analog of passive liquid crystals in
which anisotropic units consume free energy to drive emergent behavior. Similar
to liquid crystal (LC) molecules in displays, ordering and dynamics in active
nematics are sensitive to boundary conditions; however, unlike passive liquid
crystals, active nematics, such as those composed of living matter, have the
potential to regulate their boundaries through self-generated stresses. Here,
using bacterial biofilms confined by a hydrogel as a model system, we show how
a three-dimensional, living nematic can actively shape itself and its boundary
in order to regulate its internal architecture through growth-induced stresses.
We show that biofilms exhibit a sharp transition in shape from domes to lenses
upon changing environmental stiffness or cell-substrate friction, which is
explained by a theoretical model considering the competition between
confinement and interfacial forces. The growth mode defines the progression of
the boundary, which in turn determines the trajectories and spatial
distribution of cell lineages. We further demonstrate that the evolving
boundary defines the orientational ordering of cells and the emergence of
topological defects in the interior of the biofilm. Our findings reveal novel
self-organization phenomena in confined active matter and provide strategies
for guiding the development of programmed microbial consortia with emergent
material properties.


  Large industrial facilities such as particle accelerators and nuclear power
plants are critical infrastructures for scientific research and industrial
processes. These facilities are complex systems that not only require regular
maintenance and upgrades but are often inaccessible to humans due to various
safety hazards. Therefore, a virtual reality (VR) system that can quickly
replicate real-world remote environments to provide users with a high level of
spatial and situational awareness is crucial for facility maintenance planning.
However, the exact 3D shapes of these facilities are often too complex to be
accurately modeled with geometric primitives through the traditional
rasterization pipeline.
  In this work, we develop Magic NeRF Lens, an interactive framework to support
facility inspection in immersive VR using neural radiance fields (NeRF) and
volumetric rendering. We introduce a novel data fusion approach that combines
the complementary strengths of volumetric rendering and geometric
rasterization, allowing a NeRF model to be merged with other conventional 3D
data, such as a computer-aided design model. We develop two novel 3D magic lens
effects to optimize NeRF rendering by exploiting the properties of human vision
and context-aware visualization. We demonstrate the high usability of our
framework and methods through a technical benchmark, a visual search user
study, and expert reviews. In addition, the source code of our VR NeRF
framework is made publicly available for future research and development.


  Optimization of mutual synchronization between a pair of limit-cycle
oscillators with weak symmetric coupling is considered in the framework of the
phase reduction theory. By generalizing a previous study on the optimization of
cross-diffusion coupling matrices between the oscillators, we consider
optimization of mutual coupling signals to maximize the linear stability of the
synchronized state, which are functionals of the past time sequences of the
oscillator states. For the case of linear coupling, optimization of the delay
time and linear filitering of coupling signals are considered. For the case of
nonlinear coupling, general drive-response coupling is considered, and the
optimal response and driving functions are derived. The theoretical results are
exemplified by numerical simulations.


  I outline methods for calculating the solution of Monte Carlo Radiative
Transfer (MCRT) in scattering, absorption and emission processes of dust and
gas, including polarization. I provide a bibliography of relevant papers on
methods with astrophysical applications.


  We continue the study of the rational-slope generalized $q,t$-Catalan numbers
$c_{m,n}(q,t)$. We describe generalizations of the bijective constructions of
J. Haglund and N. Loehr and use them to prove a weak symmetry property
$c_{m,n}(q,1)=c_{m,n}(1,q)$ for $m=kn\pm 1$. We give a bijective proof of the
full symmetry $c_{m,n}(q,t)=c_{m,n}(t,q)$ for $\min(m,n)\le 3$. As a corollary
of these combinatorial constructions, we give a simple formula for the
Poincar\'e polynomials of compactified Jacobians of plane curve singularities
$x^{kn\pm 1}=y^n$. We also give a geometric interpretation of a relation
between rational-slope Catalan numbers and the theory of $(m,n)$-cores
discovered by J. Anderson.


  We review models of compositional growth, which were introduced to explain
the growth statistics of various quantities ranging from firm sizes to GDP. In
these models, entities are decomposed into units that grow independently. Thus,
the growth rate of the entity is the addition of the growth rates of the
composing units, with possibly heterogeneous weights. We review such models and
show that they can be understood through a unifying theoretical framework,
explaining the resulting growth rate distributions using mixtures of Gaussians.


  We study the generation of transversal oscillations in coronal loops
represented as a straight thin flux tube under the effect of an external driver
modeling the global coronal EIT wave. We investigate how the generated
oscillations depend on the nature of the driver, and the type of interaction
between the two systems. We consider the oscillations of a magnetic straight
cylinder with fixed-ends under the influence of an external driver modeling the
force due to the global EIT wave. Given the uncertainties related to the nature
of EIT waves, we first approximate the driver by an oscillatory force in time
and later by a shock with a finite width. Results show that for a harmonic
driver the dominant period in the generated oscillation belongs to the driver.
Depending on the period of driver, compared to the natural periods of the loop,
a mixture of standing modes harmonics can be initiated. In the case of a
non-harmonic driver (modeling a shock wave), the generated oscillations in the
loop are the natural periods only. The amplitude of oscillations is determined
by the position of the driver along the tube. The full diagnosis of generated
oscillations is achieved using simple numerical methods.


  In this work the open-plus-closed-loop (OPCL) method of synchronization is
used in order to synchronize the systems from the Sprott's collection of the
simplest chaotic systems. The method is general and we were looking for the
simplest coupling between master and slave system. The interval of parameters
were synchronization is achieved are obtained analytically using Routh-Hurwitz
conditions. Detailed calculations and numerical simulation are given for the
system I from the Sprott's collection. Working in the same manner for
non-linear systems based on ordinary differential equations the method can be
adopted for the teaching of the topic.


  We study an integrable Hamiltonian reducible to free fermions which is
subjected to an imperfect periodic driving with the amplitude of driving (or
kicking) randomly chosen from a binary distribution like a coin-toss problem.
The randomness present in the driving protocol destabilises the periodic steady
state, reached in the limit of perfectly periodic driving, leading to a
monotonic rise of the stroboscopic residual energy with the number of periods
($N$). We establish that a minimal deviation from the perfectly periodic
driving would always result in a {\it bounded} heating up of the system with
$N$ to an asymptotic finite value. Remarkably, exploiting the completely
uncorrelated nature of the randomness and the knowledge of the stroboscopic
Floquet operator in the perfectly periodic situation, we provide an exact
analytical formalism to derive the disorder averaged expectation value of the
residual energy through a {\it disorder operator}. This formalism not only
leads to an immense numerical simplification, but also enables us to derive an
exact analytical form for the residual energy in the asymptotic limit which is
universal, i.e, independent of the bias of coin-toss and the protocol chosen.
Furthermore, this formalism clearly establishes the nature of the monotonic
growth of the residual energy at intermediate $N$ while clearly revealing the
possible non-universal behaviour of the same.


  The properties of the momentum space quark propagator in Landau gauge are
examined for the overlap quark action in quenched lattice QCD. Numerical
calculations are done on three lattices with different lattice spacings and
similar physical volumes to explore the approach of the quark propagator toward
the continuum limit. We have calculated the nonperturbative momentum-dependent
wave function renormalization function Z(p) and the nonperturbative mass
function M(p) for a variety of bare quark masses and perform an extrapolation
to the chiral limit. We find the behavior of Z(p) and M(p) are in reasonable
agreement between the two finer lattices in the chiral limit, however the data
suggest that an even finer lattice is desirable. The large momentum behavior is
examined to determine the quark condensate.


  The realization of multiferroics in nanostructures, combined with a large
electric dipole and ferromagnetic ordering, could lead to new applications,
such as high-density multi-state data storage. Although multiferroics have been
broadly studied for decades, ferromagnetic ferroelectricity is rarely explored,
especially in two-dimensional (2D) systems. Here we report the discovery of 2D
ferromagnetic ferroelectricity in layered transition metal halide systems. On
the basis of first-principles calculations, we reveal that charged CrBr3
monolayer exhibits in-plane multiferroicity, which is ensured by the
combination of orbital and charge ordering as realized by the asymmetric
Jahn-Teller distortions of octahedral Cr-Br6 units. As an example, we further
show that (CrBr3)2Li is a ferromagnetic ferroelectric multiferroic. The
explored phenomena and mechanism of multiferroics in this 2D system are not
only useful for fundamental research in multiferroics but also enable a wide
range of applications in nano-devices.