  Though the celebrated spin echoes have been widely used to reverse quantum
dynamics, they are not applicable to systems whose constituents are beyond the
control of the su(2) algebra. Here, we design echoes to reverse quantum
dynamics of breathers in three-dimensional unitary fermions and two-dimensional
bosons and fermions with contact interactions, which are governed by an
underlying su(1,1) algebra. Geometrically, SU(1,1) echoes produce closed
trajectories on a single or multiple Poincare disks and thus could recover any
initial states without changing the sign of the Hamiltonian. In particular, the
initial shape of a breather determines the superposition of trajectories on
multiple Poincare disks and whether the revival time has period multiplication.
Our work provides physicists with a recipe to tailor collective excitations of
interacting many-body systems.


  Seawater intrusion (SWI) is a complex process, where 3D modeling is often
necessary in order to monitor and manage the affected aquifers. Here, we
present a synthetic study to test a joint hydrogeophysical inversion approach
aimed at solving the inverse problem of estimating initial and current
saltwater distribution. First, we use a 3D groundwater model for variable
density flow based on discretized flow and solute mass balance equations. In
addition to the groundwater model, a 3D geophysical model was developed for
direct current resistivity imaging and inversion. The objective function of the
coupled problem consists of data misfit and regularization terms as well as a
coupling term that relates groundwater and geophysical states. We present a
novel approach to solve the inverse problem using an Alternating Direction
Method of Multipliers (ADMM) to minimize this coupled objective function. The
sensitivities are derived analytically for the discretized system of equations,
which allows us to efficiently compute the gradients in the minimization
procedure and reduce the computational complexity of the problem. The method
was tested on different synthetic scenarios with groundwater and geophysical
data represented by solute mass fraction data and direct current resistivity
data. With the ADMM approach, we were able to obtain better estimates for the
solute distribution, compared to just considering each data set separately or
solving with a simple coupled approach.


  Workplace communications around the world were drastically altered by
Covid-19, related work-from-home orders, and the rise of remote work. To
understand these shifts, we analyzed aggregated, anonymized metadata from over
360 billion emails within 4,361 organizations worldwide. By comparing
month-to-month and year-over-year metrics, we examined changes in network
community structures over 24 months before and after Covid-19. We also examined
shifts across multiple communication media (email, instant messages, video
calls, and calendaring software) within a single global organization, and
compared them to communications shifts that were driven by changes in formal
organizational structure. We found that, in 2020, organizations around the
world became more siloed than in 2019, evidenced by increased modularity. This
shift was concurrent with decreased stability within silos. Collectively, our
analyses indicate that following the onset of Covid-19, employees began to
shift more dynamically between subcommunities (teams, workgroups or functional
areas). At the same time, once in a subcommunity, they limited their
communication to other members of that community. We term these network changes
dynamic silos. We provide initial insights into the meaning and implications of
dynamic silos for the future of work.


  We derive exact statistical properties of a class of recursive fragmentation
processes. We show that introducing a fragmentation probability 0<p<1 leads to
a purely algebraic size distribution in one dimension, P(x) ~ x^{-2p}. In d
dimensions, the volume distribution diverges algebraically in the small
fragment limit, P(V)\sim V^{-\gamma} with \gamma=2p^{1/d}. Hence, the entire
range of exponents allowed by mass conservation is realized. We demonstrate
that this fragmentation process is non-self-averaging. Specifically, the
moments Y_\alpha=\sum_i x_i^{\alpha} exhibit significant fluctuations even in
the thermodynamic limit.


  Five well-known LBV stars in M33 were observed with the Multi-Pupil Fiber
Spectrograph (MPFS) on the 6-m Russian telescope. We observed LBVs varA, varB,
varC, var2 and var83. In three of them, var2, var83, varB, large-scale nebulae
were found with sizes from 15 pc and larger. The nebula shapes are complex,
like one-side tails or conical nebulae. They all are related to their LBV
stars. In var2 and var83 stars we found radial velocity gradients 15-30 km/s
across their nebulae. The stars varA and varC do not show extended nebulae, but
nebular lines are certainty present in their spectra.


  Graphs are widely used to model the relational structure of data, and the
research of graph machine learning (ML) has a wide spectrum of applications
ranging from drug design in molecular graphs to friendship recommendation in
social networks. Prevailing approaches for graph ML typically require abundant
labeled instances in achieving satisfactory results, which is commonly
infeasible in real-world scenarios since labeled data for newly emerged
concepts (e.g., new categorizations of nodes) on graphs is limited. Though
meta-learning has been applied to different few-shot graph learning problems,
most existing efforts predominately assume that all the data from those seen
classes is gold-labeled, while those methods may lose their efficacy when the
seen data is weakly-labeled with severe label noise. As such, we aim to
investigate a novel problem of weakly-supervised graph meta-learning for
improving the model robustness in terms of knowledge transfer. To achieve this
goal, we propose a new graph meta-learning framework -- Graph Hallucination
Networks (Meta-GHN) in this paper. Based on a new robustness-enhanced episodic
training, Meta-GHN is meta-learned to hallucinate clean node representations
from weakly-labeled data and extracts highly transferable meta-knowledge, which
enables the model to quickly adapt to unseen tasks with few labeled instances.
Extensive experiments demonstrate the superiority of Meta-GHN over existing
graph meta-learning studies on the task of weakly-supervised few-shot node
classification.


  The energy of atmospheric neutrinos detected by MACRO was estimated using
multiple coulomb scattering of upward throughgoing muons. This analysis allows
a test of atmospheric neutrino oscillations, relying on the distortion of the
muon energy distribution. These results have been combined with those coming
from the upward throughgoing muon angular distribution only. Both analyses are
independent of the neutrino flux normalization and provide strong evidence,
above the 4 sigma level, in favour of neutrino oscillations.


  The [CII] 157.74 $\mu$m transition is the dominant coolant of the neutral
interstellar gas, and has great potential as a star formation rate (SFR)
tracer. Using the Herschel KINGFISH sample of 46 nearby galaxies, we
investigate the relation of [CII] surface brightness and luminosity with SFR.
We conclude that [CII] can be used for measurements of SFR on both global and
kiloparsec scales in normal star-forming galaxies in the absence of strong
active galactic nuclei (AGN). The uncertainty of the $\Sigma_{\rm
[CII]}-\Sigma_{\rm SFR}$ calibration is $\pm$0.21 dex. The main source of
scatter in the correlation is associated with regions that exhibit warm IR
colors, and we provide an adjustment based on IR color that reduces the
scatter. We show that the color-adjusted $\Sigma_{\rm[CII]}-\Sigma_{\rm SFR}$
correlation is valid over almost 5 orders of magnitude in $\Sigma_{\rm SFR}$,
holding for both normal star-forming galaxies and non-AGN luminous infrared
galaxies. Using [CII] luminosity instead of surface brightness to estimate SFR
suffers from worse systematics, frequently underpredicting SFR in luminous
infrared galaxies even after IR color adjustment (although this depends on the
SFR measure employed). We suspect that surface brightness relations are better
behaved than the luminosity relations because the former are more closely
related to the local far-UV field strength, most likely the main parameter
controlling the efficiency of the conversion of far-UV radiation into gas
heating. A simple model based on Starburst99 population-synthesis code to
connect SFR to [CII] finds that heating efficiencies are $1\%-3\%$ in normal
galaxies.


  We study the problem of estimating a multivariate convex function defined on
a convex body in a regression setting with random design. We are interested in
optimal rates of convergence under a squared global continuous $l_2$ loss in
the multivariate setting $(d\geq 2)$. One crucial fact is that the minimax
risks depend heavily on the shape of the support of the regression function. It
is shown that the global minimax risk is on the order of $n^{-2/(d+1)}$ when
the support is sufficiently smooth, but that the rate $n^{-4/(d+4)}$ is when
the support is a polytope. Such differences in rates are due to difficulties in
estimating the regression function near the boundary of smooth regions.
  We then study the natural bounded least squares estimators (BLSE): we show
that the BLSE nearly attains the optimal rates of convergence in low
dimensions, while suffering rate-inefficiency in high dimensions. We show that
the BLSE adapts nearly parametrically to polyhedral functions when the support
is polyhedral in low dimensions by a local entropy method. We also show that
the boundedness constraint cannot be dropped when risk is assessed via
continuous $l_2$ loss.
  Given rate sub-optimality of the BLSE in higher dimensions, we further study
rate-efficient adaptive estimation procedures. Two general model selection
methods are developed to provide sieved adaptive estimators (SAE) that achieve
nearly optimal rates of convergence for particular "regular" classes of convex
functions, while maintaining nearly parametric rate-adaptivity to polyhedral
functions in arbitrary dimensions. Interestingly, the uniform boundedness
constraint is unnecessary when risks are measured in discrete $l_2$ norms.


  The Virtual Brain (TVB) is now available as open-source cloud ecosystem on
EBRAINS, a shared digital research platform for brain science. It offers
services for constructing, simulating and analysing brain network models (BNMs)
including the TVB network simulator; magnetic resonance imaging (MRI)
processing pipelines to extract structural and functional connectomes;
multiscale co-simulation of spiking and large-scale networks; a domain specific
language for automatic high-performance code generation from user-specified
models; simulation-ready BNMs of patients and healthy volunteers; Bayesian
inference of epilepsy spread; data and code for mouse brain simulation; and
extensive educational material. TVB cloud services facilitate reproducible
online collaboration and discovery of data assets, models, and software
embedded in scalable and secure workflows, a precondition for research on large
cohort data sets, better generalizability and clinical translation.


  Crowdsourcing models applied to work on mobile devices continuously reach new
ways of solving sophisticated problems, now with a use of portable advanced
devices, where users are not limited to a stationary use. There exists an open
problem of quality in crowdsourcing models due the inexperienced or malicious
workers. In this paper, we propose a model and a short specification of a
platform for a bundled widely available crowdsourcing mechanism, which tries to
utilize workers individual characteristics to maximum. Analyzed solution relies
on geographical data classified by localization category. Secondly, we profile
mobile workers by precisely analyzing their activity history. Results of this
research will make an impact on better understanding the latent potential of
mobile devices users. It makes for not only better quality in results, but also
opens a possibility of implementing a "twitch crowdsourcing" or emergency
relief systems. Special tasks assigned to owners of mobile devices can help
those, which are in need of help, making them the task creators.


  We present a kinematic study of the outer regions (R_25<R<2 R_25) of 17
edge-on disk galaxies. Using deep long-slit spectroscopy (flux sensitivity a
few 10^-19 erg s^-1 cm^-2 arcsec^-2), we search for H-alpha emission, which
must be emitted at these flux levels by any accumulation of hydrogen due to the
presence of the extragalactic UV background and any other, local source of UV
flux. We present results from the individual galaxy spectra and a stacked
composite. We detect H-alpha in many cases well beyond R_25 and sometimes as
far as 2 R_25. The combination of sensitivity, spatial resolution, and
kinematic resolution of this technique thus provides a powerful complement to
21-cm observations. Kinematics in the outer disk are generally disk-like (flat
rotation curves, small velocity dispersions) at all radii, and there is no
evidence for a change in the velocity dispersion with radius. We place strong
limits, few percent, on the existence of counter-rotating gas out to 1.5 R_25.
These results suggest that thin disks extend well beyond R_25; however, we also
find a few puzzling anomalies. In ESO 323-G033 we find two emission regions
that have velocities close to the systemic velocity rather than the expected
rotation velocity. These low relative velocities are unlikely to be simply due
to projection effects and so suggest that these regions are not on disk-plane,
circular orbits. In MCG-01-31-002 we find emission from gas with a large
velocity dispersion that is co-rotating with the inner disk.


  We define the Ricci curvature on simplicial complexes by modifying the
definition of the Ricci curvature on graphs, and we prove the upper and lower
bounds of the Ricci curvature. These properties are generalizations of previous
studies. Moreover, we obtain an estimate of the eigenvalues of the Laplacian on
simplicial complexes using the Ricci curvature.


  Models with extended Higgs sectors can contain several additional Higgs
states, heavier or lighter than the SM Higgs boson. The couplings of lighter
extra states to SM particles can be strongly reduced, leading to small cross
sections for their direct production. Heavier extra states can have larger
couplings to SM particles and, moreover, have large branching fractions into
lighter extra states, notably into a SM-like Higgs boson accompagnied by
another Higgs state which can be lighter or heavier than 125$\sim$GeV.
Motivated by corresponding scenarios in the NMSSM we study the prospects for
the discovery or exclusion of cascade decays $ggF \to H_3 \to H_2 + H_1$ in the
$b\bar{b}b\bar{b}$, $b\bar{b}\tau\tau$ and $b\bar{b}\gamma\gamma$ final states
where either $H_1$ or $H_2$ can be SM-like. Significant regions of the NMSSM
parameter space can be tested by these searches. These are, however, not
confined to models of the NMSSM type.


  Evaluating multi-center molecular integrals with Cartesian Gaussian-type
basis sets has been a long-standing bottleneck in electronic structure theory
calculation for solids and molecules. We have developed a vector-coupling and
vector-uncoupling scheme to solve molecular Coulomb integrals with solid
harmonics basis functions(SHGO). Solid harmonics are eigenstates of angular
momentum, making it possible to factorize molecular integrals. By combining
solid harmonic addition, differential and product rules, the computationally
costly multi-center four-center integrals can be factored into an angular part
and a radial component dependent on the atomic positions. The potential
speed-up ratio in evaluating molecular nuclear Coulomb integrals in our method
can reach up to four orders of magnitude for atomic orbitals with high angular
momentum quantum numbers. The foundation underpinning the mathematical
efficiency is the quantum angular momentum theory, where both vector-coupling
and vector-uncoupling schemes correspond to unitary Clebsch-Gordan
transformations that act on quantum angular momentum states, influencing their
degree of entanglement. By incorporating quantum angular momentum through these
transformations, the entanglement of the states can be reduced, and the less
entanglement there is for a quantum system, the easier it is to simulate. The
highly efficient method unveiled here opens new avenues for accelerated
material and molecule design and discovery.


  The mechanisms behind waste clearance from deep within the parenchyma of the
brain remain unclear to this date. Experimental evidence has shown that one
pathway for waste clearance, termed intramural periarterial drainage (IPAD), is
the rapid drainage of interstitial fluid (ISF) via basement membranes (BM) of
the smooth muscle cells (SMC) of cerebral arteries and its failure is closely
associated with the pathology of Alzheimer's disease (AD). We have previously
shown that arterial pulsations from the heart beat are not strong enough to
drive waste clearance. Here we demonstrate computational evidence for a
mechanism for cerebral waste clearance that is driven by functional hyperaemia,
that is, the dilation of cerebral arteries as a consequence of increased
neuronal demand. This mechanism is based on our model for fluid flow through
the vascular basement membrane. It accounts for waste clearance rates observed
in mouse experiments and aligns with pathological observations as well as
recommendations to lower the individual risk of AD, such as keeping mentally
and physically active.


  We show that pointlike sets are decidable for the pseudovariety of finite
semigroups whose idempotent-generated subsemigroup is R-trivial. Notably, our
proof is constructive: we provide an explicit relational morphism which
computes the ER-pointlike subsets of a given finite semigroup.


  Phase-only spatial light modulators can be employed to structure laser light
in complex three dimensional focusing patterns, with a variety of applications.
While spatial light modulators have typical refresh frequencies of tens of Hz,
the computation time of three dimensional holograms ranges between a few
seconds and a few minutes, therefore limiting the use of the maximum refresh
rate of spatial light modulators to either pre-calculated sequences of high
quality holograms, or low quality holograms only for real time update. Here, we
propose the implementation of a recently developed compressed sensing
Gerchberg-Saxton algorithm on a consumer graphical processor allowing the
generation of high quality holograms at video rate.


  Ammonium assimilation in E. coli is regulated by two paralogous proteins
(GlnB and GlnK), which orchestrate interactions with regulators of gene
expression, transport proteins and metabolic pathways. Yet how they conjointly
modulate the activity of glutamine synthetase (GS), the key enzyme for nitrogen
assimilation, is poorly understood. We combine experiments and theory to study
the dynamic roles of GlnB and GlnK during nitrogen starvation and upshift. We
measure time-resolved in vivo concentrations of metabolites, total and
post-translationally modified proteins, and develop a concise biochemical model
of GlnB and GlnK that incorporates competition for active and allosteric sites,
as well as functional sequestration of GlnK. The model predicts the responses
of GS, GlnB and GlnK under time-varying external ammonium level in the wild
type and two genetic knock-outs. Our results show that GlnK is tightly
regulated under nitrogen-rich conditions, yet it is expressed during ammonium
run-out and starvation. This suggests a role for GlnK as a buffer of nitrogen
shock after starvation, and provides a further functional link between nitrogen
and carbon metabolisms.


  We consider directed acyclic networks with multiple sources and multiple
terminals where each source generates one i.i.d. random process over an abelian
group and all the terminals want to recover the sum of these random processes.
The different source processes are assumed to be independent. The solvability
of such networks has been considered in some previous works. In this paper we
investigate on the capacity of such networks, referred as {\it sum-networks},
and present some bounds in terms of min-cut, and the numbers of sources and
terminals.


  We show that several models of interacting XXZ spin chains subject to
boundary driving and dissipation possess a subtle kind of time-reversal
symmetry, making their steady states exactly solvable. We focus on a model with
a coherent boundary drive, showing that it exhibits a unique continuous
dissipative phase transition as a function of the boundary drive amplitude.
This transition has no analogue in the bulk closed system, or in incoherently
driven models. We also show the steady state magnetization exhibits a
surprising fractal dependence on interaction strength, something previously
associated with less easily measured infinite-temperature transport quantities
(the Drude weight). Our exact solution also directly yields driven-dissipative
double-chain models that have pure, entangled steady states that are also
current carrying.


  The theory of actual causality, defined by Halpern and Pearl, and its
quantitative measure - the degree of responsibility - was shown to be extremely
useful in various areas of computer science due to a good match between the
results it produces and our intuition. In this paper, I describe the
applications of causality to formal verification, namely, explanation of
counterexamples, refinement of coverage metrics, and symbolic trajectory
evaluation. I also briefly discuss recent applications of causality to legal
reasoning.


  We study sums of $k$-potent matrices. We show the conditions by which a
complex matrix $A$ can be expressed as a sums of $k$-potent matrices. Also we
obtain conditions by which a complex matrix $A$ can be expressed as a sum of
finite order elements. This generalize some results obtain by Wu. Also we study
the sum of $k$-potent matrices in $\mathcal{M}_{\mathcal{C}f}(F)$ with $F$ be a
field and proof that any matrix in this space can be expressed as a sum of $14$
$(k+1)$-potent matrices preserving the result obtain by Slowik.


  We study a crucial yet often overlooked issue inherent to Vision Transformers
(ViTs): feature maps of these models exhibit grid-like artifacts, which hurt
the performance of ViTs in downstream dense prediction tasks such as semantic
segmentation, depth prediction, and object discovery. We trace this issue down
to the positional embeddings at the input stage. To mitigate this, we propose a
two-stage denoising approach, termed Denoising Vision Transformers (DVT). In
the first stage, we separate the clean features from those contaminated by
positional artifacts by enforcing cross-view feature consistency with neural
fields on a per-image basis. This per-image optimization process extracts
artifact-free features from raw ViT outputs, providing clean feature estimates
for offline applications. In the second stage, we train a lightweight
transformer block to predict clean features from raw ViT outputs, leveraging
the derived estimates of the clean features as supervision. Our method, DVT,
does not require re-training the existing pre-trained ViTs, and is immediately
applicable to any Vision Transformer architecture. We evaluate our method on a
variety of representative ViTs (DINO, DeiT-III, EVA02, CLIP, DINOv2,
DINOv2-reg) and demonstrate that DVT consistently improves existing
state-of-the-art general-purpose models in semantic and geometric tasks across
multiple datasets. We hope our study will encourage a re-evaluation of ViT
design, especially regarding the naive use of positional embeddings. Our code
and checkpoints are publicly available.


  This paper is an interval dynamics counterpart of three theories founded
earlier by the authors, S. Smirnov and others in the setting of the iteration
of rational maps on the Riemann sphere: the equivalence of several notions of
non-uniform hyperbolicity, Geometric Pressure, and Nice Inducing Schemes
methods leading to results in thermodynamical formalism. We work in a setting
of generalized multimodal maps, that is smooth maps f of a finite union of
compact intervals in R into R with non-flat critical points, such that on its
maximal forward invariant set K the map f is topologically transitive and has
positive topological entropy. We prove that several notions of non-uniform
hyperbolicity of f|_K are equivalent (including uniform hyperbolicity on
periodic orbits, TCE & all periodic orbits in K hyperbolic repelling, Lyapunov
hyperbolicity, and exponential shrinking of pull-backs). We prove that several
definitions of geometric pressure P(t), that is pressure for the map f|_K and
the potential - t log |f'|, give the same value (including pressure on periodic
orbits, "tree" pressure, variational pressures and conformal pressure). Finally
we prove that, provided all periodic orbits in K are hyperbolic repelling, the
function P(t) is real analytic for t between the "condensation" and "freezing"
parameters and that for each such t there exists unique equilibrium (and
conformal) measure satisfying strong statistical properties.


  For accurate determination of particle masses accurate knowledge of the
momentum scale of the detectors is crucial. The procedure used to calibrate the
momentum scale of the LHCb spectrometer is described and illustrated using the
performance obtained with an integrated luminosity of $1.6~ fb^{-1}$ collected
during 2016 in $pp$ running. The procedure uses large samples of $J/\psi
\rightarrow \mu^+ \mu^-$ and $B^+ \rightarrow J/\psi K^+$ decays and leads to a
relative accuracy of $3 \times 10^{-4}$ on the momentum scale.


  The evolution of multi-mode instabilities in a hypersonic boundary layer and
their effects on aerodynamic heating are investigated. Experiments are
conducted in a Mach 6 wind tunnel using Rayleigh-scattering flow visualization,
fast-response pressure sensors, fluorescent temperature-sensitive paint (TSP),
and particle image velocimetry (PIV). Calculations are also performed based on
both parabolized stability equations (PSE) and direct numerical simulations
(DNS). It is found that second-mode dilatational waves, accompanied by
high-frequency alternating fluid compression and expansion, produce intense
aerodynamic heating in a small region that rapidly heats the fluid passing
through it. As a result, the surface temperature rapidly increases and results
in an overshoot over the nominal transitional value. When the dilatation waves
decay downstream, the surface temperature decreases gradually until transition
is completed. A theoretical analysis is provided to interpret the temperature
distribution affected by the aerodynamic heating.


  Although quantum computers are capable of solving problems like factoring
exponentially faster than the best-known classical algorithms, determining the
resources responsible for their computational power remains unclear. An
important class of problems where quantum computers possess an advantage is
phase estimation, which includes applications like factoring. We introduce a
new computational model based on a single squeezed state resource that can
perform phase estimation, which we call the power of one qumode. This model is
inspired by an interesting computational model known as deterministic quantum
computing with one quantum bit (DQC1). Using the power of one qumode, we
identify that the amount of squeezing is sufficient to quantify the resource
requirements of different computational problems based on phase estimation. In
particular, it establishes a quantitative relationship between the resources
required for factoring and DQC1. For example, we find the squeezing required to
factor has an exponential scaling whereas no squeezing (i.e., a coherent state)
is already sufficient to solve the hardest problem in DQC1.


  The decomposition of hydrodynamic and acoustic components of cavity flows can
aid the understanding of the flow-acoustic interaction, which produces a
variety of adverse effects in applications. We apply the approach of combining
the resolvent analysis and Doak's momentum potential theory to examine the
input-output flow-acoustic characteristics of compressible flow over an open
cavity at Re=10,000. The methodology can decompose hydrodynamic and acoustic
components from an input-output framework. We further localize the forcing at
the leading-edge and front wall of the cavity and filter with a single
component of velocity, density, and temperature forcing. For the subsonic flow
at M=0.6, The strong acoustic component appears at the trailing edge of the
cavity at a lower frequency. while as the frequency increases, the intense
acoustic structure moves close to upstream and overlap with the hydrodynamic
component. This tendency is also observed in the supersonic flow condition
M=1.4. Compared to different types of forcing, the streamwise velocity forcing
achieves the largest energy amplification. However, it substantially reduces by
moving the forcing location from the leading-edge to the front wall of the
cavity. This work provides an alternative approach to examine input-output
flow-acoustic characteristics where resonance is dominant and provides guidance
for the development of flow control strategies.


  A model for gas outflows is proposed which simultaneously explains the
correlations between the (i) equivalent width of low ionization and Ly-alpha
lines, (ii) outflow velocity, and (iii) star formation rate observed in Lyman
Break Galaxies (LBGs). Our interpretation implies that LBGs host short-lived
(30 +/- 5 Myr) starburst episodes observed at different evolutionary phases.
Initially, the starburst powers a hot wind bound by a denser cold shell, which
after about 5 Myr becomes dynamically unstable and fragments; afterwards the
fragment evolution is approximately ballistic while the hot bubble continues to
expand. As the fragments are gravitationally decelerated, their screening
ability of the starlight decreases as the UV starburst luminosity progressively
dims. LBG observations sample all these evolutionary phases. Finally, the
fragments fall back onto the galaxy after approximately 60 Myr. This phase
cannot be easily probed as it occurs when the starburst UV luminosity has
already largely faded; however, galaxies dimmer in the UV than LBGs should show
infalling gas.


  The rise in the energy spectrum of the positron ratio, observed by the PAMELA
satellite above 10 GeV, and other cosmic ray measurements, have been
interpreted as a possible signature of Dark Matter annihilation in the Galaxy.
However, the large number of free parameters, and the large astrophysical
uncertainties, make it difficult to do conclusive statements about the
viability of this scenario. Here, we perform a multi-wavelength,
multi-messenger analysis, that combines in a consistent way the constraints
arising from different astrophysical observations. We show that if standard
assumptions are made for the distribution of Dark Matter (we build models on
the recent Via Lactea II and Aquarius simulations) and the propagation of
cosmic rays, current DM models cannot explain the observed positron flux
without exceeding the observed fluxes of antiprotons or gamma-ray and radio
photons. To visualize the multi-messenger constraints, we introduce "star
plots", a graphical method that allows to show in the same plot theoretical
predictions and observational constraints for different messengers and
wavelengths.


  We propose a new method based on the invariant properties of the ansatz of
the Hirota method which have been discovered recently. This method allows one
to construct new solutions for a certain class the dissipative equations
classified by degrees of homogeneity. This algorithm is similar to the method
of ``dressing'' the solutions of integrable equations. A class of new solutions
is constructed. It is proved that all known exact solutions of the
FitzHygh-Nagumo-Semenov equation can be expressed in terms of solutions of the
linear parabolic equation. This method is compared with the Miura transforms in
the theory of Kortveg de Vris equations. This method allows on to create a
package by using the methods of computer algebra.


  Measuring public opinion is a key focus during democratic elections, enabling
candidates to gauge their popularity and alter their campaign strategies
accordingly. Traditional survey polling remains the most popular estimation
technique, despite its cost and time intensity, measurement errors, lack of
real-time capabilities and lagged representation of public opinion. In recent
years, Twitter opinion mining has attempted to combat these issues. Despite
achieving promising results, it experiences its own set of shortcomings such as
an unrepresentative sample population and a lack of long term stability. This
paper aims to merge data from both these techniques using Bayesian data
assimilation to arrive at a more accurate estimate of true public opinion for
the Brexit referendum. This paper demonstrates the effectiveness of the
proposed approach using Twitter opinion data and survey data from trusted
pollsters. Firstly, the possible existence of a time gap of 16 days between the
two data sets is identified. This gap is subsequently incorporated into a
proposed assimilation architecture. This method was found to adequately
incorporate information from both sources and measure a strong upward trend in
Leave support leading up to the Brexit referendum. The proposed technique
provides useful estimates of true opinion, which is essential to future opinion
measurement and forecasting research.


  The shallow water equations provide a useful analogue of the fully
compressible Euler equations since they have similar characteristics:
conservation laws, inertia-gravity and Rossby waves and a (quasi-) balanced
state. In order to obtain realistic simulation results, it is desirable that
numerical models have discrete analogues of these properties. Two prototypical
examples of such schemes are the 1981 Arakawa and Lamb (AL81) C-grid total
energy and potential enstrophy conserving scheme, and the 2007 Salmon (S07)
Z-grid total energy and potential enstrophy conserving scheme. Unfortunately,
the AL81 scheme is restricted to logically square, orthogonal grids; and the
S07 scheme is restricted to uniform square grids. The current work extends the
AL81 scheme to arbitrary non-orthogonal polygonal grids and the S07 scheme to
arbitrary orthogonal spherical polygonal grids in a manner that allows both
total energy and potential enstrophy conservation, by combining Hamiltonian
methods (work done by Salmon, Gassmann, Dubos and others) and Discrete Exterior
Calculus (Thuburn, Cotter, Dubos, Ringler, Skamarock, Klemp and others).
Detailed results of the schemes applied to standard test cases are deferred to
Part 2 of this series of papers.


  Cluster-level dynamic treatment regimens can be used to guide sequential,
intervention or treatment decision-making at the cluster level in order to
improve outcomes at the individual or patient-level. In a cluster-level DTR,
the intervention or treatment is potentially adapted and re-adapted over time
based on changes in the cluster that could be impacted by prior intervention,
including based on aggregate measures of the individuals or patients that
comprise it. Cluster-randomized sequential multiple assignment randomized
trials (SMARTs) can be used to answer multiple open questions preventing
scientists from developing high-quality cluster-level DTRs. In a
cluster-randomized SMART, sequential randomizations occur at the cluster level
and outcomes are at the individual level. This manuscript makes two
contributions to the design and analysis of cluster-randomized SMARTs: First, a
weighted least squares regression approach is proposed for comparing the mean
of a patient-level outcome between the cluster-level DTRs embedded in a SMART.
The regression approach facilitates the use of baseline covariates which is
often critical in the analysis of cluster-level trials. Second, sample size
calculators are derived for two common cluster-randomized SMART designs for use
when the primary aim is a between-DTR comparison of the mean of a continuous
patient-level outcome. The methods are motivated by the Adaptive Implementation
of Effective Programs Trial, which is, to our knowledge, the first-ever
cluster-randomized SMART in psychiatry.


  It is well known that an operator-valued function $\Theta$ from the Schur
class ${\bf S}(\mathfrak M,\mathfrak N)$, where $\mathfrak M$ and $\mathfrak N$
are separable Hilbert spaces, can be realized as the transfer function of a
simple conservative discrete time-invariant linear system. The known
realizations involve the function $\Theta$ itself, the Hardy spaces or the
reproducing kernel Hilbert spaces. On the other hand, as in the classical
scalar case, the Schur class operator-valued function is uniquely determined by
its so called "Schur parameters". In this paper we construct simple
conservative realizations using the Schur parameters only. It turns out that
the unitary operators corresponding to the systems take the form of five
diagonal block operator matrices, which are the analogs of
Cantero--Moral--Vel\'azquez (CMV) matrices appeared recently in the theory of
scalar orthogonal polynomials on the unit circle. We obtain new models given by
truncated block operator CMV matrices for an arbitrary completely non-unitary
contraction. It is shown that the minimal unitary dilations of a contraction in
a Hilbert space and the minimal Naimark dilations of a semi-spectral operator
measure on the unit circle can also be expressed by means of block operator CMV
matrices.


  Asymptotic symmetries of black hole spacetimes have received much attention
as a possible origin of the Bekenstein-Hawking entropy in black hole
thermodynamics. In general, it takes hard efforts to find appropriate
asymptotic conditions on a metric and a Lie algebra generating the
transformation of symmetries with which the corresponding charges are
integrable. We here propose an alternative approach to construct building
blocks of asymptotic symmetries of a given spacetime metric. Our algorithmic
approach may make it easier to explore asymptotic symmetries in any spacetime
than in conventional approaches. As an explicit application, we analyze the
asymptotic symmetries on Rindler horizon. We find a new class of symmetries
related with dilatation transformations in time and in the direction
perpendicular to the horizon, which we term superdilatations.


  We examine the general nature of nuclear odd-even mass differences by
employing neutron and proton mass relations that emphasize these effects. The
most recent mass tables are used. The possibility of a neutron excess
dependence of the staggering is examined in detail in separate regions defined
by the main nuclear shells, and a clear change in this dependency is found at
$Z=50$ for both neutrons and protons. A further separation into odd and even
neutron (proton) number produces very accurate local descriptions of the mass
differences for each type of nucleons. These odd-even effects are combined into
a global phenomenological expression, ready to use in a binding energy formula.
The results deviate from previous parametrizations, and in particular found to
be significantly superior to a recent two term, $A^{-1}$ dependence.


  If gamma-ray bursts originate in galaxies at cosmological distances, the host
galaxy should be detected if a burst error box is searched deep enough; are the
host galaxies present? We present and implement a statistical methodology which
evaluates whether the observed galaxy detections in a burst's error box are
consistent with the presence of the host galaxy, or whether all the detections
can be attributed to unrelated background galaxies. This methodology requires
the model-dependent distribution of host galaxy fluxes. While our methodology
was derived for galaxies in burst error boxes, it can be applied to other
candidate host objects (e.g., active galaxies) and to other types of error
boxes. As examples, we apply this methodology to two published studies of burst
error boxes. We find that the nine error boxes observed by Larson and McLean
(1997) are too large to discriminate between the presence or absence of host
galaxies, while the absence of bright galaxies in the four significantly
smaller error boxes observed by HST (Schaefer et al. 1997) does confirm that
there is a "no-host galaxy" problem within the "minimal" host galaxy model.


  Bounded-confidence models in social dynamics describe multi-agent systems,
where each individual interacts only locally with others. Several models are
written as systems of ordinary differential equations with discontinuous
right-hand side: this is a direct consequence of restricting interactions to a
bounded region with non-vanishing strength at the boundary. Various works in
the literature analyzed properties of solutions, such as barycenter invariance
and clustering. On the other side, the problem of giving a precise definition
of solution, from an analytical point of view, was often overlooked. However, a
rich literature proposing different concepts of solution to discontinuous
differential equations is available. Using several concepts of solution, we
show how existence is granted under general assumptions, while uniqueness may
fail even in dimension one, but holds for almost every initial conditions.
Consequently, various properties of solutions depend on the used definition and
initial conditions.


  We advance a method used to analyse the neutrino properties (masses and
mixing) in the seesaw mechanism. Assuming the hierarchical Dirac and light
neutrino masses we establish rather simple relations between the light and the
heavy neutrino parameters in the favored region of the solar and the
atmospheric neutrino experiments. A empirical condition satisfied by the RH
mixing angles is obtained.


  The relaxation processes in an ultra-cold degenerate atomic Fermi gas near a
Feshbach resonance are considered. It is shown that the relaxation rate of the
molecules being in a resonance with the atomic Fermi system is of the order of
the part of the chemical potential determined by the interaction between
resonance molecules. In this connection the lower part of the excitation
spectrum in the system of resonance molecules is not well-defined.


  We consider the associated production of a vector or Higgs boson with a jet
in hadronic collisions. When the transverse momentum $q_T$ of the boson-jet
system is much smaller than its invariant mass $Q$, the QCD perturbative
expansion is affected by large logarithmic terms that must be resummed to all
orders. We discuss the all-order resummation structure of the logarithmically
enhanced contributions up to next-to-leading logarithmic accuracy. Resummation
is performed at the differential level with respect to the kinematical
variables of the boson-jet system. Soft-parton radiation produces azimuthal
correlations that are fully accounted for in our framework. We present explicit
analytical results for the resummation coefficients up to next-to-leading order
and next-to-leading logarithmic accuracy, that include the exact dependence on
the jet radius.


  We analyze theoretically the phase diagram of a triangular triple quantum dot
with strong onsite repulsion coupled to ferromagnetic leads. This model
includes the competition of magnetic ordering of local or itinerant magnetic
moments, geometric frustration and Kondo screening. We identify all the phases
resulting from this competition. We find that three Kondo phases -- the
conventional one, the two-stage underscreened one, and the one resulting from
the ferromagnetic Kondo effect -- can be realized at zero temperature, and all
are very susceptible to the proximity of ferromagnetic leads. In particular, we
find that the quantum dots are spin-polarized in each of these phases. Further,
we discuss the fate of the phases at non-zero temperatures, where a plethora of
competing energy scales gives rise to complex landscape of crossovers. Each
Kondo regime splits into a pair of phases, one not magnetized and one
comprising magnetically polarized quantum dots. We discuss our results in the
context of heavy-fermion physics in frustrated Kondo lattices.


  The $O(a)$ improved Wilson quark action on the anisotropic lattice is
investigated. We carry out numerical simulations in the quenched approximation
at three values of lattice spacing ($a_{\sigma}^{-1}=1$--2 GeV) with the
anisotropy $\xi=a_{\sigma}/a_{\tau}=4$, where $a_{\sigma}$ and $a_{\tau}$ are
the spatial and the temporal lattice spacings, respectively. Using the
dispersion relation of mesons, the bare anisotropy $\gamma_F$ in the quark
action is numerically tuned below the charm quark mass region with the
statistical accuracy of 1 % level. The systematic uncertainties in the
calibration are examined and found to be under control in the continuum limit.
Then we compute the light hadron masses and find that they are consistent with
the result of the UKQCD Collaboration on the isotropic lattice. The effect of
the uncertainty in the calibration on the hadron spectrum for physical quark
masses is also found to be under control.


  As drought is among the natural hazards which affects people and economies
worldwide and often results in huge monetary losses sophisticated methods for
drought monitoring and decision making are needed. Several different approaches
to quantify drought have been developed during past decades. However, most of
these drought indices suffer from different shortcomings and do not account for
the multiple driving factors which promote drought conditions and their
inter-dependencies. We provide a novel methodology for the calculation of
(multivariate) drought indices, which combines the advantages of existing
approaches and omits their disadvantages. Moreover, our approach benefits from
the flexibility of vine copulas in modeling multivariate non-Gaussian
inter-variable dependence structures. A three-variate data example is used in
order to investigate drought conditions in Europe and to illustrate and reason
the different modeling steps. The data analysis shows the appropriateness of
the described methodology. Comparison to well-established drought indices shows
the benefits of our multivariate approach. The validity of the new methodology
is verified by comparing the spatial extent of historic drought events based on
different drought indices. Further, we show that the assumption of non-Gaussian
dependence structures is well-grounded in this real-world application.


  Large-amplitude Alfv\'en waves are observed in various systems in space and
laboratories, demonstrating an interesting property that the wave shapes are
stable even in the nonlinear regime. The ideal magnetohydrodynamics (MHD) model
predicts that an Alfv\'en wave keeps an arbitrary shape constant when it
propagates on a homogeneous ambient magnetic field. However, such arbitrariness
is an artifact of the idealized model that omits the dispersive effects. Only
special wave forms, consisting of two component sinusoidal functions, can
maintain the shape; we derive fully nonlinear Alfv\'en waves by an extended MHD
model that includes both the Hall and electron inertia effects. Interestingly,
these \small-scale effects" change the picture completely; the large-scale
component of the wave cannot be independent of the small scale component, and
the coexistence of them forbids the large scale component to have a free wave
form. This is a manifestation of the nonlinearity-dispersion interplay, which
is somewhat different from that of solitons.


  Experiments with diblock co-polymer melts display undulated bilayers that
emanate from defects such as triple junctions and endcaps,
\cite{batesjain_2004}. Undulated bilayers are characterized by oscillatory
perturbations of the bilayer width, which decay on a spatial length scale that
is long compared to the bilayer width. We mimic defects within the
functionalized Cahn-Hillard free energy by introducing spatially localized
inhomogeneities within its parameters. For length parameter $\varepsilon\ll1$,
we show that this induces undulated bilayer solutions whose width perturbations
decay on an $O\!\left(\varepsilon^{-1/2}\right)$ inner length scale that is
long in comparison to the $O(1)$ scale that characterizes the bilayer width.


  R Kerr's Ricci-flat Lorentz 4-manifold was shown by B Carter in 1968 to
support a classically completely integrable system of geodesics; here we
interpret this system in terms of a locally conformally symplectic structure,
which we identify (\S 2.2) using characteristic classes defined by Kerr-Schild
Cartesian coordinates (regarded as a map to the Cayley-Penrose compactification
of Minkowski space). This leads to the definition of an interesting cobordism
category of contact 3-manifolds and 4-dimensional locally conformally
symplectic cobordisms between them.


  Semimetallic osmium pyrochlore oxide Cd2Os2O7 undergoes a magnetic transition
to an all-in-all-out (AIAO)-type order at 227 K, followed by a crossover to an
AIAO insulator at around 210 K. Here, we studied the isostructural and
isoelectronic compound Hg2Os2O7 through thermodynamic measurements, muSR
spectroscopy and neutron diffraction experiments. A similar magnetic
transition, probably to an AIAO-type order, was observed at 88 K, while the
resistivity showed a decrease at the transition and remained metallic down to 2
K. Thus, the ground state of Hg2Os2O7 is most likely an AIAO semimetal, which
is analogous to the intermediate-temperature state of Cd2Os2O7. Hg2Os2O7 exists
on the verge of the metal-insulator boundary on the metal side and provides an
excellent platform for studying the electronic instability of 5d electrons with
moderate electron correlations and strong spin-orbit interactions.


  The magnetic field integrals connected with the momentum resolution are
calculated for the ATLAS inner tracking volume in a range of pseudorapidity
$|\eta| < 3$ for the cases of `ideal' and inhomogeneous solenoid fields. In the
latest case, the magnetic field map is extracted from POISSON calculations with
help of an interface program POISGT. The tracking volume is restricted by a
length of 6.8 m and by a radius of 1.06 m. The solenoid coil with an active
length of 6.3 m and with an inner radius of 1.23 m produces the magnetic flux
density of 2 T in the center of the coil.


  We present a new method for calculating the product yield of a radical pair
recombination reaction in the presence of a weak time-dependent magnetic field.
This method successfully circumvents the computational difficulties presented
by a direct solution of the Liouville-von Neumann equation for a long-lived
radical pair containing many hyperfine-coupled nuclear spins. Using a modified
formulation of Floquet theory, treating the time-dependent magnetic field as a
perturbation, and exploiting the slow radical pair recombination, we show that
one can obtain a good approximation to the product yield by considering only
nearly-degenerate sub-spaces of the Floquet space. Within a significant
parameter range, the resulting method is found to give product yields in good
agreement with exact quantum mechanical results for a variety of simple model
radical pairs. Moreover it is considerably more efficient than the exact
calculation, and it can be applied to radical pairs containing significantly
more nuclear spins. This promises to open the door to realistic theoretical
investigations of the effect of radiofrequency electromagnetic radiation on the
photochemically induced radical pair recombination reactions in the avian
retina which are believed to be responsible for the magnetic compass sense of
migratory birds.


  We develop a rapid algorithm for the evolution of stable, circular,
circumbinary discs suitable for parameter estimation and population synthesis
modelling. Our model includes disc mass and angular momentum changes, accretion
on to the binary stars, and binary orbital eccentricity pumping. We fit our
model to the post-asymptotic giant branch (post-AGB) circumbinary disc around
IRAS 08544-4431, finding reasonable agreement despite the simplicity of our
model. Our best-fitting disc has a mass of about $0.01\, \mathrm{M}_{\odot }$
and angular momentum $2.7\times 10^{52}\, \mathrm{g}\, \mathrm{cm}^{2}\,
\mathrm{s}^{-1}\simeq 9 \,\mathrm{M}_{\odot }\, \mathrm{km}\, \mathrm{s}^{-1}\,
\mathrm{au}$, corresponding to 0.0079 and 0.16 of the common-envelope mass and
angular momentum, respectively. The best-fitting disc viscosity is $\alpha
_\mathrm{disc} = 5 \times 10^{-3}$ and our tidal torque algorithm can be
constrained such that the inner edge of the disc $R_{\mathrm{in}}\sim 2a$. The
inner binary eccentricity reaches about 0.13 in our best-fitting model of IRAS
08544-4431, short of the observed 0.22. The circumbinary disc evaporates
quickly when the post-AGB star reaches a temperature of $\sim \! 6\times 10^4\,
\mathrm{K}$, suggesting that planetismals must form in the disc in about
$10^{4}\, \mathrm{yr}$ if secondary planet formation is to occur, while
accretion from the disc on to the stars at about 10 times the inner-edge
viscous rate can double the disc lifetime.


  Meson-charmonium dissociation reactions governed by the quark interchange are
studied with temperature-dependent quark potentials. Quark-antiquark
relative-motion wave functions and masses of charmonia and charmed mesons are
determined by the central spin-independent part of the potentials or by the
central spin-independent part and a smeared spin-spin interaction. The
prominent temperature dependence of the masses is found. Based on the
potentials, the wave functions, and the meson masses, we obtain
temperature-dependent cross sections for fifteen pion-charmonium and
rho-charmonium dissociation reactions. The numerical cross sections are
parametrized for future applications in hadronic matter. The particular
temperature dependence of the J/psi bound state leads to unusual behavior of
the cross sections for endothermic J/psi dissociation reactions. The quantum
numbers of psi' and chi_c can not make their difference in mass in the
temperature region 0.6T_c < T < T_c, but can make the psi' dissociation
different from the chi_c dissociation.


  We aim with the present study to provide observational evidences on whether
coronal hole spicules reach coronal temperatures. We combine multi-instrument
co-observations obtained with the SUMER/SoHO and with the EIS/SOT/XRT/Hinode.
The analysed three large spicules were found to be comprised of numerous thin
spicules which rise, rotate and descend simultaneously forming a bush-like
feature. Their rotation resembles the untwisting of a large flux rope. They
show velocities ranging from 50 to 250 km/s. We clearly associated the red- and
blue-shifted emissions in transition region lines with rotating but also with
rising and descending plasmas, respectively. Our main result is that these
spicules although very large and dynamic, show no presence in spectral lines
formed at temperatures above 300 000 K. The present paper brings out the
analysis of three Ca II H large spicules which are composed of numerous dynamic
thin spicules but appear as macrospicules in EUV lower resolution images. We
found no coronal counterpart of these and smaller spicules. We believe that the
identification of phenomena which have very different origins as macrospicules
is due to the interpretation of the transition region emission, and especially
the He II emission, wherein both chromospheric large spicules and coronal X-ray
jets are present. We suggest that the recent observation of spicules in the
coronal AIA/SDO 171 A and 211 A channels is probably due to the existence of
transition region emission there.


  The X-Ray Telescope (XRT) onboard the Hinode satellite is an X-ray imager
that observes the solar corona with the capability of diagnosing coronal
temperatures from less than 1 MK to more than 10 MK. To make full use of this
capability, Narukage et al. (Solar Phys. 269, 169, 2011) determined the
thickness of each of the X-ray focal-plane analysis filters based on
calibration measurements from the ground-based end-to-end test. However, in
their paper, the calibration of the thicker filters for observations of active
regions and flares, namely the med-Be, med-Al, thick-Al and thick-Be filters,
was insufficient due to the insufficient X-ray flux used in the measurements.
In this work, we recalibrate those thicker filters using quiescent active
region data taken with multiple filters of XRT. On the basis of our updated
calibration results, we present the revised coronal-temperature-diagnostic
capability of XRT.


  We prove the existence of singular del Pezzo surfaces that are neither
K-semistable nor contain any anticanonical polar cylinder.


  We present a multi-filtering Graph Convolution Neural Network (GCN) framework
for network embedding task. It uses multiple local GCN filters to do feature
extraction in every propagation layer. We show this approach could capture
different important aspects of node features against the existing attribute
embedding based method. We also show that with multi-filtering GCN approach, we
can achieve significant improvement against baseline methods when training data
is limited. We also perform many empirical experiments and demonstrate the
benefit of using multiple filters against single filter as well as most current
existing network embedding methods for both the link prediction and node
classification tasks.


  By using the probability approach (the Malliavin calculus), we prove the
existence of smooth fundamental solutions for degenerate kinetic Fokker-Planck
equation with anisotropic nonlocal dissipativity, where the dissipative term is
the generator of an anisotropic L\'evy process and the drift term is allowed to
be cubic growth.


  The subject of this paper is the existence and stability of solar cycles with
durations in the range of 20-250 years. Five types of data series are used: 1)
The Zurich series (1749-2009 AD), the mean annual International sunspot number
Ri, 2) The Group sunspot number series Rh (1610-1995 AD), 3) The simulated
extended sunspot Rsi number from Extended time series of Solar Activity Indices
(ESAI) (1090-2002 AD), 4) The simulated extended geomagnetic aa-index from ESAI
(1099-2002 AD), 5) The Meudon filament series (1919-1991 AD) (it is used only
particularly). Data series are smoothed over 11 years and supercenturial trends
are removed. Two principally independent methods of time series analysis are
used: the T-R periodogram analysis (both in the standard and "scanning window"
regimes) and the wavelet-analysis. The obtained results are very similar. It is
found that in all series a strong cycle with mean duration of 55-60 years
exists. It is very well expressed in the 18th and the 19th centuries. It is
less pronounced during the end of the 19th and the beginning of the 20th
centuries. On the other hand a strong and stable quasi 110-120 years and
~200-year cycles are obtained in all of these series except in Ri. In the last
series a strong mean oscillation of ~ 95 years is found, which is absent in the
other data sets. The analysis of the ESAI (1090-2002 AD) proved that the quasi
century cycle has a relatively stable doublet (~80 and ~120 years) or triplet
(~55-60, 80 and 120 years) structure during the last ~900 years. An interesting
feature in all series is the existence of significant ~29-year cycle after the
last centurial Gleissberg-Gnevishev's minimum (1898-1923 AD). Most probably the
different types of oscillations in the sub-century and century period range
correspond to cycles of different classes of active regions.


  We extend the study of the iterated elimination of strictly dominated
strategies (IESDS) from Nash strategic games to a class of qualitative games.
Also in this case, the IESDS process leads us to a kind of 'rationalizable'
result. We define several types of dominance relation and game reduction and
establish conditions under which a unique and nonempty maximal reduction
exists. We generalize, in this way, some results due to Dufwenberg and Stegeman
(2002) and Apt (2007).


  A negative-phase-velocity condition derived by Depine and Lakhtakia
[Microwave Opt Technol Lett 41 (2004) 315] for isotropic, homogeneous, passive,
dielectric-magnetic materials is inapplicable as a negative-refraction
condition for active materials.


  $\newcommand{\dist}{\operatorname{dist}}$ In this paper we define the notion
of a probabilistic neighborhood in spatial data: Let a set $P$ of $n$ points in
$\mathbb{R}^d$, a query point $q \in \mathbb{R}^d$, a distance metric $\dist$,
and a monotonically decreasing function $f : \mathbb{R}^+ \rightarrow [0,1]$ be
given. Then a point $p \in P$ belongs to the probabilistic neighborhood $N(q,
f)$ of $q$ with respect to $f$ with probability $f(\dist(p,q))$. We envision
applications in facility location, sensor networks, and other scenarios where a
connection between two entities becomes less likely with increasing distance. A
straightforward query algorithm would determine a probabilistic neighborhood in
$\Theta(n\cdot d)$ time by probing each point in $P$.
  To answer the query in sublinear time for the planar case, we augment a
quadtree suitably and design a corresponding query algorithm. Our theoretical
analysis shows that -- for certain distributions of planar $P$ -- our algorithm
answers a query in $O((|N(q,f)| + \sqrt{n})\log n)$ time with high probability
(whp). This matches up to a logarithmic factor the cost induced by
quadtree-based algorithms for deterministic queries and is asymptotically
faster than the straightforward approach whenever $|N(q,f)| \in o(n / \log n)$.
  As practical proofs of concept we use two applications, one in the Euclidean
and one in the hyperbolic plane. In particular, our results yield the first
generator for random hyperbolic graphs with arbitrary temperatures in
subquadratic time. Moreover, our experimental data show the usefulness of our
algorithm even if the point distribution is unknown or not uniform: The running
time savings over the pairwise probing approach constitute at least one order
of magnitude already for a modest number of points and queries.


  The interference gating is a novel method for robust time-resolved electron
holographic measurements by directly switching the interference. Here, a new
arrangement is presented in which a biprism in the condenser aperture as a fast
electric phase shifter is used to control the interference pattern.
High-frequency stimulation of the electric phase shifter in the gigahertz range
are performed and observed via electron holography, proving the feasibility of
interference gating in the upper picosecond range. Despite the bandwidth
limitation of 180~MHz of the current signal generator, a time resolution of 100
nanoseconds is achieved through forward correction of the control signal. With
this time resolution, it is already possible to measure the transient response
of the biasing holder system. Our method paves the way towards a closer look on
fast dynamic processes with high temporal and spatial resolution.


  A numerical simulation of silica aerogels is performed using
diffusion-limited cluster-cluster aggregation of spheres inside a cubic box
(with periodic boundary conditions). The volume fraction $c$ is taken to be
sufficiently large to get a gel structure at the end of the process. In the
case of monodisperse spheres, the wavevector dependent scattered intensity
$I(q)$ is calculated from the product of the form factor $P(q)$ of a sphere by
the structure factor $S(q)$, which is related to the Fourier transform of
$g(r)-1$, where $g(r)$ is the pair correlation function between sphere centers.
The structure factor $S(q)$ exhibits large-$q$ damped oscillations
characteristics of the short range (intra-aggregate) correlations between
spheres. These oscillations influence the $I(q)$ curve in the $q$-region
between the fractal regime and the Porod regime and quantitative comparisons
are made with experiments on colloidal aerogels. Moreover, at small-$q$ values,
$S(q)$ goes through a maximum characteristic of large range (inter-aggregate)
correlations. Quantitative fits of the maximum in the experimental $I(q)$
curves of base-catalyzed aerogel are presented. In the case of polydisperse
spheres, $I(q)$ is calculated directly from a single aggregate simulation. It
is shown that increasing polydispersity shifts the location of the cross-over
between the fractal and Porod regimes towards low $q$-value.


  CLEVER (Cross-Lipschitz Extreme Value for nEtwork Robustness) is an Extreme
Value Theory (EVT) based robustness score for large-scale deep neural networks
(DNNs). In this paper, we propose two extensions on this robustness score.
First, we provide a new formal robustness guarantee for classifier functions
that are twice differentiable. We apply extreme value theory on the new formal
robustness guarantee and the estimated robustness is called second-order CLEVER
score. Second, we discuss how to handle gradient masking, a common defensive
technique, using CLEVER with Backward Pass Differentiable Approximation (BPDA).
With BPDA applied, CLEVER can evaluate the intrinsic robustness of neural
networks of a broader class -- networks with non-differentiable input
transformations. We demonstrate the effectiveness of CLEVER with BPDA in
experiments on a 121-layer Densenet model trained on the ImageNet dataset.


  We probe the effective worldvolume theory of a set of coinciding D-branes by
switching on constant electro-magnetic fields on them. The comparison of the
mass spectrum predicted by string theory with the mass spectrum obtained from
the effective action provides insights in the structure of the effective
theory.


  In this paper, we analyze the capacity of super-resolution of one-dimensional
positive sources. In particular, we consider the same setting as in
[arXiv:1904.09186v2 [math.NA]] and generalize the results there to the case of
super-resolving positive sources. To be more specific, we consider resolving
$d$ positive point sources with $p \leqslant d$ nodes closely spaced and
forming a cluster, while the rest of the nodes are well separated. Similarly to
[arXiv:1904.09186v2 [math.NA]], our results show that when the noise level
$\epsilon \lesssim \mathrm{SRF}^{-2 p+1}$, where $\mathrm{SRF}=(\Omega
\Delta)^{-1}$ with $\Omega$ being the cutoff frequency and $\Delta$ the minimal
separation between the nodes, the minimax error rate for reconstructing the
cluster nodes is of order $\frac{1}{\Omega} \mathrm{SRF}^{2 p-2} \epsilon$,
while for recovering the corresponding amplitudes $\left\{a_j\right\}$ the rate
is of order $\mathrm{SRF}^{2 p-1} \epsilon$. For the non-cluster nodes, the
corresponding minimax rates for the recovery of nodes and amplitudes are of
order $\frac{\epsilon}{\Omega}$ and $\epsilon$, respectively. Our numerical
experiments show that the Matrix Pencil method achieves the above optimal
bounds when resolving the positive sources.


  We consider the synthesis problem on timed automata with B\"uchi objectives,
where delay choices made by a controller are subjected to small perturbations.
Usually, the controller needs to avoid punctual guards, such as testing the
equality of a clock to a constant. In this work, we generalize to a robustness
setting that allows for punctual transitions in the automaton to be taken by
controller with no perturbation. In order to characterize cycles that resist
perturbations in our setting, we introduce a new structural requirement on the
reachability relation along an accepting cycle of the automaton. This property
is formulated on the region abstraction, and generalizes the existing
characterization of winning cycles in the absence of punctual guards. We show
that the problem remains within PSPACE despite the presence of punctual guards.


  Several kinds of quantum pushdown automaton models have been proposed, and
their computational power is investigated intensively. However, for some
quantum pushdown automaton models, it is not known whether quantum models are
at least as powerful as classical counterparts or not. This is due to the
reversibility restriction. In this paper, we introduce a new quantum pushdown
automaton model that has a garbage tape. This model can overcome the
reversibility restriction by exploiting the garbage tape to store popped
symbols. We show that the proposed model can simulate any quantum pushdown
automaton with a classical stack as well as any probabilistic pushdown
automaton. We also show that our model can solve a certain promise problem
exactly while deterministic pushdown automata cannot. These results imply that
our model is strictly more powerful than classical counterparts in the setting
of exact, one-sided error and non-deterministic computation.


  We study isometric actions of finitely presented groups on
$\mathbb{R}$-trees. In this paper, we develop a relative version of the Rips
machine to study $\textit{pairs}$ of such actions. An important example of a
$\textit{pair}$ is a group action on an $\mathbb{R}$-tree and a subgroup action
on its minimal invariant subtree.


  We found a necessary and sufficient condition for the existence of the tensor
product of modules over a vertex algebra. We defined the notion of vertex
bilinear map and we provide two algebraic construction of the tensor product,
where one of them is of ring theoretical type. We show the relation between the
tensor product and the vertex homomorphisms. We prove the commutativity of the
tensor product. We also prove the associativity of the tensor product of
modules under certain necessary and sufficient condition. Finally, we show
certain functorial properties of the vertex homomorphims and the tensor
product.


  This paper studies how the static non-linear electromagnetic-vacuum spacetime
of a point nucleus with negative bare mass affects the self-adjointness of the
general-relativistic Dirac Hamiltonian for a test electron, without and with an
anomalous magnetic moment.
  The study interpolates between the previously studied extreme cases of a test
electron in (a) the Reissner--Weyl--Nordstr\"om spacetime (Maxwell's
electromagnetic vacuum), which supports a very strong curvature singularity
with negative infinite bare mass, and (b) the Hoffmann spacetime (Born or
Born--Infeld's electromagnetic vacuum) with vanishing bare mass, which features
the mildest possible curvature singularity.
  The main conclusion reached is: {on electrostatic spacetimes of a point
nucleus with a strictly negative bare mass} (which may be $-\infty$) essential
self-adjointness fails unless the radial electric field diverges sufficiently
fast at the nucleus and the anomalous magnetic moment of the electron is taken
into account.
  Thus on the Hoffmann spacetime with (strictly) negative bare mass the Dirac
Hamiltonian of a test electron, with or without anomalous magnetic moment, is
not essentially self-adjoint.
  All these operators have self-adjoint extensions, though, with the usual
essential spectrum $(-\infty,-\mEL c^2]\cup[\mEL c^2,\infty)$ and an infinite
discrete spectrum located in the gap $(-\mEL c^2,\mEL c^2)$


  For integers $k,t \geq 2$ and $1\leq r \leq t$ let $D_k(r,t;n)$ be the number
of parts among all $k$-regular partitions (i.e., partitions of $n$ where all
parts have multiplicity less than $k$) of $n$ that are congruent to $r$ modulo
$t$. Using the circle method, we obtain the asymptotic
  \[
  D_{k}(r,t;n) = \frac{3^{\frac{1}{4}}e^{\pi\sqrt{\frac{2Kn}{3}}}}{\pi t
2^{\frac{3}{4}}K^{\frac{1}{4}}n^{\frac{1}{4}}\sqrt{k}}\left(\log k +
\left(\frac{3\sqrt{K}\log k}{8\sqrt{6}\pi} -
\frac{t\pi(k-1)K^{\frac{1}{2}}}{2\sqrt{6}}\left(\frac{r}{t}-
\frac{1}{2}\right)\right)n^{-\frac{1}{2}} + O(n^{-1})\right),
  \] where $K = 1 - \frac{1}{k}$. The main term of this asymptotic does not
depend on $r$, and so if $P_k(n)$ is the total number of parts among all
$k$-regular partitions of $n$, we have that $\frac{D_k(r,t;n)}{P_k(n)} \to
\frac{1}{t}$ as $n \to \infty$. Thus, in a weak asymptotic sense, the parts are
equidistributed among congruence classes. However, inspection of the lower
order terms indicates a bias towards the lower congruence classes; that is, for
$1\leq r < s \leq t$ we have $D_k(r,t;n) \geq D_k(s,t;n)$ for sufficiently
large $n$. We make this inequality explicit, showing that for $3 \leq k \leq
10$ and $2 \leq t \leq 10$ the inequality $D_k(r,t;n) \geq D_k(s,t;n)$ holds
for all $n \geq 1$ and the strict inequality $D_k(r,t;n) > D_k(s,t;n)$ holds
for all $n \geq 17$.


  We consider the problem, as suggested by Dembo ($2003$, $2006$), of late
points of a simple random walk in two dimensions. It has been shown that the
exponents for the numbers of pairs of late points coincide with those of nearly
favorite points and high points in the Gaussian free field, whose exact values
are known. We estimate the exponents for the numbers of a multipoint set of
late points in average. While there have been observed certain similarities
between among three classes of points, our results exhibit a difference.


  For an energetic jet propagating through a weakly-coupled quark-gluon plasma,
we present the physical picture of jet quenching in longitudinal phase-space,
as emerging from the interplay between the medium-induced, quasi-democratic,
branchings and the elastic collisions responsible for the thermalization of the
soft branching products.


  The paradigm shift in the electric power grid necessitates a revisit of
existing control methods to ensure the grid's security and resilience. In
particular, the increased uncertainties and rapidly changing operational
conditions in power systems have revealed outstanding issues in terms of either
speed, adaptiveness, or scalability of the existing control methods for power
systems. On the other hand, the availability of massive real-time data can
provide a clearer picture of what is happening in the grid. Recently, deep
reinforcement learning(RL) has been regarded and adopted as a promising
approach leveraging massive data for fast and adaptive grid control. However,
like most existing machine learning (ML)-basedcontrol techniques, RL control
usually cannot guarantee the safety of the systems under control. In this
paper, we introduce a novel method for safe RL-based load shedding of power
systems that can enhance the safe voltage recovery of the electric power grid
after experiencing faults. Numerical simulations on the 39-bus IEEE benchmark
is performed to demonstrate the effectiveness of the proposed safe RL emergency
control, as well as its adaptive capability to faults not seen in the training.


  We present some recent results on the analysis of hard scattering processes
in the framework of Generalized Parton Distributions. In particular we compute
DVCS observables on unpolarized targets with the Kroll - Goloskokov model
(suited to DVMP analysis). We also discuss NLO contributions to DVCS and TCS
processes for various kinematic settings.


  We consider the finite-volume spectra of QCD in the chiral limit of massless
up and down quarks and massive strange quarks in the baryon number sectors $B =
0$ and $B = 1$ for different values of the isospin. Spontaneous symmetry
breaking gives rise to rotor spectra, as the chiral order parameter precesses
through the vacuum manifold. Baryons of different isospin influence the motion
of the order parameter through non-trivial Berry phases and associated abstract
monopole fields. Our investigation provides detailed insights into the dynamics
of spontaneous chiral symmetry breaking in QCD on a torus. It also sheds new
light on Berry phases in the context of quantum field theory. Interestingly,
the Berry gauge field resulting from QCD solves a Yang-Mills-Chern-Simons
equation of motion on the vacuum manifold $SU(2) = S^3$.


  Anomaly detection is critical in the smart industry for preventing equipment
failure, reducing downtime, and improving safety. Internet of Things (IoT) has
enabled the collection of large volumes of data from industrial machinery,
providing a rich source of information for Anomaly Detection. However, the
volume and complexity of data generated by the Internet of Things ecosystems
make it difficult for humans to detect anomalies manually. Machine learning
(ML) algorithms can automate anomaly detection in industrial machinery by
analyzing generated data. Besides, each technique has specific strengths and
weaknesses based on the data nature and its corresponding systems. However, the
current systematic mapping studies on Anomaly Detection primarily focus on
addressing network and cybersecurity-related problems, with limited attention
given to the industrial sector. Additionally, these studies do not cover the
challenges involved in using ML for Anomaly Detection in industrial machinery
within the context of the IoT ecosystems. This paper presents a systematic
mapping study on Anomaly Detection for industrial machinery using IoT devices
and ML algorithms to address this gap. The study comprehensively evaluates 84
relevant studies spanning from 2016 to 2023, providing an extensive review of
Anomaly Detection research. Our findings identify the most commonly used
algorithms, preprocessing techniques, and sensor types. Additionally, this
review identifies application areas and points to future challenges and
research opportunities.


  An important result in core-collapse supernova (CCSN) theory is that
spherically-symmetric, one-dimensional simulations routinely fail to explode,
yet multi-dimensional simulations often explode. Numerical investigations
suggest that turbulence eases the condition for explosion, but how is not fully
understood. We develop a turbulence model for neutrino-driven convection, and
show that this turbulence model reduces the condition for explosions by about
30%, in concordance with multi-dimensional simulations. In addition, we
identify which turbulent terms enable explosions. Contrary to prior
suggestions, turbulent ram pressure is not the dominant factor in reducing the
condition for explosion. Instead, there are many contributing factors, ram
pressure being only one of them, but the dominant factor is turbulent
dissipation (TD). Primarily, TD provides extra heating, adding significant
thermal pressure, and reducing the condition for explosion. The source of this
TD power is turbulent kinetic energy, which ultimately derives its energy from
the higher potential of an unstable convective profile. Investigating a
turbulence model in conjunction with an explosion condition enables insight
that is difficult to glean from merely analyzing complex multi-dimensional
simulations. An explosion condition presents a clear diagnostic to explain why
stars explode, and the turbulence model allows us to explore how turbulence
enables explosion. Though we find that turbulent dissipation is a significant
contributor to successful supernova explosions, it is important to note that
this work is to some extent qualitative. Therefore, we suggest ways to further
verify and validate our predictions with multi-dimensional simulations.


  According to quantum theory, measurements generate random outcomes, in stark
contrast with classical mechanics. This raises the question of whether there
could exist an extension of the theory which removes this indeterminism, as
suspected by Einstein, Podolsky and Rosen (EPR). Although this has been shown
to be impossible, existing results do not imply that the current theory is
maximally informative. Here we ask the more general question of whether any
improved predictions can be achieved by any extension of quantum theory. Under
the assumption that measurements can be chosen freely, we answer this question
in the negative: no extension of quantum theory can give more information about
the outcomes of future measurements than quantum theory itself. Our result has
significance for the foundations of quantum mechanics, as well as applications
to tasks that exploit the inherent randomness in quantum theory, such as
quantum cryptography.


  We consider a series of Mott insulators in unit of two orbitals each hosting
spin-1/2 electron, and by pairing two spin-1/2 into spin-1 triplet, derive the
effective exchange interaction between the adjacent units via fourth order
perturbation theory. It turns out that the biquadratic exchange interaction
between spin-1, which is one of the origins of the nematic order, arises only
in processes where the four different electrons exchange cyclically along the
twisted loop, which we call "twisted ring exchange" processes. We show that the
term becomes the same order with the Heisenberg exchange interactions when the
on-orbital Coulomb interaction is not too large. Whereas, the inter-orbital
Coulomb interactions give rise to additional processes that cancel the twisted
ring exchange, and strongly suppresses the biquadratic term. The Mott insulator
with two electrons on degenerate two orbitals is thus not an ideal platform to
study such nematic orders.


  We report the first detection of thermal water vapor emission in the 557 GHz,
$1_{10} - 1_{01}$ ground state transition of ortho-H$_2$O toward VY Canis
Majoris. In observations obtained with the Submillimeter Wave Astronomy
Satellite (SWAS), we measured a flux of $\sim 450 $Jy, in a spectrally resolved
line centered on a velocity $v_{LSR} = 25 $km s$^{-1}$ with a full width half
maximum of $\sim 35$ km s$^{-1}$, somewhat dependent on the assumed line shape.
We analyze the line shape in the context of three different radial outflow
models for which we provide analytical expressions. We also detected a weaker
557 GHz emission line from W Hydrae. We find that these and other H$_2$O
emission line strengths scale as suggested by Zubko and Elitzur (2000).


  We have succeeded in growing very high purity (99.995%) YBa_2Cu_3O_{7-delta}
crystals in BaZrO_3 crucibles and have measured Delta-lambda(T) and R_s(T) at 1
GHz in crystals with various oxygen treatments. For an oxygen vacancy level of
delta=0.007, Delta-lambda and R_s essentially reproduce our previous results
and show no sign of the existence of the two order parameter components as
recently reported by Srikanth et al. on BaZrO_3-grown crystals. For other
oxygen concentrations, we have in some cases observed deviations from the
linear low T dependence of Delta-lambda, but never any sign of a second
transition.


  The existence of a neutrino magnetic moment implies contributions to the
neutrino mass via radiative corrections. We derive model-independent
"naturalness" upper bounds on the magnetic moments of Dirac and Majorana
neutrinos, generated by physics above the electroweak scale. For Dirac
neutrinos, the bound is several orders of magnitude more stringent than present
experimental limits. However, for Majorana neutrinos the magnetic moment bounds
are weaker than present experimental limits if $\mu_\nu$ is generated by new
physics at ~ 1 TeV, and surpass current experimental sensitivity only for new
physics scales > 10 -- 100 TeV. The discovery of a neutrino magnetic moment
near present limits would thus signify that neutrinos are Majorana particles.


  In this work, we develop a fully implicit Hybrid High-Order algorithm for the
Cahn-Hilliard problem in mixed form. The space discretization hinges on local
reconstruction operators from hybrid polynomial unknowns at elements and faces.
The proposed method has several assets: (i) It supports fairly general meshes
possibly containing polygonal elements and nonmatching interfaces, (ii) it
allows arbitrary approximation orders, (iii) it has a moderate computational
cost thanks to the possibility of locally eliminating element-based unknowns by
static condensation. We perform a detailed stability and convergence study,
proving optimal convergence rates in energy-like norms. Numerical validation is
also provided using some of the most common tests in the literature.


  Self-renewal is a constitutive property of stem cells. Testing the cancer
stem cell hypothesis requires investigation of the impact of self-renewal on
cancer expansion. To understand better this impact, we propose a mathematical
model describing dynamics of a continuum of cell clones structured by the
self-renewal potential. The model is an extension of the finite
multi-compartment models of interactions between normal and cancer cells in
acute leukemias. It takes a form of a system of integro-differential equations
with a nonlinear and nonlocal coupling, which describes regulatory feedback
loops in cell proliferation and differentiation process. We show that such
coupling leads to mass concentration in points corresponding to maximum of the
self-renewal potential and the model solutions tend asymptotically to a linear
combination of Dirac measures. Furthermore, using a Lyapunov function
constructed for a finite dimensional counterpart of the model, we prove that
the total mass of the solution converges to a globally stable equilibrium.
Additionally, we show stability of the model in space of positive Radon
measures equipped with flat metric. The analytical results are illustrated by
numerical simulations.


  Infrared quadrupole modes (IRQM) of the valence electrons in light deformed
sodium clusters are studied by means of the time-dependent local-density
approximation (TDLDA). IRQM are classified by angular momentum components
$\lambda\mu =$20, 21 and 22 whose $\mu$ branches are separated by cluster
deformation. In light clusters with a low spectral density, IRQM are
unambiguously related to specific electron-hole excitations, thus giving access
to the single-electron spectrum near the Fermi surface (HOMO-LUMO region). Most
of IRQM are determined by cluster deformation and so can serve as a sensitive
probe of the deformation effects in the mean field. The IRQM branch $\lambda\mu
=$21 is coupled with the magnetic scissors mode, which gives a chance to detect
the latter. We discuss two-photon processes, Raman scattering (RS), stimulated
emission pumping (SEP), and stimulated adiabatic Raman passage (STIRAP), as the
relevant tools to observe IRQM. A new method to detect the IRQM population in
clusters is proposed.


  Two dimensional hydrodynamical disks are nonlinearly unstable to the
formation of vortices. Once formed, these vortices essentially survive forever.
What happens in three dimensions? We show with pseudospectral simulations that
in 3D a vortex in a short box forms and survives just as in 2D. But a vortex in
a tall box is unstable and is destroyed. In our simulation, the unstable vortex
decays into a transient turbulent-like state that transports angular momentum
outward at a nearly constant rate for hundreds of orbital times. The 3D
instability that destroys vortices is a generalization of the 2D instability
that forms them. We derive the conditions for these nonlinear instabilities to
act by calculating the coupling between linear modes, and thereby derive the
criterion for a vortex to survive in 3D as it does in 2D: the azimuthal extent
of the vortex must be larger than the scale height of the accretion disk. When
this criterion is violated, the vortex is unstable and decays. Because vortices
are longer in azimuthal than in radial extent by a factor that is inversely
proportional to their excess vorticity, a vortex with given radial extent will
only survive in a 3D disk if it is sufficiently weak. This counterintuitive
result explains why previous 3D simulations always yielded decaying vortices:
their vortices were too strong. We conclude that in protoplanetary disks weak
vortices can trap dust and serve as the nurseries of planet formation. Decaying
strong vortices might be responsible for the outwards transport of angular
momentum that is required to make accretion disks accrete.


  In this work we study the properties of the atomic entanglement in the
eigenstates spectrum of the inhomogeneous Tavis-Cummings Model. The
inhomogeneity is present in the coupling among the atoms with quantum
electromagnetic field. We calculate analytical expressions for the concurrence
and we found that this exhibits a strong dependence on the inhomogeneity.


  We study the mixed-state entanglement structure of chaotic quantum many-body
systems at late times using the recently developed $\textit{equilibrium
approximation}$. A rich entanglement phase diagram emerges when we generalize
this technique to evaluate the logarithmic negativity for various universality
classes of macroscopically thermalized states. Unlike in the infinite
temperature case, when we impose energy constraints at finite temperature, the
phase diagrams for the logarithmic negativity and the mutual information become
distinct. In particular, we identify a regime where the negativity is extensive
but the mutual information is sub-extensive, indicating a large amount of
$\textit{bound entanglement}$. When applied to evaporating black holes, these
results imply that there is quantum entanglement within the Hawking radiation
long before the Page time, although this entanglement may not be distillable
into EPR pairs.


  The aim of this paper is to address the effect of the carbon emission
allowance market on the production policy of a large polluter production firm.
We investigate this effect in two cases; when the large polluter cannot affect
the risk premium of the allowance market, and when it can change the risk
premium by its production. In this simple model, we ignore any possible
investment of the firm in pollution reducing technologies. We formulate the
problem of optimal production by a stochastic optimization problem. Then, we
show that, as expected, the market reduces the optimal production policy in the
first case if the firm is not given a generous initial cheap allowance package.
However, when the large producer activities can change the market risk premium,
the cut on the production and consequently pollution cannot be guaranteed. In
fact, there are cases in this model when the optimal production is {\it always}
larger than expected, and an increase in production, and thus pollution, can
increase the profit of the firm. We conclude that some of the parameters of the
market which contribute to this effect can be wisely controlled by the
regulators in order to diminish this manipulative behavior of the firm.


  We compute the eigenvalue fluctuations of uniformly distributed random
biregular bipartite graphs with fixed and growing degrees for a large class of
analytic functions. As a key step in the proof, we obtain a total variation
distance bound for the Poisson approximation of the number of cycles and
cyclically non-backtracking walks in random biregular bipartite graphs, which
might be of independent interest. We also prove a semicircle law for random
$(d_1,d_2)$-biregular bipartite graphs when $\frac{d_1}{d_2}\to\infty$. As an
application, we translate the results to adjacency matrices of uniformly
distributed random regular hypergraphs.


  We propose a Bayesian evidence framework to facilitate transfer learning from
pre-trained deep convolutional neural networks (CNNs). Our framework is
formulated on top of a least squares SVM (LS-SVM) classifier, which is simple
and fast in both training and testing, and achieves competitive performance in
practice. The regularization parameters in LS-SVM is estimated automatically
without grid search and cross-validation by maximizing evidence, which is a
useful measure to select the best performing CNN out of multiple candidates for
transfer learning; the evidence is optimized efficiently by employing Aitken's
delta-squared process, which accelerates convergence of fixed point update. The
proposed Bayesian evidence framework also provides a good solution to identify
the best ensemble of heterogeneous CNNs through a greedy algorithm. Our
Bayesian evidence framework for transfer learning is tested on 12 visual
recognition datasets and illustrates the state-of-the-art performance
consistently in terms of prediction accuracy and modeling efficiency.


  A geometric generalization of contraction theory called~$k$-contraction was
recently developed using $k$-compound matrices. In this note, we focus on the
relations between $k$-contraction and two other generalized contraction
frameworks: partial contraction (also known as virtual contraction) and
horizontal contraction. We show that in general these three notions of
contraction are different. We here provide new sufficient conditions
guaranteeing that partial contraction implies horizontal contraction, and that
horizontal contraction implies $k$-contraction. We use the Andronov-Hopf
oscillator to demonstrate some of the theoretical results.


  Charge density waves (CDW) are modulations of the electron density and the
atomic lattice that develop in some crystalline materials at low temperature.
We report an unusual example of a CDW in BaFe$_2$Al$_9$ below 100 K. In
contrast to the canonical CDW phase transition, temperature dependent physical
properties of single crystals reveal a first-order phase transition. This is
accompanied by a discontinuous change in the size of the crystal lattice. In
fact, this large strain has catastrophic consequences for the crystals causing
them to physically shatter. Single crystal x-ray diffraction reveals
super-lattice peaks in the low-temperature phase signaling the development of a
CDW lattice modulation. No similar low-temperature transitions are observed in
BaCo$_2$Al$_9$. Electronic structure calculations provide one hint to the
different behavior of these two compounds; the d-orbital states in the Fe
compound are not completely filled. Iron compounds are renowned for their
magnetism and partly filled d-states play a key role. It is therefore
surprising that BaFe$_2$Al$_9$ develops a structural modulation instead at low
temperature instead of magnetic order.


  We extend on ideas from standard thermodynamics to show that temperature can
be assigned to a general nonequilibrium quantum system. By choosing a
physically motivated complete set of observables and expanding the system state
thereupon, one can read a set of relevant, independent thermodynamic variables
which include internal energy. This expansion allows us to read a
nonequilibrium temperature as the partial derivative of the von Neumann entropy
with respect to internal energy. We show that this definition of temperature is
one of a set of thermodynamics parameters unambiguously describing the system
state. It has appealing features such as positivity for passive states and
consistency with the standard temperature for thermal states. By attributing
temperature to correlations in a bipartite system, we obtain a universal
relation which connects the temperatures of subsystems, total system as a
whole, and correlation. All these temperatures can be different even when the
composite system is in a well-defined Gibbsian thermal state.


  Localization is a fundamental task in robotics for autonomous navigation.
Existing localization methods rely on a single input data modality or train
several computational models to process different modalities. This leads to
stringent computational requirements and sub-optimal results that fail to
capitalize on the complementary information in other data streams. This paper
proposes UnLoc, a novel unified neural modeling approach for localization with
multi-sensor input in all weather conditions. Our multi-stream network can
handle LiDAR, Camera and RADAR inputs for localization on demand, i.e., it can
work with one or more input sensors, making it robust to sensor failure. UnLoc
uses 3D sparse convolutions and cylindrical partitioning of the space to
process LiDAR frames and implements ResNet blocks with a slot attention-based
feature filtering module for the Radar and image modalities. We introduce a
unique learnable modality encoding scheme to distinguish between the input
sensor data. Our method is extensively evaluated on Oxford Radar RobotCar,
ApolloSouthBay and Perth-WA datasets. The results ascertain the efficacy of our
technique.


  Limiting fragmentation in proton-proton, deuteron-nucleus and nucleus-nucleus
collisions is analyzed in the framework of the Balitsky-Kovchegov equation in
high energy QCD. Good agreement with experimental data is obtained for a wide
range of energies. Further detailed tests of limiting fragmentation at RHIC and
the LHC will provide insight into the evolution equations for high energy QCD.


  It had been a long standing problem that there is no consistent definition of
photon position operator nor photon number density in the context of quantum
theory. In this paper we derive the photon detection operator, which defines
location of photon absorption, by applying the theory of indirect measurement
to quantum electrodynamics. It is shown that the photon detection probability
depends on electric properties of a photon-absorbing atom, in particular, on
both electric and magnetic dipole moments of the atom. An experiment is
proposed, in which the complementarity of wave-particle nature of light will be
tested. It is also discussed that the complementarity is related to the
non-commutativity of the electric and the magnetic fields.


  We examine the X-ray spectral and temporal behavior of the Galactic black
hole candidate source GRS 1915+105 during its spectral state transition
observed in 1997 March - August. The source was making a slow transition from a
low-hard state to a high-soft state in about three months and during this
transition it was exhibiting a series of fast variations which can be
classified as bursts. During one type of bursts, called the irregular bursts,
it was found that the source makes rapid transitions between two intensity
states. We have analyzed the RXTE PCA data obtained on 1997 June 18 (when the
source was making rapid state transitions) and compared the results with two
sets of data each pertaining to the low hard-state and high-soft states. We
find that the power density spectrum (PDS) during the burst shows remarkable
similarity to that seen during the high-soft state of the source. The PDS
during the quiescence, on the other hand, is quite flat and is very similar to
the PDS commonly seen during the canonical low-hard state of black hole X-ray
binaries. A low frequency QPO at $\sim$3 Hz is observed during the quiescence,
a property seen during the low-hard state of the source. The X-ray spectrum of
the source during quiescence is similar to the spectrum seen during the
low-hard state of the source and the spectra during the burst and high-soft
state are very similar to each other. These observations corroborate the
suggestion made by Yadav et al. (1999) that during the irregular bursts the
source shows spectral state variations at very fast time scales. We explain
such fast state changes using the two component accretion flow model in which
the accretion disk consists of a geometrically thin (and optically thick)
standard disk co-existing with an advection dominated hot thick disk.