  The work that consists of two parts is devoted to the problem of enumerating
unrooted $r$-regular maps on the torus up to all its symmetries. We begin with
enumerating near-$r$-regular rooted maps on the torus, projective plane and the
Klein bottle. We also present the results of enumerating some special kinds of
maps on the sphere: near-$r$-regular maps, maps with multiple leaves and maps
with multiple root semi-edges. For $r=3$ and $r=4$ we obtain exact analytical
formulas. For larger $r$ we derive recurrence relations. Then using these
results we enumerate $r$-regular maps on the torus up to homeomorphisms that
preserve its orientation --- so-called sensed maps. Using the concept of a
quotient map on an orbifold we reduce this problem to enumeration of certain
classes of rooted maps. For $r=3$ and $r=4$ we obtain closed-form expressions
for the numbers of $r$-regular sensed maps by edges. All these results will be
used in the second part of the work to enumerate $r$-regular maps on the torus
up to all homeomorphisms --- so-called unsensed maps.


  In this paper we investigate a parametric resonance phenomenon of a
Kaluza-Klein mode in a $D$-dimensional generalized Kaluza-Klein theory. As the
origin of the parametric resonance we consider a small oscillation of a scale
of the compactification around a today's value of it. To make our arguments
definite and for simplicity we consider two classes of models of the
compactification: those by $S_{d}$ ($d=D-4$) and those by $S_{d_{1}}\times
S_{d_{2}}$ ($d_1\ge d_2$, $d_{1}+d_{2}=D-4$). For these models we show that
parametric resonance can occur for the Kaluza-Klein mode. After that, we give
formulas of a creation rate and a number of created quanta of the Kaluza-Klein
mode due to the parametric resonance, taking into account the first and the
second resonance band. By using the formulas we calculate those quantities for
each model of the compactification. Finally we give conditions for the
parametric resonance to be efficient and discuss cosmological implications.


  We explain how the 't Hooft expansion of correlators of half-BPS operators
can be resummed in a large-charge limit in N=4 super Yang-Mills theory. The
full correlator in the limit is given by a non-trivial function of two
variables: One variable is the charge of the BPS operators divided by the
square root of the number Nc of colors; the other variable is the octagon that
contains all the 't Hooft coupling and spacetime dependence. At each genus g in
the large Nc expansion, this function is a polynomial of degree 2g+2 in the
octagon. We find several dual matrix model representations of the correlators
in the large-charge limit. Amusingly, the number of colors in these matrix
models is formally taken to zero in the relevant limit.


  The scrape-off layer parallel heat flux decay lengths measured at ST40, a
high field, low aspect ratio spherical tokamak, have been observed to bifurcate
into two groups. The wide group matches closely with the scale of ion poloidal
Larmour radius and follows existing H-mode scalings, while the narrow group
falls up to 10 times below scalings, on the scale of ion total Larmour radius.
The onset of the narrow scrape-off layer width is observed to be associated
with suppressed magnetic fluctuations, suggesting reduced electromagnetic
turbulence levels in the SOL.


  This paper presents \proverb\, a text planner for argumentative texts.
\proverb\'s main feature is that it combines global hierarchical planning and
unplanned organization of text with respect to local derivation relations in a
complementary way. The former splits the task of presenting a particular proof
into subtasks of presenting subproofs. The latter simulates how the next
intermediate conclusion to be presented is chosen under the guidance of the
local focus.


  In this paper, we review the question of which action space is best suited
for controlling a real biped robot in combination with Sim2Real training.
Position control has been popular as it has been shown to be more sample
efficient and intuitive to combine with other planning algorithms. However, for
position control gain tuning is required to achieve the best possible policy
performance. We show that instead, using a torque-based action space enables
task-and-robot agnostic learning with less parameter tuning and mitigates the
sim-to-reality gap by taking advantage of torque control's inherent compliance.
Also, we accelerate the torque-based-policy training process by pre-training
the policy to remain upright by compensating for gravity. The paper showcases
the first successful sim-to-real transfer of a torque-based deep reinforcement
learning policy on a real human-sized biped robot. The video is available at
https://youtu.be/CR6pTS39VRE.


  We study electron correlations and their impact on magnetic properties of bcc
vanadium by a combination of density functional and dynamical mean-field
theory. The calculated uniform magnetic susceptibility {in bcc structure} is of
Pauli type at low temperatures, while it obeys the Curie-Weiss law at higher
temperatures. Thus, we qualitatively reproduce the experimental temperature
dependence of magnetic susceptibility without introducing the martensitic phase
transition. Our results for local spin-spin correlation function and local
susceptibility reveal that the Curie-Weiss behavior appears due to partial
formation of local magnetic moments, which originate from $t_{2g}$ states and
occur due to local spin correlations caused by Hund's rule coupling. At the
same time, the fermionic quasiparticles remain well-defined, while the
formation of local moments is accompanied by a deviation from the Fermi-liquid
behavior. In particular, the self-energy of the $t_{2g}$ states shows the
non-analytic frequency dependence, which is a characteristic of the
spin-freezing behavior, while the quasiparticle damping changes approximately
linearly with temperature in the intermediate temperature range $200$--$700$~K.
By analyzing the momentum dependence of static magnetic susceptibility, we find
incommensurate magnetic correlations, which may provide a mechanism for
unconventional superconductivity at low temperatures.


  We consider the problem of evacuating $k \geq 2$ mobile agents from a
unit-sided equilateral triangle through an exit located at an unknown location
on the perimeter of the triangle. The agents are initially located at the
centroid of the triangle and they can communicate with other agents at distance
at most $r$ with $0\leq r \leq 1$. An agent can move at speed at most one, and
finds the exit only when it reaches the point where the exit is located. The
agents can collaborate in the search for the exit. The goal of the {\em
evacuation problem} is to minimize the evacuation time, defined as the
worst-case time for {\em all} the agents to reach the exit. We propose and
analyze several algorithms for the problem of evacuation by $k \geq 2$ agents;
our results indicate that the best strategy to be used varies depending on the
values of $r$ and $k$. For two agents, we give three algorithms, each of which
achieves the best performance for different sub-ranges of $r$ in the range $0
\leq r \leq 1$. Finally, we show that for any $r$, evacuation of $k=6
+2\lceil(\frac{1}{r}-1)\rceil$ agents can be done in time $1+\sqrt{3}/3$, which
is optimal in terms of time, and asymptotically optimal in terms of the number
of agents.


  A toy top is defined as a rotationally symmetric body moving in a constant
gravitational field while one point on the symmetry axis is constrained to stay
in a horizontal plane. It is an integrable system similar to the Lagrange top.
Euler-Poisson equations are derived. Following Felix Klein, the special unitary
group $\rm SU(2)$ is used as configuration space and the solution is given in
terms of hyperelliptic integrals. The curve traced by the point moving in the
horizontal plane is analyzed, and a qualitative classification is achieved. The
cases in which the hyperelliptic integrals degenerate to elliptic ones are
found and the corresponding solutions are given in terms of Weierstrass
elliptic functions.


  AGB stars are major contributors to the chemical enrichment of the ISM
through nucleosynthesis and extensive mass loss. Most of our current knowledge
of AGB atmospheric and circumstellar chemistry, in particular in a C-rich
environment, is based on observations of the carbon star IRC+10216. We aim to
obtain a more generalised understanding of the chemistry in C-rich AGB CSEs by
studying a sample of three carbon stars, IRAS15194-5115, IRAS15082-4808, and
IRAS07454-7112, and test the archetypal status often attributed to IRC+10216.
We performed spatially resolved, unbiased spectral surveys in ALMA Band 3. We
identify a total of 132 rotational transitions from 49 molecular species. There
are two main morphologies of the brightness distributions: centrally-peaked
(e.g. HCN) and shell-like (e.g. C$_2$H). We estimated the sizes of the
molecular emitting regions using azimuthally-averaged radial profiles of the
line brightness distributions, and derived abundance estimates. Of the shell
distributions, the cyanopolyynes peak at slightly smaller radii than the
hydrocarbons, and CN and HNC show the most extended emission. The emitting
regions for each species are the smallest for IRAS07454-7112. We find that,
within the uncertainties of the analysis, the three stars present similar
abundances for most species, also compared to IRC+10216. We find that SiO is
more abundant in our three stars compared to IRC+10216. Our estimated isotopic
ratios match well the literature values for the sources. The observed
circumstellar chemistry appears very similar across our sample and compared to
that of IRC+10216, both in terms of the relative location of the emitting
regions and molecular abundances. This implies that, to a first approximation,
the chemical models tailored to IRC+10216 are able to reproduce the observed
chemistry in C-rich envelopes across roughly an order of magnitude in wind
density.


  Using the tight binding model and the non-equilibrium Green function method,
we study Andreev reflection in graphene-superconductor junction, where graphene
has two nonequal Dirac Cones split in energy and therefore time reversal
symmetry is broken. Due to the anti-chiral edge states of the current graphene
model, an incident electron travelling along the edges makes distinct
contribution to Andreev reflections. In a two-terminal device, because Andreev
retro-reflection is not allowed for just the anti-chiral edges, in this case
the mutual scattering between edge and bulk states is necessary, which leads
that the coefficient of Andreev retro-reflection is always symmetrical about
the incident energy. In a four-terminal junction, however, the edges are
parallel to the interface of superconductor and graphene, so at the interface
an incident electron travelling along the edges can be retro-reflected as a
hole into bulk modes, or specularly reflected as a hole into anti-chiral edge
states again. It is noted that, the coefficient of specular Andreev reflection
keeps symmetric as to the incident energy of electron which is consistent with
the reported results before, however the coefficient of Andreev
retro-reflection shows an unexpected asymmetrical behavior due to the presence
of anti-chiral edge states. Our results present some new ideas to study the
anti-chiral edge modes and Andreev reflection for a graphene model with the
broken time reversal symmetry.


  We give a proof of Lehoczky's drawdown formula for one-dimensional diffusion
processes, using the Poisson structure of the excursions of the diffusion below
its running maximum.


  We calculate the interaction potential between N atoms and NH molecules and
use it to investigate cold and ultracold collisions important for sympathetic
cooling. The ratio of elastic to inelastic cross sections is large over a wide
range of collision energy and magnetic field for most isotopic combinations, so
that sympathetic cooling of NH molecules by N atoms is a good prospect.
However, there are important effects due to a p-wave shape resonance that may
inhibit cooling in some cases. We show that scaling the reduced mass used in
the collision is approximately equivalent to scaling the interaction potential.
We then explore the dependence of the scattering properties on the reduced mass
and explain the resonant effects observed using angular-momentum-insensitive
quantum defect theory


  We consider the problem of building numerically stable algorithms for
computing Discrete Fourier Transform (DFT) of $N$- length signals with known
frequency support of size $k$. A typical algorithm, in this case, would involve
solving (possibly poorly conditioned) system of equations, causing numerical
instability. When $N$ is a power of 2, and the frequency support is a random
subset of $\mathbb{Z}_N$, we provide an algorithm that has (a possibly optimal)
$O(k \log k)$ complexity to compute the DFT while solving system of equations
that are $O(1)$ in size.


  We present a search for HI in the circumgalactic medium (CGM) of 21 massive
($\langle \log M_\star \rangle \sim 11.4$), luminous red galaxies (LRGs) at
$z\sim0.5$. Using UV spectroscopy of QSO sightlines projected within 500 kpc
($\sim R_{vir}$) of these galaxies, we detect HI absorption in 11/21
sightlines, including two partial Lyman limit systems and two Lyman limit
systems. The covering factor of $\log N(HI) \ge 16.0$ gas within the virial
radius of these LRGs is $f_c(\rho \le R_{vir}) = 0.27^{+0.11}_{-0.10}$, while
for optically-thick gas ($\log N(HI) \ge 17.2$) it is $f_c(\rho \le R_{vir}) =
0.15^{+0.10}_{-0.07}$. Combining this sample of massive galaxies with previous
galaxy-selected CGM studies, we find no strong dependence of the HI covering
factor on galaxy mass, although star-forming galaxies show marginally higher
covering factors. There is no evidence for a critical mass above which dense,
cold ($T \sim 10^4$ K) gas is suppressed in the CGM of galaxies (spanning
stellar masses $9.5 \lesssim \log M_\star \lesssim 11.8$). The metallicity
distribution in LRGs is indistinguishable from those found about lower-mass
star-forming galaxies, and we find low-metallicity gas with $[{\rm X/H}]
\approx -1.8$ (1.5% solar) and below about massive galaxies. About half the
cases show super-solar [FeII/MgII] abundances as seen previously in cool gas
near massive galaxies. While the high-metallicity cold gas seen in LRGs could
plausibly result from condensation from a corona, the low-metallicity gas is
inconsistent with this interpretation.


  A delayed feedback control framework for stabilizing unstable periodic orbits
of linear periodic time-varying systems is proposed. In this framework,
act-and-wait approach is utilized for switching a delayed feedback controller
on and off alternately at every integer multiples of the period of the system.
By analyzing the monodromy matrix of the closed-loop system, we obtain
conditions under which the closed-loop system's state converges towards a
periodic solution under our proposed control law. We discuss the application of
our results in stabilization of unstable periodic orbits of nonlinear systems
and present numerical examples to illustrate the efficacy of our approach.


  We classify germs at the origin of real analytic Lorentz metrics on R^3 which
are quasihomogeneous, in the sense that they are locally homogeneous on an open
set containing the origin in its closure, but not locally homogeneous in the
neighborhood of the origin.


  The ratio of pulsation to radial velocity (the projection factor) is
currently limiting the accuracy of the interferometric Baade-Wesselink method.
This work aims at establishing a link between the line asymmetry evolution over
the Cepheids' pulsation cycles and their projection factor, with the final
objective to improve the accuracy of the Baade-Wesselink method for distance
determinations. We present HARPS high spectral resolution observations of nine
galactic Cepheids having a good period sampling. We fit spectral line profiles
by an asymmetric bi-Gaussian to derive radial velocity, Full-Width at
Half-Maximum in the line (FWHM) and line asymmetry for all stars. We then
extract correlations curves between radial velocity and asymmetry. A geometric
model providing synthetic spectral lines, including limb-darkening, a constant
FWHM (hereafter sigma_c) and the rotation velocity is used to interpret these
correlations curves. For all stars, comparison between observations and
modelling is satisfactory, and we were able to determine the projected rotation
velocities and sigma_c for all stars. We also find a correlation between the
rotation velocity (Vrot sin i) and the period of the star: Vrot sin i = (11.5
+- 0.9) log(P) + (19.8 +- 1.0) [km/s]. Moreover, we observe a systematic shift
in observational asymmetry curves (noted gamma_O), related to the period of the
star, which is not explained by our static model: gamma_O = (10.7+-0.1) log(P)
+ (9.7+-0.2) [in %] . For long-period Cepheids, in which velocity gradients,
compression or shock waves seem to be large compared to short- or medium period
Cepheids we observe indeed a greater systematic shift in asymmetry curves.
(abridged)


  In the industry, blockchains are increasingly used as the backbone of product
and process traceability. Blockchain-based traceability participates in the
demonstration of product and/or process compliance with existing safety
standards or quality criteria. In this perspective, services and applications
built on top of blockchains are business-critical applications, because an
intended failure or corruption of the system can lead to an important
reputation loss regarding the products or the processes involved. The
development of a blockchain-based business-critical application must be then
conducted carefully, requiring a thorough justification of its dependability
and security. To this end, this paper encourages an engineering perspective
rooted in well-understood tools and concepts borrowed from the engineering of
safety-critical systems. Concretely, we use a justification framework, called
CAE (Claim, Argument, Evidence), by following an approach based on assurance
cases, in order to provide convincing arguments that a business-critical
blockchain-based application is dependable and secure. The application of this
approach is sketched with a case study based on the blockchain HYPERLEDGER
FABRIC.


  $\eta_c$-nucleus bound state energies are calculated for various nuclei.
Essential input for the calculations, namely the medium-modified $D$ and
$D^{*}$ meson masses, as well as the density distributions in nuclei, are
calculated within the quark-meson coupling (QMC) model. The attractive
potentials for the $\eta_c$ meson in the nuclear medium originate from the
in-medium enhanced $DD^{*}$ loops in the $\eta_c$ self-energy. Our results
suggest that the $\eta_c$ meson should form bound states with all the nuclei
considered.


  Aspects of Scalar Meson Dominance in semi- and non-leptonic weak pseudoscalar
meson decays are shortly discussed on the basis of the Quark-Level Linear Sigma
Model.


  Time series classification is an application of particular interest with the
increase of data to monitor. Classical techniques for time series
classification rely on point-to-point distances. Recently, Bag-of-Words
approaches have been used in this context. Words are quantized versions of
simple features extracted from sliding windows. The SIFT framework has proved
efficient for image classification. In this paper, we design a time series
classification scheme that builds on the SIFT framework adapted to time series
to feed a Bag-of-Words. We then refine our method by studying the impact of
normalized Bag-of-Words, as well as densely extract point descriptors. Proposed
adjustements achieve better performance. The evaluation shows that our method
outperforms classical techniques in terms of classification.


  Previous knowledge graph embedding approaches usually map entities to
representations and utilize score functions to predict the target entities, yet
they typically struggle to reason rare or emerging unseen entities. In this
paper, we propose kNN-KGE, a new knowledge graph embedding approach with
pre-trained language models, by linearly interpolating its entity distribution
with k-nearest neighbors. We compute the nearest neighbors based on the
distance in the entity embedding space from the knowledge store. Our approach
can allow rare or emerging entities to be memorized explicitly rather than
implicitly in model parameters. Experimental results demonstrate that our
approach can improve inductive and transductive link prediction results and
yield better performance for low-resource settings with only a few triples,
which might be easier to reason via explicit memory. Code is available at
https://github.com/zjunlp/KNN-KG.


  Let $m_{12}$, $m_{13}$, ..., $m_{n-1,n}$ be the slopes of the $\binom{n}{2}$
lines connecting $n$ points in general position in the plane. The ideal $I_n$
of all algebraic relations among the $m_{ij}$ defines a configuration space
called the {\em slope variety of the complete graph}. We prove that $I_n$ is
reduced and Cohen-Macaulay, give an explicit Gr\"obner basis for it, and
compute its Hilbert series combinatorially. We proceed chiefly by studying the
associated Stanley-Reisner simplicial complex, which has an intricate recursive
structure. In addition, we are able to answer many questions about the geometry
of the slope variety by translating them into purely combinatorial problems
concerning enumeration of trees.


  A large part of modern research, especially in the broad field of complex
systems, relies on the numerical integration of PDEs, with and without
stochastic noise. This is usually done with eiher in- house made codes or
external packages like MATLAB, Mathematica, Fenicsx, OpenFOAM, Dedalus, and
others. These packages rarely offer a good combination of speed, generality,
and the option to easily add stochasticity to the system, while in-house codes
depend on certain expertise to obtain good performance, and are usually written
for each specific use case, sacrificing modularity and reusability. This paper
introduces a package written in CUDA C++, thus enabling by default gpu
acceleration, that performs pseudo-spectral integration of generic stochastic
PDEs in flat lattices in one, two and three dimensions. This manuscript
describes how the basic functionality of cuPSS, with an example and
benchmarking, showing that cuPSS offers a considerable improvement in speed
over other popular finite-difference and spectral solvers.


  We explore the effects of a heavy fermion doublet in a simplified version of
the standard electroweak theory. We integrate out the doublet and compute the
exact effective energy functional of spatially varying gauge and Higgs fields.
We perform a variational search for a local minimum of the effective energy and
do not find evidence for a soliton carrying the quantum numbers of the
decoupled fermion doublet. The fermion vacuum polarization energy offsets the
gain in binding energy previously argued to be sufficient to stabilize a
fermionic soliton. The existence of such a soliton would have been a natural
way to maintain anomaly cancellation at the level of the states. We also see
that the sphaleron energy is significantly increased due to the quantum
corrections of the heavy doublet. We find that when the doublet is slightly
heavier than the quantum--corrected sphaleron, its decay is exponentially
suppressed owing to a new barrier. This barrier exists only for an intermediate
range of fermion masses, and a heavy enough doublet is indeed unstable.


  We report the observation of above-threshold dissociation of a multielectron
molecular system, Na$_2^+$. The process is due to continuum-continuum
transitions in a field-dressed molecular continuum. Three well resolved
fragmentation channels with different kinetic energy release patterns have been
detected, of which, two are associated with ordinary photodissociation via
light-induced potentials into Na(3s) + Na$^+$ and Na(3p) + Na$^+$, and one with
continuum-continuum transitions and above-threshold dissociation into Na(3p) +
Na$^+$. We show that when we dress this molecule with a field whose intensity
is ~3 x 10$^{12}$ W/cm$^2$, above-threshold dissociation prevails over other
processes, such as field-ionization followed by Coulomb explosion.


  In this work we define formal grammars in terms of free monoidal categories,
along with a functor from the category of formal grammars to the category of
automata. Generalising from the Booleans to arbitrary semirings, we extend our
construction to weighted formal grammars and weighted automata. This allows us
to link the categorical viewpoint on natural language to the standard machine
learning notion of probabilistic language model.


  We study the single-channel source separation problem involving orthogonal
frequency-division multiplexing (OFDM) signals, which are ubiquitous in many
modern-day digital communication systems. Related efforts have been pursued in
monaural source separation, where state-of-the-art neural architectures have
been adopted to train an end-to-end separator for audio signals (as
1-dimensional time series). In this work, through a prototype problem based on
the OFDM source model, we assess -- and question -- the efficacy of using
audio-oriented neural architectures in separating signals based on features
pertinent to communication waveforms. Perhaps surprisingly, we demonstrate that
in some configurations, where perfect separation is theoretically attainable,
these audio-oriented neural architectures perform poorly in separating
co-channel OFDM waveforms. Yet, we propose critical domain-informed
modifications to the network parameterization, based on insights from OFDM
structures, that can confer about 30 dB improvement in performance.


  Isothermal interfacial zones are investigated starting from a local energy
which can be considered as the sum of two terms: one corresponding to a medium
with a uniform composition equal to the local one and a second one associated
with the non-uniformity of the fluid. In an extended van der Waals theory, the
volume internal energy is proposed with a gradient expansion depending not only
on the gradient of density but also on the gradient of entropy. We obtain the
equation of conservative motions for non-homogeneous fluids near its critical
point. For such a medium, it is not possible to obtain shock waves. The waves
are tangential to the interface and the wave celerity is expressed depending on
thermodynamic conditions at the critical point.


  A benchmark experiment on 208Pb shows that polarized proton inelastic
scattering at very forward angles including 0{\deg} is a powerful tool for
high-resolution studies of electric dipole (E1) and spin magnetic dipole (M1)
modes in nuclei over a broad excitation energy range to test up-to-date nuclear
models. The extracted E1 polarizability leads to a neutron skin thickness
r_skin = 0.156+0.025-0.021 fm in 208Pb derived within a mean-field model [Phys.
Rev. C 81, 051303 (2010)], thereby constraining the symmetry energy and its
density dependence, relevant to the description of neutron stars.


  In this paper we study Lp-boundedness properties for area Littlewood-Paley
functions associated with heat semigroups for Hermite and Laguerre operators


  Health informatics can inform decisions that practitioners, patients,
policymakers, and researchers need to make about health and disease. Health
informatics is built upon patient health data leading to the need to codify
patient health information. Such standardization is required to compute
population statistics (such as prevalence, incidence, etc.) that are common
metrics used in fields such as epidemiology. Reliable decision-making about
health and disease rests on our ability to organize, analyze, and assess data
repositories that contain patient health data.
  While standards exist to structure and analyze patient data across patient
data sources such as health information exchanges, clinical data repositories,
and health data marketplaces, analogous best practices for rigorously defining
patient populations in health informatics contexts do not exist. Codifying best
practices for developing disease definitions could support the effective
development of clinical guidelines, inform algorithms used in clinical decision
support systems, and additional patient guidelines.
  In this paper, we present a workflow for the development of phenotype
definitions. This workflow presents a series of recommendations for defining
health and disease. Various examples within this paper are presented to
demonstrate this workflow in health informatics contexts.


  We consider a double polytropic cosmological fluid and demonstrate that, when
one constituent resembles a bare cosmological constant while the other emulates
a generalized Chaplygin gas, a good description of the Universe's large-scale
dynamics is obtained. In particular, our double polytropic reduces to the
Murnaghan equation of state, whose applications are already well established in
solid state physics and classical thermodynamics. Intriguingly, our model
approximates the conventional $\Lambda$CDM paradigm while reproducing the
collective effects of logotropic and generalized Chaplygin fluids across
different regimes. To check the goodness of our fluid description, we analyze
first order density perturbations, refining our model through various orders of
approximation, utilizing $\sigma_8$ data alongside other cosmological data
sets. Encouraging results suggest that our model, based on the Murnaghan
equation of state, outperforms the standard cosmological background within
specific approximate regimes and, on the whole, surpasses the standard
phenomenological reconstruction of dark energy.


  We prove that there are only finitely many isometry classes of even lattices
$L$ of signature $(2,n)$ for which the space of cusp forms of weight $1+n/2$
for the Weil representation of the discriminant group of $L$ is trivial. We
compute the list of these lattices. They have the property that every Heegner
divisor for the orthogonal group of $L$ can be realized as the divisor of a
Borcherds product. We obtain similar classification results in greater
generality for finite quadratic modules.


  Recent papers on approximation algorithms for the traveling salesman problem
(TSP) have given a new variant on the well-known Christofides' algorithm for
the TSP, called the Best-of-Many Christofides' algorithm. The algorithm
involves sampling a spanning tree from the solution the standard LP relaxation
of the TSP, subject to the condition that each edge is sampled with probability
at most its value in the LP relaxation. One then runs Christofides' algorithm
on the tree by computing a minimum-cost matching on the odd-degree vertices in
the tree, and shortcutting the resulting Eulerian graph to a tour. In this
paper we perform an experimental evaluation of the Best-of-Many Christofides'
algorithm to see if there are empirical reasons to believe its performance is
better than that of Christofides' algorithm. Furthermore, several different
sampling schemes have been proposed; we implement several different schemes to
determine which ones might be the most promising for obtaining improved
performance guarantees over that of Christofides' algorithm. In our
experiments, all of the implemented methods perform significantly better than
the Christofides' algorithm; an algorithm that samples from a maximum entropy
distribution over spanning trees seems to be particularly good, though there
are others that perform almost as well.


  An increasing number of proteins are being discovered with a remarkable and
somewhat surprising feature, a knot in their native structures. How the
polypeptide chain is able to knot itself during the folding process to form
these highly intricate protein topologies is not known. Here, we perform a
computational study on the 160-amino acid homodimeric protein YibK which, like
other proteins in the SpoU family of MTases, contains a deep trefoil knot in
its C-terminal region. In this study, we use a coarse-grained C-alpha-chain
representation and Langevin dynamics to study folding kinetics. We find that
specific, attractive nonnative interactions are critical for knot formation. In
the absence of these interactions, i.e. in an energetics driven entirely by
native interactions, knot formation is exceedingly unlikely. Further, we find,
in concert with recent experimental data on YibK, two parallel folding pathways
which we attribute to an early and a late formation of the trefoil knot,
respectively. For both pathways, knot formation occurs before dimerization. A
bioinformatics analysis of the SpoU family of proteins reveals further that the
critical nonnative interactions may originate from evolutionary conserved
hydrophobic segments around the knotted region.


  FUV echelle spectroscopy of the radio-quiet QSO H1821+643 (z = 0.297),
obtained with the Space Telescope Imaging Spectrograph (STIS) at 7 km/s
resolution, reveals 4 definite O VI absorption line systems and one probable O
VI absorber at 0.15 < z(abs) < 0.27. The four definite O VI absorbers are
located near galaxies and are highly displaced from the quasar in redshift;
these are likely intervening systems unrelated to the background QSO. In the
case of the strong O VI system at z(abs) = 0.22497, multiple components are
detected in Si III and O VI as well as H I Lyman series lines, and the
differing component velocity centroids and b-values firmly establish that this
is a multiphase absorption system. A weak O VI absorber is detected at z(abs) =
0.22637, i.e., offset by ~340 km/s from the z(abs) = 0.22497 system. Lya
absorption is detected at z(abs) = 0.22613, but no Lya absorption is
significantly detected at 0.22637. Other weak O VI absorbers at z(abs) =
0.24531 and 0.26659 and the probable O VI system at 0.21326 have widely diverse
O VI/H I column density ratios with N(O VI)/N(H I) ranging from <=0.14+/-0.03
to 5.2+/-1.2. The number density of O VI absorbers with rest equivalent width >
30 mA in the H1821+643 spectrum is remarkably high, dN/dz ~48, with a high
(90%) confidence that it is greater than 17. We conservatively estimate that
the cosmological mass density of the O VI systems Omega_b(O VI) > 0.0008/h_75.
With an assumed metallicity of 1/10 solar and a conservative assumption that
the fraction of oxygen in the O VI ionization stage is 0.2, we obtain Omega_b(O
VI) > 0.004/h_75. This is comparable to the combined cosmological mass density
of stars and cool gas in galaxies and X-ray emitting gas in galaxy clusters at
low redshift.


  We study two effective models developed for description of superconductors
with short-coherence length: (i) the extended Hubbard model with on-site
attraction and intersite repulsion, (ii) the model of hard-core charged bosons
on a lattice. The analysis is concentrated on the problem of phase separations
and competition between superconductivity (SS) and charge-density-wave (CDW)
orderings. The phase diagrams of the systems are shown to consist of at least
seven different states, including 3 types of phase separated (PS) states:
CDW-SS (PS1), CDW-normal (PS2) and the state of electron droplets (PS3). By
taking into account the PS states and the effects of longer-range
density-density interactions (beyond nearest neighbours) our work substantially
generalizes and modifies the conclusions of previous works concerning the
models considered.


  Assuming the Hodge conjecture for abelian varieties of CM-type, one obtains a
good category of abelian motives over the algebraic closure of a finite field
and a reduction functor to it from the category of CM-motives. Consequentely,
one obtains a morphism of gerbes of fibre functors with certain properties. We
prove unconditionally that there exists a morphism of gerbes with these
properties, and we classify them.


  After a brief review of the Maxwell-like approach to gravity we consider the
issue of the negative energy of gravitational field which is a consequence of
the field approach to the phenomenon of gravitation. Due to the existence of
the negative field energy {\it within} a mass body its total energy content is
smaller than the positive energy assigned to its mass energy. We study the
total energy content of a spherically symmetrical mass body having constant
matter density, and show that its total energy content depends on its radius.
We show that under certain circumstances, the total energy content of a mass
body achieves negative values so that the force at its surface becomes
repulsive. We apply this idea to the evolution of universe filled by matter and
the negative energy density of its gravitational field. Since the negative
energy density causes the negative pressure it might be considered as an agent
which causes the acceleration of the universe.


  We obtained precise line-of-sight radial velocities of 23 member stars of the
remote halo globular cluster Palomar 4 (Pal 4) using the High Resolution
Echelle Spectrograph (HIRES) at the Keck I telescope. We also measured the mass
function of the cluster down to a limiting magnitude of V~28 mag using archival
HST/WFPC2 imaging. We derived the cluster's surface brightness profile based on
the WFPC2 data and on broad-band imaging with the Low-Resolution Imaging
Spectrometer (LRIS) at the Keck II telescope. We find a mean cluster velocity
of 72.55+/-0.22 km/s and a velocity dispersion of 0.87+/-0.18 km/s. The global
mass function of the cluster, in the mass range 0.55<=M<=0.85 M_solar, is
shallower than a Kroupa mass function and the cluster is significantly depleted
in low-mass stars in its center compared to its outskirts. Since the relaxation
time of Pal 4 is of the order of a Hubble time, this points to primordial mass
segregation in this cluster. Extrapolating the measured mass function towards
lower-mass stars and including the contribution of compact remnants, we derive
a total cluster mass of 29800 M_solar. For this mass, the measured velocity
dispersion is consistent with the expectations of Newtonian dynamics and below
the prediction of Modified Newtonian Dynamics (MOND). Pal 4 adds to the growing
body of evidence that the dynamics of star clusters in the outer Galactic halo
can hardly be explained by MOND.


  Electromagnetically induced transparency and absorption (EIT and EIA) are
usually demonstrated by three-level atomic or atom-like systems. In contrast to
the usual case, we theoretically study the EIT and EIA in an equivalent
three-level system, which is constructed by dressing a superconducting
two-level system (qubit) dressed by a single-mode cavity field. In this
equivalent system, we find that both the EIT and the EIA can be tuned by
controlling the level-spacing of the superconducting qubit and hence
controlling the dressed system. This tunability is due to the dressed
relaxation and dephasing rates which vary parametrically with the level-spacing
of the original qubit and thus affect the transition properties of the dressed
qubit and the susceptibility. These dressed relaxation and dephasing rates
characterize the reaction of the dressed qubit to an incident probe field. We
also use recent experimental data on superconducting qubits (charge, phase, and
flux qubits) to demonstrate our approach and show the possibility of
experimentally realizing this proposal.


  Electronic health monitoring is one of the major applications of wireless
body area networks (WBANs) that helps with early detection of any abnormal
physiological symptoms. In this paper, we propose and solve an optimization
problem that maximizes the energy efficiency (EE) of WBAN consisting of sensor
nodes (SNs) equipped with energy harvesting capabilities communicating with an
aggregator. We exploit the structure of the optimization problem to provide a
sub-optimal solution at a lower computational complexity and derive the
mathematical expressions of upper and lower bounds of the source rates of the
SN. The simulation results reveal that the optimal allocation of the source
rate to energy critical SNs improves the system performance of WBAN in terms of
energy efficiency during different everyday activities.


  We investigate kinetic energy properties of an irrotational deep-water Stokes
wave. By introducing a conformal hodograph transform, we perform complex
analysis in the new variables, and show that the existence of the streamline
time-period for deep-water Stokes waves. Relying on the conformal mappings, we
prove some qualitative results about the kinetic energy such as the convexity
property of integral means of kinetic energy, the streamline time-period being
non-increasing and independent of initial data and the monotonicity and
logarithmic convexity of the total kinetic energy over a streamline
time-period. Moreover, taking advantage of the non-increasing nature of the
streamline time-period, we show that the streamline time-period strictly larger
than the wave period, which suggests the fact that there are no closed paths
for all particles in a deep-water Stokes flow and the drift of any streamline
is positive. These results allow us to quantify the observation that the
kinetic energy and the streamline time-period are larger near the free surface
and decrease with increasing the depth.


  In this paper, we introduce and explore augmented quaternions and augmented
unit quaternions, and present an augmented unit quaternion optimization model.
An augmented quaternion consist of a quaternion and a translation vector. The
multiplication rule of augmented quaternion is defined. An augmented unit
quaternion consists of a unit quaternion and a translation vector. The
augmented unit quaternions form a Lie group. By means of augmented unit
quaternions, we study the error model and kinematics. Then we formulate two
classical problems in robot research, i.e., the hand-eye calibration problem
and the simultaneous localization and mapping (SLAM) problem as augmented unit
quaternion optimization problems, which are actually real smooth spherical
equality constrained optimization problems. Comparing with the corresponding
unit dual quaternion optimization model, the augmented unit quaternion
optimization model has less variables and removes the orthogonality
constraints.


  In 2013 the Nobel Prize in Physics was awarded to Francois Englert and Peter
Higgs for their development in 1964 of the mass generation mechanism (the Higgs
mechanism) in local gauge theories. This mechanism requires the existence of a
massive scalar particle, the Higgs boson, and in 2012 the Higgs boson was
finally observed at the Large Hadron Collider after being sought for almost
half a century. In this pedagogical article we review the work of these Nobel
recipients and discuss its implications. We approach the topic from the
perspective of a dynamically generated Higgs boson that is a
fermion-antifermion bound state rather than an elementary field that appears in
an input Lagrangian. In particular, we emphasize the connection with the BCS
theory of superconductivity. We identify the double-well Higgs potential not as
a fundamental potential but as a mean-field effective Lagrangian with a
dynamical Higgs boson being generated through a residual interaction that
accompanies the mean-field Lagrangian. We discuss what we believe to be the key
challenge raised by the discovery of the Higgs boson, namely determining
whether it is elementary or composite, and suggest that the width of the Higgs
boson might serve as a suitable diagnostic for discriminating between an
elementary Higgs boson and a composite one.


  Estimating expectation values is a key subroutine in quantum algorithms.
Near-term implementations face two major challenges: a limited number of
samples required to learn a large collection of observables, and the
accumulation of errors in devices without quantum error correction. To address
these challenges simultaneously, we develop a quantum error-mitigation strategy
called ``symmetry-adjusted classical shadows,'' by adjusting classical-shadow
tomography according to how symmetries are corrupted by device errors. As a
concrete example, we highlight global $\mathrm{U(1)}$ symmetry, which manifests
in fermions as particle number and in spins as total magnetization, and
illustrate their group-theoretic unification with respective classical-shadow
protocols. We establish rigorous sampling bounds under readout errors obeying
minimal assumptions, and perform numerical experiments with a more
comprehensive model of gate-level errors derived from existing quantum
processors. Our results reveal symmetry-adjusted classical shadows as a
low-cost strategy to mitigate errors from noisy quantum experiments in the
ubiquitous presence of symmetry.


  A weight-$t$ halfspace is a Boolean function $f(x)=$sign$(w_1 x_1 + \cdots +
w_n x_n - \theta)$ where each $w_i$ is an integer in $\{-t,\dots,t\}.$ We give
an explicit pseudorandom generator that $\delta$-fools any intersection of $k$
weight-$t$ halfspaces with seed length poly$(\log n, \log k,t,1/\delta)$. In
particular, our result gives an explicit PRG that fools any intersection of any
quasipoly$(n)$ number of halfspaces of any poly$\log(n)$ weight to any
$1/$poly$\log(n)$ accuracy using seed length poly$\log(n).$ Prior to this work
no explicit PRG with non-trivial seed length was known even for fooling
intersections of $n$ weight-1 halfspaces to constant accuracy.
  The analysis of our PRG fuses techniques from two different lines of work on
unconditional pseudorandomness for different kinds of Boolean functions. We
extend the approach of Harsha, Klivans and Meka \cite{HKM12} for fooling
intersections of regular halfspaces, and combine this approach with results of
Bazzi \cite{Bazzi:07} and Razborov \cite{Razborov:09} on bounded independence
fooling CNF formulas. Our analysis introduces new coupling-based ingredients
into the standard Lindeberg method for establishing quantitative central limit
theorems and associated pseudorandomness results.


  This work is concerned with solving neural network-based feedback controllers
efficiently for optimal control problems. We first conduct a comparative study
of two prevalent approaches: offline supervised learning and online direct
policy optimization. Albeit the training part of the supervised learning
approach is relatively easy, the success of the method heavily depends on the
optimal control dataset generated by open-loop optimal control solvers. In
contrast, direct policy optimization turns the optimal control problem into an
optimization problem directly without any requirement of pre-computing, but the
dynamics-related objective can be hard to optimize when the problem is
complicated. Our results underscore the superiority of offline supervised
learning in terms of both optimality and training time. To overcome the main
challenges, dataset and optimization, in the two approaches respectively, we
complement them and propose the Pre-train and Fine-tune strategy as a unified
training paradigm for optimal feedback control, which further improves the
performance and robustness significantly. Our code is accessible at
https://github.com/yzhao98/DeepOptimalControl.


  There has been a recent surge of interest in the implementation of linear
operations such as matrix multipications using photonic integrated circuit
technology. However, these approaches require an efficient and flexible way to
perform nonlinear operations in the photonic domain. We have fabricated an
optoelectronic nonlinear device--a laser neuron--that uses excitable laser
dynamics to achieve biologically-inspired spiking behavior. We demonstrate
functionality with simultaneous excitation, inhibition, and summation across
multiple wavelengths. We also demonstrate cascadability and compatibility with
a wavelength multiplexing protocol, both essential for larger scale system
integration. Laser neurons represent an important class of optoelectronic
nonlinear processors that can complement both the enormous bandwidth density
and energy efficiency of photonic computing operations.


  Almost all the X-ray afterglows of gamma-ray bursts (GRBs) observed by the
Swift satellite have a shallow decay phase in the first thousands of seconds.
We show that in an inhomogeneous jet (multiple-subjet or patchy-shell) model
the superposition of the afterglows of off-axis subjets (patchy shells) can
have the shallow decay phase. The necessary condition for obtaining the shallow
decay phase is that gamma-ray bright subjets (patchy shells) should have
gamma-ray efficiency higher than previously estimated, and should be surrounded
by gamma-ray dim subjets (patchy shells) with low gamma-ray efficiency. Our
model predicts that events with dim prompt emission have the conventional
afterglow light curve without the shallow decay phase like GRB 050416A.


  We use string-net models to accomplish a direct, purely two-dimensional,
approach to correlators of two-dimensional rational conformal field theories.
We obtain concise geometric expressions for the objects describing bulk and
boundary fields in terms of idempotents in the cylinder category of the
underlying modular fusion category, comprising more general classes of fields
than is standard in the literature. Combining these idempotents with Frobenius
graphs on the world sheet yields string nets that form a consistent system of
correlators, i.e. a system of invariants under appropriate mapping class groups
that are compatible with factorization.
  Using markings, we extract operator products of field objects from specific
correlators; the resulting operator products are natural algebraic expressions
that make sense beyond semisimplicity. We also derive an Eckmann-Hilton
relation internal to a braided category, thereby demonstrating the utility of
string nets for understanding algebra in braided tensor categories. Finally we
introduce the notion of a universal correlator. This systematizes the treatment
of situations in which different world sheets have the same correlator and
allows for the definition of a more comprehensive mapping class group.


  We report the serendipitous discovery of VVV-WIT-12, an unusual variable
source that seems to induce variability in its surrounding nebula. The source
belongs to the rare objects that we call WITs (short for What Is This?)
discovered within the VISTA Variables in the V\'ia L\'actea (VVV) survey.
VVV-WIT-12 was discovered during a pilot search for light echoes from distant
Supernovae (SNe) in the Milky Way using the near-IR images of the VVV survey.
This source has an extremely red spectral energy distribution, consistent with
a very reddened ($A_V \sim 100$ mag) long period variable star ($P\sim1525$
days). Furthermore, it is enshrouded in a nebula that changes brightness and
color with time, apparently in synch with the central source variations. The
near-IR light curve and complementary follow-up spectroscopy observations are
consistent with a variable Young Stellar Object (YSO) illuminating its
surrounding nebula. In this case the source periodic variation along the cycles
produces an unprecedented light echo in the different regions of the nebula.


  Higher-order processes with parameterization are capable of abstraction and
application (migrated from the lambda-calculus), and thus are computationally
more expressive. For the minimal higher-order concurrency, it is well-known
that the strong bisimilarity (i.e., the strong bisimulation equality) is
decidable in absence of parameterization. By contrast, whether the strong
bisimilarity is still decidable for parameterized higher-order processes
remains unclear. In this paper, we focus on this issue. There are basically two
kinds of parameterization: one on names and the other on processes. We show
that the strong bisimilarity is indeed decidable for higher-order processes
equipped with both kinds of parameterization. Then we demonstrate how to adapt
the decision approach to build an axiom system for the strong bisimilarity. On
top of these results, we provide an algorithm for the bisimilarity checking.


  The purpose of this work is to present an improved energy conservation method
for hyperelastodynamic contact problems based on specific normal compliance
conditions. In order to determine this Improved Normal Compliance (INC) law, we
use a Moreau--Yosida $\alpha$-regularization to approximate the unilateral
contact law. Then, based on the work of Hauret--LeTallec
\cite{hauret2006energy}, we propose in the discrete framework a specific
approach allowing to respect the energy conservation of the system in adequacy
with the continuous case. This strategy (INC) is characterized by a conserving
behavior for frictionless impacts and admissible dissipation for friction
phenomena while limiting penetration. Then, we detail the numerical treatment
within the framework of the semi-smooth Newton method and primal-dual active
set strategy for the normal compliance conditions with friction. We finally
provide some numerical experiments to bring into light the energy conservation
and the efficiency of the INC method by comparing with different classical
methods from the literature throught representative contact problems.


  This paper presents an analysis of how the iris recognition is impacted by
eye diseases and an appropriate dataset comprising 2996 iris images of 230
distinct eyes (including 184 illness-affected eyes representing more than 20
different eye conditions). The images were collected in near infrared and
visible light during a routine ophthalmological practice. The experimental
study shows four valuable results. First, the enrollment process is highly
sensitive to those eye conditions that make the iris obstructed or introduce
geometrical distortions. Second, even those conditions that do not produce
visible changes to the iris structure may increase the dissimilarity among
samples of the same eyes. Third, eye conditions affecting iris geometry, its
tissue structure or producing obstructions significantly decrease the iris
recognition reliability. Fourth, for eyes afflicted by a disease, the most
prominent effect of the disease on iris recognition is to cause segmentation
errors. To our knowledge this is the first database of iris images for
disease-affected eyes made publicly available to researchers, and the most
comprehensive study of what we can expect when the iris recognition is deployed
for non-healthy eyes.


  In the present paper, we give sufficient conditions on the elements of the
continued fractions $A$ and $B$ that will assure us that the continued fraction
$A^B$ is a transcendental number. With the same condition, we establish a
transcendental measure of $A^B.$


  In this paper we provide a general solution for the dividend discount model
in order to compute the intrinsic value of a common stock that allows for
multiple stage growth rates of any predetermined number of periods. A
mathematical proof is provided for the suggested general solution. A numerical
application is also presented. The solution introduced in this paper is
expected to improve on the precision of stock valuation, which might be of
fundamental importance for investors as well as financial institutions.


  The connection between the coarse geometry of metric spaces and analytic
properties of topological groupoids is well known. One of the main results of
Skandalis, Tu and Yu is that a space admits a coarse embedding into Hilbert
space if and only if a certain associated topological groupoid is a-T-menable.
This groupoid characterisation then reduces the proof that the coarse
Baum-Connes conjecture holds for a coarsely embeddable space to known results
for a-T-menable groupoids. The property of admitting a fibred coarse embedding
into Hilbert space was introduced by Chen, Wang and Yu to provide a property
that is sufficient for the maximal analogue to the coarse Baum-Connes
conjecture and in this paper we connect this property to the traditional coarse
Baum-Connes conjecture using a restriction of the coarse groupoid and
homological algebra. Additionally we use this results to give a
characterisation of the a-T-menability for residually finite discrete groups.


  We report the discovery of eMACSJ1341-QG-1, a quiescent galaxy at $z=1.594$
located behind the massive galaxy cluster eMACSJ1341.9$-$2442 ($z=0.835$). The
system was identified as a gravitationally lensed triple image in Hubble Space
Telescope images obtained as part of a snapshot survey of the most X-ray
luminous galaxy clusters at $z>0.5$ and spectroscopically confirmed in
ground-based follow-up observations with the ESO/X-Shooter spectrograph. From
the constraints provided by the triple image, we derive a first, crude model of
the mass distribution of the cluster lens, which predicts a gravitational
amplification of a factor of $\sim$30 for the primary image and a factor of
$\sim$6 for the remaining two images of the source, making eMACSJ1341-QG-1 by
far the most strongly amplified quiescent galaxy discovered to date. Our
discovery underlines the power of SNAPshot observations of massive, X-ray
selected galaxy clusters for lensing-assisted studies of faint background
populations.


  In this paper we analyze the endoscopy for $\Sp(4,\mathbb R)$. The new
results are a precise realization of the discrete series representations (in
Section 2), a computation of their traces (Section 3) and an exact formula for
the noncommutative Poisson summation and endoscopy of for this group (in
Sections 4,5).


  Aims: The aim of this work is to compare the performance of three reaction
network integration methods used in stellar nucleosynthesis calculations. These
are the Gear's backward differentiation method, Wagoner's method (a 2nd-order
Runge-Kutta method), and the Bader-Deuflehard semi-implicit multi-step method.
  Methods: To investigate the efficiency of each of the integration methods
considered here, a test suite of temperature and density versus time profiles
is used. This suite provides a range of situations ranging from constant
temperature and density to the dramatically varying conditions present in white
dwarf mergers, novae, and x-ray bursts. Some of these profiles are obtained
separately from full hydrodynamic calculations. The integration efficiencies
are investigated with respect to input parameters that constrain the desired
accuracy and precision.
  Results: Gear's backward differentiation method is found to improve accuracy,
performance, and stability in integrating nuclear reaction networks. For
temperature-density profiles that vary strongly with time, it is found to
outperform the Bader-Deuflehard method (although that method is very powerful
for more smoothly varying profiles). Wagoner's method, while relatively fast
for many scenarios, exhibits hard-to-predict inaccuracies for some choices of
integration parameters owing to its lack of error estimations.


  We consider the problem of rate allocation in a Gaussian multiple-access
channel, with the goal of maximizing a utility function over transmission
rates. In contrast to the literature which focuses on linear utility functions,
we study general concave utility functions. We present a gradient projection
algorithm for this problem. Since the constraint set of the problem is
described by exponentially many constraints, methods that use exact projections
are computationally intractable. Therefore, we develop a new method that uses
approximate projections. We use the polymatroid structure of the capacity
region to show that the approximate projection can be implemented by a
recursive algorithm in time polynomial in the number of users. We further
propose another algorithm for implementing the approximate projections using
rate-splitting and show improved bounds on its convergence time.


  We elucidate the fate of classical symmetries which suffer from abelian
Adler-Bell-Jackiw anomalies. Instead of being completely destroyed, these
symmetries survive as non-invertible topological global symmetry defects with
worldvolume anyon degrees of freedom that couple to the bulk through a magnetic
one-form global symmetry as in the fractional hall effect. These non-invertible
chiral symmetries imply selection rules on correlation functions and arise in
familiar models of massless quantum electrodynamics and models of axions (as
well as their non-abelian generalizations). When the associated bulk magnetic
one-form symmetry is broken by the propagation of dynamical magnetic monopoles,
the selection rules of the non-invertible chiral symmetry defects are violated
non-perturbatively. This leads to technically natural exponential hierarchies
in axion potentials and fermion masses.


  Beyond individually resolvable gravitational wave events such as binary black
hole and binary neutron star mergers, the superposition of many more weak
signals coming from a multitude of sources is expected to contribute to an
overall background, the so-called stochastic gravitational wave background. In
this review, we give an overview of possible detection methods in the search
for this background and provide a detailed review of the data-analysis
techniques, focusing primarily on current Earth-based interferometric
gravitational-wave detectors. In addition, various validation techniques aimed
at reinforcing the claim of a detection of such a background are discussed as
well. We conclude this review by listing some of the astrophysical and
cosmological implications resulting from current upper limits on the stochastic
background of gravitational waves.


  Density functional theory (DFT) is an exact alternative formulation of
quantum mechanics, in which it is possible to calculate the total energy, the
spin and the charge density of many-electron systems in the ground state. In
practice, it is necessary to use uncontrolled approximations that can mainly be
verified against experimental data. Atoms and ions are simple systems, where
the approximations of DFT can be easily tested. We have calculated within DFT
the total energies, spin and higher ionization energies of all the ions of
elements with 1 $\leq$ Z $\leq$ 29. We find the calculations in close agreement
with experiment, with an error of typically less than ca. 1% for 1 $\leq$ Z
$\leq$ 29. Surprisingly, the error depends on the electronic configuration of
the ion in both local spin density approximation (LSDA) and
Perdew-Burke-Ernzerhof general gradient approximation (PBE-GGA) and independent
of both self-interaction correction (SIC) and relativistic corrections. Larger
errors are found for systems in which the spin-spin correlation is significant,
which indicates the possible benefit from an orbital-dependent formulation of
the correlation energy functional.


  Magnetic reconnection modulated by non-local disturbances in the solar
atmosphere has been investigated theoretically, but rarely observed. In this
study, employing Ha and extreme ultraviolet (EUV) images and line of sight
magnetograms, we report acceleration of reconnection by adjacent filament
eruption. In Ha images, four groups of chromospheric fibrils are observed to
form a saddle-like structure. Among them, two groups of fibrils converge and
reconnect. Two newly reconnected fibrils then form, and retract away from the
reconnection region. In EUV images, similar structures and evolution of coronal
loops are identified. Current sheet forms repeatedly at the interface of
reconnecting loops, with width and length of 1-2 and 5.3-7.2 Mm, and
reconnection rate of 0.18-0.3. It appears in the EUV low-temperature channels,
with average differential emission measure (DEM) weighed temperature and EM of
2 MK and 2.5*10^27 cm-5. Plasmoids appear in the current sheet and propagate
along it, and then further along the reconnection loops. The filament, located
at the southeast of reconnection region, erupts, and pushes away the loops
covering the reconnection region. Thereafter, the current sheet has width and
length of 2 and 3.5 Mm, and reconnection rate of 0.57. It becomes much
brighter, and appears in the EUV high-temperature channels, with average
DEM-weighed temperature and EM of 5.5 MK and 1.7*10^28 cm-5. In the current
sheet, more hotter plasmoids form. More thermal and kinetic energy is hence
converted. These results suggest that the reconnection is significantly
accelerated by the propagating disturbance caused by the nearby filament
eruption.


  Given a lattice polytope $P$ and a prime $p$, we define a function from the
set of primitive symplectic $p$-adic lattices to the rationals that extracts
the $\ell$th coefficient of the Ehrhart polynomial of $P$ relative to the given
lattice. Inspired by work of Gunnells and Rodriguez-Villegas in type
$\mathsf{A}$, we show that these functions are eigenfunctions of a suitably
defined action of the spherical symplectic Hecke algebra. Although they depend
significantly on the polytope $P$, their eigenvalues are independent of $P$ and
expressed as polynomials in $p$. We define local zeta functions that enumerate
the values of these Hecke eigenfunctions on the vertices of the affine
Bruhat--Tits buildings associated with $p$-adic symplectic groups. We compute
these zeta functions by enumerating $p$-adic lattices by their elementary
divisors and, simultaneously, one Hermite parameter. We report on a general
functional equation satisfied by these local zeta functions, confirming a
conjecture of Vankov.


  Context. Solar energetic particles observed in association with coronal mass
ejections (CMEs) are produced by the CME-driven shock waves. The acceleration
of particles is considered to be due to diffusive shock acceleration (DSA).
Aims. We aim at a better understanding of DSA in the case of quasi-parallel
shocks, in which self-generated turbulence in the shock vicinity plays a key
role. Methods. We have developed and applied a new Monte Carlo simulation code
for acceleration of protons in parallel coronal shocks. The code performs a
self-consistent calculation of resonant interactions of particles with Alfv\'en
waves based on the quasi-linear theory. In contrast to the existing Monte Carlo
codes of DSA, the new code features the full quasi-linear resonance condition
of particle pitch-angle scattering. This allows us to take anisotropy of
particle pitch-angle scattering into account, while the older codes implement
an approximate resonance condition leading to isotropic scattering.We performed
simulations with the new code and with an old code, applying the same initial
and boundary conditions, and have compared the results provided by both codes
with each other, and with the predictions of the steady-state theory. Results.
We have found that anisotropic pitch-angle scattering leads to less efficient
acceleration of particles than isotropic. However, extrapolations to particle
injection rates higher than those we were able to use suggest the capability of
DSA to produce relativistic particles. The particle and wave distributions in
the foreshock as well as their time evolution, provided by our new simulation
code, are significantly different from the previous results and from the
steady-state theory. Specifically, the mean free path in the simulations with
the new code is increasing with energy, in contrast to the theoretical result.


  A complete description of 4-by-4 matrices $\begin{bmatrix}\alpha I & C \\D &
\beta I\end{bmatrix}$, with scalar 2-by-2 diagonal blocks, for which the
numerical range is the convex hull of two non-concentric ellipses is given.
This result is obtained by reduction to the leading special case in which
$C-D^*$ also is a scalar multiple of the identity. In particular cases when in
addition $\alpha-\beta$ is real or pure imaginary, the results take an
especially simple form. An application to reciprocal matrices is provided.


  Recently, deep neural networks have been found to nearly interpolate training
data but still generalize well in various applications. To help understand such
a phenomenon, it has been of interest to analyze the ridge estimator and its
interpolation limit in high-dimensional regression models. For this motivation,
we study the ridge estimator in a rotationally sparse setting of
high-dimensional linear regression, where the signal of a response is aligned
with a small number, $d$, of covariates with large or spiked variances,
compared with the remaining covariates with small or tail variances,
\textit{after} an orthogonal transformation of the covariate vector. We
establish high-probability upper and lower bounds on the out-sample and
in-sample prediction errors in two distinct regimes depending on the ratio of
the effective rank of tail variances over the sample size $n$. The separation
of the two regimes enables us to exploit relevant concentration inequalities
and derive concrete error bounds without making any oracle assumption or
independent components assumption on covariate vectors. Moreover, we derive
sufficient and necessary conditions which indicate that the prediction errors
of ridge estimation can be of the order $O(\frac{d}{n})$ if and only if the gap
between the spiked and tail variances are sufficiently large. We also compare
the orders of optimal out-sample and in-sample prediction errors and find that,
remarkably, the optimal out-sample prediction error may be significantly
smaller than the optimal in-sample one. Finally, we present numerical
experiments which empirically confirm our theoretical findings.


  Many classes of maps are characterized as (possibly multi-valued) maps
preserving particular types of compact filters.


  Observations of QSOs at z ~ 5.7 - 6.4 show the appearance of Gunn-Peterson
troughs around z ~ 6, and a change in the slope of the IGM optical depth tau(z)
near z ~ 5.5. These results are interpreted as a signature of the end of the
reionization era, which probably started at considerably higher redshifts.
However, there also appears to be a substantial cosmic variance in the
transmission of the IGM, both along some lines of sight, and among different
lines of sight, in this intriguing redshift regime. We suggest that this is
indicative of a spatially uneven reionization, possibly caused by the
bias-driven primordial clustering of the reionization sources. There is also
some independent evidence for a strong clustering of QSOs at z ~ 4 - 5 and
galaxies around them, supporting the idea of the strong biasing of the first
luminous sources at these redshifts. Larger samples of high-z QSOs are needed
in order to provide improved, statistically significant constraints for the
models of these phenomena. We expect that the Palomar-Quest (PQ) survey will
soon provide a new set of QSOs to be used as cosmological probes in this
redshift regime.


  We have carried out a campaign to characterize the hot Jupiters WASP-5b,
WASP-44b and WASP-46b using multiband photometry collected at the
Observat\'orio do Pico Dos Dias in Brazil. We have determined the planetary
physical properties and new transit ephemerides for these systems. The new
orbital parameters and physical properties of WASP-5b and WASP-44b are
consistent with previous estimates. In the case of WASP-46b, there is some
quota of disagreement between previous results. We provide a new determination
of the radius of this planet and help clarify the previous differences. We also
studied the transit time variations including our new measurements. No clear
variation from a linear trend was found for the systems WASP-5b and WASP-44b.
In the case of WASP-46b, we found evidence of deviations indicating the
presence of a companion but statistical analysis of the existing times points
to a signal due to the sampling rather than a new planet. Finally, we studied
the fractional radius variation as a function of wavelength for these systems.
The broad-band spectrums of WASP-5b and WASP-44b are mostly flat. In the case
of WASP-46b we found a trend, but further measurements are necessary to confirm
this finding.


  In distribution compression, one aims to accurately summarize a probability
distribution $\mathbb{P}$ using a small number of representative points.
Near-optimal thinning procedures achieve this goal by sampling $n$ points from
a Markov chain and identifying $\sqrt{n}$ points with
$\widetilde{\mathcal{O}}(1/\sqrt{n})$ discrepancy to $\mathbb{P}$.
Unfortunately, these algorithms suffer from quadratic or super-quadratic
runtime in the sample size $n$. To address this deficiency, we introduce
Compress++, a simple meta-procedure for speeding up any thinning algorithm
while suffering at most a factor of $4$ in error. When combined with the
quadratic-time kernel halving and kernel thinning algorithms of Dwivedi and
Mackey (2021), Compress++ delivers $\sqrt{n}$ points with
$\mathcal{O}(\sqrt{\log n/n})$ integration error and better-than-Monte-Carlo
maximum mean discrepancy in $\mathcal{O}(n \log^3 n)$ time and $\mathcal{O}(
\sqrt{n} \log^2 n )$ space. Moreover, Compress++ enjoys the same near-linear
runtime given any quadratic-time input and reduces the runtime of
super-quadratic algorithms by a square-root factor. In our benchmarks with
high-dimensional Monte Carlo samples and Markov chains targeting challenging
differential equation posteriors, Compress++ matches or nearly matches the
accuracy of its input algorithm in orders of magnitude less time.


  Visual Place Recognition (VPR) is the process of recognising a previously
visited place using visual information, often under varying appearance
conditions and viewpoint changes and with computational constraints. VPR is
related to the concepts of localisation, loop closure, image retrieval and is a
critical component of many autonomous navigation systems ranging from
autonomous vehicles to drones and computer vision systems. While the concept of
place recognition has been around for many years, VPR research has grown
rapidly as a field over the past decade due to improving camera hardware and
its potential for deep learning-based techniques, and has become a widely
studied topic in both the computer vision and robotics communities. This growth
however has led to fragmentation and a lack of standardisation in the field,
especially concerning performance evaluation. Moreover, the notion of viewpoint
and illumination invariance of VPR techniques has largely been assessed
qualitatively and hence ambiguously in the past. In this paper, we address
these gaps through a new comprehensive open-source framework for assessing the
performance of VPR techniques, dubbed "VPR-Bench". VPR-Bench (Open-sourced at:
https://github.com/MubarizZaffar/VPR-Bench) introduces two much-needed
capabilities for VPR researchers: firstly, it contains a benchmark of 12
fully-integrated datasets and 10 VPR techniques, and secondly, it integrates a
comprehensive variation-quantified dataset for quantifying viewpoint and
illumination invariance. We apply and analyse popular evaluation metrics for
VPR from both the computer vision and robotics communities, and discuss how
these different metrics complement and/or replace each other, depending upon
the underlying applications and system requirements.


  Recent improvements in object detection are driven by the success of
convolutional neural networks (CNN). They are able to learn rich features
outperforming hand-crafted features. So far, research in traffic light
detection mainly focused on hand-crafted features, such as color, shape or
brightness of the traffic light bulb. This paper presents a deep learning
approach for accurate traffic light detection in adapting a single shot
detection (SSD) approach. SSD performs object proposals creation and
classification using a single CNN. The original SSD struggles in detecting very
small objects, which is essential for traffic light detection. By our
adaptations it is possible to detect objects much smaller than ten pixels
without increasing the input image size. We present an extensive evaluation on
the DriveU Traffic Light Dataset (DTLD). We reach both, high accuracy and low
false positive rates. The trained model is real-time capable with ten frames
per second on a Nvidia Titan Xp. Code has been made available at
https://github.com/julimueller/tl_ssd.


  Interactions between particles in quantum many-body systems play a crucial
role in determining the electric, magnetic, optical, and thermal properties of
the system. The recent progress in the laser-pulse technique has enabled the
manipulations and measurements of physical properties on ultrafast timescales.
Here, we propose a method for the direct and ultrafast probing of quantum
many-body interaction through coherent two-dimensional (2D) spectroscopy. Up to
a moderate interaction strength, the inter-particle interaction manifests
itself in the emergence of off-diagonal peaks in the 2D spectrum before all the
peaks coalesce into a single diagonal peak as the system approaches the
Mott-insulating phase in the strongly interacting regime. The evolution of the
2D spectrum as a function of the time delay between the second and third laser
pulses can provide important information on the ultrafast time variation of the
interaction.


  In the wind-driven wave regime, the Miles mechanism gives an estimate of the
growth rate of the waves under the effect of wind. We consider the case where
this growth rate, normalised with respect to the frequency of the carrier wave,
is of the order of the wave steepness. Using the method of multiple scales, we
calculate the terms which appear in the nonlinear Schr\"odinger (NLS) equation
in this regime of fast-growing waves. We define a coordinate transformation
which maps the forced NLS equation into the standard NLS with constant
coefficients, that has a number of known analytical soliton solutions. Among
these solutions, the Peregrine and the Akhmediev solitons show an enhancement
of both their lifetime and maximum amplitude which is in qualitative agreement
with the results of tank experiments and numerical simulations of dispersive
focusing under the action of wind.


  Mellin-Barnes (MB) techniques applied to integrals emerging in particle
physics perturbative calculations are summarized. New versions of AMBRE
packages which construct planar and nonplanar MB representations are shortly
discussed. The numerical package MBnumerics.m is presented for the first time
which is able to calculate with a high precision multidimensional MB integrals
in Minkowskian regions. Examples are given for massive vertex integrals which
include threshold effects and several scale parameters.


  Probabilistic denoising diffusion models (DDMs) have set a new standard for
2D image generation. Extending DDMs for 3D content creation is an active field
of research. Here, we propose TetraDiffusion, a diffusion model that operates
on a tetrahedral partitioning of 3D space to enable efficient, high-resolution
3D shape generation. Our model introduces operators for convolution and
transpose convolution that act directly on the tetrahedral partition, and
seamlessly includes additional attributes such as color. Remarkably,
TetraDiffusion enables rapid sampling of detailed 3D objects in nearly
real-time with unprecedented resolution. It's also adaptable for generating 3D
shapes conditioned on 2D images. Compared to existing 3D mesh diffusion
techniques, our method is up to 200 times faster in inference speed, works on
standard consumer hardware, and delivers superior results.


  We survey recent joint work with M. Rapoport and W. Zhang related to the
arithmetic Gan-Gross-Prasad conjecture for Shimura varieties attached to
unitary groups.


  Postnikov constructed a cellular decomposition of the totally nonnegative
Grassmannians. The poset of cells can be described (in particular) via
Grassmann necklaces. We study certain quiver Grassmannians for the cyclic
quiver admitting a cellular decomposition, whose cells are naturally labeled by
Grassmann necklaces. We show that the posets of cells coincide with the
reversed cell posets of the cellular decomposition of the totally nonnegative
Grassmannians. We investigate algebro-geometric and combinatorial properties of
these quiver Grassmannians. In particular, we describe the irreducible
components, study the action of the automorphism groups of the underlying
representations and describe the moment graphs. We also construct a resolution
of singularities for each irreducible component; the resolutions are defined as
quiver Grassmannians for an extended cyclic quiver.


  In this paper, we analyze kink-like analytical solutions in a real scalar
theory with an arcsin dynamics inspired by the arcsin electrodynamics presented
in Kruglov (2015). This analysis is done by means of the first-order formalism.
This formalism provides a framework where the equations of motion can be
simplified by preserving the linear stability of the theory. In this work, the
deformation procedure is implemented with the aim of finding exact solutions in
systems with generalized dynamics. Along with the paper, we explore how the
first-order formalism is implemented in the arcsin kinetics and how such a term
influences the kink-like solutions. As a part of the result of our paper, we
show that the kink-like solutions are similar to the ones obtained in the
standard scalar kinetic theory. We also show that the extra parameter, that
controls the non-linearities of the model, plays an essential role in the
energy densities and stability potentials. These quantities vary according to
this parameter. The goals here are to show how the first-order framework is
implemented in this arcsin scenario and to present the analytical kink-like
solutions that can be found by means of the first-order framework and
deformation method.


  We prove the equivalence in the covariant phase space of the metric and
connection formulations for Palatini gravity, with nonmetricity and torsion, on
a spacetime manifold with boundary. To this end, we will rely on the
cohomological approach provided by the relative bicomplex framework. Finally,
we discuss some of the physical implications derived from this equivalence in
the context of singularity identification through curvature invariants.


  Mathai, Melrose, and Singer introduced the notion of projective elliptic
operators on manifolds equipped with an Azumaya bundle. In this note we compute
the equivariant index of transversally elliptic operators that are the pullback
of projective elliptic operators on the trivialization of the Azumaya bundle.
It encompasses the fractional index formula of projective elliptic operator by
Mathai-Melrose-Singer.


  Motivated by the recent "Cosmos Project" observation of dark-matter
concentrations with no ordinary matter in the same place, we study the question
of the existence of compact objects made of pure dark matter. We assume that
the dark matter is neutralino, and compare its elastic and annihilation cross
sections. We find that the two cross sections are of the same order of
magnitude. This result has a straightforward and important consequence that
neutralinos comprising a compact object can not achieve thermal equilibrium. To
substantiate our arguments, by solving Oppenheimer-Volkoff equation we
constructed a model of the star made of pure neutralinos. We explicitly showed
that the condition for the thermal equilibrium supported by the Fermi pressure
is never fulfilled inside the star. This neutralino state can not be described
by the Fermi-Dirac distribution. Thus, a stable neutralino star, which is
supported by the Fermi pressure, can not exist. We also estimated that a stable
star can not contain more than a few percents of neutralinos, most of the mass
must be in the form of the standard model particles.


  We investigate here the ability of a Green-Naghdi model to reproduce strongly
nonlinear and dispersive wave propagation. We test in particular the behavior
of the new hybrid finite-volume and finite-difference splitting approach
recently developed by the authors and collaborators on the challenging
benchmark of waves propagating over a submerged bar. Such a configuration
requires a model with very good dispersive properties, because of the
high-order harmonics generated by topography-induced nonlinear interactions. We
thus depart from the aforementioned work and choose to use a new Green-Naghdi
system with improved frequency dispersion characteristics. The absence of dry
areas also allows us to improve the treatment of the hyperbolic part of the
equations. This leads to very satisfying results for the demanding benchmarks
under consideration.


  Online control design using a high-fidelity, full-order model for a bipedal
robot can be challenging due to the size of the state space of the model. A
commonly adopted solution to overcome this challenge is to approximate the
full-order model (anchor) with a simplified, reduced-order model (template),
while performing control synthesis. Unfortunately it is challenging to make
formal guarantees about the safety of an anchor model using a controller
designed in an online fashion using a template model. To address this problem,
this paper proposes a method to generate safety-preserving controllers for
anchor models by performing reachability analysis on template models while
bounding the modeling error. This paper describes how this reachable set can be
incorporated into a Model Predictive Control framework to select controllers
that result in safe walking on the anchor model in an online fashion. The
method is illustrated on a 5-link RABBIT model, and is shown to allow the robot
to walk safely while utilizing controllers designed in an online fashion.


  Optimizing manufacturing process parameters is typically a multi-objective
problem with often contradictory objectives such as production quality and
production time. If production requirements change, process parameters have to
be optimized again. Since optimization usually requires costly simulations
based on, for example, the Finite Element method, it is of great interest to
have means to reduce the number of evaluations needed for optimization. To this
end, we consider optimizing for different production requirements from the
viewpoint of a framework for system flexibility that allows us to study the
ability of an algorithm to transfer solutions from previous optimization tasks,
which also relates to dynamic evolutionary optimization. Based on the extended
Oxley model for orthogonal metal cutting, we introduce a multi-objective
optimization benchmark where different materials define related optimization
tasks, and use it to study the flexibility of NSGA-II, which we extend by two
variants: 1) varying goals, that optimizes solutions for two tasks
simultaneously to obtain in-between source solutions expected to be more
adaptable, and 2) active-inactive genotype, that accommodates different
possibilities that can be activated or deactivated. Results show that adaption
with standard NSGA-II greatly reduces the number of evaluations required for
optimization to a target goal, while the proposed variants further improve the
adaption costs, although further work is needed towards making the methods
advantageous for real applications.


  The neutrino propagating in curved spacetimes, e.g. around black holes, in
early curved universe, violates Lorentz and then CPT symmetry, at least in the
local coordinate. This occurs due to coupling of spin of the neutrino to
background spin connection which modifies the underlying dispersion relation.
This results in the neutrino asymmetry and hence as a consequence neutrino
oscillation probability gets affected.


  In this paper, we present a new class of charged rotating black brane
solutions in the higher dimensional Brans-Dicke-Born-Infeld theory and
investigate their properties. Solving the field equations directly is a
non-trivial task because they include the second derivatives of the scalar
field. We remove this difficulty through a conformal transformation. Also, we
find that the suitable Lagrangian of Einstein-Born-Infeld-dilaton gravity is
not the same as presented in \cite{DHSR}. We show that the given solutions can
present black brane, with inner and outer event horizons, an extreme black
brane or a naked singularity provided the parameters of the solutions are
chosen suitably. These black brane solutions are neither asymptotically flat
nor (anti)-de Sitter. Then we calculate finite Euclidean action, the conserved
and thermodynamic quantities through the use of counterterm method. Finally, we
argue that these quantities satisfy the first law of thermodynamics, and the
entropy does not follow the area law.


  In this paper, we will introduce the new concepts of continuous bi-g-frames
and continuous K-bi-g-frame for Hilbert spaces. Then, we examine some
characterizations properties with the help of a biframe operator. Finally, we
investigate several results about the stability of continuous bi-g-Bessel
sequence and K-bi-g-frame are produced via the use of frame theory methods.


  The betweenness centrality of graphs using random walk paths instead of
geodesics is studied. A scaling collapse with no adjustable parameters is
obtained as the graph size $N$ is varied; the scaling curve depends on the
graph model. A normalized random betweenness, that counts each walk passing
through a node only once, is also defined. It is argued to be more useful and
seen to have simpler scaling behavior. In particular, the probability for a
random walk on a preferential attachment graph to pass through the root node is
found to tend to unity as $N\rightarrow\infty.$


  I discuss effective field theories of brane-world models where different
sectors break different halves of the extended bulk supersymmetry. It is shown
how to consistently couple N=2 supersymmetric matter to N=1 superfields that
lack N=2 partners but transform in a non-linear representation of the N=2
algebra. In particular, I explain how to couple an N=2 vector to N=1 chiral
fields such that the second supersymmetry is non-linearly realized. This method
is then used to study systems where different sectors break different halves of
supersymmetry, which appear naturally in models of intersecting branes.


  Quantum memories can be regarded as quantum channels that transmit
information through time without moving it through space. Aiming at a reliable
storage of information we may thus not only encode at the beginning and decode
at the end, but also intervene during the transmission - a possibility not
captured by the ordinary capacities in Quantum Shannon Theory. In this work we
introduce capacities that take this possibility into account and study them in
particular for the transmission of quantum information via dynamical semigroups
of Lindblad form. When the evolution is subdivided and supplemented by
additional continuous semigroups acting on arbitrary block sizes, we show that
the capacity of the ideal channel can be obtained in all cases. If the
supplementary evolution is reversible, however, this is no longer the case.
Upper and lower bounds for this scenario are proven. Finally, we provide a
continuous coding scheme and simple examples showing that adding a purely
dissipative term to a Liouvillian can sometimes increase the quantum capacity.


  We introduce a new notion of influence for symmetric convex sets over
Gaussian space, which we term "convex influence". We show that this new notion
of influence shares many of the familiar properties of influences of variables
for monotone Boolean functions $f: \{\pm1\}^n \to \{\pm1\}.$
  Our main results for convex influences give Gaussian space analogues of many
important results on influences for monotone Boolean functions. These include
(robust) characterizations of extremal functions, the Poincar\'e inequality,
the Kahn-Kalai-Linial theorem, a sharp threshold theorem of Kalai, a stability
version of the Kruskal-Katona theorem due to O'Donnell and Wimmer, and some
partial results towards a Gaussian space analogue of Friedgut's junta theorem.
The proofs of our results for convex influences use very different techniques
than the analogous proofs for Boolean influences over $\{\pm1\}^n$. Taken as a
whole, our results extend the emerging analogy between symmetric convex sets in
Gaussian space and monotone Boolean functions from $\{\pm1\}^n$ to $\{\pm1\}$


  We consider a general conic mixed-binary set where each homogeneous conic
constraint $j$ involves an affine function of independent continuous variables
and an epigraph variable associated with a nonnegative function, $f_j$, of
common binary variables. Sets of this form naturally arise as substructures in
a number of applications including mean-risk optimization, chance-constrained
problems, portfolio optimization, lot-sizing and scheduling, fractional
programming, variants of the best subset selection problem, a class of sparse
semidefinite programs, and distributionally robust chance-constrained programs.
We give a convex hull description of this set that relies on simultaneous
characterization of the epigraphs of $f_j$'s, which is easy to do when all
functions $f_j$'s are submodular. Our result unifies and generalizes an
existing result in two important directions. First, it considers \emph{multiple
general convex cone} constraints instead of a single second-order cone type
constraint. Second, it takes \emph{arbitrary nonnegative functions} instead of
a specific submodular function obtained from the square root of an affine
function. We close by demonstrating the applicability of our results in the
context of a number of problem classes.


  Spatial multi-agency has been receiving growing attention from researchers
exploring many of the aspects and modalities of this phenomenon. The aim is to
develop the theoretical background needed for a multitude of applications
involving the sharing of resources by more than one agent. A traffic management
system is one of these applications. Here, a large group of mobile robots that
are operating in communication-limited, and sensory-limited modes are required
to cope with each others presence as well as the contents of their environment
while preserving their ability to reach their preset, independent goals. This
work explores the construction of a decentralized traffic controller for a
large group of agents sharing a workspace with stationary forbidden regions.
The suggested multi-agent motion controller is complete provided that a lenient
condition on the geometry of the workspace is upheld. It has a low
computational effort that linearly increases with the number of agents. The
controller is also self-organizing; therefore, it is able to deal, on its own,
with incomplete information and unexpected situations. In addition to the
above, the controller has an open structure to enable any agent to join or
leave the group without the remaining agents having to adjust the manner in
which they function. To meet these requirements, a definition of
decentralization is suggested. This definition equates decentralization to
self-organization in a group of agents operating in an artificial life mode.
The definition is used to provide guidelines for the construction of the
multi-agent controller. The controller is realized using the potential field
approach. Theoretical developments, as well as simulation results, are
provided.


  Dynamical decoupling is a technique that protects qubits against noise. The
ability to preserve quantum coherence in the presence of noise is essential for
the development of quantum devices. Here the Rigetti quantum computing platform
was used to test different dynamical decoupling sequences. The performance of
the sequences was characterized by Quantum Process Tomography and analyzed
using the quantum channels formalism. It is shown that dynamical decoupling can
reduce qubit dephasing but cannot protect against spontaneous emission.
Furthermore, from process tomography results, it was also possible to conclude
that the action of dynamical decoupling cannot be understood as a simple
modification of the qubit coherence time. It is also shown here that the
performance of dynamical decoupling on the Rigetti's qubits is limited by pulse
imperfections. However, the performance can be improved using robust dynamical
decoupling, i.e. sequences that are robust against experimental imperfections.
The sequences tested here outperformed previous dynamical decoupling sequences
tested in the same platform.


  Despite the unsettled mechanism of electricity generation from the continuous
flow of liquids on a surface, the charge-discharge theory has been widely
accepted for alternating current (AC) generation from a moving droplet. It has
been recently extended to rationalize direct current (DC) generation across a
droplet moving between two different materials. By designing a reconfigurable
contact between a metal wire and a water droplet moving on graphene, we show
that the charge-discharge theory cannot explain the reversal of current when
water-metal interfaces switch from dynamic to static. All experiments can be
described after we distinguish a dynamic from a static interface and generalize
the photovoltaic-like effect to all dynamic junctions: excited electrons and
holes in a moving interface will be separated and swept under the built-in
electrical field, leading to a DC response. This generalized theory will lead
to an understanding and the design of efficient electricity generation based on
interfacial charge transfer.


  We report results of a study of charmless B meson decays to three-body KPiPi,
KKPi and KKK final states. Measurements of branching fractions for B decays to
K+0Pi+Pi-, K+K+K-, K0K+K-, KsKsK+ and KsKsKs final states are presented. The
decays B0=>K0K+K-, B+=>KsKsK+ and B0=>KsKsKs are observed for the first time.
We also report evidence for B+=>K+K-Pi+ decay. For the three-body final states
K0K+K-, KsKsPi+, K+K+Pi- and K-Pi+Pi+ 90% confidence level upper limits are
reported. Finally, we discuss the possibility of using the three-body
B0=>KsK+K- decay for CP violation studies. The results are obtained with a 78
fb^-1 data sample collected at the Y(4S) resonance by the Belle detector
operating at the KEKB asymmetric energy e+e- collider.