  A spherical domain wall around a small black hole is formed by the Hawking
radiation from the black hole in the symmetry-broken-phase of the field theory,
e.g., the Standard Model (SM) and the Grand Unified Theory (GUT) which have a
property of the phase transition. We have obtained two types of the spherical
domain wall; (a) thermalized wall which is formed by the local heating up near
black hole and symmetry restore locally and (b) dynamical wall which is formed
by the balance between the pressure from the Hawking radiation and the pressure
from the wall tensions. The electroweak wall is formed as a thermalized wall
around a black hole with mass of the several hundred kilogram. The GUT wall is
formed as a dynamical wall around much smaller black hole. The electroweak wall
around a black hole can produce baryon number by the assumption of the
CP-broken phase in the wall. The GUT wall can supply charge into the black
hole, namely, the wall causes the spontaneous charging up of the black hole. We
propose a cosmological model which can explain the origin of the baryon number
and the cold dark matter by the primordial black hole with mass of the several
hundred kilogram.


  The epoch of reionization and formation of first stars are inter-linked
topics that are of considerable interest. We use a simplified approach for
studying formation of stars in collapsed haloes, and the resulting ionization
of the inter-galactic medium (IGM). We consider a set of LCDM models allowed by
observations of CMB temperature and polarization anisotropies for this study.
We constrain parameters related to star formation with the help of
observations. We constrain subsets of these parameters independently by using
the observed metallicity of the inter-galactic medium at z ~ 5 and the
requirement that the Thomson scattering optical depth due to an ionized IGM as
determined for the model from CMB observations be reproduced. We consider a
range of initial metalicities for star forming gas, and some variations of the
initial mass function of stars. We find that a "normal" initial mass function
(IMF) may satisfy these two constraints with a raised efficiency of star
formation as compared to that seen in the local universe. Observations require
a significant fraction of metals to escape from haloes to the IGM. We can also
place constraints on the ratio of escape fraction for metals and ionizing
photons, we find that this ratio is of order unity for most models. This
highlights the importance of using the constraints arising from enrichment of
the inter-galactic medium. (Abridged)


  With the rapid development of indoor location-based services (LBSs), the
demand for accurate localization keeps growing as well. To meet this demand, we
propose an indoor localization algorithm based on graph convolutional network
(GCN). We first model access points (APs) and the relationships between them as
a graph, and utilize received signal strength indication (RSSI) to make up
fingerprints. Then the graph and the fingerprint will be put into GCN for
feature extraction, and get classification by multilayer perceptron (MLP).In
the end, experiments are performed under a 2D scenario and 3D scenario with
floor prediction. In the 2D scenario, the mean distance error of GCN-based
method is 11m, which improves by 7m and 13m compare with DNN-based and
CNN-based schemes respectively. In the 3D scenario, the accuracy of predicting
buildings and floors are up to 99.73% and 93.43% respectively. Moreover, in the
case of predicting floors and buildings correctly, the mean distance error is
13m, which outperforms DNN-based and CNN-based schemes, whose mean distance
errors are 34m and 26m respectively.


  The absolute frequency measurement for all of the hyperfine transitions of
6P1/2 -> 7S1/2 using a self-referencing frequency comb is reported. This
transition can be used as a bench marker for the accurate atomic wave function,
and then improve the calculation of the atomic parity- non-conservation (PNC).
The frequency center is precisely determined by saturation spectroscopy
utilizing a pair of the counter-propagating laser beams intersecting with
atomic beam. Such a Doppler-free profile has been improved to 350 kHz in the
absolute frequency measurement. The 7S1/2 state hyperfine splittings have also
been deduced from our results.


  An improved understanding of the divergence-free constraint for the
incompressible Navier--Stokes equations leads to the observation that a
semi-norm and corresponding equivalence classes of forces are fundamental for
their nonlinear dynamics. The recent concept of {\em pressure-robustness}
allows to distinguish between space discretisations that discretise these
equivalence classes appropriately or not. This contribution compares the
accuracy of pressure-robust and non-pressure-robust space discretisations for
transient high Reynolds number flows, starting from the observation that in
generalised Beltrami flows the nonlinear convection term is balanced by a
strong pressure gradient. Then, pressure-robust methods are shown to outperform
comparable non-pressure-robust space discretisations. Indeed, pressure-robust
methods of formal order $k$ are comparably accurate than non-pressure-robust
methods of formal order $2k$ on coarse meshes. Investigating the material
derivative of incompressible Euler flows, it is conjectured that strong
pressure gradients are typical for non-trivial high Reynolds number flows.
Connections to vortex-dominated flows are established. Thus,
pressure-robustness appears to be a prerequisite for accurate incompressible
flow solvers at high Reynolds numbers. The arguments are supported by numerical
analysis and numerical experiments.


  Let $S$ be a minimal mass blow up solution of the critical generalized KdV
equation as constructed by Martel, Merle and Rapha\"el in arXiv:1204.4624. We
prove both time and space sharp asymptotics for $S$ close to the blow up time.
Let $Q$ be the unique ground state of (gKdV), satisfying $Q"+Q^5=Q$.
  First, we show that there exist universal smooth profiles
$Q_k\in\mathcal{S}(\mathbb{R})$ (with $Q_0=Q$) and a constant
$c_0\in\mathbb{R}$ such that, fixing the blow up time at $t=0$ and appropriate
scaling and translation parameters, $S$ satisfies, for any $m\geqslant 0$, \[
\partial_x^m S(t) - \sum_{k=0}^{[m/2]} \frac 1{t^{\frac 12+m-2k}}
Q_k^{(m-k)}\left(\frac{\cdot+ \frac1t}{t}+c_0\right)\to 0\quad \mbox{in}\ L^2
\mbox{as}\ t\downarrow 0. \] Second, we prove that, for $0<t\ll 1$, $x\leqslant
-\frac 1t -1$, \[ S(t,x) \sim - \frac 12 \|Q\|_{L^1} |x|^{-3/2}, \] and related
bounds for the derivatives of $S(t)$ of any order. We also prove
$\int_{\mathbb{R}} S(t,x)\,dx=0$.


  Digital information revolution has brought about many advantages and new
issues. The protection of ownership and the prevention of unauthorized
manipulation of digital audio, image, and video materials has become an
important concern due to the ease of editing and perfect reproduction.
Watermarking is identified as a major means to achieve copyright protection. It
is a branch of information hiding which is used to hide proprietary information
in digital media like photographs, digital music, digital video etc. In this
paper, a new image watermarking algorithm that is robust against various
attacks is presented. DWT (Discrete Wavelet Transform) and SVD (Singular Value
Decomposition) have been used to embed two watermarks in the HL and LH bands of
the host image. Simulation evaluation demonstrates that the proposed technique
withstand various attacks.


  We show that neutrino-photon reactions above $m_e$ are dominated by the
reaction $\nu \gamma \to \nu e^+ e^-$. We calculate its cross-section and see
that it is larger by several orders of magnitude than the cross-sections of
other neutrino-photon processes, for energies above $m_e$. We also discuss
potential astrophysical and cosmological consequences.


  We present photometry and spectroscopy of the slowly evolving superluminous
Type IIn SN2015da. SN2015da is extraordinary for its very high peak luminosity,
and also for sustaining a high luminosity for several years. Even at 8\,yr
after explosion, SN2015da remains as luminous as the peak of a normal SNII-P.
The total radiated energy integrated over this time period (with no bolometric
correction) is at least 1.6 FOE. Including a mild bolometric correction, adding
kinetic energy of the expanding cold dense shell of swept-up circumstellar
material (CSM), and accounting for asymmetry, the total explosion kinetic
energy was likely 5-10 FOE. Powering the light curve with CSM interaction
requires an energetic explosion and 20 Msun of H-rich CSM, which in turn
implies a massive progenitor system above 30 Msun. Narrow P Cyg features show
steady CSM expansion at 90 km/s, requiring a high average mass-loss rate of
roughly 0.1 Msun/yr sustained for 2 centuries before explosion (although
ramping up toward explosion time). No current theoretical model for single-star
pre-SN mass loss can account for this. The slow CSM, combined with broad wings
of H$\alpha$ indicating H-rich material in the unshocked ejecta, disfavor a
pulsational pair instability model for the pre-SN mass loss. Instead, violent
pre-SN binary interaction is a likely cuprit. Finally, SN2015da exhibits the
characteristic asymmetric blueshift in its emission lines from shortly after
peak until the present epoch, adding another well-studied superluminous SNeIIn
with unambiguous evidence of post-shock dust formation.


  Searches for the direct pair production of the third generation squarks are
presented in this conference report, based on proton-proton collisions at a
center-of-mass energy of 13 TeV and corresponding to an integrated luminosity
of 35.9 fb$^{-1}$, collected by the CMS detector. New techniques have been
developed to address different kinematical regimes. In absence of statistically
significant deviations from the standard model background, limits have been
derived in terms of simplified model spectra, excluding for example a stop up
to a mass of 1.05~TeV when it decays to a top and a massless neutralino.


  We prove that in wide generality the critical curve of the activated random
walk model is a continuous function of the deactivation rate, and we provide a
bound on its slope which is uniform with respect to the choice of the graph.
Moreover, we derive strict monotonicity properties for the probability of a
wide class of `increasing' events,extending previous results of Rolla and
Sidoravicius (2012). Our proof method is of independent interest and can be
viewed as a reformulation of the `essential enhancements' technique -- which
was introduced for percolation -- in the framework of Abelian networks.


  Ultra-high-energy (UHE) neutrinos, with EeV-scale energies, carry with them
unique insight into fundamental open questions in astrophysics and particle
physics. For fifty years, they have evaded discovery, but maybe not for much
longer, thanks to new UHE neutrino telescopes, presently under development. We
capitalize on this upcoming opportunity by producing state-of-the-art forecasts
of the discovery of a diffuse flux of UHE neutrinos in the next 10-20 years. By
design, our forecasts are anchored in often-overlooked nuance from theory and
experiment; we gear them to the radio array of the planned IceCube-Gen2
detector. We find encouraging prospects: even under conservative analysis
choices, most benchmark UHE neutrino flux models available in the literature
may be discovered within 10 years of detector exposure -- many sooner -- and
may be distinguished from each other. Our results validate the transformative
potential of next-generation UHE neutrino telescopes.


  The character table of the symmetric group $S_n$, of permutations of $n$
objects, is of fundamental interest in theoretical physics, combinatorics as
well as computational complexity theory. We investigate the implications of an
identity, which has a geometrical interpretation in combinatorial topological
field theories, relating the column sum of normalised central characters of
$S_n$ to a sum of structure constants of multiplication in the centre of the
group algebra of $S_n$. The identity leads to the proof that a combinatorial
computation of the column sum belongs to complexity class \shP. The sum of
structure constants has an interpretation in terms of the counting of branched
covers of the sphere. This allows the identification of a tractable subset of
the structure constants related to genus zero covers. We use this subset to
prove that the column sum for a conjugacy class labelled by partition $\lambda$
is non-vanishing if and only if the permutations in the conjugacy class are
even. This leads to the result that the determination of the vanishing or
otherwise of the column sum is in complexity class \pP. The subset gives a
positive lower bound on the column sum for any even $ \lambda$. For any
disjoint decomposition of $ \lambda$ as $\lambda_1 \sqcup \lambda_2 $ we obtain
a lower bound for the column sum at $ \lambda$ in terms of the product of the
column sums for $ \lambda_1$ and$\lambda_2$. This can be expressed as a
super-additivity property for the logarithms of column sums of normalized
characters.


  Models are developed for the motion of charge-2 Abelian Higgs vortices
through the 2-vortex moduli space $M$, with the vortices excited by their shape
mode oscillations. The models simplify to the well-known geodesic flow on $M$,
modified by a potential, when the mode oscillations are fast relative to the
moduli space motion and their amplitudes are small. When the lowest-frequency
mode is excited with a large amplitude, the geodesic flow is not a correct
description. Instead, a chaotic, or even fractal, multi-bounce structure in
vortex-vortex collisions is predicted.


  We propose to incorporate feature correlation and sequential processing into
dense optical flow estimation from event cameras. Modern frame-based optical
flow methods heavily rely on matching costs computed from feature correlation.
In contrast, there exists no optical flow method for event cameras that
explicitly computes matching costs. Instead, learning-based approaches using
events usually resort to the U-Net architecture to estimate optical flow
sparsely. Our key finding is that the introduction of correlation features
significantly improves results compared to previous methods that solely rely on
convolution layers. Compared to the state-of-the-art, our proposed approach
computes dense optical flow and reduces the end-point error by 23% on MVSEC.
Furthermore, we show that all existing optical flow methods developed so far
for event cameras have been evaluated on datasets with very small displacement
fields with a maximum flow magnitude of 10 pixels. Based on this observation,
we introduce a new real-world dataset that exhibits displacement fields with
magnitudes up to 210 pixels and 3 times higher camera resolution. Our proposed
approach reduces the end-point error on this dataset by 66%.


  The Louisiana Department of Education partnered with the Gordon A. Cain
Center at LSU to pilot a Computing High School Graduation Pathway. The first
course in the pathway, Introduction to Computational Thinking (ICT), is
designed to teach programming and reinforce mathematical practice skills of
nine-grade students, with an emphasis on promoting higher order thinking. In
2017-18, about 200 students and five teachers participated in the pilot, in
2018-2019 the participation increased to 400 students, and in the current
2019-2020 year about 800 students in 11 schools are involved. Professional
development starts with a five-week intensive summer institute, which is
complemented with follow-up Saturday sessions and coaching support during the
academic year. After describing the course content and briefly the teacher
training, we discuss the data we have collected in the last two years. The
overall student reception of the course has been positive, but the course was
categorized by most students as hard. However, the Computing Attitude Survey
analysis indicates that the difficulty of the course did not demotivate the
students. The pre-post test content assessments show that students learned not
only the language, but also general principles of programming, logic and
modeling, as well as use of variables, expressions and functions. Lessons
learned during the pilot phase motivated changes, such as emphasizing during PD
the need to provide timely feedback to students, provide detailed rubrics for
the projects and reorganize the lessons to increase the initial engagement with
the material. After two years of running pilots, the course is becoming
student-centered, where most of the code and image samples provided in the
lessons are based on code created by previous students.


  Fast and accurate performance analysis techniques are essential in early
design space exploration and pre-silicon evaluations, including software
eco-system development. In particular, on-chip communication continues to play
an increasingly important role as the many-core processors scale up. This paper
presents the first performance analysis technique that targets networks-on-chip
(NoCs) that employ weighted round-robin (WRR) arbitration. Besides fairness,
WRR arbitration provides flexibility in allocating bandwidth proportionally to
the importance of the traffic classes, unlike basic round-robin and
priority-based arbitration. The proposed approach first estimates the effective
service time of the packets in the queue due to WRR arbitration. Then, it uses
the effective service time to compute the average waiting time of the packets.
Next, we incorporate a decomposition technique to extend the analytical model
to handle NoC of any size. The proposed approach achieves less than 5% error
while executing real applications and 10% error under challenging synthetic
traffic with different burstiness levels.


  We extend monotone quasiconformal mappings from dimension n to n+1 while
preserving both monotonicity and quasiconformality. The extension is given
explicitly by an integral operator. In the case n=1 it yields a refinement of
the Beurling-Ahlfors extension.


  The energies of p-shell hypernuclear gamma rays obtained from recent
experiments using the Hyperball at BNL and KEK are used to constrain the YN
interaction which enters into shell-model calculations that include both Lambda
and Sigma configurations.


  The general solution of a 7D analogue of the 3D Euler top equation is shown
to be given by an integration over a Riemann surface with genus 9. The 7D model
is derived from the 8D $Spin(7)$ invariant self-dual Yang-Mills equation
depending only upon one variable and is regarded as a model describing
self-dual membrane instantons. Several integrable reductions of the 7D top to
lower target space dimensions are discussed and one of them gives 6, 5, 4D
descendants and the 3D Euler top associated with Riemann surfaces with genus 6,
5, 2 and 1, respectively.


  We study the relationship between decaying active region magnetic fields,
coronal holes and the global coronal magnetic structure using Global
Oscillations Network Group (GONG) synoptic magnetograms, Solar Terrestrial
RElations Observatory (STEREO) extreme ultra-violet (EUV) synoptic maps and
coronal potential-field source-surface (PFSS) models. We analyze 14 decaying
regions and associated coronal holes occurring between early 2007 and late
2010, four from cycle 23 and 10 from cycle 24. We investigate the relationship
between asymmetries in active regions' positive and negative magnetic
intensities, asymmetric magnetic decay rates, flux imbalances, global field
structure and coronal hole formation. Whereas new emerging active regions
caused changes in the large-scale coronal field, the coronal fields of the 14
decaying active regions only opened under the condition that the global coronal
structure remained almost unchanged. This was because the dominant
slowly-varying, low-order multipoles prevented opposing-polarity fields from
opening and the remnant active-region flux preserved the regions' low-order
multipole moments long after the regions had decayed. Thus the polarity of each
coronal hole necessarily matched the polar field on the side of the streamer
belt where the corresponding active region decayed. For magnetically isolated
active regions initially located within the streamer belt, the more intense
polarity generally survived to form the hole. For non-isolated regions, flux
imbalance and topological asymmetry prompted the opposite to occur in some
cases.


  In the framework of the impulse approximation we study the photoproduction of
the hypertriton $^3_{\Lambda}$H by using realistic $^3$He wave functions
obtained as solutions of Faddeev equations with the Reid soft-core potential
for different $^3_{\Lambda}$H wave functions. We obtain relatively small cross
sections of the order of 1 nb. We also find that the influence of Fermi motion
is important, while the effect of different off-shell assumptions on the cross
section is not too significant.


  This paper presents some basic elements regarding the domain of the
collaborative systems, a domain of maximum actuality and also the multiagent
systems, developed as a result of a sound study on the one-agent systems.


  The density and isospin dependences of the nonrelativistic nucleon effective
mass ($m^*$) are studied, which is a measure of the nonlocality of the single
particle (s.p.) potential. We decouple it further into the so called k-mass
($m^*_k$, i.e., the nonlocality in space) and E-mass ($m^*_E$, i.e., the
nonlocality in time). Both masses are determined and compared from the latest
versions of the nonrelativistic Brueckner-Hartree Fock (BHF) model and the
relativistic Hartree-Fock (RHF) model. The latter are achieved based on the
corresponding Schr\"{o}dinger equivalent s.p. potential in a relativistic
framework. We demonstrate the origins of different effective masses and discuss
also their neutron-proton splitting in the asymmetric matter in different
models. We find that the neutron-proton splittings of both the k-mass and the
E-mass have the same asymmetry dependences at considered densities, namely
$m^*_{k,n} > m^*_{k,p}$ and $m^*_{E,p} > m^*_{E,n}$. However, the resulting
splittings of nucleon effective masses could have different asymmetry
dependences in the two models, because they could be dominated either by that
of the k-mass (then we have $m^*_n > m^*_p$ in the BHF model) or by that of the
E-mass (then we have $m^*_p > m^*_n$ in the RHF model).


  Retirement prediction helps individuals and institutions make informed
financial, lifestyle, and workforce decisions based on estimated retirement
portfolios. This paper attempts to predict retirement using Monte Carlo
simulations, allowing one to probabilistically account for a range of
possibilities. The authors propose a model to predict the values of the
investment accounts IRA and 401(k) through the simulation of inflation rates,
interest rates, and other pertinent factors. They provide a user case study to
discuss the implications of the proposed model.


  In calculations of the inspiral of binary black holes an intermediate
approximation is needed that can bridge the post-Newtonian methods of the early
inspiral and the numerical relativity computations of the final plunge. We
describe here the periodic standing wave approximation: A numerical solution is
found to the problem of a periodic rotating binary with helically symmetric
standing wave fields, and from this solution an approximation is extracted for
the physically relevant problem of inspiral with outgoing waves. The
approximation underlying this approach has been recently confirmed with
innovative numerical methods applied to nonlinear model problems.


  The coherence of polaritons plays a fundamental role in numerous recent
experimental observations, from strong coupling to Bose-Einstein condensation,
but accessing the coherence of polaritons is a difficult task due to the high
energy of plasmons and excitons. However, surface phonon polaritons offer
similar promises at much lower energy. Here, we demonstrate the possibility to
use visible ultrafast lasers to generate and time resolve coherent surface
phonon polaritons in nanowires. We show that these modes are generated through
the ultrafast screening of the surface depletion field. By comparing
experiments and FDTD simulations, we show that this method allows the
simultaneous generation of dark and bright mode. Our observations open the way
to deeper investigations of the role of coherence in the rich polariton
physics.


  We address the nature of phase transitions in periodically driven systems
coupled to a bath. The latter enables a synchronized non-equilibrium Floquet
steady state at finite entropy, which we analyse for rapid drives within a
non-equilibrium RG approach. While the infinitely rapidly driven limit exhibits
a second order phase transition, here we reveal that fluctuations turn the
transition first order when the driving frequency is finite. This can be traced
back to a universal mechanism, which crucially hinges on the competition of
degenerate, near critical modes associated to higher Floquet Brillouin zones.
The critical exponents of the infinitely rapidly driven system -- including a
new, independent one -- can yet be probed experimentally upon smoothly tuning
towards that limit.


  Using simultaneous optical and infrared light curves of disc-bearing young
stars in NGC 2264, we perform the first multi-wavelength structure function
study of YSOs. We find that dippers have larger variability amplitudes than
bursters and symmetric variables at all timescales longer than a few hours. By
analysing optical-infrared colour time-series, we also find that the
variability in the bursters is systematically less chromatic at all timescales
than the other variability types. We propose a model of YSO variability in
which symmetric, bursting, and dipping behaviour is observed in systems viewed
at low, intermediate, and high inclinations, respectively. We argue that the
relatively short thermal timescale for the disc can explain the fact that the
infrared light curves for bursters are more symmetric than their optical
counterparts.


  Given an $\infty$-category with a set of weak equivalences which is stable
under pullback, we show that the mapping spaces of the corresponding
localization can be described as group completions of $\infty$-categories of
spans. Furthermore, we show how these $\infty$-categories of spans are the
mapping objects of an $(\infty, 2)$-category, which yields a Segal space model
for the localization after a Kan fibrant replacement.


  For a vector space $V$ the \emph{intersection graph of subspaces} of $V$,
denoted by $G(V)$, is the graph whose vertices are in a one-to-one
correspondence with proper nontrivial subspaces of $V$ and two distinct
vertices are adjacent if and only if the corresponding subspaces of $V$ have a
nontrivial (nonzero) intersection. In this paper, we study the clique number,
the chromatic number, the domination number and the independence number of the
intersection graphs of subspaces of a vector space.


  The interpretation of recent observations of bow shocks around O-stars and
the creation of corresponding models require a detailed understanding of the
associated (magneto-)hydrodynamic structures. We base our study on
three-dimensional numerical magneto-)hydrodynamical models, which are analyzed
using the dynamically relevant parameters, in particular, the (magneto)sonic
Mach numbers. The analytic Rankine-Hugoniot relation for HD and MHD are
compared with those obtained by the numerical model. In that context we also
show that the only distance which can be approximately determined is that of
the termination shock, if it is a hydrodynamical shock. For MHD shocks the
stagnation point does not, in general, lie on the inflow line, which is the
line parallel to the inflow vector and passing through the star. Thus an
estimate via the Bernoulli equation as in the HD case is, in general, not
possible. We also show that in O-star astrospheres, distinct regions exist in
which the fast, slow, Alfv\'enic, and sonic Mach numbers become lower than one,
implying sub-slow magnetosonic as well as sub-fast and sub-sonic flows.
Nevertheless, the analytic MHD Rankine Hugoniot relations can be used for
further studies of turbulence and cosmic ray modulation.


  We present exact calculations of the zero-temperature partition function, and
ground-state degeneracy (per site), $W$, for the $q$-state Potts
antiferromagnet on a variety of homeomorphic families of planar strip graphs $G
= (Ch)_{k_1,k_2,\Sigma,k,m}$, where $k_1$, $k_2$, $\Sigma$, and $k$ describe
the homeomorphic structure, and $m$ denotes the length of the strip. Several
different ways of taking the total number of vertices to infinity, by sending
(i) $m \to \infty$ with $k_1$, $k_2$, and $k$ fixed; (ii) $k_1$ and/or $k_2 \to
\infty$ with $m$, and $k$ fixed; and (iii) $k \to \infty$ with $m$ and
$p=k_1+k_2$ fixed are studied and the respective loci of points ${\cal B}$
where $W$ is nonanalytic in the complex $q$ plane are determined. The ${\cal
B}$'s for limit (i) are comprised of arcs which do not enclose regions in the
$q$ plane and, for many values of $p$ and $k$, include support for $Re(q) < 0$.
The ${\cal B}$ for limits (ii) and (iii) is the unit circle $|q-1|=1$.


  We find closed-form solutions to the stochastic game between a broker and a
mean-field of informed traders. In the finite player game, the informed traders
observe a common signal and a private signal. The broker, on the other hand,
observes the trading speed of each of his clients and provides liquidity to the
informed traders. Each player in the game optimises wealth adjusted by
inventory penalties. In the mean field version of the game, using a G\^ateaux
derivative approach, we characterise the solution to the game with a system of
forward-backward stochastic differential equations that we solve explicitly. We
find that the optimal trading strategy of the broker is linear on his own
inventory, on the average inventory among informed traders, and on the common
signal or the average trading speed of the informed traders. The Nash
equilibrium we find helps informed traders decide how to use private
information, and helps brokers decide how much of the order flow they should
externalise or internalise when facing a large number of clients.


  Functional data have been the subject of many research works over the last
years. Functional regression is one of the most discussed issues. Specifically,
significant advances have been made for functional linear regression models
with scalar response. Let $(\mathcal{H},<\cdot,\cdot>)$ be a separable Hilbert
space. We focus on the model $Y=<\Theta,X>+b+\varepsilon$, where $Y$ and
$\varepsilon$ are real random variables, $X$ is an $\mathcal{H}$-valued random
element, and the model parameters $b$ and $\Theta$ are in $\mathbb{R}$ and
$\mathcal{H}$, respectively. Furthermore, the error satisfies that
$E(\varepsilon|X)=0$ and $E(\varepsilon^2|X)=\sigma^2<\infty$. A consistent
bootstrap method to calibrate the distribution of statistics for testing $H_0:
\Theta=0$ versus $H_1: \Theta\neq 0$ is developed. The asymptotic theory, as
well as a simulation study and a real data application illustrating the
usefulness of our proposed bootstrap in practice, is presented.


  First principles studies of multiferroic materials, such as bismuth ferrite
(BFO), require methods that extend beyond standard density functional theory
(DFT). The DFT+U method is one such extension that is widely used in the study
of BFO. We present a systematic study of the effects of the U parameter on the
structural, ferroelectric and electronic properties of BFO. We find that the
structural and ferroelectric properties change negligibly in the range of U
typically considered for BFO (3-5 eV). In contrast, the electronic structure
varies significantly with U. In particular, we see large changes to the
character and curvature of the valence band maximum and conduction band
minimum, in addition to the expected increase in band gap, as U increases. Most
significantly, we find that the $t_{2g}$/$e_{g}$ ordering, expected from
crystal field theory, is inverted for U values larger than 4 eV. We therefore
recommend a U value of at most 4 eV to be applied to the Fe $d$ orbitals in
BFO. More generally, this study emphasises the need for systematic
investigations of the effects of the U parameter not merely on band gaps but on
the electronic structure as a whole, especially for strongly correlated
materials.


  Cross-lingual synthesis can be defined as the task of letting a speaker
generate fluent synthetic speech in another language. This is a challenging
task, and resulting speech can suffer from reduced naturalness, accented
speech, and/or loss of essential voice characteristics. Previous research shows
that many models appear to have insufficient generalization capabilities to
perform well on every of these cross-lingual aspects. To overcome these
generalization problems, we propose to apply the teacher-student paradigm to
cross-lingual synthesis. While a teacher model is commonly used to produce
teacher forced data, we propose to also use it to produce augmented data of
unseen speaker-language pairs, where the aim is to retain essential speaker
characteristics. Both sets of data are then used for student model training,
which is trained to retain the naturalness and prosodic variation present in
the teacher forced data, while learning the speaker identity from the augmented
data. Some modifications to the student model are proposed to make the
separation of teacher forced and augmented data more straightforward. Results
show that the proposed approach improves the retention of speaker
characteristics in the speech, while managing to retain high levels of
naturalness and prosodic variation.


  We define a new ${\mathbb Z}_2$-graded quantum (2+1)-space and show that the
extended ${\mathbb Z}_2$-graded algebra of polynomials on this ${\mathbb
Z}_2$-graded quantum space, denoted by ${\cal F}({\mathbb C}_q^{2\vert1})$, is
a ${\mathbb Z}_2$-graded Hopf algebra. We construct a right-covariant
differential calculus on ${\cal F}({\mathbb C}_q^{2\vert1})$ and define a
${\mathbb Z}_2$-graded quantum Weyl algebra and mention a few algebraic
properties of this algebra. Finally, we explicitly construct the dual ${\mathbb
Z}_2$-graded Hopf algebra of ${\cal F}({\mathbb C}_q^{2\vert1})$.


  Using Kostant's weight multiplicity formula, we describe and enumerate the
terms contributing a nonzero value to the multiplicity of a positive root $\mu$
in the adjoint representation of $\mathfrak{sl}_{r+1}(\mathbb{C})$, which we
denote $L(\tilde{\alpha})$, where $\tilde{\alpha}$ is the highest root of
$\mathfrak{sl}_{r+1}(\mathbb{C})$. We prove that the number of terms
contributing a nonzero value in the multiplicity of the positive root
$\mu=\alpha_i+\alpha_{i+1}+\cdots+\alpha_j$ with $1\leq i\leq j\leq r$ in
$L(\tilde{\alpha})$ is given by the product $F_{i}\cdot F_{r-j+1}$, where $F_n$
is the $n^{\text{th}}$ Fibonacci number. Using this result, we show that the
$q$-multiplicity of the positive root
$\mu=\alpha_i+\alpha_{i+1}+\cdots+\alpha_j$ with $1\leq i\leq j\leq r$ in the
representation $L(\tilde{\alpha})$ is precisely $q^{r-h(\mu)}$, where
$h(\mu)=j-i+1$ is the height of the positive root $\mu$. Setting $q=1$ recovers
the known result that the multiplicity of a positive root in the adjoint
representation of $\mathfrak{sl}_{r+1}(\mathbb{C})$ is one.


  Two distinct mechanisms are investigated for transferring a pure 87Rb
Bose-Einstein condensate in the F = 2, mF = 2 state into a mixture of
condensates in all the mF states within the F = 2 manifold. Some of these
condensates remain trapped whilst others are output coupled in the form of an
elementary pulsed atom laser. Here we present details of the condensate
preparation and results of the two condensate output coupling schemes. The
first scheme is a radio frequency technique which allows controllable transfer
into available mF states, and the second makes use of Majorana spin flips to
equally populate all the manifold sub-states.


  Quantization has become a predominant approach for model compression,
enabling deployment of large models trained on GPUs onto smaller form-factor
devices for inference. Quantization-aware training (QAT) optimizes model
parameters with respect to the end task while simulating quantization error,
leading to better performance than post-training quantization. Approximation of
gradients through the non-differentiable quantization operator is typically
achieved using the straight-through estimator (STE) or additive noise. However,
STE-based methods suffer from instability due to biased gradients, whereas
existing noise-based methods cannot reduce the resulting variance. In this
work, we incorporate exponentially decaying quantization-error-aware noise
together with a learnable scale of task loss gradient to approximate the effect
of a quantization operator. We show this method combines gradient scale and
quantization noise in a better optimized way, providing finer-grained
estimation of gradients at each weight and activation layer's quantizer bin
size. Our controlled noise also contains an implicit curvature term that could
encourage flatter minima, which we show is indeed the case in our experiments.
Experiments training ResNet architectures on the CIFAR-10, CIFAR-100 and
ImageNet benchmarks show that our method obtains state-of-the-art top-1
classification accuracy for uniform (non mixed-precision) quantization,
out-performing previous methods by 0.5-1.2% absolute.


  We present Atacama Large Millimeter Array (ALMA) polarization observations at
97.5 GHz of the southern hot spot of the radio galaxy 3C 445. The hot spot
structure is dominated by two bright components enshrouded by diffuse emission.
Both components show fractional polarization between 30 and 40 per cent,
suggesting the presence of shocks. The polarized emission of the western
component has a displacement of about 0.5 kpc outward with respect to the total
intensity emission, and may trace the surface of a front shock. Strong
polarization is observed in a thin strip marking the ridge of the hot spot
structure visible from radio to optical. No significant polarization is
detected in the diffuse emission between the main components, suggesting a
highly disordered magnetic field likely produced by turbulence and
instabilities in the downstream region that may be at the origin of the
extended optical emission observed in this hot spot. The polarization
properties support a scenario in which a combination of both multiple and
intermittent shock fronts due to jet dithering, and spatially distributed
stochastic second-order Fermi acceleration processes are present in the hot
spot complex.


  (Shortened Abstract) We present new X-ray data taken from the ROSAT PSPC
pointing archive for 21 clusters in the Einstein Extended Medium Sensitivity
Survey (EMSS). We have supplemented these data with new optical follow-up
observations found in the literature and overall, 32 of the original 67 z>0.14
EMSS clusters now have new information. Using this improved EMSS sample, we
have re-determined the EMSS X-ray Cluster Luminosity Function as a function of
redshift. We have removed potential mis-classifications and included our new
measurements of the clusters X-ray luminosities and redshifts. We find similar
luminosity functions to those originally presented by Henry etal (1992); albeit
with two important differences. First, we show that the original low redshift
EMSS luminosity function is insufficiently constrained. Secondly, the power law
shape of our new determination of the high redshift EMSS luminosity function
(z=0.3 to 0.6) has a shallower slope than that seen by Henry etal. We have
quantified the degree of evolution seen in the X-ray cluster luminosity using
several statistical tests. The most restrictive analysis indicates that our low
and high redshift EMSS luminosity functions are statistically different at only
the 95% level. However, other tests indicate that these luminosity functions
differ by as little as one sigma. These data are therefore, consistent with no
evolution in the X-ray cluster luminosity function out to z=0.5.


  Let $F$ be a distribution function on the integer lattice $\mathbb{Z}$ and
$S=(S_n)$ the random walk with step distribution $F$. Suppose $S$ is
oscillatory and denote by $U_{\rm a}(x)$ and $u_{\rm a}(x)$ the renewal
function and sequence, respectively, of the strictly ascending ladder height
process associated with $S$. Putting $A(x) =\int_0^x [1-F(t)-F(-t)] dt$,
$H(x)=1-F(x)+F(-x)$ we suppose
  $$A(x)/\big(xH(x)\big) \to -\infty \quad (x\to\infty).$$ Under some
additional regularity condition on the positive tail of $F$, we show that
$$u_{\rm a}(x) \sim U_{\rm a}(x)[1-F(x)]/|A(x)|$$ as $x\to\infty$ and uniformly
for $0\leq x\leq R\in \mathbb{Z}$, as $R\to\infty$ $$P [ S\; \mbox{leaves
$[0,R]$ on its upper side}\, |\, S_0=x] \, \sim\, c^{-1}A(x)u_{\rm a}(x), $$
where $c= \sum_{n=1}^\infty P[S_{n}>S_0;\, S_k < S_0$ for $0<k<n]$ and the
regularity condition is satisfied at least if $S$ is recurrent, $\limsup
[1-F(x)]/F(-x)<1$, and $x[1-F(x)]/L(x) $ ($x\geq 1$) is bounded away from zero
and infinity for some slowly varying function $L$. We also give some asymptotic
estimates of the probability that $S$ visits $R$ before entering the negative
half-line for asymptotically stable walks and obtain asymptotic behaviour of
the probability that $R$ is ever hit by $S$ conditioned to avoid the negative
half-line forever.


  To incentivize flexible resources such as Battery Energy Storage Systems
(BESSs) to offer Frequency Control Ancillary Services (FCAS), Australia's
National Electricity Market (NEM) has implemented changes in recent years
towards shorter-term bidding rules and faster service requirements. However,
firstly, existing bidding optimization methods often overlook or oversimplify
the key aspects of FCAS market procedures, resulting in an inaccurate depiction
of the market bidding process. Thus, the BESS bidding problem is modeled based
on the actual bidding records and the latest market specifications and then
formulated as a deep reinforcement learning (DRL) problem. Secondly, the
erratic decisions of the DRL agent caused by imperfectly predicted market
information increases the risk of profit loss. Hence, a Conditional Value at
Risk (CVaR)-based DRL algorithm is developed to enhance the risk resilience of
bidding strategies. Thirdly, well-trained DRL models still face performance
decline in uncommon scenarios during online operations. Therefore, a Large
Language Models (LLMs)-assisted artificial intelligence (AI)-agent interactive
decision-making framework is proposed to improve the strategy timeliness,
reliability and interpretability in uncertain new scenarios, where conditional
hybrid decision and self-reflection mechanisms are designed to address LLMs'
hallucination challenge. The experiment results demonstrate that our proposed
framework has higher bidding profitability compared to the baseline methods by
effectively mitigating the profit loss caused by various uncertainties.


  We develop a quantum duality principle for subgroups of a Poisson group and
its dual, in two formulations. Namely, in the first one we provide functorial
recipes to produce quantum coisotropic subgroups in the dual Poisson group out
of any quantum subgroup (in a tautological sense) of the initial Poisson group,
while in the second one similar recipes are given only starting from
coisotropic subgroups. In both cases this yields a Galois-type correspondence,
where a quantum coisotropic subgroup is mapped to its complementary dual;
moreover, in the first formulation quantum coisotropic subgroups are
characterized as being the fixed points in this Galois' reciprocity. By the
natural link between quantum subgroups and quantum homogeneous spaces then we
argue a quantum duality principle for homogeneous spaces too, where quantum
coisotropic spaces are the fixed elements in a suitable Galois' reciprocity.
  As an application, we provide an explicit quantization of the space of Stokes
matrices with the Poisson structure given by Dubrovin and Ugaglia.
  The *paper is actually under revision* to fix some minor, technical issues.
  The geometric objects considered here (Poisson groups, subgroups and
homogeneous spaces) are "global" - as opposed to "formal" - and quantizations
are considered as standard - i.e.non topological - Hopf algebras over the ring
of Laurent polynomials (or other non-topological rings). Instead, a
"local/formal" version of this work is developed in math.QA/0412465 - which is
in final form - due to appear in "Advances in Mathematics". The example of
Stokes matrices mentioned above is considered in math.QA/0412465 as well.


  We consider a single-hop wireless network with sources transmitting
time-sensitive information to the destination over multiple unreliable
channels. Packets from each source are generated according to a stochastic
process with known statistics and the state of each wireless channel (ON/OFF)
varies according to a stochastic process with unknown statistics. The
reliability of the wireless channels is to be learned through observation. At
every time slot, the learning algorithm selects a single pair (source, channel)
and the selected source attempts to transmit its packet via the selected
channel. The probability of a successful transmission to the destination
depends on the reliability of the selected channel. The goal of the learning
algorithm is to minimize the Age-of-Information (AoI) in the network over $T$
time slots. To analyze the performance of the learning algorithm, we introduce
the notion of AoI regret, which is the difference between the expected
cumulative AoI of the learning algorithm under consideration and the expected
cumulative AoI of a genie algorithm that knows the reliability of the channels
a priori. The AoI regret captures the penalty incurred by having to learn the
statistics of the channels over the $T$ time slots. The results are two-fold:
first, we consider learning algorithms that employ well-known solutions to the
stochastic multi-armed bandit problem (such as $\epsilon$-Greedy, Upper
Confidence Bound, and Thompson Sampling) and show that their AoI regret scales
as $\Theta(\log T)$; second, we develop a novel learning algorithm and show
that it has $O(1)$ regret. To the best of our knowledge, this is the first
learning algorithm with bounded AoI regret.


  We investigate the implications of coupling a topological quantum field
theory (TQFT) to Yang-Mills theory with $SU(N)$ gauge group in the context of
the IR-renormalon problem. Coupling a TQFT to QFT does not change the local
dynamics and perturbation theory, but it does change the bundle topology.
Crucially, the configurations with integer topological charge but fractional
action contribute to the path integral of the original theory. In the
semi-classical regime, these are critical points at infinity, called neutral
bions, and since ${\rm Arg}(g^2)=0$ is a Stokes line, their Lefschetz thimbles
are two-fold ambiguous. Therein, the ambiguity in the gluon condensate is
sourced by the neutral bions. The Fourier decomposition of multi-branched
observables at strong coupling is compatible with the saddle decomposition at
weak coupling. TQFT coupling and non-renormalization of $\theta$ angle impose
constraints and helps to identify IR-renormalon. In certain IR-CFTs, we prove
irrelevance of bions, and absence of IR-renormalons.


  Visual-Inertial Odometry (VIO) utilizes an Inertial Measurement Unit (IMU) to
overcome the limitations of Visual Odometry (VO). However, the VIO for vehicles
in large-scale outdoor environments still has some difficulties in estimating
forward motion with distant features. To solve these difficulties, we propose a
robust VIO method based on the analysis of feature confidence in forward motion
estimation using an IMU. We first formulate the VIO problem by using effective
trifocal tensor geometry. Then, we infer the feature confidence by using the
motion information obtained from an IMU and incorporate the confidence into the
Bayesian estimation framework. Experimental results on the public KITTI dataset
show that the proposed VIO outperforms the baseline VIO, and it also
demonstrates the effectiveness of the proposed feature confidence analysis and
confidence-incorporated egomotion estimation framework.


  Bar-Natan used Chinese characters to show that finite type invariants
classify string links up to homotopy. In this paper, I construct the correct
spaces of chord diagrams and Chinese characters for links up to homotopy. I use
these spaces to show that the only rational finite type invariants of link
homotopy are the pairwise linking numbers of the components.


  We present a theoretical investigation of the surface plasmon (SP) at the
interface between topologically non-trivial cylindrical core and
topological-trivial surrounding material, from the axion electrodynamics and
modified constitutive relations. We find that the topological effect always
leads to a red-shift of SP energy, while the energy red-shift decreases
monotonically as core diameter decreases. A qualitative picture based on
classical perturbation theory is given to explain these phenomena, from which
we also infer that in order to enhance the shift, the difference between the
inverse of dielectric constants of two materials shall be increased. We also
find that the surrounding magnetic environment suppresses the topological
effect. All these features can be well described by a simple ansatz surface
wave, which is in good agreement with full electromagnetic eigenmodes. In
addition, bulk plasmon energy at \omega_{P}=17.5\pm0.2eV for semiconducting
Bi2Se3 nanoparticle is observed from high-resolution Electron Energy Loss
Spectrum Image measurements.


  A new static and azimuthally symmetric magnetic monopolelike object, which
looks like a Dirac monopole when seen from far away but smoothly changes to a
dipole near the monopole position and vanishes at the origin, is discussed.
This monopolelike object is inspired by an analysis of an exactly solvable
model of Berry's phase in the parameter space. A salient feature of the
monopolelike potential ${\cal A}_{k}(r,\theta)$ with a magnetic charge $e_{M}$
is that the Dirac string is naturally described by the potential ${\cal
A}_{k}(r,\theta)$, and the origin of the Dirac string and the geometrical
center of the monopole are displaced in the coordinate space. The smooth
topology change from a monopole to a dipole takes place if the Dirac string,
when coupled to the electron, becomes unobservable by satisfying the Dirac
quantization condition. The electric charge is then quantized even if the
monopole changes to a dipole near the origin. In the transitional region from a
monopole to a dipole, a half-monopole with a magnetic charge $e_{M}/2$ appears.


  We examine how the cosmic environment affects the chemical evolution of
galaxies in the Universe by comparing the N/O ratio of dwarf galaxies in voids
with dwarf galaxies in more dense regions. Ratios of the forbidden [O III] and
[S II] transitions provide estimates of a region's electron temperature and
number density. We estimate the abundances of oxygen and nitrogen using these
temperature and density estimates and the emission line fluxes [O II] 3727, [O
III] 4959, 5007, and [N II] 6548, 6584 with the direct Te method. Using
spectroscopic observations from the Sloan Digital Sky Survey Data Release 7, we
are able to estimate the N/O ratio in 42 void dwarf galaxies and 89 dwarf
galaxies in more dense regions. The N/O ratio for void dwarfs (Mr > -17) is
slightly lower (12%) than for dwarf galaxies in denser regions. We also
estimate the nitrogen and oxygen abundances of 2050 void galaxies and 3883
galaxies in more dense regions with Mr > -20. These somewhat brighter galaxies
(but still fainter than L*) also display similar minor shifts in the N/O ratio.
The shifts in the average and median element abundance values in all absolute
magnitude bins studied are in the same direction, suggesting that the
large-scale environment may influence the chemical evolution of galaxies. We
discuss possible causes of such a large-scale environmental dependence of the
chemical evolution of galaxies, including retarded star formation and a higher
dark matter halo mass to stellar mass ratio in void galaxies.


  We have initiated the study of topology of the space of coverings on grid
domains. The space has the following constraint: while all the covering agents
can move freely (we allow overlapping) on the domain, their union must cover
the whole domain. A minimal number $N$ of the covering agents is required for a
successful covering of the domain. In this paper, we demonstrate beautiful
topological structures of this space on grid domains in 2D with $N+1$
coverings, the topology of the space has the homotopy type of $1$ dimensional
complex, regardless of the domain shape. We also present the Euler
characteristic formula which connects the topology of the space with that of
the domain itself.


  This paper continues the study of K-theoretic invariants for semigroup
C*-algebras attached to ax+b-semigroups over rings of algebraic integers in
number fields. We show that from the semigroup C*-algebra together with its
canonical commutative subalgebra, it is possible to reconstruct the zeta
function of the underlying number field as well as its ideal class group (as a
group). In addition, we give an alternative interpretation of this result in
terms of dynamical systems.


  Topological materials have recently attracted considerable attention among
materials scientists as their properties are predicted to be protected against
perturbations such as lattice distortion and chemical substitution. However,
any experimental proof of such robustness is still lacking. In this study, we
experimentally demonstrate that the topological properties of the ferromagnetic
kagome compound Co3Sn2S2 are preserved upon Ni substitution. We systematically
vary the Ni content in Co3Sn2S2 single crystals and study their magnetic and
anomalous transport properties. For the intermediate Ni substitution, we
observe a remarkable increase in the coercive field while still maintaining
significant anomalous Hall conductivity. The large anomalous Hall conductivity
of these compounds is intrinsic, consistent with first-principle calculations,
which proves its topological origin. Our results can guide further studies on
the chemical tuning of topological materials for better understanding.


  Policy compliance detection is the task of ensuring that a scenario conforms
to a policy (e.g. a claim is valid according to government rules or a post in
an online platform conforms to community guidelines). This task has been
previously instantiated as a form of textual entailment, which results in poor
accuracy due to the complexity of the policies. In this paper we propose to
address policy compliance detection via decomposing it into question answering,
where questions check whether the conditions stated in the policy apply to the
scenario, and an expression tree combines the answers to obtain the label.
Despite the initial upfront annotation cost, we demonstrate that this approach
results in better accuracy, especially in the cross-policy setup where the
policies during testing are unseen in training. In addition, it allows us to
use existing question answering models pre-trained on existing large datasets.
Finally, it explicitly identifies the information missing from a scenario in
case policy compliance cannot be determined. We conduct our experiments using a
recent dataset consisting of government policies, which we augment with expert
annotations and find that the cost of annotating question answering
decomposition is largely offset by improved inter-annotator agreement and
speed.


  We study the dynamics of Jupiter Trojans in the early phase of the Solar
system while the outer planets migrated due to their interaction with the
planetesimal disk.


  In the conventional cloud service model, computing resources are allocated
for tenants on a pay-per-use basis. However, the performance of applications
that communicate inside this network is unpredictable because network resources
are not guaranteed. To mitigate this issue, the virtual cluster (VC) model has
been developed in which network and compute units are guaranteed. Thereon, many
algorithms have been developed that are based on novel extensions of the VC
model in order to solve the online virtual cluster embedding problem (VCE) with
additional parameters. In the online VCE, the resource footprint is greedily
minimized per request which is connected with maximizing the profit for the
provider per request. However, this does not imply that a global maximization
of the profit over the whole sequence of requests is guaranteed. In fact, these
algorithms do not even provide a worst case guarantee on a fraction of the
maximum achievable profit of a certain sequence of requests. Thus, these online
algorithms do not provide a competitive ratio on the profit.
  In this thesis, two competitive online VCE algorithms and two heuristic
algorithms are presented. The competitive online VCE algorithms have different
competitive ratios on the objective function and the capacity constraints
whereas the heuristic algorithms do not violate the capacity constraints. The
worst case competitive ratios are analyzed. After that, the evaluation shows
the advantages and disadvantages of these algorithms in several scenarios with
different request patterns and profit metrics on the fat-tree and MDCube
datacenter topologies. The results show that for different scenarios, different
algorithms have the best performance with respect to certain metrics.


  The real and imaginary part of the vacuum polarisation function $\Pi(q^2)$
induced by a massive quark is calculated in perturbative QCD up to order
$\alpha_s^2$. The method is described and the results are presented. This
extends the calculation by K\"all\'en and Sabry from two to three loops.


  Genetic competence is a phenotypic state of a bacterial cell in which it is
capable of importing DNA, presumably to hasten its exploration of alternate
genes in its quest for survival under stress. Recently, it was proposed that
this transition is uncorrelated among different cells in the colony. Motivated
by several discovered signaling mechanisms which create colony-level responses,
we present a model for the influence of quorum-sensing signals on a colony of
B. Subtilis cells during the transition to genetic competence. Coupling to the
external signal creates an effective inhibitory mechanism, which results in
anti-correlation between the cycles of adjacent cells. We show that this
scenario is consistent with the specific experimental measurement, which fails
to detect some underlying collective signaling mechanisms. Rather, we suggest
other parameters that should be used to verify the role of a quorum-sensing
signal. We also study the conditions under which phenotypic spatial patterns
may emerge.


  Real-time detection of anomalies in streaming data is receiving increasing
attention as it allows us to raise alerts, predict faults, and detect
intrusions or threats across industries. Yet, little attention has been given
to compare the effectiveness and efficiency of anomaly detectors for streaming
data (i.e., of online algorithms). In this paper, we present a qualitative,
synthetic overview of major online detectors from different algorithmic
families (i.e., distance, density, tree or projection-based) and highlight
their main ideas for constructing, updating and testing detection models. Then,
we provide a thorough analysis of the results of a quantitative experimental
evaluation of online detection algorithms along with their offline
counterparts. The behavior of the detectors is correlated with the
characteristics of different datasets (i.e., meta-features), thereby providing
a meta-level analysis of their performance. Our study addresses several missing
insights from the literature such as (a) how reliable are detectors against a
random classifier and what dataset characteristics make them perform randomly;
(b) to what extent online detectors approximate the performance of offline
counterparts; (c) which sketch strategy and update primitives of detectors are
best to detect anomalies visible only within a feature subspace of a dataset;
(d) what are the tradeoffs between the effectiveness and the efficiency of
detectors belonging to different algorithmic families; (e) which specific
characteristics of datasets yield an online algorithm to outperform all others.


  A conjugacy class $C$ of a finite group $G$ is a sign conjugacy class if
every irreducible character of $G$ takes value 0, 1 or -1 on $C$. In this paper
we classify the sign conjugacy classes of the symmetric groups and thereby
verify a conjecture of Olsson.


  The High Energy cosmic Radiation Detection (HERD) facility is a space mission
designed for detecting cosmic ray (CR) electrons, $\gamma$-rays up to tens of
TeV and CR nuclei from proton to iron up to several PeV. The main instrument of
HERD is a 3-D imaging calorimeter (CALO) composed of nearly ten thousand cubic
LYSO crystals. A large dynamic range of single HERD CALO Cell (HCC) is
necessary to achieve HERD's PeV observation objectives, which means that the
response of HCC should maintain a good linearity from minimum ionizing particle
(MIP) calibration to PeV shower maximum. In order to study the linearity of HCC
over such a large energy range, a beam test has been implemented at the E2 and
E3 beam lines of BEPC. High intensity pulsed electron beam provided by E2 line
are used for producing high energy density within HCC; $\pi^{+}$/proton
provided by E3 line are used for HCC calibration. The results show that no
saturation effect occurs and the linearity of HCC is better than 10% from 30
MeV (1 MIP) to 1.1$\times$10$^{3}$ TeV (energy density is 93 TeV/cm$^{3}$),
which can meet the requirement mentioned above.


  This research note concerns the application of deep-learning-based
multi-view-imaging techniques to data from the H.E.S.S. Imaging Atmospheric
Cherenkov Telescope array. We find that the earlier the fusion of layer
information from different views takes place in the neural network, the better
our model performs with this data. Our analysis shows that the point in the
network where the information from the different views is combined is far more
important for the model performance than the method used to combine the
information.


  Various approaches of defining and determining work performed on a quantum
system are compared. Any operational definition of work, however, must allow
for two facts, first, that work characterizes a process rather than an
instantaneous state of a system, and, second, that quantum systems are
sensitive to the interactions with a measurement apparatus. We compare
different measurement scenarios on the basis of the resulting post-measurement
states and the according probabilities for finding a particular work value. In
particular, we analyze a recently proposed work-meter for the case of a
Gaussian pointer state and compare it with the results obtained by two
projective and, alternatively, two Gaussian measurements. In the limit of a
strong effective measurement strength the work distribution of projective two
energy measurements can be recovered. In the opposite limit the average of work
becomes independent of any measurement. Yet the fluctuations about this value
diverge. The performance of the work-meter is illustrated by the example of a
spin in a suddenly changing magnetic field.


  The Internal wave Dissipation, Energy and Mixing (IDEMIX) model presents a
novel way of parameterizing internal gravity waves in the atmosphere. Using a
continuous full wave spectrum in the energy balance equation and integrating
over all vertical wavenumbers and frequencies results in prognostic equations
for the energy density of gravity waves in multiple azimuthal compartments. It
includes their non-dissipative interaction with the mean flow, allowing for an
evolving and local description of momentum flux and gravity wave drag. A
saturation mechanism maintains the wave field within convective stability
limits, and an energetically consistent closure for critical-layer effects
controls how much wave flux propagates from the troposphere into the middle
atmosphere. IDEMIX can simulate zonal gravity wave drag around the mesopause,
similar to a traditional gravity wave parameterization and to a
state-of-the-art wave ray tracing model in an atmospheric circulation model. In
addition, IDEMIX shows a reversal of the gravity wave drag around the mesopause
region due to changes in the momentum flux there. When compared to empirical
model data, IDEMIX captures well the summer hemisphere flow reversal, the cold
summer mesospheric pole and the alternate positive and negative structures in
the meridional mean flow.


  It is shown that Denjoy-Carleman quasi-analytic rings of germs of functions
in two or more variables fail to satisfy the Weierstrass Preparation Theorem.
The result is proven via a non-extension theorem.


  The underlying philosophy and motivation for quantum hadrodynamics (QHD),
namely, relativistic field theories of nuclear phenomena featuring manifest
covariance, have evolved over the last quarter century in response to
successes, failures, and sharp criticisms. A recent revolution in QHD, based on
modern effective field theory and density functional theory perspectives,
explains the successes, provides antidotes to the failures, rebuts the
criticisms, and focuses the arguments in favor of a covariant representation.


  As Artificial Intelligence (AI) models are gradually being adopted in
real-life applications, the explainability of the model used is critical,
especially in high-stakes areas such as medicine, finance, etc. Among the
commonly used models, Linear Discriminant Analysis (LDA) is a widely used
classification tool that is also explainable thanks to its ability to model
class distributions and maximize class separation through linear feature
combinations. Nevertheless, real-world data is frequently incomplete,
presenting significant challenges for classification tasks and model
explanations. In this paper, we propose a novel approach to LDA under missing
data, termed \textbf{\textit{Weighted missing Linear Discriminant Analysis
(WLDA)}}, to directly classify observations in data that contains missing
values without imputation effectively by estimating the parameters directly on
missing data and use a weight matrix for missing values to penalize missing
entries during classification. Furthermore, we also analyze the theoretical
properties and examine the explainability of the proposed technique in a
comprehensive manner. Experimental results demonstrate that WLDA outperforms
conventional methods by a significant margin, particularly in scenarios where
missing values are present in both training and test sets.


  In this paper, we generalize a high order semi-Lagrangian (SL) discontinuous
Galerkin (DG) method for multi-dimensional linear transport equations without
operator splitting developed in Cai et al. (J. Sci. Comput. 73: 514-542, 2017)
to the 2D time dependent incompressible Euler equations in the vorticity-stream
function formulation and the guiding center Vlasov model. We adopt a local DG
method for Poisson's equation of these models. For tracing the characteristics,
we adopt a high order characteristics tracing mechanism based on a
prediction-correction technique. The SLDG with large time-stepping size might
be subject to extreme distortion of upstream cells. To avoid this problem, we
propose a novel adaptive time-stepping strategy by controlling the relative
deviation of areas of upstream cells.


  We propose a consideration of the properties of the two-dimensional
Ablowitz-Ladik discretization of the ubiquitous nonlinear Schrodinger (NLS)
model. We use singularity confinement techniques to suggest that the relevant
discretization should not be integrable. More importantly, we identify the
prototypical solitary waves of the model and examine their stability,
illustrating the remarkable feature that near the continuum limit, this
discretization leads to the absence of collapse and complete spectral wave
stability, in stark contrast to the standard discretization of the NLS. We also
briefly touch upon the three-dimensional case and generalizations of our
considerations therein, and also present some more exotic solutions of the
model, such as exact line solitons and discrete vortices.


  One-dimensional and quasi-one-dimensional strongly-coupled dusty plasma rings
have been created experimentally. Longitudinal (acoustic) and transverse
(optical) dispersion relations for the 1-ring were measured and found to be in
very good agreement with the theory for an unbounded straight chain of
particles interacting through a Yukawa (i.e., screened Coulomb or
Debye-H\"uckel) potential. These rings provide a new system in which to study
one-dimensional and quasi-one-dimensional physics.


  In the present paper, we address the important point of the proportionality
between the longitudinal integral lengthscale ($L$) and the characteristic mean
flow width ($\delta$) using experimental data of an axisymmetric wake and a
turbulent planar jet. This is a fundamental hypothesis when deriving the
self-similar scaling laws in free shear flows, irrespective of turbulence
dissipation scaling. We show that $L/\delta$ is indeed constant, at least in a
range of streamwise distances between 15 and 50 times the characteristic inlet
dimension ($L_{ref}$, nozzle width or wake generator size). Furthermore, we
revisit turbulence closure models such as the Prandtl mixing length
\cite{prandtl1925} and the constant eddy viscosity in the light of the
non-equilibrium dissipation scalings. We show that the mixing length model,
with $l_m\sim \delta$, does not comply with the scalings stemming from the
non-equilibrium version of the theory; we instead obtain $l_m\sim \delta
\sqrt{Re_G/Re_{0\delta}}$, where $Re_G$ and $Re_{0\delta}$ are a global and
local Reynolds number, respectively. Similarly, the eddy viscosity model holds
in the case of the non-equilibrium version of the theory provided that the eddy
viscosity is constant everywhere, not only across sections orthogonal to the
streamwise direction as in the equilibrium case. We conclude comparing the
results of the different models with each other and with experimental data and
with an improved model (following Townsend) that accounts for the intermittency
of the flow and corrects for the eddy viscosity variation across the flow
boundaries.


  We introduce a new one-person game similar to the Sudoku game. It is based on
combinatorial objects called planar binary rooted trees. It is related to the
four color conjecture. Its mathematical analysis makes use of the Tamari poset,
hence the Stasheff associahedron.


  Stochastic network-dynamics are typically assumed to be memory-less.
Involving prolonged dwells interrupted by instantaneous transitions between
nodes such Markov networks stand as a coarse-graining paradigm for chemical
reactions, gene expression, molecular machines, spreading of diseases, protein
dynamics, diffusion in energy landscapes, epigenetics and many others. However,
as soon as transitions cease to be negligibly short, as often observed in
experiments, the dynamics develops a memory. That is, state-changes depend not
only on the present state but also on the past. Here, we establish the first
thermodynamically consistent -- dissipation-preserving -- mapping of continuous
dynamics onto a network, which reveals ingrained dynamical symmetries and an
unforeseen kinetic hysteresis. These symmetries impose three independent
sources of fluctuations in state-to state kinetics that determine the `flavor
of memory'. The hysteresis between the forward/backward in time coarse-graining
of continuous trajectories implies a new paradigm for the thermodynamics of
active molecular processes in the presence of memory, that is, beyond the
assumption of local detailed balance. Our results provide a new understanding
of fluctuations in the operation of molecular machines as well as catch-bonds
involved in cellular adhesion.


  Exclusive social groups are ones in which the group members decide whether or
not to admit a candidate to the group. Examples of exclusive social groups
include academic departments and fraternal organizations. In the present paper
we introduce an analytic framework for studying the dynamics of exclusive
social groups. In our model, every group member is characterized by his
opinion, which is represented as a point on the real line. The group evolves in
discrete time steps through a voting process carried out by the group's
members. Due to homophily, each member votes for the candidate who is more
similar to him (i.e., closer to him on the line). An admission rule is then
applied to determine which candidate, if any, is admitted. We consider several
natural admission rules including majority and consensus.
  We ask: how do different admission rules affect the composition of the group
in the long term? We study both growing groups (where new members join old
ones) and fixed-size groups (where new members replace those who quit). Our
analysis reveals intriguing phenomena and phase transitions, some of which are
quite counterintuitive.


  Millimeter-wave (mmWave) radars are being increasingly integrated in
commercial vehicles to support new Adaptive Driver Assisted Systems (ADAS)
features that require accurate location and Doppler velocity estimates of
objects, independent of environmental conditions. To explore radar-based ADAS
applications, we have updated our test-bed with Texas Instrument's 4-chip
cascaded FMCW radar (TIDEP-01012) that forms a non-uniform 2D MIMO virtual
array. In this paper, we develop the necessary received signal models for
applying different direction of arrival (DoA) estimation algorithms and
experimentally validating their performance on formed virtual array under
controlled scenarios. To test the robustness of mmWave radars under adverse
weather conditions, we collected raw radar dataset (I-Q samples post
demodulated) for various objects by a driven vehicle-mounted platform,
specifically for snowy and foggy situations where cameras are largely
ineffective. Initial results from radar imaging algorithms to this dataset are
presented.


  We study the relation between qubit entanglement and Lorentzian geometry. In
an earlier paper, we had given a recipe for detecting two qubit entanglement.
The entanglement criterion is based on Partial Lorentz Transformations (PLT) on
individual qubits. The present paper gives the theoretical framework underlying
the PLT test. The treatment is based physically, on the causal structure of
Minkowski spacetime, and mathematically, on a Lorentzian Singular Value
Decomposition. A surprising feature is the natural emergence of "Energy
conditions" used in Relativity. All states satisfy a "Dominant Energy
Condition" (DEC) and separable states satisfy the Strong Energy Condition(SEC),
while entangled states violate the SEC. Apart from testing for entanglement,
our approach also enables us to construct a separable form for the density
matrix in those cases where it exists. Our approach leads to a simple graphical
three dimensional representation of the state space which shows the entangled
states within the set of all states.


  Financial time-series forecasting is one of the most challenging domains in
the field of time-series analysis. This is mostly due to the highly
non-stationary and noisy nature of financial time-series data. With progressive
efforts of the community to design specialized neural networks incorporating
prior domain knowledge, many financial analysis and forecasting problems have
been successfully tackled. The temporal attention mechanism is a neural layer
design that recently gained popularity due to its ability to focus on important
temporal events. In this paper, we propose a neural layer based on the ideas of
temporal attention and multi-head attention to extend the capability of the
underlying neural network in focusing simultaneously on multiple temporal
instances. The effectiveness of our approach is validated using large-scale
limit-order book market data to forecast the direction of mid-price movements.
Our experiments show that the use of multi-head temporal attention modules
leads to enhanced prediction performances compared to baseline models.


  We show that in the presence of spinodal instabilities which develop at a
first order phase transition, the fluctuations of conserved charges can be as
strong as those at the critical end point (CEP). In particular, the net baryon
number susceptibility diverges as the system crosses the isothermal spinodal
lines. This indicates that charge density fluctuations can be used not only to
probe the CEP but also the non--equilibrium first order chiral phase transition
in heavy ion collisions.


  The $\alpha$-stable distributions introduced by L\'evy play an important role
in probabilistic theoretical studies and their various applications, e.g., in
statistical physics, life sciences, and economics. In the present paper we
study sequences of long-range dependent random variables whose distributions
have asymptotic power law decay, and which are called $(q,\alpha)$-stable
distributions. These sequences are generalizations of i.i.d. $\alpha$-stable
distributions, and have not been previously studied. Long-range dependent
$(q,\alpha)$-stable distributions might arise in the description of anomalous
processes in nonextensive statistical mechanics, cell biology, finance. The
parameter $q$ controls dependence. If $q=1$ then they are classical i.i.d. with
$\alpha$-stable L\'evy distributions. In the present paper we establish basic
properties of $(q,\alpha)$-stable distributions, and generalize the result of
Umarov, Tsallis and Steinberg (2008), where the particular case $\alpha=2, q\in
[1,3),$ was considered, to the whole range of stability and nonextensivity
parameters $\alpha \in (0,2]$ and $q \in [1,3),$ respectively. We also discuss
possible further extensions of the results that we obtain, and formulate some
conjectures.


  We propose a scheme to directly measure the exact value of geometric quantum
discord of an arbitrary two-qubit state. We only need to perform the projective
measurement in the all anti-symmetric subspace and our scheme is parametrically
efficient in contrast to the widely adopted quantum state tomography scheme in
the sense of less parameter estimations and projectors. Moreover, the present
scheme can be easily realized with the current experimental techniques.


  We investigate the dynamics of rotating pseudo-spin-1/2 Bose-Einstein
condensates (BECs) with Rashba spin-orbit coupling (SOC) in a quasicrystalline
optical lattice (QOL). For given parameters, the system evolves from an initial
heliciform-stripe phase into a final visible vortex necklace with a giant
vortex and a hidden vortex necklace. Simultaneously, the corresponding spin
texture undergoes a transition from a meron-antimeron pair to a
half-antiskyrmion necklace. During the dynamic evolution process, the angular
momentum increases gradually, and then approaches to a convergent value.
Furthermore, typical quantum phases of rotating two-component BECs with SOC in
different external potentials are summarized.


  Despite having important cosmological implications, the reheating phase is
believed to play a crucial role in cosmology and particle physics model
building. Conventionally, the model of reheating with an arbitrary coupling of
inflaton to massless fields naturally lacks precise prediction and hence
difficult to verify through observation. In this paper, we propose a simple and
natural reheating mechanism where the particle physics model, namely the Type-I
seesaw is shown to play a major role in the entire reheating process where
inflaton is coupled with all the fields only gravitationally. Besides
successfully resolving the well-known neutrino mass and baryon asymmetry
problems, this scenario offers successful reheating, predicts distinct
primordial gravitational wave spectrum and non-vanishing lowest active neutrino
mass. Our novel mechanism opens up a new avenue of integrating particle physics
and cosmology in the context of reheating.


  Hurwitz numbers count branched covers of the Riemann sphere with specified
ramification, or equivalently, transitive permutation factorizations in the
symmetric group with specified cycle types. Monotone Hurwitz numbers count a
restricted subset of these branched covers, related to the expansion of
complete symmetric functions in the Jucys-Murphy elements, and have arisen in
recent work on the the asymptotic expansion of the
Harish-Chandra-Itzykson-Zuber integral. In previous work we gave an explicit
formula for monotone Hurwitz numbers in genus zero. In this paper we consider
monotone Hurwitz numbers in higher genera, and prove a number of results that
are reminiscent of those for classical Hurwitz numbers. These include an
explicit formula for monotone Hurwitz numbers in genus one, and an explicit
form for the generating function in arbitrary positive genus. From the form of
the generating function we are able to prove that monotone Hurwitz numbers
exhibit a polynomiality that is reminiscent of that for the classical Hurwitz
numbers, i.e., up to a specified combinatorial factor, the monotone Hurwitz
number in genus g with ramification specified by a given partition is a
polynomial indexed by g in the parts of the partition.


  We describe a realistic, renormalizable, supersymmetric ``quindecuplet''
model in which the top quark, left handed bottom quark, and up-type Higgs boson
are composite, with a compositeness scale $\sim 1-3$ TeV. The top-Higgs Yukawa
coupling is a dynamically generated strong interaction effect, and is naturally
much larger than any other Yukawa coupling. The light quark doublets and
right-handed up-type quarks are also composite but at higher energies; the
hierarchy of quark masses and mixings is due to a hierarchy in the
compositeness scales. Flavor changing neutral currents are naturally
suppressed, as is baryon number violation by Planck-scale dimension five
operators. The model predicts that the most easily observable effects would be
on $b$-quark physics and on the $\rho$ parameter. In particular a small
negative $\Delta\rho=-\epsilon$ leads to $\Delta R_b> +2\epsilon$. There are
effects on $B$ meson mixing and on flavor-changing neutral-current $b$-quark
decays to leptons which might be detectable, but not on $b\rightarrow s\gamma$.
The model also suggests the supersymmetry-breaking mass for the right handed
top squark might be considerably larger than that of the left handed top
squark.


  Recent years have seen the introduction of a range of methods for post-hoc
explainability of image classifier predictions. However, these post-hoc
explanations may not always be faithful to classifier predictions, which poses
a significant challenge when attempting to debug models based on such
explanations. To this end, we seek a methodology that can improve the
faithfulness of an explanation method with respect to model predictions which
does not require ground truth explanations. We achieve this through a novel
explanation-driven data augmentation (EDDA) technique that augments the
training data with occlusions inferred from model explanations; this is based
on the simple motivating principle that \emph{if} the explainer is faithful to
the model \emph{then} occluding salient regions for the model prediction should
decrease the model confidence in the prediction, while occluding non-salient
regions should not change the prediction. To verify that the proposed
augmentation method has the potential to improve faithfulness, we evaluate EDDA
using a variety of datasets and classification models. We demonstrate
empirically that our approach leads to a significant increase of faithfulness,
which can facilitate better debugging and successful deployment of image
classification models in real-world applications.


  We study the viscous properties of a system of weakly interacting
spin-$\frac{1}{2}$ fermions in one dimension. Accounting for the effect of
interactions on the quasiparticle energy spectrum, we obtain the bulk viscosity
of this system at low temperatures. Our result is valid for frequencies that
are small compared with the rate of fermion backscattering. For frequencies
larger than this exponentially small rate, the excitations of the system become
decoupled from the center of mass motion, and the fluid is described by
two-fluid hydrodynamics. We calculate the three transport coefficients required
to describe viscous dissipation in this regime.


  Surveys of the cosmic large-scale structure carry opportunities for building
and testing cosmological theories about the origin and evolution of the
Universe. This endeavor requires appropriate data assimilation tools, for
establishing the contact between survey catalogs and models of structure
formation. In this thesis, we present an innovative statistical approach for
the ab initio simultaneous analysis of the formation history and morphology of
the cosmic web: the BORG algorithm infers the primordial density fluctuations
and produces physical reconstructions of the dark matter distribution that
underlies observed galaxies, by assimilating the survey data into a
cosmological structure formation model. The method, based on Bayesian
probability theory, provides accurate means of uncertainty quantification. We
demonstrate the application of BORG to the Sloan Digital Sky Survey data and
describe the primordial and late-time large-scale structure in the observed
volume. We show how the approach has led to the first quantitative inference of
the cosmological initial conditions and of the formation history of the
observed structures. We then use these results for several cosmographic
projects aiming at analyzing and classifying the large-scale structure. In
particular, we build an enhanced catalog of cosmic voids probed at the level of
the dark matter distribution, deeper than with the galaxies. We present
detailed probabilistic maps of the dynamic cosmic web, and offer a general
solution to the problem of classifying structures in the presence of
uncertainty. The results described in this thesis constitute accurate
chrono-cosmography of the inhomogeneous cosmic structure.


  Communication with the goal of accurately conveying meaning, rather than
accurately transmitting symbols, has become an area of growing interest. This
paradigm, termed semantic communication, typically leverages modern
developments in artificial intelligence and machine learning to improve the
efficiency and robustness of communication systems. However, a standard model
for capturing and quantifying the details of "meaning" is lacking, with many
leading approaches to semantic communication adopting a black-box framework
with little understanding of what exactly the model is learning. One solution
is to utilize the conceptual spaces framework, which models meaning explicitly
in a geometric manner. Though prior work studying semantic communication with
conceptual spaces has shown promising results, these previous attempts involve
hand-crafting a conceptual space model, severely limiting the scalability and
practicality of the approach. In this work, we develop a framework for learning
a domain of a conceptual space model using only the raw data with high-level
property labels. In experiments using the MNIST and CelebA datasets, we show
that the domains learned using the framework maintain semantic similarity
relations and possess interpretable dimensions.


  This paper is a continuation of our first paper [10] in which we showed how
deformation theory of representation varieties can be used to study finite
simple quotients of triangle groups. While in Part I, we mainly used
deformations of the principal homomorphism from ${\rm SO}(3,\R)$, in this part
we use ${\rm PGL}_2(\R)$ as well as deformations of representations which are
very different from the principal homomorphism.


  In light of recent experimental evidence of density wave order in the
cuprates, we consider a phenomenological model of a d-wave superconductor with
coexisting charge, spin or pair density wave order of various form and wave
vector. We study the evolution of the nodal structure of the quasiparticle
energy spectrum as a function of the amplitude of the coexisting order and
perform diagrammatic linear response calculations of the low-temperature
(universal-limit) thermal conductivity. The work described herein expands upon
our past studies, which focused on a particular unit-cell-doubling charge
density wave, generalizing our techniques to a wider class of coexisting order.
We find that the question of whether the nodes of the d-wave superconductor
survive amidst a reasonable level of coexisting order is sensitive to the form
and wave vector of the order. However, in cases where the nodes do become
gapped, we identify a signature of the approach to this nodal transition, in
the low-temperature thermal conductivity, that appears to be quite general. The
amplitude of this signature is found to be disorder-dependent, which suggests a
connection between the presence of coexisting order in the underdoped cuprates
and recent observations of deviations from universal (disorder-independent)
thermal conductivity in the underdoped regime.


  We prove a comparison formula for curve-counting invariants in the setting of
the McKay correspondence, related to the crepant resolution conjecture for
Donaldson-Thomas invariants. The conjecture is concerned with comparing the
invariants of a (hard Lefschetz) Calabi-Yau orbifold of dimension three with
those of a specific crepant resolution of its coarse moduli space. We prove the
conjecture for point classes and give a conditional proof for general curve
classes. We also prove a variant of the formula for curve classes. Along the
way we identify the image of the standard heart of the orbifold under the
Bridgeland-King-Reid equivalence.


  In this work, we have studied the chemical and magnetic interactions of Fe_n;
n <= 6, clusters with a divacancy site in a graphene sheet by ab-initio density
functional calculations. Our results show significant chemical interactions
between the cluster and graphene. As a result, a complex distribution of
magnetic moments appear on the distorted Fe clusters in presence of graphene
and results in a lower average magnetic moments compared to the free clusters.
The presence of cluster also prevents the formation of 5-8-5 ringed structure
known to exhibit in a graphene sheet having a divacancy defect. The clusters
induce electronic states primarily of d-character near the Fermi level.


  It is well known that one can find a rational normal curve in $\mathbb P^n$
through $n+3$ general points. We prove a generalization of this to higher
dimensional varieties, showing that smooth varieties of minimal degree can be
interpolated through points and linear spaces.


  Communication is crucial for solving cooperative Multi-Agent Reinforcement
Learning tasks in partially observable Markov Decision Processes. Existing
works often rely on black-box methods to encode local information/features into
messages shared with other agents, leading to the generation of continuous
messages with high communication overhead and poor interpretability. Prior
attempts at discrete communication methods generate one-hot vectors trained as
part of agents' actions and use the Gumbel softmax operation for calculating
message gradients, which are all heuristic designs that do not provide any
quantitative guarantees on the expected return. This paper establishes an upper
bound on the return gap between an ideal policy with full observability and an
optimal partially observable policy with discrete communication. This result
enables us to recast multi-agent communication into a novel online clustering
problem over the local observations at each agent, with messages as cluster
labels and the upper bound on the return gap as clustering loss. To minimize
the return gap, we propose the Return-Gap-Minimization Communication (RGMComm)
algorithm, which is a surprisingly simple design of discrete message generation
functions and is integrated with reinforcement learning through the utilization
of a novel Regularized Information Maximization loss function, which
incorporates cosine-distance as the clustering metric. Evaluations show that
RGMComm significantly outperforms state-of-the-art multi-agent communication
baselines and can achieve nearly optimal returns with few-bit messages that are
naturally interpretable.


  We study classical and quantum maps on the torus phase space, in the presence
of noise. We focus on the spectral properties of the noisy evolution operator,
and prove that for any amount of noise, the quantum spectrum converges to the
classical one in the semiclassical limit. The small-noise behaviour of the
classical spectrum highly depends on the dynamics generated by the map. For a
chaotic dynamics, the outer spectrum consists in isolated eigenvalues
(``resonances'') inside the unit circle, leading to an exponential damping of
correlations. On the opposite, in the case of a regular map, part of the
spectrum accumulates along a one-dimensional ``string'' connecting the origin
with unity, yielding a diffusive behaviour. We finally study the
non-commutativity between the semiclassical and small-noise limits, and
illustrate this phenomenon by computing (analytically and numerically) the
classical and quantum spectra for some maps.


  The dielectric tensor of $\beta$-Ga$_2$O$_3$ was determined by generalized
spectroscopic ellipsometry in a wide spectral range from $0.5\,\mathrm{eV}$ to
$8.5\,\mathrm{eV}$ as well as by calculation including quasiparticle bands and
excitonic effects. The dielectric tensors obtained by both methods are in
excellent agreement with each other and the observed transitions in the
dielectric function are assigned to the corresponding valence bands. It is
shown that the off-diagonal element of the dielectric tensor reaches values up
to $|\varepsilon_{xz} | \approx 0.30 $ and cannot be neglected. Even in the
transparent spectral range where it is quite small ($|\varepsilon_{xz} | < 0.02
$) it causes a rotation of the dielectric axes around the symmetry axis of up
to $20^\circ$.


  Some basic geometric properties related to connectedness and topological
dimension 0 are discussed, especially in connection with the ultrametric
version of the triangle inequality.


  In this work, we develop a new quantum algorithm to solve a combinatorial
problem with significant practical relevance occurring in clutch manufacturing.
It is demonstrated how quantum optimization can play a role in real industrial
applications in the manufacturing sector. Using the quantum annealer provided
by D-Wave Systems, we analyze the performance of the quantum and
quantum-classical hybrid solvers and compare them to deterministic- and
random-algorithm classical benchmark solvers. The continued evolution of the
quantum technology, indicating an expectation for even greater relevance in the
future is discussed and the revolutionary potential it could have in the
manufacturing sector is highlighted.


  The LHC collider plans to start in 2007, after which millions of top quarks
will be produced at the collision points. In the first period of data taking
these events will provide an essential calibration tool for the ATLAS and CMS
detectors. During a later stage, as part of the precision measurement
programme, both detectors will determine the top mass and properties like spin,
charge and couplings. Top physics also plays a central role in the search for
new particles, both as source of a possible signal and as source of
background.}


  We introduce a general notion of flabby objects in elementary toposes and
study their basic properties. In the special case of localic toposes, this
notion reduces to the common notion of flabby sheaves, yielding a
site-independent characterization of flabby sheaves. Continuing a line of
research started by Roswitha Harting, we use flabby objects to show that an
internal notion of injective objects coincides with the corresponding external
notion, in stark contrast with the situation for projective objects. We show as
an application that higher direct images can be understood as internal
cohomology, and we study flabby objects in the effective topos.


  Solar system objects with perihelia beyond the orbit of Jupiter ($q >$ 5 AU)
are too cold for water ice to generate an appreciable coma via sublimation.
Despite this, numerous high perihelion objects (HPOs) including many comets and
recently escaped Kuiper belt objects (``Centaurs'') are observed to be active
out at least to the orbit of Saturn ($q \sim$ 10 AU). Peak equilibrium
temperatures at 10 AU ($\sim$125 K), while far too low to sublimate water ice,
are sufficient to sublimate super-volatiles such as CO and CO$_2$ ice.
Temperatures at 10 AU are also high enough to trigger the rapid crystallization
of exposed amorphous ice, thus constituting another possible driver of distant
activity. While supervolatile ices can sublimate strongly (as $r_H^{-2}$) to at
least Kuiper belt (30 AU) distances, crystallization is an exponential function
of temperature that cannot be sustained much beyond $\sim$10 AU. The
heliocentric dependence of the activity thus suggests an observational test. If
activity in high perihelion objects is triggered by crystallization, then no
examples of activity should be found with perihelia $q >>$ 10 AU. If, on the
other hand, activity is due to free sublimation of exposed supervolatile ices,
or another cause, then distant activity might be detected. We obtained
sensitive, high resolution Hubble Space Telescope observations of HPOs to
search for activity beyond the crystallization zone. No examples of activity
were detected in 53 objects with $q >$ 15 AU, consistent with the
crystallization trigger hypothesis. However, sensitivity limits are such that
we cannot reject the alternative hypothesis that mass loss is driven by the
sublimation of supervolatile ices. We also searched for binary companions in
our sample, finding none and setting an empirical 3$\sigma$ limit to the binary
fraction of $<8$\%.