  Quantum uncertainty relations have deep-rooted significance on the formalism
of quantum mechanics. Heisenberg's uncertainty relations attracted a renewed
interest for its applications in quantum information science. Robertson derived
a general form of Heisenberg's uncertainty relations for a pair of arbitrary
observables represented by Hermitian operators. In the present work, we
discover a temporal version of the Heisenberg-Robertson uncertainty relations
for the measurement of two observables at two different times, where the
dynamical uncertainties crucially depend on the time evolution of the
observables. The uncertainties not only depend on the choice of observables,
but they also depend on the times at which the physical observables are
measured. The time correlated two-time commutator dictates the trade-off
between the dynamical uncertainties. We demonstrate the dynamics of these
uncertainty relations for a spin-1/2 system and for a quantum harmonic
oscillator. The temporal uncertainty relations discovered in this work can be
experimentally verified with the present quantum technology.


  In the archetypal strongly correlated electron superconductor CeCu$_2$Si$_2$
and its Ge-substituted alloys CeCu$_2$(Si$_{1-x}$Ge$_{x}$)$_2$ two quantum
phase transitions -- one magnetic and one of so far unknown origin -- can be
crossed as a function of pressure \cite{Yuan 2003a}. We examine the associated
anomalous normal state by detailed measurements of the low temperature
resistivity ($\rho$) power law exponent $\alpha$. At the lower critical point
(at $p_{c1}$, $1\leq\alpha\leq 1.5$) $\alpha$ depends strongly on Ge
concentration $x$ and thereby on disorder level, consistent with a
Hlubina-Rice-Rosch scenario of critical scattering off antiferromagnetic
fluctuations. By contrast, $\alpha$ is independent of $x$ at the upper quantum
phase transition (at $p_{c2}$, $\alpha\simeq 1$), suggesting critical
scattering from local or Q=0 modes, in agreement with a density/valence
fluctuation approach.


  Despite the remarkable progresses made in deep-learning based depth map
super-resolution (DSR), how to tackle real-world degradation in low-resolution
(LR) depth maps remains a major challenge. Existing DSR model is generally
trained and tested on synthetic dataset, which is very different from what
would get from a real depth sensor. In this paper, we argue that DSR models
trained under this setting are restrictive and not effective in dealing with
real-world DSR tasks. We make two contributions in tackling real-world
degradation of different depth sensors. First, we propose to classify the
generation of LR depth maps into two types: non-linear downsampling with noise
and interval downsampling, for which DSR models are learned correspondingly.
Second, we propose a new framework for real-world DSR, which consists of four
modules : 1) An iterative residual learning module with deep supervision to
learn effective high-frequency components of depth maps in a coarse-to-fine
manner; 2) A channel attention strategy to enhance channels with abundant
high-frequency components; 3) A multi-stage fusion module to effectively
re-exploit the results in the coarse-to-fine process; and 4) A depth refinement
module to improve the depth map by TGV regularization and input loss. Extensive
experiments on benchmarking datasets demonstrate the superiority of our method
over current state-of-the-art DSR methods.


  Motivated by applications in architecture and design, we present a novel
method for increasing the developability of a B-spline surface. We use the
property that the Gauss image of a developable surface is 1-dimensional and can
be locally well approximated by circles. This is cast into an algorithm for
thinning the Gauss image by increasing the planarity of the Gauss images of
appropriate neighborhoods. A variation of the main method allows us to tackle
the problem of paneling a freeform architectural surface with developable
panels, in particular enforcing rotational cylindrical, rotational conical and
planar panels, which are the main preferred types of developable panels in
architecture due to the reduced cost of manufacturing.


  In the present article we describe how one can define Hausdorff measure
allowing empty elements in coverings, and using infinite countable coverings
only. In addition, we discuss how the use of different nonequivalent
interpretations of the notion "countable set", that is typical for classical
and modern mathematics, may lead to contradictions.


  In this paper, we study the weighted inequality for multilinear fractional
maximal operators and fractional integrals. We give sharp weighted estimates
for both operators.


  We briefly review how to discuss noncommutative (NC) M5-branes and
intersecting NC M5-branes from kappa-invariance of an open supermembrane action
with constant three-form fluxes. The kappa-invariance gives rise to possible
Dirichlet brane configurations. We shortly summarize a construction of
projection operators for NC M5-branes and some intersecting configurations of
NC M5-branes. A strong flux limit of them is also discussed.


  We introduce a method where successive coordinate transformations are applied
to decrease the error in the adiabatic master equation resulting from
truncation in the local adiabatic parameter. Our method reduces the nonphysical
behaviour stemming from the lack of complete positivity. The strong
environment-induced relaxation at high Cooper pair pumping frequencies leads to
adiabatic ground-state pumping only in the lowest-order approximation. We
illustrate the robustness of the frequency where the adiabaticity breaks down
using the high-order theory and show the emergence of an optimal environmental
coupling strength, for which ideal pumping is preserved for the highest
frequency. Finally, we study the effect of quantum interference on the pumped
current and give an estimate for the relaxation rate of an experimentally
measured system.


  An integer additive set-indexer (IASI) is defined as an injective function
$f:V(G)\rightarrow \mathcal{P}(\mathbb{N}_0)$ such that the induced function
$f^+:E(G) \rightarrow \mathcal{P}(\mathbb{N}_0)$ defined by $f^+ (uv) = f(u)+
f(v)$ is also injective, where $f(u)+f(v)$ is the sumset of $f(u)$ and $f(v)$
and $\mathcal{P}(\mathbb{N}_0)$ is the power set of $\mathbb{N}_0$. If
$f^+(uv)=k \forall uv\in E(G)$, then $f$ is said to be a $k$-uniform integer
additive set-indexer. An integer additive set-indexer $f$ is said to be a weak
integer additive set-indexer if $|f^+(uv)|=max(|f(u)|,|f(v)|) \forall ~ uv\in
E(G)$. We have some characteristics of the graphs which admit weak integer
additive set-indexers. In this paper, we study about the sparing number of the
corona of two graphs.


  The multi-channel Coulomb scattering problem in the adiabatic representation
is considered.
  The non-adiabatic coupling matrix is assumed to have
  a non-zero asymptotic behavior at large internuclear separations. The
asymptotic solutions at large inter-nuclear distances are {therefore}
constructed. The asymptotic boundary conditions with S-matrix and K-matrix for
the scattering problem are formulated on the basis of constructed asymptotic
solutions.


  This paper examines the fundamental problem of identifying the most important
nodes in a network. We use an axiomatic approach to this problem. Specifically,
we propose six simple properties and prove that PageRank is the only centrality
measure that satisfies all of them. Our work gives new conceptual and
theoretical foundations of PageRank that can be used to determine suitability
of this centrality measure in specific applications.


  In 2014, more than 10 million people in the US were affected by an ambulatory
disability. Thus, gait rehabilitation is a crucial part of health care systems.
The quantification of human locomotion enables clinicians to describe and
analyze a patient's gait performance in detail and allows them to base clinical
decisions on objective data. These assessments generate a vast amount of
complex data which need to be interpreted in a short time period. We conducted
a design study in cooperation with gait analysis experts to develop a novel
Knowledge-Assisted Visual Analytics solution for clinical Gait analysis
(KAVAGait). KAVAGait allows the clinician to store and inspect complex data
derived during clinical gait analysis. The system incorporates innovative and
interactive visual interface concepts, which were developed based on the needs
of clinicians. Additionally, an explicit knowledge store (EKS) allows
externalization and storage of implicit knowledge from clinicians. It makes
this information available for others, supporting the process of data
inspection and clinical decision making. We validated our system by conducting
expert reviews, a user study, and a case study. Results suggest that KAVAGait
is able to support a clinician during clinical practice by visualizing complex
gait data and providing knowledge of other clinicians.


  Degenerating the quantum queer Schur superalgebra ${\mathcal{Q}_q(n,r; R)}$
to the case $q=1$, the queer Schur superalgebra ${\mathcal{Q}(n,r)}$ is
obtained. In this article, we reconstruct the universal enveloping algebra
${U({\mathfrak{q}_n})}$ of the queer Lie superalgebra ${\mathfrak{q}_n}$ via
${\mathcal{Q}(n,r)}$, and achieve another explanation of the Schur-Weyl-Sergeev
duality. Finally, we depict the Schur-Weyl-Sergeev duality over $\mathbb{Z}$.


  We establish a correspondence between general relativity with diffeomorphism
invariance and scalar field theories with Galilean invariance: notions such as
the Levi-Civita connection and the Riemann tensor have a Galilean counterpart.
This suggests Galilean theories as the unique nontrivial alternative to gauge
theories (including general relativity). Moreover, it is shown that the
requirement of first-order Palatini formalism uniquely determines the Galileon
models with second-order field equations, similar to the Lovelock gravity
theories. Possible extensions are discussed.


  Political misinformation, astroturfing and organised trolling are online
malicious behaviours with significant real-world effects. Many previous
approaches examining these phenomena have focused on broad campaigns rather
than the small groups responsible for instigating or sustaining them. To reveal
latent (i.e., hidden) networks of cooperating accounts, we propose a novel
temporal window approach that relies on account interactions and metadata
alone. It detects groups of accounts engaging in various behaviours that, in
concert, come to execute different goal-based strategies, a number of which we
describe. The approach relies upon a pipeline that extracts relevant elements
from social media posts, infers connections between accounts based on criteria
matching the coordination strategies to build an undirected weighted network of
accounts, which is then mined for communities exhibiting high levels of
evidence of coordination using a novel community extraction method. We address
the temporal aspect of the data by using a windowing mechanism, which may be
suitable for near real-time application. We further highlight consistent
coordination with a sliding frame across multiple windows and application of a
decay factor. Our approach is compared with other recent similar processing
approaches and community detection methods and is validated against two
relevant datasets with ground truth data, using content, temporal, and network
analyses, as well as with the design, training and application of three
one-class classifiers built using the ground truth; its utility is furthermore
demonstrated in two case studies of contentious online discussions.


  PG 1553+11 was the target of a coordinated three week multiwavelength
campaign during 2003 April and May. A significant X-ray flare was observed
during the second half of this campaign. Although no optical flare was recorded
during the X-ray campaign, optical observations obtained immediately prior to
the campaign displayed a higher flux than that recorded during the campaign. An
optical flare was observed a few days after the end of the X-ray campaign and
may be related to the X-ray flare. Radio observations were made at three
frequencies, with no significant changes in flux detected near the times of the
optical and X-ray flares. The spectral energy distributions and flux ratios in
different wavebands observed for this object are compared to other X-ray
selected blazars to demonstrate how PG 1553+11 is an extreme member of this
group.


  We investigate the inverse problem of recovering the diffusion and absorption
coefficients $(\sigma,q)$ in the nonlocal diffuse optical tomography equation
$(-\text{div}( \sigma \nabla))^s u+q u =0 \text{ in }\Omega$ from the nonlocal
Dirichlet-to-Neumann (DN) map $\Lambda^s_{\sigma,q}$. The purpose of this
article is to establish the following approximation and uniqueness results.
  - Approximation: We show that solutions to the conductivity equation $
\text{div}( \sigma \nabla v)=0 \text{ in }\Omega$ can be approximated in
$H^1(\Omega)$ by solutions to the nonlocal diffuse optical tomography equation
and the DN map $\Lambda_\sigma$ related to conductivity equation can be
approximated by the nonlocal DN map $\Lambda_{\sigma,q}^s$.
  - Local uniqueness: We prove that the absorption coefficient $q$ can be
determined in a neighborhood $\mathcal{N}$ of the boundary $\partial\Omega$
provided $\sigma$ is already known in $\mathcal{N}$.
  - Global uniqueness: Under the same assumptions as for the local uniqueness
result, and if one of the potentials vanishes in $\Omega$, then one can turn
with the help of \ref{item 1 abstract} the local determination into a global
uniqueness result.
  It is worth mentioning that the approximation result relies on the
Caffarelli--Silvestre type extension technique and the geometric form of the
Hahn--Banach theorem.


  The classical spin model in planar condensed media is represented as the U(1)
Chern-Simons gauge field theory. When the vorticity of the continuous flow of
the media coincides with the statistical magnetic field, which is necessary for
the model's integrability, the theory admits zero curvature connection. This
allows me to formulate the model in terms of gauge - invariant fields whose
evolution is described by the Davey-Stewartson (DS) equations. The Self-dual
Chern-Simons solitons described by the Liouville equation are subjected to
corresponding integrable dynamics. As a by-product the 2+1-dimensional
zero-curvature representation for the DS equation is obtained as well as the
new reduction conditions related to the DS-I case. Some possible applications
for the statistical transmutation in the anyon superfluid and TQFT are briefly
discussed.


  By using the density matrix renormalization group (DMRG) technique, the
incommensurate quantum Frenkel-Kontorova model is investigated numerically. It
is found that when the quantum fluctuation is strong enough, the
\emph{g}-function featured by a saw-tooth map in the depinned state will show a
different kind of behavior, similar to a standard map, but with reduced
magnitude. The related position correlations are studied in details, which
leads to a potentially interesting application to the recently well-explored
phase transitions in cold atoms loaded in optical lattices.


  The project of Greenlees et al. on understanding rational G-spectra in terms
of algebraic categories has had many successes, classifying rational G-spectra
for finite groups, SO(2), O(2), SO(3), free and cofree G-spectra as well as
rational toral G-spectra for arbitrary compact Lie groups.
  This paper provides an introduction to the subject in two parts. The first
discusses rational G-Mackey functors, the action of the Burnside ring and
change of group functors. It gives a complete proof of the well-known
classification of rational Mackey functors for finite G. The second part
discusses the methods and tools from equivariant stable homotopy theory needed
to obtain algebraic models for rational G-spectra. It gives a summary of the
key steps in the classification of rational G-spectrain terms of a symmetric
monoidal algebraic category.
  Having these two parts in the same place allows one to clearly see the
analogy between the algebraic and topological classifications.


  This is a noncommutative-geometric study of the semiclassical dynamics of
finite topological D-brane systems. Starting from the formulation in terms of A
-infinity categories, I show that such systems can be described by the
noncommutative symplectic supergeometry of Z2-graded quivers, and give a
synthetic formulation of the boundary part of the generalized WDVV equations.
In particular, a faithful generating function for integrated correlators on the
disk can be constructed as a linear combination of quiver necklaces, i.e. a
function on the noncommutative symplectic superspace defined by the quiver's
path algebra. This point of view allows one to construct extended moduli spaces
of topological D-brane systems as non-commutative algebraic `superschemes'.
They arise by imposing further relations on a Z2-graded version of the quiver's
preprojective algebra, and passing to the subalgebra preserved by a natural
group of symmetries.


  Levenshtein introduced the problem of constructing $k$-deletion correcting
codes in 1966, proved that the optimal redundancy of those codes is $O(k\log
N)$, and proposed an optimal redundancy single-deletion correcting code (using
the so-called VT construction). However, the problem of constructing optimal
redundancy $k$-deletion correcting codes remained open. Our key contribution is
a solution to this longstanding open problem. We present a $k$-deletion
correcting code that has redundancy $8k\log n +o(\log n)$ and encoding/decoding
algorithms of complexity $O(n^{2k+1})$ for constant $k$.


  Variational quantum algorithms are tailored to perform within the constraints
of current quantum devices, yet they are limited by performance-degrading
errors. In this study, we consider a noise model that reflects realistic gate
errors inherent to variational quantum algorithms. We investigate the
decoherence of a variationally prepared quantum state due to this noise model,
which causes a deviation from the energy estimation in the variational
approach. By performing a perturbative analysis of optimized circuits, we
determine the noise threshold at which the criteria set by the stability lemma
is met. We assess our findings against the variational quantum eigensolver and
quantum approximate optimization algorithm for various problems with up to 14
qubits. Moreover, we show that certain gate errors have a significantly smaller
impact on the coherence of the state, allowing us to reduce the execution time
without compromising performance.


  We show that the Internet topology at the Autonomous System (AS) level has a
rich--club phenomenon. The rich nodes, which are a small number of nodes with
large numbers of links, are very well connected to each other. The rich--club
is a core tier that we measured using the rich--club connectivity and the
node--node link distribution. We obtained this core tier without any heuristic
assumption between the ASes. The rich--club phenomenon is a simple qualitative
way to differentiate between power law topologies and provides a criterion for
new network models. To show this, we compared the measured rich--club of the AS
graph with networks obtained using the Barab\'asi--Albert (BA) scale--free
network model, the Fitness BA model and the Inet--3.0 model.


  Recent results from real algebraic geometry and the theory of polynomial
optimization are related in a new framework to the existence question of
multivariate tight wavelet frames whose generators have at least one vanishing
moment. Namely, several equivalent formulations of the so-called Unitary
Extension Principle by Ron and Shen are interpreted in terms of hermitian sums
of squares of certain nonnegative trigonometric polynomials and in terms of
semi-definite programming. The latter together with the recent results in
algebraic geometry and semi-definite programming allow us to answer
affirmatively the long standing open question of the existence of such tight
wavelet frames in dimension $d=2$; we also provide numerically efficient
methods for checking their existence and actual construction in any dimension.
We exhibit a class of counterexamples in dimension $d=3$ showing that, in
general, the UEP property is not sufficient for the existence of tight wavelet
frames. On the other hand we provide stronger sufficient conditions for the
existence of tight wavelet frames in dimension $d > 3$ and illustrate our
results by several examples.


  Formulation of the Lagrangian approach is presented for studying features of
motions of stellar bodies with non-zero rest mass in the vicinity of
fast-spinning black holes. The structure of Lagrangian is discussed. The
general method is applied to description of body motion in the Kerr model of
space-time to transition to the problem of tidal disruption of elastic bodies
by strong gravitational field.


  Mitigating crosstalk errors, whether classical or quantum mechanical, is
critically important for achieving high-fidelity entangling gates in
multi-qubit circuits. For weakly anharmonic superconducting qubits, unwanted
$ZZ$ interactions can be suppressed by combining qubits with opposite
anharmonicity. We present experimental measurements and theoretical modeling of
two-qubit gate error for gates based on the cross resonance interaction between
a capacitively shunted flux qubit and a transmon and demonstrate the
elimination of the $ZZ$ interaction.


  Decentralized baseband processing (DBP) architecture, which partitions the
base station antennas into multiple antenna clusters, has been recently
proposed to alleviate the excessively high interconnect bandwidth, chip
input/output data rates, and detection complexity for massive multi-user
multiple-input multiple-output (MU-MIMO) systems. In this paper, we develop a
novel decentralized Gaussian message passing (GMP) detection for the DBP
architecture. By projecting the discrete probability distribution into a
complex Gaussian function, the local means and variances iteratively calculated
in each antenna cluster are fused to generate the global symbol beliefs based
on the proposed message fusion rule in the centralized processing unit. We
present the framework and analysis of the convergence of the decentralized GMP
detection based on state evolution under the assumptions of large-system limit
and Gaussian sources. Analytical results corroborated by simulations
demonstrate that nonuniform antenna cluster partition scheme exhibits higher
convergence rate than the uniform counterpart. Simulation results illustrate
that the proposed decentralized GMP detection outperforms the recently proposed
decentralized algorithms.


  Quantum control is necessary for a variety of modern quantum technologies as
it allows to optimally manipulate quantum systems. An important problem in
quantum control is to establish whether the control objective functional has
trapping behaviour or no, namely if it has or no traps -- controls from which
it is difficult to escape by local search optimization methods. Higher order
traps were previously introduced in [A. N. Pechen, D. J. Tannor, "Are there
traps in quantum control landscapes?", Phys. Rev. Lett., 106 (2011), 120402],
where 3-rd order traps were found. In this note we show that traps of
arbitrarily high order exist for controllable quantum systems with special
symmetry in the Hamiltonian.


  Recent observation of a metal-insulator phase transition in the $\nu=0$ Hall
state of graphene has inspired the idea that charge carriers in the metallic
state could be fractionally charged vortices. We examine the question of
whether vortices in particular gapped states of graphene and subject to
external magnetic and pseudo-magnetic fields could have the mid-gap zero mode
electron states which would allow them to be charged.


  In the Vlasov-Poisson equation, every configuration which is homogeneous in
space provides a stationary solution. Penrose gave in 1960 a criterion for such
a configuration to be linearly unstable. While this criterion makes sense in a
measure-valued setting, the existing results concerning nonlinear instability
always suppose some regularity with respect to the velocity variable. Here,
thanks to a multiphasic reformulation of the problem, we can prove an "almost
Lyapounov instability" result for the Vlasov-Poisson equation, and an
ill-posedness result for the kinetic Euler equation and the Vlasov-Benney
equation (two quasineutral limits of the Vlasov-Poisson equation), both around
any unstable measure.


  The process of equilibration of a colliding hard-disks system is studied in
the framework of classical mechanic. The method consists of dividing the
nonequilibrium system into the interacting subsystems; the evolution one of
these subsystems is analyzed employing generalized Lagrange and Liouville
equations. The subsystem-subsystem interaction force is considered as an
evolution parameter. The mechanism by which its system equilibrates is
described.


  String backgrounds associated with gauged $G/H$ WZNW models in general depend
non-trivially on $\alpha'$. We note, however, that there exists a local
covariant $\a'$-dependent field redefinition that relates the exact
metric-dilaton background corresponding to the $SL(2,R)/U(1)$ model to its
leading-order form ($D=2$ black hole). As a consequence, there exists a
`scheme' in which the string effective equations have the latter as an exact
solution. However, the corresponding equation for the tachyon (which, like
other Weyl anomaly coefficients, has scheme-dependent form) still contains
corrections of all orders in $\alpha'$. As a result, the `probes' (the
tachyons) still feel the $\alpha'$-corrected background. The field
redefinitions we discuss contain the dilaton terms in the metric transformation
law. We comment on exact forms of the duality transformation in different
`schemes'.


  Fast rotation is responsible for important changes in the structure and
evolution of stars. Optical long baseline interferometry now permits the study
of its effects on the stellar surface, mainly gravity darkening and flattening.
We aim to determine the fundamental parameters of the fast-rotating star
Altair, in particular its evolutionary stage, mass, and differential rotation,
using state-of-the-art stellar interior and atmosphere models together with
interferometric, spectroscopic, and asteroseismic observations. We use ESTER 2D
stellar models to produce the relevant surface parameters needed to create
intensity maps from atmosphere models. Interferometric and spectroscopic
observables are computed from these intensity maps and several stellar
parameters are then adjusted using the MCMC algorithm Emcee. We determined
Altair's equatorial radius to be 2.008 +/- 0.006 Rsun, the position angle 301.1
+/- 0.3 degrees, the inclination 50.7 +/- 1.2 degrees, and the equatorial
angular velocity 0.74 +/- 0.01 times the Keplerian angular velocity. This
angular velocity leads to a flattening of 0.220 +/- 0.003. We also deduce from
the spectroscopically derived vsini ~ 243 km/s, a true equatorial velocity of
~314 km/s corresponding to a rotation period of 7h46m (~3 c/d). The data also
impose a strong correlation between mass, metallicity, hydrogen abundance, and
core evolution. Thanks to asteroseismic data, we constrain the mass of Altair
to 1.86 +/- 0.03 Msun and further deduce its metallicity Z = 0.019 and its core
hydrogen mass fraction Xc = 0.71, assuming an initial solar hydrogen mass
fraction X = 0.739. These values suggest that Altair is ~100 Myrs old. Finally,
the 2D ESTER model also gives the internal differential rotation of Altair,
showing that its core rotates approximately 50% faster than the envelope, while
the surface differential rotation does not exceed 6%.


  In the first part, we give a self contained introduction to the theory of
cyclic systems in n-dimensional space which can be considered as immersions
into certain Grassmannians. We show how the (metric) geometries on spaces of
constant curvature arise as subgeometries of Moebius geometry which provides a
slightly new viewpoint. In the second part we characterize Guichard nets which
are given by cyclic systems as being Moebius equivalent to 1-parameter families
of linear Weingarten surfaces. This provides a new method to study families of
parallel Weingarten surfaces in space forms. In particular, analogs of Bonnet's
theorem on parallel constant mean curvature surfaces can be easily obtained in
this setting.


  Let $d$ be an integer greater than $1$, and let $t$ be fixed such that
$\frac{1}{d} < t < \frac{1}{d-1}$. We prove that for any $n_0$ chosen
sufficiently large depending upon $t$, the $d$-dimensional cubes of sidelength
$n^{-t}$ for $n \geq n_0$ can perfectly pack a cube of volume
$\sum_{n=n_0}^\infty \frac{1}{n^{dt}}$. Our work improves upon a previously
known result in the three-dimensional case for when $1/3 < t \leq 4/11 $ and
$n_0 = 1$ and builds upon recent work of Terence Tao in the two-dimensional
case.


  We introduce the class of multistage stochastic optimization problems with a
random number of stages. For such problems, we show how to write dynamic
programming equations and detail the Stochastic Dual Dynamic Programming
algorithm to solve these equations. Finally, we consider a portfolio selection
problem over an optimization period of random duration. For several instances
of this problem, we show the gain obtained using a policy that takes the random
duration of the number of stages into account over a policy built taking a
fixed number of stages (namely the maximal possible number of stages).


  This work concerns the zero Mach number limit of the compressible primitive
equations. The primitive equations with the incompressibility condition are
identified as the limiting equations. The convergence with well-prepared
initial data (i.e., initial data without acoustic oscillations) is rigorously
justified, and the convergence rate is shown to be of order $ \mathcal
O(\varepsilon) $, as $ \varepsilon \rightarrow 0^+ $, where $ \varepsilon $
represents the Mach number. As a byproduct, we construct a class of global
solutions to the compressible primitive equations, which are close to the
incompressible flows.


  We report an {\it ab initio} simulation study of changes in structural and
dynamic properties of liquid Si at 7 pressures ranging from 10.2 GPa to 24.3
GPa along the isothermal line 1150~K, which is above the minimum of the melting
line. The increase of pressure from 10.2 GPa to 16 GPa causes strong reduction
in the tetrahedral ordering of the most close neighbors. The diffusion
coefficient shows a linear decay vs drop in atomic volume, that agrees with
theoretical prediction for simple liquid metals, thus not showing any feature
at the pressures corresponding to the different crystal phase boundaries. The
Fourier-spectra of velocity autocorrelation function shows two-peak structure
at pressures 20 GPa and higher. These characteristic frequencies correspond
well to the peak frequencies of the transverse current spectral function in the
second pseudo-Brillouin zone. Two almost flat branches of short-wavelength
transverse modes were observed for all the studied pressures. We discuss the
pressure evolution of characteristic frequencies in the longitudinal and
transverse branches of collective modes.


  The steady state motion of a folded pendulum has been studied using
frequencies of drive that are mainly below the natural (resonance) frequency of
the instrument. Although the free-decay of this mechanical oscillator appears
textbook exponential, the steady state behavior of the instrument for
sub-resonance drive can be remarkably complex. Although the response cannot be
explained by linear damping models, the general features can be understood with
the nonlinear, modified Coulomb damping model developed by the author.


  For years limited Monte Carlo simulations have led to the suspicion that the
time to failure of hierarchically organized load-transfer models of fracture is
non-zero for sets of infinite size. This fact could have a profound
significance in engineering practice and also in geophysics. Here, we develop
an exact algebraic iterative method to compute the successive time intervals
for individual breaking in systems of height $n$ in terms of the information
calculated in the previous height $n-1$. As a byproduct of this method,
rigorous lower and higher bounds for the time to failure of very large systems
are easily obtained. The asymptotic behavior of the resulting lower bound leads
to the evidence that the above mentioned suspicion is actually true.


  We study Lepton Flavour Violating hadron decays of the tau lepton within the
Simplest Little Higgs model. Namely we consider $\tau \rightarrow \mu (P, V,
PP)$ where $P$ and $V$ are short for a pseudoscalar and a vector meson. We find
that, in the most positive scenarios, branching ratios for these processes are
predicted to be, at least, four orders of magnitude smaller than present
experimental bounds.


  We show that the Seifert-Weber dodecahedral space $\mathsf{SW}$ is an
$L$-space. The proof builds on our work relating Floer homology and spectral
geometry of hyperbolic three-manifolds. A direct application of our previous
techniques runs into difficulties arising from the computational complexity of
the problem. We overcome this by exploiting the large symmetry group and the
arithmetic and tetrahedral group structure of $\mathsf{SW}$ to prove that small
eigenvalues on coexact $1$-forms must have large multiplicity.


  Standard projective measurements represent a subset of all possible
measurements in quantum physics, defined by positive-operator-valued measures.
We study what quantum measurements are projective simulable, that is, can be
simulated by using projective measurements and classical randomness. We first
prove that every measurement on a given quantum system can be realised by
classical processing of projective measurements on the system plus an ancilla
of the same dimension. Then, given a general measurement in dimension two or
three, we show that deciding whether it is projective-simulable can be solved
by means of semi-definite programming. We also establish conditions for the
simulation of measurements using projective ones valid for any dimension. As an
application of our formalism, we improve the range of visibilities for which
two-qubit Werner states do not violate any Bell inequality for all
measurements. From an implementation point of view, our work provides bounds on
the amount of noise a measurement tolerates before losing any advantage over
projective ones.


  Superconducting SrTiO_{3-\delta} was obtained by annealing single crystalline
SrTiO_3 samples in ultra high vacuum. An analysis of the V(I) characteristics
revealed very small critical currents I_c which can be traced back to a
unavoidable doping inhomogeneity. R(T) curves were measured for a range of
magnetic fields B at I<<I_c, thereby probing only the sample regions with the
highest doping level. The resulting curves B_{c2}(T) show upward curvature,
both at small and strong doping. These results are discussed in the context of
bipolaronic and conventional superconductivity with Fermi surface anisotropy.
We conclude that the special superconducting properties of SrTiO_{3-\delta} can
be related to its Fermi surface and compare this finding with properties of the
recently discovered superconductor MgB_2.


  Superconducting metal dichalcogenides (MDCs) present several similarities to
the other layered superconductors like cuprates. The superconductivity in
atomically thin MDCs has been demonstrated by recent experiments, however, the
investigation of the superconductivity intertwined with other orders are
scarce. Investigating the pseudogap in atomic layers of MDCs may help to
understand the superconducting mechanism for these true two-dimensional (2D)
superconducting systems. Herein we report a pseudogap opening in the tunneling
spectra of thin layers of SnSe2 epitaxially grown on highly oriented pyrolytic
graphite (HOPG) with scanning tunneling microscopy/spectroscopy (STM/STS). A
significant V-shaped pseudogap was observed to open near the Fermi level (EF)
in the STS. And at elevated temperatures, the gap gradually evolves to a
shallow dip. Our experimental observations provide direct evidence of a
pseudogap state in the electron-doped SnSe2 atomic layers on the HOPG surface,
which may stimulate further exploration of the mechanism of superconductivity
at 2D limit in MDCs.


  The unsteady electrorotation of a drop of a viscous weakly conducting
polarizable liquid suspended in another viscous weakly conducting polarizable
liquid immiscible with the former in an applied constant uniform electric field
is theoretically investigated. The surface tension of the drop is regarded as
sufficiently large for deformation of the drop under the action of the applied
electric field and the electrohydrodynamic flow can be considered small and the
drop can be considered spherical in the calculation of the electric field and
flow. The electric field intensity and the velocity and pressure in the
electrohydrodynamic flow are sought for in the form of a series solution with
time-dependent scalar, vector, and tensor coefficients for which relations are
found allowing one to determine them. The coefficients are sought for in the
form of asymptotic expansions over the parameter, the smallness of which
corresponds to the sufficiently large viscosity of the drop with respect to
that of the surrounding liquid. The differential equations for the terms of the
dimensionless expansions up to the first and second orders with respect to this
parameter are obtained. Their stationary solutions are found in the explicit
form and their stability is investigated. Up to the terms of the second order,
transitions to deformational oscillations of the drop are established not to
occur.


  We present a study of the expectations for very-high-energy (VHE) to
ultra-high-energy (UHE) gamma-ray and neutrino emission from interacting cosmic
rays in our Galaxy as well as a comparison to the latest results for the
Galactic UHE diffuse emission. We demonstrate the importance of properly
accounting for both the mixed cosmic-ray composition and the gamma-ray
absorption. We adopt the wounded-nucleon model of nucleus interactions and
provide parameterisations of the resulting gamma-ray and neutrino production.
Nucleon shielding due to clustering inside nuclei is shown to have a measurable
effect on the production of gamma rays and is particularly evident close to
breaks and cutoffs in mixed-composition particle spectra. The change in
composition around the `knee' in the cosmic ray spectrum has a noticeable
impact on the diffuse neutrino and gamma-ray emission spectra. We show that
current and near-future detectors can probe these differences in the key energy
range from 10 TeV to 1 PeV, testing the paradigm of the universality of the
cosmic ray spectrum and composition throughout the Galaxy.


  Robust self-organization of subcellular structures is a key principle
governing the dynamics and evolution of cellular life. In fission yeast cells
undergoing division, the mitotic spindle spontaneously emerges from the
interaction of microtubules, motor proteins and the confining cell walls, and
asters and vortices have been observed to self-assemble in quasi-two
dimensional microtubule-kinesin assays. Their is no clear microscopic picture
of the role of the active motors driving this pattern formation, and the
relevance of continuum modeling to filament-scale structures remains uncertain.
Here we present results of numerical simulations of a discrete filament-motor
protein model confined to a pressurised cylindrical box. Stable spindles,
nematic configurations, asters and high-density semi-asters spontaneously
emerge, the latter pair having also been observed in cytosol confined within
emulsion droplets. State diagrams are presented delineating each stationary
state as the pressure, motor speed and motor density are varied. We further
highlight a parameter regime where vortices form exhibiting collective rotation
of all filaments, but have a finite life-time before contracting to a
semi-aster. Quantifying the distribution of life-times suggests this
contraction is a Poisson process. Equivalent systems with fixed volume exhibit
persistent vortices with stochastic switching in the direction of rotation,
with switching times obeying similar statistics to contraction times in
pressurised systems. Furthermore, we show that increasing the detachment rate
of motors from filament plus-ends can both destroy vortices and turn some
asters into vortices. Based on our findings we argue the need for a deeper
understanding of the microscopic activities underpinning macroscopic
self-organization in active gels and urge further experiments to help bridge
these lengths.


  Imanishi, Jinzenji and Kuwata provided a recipe for computing Euler number of
Grassmann manifold $G(k,N)$ using physical model and its path-integral
[S.Imanishi, M.Jinzenji and K.Kuwata, Journal of Geometry and Physics, Volume
180, October 2022, 104623]. They demonstrated that the cohomology ring of
$G(k,N)$ is represented by fermionic variables. In this study, using only
fermionic variables, we computed an integral of the Chern classes of the dual
bundle of the tautological bundle on $G(k,N)$. In other words, the intersection
number of the Schubert cycles is obtained using the fermion integral.


  The two widely accepted classes of gamma-ray bursts (GRBs), short and long,
are with confidence ascribed to mergers of compact objects and collapse of
massive stars, respectively. A third, intermediate/soft class, remains
putative. Its existence was claimed based on univariate and bivariate analyses
of GRB observables modeled with Gaussian distributions. This, however, may not
be the appropriate approach, as it has been already shown that the univariate
distributions of durations are better described by mixtures of two skewed
components rather than three Gaussian ones.
  This paper investigates whether data in the duration--hardness ratio plane is
better modeled by mixtures of skewed bivariate distributions than by normal
ones. The archival data set of the Compton Gamma-Ray Observatory/BATSE and
Fermi/GBM data from the most recent catalogue release are examined. The
preferred model is chosen based on two information criteria, Akaike ($AIC$) and
Bayesian ($BIC$). It is found that the best description is given by a
two-component mixture of skewed Student-$t$ distributions, which outperforms
any other model considered. This implies that the distribution of the studied
parameters is intrinsically skewed, introducing spurious Gaussian components,
and hence the third class is unlikely to be a real phenomenon. Its existence,
based on statistical inference, is therefore rejected as unnecessary to explain
the observations.


  The chromo-polarizability of a quarkonium state is a measure of the amplitude
of the $E1$-$E1$ chromo-electric interaction of the quarkonium with soft gluon
fields and can be measured in the heavy quarkonium decays. Based on the chiral
unitary approach, formulas with modification caused by the $S$ wave $\pi\pi$
final state interaction (FSI) for measuring the chromo-polarizabilities are
given. It is shown that the effect of the $S$ wave $\pi\pi$ FSI is very
important in extracting chromo-polarizabilities from the experimental data. The
resultant values with the FSI are reduced to about 1/3 of those determined
without the FSI. The consequences of the FSI correction in the $J/\psi$-nucleon
scattering near the threshold are also discussed. The estimated lower bound of
the total cross section is reduced from about 17 mb to 2.9 mb, which agrees
with the experimental data point and is compatible with the previously
estimated values in the literature. In order to understand the interaction of
heavy quarkonia with light hadrons at low energies better and to obtain the
chromo-polarizabilities of quarkonia accurately, more data should be
accumulated. This can be done in the $J/\psi \to \pi^+\pi^-l^+l^-$ decay at
BES-III and CLEO-c and in the $\Upsilon \to \pi^+\pi^-l^+l^-$ decay at B
factories.


  Neural networks trained with (stochastic) gradient descent have an inductive
bias towards learning simpler solutions. This makes them highly prone to
learning spurious correlations in the training data, that may not hold at test
time. In this work, we provide the first theoretical analysis of the effect of
simplicity bias on learning spurious correlations. Notably, we show that
examples with spurious features are provably separable based on the model's
output early in training. We further illustrate that if spurious features have
a small enough noise-to-signal ratio, the network's output on the majority of
examples is almost exclusively determined by the spurious features, leading to
poor worst-group test accuracy. Finally, we propose SPARE, which identifies
spurious correlations early in training and utilizes importance sampling to
alleviate their effect. Empirically, we demonstrate that SPARE outperforms
state-of-the-art methods by up to 21.1% in worst-group accuracy, while being up
to 12x faster. We also show that SPARE is a highly effective but lightweight
method to discover spurious correlations.


  The largest bodies - or dwarf planets - constitute a different class among
Kuiper belt objects and are characterised by bright surfaces and volatile
compositions remarkably different from that of smaller trans-Neptunian objects.
These compositional differences are also reflected in the visible and
near-infrared colours, and variegations across the surface can cause broadband
colours to vary with rotational phase. Here we present near-infrared J and
H-band observations of the dwarf planet (136199) Eris obtained with the
GuideDog camera of the Infrared Telescope Facility. These measurements show
that - as suspected from previous J-H measurements - the J-H colour of Eris
indeed varies with rotational phase. This suggests notable surface heterogenity
in chemical composition and/or other material properties despite the otherwise
quite homogeneous, high albedo surface, characterised by a very low amplitude
visible range light curve. While variations in the grain size of the dominant
CH4 may in general be responsible for notable changes in the J-H colour, in the
current observing geometry of the system it can only partially explain the
observed J-H variation.


  Hydrogen deuteride (HD) rotational line emission can provide reliable
protoplanetary disk gas mass measurements, but it is difficult to observe and
detections have been limited to three T-Tauri disks. No new data have been
available since the \emph{Herschel} Space Observatory mission ended in 2013. We
set out to obtain new disk gas mass constraints by analysing upper limits on HD
1-0 emission in \emph{Herschel}/PACS archival data from the DIGIT key
programme. With a focus on the Herbig Ae/Be disks, whose stars are more
luminous than T Tauris, we determine upper limits for HD in data previosly
analysed for its line detections. Their significance is studied with a grid of
models run with the DALI physical-chemical code, customised to include
deuterium chemistry. Nearly all the disks are constrained to $M_{\rm
gas}\leq0.1\,$M$_{\odot}$, ruling out global gravitational instability. A
strong constraint is obtained for the HD 163296 disk mass, $M_{\rm gas} \leq
0.067\,$M$_{\odot}$, implying $\Delta_{\rm g/d}\leq100$. This HD-based mass
limit is towards the low end of CO-based mass estimates for the disk,
highlighting the large uncertainty in using only CO and suggesting that
gas-phase CO depletion in HD 163296 is at most a factor of a few. The $M_{\rm
gas}$ limits for HD 163296 and HD 100546, both bright disks with massive
candidate protoplanetary systems, suggest disk-to-planet mass conversion
efficiencies of $M_{\rm p}/(M_{\rm gas} + M_{\rm p})\approx10$ to $40\,$% for
present-day values. Near-future observations with SOFIA/HIRMES will be able to
detect HD in the brightest Herbig~Ae/Be disks within $150\,$pc with
$\approx10\,$h integration time.


  Decentralized Parallel SGD (D-PSGD) and its asynchronous variant Asynchronous
Parallel SGD (AD-PSGD) is a family of distributed learning algorithms that have
been demonstrated to perform well for large-scale deep learning tasks. One
drawback of (A)D-PSGD is that the spectral gap of the mixing matrix decreases
when the number of learners in the system increases, which hampers convergence.
In this paper, we investigate techniques to accelerate (A)D-PSGD based training
by improving the spectral gap while minimizing the communication cost. We
demonstrate the effectiveness of our proposed techniques by running experiments
on the 2000-hour Switchboard speech recognition task and the ImageNet computer
vision task. On an IBM P9 supercomputer, our system is able to train an LSTM
acoustic model in 2.28 hours with 7.5% WER on the Hub5-2000 Switchboard (SWB)
test set and 13.3% WER on the CallHome (CH) test set using 64 V100 GPUs and in
1.98 hours with 7.7% WER on SWB and 13.3% WER on CH using 128 V100 GPUs, the
fastest training time reported to date.


  Speech Translation has always been about giving source text or audio input
and waiting for system to give translated output in desired form. In this
paper, we present the Acoustic Dialect Decoder (ADD) - a voice to voice
ear-piece translation device. We introduce and survey the recent advances made
in the field of Speech Engineering, to employ in the ADD, particularly focusing
on the three major processing steps of Recognition, Translation and Synthesis.
We tackle the problem of machine understanding of natural language by designing
a recognition unit for source audio to text, a translation unit for source
language text to target language text, and a synthesis unit for target language
text to target language speech. Speech from the surroundings will be recorded
by the recognition unit present on the ear-piece and translation will start as
soon as one sentence is successfully read. This way, we hope to give translated
output as and when input is being read. The recognition unit will use Hidden
Markov Models (HMMs) Based Tool-Kit (HTK), hybrid RNN systems with gated memory
cells, and the synthesis unit, HMM based speech synthesis system HTS. This
system will initially be built as an English to Tamil translation device.


  Criminals use malware to disrupt cyber-systems. The number of these
malware-vulnerable systems is increasing quickly as common systems, such as
vehicles, routers, and lightbulbs, become increasingly interconnected
cyber-systems. To address the scale of this problem, analysts divide malware
into classes and develop, for each class, a specialized defense. In this
project we classified malware with machine learning. In particular, we used a
supervised multi-class long short term memory (LSTM) model. We trained the
algorithm with thousands of malware files annotated with class labels (the
training set), and the algorithm learned patterns indicative of each class. We
used disassembled malware files (provided by Microsoft) and separated the
constituent data into parsed instructions, which look like human-readable
machine code text, and raw bytes, which are hexadecimal values. We are
interested in which format, text or hex, is more valuable as input for
classification. To solve this, we investigated four cases: a text-only model, a
hexadecimal-only model, a multi-input model using both text and hexadecimal
inputs, and a model based on combining the individual results. We performed
this investigation using the machine learning Python package Keras, which
allows easily configurable deep learning architectures and training. We hoped
to understand the trade-offs between the different formats. Due to the class
imbalance in the data, we used multiple methods to compare the formats, using
test accuracies, balanced accuracies (taking into account weights of classes),
and an accuracy derived from tables of confusion. We found that the multi-input
model, which allows learning on both input types simultaneously, resulted in
the best performance. Our finding expedites malware classification research by
providing researchers a suitable deep learning architecture to train a tailored
version to their malware.


  Analysis of the covariant theta-exact noncommutative (NC) gauge field theory
(GFT), inspired by high energy cosmic rays experiments, is performed in the
framework of the inelastic neutrino-nucleon scatterings. Next we have have
found neutrino two-point function and shows a closed form decoupled from the
hard ultraviolet (UV) divergent term, from softened ultraviolet/infrared
(UV/IR) mixing term, and from the finite terms as well. For a certain choice of
the noncommutative parameter theta which preserves unitarity, problematic UV
divergent and UV/IR mixing terms vanish. Non-perturbative modifications of the
neutrino dispersion relations are assymptotically independent of the scale of
noncommutativity in both, the low and high energy limits and may allow
superluminal propagation.


  We establish the multiparameter quantum Cram\'er-Rao bound for simultaneously
estimating the centroid, the separation, and the relative intensities of two
incoherent optical point sources using alinear imaging system. For equally
bright sources, the Cram\'er-Rao bound is independent of the source separation,
which confirms that the Rayleigh resolution limit is just an artifact of the
conventional direct imaging and can be overcome with an adequate strategy. For
the general case of unequally bright sources, the amount of information one can
gain about the separation falls to zero, but we show that there is always a
quadratic improvement in an optimal detection in comparison with the intensity
measurements. This advantage can be of utmost important in realistic scenarios,
such as observational astronomy.


  We investigate the effect of quantum decoherence and relaxation in neutrino
oscillations using MINOS and T2K data. The formalism of open quantum systems is
used to describe the interaction of a neutrino system with the environment,
where the strength of the interaction is regulated by a decoherence parameter
$\Gamma$. We assume an energy dependence parameterized by $\Gamma = \gamma_0
(E/\mbox{GeV})^n$, with $n=-2,0,+2$, and consider three different scenarios,
allowing the investigation of the effect of relaxation and of constraining the
solar and atmospheric sectors to the same decoherence parameter. The MINOS and
T2K data present a complementary behavior, with regard to our theoretical
model, resulting in a better sensitivity for $n = +2$ and $n = -2$,
respectively. We perform a combined analyses of both experimental data, which
also include a reactor constraint on $\sin^2 \theta_{13}$, and observe an
independence of the results to the scenarios we investigate. As highlight of
our analyses we obtain the best limit on $\gamma_0$ for the energy dependence
of $n = -2$, reporting an upper bound of $1.7 \times 10^{-23}$~GeV, at the 90\%
confidence level.


  The aggregated unfitted finite element method (AgFEM) is a methodology
recently introduced in order to address conditioning and stability problems
associated with embedded, unfitted, or extended finite element methods. The
method is based on removal of basis functions associated with badly cut cells
by introducing carefully designed constraints, which results in well-posed
systems of linear algebraic equations, while preserving the optimal
approximation order of the underlying finite element spaces. The specific goal
of this work is to present the implementation and performance of the method on
distributed-memory platforms aiming at the efficient solution of large-scale
problems. In particular, we show that, by considering AgFEM, the resulting
systems of linear algebraic equations can be effectively solved using standard
algebraic multigrid preconditioners. This is in contrast with previous works
that consider highly customized preconditioners in order to allow one the usage
of iterative solvers in combination with unfitted techniques. Another novelty
with respect to the methods available in the literature is the problem sizes
that can be handled with the proposed approach. While most of previous
references discussing linear solvers for unfitted methods are based on serial
non-scalable algorithms, we propose a parallel distributed-memory method able
to efficiently solve problems at large scales. This is demonstrated by means of
a weak scaling test defined on complex 3D domains up to 300M degrees of freedom
and one billion cells on 16K CPU cores in the Marenostrum-IV platform. The
parallel implementation of the AgFEM method is available in the large-scale
finite element package FEMPAR.


  This paper addresses the computation of normalized solid angle measure of
polyhedral cones. This is well understood in dimensions two and three. For
higher dimensions, assuming that a positive-definite criterion is met, the
measure can be computed via a multivariable hypergeometric series. We present
two decompositions of full-dimensional simplicial cones into finite families of
cones satisfying the positive-definite criterion, enabling the use of the
hypergeometric series to compute the solid angle measure of any polyhedral
cone. Additionally, our second decomposition method yields cones with a special
tridiagonal structure, reducing the number of required coordinates for the
hypergeometric series formula. Furthermore, we investigate the convergence of
the hypergeometric series for this case. Our findings provide a powerful tool
for computing solid angle measures in high-dimensional spaces.


  The CeIn3-xSnx cubic heavy fermion system presents an antiferromagnetic
transition at T_N = 10 K, for x = 0, that decreases continuously down to 0 K
upon Sn substitution at a critical concentration of x_c ~ 0.65. In the vicinity
of T_N -> 0 the system shows non-Fermi liquid behavior due to antiferromagnetic
critical fluctuations. For a high Sn content, x > 2.2, intermediate valence
effects are present. In this work we show that Gd3+-doped electron spin
resonance (ESR) probes a change in the character of the Ce 4f electron, as a
function of Sn substitution. The Gd3+ ESR results indicate a transition of the
Ce 4f spin behavior from localized to itinerant. Near the quantum critical
point, on the antiferromagnetic side of the magnetic phase diagram, both
localized and itinerant behaviors coexist.


  We present an analysis of low mass X-ray binaries (LMXBs) and globular
clusters (GCs) in five galaxies using Chandra, and HST data. Of the 186 LMXBs
within the optical fields 71 are in GCs, confirming that LMXBs are formed
particularly efficiently in GCs. However, there is no statistically significant
correlation between the distance of a GC from the center of its host galaxy and
its LMXB hosting probability. Metal-rich GCs are 3.4 times more likely to host
LMXBs than metal-poor ones. Intriguingly, the LMXBs in NGC 1399 are
preferentially in the reddest GCs of the metal-rich subsystem. This indicates
that the red peak of the color distribution itself encompasses GCs with a range
of enrichment histories. The strength of this effect varies from galaxy to
galaxy, possibly indicating differences in their metal-enrichment histories.
Field LMXBs in our program galaxies are more concentrated towards the center of
their host galaxies than GC-LMXBs. This suggests that a majority of field LMXBs
are formed in situ and have not escaped from current GCs. This is consistent
with previous specific frequency based studies. The brightest LMXBs in GCs
appear to be preferentially associated with luminous, metal-rich clusters. We
show that it is probable that some of these GCs host multiple bright LMXBs,
while the probability is much lower for metal-poor GCs. This implies that LMXBs
in more metal-rich cluster systems should reveal a longer high luminosity X-ray
tail, and show less X-ray variability than metal-poor cluster populations.
(abridged)


  Recently the renormalization group predictions on the effect of disorder on
pinning models have been put on mathematical grounds. The picture is
particularly complete if the disorder is 'relevant' or 'irrelevant' in the
Harris criterion sense: the question addressed is whether quenched disorder
leads to a critical behavior which is different from the one observed in the
pure, i.e. annealed, system. The Harris criterion prediction is based on the
sign of the specific heat exponent of the pure system, but it yields no
prediction in the case of vanishing exponent. This case is called 'marginal',
and the physical literature is divided on what one should observe for marginal
disorder, notably there is no agreement on whether a small amount of disorder
leads or not to a difference between the critical point of the quenched system
and the one for the pure system. In a previous work (arXiv:0811.0723) we have
proven that the two critical points differ at marginality of at least
exp(-c/beta^4), where c>0 and beta^2 is the disorder variance, for beta in
(0,1) and Gaussian IID disorder. The purpose of this paper is to improve such a
result: we establish in particular that the exp(-c/beta^4) lower bound on the
shift can be replaced by exp(-c(b)/beta^b), c(b)>0 for b>2 (b=2 is the known
upper bound and it is the result claimed in [Derrida, Hakim, Vannimenus, JSP
1992]), and we deal with very general distribution of the IID disorder
variables. The proof relies on coarse graining estimates and on a fractional
moment-change of measure argument based on multi-body potential modifications
of the law of the disorder.


  Blobs, or quasi-spherical emission regions containing relativistic particles
and magnetic fields, are often assumed ad hoc in emission models of
relativistic astrophysical jets, yet their physical origin is still not well
understood. Here, we employ a suite of large-scale two-dimensional
particle-in-cell simulations in electron-positron plasmas to demonstrate that
relativistic magnetic reconnection can naturally account for the formation of
quasi-spherical plasmoids filled with high-energy particles and magnetic
fields. Our simulations extend to unprecedentedly long temporal and spatial
scales, so we can capture the asymptotic physics independently of the initial
setup. We characterize the properties of the plasmoids that are continuously
generated as a self-consistent by-product of the reconnection process: they are
in rough energy equipartition between particles and magnetic fields; the upper
energy cutoff of the plasmoid particle spectrum is proportional to the plasmoid
width w, corresponding to a Larmor radius ~0.2 w; the plasmoids grow in size at
~0.1 of the speed of light, with most of the growth happening while they are
still non-relativistic (first they grow); their growth is suppressed once they
get accelerated to relativistic speeds by the field line tension, up to the
Alfven speed (then they go). The largest plasmoids, whose typical recurrence
interval is ~2.5 L/c, reach a characteristic size w ~ 0.2 L independently of
the system length L, they have nearly isotropic particle distributions and they
contain the highest energy particles, whose Larmor radius is ~0.03 L. The
latter can be regarded as the Hillas criterion for relativistic reconnection.
We briefly discuss the implications of our results for the high-energy emission
from relativistic jets and pulsar winds.


  We investigate the ultimate precision limits for quantum phase estimation in
terms of the coherence, $C$, of the probe. For pure states, we give the minimum
estimation variance attainable, $V(C)$, and the optimal state, in the
asymptotic limit when the probe system size, $n$, is large. We prove that pure
states are optimal only if $C$ scales as $n$ with a sufficiently large
proportionality factor, and that the rank of the optimal state increases with
decreasing $C$, eventually becoming full-rank. We show that the variance
exhibits a Heisenberg-like scaling, $V(C) \sim a_n/C^2$, where $a_n$ decreases
to $\pi^2/3$ as $n$ increases, leading to a dimension-independent relation.


  SOS TUTORIA UC is a student connection application aimed at facilitating
academic assistance between students through external tutoring outside of the
application. To achieve this, a responsive web application was designed and
implemented, integrated with the WeNet platform, which provides various
services for user management and user recommendation algorithms. This study
presents the development and validation of the experience in the application by
evaluating the importance of incorporating the dimension of personality traits,
according to the Big Five model, in the process of recommending students for
academic tutoring. The goal is to provide support for students to find others
with greater knowledge and with a personality that is \'different\',
\'similar\' or \'indifferent\' to their own preferences for receiving academic
assistance on a specific topic. The integration with the WeNet platform was
successful in terms of components, and the results of the recommendation system
testing were positive but have room for improvement.


  Controlling doping is essential for a successful integration of semiconductor
materials into device technologies. However, the assessment of doping levels
and the distribution of charge carriers in carbon nanotubes or other nanoscale
semiconductor materials is often either limited to a qualitative attribution of
being 'high' or 'low' or it is entirely absent. Here, we describe efforts
toward a quantitative characterization of doping in redox- or electrochemically
doped semiconducting carbon nanotubes (s-SWNTs) using VIS-NIR absorption
spectroscopy. We discuss how carrier densities up to about 0.5 $\rm nm^{-1}$
can be quantified with a sensitivity of roughly one charge per $10^4$ carbon
atoms assuming in-homogeneous or homogeneous carrier distributions.


  Motivated by a down-up Markov chain on cladograms, David Aldous conjectured
in 1999 that there exists a "diffusion on continuum trees" whose mass
partitions at any finite number of branch points evolve as Wright-Fisher
diffusions with some negative mutation rates, until some branch point
disappears. Building on previous work on interval-partition-valued processes,
we construct this conjectured process via a consistent system of stationary
evolutions of binary trees with k labeled leaves and edges decorated with
interval partitions. The interval partitions are scaled Poisson-Dirichlet
interval partitions whose interval lengths record subtree masses. They also
possess a diversity property that captures certain distances in the continuum
tree. Continuously evolving diversities give access to continuously evolving
continuum tree distances. The pathwise construction allows us to study this
"Aldous diffusion" in the Gromov-Hausdorff-Prokhorov space of rooted, weighted
R-trees. We establish the simple Markov property and path-continuity. The
Aldous diffusion is stationary with the distribution of the Brownian continuum
random tree. While the Brownian CRT is a.s. binary, we show that there is a
dense null set of exceptional times when the Aldous diffusion has a ternary
branch point, including stopping times at which the strong Markov property
fails. Our construction relates to the two-parameter Chinese restaurant
process, branching processes, and stable L\'evy processes, among other
connections. Wright-Fisher diffusions and the aforementioned processes of
Poisson-Dirichlet interval partitions arise as interesting projections of the
Aldous diffusion. Finally, one can embed Aldous's stationary down-up Markov
chain on cladograms in the Aldous diffusion and hence address a related
conjecture by David Aldous by establishing a scaling limit theorem.


  This paper details the work of the University of Groningen for the BabyLM
Challenge. We follow the idea that, like babies, language models should be
introduced to simpler concepts first and build off of that knowledge to
understand more complex concepts. We examine this strategy of
simple-then-complex through a variety of lenses, namely context size,
vocabulary, and overall linguistic complexity of the data. We find that only
one, context size, is truly beneficial to training a language model. However
this simple change to context size gives us improvements of 2 points on average
on (Super)GLUE tasks, 1 point on MSGS tasks, and 12\% on average on BLiMP
tasks. Our context-limited model outperforms the baseline that was trained on
10$\times$ the amount of data.


  Mapping the brain imaging data to networks, where each node represents a
specific area of the brain, has enabled an objective graph-theoretic analysis
of human connectome. However, the latent structure on higher-order connections
remains unexplored, where many brain regions acting in synergy perform complex
functions. Here we analyse this hidden structure using the simplicial complexes
parametrisation where the shared faces of simplexes encode higher-order
relationships between groups of nodes and emerging hyperbolic geometry. Based
on data collected within the Human Connectome Project, we perform a systematic
analysis of consensus networks of 100 female (F-connectome) and 100 male
(M-connectome) subjects by varying the number of fibres launched. Our analysis
reveals that the functional geometry of the common F\&M-connectome coincides
with the M-connectome and is characterized by a complex architecture of
simplexes to the 14th order, which is built in six anatomical communities, and
short cycles among them. Furthermore, the F-connectome has additional
connections that involve different brain regions, thereby increasing the size
of simplexes and introducing new cycles. By providing new insights into the
internal organisation of anatomical brain modules as well as into the links
between them that are essential to dynamics, these results also highlight the
functional gender-related differences


  The paper deals with the explicit calculus and the properties of the
fundamental solution K of a parabolic operator related to a semilinear equation
that models reaction diffusion systems with excitable kinetics. The initial
value problem in all of the space is analyzed together with continuous
dependence and a priori estimates of the solution. These estimates show that
the asymptotic behavior is determined by the reaction mechanism. Moreover it's
possible a rigorous singular perturbation analysis for discussing travelling
waves with their characteristic times.


  A variety of observational campaigns seek to test dark-matter models by
measuring dark-matter subhaloes at low masses. Despite their predicted lack of
stars, these subhaloes may be detectable through gravitational lensing or via
their gravitational perturbations on stellar streams. To set measurable
expectations for subhalo populations within LambdaCDM, we examine 11 Milky Way
(MW)-mass haloes from the FIRE-2 baryonic simulations, quantifying the counts
and orbital fluxes for subhaloes with properties relevant to stellar stream
interactions: masses down to 10^6 Msun, distances < 50 kpc of the galactic
center, across z = 0 - 1 (lookback time 0 - 8 Gyr). We provide fits to our
results and their dependence on subhalo mass, distance, and lookback time, for
use in (semi)analytic models. A typical MW-mass halo contains ~16 subhaloes
>10^7 Msun (~1 subhalo >10^8 Msun) within 50 kpc at z = 0. We compare our
results with dark-matter-only versions of the same simulations: because they
lack a central galaxy potential, they overpredict subhalo counts by 2-10x, more
so at smaller distances. Subhalo counts around a given MW-mass galaxy declined
over time, being ~10x higher at z = 1 than at z = 0. Subhaloes have nearly
isotropic orbital velocity distributions at z = 0. Across our simulations, we
also identified 4 analogs of Large Magellanic Cloud satellite passages; these
analogs enhance subhalo counts by 1.4-2.7 times, significantly increasing the
expected subhalo population around the MW today. Our results imply an
interaction rate of ~5 per Gyr for a stream like GD-1, sufficient to make
subhalo-stream interactions a promising method of measuring dark subhaloes.


  We show that phononic frequency conversion can be enhanced by orders of
magnitude in piezoelectric systems by heterogeneous integration of
high-mobility semiconductor films. A lithium niobate and indium gallium
arsenide heterostructure is utilized to demonstrate efficient three-wave mixing
processes at microwave frequencies, including 16% phononic power conversion
efficiency for sum-frequency generation and 1% phononic power conversion
efficiency for difference-frequency generation, as well as the most efficient
degenerate four-wave phononic mixing to date. We present a theoretical model
that accurately predicts the sum-frequency and difference-frequency generation
processes and we show that the conversion efficiency can be further enhanced by
the application of semiconductor bias fields. Laser Doppler vibrometry is then
applied to examine many three-wave and four-wave mixing processes
simultaneously in the same device. Through the use of our developed model, we
show that these nonlinearities can be enhanced far beyond what is demonstrated
here by confining phonons to smaller dimensions in waveguides and optimizing
semiconductor material properties or using 2D semiconductors.


  Traditionally, scholars in physics education research pay attention to
students solving well-structured learning activities, which provide restricted
room for collaboration and idea-generation due to their close-ended nature. In
order to encourage the socialization of information among group members, we
utilized a real-world problem where students were asked to generate a
well-structured physics task, and investigated how student groups collaborated
to create physics problems for younger students at an introductory physics
course at a university in northern Chile. Data collection consists of audio
recording the group discussions while they were collaborating to develop their
physics problems as well as the solutions they created to their problems.
Through interviews, we accessed students' perceptions on the task and its
challenges. Results suggest that generating problems is an opportunity for
students to propose ideas and make decisions regarding the goals of the
problem, concepts and procedures, contextual details and magnitudes and units
to introduce in their generated problems. In addition, we found evidence that
groups tested the validity of their creations by engaging in strategies often
observed with algebra-based physics problems, such as mathematical procedures
and qualitative descriptions of the physics embedded in the problem, yet groups
invested more time with algebra-based strategies compared to more qualitative
descriptions. Students valued the open-ended nature of the task and recognized
its benefits in utilizing physics ideas into context, which in turn enabled
collaboration in a way not experienced with traditional algebra-based problems.
These findings support the use of generative activities as a pathway for
students to engage in real-world physics problems that allow for a range and
variety of collective processes and ideas.


  Using perturbative renormalization group we study the influence of random
velocity field on the critical behaviour of directed bond percolation process
near its second-order phase transition between absorbing and active phase. We
consider Kraichnan model with finite correlation time for modelling advecting
velocity field. Using functional integral representation we are able to apply
field-theoretic renormalization group to determine possible universality
classes. The model is analyzed near its critical dimension by means of
three-parameter expansion in $\epsilon,\delta,\eta$, where $\epsilon$ is the
deviation from the Kolmogorov scaling, $\delta$ the deviation from the critical
space dimension $d_c$ and $\eta$ is the deviation from the parabolic dispersion
law for the velocity correlator. Fixed points with corresponding regions of
stability are evaluated to the leading order in the perturbation scheme.


  We discuss the very red objects found in the first field of the Caltech Faint
Galaxy Redshift Survey, for which the observations and analysis are now
complete. In this field, which is 15 arcmin$^2$ and at J005325+1234 there are
195 objects with $K_s < 20$ mag, of which 84% have redshifts. The sample
includes 24 spectroscopically confirmed Galactic stars, 136 galaxies, three
AGNs, and 32 objects without redshifts.
  About 10% of the sample has $(R-K) \ge 5$ mag. Four of these objects have
redshifts, with $0.78 \le z \le 1.23$. Three of these are based on absorption
features in the mid-UV, while the lowest redshift object shows the standard
features near 4000\AA. Many of the objects still without redshifts have been
observed spectroscopically, and no emission lines were seen in their spectra.
We believe they are galaxies with $z \sim 1 - 1.5$ that are red due to their
age and stellar content and not to some large amount of internal reddening from
dust.
  Among the many other results from this survey of interest here is a
determination of the median extinction in the mid-UV for objects with strong
emission line spectra at $z \sim 1 - 1.3$. The result is extinction by a factor
of $\sim$2 at 2400\AA.


  In this thesis an iterative scheme for the construction of operator product
expansion (OPE) coefficients is applied to determine low order coefficients in
perturbation theory for a specific toy model. We use the approach to quantum
field theory proposed by S. Hollands [arXiv:0802.2198], which is centered
around the OPE and a number of axioms on the corresponding OPE coefficients.
This framework is reviewed in the first part of the thesis.
  In the second part we apply an algorithm for the perturbative construction of
OPE coefficients to a toy model: Euclidean $\varphi^6$-theory in 3-dimensions.
Using a recently found formulation in terms of vertex operators and a
diagrammatic notation in terms of trees [arXiv:0906.5313v1], coefficients up to
second order are constructed, some general features of coefficients at
arbitrary order are presented and an exemplary comparison to the corresponding
customary method of computation is given.


  Crystal scintillators provide potential merits for the pursuit of low-energy
low-background experiments. A CsI(Tl) scintillating crystal detector is being
constructed to study low-energy neutrino physics at a nuclear reactor, while
projects are underway to adopt this technique for dark matter searches. The
choice of the geometrical parameters of the crystal modules, as well as the
optimization of the read-out scheme, are the results of an R&D program.
Crystals with 40 cm in length were developed. The detector requirements and the
achieved performance of the prototypes are presented. Future prospects for this
technique are discussed.


  Iron-rich layers are known to form in the stellar subsurface through a
combination of gravitational settling and radiative levitation. Their presence,
nature and detailed structure can affect the excitation process of various
stellar pulsation modes, and must therefore be modeled carefully in order to
better interpret Kepler asteroseismic data. In this paper, we study the
interplay between atomic diffusion and fingering convection in A-type stars,
and its role in the establishment and evolution of iron accumulation layers. To
do so, we use a combination of three-dimensional idealized numerical
simulations of fingering convection, and one-dimensional realistic stellar
models. Using the three-dimensional simulations, we first validate the mixing
prescription for fingering convection recently proposed by Brown et al. (2013),
and identify what system parameters (total mass of iron, iron diffusivity,
thermal diffusivity, etc.) play a role in the overall evolution of the layer.
We then implement the Brown et al. (2013) prescription in the Toulouse-Geneva
Evolution code to study the evolution of the iron abundance profile beneath the
stellar surface. We find, as first discussed by Th\'eado et al. (2009), that
when the concurrent settling of helium is ignored, this accumulation rapidly
causes an inversion in the mean molecular weight profile, which then drives
fingering convection. The latter mixes iron with the surrounding material very
efficiently, and the resulting iron layer is very weak. However, taking helium
settling into account partially stabilizes the iron profile against fingering
convection, and a large iron overabundance can accumulate. The opacity also
increases significantly as a result, and in some cases ultimately triggers
dynamical convection.


  In this paper we investigate the asymptotic behavior of polynomials that are
orthonormal over the interior domain of an analytic Jordan curve L with respect
to area measure. We prove that, inside L, these polynomials behave
asymptotically like a sequence of certain integrals involving the canonical
conformal map of the exterior of L onto the exterior of the unit circle and
certain meromorphic kernel function defined in terms of a conformal map of the
interior of L onto the unit disk. The error term in the integral representation
is proven to decay geometrically and sufficiently fast, allowing us to obtain
more precise asymptotic formulas for the polynomials under certain additional
geometric considerations. These formulas yield, in turn, fine results on the
location, limiting distribution and accumulation points of the zeros of the
polynomials.


  Bill James' Pythagorean formula has for decades done an excellent job
estimating a baseball team's winning percentage from very little data: if the
average runs scored and allowed are denoted respectively by ${\rm RS}$ and
${\rm RA}$, there is some $\gamma$ such that the winning percentage is
approximately ${\rm RS}^\gamma / ({\rm RS}^\gamma + {\rm RA}^\gamma)$. One
important consequence is to determine the value of different players to the
team, as it allows us to estimate how many more wins we would have given a
fixed increase in run production. We summarize earlier work on the subject, and
extend the earlier theoretical model of Miller (who estimated the run
distributions as arising from independent Weibull distributions with the same
shape parameter; this has been observed to describe the observed run data
well). We now model runs scored and allowed as being drawn from independent
Weibull distributions where the shape parameter is not necessarily the same,
and then use the Method of Moments to solve a system of four equations in four
unknowns. Doing so yields a predicted winning percentage that is consistently
better than earlier models over the last 30 MLB seasons (1994 to 2023). This
comes at a small cost as we no longer have a closed form expression but must
evaluate a two-dimensional integral of two Weibull distributions and
numerically estimate the solutions to the system of equations; as these are
trivial to do with simple computational programs it is well worth adopting this
framework and avoiding the issues of implementing the Method of Least Squares
or the Method of Maximum Likelihood.


  In this paper, we introduce a way to generalize the Euler's gamma function as
well as some related special functions. With a given polynomial in one variable
$f(t)\ge 0$, we can associate a function, so-called "gamma function associated
with $f$", defined by $\Gamma_f(s) := \int_0^\infty f^{s-1} e^{-t} dt$. This
function has many features similar to the Euler's gamma function. We also
present some initial results on the gamma-type functional equation for
$\Gamma_f(s)$ in some special cases.


  We measure the polarization of a photon gas in a dye-filled microcavity. The
polarization is obtained by a single-shot measurement of the Stokes parameters.
We find that the polarization of both the thermal cloud and the Bose-Einstein
condensate of photons (phBEC) does not differ from shot to shot. In the case of
the phBEC, we find that the polarization correlates with the polarization of
the pump pulse. The polarization of the thermal cloud is independent of
parameters varied in the experiment and is governed by a hidden anisotropy in
the system.


  A prototype tool to assist architects during the early design stage of floor
plans has been developed, consisting of an Evolutionary Program for the Space
Allocation Problem (EPSAP), which generates sets of floor plan alternatives
according to the architect's preferences; and a Floor Plan Performance
Optimization Program (FPOP), which optimizes the selected solutions according
to thermal performance criteria. The design variables subject to optimization
are window position and size, overhangs, fins, wall positioning, and building
orientation. A procedure using a transformation operator with gradient descent,
such as behavior, coupled with a dynamic simulation engine was developed for
the thermal evaluation and optimization process. However, the need to evaluate
all possible alternatives regarding designing variables being used during the
optimization process leads to an intensive use of thermal simulation, which
dramatically increases the simulation time, rendering it unpractical. An
alternative approach is a smart optimization approach, which utilizes an
oriented and adaptive search technique to efficiently find the near optimum
solution. This paper presents the search methodology for the building
orientation of floor plan designs, and the corresponding efficiency and
effectiveness indicators. The calculations are based on 100 floor plan designs
generated by EPSAP. All floor plans have the same design program, location, and
weather data, changing only their geometry. Dynamic simulation of buildings was
effectively used together with the optimization procedure in this approach to
significantly improve the designs. The use of the orientation variable has been
included in the algorithm.


  In epidemiology, identifying the effect of exposure variables in relation to
a time-to-event outcome is a classical research area of practical importance.
Incorporating propensity score in the Cox regression model, as a measure to
control for confounding, has certain advantages when outcome is rare. However,
in situations involving exposure measured with moderate to substantial error,
identifying the exposure effect using propensity score in Cox models remains a
challenging yet unresolved problem. In this paper, we propose an estimating
equation method to correct for the exposure misclassification-caused bias in
the estimation of exposure-outcome associations. We also discuss the asymptotic
properties and derive the asymptotic variances of the proposed estimators. We
conduct a simulation study to evaluate the performance of the proposed
estimators in various settings. As an illustration, we apply our method to
correct for the misclassification-caused bias in estimating the association of
PM2.5 level with lung cancer mortality using a nationwide prospective cohort,
the Nurses' Health Study (NHS). The proposed methodology can be applied using
our user-friendly R function published online.


  In this paper, we introduce a study of prolongations of representations of
Lie groups. We obtain a faithful (one-to-one) representation of TG where G is a
finite-dimensional Lie group and TG is the tangent bundle of G, by using (not
necessarily faithful) representations of G. We show that tangent functions of
Lie group actions correspond to prolonged representations. We prove that if two
representations are equivalent, then their prolongations are equivalent too. We
show that if U is an invariant subspace for a representation, then TU is an
invariant subspace for the prolongation of the given representation and vice
versa. We prove that if the prolongation of \Phi is an irreducible
representation, then \Phi is also an irreducible representation. Finally we
show that prolongations of direct sum of two representations are direct sum of
their prolongations.


  We are presenting proofs of fundamental results related to homotopy
idempotents, proofs that are sufficiently simple so that even the author can
understand them. The first one is that homotopy idempotents in the category of
pointed connected CW complexes split and the second one is that unpointed
homotopy idempotents in the category of finite-dimensional CW complexes split.
Some of our proofs rectify gaps in the existing literature.


  In this paper, we prove Sp\"ath's Character Triple Conjecture for
$p$-solvable groups. This is a conjecture proposed by Sp\"ath during the
reduction process of Dade's Projective Conjecture to quasisimple groups. In
addition, as suggested by Isaacs and Navarro, we take into account the
$p$-residue of characters.


  Recent advances using Density Functional Theory (DFT) to augment Multiplet
Ligand Field Theory (MLFT) have led to ab-initio calculations of many formerly
empirical parameters. This development makes MLFT more predictive instead of
interpretive, thus improving its value for understanding highly correlated 3d,
4d, and f-electron systems. Here, we explore a DFT + MLFT based approach for
core-to-core K{\alpha} x-ray emission spectra (XES) and evaluate its
performance for a range of transition metal systems. We find good agreement
between theory and experiment, as well as the ability to capture key spectral
trends related to spin and oxidation state. We also discuss limitations of the
model in the context of the remaining free parameters and suggest directions
forward.


  We study the effects of noise on stationary pulse solutions (bumps) in
spatially extended neural fields. The dynamics of a neural field is described
by an integrodifferential equation whose integral term characterizes synaptic
interactions between neurons in different spatial locations of the network.
Translationally symmetric neural fields support a continuum of stationary bump
solutions, which may be centered at any spatial location. Random fluctuations
are introduced by modeling the system as a spatially extended Langevin equation
whose noise term we take to be multiplicative or additive. For nonzero noise,
these bumps are shown to wander about the domain in a purely diffusive way. We
can approximate the effective diffusion coefficient using a small noise
expansion. Upon breaking the (continuous) translation symmetry of the system
using a spatially heterogeneous inputs or synapses, bumps in the stochastic
neural field can become temporarily pinned to a finite number of locations in
the network. In the case of spatially heterogeneous synaptic weights, as the
modulation frequency of this heterogeneity increases, the effective diffusion
of bumps in the network approaches that of the network with spatially
homogeneous weights.


  The diversity of Type Ia supernova (SN Ia) photometry is explored using a
grid of 130 one-dimensional models. It is shown that the observable properties
of SNe Ia resulting from Chandrasekhar-mass explosions are chiefly determined
by their final composition and some measure of ``mixing'' in the explosion. A
grid of final compositions is explored including essentially all combinations
of 56Ni, stable ``iron'', and intermediate mass elements that result in an
unbound white dwarf. Light curves (and in some cases spectra) are calculated
for each model using two different approaches to the radiation transport
problem. Within the resulting templates are models that provide good
photometric matches to essentially the entire range of observed SNe Ia. On the
whole, the grid of models spans a wide range in B-band peak magnitudes and
decline rates, and does not obey a Phillips relation. In particular, models
with the same mass of 56Ni show large variations in their light curve decline
rates. We identify the physical parameters responsible for this dispersion, and
consider physically motivated ``cuts'' of the models that agree better with the
Phillips relation. For example, models that produce a constant total mass of
burned material of 1.1 +/- Msun do give a crude Phillips relation, albeit with
much scatter. The scatter is further reduced if one restricts that set to
models that make 0.1 to 0.3 Msun of stable iron and nickel isotopes, and then
mix the ejecta strongly between the center and 0.8 Msun. We conclude that the
supernovae that occur most frequently in nature are highly constrained by the
Phillips relation and that a large part of the currently observed scatter in
the relation is likely a consequence of the intrinsic diversity of these
objects.


  The concept of asymmetric entanglement-assisted quantum error-correcting code
(asymmetric EAQECC) is introduced in this article. Codes of this type take
advantage of the asymmetry in quantum errors since phase-shift errors are more
probable than qudit-flip errors. Moreover, they use pre-shared entanglement
between encoder and decoder to simplify the theory of quantum error correction
and increase the communication capacity. Thus, asymmetric EAQECCs can be
constructed from any pair of classical linear codes over an arbitrary field.
Their parameters are described and a Gilbert-Varshamov bound is presented.
Explicit parameters of asymmetric EAQECCs from BCH codes are computed and
examples exceeding the introduced Gilbert-Varshamov bound are shown.


  We present new algorithms and fast implementations to find efficient
approximations for modelling stochastic processes. For many numerical
computations it is essential to develop finite approximations for stochastic
processes. While the goal is always to find a finite model, which represents a
given knowledge about the real data process as accurate as possible, the ways
of estimating the discrete approximating model may be quite different: (i) if
the stochastic model is known as a solution of a stochastic differential
equation, e.g., one may generate the scenario tree directly from the specified
model; (ii) if a simulation algorithm is available, which allows simulating
trajectories from all conditional distributions, a scenario tree can be
generated by stochastic approximation; (iii) if only some observed trajectories
of the scenario process are available, the construction of the approximating
process can be based on non-parametric conditional density estimates.


  We consider several computational problems related to conjugacy between
subshifts of finite type, restricted to $k$-block codes: verifying a proposed
$k$-block conjugacy, deciding if two shifts admit a $k$-block conjugacy, and
reducing the representation size of a shift via a $k$-block conjugacy. We give
a polynomial-time algorithm for verification, and show GI and NP-hardness for
deciding conjugacy and reducing representation size, respectively. Our approach
focuses on 1-block conjugacies between vertex shifts, from which we generalize
to $k$-block conjugacies and to edge shifts. We conclude with several open
problems.


  Surface transportation systems are an essential part of urban transportation
infrastructure and are susceptible to damage from earthquakes. This damage,
along with the lack of prior warning of earthquake events, may lead to severe
and unexpected disruption of normal traffic patterns, which may seriously
impair post-disaster response. Accordingly, it is important to understand and
model the performance of urban transportation systems immediately following an
earthquake, to evaluate its capability to support emergency response, e.g., the
movement of firefighters, search and rescue teams and medical personnel, and
the transportation of injured people to emergency treatment facilities. For
this purpose, a scenario-based methodology is developed to model the
performance of a transportation network immediately following an earthquake
using an agent-based model. This methodology accounts for the abrupt changes in
destination, irrational behavior of drivers, unavailability of traffic
information and the impairment to traffic capacity due to bridge damage and
building debris. An illustration using the road network of Tangshan City, China
shows that the method can capture the traffic flow characteristics immediately
after an earthquake and can determine the capability of the transportation
network to transfer injured people to hospitals considering the above factors.
Thus, it can provide rational support for evaluating the performance of the
surface transportation system under immediate post-disaster emergency
conditions.


  We present light curves of a sample of "transient" sources observed with the
All-Sky Monitor (ASM) of the Rossi X-ray Timing Explorer (RXTE). The light
curves extend over 3.5 years. They are presented in three groups: six
neutron-star systems, eight black-hole-candidate systems, and an additional
diverse set of six objects that are either transient sources (in the sense of
usually being undetectable) or persistent sources showing transient behavior.
The outburst profiles of these sources show reproducible characteristics within
one source and from source to source, as well as large variations. These
profiles together with the profiles of the hardness ratios from the ASM are a
valuable resource for the understanding of accretion instabilities. We
summarize briefly some recent work by observers on these somewhat arbitrarily
selected sources.


  Relativistic formalism of Green's functions is dicussed in QCD and QED,where
the relativistic Green's functions are constructed using the Schwinger proper
time formalism and the Fock-Feynman-Schwinger method.As a result a simple and
exact method is found for the relativistic systems,where the interaction can be
written in a time-independent form.In this case one can write the relativistic
Green's function as a one-dimensional integral of the corresponding
nonrelativistic Green's function.The explicit example for the problem of a
charge in the constant magnetic field is discussed in detail,and the exact
agreement with the Schwinger relativistic form is demonstrated. A similar
analysis is performed in the relativistiv Coulomb probem,supporting the
accuracy of the proposed relativistic formalism.


  I discuss, what really new could give Photon Colliders ($\gamma\gamma$ and
$e\gamma$) after LHC and \epe Linear Collider operations.


  We explicitly calculate the induced gravity theory at the boundary of an
asymptotically Anti-de Sitter five dimensional Einstein gravity. We also
display the action that encodes the dynamics of radial diffeomorphisms. It is
found that the induced theory is a four dimensional conformal gravity plus a
scalar field. This calculation confirms some previous results found by a
different approach.