  In order to facilitate the analysis of timing relations between individual
transitions in a signal trace, dynamic digital timing analysis offers a less
accurate but much faster alternative to analog simulations of digital circuits.
This primarily requires gate delay models that also account for the fact that
the input-to-output delay of a particular input transition also depends on the
temporal distance to the previous output transitions. In the case of
multi-input gates, the delay also experiences variations caused by multi-input
switching (MIS) effects, i.e., transitions at different inputs that occur in
close temporal proximity. In this paper, we advocate the development of hybrid
delay models for CMOS gates obtained by replacing transistors with time-variant
resistors. We exemplify our approach by applying it to a NOR gate (and, hence,
to the dual NAND gate) and a Muller C gate. We analytically solve the resulting
first-order differential equations with non-constant-coefficients, and derive
analytic expressions for the resulting MIS gate delays. The resulting formulas
not only pave the way to a sound model parametrization procedure, but are also
instrumental for implementing fast and efficient digital timing simulation. By
comparison with analog simulation data, we show that our models faithfully
represent all relevant MIS effects. Using an implementation in the Involution
Tool, we demonstrate that our model surpasses the alternative digital delay
models for NOR gates known to us in terms of accuracy, with comparably short
running times.


  Ferroelectric control of two-dimensional magnetism is promising in
fabricating electronic devices with high speed and low energy consumption. The
newly discovered layered MnBi$_2$Te$_4$(Bi$_2$Te$_3$)$_n$ and their Sb
counterparts exhibit A-type antiferromagnetism with intriguing topological
properties. Here, we propose to obtain tunable magnetic multistates in their
thin films by ferroelectrically manipulating the interlayer magnetic couplings
(IMCs) based on the Heisenberg model and first-principles calculations. Our
strategy relies on that interfacing the thin films with appropriate
ferroelectric materials can switch on/off an interlayer hopping channel between
Mn-$e_g$ orbitals as the polarizations reversed, thus resulting in a switchable
interlayer antiferromagnetism-to-ferromagnetism transition. On the other hand,
the interface effect leads to asymmetric energy barrier heights for the two
polarization states. These properties allow us to build ferroelectrically
switchable triple and quadruple magnetic states with multiple Chern numbers in
thin films. Our study reveals that ferroelectrically switchable magnetic and
topological multistates in MnBi$_2$Te$_4$ family can be obtained by rational
design for multifunctional electronic devices, which can also be applied to
other two-dimensional magnetic materials.


  We introduce electrically-poled small molecule assemblies that can serve as
the active electro-optic material in nano-scale guided-wave circuits such as
those of the silicon photonics platform. These monolithic organic materials can
be vacuum-deposited to homogeneously fill nanometer-size integrated-optics
structures, and electrically poled at higher temperatures to impart an
orientational non-centrosymmetric order that remains stable at room
temperature. An initial demonstration using the DDMEBT molecule and corona
poling delivered a material with the required high optical quality, an
effective glass transition temperature of the order of $\sim 80$ $^\circ$C, and
an electro-optic coefficient of $20$~pm/V.


  Model compression can significantly reduce the sizes of deep neural network
(DNN) models, and thus facilitates the dissemination of sophisticated, sizable
DNN models, especially for their deployment on mobile or embedded devices.
However, the prediction results of compressed models may deviate from those of
their original models. To help developers thoroughly understand the impact of
model compression, it is essential to test these models to find those deviated
behaviors before dissemination. However, this is a non-trivial task because the
architectures and gradients of compressed models are usually not available.
  To this end, we propose DFLARE, a novel, search-based, black-box testing
technique to automatically find triggering inputs that result in deviated
behaviors in image classification tasks. DFLARE iteratively applies a series of
mutation operations to a given seed image, until a triggering input is found.
For better efficacy and efficiency, DFLARE models the search problem as Markov
Chains and leverages the Metropolis-Hasting algorithm to guide the selection of
mutation operators in each iteration. Further, DFLARE utilizes a novel fitness
function to prioritize the mutated inputs that either cause large differences
between two models' outputs, or trigger previously unobserved models'
probability vectors. We evaluated DFLARE on 21 compressed models for image
classification tasks with three datasets. The results show that DFLARE
outperforms the baseline in terms of efficacy and efficiency. We also
demonstrated that the triggering inputs found by DFLARE can be used to repair
up to 48.48% deviated behaviors in image classification tasks and further
decrease the effectiveness of DFLARE on the repaired models.


  Intrinsic nonlinear elasticity deals with the deformations of elastic bodies
as isometric immersions of Riemannian manifolds into the Euclidean spaces (see
Ciarlet [9,10]). In this paper, we study the rigidity and continuity properties
of elastic bodies for the intrinsic approach to nonlinear elasticity. We first
establish a geometric rigidity estimate for mappings from Riemannian manifolds
to spheres (in the spirit of Friesecke-James-M\"{u}ller [23]), which is the
first result of this type for the non-Euclidean case as far as we know. Then we
prove the asymptotic rigidity of elastic membranes under suitable geometric
conditions. Finally, we provide a simplified geometric proof of the continuous
dependence of deformations of elastic bodies on the Cauchy-Green tensors and
second fundamental forms, which extends the Ciarlet-Mardare theorem in [18] to
arbitrary dimensions and co-dimensions.


  Current quantum orthodoxy claims that the statistical collapse of the
wave-function arises from the interaction of the measuring instrument with its
environment through the phenomenon known as environment induced decoherence.
Here it is shown that there exists a measurement scheme that is exactly
decohering without the aid of an environment. The scheme relies on the
assumption that the meter is decomposable into probe and pointer, with the
probe taken to be inaccessible for observation. Under the assumption that the
probe and the pointer initial states are momentum limited, it is shown that
coherences die out within a finite interval of time and the pointer states are
exactly orthogonal. These lead to the fundamental realization that dispersion
of correlation does not require an external infinite number of degrees of
freedom. An internal one degree of freedom is already sufficient to delocalize
the correlations and leave its subparts in a classical mixed state, so that
decoherence may occur even for isolated measuring instruments.


  In this article we construct Symmetric operations for all primes (previously
known only for p=2). These unstable operations are more subtle than the
Landweber-Novikov operations, and encode all p-primary divisibilities of
characteristic numbers. Thus, taken together (for all primes) they plug the gap
left by the Hurewitz map L ---> Z[b_1,b_2,...], providing an important
structure on Algebraic Cobordism. Applications include: questions of
rationality of Chow group elements - see [11], and the structure of the Graded
Algebraic Cobordism. We also construct Steenrod operations of T.tom Dieck-style
in Algebraic Cobordism. These unstable multiplicative operations are more
canonical and subtle than Quillen-style operations, and complement the latter.


  Graph neural networks (GNNs), as the de-facto model class for representation
learning on graphs, are built upon the multi-layer perceptrons (MLP)
architecture with additional message passing layers to allow features to flow
across nodes. While conventional wisdom commonly attributes the success of GNNs
to their advanced expressivity, we conjecture that this is not the main cause
of GNNs' superiority in node-level prediction tasks. This paper pinpoints the
major source of GNNs' performance gain to their intrinsic generalization
capability, by introducing an intermediate model class dubbed as
P(ropagational)MLP, which is identical to standard MLP in training, but then
adopts GNN's architecture in testing. Intriguingly, we observe that PMLPs
consistently perform on par with (or even exceed) their GNN counterparts, while
being much more efficient in training. This finding sheds new insights into
understanding the learning behavior of GNNs, and can be used as an analytic
tool for dissecting various GNN-related research problems. As an initial step
to analyze the inherent generalizability of GNNs, we show the essential
difference between MLP and PMLP at infinite-width limit lies in the NTK feature
map in the post-training stage. Moreover, by examining their extrapolation
behavior, we find that though many GNNs and their PMLP counterparts cannot
extrapolate non-linear functions for extremely out-of-distribution samples,
they have greater potential to generalize to testing samples near the training
data range as natural advantages of GNN architectures.


  We study perturbations of the discrete Laplacian associated to discrete
analogs of cusps and funnels. We perturb the metric and the potential in a
long-range way. We establish a propagation estimate and a Limiting Absorption
Principle away from the possible embedded eigenvalues. The approach is based on
a positive commutator technique.


  In this paper, we employ a combination of analytical and numerical techniques
to investigate the dynamics of lattice envelope vector soliton solutions
propagating within a one-dimensional chain of flexible mechanical metamaterial.
To model the system, we formulate discrete equations that describe the
longitudinal and rotational displacements of each individual rigid unit mass
using a lump element approach. By applying the multiple-scales method in the
context of a semi-discrete approximation, we derive an effective nonlinear
Schr\"odinger equation that characterizes the evolution of rotational and
slowly varying envelope waves from the aforementioned discrete motion
equations. We thus show that this flexible mechanical metamaterial chain
supports envelope vector solitons where the rotational component has the form
of either a bright or a dark soliton. In addition, due to nonlinear coupling,
the longitudinal displacement displays kink-like profiles thus forming the
2-components vector soliton. These findings, which include specific vector
envelope solutions, enrich our knowledge on the nonlinear wave solutions
supported by flexible mechanical metamaterials and open new possibilities for
the control of nonlinear waves and vibrations.


  Bootstrap percolation has been used effectively to model phenomena as diverse
as emergence of magnetism in materials, spread of infection, diffusion of
software viruses in computer networks, adoption of new technologies, and
emergence of collective action and cultural fads in human societies. It is
defined on an (arbitrary) network of interacting agents whose state is
determined by the state of their neighbors according to a threshold rule. In a
typical setting, bootstrap percolation starts by random and independent
"activation" of nodes with a fixed probability $p$, followed by a deterministic
process for additional activations based on the density of active nodes in each
neighborhood ($\theta$ activated nodes). Here, we study bootstrap percolation
on random geometric graphs in the regime when the latter are (almost surely)
connected. Random geometric graphs provide an appropriate model in settings
where the neighborhood structure of each node is determined by geographical
distance, as in wireless {\it ad hoc} and sensor networks as well as in
contagion. We derive bounds on the critical thresholds $p_c', p_c"$ such that
for all $p > p"_c(\theta)$ full percolation takes place, whereas for $p <
p'_c(\theta)$ it does not. We conclude with simulations that compare numerical
thresholds with those obtained analytically.


  We construct integrable models on flag manifold by using the symplectic
structure explicitly given in the Bruhat coordinatization of flag manifold.
They are non-commutative integrable and some of the conserved quantities are
given by the Casimir invariants. We quantize the systems using the coherent
state path integral technique and find the exact expression for the propagator
for some special cases.


  Deuteron-proton elastic scattering is considered at the energies from 880 MeV
to 2 GeV at the scattering angles $\theta^*\ge 140^\circ$. The
multiple-scattering method is used to calculate the reaction amplitude. Four
reaction mechanisms are taken into account: one-nucleon-exchange,
single-scattering, and double-scattering with a nucleon and a delta-isobar in
the intermediate state. The method allows calculating both unpolarized
differential cross section and any polarization observables.
  All the results obtained are compared to the experimental data.


  Via convex integration, we construct weak solutions to the non-resistive
electron-MHD system which do not conserve energy and magnetic helicity.


  In this paper, we consider a scale invariant Cassinian metric and a Gromov
hyperbolic metric. We discuss a distortion property of the scale invariant
Cassinian metric under M\"obius maps of a punctured ball onto another punctured
ball. We obtain a modulus of continuity of the identity map from a domain
equipped with the scale invariant Cassinian metric (or the Gromov hyperbolic
metric) onto the same domain equipped with the Euclidean metric. The
quasi-invariance properties of both the metrics under quasiconformal maps are
also established.


  We calculate the cross section of the inverse beta decay process, $\nu_e+n\to
p+e$, in a background magnetic field which is much smaller than $m_p^2/e$.
Using exact solutions of the Dirac equation in a constant magnetic field, we
find the cross section for arbitrary polarization of the initial neutrons. The
cross section depends on the direction of the incident neutrino even when the
initial neutron is assumed to be at rest and has no net polarization. Possible
implications of the result are discussed.


  We give a self contained introduction to A$_\infty$-algebras,
A$_\infty$-bimodules and maps between them. The case of A$_\infty$-bimodule-map
between $A$ and its dual space $A^{*}$, which we call $\infty$-inner-product,
will be investigated in detail. In particular, we describe the graph complex
associated to $\infty$-inner-product. In a later paper, we show how
$\infty$-inner-products can be used to model the string topology BV-algebra on
the free loop space of a Poincar\'e duality space.


  It is well known that the study of $SU(n+1)$ Toda systems is important not
only to Chern-Simons models in Physics, but also to the understanding of
holomorphic curves, harmonic sequences or harmonic maps from Riemann surfaces
to $\mathbb C\mathbb P^n$. One major goal in the study of $SU(n+1)$ Toda system
on Riemann surfaces is to completely understand the asymptotic behavior of
fully bubbling solutions. In this article we use a unified approach to study
fully bubbling solutions to general $SU(n+1)$ Toda systems and we prove three
major sharp estimates important for constructing bubbling solutions: the
closeness of blowup solutions to entire solutions, the location of blowup
points and a $\partial_z^2$ condition.


  Using the absolute detection calibration and abundant detections of the OSSOS
(Outer Solar System Origin Survey) project, we provide population measurements
for the main Kuiper Belt. For absolute magnitude $H_r<8.3$, there are 30,000
non-resonant main-belt objects, with twice as many hot-component objects than
cold, and with total mass of 0.014 $M_\Earth$, only 1/7 of which is in the cold
belt (assuming a cold-object albedo about half that of hot component objects).
We show that transneptunian objects with $5.5 < H_r < 8.3$ (rough diameters
400--100~km) have indistinguishable absolute magnitude (size) distributions,
regardless of being in the cold classical Kuiper belt (thought to be
primordial) or the `hot' population (believed to be implanted after having been
formed elsewhere). We discuss how this result was not apparent in previous
examinations of the size distribution due to the complications of fitting
assumed power-law functional forms to the detections at differing depths. This
shared size distribution is surprising in light of the common paradigm that the
hot population planetesimals formed in a higher density environment much closer
to the Sun, in an environment that also (probably later) formed larger (dwarf
planet and bigger) objects. If this paradigm is correct, % << BG added clause
our result implies that planetesimal formation was relatively insensitive to
the local disk conditions and that the subsequent planet-building process in
the hot population did not modify the shape of the planetesimal size
distribution in this 50--300~km range.


  In this paper we consider orbifold compactifications of M-theory on $S^1/{\bf
Z}_2\times T^4/{\bf Z}_2$. We discuss solutions of the local anomaly matching
conditions by twisted vector, tensor and hypermultiplets confined on the local
orbifold six-planes. In addition we consider phase-transitions among different
solutions which are mediated by M-theory fivebranes which touch the local
orbifold planes and are converted there to gauge instantons.


  We present a one-to-one correspondence between equivalence classes of
embeddings of a manifold (into a larger manifold of the same dimension) and
equivalence classes of certain distances on the manifold. This correspondence
allows us to use the Abstract Boundary to describe the structure of the `edge'
of our manifold without resorting to structures external to the manifold
itself. This is particularly important in the study of singularities within
General Relativity where singularities lie on this `edge'. The ability to talk
about the same objects, e.g., singularities, via different structures provides
alternative routes for investigation which can be invaluable in the pursuit of
physically motivated problems where certain types of information are
unavailable or difficult to use.


  LS I +61 303 is an exceptionally rare example of a high mass X-ray binary
(HMXB) that also exhibits MeV-TeV emission, making it one of only a handful of
"gamma-ray binaries". Here we present H-alpha spectra that show strong
variability during the 26.5 day orbital period and over decadal time scales. We
detect evidence of a spiral density wave in the Be circumstellar disk over part
of the orbit. The H-alpha line profile also exhibits a dramatic emission burst
shortly before apastron, observed as a redshifted shoulder in the line profile,
as the compact source moves almost directly away from the observer. We
investigate several possible origins for this red shoulder, including an
accretion disk, mass transfer stream, and a compact pulsar wind nebula that
forms via a shock between the Be star's wind and the relativistic pulsar wind.


  In this paper, we present a new variational method for sparse regression
using $L_0$ regularization. The variational parameters appear in the
approximate model in a way that is similar to Breiman's Garrote model. We refer
to this method as the variational Garrote (VG). We show that the combination of
the variational approximation and $L_0$ regularization has the effect of making
the problem effectively of maximal rank even when the number of samples is
small compared to the number of variables. The VG is compared numerically with
the Lasso method, ridge regression and the recently introduced paired mean
field method (PMF) (M. Titsias & M. L\'azaro-Gredilla., NIPS 2012). Numerical
results show that the VG and PMF yield more accurate predictions and more
accurately reconstruct the true model than the other methods. It is shown that
the VG finds correct solutions when the Lasso solution is inconsistent due to
large input correlations. Globally, VG is significantly faster than PMF and
tends to perform better as the problems become denser and in problems with
strongly correlated inputs. The naive implementation of the VG scales cubic
with the number of features. By introducing Lagrange multipliers we obtain a
dual formulation of the problem that scales cubic in the number of samples, but
close to linear in the number of features.


  The recently completed research project DEEP-ER has developed a variety of
hardware and software technologies to improve the I/O capabilities of next
generation high-performance computers, and to enable applications recovering
from the larger hardware failure rates expected on these machines.
  The heterogeneous Cluster-Booster architecture --first introduced in the
predecessor DEEP project-- has been extended by a multi-level memory hierarchy
employing non-volatile and network-attached memory devices. Based on this
hardware infrastructure, an I/O and resiliency software stack has been
implemented combining and extending well established libraries and software
tools, and sticking to standard user-interfaces. Real-world scientific codes
have tested the projects' developments and demonstrated the improvements
achieved without compromising the portability of the applications.


  We study the properties of entanglement in two-dimensional topologically
ordered phases of matter. Such phases support anyons, quasiparticles with
exotic exchange statistics. The emergent nonlocal state spaces of anyonic
systems admit a particular form of entanglement that does not exist in
conventional quantum mechanical systems. We study this entanglement by adapting
standard notions of entropy to anyonic systems. We use the algebraic theory of
anyon models (modular tensor categories) to illustrate the nonlocal
entanglement structure of anyonic systems. Using this formalism, we present a
general method of deriving the universal topological contributions to the
entanglement entropy for general system configurations of a topological phase,
including surfaces of arbitrary genus, punctures, and quasiparticle content. We
analyze a number of examples in detail. Our results recover and extend prior
results for anyonic entanglement and the topological entanglement entropy.


  The dynamics associated with a measurement-based master equation for quantum
Brownian motion are investigated. A scheme for obtaining time evolution from
general initial conditions is derived. This is applied to analyze dissipation
and decoherence in the evolution of both a Gaussian and a Schr\"{o}dinger cat
initial state. Dependence on the diffusive terms present in the master equation
is discussed with reference to both the coordinate and momentum
representations.


  Numerous experiments currently underway offer the potential to indirectly
probe new charged particles with masses at the weak scale. For example, the
tentative excess in Higgs diphoton decay and the tentative gamma-ray line in
Fermi-LAT data have recently attracted attention as possible one-loop
signatures of new charged particles. We explore the interplay between such
signals, dark matter direct detection through Higgs exchange, and measurements
of the electron EDM, by studying the size of these effects in several models.
We compute one-loop effects to explore the relationship among couplings probed
by different experiments. In particular, models in which dark matter and the
Higgs both interact with charged particles at a detectable level typically
induce, at loop level, couplings between dark matter and the Higgs that are
around the level of current direct detection sensitivity. Intriguingly,
one-loop Higgs diphoton decay and DM annihilation into two photons, two-loop
EDMs, and loop-induced direct detection rates are all coming within range of
existing experiments for approximately the same range of charged particle
masses, offering the prospect of an exciting coincidence of signals at
collider, astrophysical, underground and atomic physics measurements.


  The existence of K\"ahler-Einstein metrics on a compact K\"ahler manifold has
been the subject of intensive study over the last few decades, following Yau's
solution to Calabi's conjecture. The Ricci flow, introduced by Richard Hamilton
has become one of the most powerful tools in geometric analysis.
  We study the K\"ahler-Ricci flow on minimal surfaces of Kodaira dimension one
and show that the flow collapses and converges to a unique canonical metric on
its canonical model. Such a canonical is a generalized K\"ahler-Einstein
metric. Combining the results of Cao, Tsuji, Tian and Zhang, we give a metric
classification for K\"aher surfaces with a numerical effective canonical line
bundle by the K\"ahler-Ricci flow. In general, we propose a program of finding
canonical metrics on canonical models of projective varieties of positive
Kodaira dimension.


  We investigate closed subgroups $G \subseteq \mathrm{Sp}_{2g}(\mathbb{Z}_2)$
whose modulo-$2$ images coincide with the image $\mathfrak{S}_{2g + 1}
\subseteq \mathrm{Sp}_{2g}(\mathbb{F}_2)$ of $S_{2g + 1}$ or the image
$\mathfrak{S}_{2g + 2} \subseteq \mathrm{Sp}_{2g}(\mathbb{F}_2)$ of $S_{2g +
2}$ under the standard representation. We show that when $g \geq 2$, the only
closed subgroup $G \subseteq \mathrm{Sp}_{2g}(\mathbb{Z}_2)$ surjecting onto
$\mathfrak{S}_{2g + 2}$ is its full inverse image in
$\mathrm{Sp}_{2g}(\mathbb{Z}_2)$, while all subgroups $G \subseteq
\mathrm{Sp}_{2g}(\mathbb{Z}_2)$ surjecting onto $\mathfrak{S}_{2g + 1}$ are
open and contain the level-$8$ principal congruence subgroup of
$\mathrm{Sp}_{2g}(\mathbb{Z}_2)$. As an immediate application, we are able to
strengthen a result of Zarhin on $2$-adic Galois representations associated to
hyperelliptic curves. We also prove an elementary corollary concerning
even-degree polynomials with full Galois group.


  Let $\mathbb{F}_q$ denote the finite field with $q$ elements. In this work,
we use characters to give the number of rational points on suitable curves of
low degree over $\mathbb{F}_q$ in terms of the number of rational points on
elliptic curves. In the case where $q$ is a prime number, we give a way to
calculate these numbers. As a consequence of these results, we characterize
maximal and minimal curves given by equations of the forms $ax^3+by^3+cz^3=0$
and $ax^4+by^4+cz^4=0$.


  We derive an effective Lagrangian for meson fields. This is done in the
light-cone gauge for two-dimensional large-N_c QCD by using the bilocal
auxiliary field method. The auxiliary fields are bilocal on light-cone space
and their Fourier transformation determines the parton momentum distribution.
As the first test of our method, the 't Hooft equation is derived from the
effective Lagrangian.


  In order to better understand stellar dynamics in merging systems, such as
NGC 6240, we examine the evolution of central stellar velocity dispersion
(\sig) in dissipative galaxy mergers using a suite of binary disk merger
simulations that include feedback from stellar formation and active galactic
nuclei (AGNs). We find that $\sigma_*$ undergoes the same general stages of
evolution that were observed in our previous dissipationless simulations:
coherent oscillation, then phase mixing, followed by dynamical equilibrium. We
also find that measurements of $\sigma_*$ that are based only upon the youngest
stars in simulations consistently yield lower values than measurements based
upon the total stellar population. This finding appears to be consistent with
the so-called "$\sigma_*$ discrepancy," observed in real galaxies. We note that
quasar-level AGN activity is much more likely to occur when $\sigma_*$ is near
its equilibrium value rather than during periods of extreme $\sigma_*$.
Finally, we provide estimates of the scatter inherent in measuring $\sigma_*$
in ongoing mergers.


  The Fock-Bargmann-Hartogs domain $D_{n,m}(\mu)$ ($\mu>0$) in
$\mathbb{C}^{n+m}$ is defined by the inequality $\|w\|^2<e^{-\mu\|z\|^2},$
where $(z,w)\in \mathbb{C}^n\times \mathbb{C}^m$, which is an unbounded
non-hyperbolic domain in $\mathbb{C}^{n+m}$. Recently, Tu-Wang obtained the
rigidity result that proper holomorphic self-mappings of $D_{n,m}(\mu)$ are
automorphisms for $m\geq 2$, and found a counter-example to show that the
rigidity result isn't true for $D_{n,1}(\mu)$. In this article, we obtain a
classification of proper holomorphic mappings between $D_{n,1}(\mu)$ and
$D_{N,1}(\mu)$ with $N<2n$.


  Heinz-Dieter Zeh's discovery that the motion of macroscopic objects can not,
under typical conditions, follow the Schr\"odinger equation necessitates a
suitably modified dynamics. This unfolded a long-lasting puzzle in the open
quantum system context: what is the quantum counterpart of the classical
Brownian motion in a gas. Presented is a criticism and an open-end discussion
of the quantum linear Boltzmann and quantum Fokker-Planck equations -- with
constant respect for foundational research.


  In this paper Gaussian models of retarded and accelerated anomalous diffusion
are considered. Stochastic differential equations of fractional order driven by
single or multiple fractional Gaussian noise terms are introduced to describe
retarding and accelerating subdiffusion and superdiffusion. Short and long time
asymptotic limits of the mean squared displacement of the stochastic processes
associated with the solutions of these equations are studied. Specific cases of
these equations are shown to provide possible descriptions of retarding or
accelerating anomalous diffusion.


  CMB anisotropy experiments seeking to make maps with more pixels than the
6144 pixels used by the COBE DMR need to address the practical issues of the
computer time and storage required to make maps. A simple, repetitive scan
pattern reduces these requirements but leaves the experiment vulnerable to
systematic errors and striping in the maps. In this paper I give a time-ordered
method for map-making with one-horned experiments that has reasonable memory
and CPU needs but can handle complex COBE-like scans paths and 1/f noise.


  Deploying data- and computation-intensive applications such as large-scale AI
into heterogeneous dispersed computing networks can significantly enhance
application performance by mitigating bottlenecks caused by limited network
resources, including bandwidth, storage, and computing power. However, current
resource allocation methods in dispersed computing do not provide a
comprehensive solution that considers arbitrary topology, elastic resource
amount, reuse of computation results, and nonlinear congestion-dependent
optimization objectives. In this paper, we propose LOAM, a low-latency joint
communication, caching, and computation placement framework with a rigorous
analytical foundation that incorporates the above aspects. We tackle the
NP-hard aggregated cost minimization problem with two methods: an offline
method with a 1/2 approximation and an online adaptive method with a bounded
gap from the optimum. Through extensive simulation, the proposed framework
outperforms multiple baselines in both synthesis and real-world network
scenarios.


  We have measured excitation functions for the d+p->3He+X, (X=pi0, eta)
channels near the eta production threshold. The data were taken during a slow
ramping of the COSY internal deuteron beam scattered on a proton target. The
excitation function for the reaction d+p->3He+pi0 does not show any structure
which could originate from the decay of 3He-eta bound state. We measured also
the threshold excitation curve for the d+p->3He+X process, however, contrary to
the SATURNE results, we observe no cusp near the eta threshold.


  The critical behavior of semi-infinite systems in fixed dimensions $d<4$ is
investigated theoretically. The appropriate extension of Parisi's massive field
theory approach is presented.Two-loop calculations and subsequent Pad\'e-Borel
analyses of surface critical exponents of the special and ordinary phase
transitions yield estimates in reasonable agreement with recent Monte Carlo
results. This includes the crossover exponent $\Phi (d=3)$, for which we obtain
the values $\Phi (n=1)\simeq 0.54$ and $\Phi (n=0)\simeq 0.52$, considerably
lower than the previous $\epsilon$-expansion estimates.


  We extend applications of Furstenberg boundary theory to the study of
$C^*$-algebras associated to minimal actions $\Gamma\!\curvearrowright\! X$ of
discrete groups $\Gamma$ on locally compact spaces $X$. We introduce boundary
maps on $(\Gamma,X)$-$C^*$-algebras and investigate their applications in this
context. Among other results, we completely determine when $C^*$-algebras
generated by covariant representations arising from stabilizer subgroups are
simple. We also characterize the intersection property of locally compact
$\Gamma$-spaces and simplicity of their associated crossed products.


  We take advantage of the Shiromizu et al. covariant formalism to find out the
brane properties originating from the five dimensional bulk spacetime. Making a
different choice for the conformal factor $e^{-2b(z)}$ compared to Estrada
[24], we reach a new solution with a lot of interesting properties, where $b(z)
= ln(1/\sqrt{cosh2\mu z})$. The non-local tensor $E_{ab}$ rooted from the
5-dimensional Riemann tensor gives an anisotropic stress energy tensor on the
brane with positive energy density and negative radial pressure. The BH on the
brane looks like a black string in the 5-dimensional space, with no
singularities of the curvature invariants.


  In this paper a macroscopic quantum oscillator is introduced that consists of
a flux qubit in the form of a cantilever. The magnetic flux linked to the flux
qubit and the mechanical degrees of freedom of the cantilever are naturally
coupled. The coupling is controlled through an external magnetic field. The
ground state of the introduced flux-qubit-cantilever corresponds to a quantum
entanglement between magnetic flux and the cantilever displacement.


  Given a one-dimensional formal group of height 2, let E be the Morava
E-theory spectrum associated to its universal deformation over the Lubin-Tate
ring. By computing with moduli spaces of elliptic curves, we give an
explicitation for an algebra of Hecke operators acting on E-cohomology. This
leads to a vanishing result for Rezk's logarithmic cohomology operation on the
units of E. It identifies a family of elements in the kernel with meromorphic
modular forms whose Serre derivative is zero. Our calculation finds a
connection to logarithms of modular units. In particular, we work out an action
of Hecke operators on certain "logarithmic" q-series, in the sense of Knopp and
Mason, that agrees with our vanishing result and extends the classical Hecke
action on modular forms.


  Passive optical elements can play key roles in photonic applications such as
plasmonic integrated circuits. Here we experimentally demonstrate passive
gap-plasmon focusing and routing in two-dimensions. This is accomplished using
a high numerical-aperture metal-dielectric-metal lens incorporated into a
planar-waveguide device. Fabrication via metal sputtering, oxide deposition,
electron- and focused-ion- beam lithography, and argon ion-milling is reported
on in detail. Diffraction-limited focusing is optically characterized by
sampling out-coupled light with a microscope. The measured focal distance and
full-width-half-maximum spot size agree well with the calculated lens
performance. The surface plasmon polariton propagation length is measured by
sampling light from multiple out-coupler slits.


  An algebraic curvature tensor is called Osserman if the eigenvalues of the
associated Jacobi operator are constant on the unit sphere. A Riemannian
manifold is called conformally Osserman if its Weyl conformal curvature tensor
at every point is Osserman. We prove that a conformally Osserman manifold of
dimension $n \ne 3, 4, 16$ is locally conformally equivalent either to a
Euclidean space or to a rank-one symmetric space.


  A spin Hamiltonian, which characterizes interatomic interactions between spin
moments, is highly valuable in predicting and comprehending the magnetic
properties of materials. A deeper understanding of the microscopic origin of
magnetic interactions can open new pathways toward realizing nanometer-scale
systems for future spintronic devices. Here, we explore a method for explicitly
calculating interatomic exchange interactions in non-collinear configurations
of magnetic materials considering only a bilinear spin Hamiltonian in a local
scenario. Based on density-functional theory (DFT) calculations of dimers
adsorbed on metallic surfaces, and with a focus on the Dzyaloshinskii-Moriya
interaction (DMI) which is essential for stabilizing chiral non-collinear
magnetic states, we discuss the interpretation of the DMI when decomposed into
microscopic electron and spin densities and currents. We clarify the distinct
origins of spin currents induced in the system and their connection to the DMI.
In addition, we reveal how non-collinearity affects the usual DMI, which is
solely induced by spin-orbit coupling, and DMI-like interactions brought about
by non-collinearity. We explain how the dependence of the DMI on the magnetic
configuration establishes a connection between high-order magnetic
interactions, enabling the transition from a local to a global spin
Hamiltonian.


  We study the multiple Eisenstein series introduced by Gangl, Kaneko and
Zagier. We give a proof of (restricted) finite double shuffle relations for
multiple Eisenstein series by developing an explicit connection between the
Fourier expansion of multiple Eisenstein series and the Goncharov coproduct on
Hopf algebras of iterated integrals.


  We consider the generation of large-scale magnetic fields in slow-roll
inflation. The inflaton field is described in a supergravity framework where
the conformal invariance of the electromagnetic field is generically and
naturally broken. For each class of inflationary scenarios, we determine the
functional dependence of the gauge coupling that is consistent with the
observations on the magnetic field strength at various astrophysical scales
and, at the same time, avoid a back-reaction problem. Then, we study whether
the required coupling functions can naturally emerge in well-motivated,
possibly string-inspired, models. We argue that this is non trivial and can be
realized only for a restricted class of scenarios. This includes power-law
inflation where the inflaton field is interpreted as a modulus. However, this
scenario seems to be consistent only if the energy scale of inflation is low
and the reheating stage prolonged. Another reasonable possibility appears to be
small field models since no back-reaction problem is present in this case but,
unfortunately, the corresponding scenario cannot be justified in a stringy
framework. Finally, large field models do not lead to sensible model building.


  The Ising model is a simple statistical model for ferromagnetism. There are
analytic solutions for low dimensions and very efficient Monte Carlo methods,
such as cluster algorithms, for simulating this model in special cases. However
most approaches do not generalise to arbitrary lattices and couplings. We
present a formalism that allows one to apply Hybrid Monte Carlo (HMC)
simulations to the Ising model, demonstrating how a system with discrete
degrees of freedom can be simulated with continuous variables. Because of the
flexibility of HMC, our formalism is easily generalizable to arbitrary
modifications of the model, creating a route to leverage advanced algorithms
such as shift preconditioners and multi-level methods, developed in conjunction
with HMC.


  Every homomorphism from finite index subgroups of a universal lattices to
mapping class groups of orientable surfaces (possibly with punctures), or to
outer automorphism groups of finitely generated nonabelian free groups must
have finite image. Here the universal lattice denotes the special linear group
G=SL_m(Z[x1,...,xk]) with m at least 3 and k finite. Moreover, the same results
hold ture if universal lattices are replaced with symplectic universal lattices
Sp_{2m}(Z[x1,...,xk]) with m at least 2. These results can be regarded as a
non-arithmetization of the theorems of Farb--Kaimanovich--Masur and
Bridson--Wade. A certain measure equivalence analogue is also established. To
show the statements above, we introduce a notion of property (TT)/T ("/T"
stands for "modulo trivial part"), which is a weakening of property (TT) of N.
Monod. Furthermore, symplectic universal lattices Sp_{2m}(Z[x1,...,xk]) with m
at least 3 has the fixed point property for L^p-spaces for any p in
(1,infinity).


  Misalignments within protoplanetary discs are now commonly observed, and
features such as shadows in scattered light images indicate departure from a
co-planar geometry. VLT/SPHERE observations of the disc around HD 143006 show a
large-scale asymmetry, and two narrow dark lanes which are indicative of
shadowing. ALMA observations also reveal the presence of rings and gaps in the
disc, along with a bright arc at large radii. We present new hydrodynamic
simulations of HD 143006, and show that a configuration with both a strongly
inclined binary and an outer planetary companion is the most plausible to
explain the observed morphological features. We compute synthetic observations
from our simulations, and successfully reproduce both the narrow shadows and
the brightness asymmetry seen in IR scattered light. Additionally, we reproduce
the large dust observed in the mm continuum, due to a 10 Jupiter mass planet
detected in the CO kinematics. Our simulations also show the formation of a
circumplanetary disc, which is misaligned with respect to the outer disc. The
narrow shadows cast by the inner disc and the planet-induced "kink" in the disc
kinematics are both expected to move on a time-scale of $\sim$ 5-10 years,
presenting a potentially observable test of our model. If confirmed, HD 143006
would be the first known example of a circumbinary planet on a strongly
misaligned orbit.


  A direct calculation of the complex $\Delta I=1/2$ kaon decay amplitude is
notoriously difficult because of the presence of disconnected graphs. Here we
describe and demonstrate two practical methods to defeat this problem: the
EigCG algorithm and the use of time-separated $\pi-\pi$ sources. With a fine
tuned EigCG implementation for domain wall fermions, the calculation of light
quark propagators is accelerated by a factor of 5-10 on a variety of lattices
from small ($16^3\times32\times16$) to large ($32^3\times64\times32$). In
addition, a substantial reduction in noise is achieved by separating each of
the sources for the two pions in the time direction by 2-5 lattice spacings.
These methods are combined in a calculation of $K$ to $\pi\pi$ threshold decay
using a $24^3\times64\times16$ volume and 329 MeV pions. These methods result
in non-zero signals for both Re($A_0$) and Im($A_0$) from 138 gauge
configurations.


  Strong rescattering corrections to one-loop contributions to the parameters
of the standard electroweak model are considered.


  Reinforcement learning is an emerging approaches to facilitate multi-stage
sequential decision-making problems. This paper studies a real-time multi-stage
stochastic power dispatch considering multivariate uncertainties. Current
researches suffer from low generalization and practicality, that is, the
learned dispatch policy can only handle a specific dispatch scenario, its
performance degrades significantly if actual samples and training samples are
inconsistent. To fill these gaps, a novel contextual meta graph reinforcement
learning (Meta-GRL) for a highly generalized multi-stage optimal dispatch
policy is proposed. Specifically, a more general contextual Markov decision
process (MDP) and scalable graph representation are introduced to achieve a
more generalized multi-stage stochastic power dispatch modeling. An upper
meta-learner is proposed to encode context for different dispatch scenarios and
learn how to achieve dispatch task identification while the lower policy
learner learns context-specified dispatch policy. After sufficient offline
learning, this approach can rapidly adapt to unseen and undefined scenarios
with only a few updations of the hypothesis judgments generated by the
meta-learner. Numerical comparisons with state-of-the-art policies and
traditional reinforcement learning verify the optimality, efficiency,
adaptability, and scalability of the proposed Meta-GRL.


  Biomolecular force fields have been traditionally derived based on a mixture
of reference quantum chemistry data and experimental information obtained on
small fragments. However, the possibility to run extensive molecular dynamics
simulations on larger systems achieving ergodic sampling is paving the way to
directly using such simulations along with solution experiments obtained on
macromolecular systems. Recently, a number of methods have been introduced to
automatize this approach. Here we review these methods, highlight their
relationship with machine learning methods, and discuss the open challenges in
the field.


  In this work we analyze the longitudinal instabilities of propagating
acceleration structures that are driven by a relativistically intense laser at
the moving plasma critical layer [1]. These instabilities affect the
energy-spectra of the accelerated ion-beams in propagating critical layer
acceleration schemes [2][3]. Specifically, using analytical theory and PIC
simulations we look into three fundamental physical processes and their
interplay that are crucial to the understanding of energy spectral control by
making the laser-plasma ion accelerators stable. The interacting processes are
(i) Doppler-shifted ponderomotive bunching [1][4] (ii) potential quenching by
beam-loading [2] and (iii) two-stream instabilities. These phenomenon have been
observed in simulations analyzing these acceleration processes [5][6][7]. From
the preliminary models and results we present in this work, we can infer
measures by which these instabilities can be controlled [8] for improving the
energy-spread of the beams.


  Any Neumann quasigroup $(Q, \cdot)$ (quasigroup with Neumann identity $ x
\cdot(yz \cdot yx) = z$ is called Neumann quasigroup) can be presented in the
form $x\cdot y = x-y$, where $(Q, +)$ is an abelian group. Automorphism group
of Neumann quasigroup coincides with the group $Aut(Q, +)$. Any Schweizer
quasigroup (quasigroup with Schweizer identity $xy \cdot xz = zy$ is called
Schweizer quasigroup) is a Neumann quasigroup and vice versa. Any Neumann
quasigroup is a GA-quasigroup.


  New improvements in the measurement of both the optical solar spectrum and
laboratory wavelengths for lines of neutral iron are combined to extract
central wavelength shifts for 1446 lines observed in the Sun. This provides the
largest available database of accurate solar wavelengths useful as a reference
for comparison with other solar-type stars. It is shown how the velocity shifts
correlate with line strength, approaching a constant value, close to zero, for
lines with equivalent widths larger than 200 mA.


  We integrate for the first time the hydrodynamic
Hall-Vinen-Bekarevich-Khalatnikov equations of motion of a $^{1}S_{0}$-paired
neutron superfluid in a rotating spherical shell, using a pseudospectral
collocation algorithm coupled with a time-split fractional scheme. Numerical
instabilities are smoothed by spectral filtering. Three numerical experiments
are conducted, with the following results. (i) When the inner and outer spheres
are put into steady differential rotation, the viscous torque exerted on the
spheres oscillates quasiperiodically and persistently (after an initial
transient). The fractional oscillation amplitude ($\sim 10^{-2}$) increases
with the angular shear and decreases with the gap width. (ii) When the outer
sphere is accelerated impulsively after an interval of steady differential
rotation, the torque increases suddenly, relaxes exponentially, then oscillates
persistently as in (i). The relaxation time-scale is determined principally by
the angular velocity jump, whereas the oscillation amplitude is determined
principally by the gap width. (iii) When the mutual friction force changes
suddenly from Hall-Vinen to Gorter-Mellink form, as happens when a rectilinear
array of quantized Feynman-Onsager vortices is destabilized by a counterflow to
form a reconnecting vortex tangle, the relaxation time-scale is reduced by a
factor of $\sim 3$ compared to (ii), and the system reaches a stationary state
where the torque oscillates with fractional amplitude $\sim 10^{-3}$ about a
constant mean value. Preliminary scalings are computed for observable
quantities like angular velocity and acceleration as functions of Reynolds
number, angular shear, and gap width. The results are applied to the timing
irregularities (e.g., glitches and timing noise) observed in radio pulsars.


  In this work, a minisuperspace model for the projectable Ho\v{r}ava-Lifshitz
(HL) gravity without the detailed balance condition is investigated. The
Wheeler-deWitt equation is derived and its solutions are studied and discussed
for some particular cases where, due to HL gravity, there is a "potential
barrier" nearby $a=0$. For a vanishing cosmological constant, it is found a
normalizable wave function of the universe. When the cosmological constant is
non-vanishing, the WKB method is used to obtain solutions for the wave function
of the universe. Using the Hamilton-Jacobi equation, one discusses how the
transition from quantum to classical regime occurs and, for the case of a
positive cosmological constant, the scale factor is shown to grow
exponentially, hence recovering the GR behaviour for the late universe.


  It is shown that S-N-S weak links with an heavy-fermion metal as the weak
link (N) can be useful thermosensors. This property is due to the large
thermopower of heavy-fermion metals which is of the order 10^(-6) V/K. The
longitudinal sound can also generate voltage oscillation due to the large
Grueneisen parameter, $\Omega_{hf}\sim 10^{2}$, in heavy-fermions. Similar
effects are expected with other Kondo systems as the weak link.


  Effective complements to human judgment, artificial intelligence techniques
have started to aid human decisions in complicated social problems across the
world. In the context of United States for instance, automated ML/DL
classification models offer complements to human decisions in determining
Medicaid eligibility. However, given the limitations in ML/DL model design,
these algorithms may fail to leverage various factors for decision making,
resulting in improper decisions that allocate resources to individuals who may
not be in the most need. In view of such an issue, we propose in this paper the
method of \textit{fairgroup construction}, based on the legal doctrine of
\textit{disparate impact}, to improve the fairness of regressive classifiers.
Experiments on American Community Survey dataset demonstrate that our method
could be easily adapted to a variety of regressive classification models to
boost their fairness in deciding Medicaid Eligibility, while maintaining high
levels of classification accuracy.


  The role played by YouTube's recommendation algorithm in unwittingly
promoting misinformation and conspiracy theories is not entirely understood.
Yet, this can have dire real-world consequences, especially when
pseudoscientific content is promoted to users at critical times, such as the
COVID-19 pandemic. In this paper, we set out to characterize and detect
pseudoscientific misinformation on YouTube. We collect 6.6K videos related to
COVID-19, the Flat Earth theory, as well as the anti-vaccination and anti-mask
movements. Using crowdsourcing, we annotate them as pseudoscience, legitimate
science, or irrelevant and train a deep learning classifier to detect
pseudoscientific videos with an accuracy of 0.79.
  We quantify user exposure to this content on various parts of the platform
and how this exposure changes based on the user's watch history. We find that
YouTube suggests more pseudoscientific content regarding traditional
pseudoscientific topics (e.g., flat earth, anti-vaccination) than for emerging
ones (like COVID-19). At the same time, these recommendations are more common
on the search results page than on a user's homepage or in the recommendation
section when actively watching videos. Finally, we shed light on how a user's
watch history substantially affects the type of recommended videos.


  The Infant Mortality Rate (IMR) is the number of infants per 1000 that do not
survive until their first birthday. It is an important metric providing
information about infant health but it also measures the society's general
health status. Despite the high level of prosperity in the U.S.A., the
country's IMR is higher than that of many other developed countries.
Additionally, the U.S.A. exhibits persistent inequalities in the IMR across
different racial and ethnic groups. In this paper, we study the infant
mortality prediction using features extracted from birth certificates. We are
interested in training classification models to decide whether an infant will
survive or not. We focus on exploring and understanding the importance of
features in subsets of the population; we compare models trained for individual
races to general models. Our evaluation shows that our methodology outperforms
standard classification methods used by epidemiology researchers.


  Patient-specific therapies require that cells be manufactured in multiple
batches of small volumes, making it a challenge for conventional modes of
quality control. The added complexity of inherent variability (even within
batches) necessitates constant monitoring to ensure comparable end products.
Hence, it is critical that new non-destructive modalities of cell monitoring be
developed. Here, we study, for the first time, the use of optical spectroscopy
in the determination of cell confluency. We exploit the autofluorescence
properties of molecules found natively within cells. By applying spectral
decomposition on the acquired autofluorescence spectra, we are able to further
discern the relative contributions of the different molecules, namely flavin
adenine dinucleotide (FAD) and reduced nicotinamide adenine dinucleotide
(NADH). This is then quantifiable as redox ratios (RR) that represent the
extent of oxidation to reduction based upon the optically measured quantities
of FAD and NADH. Results show that RR is significantly higher for lower
confluencies ($\leq$50$\%$), which we attribute to the different metabolic
requirements as cells switch from individual survival to concerted
proliferation. We validate this relationship through bio-chemical assays and
autofluorescence imaging, and further confirmed through a live-dead study that
our measurement process had negligible effects on cell viability.


  Nanoporous carbon has been extensively used in a wide range of applications
ranging from water treatment to electrochemical applications, such as in energy
storage devices. An effort to relate structural to thermodynamical properties
has not been explored from an atomistic approach. In this work we present
numerical strategies to produce and study nanoporous carbon structures, using
molecular dynamics simulations and a many-body potential. We designed a
heating-quenching procedure in a thermodynamic region bounded by the critical,
and triple point densities of carbon to study an ensemble of 1750 atomic
arrangements produced at different densities, quench rates, and using graphite
and diamond unit cells as precursor structures. All these samples were
numerically characterized through the calculation of the free volumes, surface
areas, radial distribution functions, and structure factors. We found
particularly useful the potential energy dependence with $sp^3$ hybridization
content, to determine structural phases through clustering methods. Three
phases were related to graphite-like, sponge-like, and unstable states. We
showed that our results are compatible with available experiments and different
theoretical schemes, concluding that the use of Tersoff potential is a reliable
choice to produce nanoporous structures with low computational cost.


  In this work we develop a new method, named Sub-graph Permutation Equivariant
Networks (SPEN), which provides a framework for building graph neural networks
that operate on sub-graphs, while using a base update function that is
permutation equivariant, that are equivariant to a novel choice of automorphism
group. Message passing neural networks have been shown to be limited in their
expressive power and recent approaches to over come this either lack
scalability or require structural information to be encoded into the feature
space. The general framework presented here overcomes the scalability issues
associated with global permutation equivariance by operating more locally on
sub-graphs. In addition, through operating on sub-graphs the expressive power
of higher-dimensional global permutation equivariant networks is improved; this
is due to fact that two non-distinguishable graphs often contain
distinguishable sub-graphs. Furthermore, the proposed framework only requires a
choice of $k$-hops for creating ego-network sub-graphs and a choice of
representation space to be used for each layer, which makes the method easily
applicable across a range of graph based domains. We experimentally validate
the method on a range of graph benchmark classification tasks, demonstrating
statistically indistinguishable results from the state-of-the-art on six out of
seven benchmarks. Further, we demonstrate that the use of local update
functions offers a significant improvement in GPU memory over global methods.


  We use a functional approach to the Casimir effect in order to evaluate the
exact vacuum energy for a real scalar field in $d+1$ dimensions, in the
presence of backgrounds that, in a particular limit, impose Dirichlet boundary
conditions on one or two parallel surfaces. Outside of that limit, the
background may be thought of as describing finite-width mirrors with
frequency-dependent transmission and reflection coefficients. We provide new
explicit results for the Casimir energy in some particular backgrounds


  This paper is devoted to a study of infinite horizon optimal control problems
with time discounting and time averaging criteria in discrete time. It is known
that these problems are related to certain infinite-dimensional linear
programming problems, but compactness of the state constraint is a common
assumption imposed in analysis of these LP problems. In this paper, we consider
an unbounded state constraint and use Alexandroff compactification to carry out
the analysis. We also establish asymptotic relationships between the optimal
values of problems with time discounting and long-run average criteria.


  Computing Nash equilibrium policies is a central problem in multi-agent
reinforcement learning that has received extensive attention both in theory and
in practice. However, provable guarantees have been thus far either limited to
fully competitive or cooperative scenarios or impose strong assumptions that
are difficult to meet in most practical applications. In this work, we depart
from those prior results by investigating infinite-horizon \emph{adversarial
team Markov games}, a natural and well-motivated class of games in which a team
of identically-interested players -- in the absence of any explicit
coordination or communication -- is competing against an adversarial player.
This setting allows for a unifying treatment of zero-sum Markov games and
Markov potential games, and serves as a step to model more realistic strategic
interactions that feature both competing and cooperative interests. Our main
contribution is the first algorithm for computing stationary
$\epsilon$-approximate Nash equilibria in adversarial team Markov games with
computational complexity that is polynomial in all the natural parameters of
the game, as well as $1/\epsilon$. The proposed algorithm is particularly
natural and practical, and it is based on performing independent policy
gradient steps for each player in the team, in tandem with best responses from
the side of the adversary; in turn, the policy for the adversary is then
obtained by solving a carefully constructed linear program. Our analysis
leverages non-standard techniques to establish the KKT optimality conditions
for a nonlinear program with nonconvex constraints, thereby leading to a
natural interpretation of the induced Lagrange multipliers. Along the way, we
significantly extend an important characterization of optimal policies in
adversarial (normal-form) team games due to Von Stengel and Koller (GEB `97).


  Optical detection of alpha particle emitters in the environment by air
radioluminescence is a new technology that enables sensing a radiological
threat at safe distances, without putting personnel at risk or contaminating
equipment. Radioluminescence detection systems need to be fine-tuned to
efficiently capture a substantial number of photons while minimizing the
contribution from ambient ultraviolet light. The accurate simulation of
radioluminescence, in conjunction with ray tracing, facilitates the design and
optimization of such detection systems. In this work, an application within the
Geant4 framework has been developed to simulate radioluminescence photons
emitted in the vicinity of accelerated alpha particles and at the surface of
alpha radioactive samples. The application relies on existing scintillation
physics implemented in Geant4 classes such as G4OpticalPhysics and
G4Scintillation, which are used to simulate radioluminescence photons as
scintillations produced during the passage of alpha particles through air. The
application computes the ultraviolet image of alpha particles accelerated at
energies of 5.1 MeV and 8.3 MeV, as well as an extended alpha source. The
application enables optimization of experimental setups for various scenarios,
such as radiological emergency management, radiological crime scene
investigations, or decommissioning of nuclear facilities, thus minimizing the
use of costly resources and exposure to radiation.


  We consider large networks of theta neurons and use the Ott/Antonsen ansatz
to derive degree-based mean field equations governing the expected dynamics of
the networks. Assuming random connectivity we investigate the effects of
varying the widths of the in- and out-degree distributions on the dynamics of
excitatory or inhibitory synaptically coupled networks, and gap junction
coupled networks. For synaptically coupled networks, the dynamics are
independent of the out-degree distribution. Broadening the in-degree
distribution destroys oscillations in inhibitory networks and decreases the
range of bistability in excitatory networks. For gap junction coupled neurons,
broadening the degree distribution varies the values of parameters at which
there is an onset of collective oscillations. Many of the results are shown to
also occur in networks of more realistic neurons.


  Visual Question Answering (VQA) is a multi-modal task that involves answering
questions from an input image, semantically understanding the contents of the
image and answering it in natural language. Using VQA for disaster management
is an important line of research due to the scope of problems that are answered
by the VQA system. However, the main challenge is the delay caused by the
generation of labels in the assessment of the affected areas. To tackle this,
we deployed pre-trained CLIP model, which is trained on visual-image pairs.
however, we empirically see that the model has poor zero-shot performance.
Thus, we instead use pre-trained embeddings of text and image from this model
for our supervised training and surpass previous state-of-the-art results on
the FloodNet dataset. We expand this to a continual setting, which is a more
real-life scenario. We tackle the problem of catastrophic forgetting using
various experience replay methods. Our training runs are available at:
https://wandb.ai/compyle/continual_vqa_final. Our code is available at
https://github.com/AdityaKane2001/continual_vqa.


  Molecular dynamics simulation is used to study vacancy cluster formation in
$\beta$- and $\alpha$-$Si_3N_4$ with varying vacancy contents (0 - 25.6 at%).
Vacancies are randomly created in supercells, which were subsequently
heat-treated for 114 nanoseconds. The results show that both $\beta$ and
$\alpha$ can tolerate vacancies up to 12.8 at% and form clusters, confirming
previous experimental data indicating 8 at% vacancy in $\alpha$-$Si_3N_4$.
However, 25.6 at% vacancy in $\beta$ results in complete amorphization, while
the same amount in $\alpha$ results in a transformation of a semi-amorphous
$\alpha$ phase to a defective $\beta$ phase, leading to the removal of the
clusters in newly formed $\beta$. This clearly explains why cluster vacancies
are not experimentally observed in $\beta$, considering that $\beta$-$Si_3N_4$
ceramics are produced from $\alpha$. Furthermore, the lattice parameters of
both modifications increase with increasing vacancy content, revealing the
cause of different lattice constants that were previously reported for
$\alpha$-$Si_3N_4$.


  We propose an extension of {\em supersymmetric quantum mechanics} which
produces a family of isospectral hamiltonians. Our procedure slightly extends
the idea of intertwining operators. Several examples of the construction are
given. Further, we show how to build up vector coherent states of the
Gazeau-Klauder type associated to our hamiltonians.


  We describe a novel end-to-end approach using Machine Learning to reconstruct
the power spectrum of cosmological density perturbations at high redshift from
observed quasar spectra. State-of-the-art cosmological simulations of structure
formation are used to generate a large synthetic dataset of line-of-sight
absorption spectra paired with 1-dimensional fluid quantities along the same
line-of-sight, such as the total density of matter and the density of neutral
atomic hydrogen. With this dataset, we build a series of data-driven models to
predict the power spectrum of total matter density. We are able to produce
models which yield reconstruction to accuracy of about 1% for wavelengths $k
\leq 2 h Mpc^{-1}$, while the error increases at larger $k$. We show the size
of data sample required to reach a particular error rate, giving a sense of how
much data is necessary to reach a desired accuracy. This work provides a
foundation for developing methods to analyse very large upcoming datasets with
the next-generation observational facilities.


  In a scenario with two almost mass degenerate heavy sterile Majorana
neutrinos with a mass $\sim 1$ GeV, we present the semileptonic decay widths of
heavy charged pseudoscalars such as $B$ mesons, either lepton-number-violating
($B^{\pm} \to \mu^{\pm} e^{\pm} \pi^{\mp}$), or lepton-number-conserving
($B^{\pm} \to \mu^{\pm} e^{\mp} \pi^{\pm}$), mediated by such on-shell
neutrinos. It had been explained in the literature that such decays may be
eventually detected, and that they can present even detectable CP violation
effects. In this work we point out that, in addition, such decays may present
detectable effects of heavy neutrino oscillation, allowing us to extract the
oscillation length and thus the heavy neutrino mass difference $\Delta M_N$, as
well as a CP-violating Majorana phase.


  The method of graded contractions, based on the preservation of the
automorphisms of finite order, is applied to the affine Kac-Moody algebras and
their representations, to yield a new class of infinite dimensional Lie
algebras and representations. After the introduction of the horizontal and
vertical gradings, and the algorithm to find the horizontal toroidal gradings,
I discuss some general properties of the graded contractions, and compare them
with the In\"on\"u-Wigner contractions. The example of $\hat A_2$ is discussed
in detail.


  We propose a new mechanism for formation of topological defects in a U(1)
model with a local gauge symmetry. This mechanism leads to definite
predictions, which are qualitatively different from those of the Kibble-Zurek
mechanism of global theories. We confirm these predictions in numerical
simulations, and they can also be tested in superconductor experiments. We
believe that the mechanism generalizes to more complicated theories.


  We consider the downlink of cell-free massive multiple-input multiple-output
(MIMO) systems with orthogonal time frequency space (OTFS) modulation. Two
pilot-based channel estimation schemes, namely superimposed pilot-based
(SP-CHE) and embedded pilot-based channel estimation (EP-CHE), are applied to
estimate the channels at the access points (APs). The SP-CHE scheme
superimposes low power pilots onto the data symbols in the delay-Doppler domain
to avoid the spectral efficiency (SE) loss due to null guard intervals used in
the EP-CHE scheme. In the case of SP-CHE scheme, we consider a max-min fairness
optimization problem to jointly optimize the peruser pilot/data power
allocation coefficients and per-AP power control coefficients. The complicated
non-convex problem is then iteratively solved through two decoupled
sub-problems. Moreover, a max-min fairness problem is cast for the EP-CHE
scheme, where the optimization variables are the per-AP power control
coefficients. Numerical results show that the proposed resource allocation
approaches provide at most 42 and 5-fold increase in the 95%-likely per-user SE
for the SP-CHE and EP-CHE scheme, respectively, compared with the uniform power
control and in correlated shadowing fading channels.


  We prove the existence and uniqueness of a quasi-stationary distribution for
three stochastic processes derived from the model of Muller's ratchet. This
model was invented with the aim of evaluating the limitations of an asexual
reproduction mode in preventing the accumulation of deleterious mutations
through natural selection alone. The main considered model is non-classical, as
it is a stochastic diffusion evolving on an irregular set of infinite dimension
with hard killing on an hyperplane. We are nonetheless able to prove
exponential convergence in total variation to the quasi-stationary distribution
even in this case. The parameters in this last convergence result are directly
related to the core parameters of Muller's ratchet. The speed of convergence to
the quasi-stationary distribution is deduced both for the infinite dimensional
model and for approximations with a large yet finite number of potential
mutations. Likewise, we give uniform moment estimates of the empirical
distribution of mutations in the population under quasi-stationarity.


  The superposition principle is at the heart of quantum mechanics and at the
root of many paradoxes arising when trying to extend its predictions to our
everyday world. Schroedinger's cat is the prototype of such paradoxes and here,
in contrast to many others, we choose to investigate it from the operational
point of view. We experimentally demonstrate a universal strategy for producing
an unambiguously distinguishable type of superposition, that of an arbitrary
pure state and its orthogonal. It relies on only a limited amount of
information about the input state to first generate its orthogonal one. Then, a
simple change in the experimental parameters is used to produce arbitrary
superpositions of the mutually orthogonal states. Constituting a sort of
Schroedinger's black box, able to turn a whole zoo of input states into
coherent superpositions, our scheme can produce arbitrary continuous-variable
optical qubits, which may prove practical for implementing quantum technologies
and measurement tasks.


  The possibility to use the ultrashort ion bunches produced by circularly
polarized laser pulses to drive a source of fusion neutrons with sub-optical
cycle duration is discussed. A two-side irradiation of a thin foil deuterated
target produces two countermoving ion bunches, whose collision leads to an
ultrashort neutron burst. Using particle-in-cell simulations and analytical
modeling, it is evaluated that, for intensities of a few $10^{19} W cm^{-2}$,
more than $10^3$ neutrons per Joule may be produced within a time shorter than
one femtosecond. Another scheme based on a layered deuterium-tritium target is
outlined.


  For G an almost simple simply connected algebraic group defined over a field
F, Rost has shown that there exists a canonical map R_G: H^1(F, G) --> H^3(F,
Q/Z(2)). This includes the Arason invariant for quadratic forms and Rost's mod
3 invariant for Albert algebras as special cases. We show that R_G has trivial
kernel if G is quasi-split of type E_6 or E_7. A case-by-case analysis shows
that it has trivial kernel whenever G is quasi-split of low rank.


  Single Crystalline Fe3-deltaO4 (0<=delta<=0.33) films have been epitaxially
grown on InAs (001) substrates by molecular beam epitaxy using O2 as source of
active oxygen. Under optimum growth conditions in-situ real time reflection
high-energy electron diffraction patterns along with ex-situ atomic force
microscopy indicated the (001) Fe3-deltaO4 to be grown under step-flow-growth
mode with a characteristic surface reconstruction. X-ray photoelectron
spectroscopy demonstrate the possibility to obtain iron oxides with
compositions ranging from Fe3O4 to gamma-Fe2O3. Superconducting quantum
interference device magnetometer at 300K shows well behaved magnetic properties
giving therefore credibility to the promise of iron based oxides for spintronic
applications.


  The main results in this paper concern large and moderate deviations for the
radial component of a $n$-dimensional hyperbolic Brownian motion (for $n\geq
2$) on the Poincar\'{e} half-space. We also investigate the asymptotic behavior
of the hitting probability $P_\eta(T_{\eta_1}^{(n)}<\infty)$ of a ball of
radius $\eta_1$, as the distance $\eta$ of the starting point of the hyperbolic
Brownian motion goes to infinity.


  We present systematic measurements of the Casimir force between a gold-coated
plate and a sphere coated with a Hydrogen Switchable Mirror (HSM). HSMs are
shiny metals that can become transparent by hydrogenation. In spite of such a
dramatic change of the optical properties of the sphere, we did not observe any
significant decrease of the Casimir force after filling the experimental
apparatus with hydrogen. This counterintuitive result can be explained by the
Lifshitz theory that describes the Casimir attraction between metallic and
dielectric materials.


  The Lyman-Werner (LW) radiation field is a key ingredient in the
chemo-thermal evolution of gas in the Early Universe, as it dissociates H2
molecules, the primary cooling channel in an environment devoid of metals and
dust. Despite its important role, it is still not implemented in cosmological
simulations on a regular basis, in contrast to the ionising UV background. This
is in part due to uncertainty in the source modelling, their spectra and
abundance, as well as the detailed physics involved in the propagation of the
photons and their interactions with the molecules. The goal of this work is to
produce an accurate model of the LW radiation field at $z\geq6$, by
post-processing the physics-rich high-resolution FiBY simulation. Our novelties
include updated cross sections for H$_2$, H$^-$ and H$^+_2$ chemical species,
IGM absorption by neutral Hydrogen and various spectral models for Population
III and Population II stars. With our fiducial set of parameters, we show that
the mean LW intensity steadily increases by three orders of magnitude from
$z\sim23$ to $z\sim6$, while spatial inhomogeneities originate from massive
star-forming galaxies that dominate the photon budget up to a distance of
$\sim100$ proper kpc. Our model can be easily applied to other simulations or
semi-analytical models as an external radiation field that regulates the
formation of stars and massive black hole seeds in high-$z$ low-mass halos.


  The reactive process of barrier escaping from the metastable potential well
is studied together with the extension of Kramers' rate formula to the
fractional case. Characteristic quantities are computed for an thimbleful of
insight into the near barrier escaping and recrossing dynamics. Where the
stationary transmission coefficient is revealed to be larger than the usual
cases which implies less barrier recrossing. And the non-monotonic varying of
it reveals a close dependence to the fractional exponent $\alpha$. In most
cases, the near barrier behavior of the escaping dynamics is equivalent to the
diffusion in the two-dimensional non-Ohmic damping system.


  Local motion blur commonly occurs in real-world photography due to the mixing
between moving objects and stationary backgrounds during exposure. Existing
image deblurring methods predominantly focus on global deblurring,
inadvertently affecting the sharpness of backgrounds in locally blurred images
and wasting unnecessary computation on sharp pixels, especially for
high-resolution images. This paper aims to adaptively and efficiently restore
high-resolution locally blurred images. We propose a local motion deblurring
vision Transformer (LMD-ViT) built on adaptive window pruning Transformer
blocks (AdaWPT). To focus deblurring on local regions and reduce computation,
AdaWPT prunes unnecessary windows, only allowing the active windows to be
involved in the deblurring processes. The pruning operation relies on the
blurriness confidence predicted by a confidence predictor that is trained
end-to-end using a reconstruction loss with Gumbel-Softmax re-parameterization
and a pruning loss guided by annotated blur masks. Our method removes local
motion blur effectively without distorting sharp regions, demonstrated by its
exceptional perceptual and quantitative improvements compared to
state-of-the-art methods. In addition, our approach substantially reduces FLOPs
by 66% and achieves more than a twofold increase in inference speed compared to
Transformer-based deblurring methods. We will make our code and annotated blur
masks publicly available.


  This paper aims to address the major challenges of Federated Learning (FL) on
edge devices: limited memory and expensive communication. We propose a novel
method, called Partial Variable Training (PVT), that only trains a small subset
of variables on edge devices to reduce memory usage and communication cost.
With PVT, we show that network accuracy can be maintained by utilizing more
local training steps and devices, which is favorable for FL involving a large
population of devices. According to our experiments on two state-of-the-art
neural networks for speech recognition and two different datasets, PVT can
reduce memory usage by up to 1.9$\times$ and communication cost by up to
593$\times$ while attaining comparable accuracy when compared with full network
training.


  As more and more application providers transition to the cloud and deliver
their services on a Software as a Service (SaaS) basis, cloud providers need to
make their provisioning systems agile enough to meet Service Level Agreements.
At the same time they should guard against over-provisioning which limits their
capacity to accommodate more tenants. To this end we propose SQLR, a dynamic
provisioning system employing a customized model-free reinforcement learning
algorithm that is capable of reusing contextual knowledge learned from one
workload to optimize resource provisioning for other workload patterns. SQLR
achieves results comparable to those where resources are unconstrained, with
minimal overhead. Our experiments show that we can reduce the amount of
provisioned resources by almost 25% with less than 1% overall service
unavailability (due to blocking) while delivering similar response times as
those of an over-provisioned system.


  We apply equivariant localisation to the theory of $Z$-stability and
$Z$-critical metrics on a K\"ahler manifold $(X,\alpha)$, where $\alpha$ is a
K\"ahler class. We show that the invariants used to determine $Z$-stability of
the manifold, which are integrals over test configurations, can be written as a
product of equivariant classes, hence equivariant localisation can be applied.
We also study the existence of $Z$-critical K\"ahler metrics in $\alpha$, whose
existence is conjectured to be equivalent to $Z$-stability of $(X,\alpha)$. In
particular, we study a class of invariants that give an obstruction to the
existence of such metrics. Then we show that these invariants can also be
written as a product of equivariant classes. From this we give a new, more
direct proof of an existing result: the former invariants determining
$Z$-stability on a test configuration are equal to the latter invariants
related to the existence of $Z$-critical metrics on the central fibre of the
test configuration. This provides a new approach from which to derive the
$Z$-critical equation.


  Arch filament systems occur in active sunspot groups, where a fibril
structure connects areas of opposite magnetic polarity, in contrast to active
region filaments that follow the polarity inversion line. We used the GREGOR
Infrared Spectrograph (GRIS) to obtain the full Stokes vector in the spectral
lines Si I 1082.7 nm, He I 1083.0 nm, and Ca I 1083.9 nm. We focus on the
near-infrared calcium line to investigate the photospheric magnetic field and
velocities, and use the line core intensities and velocities of the helium line
to study the chromospheric plasma. The individual fibrils of the arch filament
system connect the sunspot with patches of magnetic polarity opposite to that
of the spot. These patches do not necessarily coincide with pores, where the
magnetic field is strongest. Instead, areas are preferred not far from the
polarity inversion line. These areas exhibit photospheric downflows of moderate
velocity, but significantly higher downflows of up to 30 km/s in the
chromospheric helium line. Our findings can be explained with new emerging flux
where the matter flows downward along the fieldlines of rising flux tubes, in
agreement with earlier results.


  We present the results of the charge ratio ($R$) and polarization
($P^{\mu}_{0}$) measurements using the decay electron events collected from
2008 September to 2022 June by the Super-Kamiokande detector. Because of its
underground location and long operation, we performed high precision
measurements by accumulating cosmic-ray muons. We measured the muon charge
ratio to be $R=1.32 \pm 0.02$ $(\mathrm{stat.}{+}\mathrm{syst.})$ at
$E_{\mu}\cos \theta_{\mathrm{Zenith}}=0.7^{+0.3}_{-0.2}$ $\mathrm{TeV}$, where
$E_{\mu}$ is the muon energy and $\theta_{\mathrm{Zenith}}$ is the zenith angle
of incoming cosmic-ray muons. This result is consistent with the Honda flux
model while this suggests a tension with the $\pi K$ model of $1.9\sigma$. We
also measured the muon polarization at the production location to be
$P^{\mu}_{0}=0.52 \pm 0.02$ $(\mathrm{stat.}{+}\mathrm{syst.})$ at the muon
momentum of $0.9^{+0.6}_{-0.1}$ $\mathrm{TeV}/c$ at the surface of the
mountain; this also suggests a tension with the Honda flux model of
$1.5\sigma$. This is the most precise measurement ever to experimentally
determine the cosmic-ray muon polarization near $1~\mathrm{TeV}/c$. These
measurement results are useful to improve the atmospheric neutrino simulations.


  The goal of this paper to generate a visually appealing video that responds
to music with a neural network so that each frame of the video reflects the
musical characteristics of the corresponding audio clip. To achieve the goal,
we propose a neural music visualizer directly mapping deep music embeddings to
style embeddings of StyleGAN, named Tr\"aumerAI, which consists of a music
auto-tagging model using short-chunk CNN and StyleGAN2 pre-trained on WikiArt
dataset. Rather than establishing an objective metric between musical and
visual semantics, we manually labeled the pairs in a subjective manner. An
annotator listened to 100 music clips of 10 seconds long and selected an image
that suits the music among the 200 StyleGAN-generated examples. Based on the
collected data, we trained a simple transfer function that converts an audio
embedding to a style embedding. The generated examples show that the mapping
between audio and video makes a certain level of intra-segment similarity and
inter-segment dissimilarity.


  In many reinforcement learning (RL) applications, we want policies that reach
desired states and then keep the controlled system within an acceptable region
around the desired states over an indefinite period of time. This latter
objective is called stability and is especially important when the state space
is unbounded, such that the states can be arbitrarily far from each other and
the agent can drift far away from the desired states. For example, in
stochastic queuing networks, where queues of waiting jobs can grow without
bound, the desired state is all-zero queue lengths. Here, a stable policy
ensures queue lengths are finite while an optimal policy minimizes queue
lengths. Since an optimal policy is also stable, one would expect that RL
algorithms would implicitly give us stable policies. However, in this work, we
find that deep RL algorithms that directly minimize the distance to the desired
state during online training often result in unstable policies, i.e., policies
that drift far away from the desired state. We attribute this instability to
poor credit-assignment for destabilizing actions. We then introduce an approach
based on two ideas: 1) a Lyapunov-based cost-shaping technique and 2) state
transformations to the unbounded state space. We conduct an empirical study on
various queueing networks and traffic signal control problems and find that our
approach performs competitively against strong baselines with knowledge of the
transition dynamics. Our code is available here:
https://github.com/Badger-RL/STOP.


  We present a numerical study of ground states of the dilute versions of the
Sherrington-Kirkpatrick (SK) mean-field spin glass. In contrast to so-called
"sparse" mean-field spin glasses that have been studied widely on random
networks of finite (average or regular) degree, the networks studied here are
randomly bond-diluted to an overall density $p$, such that the average degree
diverges as $\sim pN$ with the system size $N$. Ground-state energies are
obtained with high accuracy for random instances over a wide range of fixed
$p$. Since this is a NP-hard combinatorial problem, we employ the Extremal
Optimization heuristic to that end. We find that the exponent describing the
finite-size corrections, $\omega$, varies continuously with $p$, a somewhat
surprising result, as one would not expect that gradual bond-dilution would
change the $T=0$ universality class of a statistical model. For $p\to1$, the
familiar result of $\omega(p=1)\approx\frac{2}{3}$ for SK is obtained.


  The representation of a given quantity with less information is often
referred to as `quantization' and it is an important subject in information
theory. In this paper, we have considered absolutely continuous probability
measures on unit discs, squares, and the real line. For these probability
measures the optimal sets of $n$-means and the $n$th quantization errors are
calculated for some positive integers $n$.


  We present the Lya luminosity functions (LFs) derived by our deep Subaru
narrowband survey that identifies a total of 3,137 Lya emitters (LAEs) at $z =
2.2$ in five independent blank fields. The sample of these LAEs is the largest,
to date, and covers a very wide Lya luminosity range of $\log L_{Ly\alpha} =
41.7-44.4$ erg s$^{-1}$. We determine the Lya LF at $z = 2.2$ with
unprecedented accuracies, and obtain the best-fit Schechter parameters of
$L^{*}_{Ly\alpha} = 5.29^{+1.67}_{-1.13} \times 10^{42}$ erg s$^{-1}$,
$\phi^{*}_{Ly\alpha} = 6.32^{+3.08}_{-2.31} \times 10^{-4}$ Mpc$^{-3}$, and
$\alpha = -1.75^{+0.10}_{-0.09}$ showing a steep faint-end slope. We identify a
significant hump at the LF bright end ($\log L_{Ly\alpha} > 43.4$ erg
s$^{-1}$). Because all of the LAEs in the bright-end hump have (a) bright
counterpart(s) either in the X-ray, UV, or radio data, this bright-end hump is
not made by gravitational lensing magnification bias but AGNs. These AGNs allow
us to derive the AGN UV LF at $z \sim 2$ down to the faint magnitude limit of
$M_{UV} \simeq -22.5$, and to constrain the faint-end slope of AGN UV LF,
$\alpha_{AGN}=-1.2 \pm 0.1$, that is flatter than those at $z > 4$. Based on
the Lya and UV LFs from our and previous studies, we find the increase of Lya
escape fraction $f^{Ly\alpha}_{esc}$ from $z \sim 0$ to $6$ by two orders of
magnitude. This large $f^{Ly\alpha}_{esc}$ increase can be explained neither by
the evolution of stellar population nor outflow alone, but the evolution of
neutral hydrogen HI density in inter-stellar medium that enhances dust
attenuation for Lya by resonance scattering. Our uniform expanding shell models
suggest that the typical HI column density decreases from $N_{HI} \sim 7 \times
10^{19}$ ($z \sim 0$) to $\sim 1 \times 10^{18}$ cm$^{-2}$ ($z \sim 6$) to
explain the large $f^{Ly\alpha}_{esc}$ increase.


  In previous paper I construct an approximative solution of the power series
expansion in closed forms of Grand Confluent Hypergeometric (GCH) function only
up to one term of A_n's [4]. And I obtain normalized constant and orthogonal
relation of GCH function.
  In this paper I will apply three term recurrence formula [3] to the power
series expansion in closed forms of GCH function (infinite series and
polynomial) including all higher terms of A_n's.
  In general most of well-known special function with two recursive
coefficients only has one eigenvalue for the polynomial case. However this new
function with three recursive coefficients has infinite eigenvalues that make
B_n's term terminated at specific value of index n because of three term
recurrence formula [3].
  This paper is 9th out of 10 in series "Special functions and three term
recurrence formula (3TRF)". See section 6 for all the papers in the series.
Previous paper in series deals with generating functions of Lame polynomial in
the Weierstrass's form [28]. The next paper in the series describes the
integral formalism and the generating function of GCH function [30].


  Electricity load forecasting is crucial for effectively managing and
optimizing power grids. Over the past few decades, various statistical and deep
learning approaches have been used to develop load forecasting models. This
paper presents an interpretable machine learning approach that identifies load
dynamics using data-driven methods within an operator-theoretic framework. We
represent the load data using the Koopman operator, which is inherent to the
underlying dynamics. By computing the corresponding eigenfunctions, we
decompose the load dynamics into coherent spatiotemporal patterns that are the
most robust features of the dynamics. Each pattern evolves independently
according to its single frequency, making its predictability based on linear
dynamics. We emphasize that the load dynamics are constructed based on coherent
spatiotemporal patterns that are intrinsic to the dynamics and are capable of
encoding rich dynamical features at multiple time scales. These features are
related to complex interactions over interconnected power grids and different
exogenous effects. To implement the Koopman operator approach more efficiently,
we cluster the load data using a modern kernel-based clustering approach and
identify power stations with similar load patterns, particularly those with
synchronized dynamics. We evaluate our approach using a large-scale dataset
from a renewable electric power system within the continental European
electricity system and show that the Koopman-based approach outperforms a deep
learning (LSTM) architecture in terms of accuracy and computational efficiency.
The code for this paper has been deposited in a GitHub repository, which can be
accessed at the following address github.com/Shakeri-Lab/Power-Grids.


  We consider the eigenvalues of a fixed, non-normal matrix subject to a small
additive perturbation. In particular, we consider the case when the fixed
matrix is a banded Toeplitz matrix, where the bandwidth is allowed to grow
slowly with the dimension, and the perturbation matrix is drawn from one of
several different random matrix ensembles. We establish a number of
non-asymptotic results for the eigenvalues of this model, including a local law
and a rate of convergence in Wasserstein distance of the empirical spectral
measure to its limiting distribution. In addition, we define the classical
locations of the eigenvalues and prove a rigidity result showing that, on
average, the eigenvalues concentrate closely around their classical locations.
While proving these results we also establish a number of auxiliary results
that may be of independent interest, including a quantitative version of the
Tao--Vu replacement principle, a general least singular value bound that
applies to adversarial models, and a description of the limiting empirical
spectral measure for random multiplicative perturbations.


  The motion of a single hole in an arbitrary magnetic background is
investigated for the 2D t-J model. The wavefunction of the hole is described
within a generalized string picture which leads to a modified concept of spin
polarons. We calculate the one-hole spectral function using a large string
basis for the limits of a Neel ordered and a completely disordered background.
In addition we use a simple approximation to interpolate between these cases.
For the antiferromagnetic background we reproduce the well-known quasiparticle
band. In the disordered case the shape of the spectral function is found to be
strongly momentum-dependent, the quasiparticle weight vanishes for all hole
momenta. Finally, we discuss the relevance of results for the lowest energy
eigenvalue and its dispersion obtained from calculations using a polaron of
minimal size as found in the literature.


  We introduce a new approach for the numerical pricing of American options.
The main idea is to choose a finite number of suitable excessive functions
(randomly) and to find the smallest majorant of the gain function in the span
of these functions. The resulting problem is a linear semi-infinite programming
problem, that can be solved using standard algorithms. This leads to good upper
bounds for the original problem. For our algorithms no discretization of space
and time and no simulation is necessary. Furthermore it is applicable even for
high-dimensional problems. The algorithm provides an approximation of the value
not only for one starting point, but for the complete value function on the
continuation set, so that the optimal exercise region and e.g. the Greeks can
be calculated. We apply the algorithm to (one- and) multidimensional diffusions
and to L\'evy processes, and show it to be fast and accurate.


  A new method for calculating the total energy of Si systems is presented. The
method is based on the effective-medium theory concept of a reference system.
Instead of calculating the energy of an atom in the system of interest a
reference system is introduced where the local surroundings are similar. The
energy of the reference system can be calculated selfconsistently once and for
all while the energy difference to the reference system can be obtained
approximately. We propose to calculate it using the tight-binding LMTO scheme
with the Atomic-Sphere Approximation(ASA) for the potential, and by using the
ASA with charge-conserving spheres we are able to treat open system without
introducing empty spheres. All steps in the calculational method is {\em ab
initio} in the sense that all quantities entering are calculated from first
principles without any fitting to experiment. A complete and detailed
description of the method is given together with test calculations of the
energies of phonons, elastic constants, different structures, surfaces and
surface reconstructions. We compare the results to calculations using an
empirical tight-binding scheme.


  For every finitely generated recursively presented group G we construct a
finitely presented group H containing G such that G is (Frattini) embedded into
H and the group H has solvable conjugacy problem if and only if G has solvable
conjugacy problem. Moreover G and H have the same r.e. Turing degrees of the
conjugacy problem. This solves a problem by D. Collins.


  Proving equivalence between functional programs is a fundamental problem in
program verification, which often amounts to reasoning about algebraic data
types (ADTs) and compositions of structural recursions. Modern theorem provers
address this problem by applying structural induction, which is insufficient
for proving many equivalence theorems. In such cases, one has to invent a set
of lemmas, prove these lemmas by additional induction, and use these lemmas to
prove the original theorem. There is, however, a lack of systematic
understanding of what lemmas are needed for inductive proofs and how these
lemmas can be synthesized automatically. This paper presents directed lemma
synthesis, an effective approach to automating equivalence proofs by
discovering critical lemmas using program synthesis techniques. We first
identify two induction-friendly forms of propositions that give formal
guarantees to the progress of the proof. We then propose two tactics that
synthesize and apply lemmas, thereby transforming the proof goal into
induction-friendly forms. Both tactics reduce lemma synthesis to a specialized
class of program synthesis problems with efficient algorithms. Experimental
results demonstrate the effectiveness of our approach: Compared to
state-of-the-art equivalence checkers employing heuristic-based lemma
enumeration, directed lemma synthesis saves 95.47% runtime on average and
solves 38 more tasks over an extended version of the standard benchmark set.