  Consider the Schr\"odinger operator $-\triangle+\lambda V$ with non-negative
iid random potential $V$ of strength $\lambda>0$. We prove existence and
uniqueness of the associated landscape function on the whole space, and show
that its correlations decay exponentially. As a main ingredient we establish
the (annealed and quenched) exponential decay of the Green function of
$-\triangle+\lambda V$ using Agmon's positivity method, rank-one perturbation
in dimensions $d\ge 3$, and first-passage percolation in dimensions $d=1,2$.


  This paper presents a new approach to boost a single-modality (LiDAR) 3D
object detector by teaching it to simulate features and responses that follow a
multi-modality (LiDAR-image) detector. The approach needs LiDAR-image data only
when training the single-modality detector, and once well-trained, it only
needs LiDAR data at inference. We design a novel framework to realize the
approach: response distillation to focus on the crucial response samples and
avoid the background samples; sparse-voxel distillation to learn voxel
semantics and relations from the estimated crucial voxels; a fine-grained
voxel-to-point distillation to better attend to features of small and distant
objects; and instance distillation to further enhance the deep-feature
consistency. Experimental results on the nuScenes dataset show that our
approach outperforms all SOTA LiDAR-only 3D detectors and even surpasses the
baseline LiDAR-image detector on the key NDS metric, filling 72% mAP gap
between the single- and multi-modality detectors.


  In spite of its many successes, the Standard Model makes many empirical
assumptions in the Higgs and fermion sectors for which a deeper theoretical
basis is sought. Starting from the usual gauge symmetry $u(1) \times su(2)
\times su(3)$ plus the 3 assumptions: (A) scalar fields as vielbeins in
internal symmetry space \cite{framevec}, (B) the ``confinement picture'' of
symmetry breaking \cite{tHooft,Banovici}, (C) generations as ``dual'' to colour
\cite{genmixdsm}, we are led to a scheme which offers: (I) a geometrical
significance to scalar fields, (II) a theoretical criterion on what scalar
fields are to be introduced, (III) a partial explanation of why $su(2)$ appears
broken while $su(3)$ confines, (IV) baryon-lepton number (B - L) conservation,
(V) the standard electroweak structure, (VI) a 3-valued generation index for
leptons and quarks, and (VII) a dynamical system with all the essential
features of an earlier phenomenological model \cite{genmixdsm} which gave a
good description of the known mass and mixing patterns of quarks and leptons
including neutrino oscillations. There are other implications the consistency
of which with experiment, however, has not yet been systematically explored. A
possible outcome is a whole new branch of particle spectroscopy from $su(2)$
confinement, potentially as rich in details as that of hadrons from colour
confinement, which will be accessible to experiment at high energy.


  An \'etale structure over a topological space $X$ is a continuous family of
structures (in some first-order language) indexed over $X$. We give an
exposition of this fundamental concept from sheaf theory and its relevance to
countable model theory and invariant descriptive set theory. We show that many
classical aspects of spaces of countable models can be naturally framed and
generalized in the context of \'etale structures, including the Lopez-Escobar
theorem on invariant Borel sets, an omitting types theorem, and various
characterizations of Scott rank. We also present and prove the countable
version of the Joyal-Tierney representation theorem, which states that the
isomorphism groupoid of an \'etale structure determines its theory up to
bi-interpretability; and we explain how special cases of this theorem recover
several recent results in the literature on groupoids of models and functors
between them.


  e consider the experimental design problem in an online environment, an
important practical task for reducing the variance of estimates in randomized
experiments which allows for greater precision, and in turn, improved decision
making. In this work, we present algorithms that build on recent advances in
online discrepancy minimization which accommodate both arbitrary treatment
probabilities and multiple treatments. The proposed algorithms are
computational efficient, minimize covariate imbalance, and include
randomization which enables robustness to misspecification. We provide worst
case bounds on the expected mean squared error of the causal estimate and show
that the proposed estimator is no worse than an implicit ridge regression,
which are within a logarithmic factor of the best known results for offline
experimental design. We conclude with a detailed simulation study showing
favorable results relative to complete randomization as well as to offline
methods for experimental design with time complexities exceeding our algorithm.


  We report results on semileptonic $B\to\pi l\bar{\nu}$ decay form factors
near $q^2_{\rm max}$ using NRQCD heavy quark and clover light quark actions and
currents improved through $O(\alpha a)$. An inconsistency with the soft pion
relation $f^0(q^2_{\rm max})= f_B/f_{\pi}$ found in a previous work is
confirmed, and a possible solution with nonperturbative renormalization is
discussed. We find that $f^+(q^2)$ is well described by the $B^*$ pole near
$q^2_{\rm max}$, and its $1/M_B$ scaling is also consistent with the prediction
of the pole dominance model.


  We study aspects of worldsheet instantons relevant to a heterotic standard
model. The non-simply connected Calabi-Yau threefold used admits Z_3 x Z_3
Wilson lines, and a more detailed investigation shows that the homology classes
of curves are H_2(X,Z)=Z^3+Z_3+Z_3. We compute the genus-0 prepotential, this
is the first explicit calculation of the Gromov-Witten invariants of homology
classes with torsion (finite subgroups). In particular, some curve classes
contain only a single instanton. This ensures that the Beasley-Witten
cancellation of instanton contributions cannot happen on this (non-toric)
Calabi-Yau threefold.


  Federated learning (FL) approaches for saddle point problems (SPP) have
recently gained in popularity due to the critical role they play in machine
learning (ML). Existing works mostly target smooth unconstrained objectives in
Euclidean space, whereas ML problems often involve constraints or non-smooth
regularization, which results in a need for composite optimization. Addressing
these issues, we propose Federated Dual Extrapolation (FeDualEx), an extra-step
primal-dual algorithm, which is the first of its kind that encompasses both
saddle point optimization and composite objectives under the FL paradigm. Both
the convergence analysis and the empirical evaluation demonstrate the
effectiveness of FeDualEx in these challenging settings. In addition, even for
the sequential version of FeDualEx, we provide rates for the stochastic
composite saddle point setting which, to our knowledge, are not found in prior
literature.


  Au and Pt do not form homogeneous bulk alloys as they are thermodynamically
not miscible. However, we show that anodic TiO$_2$ nanotubes (NTs) can in-situ
be uniformly decorated with homogeneous AuPt alloy nanoparticles (NPs) during
their anodic growth. For this, a metallic Ti substrate containing low amounts
of dissolved Au (0.1 at%) and Pt (0.1 at%) is used for anodizing. The matrix
metal (Ti) is converted to oxide while at the oxide/metal interface direct
noble metal particle formation and alloying of Au and Pt takes place;
continuously these particles are then picked up by the growing nanotube wall.
In our experiments the AuPt alloy NPs have an average size of 4.2 nm and, at
the end of the anodic process, are regularly dispersed over the TiO$_2$
nanotubes. These alloyed AuPt particles act as excellent co-catalyst in
photocatalytic H2 generation - with a H2 production of 12.04 {\mu}L h-1 under
solar light. This represents a strongly enhanced activity as compared with
TiO$_2$ NTs decorated with monometallic particles of Au (7 {\mu}L h-1) or Pt
(9.96 {\mu}L h-1).


  Some present day results for few-nucleon bound state, two-nucleon correlation
functions and scattering observables are briefly reviewed. The old idea of the
Coulomb sum rule as a way to extract the pp correlation function is
reconsidered. It appears to be an ideal case to probe properties of the density
operator and the ground state wave functions without disturbances of final
state interactions (FSI) in exclusive electron scattering on 3He. Also
exclusive photodisintegration of 3He is regarded which appears to be promising
to identify 3N force effects.


  It is very attractive to formulate vision in terms of pattern theory
\cite{Mumford2010pattern}, where patterns are defined hierarchically by
compositions of elementary building blocks. But applying pattern theory to real
world images is currently less successful than discriminative methods such as
deep networks. Deep networks, however, are black-boxes which are hard to
interpret and can easily be fooled by adding occluding objects. It is natural
to wonder whether by better understanding deep networks we can extract building
blocks which can be used to develop pattern theoretic models. This motivates us
to study the internal representations of a deep network using vehicle images
from the PASCAL3D+ dataset. We use clustering algorithms to study the
population activities of the features and extract a set of visual concepts
which we show are visually tight and correspond to semantic parts of vehicles.
To analyze this we annotate these vehicles by their semantic parts to create a
new dataset, VehicleSemanticParts, and evaluate visual concepts as unsupervised
part detectors. We show that visual concepts perform fairly well but are
outperformed by supervised discriminative methods such as Support Vector
Machines (SVM). We next give a more detailed analysis of visual concepts and
how they relate to semantic parts. Following this, we use the visual concepts
as building blocks for a simple pattern theoretical model, which we call
compositional voting. In this model several visual concepts combine to detect
semantic parts. We show that this approach is significantly better than
discriminative methods like SVM and deep networks trained specifically for
semantic part detection. Finally, we return to studying occlusion by creating
an annotated dataset with occlusion, called VehicleOcclusion, and show that
compositional voting outperforms even deep networks when the amount of
occlusion becomes large.


  Neutrosophic set is a part of neutrosophy which studies the origin, nature,
and scope of neutralities, as well as their interactions with different
ideational spectra. Neutrosophic set is a powerful general formal framework
that has been recently proposed. However, neutrosophic set needs to be
specified from a technical point of view. To this effect, we define the
set-theoretic operators on an instance of neutrosophic set, we call it interval
neutrosophic set (INS). We prove various properties of INS, which are connected
to the operations and relations over INS. Finally, we introduce and prove the
convexity of interval neutrosophic sets.


  In the AdS/CFT description of four-dimensional QCD matter undergoing Bjorken
expansion, does the holographic energy-momentum tensor contain a Casimir-type
contribution that should not be attributed to thermal matter? When the bulk
isometry ansatz that yielded such a Casimir term for (1+1)-dimensional boundary
matter is generalised to a four-dimensional boundary, we show that a Casimir
term does not arise, owing to singularities in the five-dimensional bulk
solution. The geometric reasons are traced to a difference between the
isometries of AdS_3 and AdS_{d+1} for d>=3.


  We argue that the fundamental "atomic objects" in string theory are themelia:
extended objects that have 16 supersymmetries locally. We show that all
existing smooth horizonless microstate geometries can be seen as bound states
of themelia, and we conjecture that all such bound states with suitable KKM
charges will give rise to microstate geometries. We also construct the most
general themelion with a three-torus isometry and show that it interpolates
between superstrata and the super-maze.


  This study addresses robust automatic speech recognition (ASR) by introducing
a Conformer-based acoustic model. The proposed model builds on the wide
residual bi-directional long short-term memory network (WRBN) with
utterance-wise dropout and iterative speaker adaptation, but employs a
Conformer encoder instead of the recurrent network. The Conformer encoder uses
a convolution-augmented attention mechanism for acoustic modeling. The proposed
system is evaluated on the monaural ASR task of the CHiME-4 corpus. Coupled
with utterance-wise normalization and speaker adaptation, our model achieves
$6.25\%$ word error rate, which outperforms WRBN by $8.4\%$ relatively. In
addition, the proposed Conformer-based model is $18.3\%$ smaller in model size
and reduces total training time by $79.6\%$.


  In this paper, we present an interpolation scheme for FRQI images based on
bilinear interpolation. To accomplish this, we formulated several quantum
modules, i.e., assignment module, increment module, and quarter module, and
suffused them into our proposed quantum image interpolation circuit. The
concrete quantum circuits to accomplish up-scaling and down-scaling based on
bilinear for FRQI images are designed and the network complexities of them are
analyzed. Finally, to validate the proposed method, simulation experiments to
enlarge and reduce the test images are executed, whose results are compared
with the nearest neighbor interpolation for FRQI images. The up-scaled images
by using proposed interpolation algorithm achieve satisfactory results, and
both PSNR and SSIM values are better than those of the nearest neighbor method.


  We show that the infimum of the dual volume of the convex core of a convex
co-compact hyperbolic $3$-manifold with incompressible boundary coincides with
the infimum of the Riemannian volume of its convex core, as we vary the
geometry by quasi-isometric deformations. We deduce a linear lower bound of the
volume of the convex core of a quasi-Fuchsian manifold in terms of the length
of its bending measured lamination, with optimal multiplicative constant.


  We study two-particle long-range rapidity correlations arising in the early
stages of heavy ion collisions in the saturation/Color Glass Condensate
framework, assuming for simplicity that one colliding nucleus is much larger
than the other. We calculate the two-gluon production cross section while
including all-order saturation effects in the heavy nucleus with the
lowest-order rescattering in the lighter nucleus. We find four types of
correlations in the two-gluon production cross section: (i) geometric
correlations, (ii) HBT correlations accompanied by a back-to-back maximum,
(iii) away-side correlations, and (iv) near-side azimuthal correlations which
are long-range in rapidity. The geometric correlations (i) are due to the fact
that nucleons are correlated by simply being confined within the same nucleus
and may lead to long-range rapidity correlations for the produced particles
without strong azimuthal angle dependence. Somewhat surprisingly, long-range
rapidity correlations (iii) and (iv) have exactly the same amplitudes along
with azimuthal and rapidity shapes: one centered around \Delta \phi =\pi\ with
the other one centered around \Delta \phi =0 (here \Delta \phi\ is the
azimuthal angle between the two produced gluons). We thus observe that the
early-time CGC dynamics in nucleus-nucleus collisions generates azimuthal
non-flow correlations which are qualitatively different from jet correlations
by being long-range in rapidity. If strong enough, they have the potential of
mimicking the elliptic (and higher-order even-harmonic) flow in the di-hadron
correlators: one may need to take them into account in the experimental
determination of the flow observables.


  Four-dimensional weak-constraint variational data assimilation estimates a
state given partial noisy observations and dynamical model by minimizing a cost
function that takes into account both discrepancy between the state and
observations and model error over time. It can be formulated as a Gauss-Newton
iteration of an associated least-squares problem. In this paper, we introduce a
parameter in front of the observation mismatch and show analytically that this
parameter is crucial either for convergence to the true solution when
observations are noise-free or for boundness of the error when observations are
noisy with bounded observation noise. We also consider joint state-parameter
estimation. We illustrated theoretical results with numerical experiments using
the Lorenz 63 and Lorenz 96 models.


  We propose that the effective field theories of certain wrapped D-branes are
given by topological actions based on Born-Infeld theory. In particular, we
present a Born-Infeld version of the Abelian Donaldson-Witten theory. We then
consider wrapping D3 branes on calibrated submanifolds and for the Calabi-Yau
four-fold case, discuss how the resulting theory could give rise to a
Born-Infeld version of the ampicheiral twisted N=4 super Yang-Mills topological
field theory.


  Today, our lifestyle revolves around digital devices powered by
microprocessors of different instruction set architectures (ISA). Among them,
the most common are x86 and ARM, the brainpower of our computers and
smartphones. Reduced instruction set computing (RISC) is the basis of ARM
architecture, designed to offer greater energy efficiency. On the other hand,
principles of complex instruction set computing (CISC) are utilized by x86
processors, which handle heavier computing tasks while being more power-hungry.
The rise of smartphones over a decade has changed the laptop market. It also
influenced customers towards ARM-based energy-efficient laptops. This
transition in the computing segment is seen not only in consumers but also in
commercial settings, especially data centers. Usually, data centers are
designed to operate 24/7, where energy is a big concern. So, ARM chips have
started making their way to cloud servers. This paper comprehensively analyzes
and compares the ARM and x86 architectures to unravel the factors contributing
to ARM's increasing dominance in the market. It also explores the impact of
smartphones on the laptop market and assesses the significance of
system-on-a-chip (SoC). Focusing on the proper utilization of energy and
sustainability, our paper offers valuable insights into the growing trend of
adopting ARM processors in the computing industry.


  We give four positive formulae for the (equioriented type A) quiver
polynomials of Buch and Fulton. All four formulae are combinatorial, in the
sense that they are expressed in terms of combinatorial objects of certain
types: Zelevinsky permutations, lacing diagrams, Young tableaux, and pipe
dreams (also known as rc-graphs). Three of our formulae are multiplicity-free
and geometric, meaning that their summands have coefficient 1, and correspond
bijectively to components of a torus-invariant scheme. The remaining (presently
non-geometric) formula was conjectured for by Buch and Fulton in terms of
factor sequences of Young tableaux; our proof of it proceeds by way of a new
characterization of the tableaux counted by quiver constants. All four formulae
come naturally in ``doubled'' versions, two for `double quiver polynomials',
and the other two for their stable versions, the `double quiver functions',
where setting half the variables equal to the other half specializes to the
ordinary case.


  We study the invariant distributions for the horocycle map on
$\Gamma\backslash SL(2, \mathbb{R})$ and prove Sobolev estimates for the
cohomological equation of the horocycle map. As an application, we obtain an
estimate for the rate of equidistribution for horocycle maps on compact
manifolds.


  Sentential decision diagrams (SDDs) introduced by Darwiche in 2011 are a
promising representation type used in knowledge compilation. The relative
succinctness of representation types is an important subject in this area. The
aim of the paper is to identify which kind of Boolean functions can be
represented by SDDs of small size with respect to the number of variables the
functions are defined on. For this reason the sets of Boolean functions
representable by different representation types in polynomial size are
investigated and SDDs are compared with representation types from the classical
knowledge compilation map of Darwiche and Marquis. Ordered binary decision
diagrams (OBDDs) which are a popular data structure for Boolean functions are
one of these representation types. SDDs are more general than OBDDs by
definition but only recently, a Boolean function was presented with polynomial
SDD size but exponential OBDD size. This result is strengthened in several
ways. The main result is a quasipolynomial simulation of SDDs by equivalent
unambiguous nondeterministic OBDDs, a nondeterministic variant where there
exists exactly one accepting computation for each satisfying input. As a side
effect an open problem about the relative succinctness between SDDs and free
binary decision diagrams (FBDDs) which are more general than OBDDs is answered.


  Measurements allow efficient preparation of interesting quantum many-body
states with long-range entanglement, conditioned on additional transformations
based on measurement outcomes. Here, we demonstrate that the so-called
conformal quantum critical points (CQCP) can be obtained by performing general
single-site measurements in an appropriate basis on the cluster states in
$d\geq2$. The equal-time correlators of the said states are described by
correlation functions of certain $d$-dimensional classical models at finite
temperatures and feature spatial conformal invariance. This establishes an
exact correspondence between the measurement-prepared critical states and
conformal field theories of a range of critical spin models, including familiar
Ising models and gauge theories. Furthermore, by mapping the long-range
entanglement structure of measured quantum states into the correlations of the
corresponding thermal spin model, we rigorously establish the stability
condition of the long-range entanglement in the measurement-prepared quantum
states deviating from the ideal setting. Most importantly, we describe
protocols to decode the resulting quantum phases and transitions without
post-selection, thus transferring the exponential measurement complexity to a
polynomial classical computation. Therefore, our findings suggest a novel
mechanism in which a quantum critical wavefunction emerges, providing new
practical ways to study quantum phases and conformal quantum critical points.


  Load shedding is the last and most expensive control action against system
collapse and blackout. Achievement of an efficient emergency control to
stabilize the power system following severe disturbances, requires two key
objectives. First, preventing of further cascading outages, i.e. saving the
available and determinant power system elements and second, issuing proper
control actions to stabilize the power system inside the permissible time
frame. In this paper online contingency analysis is performed to monitor secure
and reliable operation of transmission lines. Load shedding locations are
continuously updated based on loading rate/thermal limit of lines to prevent
their outage. Simulation of severe contingencies carried out on 39 bus IEEE
standard test system in DIgSILENT power-factory validates the efficiency of
proposed method.


  Cyber-physical production systems consist of highly specialized software and
hardware components. Most components and communication protocols are not built
according to the Secure by Design principle. Therefore, their resilience to
cyberattacks is limited. This limitation can be overcome with common
operational pictures generated by security monitoring solutions. These pictures
provide information about communication relationships of both attacked and
non-attacked devices, and serve as a decision-making basis for security
officers in the event of cyberattacks. The objective of these decisions is to
isolate a limited number of devices rather than shutting down the entire
production system. In this work, we propose and evaluate a concept for finding
the devices to isolate. Our approach is based on solving the Critical Node Cut
Problem with Vulnerable Vertices (CNP-V) - an NP-hard computational problem
originally motivated by isolating vulnerable people in case of a pandemic. To
the best of our knowledge, this is the first work on applying CNP-V in context
of cybersecurity.


  The perturbative QCD predictions concerning deep inelastic scattering at low
$x$ are summarized. The theoretical framework based on the leading log $1/x$
resummation and $k_t$ factorization theorem is described and some recent
developments concerning the BFKL equation and its generalization are discussed.
The QCD expectations concerning the small $x$ behaviour of the spin dependent
structure function $g_1(x,Q^2)$ are briefly summarized and the importance of
the double logarithmic terms which sum contributions containing the leading
powers of $\alpha_s ln^2(1/x)$ is emphasised. The role of studying final states
in deep inelastic scattering for revealing the details of the underlying
dynamics at low $x$ is pointed out and some dedicated measurements, like deep
inelastic scattering accompanied by an energetic jet, the measurement of the
transverse energy flow etc., are briefly discussed.


  The dynamics of a particle in an expanding cavity is investigated in the
Klein-Gordon framework in a regime in which the single particle picture remains
valid. The cavity expansion represents a time-dependent boundary condition for
the relativistic wavefunction. We show that this expansion induces a non-local
effect on the current density throughout the cavity. Our results indicate that
a relativistic treatment still contains apparently spurious effects
traditionally associated with the unbounded velocities inherent to
non-relativistic solutions obtained from the Schroedinger equation. Possible
reasons for this behaviour are discussed.


  We study a nonlinear parabolic system for a time dependent solenoidal vector
field on $\Bbb R^3$. The nonlinear term of this new model equations is obtained
slightly modifying that of the Navier-Stokes equations. The system has the same
scaling property and the Galileian invariance as the Navier-Stokes equations.
For such system we prove the global regularity for a smooth initial data.


  Leibniz algebras are certain generalization of Lie algebras. In this paper we
give classification of non-Lie solvable (left) Leibniz algebras of dimension
$\leq 8$ with one dimensional derived subalgebra. We use the canonical forms
for the congruence classes of matrices of bilinear forms to obtain our result.
Our approach can easily be extended to classify these algebras of higher
dimensions. We also revisit the classification of three dimensional non-Lie
solvable (left) Leibniz algebras.


  We consider packings of congruent circles on a square flat torus, i.e.,
periodic (w.r.t. a square lattice) planar circle packings, with the maximal
circle radius. This problem is interesting due to a practical reason - the
problem of "super resolution of images." We have found optimal arrangements for
N=6, 7 and 8 circles. Surprisingly, for the case N=7 there are three different
optimal arrangements. Our proof is based on a computer enumeration of toroidal
irreducible contact graphs.


  In BCS superconductors, the superfluid stiffness is virtually constant at low
temperature and only slightly affected by the exponentially low density of
thermal quasiparticles. Here, we present an experimental and theoretical study
on the temperature dependence of superfluid stiffness $\Theta\left(T\right)$ in
a strongly disordered pseudo-gaped superconductor, amorphous $\text{InO}_{x}$,
which exhibits non-BCS behavior. Experimentally, we report an unusual power-law
suppression of the superfluid stiffness $\delta\Theta\left(T\right)\propto
T^{b}$ at $T\ll T_{c}$, with $b\sim1.6$, which we measured via the frequency
shift of microwave resonators. Theoretically, by combining analytical and
numerical methods to a model of a disordered superconductor with pseudogap and
spatial inhomogeneities of the superconducting order parameter, we found a
qualitatively similar low-temperature power-law behavior with exponent
$b\sim1.6-3$ being disorder-dependent. This power-law suppression of the
superfluid density occurs mainly due to the broad distribution of the
superconducting order parameter that is known to exist in such superconductors
[arXiv:1012.3630], even moderately far from the superconductor-insulator
transition. The presence of the power-law dependence
$\delta\Theta\left(T\right)\propto T^{b}$ at low $T\ll T_{c}$ demonstrates the
existence of low-energy collective excitations; in turn, it implies the
presence of a new channel of dissipation in inhomogeneous superconductors
caused by sub-gap excitations that are not quasiparticles. Our findings have
implications for the use of strongly disordered superconductors as
superinductance in quantum circuits.


  A well known result of Lozanovsky states that a Banach lattice is weakly
sequentially complete if and only if it does not contain a copy of $c_{0}$. In
the current paper we extend this result to the class of Banach $C(K)$ modules
of finite multiplicity and, as a special case, to finitely generated Banach
$C(K)$-modules. Moreover, we prove that such a module is weakly sequentially
complete if and only if each cyclic subspace of the module is weakly
sequentially complete.


  We characterize the first Alexander Z[Z]-modules of ribbon surface-links in
the 4-sphere fixing the number of components and the total genus, and then the
first Alexander Z[Z]-modules of surface-links in the 4-sphere fixing the number
of components. Using the result of ribbon torus-links, we also characterize the
first Alexander Z[Z]-modules of virtual links fixing the number of components.
For a general surface-link, an estimate of the total genus is given in terms of
the first Alexander Z[Z]-module. We show a graded structure on the first
Alexander Z[Z]-modules of all surface-links and then a graded structure on the
first Alexander Z[Z]-modules of classical links, surface-links and
higher-dimensional manifold-links.


  We show that if NC$^1 \neq$ L, then for every element $\alpha$ of the
alternating group $A_t$, circuits of depth $O(\log t)$ cannot distinguish
between a uniform vector over $(A_t)^t$ with product $= \alpha$ and one with
product $=$ identity. Combined with a recent construction by the author and
Viola in the setting of leakage-resilient cryptography [STOC '13], this gives a
compiler that produces circuits withstanding leakage from NC$^1$ (assuming
NC$^1 \neq$ L). For context, leakage from NC$^1$ breaks nearly all previous
constructions, and security against leakage from P is impossible. %In the
multi-query setting, circuits produced by this compiler use a simple secure
hardware component.
  We build on work by Cook and McKenzie [J.\ Algorithms '87] establishing the
relationship between L $=$ logarithmic space and the symmetric group $S_t$. Our
techniques include a novel algorithmic use of commutators to manipulate the
cycle structure of permutations in $A_t$.


  Recent work showed that embeddings from related languages can improve the
performance of sequence tagging, even for monolingual models. In this analysis
paper, we investigate whether the best auxiliary language can be predicted
based on language distances and show that the most related language is not
always the best auxiliary language. Further, we show that attention-based
meta-embeddings can effectively combine pre-trained embeddings from different
languages for sequence tagging and set new state-of-the-art results for
part-of-speech tagging in five languages.


  In this work, we re-think the task of speech enhancement in unconstrained
real-world environments. Current state-of-the-art methods use only the audio
stream and are limited in their performance in a wide range of real-world
noises. Recent works using lip movements as additional cues improve the quality
of generated speech over "audio-only" methods. But, these methods cannot be
used for several applications where the visual stream is unreliable or
completely absent. We propose a new paradigm for speech enhancement by
exploiting recent breakthroughs in speech-driven lip synthesis. Using one such
model as a teacher network, we train a robust student network to produce
accurate lip movements that mask away the noise, thus acting as a "visual noise
filter". The intelligibility of the speech enhanced by our pseudo-lip approach
is comparable (< 3% difference) to the case of using real lips. This implies
that we can exploit the advantages of using lip movements even in the absence
of a real video stream. We rigorously evaluate our model using quantitative
metrics as well as human evaluations. Additional ablation studies and a demo
video on our website containing qualitative comparisons and results clearly
illustrate the effectiveness of our approach. We provide a demo video which
clearly illustrates the effectiveness of our proposed approach on our website:
\url{http://cvit.iiit.ac.in/research/projects/cvit-projects/visual-speech-enhancement-without-a-real-visual-stream}.
The code and models are also released for future research:
\url{https://github.com/Sindhu-Hegde/pseudo-visual-speech-denoising}.


  Comet 67P/Churyumov-Gerasimenko was selected in 2003 as the new target of the
Rosetta mission. It has since been the subject of a detailed campaign of
observations to characterise its nucleus and activity. Here we present
previously unpublished data taken around the start of activity of the comet in
2007/8, before its last perihelion passage. We constrain the time of the start
of activity, and combine this with other data taken throughout the comet's
orbit to make predictions for its likely behaviour during 2014/5 while Rosetta
is operating. A considerable difficulty in observing 67P during the past years
has been its position against crowded fields towards the Galactic centre for
much of the time. The 2007/8 data presented here were particularly difficult,
and the comet will once again be badly placed for Earth-based observations in
2014/5. We make use of the difference image analysis (DIA) technique, which is
commonly used in variable star and exoplanet research, to remove background
sources and extract images of the comet. In addition, we reprocess a large
quantity of archival images of 67P covering its full orbit, to produce a
heliocentric lightcurve. By using consistent reduction, measurement and
calibration techniques we generate a remarkably clean lightcurve, which can be
used to measure a brightness-distance relationship and to predict the future
brightness of the comet. We determine that the comet was active around November
2007, at a pre-perihelion distance from the Sun of 4.3 AU. The comet will reach
this distance, and probably become active again, in March 2014. We find that
the dust brightness can be well described by Af\rho \propto r^-3.2
pre-perihelion and r^-3.4 post-perihelion, and that the comet has a higher
dust-to-gas ratio than average. A model fit to the photometric data suggests
that only a small fraction (1.4%) of the surface is active.


  A non--linear diffusion equation is derived by taking into account hopping
rates depending on the occupation of next neighbouring sites. There appears
additonal repulsive and attractive forces leading to a changed local mobiltiy.
The stationary and the time dependent behaviour of the system are studied based
upon the master equation approach. Different to conventional diffusion it
results a time dependent bump the position of which increases with time
described by an anomalous diffusion exponent. The fractal dimension of this
random walk is exclusively determined by the space dimension. The applicabilty
of the model to descibe glasses is discussed.


  Usually, routing models in pedestrian dynamics assume that agents have
fulfilled and global knowledge about the building's structure. However, they
neglect the fact that pedestrians possess no or only parts of information about
their position relative to final exits and possible routes leading to them. To
get a more realistic description we introduce the systematics of gathering and
using spatial knowledge. A new wayfinding model for pedestrian dynamics is
proposed. The model defines for every pedestrian an individual knowledge
representation implying inaccuracies and uncertainties. In addition,
knowledge-driven search strategies are introduced. The presented concept is
tested on a fictive example scenario.


  We investigate the thermodynamic properties of D-brane-anti-D-brane pairs and
non-BPS D-branes on the basis of boundary string field theory. We calculate the
finite temperature effective potential of N D-brane-anti-D-brane pairs in a
non-compact background and in a toroidal background. In the non-compact
background case, a phase transition occurs slightly below the Hagedorn
temperature, and the D9-anti-D9 pairs become stable. Moreover, the total energy
at the critical temperature is a decreasing function of N as long as the 't
Hooft coupling is very small. This leads to the conclusion that a large number
N of D9-anti-D9 pairs are created simultaneously near the Hagedorn temperature.
In the toroidal background case (M_{1,9-D} * T_{D}), a phase transition occurs
only if the Dp-anti-Dp pair is extended in all the non-compact directions, as
long as the 't Hooft coupling is very small. The total energy at the critical
temperature also decreases as N increases. We also calculate the finite
temperature effective potential of non-BPS D-branes, and we obtain similar
results. Then, we consider the thermodynamic balance between open strings on
these branes and closed strings in the bulk in the ideal gas approximation, and
conclude that the total energy is dominated by the open strings.


  We suggest a parameterization of the matrix element for $\bar{B}^0\to
D^{*+}\omega\pi^-$ decay using kinematic variables convenient for experimental
analysis. The contributions of intermediate $\omega\pi$- and $D^{**}$-states up
to spin 3 have been taken into account. The angular distributions for each
discussed hypothesis have been obtained and analysed using Monte-Carlo
simulation.


  We call a subset $K$ of $\mathbb C$ \emph{biholomorphically homogeneous} if
for any two points $p,q\in K$ there exists a neighborhood $U$ of $p$ and a
biholomorphism $\psi:U\to \psi(U)\subset \mathbb C$ such that $\psi(p)=q$ and
$\psi(K\cap U)= K\cap \psi(U)$. We show that a biholomorphically homogeneous
smooth curve $\gamma\subset \mathbb C$ is necessarily real-analytic.
Furthermore we show that the same holds for the homogeneity with respect of a
wider class of groups $G$ of real-analytic transformations of the plane. The
result also extends to subsets $K\subset \mathbb R^2$ which are just locally
closed.


  Social, technological and economic time series are divided by events which
are usually assumed to be random albeit with some hierarchical structure. It is
well known that the interevent statistics observed in these contexts differs
from the Poissonian profile by being long-tailed distributed with resting and
active periods interwoven. Understanding mechanisms generating consistent
statistics have therefore become a central issue. The approach we present is
taken from the Continuous Time Random Walk formalism and represents an
analytical alternative to models of non-trivial priority that have been
recently proposed. Our analysis also goes one step further by looking at the
multifractal structure of the interevent times of human decisions. We here
analyze the inter-transaction time intervals of several financial markets. We
observe that empirical data describes a subtle multifractal behavior. Our model
explains this structure by taking the pausing-time density in the form of a
superstatistics where the integral kernel quantifies the heterogeneous nature
of the executed tasks. An stretched exponential kernel provides a multifractal
profile valid for a certain limited range. A suggested heuristic analytical
profile is capable of covering a broader region.


  The self-organized dopant percolative filamentary model, entirely orbital in
character (no fictive spins), explains chemical trends in superconductive
transition temperatures Tc, assuming that Cooper pairs are formed near dopants
because attractive electron-phonon interactions outweigh repulsive Coulomb
interactions. According to rules previously used successfully for network
glasses, the host networks are marginally stable mechanically. The high Tc's
are caused by softening of the host network, enormously enhanced by large
electron-phonon interactions at interlayer dopants for states near the Fermi
energy. Background (in)homogeneities (pseudogap regions) produce novel
percolative features in phase diagrams.


  Loop quantum cosmology with a scalar field is known to be closely linked with
an inflationary phase. In this article, we study probabilistic predictions for
the duration of slow-roll inflation, by assuming a minimalist massive scalar
field as the main content of the universe. The phase of the field in its
"prebounce" oscillatory state is taken as a natural random parameter. We find
that the probability for a given number of inflationary e-folds is quite
sharply peaked around 145, which is consistent with the most favored minimum
values. In this precise sense, a satisfactory inflation is therefore a clear
prediction of loop gravity. In addition, we derive an original and stringent
upper limit on the Barbero-Immirzi parameter. The general picture of inflation,
superinflation, deflation, and superdeflation is also much clarified in the
framework of bouncing cosmologies.


  We present DLKoopman -- a software package for Koopman theory that uses deep
learning to learn an encoding of a nonlinear dynamical system into a linear
space, while simultaneously learning the linear dynamics. While several
previous efforts have either restricted the ability to learn encodings, or been
bespoke efforts designed for specific systems, DLKoopman is a generalized tool
that can be applied to data-driven learning and optimization of any dynamical
system. It can either be trained on data from individual states (snapshots) of
a system and used to predict its unknown states, or trained on data from
trajectories of a system and used to predict unknown trajectories for new
initial states. DLKoopman is available on the Python Package Index (PyPI) as
'dlkoopman', and includes extensive documentation and tutorials. Additional
contributions of the package include a novel metric called Average Normalized
Absolute Error for evaluating performance, and a ready-to-use hyperparameter
search module for improving performance.


  Jakobson and Nadirashvili \cite{JN} constructed a sequence of eigenfunctions
on $T^2$ with a bounded number of critical points, answering in the negative
the question raised by Yau \cite{Yau1} which asks that whether the number of
the critical points of eigenfunctions for the Laplacian increases with the
corresponding eigenvalues.
  The present paper finds three interesting eigenfunctions on the minimal
isoparametric hypersurface $M^n$ in $S^{n+1}(1)$. The corresponding eigenvalues
are $n$, $2n$ and $3n$, while their critical sets consist of $8$ points, a
submanifold(infinite many points) and $8$ points, respectively. On one of its
focal submanifolds, a similar phenomenon occurs.


  Robot-assisted dressing could profoundly enhance the quality of life of
adults with physical disabilities. To achieve this, a robot can benefit from
both visual and force sensing. The former enables the robot to ascertain human
body pose and garment deformations, while the latter helps maintain safety and
comfort during the dressing process. In this paper, we introduce a new
technique that leverages both vision and force modalities for this assistive
task. Our approach first trains a vision-based dressing policy using
reinforcement learning in simulation with varying body sizes, poses, and types
of garments. We then learn a force dynamics model for action planning to ensure
safety. Due to limitations of simulating accurate force data when deformable
garments interact with the human body, we learn a force dynamics model directly
from real-world data. Our proposed method combines the vision-based policy,
trained in simulation, with the force dynamics model, learned in the real
world, by solving a constrained optimization problem to infer actions that
facilitate the dressing process without applying excessive force on the person.
We evaluate our system in simulation and in a real-world human study with 10
participants across 240 dressing trials, showing it greatly outperforms prior
baselines. Video demonstrations are available on our project website
(https://sites.google.com/view/dressing-fcvp).


  Boltzmann machines (BM) are widely used as generative models. For example,
pairwise Potts models (PM), which are instances of the BM class, provide
accurate statistical models of families of evolutionarily related protein
sequences. Their parameters are the local fields, which describe site-specific
patterns of amino-acid conservation, and the two-site couplings, which mirror
the coevolution between pairs of sites. This coevolution reflects structural
and functional constraints acting on protein sequences during evolution. The
most conservative choice to describe the coevolution signal is to include all
possible two-site couplings into the PM. This choice, typical of what is known
as Direct Coupling Analysis, has been successful for predicting residue
contacts in the three-dimensional structure, mutational effects, and in
generating new functional sequences. However, the resulting PM suffers from
important over-fitting effects: many couplings are small, noisy and hardly
interpretable; the PM is close to a critical point, meaning that it is highly
sensitive to small parameter perturbations. In this work, we introduce a
general parameter-reduction procedure for BMs, via a controlled iterative
decimation of the less statistically significant couplings, identified by an
information-based criterion that selects either weak or statistically
unsupported couplings. For several protein families, our procedure allows one
to remove more than $90\%$ of the PM couplings, while preserving the predictive
and generative properties of the original dense PM, and the resulting model is
far away from criticality, hence more robust to noise.


  We propose four channels through which government guarantees affect banks'
incentives to smooth income. Empirically, we exploit two complementary settings
that represent plausible exogenous changes in government guarantees: the
increase in implicit guarantees following the creation of the Eurozone and the
removal of explicit guarantees granted to the Landesbanken. We show that
increases (decreases) in government guarantees are associated with significant
decreases (increases) in banks' income smoothing. Taken together, our results
largely corroborate the predominance of a tail-risk channel, wherein government
guarantees reduce banks' tail risk, thereby reducing managers' incentives to
engage in income smoothing.


  Successful implementations of quantum technologies require protocols and
algorithms that use as few quantum resources as possible. Many applications
require a desired quantum operation, such as rotation gates in quantum
computing or broadband pulses in NMR or MRI applications, that is not feasible
to directly implement or would require longer coherence times than achievable.
This work develops an approach that enables -- at the cost of a modestly
increased measurement repetition rate -- the exact implementation of such
operations. One proceeds by first building a library of a large number of
different approximations to the desired gate operation; by randomly selecting
these operations according to a pre-optimised probability distribution, one can
on average implement the desired operation with a rigorously controllable
approximation error. The approach relies on sophisticated tools from convex
optimisation to efficiently find optimal probability distributions. A diverse
spectrum of applications are demonstrated as (a) exactly synthesising rotations
in fault-tolerant quantum computers using only short T-depth circuits and (b)
synthesising broadband and band-selective pulses of superior performance in
quantum optimal control with (c) further applications in NMR or MRI. The
approach is very general and a broad spectrum of practical applications in
quantum technologies are explicitly demonstrated.


  Fine-Grained Visual Categorization (FGVC) is a challenging topic in computer
vision. It is a problem characterized by large intra-class differences and
subtle inter-class differences. In this paper, we tackle this problem in a
weakly supervised manner, where neural network models are getting fed with
additional data using a data augmentation technique through a visual attention
mechanism. We perform domain adaptive knowledge transfer via fine-tuning on our
base network model. We perform our experiment on six challenging and commonly
used FGVC datasets, and we show competitive improvement on accuracies by using
attention-aware data augmentation techniques with features derived from deep
learning model InceptionV3, pre-trained on large scale datasets. Our method
outperforms competitor methods on multiple FGVC datasets and showed competitive
results on other datasets. Experimental studies show that transfer learning
from large scale datasets can be utilized effectively with visual attention
based data augmentation, which can obtain state-of-the-art results on several
FGVC datasets. We present a comprehensive analysis of our experiments. Our
method achieves state-of-the-art results in multiple fine-grained
classification datasets including challenging CUB200-2011 bird, Flowers-102,
and FGVC-Aircrafts datasets.


  We use first principles calculations to investigate how deviations from
perfect chemical order affect the magneto-crystalline anisotropy energy (MAE)
in L$1_0$ FeNi. We first analyze the local chemical environment of the Fe atoms
in various partially ordered configurations, using the orbital magnetic moment
anisotropy (OMA) as proxy for a local contribution to the MAE. We are able to
identify a specific nearest neighbor configuration and use this "favorable
environment" to successfully design various structures with MAE higher than the
perfectly ordered system. However, a systematic analysis of the correlation
between local environment and OMA using smooth overlap of atomic positions
(SOAP), indicates only a partial correlation, which exists only if the
deviation from full chemical order is not too large, whereas in general no such
correlation can be identified even using up to third nearest neighbors. Guided
by the observation that the identified "favorable environment" implies an
Fe-rich composition, we investigate the effect of randomly inserting additional
Fe into the nominal Ni planes of the perfectly ordered structure. We find that
the MAE increases with Fe content, at least up to 62.5% Fe. Thus, our study
shows that the perfectly ordered case is not the one with highest MAE and that
an increased MAE can be obtained for slightly Fe-rich compositions.


  Wilson-like Dirac operators can be written in the form
$D=\gamma_\mu\nabla_\mu-\frac {ar}{2} \Delta$. For Wilson fermions the standard
two-point derivative $\nabla_\mu^{(\mathrm{std})}$ and 9-point Laplacian
$\Delta^{(\mathrm{std})}$ are used. For Brillouin fermions these are replaced
by improved discretizations $\nabla_\mu^{(\mathrm{iso})}$ and
$\Delta^{(\mathrm{bri})}$ which have 54- and 81-point stencils respectively. We
derive the Feynman rules in lattice perturbation theory for the Brillouin
action and apply them to the calculation of the improvement coefficient
${c_\mathrm{SW}}$, which, similar to the Wilson case, has a perturbative
expansion of the form
${c_\mathrm{SW}}=1+{c_\mathrm{SW}}^{(1)}g_0^2+\mathcal{O}(g_0^4)$. For $N_c=3$
we find ${c_\mathrm{SW}}^{(1)}_\mathrm{Brillouin} =0.12362580(1) $, compared to
${c_\mathrm{SW}}^{(1)}_\mathrm{Wilson} = 0.26858825(1)$, both for $r=1$.


  Planets which are smaller than Mercury and heated to sublimation temperatures
of $\sim$2000 K lose mass catastrophically in dusty evaporative winds. The
winds are observed to gust and recede largely without pattern; transit depths
from the Kepler mission vary randomly from orbit to orbit by up to a factor of
10 or more. We explain how chaotic outflows may arise by constructing a map for
the wind mass-loss rate as a function of time. The map is built on three
statements: (1) The wind mass-loss rate scales in proportion to the surface
equilibrium vapor pressure, rising exponentially with ground temperature. (2)
Because the wind takes a finite time to escape the planet's gravity well, the
surface mass-loss rate at any time determines the wind optical depth at a later
time -- the atmosphere has hysteresis. (3) The ground temperature increases
with optical depth (greenhouse effect) when the atmosphere is optically thin,
and decreases with optical depth when the atmosphere is optically thick
(nuclear winter). Statement (3) follows from how dust condenses in the face of
intense stellar irradiation. As discussed recently, condensates initially naked
before the star must be silicate-rich and iron-poor, staying cool enough for
condensation by absorbing weakly in the visible and emitting strongly in the
infrared. Later, when grains are numerous enough to self-shield from starlight,
they may accrete more iron and reverse their visible-to-infrared opacity ratio.
Depending on parameters, the map for the wind can regularly boom and bust
between a greenhouse and a nuclear winter, or erupt into chaos. Lyapunov times
are measured in orbital periods, the time for the wind to turn by Coriolis
forces away from the planet's dayside, out of the Hill sphere.


  Recognition of epileptic focal point is the important diagnosis when
screening the epilepsy patients for latent surgical cures. The accurate
localization is challenging one because of the low spatial resolution images
with more noisy data. Positron Emission Tomography (PET) has now replaced the
issues and caring a high resolution. This paper focuses the research of
automated localization of epileptic seizures in brain functional images using
symmetry based cluster approach. This approach presents a fully automated
symmetry based brain abnormality detection method for PET sequences. PET images
are spatially normalized to Digital Imaging and Communications in Medicine
(DICOM) standard and then it has been trained using symmetry based cluster
approach using Medical Image Processing, Analysis & Visualization (MIPAV) tool.
The performance evolution is considered by the metric like accuracy of
diagnosis. The obtained result is surely assists the surgeon for the automated
identification of seizures focus.


  Artificial Intelligence (AI) aims to elevate healthcare to a pinnacle by
aiding clinical decision support. Overcoming the challenges related to the
design of ethical AI will enable clinicians, physicians, healthcare
professionals, and other stakeholders to use and trust AI in healthcare
settings. This study attempts to identify the major ethical principles
influencing the utility performance of AI at different technological levels
such as data access, algorithms, and systems through a thematic analysis. We
observed that justice, privacy, bias, lack of regulations, risks, and
interpretability are the most important principles to consider for ethical AI.
This data-driven study has analyzed secondary survey data from the Pew Research
Center (2020) of 36 AI experts to categorize the top ethical principles of AI
design. To resolve the ethical issues identified by the meta-analysis and
domain experts, we propose a new utilitarian ethics-based theoretical framework
for designing ethical AI for the healthcare domain.


  By recasting the Klein--Gordon equation as an eigen-equation in the coupling
parameter $v > 0,$ the basic Klein--Gordon comparison theorem may be written
$f_1\leq f_2\implies G_1(E)\leq G_2(E)$, where $f_1$ and $f_2$, are the
monotone non-decreasing shapes of two central potentials $V_1(r) = v_1\,f_1(r)$
and $V_2(r) = v_2\, f_2(r)$ on $[0,\infty)$. Meanwhile $v_1 = G_1(E)$ and $v_2
= G_2(E)$ are the corresponding coupling parameters that are functions of the
energy $E\in(-m,\,m)$. We weaken the sufficient condition for the ground-state
spectral ordering by proving (for example in $d=1$ dimension) that if
$\int_0^x\big[f_2(t) - f_1(t)\big]\varphi_i(t)dt\geq 0$, the couplings remain
ordered $v_1 \leq v_2$ where $i = 1\, {\rm or}\, 2, $ and $\{\varphi_1,
\varphi_2\}$ are the ground-states corresponding respectively to the couplings
$\{v_1,\, v_2\}$ for a given $E \in (-m,\, m).$. This result is extended to
spherically symmetric radial potentials in $ d > 1 $ dimensions.


  Under mild hypotheses on the residual representation, we prove the
Equivariant Tamagawa Number Conjecture for modular motives with coefficients in
universal deformation rings and Hecke algebras using a novel combination of the
methods of Euler systems and Taylor-Wiles systems. We also prove the
compatibility of this conjecture with specialization.


  We analyze the impact of the leading quantum gravity effects on the
properties of black holes with nonzero angular momentum by performing a
suitable renormalization group improvement of the classical Kerr metric within
Quantum Einstein Gravity (QEG). In particular we explore the structure of the
horizons, the ergosphere, and the static limit surfaces as well as the phase
space avilable for the Penrose process. The positivity properties of the
effective vacuum energy momentum tensor are also discussed and the "dressing"
of the black hole's mass and angular momentum are investigated by computing the
corresponding Komar integrals. The pertinent Smarr formula turns out to retain
its classical form. As for their thermodynamical properties, a modified first
law of black hole thermodynamics is found to be satisfied by the improved black
holes (to second order in the angular momentum); the corresponding
Bekenstein-Hawking temperature is not proportional to the surface gravity.


  We systematically analyze the prompt emission and the early afterglow data of
a sample of 31 GRBs detected by {\em Swift} before September 2005, and estimate
the GRB radiative efficiency. BAT's narrow band inhibits a precise
determination of the GRB spectral parameters, and we have developed a method to
estimate these parameters with the hardness ratio information. The shallow
decay component commonly existing in early X-ray afterglows, if interpreted as
continuous energy injection in the external shock, suggests that the GRB
efficiency previously derived from the late-time X-ray data were not reliable.
We calculate two radiative efficiencies using the afterglow kinetic energy E_K
derived at the putative deceleration time t_{dec}) and at the break time (t_b)
when the energy injection phase ends, respectively. At t_b XRFs appear to be
less efficient than normal GRBs. However, when we analyze the data at t_{dec}
XRFs are found to be as efficient as GRBs. Short GRBs have similar radiative
efficiencies to long GRBs despite of their different progenitors. Twenty-two
bursts in the sample are identified to have the afterglow cooling frequency
below the X-ray band. Assuming \epsilon_e = 0.1, we find \eta_\gamma(t_b)
usually <10% and \eta_\gamma (t_{dec}) varying from a few percents to > 90%.
Nine GRBs in the sample have the afterglow cooling frequency above the X-ray
band for a very long time. This suggests a very small \epsilon_B and/or a very
low ambient density n.


  We investigate effects of the radiation and the moduli oscillation around the
stabilized values on the evolution of a 6-dimensional spacetime compactified on
$S^2$. In order to see the transition from the 5-dimensional space to the
3-dimensional one, we develop a procedure to pursue the spacetime evolution
with appropriate approximations, which is valid until the spacetime behaves
like 4-dimensional. In the case that the moduli stabilization process cannot be
described in the context of the 4-dimensional effective theory, it takes quite
a long time for the moduli oscillation to dominate the total energy density, in
contrast to the conventional result obtained by the 4-dimensional effective
theory approach. We also found that even if the moduli are set at the
stabilized values, they start to oscillate due to the pressure in the extra
space $S^2$ in some cases.


  We study the viability of five-dimensional gauge theories as candidates for
the origin of the Higgs field and its mechanism for spontaneous symmetry
breaking. Within the framework of lattice field theory, we consider the
simplest model of an $SU(2)$ gauge theory. We construct this theory on a
five-dimensional orbifold which explicitly breaks the gauge symmetry to $U(1)$
at the fixed points of the orbifold. Using anisotropic gauge couplings, we find
that this theory exhibits three distinct phases which we label as confined,
Higgs and hybrid. Within the Higgs phase, close to the Higgs-hybrid phase
transition, we find that the ratio of the Higgs to gauge boson masses takes
Standard Model-like values. Precisely in this region of the phase diagram, we
find dimensional reduction via localisation.


  In "Playing Pool with $\pi$", Galperin invented an extraordinary method to
learn the digits of $\pi$ by counting the collisions of billiard balls. Here I
demonstrate an exact isomorphism between Galperin's bouncing billiards and
Grover's algorithm for quantum search. This provides an illuminating way to
visualize Grover's algorithm.


  We investigate the rectification of heat current carried by electrons through
a double quantum dot (DQD) system under a temperature bias. The DQD can be
realized by molecules such as suspended carbon nanotube and be described by the
Anderson-Holstein model in presence of electron-phonon interaction. Strong
electron-phonon interaction can lead to formation of polaronic states in which
electronic states are dressed by phonon cloud. Dressed tunneling approximation
(DTA), which is nonperturbative in dealing with strong electron-phonon
interaction, is employed to obtain the heat current expression. In DTA,
self-energies are dressed by phonon cloud operator and are temperature
dependent. The temperature dependency of imaginary part of dressed retarded
self-energy gives rise to the asymmetry of the system and is the necessary
condition of thermal rectification. On top of this, one can either tune DQD
effective energy levels such that $|\bar{\epsilon}_1|\neq |\bar{\epsilon}_2|$
or have asymmetric dot-lead couplings to achieve thermal rectification. We
numerically find that increasing electron-phonon coupling and reducing inter
dot coupling can both improve thermal rectification effect, while the
electronic heat current is reduced.


  Consequences of QCD current algebra formulated on a light-like hyperplane are
derived for the forward scattering of vector and axial-vector currents on an
arbitrary hadronic target. It is shown that current algebra gives rise to a
special class of sum rules that are direct consequences of the independent
chiral symmetry that exists at every point on the two-dimensional transverse
plane orthogonal to the lightlike direction. These sum rules are obtained by
exploiting the closed, infinite-dimensional algebra satisfied by the transverse
moments of null-plane axial-vector and vector charge distributions. In the
special case of a nucleon target, this procedure leads to the Adler-Weisberger,
Gerasimov-Drell-Hearn, Cabbibo-Radicatti and Fubini-Furlan-Rossetti sum rules.
Matching to the dispersion-theoretic language which is usually invoked in
deriving these sum rules, the moment sum rules are shown to be equivalent to
algebraic constraints on forward S-matrix elements in the Regge limit.


  We introduce a fully antisymmetrized treatment of three-cluster dynamics
within the ab initio framework of the no-core shell model/resonating-group
method (NCSM/RGM). Energy-independent non-local interactions among the three
nuclear fragments are obtained from realistic nucleon-nucleon interactions and
consistent ab initio many-body wave functions of the clusters. The
three-cluster Schr\"odinger equation is solved with bound-state boundary
conditions by means of the hyperspherical-harmonic method on a Lagrange mesh.
We discuss the formalism in detail and give algebraic expressions for systems
of two single nucleons plus a nucleus. Using a soft
similarity-renormalization-group evolved chiral nucleon-nucleon potential, we
apply the method to an $^4$He+$n+n$ description of $^6$He and compare the
results to experiment and to a six-body diagonalization of the Hamiltonian
performed within the harmonic-oscillator expansions of the NCSM. Differences
between the two calculations provide a measure of core ($^4$He) polarization
effects.


  Altermagnets feature vanishing net magnetization, like antiferromagnets, but
exhibit time-reversal symmetry breaking and momentum-dependent spin-split band
structures. Motivated by the prevalence of altermagnetic materials with
non-symmorphic symmetry-dictated band degeneracies, we provide realistic
minimal models for altermagnetism by constructing tight-binding models for
nonsymmorphic space groups with a sublattice defined by two magnetic atoms.
These models can be applied to monoclinic, orthorhombic, tetragonal,
rhombohedral, hexagonal, and cubic materials and can describe d-wave, g-wave,
and i-wave altermagnetism. By examining the altermagnetic susceptibility and
mean field instabilities within a Hubbard model we reveal that these models
have altermagnetic ground states and yield a Berry curvature that is linear in
the spin-orbit coupling. We apply our models to RuO$_2$, MnF$_2$, FeSb$_2$,
$\kappa$-Cl, CrSb, and MnTe.


  In this paper, we focus on Exposure Fusion (EF) [ExposFusi2] for dynamic
scenes. The task is to fuse multiple images obtained by exposure bracketing to
create an image which comprises a high level of details. Typically, such images
are not possible to obtain directly from a camera due to hardware limitations,
e.g., a limited dynamic range of the sensor. A major problem of such tasks is
that the images may not be spatially aligned due to scene motion or camera
motion. It is known that the required alignment by image registration problems
is ill-posed. In this case, the images to be aligned vary in their intensity
range, which makes the problem even more difficult.
  To address the mentioned problems, we propose an end-to-end
\emph{Convolutional Neural Network} (CNN) based approach to learn to estimate
exposure fusion from $2$ and $3$ Low Dynamic Range (LDR) images depicting
different scene contents. To the best of our knowledge, no efficient and robust
CNN-based end-to-end approach can be found in the literature for this kind of
problem. The idea is to create a dataset with perfectly aligned LDR images to
obtain ground-truth exposure fusion images. At the same time, we obtain
additional LDR images with some motion, having the same exposure fusion
ground-truth as the perfectly aligned LDR images. This way, we can train an
end-to-end CNN having misaligned LDR input images, but with a proper ground
truth exposure fusion image. We propose a specific CNN-architecture to solve
this problem. In various experiments, we show that the proposed approach yields
excellent results.


  The interactions of the natural gas (NG) network and the electricity system
are increased by using gas-fired generation units, which use NG to produce
electricity. There are various uncertainty sources such as the forced outage of
generating units or market price fluctuations that affect the economic
operation of both NG and electricity systems. This study focuses on the
steady-state formulation of the integrated NG transmission grid and electricity
system by considering the uncertainty of electricity market price based on
information gap decision theory. The higher and lower costs than the expected
cost originated from the fluctuations of electricity market price are modelled
by the robustness and opportunity functions, respectively. The objective is to
minimise the cost of zone one while satisfying the constraints of two
interdependent systems, which can obtain revenue from selling power to its
connected zones in short-term scheduling. The capability of the proposed method
is demonstrated by applying it on a 20-node NG network and IEEE RTS 24-bus. The
proposed short-term coordination between NG and electricity infrastructures is
solved and discussed.


  Bound states in the continuum (BICs) have attracted significant interest in
recent years due to their unique optical properties, such as infinite quality
factor and wave localization. In order to improve the optical performance of
BICs based devices, more degrees of freedom are required to tune BICs in
high-dimension parameter space for practical applications. To effectively tune
more BICs, we form a 2D synthetic parameter space based on a nanohole
metasurface array. Multiple symmetry protected BIC modes with high Q factors
can be achieved at high-order symmetry point. Through manipulating asymmetry
parameters, BIC lines formed by a series of BIC modes can be found in the 2D
synthetic parameter space. Moreover, the electric field distributions are
investigated to demonstrate the generation and evolution of BICs. By measuring
the absorption spectra, the tuning of multiple BICs with synthet-ic asymmetry
parameters is experimentally explored, which agrees well with theoretical
results. Therefore, our de-sign can provide new insight for a variety of
on-chip applications, such as non-linear devices, integrated nanolasing array
and high-resolution sensors for infrared molecular detection.


  We revisit the dissociation of heavy quarkonia by thermal partons at the
next-to-leading order (NLO, also known as inelastic parton scattering
dissociation) in the Quark-Gluon Plasma (QGP). Utilizing the chromo-electric
dipole coupling from QCD multipole expansion as an effective Hamiltonian, this
has been conducted in the approach of second-order quantum mechanical
perturbation theory, which allows us to systematically incorporate the bound
state wave functions. Employing the quarkonium wave functions and binding
energies obtained from an in-medium potential model, we then numerically
evaluate the dissociation cross sections and rates for various charmonia and
bottomonia, where the infrared and collinear divergences are regularized by the
thermal masses of medium partons. We demonstrate that distinct from the leading
order (LO, also known as gluo-dissociation) counterparts peaking at relatively
low gluon energy and falling off thereafter, the NLO cross sections first grow
and then nearly saturate as the incident parton energy increases, as a result
of the outgoing parton carrying away the excess energy. The resulting NLO
dissociation rates increase with temperature and take over from the LO
counterparts toward high temperatures, similar to pertinent findings from
previous studies. We also evaluate the in-medium second-order transition
between different bound states, which may contribute to the total thermal decay
widths of heavy quarkonia in the QGP.


  Photons are fundamental excitations of the electromagnetic field and can be
captured in cavities. For a given cavity with a certain size, the fundamental
mode has a fixed frequency {\it f} which gives the photons a specific "color".
The cavity also has a typical lifetime $\tau$, which results in a finite
linewidth $\delta${\it f}. If the size of the cavity is changed fast compared
to $\tau$, and so that the frequency change $\Delta${\it f} $\gg \delta${\it
f}, then it is possible to change the "color" of the captured photons. Here we
demonstrate superconducting microwave cavities, with tunable effective lengths.
The tuning is obtained by varying a Josephson inductance at one end of the
cavity. We show data on four different samples and demonstrate tuning by
several hundred linewidths in a time $\Delta t \ll \tau$. Working in the few
photon limit, we show that photons stored in the cavity at one frequency will
leak out from the cavity with the new frequency after the detuning. The
characteristics of the measured devices make them suitable for different
applications such as dynamic coupling of qubits and parametric amplification.


  The radiation from accreting X-ray pulsars was expected to be highly
polarized, with some estimates for the polarization degree of up to 80%.
However, phase-resolved and energy-resolved polarimetry of X-ray pulsars is
required in order to test different models and to shed light on the emission
processes and the geometry of the emission region. Here we present the first
results of the observations of the accreting X-ray pulsar Vela X-1 performed
with the Imaging X-ray Polarimetry Explorer (IXPE). Vela X-1 is considered to
be the archetypal example of a wind-accreting high-mass X-ray binary system,
consisting of a highly magnetized neutron star accreting matter from its
supergiant stellar companion. The spectro-polarimetric analysis of the
phase-averaged data for Vela X-1 reveals a polarization degree (PD) of
2.3$\pm$0.4% at the polarization angle (PA) of -47.3$\pm$5.4 deg. A low PD is
consistent with the results obtained for other X-ray pulsars and is likely
related to the inverse temperature structure of the neutron star atmosphere.
The energy-resolved analysis shows the PD above 5 keV reaching 6-10%, and a 90
deg difference in the PA compared to the data in the 2-3 keV range. The
phase-resolved spectro-polarimetric analysis finds a PD in the range 0-9% with
the PA varying between -80 and 40 deg.


  We study a superweakly interacting dark matter particle motivated by minimal
walking technicolor theories. Our WIMP is a mixture of a sterile state and a
state with the charges of a standard model fourth family neutrino. We show that
the model can give the right amount of dark matter over a range of the WIMP
mass and mixing angle. We compute bounds on the model parameters from the
current accelerator data including the oblique corrections to the precision
electroweak parameters, as well as from cryogenic experiments, Super-Kamiokande
and from the IceCube experiment. We show that consistent dark matter solutions
exist which satisfy all current constraints. However, almost the entire
parameter range of the model lies within the the combined reach of the next
generation experiments.


  This PhD thesis covers breakthroughs in several areas of adaptive experiment
design: (i) (Chapter 2) Novel clinical trial designs and statistical methods in
the era of precision medicine. (ii) (Chapter 3) Multi-armed bandit theory, with
applications to learning healthcare systems and clinical trials. (iii) (Chapter
4) Bandit and covariate processes, with finite and non-denumerable set of arms.
(iv) (Chapter 5) A rigorous framework for simulation-based verification of
adaptive design properties.


  Neutron(n)-capture elements (atomic number Z>30), which can be produced in
planetary nebula (PN) progenitor stars via s-process nucleosynthesis, have been
detected in nearly 100 PNe. This demonstrates that nebular spectroscopy is a
potentially powerful tool for studying the production and chemical evolution of
trans-iron elements. However, significant challenges must be addressed before
this goal can be achieved. One of the most substantial hurdles is the lack of
atomic data for n-capture elements, particularly that needed to solve for their
ionization equilibrium (and hence to convert ionic abundances to elemental
abundances). To address this need, we have computed photoionization cross
sections and radiative and dielectronic recombination rate coefficients for the
first six ions of Se and Kr. The calculations were benchmarked against
experimental photoionization cross section measurements. In addition, we
computed charge transfer (CT) rate coefficients for ions of six n-capture
elements. These efforts will enable the accurate determination of nebular Se
and Kr abundances, allowing robust investigations of s-process enrichments in
PNe.


  Random sequential adsorption (RSA) models have been studied due to their
relevance to deposition processes on surfaces. The depositing particles are
represented by hard-core extended objects; they are not allowed to overlap.
Numerical Monte Carlo studies and analytical considerations are reported for 1D
and 2D models of multilayer adsorption processes. Deposition without screening
is investigated, in certain models the density may actually increase away from
the substrate. Analytical studies of the late stage coverage behavior show the
crossover from exponential time dependence for the lattice case to the power
law behavior in the continuum deposition. 2D lattice and continuum simulations
rule out some "exact" conjectures for the jamming coverage. For the deposition
of dimers on a 1D lattice with diffusional relaxation we find that the limiting
coverage (100%) is approached according to the ~1/t**0.5 power-law preceded,
for fast diffusion, by the mean-field crossover regime with the intermediate
~1/t behavior. In case of k-mer deposition (k>3) with diffusion the void
fraction decreases according to the power-law t**[-1/(k-1)]. In the case of RSA
of lattice hard squares in 2D with diffusional relaxation the approach to the
full coverage is ~t**(-0.5).


  We propose a new method named OnePose for object pose estimation. Unlike
existing instance-level or category-level methods, OnePose does not rely on CAD
models and can handle objects in arbitrary categories without instance- or
category-specific network training. OnePose draws the idea from visual
localization and only requires a simple RGB video scan of the object to build a
sparse SfM model of the object. Then, this model is registered to new query
images with a generic feature matching network. To mitigate the slow runtime of
existing visual localization methods, we propose a new graph attention network
that directly matches 2D interest points in the query image with the 3D points
in the SfM model, resulting in efficient and robust pose estimation. Combined
with a feature-based pose tracker, OnePose is able to stably detect and track
6D poses of everyday household objects in real-time. We also collected a
large-scale dataset that consists of 450 sequences of 150 objects.


  Einstein's photo-electric effect allows us to regard electromagnetic waves as
massless particles. Then, how is the photon helicity translated into the
electric and magnetic fields perpendicular to the direction of propagation?
This is an issue of the internal space-time symmetries defined by Wigner's
little group for massless particles. It is noted that there are three
generators for the rotation group defining the spin of a particle at rest. The
closed set of commutation relations is a direct consequence of Heisenberg's
uncertainty relations. The rotation group can be generated by three two-by-two
Pauli matrices for spin-half particles. This group of two-by-two matrices is
called SU(2), with two-component spinors. The direct product of two spinors
leads to four states leading to one spin-0 state and one spin-1 state with
three sub-states. The SU(2) group can be expanded to another group of
two-by-two matrices called SL(2,c), which serves as the covering group for the
group of Lorentz transformations. In this Lorentz-covariant regime, it is
possible to Lorentz-boost the particle at rest to its infinite-momentum or
massless state. Also in this SL(2,c) regime, there are four spin states for
each particle, as in the case of the Dirac equation. The direct product of two
SL(2,c) spinors thus leads sixteen states. Among them, four of them can be used
for the electromagnetic four-potential, and six for the Maxwell tensor. The
gauge degree of freedom is shown to be a Lorentz-boosted rotation. The
polarization of massless neutrinos is interpreted as a consequence of the gauge
invariance.


  Local differential privacy (LDP) provides a way for an untrusted data
collector to aggregate users' data without violating their privacy. Various
privacy-preserving data analysis tasks have been studied under the protection
of LDP, such as frequency estimation, frequent itemset mining, and machine
learning. Despite its privacy-preserving properties, recent research has
demonstrated the vulnerability of certain LDP protocols to data poisoning
attacks. However, existing data poisoning attacks are focused on basic
statistics under LDP, such as frequency estimation and mean/variance
estimation. As an important data analysis task, the security of LDP frequent
itemset mining has yet to be thoroughly examined. In this paper, we aim to
address this issue by presenting novel and practical data poisoning attacks
against LDP frequent itemset mining protocols. By introducing a unified attack
framework with composable attack operations, our data poisoning attack can
successfully manipulate the state-of-the-art LDP frequent itemset mining
protocols and has the potential to be adapted to other protocols with similar
structures. We conduct extensive experiments on three datasets to compare the
proposed attack with four baseline attacks. The results demonstrate the
severity of the threat and the effectiveness of the proposed attack.


  It is well understood that many-body systems driven at high frequency heat up
only exponentially slowly and exhibit a long prethermalization regime. We prove
rigorously that a certain relevant class of systems heat very slowly under weak
periodic driving at intermediate frequency as well. This class of systems are
those whose time-dependent, possibly translation-invariant, Hamiltonian is a
weak perturbation of a sum of mutually commuting terms. This condition covers
several periodically kicked systems that have been considered in the literature
recently, in particular kicked Ising models. In contrast to the high-frequency
regime, the prethermalization dynamics of our systems is in general not related
to any time-independent effective Floquet Hamiltonian. Our results also have
non-trivial implications for closed (time-independent) systems. We use the
example of an Ising model with transversal and longitudinal field to show how
they imply confinement of excitations. More generally, they show how "glassy"
kinetically constrained models emerge naturally from simple many-body
Hamiltonians, thus connecting to the topic of 'translation-invariant
localization'.


  How does Fermi surface develop in cuprates upon doping of a parent Mott
insulator, does it consist of large barrels or small pockets, which of them is
responsible for superconductivity and what is a role of the pseudogap? Those
are actively debated questions, important for understanding of high temperature
superconductivity. Here we analyze doping dependence of interlayer tunneling in
cuprates. We observe that with decreasing doping the supercurrent is rapidly
decreasing, but the quasiparticle resistance at high bias remains almost
unchanged. This indicates that Cooper pair and quasiparticle currents originate
from different parts of Brillouin zone: Cooper pairs are residing only on small
pockets, which are progressively shrinking with decreasing doping, but the
quasiparticle current is integrated over the full length of barrels, which are
only weakly doping dependent. The expanding pseudogap areas along the barrels
do not contribute to pair current. This provides direct evidence for
nonsuperconducting origin of the pseudogap.


  We present the results of a photometric study of 85 objects from the updated
sample of galaxies residing in the nearby Lynx--Cancer void. We perform our
photometry on u, g, r, and i-band images of the Sloan Digital Sky Survey. We
determine model-independent galaxy parameters such as the integrated magnitudes
and colors, effective radii and the corresponding surface brightness values,
optical radii and Holmberg radii. We analyze the radial surface brightness
profiles to determine the central brightness values and scale lengths of the
model discs. We analyze the colors of the outer parts of the galaxies and
compare them with model evolutionary tracks computed using the PEGASE2 software
package. This allowed us to estimate the time T_SF elapsed since the onset of
star formation, which turned out to be on the order of the cosmological time
T_0 for the overwhelming majority of the galaxies studied. However, for 13
galaxies of the sample the time T_SF does not exceed T_0/2 ~ 7 Gyr, and for 7
of them T_SF < 3.5 Gyr. The latter are mostly unevolved objects dominated by
low-luminosity galaxies with M_B > -13.2. We use the integrated magnitudes and
colors to estimate the stellar masses of the galaxies. We estimate the
parameter M(HI)/L_B and the gas mass fractions for void galaxies with known
HI-line fluxes. A small subgroup (about 10%) of the gas-richest void galaxies
with M(HI)/L_B > 2.5 has gas mass fractions that reach 94-99%. The outer
regions of many of these galaxies show atypically blue colors. To test various
statistical differences between void galaxies and galaxies from the samples
selected using more general criteria, we compare some of the parameters of void
galaxies with similar data for the sample of 195 galaxies from the Equatorial
Survey (ES) based on a part of the HIPASS blind HI survey. abridged


  Motivated by the standard form of string-theory amplitude, we calculate the
field-theory amplitude to complete the higher-derivative terms in type II
supergravity theories in their conventional form. We derive explicitly the $
O(\alpha'^3) $ interactions for the RR (Ramond-Ramond) fields with graviton,
B-field and dilaton in the low-energy effective action of type II superstrings.
We check our results by comparison with previous works that have been done by
the other methods, and find an exact agreement.


  We study spherically symmetric timelike thin-shells in $3+1-$dimensional bulk
spacetime with a variable equation of state for the fluid presented on the
shell. In such a fluid the angular pressure $p$ is a function of both surface
energy density $\sigma $ and the radius $R$ of the thin-shell. Explicit cases
of the thin shells connecting two non-identical cloud of strings spacetimes and
a flat Minkowski spacetime to the Schwarzschild metric are investigated.


  A comparison of ROSAT observations with simultaneous BATSE monitoring data
shows a different intensity evolution in the soft and hard X-ray band of GRS
1915+105 since 1992. In addition, fits of simultaneous ROSAT/BATSE spectra
require more than one spectral component. A short description of results of
RXTE pointed observations of GRS 1915+105 since April 1996 is also presented.


  We propose a simple approach to investigate the structural relaxation time
and glass transition of amorphous drugs. Amorphous materials are modeled as a
set of equal sized hard spheres. The structural relaxation time over many
decades in hard sphere fluids is theoretically calculated using the Elastically
Collective Nonlinear Langevin Equation theory associated with Kramer's theory.
Then, a new thermal mapping from a real material to an effective hard sphere
fluid provides temperature-dependent relaxation time, which can compare to
experiments. Numerical results quantitatively agree with previous experiments
for pharmaceutical binary mixtures having different weight ratios. We carry out
experiments to test our calculations for an ezetimibe-simvastatin-Kollidon VA64
mixture. Our approach would provide a simple but comprehensive description of
glassy dynamics in amorphous composites.


  The Galactic center excess (GCE) remains one of the most intriguing
discoveries from the Fermi Large Area Telescope (LAT) observations. We revisit
the characteristics of the GCE by first producing a new set of high-resolution
galactic diffuse gamma-ray emission templates, which are ultimately due to
cosmic-ray interactions with the interstellar medium. Using multi-messenger
observations we constrain the properties of the galactic diffuse emission. The
broad properties of the GCE that we find in this work are qualitatively
unchanged despite the introduction of this new set of templates, though its
quantitative features appear mildly different than those obtained in previous
analyses. In particular, we find a high-energy tail at higher significance than
previously reported. This tail is very prominent in the northern hemisphere,
and less so in the southern hemisphere. This strongly affects one prominent
interpretation of the excess: known millisecond pulsars are incapable of
producing this high-energy emission, even in the relatively softer southern
hemisphere, and are therefore disfavored as the sole explanation of the GCE.
The annihilation of dark matter particles of mass $40^{+10}_{-7}$ GeV (95$\%$
CL) to $b$ quarks with a cross-section of $\sigma v = 1.4^{+0.6}_{-0.3} \times
10^{-26}$ cm$^{3}$s$^{-1}$ provides a good fit to the excess especially in the
relatively cleaner southern sky. Dark matter of the same mass range
annihilating to $b$ quarks or heavier dark matter particles annihilating to
heavier Standard Model bosons can combine with millisecond pulsars to provide a
good fit to the southern hemisphere emission. As part of this paper, we make
publicly available all of our templates and the data covariance matrix we have
generated to account for systematic uncertainties.[abridged]


  The total and spectral irradiance varies over short time scales, i.e. from
days to months, and longer time scales from years to decades, centuries, and
beyond. In this talk we review the current understanding of irradiance changes
from days to decades. We present the current status of observations and discuss
proposed reconstruction approaches to understand these variations. The main
question that ultimately needs to be answered is what are the physical
processes that could explain the enhanced heating of the photosphere,
chromosphere, transition region, and corona, leading to a change in the solar
radiative output at various wavelengths. As semi-empirical models allow us to
reproduce the solar spectrum over a broad wavelength range, they offer a
powerful tool to determine the energy necessary to heat certain layers and at
the same time balance the radiative losses.


  We present a comprehensive X-ray spectroscopy and imaging study of supernova
remnant W49B using archival XMM-Newton observations. The overionization state
of the shocked ejecta in W49B is clearly indicated by the radiative
recombination continua of Si XIV, S XV, and Fe XXV, combined with the
Ly$\alpha$ lines of Ca and Fe. The line flux images of W49B indicate high
emission measures of the central bar-like region for almost all the emission
lines, while the equivalent width maps reveal a stratified structure for the
metal abundance distributions. The global spectrum of W49B is well reproduced
by a model containing one collisional ionization equilibrium (CIE) plasma
component and two recombining plasma (RP) components. The CIE plasma represents
the shocked interstellar medium, which dominates the X-ray emitting volume in
W49B with a mass $\sim450M_\odot$. The two RP components with a total mass
$\sim4.6M_\odot$ are both dominated by the ejecta material, but characterized
by different electron temperatures ($\sim1.60$ keV and $\sim0.64$ keV). The
recombination ages of the RP components are estimated as $\sim6000$ yr and
$\sim3400$ yr, respectively. We then reveal the possibility of a thermal
conduction origin for the high-temperature RP in W49B by calculating the
conduction timescale. The metal abundance ratios of the ejecta in W49B are
roughly consistent with a core-collapse explosion model with a
$\lesssim15M_\odot$ progenitor, except for a rather high Mn/Fe. A Type Ia
origin can explain the Mn abundance, while it predicts much higher ejecta
masses than observed values for all the metal species considered in our
analysis.


  The destruction of Fermi liquid behavior when a gapless Fermi surface is
coupled to a fluctuating gapless boson field is studied theoretically. This
problem arises in a number of different contexts in quantum many body physics.
Examples include fermions coupled to a fluctuating transverse gauge field
pertinent to quantum spin liquid Mott insulators, and quantum critical metals
near a Pomeranchuk transition. We develop a new controlled theoretical approach
to determining the low energy physics. Our approach relies on combining an
expansion in the inverse number (N) of fermion species with a further expansion
in the parameter \epsilon = z_b -2 where z_b is the dynamical critical exponent
of the boson field. We show how this limit allows a systematic calculation of
the universal low energy physics of these problems. The method is illustrated
by studying spinon fermi surface spin liquids, and a quantum critical metal at
a second order electronic nematic phase transition. We calculate the low energy
single particle spectra, and various interesting two particle correlation
functions. In some cases deviations from the popular Random Phase Approximation
results are found. Some of the same universal singularities are also calculated
to leading non-vanishing order using a perturbative renormalization group
calculation at small N extending previous results of Nayak and Wilczek.
Implications for quantum spin liquids, and for Pomeranchuk transitions are
discussed. For quantum critical metals at a nematic transition we show that the
tunneling density of states has a power law suppression at low energies.


  We are concerned with the two-dimensional steady supersonic reacting Euler
flow past Lipschitz bending walls that are small perturbations of a convex one,
and establish the existence of global entropy solutions when the total
variation of both the initial data and the slope of the boundary is
sufficiently small. The flow is governed by an ideal polytropic gas and
undergoes a one-step exothermic chemical reaction under the reaction rate
function that is Lipschtiz and has a positive lower bound. The heat released by
the reaction may cause the total variation of the solution to increase along
the flow direction. We employ the modified wave-front tracking scheme to
construct approximate solutions and develop a Glimm-type functional by
incorporating the approximate strong rarefaction waves and Lipschitz bending
walls to obtain the uniform bound on the total variation of the approximate
solutions. Then we employ this bound to prove the convergence of the
approximate solutions to a global entropy solution that contains a strong
rarefaction wave generated by the Lipschitz bending wall. In addition, the
asymptotic behavior of the entropy solution in the flow direction is also
analyzed.


  The Minority Game framework was recently generalized to account for the
possibility that agents adapt not only through strategy selection but also by
diversifying their response according to the kind of dynamical regime, or the
risk, they perceive. Here we study the effects of this mechanism in different
information structures. We show that both the stationary macroscopic properties
and the dynamical features depend strongly on whether the information supplied
to the system is exogenous (`random') or endogenous (`real'). In particular, in
the latter case one observes that a small amount of herding tendency suffices
to alter the collective behavior dramatically. In such cases, the dynamics is
characterized by the creation and destruction of trends, accompanied by
intermittent features like volatility clustering.


  The two-frequency problem of synchronization of the pulse train of a
passively mode locked soliton laser to an externally injected pulse train is
solved in the weak injection regime. The source and target frequency combs are
distinguished by the spacing and offset frequency mismatches. Locking diagrams
map the domain in the mismatch parameter space where stable locking of the
combs is possible. We analyze the dependence of the locking behavior on the
relative frequency and chirp of the source and target pulses, and the
conditions where the relative offset frequency has to be actively stabilized.
Locked steady states are characterized by a fixed source-target time and phase
shifts that map the locking domain.


  Let $R$ be the polydisc algebra or the Wiener algebra. It is shown that the
group $SL_n(R)$ is generated by the subgroup of elementary matrices with all
diagonal entries $1$ and at most one nonzero off-diagonal entry. The result an
easy consequence of the deep result due to Ivarsson and Kutzschebauch (Ann. of
Math. 2012).


  In this paper, we explore ordinal classification (in the context of deep
neural networks) through a simple modification of the squared error loss which
not only allows it to not only be sensitive to class ordering, but also allows
the possibility of having a discrete probability distribution over the classes.
Our formulation is based on the use of a softmax hidden layer, which has
received relatively little attention in the literature. We empirically evaluate
its performance on the Kaggle diabetic retinopathy dataset, an ordinal and
high-resolution dataset and show that it outperforms all of the baselines
employed.