  I review basic principles of the quantum mechanical measurement process in
view of their implications for a quantum theory of general relativity. It turns
out that a clock as an external classical device associated with the observer
plays an essential role. This leads me to postulate a ``principle of the
integrity of the observer''. It essentially requires the observer to be part of
a classical domain connected throughout the measurement process. Mathematically
this naturally leads to a formulation of quantum mechanics as a kind of
topological quantum field theory. Significantly, quantities with a direct
interpretation in terms of a measurement process are associated only with
amplitudes for connected boundaries of compact regions of space-time. I discuss
some implications of my proposal such as in-out duality for states,
delocalization of the ``collapse of the wave function'' and locality of the
description. Differences to existing approaches to quantum gravity are also
highlighted.


  We present some classification results for quasitoric manifolds (M) with
(p_1(M)=-\sum a_i^2) for some (a_i\in H^2(M)) which admit an action of a
compact connected Lie-group (G) such that (\dim M/G \leq 1). In contrast to
Kuroki's work we do not require that the action of (G) extends the torus action
on (M).


  In calculations of isoscalar magnetic moments of odd-odd N=Z nuclei it was
found that for medium to heavy mass nuclei large scale shell model calculations
yielded results which were very close to much simpler single j shell ones. To
understand this we compare isoscalar and isovector configuration mixing in
first order perturbation theory using a spin dependant delata interaction.The
isoscalar corrections are much smaller


  Angular dependence of gap, seen in photoemission, its evolution with doping
and temperature are interpreted on base t-t'-U Hubbard model in which a
pseudogap is a working function for electrons removing from dielectric segments
of zone boundary. Tunnel spectra in one-particle approximation display only
superconducting gap and too large asymmetry in regions aside from optimal
doping. Spectral functions confirm sharp well defined Fermi boundary at
$k_x=k_y$ direction and smoothed destructed one at the $\G(0,0)-M(\pi,0)-Y(\pi
,\pi)$ path. Both tunnel and ARPES data seem require spreading a model to
bilayer ones.


  In this paper we employ a "direct method" in order to obtain rank-k solutions
of any hyperbolic system of first order quasilinear differential equations in
many dimensions. We discuss in detail the necessary and sufficient conditions
for existence of these type of solutions written in terms of Riemann
invariants. The most important characteristic of this approach is the
introduction of specific first order side conditions consistent with the
original system of PDEs, leading to a generalization of the Riemann invariant
method of solving multi-dimensional systems of PDEs. We have demonstrated the
usefulness of our approach through several examples of hydrodynamic type
systems; new classes of solutions have been obtained in a closed form.


  The Na\"ive Mean Field (NMF) approximation is widely employed in modern
Machine Learning due to the huge computational gains it bestows on the
statistician. Despite its popularity in practice, theoretical guarantees for
high-dimensional problems are only available under strong structural
assumptions (e.g., sparsity). Moreover, existing theory often does not explain
empirical observations noted in the existing literature.
  In this paper, we take a step towards addressing these problems by deriving
sharp asymptotic characterizations for the NMF approximation in
high-dimensional linear regression. Our results apply to a wide class of
natural priors and allow for model mismatch (i.e., the underlying statistical
model can be different from the fitted model). We work under an \textit{iid}
Gaussian design and the proportional asymptotic regime, where the number of
features and the number of observations grow at a proportional rate. As a
consequence of our asymptotic characterization, we establish two concrete
corollaries: (a) we establish the inaccuracy of the NMF approximation for the
log-normalizing constant in this regime, and (b) we provide theoretical results
backing the empirical observation that the NMF approximation can be
overconfident in terms of uncertainty quantification.
  Our results utilize recent advances in the theory of Gaussian comparison
inequalities. To the best of our knowledge, this is the first application of
these ideas to the analysis of Bayesian variational inference problems. Our
theoretical results are corroborated by numerical experiments. Lastly, we
believe our results can be generalized to non-Gaussian designs and provide
empirical evidence to support it.


  During the core collapse of massive stars that do not undergo a canonical
energetic explosion, some of the hydrogen envelope of a red supergiant (RSG)
progenitor may infall onto the newborn black hole (BH). Within the Athena++
framework, we perform three-dimensional, hydrodynamical simulations of
idealized models of supergiant convection and collapse in order to assess
whether the infall of the convective envelope can give rise to
rotationally-supported material, even if the star has zero angular momentum
overall. Our dimensionless, polytropic models are applicable to the
optically-thick hydrogen envelope of non-rotating RSGs and cover a factor of 20
in stellar radius. At all radii, the specific angular momentum due to random
convective flows implies associated circularization radii of 10 - 1500 times
the innermost stable circular orbit of the BH. During collapse, the angular
momentum vector of the convective flows is approximately conserved and is
slowly varying on the timescale relevant to forming disks at small radii. Our
results indicate that otherwise failed explosions of RSGs lead to the formation
of rotationally-supported flows that are capable of driving outflows to large
radii and powering observable transients. When the BH is able to accrete most
of the hydrogen envelope, the final BH spin parameter is $\sim$ 0.5, even
though the star is non-rotating. For fractional accretion of the envelope, the
spin parameter is generally lower and never exceeds 0.8. We discuss the
implications of our results for transients produced by RSG collapse to a black
hole.


  Improving sample-efficiency and safety are crucial challenges when deploying
reinforcement learning in high-stakes real world applications. We propose
LAMBDA, a novel model-based approach for policy optimization in safety critical
tasks modeled via constrained Markov decision processes. Our approach utilizes
Bayesian world models, and harnesses the resulting uncertainty to maximize
optimistic upper bounds on the task objective, as well as pessimistic upper
bounds on the safety constraints. We demonstrate LAMBDA's state of the art
performance on the Safety-Gym benchmark suite in terms of sample efficiency and
constraint violation.


  External or internal shocks may lead to the collapse of a system consisting
of many agents. If the shock hits only one agent initially and causes it to
fail, this can induce a cascade of failures among neighoring agents. Several
critical constellations determine whether this cascade remains finite or
reaches the size of the system, i.e. leads to systemic risk. We investigate the
critical parameters for such cascades in a simple model, where agents are
characterized by an individual threshold \theta_i determining their capacity to
handle a load \alpha\theta_i with 1-\alpha being their safety margin. If agents
fail, they redistribute their load equally to K neighboring agents in a regular
network. For three different threshold distributions P(\theta), we derive
analytical results for the size of the cascade, X(t), which is regarded as a
measure of systemic risk, and the time when it stops. We focus on two different
regimes, (i) EEE, an external extreme event where the size of the shock is of
the order of the total capacity of the network, and (ii) RIE, a random internal
event where the size of the shock is of the order of the capacity of an agent.
We find that even for large extreme events that exceed the capacity of the
network finite cascades are still possible, if a power-law threshold
distribution is assumed. On the other hand, even small random fluctuations may
lead to full cascades if critical conditions are met. Most importantly, we
demonstrate that the size of the "big" shock is not the problem, as the
systemic risk only varies slightly for changes of 10 to 50 percent of the
external shock. Systemic risk depends much more on ingredients such as the
network topology, the safety margin and the threshold distribution, which gives
hints on how to reduce systemic risk.


  We consider a PT-symmetric Fermi gas with an exceptional point, representing
the critical point between PT-symmetric and symmetry broken phases. The low
energy spectrum remains linear in momentum and is identical to that of a
hermitian Fermi gas. The fermionic Green's function decays in a power law
fashion for large distances, as expected from gapless excitations, albeit the
exponent is reduced from $-1$ due to the quantum Zeno effect. In spite of the
gapless nature of the excitations, the ground state entanglement entropy
saturates to a finite value, independent of the subsystem size due to the
non-hermitian correlation length intrinsic to the system. Attractive or
repulsive interaction drives the system into the PT-symmetry broken regime or
opens up a gap and protects PT-symmetry, respectively. Our results challenge
the concept of universality in non-hermitian systems, where quantum criticality
can be masked due to non-hermiticity.


  We give an algorithm that given a graph $G$ with $n$ vertices and $m$ edges
and an integer $k$, in time $O_k(n^{1+o(1)}) + O(m)$ either outputs a rank
decomposition of $G$ of width at most $k$ or determines that the rankwidth of
$G$ is larger than $k$; the $O_k(\cdot)$-notation hides factors depending on
$k$. Our algorithm returns also a $(2^{k+1}-1)$-expression for cliquewidth,
yielding a $(2^{k+1}-1)$-approximation algorithm for cliquewidth with the same
running time. This improves upon the $O_k(n^2)$ time algorithm of Fomin and
Korhonen [STOC 2022].
  The main ingredient of our algorithm is a fully dynamic algorithm for
maintaining rank decompositions of bounded width: We give a data structure that
for a dynamic $n$-vertex graph $G$ that is updated by edge insertions and
deletions maintains a rank decomposition of $G$ of width at most $4k$ under the
promise that the rankwidth of $G$ never grows above $k$. The amortized running
time of each update is $O_k(2^{\sqrt{\log n} \log \log n})$. The data structure
furthermore can maintain whether $G$ satisfies some fixed ${\sf CMSO}_1$
property within the same running time. We also give a framework for performing
``dense'' edge updates inside a given set of vertices $X$, where the new edges
inside $X$ are described by a given ${\sf CMSO}_1$ sentence and vertex labels,
in amortized $O_k(|X| \cdot 2^{\sqrt{\log n} \log \log n})$ time. Our dynamic
algorithm generalizes the dynamic treewidth algorithm of Korhonen, Majewski,
Nadara, Pilipczuk, and Soko{\l}owski [FOCS 2023].


  In this chapter, I review the main methods and techniques of complex systems
science. As a first step, I distinguish among the broad patterns which recur
across complex systems, the topics complex systems science commonly studies,
the tools employed, and the foundational science of complex systems. The focus
of this chapter is overwhelmingly on the third heading, that of tools. These in
turn divide, roughly, into tools for analyzing data, tools for constructing and
evaluating models, and tools for measuring complexity. I discuss the principles
of statistical learning and model selection; time series analysis; cellular
automata; agent-based models; the evaluation of complex-systems models;
information theory; and ways of measuring complexity. Throughout, I give only
rough outlines of techniques, so that readers, confronted with new problems,
will have a sense of which ones might be suitable, and which ones definitely
are not.


  The space of n (ordered) points on the projective line, modulo automorphisms
of the line, is one of the most important and classical examples of an
invariant theory quotient, and is one of the first examples given in any
course. Generators for the ring of invariants have been known since the end of
the nineteenth century, but the question of the relations has remained
surprisingly open, and it was not even known that the relations have bounded
degree. We show that the ideal of relations is generated in degree at most
four, and give an explicit description of the generators. The result holds for
arbitrary weighting of the points. If all the weights are even (e.g. in the
case of equal weight for odd n), we show that the ideal of relations is
generated by quadrics. The proof is by degenerating the moduli space to a toric
variety, and following an enlarged set of generators through this degeneration.


  Here we propose an isotropic all electrical spin analyzer in a quantum ring
with spin-orbit coupling by analytically and numerically modeling how the
charge transmission rates depend on the polarization of the incident spin. The
formalism of spin transmission and polarization rates in an arbitrary direction
is also developed by analyzing the Aharonov-Bohm and the Aharonov-Casher
effects. The topological spin texture induced by the spin-orbit couplings
essentially contributes to the dynamic phase and plays an important role in
spin transport. The spin transport features derived analytically has been
confirmed numerically. This interesting two-dimensional electron system can be
designed as a spin filter, spin polarizer and general analyzer by simply tuning
the spin-orbit couplings, which paves the way for realizing the tunable and
integrable spintronics device.


  We first explain our joint work with Dirk Kreimer on the Hopf and Lie
algebras of Feynman graphs. The conceptual meaning of the concrete computations
of perturbative renormalisation is obtained from the Birkhoff decomposition in
the Riemann-Hilbert problem. The relation of the Hopf algebra of graphs with
the group of formal diffeomorphisms of complexified coupling constants allows
for a geometric interpretation of the renormalisation procedure. We then
discuss the relation between the above occurrence of the Riemann-Hilbert
problem, the interpretation of the renormalisation group as a group of
ambiguity of physical theories and the still mysterious Galois theory that
should account at Archimedian places for the connected component of identity in
the Idele class group of class field theory. This paper is the content of a
talk given in the memory of Louis Michel in January 2001, and has appeared as
such in the Poincare seminar of October 2002 in Paris.


  The paper considers the Ricci flow, coupled with the harmonic map flow
between two manifolds. We derive estimates for the fundamental solution of the
corresponding conjugate heat equation and we prove an analog of Perelman's
differential Harnack inequality. As an application, we find a connection
between the entropy functional and the best constant in the Sobolev imbedding
theorem in $\mathbb{R}^n$.


  Proliferating cell populations at steady state growth often exhibit broad
protein distributions with exponential tails. The sources of this variation and
its universality are of much theoretical interest. Here we address the problem
by asymptotic analysis of the Population Balance Equation. We show that the
steady state distribution tail is determined by a combination of protein
production and cell division and is insensitive to other model details. Under
general conditions this tail is exponential with a dependence on parameters
consistent with experiment. We discuss the conditions for this effect to be
dominant over other sources of variation and the relation to experiments.


  We introduce a covariant finite regulator for N = 4 super Yang-Mills theory
on S^4. Our formulation is based on holomorphic Chern-Simons theory on twistor
space. By switching on a large background flux, the twistor space dissolves
into a fuzzy geometry, with a finite number of points. The large N continuum
limit of the matrix model naturally approaches ordinary N = 4 SYM. We comment
on the relation between our model and the 4D quantum Hall effect.


  By acquiring two sets of tomographic measurements at distinct X-ray spectra,
the dual-energy CT (DECT) enables quantitative material-specific imaging.
However, the conventionally decomposed material basis images may encounter
severe image noise amplification and artifacts, resulting in degraded image
quality and decreased quantitative accuracy. Iterative DECT image
reconstruction algorithms incorporating either the sinogram or the CT image
prior information have shown potential advantages in noise and artifact
suppression, but with the expense of large computational resource, prolonged
reconstruction time, and tedious manual selections of algorithm parameters. To
partially overcome these limitations, we develop a domain-transformation
enabled end-to-end deep convolutional neural network (DIRECT-Net) to perform
high quality DECT material decomposition. Specifically, the proposed DIRECT-Net
has immediate accesses to mutual-domain data, and utilizes stacked convolution
neural network (CNN) layers for noise reduction and material decomposition. The
training data are numerically simulated based on the underlying physics of DECT
imaging.The XCAT digital phantom, iodine solutions phantom, and biological
specimen are used to validate the performance of DIRECT-Net. The qualitative
and quantitative results demonstrate that this newly developed DIRECT-Net is
promising in suppressing noise, improving image accuracy, and reducing
computation time for future DECT imaging.


  Modern autonomous systems, such as flying, legged, and wheeled robots, are
generally characterized by high-dimensional nonlinear dynamics, which presents
challenges for model-based safety-critical control design. Motivated by the
success of reduced-order models in robotics, this paper presents a tutorial on
constructive safety-critical control via reduced-order models and control
barrier functions (CBFs). To this end, we provide a unified formulation of
techniques in the literature that share a common foundation of constructing
CBFs for complex systems from CBFs for much simpler systems. Such ideas are
illustrated through formal results, simple numerical examples, and case studies
of real-world systems to which these techniques have been experimentally
applied.


  Previous studies have shown that the Hidden Local Symmetry (HLS) Model,
supplied with appropriate symmetry breaking mechanisms, provides an Effective
Lagrangian (BHLS) which encompasses a large number of processes within a
unified framework; a global fit procedure allows for a simultaneous description
of the e+ e- annihilation into the 6 final states $\pi^+ \pi^-$, $\pi^0
\gamma$, $\eta \gamma$, $\pi^+ \pi^- \pi^0$, $K^+ K^-$, $K_l K_s$ and includes
the dipion spectrum in the {\tau} decay and some more light meson decay partial
widths. The contribution to the muon anomalous magnetic moment $a_{th}$ of
these annihilation channels over the range of validity of the HLS model (up to
1.05 GeV) is found much improved compared to its partner derived from
integrating the measured spectra directly. However, most spectra for the
process $e^+ e^- \to \pi^+ \pi^-$ undergo overall scale uncertainties which
dominate the other sources, and one may suspect some bias in the dipion
contribution to $a_{th}$. However, an iterated fit algorithm, shown to lead to
unbiased results by a Monte Carlo study, is defined and applied succesfully to
the $e^+ e^- \to \pi^+ \pi^-$ data samples from CMD2, SND, KLOE, BaBar and
BESSIII. The iterated fit solution is shown to be further improved and leads to
a value for $a_{\mu}$ different from $a_{exp}$ above the 4 $\sigma$ level. The
contribution of the $\pi^+ \pi^-$ intermediate state up to 1.05 GeV to $a_{th}$
derived from the iterated fit benefits from an uncertainty about 3 times
smaller than the corresponding usual estimate. Therefore, global fit techniques
are shown to work and lead to improved unbiased results.


  In this work we have considered a minimal extension of Standard Model by a
local $U(1)$ gauge group in order to accommodate a stable (fermionic) Dark
Matter (DM) candidate. We have focussed on parameter regions where DM possesses
adequate self interaction, owing to the presence of a light scalar mediator
(the dark Higgs), alleviating some of the tensions in the small-scale
structures. We have studied the scenario in the light of a variety of data,
mostly from dark matter direct searches, collider searches and flavour physics
experiments, with an attempt to constrain the interactions of the standard
model (SM) particles with the ones in the Dark Sector (DS). Assuming a small
gauge kinetic mixing parameter, we find that for rather heavy DM %$\gtrsim
\mathcal{O}(1-10)\,\, {\rm GeV}$%, the most stringent bound on the mixing angle
of the Dark Higgs with the SM Higgs boson comes from dark matter direct
detection experiments, while for lighter DM, LHC constraints become more
relevant. Note that, due to the presence of very light mediators the usual
realisation of direct detection constraints in terms of momentum independent
cross sections had to be reevaluated for our scenario. In addition, we find
that the smallness of the relevant portal couplings, as dictated by data,
critically suppress the viability of DM production by the standard "freeze-out"
mechanism in such simplified scenarios. In particular, the viable DM masses are
$\lesssim \mathcal{O}(2)$ GeV $i.e.$ in the regions where direct detection
limits tend to become weak. For heavier DM with large self-interactions, we
hence conclude that non-thermal production mechanisms are favoured. Lastly,
future collider reach of such a simplified scenario has also been studied in
detail.


  As one of the most important types of (weaker) supervised information in
machine learning and pattern recognition, pairwise constraint, which specifies
whether a pair of data points occur together, has recently received significant
attention, especially the problem of pairwise constraint propagation. At least
two reasons account for this trend: the first is that compared to the data
label, pairwise constraints are more general and easily to collect, and the
second is that since the available pairwise constraints are usually limited,
the constraint propagation problem is thus important.
  This paper provides an up-to-date critical survey of pairwise constraint
propagation research. There are two underlying motivations for us to write this
survey paper: the first is to provide an up-to-date review of the existing
literature, and the second is to offer some insights into the studies of
pairwise constraint propagation. To provide a comprehensive survey, we not only
categorize existing propagation techniques but also present detailed
descriptions of representative methods within each category.


  In this work, we present the GPU implementation of the overrelaxation and
steepest descent method with Fourier acceleration methods for Laudau and
Coulomb gauge fixing using CUDA for SU(N) with N>2. A multi-GPU implementation
of the overrelaxation method is also presented using MPI and CUDA. The GPU
performance was measured on BlueWaters and compared against the gauge fixing of
the CPU MILC code.


  The model of the bosonic string with the noncommutative world-sheet geometry
is proposed in the framework of Fedosov's deformation quantization. The
re-interpretation of the model in terms of bosonic string coupled to infinite
multiplet of background fields is given and the link to the W-symmetry is
discussed. For the case of d=4 Euclidean target space, the stringy counterparts
of the Yang-Mills instantons are constructed in both commutative and
noncommutative regimes.


  Muon spin spectroscopy ($\mu$SR) is a powerful local probe technique e.g.
used for the investigation of exotic frustrated magnetism. Ab initio
simulations using Density Functional Theory with the muon treated as a
point-like defect (DFT+$\mu$) are commonly employed to determine the
interstitial lattice positions where the muon comes to rest after implantation.
These muon stopping sites are critical for accurately interpreting $\mu$SR
data. For example, for the quantum spin liquid candidate Zn-Barlowite,
DFT+$\mu$ simulations identify two types of muon stopping sites: a
higher-energy site where the muon is located between a fluorine and a bromine
atom and three similar sites near an OH group. However, our study shows that
the $\mu$SR spectra of Zn-Barlowite cannot be adequately described using muon
sites determined by the conventional DFT+$\mu$ approach. Instead, accurate
reproduction of the $\mu$SR data requires treating the muon as a spatially
extended quantum particle with a skewed wavefunction due to the anharmonicity
of the surrounding electrostatic potential. The quantum nature of the muon
significantly affects its lattice position and, consequently, the observed
$\mu$SR spectra. Our findings highlight the potential of $\mu$SR to study the
localization of quantum particles, using the muon as the probe and particle
under investigation. The light mass of the muon amplifies quantum effects,
enhancing the sensitivity of our measurements and enabling a detailed
comparison between experimental data and theoretical calculations. These
results can be directly applied to the theoretical calculations of hydrogen
localization, where quantum effects, though smaller, may still be relevant in
real materials.


  Associated to the standard $SU_{q}(n)$ R-matrices, we introduce quantum
spheres $S_{q}^{2n-1}$, projective quantum spaces $CP_{q}^{n-1}$, and quantum
Grassmann manifolds $G_{k}(C_{q}^{n})$. These algebras are shown to be
homogeneous quantum spaces of standard quantum groups and are also quantum
principle bundles in the sense of T Brzezinski and S. Majid (Comm. Math. Phys.
157,591 (1993)).


  By using the spectrum of the underlying symmetric diffusion operator, the
convergence in $L^p$-Wasserstein distance $\mathbb W_p (p\ge 1)$ is
characterized for the empirical measure $\mu_t$ of non-symmetric subordinated
diffusion processes in an abstract framework. The main results are applied to
the subordinations of several typical models, which include the (reflecting)
diffusion processes on compact manifolds, the conditional diffusion processes,
the Wright-Fisher diffusion process, and hypoelliptic diffusion processes on
{\bf SU}(2). In particular, for the (reflecting) diffusion processes on a
compact Riemannian manifold with invariant probability measure $\mu$:
  (1) the sharp limit of $t\mathbb W_2(\mu_t,\mu)^2$ is derived in $L^q(\mathbb
P)$ for concrete $q\ge 1,$ which provides a precise characterization on the
physical observation that a divergence-free perturbation accelerates the
convergence in $\mathbb W_2$;
  (2) the sharp convergence rates are presented for $(\mathbb E[\mathbb
W_{2p}(\mu_t,\mu)^{q}])^{\frac 1 q} (p,q\ge 1)$, where a critical phenomenon
appears with the critical rate $t^{-1}\log t$ as $t\to\infty$.


  We suggest a method for calculating electronic spectra in ordered and
disordered semiconductor structures (superlattices) forming double quantum
wells (QW). In our method, we represent the solution of Schr\"odinger equation
for QW potential with the help of the solution of the corresponding diffusion
equation. This is because the diffusion is the mechanism, which is primarily
responsible for amorphization (disordering) of the QW structure, leading to
so-called interface mixing. We show that the electron spectrum in such a
structure depends on the shape of the quantum well, which, in turn, corresponds
to an ordered or disordered structure. Namely, in a disordered substance, QW
typically has smooth edges, while in ordered one it has an abrupt, rectangular
shape. The present results are relevant for the heterostructures like
GaAs/AlGaAs, GaN/AlGaN, HgCdTe/CdTe, ZnSe/ZnMnSe, Si/SiGe, etc., which may be
used in high-end electronics, flexible electronics, spintronics,
optoelectronics, and energy harvesting applications.


  We carry out an independent search of Kepler photometry for small transiting
planets with sizes 0.5--8.0 times that of Earth and orbital periods between 5
and 50 days, with the goal of measuring the fraction of stars harboring such
planets. We use a new transit search algorithm, TERRA, optimized to detect
small planets. We restrict our stellar sample to include the 12,000 stars
having the lowest photometric noise in the Kepler survey. We report 129 planet
candidates having radii less than 6 Earth-radii found in 3 years of Kepler
photometry. Forty-seven of these candidates are not in Batalha et al. (2012).
We gather Keck HIRES spectra for the majority of these targets leading to
precise stellar radii and hence precise planet radii. We inject synthetic
dimmings from mock transiting planets into the actual Kepler photometry and
analyze that photometry with TERRA to assess detection completeness. We compute
the occurrence of planets as a function of planet radius and period, correcting
for the detection completeness. The resulting distribution of planet sizes
exhibits a power law rise in occurrence from 5.7 Earth-radii down to 2
Earth-radii, as found in Howard et al. (2012). That rise clearly ends at 2
Earth-radii. The occurrence of planets is consistent with constant from 2
Earth-radii toward 1 Earth-radius. This unexpected plateau in planet occurrence
at 2 Earth-radii suggests distinct planet formation processes for planets above
and below 2 Earth-radii. We find 15.1% of solar type stars---roughly one in
six---has a 1--2 Earth-radii planet with P = 5--50 days.


  Fluorides in general are characterized by big variety of crystal structures,
whereas those containing transition metals also often show sizable magnetic
properties. The tendency of fluorine to form linear chain structures in many
cases results in low-dimensional magnetism. Despite the plethora of magnetic
phenomena in fluorides, their magnetoelectric properties are less studied than
those of oxides. In the present work we theoretically study the magnetic and
magnetoelectric properties of spin-chain compounds CaFeF$_5$ and SrFeF$_5$. The
density functional theory is employed for determination of magnetic exchange
constants, which are then used in Monte Carlo calculations. The symmetry
analysis reveals that CaFeF$_5$ does not show magnetoelectric properties,
whereas SrFeF$_5$ is a multiferroic.


  The M(atrix) model has a dual realization as IIA superstring theory in the
near-horizon geometry of the supergravity D0-brane. The role of $adS_2$ in this
correspondence is reviewed, and some aspects of holography that it suggests are
discussed.


  In this paper we study the effect of the Hardy potential on existence,
uniqueness and optimal summability of solutions of the mixed local-nonlocal
elliptic problem $$-\Delta u + (-\Delta)^s u - \gamma \frac{u}{|x|^2}=f \text{
in } \Omega, \ u=0 \text{ in } \mathbb{R}^n \setminus \Omega,$$ where $\Omega$
is a bounded domain in $\mathbb{R}^n$ containing the origin and $\gamma> 0$. In
particular, we will discuss the existence, non-existence and uniqueness of
solutions in terms of the summability of $f$ and of the value of the parameter
$\gamma$.


  In this paper, the wavelet analysis is used to study the ECG signal. We show
that the high-frequency wavelet components of the ECG signal contain
information on the functioning of the heart and can be used in diagnosis. We
describe the automated classification system that separates the ECG of sick and
healthy persons using only a high-frequency ECG component.


  Many experiments that interrogate fundamental theories require detectors
whose sensitivities are limited by the laws of quantum mechanics. In
cavity-based searches for axionic dark matter, vacuum fluctuations in the two
quadratures of the cavity electromagnetic field limit the sensitivity to an
axion-induced field. In an apparatus designed to partially mimic existing axion
detectors, we demonstrate experimentally that such quantum limits can be
overcome through the use of squeezed states. By preparing a microwave cavity in
a squeezed state and measuring just the squeezed quadrature, we enhance the
spectral scan rate by a factor of $2.12 \pm 0.08$. This enhancement is in
excellent quantitative agreement with a theoretical model accounting for both
imperfect squeezing and measurement.


  This paper is devoted to the study of fractional Schr\"odinger-Poisson type
equations with magnetic field of the type \begin{equation*}
\varepsilon^{2s}(-\Delta)_{A/\varepsilon}^{s}u+V(x)u+\varepsilon^{-2t}(|x|^{2t-3}*|u|^{2})u=f(|u|^{2})u
\quad \mbox{ in } \mathbb{R}^{3}, \end{equation*} where $\varepsilon>0$ is a
parameter, $s,t\in (0, 1)$ are such that $2s+2t>3$,
$A:\mathbb{R}^{3}\rightarrow \mathbb{R}^{3}$ is a smooth magnetic potential,
$(-\Delta)^{s}_{A}$ is the fractional magnetic Laplacian,
$V:\mathbb{R}^{3}\rightarrow \mathbb{R}$ is a continuous electric potential and
$f:\mathbb{R}\rightarrow \mathbb{R}$ is a $C^{1}$ subcritical nonlinear term.
Using variational methods, we obtain the existence, multiplicity and
concentration of nontrivial solutions for $\varepsilon>0$ small enough.


  Measurements of the structure of the virtual photon in the transition region
between quasi-real photons and those far from mass-shell have been made with
the ZEUS detector at HERA, using an integrated luminosity of 38pb-1. Dijet
final states are identified, and differential cross sections are presented in
terms of xgo, an estimator of the fraction of the photon energy which takes
part in the QCD subprocess. Comparison is made to theoretical predictions.


  We study the detectability and characterization of electron beams as they
leave their acceleration site in the low corona toward interplanetary space
through their nonthermal X-ray bremsstrahlung emission. We demonstrate that the
largest interplanetary electron beams (>=10^35 electrons above 10 keV) can be
detected in X-rays with current and future instrumentation, such as RHESSI or
the X-Ray Telescope (XRT) onboard Hinode.We make a list of optimal observing
conditions and beam characteristics. Amongst others, good imaging (as opposed
to mere localization or detection in spatially integrated data) is required for
proper characterization, putting the requirement on the number of escaping
electrons (above 10 keV) to >= 3 \times 10^36 for RHESSI, >=3 \times 10^35 for
Hinode/XRT, and >=10^33 electrons for the FOXSI sounding rocket scheduled to
fly in 2011. Moreover, we have found that simple modeling hints at the
possibility that coronal soft X-ray jets could be the result of local heating
by propagating electron beams.


  In this paper, we will present a Dvali-Gabadadze-Porrati stable model in
order to perform an observational test using $H(z)$ data and radial BAO scale
in the galaxy distribution. In this vein, we study the tension between
constraints on the cosmological constant $\Lambda$ and the crossover scale
$r_c$, which is associated with the DGP model. Our results show that
observations do not favor the DGP stable model as a possible candidate to fit
the observations of the late cosmic acceleration.


  This paper studies a class of adaptive gradient based momentum algorithms
that update the search directions and learning rates simultaneously using past
gradients. This class, which we refer to as the "Adam-type", includes the
popular algorithms such as the Adam, AMSGrad and AdaGrad. Despite their
popularity in training deep neural networks, the convergence of these
algorithms for solving nonconvex problems remains an open question. This paper
provides a set of mild sufficient conditions that guarantee the convergence for
the Adam-type methods. We prove that under our derived conditions, these
methods can achieve the convergence rate of order $O(\log{T}/\sqrt{T})$ for
nonconvex stochastic optimization. We show the conditions are essential in the
sense that violating them may make the algorithm diverge. Moreover, we propose
and analyze a class of (deterministic) incremental adaptive gradient
algorithms, which has the same $O(\log{T}/\sqrt{T})$ convergence rate. Our
study could also be extended to a broader class of adaptive gradient methods in
machine learning and optimization.


  In this paper, we have studied the loops which are the semidirect products of
a loop and a group. Also, the cummutant, nuclei and the center of such loops
are studied.


  We introduce a language modeling approach for text to speech synthesis (TTS).
Specifically, we train a neural codec language model (called Vall-E) using
discrete codes derived from an off-the-shelf neural audio codec model, and
regard TTS as a conditional language modeling task rather than continuous
signal regression as in previous work. During the pre-training stage, we scale
up the TTS training data to 60K hours of English speech which is hundreds of
times larger than existing systems. Vall-E emerges in-context learning
capabilities and can be used to synthesize high-quality personalized speech
with only a 3-second enrolled recording of an unseen speaker as an acoustic
prompt. Experiment results show that Vall-E significantly outperforms the
state-of-the-art zero-shot TTS system in terms of speech naturalness and
speaker similarity. In addition, we find Vall-E could preserve the speaker's
emotion and acoustic environment of the acoustic prompt in synthesis. See
https://aka.ms/valle for demos of our work.


  In this paper we adapt previous work on rewriting string diagrams using
hypergraphs to the case where the underlying category has a traced comonoid
structure, in which wires can be forked and the outputs of a morphism can be
connected to its input. Such a structure is particularly interesting because
any traced Cartesian (dataflow) category has an underlying traced comonoid
structure. We show that certain subclasses of hypergraphs are fully complete
for traced comonoid categories: that is to say, every term in such a category
has a unique corresponding hypergraph up to isomorphism, and from every
hypergraph with the desired properties, a unique term in the category can be
retrieved up to the axioms of traced comonoid categories. We also show how the
framework of double pushout rewriting (DPO) can be adapted for traced comonoid
categories by characterising the valid pushout complements for rewriting in our
setting. We conclude by presenting a case study in the form of recent work on
an equational theory for sequential circuits: circuits built from primitive
logic gates with delay and feedback. The graph rewriting framework allows for
the definition of an operational semantics for sequential circuits.


  We analyze the stability of time-reversal (${\mathcal T}$) and lattice
four-fold ($C_4$) symmetry breaking three-dimensional higher-order topological
(HOT) Dirac semimetals (DSMs) and the associated one-dimensional hinge modes in
the presence of random pointlike charge impurities. Complementary real space
numerical and momentum space renormalization group (RG) analyses suggest that a
HOTDSM, while being a stable phase of matter for sufficiently weak disorder,
undergoes a continuous quantum phase transition into a trivial metal at finite
disorder. However, the corresponding critical exponents (numerically obtained
from the scaling of the density of states) are extremely close to the ones
found in a dirty, but first-order DSM that on the other hand preserves
${\mathcal T}$ and $C_4$ symmetries, and support two Fermi arc surface states.
This observation suggests an emergent \emph{superuniversality} (insensitive to
symmetries) in the entire family of dirty DSMs, as also predicted by a
leading-order RG analysis. As a direct consequence of the bulk-boundary
correspondence, the hinge modes in a system with open boundaries gradually fade
away with increasing randomness, and completely dissolve in the trivial
metallic phase at strong disorder.


  We establish a magnetic Agmon estimate in the case of a purely magnetic
single non-degenerate well, by means of the Fourier-Bros-Iagolnitzer transform
and microlocal exponential estimates {\`a} la Martinez-Sj{\"o}strand.


  In the present work, we investigate the electronic transport through a
T-shape double quantum dot system coupled to two normal leads and to one
superconducting lead. We explore the interplay between Kondo and Andreev states
due to proximity effects. We find that Kondo resonance is modified by the
Andreev bound states, which manifest through Fano antiresonances in the local
density of states of the embedded quantum dot and normal transmission. This
means that there is a correlation between Andreev bound states and Fano
resonances that is robust under the influence of high electronic correlation.
We have also found that the dominant couplings at the quantum dots are
characterized by a crossover region that defines the range where the Fano-Kondo
and the Andreev-Kondo effect prevail in each quantum dot. Likewise, we find
that the interaction between Kondo and Andreev bound states has a notable
influence on the Andreev transport.


  We show that if two $m$-homogeneous algebras have Morita equivalent graded
module categories, then they are quantum-symmetrically equivalent, that is,
there is a monoidal equivalence between the categories of comodules for their
associated universal quantum groups (in the sense of Manin) which sends one
algebra to the other. As a consequence, any Zhang twist of an $m$-homogeneous
algebra is a 2-cocycle twist by some 2-cocycle from its Manin's universal
quantum group.


  The duration of a gamma-ray burst (GRB) is a key indicator of its physics
origin, with long bursts perhaps associated with the collapse of massive stars
and short bursts with mergers of neutron stars.However, there is substantial
overlap in the properties of both short and long GRBs and neither duration nor
any other parameter so far considered completely separates the two groups. Here
we unambiguously classify every GRB using a machine-learning,
dimensionality-reduction algorithm, t-distributed stochastic neighborhood
embedding (t-SNE), providing a catalog separating all Swift GRBs into two
groups. Although the classification takes place only using prompt emission
light curves,every burst with an associated supernova is found in the longer
group and bursts with kilonovae in the short, suggesting along with the
duration distributions that these two groups are truly long and short GRBs. Two
bursts with a clear absence of a supernova belong to the longer class,
indicating that these might have been direct-collapse black holes, a proposed
phenomenon that may occur in the deaths of more massive stars.


  The Hierarchical Schur Complement method (HSC), and the HSC-extension, have
significantly accelerated the evaluation of the retarded Green's function,
particularly the lesser Green's function, for two-dimensional nanoscale
devices. In this work, the HSC-extension is applied to determine the solution
of non-equilibrium Green's functions (NEGF) on three-dimensional nanoscale
devices. The operation count for the HSC-extension is analyzed for a cuboid
device. When a cubic device is discretized with $N \times N \times N$ grid
points, the state-of-the-art Recursive Green Function (RGF) algorithm takes
$\mathcal{O}(N^7)$ operations, whereas the HSC-extension only requires
$\mathcal{O}(N^6)$ operations. %Realistic operation counts also depend on the
system dimensions in $xyz$-directions and the form of contact self-energy
matrix. Operation counts and runtimes are also studied for three-dimensional
nanoscale devices of practical interest: a graphene-boron\- nitride-graphene
multilayer system, a silicon nanowire, and a DNA molecule. The numerical
experiments indicate that the cost for the HSC-extension is proportional to the
solution of one linear system (or one LU-factorization) and that the runtime
speed-ups over RGF exceed three orders of magnitude when simulating realistic
devices, such as a graphene-boron nitride-graphene multilayer system with
40,000 atoms.


  We propose a simple extension of the Standard Model (SM) by adding an extra
U(1) symmetry which is hidden from the SM sector. Such a hidden U(1) has not
been considered before, and its existence at the TeV scale can be explored at
the LHC. This hidden U(1) does not couple directly to the SM particles, and
couples only to new SU(2)_L singlet exotic quarks and singlet Higgs bosons, and
is broken at the TeV scale. The dominant signals at the high energy hadron
colliders are multi lepton and multi b-jet final states with or without missing
energy. We calculate the signal rates as well as the corresponding Standard
Model background for these final states. A very distinctive signal is 6 high
p_T b-jets in the final state with no missing energy. For a wide range of the
exotic quarks masses the signals are observable above the background at the
LHC.


  Human-Center eXplainable AI (HCXAI) literature identifies the need to address
user needs. This paper examines how existing XAI research involves human users
in designing and developing XAI systems and identifies limitations in current
practices, especially regarding how researchers identify user requirements.
Finally, we propose several suggestions on how to derive better user
requirements.


  In a first paper, HIPPARCOS astrometric and kinematic data were used to
calibrate both infrared K and IRAS luminosities at the same time as kinematic
parameters of Long Period Variable stars (LPVs). Individual estimated absolute
magnitudes and a probabilistic assignation to galactic populations were deduced
from these calibrations for each LPV of our sample. Here we propose a scenario
of simultaneous stellar and circumstellar evolution according to the galactic
populations. The transitory states of S and Tc stars allow us to confirm the
location of the first dredge-up at $M_{bol}=-3.5$. There is also evidence
suggesting that a previous enrichment in s-elements from a more evolved
companion may accelerate the evolution along the AGB. The possible evolution to
OH LPVs is included in this scenario, and any of these stars may have a mass at
the limit of the capability for a C enrichment up to C/O > 1.
  A list of bright massive LPVs with peculiar envelope and luminosity
properties is proposed as Hot Bottom Burning candidates. The He-shell flash
star, R Cen, is found to be exceptionally bright and could become, before
leaving the AGB, a C-rich LPV brighter than the usual luminosity limit of
carbon stars.


  In the present work, we investigate the production of $Z_{cs}^+$ in $B^+$ and
$B_s^0$ decay, where $Z_{cs}^+$ is assigned as a $D_s^{+} \bar{D}^{\ast0} +
D_s^{\ast +}\bar{D}^0$ molecular state. By using an effective Lagrangian
approach, we evaluate the branching ratio of $B^0_s\rightarrow K^- Z^+_{cs}$
and $B^+\rightarrow \phi Z^{+}_{cs}$ via the triangle loop mechanism. The
estimated branching fractions of $B^0_s\rightarrow K^- Z^+_{cs}$ and
$B^+\rightarrow \phi Z^{+}_{cs}$ are an order of $10^{-4} $ and $10^{-5}$,
respectively. The ratio of these two branching fraction is estimated to be
about 5, which indicate that the $B_s^0 \to K^\pm Z^\mp_{cs} \to K^+ K^-
J/\psi$ may be a better process of searching $Z_{cs}$ and accessible for
further experimental measurement of the Belle II and LHCb collaborations.


  We present 1-2 arcmin spatial resolution CARMA-8 31-GHz observations towards
19 unconfirmed Planck cluster candidates, selected to have significant galaxy
overdensities from the WISE early data release and thought to be at z>1 from
the WISE colors of the putative brightest cluster galaxy (BCG). We find a
Sunyaev-Zeldovich (SZ) detection in the CARMA-8 data towards 9 candidate
clusters, where one detection is considered tentative. For each cluster
candidate we present CARMA-8 maps, a study of their radio-source environment
and we assess the reliability of the SZ detection. The CARMA SZ detections
appear to be SZ-bright, with the mean, primary-beam-corrected peak flux density
of the decrement being -2.9mJy/beam with a standard deviation of 0.8, and are
typically offset from the Planck position by approximately 80 arcsec. Using
archival imaging data in the vicinity of the CARMA SZ centroids, we present
evidence that one cluster matches Abell 586-a known z~0.2 cluster; four
candidate clusters are likely to have 0.3<z<0.7; and, for the remaining 4, the
redshift information is inconclusive. We also argue that the sensitivity limits
resulting from the cross-correlation between Planck and WISE makes it
challenging to use our selection criterion to identify clusters at z > 1.


  In this paper, we will present the author's interpretation and embellishment
of five lectures on cluster theory given by Kiyoshi Igusa during the Spring
semester of 2022 at Brandeis University. They are meant to be used as an
introduction to cluster theory from a representation-theoretic point of view.
It is assumed that the reader has some background in representations of
quivers.


  We consider steady state solutions of the massive, asymptotically flat,
spherically symmetric Einstein-Vlasov system, i.e., relativistic models of
galaxies or globular clusters, and steady state solutions of the Einstein-Euler
system, i.e., relativistic models of stars. Such steady states are embedded
into one-parameter families parameterized by their central redshift $\kappa>0$.
  We prove their linear instability when $\kappa$ is sufficiently large, i.e.,
when they are strongly relativistic, and that the instability is driven by a
growing mode.
  Our work confirms the scenario of dynamic instability proposed in the 1960s
by Zel'dovich \& Podurets (for the Einstein-Vlasov system) and by Harrison,
Thorne, Wakano, \& Wheeler (for the Einstein-Euler system).
  Our results are in sharp contrast to the corresponding non-relativistic,
Newtonian setting.
  We carry out a careful analysis of the linearized dynamics around the above
steady states and prove an exponential trichotomy result and the corresponding
index theorems for the stable/unstable invariant spaces.
  Finally, in the case of the Einstein-Euler system we prove a rigorous version
of the turning point principle which relates the stability of steady states
along the one-parameter family to the winding points of the so-called
mass-radius curve.


  Quantum information theory establishes the ultimate limits on communication
and cryptography in terms of channel capacities for various types of
information. The private capacity is particularly important because it
quantifies achievable rates of quantum key distribution. We study the power of
quantum channels with limited private capacity, focusing on channels that
dephase in random bases. These display extensive nonadditivity of private
capacity: a channel with 2 log d input qubits has a private capacity less than
2, but when used together with a second channel with zero private capacity the
joint capacity jumps to (1/2)log d. In contrast to earlier work which found
nonadditivity vanishing as a fraction of input size or conditional on unproven
mathematical assumptions, this provides a natural setting manifesting
nonadditivity of privacy of the strongest possible sort.


  The experimental hadronic density of states dN/dm, assumed to be a sum of
normalized Breit- Wigner distributions and plotted as a function of the hadron
mass m, fails to show a Hagedorn like growth beyond 2 GeV, probably due to a
lack of data. Experimental hadronic states are fitted using $\ka$ -deformed
Poincar\'e algebra and the fit is used to extrapolate for including states not
detected. For the theoretical density of states the plot is a straight line in
the log scale even beyond 2 GeV with a limiting temperature of 400 MeV.


  We present a set of results concerning the existence of Lyapunov-Krasovskii
functionals for classes of nonlinear switched systems with time-delay. In
particular, we first present a result for positive systems that relaxes
conditions recently described in \cite{SunWang} for the existence of L-K
functionals. We also provide related conditions for positive coupled
differential-difference positive systems and for systems of neutral type that
are not necessarily positive. Finally, corresponding results for discrete-time
systems are described.


  The knowledge graph (KG) stores a large amount of structural knowledge, while
it is not easy for direct human understanding. Knowledge graph-to-text
(KG-to-text) generation aims to generate easy-to-understand sentences from the
KG, and at the same time, maintains semantic consistency between generated
sentences and the KG. Existing KG-to-text generation methods phrase this task
as a sequence-to-sequence generation task with linearized KG as input and
consider the consistency issue of the generated texts and KG through a simple
selection between decoded sentence word and KG node word at each time step.
However, the linearized KG order is commonly obtained through a heuristic
search without data-driven optimization. In this paper, we optimize the
knowledge description order prediction under the order supervision extracted
from the caption and further enhance the consistency of the generated sentences
and KG through syntactic and semantic regularization. We incorporate the
Part-of-Speech (POS) syntactic tags to constrain the positions to copy words
from the KG and employ a semantic context scoring function to evaluate the
semantic fitness for each word in its local context when decoding each word in
the generated sentence. Extensive experiments are conducted on two datasets,
WebNLG and DART, and achieve state-of-the-art performances.


  We consider the dynamical properties of a simple model of vibrational surface
modes. We obtain the exact spectrum of surface excitations and discuss their
dynamical features. In addition to the usually discussed localized and
oscillatory regimes we also find a second phase transition where surface mode
frequency becomes purely imaginary and describes an overdamped regime.
Noticeably, this transition has an exact correspondence to the oscillatory -
overdamped transition of the standard oscillator with a frictional force
proportional to velocity.


  This paper systematically studies the relation between metallicity and mass
loss of massive stars. We perform one-dimensional stellar evolution simulations
and build a grid of $\sim$2000 models with initial masses ranging between 11
and 60 $M_{\odot}$ and absolute metallicities $Z$ between 0.00001 and 0.02.
Steady-state winds, comprising hot main-sequence winds and cool supergiant
winds, are the main drivers of the mass loss of massive stars in our models. We
calculate the total mass loss over the stellar lifetime for each model. Our
results reveal the existence of a critical metallicity $Z_{\rm{c}}$ at $Z \sim
10^{-3}$, where the mass loss exhibits a dramatic jump. If $Z>Z_{\rm{c}}$,
massive stars tend to evolve into cool supergiants, and a robust cool wind is
operational. In contrast, if $Z<Z_{\rm{c}}$, massive stars usually remain as
blue supergiants, wherein the cool wind is not activated and the mass loss is
generally weak. Moreover, we calculate the wind feedback in a $10^5$
$M_{\odot}$ star cluster with the Salpeter initial mass function. The kinetic
energy released by winds does not exhibit any significant transition at
$Z_{\rm{c}}$ because the wind velocity of a cool supergiant wind is low and
contributes little to the kinetic energy. The effects of critical metallicity
provide implications for the fates of metal-poor stars in the early universe.


  We re-examine collisional annihilation of superheavy dark matter particles in
dark matter density spikes in the galactic halo as a possible source of
ultrahigh energy cosmic rays. We estimate the possible flux in a way that does
not depend on detailed assumptions about the density profiles of dark matter
clumps. The result confirms that collisional annihilation is compatible with
annihilation cross sections below the unitarity bounds for superheavy dark
matter if the particles can form dense cores in dark matter substructure, and
it provides estimates for core sizes and densities. The ensuing clumpy source
distribution in the galactic halo will be tested within a few years of
operation of the Pierre Auger observatory.


  I review the issue of string and compactification scales in the weak-coupling
regimes of string theory. I explain how in the Brane World scenario a
(effectively) two-dimensional transverse space that is hierarchically larger
than the string length may replace the conventional `energy desert' described
by renormalizable supersymmetric QFT. I comment on the puzzle of unification in
this context.


  Appearance-based gaze estimation, which uses only a regular camera to
estimate human gaze, is important in various application fields. While the
technique faces data bias issues, data collection protocol is often demanding,
and collecting data from a wide range of participants is difficult. It is an
important challenge to design opportunities that allow a diverse range of
people to participate while ensuring the quality of the training data. To
tackle this challenge, we introduce a novel gamified approach for collecting
training data. In this game, two players communicate words via eye gaze through
a transparent letter board. Images captured during gameplay serve as valuable
training data for gaze estimation models. The game is designed as a physical
installation that involves communication between players, and it is expected to
attract the interest of diverse participants. We assess the game's significance
on data quality and user experience through a comparative user study.


  We consider the decay of cosmic strings that are trapped in the false vacuum
in a theory of scalar electrodynamics in 3+1 dimensions. We restrict our
analysis to the case of thin-walled cosmic strings which occur when large
magnetic flux trapped inside the string. Thus the string looks like a tube of
fixed radius, at which it is classically stable. The core of the string
contains magnetic flux in the true vacuum, while outside the string, separated
by a thin wall, is the false vacuum. The string decays by tunnelling to a
configuration which is represented by a bulge, where the region of true vacuum
within, is ostensibly enlarged. The bulge can be described as the meeting, of a
kink soliton anti-soliton pair, along the length of the string. It can be
described as a bulge appearing in the initial string, starting from the string
of small, classically stable radius, expanding to a fat string of large,
classically unstable (to expansion) radius and then returning back to the
string of small radius along its length. This configuration is the bounce point
of a corresponding O(2) symmetric instanton, which we can determine
numerically. Once the bulge appears it explodes in real time. The kink soliton
anti-soliton pair recede from each other along the length of the string with a
velocity that quickly approaches the speed of light, leaving behind a fat tube.
At the same time the radius of the fat tube that is being formed, expands
(transversely) as it is no longer classically stable, converting false vacuum
to the true vacuum with ever diluting magnetic field within. The rate of this
expansion is determined by the energy difference between the true vacuum and
the false vacuum. Our analysis could be applied to a network, of cosmic strings
formed in the very early universe or vortex lines in a superheated
superconductor.


  We figure out that the ground state of a multiple-spin exchange model
applicable to thin films of solid 3He possesses an octahedral spin nematic
order. In the presence of magnetic field, it is deformed into an
antiferro-quadrupolar order in the perpendicular spin plane, in which lattice
Z3 rotational symmetry is also broken. Furthermore, this system shows a narrow
magnetization plateau at half, m/m_{sat}=1/2, which resembles recent
magnetization measurement [H. Nema et al., Phys. Rev. Lett. 102, 075301
(2009)].


  We show how the properties of the cosmological billiards provide useful
information (spacetime dimension and $p$-form spectrum) on the oxidation
endpoint of the oxidation sequence of gravitational theories. We compare this
approach to the other available methods: $GL(n,R)$ subgroups and the
superalgebras of dualities.


  It is well known that both the heat equation with Dirichlet or Neumann
boundary conditions are null controlable as soon as the control acts in a non
trivial domain (i.e. a set of positive measure, see [10, 11, 12, 1, 6]. In this
article, we show that for any couple of initial data (u0, v0) we can achieve
the null control for both equations (Dirichlet and Neumann boundary conditions
respectively) simultaneously with the same control function for both equations.


  With the increasing adoption of robots across industries, it is crucial to
focus on developing advanced algorithms that enable robots to anticipate,
comprehend, and plan their actions effectively in collaboration with humans. We
introduce the Robot Autonomous Motion (RoAM) video dataset, which is collected
with a custom-made turtlebot3 Burger robot in a variety of indoor environments
recording various human motions from the robot's ego-vision. The dataset also
includes synchronized records of the LiDAR scan and all control actions taken
by the robot as it navigates around static and moving human agents. The unique
dataset provides an opportunity to develop and benchmark new visual prediction
frameworks that can predict future image frames based on the action taken by
the recording agent in partially observable scenarios or cases where the
imaging sensor is mounted on a moving platform. We have benchmarked the dataset
on our novel deep visual prediction framework called ACPNet where the
approximated future image frames are also conditioned on action taken by the
robot and demonstrated its potential for incorporating robot dynamics into the
video prediction paradigm for mobile robotics and autonomous navigation
research.


  On the average, one new publication on cosmic gamma-ray bursts enters the
literature every day. The total number now exceeds 4100. I present here a
complete bibliography which can be made available electronically to interested
parties.


  Realizing a large-scale fully controllable quantum system is a challenging
task in current physical research and has broad applications. Ultracold atom
and molecule arrays in optical tweezers in vacuum have been used for quantum
simulation, quantum metrology and quantum computing. Recently, quantum ground
state cooling of the center-of-mass motion of a single optically levitated
nanoparticle in vacuum was demonstrated, providing unprecedented opportunities
for studying macroscopic quantum mechanics and precision measurements. In this
work, we create a reconfigurable optically-levitated nanoparticle array in
vacuum. Our optically-levitated nanoparticle array allows full control of
individual nanoparticles to form an arbitrary pattern and detect their motion.
As a concrete example, we choose two nanoparticles without rotation signals
from an array to synthesize a nanodumbbell in-situ by merging them into one
trap. The nanodumbbell synthesized in-situ can rotate beyond 1 GHz. Our work
provides a new platform for studying macroscopic many-body physics.


  Many real-world applications based on online learning produce streaming data
that is haphazard in nature, i.e., contains missing features, features becoming
obsolete in time, the appearance of new features at later points in time and a
lack of clarity on the total number of input features. These challenges make it
hard to build a learnable system for such applications, and almost no work
exists in deep learning that addresses this issue. In this paper, we present
Aux-Drop, an auxiliary dropout regularization strategy for online learning that
handles the haphazard input features in an effective manner. Aux-Drop adapts
the conventional dropout regularization scheme for the haphazard input feature
space ensuring that the final output is minimally impacted by the chaotic
appearance of such features. It helps to prevent the co-adaptation of
especially the auxiliary and base features, as well as reduces the strong
dependence of the output on any of the auxiliary inputs of the model. This
helps in better learning for scenarios where certain features disappear in time
or when new features are to be modelled. The efficacy of Aux-Drop has been
demonstrated through extensive numerical experiments on SOTA benchmarking
datasets that include Italy Power Demand, HIGGS, SUSY and multiple UCI
datasets. The code is available at https://github.com/Rohit102497/Aux-Drop.


  In recent years, smartphones have become prevalent. Much attention is being
paid to developing and making use of mobile applications that require position
information. The Global Positioning System (GPS) is a very popular localization
technique used by these applications because of its high accuracy. However, GPS
incurs an unacceptable energy consumption, which severely limits the use of
smartphones and reduces the battery lifetime. Then an urgent requirement for
these applications is a localization strategy that not only provides enough
accurate position information to meet users' need but also consumes less
energy. In this paper, we present an energy-efficient localization strategy for
smartphone applications. On one hand, it can dynamically estimate the next
localization time point to avoid unnecessary localization operations. On the
other hand, it can also automatically select the energy-optimal localization
method. We evaluate the strategy through a series of simulations. Experimental
results show that it can significantly reduce the localization energy
consumption of smartphones while ensuring a good satisfaction degree.


  During the last few years, considerable effort has been directed towards
large-scale (>> $1 Billion US) missions to detect and characterize earth-like
planets around nearby stars, such as the Terrestrial Planet Finder
Interferometer (TPF-I) and Darwin missions. However, technological and
budgetary issues as well as shifting science priorities will likely prevent
these missions from entering Phase A until the next decade. The secondary
eclipse technique using the Spitzer Space Telescope has been used to directly
measure the temperature and emission spectrum of extrasolar planets. However,
only a small fraction of known extrasolar planets are in transiting orbits.
Thus, a simplified nulling interferometer, which produces an artificial eclipse
or occultation, and operates in the near- to mid-infrared (e.g. ~ 3 to 8 or 10
microns), can characterize the atmospheres of this much larger sample of the
known but non-transiting exoplanets. Many other scientific problems can be
addressed with a system like this, including imaging debris disks, active
galactic nuclei, and low mass companions around nearby stars. We discuss the
rationale for a probe-scale mission in the $600-800 Million range, which we
name here as the Small Prototype Planet Finding Interferometer (SPPFI).


  In a one-dimensional model for a turbulent aerosol (inertial particles
suspended in a random flow) we compute the distributions of particle-velocity
gradients and the rate of caustic formation at finite but small Kubo numbers
Ku, for arbitrary Stokes numbers St. Our results are consistent with those
obtained earlier in the limit of small Ku and and large St, such that Ku^2 St
remains constant. We show how finite-time correlations and non-ergodic effects
influence the inertial-particle dynamics at finite but small Kubo numbers.


  Coherent sheaves on general complex manifolds do not necessarily have
resolutions by finite complexes of vector bundles. However D. Toledo and Y.L.L.
Tong showed that one can resolve coherent sheaves by objects analogous to chain
complexes of holomorphic vector bundles, whose cocycle relations are governed
by a coherent infinite system of homotopies. In the modern language such
objects are obtained by the infinity-sheafification of the simplicial presheaf
of chain complexes of holomorphic vector bundles. We define a Chern character
as a map of simplicial presheaves, whereby the connected components of its
sheafification recovers the Chern character of Toledo and Tong. As a
consequence our construction extends Toledo Tong and O'Brian Toledo Tong's
definition of the Chern character to the settings of stacks and in particular
the equivariant setting. Even in the classical setting of complex manifolds,
the induced maps on higher homotopy groups provide new Chern-Simons, and higher
Chern-Simons, invariants for coherent sheaves.


  We investigate inflection structure of a synthetic language using Latin as an
example. We construct a bipartite graph in which one group of vertices
correspond to dictionary headwords and the other group to inflected forms
encountered in a given text. Each inflected form is connected to its
corresponding headword, which in some cases in non-unique. The resulting sparse
graph decomposes into a large number of connected components, to be called word
groups. We then show how the concept of the word group can be used to construct
coverage curves of selected Latin texts. We also investigate a version of the
inflection graph in which all theoretically possible inflected forms are
included. Distribution of sizes of connected components of this graphs
resembles cluster distribution in a lattice percolation near the critical
point.


  We introduce optically tunable surfaces based upon metallic gold
nanoparticles trapped in open, water-filled gold cavities. The optical
properties of the surfaces change dramatically with the presence and location
of the particles inside the cavities. The precise position of the particles is
shown to be controllable through optical forces exerted by external
illumination, thus leading to all-optical tunability, whereby the optical
response of the surfaces is tuned through externally applied light. We discuss
the performance of the cavity-particle complex in detail and provide
theoretical support for its application as a novel concept of large-scale
optically tunable system.


  For a spectrally negative L\'evy process $X$, consider $g_t$, the last time
$X$ is below the level zero before time $t\geq 0$. We use a perturbation method
for L\'evy processes to derive an It\^o formula for the three-dimensional
process $\{(g_t,t, X_t), t\geq 0 \}$ and its infinitesimal generator. Moreover,
with $U_t:=t-g_t$, the length of a current positive excursion, we derive a
general formula that allows us to calculate a functional of the whole path of $
(U, X)=\{(U_t, X_t),t\geq 0\}$ in terms of the positive and negative excursions
of the process $X$. As a corollary, we find the joint Laplace transform of
$(U_{\mathbf{e}_q}, X_{\mathbf{e}_q})$, where $\mathbf{e}_q$ is an independent
exponential time, and the q-potential measure of the process $(U, X)$.
Furthermore, using the results mentioned above, we find a solution to a general
optimal stopping problem depending on $(U, X)$ with some applications for
corporate bankruptcy. Lastly, we establish a link between the optimal
prediction of $g_{\infty}$ and optimal stopping problems in terms of $(U, X)$
as per Baurdoux and Pedraza (2020).


  Volume calculation from the Computed Tomography (CT) lung lesions data is a
significant parameter for clinical diagnosis. The volume is widely used to
assess the severity of the lung nodules and track its progression, however, the
accuracy and efficiency of previous studies are not well achieved for clinical
uses. It remains to be a challenging task due to its tight attachment to the
lung wall, inhomogeneous background noises and large variations in sizes and
shape. In this paper, we employ Halton low-discrepancy sequences to calculate
the volume of the lung lesions. The proposed method directly compute the volume
without the procedure of three-dimension (3D) model reconstruction and surface
triangulation, which significantly improves the efficiency and reduces the
complexity. The main steps of the proposed method are: (1) generate a certain
number of random points in each slice using Halton low-discrepancy sequences
and calculate the lesion area of each slice through the proportion; (2) obtain
the volume by integrating the areas in the sagittal direction. In order to
evaluate our proposed method, the experiments were conducted on the sufficient
data sets with different size of lung lesions. With the uniform distribution of
random points, our proposed method achieves more accurate results compared with
other methods, which demonstrates the robustness and accuracy for the volume
calculation of CT lung lesions. In addition, our proposed method is easy to
follow and can be extensively applied to other applications, e.g., volume
calculation of liver tumor, atrial wall aneurysm, etc.


  The model I recently proposed for the structure of quasars offers to unify
the many aspects of Type 1 AGN: emission lines, absorption lines and reflection
features. This makes the model heavily overconstrained by observation and
readily tested.
  Here I first outline the model, and then concentrate on how the model answers
objections raised since publication - with many of the tests being reported at
this meeting. I then begin to explore how these and future tests can
discriminate between this wind model and 3 well-defined alternatives.


  The Martin boundary of a Cartan-Hadamard manifold describes a fine geometric
structure at infinity, which is a sub-space of positive harmonic functions. We
describe conditions which ensure that some points of the sphere at infinity
belong to the Martin boundary as well. In the case of the universal cover of a
compact manifold with Ballmann rank one, we show that Martin points are generic
and of full harmonic measure. The result of this paper provides a partial
answer to an open problem of S. T. Yau.


  In the last few years, there has been a great interest in detecting
overlapping communities in complex networks, which is understood as dense
groups of nodes featuring a low outbound density. To date, most methods used to
compute such communities stem from the field of disjoint community detection by
either extending the concept of modularity to an overlapping context or by
attempting to decompose the whole set of nodes into several possibly
overlapping subsets. In this report we take an orthogonal approach by
introducing a metric, the cohesion, rooted in sociological considerations. The
cohesion quantifies the community-ness of one given set of nodes, based on the
notions of triangles - triplets of connected nodes - and weak ties, instead of
the classical view using only edge density. A set of nodes has a high cohesion
if it features a high density of triangles and intersects few triangles with
the rest of the network. As such, we introduce a numerical characterization of
communities: sets of nodes featuring a high cohesion. We then present a new
approach to the problem of overlapping communities by introducing the concept
of ego-munities, which are subjective communities centered around a given node,
specifically inside its neighborhood. We build upon the cohesion to construct a
heuristic algorithm which outputs a node's ego-munities by attempting to
maximize their cohesion. We illustrate the pertinence of our method with a
detailed description of one person's ego-munities among Facebook friends. We
finally conclude by describing promising applications of ego-munities such as
information inference and interest recommendations, and present a possible
extension to cohesion in the case of weighted networks.


  Image registration is a key technique in medical image analysis to estimate
deformations between image pairs. A good deformation model is important for
high-quality estimates. However, most existing approaches use ad-hoc
deformation models chosen for mathematical convenience rather than to capture
observed data variation. Recent deep learning approaches learn deformation
models directly from data. However, they provide limited control over the
spatial regularity of transformations. Instead of learning the entire
registration approach, we learn a spatially-adaptive regularizer within a
registration model. This allows controlling the desired level of regularity and
preserving structural properties of a registration model. For example,
diffeomorphic transformations can be attained. Our approach is a radical
departure from existing deep learning approaches to image registration by
embedding a deep learning model in an optimization-based registration algorithm
to parameterize and data-adapt the registration model itself.


  We review the behaviour of the Gibbs' and conditional entropies in
deterministic and stochastic systems and continue to a formulation appropriate
for a stochastically perturbed system with delayed dynamics. The underlying
question driving these investigations: ``Is the origin of the universally
observed unidirectionality of time in our universe connected to the behaviour
of entropy?''
  We focus on temporal entropic behaviour with a review of previous results in
deterministic and stochastic systems. Our emphasis is on the temporal behaviour
of the Gibbs' and conditional entropies as these entropies give equilibrium
results in concordance with experimental findings. In invertible deterministic
systems both entropies are temporally constant as has been well known for
decades. The addition of stochastic perturbations (a Wiener process) leads to
an indeterminate (either increasing or decreasing) behaviour of the Gibbs'
entropy, but the conditional entropy monotonically approaches equilibrium with
increasing time. The presence of delays in the dynamics, whether stochastically
perturbed or not, leads to situations in which the Gibbs' and conditional
entropies evolution can be oscillatory and not monotone, and may not approach
equilibrium.


  We have recently discussed an algorithm to automatically generate auxiliary
basis sets (ABSs) of the standard form for density fitting (DF) or
resolution-of-the-identity (RI) calculations in a given atomic orbital basis
set (OBS) of any form [J. Chem. Theory Comput. 2021, 17, 6886]. In this work,
we study two ways to reduce the cost of such automatically generated ABSs
without sacrificing their accuracy. We contract the ABS with a singular value
decomposition proposed by K\'allay [J. Chem. Phys. 2014, 141, 244113], used
here in a somewhat different setting. We also drop the high-angular momentum
functions from the ABS, as they are unnecessary for global fitting methods.
Studying the effect of these two types of truncations on Hartree--Fock (HF) and
second-order M{\o}ller--Plesset perturbation theory (MP2) calculations on a
chemically diverse set of first- and second-row molecules within the RI/DF
approach, we show that accurate total and atomization energies can be achieved
by a combination of the two approaches with significant reductions in the size
of the ABS. While the original approach yields ABSs whose number of functions
$N_{\text{bf}}^{\text{ABS}}$ scales with the number of functions in the OBS,
$N_{\text{OBS}}^{\text{bf}}$, as $N_{\text{ABS}}^{\text{bf}}=\gamma
N_{\text{OBS}}^{\text{bf}}$ with the prefactor $\gamma\approx\mathcal{O}(10)$,
the reduction schemes of this work afford results of essentially the same
quality as the original unpruned and uncontracted ABS with
$\gamma\approx5\text{-}6$, while an accuracy that may suffice for routine
applications is achievable with a further reduced ABS with
$\gamma\approx3\text{-}4$. The observed errors are similar at HF and MP2 levels
of theory, suggesting that the generated ABSs are highly transferable, and can
also be applied to model challenging properties with high-level methods.


  We present broadband X-ray spectral-timing analysis of the new Galactic X-ray
transient MAXI~J1348--630 using five simultaneous {\it AstroSat} and {\it
NICER} observations. Spectral analysis using {\it AstroSat} data identify the
source to be in the soft state for the first three observations and in a faint
and bright hard state for the next two. Quasi-periodic oscillations at $\sim
0.9$ and $\sim 6.9$\,Hz, belonging to the type-C and type-A class are detected.
In the soft state, the power density spectra are substantially lower (by a
factor $> 5$) for the {\it NICER} (0.5--12 keV) band compared to the {\it
AstroSat}/LAXPC (3--80 keV) one, confirming that the disk is significantly less
variable than the Comptonization component. For the first time,
energy-dependent fractional rms and time lag in the 0.5--80 keV energy band was
measured at different Fourier frequencies, using the bright hard state
observation. Hard time lag is detected for the bright hard state, while the
faint one shows evidence for soft lag. A single-zone propagation model fits the
LAXPC results in the energy band 3--80 keV with parameters similar to those
obtained for Cygnus X--1 and MAXI J1820+070. Extending the model to lower
energies, reveals qualitative similarities but having quantitative differences
with the {\it NICER} results. These discrepancies could be because the {\it
NICER} and {\it AstroSat} data are not strictly simultaneous and because the
simple propagation model does not take into account disk emission. The results
highlight the need for more joint coordinated observations of such systems by
{\it NICER} and {\it AstroSat}.


  We report the discovery of a new dwarf galaxy (NGC6503-d1) during the Subaru
extended ultraviolet (XUV) disk survey. It is a likely companion of the spiral
galaxy NGC6503. The resolved images, in B, V, R, i, and Halpha, show an
irregular appearance due to bright stars with underlying, smooth and unresolved
stellar emission. It is classified as the transition type (dIrr/dSph). Its
structural properties are similar to those of the dwarfs in the Local Group,
with a V absolute magnitude ~ -10.5, half-light radius ~400 pc, and central
surface brightness ~25.2. Despite the low stellar surface brightness
environment, one HII region was detected, though its Halpha luminosity is low,
indicating an absence of any appreciable O-stars at the current epoch. The
presence of multiple stellar populations is indicated by the color-magnitude
diagram of ~300 bright resolved stars and the total colors of the dwarf, with
the majority of its total stellar mass ~4x10^6 Msun in an old stellar
population.


  We present a method to estimate the number of irreducible components of the
Fermi varieties of periodic Schr\"odinger operators on graphs in terms of
suitable asymptotics. Our main theorem is an abstract bound for the number of
irreducible components of Laurent polynomials in terms of such asymptotics. We
then show how the abstract bound implies irreducibility in many lattices of
interest, including examples with more than one vertex in the fundamental cell
such as the Lieb lattice as well as certain models obtained by the process of
graph decoration.


  The mass reduction of satellite solar arrays results in significant panel
flexibility, so possibly striking one another dynamically leading ultimately to
structural damage. To prevent this, rubber snubbers are mounted at well chosen
points of the structure and they act as one sided linear spring; as a negative
consequence, the dynamic of these panels becomes nonlinear. The finite element
approximation is used to solve partial differential equations governing the
structural dynamic. The models are validated and adjusted with experiments done
in the ISVR laboratory, Southampton university.


  We present the first high-resolution abundance analysis of the globular
cluster VVV~CL001, which resides in a region dominated by high interstellar
reddening towards the Galactic Bulge. Using \textit{H}-band spectra acquired by
the Apache Point Observatory Galactic Evolution Experiment (APOGEE), we
identified two potential members of the cluster, and estimate from their Fe I
lines that the cluster has an average metallicity of [Fe/H] = $-2.45$ with an
uncertainty due to systematics of 0.24 dex. We find that the light-(N),
$\alpha$-(O, Mg, Si), and Odd-Z (Al) elemental abundances of the stars in
VVV~CL001 follow the same trend as other Galactic metal-poor globular clusters.
This makes VVV~CL001 possibly the most metal-poor globular cluster identified
so far within the Sun's galactocentric distance and likely one of the most
metal-deficient clusters in the Galaxy after ESO280-SC06. Applying statistical
isochrone fitting, we derive self-consistent age, distance, and reddening
values, yielding an estimated age of $11.9^{+3.12}_{-4.05}$ Gyr at a distance
of $8.22^{+1.84}_{-1.93}$ kpc, revealing that VVV~CL001 is also an old GC in
the inner Galaxy. The Galactic orbit of VVV~CL001 indicates that this cluster
lies on a halo-like orbit that appears to be highly eccentric. Both chemistry
and dynamics support the hypothesis that VVV~CL001 could be an ancient fossil
relic left behind by a massive merger event during the early evolution of the
Galaxy, likely associated with either the Sequoia or the
\textit{Gaia}-Enceladus-Sausage structures.


  We investigate the thermalization of Sachdev-Ye-Kitaev (SYK) models coupled
via random interactions following quenches from the perspective of
entanglement. Previous studies have shown that when a system of two SYK models
coupled by random two-body terms is quenched from the thermofield double state
with sufficiently low effective temperature, the R\'enyi entropies do not
saturate to the expected thermal values in the large-$N$ limit. Using numerical
large-$N$ methods, we first show that the R\'enyi entropies in a pair SYK
models coupled by two-body terms can thermalize, if quenched from a state with
sufficiently high effective temperature, and hence exhibit state-dependent
thermalization. In contrast, SYK models coupled by single-body terms appear to
always thermalize. We provide evidence that the subthermal behavior in the
former system is likely a large-$N$ artifact by repeating the quench for finite
$N$ and finding that the saturation value of the R\'enyi entropy extrapolates
to the expected thermal value in the $N \to \infty$ limit. Finally, as a finer
grained measure of thermalization, we compute the late-time spectral form
factor of the reduced density matrix after the quench. While a single SYK dot
exhibits perfect agreement with random matrix theory, both the quadratically
and quartically coupled SYK models exhibit slight deviations.


  This paper concerns the Cauchy problem of two-dimensional (2D) full
compressible magnetohydrodynamic (MHD) equations in the whole plane
$\mathbb{R}^2$ with zero density at infinity. By spatial weighted energy
method, we derive the local existence and uniqueness of strong solutions
provided that the initial density and the initial magnetic field decay not too
slowly at infinity. Note that the initial temperature does not need to decay
slowly at infinity. In particular, vacuum states at both the interior domain
and the far field are allowed.


  Electric currents circulating between charged clouds and the earth surface
during lightning discharges are responsible for considerable damages and
casualties. It is therefore important to develop better protection methods in
addition to the traditional Franklin rod. Here we present the first
demonstration that filaments formed by short and intense laser pulses can guide
lightning discharges over considerable distances. We believe that this
experimental breakthrough will lead to progress in lightning protection and
lightning physics. An experimental campaign was carried out on the S\"antis
Mountain in Northeastern Switzerland during the Summer of 2021 with a high
repetition rate terawatt laser. The guiding of an upward negative lightning
leader over a distance of 50 m was recorded by two separate high-speed cameras.
The guiding of negative lightning leaders by laser filaments was corroborated
in three other instances by VHF interferometric measurements, and the number of
X-ray bursts detected during guided lightning events was significantly
increased. While this research field has been very active for more than 20
years with many research groups around the world working to achieve this goal,
this result demonstrates lightning guiding by lasers, which may lead to the
development of a laser lightning rod. This work paves the way for new
atmospheric applications of ultrashort lasers and represents a significant step
forward in the development of a laser based lightning protection for airports,
launchpads or large infrastructures.


  We give a new approach to the dictionary learning (also known as "sparse
coding") problem of recovering an unknown $n\times m$ matrix $A$ (for $m \geq
n$) from examples of the form \[ y = Ax + e, \] where $x$ is a random vector in
$\mathbb R^m$ with at most $\tau m$ nonzero coordinates, and $e$ is a random
noise vector in $\mathbb R^n$ with bounded magnitude. For the case $m=O(n)$,
our algorithm recovers every column of $A$ within arbitrarily good constant
accuracy in time $m^{O(\log m/\log(\tau^{-1}))}$, in particular achieving
polynomial time if $\tau = m^{-\delta}$ for any $\delta>0$, and time $m^{O(\log
m)}$ if $\tau$ is (a sufficiently small) constant. Prior algorithms with
comparable assumptions on the distribution required the vector $x$ to be much
sparser---at most $\sqrt{n}$ nonzero coordinates---and there were intrinsic
barriers preventing these algorithms from applying for denser $x$.
  We achieve this by designing an algorithm for noisy tensor decomposition that
can recover, under quite general conditions, an approximate rank-one
decomposition of a tensor $T$, given access to a tensor $T'$ that is
$\tau$-close to $T$ in the spectral norm (when considered as a matrix). To our
knowledge, this is the first algorithm for tensor decomposition that works in
the constant spectral-norm noise regime, where there is no guarantee that the
local optima of $T$ and $T'$ have similar structures.
  Our algorithm is based on a novel approach to using and analyzing the Sum of
Squares semidefinite programming hierarchy (Parrilo 2000, Lasserre 2001), and
it can be viewed as an indication of the utility of this very general and
powerful tool for unsupervised learning problems.


  The Quantum Hall ground state away from $\nu = 1$ can be described by a
collection of interacting skyrmions. We show within the context of a nonlinear
sigma model, that the classical ground state away from $\nu = 1$ is a skyrmion
crystal with a generalized N\'eel order. We show that as a function of filling
$\nu$, the skyrmion crystal undergoes a triangle to square to triangle
transition at zero temperature. We argue that this structural transition,
driven by a change in the shape of the individual skyrmions, is stable to
thermal and quantum fluctuations and may be probed experimentally.


  We describe briefly the recent advances in understanding the distributed
nature of computations in the (neural) network structure of the brain. We
discuss if such artificial networks will be able to perform mathematics and
natural sciences. The problem of consciousness in such machines is addressed.
Ancient Indian ideas regarding mind-body relations and J. C. Bose's
experimental observations regarding the highly distributed computations in the
plant body is discussed.


  A key task in multi-label classification is modeling the structure between
the involved classes. Modeling this structure by probabilistic and
interpretable means enables application in a broad variety of tasks such as
zero-shot learning or learning from incomplete data. In this paper, we present
the probabilistic rule stacking learner (pRSL) which uses probabilistic
propositional logic rules and belief propagation to combine the predictions of
several underlying classifiers. We derive algorithms for exact and approximate
inference and learning, and show that pRSL reaches state-of-the-art performance
on various benchmark datasets.
  In the process, we introduce a novel multicategorical generalization of the
noisy-or gate. Additionally, we report simulation results on the quality of
loopy belief propagation algorithms for approximate inference in bipartite
noisy-or networks.


  We describe BlackHawk, a public C program for calculating the Hawking
evaporation spectra of any black hole distribution. This program allows the
users to compute the primary and secondary spectra of stable or long-lived
particles generated by Hawking radiation of the distribution of black holes,
and to study their evolution in time. The physics of Hawking radiation is
presented, and the capabilities, features and usage of BlackHawk are described
here under the form of a manual. This is the BlackHawk v2.0 manual, which is
available on the BlackHawk webpage http://blackhawk.hepforge.org/. A brief
release note summarizing the new aspects of BlackHawk v2.0 as well as
illustrating examples can be found in https://arxiv.org/abs/2108.02737.


  We proof the existence of two different topological classes of low-energy k.p
Hamiltonians for Chern insulators. Using the paradigmatic example of
single-valley two-band models, we show that k.p Hamiltonians that we dub local
have a topological invariant corresponding precisely to the Hall conductivity
and linearly dispersing chiral midgap edge states at the expansion point.
Non-local k.p Hamiltonians have a topological invariant that is twice the Hall
conductivity of the system. This class is characterized by a non-local
bulk-edge correspondence with midgap edge states appearing away from the
high-symmetry k.p expansion point.


  Privacy preserving data analysis (PPDA) has received increasing attention due
to a great variety of applications. Local differential privacy (LDP), as an
emerging standard that is suitable for PPDA, has been widely deployed into
various real-world scenarios to analyze massive data while protecting against
many forms of privacy breach. In this study, we are mainly concerned with
piecewise transformation technique (PTT) for analyzing numerical data under
local differential privacy. We provide a principled framework for PTT in the
context of LDP, based on which PTT is studied systematically. As a result, we
show that (1) many members in PTTs are asymptotically optimal when used to
obtain an unbiased estimator for mean of numerical data, and (2) for a given
privacy budget, there is PTT that reaches the theoretical low bound with
respect to variance. Next, we prove by studying two classes of PTTs in detail
that (1) there do not exist optimal PTTs compared to the well-used technique,
i.e., Duchi's scheme, in terms of the consistency noisy variance, (2) on the
other hand, one has the ability to find a great number of PTTs that are
consistently more optimal than the latter with regard to the worst-case noisy
variance, which is never reported so far. When we are restricted to consider
only the high privacy level, enough PTTs turn out to be optimal than the
well-known Laplace mechanism. Lastly, we prove that for a family of PTTs, the
correspondingly theoretical low bound of noisy variance follows
$O(\epsilon^{-2})$ when considering the high privacy level.


  We extend the noncommutative (NC) standard model to incorporate singlet
particles as cold dark matter. In the NC space-time, the singlet particles can
be coupled to the U(1) gauge field in the adjoint representation. We Study the
relic density of the singlet particles due to the NC induced interaction.
Demanding either the singlet fermion or the singlet scalar to serve as cold
dark matter and the NC induced interactions to be relevant to the dark matter
production, we obtain the corresponding relations between the NC scale and the
dark matter masses, which are consistent with some existing bounds.


  Quantum tomography is currently the mainly employed method to assess the
information of a system and therefore plays a fundamental role when trying to
characterize the action of a particular channel. Nonetheless, quantum
tomography requires the trust that the devices used in the laboratory perform
state generation and measurements correctly. This work is based on the
theoretical framework for the device-independent inference of quantum channels
that was recently developed and experimentally implemented with superconducting
qubits in [Dall'Arno, Buscemi, Vedral, arXiv:1805.01159] and [Dall'Arno,
Brandsen, Buscemi, PRSA 473, 20160721 (2017)]. Here, we present a complete
experimental test on a photonic setup of two device-independent quantum
channels falsification and characterization protocols to analyze, validate, and
enhance the results obtained by conventional quantum process tomography. This
framework has fundamental implications in quantum information processing and
may also lead to the development of new methods removing the assumptions
typically taken for granted in all the previous protocols.


  We study the big-bang nucleosynthesis (BBN) with the long-lived exotic
particle, called X. If the lifetime of X is longer than \sim 0.1 sec, its decay
may cause non-thermal nuclear reactions during or after the BBN, altering the
predictions of the standard BBN scenario. We pay particular attention to its
hadronic decay modes and calculate the primordial abundances of the light
elements. Using the result, we derive constraints on the primordial abundance
of X. Compared to the previous studies, we have improved the following points
in our analysis: The JETSET 7.4 Monte Carlo event generator is used to
calculate the spectrum of hadrons produced by the decay of X; The evolution of
the hadronic shower is studied taking account of the details of the energy-loss
processes of the nuclei in the thermal bath; We have used the most recent
observational constraints on the primordial abundances of the light elements;
In order to estimate the uncertainties, we have performed the Monte Carlo
simulation which includes the experimental errors of the cross sections and
transfered energies. We will see that the non-thermal productions of D, He3,
He4 and Li6 provide stringent upper bounds on the primordial abundance of
late-decaying particle, in particular when the hadronic branching ratio of X is
sizable. We apply our results to the gravitino problem, and obtain upper bound
on the reheating temperature after inflation.