  In this paper we compare and contrast the behavior of the posterior
predictive distribution to the risk of the maximum a posteriori estimator for
the random features regression model in the overparameterized regime. We will
focus on the variance of the posterior predictive distribution (Bayesian model
average) and compare its asymptotics to that of the risk of the MAP estimator.
In the regime where the model dimensions grow faster than any constant multiple
of the number of samples, asymptotic agreement between these two quantities is
governed by the phase transition in the signal-to-noise ratio. They also
asymptotically agree with each other when the number of samples grow faster
than any constant multiple of model dimensions. Numerical simulations
illustrate finer distributional properties of the two quantities for finite
dimensions. We conjecture they have Gaussian fluctuations and exhibit similar
properties as found by previous authors in a Gaussian sequence model, which is
of independent theoretical interest.


  Synthesizing programs from examples requires searching over a vast,
combinatorial space of possible programs. In this search process, a key
challenge is representing the behavior of a partially written program before it
can be executed, to judge if it is on the right track and predict where to
search next. We introduce a general technique for representing partially
written programs in a program synthesis engine. We take inspiration from the
technique of abstract interpretation, in which an approximate execution model
is used to determine if an unfinished program will eventually satisfy a goal
specification. Here we learn an approximate execution model implemented as a
modular neural network. By constructing compositional program representations
that implicitly encode the interpretation semantics of the underlying
programming language, we can represent partial programs using a flexible
combination of concrete execution state and learned neural representations,
using the learned approximate semantics when concrete semantics are not known
(in unfinished parts of the program). We show that these hybrid neuro-symbolic
representations enable execution-guided synthesizers to use more powerful
language constructs, such as loops and higher-order functions, and can be used
to synthesize programs more accurately for a given search budget than pure
neural approaches in several domains.


  Using a reduced model focusing on the in-plane dependence of plane Couette
flow, it is shown that the turbulent-to-laminar relaxation process can be
understood as a nucleation problem similar to that occurring at a thermodynamic
first-order phase transition. The approach, apt to deal with the large
extension of the system considered, challenges the current interpretation in
terms of chaotic transients typical of temporal chaos. The study of the
distribution of the sizes of laminar domains embedded in turbulent flow proves
that an abrupt transition from sustained spatiotemporal chaos to laminar flow
can take place at some given value of the Reynolds number R_{low}, whether or
not the local chaos lifetime, as envisioned within low-dimensional dynamical
systems theory, diverges at finite R beyond R_{low}.


  The properties of pristine, free-standing graphene monolayers prepared by
mechanical exfoliation of graphite are investigated. The graphene monolayers,
suspended over open trenches, are examined by means of spatially resolved Raman
spectroscopy of the G-, D-, and 2D-phonon modes. The G-mode phonons exhibit
reduced energies (1580 cm-1) and increased widths (14 cm-1) compared to the
response of graphene monolayers supported on the SiO2 covered substrate. From
analysis of the G-mode Raman spectra, we deduce that the free-standing graphene
monolayers are essentially undoped, with an upper bound of 2x10^11 cm-2 for the
residual carrier concentration. On the supported regions, significantly higher
and spatially inhomogeneous doping is observed. The free-standing graphene
monolayers show little local disorder, based on the very weak Raman D-mode
response. The two-phonon 2D mode of the free-standing graphene monolayers is
downshifted in frequency compared to that of the supported region of the
samples and exhibits a narrowed, positively skewed line shape.


  We study the interplay between an isostructural critical point and
dislocation mediated two-dimensional melting, using a combination of Landau and
continuum elasticity theory. If dislocations are excluded, coupling to the
elastic degrees of freedom leads to mean field critical exponents. When
dislocations are allowed, modified elastic constants lead to a new phase buried
in the solid state near the critical point. Consistent with a proposal of
Bladon and Frenkel, we find an intervening hexatic phase near the critical
point of the first-order isostructural transition line. Very close to the
critical point, a transition from the hexatic phase to a modulated bond angle
state is possible. Ising transitions in symmetrically confined two dimensional
colloidal crystals with attractive wall potentials require a different model
free energy, which we also discuss.


  Surface interactions can cause freely suspended thin liquid crystalline films
to form phases different from the bulk material, but it is not known what
happens at the surface of thick films. Edge dislocations can be used as a
marker for the boundary between the bulk center and the reconstructed surface.
We use noncontact mode atomic force microscopy to determine the depth of edge
dislocations below the surface of freely suspended thick films of
4-n-heptyloxybenzylidene-4-n-heptylaniline (7O.7) in the crystalline B phase.
3.0 +/- 0.1 nm high steps are found with a width that varies with temperature
between 56 C and 59 C. Using a strain model for the profile of liquid
crystalline layers above an edge dislocation to estimate the depth of the
dislocation, we find that the number of reconstructed surface layers increases
from 4 to 50 layers as the temperature decreases from 59 C to 56 C. This trend
tracks the behavior of the phase boundary in the thickness dependent phase
diagram of freely suspended films of 7O.7, suggesting that the surface may be
reconstructed into a smectic F region.


  A series of four sigma-Fe(100-x)Mo(x) samples was investigated with ac
magnetic susceptibility measurements. An evidence was found that the ground
magnetic state of the samples is constituted by a spin glass (SG) with the spin
glass temperature ranging between ca. 34K for x=47 and ca. 16K for x=53. The SG
state is heterogeneous and it can be divided into a weak-irreversibility and a
strong-irreversibility domains. Its figures of merit are typical of metallic
(canonical) spin glasses.


  Device fabrication often requires materials that are either reliably
conducting, reliably semiconducting, or reliably nonconducting. Bilayer
graphene (BLG) changes from a superconductor to a semiconductor depending on
it's stacking, but because it is difficult to control its stacking, it is not a
reliable material for device fabrication. Using DFTB+, this work demonstrates
that bilayers of graphenylene, net-C, and net-W can be reliably used for device
fabrication without knowing the details of their stackings. Bilayers of
graphenylene and net-C are semiconducting for all sheer displacements, net-W is
conducting for all sheer displacements, while that Type II, like BLG, is
conducting or semiconducting depending on the sheer displacement. The method
used gives bond lengths, unit cell dimensions, and band dispersion of
single-layer graphene that are consistent with previously reported values, it
correctly predicts that AB stacking is the ground state of BLG and gives an
interlayer separation that is consistent with previous studies. The bond
lengths and lattice constants of the other carbon allotropes are consistent
with previously published values. \textcolor{blue}{In order to calculate the
band structures the bilayer systems,} DFTB+ was first used to determined the
interlayer separations of the 2-D carbon allotropes under shear displacement.


  This survey tries to investigate the truths and deficiencies of prevalent
philosophy about Uncertainty Relations (UR) and Quantum Measurements (QMS). The
respective philosophy, known as being eclipsed by unfinished controversies, is
revealed to be grounded on six basic precepts. But one finds that all the
respective precepts are discredited by insurmountable deficiencies. So, in
regard to UR, the alluded philosophy discloses oneself to be an unjustified
mythology. Then UR appear either as short-lived historical conventions or as
simple and limited mathematical formulas, without any essential significance
for physics. Such a finding reinforces the Dirac's prediction that UR "`in
their present form will not survive in the physics of future"'. The noted
facets of UR motivate reconsiderations of associated debates on QMS. Mainly one
reveals that, properly, UR have not any essential connection with genuine
descriptions of QMS. For such descriptions, it is necessary that,
mathematically, the quantum observables to be considered as random variables.
The measuring scenarios with a single sampling, such are wave function collapse
or Schrodinger's cat thought experiment, are revealed as being useless
exercises. We propose to describe QMS as transmission processes for stochastic
data. Note that the above-announced revaluation of UR and QMS philosophy does
not disturb in any way the practical framework of the usual quantum mechanics.


  We study general properties of the restriction of the representations of the
finite complex reflection groups $G(de,e,r+1)$ to their maximal parabolic
subgroups of type $G(de,e,r)$, and focus notably on the multiplicity of
components. In combinatorial terms, this amounts to the following question :
which symmetries arise or disappear when one changes (exactly) one pearl in a
combinatorial necklace ?


  Electronic nematics are exotic states of matter where electronic interactions
break a rotational symmetry of the underlying lattice, in analogy to the
directional alignment without translational order in nematic liquid crystals.
Intriguingly such phases appear in the copper- and iron-based superconductors,
and their role in establishing high-temperature superconductivity remains an
open question. Nematicity may take an active part, cooperating or competing
with superconductivity, or may appear accidentally in such systems. Here we
present experimental evidence for a phase of nematic character in the heavy
fermion superconductor CeRhIn5. We observe a field-induced breaking of the
electronic tetragonal symmetry of in the vicinity of an antiferromagnetic (AFM)
quantum phase transition at Hc~50T. This phase appears in out-of-plane fields
of H*~28T and is characterized by substantial in-plane resistivity anisotropy.
The anisotropy can be aligned by a small in-plane field component, with no
apparent connection to the underlying crystal structure. Furthermore no
anomalies are observed in the magnetic torque, suggesting the absence of
metamagnetic transitions in this field range. These observations are indicative
of an electronic nematic character of the high field state in CeRhIn5. The
appearance of nematic behavior in a phenotypical heavy fermion superconductor
highlights the interrelation of nematicity and unconventional
superconductivity, suggesting nematicity to be a commonality in such materials.


  This paper is concerned with the partial information optimal control problem
of wa controlled forward-backward stochastic differential equation of jump
diffusion with correlated noises between the system and the observation.
  For this type of partial information optimal control problem, Necessary and
sufficient optimality conditions, in the form of Pontryagin maximum principle,
for the partial information optimal control are established using a unified
way. Moreover, our admissible control process $u(\cdot)$ satisfies the
following integrable condition condition: \begin{equation*} \label{eq:1.16}
\mathbb E\bigg[\int_0^T|u(t)|^4 dt\bigg]<\infty, \end{equation*}


  We study the four-point correlator $\langle \mathcal{O}_2 \mathcal{O}_2
\mathcal{D} \mathcal{D} \rangle$ in $\mathcal{N}=4$ super Yang-Mills theory
(SYM) with $SU(N)$ gauge group, where $\mathcal{O}_2$ represents the
superconformal primary operator with dimension two, while $\mathcal{D}$ denotes
a determinant operator of dimension $N$, which is holographically dual to a
giant graviton D3-brane extending along $S^5$. We analyse the integrated
correlator associated with this observable, obtained after integrating out the
spacetime dependence over a supersymmetric invariant measure. Similarly to
other classes of integrated correlators in $\mathcal{N}=4$ SYM, this integrated
correlator can be computed through supersymmetric localisation on the
four-sphere. Employing matrix-model recursive techniques, we demonstrate that
the integrated correlator can be reformulated as an infinite sum of protected
three-point functions with known coefficients. This insight allows us to
circumvent the complexity associated with the dimension-$N$ determinant
operator, significantly streamlining the large-$N$ expansion of the integrated
correlator. In the planar limit and beyond, we derive exact results for the
integrated correlator valid for all values of the 't Hooft coupling, and
investigate the resurgent properties of their strong coupling expansion.
Additionally, in the large-$N$ expansion with fixed (complexified) Yang-Mills
coupling, we deduce the $SL(2, \mathbb{Z})$ completion of these results in
terms of the non-holomorphic Eisenstein series. The proposed modular functions
are confirmed by explicit instanton calculations from the matrix model, and
agree with expectations from the holographic dual picture of known results in
type IIB string theory.


  In mixed traffic scenarios, a certain number of pedestrians might coexist in
a small area while interacting with vehicles. In this situation, every
pedestrian must simultaneously react to the surrounding pedestrians and
vehicles. Analytical modeling of such collective pedestrian motion can benefit
intelligent transportation practices like shared space design and urban
autonomous driving. This work proposed the sub-goal social force model (SG-SFM)
to describe the collective pedestrian motion under vehicle influence. The
proposed model introduced a new design of vehicle influence on pedestrian
motion, which was smoothly combined with the influence of surrounding
pedestrians using the sub-goal concept. This model aims to describe generalized
pedestrian motion, i.e., it is applicable to various vehicle-pedestrian
interaction patterns. The generalization was verified by both quantitative and
qualitative evaluation. The quantitative evaluation was conducted to reproduce
pedestrian motion in three different datasets, HBS, CITR, and DUT. It also
compared two different ways of calibrating the model parameters. The
qualitative evaluation examined the simulation of collective pedestrian motion
in a series of fundamental vehicle-pedestrian interaction scenarios. The above
evaluation results demonstrated the effectiveness of the proposed model.


  Industry 4.0 will make manufacturing processes smarter but this smartness
requires more environmental awareness, which in case of Industrial Internet of
Things, is realized by the help of sensors. This article is about industrial
pharmaceutical systems and more specifically, water purification systems.
Purified water which has certain conductivity is an important ingredient in
many pharmaceutical products. Almost every pharmaceutical company has a water
purifying unit as a part of its interdependent systems. Early detection of
faults right at the edge can significantly decrease maintenance costs and
improve safety and output quality, and as a result, lead to the production of
better medicines. In this paper, with the help of a few sensors and data mining
approaches, an anomaly detection system is built for CHRIST Osmotron water
purifier. This is a practical research with real-world data collected from
SinaDarou Labs Co. Data collection was done by using six sensors over two-week
intervals before and after system overhaul. This gave us normal and faulty
operation samples. Given the data, we propose two anomaly detection approaches
to build up our edge fault detection system. The first approach is based on
supervised learning and data mining e.g. by support vector machines. However,
since we cannot collect all possible faults data, an anomaly detection approach
is proposed based on normal system identification which models the system
components by artificial neural networks. Extensive experiments are conducted
with the dataset generated in this study to show the accuracy of the
data-driven and model-based anomaly detection methods.


  Randomized techniques play a fundamental role in theoretical computer science
and discrete mathematics, in particular for the design of efficient algorithms
and construction of combinatorial objects. The basic goal in derandomization
theory is to eliminate or reduce the need for randomness in such randomized
constructions. In this thesis, we explore some applications of the fundamental
notions in derandomization theory to problems outside the core of theoretical
computer science, and in particular, certain problems related to coding theory.
  First, we consider the wiretap channel problem which involves a communication
system in which an intruder can eavesdrop a limited portion of the
transmissions, and construct efficient and information-theoretically optimal
communication protocols for this model. Then we consider the combinatorial
group testing problem. In this classical problem, one aims to determine a set
of defective items within a large population by asking a number of queries,
where each query reveals whether a defective item is present within a specified
group of items. We use randomness condensers to explicitly construct optimal,
or nearly optimal, group testing schemes for a setting where the query outcomes
can be highly unreliable, as well as the threshold model where a query returns
positive if the number of defectives pass a certain threshold. Finally, we
design ensembles of error-correcting codes that achieve the
information-theoretic capacity of a large class of communication channels, and
then use the obtained ensembles for construction of explicit capacity achieving
codes.
  [This is a shortened version of the actual abstract in the thesis.]


  Two holomorphic Hopf differentials for surfaces of non-null parallel mean
curvature vector in S^2xS^2 and H^2xH^2 are constructed. A 1:1 correspondence
between these surfaces and pairs of constant mean curvature surfaces of S^2xR
and H^2xR is established. Using that, surfaces with vanishing Hopf
differentials (in particular spheres with parallel mean curvature vector) are
classified and a rigidity result for constant mean curvature surfaces of S^2xR
and H^2xR is proved.


  Wearable head sensor systems use different kinematic signal processing
approaches which limits field-based inter-study comparisons, especially when
artefacts are present in the signal. The aim of this study is to assess the
frequency content and characteristics of head kinematic signals from head
impact reconstruction laboratory and field-based environments to develop an
artefact attenuation filtering method (artefact attenuation method). Laboratory
impacts (n=72) on a test-dummy headform ranging from 25-150 g were conducted
and 126 elite-level rugby union players were equipped with instrumented
mouthguards (iMG) for up to four matches. Power spectral density (PSD)
characteristics of the laboratory impacts and on-field HAE (n=5694) such as the
95th percentile cumulative sum PSD frequency were utilised to develop the
artefact attenuation method. The artefact attenuation method was compared to
two other common filtering approaches (Fourth order (2x2 pole), zero-lag
Butterworth filter with 200 Hz (-6 dB) cut-off frequency (Butterworth-200Hz)
and CFC180 filter) through signal-to-noise ratio (SNR) and mixed linear effects
models for laboratory and on-field events, respectively. The artefact
attenuation method produced an overall higher SNR than the Butterworth-200Hz
and CFC180 filter and on-field peak linear acceleration (PLA) and peak angular
acceleration (PAA) values within the magnitude range tested in the laboratory.
Median PLA and PAA were higher for the CFC180 filter than the Butterworth-200Hz
(p<0.01) and artefact attenuation method (p<0.01), reporting values as high as
294 g and 31.2 krad/s2. The artefact attenuation method can be applied to all
commercially available iMG kinematic signals with adequate sample rates to
enable field-based inter-study comparisons.


  A generalised Paley map is a Cayley map for the additive group of a finite
field F, with a subgroup S=-S of the multiplicative group as generating set,
cyclically ordered by powers of a generator of S. We characterise these as the
orientably regular maps with orientation-preserving automorphism group acting
primitively and faithfully on the vertices; allowing a non-faithful primitive
action yields certain cyclic coverings of these maps. We determine the fields
of definition and the orbits of the absolute Galois group on these maps, and we
show that if (q-1)/(p-1) divides |S|, where |F|=q=p^e with p prime, then these
maps are the only orientably regular embeddings of their underlying graphs; in
particular this applies to the Paley graphs, where |S|=(q-1)/2 is even.


  We relate stability properties (i.e. moment exponents) of a stochastic
dynamical system on a compact manifold $M$ to the homotopy and integral
homology groups of $M$. In the special case of gradient Brownian systems
associated to isometric immersions of $M$ in Euclidean space, these moment
exponents can be estimated in terms of the second fundamental form of the
immersion. This yields topological obstructions to isometric immersions
generalizing results of Lawson-Simons and others. Our work also places these
authors' work into the general framework of Weitzenb\"ock formulas.


  Place recognition is an important technique for autonomous cars to achieve
full autonomy since it can provide an initial guess to online localization
algorithms. Although current methods based on images or point clouds have
achieved satisfactory performance, localizing the images on a large-scale point
cloud map remains a fairly unexplored problem. This cross-modal matching task
is challenging due to the difficulty in extracting consistent descriptors from
images and point clouds. In this paper, we propose the I2P-Rec method to solve
the problem by transforming the cross-modal data into the same modality.
Specifically, we leverage on the recent success of depth estimation networks to
recover point clouds from images. We then project the point clouds into Bird's
Eye View (BEV) images. Using the BEV image as an intermediate representation,
we extract global features with a Convolutional Neural Network followed by a
NetVLAD layer to perform matching. The experimental results evaluated on the
KITTI dataset show that, with only a small set of training data, I2P-Rec
achieves recall rates at Top-1\% over 80\% and 90\%, when localizing monocular
and stereo images on point cloud maps, respectively. We further evaluate
I2P-Rec on a 1 km trajectory dataset collected by an autonomous logistics car
and show that I2P-Rec can generalize well to previously unseen environments.


  Ponderomotive squeezing of light, where a mechanical oscillator creates
quantum correlations between the phase and amplitude of the interacting light
field, is a canonical signature of the quantum regime of optomechanics. At room
temperature, this has only been reached in pioneering experiments where an
optical restoring force controls the oscillator stiffness, akin to the
vibrational motion of atoms in an optical lattice. These include both levitated
nanoparticles and optically-trapped cantilevers. Recent advances in engineered
mechanical resonators, where the restoring force is provided by material
rigidity rather than an external optical potential, have realized ultra-high
quality factors (Q) by exploiting `soft clamping'. However entering the quantum
regime with such resonators, has so far been prevented by optical cavity
frequency fluctuations and thermal intermodulation noise. Here, we overcome
this challenge and demonstrate optomechanical squeezing at room temperature in
a phononic-engineered membrane-in-the-middle system. By using a high finesse
cavity whose mirrors are patterned with phononic crystal structures, we reduce
cavity frequency noise by more than 700-fold. In this ultra-low noise cavity,
we introduce a silicon nitride membrane oscillator whose density is modulated
by silicon nano-pillars, yielding both high thermal conductance and a localized
mechanical mode with Q of 1.8e8. These advances enable operation within a
factor of 2.5 of the Heisenberg limit, leading to squeezing of the probing
field by 1.09 dB below the vacuum fluctuations. Moreover, the long thermal
decoherence time of the membrane oscillator (more than 30 vibrational periods)
allows us to obtain conditional displaced thermal states of motion with an
occupation of 0.97 phonon, using a multimode Kalman filter. Our work extends
quantum control of engineered macroscopic oscillators to room temperature.


  Based on the general considerations of quantum mechanics and gravity the
generalized uncertainty principle (GUP) is determined in higher-dimensional
case and on the brane, respectively. The result is used to evaluate the effect
of GUP on the dynamics of evaporation and lifetime of mini black holes in the
brane-world models.


  Multi-sensor frameworks provide opportunities for ensemble learning and
sensor fusion to make use of redundancy and supplemental information, helpful
in real-world safety applications such as continuous driver state monitoring
which necessitate predictions even in cases where information may be
intermittently missing. We define this problem of intermittent instances of
missing information (by occlusion, noise, or sensor failure) and design a
learning framework around these data gaps, proposing and analyzing an
imputation scheme to handle missing information. We apply these ideas to tasks
in camera-based hand activity classification for robust safety during
autonomous driving. We show that a late-fusion approach between parallel
convolutional neural networks can outperform even the best-placed single camera
model in estimating the hands' held objects and positions when validated on
within-group subjects, and that our multi-camera framework performs best on
average in cross-group validation, and that the fusion approach outperforms
ensemble weighted majority and model combination schemes.


  Potential energy surfaces and fission barriers of superheavy nuclei are
analyzed in the macroscopic-microscopic model. The Lublin-Strasbourg Drop (LSD)
is used to obtain the macroscopic part of the energy, whereas the shell and
pairing energy corrections are evaluated using the Yukawa-folded potential. A
standard flooding technique has been used to determine the barrier heights. It
was shown the Fourier shape parametrization containing only three deformation
parameters reproduces well the nuclear shapes of nuclei on their way to
fission. In addition, the non-axial degree of freedom is taken into account to
describe better the form of nuclei around the ground state and in the saddles
region. Apart from the symmetric fission valley, a new very asymmetric fission
mode is predicted in most superheavy nuclei. The fission fragment mass
distributions of considered nuclei are obtained by solving the 3D Langevin
equations.


  In this paper, we consider a Generalized Bernstein Theorem for a type of
generalized minimal surfaces, namely minimal Plateau surfaces. We show that if
an orientable minimal Plateau surface is stable and has quadratic area growth
in $\mathbb{R}^3 $, then it is flat.


  Let $f:\Omega\to\IR^2$ be a mapping of finite distortion, where
$\Omega\subset\IR^2 .$ Assume that the distortion function $K(x,f)$ satisfies
$e^{K(\cdot, f)}\in L^p_{loc}(\Omega)$ for some $p>0.$ We establish optimal
regularity and area distortion estimates for $f$. Especially, we prove that
$|Df|^2 \log^{\beta -1}(e + |Df|) \in L^1_{loc}(\Omega) $ for every $\beta <p.$
This answers positively well known conjectures due to Iwaniec and Martin
\cite{IMbook} and to Iwaniec, Koskela and Martin \cite{IKM}.


  This is an entry for the Gallery of Fluid Motion of the 65st Annual Meeting
of the APS-DFD (fluid dynamics video). This video shows the motion of levitated
liquid droplets. The levitation is produced by the vertical vibration of a
liquid container. We made visualizations of the motion of many droplets to
study the formation of clusters and their stability.


  This paper presents a new solution for reconstructing missing data in power
system measurements. An Enhanced Denoising Autoencoder (EDAE) is proposed to
reconstruct the missing data through the input vector space reconstruction
based on the neighbor values correlation and Long Short-Term Memory (LSTM)
networks. The proposed LSTM-EDAE is able to remove the noise, extract principle
features of the dataset, and reconstruct the missing information for new
inputs. The paper shows that the utilization of neighbor correlation can
perform better in missing data reconstruction. Trained with LSTM networks, the
EDAE is more effective in coping with big data in power systems and obtains a
better performance than the neural network in conventional Denoising
Autoencoder. A random data sequence and the simulated Phasor Measurement Unit
(PMU) data of power system are utilized to verify the effectiveness of the
proposed LSTM-EDAE.


  State estimation is an essential component of autonomous systems, usually
relying on sensor fusion that integrates data from cameras, LiDARs and IMUs.
Recently, radars have shown the potential to improve the accuracy and
robustness of state estimation and perception, especially in challenging
environmental conditions such as adverse weather and low-light scenarios. In
this paper, we present a framework for ego-velocity estimation, which we call
RAVE, that relies on 3D automotive radar data and encompasses zero velocity
detection, outlier rejection, and velocity estimation. In addition, we propose
a simple filtering method to discard infeasible ego-velocity estimates. We also
conduct a systematic analysis of how different existing outlier rejection
techniques and optimization loss functions impact estimation accuracy. Our
evaluation on three open-source datasets demonstrates the effectiveness of the
proposed filter and a significant positive impact of RAVE on the odometry
accuracy. Furthermore, we release an open-source implementation of the proposed
framework for radar ego-velocity estimation accompanied with a ROS interface.


  A new variant of the DDoS attack, called Economic Denial of Sustainability
attack has emerged. Since the cloud service is based on the pay-per-use model,
the EDoS attack endeavors to scale up the resource usage over time to the point
the purveyor of the server is financially incapable of sustaining the service
due to the incurred unaffordable usage charges. The implication of the EDoS
attack is a major security implication as more elastic cloud services are being
deployed. Existing techniques to detect and mitigate such attacks are either
have low accuracy or ineffective and, in some cases, aggravate the attack even
further. Therefore, an Enhanced Mitigation Mechanism is proposed to address
these shortcomings using OpenFlow and statistical techniques, i.e. Hellinger
Distance and Entropy. The experiments clearly depicted that EMM is able to
detect and mitigate EDoS attacks with high accuracy and it is effective in
terms of resource utilization compared to existing mitigation techniques. Thus,
can be deployed in the cloud environment without the need for additional
resource requirements.


  Recent advances in deep reinforcement learning (RL) have led to considerable
progress in many 2-player zero-sum games, such as Go, Poker and Starcraft. The
purely adversarial nature of such games allows for conceptually simple and
principled application of RL methods. However real-world settings are
many-agent, and agent interactions are complex mixtures of common-interest and
competitive aspects. We consider Diplomacy, a 7-player board game designed to
accentuate dilemmas resulting from many-agent interactions. It also features a
large combinatorial action space and simultaneous moves, which are challenging
for RL algorithms. We propose a simple yet effective approximate best response
operator, designed to handle large combinatorial action spaces and simultaneous
moves. We also introduce a family of policy iteration methods that approximate
fictitious play. With these methods, we successfully apply RL to Diplomacy: we
show that our agents convincingly outperform the previous state-of-the-art, and
game theoretic equilibrium analysis shows that the new process yields
consistent improvements.


  The classical transformation of Jacobi's theta function admits a simple proof
by producing an integral representation that yields this invariance apparent.
This idea seems to have first appeared in the work of S. Ramanujan. Several
examples of this idea have been produced by Koshlyakov, Ferrar, Guinand,
Ramanujan and others. A unifying procedure to analyze these examples and
natural generalizations is presented.


  We show that a neural network whose output is obtained as the difference of
the outputs of two feedforward networks with exponential activation function in
the hidden layer and logarithmic activation function in the output node (LSE
networks) is a smooth universal approximator of continuous functions over
convex, compact sets. By using a logarithmic transform, this class of networks
maps to a family of subtraction-free ratios of generalized posynomials, which
we also show to be universal approximators of positive functions over
log-convex, compact subsets of the positive orthant. The main advantage of
Difference-LSE networks with respect to classical feedforward neural networks
is that, after a standard training phase, they provide surrogate models for
design that possess a specific difference-of-convex-functions form, which makes
them optimizable via relatively efficient numerical methods. In particular, by
adapting an existing difference-of-convex algorithm to these models, we obtain
an algorithm for performing effective optimization-based design. We illustrate
the proposed approach by applying it to data-driven design of a diet for a
patient with type-2 diabetes.


  Road network and building footprint extraction is essential for many
applications such as updating maps, traffic regulations, city planning,
ride-hailing, disaster response \textit{etc}. Mapping road networks is
currently both expensive and labor-intensive. Recently, improvements in image
segmentation through the application of deep neural networks has shown
promising results in extracting road segments from large scale, high resolution
satellite imagery. However, significant challenges remain due to lack of enough
labeled training data needed to build models for industry grade applications.
In this paper, we propose a two-stage transfer learning technique to improve
robustness of semantic segmentation for satellite images that leverages noisy
pseudo ground truth masks obtained automatically (without human labor) from
crowd-sourced OpenStreetMap (OSM) data. We further propose Pyramid
Pooling-LinkNet (PP-LinkNet), an improved deep neural network for segmentation
that uses focal loss, poly learning rate, and context module. We demonstrate
the strengths of our approach through evaluations done on three popular
datasets over two tasks, namely, road extraction and building foot-print
detection. Specifically, we obtain 78.19\% meanIoU on SpaceNet building
footprint dataset, 67.03\% and 77.11\% on the road topology metric on SpaceNet
and DeepGlobe road extraction dataset, respectively.


  We show that in order to prove that every second countable locally compact
groups with exact reduced group C*-algebra is exact in the dynamical sense
(i.e. KW-exact) it suffices to show this for totally disconnected groups.


  We present Meraculous2, an update to the Meraculous short-read assembler that
includes (1) handling of allelic variation using "bubble" structures within the
de Bruijn graph, (2) improved gap closing, and (3) an improved scaffolding
algorithm that produces more complete assemblies without compromising
scaffolding accuracy. The speed and bandwidth efficiency of the new parallel
implementation have also been substantially improved, allowing the assembly of
a human genome to be accomplished in 24 hours on the JGI/NERSC Genepool system.
To highlight the features of Meraculous2 we present here the assembly of the
diploid human genome NA12878, and compare it with previously published
assemblies of the same data using other algorithms. The Meraculous2 assemblies
are shown to have better completeness, contiguity, and accuracy than other
published assemblies for these data. Practical considerations including
pre-assembly analyses of polymorphism and repetitiveness are described.


  Neutron beam monitors are an essential diagnostic component of neutron
scattering facilities. They are used to measure neutron flux, calibrating
experiments performed on the instruments, allowing measurement of facility
performance, understanding of the effect on the neutrons of beam-line
components (such as choppers), calibration of detectors and tracking of beam
stability. Ideally beam monitors {should} not perturb the beam. Previous work
shows commercial beam monitors attenuate the beam by a few percent in the worst
case due to the 1-2 mm thick Aluminium entrance and exit windows and the
material inside. Parasitic methods of neutron beam diagnostics, where there is
no beam monitor directly in the beam, would be preferable. This paper presents
the concept of a parasitic method of monitoring the beam which can be used for
neutron chopper phasing. This is achieved by placing a gamma detector close to
a rotating chopper and measures a signal proportional to the flux absorbed by
the chopper. Neutrons interact with the Boron absorber on the chopper disc lead
to gamma emission at 480 keV. Detection of these gamma rays is used to
determine the chopper phasing and timing. Potentially information on the flux
of the beamline can be extracted. Results from a proof of concept
implementation show that diagnosis of neutron chopper phases is feasible.


  We look at generalized Delaunay graphs in the constrained setting by
introducing line segments which the edges of the graph are not allowed to
cross. Given an arbitrary convex shape $C$, a constrained Delaunay graph is
constructed by adding an edge between two vertices $p$ and $q$ if and only if
there exists a homothet of $C$ with $p$ and $q$ on its boundary that does not
contain any other vertices visible to $p$ and $q$. We show that, regardless of
the convex shape $C$ used to construct the constrained Delaunay graph, there
exists a constant $t$ (that depends on $C$) such that it is a plane $t$-spanner
of the visibility graph. Furthermore, we reduce the upper bound on the spanning
ratio for the special case where the empty convex shape is an arbitrary
rectangle to $\sqrt{2} \cdot \left( 2 l/s + 1 \right)$, where $l$ and $s$ are
the length of the long and short side of the rectangle.


  We report on simultaneous Chandra/HETGS and RXTE observations of the
transient stellar-mass black hole GRO J1655-40, made during its 2005 outburst.
Chandra reveals a line-rich X-ray absorption spectrum consistent with a disk
wind. Prior modeling of the spectrum suggested that the wind may be
magnetically driven, potentially providing insights into the nature of disk
accretion onto black holes. In this paper, we present results obtained with new
models for this spectrum, generated using three independent photoionization
codes: XSTAR, Cloudy, and our own code. Fits to the spectrum in particular
narrow wavelength ranges, in evenly spaced wavelength slices, and across a
broad wavelength band all strongly prefer a combination of high density, high
ionization, and small inner radius. Indeed, the results obtained from all three
codes require a wind that originates more than 10 times closer to the black
hole and carrying a mass flux that is on the order of 1000 times higher than
predicted by thermal driving models. If seminal work on thermally-driven disk
winds is robust, magnetic forces may play a role in driving the disk wind in
GRO J1655-40. However, even these modeling efforts must be regarded as crude
given the complexity of the spectra. We discuss these results in the context of
accretion flows in black holes and other compact objects.


  We present absorption line-strength maps for a sample of 18 Sb-Sd galaxies
observed using the integral-field spectrograph SAURON. The SAURON spectral
range allows the measurement of the Lick/IDS indices Hbeta, Fe5015 and Mgb,
which can be used to estimate the stellar population parameters. We present
here the two-dimensional line-strength maps for each galaxy. From the maps, we
learn that late-type spiral galaxies tend to have high Hbeta and low Fe5015 and
Mgb values, and that the Hbeta index has often a positive gradient over the
field, while the metal indices peak in the central region. We investigate the
relations between the central line-strength indices and their correlations with
morphological type and central velocity dispersion, and compare the observed
behaviour with that for ellipticals, lenticulars and early-type spirals from
the SAURON survey. We find that our galaxies lie below the Mg - sigma relation
determined for elliptical galaxies and that the indices show a clear trend with
morphological type. From the line-strength maps we calculate age, metallicity
and abundance ratio maps and discuss the results from a one-SSP approach and
from a two-SSP approach. Late-type galaxies are generally younger and more
metal poor than ellipticals and have abundance ratios closer to solar values.
We also explore a continuous star formation scenario, and try to recover the
star formation history using the evolutionary models of Bruzual & Charlot
(2003), assuming constant or exponentially declining star formation rate (SFR).
We find a correlation between the e-folding time-scale tau of the starburst and
the central velocity dispersion: more massive galaxies tend to have shorter
tau, suggesting that the star formation happened long ago and has now basically
ended, while for smaller objects with larger values of tau it is still active.


  The intracluster medium (ICM) is the low-density diffuse magnetized plasma in
galaxy clusters, which reaches virial temperatures of up to 10^8 K. Under these
conditions, the plasma is weakly collisional and therefore has an anisotropic
pressure tensor with respect to the local direction of the magnetic field. This
triggers very fast, Larmor-scale, pressure-anisotropy-driven kinetic
instabilities that alter magnetic field amplification. We study magnetic field
amplification through a turbulent small-scale dynamo, including the effects of
the kinetic instabilities, during the evolution of a typical massive galaxy
cluster. A specific aim of this work is to establish a redshift limit from
which a dynamo has to start to amplify the magnetic field up to equipartition
with the turbulent velocity field at redshift z=0. We implemented 1D radial
profiles for various plasma quantities for merger trees generated with the
Modified GALFORM algorithm. We assume that turbulence is driven by successive
mergers of dark matter halos and construct effective models for the Reynolds
number Re_eff dependence on the magnetic field in three different magnetization
regimes, including the effects of kinetic instabilities. The magnetic field
growth rate is calculated for the different Re_eff models. The model results in
a higher magnetic field growth rate at higher redshift. For all scenarios
considered, to reach equipartition at z=0, the amplification of the magnetic
field has to start at redshift z_start=1.5 and above. The time to reach
equipartition can be significantly shorter, in cases with systematically
smaller turbulent forcing scales, and for the highest Re_eff models. Merger
trees are useful tools for studying the evolution of magnetic fields in weakly
collisional plasmas. They could also be used to constrain the different stages
of the dynamo that could be observed by future radio telescopes.


  We propose a way to obtain holographic cosmology models for 3+1 dimensional
cosmologies vs. 3 dimensional field theories from a "dimensional reduction"
procedure, obtained by integrating over the time direction, of (modifed)
standard holographic duals of 3+1 dimensional field theories. The example of a
modified ${\cal N}=4$ SYM vs. $AdS_5\times S^5$ is presented, and in
perturbation theory doesn't match observations, though at strong coupling it
might. But the proposed mechanism is more general, and it could in principle be
applied to other top down holographic models.


  We study a large sample of 625 low-redshift brightest cluster galaxies (BCGs)
and link their morphologies to their structural properties. We derive visual
morphologies and find that ~57% of the BCGs are cD galaxies, ~13% are
ellipticals, and ~21% belong to the intermediate classes mostly between E and
cD. There is a continuous distribution in the properties of the BCG's
envelopes, ranging from undetected (E class) to clearly detected (cD class),
with intermediate classes (E/cD and cD/E) showing the increasing degrees of the
envelope presence. A minority (~7%) of BCGs have disk morphologies, with
spirals and S0s in similar proportions, and the rest (~2%) are mergers. After
carefully fitting the galaxies light distributions by using one-component
(Sersic) and two-component (Sersic+Exponential) models, we find a clear link
between the BCGs morphologies and their structures and conclude that a
combination of the best-fit parameters derived from the fits can be used to
separate cD galaxies from non-cD BCGs. In particular, cDs and non-cDs show very
different distributions in the $R_e$--$RFF$ plane, where $R_e$ is the effective
radius and $RFF$ (the residual flux fraction) measures the proportion of the
galaxy flux present in the residual images after subtracting the models. In
general, cDs have larger $R_e$ and $RFF$ values than ellipticals. Therefore we
find, in a statistically robust way, a boundary separating cD and non-cD BCGs
in this parameter space. BCGs with cD morphology can be selected with
reasonably high completeness (~75%) and low contamination (~20%). This
automatic and objective technique can be applied to any current or future BCG
sample with good quality images.


  Assistive robots enable people with disabilities to conduct everyday tasks on
their own. However, these tasks can be complex, containing both coarse reaching
motions and fine-grained manipulation. For example, when eating, not only does
one need to move to the correct food item, but they must also precisely
manipulate the food in different ways (e.g., cutting, stabbing, scooping).
Shared autonomy methods make robot teleoperation safer and more precise by
arbitrating user inputs with robot controls. However, these works have focused
mainly on the high-level task of reaching a goal from a discrete set, while
largely ignoring manipulation of objects at that goal. Meanwhile,
dimensionality reduction techniques for teleoperation map useful
high-dimensional robot actions into an intuitive low-dimensional controller,
but it is unclear if these methods can achieve the requisite precision for
tasks like eating. Our insight is that---by combining intuitive embeddings from
learned latent actions with robotic assistance from shared autonomy---we can
enable precise assistive manipulation. In this work, we adopt learned latent
actions for shared autonomy by proposing a new model structure that changes the
meaning of the human's input based on the robot's confidence of the goal. We
show convergence bounds on the robot's distance to the most likely goal, and
develop a training procedure to learn a controller that is able to move between
goals even in the presence of shared autonomy. We evaluate our method in
simulations and an eating user study. See videos of our experiments here:
https://youtu.be/7BouKojzVyk


  Starting with the relativistic Boltzmann equation where the collision term
was generalized to include gradients of the phase-space distribution function,
we recently presented a new derivation of the equations for the relativistic
dissipative fluid dynamics. We compared them with the corresponding equations
obtained in the standard Israel-Stewart and related approaches. Our method
generates all the second-order terms that are allowed by symmetry, some of
which have been missed by the traditional approaches, and the coefficients of
other terms are altered. The first-order or Navier-Stokes equation too receives
a small correction. Here we outline this work for the general audience.


  By the method of discrete transformation equations of 3-th wave hierarchy are
constructed. We present in explicit form two Poisson structures, which allow to
construct Hamiltonian operator consequent application of which leads to all
equations of this hierarchy. For calculations it will be necessary results of
previous paper \cite{1}, which for convenience of the reader we present in
corresponding place of the text. The obtained formulae are checked by
independent calculations.


  In-car Voice Assistants (VAs) play an increasingly critical role in
automotive user interface design. However, existing VAs primarily perform
simple 'query-answer' tasks, limiting their ability to sustain drivers'
long-term attention. In this study, we investigate the effectiveness of an
in-car Robot Assistant (RA) that offers functionalities beyond voice
interaction. We aim to answer the question: How does the presence of a social
robot impact user experience in real driving scenarios? Our study begins with a
user survey to understand perspectives on in-car VAs and their influence on
driving experiences. We then conduct non-driving and on-road experiments with
selected participants to assess user experiences with an RA. Additionally, we
conduct subjective ratings to evaluate user perceptions of the RA's
personality, which is crucial for robot design. We also explore potential
concerns regarding ethical risks. Finally, we provide a comprehensive
discussion and recommendations for the future development of in-car RAs.


  Synthetic control (SC) methods have gained rapid popularity in economics
recently, where they have been applied in the context of inferring the effects
of treatments on standard continuous outcomes assuming linear input-output
relations. In medical applications, conversely, survival outcomes are often of
primary interest, a setup in which both commonly assumed data-generating
processes (DGPs) and target parameters are different. In this paper, we
therefore investigate whether and when SCs could serve as an alternative to
matching methods in survival analyses. We find that, because SCs rely on a
linearity assumption, they will generally be biased for the true expected
survival time in commonly assumed survival DGPs -- even when taking into
account the possibility of linearity on another scale as in accelerated failure
time models. Additionally, we find that, because SC units follow distributions
with lower variance than real control units, summaries of their distributions,
such as survival curves, will be biased for the parameters of interest in many
survival analyses. Nonetheless, we also highlight that using SCs can still
improve upon matching whenever the biases described above are outweighed by
extrapolation biases exhibited by imperfect matches, and investigate the use of
regularization to trade off the shortcomings of both approaches.


  We establish the Haag-Kastler axioms for a class of models on the
two-dimensional de Sitter space, including the ${\mathscr P} (\varphi)_2$
model.


  As Large Language Models (LLMs) are integrated into various sectors, ensuring
their reliability and safety is crucial. This necessitates rigorous probing and
auditing to maintain their effectiveness and trustworthiness in practical
applications. Subjecting LLMs to varied iterations of a single query can unveil
potential inconsistencies in their knowledge base or functional capacity.
However, a tool for performing such audits with a easy to execute workflow, and
low technical threshold is lacking. In this demo, we introduce ``AuditLLM,'' a
novel tool designed to audit the performance of various LLMs in a methodical
way. AuditLLM's primary function is to audit a given LLM by deploying multiple
probes derived from a single question, thus detecting any inconsistencies in
the model's comprehension or performance. A robust, reliable, and consistent
LLM is expected to generate semantically similar responses to variably phrased
versions of the same question. Building on this premise, AuditLLM generates
easily interpretable results that reflect the LLM's consistency based on a
single input question provided by the user. A certain level of inconsistency
has been shown to be an indicator of potential bias, hallucinations, and other
issues. One could then use the output of AuditLLM to further investigate issues
with the aforementioned LLM. To facilitate demonstration and practical uses,
AuditLLM offers two key modes: (1) Live mode which allows instant auditing of
LLMs by analyzing responses to real-time queries; and (2) Batch mode which
facilitates comprehensive LLM auditing by processing multiple queries at once
for in-depth analysis. This tool is beneficial for both researchers and general
users, as it enhances our understanding of LLMs' capabilities in generating
responses, using a standardized auditing platform.


  We have derived high spatial resolution metallicity maps covering $\sim$42
deg$^2$ across the Small Magellanic Cloud (SMC) in an attempt to understand its
metallicity distribution and gradients up to a radius of $\sim$ 4$^{\circ}$.
Using the near-infrared VISTA Survey of the Magellanic Clouds, our data cover a
thrice larger area compared with previous studies. We identify red giant branch
(RGB) stars in spatially distinct $Y, (Y-K_{\rm s})$ colour--magnitude
diagrams. In any of our selected subregions, the RGB slope is used as an
indicator of the average metallicity, based on calibration to metallicity using
spectroscopic data. The metallicity distribution across the SMC is unimodal and
can be fitted by a Gaussian distribution with a peak at [Fe/H] = $-$0.97 dex
($\sigma$[Fe/H] = 0.05 dex). We find evidence of a shallow gradient in
metallicity ($-0.031 \pm 0.005$ dex deg$^{-1}$) from the galactic centre to
radii of 2$^{\circ}$--2.5$^{\circ}$, followed by a flat metallicity trend from
$\sim$ 3.5$^{\circ}$ to 4$^{\circ}$. We find that the SMC's metallicity
gradient is radially asymmetric. It is flatter towards the East than to the
West, hinting at mixing and/or distortion of the spatial metallicity
distribution (within the inner 3$^{\circ}$), presumably caused by tidal
interactions between the Magellanic Clouds.


  Quantum computers are getting larger and larger, but device fidelities may
not be able to keep up with the increase in qubit numbers. One way to make use
of a large device that has a limited gate depth is to run many small circuits
simultaneously. In this paper we detail our investigations into running
circuits in parallel on the Rigetti Aspen-M-1 device. We run two-qubit circuits
in parallel to solve a simple instance of the Hubbard model using the
variational quantum eigensolver. We present results for running up to 33
circuits in parallel (66 qubits), showing that with the use of error mitigation
techniques it is possible to make use of, and gain a real-time speedup from,
parallelisation on current quantum hardware. We obtain a speedup by $18\times$
for exploring the VQE energy landscape, and by more than $8\times$ for running
VQE optimisation.


  Models that can handle a wide range of speakers and acoustic conditions are
essential in speech emotion recognition (SER). Often, these models tend to show
mixed results when presented with speakers or acoustic conditions that were not
visible during training. This paper investigates the impact of cross-corpus
data complementation and data augmentation on the performance of SER models in
matched (test-set from same corpus) and mismatched (test-set from different
corpus) conditions. Investigations using six emotional speech corpora that
include single and multiple speakers as well as variations in emotion style
(acted, elicited, natural) and recording conditions are presented. Observations
show that, as expected, models trained on single corpora perform best in
matched conditions while performance decreases between 10-40% in mismatched
conditions, depending on corpus specific features. Models trained on mixed
corpora can be more stable in mismatched contexts, and the performance
reductions range from 1 to 8% when compared with single corpus models in
matched conditions. Data augmentation yields additional gains up to 4% and seem
to benefit mismatched conditions more than matched ones.


  The development of nanomaterials with a large nonlinear susceptibility is
essential for nonlinear nanophotonics. We show that
transition-metal-dichalcogenide (TMD) nanotriangles have a large effective
second-order susceptibility [$\chi^{(2)}$] at mid-infrared to near-infrared
frequencies owing to their broken centrosymmetry. $\chi^{(2)}$ is calculated
within the density-matrix formalism that accounts for dissipation and
screening. $\chi^{(2)}$ peaks in the vicinity of both two-photon resonances
(specified by the geometry) and plasmon resonances (tunable via the carrier
density). Aligning the resonances yields the values of $\chi^{(2)}$ as high as
$10^{-6}$ m/V. These findings underscore the potential of TMD nanotriangles for
nonlinear nanophotonics, particularly second-harmonic generation.


  The aim of this thesis is to develop a theoretical framework to study
parameter estimation of quantum channels. We study the task of estimating
unknown parameters encoded in a channel in the sequential setting. A sequential
strategy is the most general way to use a channel multiple times. Our goal is
to establish lower bounds (called Cramer-Rao bounds) on the estimation error.
The bounds we develop are universally applicable; i.e., they apply to all
permissible quantum dynamics. We consider the use of catalysts to enhance the
power of a channel estimation strategy. This is termed amortization. The power
of a channel for a parameter estimation is determined by its Fisher
information. Thus, we study how much a catalyst quantum state can enhance the
Fisher information of a channel by defining the amortized Fisher information.
We establish our bounds by proving that for certain Fisher information
quantities, catalyst states do not improve the performance of a sequential
estimation protocol compared to a parallel one. The technical term for this is
an amortization collapse. We use this to establish bounds when estimating one
parameter, or multiple parameters simultaneously. Our bounds apply universally
and we also cast them as optimization problems. For the single parameter case,
we establish bounds for general quantum channels using both the symmetric
logarithmic derivative (SLD) Fisher information and the right logarithmic
derivative (RLD) Fisher information. The task of estimating multiple parameters
simultaneously is more involved than the single parameter case, because the
Cramer-Rao bounds take the form of matrix inequalities. We establish a scalar
Cramer-Rao bound for multiparameter channel estimation using the RLD Fisher
information. For both single and multiparameter estimation, we provide a no-go
condition for the so-called Heisenberg scaling using our RLD-based bound.


  In this expository paper we survey some recent results on Dirichlet problems
of the form $Lu=f(x,u)$ in $\Omega$, $u\equiv0$ in $\mathbb
R^n\backslash\Omega$. We first discuss in detail the boundary regularity of
solutions, stating the main known results of Grubb and of the author and Serra.
We also give a simplified proof of one of such results, focusing on the main
ideas and on the blow-up techniques that we developed in \cite{RS-K,RS-stable}.
After this, we present the Pohozaev identities established in
\cite{RS-Poh,RSV,Grubb-Poh} and give a sketch of their proofs, which use
strongly the fine boundary regularity results discussed previously. Finally, we
show how these Pohozaev identities can be used to deduce nonexistence of
solutions or unique continuation properties.
  The operators $L$ under consideration are integro-differential operator of
order $2s$, $s\in(0,1)$, the model case being the fractional Laplacian
$L=(-\Delta)^s$.


  Let $K_1$, $K_2$ $\subset$ $R^2$ be two convex, compact sets. We would like
to know if there are commuting torus homeomorphisms $f$ and $h$ homotopic to
the identity, with lifts $\tilde f$ and $\tilde h$, such that $K_1$ and $K_2$
are their rotation sets, respectively. In this work, we proof some cases where
it cannot happen, assuming some restrictions on rotation sets.


  Hard thermal loop effective actions furnish the building blocks of resummed
thermal perturbation theory, which is expected to work as long as the
quantities under consideration are not sensitive to the nonperturbative
(chromo-)magnetostatic sector. A different breakdown of perturbation theory
occurs whenever external momenta are light-like, because the hard thermal loops
themselves develop collinear singularities. By additionally resumming
asymptotic thermal masses for hard modes these singularities are removed while
leaving the gauge invariance of the effective action intact.


  We present a new technique for rapid modeling and construction of
scientifically accurate mesoscale biological models. Resulting 3D models are
based on few 2D microscopy scans and the latest knowledge about the biological
entity represented as a set of geometric relationships. Our new technique is
based on statistical and rule-based modeling approaches that are rapid to
author, fast to construct, and easy to revise. From a few 2D microscopy scans,
we learn statistical properties of various structural aspects, such as the
outer membrane shape, spatial properties and distribution characteristics of
the macromolecular elements on the membrane. This information is utilized in 3D
model construction. Once all imaging evidence is incorporated in the model,
additional information can be incorporated by interactively defining rules that
spatially characterize the rest of the biological entity, such as mutual
interactions among macromolecules, their distances and orientations to other
structures. These rules are defined through an intuitive 3D interactive
visualization and modeling feedback loop. We demonstrate the utility of our
approach on a use case of the modeling procedure of the SARS-CoV-2 virus
particle ultrastructure. Its first complete atomistic model, which we present
here, can steer biological research to new promising directions in fighting
spread of the virus.


  In this paper, we first define a non-degenerate symmetric bilinear form on
Fq^4. Then we get an incidence matrix G of Fq^4 by the bilinear form. By its
corresponding quadratic form Q, the lines of Fq^4 are classified as isotropic
and anisotropic lines. Under this classification, we can get two sub-matrices
of G and prove their 2-rank. Key words and phrases: finite field, quadratic
form, incidence matrix.


  We give a short compendium of the main ongoing detectors and concepts capable
of performing accurate sub-100 ps timing at high particle fluxes and on large
areas, through technologies based on gaseous media. We briefly discuss the
state-of-the-art, technological limitations and prospects, and a new bizarre
idea.


  XSEN (Cross Section of Energetic Neutrinos) is a small experiment designed to
study, for the first time, neutrino-nucleon interactions (including the tau
flavour) in the 0.5-1 TeV neutrino energy range. The detector will be installed
in the decommissioned TI18 tunnel and uses nuclear emulsions. Its simplicity
allows construction and installation before the LHC Run 3, 2021-2023; with
150/fb in Run3, the experiment can record up to two thousand neutrino
interactions, and up to a hundred tau neutrino events. The XSEN detector
intercepts the intense neutrino flux, generated by the LHC beams colliding in
IP1, at large pseudo-rapidities, where neutrino energies can exceed the TeV.
Since the neutrino-N interaction cross section grows almost linearly with
energy, the detector can be light and still collect a considerable sample of
neutrino interactions. In our proposal, the detector weighs less than 3 tons.
It is lying slightly above the ideal prolongation of the LHC beam from the
straight section; this configuration, off the beam axis, although very close to
it, enhances the contribution of neutrinos from c and b decays, and
consequently of tau neutrinos. The detector fits in the TI18 tunnel without
modifications. We plan for a demonstrator experiment in 2021 with a small
detector of about 0.5 tons; with 25/fb, nearly a hundred interactions of
neutrinos of about 1 TeV can be recorded. The aim of this pilot run is a good
in-situ characterisation of the machine-generated backgrounds, an experimental
verification of the systematic uncertainties and efficiencies, and a tuning of
the emulsion analysis infrastructure and efficiency. This Letter provides an
overview of the experiment motivations, location, design constraints,
technology choice, and operation.


  As communication systems that employ millimeter wave (mmWave) frequency bands
must use large antenna arrays to overcome the severe propagation loss of mmWave
signals, hybrid beamforming has been considered as an integral component of
mmWave communications. Recently, intelligent reflecting surface (IRS) has been
proposed as an innovative technology that can significantly improve the
performance of mmWave communication systems through the use of low-cost passive
reflecting elements. In this paper, we study IRS-aided mmWave multiple-input
multiple-output (MIMO) systems with hybrid beamforming architectures. We first
exploit the sparse-scattering structure and large dimension of mmWave channels
to develop the joint design of IRS reflection matrix and hybrid beamformer for
narrowband MIMO systems. Then, we generalize the proposed joint design to
broadband MIMO systems with orthogonal frequency division multiplexing (OFDM)
modulation by leveraging the angular sparsity of frequency-selective mmWave
channels. Simulation results demonstrate that the proposed joint designs can
significantly enhance the spectral efficiency of the systems of interest and
achieve superior performance over the existing designs.


  The Cayley graph construction provides a natural grid structure on a finite
vector space over a field of prime or prime square cardinality, where the
characteristic is congruent to 3 modulo 4, in addition to the quadratic residue
tournament structure on the prime subfield. Distance from the null vector in
the grid graph defines a Manhattan norm. The Hermitian inner product on these
spaces over finite fields behaves in some respects similarly to the real and
complex case. An analogue of the Cauchy-Schwarz inequality is valid with
respect to the Manhattan norm. With respect to the non-transitive order
provided by the quadratic residue tournament, an analogue of the Cauchy-Schwarz
inequality holds in arbitrarily large neighborhoods of the null vector, when
the characteristic is an appropriate large prime.


  We study the existence of solutions $(\underline u,\lambda_{\underline u})\in
H^1(\mathbb{R}^N; \mathbb{R}) \times \mathbb{R}$ to \[ -\Delta u + \lambda u =
f(u) \quad \text{in } \mathbb{R}^N \] with $N \ge 3$ and prescribed $L^2$ norm,
and the dynamics of the solutions to \[ \begin{cases} \mathrm{i} \partial_t
\Psi + \Delta \Psi = f(\Psi)\\ \Psi(\cdot,0) = \psi_0 \in H^1(\mathbb{R}^N;
\mathbb{C}) \end{cases} \] with $\psi_0$ close to $\underline u$. Here, the
nonlinear term $f$ has mass-subcritical growth at the origin,
mass-supercritical growth at infinity, and is more general than the sum of two
powers. Under different assumptions, we prove the existence of a locally
least-energy solution, the orbital stability of all such solutions, the
existence of a second solution with higher energy, and the strong instability
of such a solution.


  Measurements of fractional multiples of the {\nu}=2 plateau quantized Hall
resistance (R_H {\approx} 12906 {\Omega}) were enabled by the utilization of
multiple current terminals on millimetre-scale graphene p-n junction devices
fabricated with interfaces along both lateral directions. These quantum Hall
resistance checkerboard devices have been demonstrated to match quantized
resistance outputs numerically calculated with the LTspice circuit simulator.
From the devices' functionality, more complex embodiments of the quantum Hall
resistance checkerboard were simulated to highlight the parameter space within
which these devices could operate. Moreover, these measurements suggest that
the scalability of p-n junction fabrication on millimetre or centimetre scales
is feasible with regards to graphene device manufacturing by using the far more
efficient process of standard ultraviolet lithography.


  We construct the time evolution for states of Glauber dynamics for a spatial
infinite particle system in terms of generating functionals. This is carried
out by an Ovsjannikov-type result in a scale of Banach spaces, leading to a
local (in time) solution which, under certain initial conditions, might be
extended to a global one. An application of this approach to Vlasov-type
scaling in terms of generating functionals is considered as well.


  Let $S=(C \times D)/G$ be a surface isogenous to a higher product of unmixed
type with $p_g=q=0$, $G=(\mathbb{Z}/2)^3$ or $(\mathbb{Z}/2)^4$. We construct
exceptional sequences of maximal length and quasiphantom categories on $S$.


  This work introduces a novel estimation method, called LOVE, of the entries
and structure of a loading matrix A in a sparse latent factor model X = AZ + E,
for an observable random vector X in Rp, with correlated unobservable factors Z
\in RK, with K unknown, and independent noise E. Each row of A is scaled and
sparse. In order to identify the loading matrix A, we require the existence of
pure variables, which are components of X that are associated, via A, with one
and only one latent factor. Despite the fact that the number of factors K, the
number of the pure variables, and their location are all unknown, we only
require a mild condition on the covariance matrix of Z, and a minimum of only
two pure variables per latent factor to show that A is uniquely defined, up to
signed permutations. Our proofs for model identifiability are constructive, and
lead to our novel estimation method of the number of factors and of the set of
pure variables, from a sample of size n of observations on X. This is the first
step of our LOVE algorithm, which is optimization-free, and has low
computational complexity of order p2. The second step of LOVE is an easily
implementable linear program that estimates A. We prove that the resulting
estimator is minimax rate optimal up to logarithmic factors in p. The model
structure is motivated by the problem of overlapping variable clustering,
ubiquitous in data science. We define the population level clusters as groups
of those components of X that are associated, via the sparse matrix A, with the
same unobservable latent factor, and multi-factor association is allowed.
Clusters are respectively anchored by the pure variables, and form overlapping
sub-groups of the p-dimensional random vector X. The Latent model approach to
OVErlapping clustering is reflected in the name of our algorithm, LOVE.


  Interferometry is one of the central organizing principles of optics. Key to
interferometry is the concept of optical delay, which facilitates spectral
analysis in terms of time-harmonics. In contrast, when analyzing a beam in a
Hilbert space spanned by spatial modes -- a critical task for spatial-mode
multiplexing and quantum communication -- basis-specific principles are invoked
that are altogether distinct from that of `delay.' Here, we extend the
traditional concept of temporal delay to the spatial domain, thereby enabling
the analysis of a beam in an arbitrary spatial-mode basis -- exemplified using
Hermite-Gaussian and radial Laguerre-Gaussian modes. Such generalized delays
correspond to optical implementations of fractional transforms; for example,
the fractional Hankel transform is the generalized delay associated with the
space of Laguerre-Gaussian modes, and an interferometer incorporating such a
`delay' obtains modal weights in the associated Hilbert space. By implementing
an inherently stable, reconfigurable spatial-light-modulator-based
polarization- interferometer, we have constructed a `Hilbert-space analyzer'
capable of projecting optical beams onto any modal basis.


  The physical world obeys the rules of quantum, as opposed to classical,
physics. Since the playing of any particular game requires physical resources,
the question arises as to how Game Theory itself would change if it were
extended into the quantum domain. Here we provide a general formalism for {\em
quantum} games, and illustrate the explicit application of this new formalism
to a quantized version of the well-known prisoner's dilemma game.


  We develop a novel Bayesian methodology aimed at reliably and precisely
inferring the distribution of dark matter within the Milky Way using rotation
curve data. We identify a subset of the available rotation curve tracers that
are mutually consistent with each other, thus eliminating data sets that might
suffer from systematic bias. We investigate three different models for the mass
distribution of the luminous (baryonic) component that bracket the range of
likely morphologies. We demonstrate the statistical performance of our method
on simulated data in terms of coverage, fractional distance, and mean squared
error. Applying it to Milky Way data we measure the local dark matter density
at the solar circle $\rho_0$ to be $\rho_0 = 0.43\pm
0.02(\rm{stat})\pm0.01(\rm{sys})$ GeV/cm$^3$, with an accuracy $\sim$ 6%. This
result is robust to the assumed baryonic morphology. The scale radius and inner
slope of the dark matter profile are degenerate and cannot be individually
determined with high accuracy. We show that these results are robust to several
possible residual systematic errors in the rotation curve data.


  In this paper we extend the results given in \cite{Mo18} to the
$n$-dimensional case the fractional powers of Bessel operators. Moreover, we
established a Liouville type theorems for these operators. This extend the
result obtained in \cite{GMQ18} for Bessel operators.


  In this work, we derive a $\gamma$-robust a posteriori error estimator for
finite element approximations of the Allen-Cahn equation with variable
non-degenerate mobility. The estimator utilizes spectral estimates for the
linearized steady part of the differential operator as well as a conditional
stability estimate based on a weighted sum of Bregman distances, based on the
energy and a functional related to the mobility. A suitable reconstruction of
the numerical solution in the stability estimate leads to a fully computable
estimator.


  In this paper, we use simulated swarms of robots to further explore the
aggregation dynamics generated by these simple individual mechanisms. Our
objective is to study the introduction of "informed robots", and to study how
many of these are needed to direct the aggregation process toward a pre-defined
site among those available in the environment. Informed robots are members of a
group that selectively avoid the site/s where no aggregate should emerge, and
stop only on the experimenter predefined site/s for aggregation. We study the
aggregation process with informed robots in three different scenarios: two that
are morphologically symmetric, whereby the different types of aggregation site
are equally represented in the environment; and an asymmetric scenario, whereby
the target site has an area that is half the area of the sites that should be
avoided. We first show what happens when no robot in the swarm is informed: in
symmetric environments, the swarm is able to break the symmetry and aggregates
on one of the two types of site at random, not necessarily on the target site,
while in the asymmetric environment, the swarm tends to aggregate on the sites
that are most represented in terms of area. As a further valuable contribution
of this study, we provide analytical results by studying a system of Ordinary
Differential Equations' (ODEs) that is an extension of a well known model.
Using this model, we show how, for certain values of the parameters, the model
can predict the dynamics observed with simulated robots in one of the two
symmetric scenarios.


  Within the next few years, several instruments aiming at imaging extrasolar
planets will see first light. In parallel, low mass planets are being searched
around red dwarfs which offer more favorable conditions, both for radial
velocity detection and transit studies, than solar-type stars. We review recent
advancements in modeling the stellar to substellar transition. The revised
solar oxygen abundances and cloud models allow to reproduce the photometric and
spectroscopic properties of this transition to a degree never achieved before,
but problems remain in the important M-L transition characteristic of the
effective temperature range of characterizable exoplanets.


  We derive the statistics of the signals generated by shape fluctuations of
large molecules studied by feedback tracking microscopy. We account for the
influence of intramolecular dynamics on the response of the tracking system,
and derive a general expression for the fluorescence autocorrelation function
that applies when those dynamics are linear. We show that tracking provides
enhanced sensitivity to translational diffusion, molecular size, heterogeneity
and long time-scale decays in comparison to traditional fluorescence
correlation spectroscopy. We demonstrate our approach by using a
three-dimensional tracking microscope to study genomic $\lambda$-phage DNA
molecules with various fluorescence label configurations.


  AC optimal power flow (AC OPF) is a fundamental problem in power system
operations. Accurately modeling the network physics via the AC power flow
equations makes AC OPF a challenging nonconvex problem. To search for global
optima, recent research has developed a variety of convex relaxations that
bound the optimal objective values of AC OPF problems. The well-known QC
relaxation convexifies the AC OPF problem by enclosing the non-convex terms
(trigonometric functions and products) within convex envelopes. The accuracy of
this method strongly depends on the tightness of these envelopes. This paper
proposes two improvements for tightening QC relaxations of OPF problems. We
first consider a particular nonlinear function whose projections are the
nonlinear expressions appearing in the polar representation of the power flow
equations. We construct a convex envelope around this nonlinear function that
takes the form of a polytope and then use projections of this envelope to
obtain convex expressions for the nonlinear terms. Second, we use certain
characteristics of the sine and cosine expressions along with the changes in
their curvature to tighten this convex envelope. We also propose a coordinate
transformation that rotates the power flow equations by an angle specific to
each bus in order to obtain a tighter envelope. We demonstrate these
improvements relative to a state-of-the-art QC relaxation implementation using
the PGLib-OPF test cases. The results show improved optimality gaps in 68% of
these cases.


  Since its discovery more than a century ago, superconductivity has been at
the epicentre of condensed matter physics research. The electron phonon
coupling in conventional superconductors, which obeys BCS theory, causes an
attractive interaction, resulting in a unique isotropic and fixed sign pairing
symmetry ground state. Exotic pairing symmetries are hard to come by in this
favourable interaction. While unconventional superconductivity is still a
mystery, the potential for novel and exotic coupling symmetries due to the
interplay of structural symmetries and Fermi surface (FS) topology makes it a
fascinating research issue. In this thesis, we have investigated the magnetic,
transport, and microscopic properties of the conventional superconductors
HfIrSi, ZrIrSi, and novel superconductors ThCoC$_{2}$, CeIr$_{3}$, primarily
through the use of a variety of complementary experimental techniques such as
low temperature resistivity, magnetization, heat capacity, and muon spin
rotation and relaxation measurements.


  In actual implementations of magnetic control laws for spacecraft attitude
stabilization, the time in which Earth magnetic field is measured must be
separated from the time in which magnetic dipole moment is generated. The
latter separation translates into the constraint of being able to genere only
piecewise-constant magnetic dipole moment. In this work we present attitude
stabilization laws using only magnetic actuators that take into account of the
latter aspect. Both a state feedback and an output feedback are presented, and
it is shown that the proposed design allows for a systematic selection of the
sampling period.


  The combination of graphene with semiconductor materials in heterostructure
photodetectors, has enabled amplified detection of femtowatt light signals
using micron-scale electronic devices. Presently, the speed of such detectors
is limited by long-lived charge traps and impractical strategies, e.g. the use
of large gate voltage pulses, have been employed to achieve bandwidths suitable
for applications, such as video-frame-rate imaging. Here, we report atomically
thin graphene-WS$_2$ heterostructure photodetectors encapsulated in an ionic
polymer, which are uniquely able to operate at bandwidths up to 1.5 kHz, whilst
maintaining internal gain as large as $10^6$. Highly mobile ions and a
nanometre scale Debye length of the ionic polymer are used to screen charge
traps and tune the Fermi level of graphene over an unprecedented range at the
interface with WS$_2$. We observe a responsivity $R=10^6$ A W$^{-1}$ and
detectivity $D^*=3.8\times10^{11}$ Jones, approaching that of single photon
counters. The combination of both high responsivity and fast response times
makes these photodetectors suitable for video-frame-rate imaging applications.


  The cosmic-ray (CR) accelerator at the galactic centre (GC) is not yet
established by current observations. Here we investigate the
radiative-inefficient accretion flow (RIAF) of Sagittarius A* (SgrA*) as a CR
accelerator assuming acceleration by turbulent magnetic reconnection, and
derive possible emission fluxes of CRs interacting within the RIAF (the central
$\sim10^{13}$cm). The target environment of the RIAF is modelled with
numerical, general relativistic magneto-hydrodynamics (GRMHD) together with
leptonic radiative transfer simulations. The acceleration of the CRs is not
computed here. Instead, we inject CRs constrained by the magnetic reconnection
power of the accretion flow and compute the emission/absorption of
$\gamma$-rays due to these CRs interacting with the RIAF, through Monte Carlo
simulations employing the {\tt CRPropa 3} code. The resulting very-high-energy
(VHE) fluxes are not expected to reproduce the point source HESS J1745-290 as
the emission of this source is most likely produced at pc scales. The emission
profiles derived here intend to trace the VHE signatures of the RIAF as a CR
accelerator and provide predictions for observations of the GC with improved
angular resolution and differential flux sensitivity as those of the
forthcoming Cherenkov Telescope Array (CTA). Within the scenario presented
here, we find that for mass accretion rates $\gtrsim
10^{-7}$M$_\odot$yr$^{-1}$, the RIAF of SgrA* produces VHE fluxes which are
consistent with the H.E.S.S. upper limits for the GC and potentially observable
by the future CTA. The associated neutrino fluxes are negligible compared with
the diffuse neutrino emission measured by the IceCube.


  Time series and sequential data have gained significant attention recently
since many real-world processes in various domains such as finance, education,
biology, and engineering can be modeled as time series. Although many
algorithms and methods such as the Kalman filter, hidden Markov model, and long
short term memory (LSTM) are proposed to make inferences and predictions for
the data, their usage significantly depends on the application, type of the
problem, available data, and sufficient accuracy or loss. In this paper, we
compare the supervised and unsupervised hidden Markov model to LSTM in terms of
the amount of data needed for training, complexity, and forecasting accuracy.
Moreover, we propose various techniques to discretize the observations and
convert the problem to a discrete hidden Markov model under stationary and
non-stationary situations. Our results indicate that even an unsupervised
hidden Markov model can outperform LSTM when a massive amount of labeled data
is not available. Furthermore, we show that the hidden Markov model can still
be an effective method to process the sequence data even when the first-order
Markov assumption is not satisfied.


  We comment on the Lee-Yang zero analysis for the study of the phase structure
of QCD at high temperature and baryon number density by Monte-Carlo
simulations. We find that the sign problem for non-zero density QCD induces a
serious problem in the finite volume scaling analysis of the Lee-Yang zeros for
the investigation of the order of the phase transition. If the sign problem
occurs at large volume, the Lee-Yang zeros will always approach the real axis
of the complex parameter plane in the thermodynamic limit. This implies that a
scaling behavior which would suggest a crossover transition will not be
obtained. To clarify this problem, we discuss the Lee-Yang zero analysis for
SU(3) pure gauge theory as a simple example without the sign problem, and then
consider the case of non-zero density QCD. It is suggested that the
distribution of the Lee-Yang zeros in the complex parameter space obtained by
each simulation could be more important information for the investigation of
the critical endpoint in the $(T, \mu_q)$ plane than the finite volume scaling
behavior.


  We show that the present experimental LEP average R=\Gamma_h/\Gamma_l= 20.795
+- 0.040 is not unambiguous due to the presence of substantial systematic
effects which cannot be interpreted within gaussian statistics. We find by
Montecarlo simulation that the C.L. of the original LEP sample is only 3.8
\cdot 10^{-4}. We suggest that a reliable extimate of the true R-value is
20.60< R < 20.98 which produces only a very poor determination of the strong
coupling constant at the Z mass scale, 0.10< \alpha_s(M_z)< 0.15.


  The $O(\alpha)$ QED and electroweak radiative corrections to neutrino
deuteron reactions is investigated with particular emphasis given to the
constant terms, which have not been treated properly in the literature. This
problem is related to the definition of the axial-vector coupling constant
$g_{A}$ as to the inclusion of radiative corrections. After proper calculations
of the constants for the Fermi and Gamow-Teller transitions, we find the
radiative correction to the neutral current induced reaction, with the usually
adopted definition of $g_{A}$, is 1.017 for the Higgs boson mass $m_{H}=1.5
m_{Z}$. This value is close to that given by Kurylov et al., but this is due to
an accidental cancellation of the errors, between those caused by putative
identification of constant terms for the Fermi and Gamow-Teller transitions for
the charged current reactions and minor errors in their treatment of the
constant terms for the neutral current induced reactions.


  Convolutional dictionary learning (CDL), the problem of estimating
shift-invariant templates from data, is typically conducted in the absence of a
prior/structure on the templates. In data-scarce or low signal-to-noise ratio
(SNR) regimes, learned templates overfit the data and lack smoothness, which
can affect the predictive performance of downstream tasks. To address this
limitation, we propose GPCDL, a convolutional dictionary learning framework
that enforces priors on templates using Gaussian Processes (GPs). With the
focus on smoothness, we show theoretically that imposing a GP prior is
equivalent to Wiener filtering the learned templates, thereby suppressing
high-frequency components and promoting smoothness. We show that the algorithm
is a simple extension of the classical iteratively reweighted least squares
algorithm, independent of the choice of GP kernels. This property allows one to
experiment flexibly with different smoothness assumptions. Through simulation,
we show that GPCDL learns smooth dictionaries with better accuracy than the
unregularized alternative across a range of SNRs. Through an application to
neural spiking data, we show that GPCDL learns a more accurate and
visually-interpretable smooth dictionary, leading to superior predictive
performance compared to non-regularized CDL, as well as parametric
alternatives.


  Renormalization group flows of quiver gauge theories play a central role in
determining the low-energy properties of string vacua. We demonstrate that
useful predictions about the RG dynamics of a quiver gauge theory may be
extracted from the global structure of its quiver diagram. For quiver theories
of a certain type, we develop an efficient and practical method for determining
which superpotential deformations generate a flow to an interacting conformal
fixed point.


  Using a sample of about 10 billion $J/\psi$ events collected at a
center-of-mass energy $\sqrt s = 3.097$ GeV with the BESIII detector, the
electromagnetic Dalitz decays $J/\psi \to e^+e^- \pi^+ \pi^- \eta'$, with
$\eta'\to\gamma\pi^+ \pi^-$ and $\eta'\to\pi^+\pi^-\eta$, have been studied.
The decay $J/\psi \to e^+ e^- X(1835)$ is observed with a significance of
$15\sigma$, and the transition form factor of $J/\psi\to e^+e^-X(1835)$ is
presented for the first time. The intermediate states $X(2120)$ and $X(2370)$
are also observed in the $\pi^+ \pi^- \eta'$ invariant mass spectrum with
significances of $5.3\sigma$ and $7.3\sigma$. The corresponding product
branching fractions for $J/\psi\to e^+e^-X$, $X\to\pi^+\pi^-\eta'$ $(X=X(1835),
X(2120)$ and $X(2370))$, are reported.


  Consider a generic triangle in the upper half of the complex plane with one
side on the real line. This paper presents a tailored construction of a
discrete random walk whose continuum limit is a Brownian motion in the
triangle, reflected instantaneously on the left and right sides with constant
reflection angles. Starting from the top of the triangle, it is evident from
the construction that the reflected Brownian motion lands with the uniform
distribution on the base. Combined with conformal invariance and the locality
property, this uniform exit distribution allows us to compute distribution
functions characterizing the hull generated by the reflected Brownian motion.


  Only three magnetic $\delta$ Scuti stars are known as of today. HD 41641 is a
$\delta$ Scuti star showing chemical peculiarities and rotational modulation of
its light-curve, making it a good magnetic candidate. We acquired
spectropolarimetric observations of this star with Narval at TBL to search for
the presence of a magnetic field and characterize it. We indeed clearly detect
a magnetic field in HD 41641, making it the fourth known magnetic $\delta$
Scuti star. Our analysis shows that the field is of fossil origin, like
magnetic OBA stars, but with a complex field structure rather than the much
more usual dipolar structure.


  We have devised an alternative approach to sifting integers in the sieve of
Eratosthenes that helps refine the error term. Instead of eliminating all
multiples of a prime number $p<z$ in the traditional sieve method, our approach
solely eliminates multiples of $p$ that have the minimum prime factor of $p$.
By leveraging the density of integers with the least prime factor $p$ in this
sieve technique, we obtain a reduced error term and an upper bound of $\pi(x)$
that accurately reflects the prime number theorem.


  This paper presents a list of suggested stars for radial velocity
measurements. We explain here in brief the research project for which the
radial velocity of the "slow movers" i.e. small proper motion stars are
necessary. Basing on this study we prepared a list of 1100 stellar targets with
very accurate positions, proper motions and trigonometric parallaxes but
without radial velocity measurements. Distributions of stellar brightnesses and
spectral types among these stars are presented as well as its "most wanted"
subset. We announce the begin of the radial velocity measurements to be
conducted with our new echelle spectrograph just put into operation and offer
some coordination for observations of targets that cannot be reached from our
location.


  Extending the eavesdropping strategy devised by Zhang, Li and Guo [Phys. Rev.
A 63, 036301 (2001)], we show that the multiparty quantum communication
protocol based on entanglement swapping, which was proposed by Cabello
[quant-ph/0009025], is not secure. We modify the protocol so that entanglement
swapping can secure multiparty quantum communication, such as multiparty
quantum key distribution and quantum secret sharing of classical information,
and show that the modified protocol is secure against the Zhang-Li-Guo's
strategy for eavesdropping as well as the basic intercept-resend attack.


  We present some more foundations for a theory of real structure in operator
spaces and algebras, in particular concerning the real case of the theory of
injectivity, and the injective, ternary, and $C^*$-envelope. We consider the
interaction between these topics and the complexification. We also generalize
many of these results to the setting of operator spaces and systems acted upon
by a group.


  In this note, we discuss the impact of the COVID-19 outbreak from the
perspective of the market-structure. We observe that the US market-structure
has dramatically changed during the past four weeks and that the level of
change has followed the number of infected cases reported in the USA.
Presently, market-structure resembles most closely the structure during the
middle of the 2008 crisis but there are signs that it may be starting to evolve
into a new structure altogether. This is the first article of a series where we
will be analyzing and discussing market-structure as it evolves to a state of
further instability or, more optimistically, stabilization and recovery.


  Developments in deep generative models have allowed for tractable learning of
high-dimensional data distributions. While the employed learning procedures
typically assume that training data is drawn i.i.d. from the distribution of
interest, it may be desirable to model distinct distributions which are
observed sequentially, such as when different classes are encountered over
time. Although conditional variations of deep generative models permit multiple
distributions to be modeled by a single network in a disentangled fashion, they
are susceptible to catastrophic forgetting when the distributions are
encountered sequentially. In this paper, we adapt recent work in reducing
catastrophic forgetting to the task of training generative adversarial networks
on a sequence of distinct distributions, enabling continual generative
modeling.


  The limit relations for the partial derivatives of the two-electron atomic
wave functions at the two-particle coalescence lines have been obtained
numerically using accurate CFHHM wave functions. The asymptotic solutions of
the proper two-electron Schrodinger equation have been derived for both
electron-nucleus and electron-electron coalescence. It is shown that the
solutions for the electron-nucleus coalescence correspond to the ground and
singly excited bound states, including triplet ones. The proper solutions at
small distances $R$ from the triple coalescence point were presented as the
second order expansion on R and lnR. The vanishing of the Fock's logarithmic
terms at the electron-nucleus coalescence line was revealed in the frame of
this expansion, unlike the case of electron-electron coalescence. On the basis
of the obtained boundary solutions the approximate wave function corresponding
to both coalescence lines have been proposed in the two-exponential form with
no variational parameters.


  The GUT value of Weinberg's angle is also the value that minimises the total
square matrix elements of $Z^0$ decay, independently of any GUT consideration,
and thus the one that maximises the neutrino branching ratio against total
width. We review the proof of this result and some related facts.


  We give a characterization of the invariant measures for the exclusion
process on the integers with certain reversible transition kernels. Some
examples include all nearest-neighbor kernels with asymptotic mean zero. One
tool used is a necessary and sufficient condition for reversible measures to be
extremal in the set of all invariant measures which is an interesting result in
its own right.


  The ability to map the cosmological expansion has developed enormously,
spurred by the turning point one decade ago of the discovery of cosmic
acceleration. The standard model of cosmology has shifted from a matter
dominated, standard gravity, decelerating expansion to the present search for
the origin of acceleration in the cosmic expansion. We present a wide ranging
review of the tools, challenges, and physical interpretations. The tools
include direct measures of cosmic scales through Type Ia supernova luminosity
distances, and angular distance scales of baryon acoustic oscillation and
cosmic microwave background density perturbations, as well as indirect probes
such as the effect of cosmic expansion on the growth of matter density
fluctuations. Accurate mapping of the expansion requires understanding of
systematic uncertainties in both the measurements and the theoretical
framework, but the result will give important clues to the nature of the
physics behind accelerating expansion and to the fate of the universe.