  Separated spin-up and spin-down quantum kinetics is derived for more detailed
research of the spin-electron acoustic waves. Kinetic theory allows to obtain
spectrum of the spin-electron acoustic waves including effects of occupation of
quantum states more accurately than quantum hydrodynamics. We apply quantum
kinetic to calculate the Landau damping of the spin-electron acoustic waves. We
have considered contribution of ions dynamics in the spin-electron acoustic
wave spectrum. We obtain contribution of ions in the Landau damping in
temperature regime of classic ions. Kinetic analysis for ion-acoustic, zero
sound, and Langmuir waves at separated spin-up and spin-down electron dynamics
is presented as well.


  Using a TE/TM decomposition for an angular plane-wave spectrum of free random
electromagnetic waves and matched boundary conditions, we derive the
probability density function for the energy density of the vector electric
field in the presence of a semi-infinite isotropic medium. The theoretical
analysis is illustrated with calculations and results for good electric
conductors and for a lossless dielectric half-space. The influence of the
permittivity and conductivity on the intensity, random polarization,
statistical distribution and standard deviation of the field is investigated,
both for incident plus reflected fields and for refracted fields. External
refraction is found to result in compression of the fluctuations of the random
field.


  Stability of matter with Coulomb forces has been proved for non-relativistic
dynamics, including arbitrarily large magnetic fields, and for relativistic
dynamics without magnetic fields. In both cases stability requires that the
fine structure constant alpha be not too large. It was unclear what would
happen for both relativistic dynamics and magnetic fields, or even how to
formulate the problem clearly. We show that the use of the Dirac operator
allows both effects, provided the filled negative energy `sea' is defined
properly. The use of the free Dirac operator to define the negative levels
leads to catastrophe for any alpha, but the use of the Dirac operator with
magnetic field leads to stability.


  We analyze the behavior of the trace of the resolvent of an elliptic cone
differential operator as the spectral parameter tends to infinity. The
resolvent splits into two components, one associated with the minimal extension
of the operator, and another, of finite rank, depending on the particular
choice of domain. We give a full asymptotic expansion of the first component
and expand the component of finite rank in the case where the domain is
stationary. The results make use, and develop further, our previous
investigations on the analytic and geometric structure of the resolvent. The
analysis of nonstationary domains, considerably more intricate, is pursued
elsewhere.


  Recently, a silicon micromachining method to produce tetrahedral silicon
particles was discovered. In this report we determine, using band structure
calculations, the optical properties of diamond-lattice photonic crystals when
assembled from such particles. We show that crystal structures built from
silicon tetrahedra are expected to display small stop gaps. Wide photonic band
gaps appear when truncated tetrahedral particles are used to build the photonic
crystals. With truncated tetrahedral particles a band gap with a width of 23.6%
can be achieved, which is more than twice as wide compared to band gaps in
self-assembled diamond-lattices of hard-spheres. The width of the band gap is
insensitive to small deviations from the optimal amount of truncation. This
work paves the way to a novel class of silicon diamond-lattice band gap
crystals that can be obtained through self-assembly. Such a self-assembly
approach would allow for easy integration of these highly photonic crystals in
existing silicon microfluidic and -electronic systems.


  The development of superresolution techniques, i.e., allowing for efficient
resolution below the Rayleigh limit, became one of the important branches in
contemporary optics and metrology. Recent findings show that perfect spatial
mode demultiplexing (SPADE) into Hermite-Gauss modes followed by photon
counting enables one to reach the quantum limit of precision in the task of
estimation of separation between two weak stationary sources in the
sub-Rayleigh regime. In order to check the limitations of the method, various
imperfections such as misalignment or crosstalk between the modes were
considered.
  Possible applications of the method in microscopy call for the adaptive
measurement scheme, as the position of the measured system can evolve in time,
causing non-negligible misalignment. In this paper, we examine the impact of
Brownian motion of the center of the system of two weak incoherent sources of
arbitrary relative brightness on adaptive SPADE measurement precision limits.
The analysis is carried out using Fisher information, from which the limit of
precision can be obtained by Cram\'er-Rao bound. As a result, we find that
Rayleigh's curse is present in such a scenario; however, SPADE measurement can
outperform perfect direct imaging. What is more, a suitable adjustment of the
measurement time between alignments allows measurement with near-optimal
precision.


  In this paper, we address the virtualization and the centralization of
real-time network functions, notably in the framework of Cloud RAN (C-RAN). We
thoroughly analyze the required fronthaul capacity for the deployment of the
proposed C-RAN architecture. We are specifically interested in the performance
of the software based channel coding function. We develop a dynamic
multi-threading approach to achieve parallel computing on a multi-core
platform. Measurements from an OAI-based testbed show important gains in terms
of latency; this enables the increase of the distance between the radio
elements and the virtualized RAN functions and thus a higher aggregation of
gNodeBs in edge data centers, referred to as Central Offices (COs).


  Understanding protein function is one of the keys to understanding life at
the molecular level. It is also important in several scenarios including human
disease and drug discovery. In this age of rapid and affordable biological
sequencing, the number of sequences accumulating in databases is rising with an
increasing rate. This presents many challenges for biologists and computer
scientists alike. In order to make sense of this huge quantity of data, these
sequences should be annotated with functional properties. UniProtKB consists of
two components: i) the UniProtKB/Swiss-Prot database containing protein
sequences with reliable information manually reviewed by expert bio-curators
and ii) the UniProtKB/TrEMBL database that is used for storing and processing
the unknown sequences. Hence, for all proteins we have available the sequence
along with few more information such as the taxon and some structural domains.
Pairwise similarity can be defined and computed on proteins based on such
attributes. Other important attributes, while present for proteins in
Swiss-Prot, are often missing for proteins in TrEMBL, such as their function
and cellular localization. The enormous number of protein sequences now in
TrEMBL calls for rapid procedures to annotate them automatically. In this work,
we present DistNBLP, a novel Distributed Neighborhood-Based Label Propagation
approach for large-scale annotation of proteins. To do this, the functional
annotations of reviewed proteins are used to predict those of non-reviewed
proteins using label propagation on a graph representation of the protein
database. DistNBLP is built on top of the "akka" toolkit for building resilient
distributed message-driven applications.


  For a decade now, evidence has accumulated that giant molecular clouds
located within the central molecular zone of our Galaxy reflect X-rays coming
from past outbursts of the supermassive black hole Sgr A*. However, the number
of illuminating events as well as their ages and durations are still unresolved
questions. We aim to reconstruct parts of the history of Sgr A* by studying
this reflection phenomenon in the molecular complex Sgr C and by determining
the line-of-sight positions of its main bright substructures. Using
observations made with XMM-Newton and Chandra between 2000 and 2014, we
investigated the variability of the reflected emission. We carried out an
imaging and a spectral analysis. We also used a Monte Carlo model of the
reflected spectra to constrain the line-of-sight positions of the brightest
clumps, and hence to assign an approximate date to the associated illuminating
events. We show that the emission from Sgr C exhibits significant variability
in both space and time, which confirms its reflection origin. The most likely
illuminating source is Sgr A*. We report two distinct variability timescales,
as one clump undergoes a sudden rise and fall in about 2005, while two others
vary smoothly throughout the whole 2000-2014 period. By fitting the Monte Carlo
model to the data, we are able to place tight constraints on the 3D positions
of the clumps. These two independent approaches provide a consistent picture of
the past activity of Sgr A*, since the two slowly varying clumps are located on
the same wavefront, while the rapidly varying clump corresponds to a different
wavefront, that is, to a different illuminating event. We show that Sgr A*
experienced at least two powerful outbursts in the past 300 years, and for the
first time, we provide an estimation of their age. Extending this approach to
other molecular complexes will allow this scenario to be tested further.


  We report the characterization of Bi$_2$Te$_2$Se crystals obtained by the
modified Bridgman and Bridgman-Stockbarger crystal growth techniques. X-ray
diffraction study confirms an ordered Se-Te distribution in the inner and outer
chalcogen layers, respectively, with a small amount of mixing. The crystals
displaying high resistivity ($> 1 \mathrm{\Omega cm}$) and low carrier
concentration ($\sim 5\times 10^{16}$/cm$^3$) at 4 K were found in the central
region of the long Bridgman-Stockbarger crystal, which we attribute to very
small differences in defect density along the length of the crystal rod.
Analysis of the temperature dependent resistivities and Hall coefficients
reveals the possible underlying origins of the donors and acceptors in this
phase.


  In multivariate statistics, the question of finding direct interactions can
be formulated as a problem of network inference - or network reconstruction -
for which the Gaussian graphical model (GGM) provides a canonical framework.
Unfortunately, the Gaussian assumption does not apply to count data which are
encountered in domains such as genomics, social sciences or ecology.
  To circumvent this limitation, state-of-the-art approaches use two-step
strategies that first transform counts to pseudo Gaussian observations and then
apply a (partial) correlation-based approach from the abundant literature of
GGM inference. We adopt a different stance by relying on a latent model where
we directly model counts by means of Poisson distributions that are conditional
to latent (hidden) Gaussian correlated variables. In this multivariate Poisson
lognormal-model, the dependency structure is completely captured by the latent
layer. This parametric model enables to account for the effects of covariates
on the counts.
  To perform network inference, we add a sparsity inducing constraint on the
inverse covariance matrix of the latent Gaussian vector. Unlike the usual
Gaussian setting, the penalized likelihood is generally not tractable, and we
resort instead to a variational approach for approximate likelihood
maximization. The corresponding optimization problem is solved by alternating a
gradient ascent on the variational parameters and a graphical-Lasso step on the
covariance matrix.
  We show that our approach is highly competitive with the existing methods on
simulation inspired from microbiological data. We then illustrate on three
various data sets how accounting for sampling efforts via offsets and
integrating external covariates (which is mostly never done in the existing
literature) drastically changes the topology of the inferred network.


  Analytical solutions of dispersion relations in the nuclear optical model
have been found for both imaginary volume and surface potentials. A standard
Brown-Rho shape has been assumed for the volume imaginary term and a Brown-Rho
shape multiplied by a decreasing exponential for the surface contribution. The
analytical solutions are valid for any even value of the exponent appearing in
these functional forms.


  In the framework of Carrol-Field-Jackiw electrodynamics we calculate the
spectral distribution of the Cherenkov radiation (CHR) produced by a charge
moving at constant velocity in a chiral medium. We find zero, one or two
Cherenkov angles according to the relation between the velocity of the particle
and the refraction index of the medium.


  Textual descriptions of the physical world implicitly mention commonsense
facts, while the commonsense knowledge bases explicitly represent such facts as
triples. Compared to dramatically increased text data, the coverage of existing
knowledge bases is far away from completion. Most of the prior studies on
populating knowledge bases mainly focus on Freebase. To automatically complete
commonsense knowledge bases to improve their coverage is under-explored. In
this paper, we propose a new task of mining commonsense facts from the raw text
that describes the physical world. We build an effective new model that fuses
information from both sequence text and existing knowledge base resource. Then
we create two large annotated datasets each with approximate 200k instances for
commonsense knowledge base completion. Empirical results demonstrate that our
model significantly outperforms baselines.


  We review our recent contributions on shot noise for entangled electrons and
spin-polarized currents in novel mesoscopic geometries. We first discuss some
of our recent proposals for electron entanglers involving a superconductor
coupled to a double dot in the Coulomb blockade regime, a superconductor
tunnel-coupled to Luttinger-liquid leads, and a triple-dot setup coupled to
Fermi leads. We calculate current and shot noise for spin-polarized currents
and entangled/unentangled electron pairs in a beam-splitter geometry with a
\textit{local} Rashba spin-orbit (s-o) interaction in the incoming leads. We
find \textit{continuous} bunching and antibunching behaviors for the
\textit{entangled} pairs -- triplet and singlet -- as a function of the Rashba
rotation angle. In addition, we find that unentangled triplets and the
entangled one exhibit distinct shot noise. Shot noise for spin-polarized
currents shows sizable oscillations as a function of the Rashba phase. This
happens only for electrons injected perpendicular to the Rashba rotation axis;
spin-polarized carriers along the Rashba axis are noiseless. We find an
additional spin rotation for electrons with energies near the crossing of the
bands where s-o induced interband coupling is relevant. This gives rise to an
additional modulation of the noise for both electron pairs and spin-polarized
currents. Finally, we briefly discuss shot noise for a double dot near the
Kondo regime.


  We compiled a list of more than 3500 eclipsing binaries located in and near
the Northern Continuous Viewing Zone (NCVZ) of the TESS space telescope that
have a sufficient amount of TESS photometry to search for additional hidden
components in these systems. We obtained the TESS light curves of all targets
in an automated way applying convolution-aided differential photometry on the
TESS Full-Frame Images from all available sectors up to Sector 60. Using a new
self-developed Python GUI, we visually vetted all of these light curves,
determined the eclipsing periods of the objects and calculated their eclipse
timing variations (ETVs). The ETV curves were used in order to search for
nonlinear variations that could be attributed to a light travel time effect
(LTTE) or dynamical perturbations caused by additional components in these
systems. We pre-selected 351 such candidates and tried to model their ETVs with
the analytic formulae of pure LTTE or the combination of LTTE and dynamical
perturbations. In total we could fit a model solution for the ETVs of 135
hierarchical triple candidates in which 10 systems were already known in the
literature and the remainder of the 125 systems are new discoveries. Among
these systems, there are some more noteworthy ones, such as five tight triples
very close to their dynamical stability limit with a period ratio of less than
20 and three newly discovered triply eclipsing triples. We point out that
dynamical perturbations are occurring in GZ Dra, which turns out to be a
triple. We also made a comparison of the distributions of some orbital
parameters coming from our solutions with those from the Kepler sample derived
by Borkovits et al. (2016). Finally, we checked the correlations between the
available parameters for systems that have Gaia Non-Single Star orbital
solutions with those from our ETV solutions. (Abridged)


  Anisotropic light transport is extremely common among scattering materials,
yet a comprehensive picture of how macroscopic diffusion is determined by
microscopic tensor scattering coefficients is not fully established yet. In
this work, we present a theoretical and experimental study of diffusion in
structurally anisotropic media with uniaxially symmetric scattering
coefficients. Exact analytical relations are derived in the case of
index-matched turbid media, unveiling the general relation between microscopic
scattering coefficients and the resulting macroscopic diffusion tensor along
different directions. Excellent agreement is found against anisotropic Monte
Carlo simulations up to high degrees of anisotropy, in contrast with previously
proposed approaches. The obtained solutions are used to analyze experimental
measurements of anisotropic light transport in polystyrene foam samples under
different degrees of uniaxial compression, providing a practical example of
their applicability.


  We perform a tomographic structure growth and expansion rate analysis using
the monopole, quadrupole and hexadecapole of the redshift-space galaxy power
spectrum derived from the Sloan Digital Sky Survey (SDSS-III) Baryon
Oscillation Spectroscopic Survey (BOSS) Data Release 12 combined sample, which
covers the redshift range of $0.20<z<0.75$. By allowing for overlap between
neighbouring redshift slices in order to extract information on the light-cone,
we successfully obtain joint BAO and RSD constraints with a precision of
$2-3\%$ for $D_A$, $3-10\%$ for $H$ and $9-12\%$ for $f\sigma_8$ with a
redshift resolution of $\Delta z\sim0.04$. Our measurement is consistent with
that presented in arXiv:1709.05173, where the analysis is performed in
configuration space. We apply our measurement to constrain the $f(R)$ gravity
model, and find that the 95\% CL upper limit of ${\rm log_{10}}B_0$ can be
reduced by 11\% by our tomographic BAO and RSD measurement.


  We predict the existence of triple point fermions in the band structure of
several half-Heusler topological insulators by $ab~initio$ calculations and the
Kane model. We find that many half-Heusler compounds exhibit multiple triple
points along four independent $C_3$ axes, through which the doubly degenerate
conduction bands and the nondegenerate valence band cross each other linearly
nearby the Fermi energy. When projected from the bulk to the (111) surface,
most of these triple points are located far away from the surface
$\bar{\Gamma}$ point, as distinct from previously reported triple point fermion
candidates. These isolated triple points give rise to Fermi arcs on the
surface, that can be readily detected by photoemission spectroscopy or scanning
tunneling spectroscopy.


  Exactly solvable model of two Rydberg-dressed atoms moving in a
quasi-two-dimensional harmonic trap is introduced and its properties are
investigated. Depending on the strength of inter-particle interactions and the
critical range of the potential, the two-particle eigenstates are classified
with respect to the excitations of the center-of-mass motion, relative angular
momentum, and relative distance variable. Having these solutions in hand, we
discuss inter-particle correlations as functions of interaction parameters. We
also present a straightforward prescription of how to generalize obtained
solutions to higher dimensions.


  A novel coding strategy for block-based compressive sens-ing named spatially
directional predictive coding (SDPC) is proposed, which efficiently utilizes
the intrinsic spatial cor-relation of natural images. At the encoder, for each
block of compressive sensing (CS) measurements, the optimal pre-diction is
selected from a set of prediction candidates that are generated by four
designed directional predictive modes. Then, the resulting residual is
processed by scalar quantiza-tion (SQ). At the decoder, the same prediction is
added onto the de-quantized residuals to produce the quantized CS measurements,
which is exploited for CS reconstruction. Experimental results substantiate
significant improvements achieved by SDPC-plus-SQ in rate distortion
performance as compared with SQ alone and DPCM-plus-SQ.


  Let $H^4$ denote the hyperbolic four-space. Given a bordered Riemann surface,
$M$, we prove that every smooth conformal superminimal immersion $\overline
M\to H^4$ can be approximated uniformly on compacts in $M$ by proper conformal
superminimal immersions $M\to H^4$. In particular, $H^4$ contains properly
immersed conformal superminimal surfaces normalised by any given open Riemann
surface of finite topological type without punctures. The proof uses the
analysis of holomorphic Legendrian curves in the twistor space of $H^4$.


  A light $Z'$ vector boson coupled to the second and third lepton generations
through $L_{\mu}-L_{\tau}$ current with mass below 200 MeV provides a very
viable explanation in terms of new physics to the recently confirmed
$(g-2)_\mu$ anomaly. This boson can be produced in the bremsstrahlung reaction
$\mu N \rightarrow \mu N Z'$ after a high energy muon beam collides with a
target. NA64$\mu$ is a fixed-target experiment using a 160 GeV muon beam from
the CERN Super Proton Synchrotron accelerator looking for the $Z'$ production
and its subsequent decays, $Z'\rightarrow invisible$. In this paper, we present
the study of the NA64$\mu$ sensitivity to search for such a $Z'$. This includes
a realistic beam simulation, the detailed detectors description and a
discussion about the main potential background sources. A pilot run is
scheduled in order to validate the simulation results. If those are confirmed,
NA64$\mu$ will be able to explore all the remaining phase space which could
provide an explanation for the $g-2$ muon anomaly.


  We show, theoretically and experimentally, that a sheet formed by two
confocal lenticular arrays can flip one component of the local light-ray
direction. Ray-optically, such a sheet is equivalent to a Dove-prism sheet, an
example of a METATOY (metamaterial for light rays), a structure that changes
the direction of transmitted light rays in a way that cannot be performed
perfectly wave-optically.


  The measurement of the wavelength of light using speckle is a promising tool
for the realization of compact and precise wavemeters and spectrometers.
However, the resolution of these devices is limited by strong correlations
between the speckle patterns produced by closely-spaced wavelengths. Here, we
show how principal component analysis of speckle images provides a route to
overcome this limit. Using this, we demonstrate a compact wavemeter which
measures wavelength changes of a stabilized diode laser of 5.3 am, eight orders
of magnitude below the speckle correlation limit.


  In this paper, we analyze and discuss the well-posedness of a new variant of
the so-called sweeping process, introduced by J.J. Moreau in the early 70's
\cite{More71} with motivation in plasticity theory. In this variant, the normal
cone to the (mildly non-convex) prox-regular moving set $C(t)$, supposed to
have an absolutely continuous variation, is perturbed by a sum of a
Carath\'{e}odory mapping and an integral forcing term. The integrand of the
forcing term depends on two time-variables, that is, we study a general
integro-differential sweeping process of Volterra type. By setting up an
appropriate semi-discretization method combined with a new Gronwall-like
inequality (differential inequality), we show that the integro-differential
sweeping process has one and only one absolutely continuous solution. We also
establish the continuity of the solution with respect to the initial value. The
results of the paper are applied to the study of nonlinear integro-differential
complementarity systems which are combination of Volterra integro-differential
equations with nonlinear complementarity constraints. Another application is
concerned with non-regular electrical circuits containing time-varying
capacitors and nonsmooth electronic device like diodes. Both applications
represent an additional novelty of our paper.


  Univariate delta Gon\v{c}arov polynomials arise when the classical
Gon\v{c}arov interpolation problem in numerical analysis is modified by
replacing derivatives with delta operators. When the delta operator under
consideration is the backward difference operator, we acquire the univariate
difference Gon\v{c}arov polynomials, which have a combinatorial relation to
lattice paths in the plane with a given right boundary. In this paper, we
extend several algebraic and analytic properties of univariate difference
Gon\v{c}arov polynomials to the multivariate case. We then establish a
combinatorial interpretation of multivariate difference Gon\v{c}arov
polynomials in terms of certain constraints on $d$-tuples of non-decreasing
integer sequences. This motivates a connection between multivariate difference
Gon\v{c}arov polynomials and a higher-dimensional generalized parking function,
the $\boldsymbol{U}$-parking function, from which we derive several enumerative
results based on the theory of multivariate delta Gon\v{c}arov polynomials.


  We study the production of proton, antiproton and net-proton at \AGS, \SPS
and \RHIC within the framework non-uniform flow model(NUFM) in this paper. It
is found that the system of RHIC has stronger longitudinally non-uniform
feature than AGS and SPS, which means that nuclei at RHIC energy region is much
more transparent. The NUFM model provides a very good description of all proton
rapidity at whole AGS, SPS and RHIC. It is shown that our analysis relates
closely to the study of nuclear stopping and longitudinally non-uniform flow
distribution of experiment. This comparison with AGS and SPS help us to
understand the feature of particle stopping of thermal freeze-out at RHIC
experiment.


  Coulomb interaction, following an inverse-square force-law, quantifies the
amount of force between two stationary and electrically charged particles. The
long-range nature of Coulomb interactions poses a major challenge to molecular
dynamics simulations which are major tools for problems at the nano-/micro-
scale. Various algorithms are developed to calculate the pairwise Coulomb
interactions to a linear scaling but the poor scalability limits the size of
simulated systems. Here, we conduct an efficient molecular dynamics algorithm
with the random batch Ewald method on all-atom systems where the complete
Fourier components in the Coulomb interaction are replaced by randomly selected
mini-batches. By simulating the $N$-body systems up to 100 million particles
using $10$ thousand CPU cores, we show that this algorithm furnishes $O(N)$
complexity, almost perfect scalability and an order of magnitude faster
computational speed when compared to the existing state-of-the-art algorithms.
Further examinations of our algorithm on distinct systems, including pure
water, micro-phase-separated electrolyte and protein solution demonstrate that
the spatiotemporal information on all time and length scales investigated and
thermodynamic quantities derived from our algorithm are in perfect agreement
with those obtained from the existing algorithms. Therefore, our algorithm
provides a breakthrough solution on scalability of computing the Coulomb
interaction. It is particularly useful and cost-effective to simulate
ultra-large systems, which was either impossible or very costing to conduct
using existing algorithms, thus would benefit the broad community of sciences.


  Let $F : \mathbb{R}^n \times \mathbb{R}^{N\times n} \rightarrow \mathbb{R}^N$
be a Caratheodory map. In this paper we consider the problem of existence and
uniqueness of weakly differentiable global strong a.e. solutions $u:
\mathbb{R}^n \longrightarrow \mathbb{R}^N$ to the fully nonlinear PDE system
\[\label{1} \tag{1} F(\cdot,Du ) \,=\, f, \ \ \text{ a.e. on }\mathbb{R}^n, \]
when $ f\in L^2(\mathbb{R}^n)^N$. This problem has not been considered before.
By introducing an appropriate notion of ellipticity, we prove existence of
solution to \eqref{1} in a tailored Sobolev "energy" space (known also as the
J.L. Lions space) and a uniqueness a priori estimate. The proof is based on the
solvability of the linearised problem by Fourier transform methods and a
"perturbation device" which allows to use of Campanato's notion of near
operators, an idea developed for the 2nd order case.


  We show that certain CP-odd momentum correlations in the production and
subsequent decay of tau pairs in $e^+e^-$ collisions get enhanced when the
electron beam is longitudinally polarized. Analytic expressions for these
correlations are obtained when $\tau^+\tau^-$ have a ``weak" dipole form factor
(WDFF) coupling to $Z$ in the case of two-body decay modes of the $\tau$.
Expressions of the variance of these correlations due to the standard model
interactions are also presented. For $e^+e^-$ collisions at the $Z$ peak, a
sensitivity of about $10^{-17} e$ cm for the real part of the $\tau$ WDFF and
$3\times 10^{-17} e$ cm for the imaginary part of the $\tau$ WDFF can be
reached using $\pi$ and $\rho$ channels (which are the most sensitive channels)
in $\tau$ decay, with $10^6\, Z$'s likely to be available at the SLC at
Stanford with $e^-$ polarization of 62\%-75\%.


  New data are reported for polyvinylidene fluoride (PVDF), polyphenylene
sulfide (PPS), and two forms of polyetherimide (PEI, branded ULTEM 1010 and
9085). Data for starting filaments and both simple and complex printed parts
are reported. PVDF filaments and simple printed beads, were found to have
values of approximately 30 and 50 ppt for Th-232 and U-238, respectively, while
a more complex spring clip part had slightly elevated Th-232 levels of 65 ppt,
with U-238 remaining at 50 ppt. PPS filament was found to have concentrations
of 270 and 710 ppt for Th-232 and U-238, respectively, and were not chosen to
be printed as those levels were already higher than other material options.
ULTEM 1010 filaments and printed complex spring clip parts were found to have
concentrations of around 5 and 7 ppt for Th-232 and U-238, respectively,
illustrating no significant contamination from the printing process. ULTEM 9085
filaments were found to have concentrations of around 9 and 5 ppt for Th-232
and U-238, respectively, while the printed complex spring clip part was found
to have slightly elevated concentrations of 25 and 7 ppt for Th-232 and U-238,
respectively. These results were all obtained using a novel dry ashing method
in crucibles constructed of ultralow background electroformed copper or, when
applicable, microwave-assisted wet ashing digestion. Samples and process blanks
were spiked with Th-229 and U-233 as internal standards prior to dry/wet ashing
and determinations were made by inductively coupled plasma mass spectrometry
(ICP-MS). In order to maintain high radiopurity levels, pre-cleaning the
filaments before printing and post-cleaning the parts is recommended, although
the printing process itself has shown to contribute very minute amounts of
radiocontaminants.


  The observation of CP violation effects is becoming more and more significant
in a variety of channels, due to the impressive experimental effort of the last
years. We review recent progress in Bs semileptonic decays and in Bs decays
into CP eigenstates.


  In this thesis, we theoretically predict the normal characteristics of Very
Low Frequency (3~30 kHz) radio wave propagation through Earth-ionosphere
waveguide corresponding to normal behavior of the D-region ionosphere. We took
the VLF narrow band data from the receivers of Indian Centre for Space Physics
(ICSP) to validate our models. Detection of sudden ionospheric disturbances
(SIDs) are common to all the measurements. We apply our theoretical models to
infer the D-region characteristics and to reproduce the observed VLF signal
behavior corresponding to such SIDs.
  We develop a code based on ray theory to simulate the diurnal behavior of VLF
signals over short propagation paths (2000~3000 km). The diurnal variation from
this code are comparable to the variation obtained from a more general Long
Wave Propagation Capability (LWPC) code which is based on mode theory approach.
We simulate the observational results obtained during the Total Solar Eclipse
of July 22, 2009 in India. We also report and simulate a historic event,
namely, the lunar occultation of a solar flare during the annular solar eclipse
of 15th January, 2010 and find the effects on the D-region electron density
profiles.


  Associated to any closed quantum subgroup $G\subset U_N^+$ and any index set
$I\subset\{1,\ldots,N\}$ is a certain homogeneous space $X_{G,I}\subset
S^{N-1}_{\mathbb C,+}$, called affine homogeneous space. We discuss here the
abstract axiomatization of the algebraic manifolds $X\subset S^{N-1}_{\mathbb
C,+}$ which can appear in this way, by using Tannakian duality methods.


  A broad goal in natural language processing (NLP) is to develop a system that
has the capacity to process any natural language. Most systems, however, are
developed using data from just one language such as English. The SIGMORPHON
2020 shared task on morphological reinflection aims to investigate systems'
ability to generalize across typologically distinct languages, many of which
are low resource. Systems were developed using data from 45 languages and just
5 language families, fine-tuned with data from an additional 45 languages and
10 language families (13 in total), and evaluated on all 90 languages. A total
of 22 systems (19 neural) from 10 teams were submitted to the task. All four
winning systems were neural (two monolingual transformers and two massively
multilingual RNN-based models with gated attention). Most teams demonstrate
utility of data hallucination and augmentation, ensembles, and multilingual
training for low-resource languages. Non-neural learners and manually designed
grammars showed competitive and even superior performance on some languages
(such as Ingrian, Tajik, Tagalog, Zarma, Lingala), especially with very limited
data. Some language families (Afro-Asiatic, Niger-Congo, Turkic) were
relatively easy for most systems and achieved over 90% mean accuracy while
others were more challenging.


  We consider a class of consensus systems driven by a nonlinear input. Such
systems arise in a class of IoT applications. Our objective in this paper is to
determine conditions under which a certain partially distributed system
converges to a Lur'e-like scalar system, and to provide a rigorous proof of its
stability. Conditions are derived for the non-uniform convergence and stability
of such a system and an example is given of a speed advisory system where such
a system arises in real engineering practice.


  Despite the clear-cut prediction and subsequent experimental detection of the
weak interaction bosons, the Higgs sector of the standard model of elementary
particle physics has long remained one of its most obscure features. Here, it
is demonstrated through a very basic argument that standard accounts of the
Higgs mechanism suffer from a serious conceptual consistency problem, in that
they incorrectly identify physical degrees of freedom. The point at issue, is
that the reasoning which leads to a removal of the unphysical excitation modes
is valid in both phases of the theory - i.e. both after and before the phase
transition occurs. Consistently removing unphysical degrees of freedom implies
a discrepancy in the number of physical degrees of freedom. In particular, the
longitudinally polarized, massive gauge boson degrees of freedom do not have
physical counterparts before the phase transition and are thus effectively
"created ex nihilio" at the transition, within the context of ordinary Higgs
models. Possible scenarios for removing the discrepancy are briefly considered.
The results obtained here strongly indicate that although standard,
perturbative formulations of the Higgs mechanism provide a convenient
parametrization of electroweak physics over a certain range of scales, they
cannot provide a sensible explanation of all relevant physical degrees of
freedom involved.


  The holographic RG flow in AdS/CFT correspondence naturally defines a
holographic scheme in which the central charge c and the beta function are
related by a universal formula. We perform some checks of that formula and we
compare it with quantum field theory expectations. We discuss alternative
definitions of the c-function. In particular, we compare, for a particular
supersymmetric flow, the holographic c-function with the central charge
computed directly from the two-point function of the stress-energy tensor.


  In this paper, we first generalize the class of linear codes by Ding and Ding
(IEEE TIT, 61(11), pp. 5835-5842, 2015). Then we mainly study the augmented
codes of this generalized class of linear codes. For one thing, we use Gaussian
sums to determine the parameters and weight distributions of the augmented
codes in some cases. It is shown that the augmented codes are self-orthogonal
and have only a few nonzero weights. For another thing, the locality of the
augmented codes is proved to be 2, which indicates the augmented codes are
useful in distributed storage. Besides, the augmented codes are projective as
the minimum distance of their duals is proved to be 3. In particular, we obtain
several (almost) optimal linear codes and locally recoverable codes.


  We study the shadows cast by rotating hairy black holes with two non-trivial
time-periodic scalar fields having a non-flat Gaussian curvature of the target
space spanned by the scalar fields. Such black holes are a viable alternative
to the Kerr black hole, having a much more complicated geodesic structure and
resulting shadows. We investigate how a nontrivial Gauss curvature alters the
pictures for different amounts of scalar hair around the black holes,
quantified by a normalized charge. Our results show that for high values of
this charge, close to a boson star limit, chaotic shadows are observed with
multiple small disconnected components for all considered Gaussian curvatures.
For moderately large amounts of scalar hair and corresponding normalized
charge, although the shadows still exhibit chaotic behavior, a dominant shadow
component emerges, the size and shape of which are substantially influenced by
the Gaussian curvature. For instance, highly chaotic shadows for flat target
space, start developing a large central shadow region with the increase of the
Gauss curvature even for black holes with substantially heavy scalar hair. For
lower values of the normalized charge, the shadows resemble qualitatively the
Kerr black hole while the Gaussian curvature has a small impact on their
properties.


  The interplay between global constraints and local material properties of
chain molecules is a subject of emerging interest. Studies of molecules that
are intrinsically chiral, such as double-stranded DNA, is one example. Their
properties generally depend on the local geometry, i.e. on curvature and
torsion, yet the paths of closed molecules are globally restricted by topology.
Molecules that fulfill a twist neutrality condition, a zero sum rule for the
incremental change in the rate of winding along the curve, will behave
neutrally to strain. This has implications for plasmids. For small circular
microDNAs it follows that there must exist a minimum length for these to be
double-stranded. It also follows that all microDNAs longer than the minimum
length must be concave. This counterintuitive result is consistent with the
kink-like appearance which has been observed for circular DNA. A prediction for
the total negative curvature of a circular microDNA is given as a function of
its length.


  The massive continuum limit of the 1+1 dimensional O(2) nonlinear
$\sigma$-model (XY model) is studied using its equivalence to the Sine-Gordon
model at its asymptotically free point. It is shown that leading lattice
artifacts are universal but they vanish only as inverse powers of the logarithm
of the correlation length. Such leading artifacts are calculated for the case
of the scattering phase shifts and the correlation function of the Noether
current using the bootstrap S-matrix and perturbation theory respectively.


  In the context of continuous first-order logic, special attention is often
given to theories that are somehow continuous in an 'essential' way. A common
feature of such theories is that they do not interpret any infinite discrete
structures. We investigate a stronger condition that is easier to establish and
use it to give an example of a strictly simple continuous theory that does not
interpret any infinite discrete structures: the theory of richly branching
$\mathbb{R}$-forests with generic binary predicates. We also give an example of
a superstable theory that fails to satisfy this stronger condition but
nevertheless does not interpret any infinite discrete structures.


  Provably efficient Model-Based Reinforcement Learning (MBRL) based on
optimism or posterior sampling (PSRL) is ensured to attain the global
optimality asymptotically by introducing the complexity measure of the model.
However, the complexity might grow exponentially for the simplest nonlinear
models, where global convergence is impossible within finite iterations. When
the model suffers a large generalization error, which is quantitatively
measured by the model complexity, the uncertainty can be large. The sampled
model that current policy is greedily optimized upon will thus be unsettled,
resulting in aggressive policy updates and over-exploration. In this work, we
propose Conservative Dual Policy Optimization (CDPO) that involves a
Referential Update and a Conservative Update. The policy is first optimized
under a reference model, which imitates the mechanism of PSRL while offering
more stability. A conservative range of randomness is guaranteed by maximizing
the expectation of model value. Without harmful sampling procedures, CDPO can
still achieve the same regret as PSRL. More importantly, CDPO enjoys monotonic
policy improvement and global optimality simultaneously. Empirical results also
validate the exploration efficiency of CDPO.


  We introduce an integrable impurity model in which both electrons and
impurity have spin and flavour degrees of freedom. This model is a
generalization of the multi-channel Kondo model and closely related with
resonant tunneling through quantum dot. The Hamiltonian is exactly diagonalized
by means of the Bethe ansatz.


  Dark matter with a non-zero self-interacting cross section ($\sigma_{\rm
SIDM}$) has been posited as a solution to a number of outstanding astrophysical
mysteries. Many studies of merging galaxy clusters have given constraints on
$\sigma_{\rm SIDM}$ based on the spatial offset between the member galaxy
population and the dark matter distribution. Assuming $\sigma_{\rm SIDM} = 0$,
how likely is it for us to see the galaxy-DM offset values observed in merging
clusters of galaxies? To answer this question, we formulate a hypothesis test
using data from Illustris, a $\Lambda$CDM cosmological simulation. We select 43
Illustris clusters and their galaxy members at z~0 and examine the accuracy of
commonly used galaxy summary statistics, including kernel-density-estimation
(KDE) luminosity peak, KDE number density peak, shrinking aperture, centroid
and the location of the brightest cluster galaxy (BCG). We use the dark-matter
particles to reproduce commonly adopted methods to identify dark-matter peaks
based on gravitational lensing cluster maps. By analysing each cluster in 768
projections, we determine the optimistic noise floor in the measurements of the
galaxy-DM offsets. We find that the choice of the galaxy summary statistics
affects the inferred offset values substantially, with the BCG and the
luminosity peak giving the tightest 68-th percentile offset levels, $\lesssim$
4 kpc and $\lesssim$ 32 kpc, respectively. Shrinking aperture, number density
and centroid give a large offset scatter of about 50-100 kpc at the 68-th
percentile level, even for clusters with only one dominant mass component. Out
of the 15 reported offsets from observed merging clusters that we examined, 13
of them are consistent with Illustris unrelaxed cluster offsets at the 2-sigma
(95-th percentile) level, i.e. consistent with the hypothesis that $\Lambda$CDM
is the true underlying physical model.


  We consider a Hamiltonian action of n-dimensional torus, T^n, on a compact
symplectic manifold (M,\omega) with d isolated fixed points. For every fixed
point p there exists (though not unique) a class a_p in H^*_{T}(M; Q) such that
the collection {a_p}, over all fixed points, forms a basis for H^*_{T}(M; Q) as
an H^*(BT; Q) module. The map induced by the inclusion, \iota^*:H^*_{T}(M; Q)
\rightarrow H^*_{T}(M^{T}; Q)= \oplus_{j=1}^{d}Q[x_1, ..., x_n] is injective.
We use such classes {a_p} to give necessary and sufficient conditions for
f=(f_1, ...,f_d) in \oplus_{j=1}^{d}Q[x_1, ..., x_n] to be in the image of
\iota^*, i.e. to represent an equiviariant cohomology class on M. In the case
when T is a circle and present these conditions explicitly. We explain how to
combine this 1-dimensional solution with Chang-Skjelbred Lemma in order to
obtain the result for a torus T of any dimension. Moreover, for a GKM
T-manifold M our techniques give combinatorial description of H^*_{K}(M; Q),
for a generic subgroup K \hookrightarrow T, even if M is not a GKM K-manifold.


  We address the problem of fundamental limitations of information extraction
from the environment in open quantum systems. We derive a model-independent,
hybrid quantum-classical solution of open dynamics in the recoil-less limit,
which includes environmental degrees of freedom. Specifying to the celebrated
Caldeira-Leggett model of hot thermal environments, ubiquitous in everyday
situations, we reveal the existence of a new lengthscale, called
distinguishability length, different from the well-known thermal de Broglie
wavelength that governs the decoherence. Interestingly, a new integral kernel,
called Quantum Fisher Information kernel, appears in the analysis. It
complements the well-known dissipation and noise kernels and satisfies
disturbance-information gain type of relations, similar to the famous
fluctuation-dissipation relation. Our results complement the existing
treatments of the Caldeira-Legget model from a non-standard and highly
non-trivial perspective of information dynamics in the environment. This leads
to a full picture of how the open evolution looks like from both the system and
the environment points of view, as well as sets limits on the precision of
indirect observations.


  The behavior decision-making subsystem is a key component of the autonomous
driving system, which reflects the decision-making ability of the vehicle and
the driver, and is an important symbol of the high-level intelligence of the
vehicle. However, the existing rule-based decision-making schemes are limited
by the prior knowledge of designers, and it is difficult to cope with complex
and changeable traffic scenarios. In this work, an advanced deep reinforcement
learning model is adopted, which can autonomously learn and optimize driving
strategies in a complex and changeable traffic environment by modeling the
driving decision-making process as a reinforcement learning problem.
Specifically, we used Deep Q-Network (DQN) and Proximal Policy Optimization
(PPO) for comparative experiments. DQN guides the agent to choose the best
action by approximating the state-action value function, while PPO improves the
decision-making quality by optimizing the policy function. We also introduce
improvements in the design of the reward function to promote the robustness and
adaptability of the model in real-world driving situations. Experimental
results show that the decision-making strategy based on deep reinforcement
learning has better performance than the traditional rule-based method in a
variety of driving tasks.


  We study several interesting examples of Biangular Tight Frames (BTFs) -
basis-like sets of unit vectors admitting exactly two distinct frame angles
(ie, pairwise absolute inner products) - and examine their relationships with
Equiangular Tight Frames (ETFs) - basis-like systems which admit exactly one
frame angle.
  We demonstrate a smooth parametrization BTFs, where the corresponding frame
angles transform smoothly with the parameter, which "passes through" an ETF
answers two questions regarding the rigidity of BTFs. We also develop a general
framework of so-called harmonic BTFs and Steiner BTFs - which includes the
equiangular cases, surprisingly, the development of this framework leads to a
connection with the famous open problem(s) regarding the existence of Mersenne
and Fermat primes. Finally, we construct a (chordally) biangular tight set of
subspaces (ie, a tight fusion frame) which "Pl\"ucker embeds" into an ETF.


  Let $q$ be a prime. We give an elementary proof of the fact that for any
$k\in\mathbb{N}$, the proportion of $k$-element subsets of $\mathbb{Z}$ that
contain a $q^{th}$ power modulo almost every prime, is zero. This result holds
regardless of whether the proportion is measured additively or
multiplicatively. More specifically, the number of $k$-element subsets of $[-N,
N]\cap\mathbb{Z}$ that contain a $q^{th}$ power modulo almost every prime is no
larger than $a_{q,k} N^{k-(1-\frac{1}{q})}$, for some positive constant
$a_{q,k}$. Furthermore, the number of $k$-element subsets of $\{\pm
p_{1}^{e_{1}} p_{2}^{e_{2}} \cdots p_{N}^{e_{N}} : 0 \leq e_{1}, e_{2}, \ldots,
e_{N}\leq N\}$ that contain a $q^{th}$ power modulo almost every prime is no
larger than $m_{q,k} \frac{N^{Nk}}{q^{N}}$ for some positive constant
$m_{q,k}$.


  The three areas of realistic forward rendering, per-pixel inverse rendering,
and generative image synthesis may seem like separate and unrelated sub-fields
of graphics and vision. However, recent work has demonstrated improved
estimation of per-pixel intrinsic channels (albedo, roughness, metallicity)
based on a diffusion architecture; we call this the RGB$\rightarrow$X problem.
We further show that the reverse problem of synthesizing realistic images given
intrinsic channels, X$\rightarrow$RGB, can also be addressed in a diffusion
framework.
  Focusing on the image domain of interior scenes, we introduce an improved
diffusion model for RGB$\rightarrow$X, which also estimates lighting, as well
as the first diffusion X$\rightarrow$RGB model capable of synthesizing
realistic images from (full or partial) intrinsic channels. Our
X$\rightarrow$RGB model explores a middle ground between traditional rendering
and generative models: we can specify only certain appearance properties that
should be followed, and give freedom to the model to hallucinate a plausible
version of the rest.
  This flexibility makes it possible to use a mix of heterogeneous training
datasets, which differ in the available channels. We use multiple existing
datasets and extend them with our own synthetic and real data, resulting in a
model capable of extracting scene properties better than previous work and of
generating highly realistic images of interior scenes.


  Beginning in 2016, the IceCube Neutrino Observatory has sent out alerts in
real time containing the information of high-energy ($E \gtrsim 100$~TeV)
neutrino candidate events with moderate-to-high ($\gtrsim 30$\%) probability of
astrophysical origin. In this work, we use a recent catalog of such alert
events, which, in addition to events announced in real-time, includes events
that were identified retroactively, and covers the time period of 2011-2020. We
also search for additional, lower-energy, neutrinos from the arrival directions
of these IceCube alerts. We show how performing such an analysis can constrain
the contribution of rare populations of cosmic neutrino sources to the diffuse
astrophysical neutrino flux. After searching for neutrino emission coincident
with these alert events on various timescales, we find no significant evidence
of either minute-scale or day-scale transient neutrino emission or of steady
neutrino emission in the direction of these alert events. This study also shows
how numerous a population of neutrino sources has to be to account for the
complete astrophysical neutrino flux. Assuming sources have the same
luminosity, an $E^{-2.5}$ neutrino spectrum and number densities that follow
star-formation rates, the population of sources has to be more numerous than
$7\times 10^{-9}~\textrm{Mpc}^{-3}$. This number changes to $3\times
10^{-7}~\textrm{Mpc}^{-3}$ if number densities instead have no cosmic
evolution.


  A continuous train of irregularly spaced spikes, peculiar of homoclinic
chaos, transforms into clusters of regularly spaced spikes, with quiescent
periods in between (bursting regime), by feeding back a low frequency portion
of the dynamical output. Such autonomous bursting results to be extremely
robust against noise; we provide experimental evidence of it in a CO2 laser
with feedback. The phenomen here presented display qualitative analogies with
bursting phenomena in neurons.


  We study homogeneous instantons on the seven dimensional Stiefel manifold V
in the context of G2 and Sasakian geometry. According to the reductive
decomposition of V we provide an explicit description of all invariant G2 and
Sasakian structures. In particular, we characterise the invariant G2-
structures inducing a Sasakian metric, among which the well known nearly
parallel G2-structure (Sasaki- Einstein) is included. As a consequence, we
classify the invariant connections on homogeneous principal bundles over V with
gauge group U(1) and SO(3), satisfying either the G2 or the Sasakian instanton
condition. Finally, we analyse the Yang Mills condition for those invariant
connections.


  We develop a generalization of Nesterov's accelerated gradient descent method
which is designed to deal with orthogonality constraints. To demonstrate the
effectiveness of our method, we perform numerical experiments which demonstrate
that the number of iterations scales with the square root of the condition
number, and also compare with existing state-of-the-art quasi-Newton methods on
the Stiefel manifold. Our experiments show that our method outperforms existing
state-of-the-art quasi-Newton methods on some large, ill-conditioned problems.


  We report the identification of a very low mass new binary system 2MASS
J10274572+0629104, based on Kepler K2 photometry and Gaia DR2 astrometry. The
K2 light curve is consistent with a beat pattern of two periodic signals, and
using Lomb-Scargle periodogram, we find two rotation periods of 0.2114 \pm
0.0002 day and 0.2199 \pm 0.0003 day.We conclude that these rotation periods
arise from two stars with similar spectral types of M6, and have near equal
luminosity. It is the first ultracool binary system to be identified based on
beat patterns in the light curve. Near-infrared spectroscopy yields RV = -9.8
\pm 0.6 km s^-1, v sin i = 21.5 \pm 1.1 km s^-1, T_eff = 3110 \pm 40 K, and log
g = 5.2 \pm 0.2. The motions are consistent with a young age, as are the
rotation periods, but the source does not appear to be part of any known moving
group. Furthermore, we detected three strong white light flares in the K2 light
curve, with estimated total bolometric (UV/optical/IR) energies to be 2.6 X
10^33, 5.0 X 10^33, and 3.5 X 10^33 erg respectively.


  We present new bounds for the numerical radius of bounded linear operators
and $2\times 2$ operator matrices. We apply upper bounds for the numerical
radius to the Frobenius companion matrix of a complex monic polynomial to
obtain new estimations for zeros of that polynomial. We also show with
numerical examples that our new estimations improve on the existing
estimations.


  We discuss a new approach to the investigation of the nature of the mass gap
in spin systems with continuous global symmetries which is much analogous to
the method of abelian projection in the gauge theories. We suggest that the
abelian degrees of freedom, in particular, abelian vortices are responsible for
the mass gap generation phenomena in the non-abelian spin systems. To check our
hypothesis we study numerically the three-dimensional SU(2) spin model in the
Maximal Abelian projection. We find that the abelian mass gap in the projected
theory coincides with the full non-abelian mass gap within numerical errors.
The study of the percolation properties of the abelian vortex trajectories
shows that the phase transition and the mass gap generation in the 3D SU(2)
spin model are driven by the abelian vortex condensation.


  We report a compact, cost-effective and field-portable lensless imaging
platform for quantitative microscopy. In this platform, the object is placed on
top of an image sensor chip without using any lens. We use a low-cost galvo
scanner to rapidly scan an unknown laser speckle pattern on the object. To
address the positioning repeatability and accuracy issues, we directly recover
the positional shifts of the speckle pattern based on the phase correlation of
the captured images. To bypass the resolution limit set by the imager pixel
size, we employ a sub-sampled ptychographic phase retrieval process to recover
the complex object. We validate our approach using a resolution target, a phase
target, and a biological sample. Our results show that accurate, high-quality
complex images can be obtained from a lensless dataset with as few as ~10
images. We also demonstrate the reported approach to achieve a 6.4 mm by 4.6 mm
field of view and a half pitch resolution of 1 miron. The reported approach may
provide a quantitative lensless imaging strategy for addressing point-of-care,
global-health, and telemedicine related challenges.


  Orbital debris presents a growing risk to space operations, and is becoming a
significant source of contamination of astronomical images. Much of the debris
population is uncatalogued, making the impact more difficult to assess. We
present initial results from the first ten nights of commissioning observations
with the International Liquid Mirror Telescope, in which images were examined
for streaks produced by orbiting objects including satellites, rocket bodies
and other forms of debris. We detected 83 streaks and performed a correlation
analysis to attempt to match these with objects in the public database. 48\% of
these objects were uncorrelated, indicating substantial incompleteness in the
database, even for some relatively-bright objects. We were able to detect
correlated objects to an estimated magnitude of 14.5 and possibly about two
magnitudes greater for the faintest uncorrelated object.


  Let G be a connected simple algebraic group over an algebraically closed
field k of characteristic p > 0, and g := Lie(G). We additionally assume that G
is standard and is of type An. Motivated by the investigation of the geometric
properties of the varieties E(r, g) of r-dimensional elementary subalgebras of
a restricted Lie algebra g, we will show in this article the irreducible
components of E(rkp(g)-1,g) when rkp(g) is the maximal dimension of an
elementary subalgebra of g.


  We announce recent results on a connection between factorization statistics
of polynomials over a finite field and the structure of the cohomology of
configurations in $\mathbb{R}^3$ as a representation of the symmetric group.
This connection parallels a result of Church, Ellenberg, and Farb relating
factorization statistics of squarefree polynomials and the cohomology of
configurations in $\mathbb{R}^2$.


  Critical properties of QCD and the chiral condensate at finite density are
analytically studied on an anisotropic lattice in the approximation SU(N)
\simeq Z(N). Asymptotic behavior of the partition function and its continuum
limit are discussed.


  We compute the gluon polarization $\Delta G$ and the gluon total angular
momentum $J_g$ in the Isgur-Karl quark model. Taking into account
self-interaction contributions, we obtain for both quantities a positive value
of about 0.24 at the model scale $\mu_0^2 \simeq 0.25$ GeV$^2$. This estimate
is reasonably close to the expectation from polarized deep inelastic scattering
analyses.


  In this paper we present an application where we put together two methods for
clustering and classification into a force aggregation method. Both methods are
based on conflicts between elements. These methods work with different type of
elements (intelligence reports, vehicles, military units) on different
hierarchical levels using specific conflict assessment methods on each level.
We use Dempster-Shafer theory for conflict calculation between elements,
Dempster-Shafer clustering for clustering these elements, and templates for
classification. The result of these processes is a complete force aggregation
on all levels handled.


  We investigate the rotation sets of open billiards in $\mathbb{R}^N$ for the
natural observable related to a starting point of a given billiard trajectory.
We prove that the general rotation set is convex and the set of all convex
combinations of rotation vectors of periodic trajectory $P_\phi$ is dense in
it. We provide a constructive proof which illustrates that the set $P_\phi$ is
dense in the pointwise rotation set, and the closure of the pointwise rotation
set is convex. We also consider a class of billiards consisting of three
obstacles and construct a sequence in the symbol space such that its rotation
vector is not defined.


  Lack of awareness and knowledge of microservices-specific security challenges
and solutions often leads to ill-informed security decisions in microservices
system development. We claim that identifying and leveraging security
discussions scattered in existing microservices systems can partially close
this gap. We define security discussion as "a paragraph from developer
discussions that includes design decisions, challenges, or solutions relating
to security". We first surveyed 67 practitioners and found that securing
microservices systems is a unique challenge and that having access to security
discussions is useful for making security decisions. The survey also confirms
the usefulness of potential tools that can automatically identify such security
discussions. We developed fifteen machine/deep learning models to automatically
identify security discussions. We applied these models on a manually
constructed dataset consisting of 4,813 security discussions and 12,464
non-security discussions. We found that all the models can effectively identify
security discussions: an average precision of 84.86%, recall of 72.80%,
F1-score of 77.89%, AUC of 83.75% and G-mean 82.77%. DeepM1, a deep learning
model, performs the best, achieving above 84% in all metrics and significantly
outperforms three baselines. Finally, the practitioners' feedback collected
from a validation survey reveals that security discussions identified by DeepM1
have promising applications in practice.


  This paper is no longer active and will NOT appear in print. For new data and
analysis, please see: arXiv:0903.2220


  We revisit multivariate extreme value theory modeling by emphasizing
multivariate regular variations and the multivariate Breiman Lemma. This allows
us to recover in a simple framework the most popular multivariate extreme value
distributions, such as the logistic, negative logistic, Dirichlet, extremal-$t$
and H\"usler-Reiss models. In a second part of the paper, we focus on the
H\"usler-Reiss Pareto model and its surprising exponential family property.
After a thorough study of this exponential family structure, we focus on
maximum likelihood estimation. We also consider the generalized H\"usler-Reiss
Pareto model with different tail indices and a likelihood ratio test for
discriminating constant tail index versus varying tail indices.


  This is a companion paper to our recent work [9], where we studied the
interior Bernoulli free boundary for the infinity Laplacian. Here we consider
its variational side, which corresponds to the supremal version of the
Alt--Caffarelli minimization problem.


  For defining the optimal machine learning algorithm, the decision was not
easy for which we shall choose. To help future researchers, we describe in this
paper the optimal among the best of the algorithms. We built a synthetic data
set and performed the supervised machine learning runs for five different
algorithms. For heterogeneous rock fabric, we identified Random Forest, among
others, to be the appropriate algorithm.


  We explain how dispersionless integrable hierarchy in 2d topological field
theory arises from the Kodaira-Spencer gravity (BCOV theory). The infinitely
many commuting Hamiltonians are given by the current observables associated to
the infinite abelian symmetries of the Kodaira-Spencer gravity. We describe a
BV framework of effective field theories that leads to the B-model
interpretation of dispersionless integrable hierarchy.


  Ginzburg-Landau functional is derived for a system possessing both chiral and
diquark condensates. Anderson theorem for such a system is formulated and
proved.


  The Hamiltonian formulation of the Holst action in presence of a massless
fermion field with a non-minimal Lagrangian is performed without any
restriction on the local Lorentz frame. It is outlined that the phase space
structure does not resemble that one of a background independent Lorentz gauge
theory, as some additional constraints are present. Proper phase space
coordinates are introduced, such that SU(2) connections can be defined and the
vanishing of conjugate momenta to boost variables is predicted. Finally, it is
demonstrated that for a particular value of the non-minimal parameter the
kinematics coincides with that one of a background independent SU(2) gauge
theory and the Immirzi parameter becomes the coupling constant of such an
interaction between fermions and the gravitational field.


  The in vivo observation of the human retina at the cellular level is crucial
to detect lesions before irreversible visual loss occurs, to follow the time
course of retinal diseases and to evaluate and monitor the early effects of
treatments. Despite the phenomenal advances in optical coherence tomography
(OCT) and adaptive optics systems, in vivo imaging of several retinal cells is
still elusive. Here we propose a radically different method compared to OCT,
called transscleral optical phase imaging (TOPI), which allows to image retinal
cells with high contrast, high resolution, and within an acquisition time
suitable for clinical use. TOPI relies on high-angle oblique illumination of
the retina, combined with adaptive optics, to enhance the phase contrast of
transparent cells. We first present in-vivo images of retinal cells, from the
retinal pigment epithelium (RPE) to the nerve and vascular layers of the
retina, in eleven healthy volunteers without pupil dilation. The morphology of
the cells in vivo is then compared to that of images obtained with the same
technique applied on ex vivo human RPE and pig retinas. Finally, we demonstrate
the ability of high resolution phase microscopy to image pericytes and
microglia around rat retinal capillaries. Our results show the ability of TOPI
to image and quantify retinal cells up to the RPE depth within a maximum time
of 9 seconds over a field of view of 4.4 x 4.4{\deg}, opening new avenue in the
in vivo exploration of the deepest layer of the retina in healthy and diseased
eyes.


  We consider the problem of approximating a linear cocycle (or, more
generally, a vector bundle automorphism) over a fixed base dynamics by another
cocycle admitting a dominated splitting. We prove that the possibility of doing
so depends only on the homotopy class of the cocycle, provided that the base
dynamics is a minimal diffeomorphism and the fiber dimension is least 3. This
result is obtained by means of a general theorem on the existence of almost
invariant sections for fiberwise isometries of bundles with compact fibers and
finite fundamental group. The main novelty of the proofs is the use of a
quantitative homotopy result due to Calder, Siegel, and Williams.


  For a pair of finitely generated modules $M$ and $N$ over a codimension $c$
complete intersection ring $R$ with $\ell(M\otimes_RN)$ finite, we pay special
attention to the inequality $\dim M+\dim N \leq \dim R +c$. In particular, we
develop an extension of Hochster's theta invariant whose nonvanishing detects
equality. In addition, we consider a parallel theory where dimension and
codimension are replaced by depth and complexity, respectively.


  We determine the essential spectrum of Hamiltonians with N-body type
interactions that have radial limits at infinity. This extends the HVZ-theorem,
which treats perturbations of the Laplacian by potentials that tend to zero at
infinity. Our proof involves $C^*$-algebra techniques that allows one to treat
large classes of operators with local singularities and general behavior at
infinity. In our case, the configuration space of the system is a finite
dimensional, real vector space $X$, and we consider the $C^*$-algebra
$\mathcal{E}(X)$ of functions on $X$ generated by functions of the form
$v\circ\pi_Y$, where $Y$ runs over the set of all linear subspaces of $X$,
$\pi_Y$ is the projection of $X$ onto the quotient $X/Y$, and
$v:X/Y\to\mathbb{C}$ is a continuous function that has uniform radial limits at
infinity. The group $X$ acts by translations on $\mathcal{E}(X)$, and hence the
crossed product $\mathscr{E}(X) := \mathcal{E}(X)\rtimes X$ is well defined;
the Hamiltonians that are of interest to us are the self-adjoint operators
affiliated to it. We determine the characters of $\mathcal{E}(X)$. This then
allows us to describe the quotient of $\mathscr{E}(X)$ with respect to the
ideal of compact operators, which in turn gives a formula for the essential
spectrum of any self-adjoint operator affiliated to $\mathscr(X)$.


  Primary and secondary education is a crucial stage to build a strong
foundation before diving deep into specialised subjects in colleges and
universities. To excel in the current education system, students are required
to have a deep understanding of knowledge according to standardized curriculums
and syllabus, and exam-related problem solving skills. In current school
settings, this learning normally occurs in large classes of 30-40 students per
class. Such a ``one size fits all'' approach may not be effective, as different
students proceed on their learning in different ways and pace. To address this
problem, we propose the Self-Evolving Adaptive Learning (SEAL) system for
personalized education at scale.


  This paper provides a new geospatial perspective on whether or not Zipf's law
holds for all cities or for the largest cities in the United States using a
massive dataset and its computing. A major problem around this issue is how to
define cities or city boundaries. Most of the investigations of Zipf's law rely
on the demarcations of cities imposed by census data, e.g., metropolitan areas
and census-designated places. These demarcations or definitions (of cities) are
criticized for being subjective or even arbitrary. Alternative solutions to
defining cities are suggested, but they still rely on census data for their
definitions. In this paper we demarcate urban agglomerations by clustering
street nodes (including intersections and ends), forming what we call natural
cities. Based on the demarcation, we found that Zipf's law holds remarkably
well for all the natural cities (over 2-4 million in total) across the United
States. There is little sensitivity for the holding with respect to the
clustering resolution used for demarcating the natural cities. This is a big
contrast to urban areas, as defined in the census data, which do not hold
stable for Zipf's law.
  Keywords: Natural cities, power law, data-intensive geospatial computing,
scaling of geographic space


  We introduce a new perturbation for the operator curl related to connections
with nonabelian gauge groups. We also prove that the perturbed operator is
unitary equivalent to the operator curl if the corresponding connection is
close enough to the trivial one with respect to a certain topology on the space
of connections.


  We analyse, using Inhomogenous Mode-Coupling Theory, the critical scaling
behaviour of the dynamical susceptibility at a distance epsilon from continuous
second-order glass transitions. We find that the dynamical correlation length
xi behaves generically as epsilon^{-1/3} and that the upper critical dimension
is equal to six. More surprisingly, we find activated dynamic scaling, where xi
grows with time as [ln(t)]^2 exactly at criticality. All these results suggest
a deep analogy between the glassy behaviour of attractive colloids or randomly
pinned supercooled liquids and that of the Random Field Ising Model.


  We employ a recently-developed transfer-matrix formulation of scattering
theory in two dimensions to study a class of scattering setups modeled by real
potentials. The transfer matrix for these potentials is related to the
time-evolution operator for an associated pseudo-Hermitian Hamiltonian operator
$\widehat{\mathbf{H}}$ which develops an exceptional point for a discrete set
of incident wavenumbers. We use the spectral properties of this operator to
determine the transfer matrix of these potentials and solve their scattering
problem. We apply our general results to explore the scattering of waves by a
waveguide of finite length in two dimensions, where the source of the incident
wave and the detectors measuring the scattered wave are positioned at spatial
infinities while the interior of the waveguide, which is filled with an
inactive material, forms a finite rectangular region of the space. The study of
this model allows us to elucidate the physical meaning and implications of the
presence of the real and complex eigenvalues of $\widehat{\mathbf{H}}$ and its
exceptional points. Our results reveal the relevance of the concepts of
pseudo-Hermitian operator and exceptional point in the standard quantum
mechanics of closed systems where the potentials are required to be real.


  We investigate the QCD phase diagram in the strong-coupling lattice QCD with
fluctuation and $1/g^2$ effects by using the auxiliary field Monte-Carlo
simulations. The complex phase of the Fermion determinant at finite chemical
potential is found to be suppressed by introducing a complex shift of integral
path for one of the auxiliary fields, which corresponds to introducing a
repulsive vector mean field for quarks. The obtained phase diagram in the
chiral limit shows suppressed $T_c$ in the second order phase transition region
compared with the strong-coupling limit results. We also argue that we can
approximately guess the statistical weight cancellation from the complex phase
in advance in the case where the complex phase distribution is Gaussian. We
demonstrate that correct expectation values are obtained by using this guess in
the importance sampling (preweighting).


  We consider a stochastic heat equation driven by a space-time white noise and
with a singular drift, where a local-time in space appears. The process we
study has an explicit invariant measure of Gibbs type, with a non-convex
potential. We obtain existence of a Markov solution, which is associated with
an explicit Dirichlet form. Moreover we study approximations of the stationary
solution by means of a regularization of the singular drift or by a
finite-dimensional projection.


  Let C be a nonempty, bounded, closed, and convex subset of a Banach space X
and $T : C \rightarrow C$ be a monotone asymptotic nonexpansive mapping. In
this paper, we investigate the existence of fixed points of T. In particular,
we establish an analogue to the original Goebel and Kirk's fixed point theorem
for asymptotic nonexpansive mappings.


  Demand outstrips available resources in most situations, which gives rise to
competition, interaction and learning. In this article, we review a broad
spectrum of multi-agent models of competition (El Farol Bar problem, Minority
Game, Kolkata Paise Restaurant problem, Stable marriage problem, Parking space
problem and others) and the methods used to understand them analytically. We
emphasize the power of concepts and tools from statistical mechanics to
understand and explain fully collective phenomena such as phase transitions and
long memory, and the mapping between agent heterogeneity and physical disorder.
As these methods can be applied to any large-scale model of competitive
resource allocation made up of heterogeneous adaptive agent with non-linear
interaction, they provide a prospective unifying paradigm for many scientific
disciplines.


  The measurement of the mixing-induced CP-violating phase $\phi_s$ in the
$B^0_s - \bar{B}^0_s$ system is one of the key goals of the LHCb experiment,
and provides an excellent opportunity to search for New Physics beyond Standard
Model. Using Run-I data, $\phi_s$ has been measured in several decay channels.
These proceedings briefly summarise the previous LHCb Run-I results of $\phi_s$
measurement, and show the most recent results obtained by analysing the decay
channel $B^0_s \to J/\psi K^+ K^-$ in the $K^+ K^-$ mass region above the
$\phi$(1020) resonance.


  This paper analyzes independence concepts for sets of probability measures
associated with directed acyclic graphs. The paper shows that epistemic
independence and the standard Markov condition violate desirable separation
properties. The adoption of a contraction condition leads to d-separation but
still fails to guarantee a belief separation property. To overcome this
unsatisfactory situation, a strong Markov condition is proposed, based on
epistemic independence. The main result is that the strong Markov condition
leads to strong independence and does enforce separation properties; this
result implies that (1) separation properties of Bayesian networks do extend to
epistemic independence and sets of probability measures, and (2) strong
independence has a clear justification based on epistemic independence and the
strong Markov condition.


  We prove that every profinite $n$-ary group $(G, f)=\Gf$ has a unique Haar
measure $m_p$ and further for every measurable subset $A\subseteq G$, we have
$$ m_p(A)=m(A)=(n-1)m^{\ast}(A) $$ where $m$ and $m^{\ast}$ are the normalized
Haar measures of the profinite groups $(G, \bullet)$ and the Post cover
$G^{\ast}$, respectively.


  The large-scale integration of Distributed Energy Resources (DERs) into the
electric power system offers new opportunities to ensure stability. For
example, Active Distribution Networks (ADNs) can be used in (sub-)transmission
systems in the emergency state, as far as high robustness and performance of
the ADN control are guaranteed. This paper presents an adaptive control system
for ADN's cross-voltage-level power flow control. For this purpose, the gain
scheduling approach is used. Furthermore, this work introduces a method for
control parameter tuning. In order to validate the control parameter tuning,
the adaptive control system is analyzed regarding robustness and performance
using an exemplary medium voltage grid. In addition, the influence of
uncertainties is examined. Finally, the operation of the adaptive control
system is demonstrated by performing time-domain simulations.


  I summarize Density Functional Theory (DFT) in a language familiar to quantum
field theorists, and introduce several apparently novel ideas for constructing
{\it systematic} approximations for the density functional. I also note that,
at least within the large $K$ approximation ($K$ is the number of electron spin
components), it is easier to compute the quantum effective action of the
Coulomb photon field, which is related to the density functional by algebraic
manipulations in momentum space.


  The Stefan-Boltzmann law yields a fundamental constraint on the geometry of
inner accretion disks in black-hole X-ray binaries. It follows from considering
the irradiating flux and the effective temperature of the inner parts of the
disk, which implies that a strong quasi-thermal component with the average
energy higher than that of a blackbody at the effective temperature has to be
present whenever relativistic Fe K fluorescence and reflection features are
observed. The apparent absence of such quasi-thermal component with the color
temperature of $\sim$1 keV in high-luminosity hard states is not compatible
with a strongly irradiated disk extending close to the innermost stable
circular orbit. Instead, the disk should be either truncated at a relatively
large radius or irradiated by a corona at a large height, which would reduce
the effective temperature and bring it to an agreement with the data. We also
study constraints on disk/corona models following from comparing the disk
densities fitted in literature using variable-density reflection codes with
those calculated by us from the ionization parameter, the luminosity and the
disk inner radius. We find that the fitted densities are much higher/lower in
the hard/soft state of binaries, implying significant problems with the used
assumptions and methods.


  A search for the flavour-changing neutral-current decay $t\to qZ$ is
presented. Data collected by the ATLAS detector during 2012 from proton-proton
collisions at the Large Hadron Collider at a centre-of-mass energy of
$\sqrt{s}=8$ TeV, corresponding to an integrated luminosity of 20.3 fb$^{-1}$,
are analysed. Top-quark pair-production events with one top quark decaying
through the $t\to qZ$ ($q=u,c$) channel and the other through the dominant
Standard Model mode $t\to bW$ are considered as signal. Only the decays of the
$Z$ boson to charged leptons and leptonic $W$ boson decays are used. No
evidence for a signal is found and an observed (expected) upper limit on the
$t\to qZ$ branching ratio of $7\times 10^{-4}$ ($8\times 10^{-4}$) is set at
the 95% confidence level.


  A simplified model of a redundant power grid is used to study integration of
fluctuating renewable generation. The grid consists of large number of
generator and consumer nodes. The net power consumption is determined by the
difference between the gross consumption and the level of renewable generation.
The gross consumption is drawn from a narrow distribution representing the
predictability of aggregated loads, and we consider two different distributions
representing wind and solar resources. Each generator is connected to D
consumers, and redundancy is built in by connecting R of these consumers to
other generators. The lines are switchable so that at any instance each
consumer is connected to a single generator. We explore the capacity of the
renewable generation by determining the level of "firm" generation capacity
that can be displaced for different levels of redundancy R. We also develop
message-passing control algorithm for finding switch settings where no
generator is overloaded.


  We show the existence of uniformly bounded sequences of increasing numbers of
orthonormal sections of powers $L^k$ of a positive holomorphic line bundle $L$
on a compact K\"ahler manifold $M$. In particular, we construct for each
positive integer $k$, orthonormal sections $s^k_1,\dots,s^k_{n_k}$ in
$H^0(M,L^k)$, $n_k\ge\beta\dim H^0(M,L^k)$, such that $\{s^k_j\}$ is a
uniformly bounded family, where $\beta$ is an explicit positive constant
depending only on the dimension of $M$. For $m=1$, we can take $\beta=.99564$.


  We use MERLIN, VLA and VLBA observations of Galactic \HI absorption towards
3C~138 to estimate the structure function of the \HI opacity fluctuations at AU
scales. Using Monte Carlo simulations, we show that there is likely to be a
significant bias in the estimated structure function at signal-to-noise ratios
characteristic of our observations, if the structure function is constructed in
the manner most commonly used in the literature. We develop a new estimator
that is free from this bias and use it to estimate the true underlying
structure function slope on length scales ranging $5$ to $40$~AU. From a power
law fit to the structure function, we derive a slope of $0.81^{+0.14}_{-0.13}$,
i.e. similar to the value observed at parsec scales. The estimated upper limit
for the amplitude of the structure function is also consistent with the
measurements carried out at parsec scales. Our measurements are hence
consistent with the \HI opacity fluctuation in the Galaxy being characterized
by a power law structure function over length scales that span six orders of
magnitude. This result implies that the dissipation scale has to be smaller
than a few AU if the fluctuations are produced by turbulence. This inferred
smaller dissipation scale implies that the dissipation occurs either in (i)
regions with densities $\gtrsim 10^3 $cm$^-3$ (i.e. similar to that inferred
for "tiny scale" atomic clouds or (ii) regions with a mix of ionized and atomic
gas (i.e. the observed structure in the atomic gas has a magneto-hydrodynamic
origin).


  Racial diversity has become increasingly discussed within the AI and
algorithmic fairness literature, yet little attention is focused on justifying
the choices of racial categories and understanding how people are racialized
into these chosen racial categories. Even less attention is given to how racial
categories shift and how the racialization process changes depending on the
context of a dataset or model. An unclear understanding of \textit{who}
comprises the racial categories chosen and \textit{how} people are racialized
into these categories can lead to varying interpretations of these categories.
These varying interpretations can lead to harm when the understanding of racial
categories and the racialization process is misaligned from the actual
racialization process and racial categories used. Harm can also arise if the
racialization process and racial categories used are irrelevant or do not exist
in the context they are applied.
  In this paper, we make two contributions. First, we demonstrate how racial
categories with unclear assumptions and little justification can lead to
varying datasets that poorly represent groups obfuscated or unrepresented by
the given racial categories and models that perform poorly on these groups.
Second, we develop a framework, CIRCSheets, for documenting the choices and
assumptions in choosing racial categories and the process of racialization into
these categories to facilitate transparency in understanding the processes and
assumptions made by dataset or model developers when selecting or using these
racial categories.


  In this paper we analyze in the Wilson loop context the parallel transport of
vectors and spinors around a closed loop in the background space-time of a
rotating black string in order to classify its global properties. We also
examine particular closed orbits in this space-time and verify the Mandelstam
relations.


  If you fall into a real astronomical black hole (choosing a supermassive
black hole, to make sure that the tidal forces don't get you first), then you
will probably meet your fate not at a central singularity, but rather in the
exponentially growing, relativistic counter-streaming instability at the inner
horizon first pointed out by Poisson & Israel (1990), who called it mass
inflation. The chief purpose of this paper is to present a clear exposition of
the physical cause and consequence of inflation in spherical, charged black
holes. Inflation acts like a particle accelerator in that it accelerates cold
ingoing and outgoing streams through each other to prodigiously high energies.
Inflation feeds on itself: the acceleration is powered by the gravity produced
by the streaming energy. The paper: (1) uses physical arguments to develop
simple approximations that follow the evolution of inflation from ignition,
through inflation itself, to collapse; (2) confirms that the simple
approximations capture accurately the results of fully nonlinear one- and
two-fluid self-similar models; (3) demonstrates that, counter-intuitively, the
smaller the accretion rate, the more rapidly inflation exponentiates; (4) shows
that in single perfect-fluid models, inflation occurs only if the sound speed
equals the speed of light, supporting the physical idea that inflation in
single fluids is driven by relativistic counter-streaming of waves; (5) shows
that what happens during inflation up to the Planck curvature depends not on
the distant past or future, but rather on events happening only a few hundred
black hole crossing times into the past or future; (6) shows that, if quantum
gravity does not intervene, then the generic end result of inflation is not a
general relativistic null singularity, but rather a spacelike singularity at
zero radius.


  This report outlines the objectives, methodology, challenges, and results of
the first Fuzzing Competition held at SBFT 2023. The competition utilized
FuzzBench to assess the code-coverage performance and bug-finding efficacy of
eight participating fuzzers over 23 hours. The competition was organized in
three phases. In the first phase, participants were asked to integrate their
fuzzers into FuzzBench and allowed them to privately run local experiments
against the publicly available benchmarks. In the second phase, we publicly ran
all submitted fuzzers on the publicly available benchmarks and allowed
participants to fix any remaining bugs in their fuzzers. In the third phase, we
publicly ran all submitted fuzzers plus three widely-used baseline fuzzers on a
hidden set and the publicly available set of benchmark programs to establish
the final results.


  We present a method for novel view synthesis from input images that are
freely distributed around a scene. Our method does not rely on a regular
arrangement of input views, can synthesize images for free camera movement
through the scene, and works for general scenes with unconstrained geometric
layouts. We calibrate the input images via SfM and erect a coarse geometric
scaffold via MVS. This scaffold is used to create a proxy depth map for a novel
view of the scene. Based on this depth map, a recurrent encoder-decoder network
processes reprojected features from nearby views and synthesizes the new view.
Our network does not need to be optimized for a given scene. After training on
a dataset, it works in previously unseen environments with no fine-tuning or
per-scene optimization. We evaluate the presented approach on challenging
real-world datasets, including Tanks and Temples, where we demonstrate
successful view synthesis for the first time and substantially outperform prior
and concurrent work.


  All inextendible null geodesics in four dimensional de Sitter space dS^4 are
complete and globally achronal. This achronality is related to the fact that
all observer horizons in dS^4 are eternal, i.e. extend from future infinity
scri^+ all the way back to past infinity scri^-. We show that the property of
having a null line (inextendible achronal null geodesic) that extends from
scri^- to scri^+ characterizes dS^4 among all globally hyperbolic and
asymptotically de Sitter spacetimes satisfying the vacuum Einstein equations
with positive cosmological constant. This result is then further extended to
allow for a class of matter models that includes perfect fluids.


  The transition from deterministic to distributed chaos/turbulence at the
increase of Rayleigh number (from $10^4$ to $10^8$) in Rayleigh-B\'{e}nard
convection, controlled by generalized Birkhoff-Saffman invariant, has been
studied using the results of direct numerical simulations. The applications of
this approach to rotating Rayleigh-B\'{e}nard convection, to stably stratified
flows, and to observations in the atmosphere and in the solar photosphere have
been briefly discussed.


  The notion of spherically symmetric superfunctions as functions invariant
under the orthosymplectic group is introduced. This leads to dimensional
reduction theorems for differentiation and integration in superspace. These
spherically symmetric functions can be used to solve orthosymplectically
invariant Schroedinger equations in superspace, such as the (an)harmonic
oscillator or the Kepler problem. Finally the obtained machinery is used to
prove the Funk-Hecke theorem and Bochner's relations in superspace.


  Following a polynomial approach, many robust fixed-order controller design
problems can be formulated as optimization problems whose set of feasible
solutions is modelled by parametrized polynomial matrix inequalities (PMI).
These feasibility sets are typically nonconvex. Given a parametrized PMI set,
we provide a hierarchy of linear matrix inequality (LMI) problems whose optimal
solutions generate inner approximations modelled by a single polynomial
sublevel set. Those inner approximations converge in a strong analytic sense to
the nonconvex original feasible set, with asymptotically vanishing
conservatism. One may also impose the hierarchy of inner approximations to be
nested or convex. In the latter case they do not converge any more to the
feasible set, but they can be used in a convex optimization framework at the
price of some conservatism. Finally, we show that the specific geometry of
nonconvex polynomial stability regions can be exploited to improve convergence
of the hierarchy of inner approximations.


  We compute the symbol of the first two-loop amplitudes in planar ${\cal N}=4$
SYM with algebraic letters, the eight-point NMHV amplitude (or the dual octagon
Wilson loops). We show how to apply $\bar{Q}$ equations for computing the
differential of two-loop $n$-point NMHV amplitudes and present the result for
n=8 explicitly. The symbol alphabet for octagon consists of 180 independent
rational letters and 18 algebraic ones involving Gram-determinant square roots.
We comment on all-loop predictions for final entries and aspects of the result
valid for all multiplicities.


  We consider some fractional extensions of the recursive differential equation
governing the Poisson process, by introducing combinations of different
fractional time-derivatives. We show that the so-called "Generalized
Mittag-Leffler functions" (introduced by Prabhakar [20]) arise as solutions of
these equations. The corresponding processes are proved to be renewal, with
density of the intearrival times (represented by Mittag-Leffler functions)
possessing power, instead of exponential, decay, for t tending to infinite. On
the other hand, near the origin the behavior of the law of the interarrival
times drastically changes for the parameter fractional parameter varying in the
interval (0,1). For integer values of the parameter, these models can be viewed
as a higher-order Poisson processes, connected with the standard case by simple
and explict relationships.


  Learning-based control schemes have recently shown great efficacy performing
complex tasks for a wide variety of applications. However, in order to deploy
them in real systems, it is of vital importance to guarantee that the system
will remain safe during online training and execution. Among the currently most
popular methods to tackle this challenge, Control Barrier Functions (CBFs)
serve as mathematical tools that provide a formal safety-preserving control
synthesis procedure for systems with known dynamics. In this paper, we first
introduce a model-uncertainty-aware reformulation of CBF-based safety-critical
controllers using Gaussian Process (GP) regression to bridge the gap between an
approximate mathematical model and the real system. Compared to previous
approaches, we study the feasibility of the resulting robust safety-critical
controller. This feasibility analysis results in a set of richness conditions
that the available information about the system should satisfy to guarantee
that a safe control action can be found at all times. We then use these
conditions to devise an event-triggered online data collection strategy that
ensures the recursive feasibility of the learned safety-critical controller.
Our proposed methodology endows the system with the ability to reason at all
times about whether the current information at its disposal is enough to ensure
safety or if new measurements are required. This, in turn, allows us to provide
formal results of forward invariance of a safe set with high probability, even
in a priori unexplored regions. Finally, we validate the proposed framework in
numerical simulations of an adaptive cruise control system and a kinematic
vehicle.


  We have studied the relaxation dynamics of optically excited electrons in
molybdenum and rhodium by means of time resolved two-photon photoemission
spectroscopy (TR-2PPE) and ab initio electron self-energy calculations
performed within the GW and GW+T approximations. Both theoretical approaches
reproduce qualitatively the experimentally observed trends and differences in
the lifetimes of excited electrons in molybdenum and rhodium. For excitation
energies exceeding the Fermi energy by more than 1 eV, the GW+T theory yields
lifetimes in quantitative agreement with the experimental results. As one of
the relevant mechanisms causing different excited state lifetime in Mo and Rh
we identify the occupation of the 4d bands. An increasing occupation of the 4d
bands results in an efficient decrease of the lifetime even for rather small
excitation energies of a few 100 meV.


  A \textit{walker} is a droplet of liquid that self-propels on the free
surface of an oscillating bath of the same liquid through feedback between the
droplet and its wave field. We have studied walking droplets in the presence of
two driving frequencies and have observed a new class of walking droplets,
which we coin \textit{superwalkers}. Superwalkers may be more than double the
size of the largest walkers, may travel at more than triple the speed of the
fastest ones, and enable a plethora of novel multi-droplet behaviors.