  In this paper, it is presented a methodology for implementing arbitrarily
constructed time-homogenous Markov chains with biochemical systems. Not only
discrete but also continuous-time Markov chains are allowed to be computed. By
employing chemical reaction networks (CRNs) as a programmable language,
molecular concentrations serve to denote both input and output values. One
reaction network is elaborately designed for each chain. The evolution of
species' concentrations over time well matches the transient solutions of the
target continuous-time Markov chain, while equilibrium concentrations can
indicate the steady state probabilities. Additionally, second-order Markov
chains are considered for implementation, with bimolecular reactions rather
that unary ones. An original scheme is put forward to compile unimolecular
systems to DNA strand displacement reactions for the sake of future physical
implementations. Deterministic, stochastic and DNA simulations are provided to
enhance correctness, validity and feasibility.


  This paper focuses on order-preserving logics defined from varieties of
distributive lattices with negation, and in particular on the problem of
whether these can be axiomatized by means of finite Hilbert calculi. On the
side of negative results, we provide a syntactic condition on the equational
presentation of a variety that entails failure of finite axiomatizability for
the corresponding logic. An application of this result is that the logic of all
distributive lattices with negation is not finitely axiomatizable; likewise, we
establish that the order-preserving logic of the variety of all Ockham algebras
is also not finitely axiomatizable. On the positive side, we show that an
arbitrary subvariety of semi-De Morgan algebras is axiomatized by a finite
number of equations if and only if the corresponding order-preserving logic is
axiomatized by a finite Hilbert calculus. This equivalence also holds for every
subvariety of a Berman variety of Ockham algebras. We obtain, as a corollary, a
new proof that the implication-free fragment of intuitionistic logic is
finitely axiomatizable, as well as a new Hilbert calculus for it. Our proofs
are constructive in that they allow us to effectively convert an equational
presentation of a variety of algebras into a Hilbert calculus for the
corresponding order-preserving logic, and vice versa. We also consider the
assertional logics associated to the above-mentioned varieties, showing in
particular that the assertional logics of finitely axiomatizable subvarieties
of semi-De Morgan algebras are finitely axiomatizable as well.


  We demonstrate a new technique for detecting radio transients based on
interferometric closure quantities. The technique uses the bispectrum, the
product of visibilities around a closed-loop of baselines of an interferometer.
The bispectrum is calibration independent, resistant to interference, and
computationally efficient, so it can be built into correlators for real-time
transient detection. Our technique could find celestial transients anywhere in
the field of view and localize them to arcsecond precision. At the Karl G.
Jansky Very Large Array (VLA), such a system would have a high survey speed and
a 5-sigma sensitivity of 38 mJy on 10 ms timescales with 1 GHz of bandwidth.
The ability to localize dispersed millisecond pulses to arcsecond precision in
large volumes of interferometer data has several unique science applications.
Localizing individual pulses from Galactic pulsars will help find X-ray
counterparts that define their physical properties, while finding host galaxies
of extragalactic transients will measure the electron density of the
intergalactic medium with a single dispersed pulse. Exoplanets and active stars
have distinct millisecond variability that can be used to identify them and
probe their magnetospheres. We use millisecond time scale visibilities from the
Allen Telescope Array (ATA) and VLA to show that the bispectrum can detect
dispersed pulses and reject local interference. The computational and data
efficiency of the bispectrum will help find transients on a range of time
scales with next-generation radio interferometers.


  In this work, we investigate differential chaos shift keying (DCSK), a
communication-based waveform, in the context of wireless power transfer (WPT).
Particularly, we present a DCSK-based WPT architecture, that employs an analog
correlator at the receiver in order to boost the energy harvesting (EH)
performance. By taking into account the nonlinearities of the EH process, we
derive closed-form analytical expressions for the peak-to-average-power-ratio
of the received signal as well as the harvested power. Nontrivial design
insights are provided, where it is shown how the parameters of the transmitted
waveform affects the EH performance. Furthermore, it is demonstrated that the
employment of a correlator at the receiver achieves significant EH gains in
DCSK-based WPT systems.


  Fingerprint recognition techniques are immensely dependent on quality of the
fingerprint images. To improve the performance of recognition algorithm for
poor quality images an efficient enhancement algorithm should be designed.
Performance improvement of recognition algorithm will be more if enhancement
process is adaptive to the fingerprint quality (wet, dry or normal). In this
paper, a quality adaptive fingerprint enhancement algorithm is proposed. The
proposed fingerprint quality assessment algorithm clusters the fingerprint
images in appropriate quality class of dry, wet, normal dry, normal wet and
good quality using fuzzy c-means technique. It considers seven features namely,
mean, moisture, variance, uniformity, contrast, ridge valley area uniformity
and ridge valley uniformity into account for clustering the fingerprint images
in appropriate quality class. Fingerprint images of each quality class undergo
through a two-stage fingerprint quality enhancement process. A quality adaptive
preprocessing method is used as front-end before enhancing the fingerprint
images with Gabor, short term Fourier transform and oriented diffusion
filtering based enhancement techniques. Experimental results show improvement
in the verification results for FVC2004 datasets. Significant improvement in
equal error rate is observed while using quality adaptive preprocessing based
approaches in comparison to the current state-of-the-art enhancement
techniques.


  We report on the synthesis, scanning tunneling microscopy (STM) and
theoretical modeling of the electrostatic and transport properties of
one-dimensional organic heterostructures consisting of contiguous lines of CF3-
and OCH3-substituted styrene molecules on silicon. The electrostatic fields
emanating from these polar molecules are found, under appropriate conditions,
to strongly influence electrical conduction through nearby molecules and the
underlying substrate. For suitable alignment of the OCH3 groups of the
OCH3-styrene molecules in the molecular chain, their combined electric fields
are shown by ab initio density functional calculations to give rise to
potential profiles along the OCH3-styrene chain that result in strongly
enhanced conduction through OCH3-styrene molecules near the heterojunction for
moderately low negative substrate bias, as is observed experimentally. Under
similar bias conditions, dipoles associated with the CF3 groups are found in
both experiment and in theory to depress transport in the underlying silicon.
Under positive substrate bias, simulations suggest that the differing
structural and electrostatic properties of the CF3-styrene molecules may lead
to a more sharply localized conduction enhancement near the heterojunction at
low temperatures. Thus choice of substituents, their attachment site on the
host styrene molecules on silicon and the orientations of the molecular dipole
and higher multipole moments provide a means of differentially tuning transport
on the molecular scale.


  This paper describes a novel system for automatic classification of images
obtained from Anti-Nuclear Antibody (ANA) pathology tests on Human Epithelial
type 2 (HEp-2) cells using the Indirect Immunofluorescence (IIF) protocol. The
IIF protocol on HEp-2 cells has been the hallmark method to identify the
presence of ANAs, due to its high sensitivity and the large range of antigens
that can be detected. However, it suffers from numerous shortcomings, such as
being subjective as well as time and labour intensive. Computer Aided
Diagnostic (CAD) systems have been developed to address these problems, which
automatically classify a HEp-2 cell image into one of its known patterns (eg.
speckled, homogeneous). Most of the existing CAD systems use handpicked
features to represent a HEp-2 cell image, which may only work in limited
scenarios. We propose a novel automatic cell image classification method termed
Cell Pyramid Matching (CPM), which is comprised of regional histograms of
visual words coupled with the Multiple Kernel Learning framework. We present a
study of several variations of generating histograms and show the efficacy of
the system on two publicly available datasets: the ICPR HEp-2 cell
classification contest dataset and the SNPHEp-2 dataset.


  Over the past decades, atomistic simulations of chemical, biological and
materials systems have become increasingly precise and predictive thanks to the
development of accurate and efficient techniques that describe the quantum
mechanical behavior of electrons. However, the overwhelming majority of such
simulations still assume that the nuclei behave as classical particles. While
historically this approximation could sometimes be justified due to complexity
and computational overhead, the lack of nuclear quantum effects has become one
of the biggest sources of error when systems containing light atoms are treated
using current state-of-the-art descriptions of chemical interactions. Over the
past decade, this realization has spurred a series of methodological advances
that have led to dramatic reductions in the cost of including these important
physical effects in the structure and dynamics of chemical systems. Here we
show how these developments are now allowing nuclear quantum effects to become
a mainstream feature of molecular simulations. These advances have led to new
insights into chemical processes in the condensed phase and open the door to
many exciting future opportunities.


  The cataclysmic contagion based calamity -- Covid-19 has shown us a clear
need for a comprehensive community based strategy that overcomes the sheer
complexity of controlling it and the caveats of current methods. In this
regard, as seen in earlier epidemics, testing has always been an integral part
of containment policy. But one has to consider the optimality of a testing
scheme based on the resultant disease spread in the community and not based on
purely increasing testing efficiency. Therefore, taking a decision is no easy
feat and must consider the community utility constrained by its priorities,
budget, risks, collateral and abilities which can be encoded into the
optimization of the strategy. We thus propose a simple pooling strategy that is
easy to customize and practical to implement, unlike other complex and
computationally intensive methods.


  Natural protein sequences contain a record of their history. A common
constraint in a given protein family is the ability to fold to specific
structures, and it has been shown possible to infer the main native ensemble by
analyzing covariations in extant sequences. Still, many natural proteins that
fold into the same structural topology show different stabilization energies,
and these are often related to their physiological behavior. We propose a
description for the energetic variation given by sequence modifications in
repeat proteins, systems for which the overall problem is simplified by their
inherent symmetry. We explicitly account for single amino acid and pair-wise
interactions and treat higher order correlations with a single term. We show
that the resulting force field can be interpreted with structural detail. We
trace the variations in the energetic scores of natural proteins and relate
them to their experimental characterization. The resulting energetic force
field allows the prediction of the folding free energy change for several
mutants, and can be used to generate synthetic sequences that are statistically
indistinguishable from the natural counterparts.


  Given a smooth foliation on a closed manifold, basic forms are differential
forms that can be expressed locally in terms of the transverse variables. The
space of basic forms yields a differential complex, because the exterior
derivative fixes this set. The basic cohomology is the cohomology of this
complex, and this has been studied extensively. Given a Riemannian metric, the
adjoint of the exterior derivative maps the orthogonal complement of the basic
forms to itself, and we call the resulting cohomology the "antibasic
cohomology". Although these groups are defined using the metric, the dimensions
of the antibasic cohomology groups are invariant under diffeomorphism and
metric changes. If the underlying foliation is Riemannian, the groups are
foliated homotopy invariants that are independent of basic cohomology and
ordinary cohomology of the manifold. For this class of foliations we use the
codifferential on antibasic forms to obtain the corresponding Laplace operator,
develop its analytic properties, and prove a Hodge theorem. We then find some
topological and geometric properties that impose restrictions on the antibasic
Betti numbers.


  In this work, we investigate the question of how knowledge about expectations
$\mathbb{E}(f_i(X))$ of a random vector $X$ translate into inequalities for
$\mathbb{E}(g(X))$ for given functions $f_i$, $g$ and a random vector $X$ whose
support is contained in some set $S\subseteq \mathbb{R}^n$. We show that there
is a connection between the problem of obtaining tight expectation inequalities
in this context and properties of convex hulls, allowing us to rewrite it as an
optimization problem. The results of these optimization problems not only
arrive at sharp bounds for $\mathbb{E}(g(X))$ but in some cases also yield
discrete probability measures where equality holds.
  We develop an analytical approach that is particularly suited for studying
the Jensen gap problem when the known information are the average and variance,
as well as a numerical approach for the general case, that reduces the problem
to a convex optimization; which in a sense extends known results about the
moment problem.


  It is shown that a change of variable in 1-dim Schroedinger equation applied
to the Borel summable fundamental solutions [Giller] is equivalent to Borel
resummation of the fundamental solutions multiplied by suitably chosen
$\hbar$-dependent constant. This explains why change of variable can improve
JWKB formulae [Giller, Milczarski]. It is shown also that a change of variable
alone cannot provide us with the exact JWKB formulae.


  Predicting unseen weather phenomena is an important issue for disaster
management. In this paper, we suggest a model for a convolutional
sequence-to-sequence autoencoder for predicting undiscovered weather situations
from previous satellite images. We also propose a symmetric skip connection
between encoder and decoder modules to produce more comprehensive image
predictions. To examine our model performance, we conducted experiments for
each suggested model to predict future satellite images from historical
satellite images. A specific combination of skip connection and
sequence-to-sequence autoencoder was able to generate closest prediction from
the ground truth image.


  We study the real economic activity in the Bitcoin blockchain that involves
transactions from/to retail users rather than between organizations such as
marketplaces, exchanges, or other services. We first introduce a heuristic
method to classify Bitcoin players into three main categories: Frequent
Receivers (FR), Neighbors of FR, and Others. We show that most real
transactions involve Frequent Receivers, representing a small fraction of the
total value exchanged according to the blockchain, but a significant fraction
of all payments, raising concerns about the centralization of the Bitcoin
ecosystem. We also conduct a weekly pattern analysis of activity, providing
insights into the geographical location of Bitcoin users and allowing us to
quantify the bias of a well-known dataset for actor identification.


  We investigate the distribution of particle acceleration sites, independently
of the actual acceleration mechanism, during plasmoid-dominated, relativistic
collisionless magnetic reconnection by analyzing the results of a
particle-in-cell numerical simulation. The simulation is initiated with
Harris-type current layers in pair plasma with no guide magnetic field,
negligible radiative losses, no initial perturbation, and using periodic
boundary conditions. We find that the plasmoids develop a robust internal
structure, with colder dense cores and hotter outer shells, that is recovered
after each plasmoid merger on a dynamical time scale. We use spacetime diagrams
of the reconnection layers to probe the evolution of plasmoids, and in this
context we investigate the individual particle histories for a representative
sample of energetic electrons. We distinguish three classes of particle
acceleration sites associated with (1) magnetic X-points, (2) regions between
merging plasmoids, and (3) the trailing edges of accelerating plasmoids. We
evaluate the contribution of each class of acceleration sites to the final
energy distribution of energetic electrons -- magnetic X-points dominate at
moderate energies, and the regions between merging plasmoids dominate at higher
energies. We also identify the dominant acceleration scenarios, in order of
decreasing importance -- (1) single acceleration between merging plasmoids, (2)
single acceleration at a magnetic X-point, and (3) acceleration at a magnetic
X-point followed by acceleration in a plasmoid. Particle acceleration is absent
only in the vicinity of stationary plasmoids. The effect of magnetic mirrors
due to plasmoid contraction does not appear to be significant in relativistic
reconnection.


  We present integrated JHK_s 2MASS photometry and a compilation of
integrated-light optical photoelectric measurements for 84 star clusters in the
Magellanic Clouds. These clusters range in age from ~200 Myr to >10 Gyr, and
have [Fe/H] values from -2.2 to -0.1 dex. We find a spread in the intrinsic
colours of clusters with similar ages and metallicities, at least some of which
is due to stochastic fluctuations in the number of bright stars residing in
low-mass clusters. We use 54 clusters with the most reliable age and
metallicity estimates as test particles to evaluate the performance of four
widely used SSP models in the optical/NIR colour-colour space. All models
reproduce the reddening-corrected colours of the old (>10 Gyr) globular
clusters quite well, but model performance varies at younger ages. In order to
account for the effects of stochastic fluctuations in individual clusters, we
provide composite B-V, B-J, V-J, V-Ks and J-Ks colours for Magellanic Cloud
clusters in several different age intervals. The accumulated mass for most
composite clusters are higher than that needed to keep luminosity variations
due to stochastic fluctuations below the 10% level. The colours of the
composite clusters are clearly distinct in optical-NIR colour-colour space for
the following intervals of age: >10 Gyr, 2-9 Gyr, 1-2 Gyr, and 200 Myr-1 Gyr.
This suggests that a combination of optical plus NIR colours can be used to
differentiate clusters of different age and metallicity.


  A proper ideal $P$ of a commutative ring with identity is an almost prime
ideal if $ab \in P{\setminus}P^2$ implies $a \in P$ or $b \in P$. In this paper
we define almost prime ideals of a noncommutative ring, and provide some
equivalent definitions. We also examine some cases such that all right ideals
of a noncommutative ring are almost prime right ideals.


  Finding point-level correspondences is a fundamental problem in ultrasound
(US), since it can enable US landmark tracking for intraoperative image
guidance in different surgeries, including head and neck. Most existing US
tracking methods, e.g., those based on optical flow or feature matching, were
initially designed for RGB images before being applied to US. Therefore domain
shift can impact their performance. Training could be supervised by
ground-truth correspondences, but these are expensive to acquire in US. To
solve these problems, we propose a self-supervised pixel-level tracking model
called PIPsUS. Our model can track an arbitrary number of points in one forward
pass and exploits temporal information by considering multiple, instead of just
consecutive, frames. We developed a new self-supervised training strategy that
utilizes a long-term point-tracking model trained for RGB images as a teacher
to guide the model to learn realistic motions and use data augmentation to
enforce tracking from US appearance. We evaluate our method on neck and oral US
and echocardiography, showing higher point tracking accuracy when compared with
fast normalized cross-correlation and tuned optical flow. Code will be
available once the paper is accepted.


  In this work we report on using light-front dynamics to describe generalized
parton distributions, which are correlation functions encountered in virtual
Compton scattering at large momentum transfer. This two photon process requires
pair annihilation contributions which are subtle to handle in light-front
dynamics. We are careful to derive such contributions in the light-front
Bethe-Salpeter formalism. This derivation highlights the connection to the Fock
space picture as well as provides a toy model for generalized parton
distributions.Ultimately we use light-front dynamics to build a
phenomenological parametrization for the proton's generalized parton
distributions. This task is non-trivial due to the field theoretic constraints
required of these distributions. To meet the constraints imposed by Lorentz
covariance, we approach generalized parton distributions from the perspective
of double distributions. Despite avid phenomenological use, surprisingly little
work has been done to calculate double distributions. We first focus on a
number of simple pedagogical examples and demonstrate how double distributions
can be correctly determined. The double distributions we derive, including
those for the proton, satisfy known constraints and are adequate for
phenomenological estimates of cross sections. The models used allow one to
study the interplay between the light-front formulation and Lorentz covariance.


  We introduce PARQR, a tool for online education forums that reduces duplicate
posts by 40\% in a degree seeking online masters program at a top university.
Instead of performing a standard keyword search, PARQR monitors questions as
students compose them and continuously suggests relevant posts. In testing,
PARQR correctly recommends a relevant post, if one exists, 73.5\% of the time.
We discuss PARQR's design, initial experimental results comparing different
semesters with and without PARQR, and interviews we conducted with teaching
instructors regarding their experience with PARQR.


  We give a review of the mathematical and physical properties of the
celebrated family of Calogero-like models and related spin chains.


  In this paper, we introduce matrix weighted Bourgain-Morrey spaces and obtain
two sufficient conditions for precompact sets in matrix weighted
Bourgain-Morrey spaces. We prove that the dyadic average operator is bounded on
some matrix weighted Bourgain-Morrey spaces. With this result, we obtain the
necessity for precompact sets in some matrix weighted Bourgain-Morrey spaces.


  Powerful radio sources associated with super-massive black holes are among
the most luminous objects in the Universe, and are frequently recognized both
as cosmological probes and active constituents in the evolution of galaxies. We
present alignments between radio jets and cold molecular gas in the environment
of distant radio galaxies, and show that the brightness of the radio
synchrotron source can be enhanced by its interplay with the molecular gas. Our
work is based on CO J>1 observations with the Atacama Large
Millimeter/submillimeter Array (ALMA) of three radio galaxies with redshifts in
the range 1.4 < z < 2.1, namely MRC 0114-211 (z = 1.41), MRC 0156-252 (z =
2.02), and MRC 2048-272 (z = 2.05). These ALMA observations support previous
work that found molecular gas out to 50 kpc in the circumgalactic environment,
based on a CO(1-0) survey performed with the Australia Telescope Compact Array
(ATCA). The CO emission is found along the radio axes but beyond the main radio
lobes. When compared to a large sample of high-z radio galaxies from the
literature, we find that the presence of this cold molecular medium correlates
with an increased flux-density ratio of the main vs. counter lobe. This suggest
that the radio lobe brightens when encountering cold molecular gas in the
environment. While part of the molecular gas is likely related to the
interstellar medium (ISM) from either the host or a companion galaxy, a
significant fraction of the molecular gas in these systems shows very low
excitation, with r$_{2-1/1-0}$ and r$_{3-2/1-0}$ values $\lesssim$0.2. This
could be part of the circumgalactic medium (CGM).


  We study the formation of globular clusters (GCs) in a Milky Way-size galaxy
using a high-resolution cosmological simulation. The clusters in our model form
in the dense cores of supergiant molecular clouds in the gaseous disks of
high-redshift galaxies. The properties of clusters are estimated using a
physically-motivated subgrid model of the isothermal cloud collapse. The first
clusters in the simulation form at z ~ 12, while we conjecture that the best
conditions for GC formation appear to be at z ~ 3-5. Most clusters form in the
progenitor galaxies of the virial mass >10^9 Msun and the total mass of the
cluster population is strongly correlated with the mass of its host galaxy with
a fraction ~2x10^-4 of the galactic baryons being in the form of GCs. In
addition, the mass of the GC population and the maximum cluster mass in a given
region strongly correlate with the local average star formation rate. We find
that the mass, size, and metallicity distributions of the cluster population
identified in the simulation are remarkably similar to the corresponding
distributions of the Milky Way globulars. We find no clear mass-metallicity or
age-metallicity correlations for the old clusters. The zero-age cluster mass
function can be approximated by a power-law, dN/dM ~ M^-alpha, with alpha ~ 2,
in agreement with the mass function of young stellar clusters in starbursting
galaxies. However, the shape of the zero-age mass function may be better
described by the high-mass tail of a lognormal distribution which peaks at
~10^3 Msun. We discuss in detail the origin, universality, and dynamical
evolution of the globular cluster mass function. Our results indicate that
globular clusters with properties similar to those of observed clusters can
form naturally within young dense gaseous disks at z >~ 3 in the LCDM
cosmology.


  A MATLAB program has been developed for simulation of polymer blend
self-assembly with nano-scaled features. The Cahn-Hilliard equation is
implemented to calculate the free energy profile of the polymer blends. The
Flory-Huggins type of energy is used to estimate the local free energy. The
program is capable of quantitatively simulate the phase separation of polymer
blends. The effects such as the substrate functionalization, solvent
evaporation, and polymer materials properties are included in the program. The
program can estimate the model parameters from the real experimental processing
parameters and the material properties. The simulation results can be evaluated
quantitatively and compared with the experimental results with analysis tools
included in the program.


  We study the chromatic polynomial P_G(q) for m \times n square- and
triangular-lattice strips of widths 2\leq m \leq 8 with cyclic boundary
conditions. This polynomial gives the zero-temperature limit of the partition
function for the antiferromagnetic q-state Potts model defined on the lattice
G. We show how to construct the transfer matrix in the Fortuin--Kasteleyn
representation for such lattices and obtain the accumulation sets of chromatic
zeros in the complex q-plane in the limit n\to\infty. We find that the
different phases that appear in this model can be characterized by a
topological parameter. We also compute the bulk and surface free energies and
the central charge.


  We prove that the stationary magnetic potential vector and the electrostatic
potential entering the dynamic magnetic Schr\"odinger equation can be Lipschitz
stably retrieved through finitely many local boundary measurements of the
solution. The proof is by means of a specific global Carleman estimate for the
Schr\"odinger equation, established in the first part of the paper.


  An algorithm is proposed to verify whether a finite game is a weighted
potential game (WPG) without pre-knowledge on its weights. Then the algorithm
is also applied to find the closest WPG for a given finite game. The concept
and criterion of near weighted potential games (NWPGs) are given, indicating
the evolutionary equivalence between a finite game and its closest WPG. Based
on this, a method is proposed for replacing PGs by NWPGs in game theoretic
control, which improved the applicability of PG-based optimization.


  A new analytical expression for the size-dependent bandgap of colloidal
semiconductor nanocrystals is proposed within the framework of the finite-depth
square-well effective mass approximation in order to provide a quantitative
description of the quantum confinement effect. This allows one to convert
optical spectroscopic data (photoluminescence spectrum and absorbance edge)
into accurate estimates for the particle size distributions of colloidal
systems even if the traditional effective mass model is expected to fail, which
occurs typically for very small particles belonging to the so-called strong
confinement limit. By applying the reported theoretical methodologies to CdTe
nanocrystals synthesized through wet chemical routes, size distributions are
inferred and compared directly to those obtained from atomic force microscopy
and transmission electron microscopy. This analysis can be used as a
complementary tool for the characterization of nanocrystal samples of many
other systems such as the II-VI and III-V semiconductor materials.


  It is known that the empirical spectral distribution of random matrices
obtained from linear codes of increasing length converges to the well-known
Marchenko-Pastur law, if the Hamming distance of the dual codes is at least 5.
In this paper, we prove that the convergence in probability is at least of the
order $n^{-1/4}$ where $n$ is the length of the code.


  We calculate the one-loop induced couplings of two gaugino-like neutralinos
to the $Z$ and Higgs bosons in the Minimal Supersymmetric Standard Model. These
couplings, which vanish at the tree level, can be generated through loops
involving fermions and sfermions. We show that, while the neutralino
contribution to the invisible $Z$ boson decay width remains small, the loop
induced couplings to the lightest Higgs boson might be sufficiently large to
yield a rate of invisible decays of this Higgs boson that should be detectable
at future $e^+e^-$ colliders. We also study the implications of these couplings
for direct searches of Dark Matter and show that they can modify appreciably
the neutralino-nucleon elastic cross section for some parameter range.


  The ground state phase diagram of the dimerized spin-1/2 XX honeycomb model
in presence of a transverse magnetic field (TF) is known. With the absence of
the magnetic field, two quantum phases, namely, the N\'eel and the dimerized
phases have been identified. Moreover, canted N\'eel and the paramagnetic (PM)
phases also emerge by applying the magnetic field. In this paper, using two
complementary numerical exact techniques, Lanczos exact diagonalization, and
Density matrix renormalization group (DMRG) methods, we study this model by
focusing on the quantum correlations, the concurrence, and the quantum discord
(QD) among nearest-neighbor spins. We show that the quantum correlations can
capture the position of the quantum critical points in the whole range of the
ground state phase diagram consistent with previous results. Although the
concurrence and the QD are short-range, informative about long-ranged critical
correlations. In addition, we address a "magnetic-entanglement" behavior that
starts from an entangled field around the saturation field.


  Galaxy morphologies, kinematics, and stellar populations are thought to be
linked to each other. However, both simulations and observations have pointed
out mismatches therein. In this work, we study the nature and origin of the
present-day quenched, bulge-dominated, but dynamically cold galaxies within a
stellar mass range of
$10.3\,\leqslant\,\log\,M_{\ast}/\mathrm{M_{\odot}}\,\leqslant\,11.2$ in the
IllustrisTNG-100 Simulation. We compare these galaxies with a population of
normal star-forming dynamically cold disc galaxies and a population of normal
quenched dynamically hot elliptical galaxies within the same mass range. The
populations of the present-day quenched and bulge-dominated galaxies (both
being dynamically cold and hot) used to have significantly higher
star-formation rates and flatter morphologies at redshift of $z\sim 2$. They
have experienced more frequent larger mass-ratio mergers below $z \sim 0.7$ in
comparison to their star-forming disc counterparts, which is responsible for
the formation of their bulge-dominated morphologies. The dynamically cold
populations (both being star-forming and quenched) have experienced more
frequent prograde and tangential mergers especially below $z \sim 1$, in
contrast to the dynamically hot ellipticals, which have had more retrograde and
radial mergers. Such different merging histories can well explain the
differences on the cold and hot dynamical status among these galaxies. We point
out that the real-world counterparts of these dynamically cold and hot
bulge-dominated quenched populations are the fast- and slow-rotating early-type
galaxies, respectively, as seen in observations and hence reveal the different
evolution paths of these two distinct populations of early-type galaxies.


  We develop a general scheme for an analysis of macroscopic qudit systems: a)
introduce a set of collective observables, which characterizes the macroscopic
properties of qudits in an optimal way; b) construct projected
$\tilde{Q}$-functions for $N$ qudit systems, containing full macroscopic
information; c) propose a collective tomographic protocol both for a general
and symmetric $N$-qudit states. The example of $N$-qutrit is analyzed in
details and compared to $N$-qubit case


  The possibility of obtaining an open set of regular cosmological models is
discussed. Cylindrical stiff perfect fluid cosmologies are studied in detail.
The condition for geodesic completeness is easy to check. A large family of
non-singular models is found therein.


  The flow inside a fluid damper where a piston reciprocates sinusoidally
inside an outer casing containing high-viscosity silicone oil is simulated
using a Finite Volume method, at various excitation frequencies. The oil is
modelled by the Carreau-Yasuda (CY) and Phan-Thien \& Tanner (PTT) constitutive
equations. Both models account for shear-thinning but only the PTT model
accounts for elasticity. The CY and other generalised Newtonian models have
been previously used in theoretical studies of fluid dampers, but the present
study is the first to perform full two-dimensional (axisymmetric) simulations
employing a viscoelastic constitutive equation. It is found that the CY and PTT
predictions are similar when the excitation frequency is low, but at medium and
higher frequencies the CY model fails to describe important phenomena that are
predicted by the PTT model and observed in experimental studies found in the
literature, such as the hysteresis of the force-displacement and force-velocity
loops. Elastic effects are quantified by applying a decomposition of the damper
force into elastic and viscous components, inspired from LAOS (Large Amplitude
Oscillatory Shear) theory. The CY model also overestimates the damper force
relative to the PTT, because it underpredicts the flow development length
inside the piston-cylinder gap. It is thus concluded that (a) fluid elasticity
must be accounted for and (b) theoretical approaches that rely on the
assumption of one-dimensional flow in the piston-cylinder gap are of limited
accuracy, even if they account for fluid viscoelasticity. The consequences of
using lower-viscosity silicone oil are also briefly examined.


  Let $\mathcal{P}$ and $\mathcal{P}'$ be $3$-dimensional convex polytopes in
$\mathbb{R}^3$ and $S \subseteq \mathbb{R}^3$ be a non-empty intersection of an
open set with a sphere. As a consequence of a somewhat more general result it
is proved that $\mathcal{P}$ and $\mathcal{P}'$ coincide up to translation
and/or reflection in a point if $|\int_{\mathcal{P}}
e^{-i\mathbf{s}\cdot\mathbf{x}} \,\mathbf{dx}| = |\int_{\mathcal{P}'}
e^{-i\mathbf{s}\cdot\mathbf{x}} \,\mathbf{dx}|$ for all $\mathbf{s} \in S$.
This can be applied to the field of crystallography regarding the question
whether a nanoparticle modelled as a convex polytope is uniquely determined by
the intensities of its X-ray diffraction pattern on the Ewald sphere.


  Monte Carlo methods are often necessary for the implementation of optimal
Bayesian estimators. A fundamental technique that can be used to generate
samples from virtually any target probability distribution is the so-called
rejection sampling method, which generates candidate samples from a proposal
distribution and then accepts them or not by testing the ratio of the target
and proposal densities. The class of adaptive rejection sampling (ARS)
algorithms is particularly interesting because they can achieve high acceptance
rates. However, the standard ARS method can only be used with log-concave
target densities. For this reason, many generalizations have been proposed.
  In this work, we investigate two different adaptive schemes that can be used
to draw exactly from a large family of univariate probability density functions
(pdf's), not necessarily log-concave, possibly multimodal and with tails of
arbitrary concavity. These techniques are adaptive in the sense that every time
a candidate sample is rejected, the acceptance rate is improved. The two
proposed algorithms can work properly when the target pdf is multimodal, with
first and second derivatives analytically intractable, and when the tails are
log-convex in a infinite domain. Therefore, they can be applied in a number of
scenarios in which the other generalizations of the standard ARS fail. Two
illustrative numerical examples are shown.


  Quantum experiments yield random data. We show that the most efficient way to
store this empirical information by a finite number of bits is by means of the
vector of square roots of observed relative frequencies. This vector has the
unique property that its dispersion becomes invariant of the underlying
probabilities, and therefore invariant of the physical parameters. This also
extends to the complex square roots, and it remains true under a unitary
transformation. This reveals quantum theory as a theory for making predictions
which are as accurate as the input information, without any statistical loss.
Our analysis also suggests that from the point of view of information a
slightly more accurate theory than quantum theory should be possible.


  Photodetector nonlinearity, the main limiting factor in terms of optical
power in the detection chain, is corrected to improve the signal-to-noise ratio
of a short-time measurement in dual-comb spectroscopy. An iterative correction
algorithm minimizing out-of-band spectral artifacts based on nonlinearity
correction methods used in classical Fourier-transform spectrometers is
presented. The exactitude of the nonlinearity correction is validated using a
low power linear measurement. Spectroscopic lines of H$^{12}$CN are provided
and the error caused by the saturation of the detector is corrected yielding
residuals limited by the measurement noise.


  We study rational cuspidal curves in Hirzebruch surfaces. We provide two
obstructions for the existence of rational cuspidal curves in Hirzebruch
surfaces with prescribed types of singular points. The first result comes from
Heegaard--Floer theory and is a generalization of a result by Livingston and
the first author. The second criterion is obtained by comparing the spectrum of
a suitably defined link at infinity of a curve with spectra of its singular
points.


  In this paper we study the calculation of multiloop Feynman integrals that
cannot be expressed in terms of multiple polylogarithms. We show in detail how
certain types of two- and three-point functions at two loops, which appear in
the calculation of higher order corrections in QED, QCD and in the electroweak
theory (EW), can naturally be expressed in terms of a recently introduced
elliptic generalisation of multiple polylogarithms by direct integration over
their Feynman parameter representation. Moreover, we show that in all examples
that we considered a basis of pure Feynman integrals can be found.


  We compute certain Ext and Tor groups in the category of all functors from an
Z/p-linear additive category A to vector spaces in terms of Ext and Tor
computed in the full subcategory of additive functors from A to vector spaces.
We thus obtain group homology computations for general lineargroups.


  Multi-fluid models have recently been proposed as an approach to improving
the representation of convection in weather and climate models. This is an
attractive framework as it is fundamentally dynamical, removing some of the
assumptions of mass-flux convection schemes which are invalid at current model
resolutions. However, it is still not understood how best to close the
multi-fluid equations for atmospheric convection. In this paper we develop a
simple two-fluid, single-column model with one rising and one falling fluid. No
further modelling of sub-filter variability is included. We then apply this
model to Rayleigh-B\'{e}nard convection, showing that, with minimal closures,
the correct scaling of the heat flux (Nu) is predicted over six orders of
magnitude of buoyancy forcing (Ra). This suggests that even a very simple
two-fluid model can accurately capture the dominant coherent overturning
structures of convection.


  We discuss positive closed currents and Fubini-Study currents on orbifolds,
as well as Bergman kernels of singular Hermitian orbifold line bundles. We
prove that the Fubini-Study currents associated to high powers of a
semipositive singular line bundle converge weakly to the curvature current on
the set where the curvature is strictly positive, generalizing a well-known
theorem of Tian. We include applications to the asymptotic distribution of
zeros of random holomorphic sections.


  We study the temporal evolution of the circuit complexity for a subsystem in
harmonic lattices after a global quantum quench of the mass parameter, choosing
the initial reduced density matrix as the reference state. Upper and lower
bounds are derived for the temporal evolution of the complexity for the entire
system. The subsystem complexity is evaluated by employing the Fisher
information geometry for the covariance matrices. We discuss numerical results
for the temporal evolutions of the subsystem complexity for a block of
consecutive sites in harmonic chains with either periodic or Dirichlet boundary
conditions, comparing them with the temporal evolutions of the entanglement
entropy. For infinite harmonic chains, the asymptotic value of the subsystem
complexity is studied through the generalised Gibbs ensemble.


  We study webs of D3- and D5-branes in type IIB supergravity. These webs
preserve at least 8 supercharges. By solving the Killing spinor equations we
determine the form of supergravity solutions for the system. We then turn to
the sub-class of the intersecting D3/D5 brane system and elucidate some of its
features.


  We study the evolution of averaged transconductances in three-terminal
Josephson junctions when the superconducting leads are led throughout a
topological phase transition from an $s$-wave to a $p$-wave (Majorana) phase by
an in-plane magnetic field $B_x$. We provide a complete description of this
transition as a function of $B_x$ and a magnetic flux $\Phi$ threading the
junction. For that we use a spinful model within a formalism that allows to
treat on equal footing the contribution to the transconductance from both the
Andreev subgap levels and the continuum spectrum. We unveil a fractionalization
in the quantization of the transconductance due to the presence of Majorana
quasiparticles, reflecting the effective pumping of half a Cooper pair charge
in the $p$-wave regime.


  This document is part of a series of near real-time weekly influenza
forecasts made during the 2012-2013 influenza season. Here we present results
of a forecast initiated following assimilation of observations for Week 51
(i.e. the forecast begins December 23, 2012) for municipalities in the United
States. The forecast was made on December 28, 2012. Results from forecasts
initiated the four previous weeks (Weeks 47-50) are also presented. Predictions
generated with an alternate SIRS model, run without absolute humidity forcing
(no AH), are also presented.


  We study the deformation theory of a Q-Fano 3-fold with only terminal
singularities. First, we show that the Kuranishi space of a Q-Fano 3-fold is
smooth. Second, we show that every Q-Fano 3-fold with only "ordinary" terminal
singularities is Q-smoothable, that is, it can be deformed to a Q-Fano 3-fold
with only quotient singularities. Finally, we prove Q-smoothability of a Q-Fano
3-fold assuming the existence of a Du Val anticanonical element. As an
application, we get the genus bound for primary Q-Fano 3-folds with Du Val
anticanonical elements.


  Let $G$ be a profinite group in which for every element $x\in G$ there exists
a natural number $q=q(x)$ such that $x^q$ is Engel. We show that $G$ is locally
virtually nilpotent. Further, let $p$ be a prime and $G$ a finitely generated
profinite group in which for every $\gamma_k$-value $x\in G$ there exists a
natural $p$-power $q=q(x)$ such that $x^q$ is Engel. We show that $\gamma_k(G)$
is locally virtually nilpotent.


  In this paper, we propose a novel deep learning architecture combining
stacked Bi-directional LSTM and LSTMs with the Siamese network architecture for
segmentation of brain fibers, obtained from tractography data, into
anatomically meaningful clusters. The proposed network learns the structural
difference between fibers of different classes, which enables it to classify
fibers with high accuracy. Importantly, capturing such deep inter and intra
class structural relationship also ensures that the segmentation is robust to
relative rotation among test and training data, hence can be used with
unregistered data. Our extensive experimentation over order of
hundred-thousands of fibers show that the proposed model achieves
state-of-the-art results, even in cases of large relative rotations between
test and training data.


  Galinier, Habib, and Paul introduced the reduced clique graph of a chordal
graph $G$. The nodes of the reduced clique graph are the maximal cliques of
$G$, and two nodes are joined by an edge if and only if they form a
non-disjoint separating pair of cliques in $G$. In this case the weight of the
edge is the size of the intersection of the two cliques. A clique tree of $G$
is a tree with the maximal cliques of $G$ as its nodes, where for any $v\in
V(G)$, the subgraph induced by the nodes containing $v$ is connected. Galinier
et al.\ prove that a spanning tree of the reduced clique graph is a clique tree
if and only if it has maximum weight, but their proof contains an error. We
explain and correct this error.
  In addition, we initiate a study of the structure of reduced clique graphs by
proving that they cannot contain any induced cycle of length five (although
they may contain induced cycles of length three or any even integer greater
than two). We show that no cycle of length four or more is isomorphic to a
reduced clique graph. We prove that the class of clique graphs of chordal
graphs is not comparable to the class of reduced clique graphs of chordal
graphs by providing examples that are in each of these classes without being in
the other.


  We present methods for online linear optimization that take advantage of
benign (as opposed to worst-case) sequences. Specifically if the sequence
encountered by the learner is described well by a known "predictable process",
the algorithms presented enjoy tighter bounds as compared to the typical worst
case bounds. Additionally, the methods achieve the usual worst-case regret
bounds if the sequence is not benign. Our approach can be seen as a way of
adding prior knowledge about the sequence within the paradigm of online
learning. The setting is shown to encompass partial and side information.
Variance and path-length bounds can be seen as particular examples of online
learning with simple predictable sequences.
  We further extend our methods and results to include competing with a set of
possible predictable processes (models), that is "learning" the predictable
process itself concurrently with using it to obtain better regret guarantees.
We show that such model selection is possible under various assumptions on the
available feedback. Our results suggest a promising direction of further
research with potential applications to stock market and time series
prediction.


  Landau's theorem on conjugacy classes asserts that there are only finitely
many finite groups, up to isomorphism, with exactly $k$ conjugacy classes for
any positive integer $k$. We show that, for any positive integers $n$ and $s$,
there exists only a finite number of finite groups $G$, up to isomorphism,
having a normal subgroup $N$ of index $n$ which contains exactly $s$
non-central $G$-conjugacy classes. We provide upper bounds for the orders of
$G$ and $N$, which are used by using GAP to classify all finite groups with
normal subgroups having a small index and few $G$-classes. We also study the
corresponding problems when we only take into account the set of $G$-classes of
prime-power order elements contained in a normal subgroup.


  Reflection moveout of pure modes recorded on conventional-length spreads is
described by a normal-moveout (NMO) velocity that depends on the orientation of
the common-midpoint (CMP) line. Here, we introduce the concept of NMO-velocity
surfaces, obtained by plotting the NMO velocity as the radius-vector along all
possible directions in 3-D space, and use it to develop Dix-type averaging and
differentiation algorithms in anisotropic heterogeneous media.
  The intersection of the NMO-velocity surface with the horizontal plane
represents the NMO ellipse that can be estimated from wide-azimuth reflection
data. We demonstrate that the NMO ellipse and conventional-spread moveout as a
whole can be modeled by Dix-type averaging of specifically oriented
cross-sections of the NMO-velocity surfaces along the zero-offset reflection
raypath. This formalism is particularly simple to implement for a stack of
homogeneous anisotropic layers separated by plane dipping boundaries. Since our
method involves computing just a single (zero-offset) ray for a given
reflection event, it can be efficiently used in anisotropic stacking-velocity
tomography.


  Electronic data is growing at increasing rates, in both size and
connectivity: the increasing presence of, and interest in, relationships
between data. An example is the Twitter social network graph. Due to this
growth demand is increasing for technologies that can process such data.
Currently relational databases are the predominant technology, but they are
poorly suited to processing connected data as they are optimized for
index-intensive operations. Conversely, graph databases are optimized for graph
computation. They link records by direct references, avoiding index lookups,
and enabling retrieval of adjacent elements in constant time, regardless of
graph size. However, as data volume increases these databases outgrow the
resources of one computer and data partitioning becomes necessary. We evaluate
the viability of using graph partitioning algorithms to partition graph
databases. A prototype partitioned database was developed. Three partitioning
algorithms explored and one implemented. Three graph datasets were used: two
real and one synthetically generated. These were partitioned in various ways
and the impact on database performance measured. We defined one synthetic
access pattern per dataset and executed each on the partitioned datasets.
Evaluation took place in a simulation environment, ensuring repeatability and
allowing measurement of metrics like network traffic and load balance. Results
show that compared to random partitioning the partitioning algorithm reduced
traffic by 40-90%. Executing the algorithm intermittently during usage
maintained partition quality, while requiring only 1% the computation of
initial partitioning. Strong correlations were found between theoretic quality
metrics and generated network traffic under non-uniform access patterns.


  We argue that the main reason of crisis in quantum theory is that nature,
which is fundamentally discrete and even finite, is described by classical
mathematics involving the notions of infinitely small, continuity etc.
Moreover, since classical mathematics has its own foundational problems which
cannot be resolved (as follows, in particular, from G\"{o}del's incompleteness
theorems), the ultimate physical theory cannot be based on that mathematics. In
the first part of the work we discuss inconsistencies in standard quantum
theory and reformulate the theory such that it can be naturally generalized to
a formulation based on finite mathematics. It is shown that: a) as a
consequence of inconsistent definition of standard position operator,
predictions of the theory contradict the data on observations of stars; b) the
cosmological acceleration and gravity can be treated simply as {\it
kinematical} manifestations of quantum de Sitter symmetry, {\it i.e. the
cosmological constant problem does not exist, and for describing those
phenomena the notions of dark energy, space-time background and gravitational
interaction are not needed}. In the second part we prove that classical
mathematics is a special degenerate case of finite mathematics in the formal
limit when the characteristic $p$ of the field or ring in the latter goes to
infinity. {\bf This implies that mathematics describing nature at the most
fundamental level involves only a finite number of numbers while the notions of
limit and infinitely small/large and the notions constructed from them (e.g.
continuity, derivative and integral) are needed only in calculations describing
nature approximately}. In a quantum theory based on finite mathematics, the de
Sitter gravitational constant depends on $p$ and disappears in the formal limit
$p\to\infty$, i.e. gravity is a consequence of finiteness of nature.


  This letter provides a stochastic geometry (SG)-based coverage probability
(CP) analysis of an indoor terahertz (THz) downlink assisted by a single
reconfigurable intelligent surface (RIS) panel. Specifically, multiple access
points (AP) deployed on the ceiling of a hall (each equipped with multiple
antennas) need to serve multiple user equipment (UE) nodes. Due to presence of
blockages, a typical UE may either get served via a direct link, the RIS, or
both links (the composite link). The locations of the APs and blockages are
modelled as a Poisson point process (PPP) and SG framework is utilized to
compute the CP, at a reference UE for all the three scenarios. Monte-Carlo
simulation results validate our theoretical analysis.


  We find an explicit closed form for the subword complexity of the infinite
fixed point of the morphism sending $a \rightarrow aab$ and $b \rightarrow b$.
This morphism is then generalized in three different ways, and we find similar
explicit expressions for the subword complexity of the generalizations.


  Let $G$ be a graph with adjacency matrix $A$. The transition matrix
corresponding to $G$ is defined by $H(t):=\exp{\left(itA\right)}$, $t\in\Rl$.
The graph $G$ is said to have perfect state transfer (PST) from a vertex $u$ to
another vertex $v$, if there exist $\tau\in\Rl$ such that the $uv$-th entry of
$H(\tau)$ has unit modulus. The graph $G$ is said to be periodic at
$\tau\in\Rl$ if there exist $\gamma\in\Cl$ with $|\gamma|=1$ such that
$H(\tau)=\gamma I$, where $I$ is the identity matrix. A $\mathit{gcd}$-graph is
a Cayley graph over a finite abelian group defined by greatest common divisors.
In this paper, we construct classes of $\mathit{gcd}$-graphs having periodicity
and perfect state transfer.


  A real Bott tower is obtained as the orbit space of the $n$-torus $T^n$ by
the free action of an elementary abelian 2-group $(\mathbb{Z}_2)^n$. This paper
deals with the classification of 5-dimensional real Bott towers and study
certain type of $n$-dimensional real Bott towers ($n\geq 6$).


  Joint multimodal functional data acquisition, where functional data from
multiple modes are measured simultaneously from the same subject, has emerged
as an exciting modern approach enabled by recent engineering breakthroughs in
the neurological and biological sciences. One prominent motivation to acquire
such data is to enable new discoveries of the underlying connectivity by
combining multimodal signals. Despite the scientific interest, there remains a
gap in principled statistical methods for estimating the graph underlying
multimodal functional data. To this end, we propose a new integrative framework
that models the data generation process and identifies operators mapping from
the observation space to the latent space. We then develop an estimator that
simultaneously estimates the transformation operators and the latent graph.
This estimator is based on the partial correlation operator, which we
rigorously extend from the multivariate to the functional setting. Our
procedure is provably efficient, with the estimator converging to a stationary
point with quantifiable statistical error. Furthermore, we show recovery of the
latent graph under mild conditions. Our work is applied to analyze
simultaneously acquired multimodal brain imaging data where the graph indicates
functional connectivity of the brain. We present simulation and empirical
results that support the benefits of joint estimation.


  A periodic lattice in Euclidean space is the infinite set of all integer
linear combinations of basis vectors. Any lattice can be generated by
infinitely many different bases. This ambiguity was only partially resolved,
but standard reductions remained discontinuous under perturbations modelling
crystal vibrations. This paper completes a continuous classification of
2-dimensional lattices up to Euclidean isometry (or congruence), rigid motion
(without reflections), and similarity (with uniform scaling). The new
homogeneous invariants allow easily computable metrics on lattices considered
up to the equivalences above. The metrics up to rigid motion are especially
non-trivial and settle all remaining questions on (dis)continuity of lattice
bases. These metrics lead to real-valued chiral distances that continuously
measure a lattice deviation from a higher-symmetry neighbour.


  The purpose of this paper is to establish the equivalence between Lagrangian
and classical formulations for the stochastic incompressible Euler equations,
the proof is based in Ito-Wentzell-Kunita formula and stochastic analysis
techniques. Moreover, we prove a local existence result for the Lagrangian
formulation in suitable Sobolev Spaces.


  The relativistic four-quark equations in the framework of the dispersion
relation technique are derived. The four-quark amplitudes of the scalar
tetraquarks with open bottom, including u, d, s and bottom quarks, are
constructed. The poles of these amplitudes determine the masses and widths of
scalar tetraquarks.


  As a pedagogical exercise, we derive the shape of a particularly elegant
pop-up card design, and show that it connects to a classically studied plane
curve that is (among other interpretations) a caustic of a circle.


  We present a point value characterization for elements of the elementary full
Colombeau algebra G^e and the diffeomorphism invariant full Colombeau algebra
G^d. Moreover, several results from the special algebra G^s about generalized
numbers and invertibility are extended to the elementary full algebra.


  We present a theoretical analysis of phase separation in the presence of a
spatially periodic forcing of wavenumber q traveling with a velocity v. By an
analytical and numerical study of a suitably generalized 2d-Cahn-Hilliard model
we find as a function of the forcing amplitude and the velocity three different
regimes of phase separation. For a sufficiently large forcing amplitude a
spatially periodic phase separation of the forcing wavenumber takes place,
which is dragged by the forcing with some phase delay. These locked solutions
are only stable in a subrange of their existence and beyond their existence
range the solutions are dragged irregularly during the initial transient period
and otherwise rather regular. In the range of unstable locked solutions a
coarsening dynamics similar to the unforced case takes place. For small and
large values of the forcing wavenumber analytical approximations of the
nonlinear solutions as well as for the range of existence and stability have
been derived.


  In recent years, X-ray observations with Chandra and XMM-Newton have
significantly increased our understanding of rotation-powered (radio)
millisecond pulsars (MSPs). Deep Chandra studies of several globular clusters
have detected X-ray counterparts to a host of MSPs, including 19 in 47 Tuc
alone. These surveys have revealed that most MSPs exhibit thermal emission from
their heated magnetic polar caps. Realistic models of this thermal X-ray
emission have provided important insight into the basic physics of pulsars and
neutron stars. In addition, intrabinary shock X-ray radiation observed in
``black-widow'' and peculiar globular cluster ``exchanged'' binary MSPs give
interesting insight into MSP winds and relativistic shock. Thus, the X-ray band
contains valuable information regarding the basic properties of MSPs that are
not accesible by radio timing observations.


  In 21st century America, to many observers, the idea that 10's of millions of
Americans could lose power and heat for multiple days in the middle of a record
cold snap, was unthinkable. It came as an even greater surprise that it would
be Texas - arguably one of the world's energy capitals - that failed to provide
sufficient power to its residents. This paper explores the events that led to
the outage, the experiences of those who lived through it, and the situation in
Texas one to two months after the event. We have taken an ethnographic approach
to capture both the empirical aspects of the situation, and the more
interpretive descriptions of the accounts and thoughts of the participants. We
believe this ethnography of events in Texas can serve as foundational evidence
and therefore can be generalized to a wide variety of situations and
methodologies.


  On a daily basis, law enforcement officers struggle with suspects using
mobile communication applications for criminal activities. These mobile
applications replaced SMS-messaging and evolved the last few years from
plain-text data transmission and storage to an encrypted version. Regardless of
the benefits for all law abiding citizens, this is considered to be the
downside for criminal investigations. Normal smartphone, computer or network
investigations do no longer provide the contents of the communication in
real-time when suspects are using apps like WhatsApp, Signal or Telegram. Among
them, WhatsApp is one of the most common smartphone applications for
communication, both criminal as well as legal activities. Early 2016 WhatsApp
introduced end-to-end encryption for all users, immediately keeping law
enforcement officers around the world in the dark. Existing research to
recuperate the position of law enforcement is limited to a single field of
investigation and often limited to post mortem research on smartphone or
computer while wiretapping is limited to metadata information. Therefore, it
provides only historical data or metadata while law enforcement officers want a
continuous stream of live and substantive information. This paper identified
that gap in available scenarios for law enforcement investigations and
identified a gap in methods available for forensic acquiring and processing
these scenarios. In this paper, we propose a forensic approach to create
real-time insight in the WhatsApp communication. Our approach is based on the
wiretapping, decrypting WhatsApp databases, open source intelligence and
WhatsApp Web communication analysis. We also evaluate our method with different
scenarios in WhatsApp forensics to prove its feasibility and efficiency.


  Style is a significant component of natural language text, reflecting a
change in the tone of text while keeping the underlying information the same.
Even though programming languages have strict syntax rules, they also have
style. Code can be written with the same functionality but using different
language features. However, programming style is difficult to quantify, and
thus as part of this work, we define style attributes, specifically for Python.
To build a definition of style, we utilized hierarchical clustering to capture
a style definition without needing to specify transformations. In addition to
defining style, we explore the capability of a pre-trained code language model
to capture information about code style. To do this, we fine-tuned pre-trained
code-language models and evaluated their performance in code style transfer
tasks.


  Next-generation optoelectronic devices and photonic circuitry will have to
incorporate on-chip compatible nanolaser sources. Semiconductor nanowire lasers
have emerged as strong candidates for integrated systems with applications
ranging from ultrasensitive sensing, to data communication technologies.
Despite significant advances in their fundamental aspects, the integration
within scalable photonic circuitry remains challenging. Here we report on the
realization of hybrid photonic devices consisting of nanowire lasers integrated
with wafer-scale lithographically designed V-groove plasmonic waveguides. We
present experimental evidence of the lasing emission and coupling into the
propagating modes of the V-grooves, enabling on-chip routing of coherent and
sub-diffraction confined light with room temperature operation. Theoretical
considerations suggest that the observed lasing is enabled by a waveguide
hybrid photonic-plasmonic mode. This work represents a major advance towards
the realization of application-oriented photonic circuits with integrated
nanolaser sources.


  The basic motivation behind this work is to raise the question that whether
post selection can be considered a valid physical transformation (on
probability space) or not. We study the consequences of both answers set in a
device (theory) independent framework, based only on observed statistics. We
start with taking up post-selection as an assumption and model the same using
independent devices governed by Boolean functions. We establish analogy between
the post selection functions and the general probabilistic games in a two party
binary input-output scenario. As an observation, we categorize all possible
post-selection functions based on the effect on a uniform input probability
distribution. We find that post-selection can transform simple no signaling
probability distributions to signaling. Similarly, solving NP complete problems
is easy independent of classical or quantum computation (in particular we prove
that Post RP = NP). Finally, we demonstrate an instance of the violation of the
pigeon hole principle independent of underlying theory. As result of our theory
independent modeling we conclude that post-selection as an assumption adds
power to the underlying theory. In particular, quantum mechanics benefits more
with the post-selection assumption, only because it admits a more general set
of allowed probabilities as compared to the local hidden variable model.
Without the assumption we associate a device independent efficiency factor to
quantify the cost of post selection. Our study shows that in the real world
post-selection is not efficient enough to be of any advantage. But from an
adversarial perspective it is still of significance. As an application, we
obtain robust bounds on faking the bell violation in terms of minimum
efficiency required using post selection.


  We present a simple quantum open system to show quantitatively how
entanglement decoherence is related to the energy transfer between the system
of interest and its environment. Particularly, in the case of the exact
entanglement decoherence of two qubits, we find an upper bound for the energy
transfer between the two-qubit system and its environments.


  Antipredator behavior is present in many biological systems where individuals
collectively react to an imminent attack. The antipredator response may
influence spatial pattern formation and ecosystem stability but requires an
organism's cost to contribute to the collective effort. We investigate a
nonhierarchical tritrophic system, whose predator-prey interactions are
described by the rock-paper-scissors game rules. In our spatial stochastic
simulations, the radius of antipredator response defines the maximum prey group
size that disturbs the predator's action, determining the individual cost to
participate in antipredator strategies. We consider that each organism
contributes equally to the collective effort, having its mobility limited by
the proportion of energy devoted to the antipredator reaction. Our outcomes
show that the antipredator response leads to spiral patterns, with the
segregation of organisms of the same species occupying departed spatial
domains. We found that a less localized antipredator response increases the
average size of the single-species patches, improving the protection of
individuals against predation. Finally, our findings show that although the
increase of the predation risk for a more localized antipredator response, the
high mobility constraining benefits species coexistence. Our results may help
ecologists understand the mechanisms leading to the stability of biological
systems where locality is crucial to behavioral interactions among species.


  Identifying frequencies with low signal-to-noise ratios in time series of
stellar photometry and spectroscopy, and measuring their amplitude ratios and
peak widths accurately, are critical goals for asteroseismology. These are also
challenges for time series with gaps or whose data are not sampled at a
constant rate, even with modern Discrete Fourier Transform (DFT) software. Also
the False-Alarm Probability introduced by Lomb and Scargle is an approximation
which becomes less reliable in time series with longer data gaps. A rigorous
statistical treatment of how to determine the significance of a peak in a DFT,
called SigSpec, is presented here. SigSpec is based on an analytical solution
of the probability that a DFT peak of a given amplitude does not arise from
white noise in a non-equally spaced data set. The underlying Probability
Density Function (PDF) of the amplitude spectrum generated by white noise can
be derived explicitly if both frequency and phase are incorporated into the
solution. In this paper, I define and evaluate an unbiased statistical
estimator, the "spectral significance", which depends on frequency, amplitude,
and phase in the DFT, and which takes into account the time-domain sampling. I
also compare this estimator to results from other well established techniques
and demonstrate the effectiveness of SigSpec with a few examples of ground- and
space-based photometric data, illustratring how SigSpec deals with the effects
of noise and time-domain sampling in determining significant frequencies.


  We show that a direct limit of projective contramodules (over a right linear
topological ring) is projective if it has a projective cover. A similar result
is obtained for $\infty$-strictly flat contramodules of projective dimension
not exceeding $1$, using an argument based on the notion of the topological
Jacobson radical. Covers and precovers of direct limits of more general classes
of objects, both in abelian categories with exact and with nonexact direct
limits, are also discussed, with an eye towards the Enochs conjecture about
covers and direct limits, using locally split (mono)morphisms as the main
technique. In particular, we offer a simple elementary proof of the Enochs
conjecture for the left class of an $n$-tilting cotorsion pair in an abelian
category with exact direct limits.


  I present new results for the Standard-Model predictions of the differential
decay rates for $H\to \ell^{+} \ell^{-} \gamma$, where $\ell=e, \mu$, and the
forward-backward asymmetries defined in terms of the flight direction of the
photon corresponding to the lepton momenta. The results dependend on the cuts
on energies and invariant masses of the final state particles. For standard
choices of these cuts the branching ratios $B(H\to e \bar e \gamma)=5.8\cdot
10^{-5}$ and $B(H\to \mu \bar \mu \gamma)=6.4\cdot 10^{-5}$ as well as the
forward-backward asymmetries $\mathcal{A}^{(e)}_{\text{FB}}=0.343$ and
$\mathcal{A}^{(\mu)}_{\text{FB}}=0.255$ have been found.


  This work tackles the problem of task-oriented dexterous hand pose synthesis,
which involves generating a static hand pose capable of applying a
task-specific set of wrenches to manipulate objects. Unlike previous approaches
that focus solely on force-closure grasps, which are unsuitable for
non-prehensile manipulation tasks (\textit{e.g.}, turning a knob or pressing a
button), we introduce a unified framework covering force-closure grasps,
non-force-closure grasps, and a variety of non-prehensile poses. Our key idea
is a novel optimization objective quantifying the disparity between the Task
Wrench Space (TWS, the desired wrenches predefined as a task prior) and the
Grasp Wrench Space (GWS, the achievable wrenches computed from the current hand
pose). By minimizing this objective, gradient-based optimization algorithms can
synthesize task-oriented hand poses without additional human demonstrations.
Our specific contributions include 1) a fast, accurate, and differentiable
technique for estimating the GWS boundary; 2) a task-oriented objective
function based on the disparity between the estimated GWS boundary and the
provided TWS boundary; and 3) an efficient implementation of the synthesis
pipeline that leverages CUDA accelerations and supports large-scale
paralleling. Experimental results on 10 diverse tasks demonstrate a 72.6\%
success rate in simulation. Furthermore, real-world validation for 4 tasks
confirms the effectiveness of synthesized poses for manipulation. Notably,
despite being primarily tailored for task-oriented hand pose synthesis, our
pipeline can generate force-closure grasps 50 times faster than DexGraspNet
while maintaining comparable grasp quality. Project page:
https://pku-epic.github.io/TaskDexGrasp/.


  The aim of this paper is to present some results about generation,
sectoriality and gradient estimates both for the semigroup and for the
resolvent of suitable realizations of the operators [\Ab u(x)=\gamma xu"(x) + b
u'(x),] with constants $\gamma >0$ and $b\geq 0$, in the space $C([0,\infty])$


  We test the reproducibility of X-ray reflectometry(XRR) measurements and
optimizations using an National Metrology Institute of Japan (NMIJ)/National
Institute of Advanced Industrial Science and Technology (AIST) pre-standard.
Based on bootstrap analysis of repeated refinements, using several CPU-years of
time, we provide concrete recommendations of best practices for ensuring the
reproducibility of XRR model fitting results. These recommendations can be used
to study both instrument repeatability and cross-instrument reproducibility.
Because the recommendations used optimizations methods available in commonly
used commercial software, they can quickly be applied both in research and
analytical laboratories, as well as fabrication environments.


  We consider the head-on collision of equal-mass neutron stars boosted towards
each other and we study the behavior of such systems near the threshold of
black-hole formation. In particular, we confirm the previous findings by [1]
that a type-I critical phenomenon can be observed by fine-tuning the initial
mass of the two neutron stars. At the same time, we argue against the
interpretation that the critical solution is not a perturbed spherical star and
show instead that the metastable star corresponds to a (perturbed) equilibrium
solution on the unstable branch of the equilibrium configurations. As a result,
the head-on collision of two neutron stars near the critical threshold can be
seen as a transition in the space of configurations from an initial stable
solution over to a critical metastable one which can either migrate to a stable
solution or collapse to a black hole. The critical exponent for this process
shows a fine structure which was already observed in the case of the critical
collapse of scalar fields but never before for perfect fluids.


  The H-index of a node in a static network is the maximum value $h$ such that
at least $h$ of its neighbors have a degree of at least $h$. Recently, a
generalized version, the $n$-th order H-index, was introduced, allowing to
relate degree centrality, H-index, and the $k$-core of a node. We extend the
$n$-th order H-index to temporal networks and define corresponding temporal
centrality measures and temporal core decompositions. Our $n$-th order temporal
H-index respects the reachability in temporal networks leading to node
rankings, which reflect the importance of nodes in spreading processes. We
derive natural decompositions of temporal networks into subgraphs with strong
temporal coherence. We analyze a recursive computation scheme and develop a
highly scalable streaming algorithm. Our experimental evaluation demonstrates
the efficiency of our algorithms and the conceptional validity of our approach.
Specifically, we show that the $n$-th order temporal H-index is a strong
heuristic for identifying super-spreaders in evolving social networks and
detects temporally well-connected components.


  This paper addresses the problem of constructing a cycle-level intersection
theory for toric varieties. We show that by making one global choice, we can
determine a cycle representative for the intersection of an equivariant Cartier
divisor with an invariant cycle on a toric variety. For a toric variety defined
by a fan in N, the choice consists of giving an inner product or a complete
flag for M_Q=Hom(N,Q), or more generally giving for each cone sigma in the fan
a linear subspace of M_Q complementary to the subspace of M_Q perpendicular to
sigma, satisfying certain compatibility conditions.
  We show that these intersection cycles have properties analogous to the usual
intersections modulo rational equivalence. If X is simplicial (for instance, if
X is non-singular), we obtain a commutative ring structure on the invariant
cycles of X with rational coefficients. This ring structure determines cycles
representing certain characteristic classes of the toric variety. We also
discuss how to define intersection cycles that require no choices, at the
expense of increasing the size of the coefficient field.


  We revisit for 714 SNeIa the discrepancy between the red-shift associated to
the distance modulus $\mu$ and the spectroscopic red-shift. Previous work has
shown that the total red-shift $z$ might be a combination of the expansion
red-shift $z_{\rm C}$ and of a static, blue or red shift $z_{\rm LSV}(r)$, $r$
being the comoving distance. The latter is due to the energy non-conservation
of the photon propagating through Electro-Magnetic (EM) background fields (host
galaxy, intergalactic and Milky Way), under Lorentz(-Poincar\'e) Symmetry
Violation (LSV), associated to the Standard-Model Extension (SME). The
non-conservation stems from the vacuum expectation value of the vector and
tensor LSV fields. For zero radiation $\Omega_{\rm rad}$ and curvature
$\Omega_{\rm k}$ densities, and matter density $\Omega_m = 0.28$, the SN1a
positions in the ($\mu$, z) plan are recovered according to the different
strengths, orientations, alignments and space-time dependencies of the EM
fields and LSV components. The LSV vacuum energy may be thus tantamount to
$\Omega_\Lambda \simeq 0.7$, but unrelated to an accelerated expansion. We
present models with red or blue-shifts $z_{\rm LSV}$, below $10\%$ of $z$. The
$\nu$ frequency variation is below $10^{-19} \Delta \nu/\nu$ per m.


  We study the radiative properties -- the Lamb shift, Purcell decay rate and
the spontaneous emission dynamics -- of an artificial atom coupled to a long,
multimode cavity formed by an array of Josephson junctions. Introducing a
tunable coupling element between the atom and the array, we demonstrate that
such a system can exhibit a crossover from a perturbative to non-perturbative
regime of light-matter interaction as one strengthens the coupling between the
atom and the Josephson junction array (JJA). As a consequence, the concept of
spontaneous emission as the occupation of the local atomic site being governed
by a single complex-valued exponent breaks down. This breakdown, we show, can
be interpreted in terms of formation of hybrid atom-resonator modes with
radiative losses that are non-trivially related to the effective coupling
between individual modes. We develop a singular function expansion approach for
the description of the open quantum system dynamics in such a multimode
non-perturbative regime. This modal framework generalizes the normal mode
description of quantum fields in a finite volume, incorporating exact radiative
losses and incident quantum noise at the delimiting surface. Our results are
pertinent to recent experiments with Josephson atoms coupled to high impedance
Josephson junction arrays.


  We simulate the propagation of a shock front through the galactic halo
induced by an explosion and/or a starburst at the galactic center. A huge
dumbbell ($\Omega$)-shaped shock front produced by an explosion of energy
$3\times 10^{56}$ ergs about fifteen million years ago can mimic the radio and
X-ray North Polar Spur as well the southern large X-ray spur. The post-shock
high-temperature gas in the corona will explain the observed X-ray bulge around
the galactic center. Key workds Galaxy: center -- Galaxy: halo -- Radio
continuum: general -- Shock wave -- X-rays: general


  Several well-studied online resource allocation problems can be formulated in
terms of infinite, increasing sequences of positive values, in which each
element is associated with a corresponding allocation value. Examples include
problems such as online bidding, searching for a hidden target on an unbounded
line, and designing interruptible algorithms based on repeated executions. The
performance of the online algorithm, in each of these problems, is measured by
the competitive ratio, which describes the multiplicative performance loss due
to the absence of full information on the instance.
  We study such competitive sequencing problems in a setting in which the
online algorithm has some (potentially) erroneous information, expressed as a
$k$-bit advice string, for some given $k$. We first consider the untrusted
advice setting of [Angelopoulos et al, ITCS 2020], in which the objective is to
quantify performance considering two extremes: either the advice is either
error-free, or it is generated by a (malicious) adversary. Here, we show a
Pareto-optimal solution, using a new approach for applying the functional-based
lower-bound technique due to [Gal, Israel J. Math. 1972]. Next, we study a
nascent noisy advice setting, in which a number of the advice bits may be
erroneous; the exact error is unknown to the online algorithm, which only has
access to a pessimistic estimate (i.e., an upper bound on this error). We give
improved upper bounds, but also the first lower bound on the competitive ratio
of an online problem in this setting. To this end, we combine ideas from robust
query-based search in arrays, and fault-tolerant contract scheduling. Last, we
demonstrate how to apply the above techniques in robust optimization without
predictions, and discuss how they can be applicable in the context of more
general online problems.


  We complete the derivation of the Cornwall-Jackiw-Tomboulis effective
potential for quark propagator at finite temperature and finite quark chemical
potential in the real-time formalism of thermal field theory and in Landau
gauge. In the approximation that the function $A(p^2)$ in inverse quark
propagator is replaced by unity, by means of the running gauge coupling and the
quark mass function invariant under the renormalization group in zero
temperature Quantum Chromadynamics (QCD), we obtain a calculable expression for
the thermal effective potential which will be a useful means to research chiral
phase transition in QCD in the real-time formalism.


  For a large class of linear neutral type systems the problem of eigenvalues
and eigenvectors assignment is investigated, i.e. finding the system which has
the given spectrum and almost all, in some sense, eigenvectors.


  We consider two quantum cryptographic schemes relying on encoding the key
into qudits, i.e. quantum states in a d-dimensional Hilbert space. The first
cryptosystem uses two mutually unbiased bases (thereby extending the BB84
scheme), while the second exploits all the d+1 available such bases (extending
the six-state protocol for qubits). We derive the information gained by a
potential eavesdropper applying a cloning-based individual attack, along with
an upper bound on the error rate that ensures unconditional security against
coherent attacks.


  Anomaly detection from a single image is challenging since anomaly data is
always rare and can be with highly unpredictable types. With only anomaly-free
data available, most existing methods train an AutoEncoder to reconstruct the
input image and find the difference between the input and output to identify
the anomalous region. However, such methods face a potential problem - a coarse
reconstruction generates extra image differences while a high-fidelity one may
draw in the anomaly. In this paper, we solve this contradiction by proposing a
two-stage approach, which generates high-fidelity yet anomaly-free
reconstructions. Our Unsupervised Two-stage Anomaly Detection (UTAD) relies on
two technical components, namely the Impression Extractor (IE-Net) and the
Expert-Net. The IE-Net and Expert-Net accomplish the two-stage anomaly-free
image reconstruction task while they also generate intuitive intermediate
results, making the whole UTAD interpretable. Extensive experiments show that
our method outperforms state-of-the-arts on four anomaly detection datasets
with different types of real-world objects and textures.


  Cybersecurity is an inherent characteristic that should be addressed before
the large deployment of smart city applications. Recently, Blockchain appears
as a promising technology to provide several cybersecurity aspects of smart
city applications. This paper provides a comprehensive review of the existing
blockchain-based solutions for the cybersecurity of the main smart city
applications, namely smart healthcare, smart transportation, smart agriculture,
supply chain management, smart grid, and smart homes. We describe the existing
solutions and we discuss their merits and limits. Moreover, we define the
security requirements of each smart city application and we give a mapping of
the studied solutions to these defined requirements. Additionally, future
directions are given. We believe that the present survey is a good starting
point for every researcher in the fields of cybersecurity, blockchain, and
smart cities.


  We develop a method for comparing hierarchical image representations in terms
of their ability to explain perceptual sensitivity in humans. Specifically, we
utilize Fisher information to establish a model-derived prediction of
sensitivity to local perturbations of an image. For a given image, we compute
the eigenvectors of the Fisher information matrix with largest and smallest
eigenvalues, corresponding to the model-predicted most- and least-noticeable
image distortions, respectively. For human subjects, we then measure the amount
of each distortion that can be reliably detected when added to the image. We
use this method to test the ability of a variety of representations to mimic
human perceptual sensitivity. We find that the early layers of VGG16, a deep
neural network optimized for object recognition, provide a better match to
human perception than later layers, and a better match than a 4-stage
convolutional neural network (CNN) trained on a database of human ratings of
distorted image quality. On the other hand, we find that simple models of early
visual processing, incorporating one or more stages of local gain control,
trained on the same database of distortion ratings, provide substantially
better predictions of human sensitivity than either the CNN, or any combination
of layers of VGG16.


  We consider the moduli space of holomorphic principal bundles for reductive
Lie groups over Riemann surfaces (possibly with boundaries) and equipped with
meromorphic connections. We associate to this space a point-wise notion of
quantum spectral curve whose generalized periods define a new set of moduli. We
define homology cycles and differential forms of the quantum spectral curve,
allowing to derive quantum analogs of the form-cycle duality and Riemann
bilinear identities of classical geometry. A tau-function is introduced for
this system in the form of a theta-series and in such a way that the variations
of its coefficients with respect to moduli, isomonodromic or not, can be
computed as quantum period integrals. This lays new grounds to relate our study
to that of integrable hierarchies, isomonodromic deformation of meromorphic
connections and non-perturbative topological string theory. In turn, we define
amplitudes on the quantum spectral curve which have an interpretation in
conformal field theory when the Lie algebra is assumed to be simply-laced: they
coincide with correlation functions involving twisted chiral fields of an
affine Lie algebra at level one. The singularities at the punctures are
interpreted as primary fields of the associated Casimir W-algebra. The
amplitudes are moreover related by W-constraints, so-called loop equations,
allowing one to compute recursively a certain asymptotic expansion of the
tau-function, namely the one corresponding both to the heavy-charge regime of
conformal field theory and to the weak-coupling regime of topological string
theory.


  We study numerically the ground-state phase diagram of the
bilinear-biquadratic spin-1 chain near the ferromagnetic instability point,
where the existence of a gapped or gapless nondimerized quantum nematic phase
has been suggested. Our results, obtained by a highly accurate density-matrix
renormalization-group (DMRG) calculation are consistent with the view that the
order parameter characterizing the dimer phase vanishes only at the point where
the system becomes ferromagnetic, although the existence of a gapped or gapless
nondimerized phase in a very narrow parameter range between the ferromagnetic
and the dimerized regimes cannot be ruled out.


  Metric learning is an important problem in machine learning. It aims to group
similar examples together. Existing state-of-the-art metric learning approaches
require class labels to learn a metric. As obtaining class labels in all
applications is not feasible, we propose an unsupervised approach that learns a
metric without making use of class labels. The lack of class labels is
compensated by obtaining pseudo-labels of data using a graph-based clustering
approach. The pseudo-labels are used to form triplets of examples, which guide
the metric learning. We propose a probabilistic loss that minimizes the chances
of each triplet violating an angular constraint. A weight function, and an
orthogonality constraint in the objective speeds up the convergence and avoids
a model collapse. We also provide a stochastic formulation of our method to
scale up to large-scale datasets. Our studies demonstrate the competitiveness
of our approach against state-of-the-art methods. We also thoroughly study the
effect of the different components of our method.


  Domination in graphs has long been studied and is applied to signal
distribution problem. For example, telecommunication companies want to spread
the signal from broadcast stations by transmitting varying signal strength to
all receiving stations. This problem can be interpreted in a term of graph
theory. Assume that broadcast companies need to spread the signal in graphs by
using broadcast stations with varying signal strength so that the signal could
be sent to all the vertices. However, broadcast stations with stronger signal
are generally more expensive. The distribution of signal was configured to
cover all stations with minimum total cost of signal called the
$\gamma_b-$dominating broadcast number. This paper shows another proof of the
$\gamma_b-$dominating broadcast number of cycle graphs and sunlet graphs as a
foundation for the further result. I also consider the $\gamma_b-$dominating
broadcast number of a generalized version of sunlet graphs whose vertices on
the cycle are equally extended by the path, called the sunlet graph with degree
$n$. To obtain the optimal cost of the signal distribution for this extended
version, we show that it is sufficient to use only one broadcast station at a
vertex on the cycle with the signal cost equal to the radius of the sunlet
graph with degree $n$.


  This paper proposes a scientifically reasonable polarization mode dispersion
(PMD) emulator (PMDE) for coherent optical fiber transmission. Guidelines are
physically correct modeling of the polarization-dispersive fiber, the
time-variable polarization transformations occurring in there, including
emulation of polarization events caused by lightning strikes, the adoption of
acceptable compromise to keep implementation cost low enough and competitive
industrial basis for production of such PMDE. We propse a PMDE consisting of N
differential group delay (DGD) sections placed between N+1 time-variable
general retarders or polarization scramblers. These should be general
elliptical retarders, capable of changing polarization with rates up to 20
Mrad/s on the Poincar\'e sphere. That should include bursts of polarization
rotations forth and back at up to 20 Mrad/s. The DGD sections can be fixed or
variable and should be able to constitute a total PMD of alternatively, say, 20
ps, 50 ps, 100 ps, 200 ps, or another set of various discrete values. We
propose even N and equal individual DGDs, which allows the total PMDE to assume
a neutral state without any PMD of whatever order. Number N may be chosen
relatively small; N = 2 seems acceptable. A variety of component and subsystem
suppliers is available, and the proposed PMDE is available on the market.


  We construct a simple accretion model of a rotating pressureless gas sphere
onto a Schwarzschild black hole. We show how to build analytic solutions in
terms of Jacobi elliptic functions. This construction represents a general
relativistic generalisation of the Newtonian accretion model first proposed by
Ulrich (1976). In exactly the same form as it occurs for the Newtonian case,
the flow naturally predicts the existence of an equatorial rotating accretion
disc about the hole. However, the radius of the disc increases monotonically
without limit as the flow reaches its maximum allowed angular momentum.


  In 2015, Guglielmi and Badia discussed optimal strategies in a particular
type of service system with two strategic servers. In their setup, each server
can either be active or inactive and an active server can be requested to
transmit a sequence of packets. The servers have varying probabilities of
successfully transmitting when they are active, and both servers receive a unit
reward if the sequence of packets is transmitted successfully. Guglielmi and
Badia provided an analysis of optimal strategies in four scenarios: where each
server does not know the other's successful transmission probability; one of
the two servers is always inactive; each server knows the other's successful
transmission probability; and they are willing to cooperate.
  Unfortunately the analysis in Guglielmi and Badia contained errors. In this
paper we correct these errors. We discuss three cases where both servers (I)
communicate and cooperate; (II) neither communicate nor cooperate; (III)
communicate but do not cooperate. In particular, we obtain the unique Nash
equilibrium strategy in Case II through a Bayesian game formulation, and
demonstrate that there is a region in the parameter space where there are
multiple Nash equilibria in Case III. We also quantify the value of
communication or cooperation by comparing the social welfare in the three
cases, and propose possible regulations to make the Nash equilibrium strategy
the socially optimal strategy for both Cases II and III.