  Graph neural networks (GNNs) are machine learning models specialized for
graph data and widely used in many applications. To train GNNs on large graphs
that exceed CPU memory, several systems store data on disk and conduct
out-of-core processing. However, these systems suffer from either read
amplification when reading node features that are usually smaller than a disk
page or degraded model accuracy by treating the graph as disconnected
partitions. To close this gap, we build a system called DiskGNN, which achieves
high I/O efficiency and thus fast training without hurting model accuracy. The
key technique used by DiskGNN is offline sampling, which helps decouple graph
sampling from model computation. In particular, by conducting graph sampling
beforehand, DiskGNN acquires the node features that will be accessed by model
computation, and such information is utilized to pack the target node features
contiguously on disk to avoid read amplification. Besides, \name{} also adopts
designs including four-level feature store to fully utilize the memory
hierarchy to cache node features and reduce disk access, batched packing to
accelerate the feature packing process, and pipelined training to overlap disk
access with other operations. We compare DiskGNN with Ginex and MariusGNN,
which are state-of-the-art systems for out-of-core GNN training. The results
show that DiskGNN can speed up the baselines by over 8x while matching their
best model accuracy.


  We present a self-consistent comparison of the rise times for low- and
high-redshift Type Ia supernovae. Following previous studies, the early light
curve is modeled using a t-squared law, which is then mated with a modified
Leibundgut template light curve. The best-fit t-squared law is determined for
ensemble samples of low- and high-redshift supernovae by fitting simultaneously
for all light curve parameters for all supernovae in each sample. Our method
fully accounts for the non-negligible covariance amongst the light curve
fitting parameters, which previous analyses have neglected. Contrary to Riess
et al. (1999), we find fair to good agreement between the rise times of the
low- and high-redshift Type Ia supernovae. The uncertainty in the rise time of
the high-redshift Type Ia supernovae is presently quite large (roughly +/- 1.2
days statistical), making any search for evidence of evolution based on a
comparison of rise times premature. Furthermore, systematic effects on rise
time determinations from the high-redshift observations, due to the form of the
late-time light curve and the manner in which the light curves of these
supernovae were sampled, can bias the high-redshift rise time determinations by
up to +3.6/-1.9 days under extreme situations. The peak brightnesses - used for
cosmology - do not suffer any significant bias, nor any significant increase in
uncertainty.


  We discuss a model based on a hidden $U(1)_X$ gauge symmetry in which
neutrino mass is induced at two-loop level by effects of interactions among
particles in hidden sector and the Standard Model leptons. Since neutrino mass
is suppressed by two-loop, its associate Yukawa couplings can be sizable and it
would affect lepton flavor phenomenology. We analyze neutrino mass matrix,
lepton flavor violating processes, electron/muon $g-2$ and dark matter
annihilation cross section which are induced via interactions among Standard
Model leptons and particles in $U(1)_X$ hidden sector, and their interactions
can be sizable in our scenario. Performing numerical analysis, we show expected
ratios for these processes using allowed parameters which can fit the neutrino
data and satisfy flavor constraints.


  Zamolodchikov periodicity is periodicity of certein recursions associated
with box products $X \square Y$ of two finite type Dynkin diagrams. We suggest
an affine analog of Zamolodchikov periodicity, which we call Zamolodchikov
integrability. We conjecture that it holds for products $X \square Y$, where
$X$ is a finite type Dynkin diagram and $Y$ is an extended Dynkin diagram. We
prove this conjecture for the case of $A_m \square A_{2n-1}^{(1)}$. The proof
employs cluster structures in certain classical rings of invariants, previously
studied by S. Fomin and the author.


  There are currently two philosophies for building grammars and parsers --
Statistically induced grammars and Wide-coverage grammars. One way to combine
the strengths of both approaches is to have a wide-coverage grammar with a
heuristic component which is domain independent but whose contribution is tuned
to particular domains. In this paper, we discuss a three-stage approach to
disambiguation in the context of a lexicalized grammar, using a variety of
domain independent heuristic techniques. We present a training algorithm which
uses hand-bracketed treebank parses to set the weights of these heuristics. We
compare the performance of our grammar against the performance of the IBM
statistical grammar, using both untrained and trained weights for the
heuristics.


  We investigate the scale-dependence, or the runnings, of linear and second
order density perturbations generated in various curvaton scenarios. We argue
that the second order perturbations, i.e. non-Gaussianity, can strongly depend
on the scale, even when the linear perturbations are nearly scale-invariant. We
present analytic formulae for the runnings from curvatons with general energy
potentials, and clarify the conditions under which fNL becomes strongly
scale-dependent. From the point of view of the fNL running, curvaton potentials
can be classified into roughly two categories by whether the potential flattens
or steepens compared to a quadratic one. As such examples, we study
pseudo-Nambu-Goldstone curvatons, and self-interacting curvatons, respectively.
The dynamics of non-quadratic curvatons and the behaviors of the resulting
density perturbations are clarified by analytical methods. Then we also study
models where multiple source can be responsible for density perturbations such
as the multi-curvaton, and mixed curvaton and inflaton models where the running
of fNL can also be large due to their multi-source nature. We make quantitative
analysis for each curvaton scenario and discuss in what cases the
scale-dependence, in particular, of fNL can be large enough to be probed with
future CMB experiments.


  We demonstrate using scanning tunneling microscopy and spectroscopy the
electron quantization within metallic Au atomic wires self-assembled on a
Si(111) surface and segmented by adatom impurities. The local electronic states
of wire segments with a length up to 10 nm are investigated as terminated by
two neighboring Si adatoms. One dimensional (1D) quantum well states are well
resolved by their spatial distributions and the inverse-length-square
dependence in their energies. The quantization also results in the quantum
oscillation of the conductance at the Fermi level. These results deny the
dopant role of the adatoms assumed for a long time but indicate their strong
scattering nature. The present approach provides a new and convenient platform
to investigate 1D quantum phenomena with atomic precision.


  We explore the Cauchy and a new heavy tailed (Fuquene, Perez and Pericchi
(2011)) priors to estimate proportions on small areas. Hierarchical models and
the Binomial likelihood in the exponential family form are used. We believe
that the heavy tailed priors in survey sampling settings could be more
effective than the choice of noninformative priors to eliminate antipathy
towards methods that involve subjective elements or assumptions. To illustrate
the robust Bayesian approach, we apply this methodology in a popular example:
"the clement problem". Finally, we recommend to use the Cauchy prior in absence
or presence of outliers within the small areas and the Fuquene et al. (2011)
prior when the outlier is a particular small area.


  Research into the automatic acquisition of lexical information from corpora
is starting to produce large-scale computational lexicons containing data on
the relative frequencies of subcategorisation alternatives for individual
verbal predicates. However, the empirical question of whether this type of
frequency information can in practice improve the accuracy of a statistical
parser has not yet been answered. In this paper we describe an experiment with
a wide-coverage statistical grammar and parser for English and
subcategorisation frequencies acquired from ten million words of text which
shows that this information can significantly improve parse accuracy.


  We employ the Yukawa coupling unification condition, y_t= y_b= y_tau at
M_GUT, inspired by supersymmetric SO(10) models, to estimate the lightest Higgs
boson mass as well as masses of the associated squarks and gluino. We employ
non-universal soft masses, dictated by SO(10) symmetry, for the gauginos.
Furthermore, the soft masses for the two scalar Higgs doublets are set equal at
M_GUT, and in some examples these are equal to the soft masses for scalars in
the matter multiplets. For mu > 0, M_2 > 0, where M_2 denotes the SU(2) gaugino
mass, essentially perfect t-b-tau Yukawa unification is possible, and it
predicts a Higgs mass of 122 - 124 GeV with a theoretical uncertainty of about
3 GeV. The corresponding gluino and the first two family squarks have masses 3
TeV. We present some LHC testable benchmark points which also show the presence
of neutralino-stau coannihilation in this scenario. The well-known MSSM
parameter tan beta~47.


  This paper introduces the Banzhaf and Banzhaf-Owen values as novel centrality
measures for ranking terrorists in a network. This new approach let integrate
the complete topology (i.e. nodes and edges) of the network and a coalitional
structure on the nodes of the network. More precisely, the characteristics of
the nodes (e.g., terrorists) of the network and their possible relationships
(e.g., types of communication links), as well as coalitional information (e.g.
level of hierarchies) independent of the network. First, for both centrality
measures, we provide approximation algorithms and the corresponding R-codes.
Second, as illustration, we rank the members of the Zerkani network,
responsible for the attacks in Paris (2015) and Brussels (2016). Finally, we
give a comparison between the rankings established by Banzhaf and Banzhaf-Owen
and the rankings obtained when using the Shapley value (cf. Hamers et al.,
2019) and the Owen value as centrality measures


  In the context of topcolor assisted technicolor(TC2) models, we study the
production of the top-pions $\pi_{t}^{0,\pm}$ with single top quark via the
processes $p\bar{p} \to t\pi_{t}^{0}+X$ and $p\bar{p} \to t\pi_{t}^{\pm}+X$,
and discuss the possibility of detecting these new particles at Tevatron and
LHC. We find that it is very difficult to observe the signals of these
particles via these processes at Tevatron, while the neutral and charged
top-pions $\pi_{t}^{0}$ and $\pi_{t}^{\pm}$ can be detecting via considering
the same sign top pair $tt\bar{c}$ event and the $tt\bar{b}$ (or $t\bar{t}b$)
event at LHC, respectively.


  The promise of quantum computing lies in harnessing programmable quantum
devices for practical applications such as efficient simulation of quantum
materials and condensed matter systems. One important task is the simulation of
geometrically frustrated magnets in which topological phenomena can emerge from
competition between quantum and thermal fluctuations. Here we report on
experimental observations of relaxation in such simulations, measured on up to
1440 qubits with microsecond resolution. By initializing the system in a state
with topological obstruction, we observe quantum annealing (QA) relaxation
timescales in excess of one microsecond. Measurements indicate a dynamical
advantage in the quantum simulation over the classical approach of
path-integral Monte Carlo (PIMC) fixed-Hamiltonian relaxation with multiqubit
cluster updates. The advantage increases with both system size and inverse
temperature, exceeding a million-fold speedup over a CPU. This is an important
piece of experimental evidence that in general, PIMC does not mimic QA dynamics
for stoquastic Hamiltonians. The observed scaling advantage, for simulation of
frustrated magnetism in quantum condensed matter, demonstrates that near-term
quantum devices can be used to accelerate computational tasks of practical
relevance.


  Bacillus subtilis ATCC6633 produces mycosubtilin, a non-ribosomally
synthesized lipopeptide of the iturin family which presents antagonistic
activities toward various phytopathogens. Different homologues with fatty acid
moiety varying from C 15 to C 17 are usually co-produced, with their biological
activities increasing with the number of carbons in the fatty acid chain. In
the present report, we highlight that growth temperature modulates both the
extent of mycosubtilin production and the relative abundance of the different
homologues. A 30-fold increase in mycosubtilin production was observed when the
temperature was decreased from 37 C to 25 C for both strain ATCC6633 and its
derivative BBG100, a constitutive mycosubtilin overproducer. However, no
significant difference in either the expression of the mycosubtilin synthetase
encoding genes or in the intracellular synthetase concentration could be found,
suggesting that the observed phenotype originated from a higher mycosubtilin
synthetase turnover at lower temperature. We also point out that lower growth
temperature leads to an increased proportion of odd-numbered fatty acid
homologues as a consequence of de novo synthesis of C 17 anteiso fatty acid
following cell adaptation to low temperatures.


  Active colloidal microswimmers serve as archetypical active fluid systems,
and as models for biological swimmers. Here, by studying in detail their
velocity traces, we find robust power-law intermittency with system-dependent
exponential cut off. We model the motion by an interplay of the field
gradient-dependent active force and the locally fluctuating hydrodynamic drag,
set by the wetting properties of the substrate. The model closely describes the
velocity distributions of two disparate swimmer systems: AC field activated and
catalytic swimmers. The generality is highlighted by the collapse of all data
in a single master curve, suggesting the applicability to further systems, both
synthetic and biological.


  Chamorro and Virbhadra studied, using the energy-momentum complex of
Einstein, the energy distribution associated with static spherically symmetric
charged dilaton black holes for an arbitrary value of the coupling parameter
$\gamma$ which controls the strength of the dilaton to the Maxwell field. We
study the same in Tolman's prescription and get the same result as obtained by
Chamorro and Virbhadra. The energy distribution of charged dilaton black holes
depends on the value of $\gamma$ and the total energy is independent of this
parameter.


  Radio Frequency Identification (RFID) systems are among the most widespread
computing technologies with technical potential and profitable opportunities in
numerous applications worldwide. Further, RFID is the core technology behind
the Internet of Things (IoT), which can accomplish the real-time transmission
of information between objects without manual operation. However, RFID security
has been taken for granted for several years, causing multiple vulnerabilities
that can even damage human functionalities. The latest ISO/IEC 18000-63:2015
standard concerning RFID dates to 2015, and much freedom has been given to
manufacturers responsible for making their devices secure. The lack of a
substantial standard for devices that implement RFID technology creates many
vulnerabilities that expose end-users to elevated risk. Hence, this paper gives
the reader a clear overview of the technology, and it analyzes 23 well-known
RFID attacks such as Reverse Engineering, Buffer Overflow, Eavesdropping, and
Malware. Moreover, given the exceptional capabilities and utilities of RFID
devices, this paper has focused on security measures and defenses for
protecting them, such as Active Jamming, Shielding tag, and Authentication.


  Industrial automation systems (IASs) are commonly developed using the
languages defined by the IEC 61131 standard and are executed on PLCs. In this
paper, a system-based approach for the development of IASs is adopted. A
framework is described to refine the UML model of the software part, which is
extracted from the SysML system model, and get the implementation code. Two
implementation alternatives are considered to exploit PLCs but also the recent
deluge of embedded boards in the market. For PLC targets, the new version of
IEC 61131 that supports Object-Orientation is adopted, while Java is used for
embedded boards. The case study was developed as a lab exercise for teaching
the various technologies that address challenges in the domain of
cyber-physical systems where Internet of Things (IoT) would be the glue
regarding their cyber interfaces.


  The detection of multi-TeV gamma-rays from the afterglow phase of GRB 190829A
by High Energy Stereoscopic System (H.E.S.S.) telescope is an addition to the
already existing list of two more GRBs observed in the very high energy (VHE)
gamma-rays in recent years. Jets of blazars and GRBs have many similarities and
the photohadronic model is very successful in explaining the VHE gamma-ray
spectra from the high energy blazars. Recently, the photohadronic model has
been successfully applied to study the sub-TeV gamma-rays from the afterglow
phases of GRB 180720B and GRB 190114C. We employed this model again to explain
the VHE spectra observed for the two consecutive nights from GRB 190829A. We
show that the spectra of GRB 190829A can be due to the interactions of high
energy protons with the synchrotron self-Compton photons in the forward shock
region of the GRB jet, similar to the low emission state of the VHE flaring
events of high energy blazars. We speculate that, if in future, it is possible
to observe the VHE gamma-ray spectra from nearby GRBs in their afterglow
phases, then some of them could only be explained by employing two different
spectral indices. If confirmed, such VHE spectra could be interpreted as a
result of the interactions of the high energy protons with the photons, both
from the synchrotron background and the synchrotron self-Compton background in
the forward shock region.


  We study a general class of PT-symmetric tridiagonal Hamiltonians with purely
imaginary interaction terms in the quasi-hermitian representation of quantum
mechanics. Our general Hamiltonian encompasses many previously studied lattice
models as special cases. We provide numerical results regarding domains of
observability and exceptional points, and discuss the possibility of explicit
construction of general metric operators (which in turn determine all the
physical Hilbert spaces). The condition of computational simplicity for the
metrics motivates the introduction of certain one-parametric special cases,
which consequently admit closed-form extrapolation patterns of the
low-dimensional results.


  In this paper, we introduce a new class of codes, called weighted
parity-check codes, where each parity-check bit has a weight that indicates its
likelihood to be one (instead of fixing each parity-check bit to be zero). It
is applicable to a wide range of settings, e.g. asymmetric channels, channels
with state and/or cost constraints, and the Wyner-Ziv problem, and can provably
achieve the capacity. For the channels with state (Gelfand-Pinsker) setting,
the proposed coding scheme has two advantages compared to the nested linear
code. First, it achieves the capacity of any channel with state (e.g.
asymmetric channels). Second, simulation results show that the proposed code
achieves a smaller error rate compared to the nested linear code. We also
discuss a sparse construction where the belief propagation algorithm can be
applied to improve the coding efficiency.


  Lattices are very important objects in the effort to construct cryptographic
primitives that are secure against quantum attacks. A central problem in the
study of lattices is that of finding the shortest non-zero vector in the
lattice. Asymptotically, sieving is the best known technique for solving the
shortest vector problem, however, sieving requires memory exponential in the
dimension of the lattice. As a consequence, enumeration algorithms are often
used in place of sieving due to their linear memory complexity, despite their
super-exponential runtime. In this work, we present a heuristic quantum sieving
algorithm that has memory complexity polynomial in the size of the length of
the sampled vectors at the initial step of the sieve. In other words, unlike
most sieving algorithms, the memory complexity of our algorithm does not depend
on the number of sampled vectors at the initial step of the sieve.


  We present results from STAR on 3-particle azimuthal correlations for a
$3<p_T<4$ GeV/c trigger particle with two softer $1<p_T<2$ GeV/c particles.
Results are shown for pp, d+Au and high statistics Au+Au collisions at
$\sqrt{s_{NN}}=200 GeV$. We observe a 3-particle correlation in central Au+Au
collisions which may indicate the presence of conical emission. In addition,
the dependence of the observed signal angular position on the $p_T$ of the
associated particles can be used to distinguish conical flow from simple
QCD-\v{C}erenkov radiation. An important aspect of the analysis is the
subtraction of combinatorial backgrounds. Systematic uncertainties due to this
subtraction and the flow harmonics $v_2$ and $v_4$ are investigated in detail.


  We have calculated the large-$q$ series of the energy cumulants, the
magnetization cumulants and the correlation length at the first order phase
transition point both in the ordered and disordered phases for the $q$-state
Potts model in two dimensions. The series enables us to estimate the numerical
values of the quantities more precisely by a factor of $10^2 - 10^4$ than the
Monte Carlo simulations. From the large-$q$ series of the eigenvalues of the
transfer matrix, we also find that the excited states form a continuum spectrum
and there is no particle state at the first order phase transition point.


  Motivated by problems arising in digital advertising, we introduce the task
of training differentially private (DP) machine learning models with
semi-sensitive features. In this setting, a subset of the features is known to
the attacker (and thus need not be protected) while the remaining features as
well as the label are unknown to the attacker and should be protected by the DP
guarantee. This task interpolates between training the model with full DP
(where the label and all features should be protected) or with label DP (where
all the features are considered known, and only the label should be protected).
We present a new algorithm for training DP models with semi-sensitive features.
Through an empirical evaluation on real ads datasets, we demonstrate that our
algorithm surpasses in utility the baselines of (i) DP stochastic gradient
descent (DP-SGD) run on all features (known and unknown), and (ii) a label DP
algorithm run only on the known features (while discarding the unknown ones).


  Which programming error messages are the most common? We investigate this
question, motivated by writing error explanations for novices. We consider
large data sets in Python and Java that include both syntax and run-time
errors. In both data sets, after grouping essentially identical messages, the
error message frequencies empirically resemble Zipf-Mandelbrot distributions.
We use a maximum-likelihood approach to fit the distribution parameters. This
gives one possible way to contrast languages or compilers quantitatively.


  A nonparametric family of conditional distributions is introduced, which
generalizes conditional exponential families using functional parameters in a
suitable RKHS. An algorithm is provided for learning the generalized natural
parameter, and consistency of the estimator is established in the well
specified case. In experiments, the new method generally outperforms a
competing approach with consistency guarantees, and is competitive with a deep
conditional density model on datasets that exhibit abrupt transitions and
heteroscedasticity.


  In this work, we use the AdS/CFT correspondence to study the behavior of a
triply heavy baryon within anisotropic backgrounds. Beginning with the total
action of the three quarks, we derive the balance equation for the three-quark
system and compute the separation distance and potential energy. Our results
reveal a consistent decrease in both the separation distance and potential
energy for the A configuration and the B configuration as the anisotropy
coefficient $a$ increases. This suggests that the presence of an anisotropic
background promotes the dissolution of the three-quark system. Additionally, we
compare the potential energies of the A and B configurations and observe that
the A configuration has a slightly smaller potential energy, suggesting greater
stability compared to the B configuration.


  Entity Alignment (EA) aims to find equivalent entity pairs between KGs, which
is the core step of bridging and integrating multi-source KGs. In this paper,
we argue that existing GNN-based EA methods inherit the inborn defects from
their neural network lineage: weak scalability and poor interpretability.
Inspired by recent studies, we reinvent the Label Propagation algorithm to
effectively run on KGs and propose a non-neural EA framework -- LightEA,
consisting of three efficient components: (i) Random Orthogonal Label
Generation, (ii) Three-view Label Propagation, and (iii) Sparse Sinkhorn
Iteration. According to the extensive experiments on public datasets, LightEA
has impressive scalability, robustness, and interpretability. With a mere tenth
of time consumption, LightEA achieves comparable results to state-of-the-art
methods across all datasets and even surpasses them on many.


  Proteins are essential components of living systems, capable of performing a
huge variety of tasks at the molecular level, such as recognition, signalling,
copy, transport, ... The protein sequences realizing a given function may
largely vary across organisms, giving rise to a protein family. Here, we
estimate the entropy of those families based on different approaches, including
Hidden Markov Models used for protein databases and inferred statistical models
reproducing the low-order (1-and 2-point) statistics of multi-sequence
alignments. We also compute the entropic cost, that is, the loss in entropy
resulting from a constraint acting on the protein, such as the fixation of one
particular amino-acid on a specific site, and relate this notion to the escape
probability of the HIV virus. The case of lattice proteins, for which the
entropy can be computed exactly, allows us to provide another illustration of
the concept of cost, due to the competition of different folds. The relevance
of the entropy in relation to directed evolution experiments is stressed.


  We determine the exact threshold of satisfiability for random instances of a
particular NP-complete constraint satisfaction problem (CSP). This is the first
random CSP model for which we have determined a precise linear satisfiability
threshold, and for which random instances with density near that threshold
appear to be computationally difficult. More formally, it is the first random
CSP model for which the satisfiability threshold is known and which shares the
following characteristics with random k-SAT for k >= 3. The problem is
NP-complete, the satisfiability threshold occurs when there is a linear number
of clauses, and a uniformly random instance with a linear number of clauses
asymptotically almost surely has exponential resolution complexity.


  The standard efficient testing procedures in the Generalized Inverse Gaussian
(GIG) family (also known as Halphen Type A family) are likelihood ratio tests,
hence rely on Maximum Likelihood (ML) estimation of the three parameters of the
GIG. The particular form of GIG densities, involving modified Bessel functions,
prevents in general from a closed-form expression for ML estimators, which are
obtained at the expense of complex numerical approximation methods. On the
contrary, Method of Moments (MM) estimators allow for concise expressions, but
tests based on these estimators suffer from a lack of efficiency compared to
likelihood ratio tests. This is why, in recent years, trade-offs between ML and
MM estimators have been proposed, resulting in simpler yet not completely
efficient estimators and tests. In the present paper, we do not propose such a
trade-off but rather an optimal combination of both methods, our tests
inheriting efficiency from an ML-like construction and simplicity from the MM
estimators of the nuisance parameters. This goal shall be reached by attacking
the problem from a new angle, namely via the Le Cam methodology. Besides
providing simple efficient testing methods, the theoretical background of this
methodology further allows us to write out explicitly power expressions for our
tests. A Monte Carlo simulation study shows that, also at small sample sizes,
our simpler procedures do at least as good as the complex likelihood ratio
tests. We conclude the paper by applying our findings on two real-data sets.


  We present a formalism based on first principles of quantum electrodynamics
at nonzero temperature which permits to calculate the Casimir-Polder
interaction between an atom and a graphene sheet with arbitrary mass gap and
chemical potential, including graphene-coated substrates. The free energy and
force of the Casimir-Polder interaction are expressed via the polarization
tensor of graphene in (2+1)-dimensional space-time in the framework of the
Dirac model. The obtained expressions are used to investigate the influence of
the chemical potential of graphene on the Casimir-Polder interaction.
Computations are performed for an atom of metastable helium interacting with
either a free-standing graphene sheet or a graphene-coated substrate made of
amorphous silica. It is shown that the impacts of the nonzero chemical
potential and the mass gap on the Casimir-Polder interaction are in opposite
directions by increasing and decreasing the magnitudes of the free energy and
force, respectively. It turns out, however, that the temperature-dependent part
of the Casimir-Polder interaction is decreased by a nonzero chemical potential,
whereas the mass gap increases it compared to the case of undoped, gapless
graphene. The physical explanation for these effects is provided. Numerical
computations of the Casimir-Polder interaction are performed at various
temperatures and atom-graphene separations.


  Human brain performs remarkably well in segregating a particular speaker from
interfering ones in a multi-speaker scenario. It has been recently shown that
we can quantitatively evaluate the segregation capability by modelling the
relationship between the speech signals present in an auditory scene and the
cortical signals of the listener measured using electroencephalography (EEG).
This has opened up avenues to integrate neuro-feedback into hearing aids
whereby the device can infer user's attention and enhance the attended speaker.
Commonly used algorithms to infer the auditory attention are based on linear
systems theory where the speech cues such as envelopes are mapped on to the EEG
signals. Here, we present a joint convolutional neural network (CNN) - long
short-term memory (LSTM) model to infer the auditory attention. Our joint
CNN-LSTM model takes the EEG signals and the spectrogram of the multiple
speakers as inputs and classifies the attention to one of the speakers. We
evaluated the reliability of our neural network using three different datasets
comprising of 61 subjects where, each subject undertook a dual-speaker
experiment. The three datasets analysed corresponded to speech stimuli
presented in three different languages namely German, Danish and Dutch. Using
the proposed joint CNN-LSTM model, we obtained a median decoding accuracy of
77.2% at a trial duration of three seconds. Furthermore, we evaluated the
amount of sparsity that our model can tolerate by means of magnitude pruning
and found that the model can tolerate up to 50% sparsity without substantial
loss of decoding accuracy.


  Ultraluminous X-ray sources (ULXs) represent an extreme class of accreting
compact objects: from the identification of some of the accretors as neutron
stars to the detection of powerful winds travelling at 0.1-0.2 c, the
increasing evidence points towards ULXs harbouring stellar-mass compact objects
undergoing highly super-Eddington accretion. Measuring their intrinsic
properties, such as the accretion rate onto the compact object, the outflow
rate, the masses of accretor/companion -- hence their progenitors, lifetimes,
and future evolution -- is challenging due to ULXs being mostly extragalactic
and in crowded fields. Yet ULXs represent our best opportunity to understand
super-Eddington accretion physics and the paths through binary evolution to
eventual double compact object binaries and gravitational wave sources. Through
a combination of end-to-end and single-source simulations, we investigate the
ability of HEX-P to study ULXs in the context of their host galaxies and
compare it to XMM-Newton and NuSTAR, the current instruments with the most
similar capabilities. HEX-P's higher sensitivity, which is driven by its narrow
point-spread function and low background, allows it to detect pulsations and
broad spectral features from ULXs better than XMM-Newton and NuSTAR. We
describe the value of HEX-P in understanding ULXs and their associated key
physics, through a combination of broadband sensitivity, timing resolution, and
angular resolution, which make the mission ideal for pulsation detection and
low-background, broadband spectral studies.


  We show that every internal biequivalence in a tricategory T is part of a
biadjoint biequivalence. We give two applications of this result, one for
transporting monoidal structures and one for equipping a monoidal bicategory
with invertible objects with a coherent choice of those inverses.


  We perform a model independent study of freeze-in of massive particle dark
matter (DM) by adopting an effective field theory framework. Considering the
dark matter to be a gauge singlet Majorana fermion, odd under a stabilising
symmetry $Z_2$ under which all standard model (SM) fields are even, we write
down all possible DM-SM operators upto and including mass dimension eight. For
simplicity of the numerical analysis we restrict ourselves only to the scalar
operators in SM as well as in the dark sector. We calculate the DM abundance
for each such dimension of operator considering both UV and IR freeze-in
contributions which can arise before and after the electroweak symmetry
breaking respectively. After constraining the cut-off scale and reheat
temperature of the universe from the requirement of correct DM relic abundance,
we also study the possibility of connecting the origin of neutrino mass to the
same cut-off scale by virtue of lepton number violating Weinberg operators. We
thus compare the bounds on such cut-off scale and corresponding reheat
temperature required for UV freeze-in from the origin of light neutrino mass as
well as from the requirement of correct DM relic abundance. We also briefly
comment upon the possibilities of realising such DM-SM effective operators in a
UV complete model.


  A simulation framework based on the level-set and the immersed boundary
methods (LS-IBM) has been developed for reactive transport problems in porous
media involving a moving solid-fluid interface. The interface movement due to
surface reactions is tracked by the level-set method, while the immersed
boundary method captures the momentum and mass transport at the interface. The
proposed method is capable of accurately modeling transport near evolving
boundaries in Cartesian grids. The framework formulation guarantees second
order accuracy in space. Since the interface velocity is only defined at the
moving boundary, an interface velocity propagation method is also proposed. The
method can be applied to other moving interface problems of the ``Stefan''
type. Here, we validate the proposed LS-IBM both for flow and transport close
to an immersed object with reactive boundaries as well as for crystal growth.
The proposed method provides a powerful tool to model more realistic problems
involving moving reactive interfaces in complex domains.


  Recently, Scullard and Ziff noticed that a broad class of planar percolation
models are self-dual under a simple condition that, in a parametrized version
of such a model, reduces to a single equation. They state that the solution of
the resulting equation gives the critical point. However, just as in the
classical case of bond percolation on the square lattice, self-duality is
simply the starting point: the mathematical difficulty is precisely showing
that self-duality implies criticality. Here we do so for a generalization of
the models considered by Scullard and Ziff. In these models, the states of the
bonds need not be independent; furthermore, increasing events need not be
positively correlated, so new techniques are needed in the analysis. The main
new ingredients are a generalization of Harris's Lemma to products of partially
ordered sets, and a new proof of a type of Russo-Seymour-Welsh Lemma with
minimal symmetry assumptions.


  We consider a solution to a parametric family of the Cauchy problems for
$m$th-order linear differential equations with constant coefficients.
Parameters of the family are the coefficients of the differential equation and
the initial values of the solution and its derivatives up to the
$(m-1)$th-order (by a solution to a family of problems we mean a function of
the parameters of the given family that maps each tuple of parameters to a
solution to the problem with these parameters). We obtain an exponential-power
estimate for the functions of this parametric family that is uniform (with
respect to parameters) on any bounded set. We also prove that the maximal
element of the set of real parts of monic polynomial roots is a continuous
function (of the coefficients of the polynomial). The continuity of this
element is used for obtaining the estimate mentioned above (since to each tuple
of coefficients of the differential equation there corresponds its
characteristic polynomial with these coefficients, the set of the roots of the
characteristic polynomial and the maximal element of this set are also
functions of the coefficients of the differential equation).


  We start with a curve over an algebraically closed ground field of positive
characteristic $p>0$. By using specialization techniques, under suitable
natural coprimality conditions, we prove a cohomological Simpson Correspondence
between the moduli space of Higgs bundles and the one of connections on the
curve. We also prove a new $p$-multiplicative periodicity concerning the
cohomology rings of Dolbeault moduli spaces of degrees differing by a factor of
$p$. By coupling this $p$-periodicity in characteristic $p$ with
lifting/specialization techniques in mixed characteristic, we find, in
arbitrary characteristic, cohomology ring isomorphisms between the cohomology
rings of Dolbeault moduli spaces for different degrees coprime to the rank. It
is interesting that this last result is proved as follows: we prove a weaker
version in positive characteristic; we lift and strengthen the weaker version
to the result in characteristic zero; finally, we specialize the result to
positive characteristic. The moduli spaces we work with admit certain natural
morphisms (Hitchin, de Rham-Hitchin, Hodge-Hitchin), and all the cohomology
ring isomorphisms we find are filtered isomorphisms for the resulting perverse
Leray filtrations.


  Solutions of stationary Fokker-Planck equations in the narrow beam regime are
commonly approximated by either ballistic linear transport or by a Fermi
pencil-beam equation. We present a rigorous approximation analysis of these
three models in a half-space geometry. Error estimates are obtained in a
1-Wasserstein sense, which is an adapted metric to quantify beam spreading. The
required well-posedness and regularity results for the stationary Fokker-Planck
equation with singular internal and boundary sources are also presented in
detail.


  Given an arrangement of lines in the plane, what is the minimum number $c$ of
colors required to color the lines so that no cell of the arrangement is
monochromatic? In this paper we give bounds on the number c both for the above
question, as well as some of its variations. We redefine these problems as
geometric hypergraph coloring problems. If we define $\Hlinecell$ as the
hypergraph where vertices are lines and edges represent cells of the
arrangement, the answer to the above question is equal to the chromatic number
of this hypergraph. We prove that this chromatic number is between $\Omega
(\log n / \log\log n)$. and $O(\sqrt{n})$.
  Similarly, we give bounds on the minimum size of a subset $S$ of the
intersections of the lines in $\mathcal{A}$ such that every cell is bounded by
at least one of the vertices in $S$. This may be seen as a problem on guarding
cells with vertices when the lines act as obstacles. The problem can also be
defined as the minimum vertex cover problem in the hypergraph $\Hvertexcell$,
the vertices of which are the line intersections, and the hyperedges are
vertices of a cell. Analogously, we consider the problem of touching the lines
with a minimum subset of the cells of the arrangement, which we identify as the
minimum vertex cover problem in the $\Hcellzone$ hypergraph.


  We examine a large class of inhomogeneous spherically symmetric spacetimes
that generalize the Lemaitre-Tolman-Bondi dust solutions to nonzero pressure
("LTB spacetimes"). Local covariant LTB objects can be expressed as
perturbations of covariant quasi-local (QL) scalars that satisfy evolution
equations of equivalent Friedman-Lemaitre-Robertson-Walker (FLRW) scalars.
Thus, the dynamics of these spacetimes can be rigorously described as
non-linear, gauge invariant and covariant perturbations on a formal FLRW
background given by the QL scalars. Since LTB spacetimes are compatible with a
wide variety of "equations of state" and theoretical assumptions, they provide
an ideal framework for numerical models of cosmological sources under idealized
but fully non-linear conditions. As an illustrative example, we briefly examine
the formation of a black hole in an expanding Chaplygin gas universe.


  We consider a state-dependent, time-dependent, discrete random walks
$X_t^{\{a_n\}}$ defined on natural numbers $\mathbb{N}$ (bent to a "stair" in
$\mathbb{N}^2$) where the random walk depends on input of a positive
deterministic sequence $\{a_n\}$. This walk has the peculiar property that if
we set $a_n$ to be $+\infty$ for all $n$, it converges to a stationary
distribution $\pi(\cdot)$; but if $a_n$ is uniformly bounded (over all $n$) by
any upper bound $a \in (0,\infty)$, this walk diverges to infinity with
probability 1. It is thus interesting to consider the intermediate case where
$a_n<\infty$ for all $n$ but $a_n$ eventually tends to $+\infty$.
  (Latuszynski et al., 2013) first defined this walk and conjectured that a
particular choice of sequence $\{a_n\}$ exists such that (i) $a_n \to \infty$
and, (ii) $P(X_t^{\{a_n\}} \to \infty )=1$. They managed to construct a
sequence $\{a_n\}$ that satisfies (i) and $P(X_t^{\{a_n\}}\to \infty)>0$, which
is weaker than (ii).
  In this paper, we obtain a stronger result: for any $\sigma<1$, there exists
a choice of $\{a_n\}$ so that $P(X_t\to \infty)\ge \sigma$. Our result does not
apply when $\sigma=1$, the original conjecture remains open. We record our
method here for technical interests.


  Existing low-light image enhancement techniques are mostly not only difficult
to deal with both visual quality and computational efficiency but also commonly
invalid in unknown complex scenarios. In this paper, we develop a new
Self-Calibrated Illumination (SCI) learning framework for fast, flexible, and
robust brightening images in real-world low-light scenarios. To be specific, we
establish a cascaded illumination learning process with weight sharing to
handle this task. Considering the computational burden of the cascaded pattern,
we construct the self-calibrated module which realizes the convergence between
results of each stage, producing the gains that only use the single basic block
for inference (yet has not been exploited in previous works), which drastically
diminishes computation cost. We then define the unsupervised training loss to
elevate the model capability that can adapt to general scenes. Further, we make
comprehensive explorations to excavate SCI's inherent properties (lacking in
existing works) including operation-insensitive adaptability (acquiring stable
performance under the settings of different simple operations) and
model-irrelevant generality (can be applied to illumination-based existing
works to improve performance). Finally, plenty of experiments and ablation
studies fully indicate our superiority in both quality and efficiency.
Applications on low-light face detection and nighttime semantic segmentation
fully reveal the latent practical values for SCI. The source code is available
at https://github.com/vis-opt-group/SCI.


  Item non-response in surveys is usually handled by single imputation, whose
main objective is to reduce the non-response bias. Imputation methods need to
be adapted to the study variable. For instance, in business surveys, the
interest variables often contain a large number of zeros. Motivated by a
mixture regression model, we propose two imputation procedures for such data
and study their statistical properties. We show that these procedures preserve
the distribution function if the imputation model is well specified. The
results of a simulation study illustrate the good performance of the proposed
methods in terms of bias and mean square error.


  To alleviate green house effect, high network energy efficiency (EE) has
increasingly become an important research target in wireless green
communications. Therefore, the investigation for resource management to
mitigate the co-tier interference in the small cell network (SCN) is provided.
Moreover, with the merits of cloud radio access network (C-RAN), small cell
base stations (SBSs) can be decomposed of a central small cell (CSC) and remote
small cells (RSCs). To achieve the coordination, the split medium access
control (MAC) based functional splitting is adopted with scheduler deployed at
CSCs and retransmission functions left at RSCs. However, limited fronthaul has
a compelling impact at RSCs due to requirements of user quality-of-service
(QoS). Accordingly, a traffic control-based user association and resource
allocation (TURA) scheme is proposed for a centralized resource management. To
deal with the infeasibility to control all RSCs by CSC, we propose a hybrid
controlled user and resource management (HARM) scheme. A CSC performs TURA for
RSCs to mitigate intra-group interference within localized C-RANs, whereas the
CSCs among separate C-RANs conduct cooperative resource competition (CRC) game
for alleviating inter-group interference. Based on regret-based learning
algorithm, the proposed schemes are analytically proved to reach the correlated
equilibrium (CE). Simulation results have validated the effect of traffic
control in TURA scheme and the convergence of CRC. Moreover, the comparison of
the proposed TURA, HARM, and CRC schemes with the benchmark is revealed. It is
observed that the TURA scheme outperforms the other schemes under ideal
fronthaul control, whilst the proposed HARM scheme can sustain EE performance
considering feasible implementation.


  We propose a generalized parity-time ($\mathcal{PT}$) -symmetric Li\'enard
oscillator with two different orders of nonlinear position-dependent
dissipation. We study the stability of the stationary states by using the
eigenvalues of Jacobian and evaluate the stability threshold thereafter. In the
first order nonlinear damping model, we discover that the temporal evolution of
both gain and lossy oscillators attains a complete convergence towards the
stable stationary state leading to the emergence of oscillation and amplitude
deaths. Also, the system displays a remarkable manifestation of transient chaos
in the lossy oscillator while the gain counterpart exhibits blow-up dynamics
for certain choice of initial conditions and control parameters. Employing an
external driving force on the loss oscillator, we find that the blow-up
dynamics can be controlled and a pure aperiodic state is achievable. On the
other hand, the second order nonlinear damping model yields a completely
different dynamics on contrary to the first order where the former reveals a
conventional quasi-periodic route to chaos upon decreasing the natural
frequency of both gain and loss oscillators. An electronic circuit scheme for
the experimental realization of the proposed system has also been put forward.


  This paper proposes a novel approach that combines variational integration
with the bonded discrete element method (BDEM) to achieve faster and more
accurate fracture simulations. The approach leverages the efficiency of
implicit integration and the accuracy of BDEM in modeling fracture phenomena.
We introduce a variational integrator and a manifold optimization approach
utilizing a nullspace operator to speed up the solving of
quaternion-constrained systems. Additionally, the paper presents an element
packing and surface reconstruction method specifically designed for bonded
discrete element methods. Results from the experiments prove that the proposed
method offers 2.8 to 12 times faster state-of-the-art methods.


  We review the well-known slice theorem of Ebin for the action of the
diffeomorphism group on the space of Riemannian metrics of a closed manifold.
We present advances in the study of the spaces of Riemannian metrics, and
produce a more concise proof for the existence of slices.


  Due to the effectiveness of using machine learning in physics, it has been
widely received increased attention in the literature. However, the notion of
applying physics in machine learning has not been given much awareness to. This
work is a hybrid of physics and machine learning where concepts of physics are
used in machine learning. We propose the supervised Gravitational
Dimensionality Reduction (GDR) algorithm where the data points of every class
are moved to each other for reduction of intra-class variances and better
separation of classes. For every data point, the other points are considered to
be gravitational particles, such as stars, where the point is attracted to the
points of its class by gravity. The data points are first projected onto a
spacetime manifold using principal component analysis. We propose two variants
of GDR -- one with the Newtonian gravity and one with the Einstein's general
relativity. The former uses Newtonian gravity in a straight line between points
but the latter moves data points along the geodesics of spacetime manifold. For
GDR with relativity gravitation, we use both Schwarzschild and Minkowski metric
tensors to cover both general relativity and special relativity. Our
simulations show the effectiveness of GDR in discrimination of classes.


  We give a greedy learning algorithm for reconstructing an evolutionary tree
based on a certain harmonic average on triplets of terminal taxa. After the
pairwise distances between terminal taxa are estimated from sequence data, the
algorithm runs in O(n^2) time using O(n) work space, where n is the number of
terminal taxa. These time and space complexities are optimal in the sense that
the size of an input distance matrix is n^2 and the size of an output tree is
n. Moreover, in the Jukes-Cantor model of evolution, the algorithm recovers the
correct tree topology with high probability using sample sequences of length
polynomial in (1) n, (2) the logarithm of the error probability, and (3) the
inverses of two small parameters.


  Generalizing some earlier techniques due to the second author, we show that
Menas' theorem which states that the least cardinal kappa which is a measurable
limit of supercompact or strongly compact cardinals is strongly compact but not
2^kappa supercompact is best possible. Using these same techniques, we also
extend and give a new proof of a theorem of Woodin and extend and give a new
proof of an unpublished theorem due to the first author.


  In the X-ray spectra of AGNs, a noticeable excess of soft X-rays is typically
detected beyond the extrapolation of the power-law trend observed between 2-10
keV. In the scenario of warm Comptonization, observations propose a warm corona
temperature ranging from 0.1-1 keV and an optical depth of approximately 10-20.
Furthermore, according to radiative constraints derived from spectral analyses
employing Comptonization models, it is suggested that the majority of the
accretion power is released within the warm corona, while the disk beneath it
is largely non-dissipative, emitting mainly the reprocessed radiation from the
corona. We test the dissipative warm corona model using the radiative transfer
code-TITAN/NOAR on a sample of 82 XMM-Newton observations of AGNs. Through
spectral modeling of the X-ray data, we aim to estimate the total amount of
internal heating inside the warm corona situated on top of the accretion disk.
By modeling the 0.3-10 keV EPIC-pn spectra, we estimate the internal heating
and optical depth of the warm corona and check their correlations with global
parameters blackhole parameters. From model normalization, we compute the
radial extent of warm corona on top of cold accretion disk. Our model infers
the presence of dissipative warm corona, with optical depths distributed in the
range 6-30 and total internal heating in the range 1-29 x 1e-23 erg/s-cm3. The
extent of warm corona is spread across a large range from 7-408 gravitational
radii, and we find that warm corona is more extended for larger accretion
rates. Soft excess emission is ubiquitous in AGNs across wide mass range and
accretion rate. We confirm that warm corona responsible for producing the
soft-excess is highly dissipative in nature with larger optical depths being
associated with lower internal heating and vice versa. The cold standard
accretion disk regulates the extent of warm corona.


  We study self-regulating processes modeling biological transportation
networks. Firstly, we write the formal $L^2$-gradient flow for the symmetric
tensor valued diffusivity $D$ of a broad class of entropy dissipations
associated with a purely diffusive model. The introduction of a prescribed
electric potential leads to the Fokker-Planck equation, for whose entropy
dissipations we also investigate the formal $L^2$-gradient flow. We derive an
integral formula for the second variation of the dissipation functional,
proving convexity (in dependence of diffusivity tensor) for a quadratic entropy
density modeling Joule heating. Finally, we couple in the Poisson equation for
the electric potential obtaining the Poisson-Nernst-Planck system. The formal
gradient flow of the associated entropy loss functional is derived, giving an
evolution equation for $D$ coupled with two auxiliary elliptic PDEs.


  Young, rapidly rotating neutron stars could accelerate protons to energies of
$\sim 1$ PeV close to the stellar surface, which scatter with x-rays from the
stellar surface through the $\Delta$ resonance and produce pions. The pions
subsequently decay to produce muon neutrinos. We find that the energy spectrum
of muon neutrinos consists of a sharp rise at $\sim 50$ TeV, corresponding to
the onset of the resonance, above which the flux drops as $\epsilon_\nu^{-2}$
up to an upper-energy cut-off that is determined by either kinematics or by the
maximum energy to which protons are accelerated. We predict event rates as high
as 10-50 km$^{-2}$ yr$^{-1}$ from relatively young, close neutron stars. Such
fluxes would be detectable by IceCube.


  The dynamics of chiral nuclei is investigated for the first time with the
time-dependent and tilted axis cranking covariant density functional theories
on a three-dimensional space lattice in a microscopic and self-consistent way.
The experimental energies of the two pairs of the chiral doublet bands in
$^{135}$Nd are well reproduced without any adjustable parameters beyond the
well-defined density functional. A novel mechanism, i.e., chiral precession, is
revealed from the microscopic dynamics of the total angular momentum in the
body-fixed frame, whose harmonicity is associated with a transition from the
planar into aplanar rotations with the increasing spin. This provides a fully
microscopic and dynamical view to understand the chiral excitations in nuclei.


  Radiation dosimetry systems are complex systems, comprised of a milieu of
components, designed for determining absorbed dose after exposure to ionizing
radiation. Although many materials serve as absorbing media for measurement,
thermoluminescent dosimeters represent some of the more desirable materials
available; yet, reliability studies have revealed a clear and definite
decrement in dosimeter sensitivity after repeated use. Unfortunately, repeated
use of any such material for absorbing media in ionizing radiation dosimetry
will in time experience performance decrements; thus, in order to achieve the
most accuracy and/or precision in dosimetry, it is imperative proper
compensation be made in calibration. Yet, analysis proves the majority of the
measured decrement in sensitivity experienced by dosimeters is attributable to
drift noise and not to any degradation in dosimeter performance, at least, not
to any great degree. In addition to investigating dosimeter reliability,
implications for metrological traceability and influences for calibration, this
monograph addresses certain errors in applied statistics, which are rather
alarming habits found in common usage throughout the radiation dosimetry
community. This monograph can also be considered a systems analysis of sorts;
because, attention to such key topics, so general and essential in nature,
produces an effective system analysis, where each principle covered aptly
applies to radiation dosimetry systems in general.


  Qudit gates for high-dimensional quantum computing can be synthesized with
high precision using numerical quantum optimal control techniques. Large
circuits are broken down into modules and the tailored pulses for each module
can be used as primitives for a qudit compiler. Application of the pulses of
each module in the presence of extra modes may decrease their effectiveness due
to crosstalk. In this paper, we address this problem by simulating qudit
dynamics for circuit quantum electrodynamics (cQED) systems. As a test case, we
take pulses for single-qudit SWAP gates optimized in isolation and then apply
them in the presence of spectator modes each of which are in Fock states. We
provide an experimentally relevant scaling formula that can be used as a bound
on the fidelity decay. Our results show that frequency shift from spectator
mode populations has to be $\lesssim 0.1\%$ of the qudit's nonlinearity in
order for high-fidelity single-qudit gates to be useful in the presence of
occupied spectator modes.


  We show that the bandwidth of a square two-dimensional grid of arbitrary size
can be reduced if two (but not less than two) edges are deleted. The two
deleted edges may not be chosen arbitrarily, but they may be chosen to share a
common endpoint or to be non-adjacent.
  We also show that the bandwidth of the rectangular n by m (m greater or equal
to n) grid can be reduced by k, for all k that are sufficiently small, if
m-n+2k edges are deleted.


  An interesting phenomenon in combinatorics on words is when every recurrent
word satisfying some avoidance constraints has the same factor set as a morphic
word. An early example is the Hall-Thue word, fixed point of the morphism
$\texttt{0}\to\texttt{012}$, $\texttt{1}\to\texttt{02}$,
$\texttt{2}\to\texttt{1}$, which is essentially the only ternary word avoiding
squares and the words \texttt{010} and \texttt{212}. We provide some examples
of this phenomenon from various contexts.


  A re-analysis of Lauer \& Postman's (1994; LP) finding that the Abell cluster
inertial frame (ACIF), defined by the 119 Abell clusters within 15,000 km/s, is
moving at almost 700 km/s with respect to the cosmic microwave background. Such
a motion is inconsistent with most cosmological models at a confidence level of
95% or higher. We obtain an exact expression for a cluster's peculiar velocity
in terms of the residual magnitude about the mean relation between the metric
luminosity of brightest cluster galaxies and the slope of their luminosity
profiles. We compare this to the approximation used by LP. We develop a maximum
likelihood procedure for recovering the Local Group motion from the scatter in
this relation which yields an unbiased estimate for the motion with
significantly smaller uncertainties than LP's method. We re-analyse LP's data
and find that the Local Group is moving relative to the ACIF at 626 (+/-242)
km/s towards l=216, b=-28 (+/-20). This implies that the ACIF is itself moving
relative to the cosmic microwave background at 764 (+/-160) km/s towards l=341,
b=49 (+/-20). This motion is consistent with that derived by LP but has a 10%
larger amplitude and 20% smaller errors, making it even harder to reconcile
with cosmological models.


  In dimension-less theories of dynamical generation of the weak scale, the
Universe can undergo a period of low-scale inflation during which all particles
are massless and super-cool. This leads to a new mechanism of generation of the
cosmological Dark Matter (DM) relic density: super-cooling can easily suppress
the amount of DM to the desired level. This is achieved for TeV-scale DM, if
super-cooling ends when quark condensates form at the QCD phase transition.
Along this scenario, the baryon asymmetry can be generated either at the phase
transition or through leptogenesis. We show that the above mechanism takes
place in old and new dimension-less models.


  In this paper, we revisit the classical results on the generalized St.
Petersburg sums. We determine the limit distribution of the St. Petersburg sum
conditioning on its maximum, and we analyze how the limit depends on the value
of the maximum. As an application, we obtain an infinite sum representation of
the distribution function of the possible semistable limits. In the
representation, each term corresponds to a given maximum, in particular this
result explains that the semistable behavior is caused by the typical values of
the maximum.


  We present an overview of eclipsing systems of the HW-Virginis type, based on
space observations from the TESS Mission. We perform a detailed analysis of the
properties of AA Dor, which was monitored for almost a full year. This
excellent time-series dataset permitted us to search for both stellar
pulsations and eclipse timing variations. In addition, we used the
high-precision trigonometric parallax from Gaia Early Data Release 3 to make an
independent determination of the fundamental stellar parameters. No convincing
pulsations were detected down to a limit of 76 parts per million, however we
detected one peak with false alarm probability of 0.2%. 20 sec cadences being
collected during Year 3 should confirm or reject our detection. From eclipse
timing measurements we were able to confirm that the orbital period is stable,
with an upper limit to any period change of 5.75 $\cdot$ 10$^{-13}$ s/s. The
apparent offset of the secondary eclipse is consistent with the predicted
R{\o}mer delay when the primary mass is that of a canonical extended horizontal
branch star. Using parallax and a spectral energy distribution corroborates
that the mass of the primary in AA Dor is canonical, and its radius and
luminosity is consistent with an evolutionary state beyond core helium burning.
The mass of the secondary is found to be at the limit of hydrogen burning.


  We show that three-dimensional massive gravity admits Lifshitz metrics with
generic values of the dynamical exponent z as exact solutions. At the point
z=3, exact black hole solutions which are asymptotically Lifshitz arise. These
spacetimes are three-dimensional analogues of those that were recently proposed
as gravity duals for scale invariant fixed points.


  Robotic platforms serve different use cases ranging from experiments for
prototyping assistive applications up to embedded systems for realizing
cyber-physical systems in various domains. We are using 1:10 scale miniature
vehicles as a robotic platform to conduct research in the domain of
self-driving cars and collaborative vehicle fleets. Thus, experiments with
different sensors like e.g.~ultra-sonic, infrared, and rotary encoders need to
be prepared and realized using our vehicle platform. For each setup, we need to
configure the hardware/software interface board to handle all sensors and
actors. Therefore, we need to find a specific configuration setting for each
pin of the interface board that can handle our current hardware setup but which
is also flexible enough to support further sensors or actors for future use
cases. In this paper, we show how to model the domain of the configuration
space for a hardware/software interface board to enable model checking for
solving the tasks of finding any, all, and the best possible pin configuration.
We present results from a formal experiment applying the declarative languages
Alloy and Prolog to guide the process of engineering the hardware/software
interface for robotic platforms on the example of a configuration complexity up
to ten pins resulting in a configuration space greater than 14.5 million
possibilities. Our results show that our domain model in Alloy performs better
compared to Prolog to find feasible solutions for larger configurations with an
average time of 0.58s. To find the best solution, our model for Prolog performs
better taking only 1.38s for the largest desired configuration; however, this
important use case is currently not covered by the existing tools for the
hardware used as an example in this article.


  Relations between the thermodynamics and dynamics of supercooled liquids
approaching a glass transition have been proposed over many years. The
potential energy surface of model liquids has been increasingly studied since
it provides a connection between the configurational component of the partition
function on one hand, and the system dynamics on the other. This connection is
most obvious at low temperatures, where the motion of the system can be
partitioned into vibrations within a basin of attraction and infrequent
inter-basin transitions. In this work, we present a description of the
potential energy surface properties of supercooled liquid water. The dynamics
of this model has been studied in great details in the last years.
Specifically, we locate the minima sampled by the liquid by ``quenches'' from
equilibrium configurations generated via molecular dynamics simulations. We
calculate the temperature and density dependence of the basin energy,
degeneracy, and shape. The temperature dependence of the energy of the minima
is qualitatively similar to simple liquids, but has anomalous density
dependence. The unusual density dependence is also reflected in the
configurational entropy, the thermodynamic measure of degeneracy. Finally, we
study the structure of simulated water at the minima, which provides insight on
the progressive tetrahedral ordering of the liquid on cooling.


  Magnetic ground state of Rh-doped Kondo semiconductor CeRu$_2$Al$_{10}$
[Ce(Ru$_{1-x}$Rh$_x$)$_2$Al$_{10}$] is investigated by muon-spin relaxation
method. Muon-spin precession with two frequencies is observed in the $x$ = 0
sample, while only one frequency is present in the $x$ = 0.05 and 0.1 samples,
which is attributed to the broad static field distribution at the muon site.
The internal field at the muon site is enhanced from about 180 G in $x$ = 0
sample to about 800 G in the Rh-doped samples, supporting the spin-flop
transition as suggested by macroscopic measurements, and the boundary of
different magnetic ground states is identified around $x$ = 0.03. The drastic
change of magnetic ground state by a small amount of Rh-doping (3%) indicates
that the magnetic structure in CeRu$_2$Al$_{10}$ is not robust and can be
easily tuned by external perturbations such as electron doping. The anomalous
temperature dependence of internal field in CeRu$_2$Al$_{10}$ is suggested to
be attributed to the hyperfine interaction between muons and conduction
electrons.


  We propose an effective model to describe the bias induced on cosmological
observables by Laniakea, the gravitational supercluster hosting the Milky Way,
which was defined using peculiar velocity data from Cosmicflows-4 (CF4). The
structure is well described by an ellipsoidal shape exhibiting triaxial
expansion, reasonably approximated by a constant expansion rate along the
principal axes. Our best fits suggest that the ellipsoid, after subtracting the
background expansion, contracts along the two smaller axes and expands along
the longest one, predicting an average expansion of $\sim -1.1
~\rm{km}/\rm{s}/\rm{Mpc}$. The different expansion rates within the region,
relative to the mean cosmological expansion, induce line-of-sight-dependent
corrections in the computation of luminosity distances. We apply these
corrections to two low-redshift datasets: the Pantheon+ catalog of type Ia
Supernovae (SN~Ia), and 63 measurements of Surface Brightness Fluctuations
(SBF) of early-type massive galaxies from the MASSIVE survey. We find
corrections on the distances of order $\sim 2-3\%$, resulting in a shift in the
inferred best-fit values of the Hubble constant $H_0$ of order $\Delta
H_0^{\rm{SN~Ia}}\approx 0.5 ~\rm{km}/\rm{s}/\rm{Mpc}$ and $\Delta
H_0^{\rm{SBF}}\approx 1.1 ~\rm{km}/\rm{s}/\rm{Mpc}$, seemingly worsening the
Hubble tension.


  We show that irreducibility is not a first-order definable property of real
algebraic varieties. The proof is based on the recent o-minimality result for
the exponential function. We conjecture that irreducibility is not a definable
property of complex algebraic varieties.


  The photometric observations from the recent decade revolutionized our view
on classical pulsators. Low-amplitude signals have been detected
photometrically in addition to the dominant high-amplitude radial mode
pulsations in many RR Lyrae stars and classical Cepheids. First overtone (1O)
pulsators with an additional low-amplitude signal at a period ratio of around
0.61 with the main mode, the so-called 0.61 stars, form the most populous group
among these stars. The nature of this signal has been attributed to non-radial
pulsations. Another mysterious group are stars, where the additional signal
forms a period ratio of around 0.68 - the 0.68 stars. The origin of the signal
remains unknown. Here, we search for similar phenomena in spectroscopic
observations of 1O classical Cepheids collected as part of the VELOCE project.
We performed frequency analysis of several parameters derived from
cross-correlation functions (CCFs), including radial velocity, FWHM, bisector
inverse span, and CCF depth. Using standard prewhitening, we searched for
additional low-amplitude signals. We identify the location of these stars in
various sequences of the Petersen diagram. We detect additional signals in four
1O classical Cepheids: BG Cru, QZ Nor, V391 Nor, and V411 Lac. We classified BG
Cru, QZ Nor, and V391 Nor as 0.61 stars based on period ratios. V411 Lac,
however, exhibits a ratio of 0.68 between the two modes, and the additional
signal has a longer period. This kind of multiperiodicity remains unexplained.
VELOCE CCFs yield the first spectroscopic detections of non-radial pulsation
modes in classical Cepheids. This opens an asteroseismic window for pursuing a
more detailed understanding of these important stars. While the 0.61 signal of
BG Cru, QZ Nor, V391 Nor is understood to originate due to non-radial modes of
moderate degrees, the 0.68 signal of V411 Lac still lacks a physical
explanation.


  Standard cosmological models rely on an approximate treatment of gravity,
utilizing solutions of the linearized Einstein equations as well as physical
approximations. In an era of precision cosmology, we should ask: are these
approximate predictions sufficiently accurate for comparison to observations,
and can we draw meaningful conclusions about properties of our Universe from
them? In this work we examine the accuracy of linearized gravity in the
presence of collisionless matter and a cosmological constant utilizing fully
general relativistic simulations. We observe the gauge-dependence of
corrections to linear theory, and note the amplitude of these corrections. For
perturbations whose amplitudes are in line with expectations from the standard
$\Lambda$CDM model, we find that the full, general relativistic metric is
well-described by linear theory in Newtonian and harmonic gauges, while the
metric in comoving-synchronous gauge is not. For the largest observed
structures in our Universe, our results suggest that corrections to linear
gravitational theory can reach or surpass the percent-level.


  We give a transport proof of a discrete version of the displacement convexity
of entropy on integers (Z), and get, as a consequence, two discrete forms of
the Pr{\'e}kopa-Leindler Inequality : the Four Functions Theorem of Ahlswede
and Daykin on the discrete hypercube [1] and a recent result on Z due to
Klartag and Lehec [16].


  Recent experiments on triangular lattice organic Mott insulators have found
evidence for a 2D spin liquid in proximity to the metal-insulator transition. A
Gutzwiller wavefunction study of the triangular lattice Heisenberg model with
appropriate four-spin ring exchanges has found that the projected spinon Fermi
sea state has a low variational energy. This wavefunction, together with a
slave particle gauge theory, suggests that such spin liquid possesses spin
correlations that are singular along surfaces in momentum space ("Bose
surfaces"). Signatures of this state, which we refer to as a "Spin Bose-Metal"
(SBM), are expected to be manifest in quasi-1D ladder systems: The discrete
transverse momenta cut through the 2D Bose surface leading to a distinct
pattern of 1D gapless modes. Here we search for a quasi-1D descendant of the
triangular lattice SBM state by exploring the Heisenberg plus ring model on a
two-leg strip (zigzag chain). Using DMRG, variational wavefunctions, and a
Bosonization analysis, we map out the full phase diagram. Without ring exchange
the model is equivalent to the J_1 - J_2 Heisenberg chain, and we find the
expected Bethe-chain and dimerized phases. Remarkably, moderate ring exchange
reveals a new gapless phase over a large swath of the phase diagram. Spin and
dimer correlations possess particular singular wavevectors and allow us to
identify this phase as the hoped for quasi-1D descendant SBM state. We derive a
low energy theory and find three gapless modes and one Luttinger parameter
controlling all power laws. Potential instabilities out of the zigzag SBM give
rise to other interesting phases such as a period-3 VBS or a period-4 Chirality
order, which we discover in the DMRG; we also find an interesting SBM state
with partial ferromagnetism.


  Since the discovery of Quasi-stellar Objects (QSOs), also known as quasars,
they have been traditionally subdivided as radio-loud and radio-quiet sources.
Whether such division is a misleading effect from a highly heterogeneous single
population of objects, or real has yet to be answered. Such dichotomy has been
evidenced by observations of the flux ratio between the optical and radio
emissions (usually $B$-band and 5 GHz). Evidence of two populations in quasars
and samples of a wide diversity of AGNs has been accumulated over the years.
Other quantities beyond radio loudness also seem to show the signature of the
existence of two different populations of AGN. To verify the existence of a
dichotomy through different parameters, we employed a soft clustering scheme,
based on the Gaussian Mixture Model (GMM), to classify these objects
simultaneously using the following parameters: black hole mass, colour and $R$
loudness index, as well as the usual radio and $B$-band luminosity. To
investigate whether different kinds of AGNs manifest any population dichotomy,
we applied GMM to four independent catalogues composed of both optical and
radio information. Our results indicate the persistence of a dichotomy in all
datasets, although the discriminating power differs for different choices of
parameters. Although the Radio Loudness parameter alone does not seem to be
enough to display the dichotomy, the evidence of two populations of AGNs could
persist even if we consider other parameters. Our research suggests that the
dichotomy is not a misleading effect but real.


  We show that for any block algebra B of a finite group over an algebraically
closed field of prime characteristic the dimension of HH^n(B) is bounded by a
function depending only on the nonnegative integer n and the defect of B. The
proof uses in particular a theorem of Brauer and Feit which implies the result
for n=0.


  Quantum dense coding plays an important role in quantum cryptography
communication, and how to select a set of appropriate unitary operators to
encode message is the primary work in the design of quantum communication
protocols. Shukla et al. proposed a preliminary method for unitary operator
construction based on Pauli group under multiplication, which is used for dense
coding in quantum dialogue. However, this method lacks feasible steps or
conditions, and cannot construct all the possible unitary operator sets. In
this study, a feasible solution of constructing unitary operator sets for
quantum maximal dense coding is proposed, which aims to use minimum qubits to
maximally encode a class of t-qubit symmetric states. These states have an even
number of superposition items, and there is at least one set of t/2 qubits
whose superposition items are orthogonal to each other. Firstly, we propose the
procedure and the corresponding algorithm for constructing 2^t-order
multiplicative modified generalized Pauli subgroups (multiplicative MGP
subgroups). Then, two conditions for t-qubit symmetric states are given to
select appropriate unitary operator sets from the above subgroups. Finally, we
take 3-qubit GHZ, 4-qubit W, 4-qubit cluster and 5-qubit cluster states as
examples, and demonstrate how to find all unitary operator sets for maximal
dense coding through our construction solution, which shows that our solution
is feasible and convenient.


  Using a previously well-tested numerical model, we demonstrate theoretically
that good acoustophoresis can be obtained in a microchannel embedded in an
acoustically soft, all-polymer chip, by excitation of whole-system ultrasound
resonances. In contrast to conventional techniques based on a standing bulk
acoustic wave inside a liquid-filled microchannel embedded in an elastic,
acoustically hard material, such as glass or silicon, the proposed whole-system
resonance does not need a high acoustic contrast between the liquid and
surrounding solid. Instead, it relies on the very high acoustic contrast
between the solid and the surrounding air. In microchannels of usual
dimensions, we demonstrate the existence of whole-system resonances in an
all-polymer device, which support acoustophoresis of a quality fully comparable
to that of a conventional hard-walled system. Our results open up for using
cheap and easily processable polymers in a controlled manner to design and
fabricate microfluidic devices for single-use acoustophoresis.


  We present an educational path on the magnetic vector potential A addressed
to undergraduate students and to pre-service physics teachers. Starting from
the generalized Ampere-Laplace law, in the framework of a slowly varying
time-dependent field approximation, the magnetic vector potential is written in
terms of its empirical referent, i. e. the conduction current. Therefore, once
the currents are known, our approach allows a clear and univocal physical
determination of A overcoming the mathematical indeterminacy due to the gauge
transformations. We have no need to fix a gauge, since for slowly varying
time-dependent electric and magnetic fields, the natural gauge for A is the
Coulomb one. We stress the difference between our approach and those usually
presented in the literature. Finally, a physical interpretation of the magnetic
vector potential is discussed and some examples of calculation of A are
analysed.


  We performed a combined study of the (001)-cleavage plane of lanthanum
hexaboride (LaB$_\text{6}$) using scanning tunneling microscopy (STM) and
density functional theory (DFT). Experimentally, we found a (2$\times$1)
reconstructed surface on a local scale. The reconstruction is only short-range
ordered and tends to order perpendicularly to step edges. At larger distances
from surface steps, the reconstruction evolves to a labyrinth-like pattern.
These findings are supported by low-energy electron diffraction (LEED)
experiments. Slab calculations within the framework of DFT shows that the
atomic structure consists of parallel lanthanum chains on top of boron
octahedra. Scanning tunneling spectroscopy (STS) shows a prominent spectral
feature at -0.6 eV. Using DFT, we identify this structure as a surface
resonance of the (2$\times$1) reconstructed LaB$_\text{6}$ (100)-surface which
is dominated by boron dangling bond-states and lanthanum d-states.


  A subgroup of a finite group is wide if each prime divisor of the group order
divides the subgroup order. We obtain the description of finite soluble groups
with no wide subgroups. We also prove that a finite soluble group with
nilpotent wide subgroups has the quotient group by its hypercenter with no wide
subgroups.


  Let $U(G)$ be a maximal unipotent subgroup of one of classical groups
$G=GL(V),O(V),Sp(V)$. Let $W$ be a direct sum of copies of $V$ and its dual
$V*$. For the natural action $U(G):W$, we describe a minimal system of
homogeneous generators for the algebra of $U(G)$-invariant regular functions on
$W$. For $G=GL(V)$, we also describe the syzygies among these generators in
some particular cases.


  Many-body non-equilibrium steady states can be described by a Landau-Ginzburg
theory if one allows non-analytic terms in the potential. We substantiate this
claim by working out the case of the Ising magnet in contact with a thermal
bath and undergoing stochastic reheating: It is reset to a paramagnet at random
times. By a combination of stochastic field theory and Monte Carlo simulations,
we unveil how the usual $\varphi^4$ potential is deformed by non-analytic
operators of intrinsic non-equilibrium nature. We demonstrate their infrared
relevance at low temperatures by a renormalization-group analysis of the
non-equilibrium steady state. The equilibrium ferromagnetic fixed point is thus
destabilized by stochastic reheating, and we identify the new non-equilibrium
fixed point.


  Inferring how an epidemic will progress and what actions to take when
presented with limited information is of critical importance for
epidemiologists and health professionals. In real world settings, epidemiology
data can be scarce or subject to reporting errors. In this project there are
different epidemic scenarios simulated and, using hidden Markov Chains, it is
attempted to mimic the imperfect data an epidemiologist will encounter.
Furthermore, different kinds of compartmental models are modelled using the
particle Markov Chain Monte Carlo algorithm with a variation of the adaptive
Metropolis-Hastings algorithm to estimate the posterior density of the
parameters underlying the models. Moreover, the sensitivity of these algorithms
is investigated when subjected with changes in the dataset. This is
accomplished by limiting the information provided, while using an adaptive
approach on the posterior covariance of the parameters.


  In this paper some general theory is presented for locally stationary
processes based on the stationary approximation and the stationary derivative.
Laws of large numbers, central limit theorems as well as deterministic and
stochastic bias expansions are proved for processes obeying an expansion in
terms of the stationary approximation and derivative. In addition it is shown
that this applies to some general nonlinear non-stationary Markov-models. In
addition the results are applied to derive the asymptotic properties of maximum
likelihood estimates of parameter curves in such models.


  Flowing blood displays a phenomenon called margination, in which leukocytes
and platelets are preferentially found near blood vessel walls, while
erythrocytes are depleted from these regions. Here margination is investigated
using direct hydrodynamic simulations of a binary suspension of stiff (s) and
floppy (f) capsules, as well as a stochastic model that incorporates the key
particle transport mechanisms in suspensions -- wall-induced hydrodynamic
migration and shear-induced pair collisions. The stochastic model allows the
relative importance of these two mechanisms to be directly evaluated and
thereby indicates that margination, at least in the dilute case, is largely due
to the differential dynamics of homogeneous (e.g. s-s) and heterogeneous (s-f)
collisions


  General expressions are given for the generation of Primordial Black Holes
(PBH) in a universe with a presently accelerated expansion due to a(n
effective) cosmological constant. We give expressions both for a powerlaw
scalefree primordial spectrum and for spectra which are not of that type.
Specializing to the case of a pure cosmological constant $\Lambda$ and assuming
flatness, we show that a comological constant with $\Omega_{\Lambda,0}=0.7$
will decrease the mass variance at the PBH formation time by about 15% compared
with a critical density universe.


  We formulate a renormalized running coupling expansion for the
$\beta$--function and the potential of the renormalized $\phi^4$--trajectory on
four dimensional Euclidean space-time. Renormalization invariance is used as a
first principle. No reference is made to bare quantities. The expansion is
proved to be finite to all orders of perturbation theory. The proof includes a
large momentum bound on the connected free propagator amputated vertices.


  Thirty years ago, theorists showed that a properly designed combination of
incident waves could be fully transmitted through (or reflected by) a
disordered medium, based on the existence of propagation channels which are
essentially either closed or open (bimodal law). In this Letter, we study
elastic waves in a disordered waveguide and present direct experimental
evidence of the bimodal law. Full transmission and reflection are achieved. The
wave field is monitored by laser interferometry and highlights the interference
effects that take place within the scattering medium.


  Previous work in Indonesian part-of-speech (POS) tagging are hard to compare
as they are not evaluated on a common dataset. Furthermore, in spite of the
success of neural network models for English POS tagging, they are rarely
explored for Indonesian. In this paper, we explored various techniques for
Indonesian POS tagging, including rule-based, CRF, and neural network-based
models. We evaluated our models on the IDN Tagged Corpus. A new
state-of-the-art of 97.47 F1 score is achieved with a recurrent neural network.
To provide a standard for future work, we release the dataset split that we
used publicly.


  This expository paper is written in celebration of Boris Zilber's 75th
birthday. We discuss Ax-Schanuel type statements focusing on the case of
positive characteristic.


  Weak lensing by large-scale structure is a powerful technique to probe the
dark components of the universe. To understand the measurement process of weak
lensing and the associated systematic effects, image simulations are becoming
increasingly important. For this purpose we present a first implementation of
the $\textit{Monte Carlo Control Loops}$ ($\textit{MCCL}$; Refregier & Amara
2014), a coherent framework for studying systematic effects in weak lensing. It
allows us to model and calibrate the shear measurement process using image
simulations from the Ultra Fast Image Generator (UFig; Berge et al. 2013). We
apply this framework to a subset of the data taken during the Science
Verification period (SV) of the Dark Energy Survey (DES). We calibrate the UFig
simulations to be statistically consistent with DES images. We then perform
tolerance analyses by perturbing the simulation parameters and study their
impact on the shear measurement at the one-point level. This allows us to
determine the relative importance of different input parameters to the
simulations. For spatially constant systematic errors and six simulation
parameters, the calibration of the simulation reaches the weak lensing
precision needed for the DES SV survey area. Furthermore, we find a sensitivity
of the shear measurement to the intrinsic ellipticity distribution, and an
interplay between the magnitude-size and the pixel value diagnostics in
constraining the noise model. This work is the first application of the
$\textit{MCCL}$ framework to data and shows how it can be used to methodically
study the impact of systematics on the cosmic shear measurement.


  We consider inflationary magnetogenesis where the conformal symmetry is
broken by the term $f^2(\phi) F_{\alpha\beta} F^{\alpha\beta}$. We assume that
the magnetic field power spectrum today between 0.1 and $10^4$ Mpc is a power
law, with upper and lower limits from observation. This fixes $f$ to be close
to a power law in conformal time in the window during inflation when the modes
observed today are generated. In contrast to previous work, we do not make any
assumptions about the form of $f$ outside these scales. We cover all possible
reheating histories, described by an average equation of state $-1/3 <\bar{w}
<1$. Requiring that strong coupling and large backreaction are avoided both at
the background and perturbative level, we find the bound $\delta_{B_0} < 5
\times10^{-15} \left( \frac{r}{0.07} \right)^{1/2} \kappa \mathrm{G}$ for the
magnetic field generated by inflation, where $r$ is the tensor-to-scalar ratio
and $\kappa$ is a constant related to the form of $f$. This estimate has an
uncertainty of one order of magnitude related to our approximations. The
parameter $\kappa$ is $<100$, and values $\gtrsim1$ require a highly fine-tuned
form of $f$; typical values are orders of magnitude smaller.


  This paper is devoted to proposing a general weighted low-rank recovery model
and designing a fast SVD-free computational scheme to solve it. First, our
generic weighted low-rank recovery model unifies several existing approaches in
the literature.~Moreover, our model readily extends to the non-convex setting.
Algorithm-wise, most first-order proximal algorithms in the literature for
low-rank recoveries require computing singular value decomposition (SVD). As
SVD does not scale appropriately with the dimension of the matrices, these
algorithms become slower when the problem size becomes larger. By incorporating
the variational formulation of the nuclear norm into the sub-problem of
proximal gradient descent, we avoid computing SVD, which results in significant
speed-up. Moreover, our algorithm preserves the rank identification property of
nuclear norm [33] which further allows us to design a rank continuation scheme
that asymptotically achieves the minimal iteration complexity. Numerical
experiments on both toy examples and real-world problems, including structure
from motion (SfM) and photometric stereo, background estimation, and matrix
completion, demonstrate the superiority of our proposed algorithm.


  Excited states of the neutron-rich isotopes $^{42,44}$S and $^{41,43}$P have
been studied via inverse-kinematics proton scattering from a liquid hydrogen
target, using the GRETINA $\gamma$-ray tracking array to extract inelastic
scattering cross sections. Deformation lengths of the $2^+_1$ excitations in
$^{42,44}$S have been determined and, when combined with deformation lengths
determined with electromagnetic probes, yield the ratio of neutron-to-proton
matrix elements $M_n/M_p$ for the $2^+_1$ excitations in these nuclei. The
present results for $^{41,43}$P$(p,p')$ are used to compare two shell model
interactions, SDPF-U and SDPF-MU. As in a recent study of $^{42}$Si, the
present results on $^{41,43}$P favor the SDPF-MU interaction.


  We use deep J and Ks images of the Antennae (NGC 4038/9) obtained with WIRC
on the Palomar 200-inch telescope, together with the Chandra X-ray source list
of Zezas et al. (2002a), to search for IR counterparts to X-ray point sources.
We establish an X-ray/IR astrometric frame tie with 0.5" rms residuals over a
\~4.3' field. We find 13 ``strong'' IR counterparts brighter than Ks = 17.8 mag
and < 1.0" from X-ray sources, and an additional 6 ``possible'' IR counterparts
between 1.0" and 1.5" from X-ray sources. The surface density of IR sources
near the X-ray sources suggests only ~2 of the ``strong'' counterparts and ~3
of the ``possible'' counterparts are chance superpositions of unrelated
objects.
  Comparing both strong and possible IR counterparts to our photometric study
of ~220 Antennae, IR clusters, we find the IR counterparts to X-ray sources are
\~1.2 mag more luminous in Ks than average non-X-ray clusters. We also note
that the X-ray/IR matches are concentrated in the spiral arms and ``overlap''
regions of the Antennae. This implies that these X-ray sources lie in the most
``super'' of the Antennae's Super Star Clusters, and thus trace the recent
massive star formation history here. Based on the N_H inferred from the X-ray
sources without IR counterparts, we determine that the absence of most of the
``missing'' IR counterparts is because they are intrinsically less luminous in
the IR, implying that they trace a different (possibly older) stellar
population.


  By connecting two antennas, Kashima 34~m and Nobeyama 45~m, an east-west
baseline of 200~km is formed. At that time, because Nobeyama 45~m had the
world's number one sensitivity in the 43~GHz band, and also Kashima 34~m was
the world's third-largest one, the Kashima-Nobeyama baseline provided the
highest sensitivity at 43~GHz VLBI (Figure 1). The construction of the Kashima
34~m antenna began in 1988, also almost at the same time, a domestic project of
mm-VLBI (KNIFE, Kashima Nobeyama INterFrermeter) started. Nobeyama Radio
Observatory provided the first cooled-HEMT 43~GHz receiver in the world to the
Kashima 34~m. In October 1989, the first fringe at 43~GHz was detected. We here
review the achievements of the KNIFE at that time.


  We present the exact solutions of various directed walk models of polymers
confined to a slit and interacting with the walls of the slit via an attractive
potential. We consider three geometric constraints on the ends of the polymer
and concentrate on the long chain limit. Apart from the general interest in the
effect of geometrical confinement this can be viewed as a two-dimensional model
of steric stabilization and sensitized flocculation of colloidal dispersions.
We demonstrate that the large width limit admits a phase diagram that is
markedly different from the one found in a half-plane geometry, even when the
polymer is constrained to be fixed at both ends on one wall. We are not able to
find a closed form solution for the free energy for finite width, at all values
of the interaction parameters, but we can calculate the asymptotic behaviour
for large widths everywhere in the phase plane. This allows us to find the
force between the walls induced by the polymer and hence the regions of the
plane where either steric stabilization or sensitized flocculation would occur.


  Time-Dependent Density Functional Theory (TDDFT) has recently been extended
to describe many-body open quantum systems (OQS) evolving under non-unitary
dynamics according to a quantum master equation. In the master equation
approach, electronic excitation spectra are broadened and shifted due to
relaxation and dephasing of the electronic degrees of freedom by the
surrounding environment. In this paper, we develop a formulation of TDDFT
linear-response theory (LR-TDDFT) for many-body electronic systems evolving
under a master equation, yielding broadened excitation spectra. This is done by
mapping an interacting open quantum system onto a non-interacting open
Kohn-Sham system yielding the correct non-equilibrium density evolution. A
pseudo-eigenvalue equation analogous to the Casida equations of usual LR-TDDFT
is derived for the Redfield master equation, yielding complex energies and Lamb
shifts. As a simple demonstration, we calculate the spectrum of a C$^{2+}$ atom
in an optical resonator interacting with a bath of photons. The performance of
an adiabatic exchange-correlation kernel is analyzed and a first-order
frequency-dependent correction to the bare Kohn-Sham linewidth based on
Gorling-Levy perturbation theory is calculated.


  Diabetic eye diseases, particularly Diabetic Retinopathy,is the leading cause
of vision loss worldwide and can be prevented by early diagnosis through annual
eye-screenings. However, cost, healthcare disparities, cultural limitations,
etc. are the main barriers against regular screening. Eye-screenings conducted
in community events with native-speaking staffs can facilitate regular check-up
and development of awareness among underprivileged communities compared to
traditional clinical settings. However, there are not sufficient technology
support for carrying out the screenings in community settings with
collaboration from community partners using native languages. In this paper, we
have proposed and discussed the development of our software framework, "Mobile
Teleophthalomogy in Community Settings (mTOCS)", that connects the community
partners with eye-specialists and the Health Department staffs of respective
cities to expedite this screening process. Moreover, we have presented the
analysis from our study on the acceptance of community-based screening methods
among the community participants as well as on the effectiveness of mTOCS among
the community partners. The results have evinced that mTOCS has been capable of
providing an improved rate of eye-screenings and better health outcomes.