  Formation of p+ contact on Germanium is important for applications in diode
detector and other electronic devices. In this work, thermally deposited Al on
Ge crystal is annealed at 350oC followed by slow cooling for solid-state
regrowth of Al-Ge p+ contact on Ge. Depth profile analysis by secondary ion
mass spectrometry (SIMS) is carried out to investigate the occurrence of Al and
Ge along the depth of the regrown Al-Ge layer. Evidence of regrowth is observed
due to inter-diffusion of both Ge and Al across the layers although Ge
diffusion in Al layer is found to be more prevalent. Thickness of the
evaporated Al layer is varied to understand the diffusion profile of Al, Ge and
estimate the depth of Al incorporation in Ge crystal underneath. Hall
measurement at different depth of Al-Ge regrown layer reveals that Al impurity
induces p+ doping in p-type Ge and its concentration gradually reduces towards
the Ge crystal. Top surface of the Al-Ge layer exhibits lowest sheet resistance
that varies with the thickness of the as deposited Al layer.


  The integration of empirical data in computational frameworks to model the
spread of infectious diseases poses challenges that are becoming pressing with
the increasing availability of high-resolution information on human mobility
and contacts. This deluge of data has the potential to revolutionize the
computational efforts aimed at simulating scenarios and designing containment
strategies. However, the integration of detailed data sources yields models
that are less transparent and general. Hence, given a specific disease model,
it is crucial to assess which representations of the raw data strike the best
balance between simplicity and detail. We consider high-resolution data on the
face-to-face interactions of individuals in a hospital ward, obtained by using
wearable proximity sensors. We simulate the spread of a disease in this
community by using an SEIR model on top of different mathematical
representations of the contact patterns. We show that a contact matrix that
only contains average contact durations fails to reproduce the size of the
epidemic obtained with the high-resolution contact data and also to identify
the most at-risk classes. We introduce a contact matrix of probability
distributions that takes into account the heterogeneity of contact durations
between (and within) classes of individuals, and we show that this
representation yields a good approximation of the epidemic spreading properties
obtained by using the high-resolution data. Our results mark a step towards the
definition of synopses of high-resolution dynamic contact networks, providing a
compact representation of contact patterns that can correctly inform
computational models designed to discover risk groups and evaluate containment
policies. We show that this novel kind of representation can preserve in
simulation quantitative features of the epidemics that are crucial for their
study and management.


  The Graphical House Allocation problem asks: how can $n$ houses (each with a
fixed non-negative value) be assigned to the vertices of an undirected graph
$G$, so as to minimize the "aggregate local envy", i.e., the sum of absolute
differences along the edges of $G$? This problem generalizes the classical
Minimum Linear Arrangement problem, as well as the well-known House Allocation
Problem from Economics, the latter of which has notable practical applications
in organ exchanges. Recent work has studied the computational aspects of
Graphical House Allocation and observed that the problem is NP-hard and
inapproximable even on particularly simple classes of graphs, such as vertex
disjoint unions of paths. However, the dependence of any approximations on the
structural properties of the underlying graph had not been studied.
  In this work, we give a complete characterization of the approximability of
the Graphical House Allocation problem. We present algorithms to approximate
the optimal envy on general graphs, trees, planar graphs, bounded-degree
graphs, bounded-degree planar graphs, and bounded-degree trees. For each of
these graph classes, we then prove matching lower bounds, showing that in each
case, no significant improvement can be attained unless P = NP. We also present
general approximation ratios as a function of structural parameters of the
underlying graph, such as treewidth; these match the aforementioned tight upper
bounds in general, and are significantly better approximations for many natural
subclasses of graphs. Finally, we present constant factor approximation schemes
for the special classes of complete binary trees and random graphs.


  We present a lattice of distributed program specifications, whose ordering
represents implementability/refinement. Specifications are modelled by families
of subsets of relative execution traces, which encode the local orderings of
state transitions, rather than their absolute timing according to a global
clock. This is to overcome fundamental physical difficulties with
synchronisation. The lattice of specifications is assembled and analysed with
several established mathematical tools. Sets of nondegenerate cells of a
simplicial set are used to model relative traces, presheaves model the
parametrisation of these traces by a topological space of variables, and
information algebras reveal novel constraints on program correctness. The
latter aspect brings the enterprise of program specification under the widening
umbrella of contextual semantics introduced by Abramsky et al. In this model of
program specifications, contextuality manifests as a failure of a consistency
criterion comparable to Lamport's definition of sequential consistency. The
theory of information algebras also suggests efficient local computation
algorithms for the verification of this criterion. The novel constructions in
this paper have been verified in the proof assistant Isabelle/HOL.


  I argue that the rotation of white dwarfs is not a remnant of the angular
momentum of their main sequence progenitors but a result of the mass loss
process on the AGB. Weak magnetic fields, if present in stellar interiors, are
likely to maintain approximately uniform rotation in stars, both on the main
sequence and on the giant branches. The nearly uniform rotation of the core of
the Sun is evidence for the existence of such fields. Exactly axisymmetric mass
loss on the AGB from uniformly rotating stars would lead lead to white dwarfs
with very long rotation periods ($>$ 10 yr). Small random non-axisymmetries
($\sim 10^{-3}$) in the mass loss process, on the other hand, add sufficient
angular momentum to explain the observed rotation periods around one day. The
process illustrated with a computation of the probability distribution of the
rotation periods under the combined influence of random forcing by weak
nonaxisymmetries and angular momentum loss in the AGB superwind. Such
asymmetries can in principle be observed by proper motion studies of the clumps
in interferometric images of SiO maser emission.


  The research team has utilized an integrated dataset, consisting of
anonymized location data, COVID-19 case data, and census population
information, to study the impact of COVID-19 on human mobility. The study
revealed that statistics related to social distancing, namely trip rate, miles
traveled per person, and percentage of population staying at home have all
showed an unexpected trend, which we named social distancing inertia. The
trends showed that as soon as COVID-19 cases were observed, the statistics
started improving, regardless of government actions. This suggests that a
portion of population who could and were willing to practice social distancing
voluntarily and naturally reacted to the emergence of COVID-19 cases. However,
after about two weeks, the statistics saturated and stopped improving, despite
the continuous rise in COVID-19 cases. The study suggests that there is a
natural behavior inertia toward social distancing, which puts a limit on the
extent of improvement in the social-distancing-related statistics. The national
data showed that the inertia phenomenon is universal, happening in all the U.S.
states and for all the studied statistics. The U.S. states showed a
synchronized trend, regardless of the timeline of their statewide COVID-19 case
spreads or government orders.


  We pursue the investigation of the validity of our recently proposed quantum
mechanically correlated statistical hadron gas model (HRG) inspired by a
Beth-Uhlenbeck corrected form of the equation of state (EoS) to the ideal
hadron resonance gas model (IHRG). We calculate the ratios of some particle
yields of equal masses, namely ($\bar{p} / p$,$K^-/ K^+$, $\pi^-/ \pi^+$,
$\bar{\Lambda}/ \Lambda$, $\bar{\Sigma}/ \Sigma$, $\bar{\Omega}/ \Omega$), and
some particle yield with unequal masses, namely ($p/ \pi^+$, $k^+/ \pi^+$,
$k^-/ \pi^-$, $\Lambda/ \pi^-$, $\bar{p}/ \pi^-$, $\Omega/\pi^-$). We then
study the center-of-mass energy variation of these ratios of particle yields
obtained by our proposed HRG model. Our model results are then confronted with
the corresponding calculations obtained using the ideal hadron resonance gas
(IHRG) model, the Cosmic Ray Monte Carlo (CRMC) EPOS $1.99$ simulations, as
well as the experimental data from AGS, SPS, RHIC, and ALICE. Our proposed HRG
model results generally show very close agreement with the experimental data
compared with the other models considered. Especially remarkable is the very
good matching obtained by our new HRG model with the experimental data of
$\bar{p}/ \pi^-$ and $p/ \pi^+$, which suggests that our HRG model might be
helpful in describing the famous proton anomaly at top RHIC and LHC energies.
However, some experimental data of the ratios of hadron pairs of unequal mass
and (multi)strange content, like $\Lambda/ \pi^-$ and $\Omega/ \pi^-$, appear
to be quite underestimated by both our HRG model and the IHRG model, which
alert further investigation of the suitability of the thermal hadron gas
model(s) and thereby motivate the need for further modification.


  A general form of the effective mass Schrodinger equation is solved exactly
for Hulthen potential. Nikiforov-Uvarov method is used to obtain energy
eigenvalues and the corresponding wave functions. A free parameter is used in
the transformation of the wave function.


  We perform a joint analysis of the auto and cross-correlations between three
cosmic fields: the galaxy density field, the galaxy weak lensing shear field,
and the cosmic microwave background (CMB) weak lensing convergence field. These
three fields are measured using roughly 1300 sq. deg. of overlapping optical
imaging data from first year observations of the Dark Energy Survey and
millimeter-wave observations of the CMB from both the South Pole Telescope
Sunyaev-Zel'dovich survey and Planck. We present cosmological constraints from
the joint analysis of the two-point correlation functions between galaxy
density and galaxy shear with CMB lensing. We test for consistency between
these measurements and the DES-only two-point function measurements, finding no
evidence for inconsistency in the context of flat $\Lambda$CDM cosmological
models. Performing a joint analysis of five of the possible correlation
functions between these fields (excluding only the CMB lensing autospectrum)
yields $S_{8}\equiv \sigma_8\sqrt{\Omega_{\rm m}/0.3} =
0.782^{+0.019}_{-0.025}$ and $\Omega_{\rm m}=0.260^{+0.029}_{-0.019}$. We test
for consistency between these five correlation function measurements and the
Planck-only measurement of the CMB lensing autospectrum, again finding no
evidence for inconsistency in the context of flat $\Lambda$CDM models.
Combining constraints from all six two-point functions yields
$S_{8}=0.776^{+0.014}_{-0.021}$ and $\Omega_{\rm m}= 0.271^{+0.022}_{-0.016}$.
These results provide a powerful test and confirmation of the results from the
first year DES joint-probes analysis.


  In this paper we prove the existence of a nontrivial solution to the
nonlinear Schrodinger-Maxwell equations in $\R^3,$ assuming on the nonlinearity
the general hypotheses introduced by Berestycki & Lions.


  Earning any advanced degree in physics or astronomy is an arduous process and
major accomplishment. However, not every journey to the Ph.D. is paved equally.
Every year, there are hundreds of students who earn terminal master's degrees
in physics and astronomy in the United States. A master's degree on its own is
sufficient qualification for many good careers, but for a portion of these
students, the master's degree is not the final step in graduate education. When
students with master's degrees decide to continue their education and are
accepted to Ph.D. programs, they often find that their credits do not transfer
and that they will be required to re-do large portions of their master's degree
at their new Ph.D.-granting institution. Here we discuss the need for gathering
more data to understand both the different pathways to a Ph.D. and the students
that choose each route. We also discuss some of the challenges faced by
students that earn a master's degree before beginning a Ph.D. program. As
students in the physical sciences that complete a master's and a Ph.D. at
different schools take over 2 years longer to reach a Ph.D. than students that
get both degrees from the same school, we suggest steps that can be taken to
help these students succeed in a timely manner.


  We analyse the rest-frame (U-V) colour-magnitude relation for 2 clusters at
redshift 0.7 and 0.8, drawn from the ESO Distant Cluster Survey. By comparing
with the population of red galaxies in the Coma cluster, we show that the high
redshift clusters exhibit a deficit of passive faint red galaxies. Our results
show that the red-sequence population cannot be explained in terms of a
monolithic and synchronous formation scenario. A large fraction of faint
passive galaxies in clusters today has moved onto the red sequence relatively
recently as a consequence of the fact that their star formation activity has
come to an end at z<0.8.


  We show that in the isentropic scenario the first order thermodynamical
particle creation model gives an emergent universe solution even when the
chemical potential is non-zero. However there exists no emergent universe
scenario in the second order non-equilibrium theory for the particle creation
model. We then point out a correspondence between the particle creation model
with barotropic equation of state and the equation of state giving rise to an
emergent universe without particle creation in spatially flat FRW cosmology.


  This note shows there are infinitely many finite groups G, such that every
connected Cayley graph on G has a hamiltonian cycle, and G is not solvable.
Specifically, for every prime p that is congruent to 1, modulo 30, we show
there is a hamiltonian cycle in every connected Cayley graph on the direct
product of the cyclic group of order p with the alternating group A_5 on five
letters.


  Limit theorems, including the large deviation principle, are established for
random point processes (fields), which describe the position distributions of
the perfect boson gas in the regime of the Bose-Einstein condensation. We
compare these results with those for the case of the normal phase.


  By a classical theorem of Harvey Friedman (1973), every countable nonstandard
model $\mathcal{M}$ of a sufficiently strong fragment of ZF has a proper
rank-initial self-embedding $j$, i.e., $j$ is a self-embedding of $\mathcal{M}$
such that $j[\mathcal{M}]\subsetneq\mathcal{M}$, and the ordinal rank of each
member of $j[\mathcal{M}]$ is less than the ordinal rank of each element of
$\mathcal{M}\setminus j[\mathcal{M}]$. Here we investigate the larger family of
proper initial-embeddings $j$ of models $\mathcal{M}$ of fragments of set
theory, where the image of $j$ is a transitive submodel of $\mathcal{M}$.


  We consider the time-dependent Hamiltonian $H(t)= {1 \over 2} p^2 -E(t) \cdot
x + V(t,x)$ on $L^2(R^n)$, where the external electric field $E(t)$ and the
short-range electric potential $V(t,x)$ are time-periodic with the same period.
It is well-known that the short-range notion depends on the mean value $E\_0$
of the external field. When $E\_0=0$, we show that the high energy limit of the
scattering operators determines uniquely $V(t,x)$. In the other case, the same
result holds in dimension $n \geq 3$ for generic sghort-range potentials. In
dimension 2, one has to assume a stronger decay on the electric potential.


  Internet of Things (IoT) has already proven to be the building block for
next-generation Cyber-Physical Systems (CPSs). The considerable amount of data
generated by the IoT devices needs latency-sensitive processing, which is not
feasible by deploying the respective applications in remote Cloud datacentres.
Edge/Fog computing, a promising extension of Cloud at the IoT-proximate
network, can meet such requirements for smart CPSs. However, the structural and
operational differences of Edge/Fog infrastructure resist employing Cloud-based
service regulations directly to these environments. As a result, many research
works have been recently conducted, focusing on efficient application and
resource management in Edge/Fog computing environments. Scalable Edge/Fog
infrastructure is a must to validate these policies, which is also challenging
to accommodate in the real-world due to high cost and implementation time.
Considering simulation as a key to this constraint, various software has been
developed that can imitate the physical behaviour of Edge/Fog computing
environments. Nevertheless, the existing simulators often fail to support
advanced service management features because of their monolithic architecture,
lack of actual dataset, and limited scope for a periodic update. To overcome
these issues, we have developed multiple simulation models for service
migration, dynamic distributed cluster formation, and microservice
orchestration for Edge/Fog computing in this work and integrated with the
existing iFogSim simulation toolkit for launching it as iFogSim2. The
performance of iFogSim2 and its built-in policies are evaluated using three use
case scenarios and compared with the contemporary simulators and benchmark
policies under different settings. Results indicate that the proposed solution
outperform others in service management time, network usage, ram consumption,
and simulation time.


  Question-answering systems have revolutionized information retrieval, but
linguistic and cultural boundaries limit their widespread accessibility. This
research endeavors to bridge the gap of the absence of efficient QnA datasets
in low-resource languages by translating the English Question Answering Dataset
(SQuAD) using a robust data curation approach. We introduce MahaSQuAD, the
first-ever full SQuAD dataset for the Indic language Marathi, consisting of
118,516 training, 11,873 validation, and 11,803 test samples. We also present a
gold test set of manually verified 500 examples. Challenges in maintaining
context and handling linguistic nuances are addressed, ensuring accurate
translations. Moreover, as a QnA dataset cannot be simply converted into any
low-resource language using translation, we need a robust method to map the
answer translation to its span in the translated passage. Hence, to address
this challenge, we also present a generic approach for translating SQuAD into
any low-resource language. Thus, we offer a scalable approach to bridge
linguistic and cultural gaps present in low-resource languages, in the realm of
question-answering systems. The datasets and models are shared publicly at
https://github.com/l3cube-pune/MarathiNLP .


  The possible anomaly of the tensor current divergence equation in U(1) gauge
theories is calculated by means of perturbative method. It is found that the
tensor current divergence equation is free of anomalies.


  The Whitney group $K_1(A)$ is isomorphic to $A^\times \times
\operatorname{SK}_1(A)$ for some subgroup $\operatorname{SK}_1(A)$, where $A$
is a commutative ring and $A^\times$ denotes the set of units in $A$. Consider
an o-minimal expansion of a real closed field $\mathcal
R=(R,0,1,+,\cdot,\ldots)$. Let $M$ be an affine definable $C^r$ manifold, where
$r$ is a nonnegative integer. We demonstrate its homotopy theorem and that the
group $\operatorname{SK}_1(C_{\text{df}}^r)$ is isomorphic to
$\operatorname{SK}_1(C_{\text{df}}^0(M))$, where $C_{\text{df}}^r(M)$ denotes
the ring of definable $C^r$ functions on $M$.


  Let $E$ be a closed set in the Riemann sphere $\widehat{\mathbb{C}}$. We
consider a holomorphic motion $\phi$ of $E$ over a complex manifold $M$, that
is, a holomorphic family of injections on $E$ parametrized by $M$. It is known
that if $M$ is the unit disk $\Delta$ in the complex plane, then any
holomorphic motion of $E$ over $\Delta$ can be extended to a holomorphic motion
of the Riemann sphere over $\Delta$. In this paper, we consider conditions
under which a holomorphic motion of $E$ over a non-simply connected Riemann
surface $X$ can be extended to a holomorphic motion of $\widehat{\mathbb{C}}$
over $X$. Our main result shows that a topological condition, the triviality of
the monodromy, gives a necessary and sufficient condition for a holomorphic
motion of $E$ over $X$ to be extended to a holomorphic motion of
$\widehat{\mathbb{C}}$ over $X$. We give topological and geometric conditions
for a holomorphic motion over a Riemann surface to be extended. We also apply
our result to a lifting problem for holomorphic maps to Teichm\"uller spaces.


  Cluster randomization trials commonly employ multiple endpoints. When a
single summary of treatment effects across endpoints is of primary interest,
global hypothesis testing/effect estimation methods represent a common analysis
strategy. However, specification of the joint distribution required by these
methods is non-trivial, particularly when endpoint properties differ. We
develop rank-based interval estimators for a global treatment effect referred
to as the "global win probability," or the probability that a treatment
individual responds better than a control individual on average. Using
endpoint-specific ranks among the combined sample and within each arm, each
individual-level observation is converted to a "win fraction" which quantifies
the proportion of wins experienced over every observation in the comparison
arm. An individual's multiple observations are then replaced by a single
"global win fraction," constructed by averaging win fractions across endpoints.
A linear mixed model is applied directly to the global win fractions to recover
point, variance, and interval estimates of the global win probability adjusted
for clustering. Simulation demonstrates our approach performs well concerning
coverage and type I error, and methods are easily implemented using standard
software. A case study using publicly available data is provided with
corresponding R and SAS code.


  We study a one-loop induced radiative neutrino model with an inert isospin
triplet scalar field, in which we discuss current neutrino oscillation data,
lepton flavor violations, muon anomalous magnetic moment, and a dark matter
candidate. We show global analysis combining all the constraints, and briefly
mention another possibility.


  We expand upon a new theoretical framework for Diffusion Limited Aggregation
and associated Dielectric Breakdown Models in two dimensions [R. C. Ball and E.
Somfai, Phys. Rev. Lett. 89, 135503 (2002)]. Key steps are understanding how
these models interrelate when the ultra-violet cut-off strategy is changed, the
analogy with turbulence and the use of logarithmic field variables. Within the
simplest, Gaussian, truncation of mode-mode coupling, all properties can be
calculated. The agreement with prior knowledge from simulations is encouraging,
and a new superuniversality of the tip scaling exponent is discussed. We find
angular resonances relatable to the cone angle theory, and we are led to
predict a new Screening Transition in the DBM at large eta.


  The title reaction is studied using a quasi-classical trajectory method for
collision energies between 0.1 meV and 10 eV, considering the vibrational
excitation of H$_2^+$ reactant. A new potential energy surface is developed
based on a Neural Network many body correction of a triatomics-in-molecules
potential, which significantly improves the accuracy of the potential up to
energies of 17 eV, higher than in other previous fits.The effect of the fit
accuracy and the non-adiabatic transitions on the dynamics are analyzed in
detail.The reaction cross section for collision energies above 1 eV increases
significantly with the increasing of the vibrational excitation of
H$_2^+$($v'$), for values up to $v'$=6. The total reaction cross section
(including the double fragmentation channel) obtained for $v'$=6 matches the
new experimental results obtained by Savic, Schlemmer and Gerlich [Chem. Phys.
Chem. 21 (13), 1429.1435(2020)]. The differences among several experimental
setups, for collision energies above 1 eV, showing cross sections
scattered/dispersed over a rather wide interval, can be explained by the
differences in the vibrational excitations obtained in the formation of H$_2^+$
reactants. On the contrary, for collision energies below 1 eV, the cross
section is determined by the long range behavior of the potential and do not
depend strongly on the vibrational state of H$_2^+$. In addition in this study,
the calculated reaction cross sections are used in a plasma model and compared
with previous results. We conclude that the efficiency of the formation of
H$_3^+$ in the plasma is affected by the potential energy surface used.


  We report the serendipitous discovery of an extended stellar halo surrounding
the low-mass galaxy Ark 227 ($M_\ast=5\times10^9 M_\odot$; d=35 Mpc) in deep
JWST NIRCam imaging from the Blue Jay Survey. The F200W-F444W color provides
robust star-galaxy separation, enabling the identification of stars at very low
density. By combining resolved stars at large galactocentric distances with
diffuse emission from NIRCam and Dragonfly imaging at smaller distances, we
trace the surface brightness and color profiles of this galaxy over the entire
extent of its predicted dark matter halo, from 0.1-100 kpc. Controlled N-body
simulations have predicted that minor mergers create "accretion shelves" in the
surface brightness profile at large radius. We observe such a feature in Ark
227 at 10-20 kpc, which, according to models, could be caused by a merger with
total mass ratio 1:10. The metallicity declines over this radial range, further
supporting the minor merger scenario. There is tentative evidence of a second
shelf at $\mu_V\approx 35$ mag arcsec$^{-2}$ extending from 50-100 kpc, along
with a corresponding drop in metallicity. The stellar mass in this outermost
envelope is $\approx10^7M_\odot$. These results suggest that Ark 227
experienced multiple mergers with a spectrum of lower-mass galaxies -- a
scenario that is broadly consistent with the hierarchical growth of structure
in a cold dark matter-dominated universe. Finally, we identify an ultra-faint
dwarf associated with Ark 227 with $M_\ast\approx10^5 M_\odot$ and
$\mu_{V,e}=28.1$ mag arcsec$^{-2}$, demonstrating that JWST is capable of
detecting very low-mass dwarfs to distances of at least ~30 Mpc.


  The problems of neutrino masses, matter-antimatter asymmetry, and dark matter
could be successfully addressed by postulating right-handed neutrinos with
Majorana masses below the electroweak scale. In this work, leptonic decays of
$W$ bosons extracted from 32.9 fb$^{-1}$ to 36.1 fb$^{-1}$ of 13 TeV
proton-proton collisions at the LHC are used to search for heavy neutral
leptons (HNLs) that are produced through mixing with muon or electron
neutrinos. The search is conducted using the ATLAS detector in both prompt and
displaced leptonic decay signatures. The prompt signature requires three
leptons produced at the interaction point (either $\mu\mu e$ or $e e\mu$) with
a veto on same-flavour opposite-charge topologies. The displaced signature
comprises a prompt muon from the $W$ boson decay and the requirement of a
dilepton vertex (either $\mu\mu$ or $\mu e$) displaced in the transverse plane
by 4-300 mm from the interaction point. The search sets constraints on the HNL
mixing to muon and electron neutrinos for HNL masses in the range 4.5-50 GeV.


  Variance parameter estimation in linear mixed models is a challenge for many
classical nonlinear optimization algorithms due to the positive-definiteness
constraint of the random effects covariance matrix. We take a completely novel
view on parameter estimation in linear mixed models by exploiting the intrinsic
geometry of the parameter space. We formulate the problem of residual maximum
likelihood estimation as an optimization problem on a Riemannian manifold.
Based on the introduced formulation, we give geometric higher-order information
on the problem via the Riemannian gradient and the Riemannian Hessian. Based on
that, we test our approach with Riemannian optimization algorithms numerically.
Our approach yields a higher quality of the variance parameter estimates
compared to existing approaches.


  This work is a mathematician's attempt to understand intuitionistic logic. It
can be read in two ways: as a research paper interspersed with lengthy
digressions into rethinking of standard material; or as an elementary (but
highly unconventional) introduction to first-order intuitionistic logic. For
the latter purpose, no training in formal logic is required, but a modest
literacy in mathematics, such as topological spaces and posets, is assumed.
  The main theme of this work is the search for a formal semantics adequate to
Kolmogorov's informal interpretation of intuitionistic logic (whose simplest
part is more or less the same as the so-called BHK interpretation). This search
goes beyond the usual model theory, based on Tarski's notion of semantic
consequence, and beyond the usual formalism of first-order logic, based on
schemata. Thus we study formal semantics of a simplified version of Paulson's
meta-logic, used in the Isabelle prover.
  By interpreting the meta-logical connectives and quantifiers constructively,
we get a generalized model theory, which covers, in particular,
realizability-type interpretations of intuitionistic logic. On the other hand,
by analyzing Kolmogorov's notion of semantic consequence (which is an
alternative to Tarski's standard notion), we get an alternative model theory.
By using an extension of the meta-logic, we further get a generalized
alternative model theory, which suffices to formalize Kolmogorov's semantics.
  On the other hand, we also formulate a modification of Kolmogorov's
interpretation, which is compatible with the usual, Tarski-style model theory.
Namely, it can be formalized by means of sheaf-valued models, which turn out to
be a special case of Palmgren's categorical models; intuitionistic logic is
complete with respect to this semantics.


  Snapshot recording durations at each process contribute to the overall
efficiency of the algorithm. In this paper we are presenting the observed
variations in snapshot recording durations at processes in a distributed
system. We conclude with key characteristics of a reliable and effective
snapshot algorithm. Simulations were achieved using SimGrid Java API.


  Random survival forests (RSF) are a powerful method for risk prediction of
right-censored outcomes in biomedical research. RSF use the log-rank split
criterion to form an ensemble of survival trees. The most common approach to
evaluate the prediction accuracy of a RSF model is Harrell's concordance index
for survival data ('C index'). Conceptually, this strategy implies that the
split criterion in RSF is different from the evaluation criterion of interest.
This discrepancy can be overcome by using Harrell's C for both node splitting
and evaluation. We compare the difference between the two split criteria
analytically and in simulation studies with respect to the preference of more
unbalanced splits, termed end-cut preference (ECP). Specifically, we show that
the log-rank statistic has a stronger ECP compared to the C index. In
simulation studies and with the help of two medical data sets we demonstrate
that the accuracy of RSF predictions, as measured by Harrell's C, can be
improved if the log-rank statistic is replaced by the C index for node
splitting. This is especially true in situations where the censoring rate or
the fraction of informative continuous predictor variables is high. Conversely,
log-rank splitting is preferable in noisy scenarios. Both C-based and log-rank
splitting are implemented in the R~package ranger. We recommend Harrell's C as
split criterion for use in smaller scale clinical studies and the log-rank
split criterion for use in large-scale 'omics' studies.


  We study 87 Extremely Red Objects (EROs), selected both to have color redder
than R-[3.6] = 4.0, and to have confirmed spectroscopic redshifts. Together,
these two constraints result in this sample populating a fairly narrow redshift
range at 0.76 < z < 1.42. The key new ingredient included here is deep Spitzer
Space Telescope InfraRed Array Camera (IRAC) data. Based on [3.6]-[8.0] color,
we demonstrate that it is possible to classify EROs into early-type, dusty
starburst, or power-law (AGN) types. We present ultraviolet to mid-infrared
spectral energy distributions (SEDs) and Advanced Camera for Surveys (ACS)
images, both of which support our simple IRAC color classification.


  Superhydrides have complex hydrogenic sublattices and are important
prototypes for studying metallic hydrogen and high-temperature superconductors.
Encouraged by the results on LaH10, in consideration of the differences between
La and Pr, Pr-H system is especially worth studying because of the magnetism
and valence-band f-electrons in element Pr. Here we successfully synthesized
praseodymium superhydrides (PrH9) in laser-heated diamond anvil cells.
Synchrotron X-ray diffraction (XRD) analysis demonstrated the presence of
previously predicted F43m-PrH9 and unexpected P63/mmc-PrH9 phases. Moreover,
Fm3m-PrH3, P4/nmm-PrH(3-{\delta}) and Fm3m-PrH(1+x) were found below 52 GPa.
F43m-PrH9 and P63/mmc-PrH9 were stable above 100 GPa in experiment.
Experimental studies of electrical resistance in the PrH9 sample showed the
emergence of superconducting transition (Tc) below 9K and a dependent Tc on
applied magnetic field. Theoretical calculations indicate that magnetic order
and electron-phonon interaction coexist in a very close range of pressures in
the PrH9 sample which may contribute to its low superconducting temperature Tc.
Our results highlight the intimate connections among hydrogenic sublattices,
density of states, magnetism and superconductivity in Pr-based superhydrides.


  Recent efforts to obtain high data rates in wireless systems have focused on
what can be achieved in systems that have nonlinear or coarsely quantized
transceiver architectures. Estimating the channel in such a system is
challenging because the nonlinearities distort the channel estimation process.
It is therefore of interest to determine how much training is needed to
estimate the channel sufficiently well so that the channel estimate can be used
during data communication. We provide a way to determine how much training is
needed by deriving a lower bound on the achievable rate in a training-based
scheme that can be computed and analyzed even when the number of antennas is
very large. This lower bound can be tight, especially at high SNR. One
conclusion is that the optimal number of training symbols may paradoxically be
smaller than the number of transmitters for systems with coarsely-quantized
transceivers. We show how the training time can be strongly dependent on the
number of receivers, and give an example where doubling the number of receivers
reduces the training time by about 37 percent.


  We describe a singular variety associated to the smallest degree Pinchuk map
and calculate its intersection homology. The result describes the geometry at
infinity of the Pinchuk's map.


  The boundary of symmetry-protected topological states (SPTs) can harbor new
quantum anomaly phenomena. In this work, we characterize the bosonic anomalies
introduced by the 1+1D non-onsite-symmetric gapless edge modes of 2+1D bulk
bosonic SPTs with a generic finite Abelian group symmetry (isomorphic to
$G=\prod_i Z_{N_i}=Z_{N_1} \times Z_{N_2} \times Z_{N_3} \times ...$). We
demonstrate that some classes of SPTs (termed "Type II") trap fractional
quantum numbers (such as fractional $Z_N$ charges) at the 0D kink of the
symmetry-breaking domain walls; while some classes of SPTs (termed "Type III")
have degenerate zero energy modes (carrying the projective representation
protected by the unbroken part of the symmetry), either near the 0D kink of a
symmetry-breaking domain wall, or on a symmetry-preserving 1D system
dimensionally reduced from a thin 2D tube with a monodromy defect 1D line
embedded. More generally, the energy spectrum and conformal dimensions of
gapless edge modes under an external gauge flux insertion (or twisted by a
branch cut, i.e., a monodromy defect line) through the 1D ring can distinguish
many SPT classes. We provide a manifest correspondence from the physical
phenomena, the induced fractional quantum number and the zero energy mode
degeneracy, to the mathematical concept of cocycles that appears in the group
cohomology classification of SPTs, thus achieving a concrete physical
materialization of the cocycles. The aforementioned edge properties are
formulated in terms of a long wavelength continuum field theory involving
scalar chiral bosons, as well as in terms of Matrix Product Operators and
discrete quantum lattice models. Our lattice approach yields a regularization
with anomalous non-onsite symmetry for the field theory description. We also
formulate some bosonic anomalies in terms of the Goldstone-Wilczek formula.


  Let R be a local Cohen-Macaulay ring, let I be an R-ideal, and let G be the
associated graded ring of I. We give an estimate for the depth of G when G is
not necessarily Cohen-Macaulay. We assume that I is either equimultiple, or has
analytic deviation one, but we do not have any restriction on the reduction
number. We also give a general estimate for the depth of G involving the first
r+l powers of I, where r denotes the Castelnuovo regularity of G and l denotes
the analytic spread of I.


  The constrained Hamiltonian formalism is worked out for the theories where
the gauge symmetry parameters are unfree, being restricted by differential
equations. The Hamiltonian BFV-BRST embedding is elaborated for this class of
gauge theories. The general formalism is exemplified by the linearized
unimodular gravity.


  Quantum Monte Carlo methods are accurate and promising many body techniques
for electronic structure calculations which, in the last years, are
encountering a growing interest thanks to their favorable scaling with the
system size and their efficient parallelization, particularly suited for the
modern high performance computing facilities. The ansatz of the wave function
and its variational flexibility are crucial points for both the accurate
description of molecular properties and the capabilities of the method to
tackle large systems. In this paper, we extensively analyze, using different
variational ansatzes, several properties of the water molecule, namely: the
total energy, the dipole and quadrupole momenta, the ionization and atomization
energies, the equilibrium configuration, and the harmonic and fundamental
frequencies of vibration. The investigation mainly focuses on variational Monte
Carlo calculations, although several lattice regularized diffusion Monte Carlo
calculations are also reported. Through a systematic study, we provide a useful
guide to the choice of the wave function, the pseudo potential, and the basis
set for QMC calculations. We also introduce a new strategy for the definition
of the atomic orbitals involved in the Jastrow - Antisymmetrised Geminal power
wave function, in order to drastically reduce the number of variational
parameters. This scheme significantly improves the efficiency of QMC energy
minimization in case of large basis sets.


  NGC 2071 is a star-forming region that overlaps with three $\gamma$-ray
sources detected by the Fermi Space Telescope. We propose that strong flare
activity in T Tauri stars could produce $\gamma$-ray emission in a way that
makes them a counterpart to some unidentified sources detected by the Large
Area Telescope aboard the Fermi satellite. We have performed a spectral and
temporal analysis for two Fermi data sets: the first 2 yr and the entire 14 yr
of observations. We have found that the $\gamma$-ray source is detectable at
3.2$\sigma$ above the background at energies above 100 GeV during the first 2
yr of observation. The analysis of the expected frequency of the highest energy
flares occurring in T Tauri stars is consistent with our estimate. In addition,
we have determined the minimum energy of the flare that would produce
$\gamma$-ray emission, which is $\sim 5 \times 10^{37}$ erg. This agreement
becomes a hard observational constraint supporting previous hypotheses about
rare flares as the origin of unidentified $\gamma$-ray sources in star-forming
regions.


  We examine in detail the causes of the structural transitions that occur for
those small Lennard-Jones clusters that have a non-icosahedral global minima.
Based on the principles learned from these examples we develop a method to
construct structural phase diagrams that show in a coarse-grained manner how
the equilibrium structure of large clusters depends on both size and
temperature. The method can be augmented to account for anharmonicity and
quantum effects. Our results illustrate that the vibrational entropy can play a
crucial role in determining the equilibrium structure of a cluster.


  In the present work we have analyzed a fermionic infinite-ranged Ising spin
glass with a local BCS coupling in the presence of transverse field. This model
has been obtained by tracing out the conduction electrons degrees of freedom in
a superconducting alloy. The transverse field \Gamma is applied in the
resulting effective model. The problem is formulated in the path integral
formalism where the spins operators are represented by bilinear combination of
Grassmann fields. The problem can be solved by combining previous approaches
used to study a fermionic Heisenberg spin glass and a Ising spin glass in a
transverse field. The results are show in a phase diagram T/J {\it versus}
\Gamma/J (J is the standard deviation of the random coupling J_{ij}) for
several values of g (the strength of the pairing interaction). For small g, the
line transition T_c(\Gamma) between the normal paramagnetic phase and the spin
glass phase decreases when increases \Gamma, until it reaches a quantum
critical point. For increasing g, a PAIR phase (where there is formation of
local pairs) has been found which disappears when is close to \Gamma_c showing
that the transverse field tends to inhibited the PAIR phase.


  The main goal of this work is to estimate the actual number of cases of
Covid-19 in Spain in the period 01-31-2020 / 06-01-2020 by Autonomous
Communities. Based on these estimates, this work allows us to accurately
re-estimate the lethality of the disease in Spain, taking into account
unreported cases. A hierarchical Bayesian model recently proposed in the
literature has been adapted to model the actual number of Covid-19 cases in
Spain. The results of this work show that the real load of Covid-19 in Spain in
the period considered is well above the data registered by the public health
system. Specifically, the model estimates show that, cumulatively until June
1st, 2020, there were 2,425,930 cases of Covid-19 in Spain with characteristics
similar to those reported (95\% credibility interval: 2,148,261 - 2,813,864),
from which were actually registered only 518,664. Considering the results
obtained from the second wave of the Spanish seroprevalence study, which
estimates 2,350,324 cases of Covid-19 produced in Spain, in the period of time
considered, it can be seen that the estimates provided by the model are quite
good. This work clearly shows the key importance of having good quality data to
optimize decision-making in the critical context of dealing with a pandemic.


  Cyclotron Radiation Emission Spectroscopy (CRES) is an approach to measuring
the energy of an electron trapped in an externally applied magnetic field. The
bare electron can come from different interactions, including photoelectric
absorption, Compton scatters, beta decay, and pair production. CRES relies on
measuring the frequency of the electron's cyclotron motion, and because the
measurement times extend over $10^6$-$10^7$ cycles, the energy resolution is on
the order of a single electronvolt. To date, CRES has only been performed on
internal beta-emitting radioisotopes, but the technology can be applied to
X-ray spectrometery through appropriate selection of a target gas and
sufficient intensity of the distinct X-ray source. The applications of this
technology range from high-precision measurements of atomic energy levels, to
calibrations of basic science experiments, to trace element identification. In
this work we explore the use of CRES for X-ray spectroscopy within the rubric
of measuring the energy levels of argon, although the principles are broadly
applicable to many other situations. The issues we explore include target
material, density, electron trapping depth, noise levels, and overall
efficiency. We also discuss spectral deconvolution and how the multiple peaks
obtained from a single target / source pair can be used to enhance the
robustness of the measurement.


  Unique and highly tunable optical properties of PT-symmetric systems and
metamaterials enable a plenty of entirely new linear and nonlinear optical
phenomena with numerous applications, e.g., for designing subdiffraction
lenses, nonreciprocal devices, etc. Therefore, the artificial media with the PT
symmetry attract ever-increasing attention and are now a subject for intensive
investigations. One of the commonly used methods providing information about
the optical response of artificial nanostructural media is a so-called
effective medium theory. Here we examine the possibility of utilizing the
effective medium theory for a comprehensive analysis of PT-symmetric
multilayered systems composed of alternating loss and gain slabs. We show that
applicability of local effective material parameters (or Maxwell Garnett
approximation) is very limited and cannot be exploited for a prediction of
exceptional points marking a PT symmetry breaking. On the other hand, nonlocal
bianisotropic effective medium parameters can be reliably used, if the
thickness of a unit cell is much smaller than the radiation wavelength. In the
case of obliquely incident plane waves, we reveal the limitation on the
loss-gain coefficient, which should not be too large compared with the real
part of the permittivity. We believe that our findings can improve the
fundamental understanding of physics behind PT-symmetric systems and advance
the development of auxiliary tools for analyzing their peculiar optical
response.


  We propose an efficient analytical method for estimating the luminosity
distance in a homogenous Friedmann-Lema\^itre-Robertson-Walker (FLRW) model of
the Universe. This method is based on the homotopy perturbation method (HPM),
which has high accuracy in many nonlinear problems, and can be easily
implemented. For analytical calculation of the luminosity distance, we offer to
proceed not from the computation of the integral, which determines it, but from
the solution of a certain differential equation with corresponding initial
conditions. Solving this equation by means of HPM, we obtain the approximate
analytical expressions for the luminosity distance as a function of redshift
for two different types of homotopy. Possible extension of this method to other
cosmological models is also discussed.


  While end-to-end models have shown great success on the Automatic Speech
Recognition task, performance degrades severely when target sentences are
long-form. The previous proposed methods, (partial) overlapping inference are
shown to be effective on long-form decoding. For both methods, word error rate
(WER) decreases monotonically when overlapping percentage decreases. Setting
aside computational cost, the setup with 50% overlapping during inference can
achieve the best performance. However, a lower overlapping percentage has an
advantage of fast inference speed. In this paper, we first conduct
comprehensive experiments comparing overlapping inference and partial
overlapping inference with various configurations. We then propose
Voice-Activity-Detection Overlapping Inference to provide a trade-off between
WER and computation cost. Results show that the proposed method can achieve a
20% relative computation cost reduction on Librispeech and Microsoft Speech
Language Translation long-form corpus while maintaining the WER performance
when comparing to the best performing overlapping inference algorithm. We also
propose Soft-Match to compensate for similar words mis-aligned problem.


  The main motivation of the current study is to propose a high-pressure
hydrogen injection as an hybrid active flow control technique in order to
manipulate the flow-field in front of a blunt nose during hypersonic flight.
Hydrogen injection can lead to self-igition under the right environment
conditions in a stagnation zone, and may cause thermal heat addition through
combustion and provide the counterjet effect together by pushing bow shock
upstream. The axisymmetric numerical simulations for the hemispherical blunt
nose are performed at a Mach 6 freestream flow with 10000 Pa pressure and 293 K
temperature. The sonic and supersonic hydrogen and air injections are compared
for drag reduction at the same stagnation pressure ratio $PR$ and momentum
ratio ($R_{MA}$). The sonic air and hydrogen injection scenarios show similar
performance in terms of drag reduction and similar SPM flow features, but
hydrogen injection has a mass flow rate 3.76 times lower than air. Supersonic
hydrogen injection at $M_j$ 2.94 behaves differently than supersonic air
injection and can achieve up to 60 % drag reduction at lower PR and LPM mode
with lower mass flow rate. Additionally, air injection achieves a drag
reduction of 40 % in SPM mode at higher PR with very high mass flow rate.


  We report on the phonon spectrum of Ba3Cr2O8 determined by infrared
spectroscopy, and on specific heat measurements across the Jahn-Teller
transition in magnetic fields up to 9 T. Phonon modes split below the
Jahn-Teller transition, which occurs at T_{JT} = 70 K as detected by specific
heat measurements. The field-dependent specific heat data is analyzed in terms
of the contributions from lattice, magnetic and orbital degrees of freedom. In
contrast to the isostructural compound Sr3Cr2O8 our analysis does not indicate
the existence of orbital fluctuations below the Jahn-Teller transition in
Ba3Cr2O8.


  Word sense disambiguation primarily addresses the lexical ambiguity of common
words based on a predefined sense inventory. Conversely, proper names are
usually considered to denote an ad-hoc real-world referent. Once the reference
is decided, the ambiguity is purportedly resolved. However, proper names also
exhibit ambiguities through appellativization, i.e., they act like common words
and may denote different aspects of their referents. We proposed to address the
ambiguities of proper names through the light of regular polysemy, which we
formalized as dot objects. This paper introduces a combined word sense
disambiguation (WSD) model for disambiguating common words against Chinese
Wordnet (CWN) and proper names as dot objects. The model leverages the
flexibility of a gloss-based model architecture, which takes advantage of the
glosses and example sentences of CWN. We show that the model achieves
competitive results on both common and proper nouns, even on a relatively
sparse sense dataset. Aside from being a performant WSD tool, the model further
facilitates the future development of the lexical resource.


  This is a Reply on the proceeding comment on our paper titled "Classical
Simulations Including Electron Correlations for Sequential Double Ionization".


  The classical phase of the matrix model of 11-dimensional M-theory is
complex, infinite-dimensional Hilbert space. As a complex manifold, the latter
admits a continuum of nonequivalent, complex-differentiable structures that can
be placed in 1-to-1 correspondence with families of coherent states in the
Hilbert space of quantum states. The moduli space of nonbiholomorphic complex
structures on classical phase space turns out to be an infinite-dimensional
symmetric space. We argue that each choice of a complex differentiable
structure gives rise to a physically different notion of an elementary quantum.


  Recent adaptive optics systems in astronomy achieve high-angular resolution.
With the extreme stability of the images, detection at very low fluxes can be
reached using a coronograph at the diffraction limit of the telescopes. This
paper is an overview of the issues of stellar coronography used at the
diffraction limit. Image formation through such a system is illustrated by
numerical simulations. The description of a coronograph implemented on the VLT
adaptive optics prototype, COME-ON, is presented as well as the first
observations.


  This paper investigates further how the presence of a single reflecting plane
wall modifies the usual Planckian forms in the thermodynamics of the massless
scalar radiation in $N$-dimensional Minkowski spacetime. This is done in a
rather unconventional way by integrating the energy density over space to
obtain the internal energy and from that the Helmholtz free energy. The
reflecting wall is modelled by assuming the Dirichlet or the Neumann boundary
conditions on the wall. It is found that when $N>2$ integration over space
eliminates dependence on the curvature coupling parameter $\xi$. Unexpectedly
though, when $N=2$, the internal energy and the corresponding thermodynamics
turn out to be dependent on $\xi$. For instance, the correction to the
two-dimensional Planckian heat capacity is $\mp \xi k_{B}$ (minus for
Dirichlet, plus for Neumann). Other aspects of this dependence on $\xi$ are
also discussed. Results are confronted with those in the literature concerning
related setups of reflecting walls (such as slabs) where conventional (i.e.,
global) approaches to obtain thermodynamics have been used.


  In this paper, we derive an inverse result for bivariate Kantorovich type
sampling series for the space of all continuous functions with upto second
order partial derivatives are continuous and bounded on $R^2.$ Further, we
prove the rate of approximation in the Bogel space of continuous functions for
the GBS (Generalized Boolean Sum) of these operators. Finally, we give some
examples for the kernel to which the theory can be applied


  Recent works have shown that transformers can solve contextual reasoning
tasks by internally executing computational graphs called circuits. Circuits
often use attention to logically match information from subspaces of the
representation, e.g. using position-in-sequence to identify the previous token.
In this work, we consider a semantic subspace to be any independent subspace of
the latent representation that can fully determine an attention distribution.
We show that Pre-Norm, the placement of normalisation layer used by
state-of-the-art transformers, violates this ability unless the model learns a
strict representation structure of orthogonal spheres. This is because it
causes linear subspaces to interfere through their common normalisation factor.
Theoretically, we analyse circuit stability by modelling this interference as
random noise on the $L_2$-norms of the query/key/value vectors, predicting a
phenomenon of circuit collapse when sparse-attention shifts to a different
token. Empirically, we investigate the sensitivity of real-world models trained
for mathematical addition, observing a 1% rate of circuit collapse when the
norms are artificially perturbed by $\lesssim$10%. We contrast Pre-Norm with
QKV-Norm, which places normalisation after the attention head's linear
operators. Theoretically this relaxes the representational constraints.
Empirically we observe comparable in-distribution but worse out-of-distribution
performance.


  We present a comprehensive study performed with high-resolution
angle-resolved photoemission spectroscopy on triple-layered Bi2Sr2Ca2Cu3O10+d
single crystals. By measurements above TC the Fermi surface topology defined by
the Fermi level crossings of the CuO2-derived band was determined. A hole-like
Fermi surface as for single and double-CuO2 layered Bi-based cuprates is found,
giving new input to the current debate of the general Fermi surface topology of
the high Tc superconductors. Furthermore, we present measurements of the
superconducting gap of Bi-2223 and show that there are clear indications for a
strong anisotropy of the superconducting gap. The universal properties of this
phase in comparison to the other Bi-based cuprates will be discussed.


  In this paper, we propose a new multi-armed bandit problem called the
Gambler's Ruin Bandit Problem (GRBP). In the GRBP, the learner proceeds in a
sequence of rounds, where each round is a Markov Decision Process (MDP) with
two actions (arms): a continuation action that moves the learner randomly over
the state space around the current state; and a terminal action that moves the
learner directly into one of the two terminal states (goal and dead-end state).
The current round ends when a terminal state is reached, and the learner incurs
a positive reward only when the goal state is reached. The objective of the
learner is to maximize its long-term reward (expected number of times the goal
state is reached), without having any prior knowledge on the state transition
probabilities. We first prove a result on the form of the optimal policy for
the GRBP. Then, we define the regret of the learner with respect to an
omnipotent oracle, which acts optimally in each round, and prove that it
increases logarithmically over rounds. We also identify a condition under which
the learner's regret is bounded. A potential application of the GRBP is optimal
medical treatment assignment, in which the continuation action corresponds to a
conservative treatment and the terminal action corresponds to a risky treatment
such as surgery.


  We use a sample of blue horizontal branch (BHB) stars from the Sloan Digital
Sky Survey Data Release 7 to explore the structure of the tidal tails from the
Sagittarius Dwarf Galaxy. We use a method yielding BHB star candidates with up
to ~70% purity from photometry alone. The resulting sample has a distance
precision of roughly 5% and can probe distances in excess of 100 kpc. Using
this sample, we identify a possible extension to the trailing arm at distances
of 60-80 kpc from the Sun with an estimated significance of at least 3.8 sigma.
Current models predict that a distant `returning' segment of the debris stream
should exist, but place it substantially closer to the Sun where no debris is
observed in our data. Exploiting the distance precision of our tracers, we
estimate the mean line-of-sight thickness of the leading arm to be ~3 kpc, and
show that the two `bifurcated' branches of the debris stream differ by only 1-2
kpc in distance. With a spectroscopic very pure BHB star subsample, we estimate
the velocity dispersion in the leading arm, 37 km s^-1, which is in reasonable
agreement with models of Sgr disruption. We finally present a sample of
high-probability Sgr BHB stars in the leading arm of Sgr, selected to have
distances and velocities consistent with Sgr membership, to allow further
study.


  Large samples of globular clusters (GC) with precise multi-wavelength
photometry are becoming increasingly available and can be used to constrain the
formation history of galaxies. We present the results of an analysis of Milky
Way (MW) and Virgo core GCs based on five optical-near-infrared colors and ten
synthetic stellar population models. For the MW GCs, the models tend to agree
on photometric ages and metallicities, with values similar to those obtained
with previous studies. When used with Virgo core GCs, for which photometry is
provided by the Next Generation Virgo cluster Survey (NGVS), the same models
generically return younger ages. This is a consequence of the systematic
differences observed between the locus occupied by Virgo core GCs and models in
panchromatic color space. Only extreme fine-tuning of the adjustable parameters
available to us can make the majority of the best-fit ages old. Although we
cannot exclude that the formation history of the Virgo core may lead to more
conspicuous populations of relatively young GCs than in other environments, we
emphasize that the intrinsic properties of the Virgo GCs are likely to differ
systematically from those assumed in the models. Thus, the large wavelength
coverage and photometric quality of modern GC samples, such as used here, is
not by itself sufficient to better constrain the GC formation histories. Models
matching the environment-dependent characteristics of GCs in multi-dimensional
color space are needed to improve the situation.


  A counterpoint theory for the whole continuum of the octave is obtained from
Mazzola's model via extended counterpoint symmetries, and some of its
properties are discussed.


  We address multi-robot geometric task-and-motion planning (MR-GTAMP) problems
in synchronous, monotone setups. The goal of the MR-GTAMP problem is to move
objects with multiple robots to goal regions in the presence of other movable
objects. We focus on collaborative manipulation tasks where the robots have to
adopt intelligent collaboration strategies to be successful and effective,
i.e., decide which robot should move which objects to which positions, and
perform collaborative actions, such as handovers. To endow robots with these
collaboration capabilities, we propose to first collect occlusion and
reachability information for each robot by calling motion-planning algorithms.
We then propose a method that uses the collected information to build a graph
structure which captures the precedence of the manipulations of different
objects and supports the implementation of a mixed-integer program to guide the
search for highly effective collaborative task-and-motion plans. The search
process for collaborative task-and-motion plans is based on a Monte-Carlo Tree
Search (MCTS) exploration strategy to achieve exploration-exploitation balance.
We evaluate our framework in two challenging MR-GTAMP domains and show that it
outperforms two state-of-the-art baselines with respect to the planning time,
the resulting plan length and the number of objects moved. We also show that
our framework can be applied to underground mining operations where a robotic
arm needs to coordinate with an autonomous roof bolter. We demonstrate plan
execution in two roof-bolting scenarios both in simulation and on robots.


  We consider the sequence of nodal counts for eigenfunctions of the
Laplace-Beltrami operator in two dimensional domains. It was conjectured
recently that this sequence stores some information pertaining to the geometry
of the domain, and we show explicitly that this is the case for the family of
rectangular domains with Dirichlet boundary conditions.


  We consider the transverse force on a moving vortex with the acoustic metric
using the $\phi $-mapping topological current theory. In the frame of effective
spacetime geometry the vortex appear naturally by virtue of the vortex tensor
in the Lorentz spacetime and we show that it is just the vortex derived with
the order parameter in the condensed matter. With the usual Lagrangian we
obtain the equation of motion for the vortex. At last, we show that the
transverse force on the moving vortex in our equation is just the usual Magnus
force in a simple model.


  We demonstrate theoretically that the spin polarization of current can be
electrically amplified within nonmagnetic semiconductors by exploiting the fact
the spin current, compared to the charge current, is weakly perturbed by
electric driving forces. As a specific example, we consider a T-shaped current
branching geometry made entirely of a nonmagnetic semiconductor, where the
current is injected into one of the branches (input branch) and splits into the
other two branches (output branches). We show that when the input current has a
moderate spin polarization, the spin polarization in one of the output branches
can be higher than the spin polarization in the input branch and may reach 100%
when the relative magnitudes of current-driving electric fields in the two
output branches are properly tuned. The proposed amplification scheme does not
use ferromagnets or magnetic fields, and does not require low temperature
operation, providing an efficient way to generate a highly spin polarized
current in nonmagnetic semiconductors at room temperature.


  The Quantum Random Energy Model (QREM) is a random matrix of Anderson-type
which describes effects of a transversal magnetic field on Derrida's spin
glass. The model exhibits a glass phase as well as a classical and a quantum
paramagnetic phase. We analyze in detail the low-energy spectrum and establish
a localization-delocalization transition for the corresponding eigenvectors of
the QREM. Based on a combination of random matrix and operator techniques as
well as insights in the random geometry, we derive next-to-leading order
asymptotics for the ground-state energy and eigenvectors in all regimes of the
parameter space. Based on this, we also deduce the next-to-leading order of the
free energy, which turns out to be deterministic and on order one in the system
size in all phases of the QREM. As a result, we determine the nature of the
fluctuations of the free energy in the spin glass regime.


  We show that affine coordinate subspaces of dimension at least two in
Euclidean space are of Khintchine type for divergence. For affine coordinate
subspaces of dimension one, we prove a result which depends on the dual
Diophantine type of the base point of the subspace. These results provide
evidence for the conjecture that all affine subspaces of Euclidean space are of
Khintchine type for divergence. We also prove a partial analogue regarding the
Hausdorff measure theory. Furthermore, we obtain various results relating
weighted Diophantine approximation and Dirichlet improvability. In particular,
we show that weighted badly approximable vectors are weighted Dirichlet
improvable, thus generalising a result by Davenport and Schmidt. We also
provide a relation between non-singularity and twisted inhomogeneous
approximation. This extends a result of Shapira to the weighted case.


  Excitonic spectra are calculated for free-standing, surface passivated InAs
quantum dots using atomic pseudopotentials for the single-particle states and
screened Coulomb interactions for the two-body terms. We present an analysis of
the single particle states involved in each excitation in terms of their
angular momenta and Bloch-wave parentage. We find that (i) in agreement with
other pseudopotential studies of CdSe and InP quantum dots, but in contrast to
k.p calculations, dot states wavefunction exhibit strong odd-even angular
momentum envelope function mixing (e.g. $s$ with $p$) and large
valence-conduction coupling. (ii) While the pseudopotential approach produced
very good agreement with experiment for free-standing, colloidal CdSe and InP
dots, and for self-assembled (GaAs-embedded) InAs dots, here the predicted
spectrum does {\em not} agree well with the measured (ensemble average over dot
sizes) spectra. (1) Our calculated excitonic gap is larger than the PL measure
one, and (2) while the spacing between the lowest excitons is reproduced, the
spacings between higher excitons is not fit well. Discrepancy (1) could result
from surface states emission. As for (2), agreement is improved when account is
taken of the finite size distribution in the experimental data. (iii) We find
that the single particle gap scales as $R^{-1.01}$ (not $R^{-2}$), that the
screened (unscreened) electron-hole Coulomb interaction scales as $R^{-1.79}$
($R^{-0.7}$), and that the eccitonic gap sclaes as $R^{-0.9}$. These scaling
laws are different from those expected from simple models.


  In this note, we shall consider the existence of invariant measures for a
class of infinite dimensional stochastic functional differential equations with
delay whose driving semigroup is eventually norm continuous. The results
obtained are applied to stochastic heat equations with distributed delays which
appear in such terms having the highest order partial derivatives. In the
systems, the associated driving semigroups are generally non eventually
compact.


  On complex algebraic varieties, height functions arising in combinatorial
applications fail to be proper. This complicates the description and
computation via Morse theory of key topological invariants. Here we establish
checkable conditions under which the behavior at infinity may be ignored, and
the usual theorems of classical and stratified Morse theory may be applied.
This allows for simplified arguments in the field of analytic combinatorics in
several variables, and forms the basis for new methods applying to problems
beyond the reach of previous techniques.


  We investigate the large-scale statistics of a passive scalar transported by
a turbulent velocity field. At scales larger than the characteristic
lengthscale of scalar injection, yet smaller than the correlation length of the
velocity, the advected field displays persistent long-range correlations due to
the underlying turbulent velocity. These induce significant deviations from
equilibrium statistics for high-order scalar correlations, despite the absence
of scalar flux.


  The present work extends and deepens previous examinations of the evolution
of globular cluster orbits in elliptical galaxies, by means of numerical
integrations of a wide set of orbits in 5 self-consistent triaxial galactic
models characterized by a central core and different axial ratios. These models
constitute a valid and complete representation of regular orbits in elliptical
galaxies. Dynamical friction is definitely shown to be an efficient cause of
evolution for the globular cluster systems in elliptical galaxies of any mass
and axial ratios. Moreover, our statistically significant sample of computed
orbits confirm that the globular cluster orbital decay times are, in a wide
range of realistic initial conditions, much shorter than the age of the
galaxies. Consequently, the huge quantity of mass carried into the innermost
galactic region in form of decayed globular clusters have likely contributed
significantly in feeding and accreting a compact object therein.


  Generalizable manipulation requires that robots be able to interact with
novel objects and environment. This requirement makes manipulation extremely
challenging as a robot has to reason about complex frictional interaction with
uncertainty in physical properties of the object. In this paper, we study
robust optimization for control of pivoting manipulation in the presence of
uncertainties. We present insights about how friction can be exploited to
compensate for the inaccuracies in the estimates of the physical properties
during manipulation. In particular, we derive analytical expressions for
stability margin provided by friction during pivoting manipulation. This margin
is then used in a bilevel trajectory optimization algorithm to design a
controller that maximizes this stability margin to provide robustness against
uncertainty in physical properties of the object. We demonstrate our proposed
method using a 6 DoF manipulator for manipulating several different objects.


  We investigate a new scheme for astronomical spectrograph calibration using
the laser frequency comb at the Solar Vacuum Tower Telescope on Tenerife. Our
concept is based upon a single-mode fiber channel, that simultaneously feeds
the spectrograph with comb light and sunlight. This yields nearly perfect
spatial mode matching between the two sources. In combination with the absolute
calibration provided by the frequency comb, this method enables extremely
robust and accurate spectroscopic measurements. The performance of this scheme
is compared to a sequence of alternating comb and sunlight, and to absorption
lines from Earth's atmosphere. We also show how the method can be used for
radial-velocity detection by measuring the well-explored 5-minute oscillations
averaged over the full solar disk. Our method is currently restricted to solar
spectroscopy, but with further evolving fiber-injection techniques it could
become an option even for faint astronomical targets.


  Variational perturbation theory is used to determine the decay rates of
metastable states across a cubic barrier of arbitrary height. For high
barriers, a variational resummation procedure is applied to the complex energy
eigenvalues obtained from a WKB expansion; for low barriers, the variational
resummation procedure converts the non-Borel-summable
Rayleigh-Schr\"o\-din\-ger expansion into an exponentially fast convergent one.
The results in the two regimes match and yield very accurate imaginary parts of
the energy eigenvalues. This is demonstrated by comparison with the complex
eigenvalues from solutions of the Schr\"odinger equation via the
complex-coordinate rotation method.


  We investigate quantum channels, which after a finite number $k$ of repeated
applications erase all input information, i.e., channels whose $k$-th power
(but no smaller power) is a completely depolarizing channel. We show that on a
system with Hilbert space dimension $d$, the order is bounded by $k\leq d^2-1$,
and give an explicit construction scheme for such channels. We also consider
strictly forgetful memory channels, i.e., channels with an additional input and
output in every step, which after exactly $k$ steps retain no information about
the initial memory state. We establish an explicit representation for such
channels showing that the same bound applies for the memory depth $k$ in terms
of the memory dimension $d$.


  We develop an efficient quantum implementation of an important signal
processing algorithm for line spectral estimation: the matrix pencil method,
which determines the frequencies and damping factors of signals consisting of
finite sums of exponentially damped sinusoids. Our algorithm provides a quantum
speedup in a natural regime where the sampling rate is much higher than the
number of sinusoid components. Along the way, we develop techniques that are
expected to be useful for other quantum algorithms as well - consecutive phase
estimations to efficiently make products of asymmetric low rank matrices
classically accessible and an alternative method to efficiently exponentiate
non-Hermitian matrices. Our algorithm features an efficient quantum-classical
division of labor: The time-critical steps are implemented in quantum
superposition, while an interjacent step, requiring only exponentially few
parameters, can operate classically. We show that frequencies and damping
factors can be obtained in time logarithmic in the number of sampling points,
exponentially faster than known classical algorithms.


  Normalizing flows are machine-learned maps between different lattice theories
which can be used as components in exact sampling and inference schemes.
Ongoing work yields increasingly expressive flows on gauge fields, but it
remains an open question how flows can improve lattice QCD at state-of-the-art
scales. We discuss and demonstrate two applications of flows in replica
exchange (parallel tempering) sampling, aimed at improving topological mixing,
which are viable with iterative improvements upon presently available flows.


  The formalism of rainbow gravity is studied in a cosmological setting. We
consider the very early universe which is radiation dominated. A novel
treatment in our paper is to look for an ``averaged'' cosmological metric
probed by radiation particles themselves. Taking their cosmological evolution
into account, we derive the modified Friedmann-Robertson-Walker(FRW) equations
which is a generalization of the solution presented by Magueijo and Smolin.
Based on this phenomenological cosmological model we argue that the spacetime
curvature has an upper bound such that the cosmological singularity is absent.
These modified $FRW$ equations can be treated as effective equations in the
semi-classical framework of quantum gravity and its analogy with the one
recently proposed in loop quantum cosmology is also discussed.


  HPC environments have traditionally been designed to meet the compute demand
of scientific applications and data has only been a second order concern. With
science moving toward data-driven discoveries relying more on correlations in
data to form scientific hypotheses, the limitations of HPC approaches become
apparent: Architectural paradigms such as the separation of storage and compute
are not optimal for I/O intensive workloads (e.g. for data preparation,
transformation and SQL). While there are many powerful computational and
analytical libraries available on HPC (e.g. for scalable linear algebra), they
generally lack the usability and variety of analytical libraries found in other
environments (e.g. the Apache Hadoop ecosystem). Further, there is a lack of
abstractions that unify access to increasingly heterogeneous infrastructure
(HPC, Hadoop, clouds) and allow reasoning about performance trade-offs in this
complex environment. At the same time, the Hadoop ecosystem is evolving rapidly
and has established itself as de-facto standard for data-intensive workloads in
industry and is increasingly used to tackle scientific problems. In this paper,
we explore paths to interoperability between Hadoop and HPC, examine the
differences and challenges, such as the different architectural paradigms and
abstractions, and investigate ways to address them. We propose the extension of
the Pilot-Abstraction to Hadoop to serve as interoperability layer for
allocating and managing resources across different infrastructures. Further,
in-memory capabilities have been deployed to enhance the performance of
large-scale data analytics (e.g. iterative algorithms) for which the ability to
re-use data across iterations is critical. As memory naturally fits in with the
Pilot concept of retaining resources for a set of tasks, we propose the
extension of the Pilot-Abstraction to in-memory resources.


  Hole-doped high-temperature cuprate superconductors below optimum doping have
small electron-like Fermi surfaces occupying a small fraction of the Brillouin
zone. There is strong evidence that this is linked to charge density wave (CDW)
order, which reconstructs the large hole-like Fermi surfaces predicted by band
structure calculations . Recent experiments have revealed the structure of the
two CDW components in the benchmark bilayer material YBa$_2$Cu$_3$O$_{7-x}$ in
high field where quantum oscillation (QO) measurements are performed. We have
combined these results with a tight-binding description of the bands in an
isolated bilayer to give a minimal model revealing the essential physics of the
situation. Here we show that this approach, combined with the effects of
spin-orbit interactions and the pseudogap, gives a good qualitative description
of the multiple frequencies seen in the QO observations in this material.
Magnetic breakdown through weak CDW splitting of the bands will lead to a
field-dependence of the QO spectrum and to the observed fourfold symmetry of
the results in tilted fields.


  We quantified and calibrated the metallicity and temperature sensitivities of
colors derived from nine Wide Field Camera 3 (WFC3) filters aboard the Hubble
Space Telescope using Dartmouth isochrones and Kurucz atmospheres models. The
theoretical isochrone colors were tested and calibrated against observations of
five well studied galactic clusters: M92, NGC 6752, NGC 104, NGC 5927, and NGC
6791, all of which have spectroscopically determined metallicities spanning
-2.30 < [Fe/H] < +0.4. We found empirical corrections to the Dartmouth
isochrone grid for each of the following color magnitude diagrams (CMD)
(F555W--F814W, F814W), (F336W-F555W, F814W), (F390M-F555W, F814W) and
(F390W-F555W, F814W). Using the empirical corrections we tested the accuracy
and spread of the photometric metallicities assigned from CMDs and color-color
diagrams (which are necessary to break the age-metallicity degeneracy). Testing
three color-color diagrams [(F336W-F555W),(F390M-F555W),(F390W-F555W), vs
(F555W-F814W)], we found the colors (F390M-F555W) and (F390W-F555W), to be the
best suited to measure photometric metallicities. The color (F390W-F555W)
requires much less integration time, but generally produces wider metallicity
distributions, and, at very-low metallicity, the MDF from (F390W-F555W) is ~60%
wider than that from (F390M-F555W). Using the calibrated isochrones we
recovered the overall cluster metallicity to within ~0.1 dex in [Fe/H] when
using CMDs (i.e. when the distance, reddening and ages are approximately
known). The measured metallicity distribution function (MDF) from color-color
diagrams show this method measures metallicities of stellar clusters of unknown
age and metallicity with an accuracy of ~0.2 - 0.5 dex using F336W--F555W,
~0.15 - 0.25 dex using F390M-F555W, and ~0.2 - 0.4 dex with F390W-F555W, with
the larger uncertainty pertaining to the lowest metallicity range.


  We present predictions of the evolution of the light elements, Li, Be, and B,
in the early epochs of the Galactic halo, using a model of supernova-induced
chemical evolution based on contributions from supernovae (SNe) and cosmic rays
(CRs). The most important prediction from our model is that the abundances of
light elements in extremely metal-poor stars might be used as age indicators in
the very early stages of an evolving halo population, at times when metallicity
in most stars are dominated by local metal enrichment due to nearby SN events,
and is poorly correlated with age. Our results show that the best ``cosmic
clock'' is the $^6$Li abundance. We have derived relationships among various
cosmic-ray parameters. Although our model is successful for certain sets of
cosmic-ray parameters, larger energy should be absorbed by energetic particles
from each SN than required to the current situation of Galactic disk. We
discuss an alternative hypothesis of AGN activity in the early Galaxy as
another possible accelerator of CRs.


  We provide a model to study memory effects in quantum Gaussian channels with
additive classical noise over an arbitrary number of uses. The correlation
among different uses is introduced by contiguous two-mode interactions.
Numerical results for few modes are presented. They confirm the possibility to
enhance the classical information rate with the aid of entangled inputs, and
show a likely asymptotic behavior that should lead to the full capacity of the
channel.


  This project investigates numerical methods for solving fully coupled
forward-backward stochastic differential equations (FBSDEs) of McKean-Vlasov
type. Having numerical solvers for such mean field FBSDEs is of interest
because of the potential application of these equations to optimization
problems over a large population, say for instance mean field games (MFG) and
optimal mean field control problems. Theory for this kind of problems has met
with great success since the early works on mean field games by Lasry and
Lions, see \cite{Lasry_Lions}, and by Huang, Caines, and Malham\'{e}, see
\cite{Huang}. Generally speaking, the purpose is to understand the continuum
limit of optimizers or of equilibria (say in Nash sense) as the number of
underlying players tends to infinity. When approached from the probabilistic
viewpoint, solutions to these control problems (or games) can be described by
coupled mean field FBSDEs, meaning that the coefficients depend upon the own
marginal laws of the solution. In this note, we detail two methods for solving
such FBSDEs which we implement and apply to five benchmark problems. The first
method uses a tree structure to represent the pathwise laws of the solution,
whereas the second method uses a grid discretization to represent the time
marginal laws of the solutions. Both are based on a Picard scheme; importantly,
we combine each of them with a generic continuation method that permits to
extend the time horizon (or equivalently the coupling strength between the two
equations) for which the Picard iteration converges.


  Reconfigurable Intelligent Surfaces (RISs) are expected to play a crucial
role in reaching the key performance indicators (KPIs) for future 6G networks.
Their competitive edge over conventional technologies lies in their ability to
control the wireless environment propagation properties at will, thus
revolutionizing the traditional communication paradigm that perceives the
communication channel as an uncontrollable black box. As RISs transition from
research to market, practical deployment issues arise. Major roadblocks for
commercially viable RISs are i) the need for a fast and complex control channel
to adapt to the ever-changing wireless channel conditions, and ii) an extensive
grid to supply power to each deployed RIS. In this paper, we question the
established RIS practices and propose a novel RIS design combining
self-configuration and energy self-sufficiency capabilities. We analyze the
feasibility of devising fully-autonomous RISs that can be easily and seamlessly
installed throughout the environment, following the new Internet-of-Surfaces
(IoS) paradigm, requiring modifications neither to the deployed mobile network
nor to the power distribution system. In particular, we introduce ARES, an
Autonomous RIS with Energy harvesting and Self-configuration solution. ARES
achieves outstanding communication performance while demonstrating the
feasibility of energy harvesting (EH) for RISs power supply in future
deployments.


  Many physical situations are characterized by interfaces with a non trivial
shape so that relevant geometric features, such as interfacial area, curvature
or unit normal vector, can be used as main indicators of the topology of the
interface. We analyze the evolution equations for a set of geometrical
quantities that characterize the interface in two-phase flows. Several
analytical relations for the interfacial area density are reviewed and
presented, clarifying the physical significance of the different quantities
involved and specifying the hypotheses under which each transport equation is
valid. Moreover, evolution equations for the unit normal vector and for the
curvature are analyzed. The impact of different formulations is then assessed
in numerical simulations of rising bubble benchmarks.


  Text-to-3D generation has shown promising results, yet common challenges such
as the Multi-face Janus problem and extended generation time for high-quality
assets. In this paper, we address these issues by introducing a novel
three-stage training pipeline called GradeADreamer. This pipeline is capable of
producing high-quality assets with a total generation time of under 30 minutes
using only a single RTX 3090 GPU. Our proposed method employs a Multi-view
Diffusion Model, MVDream, to generate Gaussian Splats as a prior, followed by
refining geometry and texture using StableDiffusion. Experimental results
demonstrate that our approach significantly mitigates the Multi-face Janus
problem and achieves the highest average user preference ranking compared to
previous state-of-the-art methods. The project code is available at
https://github.com/trapoom555/GradeADreamer.


  The quasi-isotropic expansion for a simple two-fluid cosmological model,
including radiation and string gas is constructed. The first non-trivial order
expressions for the metric coefficients, energy densities and velocities are
explicitly written down. Their small and large time asymptotics are studied. It
is found that the large time asymptotic for the anisotropic component of the
metric coefficients grows faster than that of the isotropic
(trace-proportional) component.


  The discovery of new low-dimensional transition metal chalcogenides is
contributing to the already prosperous family of these materials. In this
study, needle-shaped single crystals of a new quasi-one-dimensional material
(Nb$_4$Se$_{15}$I$_2$)I$_2$ were grown by chemical vapor transport, and the
structure was solved by single crystal X-ray diffraction (XRD). The new
structure has one-dimensional (Nb$_4$Se$_{15}$I$_2$)$_n$ chains along the [101]
direction, with two I$^-$ ions per formula unit directly bonded to Nb$^{5+}$.
The other two I$^-$ ions are loosely coordinated and intercalate between the
chains. Individual chains are chiral, and stack along the $b$ axis in opposing
directions, giving space group $P2_1/c$. The phase purity and crystal structure
was verified by powder XRD. Density functional theory calculations show
(Nb$_4$Se$_{15}$I$_2$)I$_2$ to be a semiconductor with a direct band gap of
around 0.6 eV. Resistivity measurements of bulk crystals and micro-patterned
devices demonstrate that (Nb$_4$Se$_{15}$I$_2$)I$_2$ has an activation energy
of around 0.1 eV, and no anomaly or transition was seen upon cooling.
(Nb$_4$Se$_{15}$I$_2$)I$_2$ does not undergo structural phase transformation
from room temperature down to 8.2 K, based on cryogenic temperature single
crystal XRD. This compound represents a well-characterized and valence-precise
member of a diverse family of anisotropic transition metal chalcogenides.


  We prove the convergence of the density on the scale $Z^{-1}$ to the density
of the Bohr atom (with infinitely many electrons) (strong Scott conjecture) for
a model that is known to describe heavy atoms accurately.


  Frequent itemset mining leads to the discovery of associations and
correlations among items in large transactional databases. Apriori is a
classical frequent itemset mining algorithm, which employs iterative passes
over database combining with generation of candidate itemsets based on frequent
itemsets found at the previous iteration, and pruning of clearly infrequent
itemsets. The Dynamic Itemset Counting (DIC) algorithm is a variation of
Apriori, which tries to reduce the number of passes made over a transactional
database while keeping the number of itemsets counted in a pass relatively low.
In this paper, we address the problem of accelerating DIC on the Intel Xeon Phi
many-core system for the case when the transactional database fits in main
memory. Intel Xeon Phi provides a large number of small compute cores with
vector processing units. The paper presents a parallel implementation of DIC
based on OpenMP technology and thread-level parallelism. We exploit the
bit-based internal layout for transactions and itemsets. This technique reduces
the memory space for storing the transactional database, simplifies the support
count via logical bitwise operation, and allows for vectorization of such a
step. Experimental evaluation on the platforms of the Intel Xeon CPU and the
Intel Xeon Phi coprocessor with large synthetic and real databases showed good
performance and scalability of the proposed algorithm.


  When smartphone cameras are used to take photos of digital screens, usually
moire patterns result, severely degrading photo quality. In this paper, we
design a wavelet-based dual-branch network (WDNet) with a spatial attention
mechanism for image demoireing. Existing image restoration methods working in
the RGB domain have difficulty in distinguishing moire patterns from true scene
texture. Unlike these methods, our network removes moire patterns in the
wavelet domain to separate the frequencies of moire patterns from the image
content. The network combines dense convolution modules and dilated convolution
modules supporting large receptive fields. Extensive experiments demonstrate
the effectiveness of our method, and we further show that WDNet generalizes to
removing moire artifacts on non-screen images. Although designed for image
demoireing, WDNet has been applied to two other low-levelvision tasks,
outperforming state-of-the-art image deraining and derain-drop methods on the
Rain100h and Raindrop800 data sets, respectively.


  Yang-Baxter R operators symmetric with respect to the orthogonal and
symplectic algebras are considered in an uniform way. Explicit forms for the
spinorial and metaplectic R operators are obtained. L operators, obeying the
RLL relation with the orthogonal or symplectic fundamental R matrix, are
considered in the interesting cases, where their expansion in inverse powers of
the spectral parameter is truncated. Unlike the case of special linear algebra
symmetry the truncation results in additional conditions on the Lie algebra
generators of which the L operators is built and which can be fulfilled in
distinguished representations only. Further, generalised L operators, obeying
the modified RLL relation with the fundamental R matrix replaced by the
spinorial or metaplectic one, are considered in the particular case of linear
dependence on the spectral parameter. It is shown how by fusion with respect to
the spinorial or metaplectic representation these first order spinorial L
operators reproduce the ordinary L operators with second order truncation.


  In this paper we introduce and study a geometric heat flow to find Killing
vector fields on closed Riemannian manifolds with positive sectional curvature.
We study its various properties, prove the global existence of the solution of
this flow, discuss its convergence and possible applications, and its relation
to the Navier-Stokes equations on manifolds and Kazdan-Warner-Bourguignon-Ezin
identity for conformal Killing vector fields. We also provide two new
criterions on the existence of Killing vector fields. The similar flow to
finding holomorphic vector fields on K\"ahler manifolds will be studied in
\cite{LL2}.


  We determine which three-manifolds are dominated by products. The result is
that a closed, oriented, connected three-manifold is dominated by a product if
and only if it is finitely covered either by a product or by a connected sum of
copies of the product of the two-sphere and the circle. This characterization
can also be formulated in terms of Thurston geometries, or in terms of purely
algebraic properties of the fundamental group. We also determine which
three-manifolds are dominated by non-trivial circle bundles, and which
three-manifold groups are presentable by products.


  The attention mechanism has gained significant recognition in the field of
computer vision due to its ability to effectively enhance the performance of
deep neural networks. However, existing methods often struggle to effectively
utilize spatial information or, if they do, they come at the cost of reducing
channel dimensions or increasing the complexity of neural networks. In order to
address these limitations, this paper introduces an Efficient Local Attention
(ELA) method that achieves substantial performance improvements with a simple
structure. By analyzing the limitations of the Coordinate Attention method, we
identify the lack of generalization ability in Batch Normalization, the adverse
effects of dimension reduction on channel attention, and the complexity of
attention generation process. To overcome these challenges, we propose the
incorporation of 1D convolution and Group Normalization feature enhancement
techniques. This approach enables accurate localization of regions of interest
by efficiently encoding two 1D positional feature maps without the need for
dimension reduction, while allowing for a lightweight implementation. We
carefully design three hyperparameters in ELA, resulting in four different
versions: ELA-T, ELA-B, ELA-S, and ELA-L, to cater to the specific requirements
of different visual tasks such as image classification, object detection and
sementic segmentation. ELA can be seamlessly integrated into deep CNN networks
such as ResNet, MobileNet, and DeepLab. Extensive evaluations on the ImageNet,
MSCOCO, and Pascal VOC datasets demonstrate the superiority of the proposed ELA
module over current state-of-the-art methods in all three aforementioned visual
tasks.


  Based on experiments of the compaction of granular materials under periodic
shear of a packing of glass beads, a minimal model for the dynamics of the
packing density as a function of time is proposed. First, a random ``energy
landscape'' is created by a random walk (RW) in energy. Second, an ensemble of
RWs is performed for various temperatures in different temperature-time
sequences. We identify the minimum (mean) of the energy landscape with the
maximum (random) density. The temperature scaled by the step-size of the energy
landscape determines the dynamics of the system and can be regarded as the
agitation or shear amplitude. The model reproduces qualitatively both tapping
and shear experiments.
  {\bf Key-words}: Compaction, crystallization, Sinai-diffusion, random walks,
quenched disorder


  Multimodal recommender systems utilizing multimodal features (e.g., images
and textual descriptions) typically show better recommendation accuracy than
general recommendation models based solely on user-item interactions.
Generally, prior work fuses multimodal features into item ID embeddings to
enrich item representations, thus failing to capture the latent semantic
item-item structures. In this context, LATTICE proposes to learn the latent
structure between items explicitly and achieves state-of-the-art performance
for multimodal recommendations. However, we argue the latent graph structure
learning of LATTICE is both inefficient and unnecessary. Experimentally, we
demonstrate that freezing its item-item structure before training can also
achieve competitive performance. Based on this finding, we propose a simple yet
effective model, dubbed as FREEDOM, that FREEzes the item-item graph and
DenOises the user-item interaction graph simultaneously for Multimodal
recommendation. Theoretically, we examine the design of FREEDOM through a graph
spectral perspective and demonstrate that it possesses a tighter upper bound on
the graph spectrum. In denoising the user-item interaction graph, we devise a
degree-sensitive edge pruning method, which rejects possibly noisy edges with a
high probability when sampling the graph. We evaluate the proposed model on
three real-world datasets and show that FREEDOM can significantly outperform
current strongest baselines. Compared with LATTICE, FREEDOM achieves an average
improvement of 19.07% in recommendation accuracy while reducing its memory cost
up to 6$\times$ on large graphs. The source code is available at:
https://github.com/enoche/FREEDOM.