  Plasmodium vivax is one of the most geographically widespread malaria
parasites in the world due to its ability to remain dormant in the human liver
as hypnozoites and subsequently reactivate after the initial infection (i.e.
relapse infections). More than 80% of P. vivax infections are due to hypnozoite
reactivation. Mathematical modelling approaches have been widely applied to
understand P. vivax dynamics and predict the impact of intervention outcomes.
In this article, we provide a scoping review of mathematical models that
capture P. vivax transmission dynamics published between January 1988 and May
2023 to provide a comprehensive summary of the mathematical models and
techniques used to model P. vivax dynamics. We aim to assist researchers
working on P. vivax transmission and other aspects of P. vivax malaria by
highlighting best practices in currently published models and highlighting
where future model development is required. We provide an overview of the
different strategies used to incorporate the parasite's biology, use of
multiple scales (within-host and population-level), superinfection, immunity,
and treatment interventions. In most of the published literature, the rationale
for different modelling approaches was driven by the research question at hand.
Some models focus on the parasites' complicated biology, while others
incorporate simplified assumptions to avoid model complexity. Overall, the
existing literature on mathematical models for P. vivax encompasses various
aspects of the parasite's dynamics. We recommend that future research should
focus on refining how key aspects of P. vivax dynamics are modelled, including
spatial heterogeneity in exposure risk, the accumulation of hypnozoite
variation, the interaction between P. falciparum and P. vivax, acquisition of
immunity, and recovery under superinfection.


  Deep learning approaches for diffusion MRI have so far focused primarily on
voxel-based segmentation of lesions or white-matter fiber tracts. A drawback of
representing tracts as volumetric labels, rather than sets of streamlines, is
that it precludes point-wise analyses of microstructural or geometric features
along a tract. Traditional tractography pipelines, which do allow such
analyses, can benefit from detailed whole-brain segmentations to guide tract
reconstruction. Here, we introduce fast, deep learning-based segmentation of
170 anatomical regions directly on diffusion-weighted MR images, removing the
dependency of conventional segmentation methods on T 1-weighted images and slow
pre-processing pipelines. Working natively in diffusion space avoids non-linear
distortions and registration errors across modalities, as well as interpolation
artifacts. We demonstrate consistent segmentation results between 0 .70 and 0
.87 Dice depending on the tissue type. We investigate various combinations of
diffusion-derived inputs and show generalization across different numbers of
gradient directions. Finally, integrating our approach to provide anatomical
priors for tractography pipelines, such as TRACULA, removes hours of
pre-processing time and permits processing even in the absence of high-quality
T 1-weighted scans, without degrading the quality of the resulting tract
estimates.


  The Earth Trojans are co-orbitals librating around the Lagrange points $L_4$
or $L_5$ of the Sun-Earth system. Although many numerical studies suggest that
they can maintain their dynamical status and be stable on timescales up to a
few tens of thousands of years or even longer, they remain an elusive
population. Thus far only one transient member (2010 TK$_7$) has been
discovered serendipitously. Here, we present a dynamical study of asteroid 2020
XL$_5$. With our meticulous followup astrometric observations of the object, we
confirmed that it is a new Earth Trojan. However, its eccentric orbit brings it
close encounters with Venus on a frequent basis. Based on our N-body
integration, we found that the asteroid was captured into the current Earth
Trojan status in the 15th century, and then it has a likelihood of 99.5% to
leave the $L_4$ region within the next $\sim$10 kyr. Therefore, it is most
likely that 2020 XL$_5$ is dynamically unstable over this timescale.


  Policy Brief on "AstroInformatics, Recommendations for Global Collaboration",
distilled from panel discussions during S20 Policy Webinar on Astroinformatics
for Sustainable Development held on 6-7 July 2023.
  The deliberations encompassed a wide array of topics, including broad
astroinformatics, sky surveys, large-scale international initiatives, global
data repositories, space-related data, regional and international collaborative
efforts, as well as workforce development within the field. These discussions
comprehensively addressed the current status, notable achievements, and the
manifold challenges that the field of astroinformatics currently confronts.
  The G20 nations present a unique opportunity due to their abundant human and
technological capabilities, coupled with their widespread geographical
representation. Leveraging these strengths, significant strides can be made in
various domains. These include, but are not limited to, the advancement of STEM
education and workforce development, the promotion of equitable resource
utilization, and contributions to fields such as Earth Science and Climate
Science.
  We present a concise overview, followed by specific recommendations that
pertain to both ground-based and space data initiatives. Our team remains
readily available to furnish further elaboration on any of these proposals as
required. Furthermore, we anticipate further engagement during the upcoming G20
presidencies in Brazil (2024) and South Africa (2025) to ensure the continued
discussion and realization of these objectives.
  The policy webinar took place during the G20 presidency in India (2023).
Notes based on the seven panels will be separately published.


  Murray, Roberts and Wockel showed that there is no strict model of the string
2-group using the free loop group. Instead, they construct the next best thing,
a coherent model for the string 2-group using the free loop group, with
explicit formulas for all structure. Based on their expectations, we build a
category of 2-representations for coherent Lie 2-groups and some concrete
examples. We also discuss the relation between this category of
2-representations and the category of representations. In addition, we
construct a model of equivariant 2-vector bundles. At the end, we discuss the
adjoint action on the string 2-representations.


  We propose a new testing framework applicable to both the two-sample problem
on point processes and the community detection problem on rectangular arrays of
point processes, which we refer to as longitudinal networks; the latter problem
is useful in situations where we observe interactions among a group of
individuals over time. Our framework is based on a multiscale discretization
scheme that consider not just the global null but also a collection of nulls
local to small regions in the domain; in the two-sample problem, the local
rejections tell us where the intensity functions differ and in the longitudinal
network problem, the local rejections tell us when the community structure is
most salient. We provide theoretical analysis for the two-sample problem and
show that our method has minimax optimal power under a Holder continuity
condition. We provide extensive simulation and real data analysis demonstrating
the practicality of our proposed method.


  The notion of super weak compactness for subsets of Banach spaces is a
strengthening of the weak compactness that can be described as a local version
of super-reflexivity. A recent result of K. Tu which establishes that the
closed convex hull of a super weakly compact set is super weakly compact has
removed the main obstacle to further development of the theory. In this paper
we provide a variety of results around super weak compactness in order to show
the great scope of this notion. We also give non linear characterizations of
super weak compactness in terms of the (non) embeddability of special trees and
graphs. We conclude with a few relevant examples of super weakly compact sets
in non super-reflexive Banach spaces.


  We prove a pro-$p$ version of Sela's theorem stating that a finitely
generated group is $k$-acylindrically accessible. This result is then used to
prove that $\mathrm{PD}^n$ pro-$p$ groups admit a unique $k$-acylindrical
JSJ-decomposition.


  Very fast variability on scales of minutes is regularly observed in Blazars.
The assumption that these flares are emerging from the dominant emission zone
of the very high energy (VHE) radiation within the jet challenges current
acceleration and radiation models. In this work we use a spatially resolved and
time dependent synchrotron-self-Compton (SSC) model that includes the full time
dependence of Fermi-I acceleration. We use the (apparent) orphan $\gamma$-ray
flare of \textit{Mrk501} during MJD 54952 and test various flare scenarios
against the observed data. We find that a rapidly variable external radiation
field can reproduce the high energy lightcurve best. However, the effect of the
strong inverse Compton (IC) cooling on other bands and the X-ray observations
are constraining the parameters to rather extreme ranges. Then again other
scenarios would require parameters even more extreme or stronger physical
constraints on the rise and decay of the source of the variability which might
be in contradiction with constraints derived from the size of the black hole's
ergosphere.


  The SNO+ neutrino detector is an acrylic sphere of radius 6 m filled with
liquid scintillator, immersed in a water-filled underground cavern, with a thin
vertical neck (radius 0.75 m) extending upwards about 7 m from the sphere to a
purified nitrogen cover gas. To explain a period of unexpected motion of the
scintillator, time-dependent flow simulations have been performed using
OpenFoam. It appears that the motion, inferred from subsequent 24 h-averaged
patterns of transient $^{222}\mathrm{Rn}$ contamination introduced during
earlier recirculation of scintillator, can be explained as owing to heat
transfer through the detector wall that induced buoyant flow in a thin wall
boundary layer. This mechanism can result in transport of contaminant, should
it be introduced, down the neck to the sphere on a time scale of several hours.
If the scintillator happens to be thermally stratified, the same forcing
produces internal gravity waves in the spherical flow domain, at the
Brunt-V\"{a}is\"{a}l\"{a} frequency. Nevertheless, oscillatory motion being by
its nature non-diffusive, simulations confirm that imposing strong thermal
stratification over the depth of the neck can mitigate mixing due to transient
heat fluxes.


  Urban planning is increasingly data driven, yet the challenge of designing
with data at a city scale and remaining sensitive to the impact at a human
scale is as important today as it was for Jane Jacobs. We address this
challenge with Urban Mosaic,a tool for exploring the urban fabric through a
spatially and temporally dense data set of 7.7 million street-level images from
New York City, captured over the period of a year. Working in collaboration
with professional practitioners, we use Urban Mosaic to investigate questions
of accessibility and mobility, and preservation and retrofitting. In doing so,
we demonstrate how tools such as this might provide a bridge between the city
and the street, by supporting activities such as visual comparison of
geographically distant neighborhoods,and temporal analysis of unfolding urban
development.


  This paper demonstrates sufficient conditions for the existence of KAM tori
in a singly thermostated, integrable hamiltonian system with $n$ degrees of
freedom with a focus on the generalized, variable-mass thermostats of order
2--which include the Nos\'e thermostat, the logistic thermostat of Tapias,
Bravetti and Sanders, and the Winkler thermostat. It extends Theorem 3.2 of
Legoll, Luskin & Moeckel, (Non-ergodicity of Nos\'e-Hoover dynamics,
Nonlinearity, 22 (2009), pp. 1673--1694) to prove that a "typical" singly
thermostated, integrable, real-analytic hamiltonian possesses a
positive-measure set of invariant tori when the thermostat is weakly coupled.
It also demonstrates a class of integrable hamiltonians, which, for a
full-measure set of couplings, satisfies the same conclusion.


  A Yang-Mills theory linear in the scalar curvature for 2d gravity with
symmetry generated by the semidirect product formed with the Lie derivative of
the algebra of diffeomorphisms with the two-dimensional Abelian algebra is
formulated. As compared with dilaton models, the role of the dilaton is played
by the dual field strength of a $U(1)$ gauge field. All vacuum solutions are
found. They are either black holes or have constant scalar curvature. Those
with constant scalar curvature have constant dual field strength. In
particular, solutions with vanishing cosmological constant but nonzero scalar
curvature exist. In the conformal-Lorenz gauge, the model has a CFT
interpretation whose residual symmetry combines holomorphic diffeomorphisms
with a subclass of U(1) gauge transformations while preserving dS2 and AdS2
boundary conditions. This is the same symmetry as in Jackiw-Teitelboim-Maxwell
gravity considered by Hartman and Strominger. It is argued that this is the
only nontrivial Yang-Mills model linear in the scalar curvature that exists for
real Lie algebras of dimension four.


  We summarize how the approach to the black-disk regime (BDR) of strong
interactions at TeV energies influences rapidity gap survival in exclusive hard
diffraction pp -> p + H + p (H = dijet, Qbar-Q, Higgs). Employing a recently
developed partonic description of such processes, we discuss (a) the
suppression of diffraction at small impact parameters by soft spectator
interactions in the BDR; (b) further suppression by inelastic interactions of
hard spectator partons in the BDR; (c) correlations between hard and soft
interactions. Hard spectator interactions substantially reduce the rapidity gap
survival probability at LHC energies compared to previously reported estimates.


  The state space of an operator system of $n$-by-$n$ matrices has, in a sense,
many normal cones. Merely this convex geometrical property implies smoothness
qualities and a clustering property of exposed faces. The latter holds since
each exposed face is an intersection of maximal exposed faces. An isomorphism
translates these results to the lattice of ground state projections of the
operator system. We work on minimizing the assumptions under which a convex set
has the mentioned properties.


  We consider an action of the automorphism group $\mathrm{Aut}(F_n)$ of the
free group $F_n$ of rank $n$ on the filtered vector space $A_d(n)$ of Jacobi
diagrams of degree $d$ on $n$ oriented arcs. This action induces on the
associated graded vector space of $A_d(n)$, which is identified with the space
$B_d(n)$ of open Jacobi diagrams, an action of the general linear group
$\mathrm{GL}(n,Z)$ and an action of the graded Lie algebra of the
IA-automorphism group of $F_n$ associated with its lower central series. We use
these actions on $B_d(n)$ to study the $\mathrm{Aut}(F_n)$-module structure of
$A_d(n)$. In particular, we consider the case where $d=2$ in detail and give an
indecomposable decomposition of $A_2(n)$. We also construct a polynomial
functor $A_d$ of degree $2d$ from the opposite category of the category of
finitely generated free groups to the category of filtered vector spaces, which
includes the $\mathrm{Aut}(F_n)$-module structure of $A_d(n)$ for all $n\geq
0$.


  Deep learning models are the state-of-the-art methods for semantic point
cloud segmentation, the success of which relies on the availability of
large-scale annotated datasets. However, it can be extremely time-consuming and
prohibitively expensive to compile such datasets. In this work, we propose an
active learning approach to maximize model performance given limited annotation
budgets. We investigate the appropriate sample granularity for active selection
under realistic annotation cost measurement (clicks), and demonstrate that
super-point based selection allows for more efficient usage of the limited
budget compared to point-level and instance-level selection. We further exploit
local consistency constraints to boost the performance of the super-point based
approach. We evaluate our methods on two benchmarking datasets (ShapeNet and
S3DIS) and the results demonstrate that active learning is an effective
strategy to address the high annotation costs in semantic point cloud
segmentation.


  We apply the method of Lyapunov-Schmidt reduction to study large
area-constrained Willmore surfaces in Riemannian 3-manifolds asymptotic to
Schwarzschild. In particular, we prove that the end of such a manifold is
foliated by distinguished area-constrained Willmore spheres. The leaves are the
unique area-constrained Willmore spheres with large area, non-negative Hawking
mass, and distance to the center of the manifold at least a small multiple of
the area radius. Unlike previous related work, we only require that the scalar
curvature satisfies mild asymptotic conditions. We also give explicit examples
to show that these conditions on the scalar curvature are necessary.


  The cell motility problem has been investigated for a long time. Today, many
biologists, physicists, and mathematicians are looking for new research
instruments for this process. A simple 2D model of a free-boundary cell moving
on a homogeneous isotropic surface is presented in the paper. It describes the
dynamics of the complex actomyosin liquid, whose special properties influence
the boundary dynamics and cell motility. The model consists of a system of
equations with the free boundary domain and contains a non-local term. In this
work, we present a numerical solution of this problem.


  We study the relation between the directed polymer and the directed
percolation models, for the case of a disordered energy landscape where the
energies are taken from bimodal distribution. We find that at the critical
concentration of the directed percolation, the directed polymer undergoes a
transition from the directed polymer universality class to the directed
percolation universality class. We also find that directed percolation clusters
affect the characterisrics of the directed polymer below the critical
concentration.


  We use inelastic neutron scattering to demonstrate that at low temperatures,
the low frequency magnetic fluctuations in YBa_2Cu_3O_{6.6} ($T_c=62.7$ K) are
incommensurate, being found at positions displaced by $\pm\delta$ ($0.057\pm
0.006$ r.l.u.) along the $[\pi,\pi]$ direction from the wave vector $(\pi,\pi)$
associated with the antiferromagnetic order of the parent insulator,
YBa_2Cu_3O_{6}. The dynamical susceptibility $\chi''(q,\omega)$ at the
incommensurate positions increases on cooling below $T_c$, accompanied by a
suppression of magnetic fluctuations at the commensurate points.


  A series of self-consistent, three-dimensional continuum radiative transfer
models are constructed of the pre-protostellar core L1544, with the results
compared with existing SCUBA and ISO data. The source is well-fit by a prolate
spheroid, having an ellipsoidal power-law density distribution of index m ~ 2
(1.75 < m < 2.25) in to at least r ~ 1600AU. For r<1600 AU, the data are
consistent with either an extension of the power law to smaller radii, or a
flattened (Bonner-Ebert like) density distribtion. We can further constrain the
optical depth along the short axis at 1300um to be ~ 5e-3, the central
luminosity to be L < 1e-3 solar luminosities, the long axis diameter D ~ 0.1
pc, the axis ratio to be q ~ 2, and the external ISRF to be similar to that
defined by Mathis, Mezger, & Panagia (1983) to within 50 per cent. The outer
diameter and axis ratio may each be somewhat larger due to potential on-source
chopping in the observations, and the projection of the long axis onto the
plane of the sky. While these results are similar to those inferred directly
from observations or spherical modeling due to the source transparency at
submillimeter wavelengths, we infer a smaller size, lower mass, and higher
optical depth / column density, exposed to a stronger external radiation field
than previously assumed. Finally, we find that both the spectral energy
distribution (SED) and surface brightness distribution are necessary to
constrain the source properties in this way.


  In this paper, we introduce a criterion for maximal operators associated with
Fourier multipliers to be bounded on $L^p(\mathbb{R}^d)$. Noteworthy examples
satisfying the criterion are multipliers of the Mikhlin type or limited decay
which are not necessarily radial. To do so, we make use of modified square
function estimates and bilinear interpolation. In result, we obtain convergence
results for fractional half-wave equations and surface averages as well as the
$L^p$ boundedness for the maximal operators.


  We introduce the two substructural propositional logics KL, KL+, which use
disjunction, fusion and a unary, (quasi-)exponential connective. For both we
prove strong completeness with respect to the interpretation in Kleene algebras
and a variant thereof. We also prove strong completeness for language models,
where each logic comes with a different interpretation. We show that for both
logics the cut rule is admissible and both have a decidable consequence
relation.


  In this paper we introduce two new ways to split ramification of Brauer
classes on surfaces using stacks. Each splitting method gives rise to a new
moduli space of twisted stacky vector bundles. By studying the structure of
these spaces we prove new results on the standard period-index conjecture. The
first yields new bounds on the period-index relation for classes on curves over
higher local fields, while the second can be used to relate the Hasse principle
for forms of moduli spaces of stable vector bundles on pointed curves over
global fields to the period-index problem for Brauer groups of arithmetic
surfaces. We include an appendix by Daniel Krashen showing that the local
period-index bounds are sharp.


  In this note we prove that the ball is a maximiser of some Schatten $p$-norms
of the Riesz potential operators among all domains of a given measure in
$\mathbb R^{d}$. In particular, the result is valid for the polyharmonic Newton
potential operator, which is related to a nonlocal boundary value problem for
the poly-Laplacian extending the one considered by M. Kac in the case of the
Laplacian, so we obtain and isoperimetric inequalities for its eigenvalues as
well, namely, analogues of Rayleigh-Faber-Krahn and Hong-Krahn-Szeg\"o
inequalities.


  All information about primary cosmic rays above the knee has been obtained
from results of EAS investigations. At that, two alternative approaches exist:
cosmophysical and nuclear physical. In the frame of the first one, all changes
in measured EAS characteristics are explained by the changes in energy spectrum
and mass composition of primary cosmic rays. In this paper, the second approach
is considered, in frame of which corresponding changes in EAS parameters are
explained by changes of interaction model above the knee. Some experimental
possibilities of proof of the correctness of the nuclear physical approach are
considered.


  Let $H_n$ be the linear heptagonal networks with $2n$ heptagons. We study the
structure properties and the eigenvalues of the linear heptagonal networks.
According to the Laplacian polynomial of $H_n$, we utilize the decomposition
theorem. Thus, the Laplacian spectrum of $H_n$ is created by eigenvalues of a
pair of matrices: $L_A$ and $L_S$ of order number $5n+1$ and $4n+1$,
respectively. On the basis of the roots and coefficients of their
characteristic polynomials of $L_A$ and $L_S$, we not only get the explicit
forms of Kirchhoff index, but also corresponding total complexity of $H_n$.


  Motivated by the growing interest in mobile systems, we study the dynamics of
information dissemination between agents moving independently on a plane.
Formally, we consider $k$ mobile agents performing independent random walks on
an $n$-node grid. At time $0$, each agent is located at a random node of the
grid and one agent has a rumor. The spread of the rumor is governed by a
dynamic communication graph process ${G_t(r) | t \geq 0}$, where two agents are
connected by an edge in $G_t(r)$ iff their distance at time $t$ is within their
transmission radius $r$. Modeling the physical reality that the speed of radio
transmission is much faster than the motion of the agents, we assume that the
rumor can travel throughout a connected component of $G_t$ before the graph is
altered by the motion. We study the broadcast time $T_B$ of the system, which
is the time it takes for all agents to know the rumor. We focus on the sparse
case (below the percolation point $r_c \approx \sqrt{n/k}$) where, with high
probability, no connected component in $G_t$ has more than a logarithmic number
of agents and the broadcast time is dominated by the time it takes for many
independent random walks to meet each other. Quite surprisingly, we show that
for a system below the percolation point the broadcast time does not depend on
the relation between the mobility speed and the transmission radius. In fact,
we prove that $T_B = \tilde{O}(n / \sqrt{k})$ for any $0 \leq r < r_c$, even
when the transmission range is significantly larger than the mobility range in
one step, giving a tight characterization up to logarithmic factors. Our result
complements a recent result of Peres et al. (SODA 2011) who showed that above
the percolation point the broadcast time is polylogarithmic in $k$.


  We review the recently proposed Trans-Planckian Censorship Conjecture that
stems from the Trans-Planckian problem of cosmological perturbations. We
analyze the implications and constraints that TCC introduces in different
frameworks of viable inflation. We revisit the case of slow-roll scalar field
inflation and we investigate the cases of slow-roll $f(R)$ and
$f(R,\phi)$-gravity. Finally, we consider the conjecture in the context of
constant-roll scalar field inflation.


  Q-exchangeable ergodic distributions on the infinite symmetric group were
classified by Gnedin-Olshanski (2012). In this paper, we study a specific
linear combination of the ergodic measures and call it the Mallows product
measure. From a particle system perspective, the Mallows product measure is a
reversible stationary blocking measure of the infinite-species ASEP and it is a
natural multi-species extension of the Bernoulli product blocking measures of
the one-species ASEP. Moreover, the Mallows product measure can be viewed as
the universal product blocking measure of interacting particle systems coming
from random walks on Hecke algebras.
  For the random infinite permutation distributed according to the Mallows
product measure we have computed the joint distribution of its neighboring
displacements, as well as several other observables. The key feature of the
obtained formulas is their remarkably simple product structure. We project
these formulas to ASEP with finitely many species, which in particular recovers
a recent result of Adams-Balazs-Jay, and also to ASEP(q,M).
  Our main tools are results of Gnedin-Olshanski about ergodic Mallows measures
and shift-invariance symmetries of the stochastic colored six vertex model
discovered by Borodin-Gorin-Wheeler and Galashin.


  he ethical implications of algorithmic systems have been much discussed in
both HCI and the broader community of those interested in technology design,
development and policy. In this paper, we explore the application of one
prominent ethical framework - Fairness, Accountability, and Transparency - to a
proposed algorithm that resolves various societal issues around food security
and population ageing. Using various standardised forms of algorithmic audit
and evaluation, we drastically increase the algorithm's adherence to the FAT
framework, resulting in a more ethical and beneficent system. We discuss how
this might serve as a guide to other researchers or practitioners looking to
ensure better ethical outcomes from algorithmic systems in their line of work.


  In this paper, we present a method for unconstrained end-to-end head pose
estimation. We address the problem of ambiguous rotation labels by introducing
the rotation matrix formalism for our ground truth data and propose a
continuous 6D rotation matrix representation for efficient and robust direct
regression. This way, our method can learn the full rotation appearance which
is contrary to previous approaches that restrict the pose prediction to a
narrow-angle for satisfactory results. In addition, we propose a geodesic
distance-based loss to penalize our network with respect to the SO(3) manifold
geometry. Experiments on the public AFLW2000 and BIWI datasets demonstrate that
our proposed method significantly outperforms other state-of-the-art methods by
up to 20\%. We open-source our training and testing code along with our
pre-trained models: https://github.com/thohemp/6DRepNet.


  Large scale machine learning (ML) systems such as the Alexa automatic speech
recognition (ASR) system continue to improve with increasing amounts of
manually transcribed training data. Instead of scaling manual transcription to
impractical levels, we utilize semi-supervised learning (SSL) to learn acoustic
models (AM) from the vast firehose of untranscribed audio data. Learning an AM
from 1 Million hours of audio presents unique ML and system design challenges.
We present the design and evaluation of a highly scalable and resource
efficient SSL system for AM. Employing the student/teacher learning paradigm,
we focus on the student learning subsystem: a scalable and robust data pipeline
that generates features and targets from raw audio, and an efficient model
pipeline, including the distributed trainer, that builds a student model. Our
evaluations show that, even without extensive hyper-parameter tuning, we obtain
relative accuracy improvements in the 10 to 20$\%$ range, with higher gains in
noisier conditions. The end-to-end processing time of this SSL system was 12
days, and several components in this system can trivially scale linearly with
more compute resources.


  The vast majority of textual content is unstructured, making automated
classification an important task for many applications. The goal of text
classification is to automatically classify text documents into one or more
predefined categories. Recently proposed simple architectures for text
classification such as Convolutional Neural Networks for Sentence
Classification by Kim, Yoon showed promising results. In this paper, we propose
incorporating an attention mechanism into the network to boost its performance,
we also propose WordRank for vocabulary selection to reduce the network
embedding parameters and speed up training with minimum accuracy loss. By
adopting the proposed ideas TextCNN accuracy on 20News increased from 94.79 to
96.88, moreover, the number of parameters for the embedding layer can be
reduced substantially with little accuracy loss by using WordRank. By using
WordRank for vocabulary selection we can reduce the number of parameters by
more than 5x from 7.9M to 1.5M, and the accuracy will only decrease by 1.2%.


  We have derived Fe abundances of 16 solar-type Pleiades dwarfs by means of an
equivalent width analysis of Fe I and Fe II lines in high-resolution spectra
obtained with the Hobby - Eberly Telescope and High Resolution Spectrograph.
Abundances derived from Fe II lines are larger than those derived from Fe I
lines (herein referred to as over-ionization) for stars with Teff < 5400 K, and
the discrepancy (deltaFe = [Fe II/H] - [Fe I/H]) increases dramatically with
decreasing Teff, reaching over 0.8 dex for the coolest stars of our sample. The
Pleiades joins the open clusters M 34, the Hyades, IC 2602, and IC 2391, and
the Ursa Major moving group, demonstrating ostensible over-ionization trends.
The Pleiades deltaFe abundances are correlated with Ca II infrared triplet and
Halpha chromospheric emission indicators and relative differences therein.
Oxygen abundances of our Pleiades sample derived from the high-excitation O I
triplet have been previously shown to increase with decreasing Teff, and a
comparison with the deltaFe abundances suggests that the over-excitation
(larger abundances derived from high excitation lines relative to low
excitation lines) and over-ionization effects that have been observed in cool
open cluster and disk field main sequence (MS) dwarfs share a common origin.
Star-to-star Fe I abundances have low internal scatter, but the abundances of
stars with Teff < 5400 K are systematically higher compared to the warmer
stars. The cool star [Fe I/H] abundances cannot be connected directly to
over-excitation effects, but similarities with the deltaFe and O I triplet
trends suggest the abundances are dubious. Using the [Fe I/H] abundances of
five stars with Teff > 5400 K, we derive a mean Pleiades cluster metallicity of
[Fe/H] = +0.01 +/- 0.02.


  We discuss some special property of the Farey sequence. We show in each term
of the Farey sequence, ratio of the sum of elements in the denominator and the
sum of elements in the numerator is exactly two. We also show that the Farey
sequence contains a palindromic structure.


  Non-Orthogonal Multiple Access (NOMA) and Fog Radio Access Networks (FRAN)
are promising candidates within the 5G and beyond systems. This work examines
the benefit of adopting NOMA in an FRAN architecture with constrained capacity
fronthaul. The paper proposes methods for optimizing joint scheduling and power
adaptation in the downlink of a NOMA-based FRAN with multiple resource blocks
(RB). We consider a mixed-integer optimization problem which maximizes a
network-wide rate-based utility function subject to fronthaul-capacity
constraints, so as to determine i) the user-to-RB assignment, ii) the allocated
power to each RB, and iii) the power split levels of the NOMA users in each RB.
The paper proposes a feasible decoupled solution for such non-convex
optimization problem using a three-step hybrid centralized/distributed
approach. The proposed solution complies with FRAN operation that aims to
partially shift the network control to the FAPs, so as to overcome delays due
to fronthaul rate constraints. The paper proposes and compares two distinct
methods for solving the assignment problem, namely the Hungarian method, and
the Multiple Choice Knapsack method. The power allocation and the NOMA power
split optimization, on the other hand, are solved using the alternating
direction method of multipliers (ADMM). Simulations results illustrate the
advantages of the proposed methods compared to different baseline schemes
including the conventional Orthogonal Multiple Access (OMA), for different
utility functions and different network environments.


  Recently, a new two-dimensional carbon allotrope, named biphenylene network
(BPN) was experimentally realized. The BPN structure is composed of four-,
six-, and eight-membered rings of sp$^2$-hybridized carbon atoms. In this work,
we carried out fully-atomistic reactive (ReaxFF) molecular dynamics simulations
to study the thermomechanical properties and fracture patterns of non-defective
and defective (nanocracks) BPN. Our results show that under uniaxial tensile
loading, BPN is converted into four distinct morphologies before fracture
starts. This conversion process is dependent on the stretching direction. Some
of the formed structures are mainly formed by eight-membered rings, which have
different shapes in each morphology. In one of them, a graphitization process
was observed before the complete fracture. Importantly, in the presence of
nanocracks, no new morphologies are formed. BPN exhibits a distinct fracture
process when contrasted to graphene. After the critical strain threshold, the
graphene transitions from an elastic to a brittle regime, while BPN can exhibit
different inelastic stages. These stages are associated with the appearance of
new morphologies. However, BPN shares some of the exceptional graphene
properties. Its calculated Young's modulus and melting point values are
comparable to the graphene ones, about 1019.4 GPa and 4024K, respectively.


  We investigate the question: if an AI agent is known to be safe in one
setting, is it also safe in a new setting similar to the first? This is a core
question of AI alignment--we train and test models in a certain environment,
but deploy them in another, and we need to guarantee that models that seem safe
in testing remain so in deployment. Our notion of safety is based on
power-seeking--an agent which seeks power is not safe. In particular, we focus
on a crucial type of power-seeking: resisting shutdown. We model agents as
policies for Markov decision processes, and show (in two cases of interest)
that not resisting shutdown is "stable": if an MDP has certain policies which
don't avoid shutdown, the corresponding policies for a similar MDP also don't
avoid shutdown. We also show that there are natural cases where safety is _not_
stable--arbitrarily small perturbations may result in policies which never shut
down. In our first case of interest--near-optimal policies--we use a
bisimulation metric on MDPs to prove that small perturbations won't make the
agent take longer to shut down. Our second case of interest is policies for
MDPs satisfying certain constraints which hold for various models (including
language models). Here, we demonstrate a quantitative bound on how fast the
probability of not shutting down can increase: by defining a metric on MDPs;
proving that the probability of not shutting down, as a function on MDPs, is
lower semicontinuous; and bounding how quickly this function decreases.


  We consider the 0-1 Penalized Knapsack Problem (PKP). Each item has a profit,
a weight and a penalty and the goal is to maximize the sum of the profits minus
the greatest penalty value of the items included in a solution. We propose an
exact approach relying on a procedure which narrows the relevant range of
penalties, on the identification of a core problem and on dynamic programming.
The proposed approach turns out to be very effective in solving hard instances
of PKP and compares favorably both to commercial solver CPLEX 12.5 applied to
the ILP formulation of the problem and to the best available exact algorithm in
the literature. Then we present a general inapproximability result and
investigate several relevant special cases which permit fully polynomial time
approximation schemes (FPTASs).


  We extend some rate of convergence results of greedy quantization sequences
already investigated in arXiv:1409.0732 [math.PR]. We show, for a more general
class of distributions satisfying a certain control, that the quantization
error of these sequences have an $n^{-\frac1d}$ rate of convergence and that
the distortion mismatch property is satisfied. We will give some non-asymptotic
Pierce type estimates. The recursive character of greedy vector quantization
allows some improvements to the algorithm of computation of these sequences and
the implementation of a recursive formula to quantization-based numerical
integration. Furthermore, we establish further properties of sub-optimality of
greedy quantization sequences.


  The Hipparcos mission (1989-1993) resulted in the first space-based stellar
catalogue including measurements of positions, parallaxes and annual proper
motions accurate to about one milli-arcsecond. More space astrometry missions
will follow in the near future. The ultra-small Japanese mission Nano-JASMINE
(launch in late 2013) will determine positions and annual proper motions with
some milli-arcsecond accuracy. In mid 2013 the next-generation ESA mission Gaia
will deliver some tens of micro-arcsecond accurate astrometric parameters.
Until the final Gaia catalogue is published in early 2020 the best way of
improving proper motion values is the combination of positions from different
missions separated by long time intervals. Rather than comparing positions from
separately reduced catalogues, we propose an optimal method to combine the
information from the different data sets by making a joint astrometric
solution. This allows to obtain good results even when each data set alone is
insufficient for an accurate reduction. We demonstrate our method by combining
Hipparcos and simulated Nano-JASMINE data in a joint solution. We show a
significant improvement over the conventional catalogue combination.


  In [Math. Proc. Cambridge Philos. Soc. 64 (1968), 251-264], P.M. Cohn
famously claimed that a commutative domain is atomic if and only if it
satisfies the ascending chain condition on principal ideals (ACCP). Some years
later, a counterexample was provided by A. Grams in [Math. Proc. Cambridge
Philos. Soc. 75 (1974), 321-329]: Every commutative domain with the ACCP is
atomic, but not vice versa. This has led to the question of finding a sensible
(ideal-theoretic) characterization of atomicity.
  The question (explicitly stated on p. 3 of A. Geroldinger and F.
Halter-Koch's 2006 monograph on factorization) is still open. We settle it
using the language of monoids and preorders.


  An attempt is made to present the contribution of the scalar unparticle on
the Z-production cross-section at International Linear Colliders (ILC) with
polarized initial beams in the Randall-Sundrum model. The cross-sections depend
strongly on the polarization of $e^{-}$, $e^{+}$ initial beams, the center of
mass energy $\sqrt{s} $, the scaling dimension $d_{U}$ of the unparticle
operator $\mathcal{O}_{U}$ and the energy scale $\Lambda_{U}$. The results
indicate that with the effect of the scalar propagators in the s-channel,
including radion, Higgs and scalar unparticle, the cross-section for the ZZ
production is enhanced and larger than that in the Standard model under the
same conditions.


  Managing the dynamic regions in the photometric loss formulation has been a
main issue for handling the self-supervised depth estimation problem. Most
previous methods have alleviated this issue by removing the dynamic regions in
the photometric loss formulation based on the masks estimated from another
module, making it difficult to fully utilize the training images. In this
paper, to handle this problem, we propose an isometric self-sample-based
learning (ISSL) method to fully utilize the training images in a simple yet
effective way. The proposed method provides additional supervision during
training using self-generated images that comply with pure static scene
assumption. Specifically, the isometric self-sample generator synthesizes
self-samples for each training image by applying random rigid transformations
on the estimated depth. Thus both the generated self-samples and the
corresponding training image always follow the static scene assumption. We show
that plugging our ISSL module into several existing models consistently
improves the performance by a large margin. In addition, it also boosts the
depth accuracy over different types of scene, i.e., outdoor scenes (KITTI and
Make3D) and indoor scene (NYUv2), validating its high effectiveness.


  This paper develops and analyzes a fully discrete finite element method for a
class of semilinear stochastic partial differential equations (SPDEs) with
multiplicative noise. The nonlinearity in the diffusion term of the SPDEs is
assumed to be globally Lipschitz and the nonlinearity in the drift term is only
assumed to satisfy a one-side Lipschitz condition. The semilinear SPDEs
considered in this paper is a direct generalization of the SODEs considered in
[13]. There are several difficulties which need to be overcome for this
generalization. First, obviously the spatial discretization, which does not
appear in the SODE case, adds an extra layer of difficulty. It turns out a
special discretization must be designed to guarantee certain properties for the
numerical scheme and its stiffness matrix. In this paper we use a finite
element interpolation technique to discretize the nonlinear drift term. Second,
in order to prove the strong convergence of the proposed fully discrete finite
element method, stability estimates for higher order moments of the
$H^1$-seminorm of the numerical solution must be established, which are
difficult and delicate. A judicious combination of the properties of the drift
and diffusion terms and a nontrivial technique borrowed from [16] is used in
this paper to achieve the goal. Finally, stability estimates for the second and
higher order moments of the $L^2$-norm of the numerical solution is also
difficult to obtain due to the fact that the mass matrix may not be diagonally
dominant. This is done by utilizing the interpolation theory and the higher
moment estimates for the $H^1$-seminorm of the numerical solution. After
overcoming these difficulties, it is proved that the proposed fully discrete
finite element method is convergent in strong norms with nearly optimal rates
of convergence.


  We present a study of the structural properties and metallicity distribution
of the nearby peculiar galaxy NGC3077. Using data from our survey of the M81
Group with the Hyper Suprime-Cam on the Subaru Telescope, we construct deep
color-magnitude diagrams that are used to probe the old red giant branch
population of NGC3077. We map these stars out to and beyond the nominal tidal
radius, which allows us to derive the structural properties and stellar content
of the peripheral regions. We show that NGC3077 has an extended stellar halo
and pronounced ``S-shaped" tidal tails that diverge from the radial profile of
the inner region. The average metallicity of the old population in NGC3077 is
estimated from individual RGBs to be $\rm{[M/H]}=-0.98 \pm 0.26$, which
decreases with the distance from the galaxy center as $\rm{[M/H]}=-0.17$ dex
$\rm{R_{h}}^{-1}$. The metallicity of the S-shaped structure is similar to that
of the regions lying at $r\sim4\times\rm{R_{h}} (\sim 30$~kpc), indicating that
the stellar constituents of the tidal tails have come from the outer envelope
of NGC3077. These results suggest that this peculiar galaxy was probably a
rather normal dwarf elliptical galaxy before the tidal interaction with M81 and
M82. We also examine the evidence in our dataset for the six recently-reported
ultra-faint dwarf candidates around NGC3077. We recover a spatial overdensity
of sources coinciding with only one of these.


  Online Social Networks (OSN) are among the most popular applications in
today's Internet. Decentralized online social networks (DOSNs), a special class
of OSNs, promise better privacy and autonomy than traditional centralized OSNs.
However, ensuring availability of content when the content owner is not online
remains a major challenge. In this paper, we rely on the structure of the
social graphs underlying DOSN for replication. In particular, we propose that
friends, who are anyhow interested in the content, are used to replicate the
users content. We study the availability of such natural replication schemes
via both theoretical analysis as well as simulations based on data from OSN
users. We find that the availability of the content increases drastically when
compared to the online time of the user, e. g., by a factor of more than 2 for
90% of the users. Thus, with these simple schemes we provide a baseline for any
more complicated content replication scheme.


  For the first time nanoparticles of CdP2 and CdP4 semiconductors were
prepared and studied. The nanoparticles were prepared by incorporation into
zeolite Na-X matrix. Absorption and photoluminescence (PL) spectra of CdP2 and
CdP4 nanoparticles were measured at the temperature of 77 K. Two bands were
observed in both the absorption and PL spectra of CdP2 nanoparticles
demonstrating the blue shift from the line of free exciton in bulk crystal.
Single band was observed in both the absorption and PL spectra of CdP4
nanoparticles demonstrating the blue shift from the spectra of bulk crystal. We
attribute the bands to some stable nanoparticles of CdP2 and CdP4 with size
less than the size of zeolite Na-X supercage. We observed Stokes shift of the
PL bands with respect to the absorption bands for both CdP2 and CdP4
nanoparticles.


  Efficient algorithms are being developed to search for strong gravitational
lens systems owing to increasing large imaging surveys. Neural networks have
been successfully used to discover galaxy-scale lens systems in imaging surveys
such as the Kilo Degree Survey, Hyper-Suprime Cam (HSC) Survey and Dark Energy
Survey over the last few years. Thus, it has become imperative to understand
how some of these networks compare, their strengths and the role of the
training datasets as most of the networks make use of supervised learning
algorithms. In this work, we present the first-of-its-kind systematic
comparison and benchmarking of networks from four teams that have analysed the
HSC Survey data. Each team has designed their training samples and developed
neural networks independently but coordinated apriori in reserving specific
datasets strictly for test purposes. The test sample consists of mock lenses,
real (candidate) lenses and real non-lenses gathered from various sources to
benchmark and characterise the performance of each of the network. While each
team's network performed much better on their own constructed test samples
compared to those from others, all networks performed comparable on the test
sample with real (candidate) lenses and non-lenses. We also investigate the
impact of swapping the training samples amongst the teams while retaining the
same network architecture. We find that this resulted in improved performance
for some networks. These results have direct implications on measures to be
taken for lens searches with upcoming imaging surveys such as the Rubin-Legacy
Survey of Space and Time, Roman and Euclid.


  In this work, we consider optimal state discrimination for a quantum system
that interacts with an environment, i.e., states evolve under a quantum
channel. We show the conditions on a quantum channel and an ensemble of states
such that a measurement for optimal state discrimination is preserved. In
particular, we show that when an ensemble of states with equal {\it a priori}
probabilities is given, an optimal measurement can be preserved over any
quantum channel by applying local operations and classical communication, that
is, by manipulating the quantum states before and after the channel
application. Examples are provided for illustration. Our results can be readily
applied to quantum communication protocols over various types of noise.


  Fracturing in reservoir rocks is an important issue for the petroleum
industry - as productivity can be enhanced by a controlled fracturing
operation. Fracturing also has a big impact on CO2 storage, geothermal
installation and gas production at and from the reservoir rocks. Therefore,
understanding the fracturing behavior of different types of reservoir rocks is
a basic need for planning field operations towards these activities. In our
study, the fracturing of rock sample is monitored by Acoustic Emission (AE) and
post-experiment Computer Tomography (CT) scans. The fracturing experiments have
been performed on hollow cylinder cores of different rocks - sandstones and
chalks. Our analysis show that the amplitudes and energies of acoustic events
clearly indicate initiation and propagation of the main fractures. The
amplitudes of AE events follow an exponential distribution while the energies
follow a power law distribution. Time-evolution of the radial strain measured
in the fracturing-test will later be compared to model predictions of fracture
size.


  We give an exact formula, as a function of m and q, for the maximum order of
the elements of the finite symplectic group Sp(2m,q), with q even, and of its
automorphism group.


  Inspired by [6, 7], we study the boundary regularity of constant curvature
hypersurfaces in the hyperbolic space $\mathbb{H}^{n+1}$, which have prescribed
asymptotic boundary at infinity. Through constructing the boundary expansions
of the solutions, we derive the optimal regularity of the solutions. Moreover,
we obtain an equivalent condition that guarantees the smoothness of the
solutions.


  We have carried out three-dimensional Navier-Stokes simulations, from
quiescent conditions to the limit cycle, of a traveling-wave thermoacoustic
heat engine (TAE) composed of a long variable-area resonator shrouding a
smaller annular tube, which encloses the hot (HHX) and ambient (AHX)
heat-exchangers, and the regenerator (REG). Simulations are wall-resolved, with
no-slip and adiabatic conditions enforced at all boundaries, while the heat
transfer and drag due to the REG and HXs are modeled. HHX temperatures have
been investigated in the range 440K - 500K with AHX temperature fixed at 300K.
The initial exponential growth of acoustic energy is due to a network of
traveling waves amplified by looping around the REG/HX unit in the direction of
the imposed temperature gradient. A simple analytical model demonstrates that
such thermoacoustic instability is a Lagrangian thermodynamic process
resembling a Stirling cycle. A system-wide linear stability model based on
Rott's theory is able to accurately predict the frequency and the growth rate,
exhibiting properties consistent with a supercritical Hopf bifurcation. The
limit cycle is governed by acoustic streaming -- a rectified flow resulting
from high-amplitude acoustics. Its key features are explained with an axially
symmetric incompressible model driven by the wave-induced stresses extracted
from the compressible calculations. These features include Gedeon streaming and
mean recirculations due to flow separation. The first drives the mean advection
of hot fluid from the HHX to a secondary heat exchanger (AHX2), in the thermal
buffer tube (TBT), necessary to achieve saturation of the acoustic energy
growth. The direct evaluation of the energy fluxes reveals that the efficiency
of the device deteriorates with the drive ratio and that the acoustic power in
the TBT is balanced primarily by the mean advection and thermoacoustic heat
transport.


  In this note, I would like to discuss an approach to the construction of
Green's function on algebraic surfaces, indicated by Manin, towards the
computation of the Green's function on surfaces using Schottky uniformization.
We shall see that the exact geometric interpretation of the formula mentioned
there is obscure, and try to remedy the situation by investigating convergence
of deformations of that formula.


  We investigate the random bipartite optimal matching problem on a flat torus
in two-dimensions, considering general strictly convex power costs of the
distance. We extend the successful ansatz first introduced by Caracciolo et al.
for the quadratic case, involving a linear Poisson equation, to a non-linear
equation of $q$-Poisson type, allowing for a more comprehensive analysis of the
optimal transport cost. Our results establish new asymptotic connections
between the energy of the solution to the PDE and the optimal transport cost,
providing insights on their asymptotic behavior.


  The normalized state $\ket{\psi(t)}=c_1(t)\ket{1}+c_2(t)\ket{2}$ of a single
two-level system performs oscillations under the influence of a resonant
driving field. It is assumed that only one realization of this process is
available. We show that it is possible to approximately visualize in real time
the evolution of the system as far as it is given by $|c_2(t)|^2$. For this
purpose we use a sequence of particular unsharp measurements separated in time.
They are specified within the theory of generalized measurements in which
observables are represented by positive operator valued measures (POVM). A
realization of the unsharp measurements may be obtained by coupling the
two-level system to a meter and performing the usual projection measurements on
the meter only.


  We detail a procedure for the computation of the polynomial form of an
electronic combinational circuit from the design equations in a truth table.
The method uses the Buchberger algorithm rather than current traditional
methods based on search algorithms. We restrict the analysis to a single
output, but the procedure can be generalized to multiple outputs. The procedure
is illustrated with the design of a simple arithmetic and logic unit with two
3-bit operands and two control bits.


  We investigate the effects of environmental dielectric screening on the
electronic dispersion and the band gap in the atomically-thin, quasi
two-dimensional (2D) semiconductor WS$_2$ using correlative angle-resolved
photoemission and optical spectroscopies, along with first-principles
calculations. We find the main effect of increased environmental screening to
be a reduction of the band gap, with little change to the electronic dispersion
of the band structure. These essentially rigid shifts of the bands results from
the special spatial structure of the changes in the Coulomb potential induced
by the dielectric environment in the 2D limit. Our results suggest dielectric
engineering as a non-invasive method of tailoring the band structure of 2D
semiconductors and provide guidance for understanding the electronic properties
of 2D materials embedded in multilayer heterostructures.


  We show that unsupervised sequence-segmentation performance can be
transferred to extremely low-resource languages by pre-training a Masked
Segmental Language Model (Downey et al., 2021) multilingually. Further, we show
that this transfer can be achieved by training over a collection of
low-resource languages that are typologically similar (but phylogenetically
unrelated) to the target language. In our experiments, we transfer from a
collection of 10 Indigenous American languages (AmericasNLP, Mager et al.,
2021) to K'iche', a Mayan language. We compare our multilingual model to a
monolingual (from-scratch) baseline, as well as a model pre-trained on Quechua
only. We show that the multilingual pre-trained approach yields consistent
segmentation quality across target dataset sizes, exceeding the monolingual
baseline in 6/10 experimental settings. Our model yields especially strong
results at small target sizes, including a zero-shot performance of 20.6 F1.
These results have promising implications for low-resource NLP pipelines
involving human-like linguistic units, such as the sparse transcription
framework proposed by Bird (2020).


  We propose two approaches for determining the native basins in off-lattice
models of proteins. The first of them is based on exploring the saddle points
on selected trajectories emerging from the native state. In the second
approach, the basin size can be determined by monitoring random distortions in
the shape of the protein around the native state. Both techniques yield the
similar results. As a byproduct, a simple method to determine the folding
temperature is obtained.


  The first result in this study is a non-existence theorem for
$\alpha-$harmonic mappings. Additionally, a direct connection between the
$\alpha-$ harmonic and harmonic maps is made possible via conformal
deformation. Second, the instability of non-constant $\alpha$-harmonic maps is
investigated with regard to the target manifold's Ricci curvature requirements.
Next, the concept of $\alpha-$stable manifolds and their physical applications
are explored. Finally, it is investigated the $\alpha-$stability of compact
Riemannian manifolds that admit a non-isometric conformal vector field as well
as the Einstein Riemannian manifolds under certain assumption on the smallest
positive eigenvalue of its Laplacian operator on functions.


  Unitary representations of centrally extended mapping class groups $\tilde
M_{g,1}, g\geq 1$ are given in terms of a rational Hopf algebra $H$, and a
related generalization of the Verlinde formula is presented. Formulae
expressing the traces of mapping class group elements in terms of the fusion
rules, quantum dimensions and statistics phases are proposed.


  In spintronics, the ability to transport magnetic information often depends
on the existence of a spin current traveling between two different magnetic
objects acting as source and probe. A large fraction of this information never
reaches the probe and is lost because the spin current tends to travel
omni-directionally. We propose that a curved boundary between a gated and a
non-gated region within graphene acts as an ideal lens for spin currents
despite being entirely of non-magnetic nature. We show as a proof of concept
that such lenses can be utilized to redirect the spin current that travels away
from a source onto a focus region where a magnetic probe is located, saving a
considerable fraction of the magnetic information that would be otherwise lost.


  In 2021, Kashiwara-Kim-Oh-Park constructed cluster algebra structures on the
Grothendieck rings of certain monoidal subcategories of the category of
finite-dimensional representations of a quantum loop algebra, generalizing
Hernandez-Leclerc's pioneering work from 2010. They stated the problem of
finding explicit quivers for the seeds they used. We provide a solution by
using Palu's generalized mutation rule applied to the cluster categories
associated with certain algebras of global dimension at most 2, for example
tensor products of path algebras of representation-finite quivers. Thus, our
method is based on (and contributes to) the bridge, provided by cluster
combinatorics, between the representation theory of quantum groups and that of
quivers with relations.


  We study the Morava $E$-theory (at a prime $p$) of $BGL_d(F)$, where $F$ is a
finite field with $|F|=1\pmod{p}$. Taking all $d$ together, we obtain a
structure with two products $\times$ and $\bullet$. We prove that it is a
polynomial ring under $\times$, and that the module of $\times$-indecomposables
inherits a $\bullet$-product, and we describe the structure of the resulting
ring. In the process, we prove many auxiliary structural results.


  Past research on interactive decision making problems (bandits, reinforcement
learning, etc.) mostly focuses on the minimax regret that measures the
algorithm's performance on the hardest instance. However, an ideal algorithm
should adapt to the complexity of a particular problem instance and incur
smaller regrets on easy instances than worst-case instances. In this paper, we
design the first asymptotic instance-optimal algorithm for general interactive
decision making problems with finite number of decisions under mild conditions.
On every instance $f$, our algorithm outperforms all consistent algorithms
(those achieving non-trivial regrets on all instances), and has asymptotic
regret $\mathcal{C}(f) \ln n$, where $\mathcal{C}(f)$ is an exact
characterization of the complexity of $f$. The key step of the algorithm
involves hypothesis testing with active data collection. It computes the most
economical decisions with which the algorithm collects observations to test
whether an estimated instance is indeed correct; thus, the complexity
$\mathcal{C}(f)$ is the minimum cost to test the instance $f$ against other
instances. Our results, instantiated on concrete problems, recover the
classical gap-dependent bounds for multi-armed bandits [Lai and Robbins, 1985]
and prior works on linear bandits [Lattimore and Szepesvari, 2017], and improve
upon the previous best instance-dependent upper bound [Xu et al., 2021] for
reinforcement learning.


  When waves impinge on a disordered material they are back-scattered and form
a highly complex interference pattern. Suppressing any such distortions in the
free propagation of a wave is a challenging task with many applications in a
number of different disciplines. In a recent theoretical proposal, it was
pointed out that both perfect transmission through disorder as well as a
complete suppression of any variation in a wave intensity can be achieved by
adding a continuous gain-loss distribution to the disorder. Here we show that
this abstract concept can be implemented in a realistic acoustic system. Our
prototype consists of an acoustic waveguide containing several inclusions that
scatter the incoming wave in a passive configuration and provide the gain or
loss when being actively controlled. Our measurements on this non-Hermitian
acoustic metamaterial demonstrate unambiguously the creation of a
reflectionless scattering wave state that features a unique form of discrete
constant-amplitude pressure waves. In addition to demonstrating that gain-loss
additions can turn localised systems into transparent ones, we expect our
proof-of-principle demonstration to trigger interesting new developments not
only in sound engineering, but also in other related fields such as in
non-Hermitian photonics.


  In this paper, the notion of generic transversality and its characterization
are given. The characterization is also a further improvement of the basic
transversality result and its strengthening which was given by John Mather.


  Ar{\i}kan's polar coding, is by now a well studied technique that allows
achieving the symmetric capacity of binary input memoryless channels with low
complexity encoding and decoding, provided that the polar decoding architecture
is used and the decoding metric is matched to the true channel. In this paper,
we analyze communication rates that are achievable when the polar
coding/decoding architecture is used with the decoder using an incorrect model
of the channel. We define the `polar mismatched capacity' as an analogue of the
classical mismatched capacity, give an expression for it, and derive bounds on
it.


  Observational astrophysics started when spectroscopy could be applied to
astronomy. Similarly, observational work on stellar magnetic fields became
possible with the application of spectro-polarimetry. In recent decades there
have been dramatic advances in the observational tools for spectro-polarimetry.
The four Stokes parameters that provide a complete representation of partially
polarized light can now be simultaneously imaged with megapixel array detectors
with high polarimetric precision (0.001% in the degree of polarization). This
has led to new insights about the nature and properties of the magnetic field,
and has helped pave the way for the use of the Hanle effect as a diagnostic
tool beside the Zeeman effect. The magnetic structuring continues on scales
orders of magnitudes smaller than the resolved ones, but various types of
spectro-polarimetric signatures can be identified, which let us determine the
field strengths and angular distributions of the field vectors in the spatially
unresolved domain. Here we review the observational properties of the magnetic
field, from the global patterns to the smallest scales at the magnetic
diffusion limit, and relate them to the global and local dynamos.


  The recent discoveries of high-energy cosmic neutrinos and gravitational
waves from astrophysical objects have led to the new era of multi-messenger
astrophysics. In particular, electromagnetic follow-up observations triggered
by these cosmic signals proved to be highly successful and brought about new
opportunities in the time-domain astronomy. Here we review high-energy particle
production in various classes of astrophysical transient phenomena related to
black holes and neutron stars, and discuss how high-energy emission can be used
to reveal the underlying physics of neutrino and gravitational-wave sources.


  Modern applications can generate a large amount of data from different
sources with high velocity, a combination that is difficult to store and
process via traditional tools. Hadoop is one framework that is used for the
parallel processing of a large amount of data in a distributed environment,
however, various challenges can lead to poor performance. Two particular issues
that can limit performance are the high access time for I/O operations and the
recomputation of intermediate data. The combination of these two issues can
result in resource wastage. In recent years, there have been attempts to
overcome these problems by using caching mechanisms. Due to cache space
limitations, it is crucial to use this space efficiently and avoid cache
pollution (the cache contains data that is not used in the future). We propose
Hadoop-oriented SVM-LRU (HSVM- LRU) to improve Hadoop performance. For this
purpose, we use an intelligent cache replacement algorithm, SVM-LRU, that
combines the well-known LRU mechanism with a machine learning algorithm, SVM,
to classify cached data into two groups based on their future usage.
Experimental results show a significant decrease in execution time as a result
of an increased cache hit ratio, leading to a positive impact on Hadoop
performance.


  The multiple lobes of high order Hermite-Gaussian (HG) laser modes differ in
terms of shape, size, and optical energy distribution. Here, we introduce a
generic numerical method that redistributes optical energy among the lobes of
high order HG modes such that all the identical low intense lobes become both
moderate or high intense lobes and vice-versa, in a controlled manner. Further,
the modes which consist of only two types of intensity distribution among its
multiple lobes are transformed together into all high intense lobes.
Furthermore, in some cases, moderate intense lobes together with high intense
lobes become high intense lobes, and moderate intense lobes together with low
intense lobes become high intense lobes. Such controlled modulation of optical
energy may offer efficient and selective utilization of each lobe of HG modes
in most applications like particle manipulation, optical lithography, and the
method can be used in other fields like nonlinear frequency conversion and
shaping ultrafast optical pulses.


  Rayleigh-Benard convection is not only a classical problem in fluid dynamics
but plays also an important role in many metallurgical and crystal growth
applications. The measurement of the flow field and of the dynamics of the
emerging large-scale circulation in liquid metals is a challenging task due to
the opaqueness and the high temperature of the melts. Contactless inductive
flow tomography is a technique to visualize the mean three-dimensional flow
structure in liquid metals by measuring the flow induced magnetic field
perturbations under the influence of one or several applied magnetic fields. In
this paper, we present first measurements of the flow induced magnetic field in
a Rayleigh-Benard setup, which are also used to investigate the dynamics of the
large-scale circulation. Additionally, we investigate numerically the quality
of the reconstruction of the three-dimensional flow field for different sensor
configurations.


  Primordial magnetic fields (PMF) damp at scales smaller than the photon
diffusion and free-streaming scale. This leads to heating of ordinary matter
(electrons and baryons), which affects both the thermal and ionization history
of our Universe. Here, we study the effect of heating due to ambipolar
diffusion and decaying magnetic turbulence. We find that changes to the
ionization history computed with recfast are significantly overestimated when
compared with CosmoRec. The main physical reason for the difference is that the
photoionization coefficient has to be evaluated using the radiation temperature
rather than the matter temperature. A good agreement with CosmoRec is found
after changing this aspect. Using Planck 2013 data and considering only the
effect of PMF-induced heating, we find an upper limit on the r.m.s. magnetic
field amplitude of B0 < 1.1 nG (95% c.l.) for a stochastic background of PMF
with a nearly scale-invariant power spectrum. We also discuss uncertainties
related to the approximations for the heating rates and differences with
respect to previous studies. Our results are important for the derivation of
constraints on the PMF power spectrum obtained from measurements of the cosmic
microwave background anisotropies with full-mission Planck data. They may also
change some of the calculations of PMF-induced effects on the primordial
chemistry and 21cm signals.


  In 2006, Restorff completed the classification of all Cuntz-Krieger algebras
with finitely many ideals (i.e., those that are purely infinite) up to stable
isomorphism. He left open the questions concerning strong classification up to
stable isomorphism and unital classification. In this paper, we address both
questions. We show that any isomorphism between the reduced filtered K-theory
of two Cuntz-Krieger algebras with finitely many ideals lifts to a
*-isomorphism between the stabilized Cuntz-Krieger algebras. As a result, we
also obtain strong unital classification.


  While purely data-driven assessment is feasible for the first levels of the
Structural Health Monitoring (SHM) process, namely damage detection and
arguably damage localization, this does not hold true for more advanced
processes. The tasks of damage quantification and eventually residual life
prognosis are invariably linked to availability of a representation of the
system, which bears physical connotation. In this context, it is often
desirable to assimilate data and models, into what is often termed a digital
twin of the monitored system.
  One common take to such an end lies in exploitation of structural mechanics
models, relying on use of Finite Element approximations. proper updating of
these models, and their incorporation in an inverse problem setting may allow
for damage quantification and localization, as well as more advanced tasks,
including reliability analysis and fatigue assessment. However, this may only
be achieved by means of repetitive analyses of the forward model, which implies
considerable computational toll, when the model used is a detailed FE
representation. In tackling this issue, reduced order models can be adopted,
which retain the parameterisation and link to the parameters regulating the
physical properties, albeit greatly reducing the computational burden.
  In this work a detailed FE model of a wind turbine tower is considered,
reduced forms of this model are found using both the Craig Bampton and Dual
Craig Bampton methods. These reduced order models are then used and compared in
a Transitional Markov Chain Monte Carlo procedure to localise and quantify
damage which is introduced to the system.


  We consider a system of real-valued spins interacting with each other through
a mean-field Hamiltonian that depends on the empirical magnetization of the
spins via a general potential. The system is subjected to a stochastic dynamics
where the spins perform independent Brownian motions. As in \cite{FedHoMa13},
which considers the Curie-Weiss model with Ising spins interacting via a
quadratic potential and subjected to independent spins flips, we follow the
program outlined in \cite{vEFedHoRe10}. We show that in the thermodynamic limit
the system is non-Gibbs at time $t \in (0,\infty)$ if and only if there exists
an $\alpha \in \mathbb{R}$ such that the large deviation rate function for the
trajectory of the magnetization conditional on hitting the value $\alpha$ at
time $t$ has multiple global minimizers. We further show that different
minimizing trajectories are different at time $t=0$. We give conditions on the
potential under which the system is Gibbs at time $t=0$, classify the possible
scenarios of being Gibbs at time $t \in (0,\infty)$ in terms of the second
difference quotient of the potential, and show that the system cannot become
Gibbs once it has become non-Gibbs, i.e., there is a unique and explicitly
computable crossover time $t_c \in [0,\infty]$ from Gibbs to non-Gibbs. We give
examples of immediate loss of Gibbsianness ($t_c=0$), short-time conservation
of Gibbsianness, large-time loss of Gibbsianness ($t_c\in (0,\infty)$), and
preservation of Gibbsianness ($t_c=\infty$). Depending on the potential, the
system can be Gibbs or non-Gibbs at the cross-over time time $t=t_c$.


  Let X be a smooth, connected, dimension n, quasi-projective variety imbedded
in \PP_N. Consider integers {k_1,...,k_r}, with k_i>0, and the Hilbert Scheme
H_{k_1,...,k_r}(X) of aligned, finite, degree \sum k_i, subschemes of X, with
multiplicities k_i at points x_i (possibly coinciding). The expected dimension
of H_{k_1,...,k_r}(X) is 2N-2+r-(\sum k_i)(N-n). We study the locus of points
where H_{k_1,...,k_r}(X) is not smooth of expected dimension and we prove that
the lines carrying this locus do not fill up \PP_N


  Manufacturing of products, nowadays, due to the advances in Information
Technologies (IT) that turn products into smart devices, and the evolution in
device connectivity, becomes increasingly complex. Connected product networks
(CPN) and cyber-physical systems (CPS) are bringing new challenges to
manufacturing companies. These challenges, among others things, lead to
increased demands for optimisation and personalisation of production processes.
This move, which as a result drives the market of machines and products, poses
new challenges to the manufacturing domain that needs flexible solutions to
replace the rigid traditional methodologies and tools. The current work
suggests a cloud-based platform for optimisation of machines, products and
processes, allowing for situational awareness on the users' site, involving
technologies for event prediction and optimisation.


  Pointwise matches between two time series are of great importance in time
series analysis, and dynamic time warping (DTW) is known to provide generally
reasonable matches. There are situations where time series alignment should be
invariant to scaling and offset in amplitude or where local regions of the
considered time series should be strongly reflected in pointwise matches. Two
different variants of DTW, affine DTW (ADTW) and regional DTW (RDTW), are
proposed to handle scaling and offset in amplitude and provide regional
emphasis respectively. Furthermore, ADTW and RDTW can be combined in two
different ways to generate alignments that incorporate advantages from both
methods, where the affine model can be applied either globally to the entire
time series or locally to each region. The proposed alignment methods
outperform DTW on specific simulated datasets, and one-nearest-neighbor
classifiers using their associated difference measures are competitive with the
difference measures associated with state-of-the-art alignment methods on real
datasets.


  We studied the weak-lined T Tauri star Hubble 4, a known long-period binary,
and its starspot phenomena. We used optical radial velocity (RV) data taken
over a span of 14 years (2004-2010, 2017-2019) at the McDonald Observatory 2.7m
Harlan J. Smith telescope and single epoch imaging from the HST/WFC3
instrument. The observed and apparent RV variations show contributions,
respectively, from the binary motion as well as from a large spot group on one
of the stars, presumed to be the primary. Fitting and removing the orbital
signal from the RVs, we found the lower bound on the lifetime of a previously
identified large spot group on the surface of the star to be at least 5.1
years. A $\sim5$ year lower limit is a long, but not unprecedented, duration
for a single spot group. The later epoch data indicate significant spot
evolution has occurred, placing an upper bound on the spot group lifetime at 12
years. We find that pre-main sequence evolutionary models for the age of Taurus
($\sim2$ Myr), combined with component mass estimates from the literature,
permit us to reproduce the HST relative photometry and the binary-induced
contribution to the apparent RV variations. The long-lived star spot we find on
Hubble 4 has significant implications for dynamo models in young stars, as it
adds evidence for long lifetimes of magnetic field topologies. There are also
significant implications for young star exoplanet searches as long-lived
coherent RV signals may be spot-induced and not the result of planetary motion.
(This paper includes data taken at The McDonald Observatory of The University
of Texas at Austin.)


  The Desktop Grid offers solutions to overcome several challenges and to
answer increasingly needs of scientific computing. Its technology consists
mainly in exploiting resources, geographically dispersed, to treat complex
applications needing big power of calculation and/or important storage
capacity. However, as resources number increases, the need for scalability,
self-organisation, dynamic reconfigurations, decentralisation and performance
becomes more and more essential. Since such properties are exhibited by P2P
systems, the convergence of grid computing and P2P computing seems natural. In
this context, this paper evaluates the scalability and performance of P2P tools
for discovering and registering services. Three protocols are used for this
purpose: Bonjour, Avahi and Free-Pastry. We have studied the behaviour of
theses protocols related to two criteria: the elapsed time for registrations
services and the needed time to discover new services. Our aim is to analyse
these results in order to choose the best protocol we can use in order to
create a decentralised middleware for desktop grid.


  Brumer and Kramer gave bounds on local conductor exponents for an abelian
variety $A/\mathbb Q$ in terms of the dimension of $A$ and the localization
prime $p$. Here we give improved bounds in the case that $A$ has maximal real
multiplication, i.e., $A$ is isogenous to a factor of the Jacobian of a modular
curve $X_0(N)$. In many cases, these bounds are sharp. The proof relies on
showing that the rationality field of a newform for $\Gamma_0(N)$, and thus the
endomorphism algebra of $A$, contains $\mathbb Q(\zeta_{p^r})^+$ when $p$
divides $N$ to a sufficiently high power. We also deduce that certain
divisibility conditions on $N$ determine the endomorphism algebra when $A$ is
simple.


  Interaction between vehicles and pedestrians is seen in many areas such as
crosswalks and intersections. In this paper, we study a totally asymmetric
simple exclusion process with a bottleneck at a boundary caused by an
interaction. Due to the time-dependent effect originating from the speed of
pedestrians, the flow of the model varies even if the average hopping
probability at the last site is the same. We analyze the phenomenon by using
two types of approximations: (2+1)-cluster approximation and isolated
rarefaction wave approximation. The approximate results capture intriguing
features of the model. Moreover, we discuss the situation where vehicles turn
right at the intersection by adding a traffic light at the boundary condition.
The result suggests that pedestrian scrambles are valid to eliminate traffic
congestion in the right turn lane.


  We present new observations of MRG-M2129, a quiescent galaxy at z = 2.15 with
the Atacama Large Millimeter/submillimeter Array (ALMA). With the combination
of the gravitational lensing effect by the foreground cluster and the angular
resolution provided by ALMA, our data reveal 1.2 mm continuum emission at
$\sim130$ pc angular resolution. Compact dust continuum is detected at 7.9
$\sigma$ in the target but displaced from its stellar peak position by $62 \pm
38$ mas, or $\sim169 \pm 105$ pc in the source plane. We find considerably high
dust-to-stellar mass ratio, $4 \times 10^{-4}$. From non-detection of the [C i]
3P2 -> 3P1 line, we then derive $3 \sigma$ upper limits on the molecular
gas-to-dust mass ratio $\delta_\mathrm{GDR} < 60$ and the molecular
gas-to-stellar mass ratio fH2 < 2.3%. The derived $\delta_\mathrm{GDR}$ is
$>2\times$ smaller than the typical value assumed for quiescent galaxies in the
literature. Our study supports that there exists a broad range of
$\delta_\mathrm{GDR}$ and urges submillimeter follow-up observations of
quenching/recently quenched galaxies at similar redshifts. Based on the derived
low $\delta_\mathrm{GDR}$ and other observed dust properties, we argue that the
central black hole is still active and regulates star formation in the system.
Our study exhibits a rare case of a gravitationally lensed type 2 QSO harbored
by a quiescent galaxy.


  Directed information transmission is paramount for many social, physical, and
biological systems. For neural systems, scientists have studied this problem
under the paradigm of feedforward networks for decades. In most models of
feedforward networks, activity is exclusively driven by excitatory neurons and
the wiring patterns between them, while inhibitory neurons play only a
stabilizing role for the network dynamics. Motivated by recent experimental
discoveries of hippocampal circuitry, cortical circuitry, and the diversity of
inhibitory neurons throughout the brain, here we illustrate that one can
construct such networks even if the connectivity between the excitatory units
in the system remains random. This is achieved by endowing inhibitory nodes
with a more active role in the network. Our findings demonstrate that apparent
feedforward activity can be caused by a much broader network-architectural
basis than often assumed.


  Let $N$ be the number of triangles in an Erd\H{o}s-R\'enyi graph
$\mathcal{G}(n,p)$ on $n$ vertices with edge density $p=d/n,$ where $d>0$ is a
fixed constant. It is well known that $N$ weakly converges to the Poisson
distribution with mean ${d^3}/{6}$ as $n\rightarrow \infty$. We address the
upper tail problem for $N,$ namely, we investigate how fast $k$ must grow, so
that the probability of $\{N\ge k\}$ is not well approximated anymore by the
tail of the corresponding Poisson variable. Proving that the tail exhibits a
sharp phase transition, we essentially show that the upper tail is governed by
Poisson behavior only when $k^{1/3} \log k< (\frac{3}{\sqrt{2}})^{2/3} \log n$
(sub-critical regime) as well as pin down the tail behavior when $k^{1/3} \log
k> (\frac{3}{\sqrt{2}})^{2/3} \log n$ (super-critical regime). We further prove
a structure theorem, showing that the sub-critical upper tail behavior is
dictated by the appearance of almost $k$ vertex-disjoint triangles whereas in
the supercritical regime, the excess triangles arise from a clique like
structure of size approximately $(6k)^{1/3}$. This settles the long-standing
upper-tail problem in this case, answering a question of Aldous, complementing
a long sequence of works, spanning multiple decades, culminating in (Harel,
Moussat, Samotij,'19) which analyzed the problem only in the regime $p\gg
\frac{1}{n}.$ The proofs rely on several novel graph theoretical results which
could have other applications.


  On a compact group the Haar probability measure plays the role of uniform
distribution. The entropy and rate distortion theory for this uniform
distribution is studied. New results and simplified proofs on convergence of
convolutions on compact groups are presented and they can be formulated as
entropy increases to its maximum. Information theoretic techniques and Markov
chains play a crucial role. The convergence results are also formulated via
rate distortion functions. The rate of convergence is shown to be exponential.


  We study the decay of unstable states by formulating quantum tunneling as a
time-of-arrival problem: we determine the detection probability for particles
at a detector located a distance L from the tunneling region. For this purpose,
we use a Positive-Operator-Valued-Measure (POVM) for the time-of-arrival
determined in quant-ph/0509020 [JMP 7, 122106 (2006)]. This only depends on the
initial state, the Hamiltonian and the location of the detector. The POVM above
provides a well-defined probability density and an unambiguous interpretation
of all quantities involved. We demonstrate that the exponential decay only
arises if three specific mathematical conditions are met. Their physical
content is the following: (i) the decay time is much larger than any
microscopic timescale, so that the fine details of the initial state can be
ignored, (ii) there is no quantum coherence between the different `attempts' of
the particle to traverse the barrier, and (iii) the transmission probability
varies little within the momentum spread of the initial state. We also
determine the long time limits of the decay probability and we identify
regimes, in which the decays have no exponential phase.


  Using the established $d$-concavity of the $k$-Hessian type functions
$F_k(R)=\log(S_k(R)),$ whose variables are nonsymmetric matrices, we prove $
C^{2, \alpha}(\overline{\Omega}) $ estimates for strictly $(\delta,
\widetilde{\gamma}_k) $-admissible solutions to the Dirichlet problem without
the well-known regularity condition. A necessary condition for the existence of
strictly $\delta$-admissible solutions to the equations is given. By the method
of continuity, we provide some sufficient conditions for the unique solvability
in the class of strictly $(\delta,\widetilde{\gamma}_k)$-admissible solutions
to the Dirichlet problem, provided that those skew-symmetric matrices in the
equations are sufficiently small in some sense.


  Persona-driven role-playing (PRP) aims to build AI characters that can
respond to user queries by faithfully sticking with all persona statements.
Unfortunately, existing faithfulness criteria for PRP are limited to
coarse-grained LLM-based scoring without a clear definition or formulation.
This paper presents a pioneering exploration to quantify PRP faithfulness as a
fine-grained and explainable criterion, which also serves as a reliable
reference for optimization. Our criterion first discriminates persona
statements into active and passive constraints by identifying the
query-statement relevance. Then, we incorporate all constraints following the
principle that the AI character's response should be (a) entailed by active
(relevant) constraints and (b) not contradicted by passive (irrelevant)
constraints. We translate this principle mathematically into a novel
Active-Passive-Constraint (APC) score, a constraint-wise sum of natural
language inference (NLI) scores weighted by relevance scores. In practice, we
build the APC scoring system by symbolically distilling small discriminators
from GPT-4 for efficiency. We validate the quality of the APC score against
human evaluation based on example personas with tens of statements, and the
results show a high correlation. We further leverage it as a reward system in
direct preference optimization (DPO) for better AI characters. Our experiments
offer a fine-grained and explainable comparison between existing PRP
techniques, revealing their advantages and limitations. We further find
APC-based DPO to be one of the most competitive techniques for sticking with
all constraints and can be well incorporated with other techniques. We then
extend the scale of the experiments to real persons with hundreds of statements
and reach a consistent conclusion.


  We prove two general results concerning spectral sequences of
$\mathbf{FI}$-modules. These results can be used to significantly improve
stable ranges in a large portion of the stability theorems for
$\mathbf{FI}$-modules currently in the literature. We work this out in detail
for the cohomology of configuration spaces where we prove a linear stable range
and the homology of congruence subgroups of general linear groups where we
prove a quadratic stable range. Previously, the best stable ranges known in
these examples were exponential. Up to an additive constant, our work on
congruence subgroups verifies a conjecture of Djament.


  Canonical quantization has served wonderfully for the quantization of a vast
number of classical systems. That includes single classical variables, such as
$p$ and $q$, and numerous classical Hamiltonians $H(p,q)$, as well as field
theories, such as $\pi(x)$ and $ \phi(x)$, and many classical Hamiltonians
$H(\pi,\phi)$. However, in all such systems there are situations for which
canonical quantization fails. This includes certain particle and field theory
problems. Affine quantization involves a simple recombination of classical
variables that lead to a new chapter in the process of quantization, and which
is able to solve a vast variety of normally insoluble systems, such as quartic
interactions in scalar field theory in spacetime dimensions 4 and higher, as
well as the quantization of Einstein's gravity in 4 spacetime dimensions.


  This paper describes two-fold approach towards utilizing Triple Modular
Redundancy (TMR) in Wireless Adhoc Network (AdocNet). A distributed
checkpointing and recovery protocol is proposed. The protocol eliminates
useless checkpoints and helps in selecting only dependent processes in the
concerned checkpointing interval, to recover. A process starts recovery from
its last checkpoint only if it finds that it is dependent (directly or
indirectly) on the faulty process. The recovery protocol also prevents the
occurrence of missing or orphan messages. In AdocNet, a set of three nodes
(connected to each other) is considered to form a TMR set, being designated as
main, primary and secondary. A main node in one set may serve as primary or
secondary in another. Computation is not triplicated, but checkpoint by main is
duplicated in its primary so that primary can continue if main fails.
Checkpoint by primary is then duplicated in secondary if primary fails too.


  We show that error distributions of a compilation of 28 recent independent
measurements of the distance from the Sun to the Galactic center, $R_{0}$, are
wider than a standard Gaussian and best fit by an $n=4$ Student's $t$
probability density function. Given this non-Gaussianity, the results of our
median statistics analysis, summarized as $R_{0}=8.0 \pm 0.3$ kpc ($2\sigma$
error), probably provides the most reliable estimate of $R_{0}$.


  We report experimental studies of synchronization phenomena in a pair of
biological neurons that interact through naturally occurring, electrical
coupling. When these neurons generate irregular bursts of spikes, the natural
coupling synchronizes slow oscillations of membrane potential, but not the fast
spikes. By adding artificial electrical coupling we studied transitions between
synchrony and asynchrony in both slow oscillations and fast spikes. We discuss
the dynamics of bursting and synchronization in living neurons with distributed
functional morphology.


  In a recent article, Faraoni proposed an alternative procedure to solve the
Friedman-Lemaitre-Robertson-Walker (FLRW) cosmological equations. The basic
result of that paper was obtained long ago through a different approach, which
seems to be little known and deserves closer attention due to its pedagogical
interest. The broad importance of this method is readily recognized by
examining some additional cases not considered by Faraoni. Its instructive
potential for introductory courses on cosmology has been positively verified by
the author in many lectures during the last decade.


  The efficiency of two Bayesian order estimators is studied. By using
nonparametric techniques, we prove new underestimation and overestimation
bounds. The results apply to various models, including mixture models. In this
case, the errors are shown to be $O(e^{-an})$ and $O((\log n)^b/\sqrt{n})$
($a,b>0$), respectively.


  Daily deals sites such as Groupon offer deeply discounted goods and services
to tens of millions of customers through geographically targeted daily e-mail
marketing campaigns. In our prior work we observed that a negative side effect
for merchants using Groupons is that, on average, their Yelp ratings decline
significantly. However, this previous work was essentially observational,
rather than explanatory. In this work, we rigorously consider and evaluate
various hypotheses about underlying consumer and merchant behavior in order to
understand this phenomenon, which we dub the Groupon effect. We use statistical
analysis and mathematical modeling, leveraging a dataset we collected spanning
tens of thousands of daily deals and over 7 million Yelp reviews. In
particular, we investigate hypotheses such as whether Groupon subscribers are
more critical than their peers, or whether some fraction of Groupon merchants
provide significantly worse service to customers using Groupons. We suggest an
additional novel hypothesis: reviews from Groupon subscribers are lower on
average because such reviews correspond to real, unbiased customers, while the
body of reviews on Yelp contain some fraction of reviews from biased or even
potentially fake sources. Although we focus on a specific question, our work
provides broad insights into both consumer and merchant behavior within the
daily deals marketplace.


  Stimulated by practical applications arising from viral marketing. This paper
investigates a novel Budgeted $k$-Submodular Maximization problem defined as
follows: Given a finite set $V$, a budget $B$ and a $k$-submodular function $f:
(k+1)^V \mapsto \mathbb{R}_+$, the problem asks to find a solution $\s=(S_1,
S_2, \ldots, S_k)$, each element $e \in V$ has a cost $c_i(e)$ to be put into
$i$-th set $S_i$, with the total cost of $s$ does not exceed $B$ so that
$f(\s)$ is maximized. To address this problem, we propose two streaming
algorithms that provide approximation guarantees for the problem. In
particular, in the case of each element $e$ has the same cost for all $i$-th
sets, we propose a deterministic streaming algorithm which provides an
approximation ratio of $\frac{1}{4}-\epsilon$ when $f$ is monotone and
$\frac{1}{5}-\epsilon$ when $f$ is non-monotone. For the general case, we
propose a random streaming algorithm that provides an approximation ratio of
$\min\{\frac{\alpha}{2}, \frac{(1-\alpha)k}{(1+\beta)k-\beta} \}-\epsilon$ when
$f$ is monotone and $\min\{\frac{\alpha}{2},
\frac{(1-\alpha)k}{(1+2\beta)k-2\beta} \}-\epsilon$ when $f$ is non-monotone in
expectation, where $\beta=\max_{e\in V, i , j \in [k], i\neq j}
\frac{c_i(e)}{c_j(e)}$ and $\epsilon, \alpha$ are fixed inputs.


  Compared with the traditional hashing methods, deep hashing methods generate
hash codes with rich semantic information and greatly improves the performances
in the image retrieval field. However, it is unsatisfied for current deep
hashing methods to predict the similarity of hard examples. It exists two main
factors affecting the ability of learning hard examples, which are weak key
features extraction and the shortage of hard examples. In this paper, we give a
novel end-to-end model to extract the key feature from hard examples and obtain
hash code with the accurate semantic information. In addition, we redesign a
hard pair-wise loss function to assess the hard degree and update penalty
weights of examples. It effectively alleviates the shortage problem in hard
examples. Experimental results on CIFAR-10 and NUS-WIDE demonstrate that our
model outperformances the mainstream hashing-based image retrieval methods.