  We prove that given any $\epsilon>0$, random integral $n\times n$ matrices
with independent entries that lie in any residue class modulo a prime with
probability at most $1-\epsilon$ have cokernels asymptotically (as
$n\rightarrow\infty$) distributed as in the distribution on finite abelian
groups that Cohen and Lenstra conjecture as the distribution for class groups
of imaginary quadratic fields. This is a refinement of a result on the
distribution of ranks of random matrices with independent entries in
$\mathbb{Z}/p\mathbb{Z}$. This is interesting especially in light of the fact
that these class groups are naturally cokernels of square matrices. We also
prove the analogue for $n\times (n+u)$ matrices.


  This paper describes our submission to Task 10 at SemEval 2023-Explainable
Detection of Online Sexism (EDOS), divided into three subtasks. The recent rise
in social media platforms has seen an increase in disproportionate levels of
sexism experienced by women on social media platforms. This has made detecting
and explaining online sexist content more important than ever to make social
media safer and more accessible for women. Our approach consists of
experimenting and finetuning BERT-based models and using a Majority Voting
ensemble model that outperforms individual baseline model scores. Our system
achieves a macro F1 score of 0.8392 for Task A, 0.6092 for Task B, and 0.4319
for Task C.


  We look at the prospects for detecting light bosons, $X$, at proposed Z
factories assuming a production of $10^{12}$ Z bosons. Such a large yield is
within the design goals of future FCC-ee and CEPC colliders. Specifically we
look at the cases where $X$ is either a singlet scalar which mixes with the
standard model Higgs or a vector boson with mass $1\lesssim M_X \lesssim 80$
GeV. We find that several channels are particularly promising for discovery
prospects. In particular $Z\rightarrow f \bar{f} X$ and $Z \rightarrow V_Q X$
gives a promising signal above a very clean standard model background. We also
discuss several channels that have too large a background to be useful.


  Variational wave functions based on a Margenau-Brink cluster model with short
range and state dependent correlations, and angular momentum projection are
obtained for some nuclei with $12 \leq A \leq 16$. The calculations have been
carried out starting from the nucleon-nucleon interaction by using the
Variational Monte Carlo method. The configuration used consists of three alpha
clusters located at the apexes of an equilateral triangle, and an additional
cluster, not necessarily of alpha type, forming a tetrahedron. This cluster is
located at the top of its height. Short-range and state dependent correlations
are included by means of a central Jastrow factor and a linear operatorial
correlation factor respectively. Angular momentum projection is performed by
using the Peierls-Yoccoz operators. Optimal structures are obtained for all the
nuclei studied. Some aspects of our methodology have been tested by comparing
with previous calculations carried out without short range correlations. The
binding energy, the root mean square radius, and the one- and two-body
densities are reported. The effects of correlations on both the energy and the
nucleon distribution are analyzed systematically.


  Position measurements at the quantum level are vital for many applications,
but also challenging. Typically, methods based on optical phase shifts are
used, but these methods are often weak and difficult to apply to many
materials. An important example is graphene, which is an excellent mechanical
resonator due to its small mass and an outstanding platform for
nanotechnologies, but is largely transparent. Here, we present a novel
detection scheme based upon the strong, dispersive vacuum interactions between
a graphene sheet and a quantum emitter. In particular, the mechanical
displacement causes strong changes in the vacuum-induced shifts of the
transition frequency of the emitter, which can be read out via optical fields.
We show that this enables strong quantum squeezing of the graphene position on
time scales short compared to the mechanical period.


  Optimization in the presence of sharp (non-Lipschitz), unpredictable (w.r.t.
time and amount) changes is a challenging and largely unexplored problem of
great significance. We consider the class of piecewise Lipschitz functions,
which is the most general online setting considered in the literature for the
problem, and arises naturally in various combinatorial algorithm selection
problems where utility functions can have sharp discontinuities. The usual
performance metric of $\mathit{static}$ regret minimizes the gap between the
payoff accumulated and that of the best fixed point for the entire duration,
and thus fails to capture changing environments. Shifting regret is a useful
alternative, which allows for up to $s$ environment shifts. In this work we
provide an $O(\sqrt{sdT\log T}+sT^{1-\beta})$ regret bound for
$\beta$-dispersed functions, where $\beta$ roughly quantifies the rate at which
discontinuities appear in the utility functions in expectation (typically
$\beta\ge1/2$ in problems of practical interest). We also present a lower bound
tight up to sub-logarithmic factors. We further obtain improved bounds when
selecting from a small pool of experts. We empirically demonstrate a key
application of our algorithms to online clustering problems on popular
benchmarks.


  We propose an architecture to jointly learn word and label embeddings for
slot filling in spoken language understanding. The proposed approach encodes
labels using a combination of word embeddings and straightforward word-label
association from the training data. Compared to the state-of-the-art methods,
our approach does not require label embeddings as part of the input and
therefore lends itself nicely to a wide range of model architectures. In
addition, our architecture computes contextual distances between words and
labels to avoid adding contextual windows, thus reducing memory footprint. We
validate the approach on established spoken dialogue datasets and show that it
can achieve state-of-the-art performance with much fewer trainable parameters.


  We construct multimonopole solutions containing N-1 distinct fundamental
monopoles in SU(N) gauge theory. When the gauge symmetry is spontaneously
broken to U(1)^{N-1}, the monopoles are all massive, and we show that the
fields can be written in terms of elementary function for all values of the
monopole positions and phases. In the limit of unbroken U(1) X SU(N-2) X U(1)
symmetry, the configuration can be viewed as containing a pair of massive
monopoles, each carrying both U(1) and SU(N-2) magnetic charges, together with
N-3 massless monopoles that condense into a cloud of non-Abelian fields. We
obtain explicit expressions for the fields in the latter case and use these to
analyze the properties of the non-Abelian cloud.


  In medical research, individual-level patient data provide invaluable
information, but the patients' right to confidentiality remains of utmost
priority. This poses a huge challenge when estimating statistical models such
as linear mixed models, which is an extension of linear regression models that
can account for potential heterogeneity whenever data come from different data
providers. Federated learning algorithms tackle this hurdle by estimating
parameters without retrieving individual-level data. Instead, iterative
communication of parameter estimate updates between the data providers and
analyst is required. In this paper, we propose an alternative framework to
federated learning algorithms for fitting linear mixed models. Specifically,
our approach only requires the mean, covariance, and sample size of multiple
covariates from different data providers once. Using the principle of
statistical sufficiency within the framework of likelihood as theoretical
support, this proposed framework achieves estimates identical to those derived
from actual individual-level data. We demonstrate this approach through real
data on 15 068 patient records from 70 clinics at the Children's Hospital of
Pennsylvania (CHOP). Assuming that each clinic only shares summary statistics
once, we model the COVID-19 PCR test cycle threshold as a function of patient
information. Simplicity, communication efficiency, and wider scope of
implementation in any statistical software distinguish our approach from
existing strategies in the literature.


  In this second paper of the series we continue to spell out a new program for
quantum gravity, grounded in the notion of corner symmetry algebra and its
representations. Here we focus on tetrad gravity and its corner symplectic
potential. We start by performing a detailed decomposition of the various
geometrical quantities appearing in BF theory and tetrad gravity. This provides
a new decomposition of the symplectic potential of BF theory and the simplicity
constraints. We then show that the dynamical variables of the tetrad gravity
corner phase space are the internal normal to the spacetime foliation, which is
conjugated to the boost generator, and the corner coframe field. This allows us
to derive several key results. First, we construct the corner Lorentz charges.
In addition to sphere diffeomorphisms, common to all formulations of gravity,
these charges add a local $\mathfrak{sl}(2,\mathbb{C})$ component to the corner
symmetry algebra of tetrad gravity. Second, we also reveal that the corner
metric satisfies a local $\mathfrak{sl}(2,\mathbb{R})$ algebra, whose Casimir
corresponds to the corner area element. Due to the space-like nature of the
corner metric, this Casimir belongs to the unitary discrete series, and its
spectrum is therefore quantized. This result, which reconciles discreteness of
the area spectrum with Lorentz invariance, is proven in the continuum and
without resorting to a bulk connection. Third, we show that the corner phase
space explains why the simplicity constraints become non-commutative on the
corner. This fact requires a reconciliation between the bulk and corner
symplectic structures, already in the classical continuum theory. Understanding
this leads inevitably to the introduction of edge modes.


  It has been suggested that the peanut-shaped bulges seen in some edge-on disk
galaxies are due to the presence of a central bar. Although bars cannot be
detected photometrically in edge-on galaxies, we show that barred potentials
produce a strong kinematic signature in the form of double-peaked line-of-sight
velocity distributions with a characteristic ``figure-of-eight'' variation with
radius. We have obtained spectroscopic observations of two edge-on galaxies
with peanut-shaped bulges (NGC~5746 and NGC~5965), and they reveal exactly such
line-of-sight velocity distributions in both their gaseous (emission line) and
their stellar (absorption line) components. These observations provide strong
observational evidence that peanut-shaped bulges are a by-product of bar
formation.


  We study the problem of minimizing the supremum norm, on a segment of the
real line or on a compact set in the plane, by polynomials with integer
coefficients. The extremal polynomials are naturally called integer Chebyshev
polynomials. Their factors, zero distribution and asymptotics are the main
subjects of this paper. In particular, we show that the integer Chebyshev
polynomials for any infinite subset of the real line must have infinitely many
distinct factors, which answers a question of Borwein and Erd\'{e}lyi.
Furthermore, it is proved that the accumulation set for their zeros must be of
positive capacity in this case.
  We also find the first nontrivial examples of explicit integer Chebyshev
constants for certain classes of lemniscates. Since it is rarely possible to
obtain an exact value of integer Chebyshev constant, good estimates are of
special importance.
  Introducing the methods of weighted potential theory, we generalize and
improve the Hilbert-Fekete upper bound for integer Chebyshev constant. These
methods also give bounds for the multiplicities of factors of integer Chebyshev
polynomials, and lower bounds for integer Chebyshev constant. Moreover, all the
mentioned bounds can be found numerically, by using various extremal point
techniques, such as weighted Leja points algorithm. Applying our results in the
classical case of the segment $[0,1]$, we improve the known bounds for the
integer Chebyshev constant and the multiplicities of factors of the integer
Chebyshev polynomials.


  We prove existence and uniqueness results for solutions to a class of optimal
transportation problems with infinitely many marginals, supported on the real
line. We also provide a characterization of the solution with an explicit
formula. We then show that this result implies an infinite dimensional
rearrangement inequality, and use it to derive upper bounds on solutions to
parabolic PDE via the Feynman-Kac formula. This result can be used to provide
model independent bounds on the prices of certain derivatives in mathematical
finance. As an another application, we obtain refined phase-space bounds in
quantum physics.


  This paper investigates a statistical procedure for testing the equality of
two independently estimated covariance matrices when the number of potentially
dependent data vectors is large and proportional to the size of the vectors,
that is, the number of variables. Inspired by the spike models used in random
matrix theory, we concentrate on the largest eigenvalues of the matrices in
order to determine significant differences. To avoid false rejections we must
guard against residual spikes and need a sufficiently precise description of
the properties of the largest eigenvalues under the null hypothesis. In this
paper, we extend arXiv:2002.12741 for perturbation of order $1$ and
arXiv:2002.12703 studying simpler statistic. The residual spike introduce in
the first paper is investigated and leads to a statistic that results in a good
test of equality of two populations. Simulations show that this new test does
not rely on some hypotheses that were necessary for the proofs and in the
second paper.


  For time-delay systems, it is known that global asymptotic stability is
guaranteed by the existence of a Lyapunov-Krasovskii functional that dissipates
in a point-wise manner along solutions, namely whose dissipation rate involves
only the current value of the solution's norm. So far, the extension of this
result to global exponential stability (GES) holds only for systems ruled by a
globally Lipschitz vector field and remains largely open for the input-to-state
stability (ISS) property. In this paper, we rely on the notion of exponential
ISS to extend the class of systems for which GES or ISS can be concluded from a
point-wise dissipation. Our results in turn show that these properties still
hold in the presence of a sufficiently small additional term involving the
whole state history norm. We provide explicit estimates of the tolerable
magnitude of this extra term and show through an example how it can be used to
assess robustness with respect to modeling uncertainties.


  N=1 supersymmetric U(N) gauge theory with adjoint matter $\Phi$ and a
polynomial superpotential $\Tr W(\Phi)$ has been much studied recently. The
classical theory has several vacua labeled by integers $(N_1,N_2,...,N_k)$,
with the classical unbroken gauge group $\prod_i U(N_i)$. Quantum mechanically,
each classical vacuum leads to $\prod_i N_i$ different vacua. As the parameters
of $W(\Phi)$ are varied, these vacua change in a continuous (and holomorphic)
fashion. We find that vacua associated with $(N_1,N_2,...,N_k)$ can be
continuously transformed to vacua with $(\tilde N_1,\tilde N_2,...,\tilde
N_k)$, thus leading to a new kind of duality. Traditional order parameters,
like the Wilson loop and 't Hooft loop, sometimes distinguish different phases.
We also find phases that are not distinguished by conventional order
parameters. The whole picture of the phase diagram is reminiscent of the phase
diagram of $M$-theory.


  We find two combinatorial identities on the theta series of the root lattices
of the finite-dimensional simple Lie algebras of type $D_{4n}$ and the cosets
in their integral duals, in terms of the well-known Essenstein series $E_4(z)$
and Ramanujan series $\Dlt_{24}(z)$. Using these two identities, we determine
the theta series of certain infinite families of postive definite even
unimodular lattices obtained by gluing finite copies of the root lattices of
the finite-dimensional simple Lie algebras of type
  $D_{2n}$. It turns out that these theta series are weighted symmetric
polynomials of two fixed families of polynomials of $E_4(z)$ and
$\Dlt_{24}(z)$.


  Given the final ranking of a competition, how should the total prize
endowment be allocated among the competitors? We study consistent prize
allocation rules satisfying elementary solidarity and fairness principles. In
particular, we axiomatically characterize several families of rules satisfying
anonymity, order preservation, and endowment monotonicity, which all fall
between the Equal Division rule and the Winner-Takes-All rule. Specific
characterizations of rules and subfamilies are directly obtained. To our
knowledge, this paper is the first that develops and motivates prize allocation
rules for rank-order competitions directly from axioms.


  We study the unzipping of double stranded DNA (dsDNA) by applying a pulling
force at a fraction $s$ $(0 \le s \le 1)$ from the anchored end. From exact
analytical and numerical results, the complete phase diagram is presented. The
phase diagram shows a strong ensemble dependence for various values of $s$. In
addition, we show the existence of an ``eye'' phase and a triple point.


  Automatic analysis of human behaviour is a fundamental prerequisite for the
creation of machines that can effectively interact with- and support humans in
social interactions. In MultiMediate'23, we address two key human social
behaviour analysis tasks for the first time in a controlled challenge:
engagement estimation and bodily behaviour recognition in social interactions.
This paper describes the MultiMediate'23 challenge and presents novel sets of
annotations for both tasks. For engagement estimation we collected novel
annotations on the NOvice eXpert Interaction (NOXI) database. For bodily
behaviour recognition, we annotated test recordings of the MPIIGroupInteraction
corpus with the BBSI annotation scheme. In addition, we present baseline
results for both challenge tasks.


  I formulate and characterize the following two-stage choice behavior. The
decision maker is endowed with two preferences. She shortlists all maximal
alternatives according to the first preference. If the first preference is
decisive, in the sense that it shortlists a unique alternative, then that
alternative is the choice. If multiple alternatives are shortlisted, then, in a
second stage, the second preference vetoes its minimal alternative in the
shortlist, and the remaining members of the shortlist form the choice set. Only
the final choice set is observable. I assume that the first preference is a
weak order and the second is a linear order. Hence the shortlist is fully
rationalizable but one of its members can drop out in the second stage, leading
to bounded rational behavior. Given the asymmetric roles played by the
underlying binary relations, the consequent behavior exhibits a minimal
compromise between two preferences. To our knowledge it is the first Choice
function that satisfies Sen's $\beta$ axiom of choice,but not $\alpha$.


  We demonstrate that it is not necessary to substantially break the mass
degeneracy between the Standard Model Higgs boson doublet and the corresponding
scalar leptoquark, where these two fields comprise a single five-dimensional
$SU(5)$ representation. More precisely, we show that the experimental data on
partial proton decay lifetimes cannot place any meaningful bound on the mass of
the scalar leptoquark, a.k.a. the color triplet, if one includes effects of
higher-dimensional operators within the Georgi-Glashow model. We also point out
that the complete suppression of proton decay via the scalar leptoquark
mediation is compatible with the partial suppression of the gauge mediated
two-body proton decay signatures. Finally, we derive a proper limit on the
cutoff scale of the aforementioned higher-dimensional operators and outline how
this scenario could be tested.


  A most fundamental and longstanding goal in spintronics is to electrically
tune highly efficient spin injectors and detectors, preferably compatible with
nanoscale electronics. Here, we demonstrate all these points using
semiconductor quantum dots (QDs), individually spin-polarized by ferromagnetic
split-gates (FSGs). As a proof of principle, we fabricated a double QD spin
valve consisting of two weakly coupled semiconducting QDs in an InAs nanowire
(NW), each with independent FSGs that can be magnetized in parallel or
anti-parallel. In tunneling magnetoresistance (TMR) experiments at zero
external magnetic field, we find a strongly reduced spin valve conductance for
the two anti-parallel configurations, with a single QD polarization of $\sim
27\%$. The TMR can be significantly improved by a small external field and
optimized gate voltages, which results in a continuously electrically tunable
TMR between $+80\%$ and $-90\%$. A simple model quantitatively reproduces all
our findings, suggesting a gate tunable QD polarization of $\pm 80\%$. Such
versatile spin-polarized QDs are suitable for various applications, for example
in spin projection and correlation experiments in a large variety of
nanoelectronics experiments.


  We propose a new method for robust PCA -- the task of recovering a low-rank
matrix from sparse corruptions that are of unknown value and support. Our
method involves alternating between projecting appropriate residuals onto the
set of low-rank matrices, and the set of sparse matrices; each projection is
{\em non-convex} but easy to compute. In spite of this non-convexity, we
establish exact recovery of the low-rank matrix, under the same conditions that
are required by existing methods (which are based on convex optimization). For
an $m \times n$ input matrix ($m \leq n)$, our method has a running time of
$O(r^2mn)$ per iteration, and needs $O(\log(1/\epsilon))$ iterations to reach
an accuracy of $\epsilon$. This is close to the running time of simple PCA via
the power method, which requires $O(rmn)$ per iteration, and
$O(\log(1/\epsilon))$ iterations. In contrast, existing methods for robust PCA,
which are based on convex optimization, have $O(m^2n)$ complexity per
iteration, and take $O(1/\epsilon)$ iterations, i.e., exponentially more
iterations for the same accuracy.
  Experiments on both synthetic and real data establishes the improved speed
and accuracy of our method over existing convex implementations.


  Given an untrimmed video, repetitive actions counting aims to estimate the
number of repetitions of class-agnostic actions. To handle the various length
of videos and repetitive actions, also optimization challenges in end-to-end
video model training, down-sampling is commonly utilized in recent
state-of-the-art methods, leading to ignorance of several repetitive samples.
In this paper, we attempt to understand repetitive actions from a full temporal
resolution view, by combining offline feature extraction and temporal
convolution networks. The former step enables us to train repetition counting
network without down-sampling while preserving all repetition regardless of the
video length and action frequency, and the later network models all frames in a
flexible and dynamically expanding temporal receptive field to retrieve all
repetitions with a global aspect. We experimentally demonstrate that our method
achieves better or comparable performance in three public datasets, i.e.,
TransRAC, UCFRep and QUVA. We expect this work will encourage our community to
think about the importance of full temporal resolution.


  The interference pattern produced by a quantum particle in Young's
double-slit setup is attributed to the particle's wavefunction having gone
through both slits. In the path integral formulation, this interference
involves a superposition of paths, going through either slit, linking the
source to the detection point. We show how these paths superpositions can in
principle be observed by implementing a series of minimally-perturbing weak
measurements between the slits and the detection plane. We further propose a
simplified protocol in order to observe these "weak trajectories" with single
photons.


  The behavior of QCD at high baryon density and low temperature is crucial to
understanding the properties of neutron stars and gravitational waves emitted
during their mergers. In this paper we study small systems of baryons in
periodic boundary conditions to probe the properties of QCD at high baryon
density. By comparing calculations based on nucleon degrees of freedom to
simple quark models we show that specific features of the nuclear spectrum,
including shell structure and nucleon pairing, emerge if nucleons are the
primary degrees of freedom. Very small systems should also be amenable to
studies in lattice QCD, unlike larger systems where the fermion sign problem is
much more severe. Through comparisons of lattice QCD and nuclear calculations
it should be possible to gain, at at least a semi-quantitative level, more
understanding of the cold dense equation of state as probed in neutron stars.


  The inversion and volume effects on magnetism in a spinel-type magnetically
frustrated compound, CoAl2O4, and its gallium-substituted system, CoAl2-xGaxO4,
were investigated. Magnetically frustrated Co2+ with spin S = 3/2 on the
tetrahedral site formed a diamond lattice in CoAl2O4 located in the vicinity of
the magnetic phase boundary between Neel and spin-spiral states. In the
Ga-substituted system, the number of Co ions, the so-called inversion h
dominating the octahedral site, increased with increasing x. From comprehensive
crystallographic, magnetic, and thermal measurements, increments of both volume
and inversion strongly reduced the Neel point, while the latter also induced a
spin-glass state above the critical value of hc = 0.09. In the spin glass
state, h > hc, the orbital degree of freedom of Co2+ ions in the octahedral
site appeared in the magnetic entropy, which couples strongly with that of
spin, even above the magnetic transitions. Above h ~ hc, the field-induced
quenched magnetic moment appeared above the transitions. Therefore, a short
range ordered state emerged among the paramagnetic, antiferromganetic, and
spin-glass states in the magnetic phase diagram.


  Exact analytic expressions for various characteristics of the hyperbolic-type
orbits of a particle in the Schwarzschild geometry are presented. A useful
simple approximation formula is given for the case when the deviation from the
Newtonian hyperbolic path is very small.


  We prove continuity on domains up to the boundary for n/2-polyharmonic maps
into manifolds. Technically, we show how to adapt Helein's direct approach to
the fractional setting. This extends a remark by the author that this is
possible in the setting of Riviere's famous regularity result for critical
points of conformally invariant variational functionals. Moreover, pointwise
behavior for the involved three-commutators is established. Continuity up to
the boundary is then obtained via an adaption of Hildebrandt and Kaul's
technique to the non-local setting.


  We propose a high-statistics measurement of few body nuclear structure and
short range correlations in quasi-elastic scattering at 6.6 GeV from $^2$H,
$^3$He and $^3$H targets in Hall B with the CLAS12 detector.
  We will measure absolute cross sections for $(e,e'p)$ and $(e,e'pN)$
quasi-elastic reaction channels up to a missing momentum $p_{miss} \approx 1$
GeV/c over a wide range of $Q^2$ and $x_B$ and construct the isoscalar sum of
$^3$H and $^3$He. We will compare $(e,e'p)$ cross sections to nuclear theory
predictions using a wide variety of techniques and $NN$ interactions in order
to constrain the $NN$ interaction at short distances. We will measure
$(e,e'pN)$ quasi-elastic reaction cross sections and $(e,e'pN)/(e,e'p)$ ratios
to understand short range correlated (SRC) $NN$ pairs in the simplest
non-trivial system. $^3$H and $^3$He, being mirror nuclei, exploit the maximum
available isospin asymmetry. They are light enough that their ground states are
readily calculable, but they already exhibit complex nuclear behavior,
including $NN$ SRCs. We will also measure $^2$H$(e,e'p)$ in order to help
theorists constrain non-quasielastic reaction mechanisms in order to better
calculate reactions on $A=3$ nuclei. Measuring all three few body nuclei
together is critical, in order to understand and minimize different reaction
effects, such as single charge exchange final state interactions, in order to
test ground-state nuclear models.
  We will also measure the ratio of inclusive $(e,e')$ quasi-elastic cross
sections (integrated over $x_B$) from $^3$He and $^3$H in order to extract the
neutron magnetic form factor $G_M^n$ at small and moderate values of $Q^2$. We
will measure this at both 6.6 GeV and 2.2 GeV.


  Inspired by Internet ad auction applications, we study the problem of
allocating a single item via an auction when bidders place very different
values on the item. We formulate this as the problem of prior-free auction and
focus on designing a simple mechanism that always allocates the item. Rather
than designing sophisticated pricing methods like prior literature, we design
better allocation methods. In particular, we propose quasi-proportional
allocation methods in which the probability that an item is allocated to a
bidder depends (quasi-proportionally) on the bids.
  We prove that corresponding games for both all-pay and winners-pay
quasi-proportional mechanisms admit pure Nash equilibria and this equilibrium
is unique. We also give an algorithm to compute this equilibrium in polynomial
time. Further, we show that the revenue of the auctioneer is promisingly high
compared to the ultimate, i.e., the highest value of any of the bidders, and
show bounds on the revenue of equilibria both analytically, as well as using
experiments for specific quasi-proportional functions. This is the first known
revenue analysis for these natural mechanisms (including the special case of
proportional mechanism which is common in network resource allocation
problems).


  "Approximate Bayesian Computation" (ABC) represents a powerful methodology
for the analysis of complex stochastic systems for which the likelihood of the
observed data under an arbitrary set of input parameters may be entirely
intractable-the latter condition rendering useless the standard machinery of
tractable likelihood-based, Bayesian statistical inference (e.g. conventional
Markov Chain Monte Carlo simulation; MCMC). In this article we demonstrate the
potential of ABC for astronomical model analysis by application to a case study
in the morphological transformation of high redshift galaxies. To this end we
develop, first, a stochastic model for the competing processes of merging and
secular evolution in the early Universe; and second, through an ABC-based
comparison against the observed demographics of massive (M_gal > 10^11 M_sun)
galaxies (at 1.5 < z < 3) in the CANDELS/EGS dataset we derive posterior
probability densities for the key parameters of this model. The "Sequential
Monte Carlo" (SMC) implementation of ABC exhibited herein, featuring both a
self-generating target sequence and self-refining MCMC kernel, is amongst the
most efficient of contemporary approaches to this important statistical
algorithm. We highlight as well through our chosen case study the value of
careful summary statistic selection, and demonstrate two modern strategies for
assessment and optimisation in this regard. Ultimately, our ABC analysis of the
high redshift morphological mix returns tight constraints on the evolving
merger rate in the early Universe and favours major merging (with disc survival
or rapid reformation) over secular evolution as the mechanism most responsible
for building up the first generation of bulges in early-type disks.


  We study translation invariant stochastic processes on $\mathbb{R}^d$ or
$\mathbb{Z}^d$ whose diffraction spectrum or structure function $S(k)$, i.e.
the Fourier transform of the truncated total pair correlation function,
vanishes on an open set $U$ in the wave space. A key family of such processes
are stealthy hyperuniform point processes, for which the origin $k=0$ is in
$U$; these are of much current physical interest. We show that all such
processes exhibit the following remarkable maximal rigidity : namely, the
configuration outside a bounded region determines, with probability 1, the
exact value (or the exact locations of the points) of the process inside the
region. In particular, such processes are completely determined by their tail.
In the 1D discrete setting (i.e. $\mathbb{Z}$-valued processes on
$\mathbb{Z}$), this can also be seen as a consequence of a recent theorem of
Borichev, Sodin and Weiss; in higher dimensions or in the continuum, such a
phenomenon seems novel. For stealthy hyperuniform point processes, we prove the
Zhang-Stillinger-Torquato conjecture that such processes have bounded holes
(empty regions), with a universal bound that depends inversely on the size of
$U$.


  The Zwicky Transient Facility (ZTF), a public-private enterprise, is a new
time domain survey employing a dedicated camera on the Palomar 48-inch Schmidt
telescope with a 47 deg$^2$ field of view and 8 second readout time. It is well
positioned in the development of time domain astronomy, offering operations at
10% of the scale and style of the Large Synoptic Survey Telescope (LSST) with a
single 1-m class survey telescope. The public surveys will cover the observable
northern sky every three nights in g and r filters and the visible Galactic
plane every night in g and r. Alerts generated by these surveys are sent in
real time to brokers. A consortium of universities which provided funding
("partnership") are undertaking several boutique surveys. The combination of
these surveys producing one million alerts per night allows for exploration of
transient and variable astrophysical phenomena brighter than r $\sim$ 20.5 on
timescales of minutes to years. We describe the primary science objectives
driving ZTF including the physics of supernovae and relativistic explosions,
multi-messenger astrophysics, supernova cosmology, active galactic nuclei and
tidal disruption events, stellar variability, and Solar System objects.


  This note deals with the relationship between the total number of $k$-walks
in a graph, and the sum of the $k$-th powers of its vertex degrees. In
particular, it is shown that the the number of all $k$-walks is upper bounded
by the sum of the $k$-th powers of the degrees.


  For mobile robots range sensors are important to perceive the environment.
Sensors that can measure in a 3D volume are especially significant for outdoor
robotics, because this environment is often highly unstructured. The quality of
the data gathered by those sensors influences all algorithms relying on it. In
this paper thus the precision of several 2D and 2.5D sensors is measured at
different ranges and different incidence angles. The results of all tests are
presented and analyzed.


  It is shown that local distinguishability of orthogonal mixed states can be
completely characterized by local distinguishability of their supports
irrespective of entanglement and mixedness of the states. This leads to two
kinds of upper bounds on the number of perfect LOCC distinguishable orthogonal
mixed states. The first one depends only on pure-state entanglement within the
supports of the states, and therefore may be easy to compute in many instances.
The second bound is optimal in the sense that it optimizes the bounding
quantities, not necessarily function of entanglement alone, over all orthogonal
mixed state ensembles (satisfying certain conditions) admissible within the
supports of the density matrices.


  We study the nonrelativistic limit of the quantum theory of a Chern-Simons
field minimally coupled to a scalar field with quartic self-interaction. The
renormalization of the relativistic model, in the Coulomb gauge, is discussed.
We employ a procedure to calculate scattering amplitudes for low momenta that
generates their $|p|/m$ expansion and separates the contributions coming from
high and low energy intermediary states. The two body scattering amplitude is
calculated up to order $p^2/m^2$. It is shown that the existence of a critical
value of the self-interaction parameter for which the 2-particle scattering
amplitude reduces to the Aharonov-Bohm one is a strictly nonrelativistic
feature. The subdominant terms correspond to relativistic corrections to the
Aharonov-Bohm scattering. A nonrelativistic reduction scheme and an effective
nonrelativistic Lagrangian to account for the relativistic corrections are
proposed.


  For fine-grained categorization tasks, videos could serve as a better source
than static images as videos have a higher chance of containing discriminative
patterns. Nevertheless, a video sequence could also contain a lot of redundant
and irrelevant frames. How to locate critical information of interest is a
challenging task. In this paper, we propose a new network structure, known as
Redundancy Reduction Attention (RRA), which learns to focus on multiple
discriminative patterns by sup- pressing redundant feature channels.
Specifically, it firstly summarizes the video by weight-summing all feature
vectors in the feature maps of selected frames with a spatio-temporal soft
attention, and then predicts which channels to suppress or to enhance according
to this summary with a learned non-linear transform. Suppression is achieved by
modulating the feature maps and threshing out weak activations. The updated
feature maps are then used in the next iteration. Finally, the video is
classified based on multiple summaries. The proposed method achieves out-
standing performances in multiple video classification datasets. Further- more,
we have collected two large-scale video datasets, YouTube-Birds and
YouTube-Cars, for future researches on fine-grained video categorization. The
datasets are available at http://www.cs.umd.edu/~chenzhu/fgvc.


  As part of our radial velocity survey of low Galactic latitude structures
that surround the Galactic disc, we report the detection of the so called
Monoceros Ring in the foreground of the Carina dwarf galaxy at Galactic
coordinates (l,b)=(260,-22) based on VLT/FLAMES observations of the dwarf
galaxy. At this location, 20 degrees in longitude greater than previous
detections, the Ring has a mean radial velocity of 145+/-5 km/s and a velocity
dispersion of only 17+/-5 km/s. Based on Keck/DEIMOS observations, we also
determine that the Ring has a mean radial velocity of -75+/-4 km/s in the
foreground of the Andromeda galaxy at (l,b)\sim(122,-22), along with a velocity
dispersion of 26+/-3 km/s. These two kinematic detections are both highly
compatible with known characteristics of the structure and, along with previous
detections provide radial velocity values of the Ring over the 120<l<260 range.
This should add strong constraints on numerical models of the accretion of the
dwarf galaxy that is believed to be the progenitor of the Ring.


  3D scene flow characterizes how the points at the current time flow to the
next time in the 3D Euclidean space, which possesses the capacity to infer
autonomously the non-rigid motion of all objects in the scene. The previous
methods for estimating scene flow from images have limitations, which split the
holistic nature of 3D scene flow by estimating optical flow and disparity
separately. Learning 3D scene flow from point clouds also faces the
difficulties of the gap between synthesized and real data and the sparsity of
LiDAR point clouds. In this paper, the generated dense depth map is utilized to
obtain explicit 3D coordinates, which achieves direct learning of 3D scene flow
from 2D images. The stability of the predicted scene flow is improved by
introducing the dense nature of 2D pixels into the 3D space. Outliers in the
generated 3D point cloud are removed by statistical methods to weaken the
impact of noisy points on the 3D scene flow estimation task. Disparity
consistency loss is proposed to achieve more effective unsupervised learning of
3D scene flow. The proposed method of self-supervised learning of 3D scene flow
on real-world images is compared with a variety of methods for learning on the
synthesized dataset and learning on LiDAR point clouds. The comparisons of
multiple scene flow metrics are shown to demonstrate the effectiveness and
superiority of introducing pseudo-LiDAR point cloud to scene flow estimation.


  We study the spontaneous de-excitation and excitation of accelerated atoms on
arbitrary stationary trajectories (``generalized Unruh effect''). We consider
the effects of vacuum fluctuations and radiation reaction separately. We show
that radiation reaction is generally not altered by stationary acceleration,
whereas the contribution of vacuum fluctuations differs for all stationary
accelerated trajectories from its inertial value. Spontaneous excitation from
the ground state occurs for all { accelerated stationary} trajectories and is
therefore the ``normal case''. We furthermore show that the radiative energy
shift (``Lamb shift'') of a two-level atom is modified by acceleration for all
stationary trajectories. Again only vacuum fluctuations give rise to the shift.
Our results are illustrated for the special case of an atom in circular motion,
which may be experimentally relevant.


  Abundance studies of solar-type stars revealed a small fraction of objects
with extreme depletion of beryllium. We investigate the possible link between
the beryllium depletion and the presence of companions. The classical methods
(radial velocity, astrometry, imaging) used to search for binary companions
were exploited. We also performed a chemical analysis to identify binaries by
the alteration in abundances that is produced by the accretion of material lost
by a former evolved companion. We found that all the four previously
investigated stars that were found to be ultra--depleted in Be are binaries. In
two cases the companion is a white dwarf, and in the other two cases the
companion might be a white dwarf or a main-sequence star. One new barium star
was identified. We speculate that the interaction with the white dwarf
progenitor caused an alteration in the abundance pattern of the star, which
resulted in severe beryllium depletion. Possible mechanisms such as
thermohaline mixing, episodic accretion, and rotational mixing are discussed.
We also briefly discuss predictions for validating this scenario


  We study the charge of a small normal island connected by a tunnel junction
to a superconducting lead. Unlike the N-I-N case, the steps of the Coulomb
staircase remain sharp even if the conductance of the tunneling barrier exceeds
e^2/h. One can observe the transition from sharp steps to the smeared ones by
applying magnetic field to destroy the superconductivity.


  Coherence times of electron spins bound to phosphorus donors have been
measured, using a standard Hahn echo technique, to be up to 20 ms in
isotopically pure silicon with [P]$ = 10^{14}$ cm$^{-3}$ and at temperatures
$\leq 4 $K. Although such times are exceptionally long for electron spins in
the solid state, they are nevertheless limited by donor electron spin-spin
interactions. Suppressing such interactions requires even lower donor
concentrations, which lie below the detection limit for typical electron spin
resonance (ESR) spectrometers. Here we describe an alternative method for
phosphorus donor ESR detection, exploiting the spin-to-charge conversion
provided by the optical donor bound exciton transition. We characterise the
method and its dependence on laser power and use it to measure a coherence time
of $T_2 = 130 $ms for one of the purest silicon samples grown to-date ([P]$ =
5\times 10^{11} $cm$^{-3}$). We then benchmark this result using an alternative
application of the donor bound exciton transition: optically polarising the
donor spins before using conventional ESR detection at 1.7~K for a sample with
[P]$ = 4\times10^{12} $cm$^{-3}$, and measuring in this case a $T_2$ of 350 ms.


  The spin-resolved thermoelectric transport properties of correlated nanoscale
junctions, consisting of a quantum dot/molecule asymmetrically coupled to
external ferromagnetic contacts, are studied theoretically in the
far-from-equilibrium regime. One of the leads is assumed to be strongly coupled
to the quantum dot resulting in the development of the Kondo effect. The
spin-dependent current flowing through the system, as well as the
thermoelectric properties, are calculated by performing a perturbation
expansion with respect to the weakly coupled electrode, while the Kondo
correlations are captured accurately by using the numerical renormalization
group method. In particular, we determine the differential and nonequilibrium
Seebeck effects of the considered system in different magnetic configurations
and uncover the crucial role of spin-dependent tunneling on the device
performance. Moreover, by allowing for spin accumulation in the leads, which
gives rise to finite spin bias, we shed light on the behavior of the
nonequilibrium spin Seebeck effect.


  In this paper we extend Chandrasekhar and von Neumann's analysis of the
statistics of the gravitational field to systems in which particles (e.g.
stars, galaxies) are not homogeneously distributed. We derive a distribution
function W({F},dF/dt) giving the joint probability that a test particle is
subject to a force F and an associated rate of change of F given by dF/dt. We
calculate the first moment of dF/dt to study the effects of inhomogenity on
dynamical friction.


  The Liouville-Lanczos approach to linear-response time-dependent
density-functional theory is generalized so as to encompass electron
energy-loss and inelastic X-ray scattering spectroscopies in periodic solids.
The computation of virtual orbitals and the manipulation of large matrices are
avoided by adopting a representation of response orbitals borrowed from
(time-independent) density-functional perturbation theory and a suitable
Lanczos recursion scheme. The latter allows the bulk of the numerical work to
be performed at any given transferred momentum only once, for a whole extended
frequency range. The numerical complexity of the method is thus greatly
reduced, making the computation of the loss function over a wide frequency
range at any given transferred momentum only slightly more expensive than a
single standard ground-state calculation, and opening the way to computations
for systems of unprecedented size and complexity. Our method is validated on
the paradigmatic examples of bulk silicon and aluminum, for which both
experimental and theoretical results already exist in the literature.


  We report the detection of hard X-ray emission components in the spectra of
six nearby, giant elliptical galaxies observed with the ASCA satellite. The
systems studied, which exhibit strong dynamical evidence for supermassive black
holes in their nuclei, are M87, NGC 1399 and NGC 4696 (the dominant galaxies of
the Virgo, Fornax and Centaurus clusters, respectively) and NGC 4472, 4636 and
4649 (three further giant ellipticals in the Virgo cluster). The ASCA data for
all six sources provide clear evidence for hard emission components, which can
be parameterized by power-law models with photon indices in the range \Gamma =
0.6-1.5 (mean value 1.2) and intrinsic 1-10 keV luminosities of 2 \times
10^{40} - 2 \times 10^{42} erg/s. Our results imply the identification of a new
class of accreting X-ray source, with X-ray spectra significantly harder than
those of binary X-ray sources, Seyfert nuclei or low luminosity AGN, and
bolometric luminosities relatively dominated by their X-ray emission. We
discuss various possible origins for the hard X-ray emission and argue that it
is most likely to be due to accretion onto the central supermassive black
holes, via low-radiative efficiency accretion coupled with strong outflows. In
the case of M87, our detected power-law flux is in good agreement with a
previously-reported measurement from ROSAT High Resolution Imager observations,
which were able to resolve the jet from the nuclear X-ray emission components.
We confirm previous results showing that the use of multiphase models in the
analysis of the ASCA data leads to determinations of approximately solar
emission-weighted metallicities for the X-ray gas in the galaxies. We also
present results on the individual element abundances in NGC 4636.


  We study the spectra of heavy-light and heavy-heavy mesons containing charm
quarks, including higher spin states. We use two sets of $N_f = 2 + 1$ gauge
configurations, one set from QCDSF using the SLiNC action, and the other
configurations from the Budapest-Marseille-Wuppertal collaboration, using the
HEX smeared clover action. To extract information about the excited states, we
choose a suitable basis of operators to implement the variational method.


  We present TEM images of the interior of metal whiskers (MW) grown on
electroplated Sn films. Along with earlier published information, our
observations focus on a number of questions, such as why MWs' diameters are in
the micron range (significantly exceeding the typical nano-sizes of nuclei in
solids), why the diameters remain practically unchanged in the course of MW
growth, what is the nature of MW diameter stochasticity, and what is the origin
of the well-known striation structure of MW side surfaces. In an attempt to
address such questions we performed an in-depth study of MW structure at the
nanoscale by detaching a MW from its original film, reducing its size to a thin
slice by cutting its sides by a focused ion beam, and performing TEM on that
structure. Our observations revealed a rich nontrivial morphology suggesting
that MW may consist of many side by side grown filaments. This structure
appears to extend to the outside whisker surface and be the reason for the
striation. In addition, we put forward a theory where nucleation of multiple
thin metal needles results into micron-scale and larger MW diameters. This
theory is developed in the average field approximation similar to the
roughening transitions of metal surfaces. The theory also predicts MW
nucleation barriers and other observed features.


  The three-dimensional generalized tropical climate model with partial
viscosity and damping is considered in this paper. Global well-posedness of
solutions of the three-dimensional generalized tropical climate model with
partial viscosity and damping is proved for $\alpha\geq\frac{3}{2}$ and
$\beta\geq4$. Global smooth solution of the three-dimensional generalized
tropical climate model with partial viscosity and damping is proved in
$H^s(\mathbb R^3)$ $(s>2)$ for $\alpha\geq\frac{3}{2}$ and $4\leq\beta\leq5$.


  Generating a set of high-quality correspondences or matches is one of the
most critical steps in point cloud registration. This paper proposes a learning
framework COTReg by jointly considering the pointwise and structural matchings
to predict correspondences of 3D point cloud registration. Specifically, we
transform the two matchings into a Wasserstein distance-based and a
Gromov-Wasserstein distance-based optimizations, respectively. Thus the task of
establishing the correspondences can be naturally reshaped to a coupled optimal
transport problem. Furthermore, we design a network to predict the confidence
score of being an inlier for each point of the point clouds, which provides the
overlap region information to generate correspondences. Our correspondence
prediction pipeline can be easily integrated into either learning-based
features like FCGF or traditional descriptors like FPFH. We conducted
comprehensive experiments on 3DMatch, KITTI, 3DCSR, and ModelNet40 benchmarks,
showing the state-of-art performance of the proposed method.


  We extend the existing enumeration of neck tie-knots to include tie-knots
with a textured front, tied with the narrow end of a tie. These tie-knots have
gained popularity in recent years, based on reconstructions of a costume detail
from The Matrix Reloaded, and are explicitly ruled out in the enumeration by
Fink and Mao (2000).
  We show that the relaxed tie-knot description language that comprehensively
describes these extended tie-knot classes is context free. It has a regular
sub-language that covers all the knots that originally inspired the work.
  From the full language, we enumerate 266 682 distinct tie-knots that seem
tie-able with a normal neck-tie. Out of these 266 682, we also enumerate 24 882
tie-knots that belong to the regular sub-language.


  We prove a degeneration formula for Donaldson-Thomas theory on Calabi-Yau
4-folds, and apply it to compute zero dimensional invariants on $\mathbb{C}^4$
and on any local curve.


  In this technical report we describe the IDLAB top-scoring submissions for
the VoxCeleb Speaker Recognition Challenge 2020 (VoxSRC-20) in the supervised
and unsupervised speaker verification tracks. For the supervised verification
tracks we trained 6 state-of-the-art ECAPA-TDNN systems and 4 Resnet34 based
systems with architectural variations. On all models we apply a large margin
fine-tuning strategy, which enables the training procedure to use higher margin
penalties by using longer training utterances. In addition, we use
quality-aware score calibration which introduces quality metrics in the
calibration system to generate more consistent scores across varying levels of
utterance conditions. A fusion of all systems with both enhancements applied
led to the first place on the open and closed supervised verification tracks.
The unsupervised system is trained through contrastive learning. Subsequent
pseudo-label generation by iterative clustering of the training embeddings
allows the use of supervised techniques. This procedure led to the winning
submission on the unsupervised track, and its performance is closing in on
supervised training.


  The MARTINI numerical simulation allows for direct comparison of theoretical
model calculations and the latest results for dijet asymmetry from the ATLAS
and CMS collaborations. In this paper, partons are simulated as undergoing
radiative and collisional processes throughout the evolution of central
lead-lead collisions at the Large Hadron Collider. Using hydrodynamical
background evolution determined by a simulation which fits well with the data
on charged particle multiplicities from ALICE and a value of $\alpha_s\approx
0.25-0.3$, the dijet asymmetry is found to be consistent with partonic energy
loss in a hot, strongly-interacting medium.


  The Bogoliubov procedure in quantum field theory is used to describe a
relativistic almost ideal Bose gas at zero temperature. Special attention is
given to the study of a vortex. The radius of the vortex in the field
description is compared to that obtained in the relativistic fluid
approximation. The Kelvin waves are studied and, for long wavelengths, the
dispersion relation is obtained by an asymptotic matching method and compared
with the non relativistic result.


  The disk complex of a surface in a 3-manifold is used to define its {\it
topological index}. Surfaces with well-defined topological index are shown to
generalize well-known classes, such as incompressible, strongly irreducible,
and critical surfaces. The main result is that one may always isotope a surface
$H$ with topological index $n$ to meet an incompressible surface $F$ so that
the sum of the indices of the components of $H \setminus N(F)$ is at most $n$.
This theorem and its corollaries generalize many known results about surfaces
in 3-manifolds, and often provides more efficient proofs. The paper concludes
with a list of questions and conjectures, including a natural generalization of
Hempel's {\it distance} to surfaces with topological index $\ge 2$.


  The fractional operators together with exponential quantum in coordinate and
momentum space corresponding to the power of observables are introduced. Based
on an exponential relation between energy and momentum, the fractional
Schr\"odinger equations for the free particle and the one in potential fields
in heterogeneous complex media are found. The fractional equation of motion and
the fractional virial theorem for anomalous quantum mechanics are then
developed. Applying the fractional virial theorem, we derive an anomalous
hydrogen atom whose transition energy values are much higher than that of Bohr
hydrogen atom. The anomalous Heisenberg picture being equivalent to the
fractional Schr\"odinger picture is also discussed.


  We study entire solutions of the biharmonic heat equation on complete
Riemannian manifolds without boundary. We provide exponential decay estimates
for the biharmonic heat kernel under assumptions on the lower bound of Ricci
curvature and noncollapsing of unit balls. And we prove a uniqueness criteria
for the Cauchy problem. As corollaries we prove the conservation law for the
biharmonic heat kernel and a uniform L-infinite estimate for entire solutions
starting with bounded initial data.


  We present a calculation of the fourth-order (NLO) contribution to
spin-dependent Compton scattering in heavy-baryon chiral perturbation theory,
and we give results for the four spin polarisabilities. No low-energy
constants, except for the anomalous magnetic moments of the nucleon, enter at
this order. For forward scattering the fourth-order piece of the spin
polarisability of the proton turns out to be almost twice the size of the
leading piece, with the opposite sign. This leads to the conclusion that no
prediction can currently be made for this quantity. For backward scattering the
fourth-order contribution is much smaller than the third-order piece which is
dominated by the anomalous scattering, and so cannot explain the discrepancy
between the CPT result and the current best experimental determination.


  We investigate the equilibrium and radial stability of spherically symmetric
relativistic stars, considering a polytropic equation of state (EoS), within
the framework of $f(R,T)$ gravity with a conservative energy-momentum tensor.
Both modified stellar structure equations and Chandrasekhar's pulsation
equations are derived for the $f(R,T)= R+ h(T)$ gravity model, where the
function $h(T)$ assumes a specific form in order to safeguard the conservation
equation for the energy-momentum tensor. The neutron star properties, such as
radius, mass, binding energy and oscillation spectrum are studied in detail.
Our results show that a cusp -- which signals the appearance of instability --
is formed when the binding energy is plotted as a function of the compact star
proper mass. We find that the squared frequency of the fundamental vibration
mode passes through zero at the central-density value corresponding to such a
cusp where the binding energy is a minimum.


  We consider the case of a chiral soliton lattice subjected to uniaxial
elastic strain applied perpendicular to the chiral axis and derive through
analytical modelling the phase diagram of magnetic states supported in the
presence of an external magnetic field. The strain induced anisotropies give
rise to three distinct non-trivial spin textures, depending on the nature of
the strain, and we show how these states may be identified by their signatures
in Lorentz transmission electron microscopy (TEM). Experimental TEM
measurements of the Fresnel contrast in a strained sample of the prototypical
monoaxial chrial helimagnet CrNb$_3$S$_6$ are reported and compare well with
the modelled contrast. Our results demonstrate an additional degree of freedom
that may be used to tailor the magnetic properties of helimagnets for
fundamental research and applications in the areas of spintronics and the
emerging field of strain manipulated spintronics.


  Unmanned Aerial Vehicles (UAV), commonly known as drones, have many potential
uses in real world applications. Drones require advanced planning and
navigation algorithms to enable them to safely move through and interact with
the world around them. This paper presents an extended potential field
controller (ePFC) which enables an aerial robot, or drone, to safely track a
dynamic target location while simultaneously avoiding any obstacles in its
path. The ePFC outperforms a traditional potential field controller (PFC) with
smoother tracking paths and shorter settling times. The proposed ePFC's
stability is evaluated by Lyapunov approach, and its performance is simulated
in a Matlab environment. Finally, the controller is implemented on an
experimental platform in a laboratory environment which demonstrates the
effectiveness of the controller.


  Let L/K be a finite Galois extension of complete local fields with finite
residue fields and let G=Gal(L/K). Let G_1 and G_2 be the first and second
ramification groups. Thus L/K is tamely ramified when G_1 is trivial and we say
that L/K is weakly ramified when G_2 is trivial. Let O_L be the valuation ring
of L and let P_L be its maximal ideal. We show that if L/K is weakly ramified
and n is congruent to 1 mod |G_1| then P_L^n is free over the group ring
O_K[G], and we construct an explicit generating element. Under the additional
assumption that L/K is wildly ramified, we then show that every free generator
of P_L over O_K[G] is also a free generator of O_L over its associated order in
the group algebra K[G]. Along the way, we prove a `splitting lemma' for local
fields, which may be of independent interest.


  The operator that intertwines between the $\mathbb{Z}_2$ - Dunkl operator and
the derivative is shown to have a realization in terms of the oscillator
operators in one dimension. This observation rests on the fact that the Dunkl
intertwining operator maps the Hermite polynomials on the generalized Hermite
polynomials.


  The increasing need to store large amounts of information with an
ultra-dense, reliable, low power and low cost memory device is driving
aggressive efforts to improve upon current perpendicular magnetic recording
technology. However, the difficulties in fabricating small grain recording
media while maintaining thermal stability and a high signal-to-noise ratio
motivate development of alternative methods, such as the patterning of magnetic
nano-islands and utilizing energy-assist for future applications. In addition,
both from sensor and memory perspective three-dimensional spintronic devices
are highly desirable to overcome the restrictions on the functionality in the
planar structures. Here we demonstrate a three-dimensional magnetic-memory
(magnetic page memory) based on thermally assisted and stray-field induced
transfer of domains in a vertical stack of magnetic nanowires with
perpendicular anisotropy. Using spin-torque induced domain shifting in such a
device with periodic pinning sites provides additional degrees of freedom by
allowing lateral information flow to realize truly three-dimensional
integration.


  We study the impact of picosecond precision timing detection systems on the
LHC experiments' long-lived particle search program during the HL-LHC era. We
develop algorithms that allow us to reconstruct the mass of such charged
particles and perform particle identification using the time-of-flight
measurement. We investigate the reach for benchmark scenarios as a function of
the timing resolution, and find sensitivity improvement of up to a factor of
ten, depending on the new heavy particle mass.


  If the transverse jet B fields observed in BL Lac objects on parsec scales
represent the toroidal component of the jet B fields, this should give rise to
rotation-measure gradients across the jets, due to the systematic change in the
line-of-sight component of the jet B field. We have found evidence for such
rotation-measure gradients in one-third to one-half of the 1 Jy BL Lac objects
we have analyzed. We present and discuss these new results, together with some
of their implications for our understanding of the parsec-scale jets of AGN.


  We show that the full global symmetry groups of all the D-dimensional maximal
supergravities can be described in terms of the closure of the internal general
coordinate transformations of the toroidal compactifications of D=11
supergravity and of type IIB supergravity, with type IIA/IIB T-duality
providing an intertwining between the two pictures. At the quantum level, the
part of the U-duality group that corresponds to the surviving discretised
internal general coordinate transformations in a given picture leaves the
internal torus invariant, while the part that is not described by internal
general coordinate transformations can have the effect of altering the size or
shape of the internal torus. For example, M-theory compactified on a large
torus T^n can be related by duality to a compactification on a small torus, if
and only if n\ge 3. We also discuss related issues in the toroidal
compactification of the self-dual string to D=4. An appendix includes the
complete results for the toroidal reduction of the bosonic sector of type IIB
supergravity to arbitrary dimensions D\ge3.


  Phase field methods have been widely used to study phase transitions and
polarization switching in ferroelectric thin films. In this paper, we develop
an efficient numerical scheme for the variational phase field model based on
variational forms of the electrostatic energy and the relaxation dynamics of
the polarization vector. The spatial discretization combines the Fourier
spectral method with the finite difference method to handle three-dimensional
mixed boundary conditions. It allows for an efficient semi-implicit
discretization for the time integration of the relaxation dynamics. This method
avoids explicitly solving the electrostatic equilibrium equation (a Poisson
equation) and eliminates the use of associated Lagrange multipliers. We present
several numerical examples including phase transitions and polarization
switching processes to demonstrate the effectiveness of the proposed method.


  Three-dimensional topological insulators are a class of Dirac materials,
wherein strong spin-orbit coupling leads to two-dimensional surface states. The
latter feature spin-momentum locking, i.e., each momentum vector is associated
with a spin locked perpendicularly to it in the surface plane. While the
principal spin generation capability of topological insulators is well
established, comparatively little is known about the interaction of the spins
with external stimuli like polarized light. We observe a helical,
bias-dependent photoconductance at the lateral edges of topological Bi2Te2Se
platelets for perpendicular incidence of light. The same edges exhibit also a
finite bias-dependent Kerr angle, indicative of spin accumulation induced by a
transversal spin Hall effect in the bulk states of the Bi2Te2Se platelets. A
symmetry analysis shows that the helical photoconductance is distinct to common
longitudinal photoconductance and photocurrent phenomena, but consistent with
the accumulated spins being transported in the side facets of the platelets.
Our findings demonstrate that spin effects in the facets of 3D topological
insulators can be addressed and read-out in optoelectronic devices even at room
temperatures.


  We introduce PC2WF, the first end-to-end trainable deep network architecture
to convert a 3D point cloud into a wireframe model. The network takes as input
an unordered set of 3D points sampled from the surface of some object, and
outputs a wireframe of that object, i.e., a sparse set of corner points linked
by line segments. Recovering the wireframe is a challenging task, where the
numbers of both vertices and edges are different for every instance, and
a-priori unknown. Our architecture gradually builds up the model: It starts by
encoding the points into feature vectors. Based on those features, it
identifies a pool of candidate vertices, then prunes those candidates to a
final set of corner vertices and refines their locations. Next, the corners are
linked with an exhaustive set of candidate edges, which is again pruned to
obtain the final wireframe. All steps are trainable, and errors can be
backpropagated through the entire sequence. We validate the proposed model on a
publicly available synthetic dataset, for which the ground truth wireframes are
accessible, as well as on a new real-world dataset. Our model produces
wireframe abstractions of good quality and outperforms several baselines.


  Hadronic resonance production plays an important role both in elementary and
in nucleus-nucleus collisions. In heavy-ion collisions, since the lifetimes of
short-lived resonances are comparable with the lifetime of the late hadronic
phase, regeneration and rescattering effects become important and ratios of
yields of resonances relative to those of longer lived particles can be used to
estimate the time interval between the chemical and kinetic freeze-out. The
measurements in pp and p--Pb collisions constitute a reference for nuclear
collisions and provide information for tuning event generators inspired by
Quantum Chromodynamics.


  Recent direct experimental observation of multiple highly-dispersive C$_{60}$
valence bands has allowed for a detailed analysis of the unique photoemission
traits of these features through photon energy- and polarization-dependent
measurements. Previously obscured dispersions and strong photoemission traits
are now revealed by specific light polarizations. The observed intensity
effects prove the locking in place of the C$_{60}$ molecules at low
temperatures and the existence of an orientational order imposed by the
substrate chosen. Most importantly, photon energy- and polarization-dependent
effects are shown to be intimately linked with the orbital character of the
C$_{60}$ band manifolds which allows for a more precise determination of the
orbital character within the HOMO-2. Our observations and analysis provide
important considerations for the connection between molecular and crystalline
C$_{60}$ electronic structure, past and future band structure studies, and for
increasingly popular C$_{60}$ electronic device applications, especially those
making use of heterostructures.


  The behavior of molecular nanomagnets in periodic magnetic field transverse
to the easy axis direction is investigated. It is shown that at sufficiently
strong field the tunneling time can be considerably reduced.


  We discuss the topics mentioned in the title by scrutinizing and improving
the $0^{-+}$ di-gluonia sum rules within the standard SVZ-expansion at N2LO
without instantons. First, we reconsider the estimate of the slope of the
topological charge $\chi'(0)=24.3(3.4)$ MeV which imply $0.144(5) [\rm data:
0.145(13)]$ for the first moment of the polarized proton structure function
(proton spin) and $G_A^{(0)} = 0.337(50) [\rm data=0.330(39)]$ for the singlet
form factor of the axial current. Second, we work with high degree moments and
parametrize the spectral function beyond the minimal duality ansatz: "One
resonance plus QCD continuum" to get the $0^{-+}$ di-gluonia spectra. Then, we
obtain three groups of gluonia: The familiar light $\eta_1$ [singlet gluon
component of the $\eta'(958)$] with $[M_{\eta_1},f_{\eta_1}]= [825 , 905(72)]$;
The two new medium gluonia with $M_{P_{1a}}=1338(112)$ MeV and
$[M_{P_{1b}}=1462(117) $ MeV or their mean
$[M_{P_1},f_{P_1}]=[1397(81),594(144)]$ MeV which support the gluonium nature
of the candidate $\eta(1405)$ and may bring a small gluon piece to the
$\eta(1295)$; Their 1st radial excitations: $M_{P'_{1a}}=1508(226)$ MeV and
$M_{P'_{1b}}=1553(139)$ MeV with their mean:
$[M_{P'_1},f_{P'_1}]=[1541(118),205(282)]$ MeV which may be identified (up to
some eventual mixings with $\bar qq$ states) with the $\eta(1475,1700)$ states;
The heavy gluonium with : $[M_{P_2}, f_{P_2}]=[2751(140),500(43)]$ MeV
comparable with the lattice results. One can remark the (natural) one to one
correspondence between the pseudoscalar gluonia and their chiral scalar
analogue from Ref.1: $\sigma(1)\to \eta_1;~G_1(1.55)\to P_{1};
[\sigma'(1.1),G'(1.56)]\to P'_{1a,1b};~G_2(3)\to P_2$ which is mainly due to
the importance of QCD PT in the sum rule analysis that are almost equal in
these two channels. Results for the spectra are in Table 2.


  A fine-grained provenance-based access control policy model is proposed in
this paper, in order to improve the express performance of existing model. This
method employs provenance as conditions to determine whether a piece of data
can be accessed because historical operations performed on data could reveal
clues about its sensitivity and vulnerability. Particularly, our proposed work
provides a four-valued decision set which allows showing status to match a
restriction particularly. This framework consists of target policy, access
control policy, and policy algebras. With the complete definition and algebra
system construction, a practical fine-grained access control policy model is
developed.


  We derive conditional stability estimates for inverse scattering problems
related to time harmonic magnetic Schr\"odinger equation. We prove logarithmic
type estimates for retrieving the magnetic (up to a gradient) and electric
potentials from near field or far field maps. Our approach combines techniques
from similar results obtained in the literature for inhomogeneous inverse
scattering problems based on the use of geometrical optics solutions.


  Weather regimes describe the large-scale atmospheric circulation in the
mid-latitudes in terms of a few circulation states that modulate regional
surface weather. Subseasonal forecasts of prevailing weather regimes have
proven skillful and valuable to energy applications. Previous studies have
mainly focused on the mean surface weather associated with a regime. However,
we show in this paper that variability of surface weather within a regime
cannot be ignored. These intra-regime variations, caused by different
`subflavors' of the same regime, can be captured by continuous regime indices
and allow a refined application of weather regimes. Here we discuss wintertime
temperature and wind speed regime anomalies for four selected countries, and
provide guidance on the operational use and interpretation of regime forecasts.
In an accompanying supplementary dataset we provide similar analysis for all
European countries, seasons and key energy variables, useful as an applied
reference.


  The 5-qubit quantum computer prototypes that IBM has given open access to on
the cloud allow the implementation of real experiments on a quantum processor.
We present the results obtained in five experimental tests performed on these
computers: dense coding, quantum Fourier transforms, Bell's inequality,
Mermin's inequalities (up to $n=5$) and the construction of the prime state
$|p_3\rangle$. These results serve to assess the functioning of the IBM 5Q
chips.


  Deep learning has made significant advances in creating efficient
representations of time series data by automatically identifying complex
patterns. However, these approaches lack interpretability, as the time series
is transformed into a latent vector that is not easily interpretable. On the
other hand, Symbolic Aggregate approximation (SAX) methods allow the creation
of symbolic representations that can be interpreted but do not capture complex
patterns effectively. In this work, we propose a set of requirements for a
neural representation of univariate time series to be interpretable. We propose
a new unsupervised neural architecture that meets these requirements. The
proposed model produces consistent, discrete, interpretable, and visualizable
representations. The model is learned independently of any downstream tasks in
an unsupervised setting to ensure robustness. As a demonstration of the
effectiveness of the proposed model, we propose experiments on classification
tasks using UCR archive datasets. The obtained results are extensively compared
to other interpretable models and state-of-the-art neural representation
learning models. The experiments show that the proposed model yields, on
average better results than other interpretable approaches on multiple
datasets. We also present qualitative experiments to asses the interpretability
of the approach.


  There are many resources useful for processing images, most of them freely
available and quite friendly to use. In spite of this abundance of tools, a
study of the processing methods is still worthy of efforts. Here, we want to
discuss the possibilities arising from the use of fractional differential
calculus. This calculus evolved in the research field of pure mathematics until
1920, when applied science started to use it. Only recently, fractional
calculus was involved in image processing methods. As we shall see, the
fractional calculation is able to enhance the quality of images, with
interesting possibilities in edge detection and image restoration. We suggest
also the fractional differentiation as a tool to reveal faint objects in
astronomical images.


  The development of efficient sources of single photons and entangled photon
pairs emitting in the low-loss wavelength region around 1550 nm is crucial for
long-distance quantum communication. Moreover, direct fiber coupling and
electrical carrier injection are highly desirable for deployment in compact and
user-friendly systems integrated with the existing fiber infrastructure. Here
we present a detailed design study of circular Bragg gratings etched in InP
slabs and operating in the telecom C-band. These devices enable the
simultaneous enhancement of the X and XX spectral lines, with collection
efficiency in NA=0.65 close to 90% for the wavelength range 1520-1580 nm and
Purcell factor up to 15. We also investigate the coupling into single mode
fiber, which exceeds 70% in UHNA4. Finally, we propose a modified device design
directly compatible with electrical carrier injection, reporting Purcell
factors up to 20 and collection efficiency in NA=0.65 close to 70% for the
whole telecom C-band.


  Extending a previous paper, we present a generalization in dimension 3 of the
traditional Szebehely-type inverse problem. In that traditional setting, the
data are curves determined as the intersection of two families of surfaces, and
the problem is to find a potential V such that the Lagrangian L = T - V, where
T is the standard Euclidean kinetic energy function, generates integral curves
which include the given family of curves. Our more general way of posing the
problem makes use of ideas of the inverse problem of the calculus of variations
and essentially consists of allowing more general kinetic energy functions,
with a metric which is still constant, but need not be the standard Euclidean
one. In developing our generalization, we review and clarify different aspects
of the existing literature on the problem and illustrate the relevance of the
newly introduced additional freedom with many examples.


  Cities are the drivers of socio-economic innovation, and are also forced to
address the accelerating risk of failure in providing essential services such
as water supply today and in the future. Here, we investigate the resilience of
urban water supply security, which is defined in terms of the services that
citizens receive. The resilience of services is determined by the availability
and robustness of critical system elements, or 'capitals' (water resources,
infrastructure, finances, management efficacy and community adaptation). We
translate quantitative information about this portfolio of capitals from seven
contrasting cities on four continents into parameters of a coupled systems
dynamics model. Water services are disrupted by recurring stochastic shocks,
and we simulate the dynamics of impact and recovery cycles. Resilience emerges
under various constraints, expressed in terms of each city's capital portfolio.
Systematic assessment of the parameter space produces the urban water
resilience landscape, and we determine the position of each city along a
continuous gradient from water insecure and non-resilient to secure and
resilient systems. In several cities stochastic disturbance regimes challenge
steady-state conditions and drive system collapse. While water insecure and
non-resilient cities risk being pushed into a poverty trap, cities which have
developed excess capitals risk being trapped in rigidity and crossing a tipping
point from high to low services and collapse. Where public services are
insufficient, community adaptation improves water security and resilience to
varying degrees. Our results highlight the need for resilience thinking in the
governance of urban water systems under global change pressures.


  We develop a quantitative semiclassical theory for the resosnant tunneling
through a quantum well in a tilted magnetic field. It is shown, that in the
leading semiclassical approximation the tunneling current depends only on
periodic orbits within the quantum well. Further corrections (due to e.g.
"ghost" effect) can be expressed in terms of closed, but non-periodic orbits,
started at the "injection point". The results of the semiclassical theory are
shown to be in good agreement with both the experimental data and numerical
calculations.


  H-alpha emission from supernova remnants (SNRs) implies the existence of
neutral hydrogen in the circumstellar medium. Some of the neutral particles
penetrating the shock are ionized by the charge exchange process and make a
cold ion beam in the shock downstream region. We perform linear analyses of
collisionless plasma instabilities between the cold beam and the hot downstream
plasma. We find that, under typical SNR conditions, either the resonant
instability or the Weibel instability is the most unstable. This mechanism may
amplify the magnetic field to more than 100 micro G and changes the shock
structure. As a result, the radio spectrum and the large magnetic field can be
explained, apart from the widely discussed Bell's mechanism.


  Recent studies have validated the association between cardiovascular disease
(CVD) risk and retinal fundus images. Combining deep learning (DL) and portable
fundus cameras will enable CVD risk estimation in various scenarios and improve
healthcare democratization. However, there are still significant issues to be
solved. One of the top priority issues is the different camera differences
between the databases for research material and the samples in the production
environment. Most high-quality retinography databases ready for research are
collected from high-end fundus cameras, and there is a significant domain
discrepancy between different cameras. To fully explore the domain discrepancy
issue, we first collect a Fundus Camera Paired (FCP) dataset containing
pair-wise fundus images captured by the high-end Topcon retinal camera and the
low-end Mediwork portable fundus camera of the same patients. Then, we propose
a cross-laterality feature alignment pre-training scheme and a self-attention
camera adaptor module to improve the model robustness. The cross-laterality
feature alignment training encourages the model to learn common knowledge from
the same patient's left and right fundus images and improve model
generalization. Meanwhile, the device adaptation module learns feature
transformation from the target domain to the source domain. We conduct
comprehensive experiments on both the UK Biobank database and our FCP data. The
experimental results show that the CVD risk regression accuracy and the result
consistency over two cameras are improved with our proposed method. The code is
available here:
\url{https://github.com/linzhlalala/CVD-risk-based-on-retinal-fundus-images}


  We consider a strong Markov process with killing and prove an approximation
method for the distribution of the process conditioned not to be killed when it
is observed. The method is based on a Fleming-Viot type particle system with
rebirths, whose particles evolve as independent copies of the original strong
Markov process and jump onto each others instead of being killed. Our only
assumption is that the number of rebirths of the Fleming-Viot type system
doesn't explode in finite time almost surely and that the survival probability
of the original process remains positive in finite time. The approximation
method generalizes previous results and comes with a speed of convergence. A
criterion for the non-explosion of the number of rebirths is also provided for
general systems of time and environment dependent diffusion particles. This
includes, but is not limited to, the case of the Fleming-Viot type system of
the approximation method. The proof of the non-explosion criterion uses an
original non-attainability of $(0,0)$ result for pair of non-negative
semi-martingales with positive jumps.


  When there is a dispute between players on how to divide multiple divisible
assets, how should it be resolved? In this paper we introduce a multi-asset
game model that enables cooperation between multiple agents who bargain on
sharing K assets, when each player has a different value for each asset. It
thus extends the sequential discrete Raiffa solution and the Talmud rule
solution to multi-asset cases. keyword: resource allocation, game theory,
Raiffa Bargaining Solution, Aumann Bankruptcy, non-transferable commodities


  We investigate the thermodynamics of non-relativistic and relativistic ideal
gases on the spacetime with noncommutative fuzzy geometry. We first find that
the heat capacities of the non-relativistic ideal boson and fermion on the
fuzzy two-sphere have different values, contrast to that on the commutative
geometry. We calculate the "statistical interparticle potential" therein and
interprete this property as a result that the non-commutativity of the fuzzy
sphere has an inclination to enhance the statistical "attraction (repulsion)
interparticle potential" between boson (fermion). We also see that at high
temperature the heat capacity approaches to zero. We next evaluate the heat
capacities of the non-relativistic ideal boson and fermion on the product of
the 1+D (with D=2,3) Minkowski spacetime by a fuzzy two-sphere and see that the
fermion capacity could be a decreasing function of temperature in
high-temperature limit, contrast to that always being an increasing function on
the commutative geometry. Also, the boson and fermion heat capacities both
approach to that on the 1+D Minkowski spacetime in high-temperature limit. We
discuss these results and mention that the properties may be traced to the
mechanism of "thermal reduction of the fuzzy space". We also investigate the
same problems in the relativistic system with free Klein-Gordon field and Dirac
field and find the similar properties.


  Perverse-Hodge complexes are objects in the derived category of coherent
sheaves obtained from Hodge modules associated with Saito's decomposition
theorem. We study perverse-Hodge complexes for Lagrangian fibrations and
propose a symmetry between them. This conjectural symmetry categorifies the
"Perverse = Hodge" identity of the authors and specializes to Matsushita's
theorem on the higher direct images of the structure sheaf. We verify our
conjecture in several cases by making connections with variations of Hodge
structures, Hilbert schemes, and Looijenga-Lunts-Verbitsky Lie algebras.


  Optical interferometry is a powerful tool to investigate the close
environment of AGB stars. With a spatial resolution of a few milli-arcseconds,
it is even possible to image directly the surface of angularly large objects.
This is of special interest forMira stars and red supergiants for which the
dust-wind is initiated from or very close to the photosphere by an interplay
between pulsation and convection. Based on two-epoch interferometric
observations of the Mira star X Hya, we present how the variation of the
angular size with wavelength challenges pulsation models and how reconstructed
images can reveal the evolution of the object shape and of its asymmetric
structures.


  Machines that can replicate human intelligence with type 2 reasoning
capabilities should be able to reason at multiple levels of spatio-temporal
abstractions and scales using internal world models. Devising formalisms to
develop such internal world models, which accurately reflect the causal
hierarchies inherent in the dynamics of the real world, is a critical research
challenge in the domains of artificial intelligence and machine learning. This
thesis identifies several limitations with the prevalent use of state space
models (SSMs) as internal world models and propose two new probabilistic
formalisms namely Hidden-Parameter SSMs and Multi-Time Scale SSMs to address
these drawbacks. The structure of graphical models in both formalisms
facilitates scalable exact probabilistic inference using belief propagation, as
well as end-to-end learning via backpropagation through time. This approach
permits the development of scalable, adaptive hierarchical world models capable
of representing nonstationary dynamics across multiple temporal abstractions
and scales. Moreover, these probabilistic formalisms integrate the concept of
uncertainty in world states, thus improving the system's capacity to emulate
the stochastic nature of the real world and quantify the confidence in its
predictions. The thesis also discuss how these formalisms are in line with
related neuroscience literature on Bayesian brain hypothesis and predicitive
processing. Our experiments on various real and simulated robots demonstrate
that our formalisms can match and in many cases exceed the performance of
contemporary transformer variants in making long-range future predictions. We
conclude the thesis by reflecting on the limitations of our current models and
suggesting directions for future research.


  We present the results of our power spectral density analysis for the BL Lac
object OJ\,287, utilizing the {\it Fermi}-LAT survey at high-energy
$\gamma$-rays, {\it Swift}-XRT in X-rays, several ground-based telescopes and
the {\it Kepler} satellite in the optical, and radio telescopes at GHz
frequencies. The light curves are modeled in terms of continuous-time
auto-regressive moving average (CARMA) processes. Owing to the inclusion of the
{\it Kepler} data, we were able to construct \emph{for the first time} the
optical variability power spectrum of a blazar without any gaps across $\sim6$
dex in temporal frequencies. Our analysis reveals that the radio power spectra
are of a colored-noise type on timescales ranging from tens of years down to
months, with no evidence for breaks or other spectral features. The overall
optical power spectrum is also consistent with a colored noise on the
variability timescales ranging from 117 years down to hours, with no hints of
any quasi-periodic oscillations. The X-ray power spectrum resembles the radio
and optical power spectra on the analogous timescales ranging from tens of
years down to months. Finally, the $\gamma$-ray power spectrum is noticeably
different from the radio, optical, and X-ray power spectra of the source: we
have detected a characteristic relaxation timescale in the {\it Fermi}-LAT
data, corresponding to $\sim 150$\,days, such that on timescales longer than
this, the power spectrum is consistent with uncorrelated (white) noise, while
on shorter variability timescales there is correlated (colored) noise.


  We provide a graphical description of the entanglement of pure-state
multiparty systems based on an analogy between a bipartite purity analysis and
the centroid of a collection of point masses. This description applies to
quantum systems with $N$ parties, each with an arbitrary number of (discrete)
states. The case of $N$ qubits is highlighted for simplicity. This geometric
description illustrates some of the restrictions in the form of inequalities
that apply to entanglement in multiparty systems.


  We present the discovery of substellar-mass companions to three giant stars
by the ongoing Penn State-Toru\'n Planet Search (PTPS) conducted with the 9.2 m
Hobby-Eberly Telescope. The most massive of the three stars, K2-giant HD
240237, has a 5.3 MJ minimum mass companion orbiting the star at a 746-day
period. The K0-giant BD +48 738 is orbited by a > 0.91 MJ planet which has a
period of 393 days and shows a non-linear, long-term radial velocity trend that
indicates a presence of another, more distant companion, which may have a
substellar mass or be a low-mass star. The K2-giant HD 96127, has a > 4.0 MJ
mass companion in a 647-day orbit around the star. The two K2-giants exhibit a
significant RV noise that complicates the detection of low-amplitude, periodic
variations in the data. If the noise component of the observed RV variations is
due to solar-type oscillations, we show, using all the published data for the
substellar companions to giants, that its amplitude is anti-correlated with
stellar metallicity.


  We show how one can obtain an asymptotic expression for some special
functions satisfying a second order differential equation with a very explicit
error term starting from appropriate upper bounds.
  We will work out the details for the Bessel function $J_\nu (x)$ and the Airy
function $Ai(x)$ and find a sharp approximation for their zeros.
  We also answer the question raised by Olenko by showing that
  $$c_1 | \nu^2-1/4\,| < \sup_{x \ge 0} x^{3/2}|J_\nu(x)-\sqrt{\frac{2}{\pi x}}
\, \cos (x-\frac{\pi \nu}{2}-\frac{\pi}{4}\,)| <c_2 |\nu^2-1/4\,|, $$ $ \nu \ge
-1/2 \, ,$ for some explicit numerical constants $c_1$ and $c_2.$


  Discriminativeness is a desirable feature of image captions: captions should
describe the characteristic details of input images. However, recent
high-performing captioning models, which are trained with reinforcement
learning (RL), tend to generate overly generic captions despite their high
performance in various other criteria. First, we investigate the cause of the
unexpectedly low discriminativeness and show that RL has a deeply rooted side
effect of limiting the output words to high-frequency words. The limited
vocabulary is a severe bottleneck for discriminativeness as it is difficult for
a model to describe the details beyond its vocabulary. Then, based on this
identification of the bottleneck, we drastically recast discriminative image
captioning as a much simpler task of encouraging low-frequency word generation.
Hinted by long-tail classification and debiasing methods, we propose methods
that easily switch off-the-shelf RL models to discriminativeness-aware models
with only a single-epoch fine-tuning on the part of the parameters. Extensive
experiments demonstrate that our methods significantly enhance the
discriminativeness of off-the-shelf RL models and even outperform previous
discriminativeness-aware methods with much smaller computational costs.
Detailed analysis and human evaluation also verify that our methods boost the
discriminativeness without sacrificing the overall quality of captions.


  Accurate simulation of the printing process is essential for improving print
quality, reducing waste, and optimizing the printing parameters of
extrusion-based additive manufacturing. Traditional additive manufacturing
simulations are very compute-intensive and are not scalable to simulate even
moderately-sized geometries. In this paper, we propose a general framework for
creating a digital twin of the dynamic printing process by performing physics
simulations with the intermediate print geometries. Our framework takes a
general extrusion-based additive manufacturing G-code, generates an
analysis-suitable voxelized geometry representation from the print schedule,
and performs physics-based (transient thermal and phase change) simulations of
the printing process. Our approach leverages parallel adaptive octree meshes
for both voxelated geometry representation as well as for fast simulations to
address real-time predictions. We demonstrate the effectiveness of our method
by simulating the printing of complex geometries at high voxel resolutions with
both sparse and dense infills. Our results show that this approach scales to
high voxel resolutions and can predict the transient heat distribution as the
print progresses. This work lays the computational and algorithmic foundations
for building real-time digital twins and performing rapid virtual print
sequence exploration to improve print quality and further reduce material
waste.


  Representation based classification method (RBCM) remains one of the hottest
topics in the community of pattern recognition, and the recently proposed
non-negative representation based classification (NRC) achieved impressive
recognition results in various classification tasks. However, NRC ignores the
relationship between the coding and classification stages. Moreover, there is
no regularization term other than the reconstruction error term in the
formulation of NRC, which may result in unstable solution leading to
misclassification. To overcome these drawbacks of NRC, in this paper, we
propose a class-specific residual constraint non-negative representation (CRNR)
for pattern classification. CRNR introduces a class-specific residual
constraint into the formulation of NRC, which encourages training samples from
different classes to competitively represent the test sample. Based on the
proposed CRNR, we develop a CRNR based classifier (CRNRC) for pattern
classification. Experimental results on several benchmark datasets demonstrate
the superiority of CRNRC over conventional RBCM as well as the recently
proposed NRC. Moreover, CRNRC works better or comparable to some
state-of-the-art deep approaches on diverse challenging pattern classification
tasks. The source code of our proposed CRNRC is accessible at
https://github.com/yinhefeng/CRNRC.