  We consider the monomer-dimer model, whose realisations are spanning
sub-graphs of a given graph such that every vertex has degree zero or one. The
measure depends on a parameter, the monomer activity, which rewards the total
number of monomers. We consider general correlation functions including
monomer-monomer correlations and dimer-dimer covariances. We show that these
correlations decay exponentially fast with the distance if the monomer activity
is strictly positive. Our result improves a previous upper bound from van den
Berg and is of interest due to its relation to truncated spin-spin correlations
in classical spin systems. Our proof is based on the cluster expansion
technique.


  Image annotation is one essential prior step to enable data-driven
algorithms. In medical imaging, having large and reliably annotated data sets
is crucial to recognize various diseases robustly. However, annotator
performance varies immensely, thus impacts model training. Therefore, often
multiple annotators should be employed, which is however expensive and
resource-intensive. Hence, it is desirable that users should annotate unseen
data and have an automated system to unobtrusively rate their performance
during this process. We examine such a system based on whole slide images
(WSIs) showing lung fluid cells. We evaluate two methods the generation of
synthetic individual cell images: conditional Generative Adversarial Networks
and Diffusion Models (DM). For qualitative and quantitative evaluation, we
conduct a user study to highlight the suitability of generated cells. Users
could not detect 52.12% of generated images by DM proofing the feasibility to
replace the original cells with synthetic cells without being noticed.


  We compute cones of effective cycles on some blowups of projective spaces in
general sets of lines.


  Besides being a fascinating class of new materials, magnetic molecules
provide the opportunity to study concepts of condensed matter physics in zero
dimensions. This contribution will exemplify the impact of molecular magnetism
on concepts of frustrated spin systems. We will discuss spin rings and the
unexpected rules that govern their low-energy behavior. Rotational bands, which
are experimentally observed in various molecular magnets, provide a useful,
simplified framework for characterizing the energy spectrum, but there are also
deviations thereof with far-reaching consequences. It will be shown that
localized independent magnons on certain frustrated spin systems lead to giant
magnetization jumps, a new macroscopic quantum effect. In addition a
frustration-induced metamagnetic phase transitions will be discussed, which
demonstrates that hysteresis can exist without anisotropy. Finally, it is
demonstrated that frustrated magnetic molecules could give rise to an enhanced
magnetocaloric effect.


  In this paper, we present a numerical study of the properties of the flow
produced by the collision of a magnetized anisotropic pulsar wind with its
environment in binary system. We compare the impact of both the magnetic field
and the wind anisotropy to the benchmark case of a purely hydrodynamical (HD)
interaction of isotropic winds, which has been studied in detail by Bogovalov
et al. (2008). We consider the interaction in axisymmetric approximation, i.e.
the pulsar rotation axis is assumed to be oriented along the line between the
pulsar and the optical star and the effects related to the pulsar orbiting are
neglected. The impact of the magnetic field is studied for the case of weak
magnetization (with magnetization parameter $\sigma<0.1$), which is consistent
with conventional models of pulsar winds. The effects related to anisotropy in
pulsar winds are modeled assuming that the kinetic energy flux in a
non-magnetized pulsar wind is strongly anisotropic, with the minimum at the
pulsar rotation axis and the maximum in the perpendicular direction. We show
that, although both considered effects change the shape of the region occupied
by the terminated pulsar wind, their impact appears to be small. In particular,
for the magnetization of the pulsar wind below 0.1, the magnetic field pressure
remains well below the plasma pressure in the post-shock region. Thus, in the
case of interaction of a pulsar with the stellar wind environment (opposite to
the case of plerions, i.e. the pulsar interaction with the interstellar medium,
when the magnetic field becomes dynamically important independently on the wind
magnetization) the HD approach represents a feasible approximation for
numerical modelling.


  We show that it is possible to construct a well-defined effective field
theory incorporating string winding modes without using strong constraint in
double field theory. We show that X-ray (Radon) transform on a torus is
well-suited for describing weakly constrained double fields, and any weakly
constrained fields are represented as a sum of strongly constrained fields.
Using inverse X- ray transform we define a novel binary operation which is
compatible with the level matching constraint. Based on this formalism, we
construct a consistent gauge transform and gauge invariant action without using
strong constraint. We then discuss the relation of our result to the closed
string field theory. Our construction suggests that there exists an effective
field theory description for massless sector of closed string field theory on a
torus in an associative truncation.


  The electrochemical switching of SrCoOx-based non-volatile memory with
thin-film-transistor structure was examined by using liquid-leakage-free
electrolytes with different conductivity (s) as the gate insulator. We first
examined leakage-free water, which is incorporated in the amorphous (a-) 12CaO
7Al2O3 film with nanoporous structure (CAN), but the electrochemical
oxidation/reduction of SrCoOx layer required the application of high gate
voltage (Vg) up to 20 V for a very long retention-time (t) 40 minutes,
primarily due to the low s (2.0 x 10-8 S cm-1 at RT) of leakage-free water.We
then controlled the s of leakage-free electrolyte, infiltrated in the a-NaxTaO3
film with nanopillar array structure, from 8.0 x 10-8 S cm-1 to 2.5 x 10-6 S
cm-1 at RT by changing the x = 0.01-1.0. As the result, the t, required for the
metallization of SrCoOx layer under small Vg = -3 V, becomes two orders of
magnitude shorter with increase of the s of the a-NaxTaO3 leakage-free
electrolyte. These results indicate that the ion migration in the leakage-free
electrolyte is the rate-determining step for the electrochemical switching,
compared to the other electrochemical process, and the high s of the
leakage-free electrolyte is the key factor for the development of the
non-volatile SrCoOx-based electro-magnetic phase switching device.


  The Dalitz plot slope parameters g, h and k for the K- -> pi0 pi0 pi- decay
have been measured using in-flight decays detected with the ISTRA+ setup
operating in the 25 GeV negative secondary beam of the U-70 PS. About 252 K
events with four-momenta measured for the pi- and four involved photons were
used for the analysis. The values obtained g=0.627+/-0.004(stat)+/-0.010(syst),
h=0.046+/-0.004(stat)+/-0.012(syst), k=0.001+/-0.001(stat)+/-0.002(syst) are
consistent with the world averages dominated by K+ data, but have significantly
smaller errors.


  In these lectures we report recent work on the exact quantization of
dimensionally reduced gravity, i.e. 2d non-linear (G/H)-coset space
sigma-models coupled to gravity and a dilaton. Using methods developed in the
context of flat space integrable systems, the Wheeler-DeWitt equations for
these models can be reduced to a modified version of the Knizhnik-Zamolodchikov
equations from conformal field theory, the insertions given by singularities in
the spectral parameter plane. This basic result in principle permits the
explicit construction of solutions, i.e. physical states of the quantized
theory. In this way, we arrive at integrable models of quantum gravity with
infinitely many self-interacting propagating degrees of freedom.


  We constrain the shape of the Milky Way's halo by dynamical modeling of the
observed phase-space tracks of the Pal 5 and GD-1 tidal streams. We find that
the only information about the potential gleaned from the tracks of these
streams are precise measurements of the shape of the gravitational
potential---the ratio of vertical to radial acceleration---at the location of
the streams, with weaker constraints on the radial and vertical accelerations
separately. The latter will improve significantly with precise proper-motion
measurements from Gaia. We measure that the overall potential flattening is
0.95 +/- 0.04 at the location of GD-1 ([R,z] ~ [12.5,6.7] kpc) and 0.94 +/-
0.05 at the position of Pal 5 ([R,z] ~ [8.4,16.8] kpc). Combined with
constraints on the force field near the Galactic disk, we determine that the
axis ratio of the dark-matter halo's density distribution is 1.05 +/- 0.14
within the inner 20 kpc, with a hint that the halo becomes more flattened near
the edge of this volume. The halo mass within 20 kpc is 1.1 +/- 0.1 x 10^{11}
M_sun. A dark-matter halo this close to spherical is in tension with the
predictions from numerical simulations of the formation of dark-matter halos.


  Purpose: Segmentation of organs-at-risk (OARs) is a bottleneck in current
radiation oncology pipelines and is often time consuming and labor intensive.
In this paper, we propose an atlas-based semi-supervised registration algorithm
to generate accurate segmentations of OARs for which there are ground truth
contours and rough segmentations of all other OARs in the atlas. To the best of
our knowledge, this is the first study to use learning-based registration
methods for the segmentation of head and neck patients and demonstrate its
utility in clinical applications. Methods: Our algorithm cascades rigid and
deformable deformation blocks, and takes on an atlas image (M), set of
atlas-space segmentations (S_A), and a patient image (F) as inputs, while
outputting patient-space segmentations of all OARs defined on the atlas. We
train our model on 475 CT images taken from public archives and Stanford RadOnc
Clinic (SROC), validate on 5 CT images from SROC, and test our model on 20 CT
images from SROC. Results: Our method outperforms current state of the art
learning-based registration algorithms and achieves an overall dice score of
0.789 on our test set. Moreover, our method yields a performance comparable to
manual segmentation and supervised segmentation, while solving a much more
complex registration problem. Whereas supervised segmentation methods only
automate the segmentation process for a select few number of OARs, we
demonstrate that our methods can achieve similar performance for OARs of
interest, while also providing segmentations for every other OAR on the
provided atlas. Conclusions: Our proposed algorithm has significant clinical
applications and could help reduce the bottleneck for segmentation of head and
neck OARs. Further, our results demonstrate that semi-supervised diffeomorphic
registration can be accurately applied to both registration and segmentation
problems.


  We investigate the properties of categories of G_C-flat R-modules where C is
a semidualizing module over a commutative noetherian ring R. We prove that the
category of all G_C-flat R-modules is part of a weak AB-context, in the
terminology of Hashimoto. In particular, this allows us to deduce the existence
of certain Auslander-Buchweitz approximations for R-modules of finite G_C-flat
dimension. We also prove that two procedures for building R-modules from
complete resolutions by certain subcategories of G_C-flat R-modules yield only
the modules in the original subcategories.


  Vehicle-to-everything (V2X) perception is an innovative technology that
enhances vehicle perception accuracy, thereby elevating the security and
reliability of autonomous systems. However, existing V2X perception methods
focus on static scenes from mainly vehicle-based vision, which is constrained
by sensor capabilities and communication loads. To adapt V2X perception models
to dynamic scenes, we propose to build V2X perception from road-to-vehicle
vision and present Adaptive Road-to-Vehicle Perception (AR2VP) method. In
AR2VP,we leverage roadside units to offer stable, wide-range sensing
capabilities and serve as communication hubs. AR2VP is devised to tackle both
intra-scene and inter-scene changes. For the former, we construct a dynamic
perception representing module, which efficiently integrates vehicle
perceptions, enabling vehicles to capture a more comprehensive range of dynamic
factors within the scene.Moreover, we introduce a road-to-vehicle perception
compensating module, aimed at preserving the maximized roadside unit perception
information in the presence of intra-scene changes.For inter-scene changes, we
implement an experience replay mechanism leveraging the roadside unit's storage
capacity to retain a subset of historical scene data, maintaining model
robustness in response to inter-scene shifts. We conduct perception experiment
on 3D object detection and segmentation, and the results show that AR2VP excels
in both performance-bandwidth trade-offs and adaptability within dynamic
environments.


  Federated Learning (FL) is a decentralized machine learning protocol that
allows a set of participating agents to collaboratively train a model without
sharing their data. This makes FL particularly suitable for settings where data
privacy is desired. However, it has been observed that the performance of FL is
closely tied with the local data distributions of agents. Particularly, in
settings where local data distributions vastly differ among agents, FL performs
rather poorly with respect to the centralized training. To address this
problem, we hypothesize the reasons behind the performance degradation, and
develop some techniques to address these reasons accordingly. In this work, we
identify four simple techniques that can improve the performance of trained
models without incurring any additional communication overhead to FL, but
rather, some light computation overhead either on the client, or the
server-side. In our experimental analysis, combination of our techniques
improved the validation accuracy of a model trained via FL by more than 12%
with respect to our baseline. This is about 5% less than the accuracy of the
model trained on centralized data.


  A new formulation is presented for a variational calculation of $N$-body
systems on a correlated Gaussian basis with arbitrary angular momenta. The
rotational motion of the system is described with a single spherical harmonic
of the total angular momentum $L$, and thereby needs no explicit coupling of
partial waves between particles. A simple generating function for the
correlated Gaussian is exploited to derive the matrix elements. The formulation
is applied to various Coulomb three-body systems such as $e^-e^-e^+, tt\mu,
td\mu$, and $\alpha e^-e^-$ up to $L=4$ in order to show its usefulness and
versatility. A stochastic selection of the basis functions gives good results
for various angular momentum states.


  With a large number of software tools dedicated to the visualisation and/or
demonstration of properties of geometric constructions and also with the
emerging of repositories of geometric constructions, there is a strong need of
linking them, and making them and their corpora, widely usable. A common
setting for interoperable interactive geometry was already proposed, the i2g
format, but, in this format, the conjectures and proofs counterparts are
missing. A common format capable of linking all the tools in the field of
geometry is missing. In this paper an extension of the i2g format is proposed,
this extension is capable of describing not only the geometric constructions
but also the geometric conjectures. The integration of this format into the
Web-based GeoThms, TGTP and Web Geometry Laboratory systems is also discussed.


  We elaborate on the functional integral describing the stochastic dynamics of
a spectator field during inflation, comparing its diagrammatic expansion to
that obtained directly from a perturbative solution of the corresponding
Langevin equation. We state Feynman rules for computing arbitrary temporal
$n$-point functions and perform some illustrative computations for a
$\lambda\phi^4$ interaction, paying attention to the role played by a
functional Jacobian determinant in the path integral. We also briefly consider
the case when the field contributes to the expansion rate, making the noise
multiplicative, which introduces additional vertices.


  Precategories generalize both the notions of strict $n$-category and
sesquicategory: their definition is essentially the same as the one of strict
$n$-categories, excepting that we do not require the various interchange laws
to hold. Those have been proposed as a framework in which one can express
semi-strict definitions of weak higher categories: in dimension 3, Gray
categories are an instance of them and have been shown to be equivalent to
tricategories, and definitions of semi-strict tetracategories have been
proposed, and used as the basis of proof assistants such as Globular. In this
article, we are mostly interested in free precategories. Those can be presented
by generators and relations, using an appropriate variation on the notion of
polygraph (aka computad), and earlier works have shown that the theory of
rewriting can be generalized to this setting, enjoying most of the fundamental
constructions and properties which can be found in the traditional theory,
contrarily to polygraphs for strict categories. We further study here why this
is the case, by providing several results which show that precategories and
their associated polygraphs bear properties which ensure that we have a good
syntax for those. In particular, we show that the category of polygraphs for
precategories form a presheaf category.


  Compressed sensing is a method that allows a significant reduction in the
number of samples required for accurate measurements in many applications in
experimental sciences and engineering. In this work, we show that compressed
sensing can also be used to speed up numerical simulations. We apply compressed
sensing to extract information from the real-time simulation of atomic and
molecular systems, including electronic and nuclear dynamics. We find that for
the calculation of vibrational and optical spectra the total propagation time,
and hence the computational cost, can be reduced by approximately a factor of
five.


  We solve the double exchange model in the presence of arbitrary
substitutional disorder by using a self consistently generated effective
Hamiltonian for the spin degrees of freedom. The magnetic properties are
studied through classical Monte Carlo while the effective exchange, $D_{ij}$,
are calculated by solving the disordered fermion problem, and renormalised
self-consistently with increasing temperature. We present exact results on the
conductivity, magnetoresistance, optical response and `real space' structure of
the inhomogeneous ferromagnetic state, and compare our results with charge
dynamics in disordered La_{1-x}Sr_xMnO_3. The large sizes, ${\cal O} (10^3)$,
accessible within our method allows a complete, controlled calculation on the
disordered strongly interacting problem.


  Motivated by the recent experiments [H. Kadau et al., Nature (London) 530,
194 (2016); I. Ferrier-Barbut et al., arXiv:1601.03318] and theoretical
prediction (F. W\"achtler and L. Santos, arXiv:1601.04501), the ground state of
a dysprosium Bose-Einstein condensate with strong dipole-dipole interaction is
studied using the path-integral Monte Carlo method. It is shown that quantum
fluctuation can stabilize the condensate against dipolar collapse.


  RHII and starbursts are both powered by massive stars. They are the main
contributors to the heating of the ISM via radiative and mechanical energy.
Techniques to derive the stellar content and the evolutionary state of RHIIs
and starbursts from their ultraviolet and optical integrated light are
reviewed. A prototypical RHII (NGC 604) and nuclear starburst (NGC 7714) are
discussed in more detail. The results reveal the necessity of multiwavelength
analyses of these objects to estimate their stellar content and their
evolutionary state in a consistent way.


  The 1-loop self-energy of a Dirac electron of mass m propagating in a thin
medium simulating graphene in an external magnetic field B is investigated in
Quantum Field Theory. Equivalence is shown with the so-called reduced QED_{3+1}
on a 2-brane. Schwinger-like methods are used to calculate the self-mass \delta
m_{LLL} of the electron when it lies in the lowest Landau level. Unlike in
standard QED_{3+1}, it does not vanish at the limit m -> 0 :\delta m_{LLL} ->
(\alpha/2)\sqrt{pi/2}sqrt{\hbar|e|B/c^2}; all Landau levels of the virtual
electron are taken into account and on mass-shell renormalization conditions
are implemented. Restricting to the sole lowest Landau level of the virtual
electron is explicitly shown to be inadequate. Resummations at higher orders
lie beyond the scope of this work.


  Convolutional neural networks demonstrated outstanding empirical results in
computer vision and speech recognition tasks where labeled training data is
abundant. In medical imaging, there is a huge variety of possible imaging
modalities and contrasts, where annotated data is usually very scarce. We
present two approaches to deal with this challenge. A network pretrained in a
different domain with abundant data is used as a feature extractor, while a
subsequent classifier is trained on a small target dataset; and a deep
architecture trained with heavy augmentation and equipped with sophisticated
regularization methods. We test the approaches on a corpus of X-ray images to
design an anatomy detection system.


  This note contains a (short) proof of the following generalisation of the
Friedman--Mineyev theorem (earlier known as the Hanna Neumann conjecture): if
$A$ and $B$ are nontrivial free subgroups of a virtually free group containing
a free subgroup of index $n$, then $rank(A\cap B)-1\leqslant
n\cdot(rank(A)-1)\cdot(rank(B)-1)$. In addition, we obtain a
virtually-free-product analogue of this result.


  We report the first measurement of $\Lambda_c^+$ (average of $\Lambda_c^+$
and $\bar{\Lambda}_c^-$) baryon production and significantly improved
measurement of $D_s^+$ (average of $D_s^+$ and $D_s^-$) meson production,
within the rapidity range of $\left|y\right| < 1$ in Au+Au collisions at
$\sqrt{s_{\rm NN}}$ = 200 GeV from the STAR experiment. The transverse momentum
spectra of $\Lambda_c^+$ and $D_s^+$ as well as their yield ratios to that of
$D^0$ meson are also presented and compared to theoretical calculations.Both
the $\Lambda_c^+/D^0$ and $D_s^+/D^0$ ratios are found to be significantly
enhanced in Au+Au collisions with respect to those in p+p collisions predicted
by PYTHIA. A model calculation including coalescence hadronization and
thermalized charm quarks is consistent with the measured $\Lambda_c^+/D^0$
ratio. On the other hand, the TAMU model seems to underestimate the $D_s^+/D^0$
ratio measured in Au+Au collisions in the applicable kinematic region.


  In this article, we present an algorithm to compute the 9th Dedekind Number.
The key aspects are the use of matrix multiplication and symmetries in the free
distributive lattice, which are detected with techniques from Formal Concept
Analysis.


  In this paper, we investigate simultaneously transmitting and reflecting
reconfigurable intelligent surfaces (STAR-RIS), which enables to communicate
with users both sides by transmitting signals to users forward and reflecting
signals to users backward simultaneously. We consider a communicatio system
with a STAR-RIS, a base station (BS) and many users to maximize the minimum
user energy efficiency (EE) by jointly optimizing the active beamforming,
transmission and reflection coefficients with BS power consumption limited. To
solve this optimization problem efficiently, we divide it into two sub-problems
to optimize the transmitting beamforming matrix and phase shifts of STAR-RIS
seperately. With the two subproblems fixed, an Alternating Optimization (AO)
method is proposed to solve the maximize minmum user EE fair optimization
problem. Numerical results can demonstrate that STAR-RIS behaves better than
traditional reflecting-only RIS, and the algorithm we desigend can maximize the
minum EE problem efficienty to ensure user fairness.


  We consider two combinatorial principles, ${\sf{ERT}}$ and ${\sf{ECT}}$. Both
are easily proved in ${\sf{RCA}}_0$ plus ${\Sigma^0_2}$ induction. We give two
proofs of ${\sf{ERT}}$ in ${\sf{RCA}}_0$, using different methods to eliminate
the use of ${\Sigma^0_2}$ induction. Working in the weakened base system
${\sf{RCA}}_0^*$, we prove that ${\sf{ERT}}$ is equivalent to ${\Sigma^0_1}$
induction and ${\sf{ECT}}$ is equivalent to ${\Sigma^0_2}$ induction. We
conclude with a Weihrauch analysis of the principles, showing ${\sf{ERT}}
{\equiv_{\rm W}} {\sf{LPO}}^* {<_{\rm W}}{{\sf{TC}}_{\mathbb N}}^* {\equiv_{\rm
W}} {\sf{ECT}}$.


  We have found a new class of time dependent partial waves which are solutions
of time dependent Schr\"odinger equation for three dimensional harmonic
oscillator. We also showed the decomposition of coherent states of harmonic
oscillator into these partial waves. This decomposition appears perticularly
convenient for a description of the dynamics of a wave packet representing a
particle with spin when the spin--orbit interaction is present in the
hamiltonian. An example of an evolution of a localized wave packet into a torus
and backwards, for a particular initial conditions is analysed in analytical
terms and shown with a computer graphics.


  During the 2017 NBA playoffs, Celtics coach Brad Stevens was faced with a
difficult decision when defending against the Cavaliers: "Do you double and
risk giving up easy shots, or stay at home and do the best you can?" It's a
tough call, but finding a good defensive strategy that effectively incorporates
doubling can make all the difference in the NBA. In this paper, we analyze
double teaming in the NBA, quantifying the trade-off between risk and reward.
Using player trajectory data pertaining to over 643,000 possessions, we
identified when the ball handler was double teamed. Given these data and the
corresponding outcome (i.e., was the defense successful), we used deep
reinforcement learning to estimate the quality of the defensive actions. We
present qualitative and quantitative results summarizing our learned defensive
strategy for defending. We show that our policy value estimates are predictive
of points per possession and win percentage. Overall, the proposed framework
represents a step toward a more comprehensive understanding of defensive
strategies in the NBA.


  In this article, we analyse the Bistritzer--MacDonald (BM) model (also known
as the continuum model) of twisted bilayer graphene (TBG) with an additional
external magnetic field. We provide an explicit semiclassical asymptotic
expansion of the density of states (DOS) in the limit of strong magnetic
fields. The explicit expansion of the DOS enables us to study magnetic response
properties such as magnetic oscillations which includes Shubnikov-de Haas and
de Haas-van Alphen oscillations as well as the integer quantum Hall effect. In
particular, we elucidate the role played by different types of interlayer
tunnelings ($AA^{\prime}$/$BB^{\prime}$ vs. $AB^{\prime}$/$BA^{\prime}$) in the
study of the DOS, and magnetic properties.


  Let $F(G)$ and $b(G)$ respectively denote the Fitting subgroup and the
largest degree of an irreducible complex character of a finite group $G$. A
well-known conjecture of D. Gluck claims that if $G$ is solvable then
$|G:F(G)|\leq b(G)^{2}$. We confirm this conjecture in the case where $|F(G)|$
is coprime to 6. We also extend the problem to arbitrary finite groups and
prove several results showing that the largest irreducible character degree of
a finite group strongly controls the group structure.


  We study how the components of hadronic wave functions in light-cone
quantization depend on the ultraviolet cut-off by relating them in a systematic
way to the matrix elements of a class of quark-gluon operators between the QCD
vacuum and the hadrons. From this, we derive an infinite set of scale-evolution
equations for the individual contributions to parton distributions from the
Fock expansion. When summed over all the contributions, we recover the
well-known DGLAP equation.


  The $p$-widths of a closed Riemannian manifold are a nonlinear analogue of
the spectrum of its Laplace--Beltrami operator, which corresponds to areas of a
certain min-max sequence of possibly singular minimal submanifolds. We show
that the $p$-widths of any closed Riemannian two-manifold correspond to a union
of closed immersed geodesics, rather than simply geodesic nets.
  We then prove optimality of the sweepouts of the round two-sphere constructed
from the zero set of homogeneous polynomials, showing that the $p$-widths of
the round sphere are attained by $\lfloor \sqrt{p}\rfloor$ great circles. As a
result, we find the universal constant in the Liokumovich--Marques--Neves--Weyl
law for surfaces to be $\sqrt{\pi}$.
  En route to calculating the $p$-widths of the round two-sphere, we prove two
additional new results: a bumpy metrics theorem for stationary geodesic nets
with fixed edge lengths, and that, generically, stationary geodesic nets with
bounded mass and bounded singular set have Lusternik--Schnirelmann category
zero.


  In this paper we follow our previous research in the area of Computerized
Adaptive Testing (CAT). We present three different methods for CAT. One of
them, the item response theory, is a well established method, while the other
two, Bayesian and neural networks, are new in the area of educational testing.
In the first part of this paper, we present the concept of CAT and its
advantages and disadvantages. We collected data from paper tests performed with
grammar school students. We provide the summary of data used for our
experiments in the second part. Next, we present three different model types
for CAT. They are based on the item response theory, Bayesian networks, and
neural networks. The general theory associated with each type is briefly
explained and the utilization of these models for CAT is analyzed. Future
research is outlined in the concluding part of the paper. It shows many
interesting research paths that are important not only for CAT but also for
other areas of artificial intelligence.


  Let $\mathcal{M}_i$ be a family of $\mathrm{II}_1$-factors, containing a
common $\mathrm{II}_1$-subfactor $\mathcal{N}$, such that
$[\mathcal{M}_i:\mathcal{N}] \in \mathbb{N}_0$ for all $i$. Furthermore, let
$\phi \colon \mathbb{N}_0 \to \mathbb{C}$. We show that if a Hankel matrix
related to $\phi$ is trace-class, then there exists a unique completely bounded
map $M_\phi$ on the amalgamated free product of the $\mathcal{M}_i$ with
amalgamation over $\mathcal{N}$, which acts as an radial multiplier. Hereby we
extend a result of U. Haagerup and the author for radial multipliers on reduced
free products of unital $C^*$- and von Neumann algebras.


  Over the past decade, domain adaptation has become a widely studied branch of
transfer learning that aims to improve performance on target domains by
leveraging knowledge from the source domain. Conventional domain adaptation
methods often assume access to both source and target domain data
simultaneously, which may not be feasible in real-world scenarios due to
privacy and confidentiality concerns. As a result, the research of Source-Free
Domain Adaptation (SFDA) has drawn growing attention in recent years, which
only utilizes the source-trained model and unlabeled target data to adapt to
the target domain. Despite the rapid explosion of SFDA work, yet there has no
timely and comprehensive survey in the field. To fill this gap, we provide a
comprehensive survey of recent advances in SFDA and organize them into a
unified categorization scheme based on the framework of transfer learning.
Instead of presenting each approach independently, we modularize several
components of each method to more clearly illustrate their relationships and
mechanics in light of the composite properties of each method. Furthermore, we
compare the results of more than 30 representative SFDA methods on three
popular classification benchmarks, namely Office-31, Office-home, and VisDA, to
explore the effectiveness of various technical routes and the combination
effects among them. Additionally, we briefly introduce the applications of SFDA
and related fields. Drawing from our analysis of the challenges facing SFDA, we
offer some insights into future research directions and potential settings.


  The disc structure of the Milky Way is marked by a chemical dichotomy, with
high-alpha and low-alpha abundance sequences, traditionally identified with the
geometric thick and thin discs. This identification is aided by the old ages of
the high-alpha stars, and lower average ages of the low-alpha ones. Recent
large scale surveys such as APOGEE have provided a wealth of data on this
chemical structure, including showing that an identification of chemical and
geometric thick discs is not exact, but the origin of the chemical dichotomy
has remained unclear. Here we demonstrate that a dichotomy arises naturally if
the early gas-rich disc fragments, leading to some fraction of the star
formation occurring in clumps of the type observed in high-redshift galaxies.
These clumps have high star formation rate density. They, therefore, enrich
rapidly, moving from the low-alpha to the high-alpha sequence, while more
distributed star formation produces the low-alpha sequence. We demonstrate that
this model produces a chemically-defined thick disc that has many of the
properties of the Milky Way's thick disc. Because clump formation is common in
high redshift galaxies, we predict that chemical bimodalities are common in
massive galaxies.


  A calculation method for higher-order moments of physical quantities,
including magnetization and energy, based on the higher-order tensor
renormalization group is proposed. The physical observables are represented by
impurity tensors. A systematic summation scheme provides coarse-grained tensors
including multiple impurities. Our method is compared with the Monte Carlo
method on the two-dimensional Potts model. While the nature of the transition
of the $q$-state Potts model has been known for a long time owing to the
analytical arguments, a clear numerical confirmation has been difficult due to
extremely long correlation length in the weakly first-order transitions, e.g.,
for $q=5$. A jump of the Binder ratio precisely determines the transition
temperature. The finite-size scaling analysis provides critical exponents and
distinguishes the weakly first-order and the continuous transitions.


  In this paper we revisit the Adler-Bobenko-Suris H2 equation. The H2 equation
is linearly related to the $S^{(0,0)}$ and $S^{(1,0)}$ variables in the Cauchy
matrix scheme. We elaborate the coupled quad-system of $S^{(0,0)}$ and
$S^{(1,0)}$ in terms of their 3-dimensional consistency, Lax pair, bilinear
form and continuum limits. It is shown that $S^{(1,0)}$ itself satisfies a
9-point lattice equation and in continuum limit $S^{(1,0)}$ is related to the
eigenfunction in the Lax pair of the Korteweg-de Vries equation.


  We empirically verify that the market capitalisations of coins and tokens in
the cryptocurrency universe follow power-law distributions with significantly
different values, with the tail exponent falling between 0.5 and 0.7 for coins,
and between 1.0 and 1.3 for tokens. We provide a rationale for this, based on a
simple proportional growth with birth & death model previously employed to
describe the size distribution of firms, cities, webpages, etc. We empirically
validate the model and its main predictions, in terms of proportional growth
(Gibrat's law) of the coins and tokens. Estimating the main parameters of the
model, the theoretical predictions for the power-law exponents of coin and
token distributions are in remarkable agreement with the empirical estimations,
given the simplicity of the model. Our results clearly characterize coins as
being "entrenched incumbents" and tokens as an "explosive immature ecosystem",
largely due to massive and exuberant Initial Coin Offering activity in the
token space. The theory predicts that the exponent for tokens should converge
to 1 in the future, reflecting a more reasonable rate of new entrants
associated with genuine technological innovations.


  Fractional evolution equations lack generally accessible and well-converged
codes excepting anomalous diffusion. A particular equation of strong interest
to the growing intersection of applied mathematics and quantum information
science and technology is the fractional Schr\"odinger equation, which
describes sub-and super-dispersive behavior of quantum wavefunctions induced by
multiscale media. We derive a computationally efficient sixth-order split-step
numerical method to converge the eigenfunctions of the FSE to arbitrary
numerical precision for arbitrary fractional order derivative. We demonstrate
applications of this code to machine precision for classic quantum problems
such as the finite well and harmonic oscillator, which take surprising twists
due to the non-local nature of the fractional derivative. For example, the
evanescent wave tails in the finite well take a Mittag-Leffer-like form which
decay much slower than the well-known exponential from integer-order derivative
wave theories, enhancing penetration into the barrier and therefore quantum
tunneling rates. We call this effect \emph{fractionally enhanced quantum
tunneling}. This work includes an open source code for communities from quantum
experimentalists to applied mathematicians to easily and efficiently explore
the solutions of the fractional Schr\"odinger equation in a wide variety of
practical potentials for potential realization in quantum tunneling enhancement
and other quantum applications.


  We report a preliminary measurement of the slope parameter $\alpha$ for the
$\eta\to 3\piz$ decay carried out with KLOE at DA$\Phi$NE; where $\alpha$ is
the parameter describing the energy dependence of the square of the matrix
element for this decay. By fitting the event density in the Dalitz plot with a
collected statistic of 420 pb$^{-1}$ we determine $\alpha = -0.027 \pm 0.004
(stat) ^{+0.004}_{-0.006} (syst)$. This result is consistent with current
chiral perturbation theory calculations within the unitary approach.


  We investigate the new agegraphic dark energy scenario in a universe governed
by Horava-Lifshitz gravity. We consider both the detailed and non-detailed
balanced version of the theory, we impose an arbitrary curvature, and we allow
for an interaction between the matter and dark energy sectors. Extracting the
differential equation for the evolution of the dark energy density parameter
and performing an expansion of the dark energy equation-of-state parameter, we
calculate its present and its low-redshift value as functions of the dark
energy and curvature density parameters at present, of the Horava-Lifshitz
running parameter $\lambda$, of the new agegraphic dark energy parameter $n$,
and of the interaction coupling $b$. We find that $w_0=-0.82^{+0.08}_{-0.08}$
and $w_1=0.08^{+0.09}_{-0.07}$. Although this analysis indicates that the
scenario can be compatible with observations, it does not enlighten the
discussion about the possible conceptual and theoretical problems of
Horava-Lifshitz gravity.


  Motivated by the study of the maximal operator for the Schr\"{o}dinger
equation on the one-dimensional torus $ \mathbb{T}^1 $, it is conjectured that
for any complex sequence $ \{b_n\}_{n=1}^N $, $$ \left\| \sup_{t\in [0,N^2]}
\left|\sum_{n=1}^N b_n e \left(x\frac{n}{N} + t\frac{n^2}{N^2} \right) \right|
\right\|_{L^4([0,N])} \leq C_\epsilon N^{\epsilon} N^{\frac{1}{2}}
\|b_n\|_{\ell^2} $$ In this note, we show that if we replace the sequence $
\{\frac{n^2}{N^2}\}_{n=1}^N $ by an arbitrary sequence $ \{a_n\}_{n=1}^N $ with
only some convex properties, then $$ \left\| \sup_{t\in [0,N^2]}
\left|\sum_{n=1}^N b_n e \left(x\frac{n}{N} + ta_n \right) \right|
\right\|_{L^4([0,N])} \leq C_\epsilon N^\epsilon N^{\frac{7}{12}}
\|b_n\|_{\ell^2}. $$ We further show that this bound is sharp up to a
$C_\epsilon N^\epsilon$ factor.


  In this paper we find a complete characterization of plateaued Boolean
functions in terms of the associated Cayley graphs. Precisely, we show that a
Boolean function $f$ is $s$-plateaued (of weight $=2^{(n+s-2)/2}$) if and only
if the associated Cayley graph is a complete bipartite graph between the
support of $f$ and its complement (hence the graph is strongly regular of
parameters $e=0,d=2^{(n+s-2)/2}$). Moreover, a Boolean function $f$ is
$s$-plateaued (of weight $\neq 2^{(n+s-2)/2}$) if and only if the associated
Cayley graph is strongly $3$-walk-regular (and also strongly
$\ell$-walk-regular, for all odd $\ell\geq 3$) with some explicitly given
parameters.


  Three-body states are critical to the dynamics of many hadronic resonances.
We show that lattice QCD calculations have reached a stage where these states
can be accurately resolved. We perform a calculation over a wide range of
parameters and find all states below inelastic threshold agree with predictions
from a state-of-the-art phenomenological formalism. This also illustrates the
reliability of the formalism used to connect lattice QCD results to infinite
volume physics. Our calculation is performed using three positively charged
pions, with different lattice geometries and quark masses.


  Atomic contacts made of ferromagnetic metals present zero-bias anomalies in
the differential conductance due to the Kondo effect. These systems provide a
unique opportunity to perform a statistical analysis of the Kondo parameters in
nanostructures since a large number of contacts can be easily fabricated using
break-junction techniques. The details of the atomic structure differ from one
contact to another so a large number of different configurations can be
statistically analyzed. Here we present such a statistical analysis of the
Kondo effect in atomic contacts made from the ferromagnetic transition metals
Ni, Co and Fe. Our analysis shows clear differences between materials that can
be understood by fundamental theoretical considerations. This combination of
experiments and theory allow us to extract information about the origin and
nature of the Kondo effect in these systems and to explore the influence of
geometry and valence in the Kondo screening of atomic-sized nanostructures.


  This paper extends joint work with R. Friedman to show that the closure of
the locus of intermediate Jacobians of smooth cubic threefolds, in the moduli
space of principally polarized abelian varieties (ppav's) of dimension five, is
an irreducible component of the locus of ppav's whose theta divisor has a point
of multiplicity three or more. This paper also gives a sharp bound on the
multiplicity of a point on the theta divisor of an irreducible ppav of
dimension less than or equal to five; for dimensions four and five, this
improves the bound due to J. Koll\'ar, R. Smith-R. Varley, and L. Ein-R.
Lazarsfeld.


  The aim of the paper is to describe autocompact objects in Ab5-categories,
i.e. objects in cocomplete abelian categories with exactness preserving
filtered colimits of exact sequences, whose covariant Hom-functor commutes with
copowers of the object itself. A characterization of non-autocompact object is
given, a general criterion of autocompactness of an object via the structure of
its endomorphism ring is presented and a criterion of autocompactness of
products is proven.


  We report a new class of rotating charged solutions in 2+1 dimensions. These
solutions are obtained for Einstein-Maxwell gravity coupled to a dilaton field
with selfdual electromagnetic fields. The mass and the angular momentum of
these solutions computed at spatial infinity are finite. The class of solutions
considered here have naked singularities and are asymptotically flat.


  In this monograph we develop magnetic pseudodifferential theory for
operator-valued and equivariant operator-valued functions and distributions
from first principles. These have found plentiful applications in mathematical
physics, including in rigorous perturbation theory for slow-fast systems and
perturbed periodic operators. Yet, a systematic treatise was hitherto missing.
While many of the results can be found piecemeal in appendices and as sketches
in other articles, this article does contain new results. For instance, we have
established Beals-type commutator criteria for both cases, which then imply the
existence of Moyal resolvents for (equivariant) selfadjoint-operator-valued,
elliptic H\"ormander symbols and allows one to construct functional calculi.
What is more, we give criteria on the function under which a magnetic
pseudodifferential operator is (locally) trace class. Our aims for this article
are three-fold: (1) Create a single, solid work that colleagues can refer to.
(2) Be pedagogical and precise. And (3) give a straightforward strategy for
extending results from the operator-valued to the equivariant case, pointing
out some caveats and pitfalls that need to be kept in mind.


  Classical Gon\v{c}arov polynomials arose in numerical analysis as a basis for
the solutions of the Gon\v{c}arov interpolation problem. These polynomials
provide a natural algebraic tool in the enumerative theory of parking
functions. By replacing the differentiation operator with a delta operator and
using the theory of finite operator calculus, Lorentz, Tringali and Yan
introduced the sequence of generalized Gon\v{c}arov polynomials associated to a
pair $(\Delta, Z)$ of a delta operator $\Delta$ and an interpolation grid $Z$.
Generalized Gon\v{c}arov polynomials share many nice algebraic properties and
have a connection with the theories of binomial enumeration and order
statistics. In this paper we give a complete combinatorial interpretation for
any sequence of generalized Gon\v{c}arov polynomials. First, we show that they
can be realized as weight enumerators in partition lattices. Then, we give a
more concrete realization in exponential families and show that these
polynomials enumerate various enriched structures of vector parking functions.


  This chapter investigates the complexities surrounding the iron
biogeochemical cycle from the Archean to present, with a focus on assessing the
balance between iron sources and sinks during long periods of Earth's history
with relatively invariable redox conditions, when steady state can be safely
assumed. Currently, the residence time of iron in the ocean may be as short as
approximately 5 years. The input flux of iron is highly sensitive to redox
cycling in sediments, while its removal primarily occurs through dispersed
processes of oxidation and precipitation. In the Archean, we find a significant
imbalance between continental and hydrothermal inputs, which collectively
contribute between 61,500 to 263,000 Gg/yr of dissolved iron to the oceans, and
the most obvious sinks such as iron formations (IFs), which sequester up to
~43,000 Gg/yr of iron. A possible solution to this imbalance involves the
dispersed abiotic precipitation and removal of iron as silicates, sulfides, and
carbonates in marine basins. Additionally, we calculate the residence time of
dissolved iron in the Archean oceans to be between 6 kyr and 3 Myr, which is
significantly longer than the ocean mixing timescale. Our estimates indicate
that under the anoxic Archean atmosphere, the iron cycle was more protracted
than today, and the isotopic compositions and concentrations of dissolved iron
were likely more uniform. Distinct water bodies were likely confined to limited
areas or specific, dynamic systems with intense iron turnover, such as regions
where deep-sea upwelling currents brought hydrothermal iron to photic zones
rich in biotic or abiotic oxidants.


  We present the thermodynamic Bethe ansatz as a way to factorize the partition
function of a 2d field theory, in particular, a conformal field theory and we
compare it with another approach to factorization due to K. Schoutens which
consists of diagonalizing matrix recursion relations between the partition
functions at consecutive levels. We prove that both are equivalent, taking as
examples the SU(2) spinons and the 3-state Potts model. In the latter case we
see that there are two different thermodynamic Bethe ansatz equation systems
with the same physical content, of which the second is new and corresponds to a
one-quasiparticle representation, as opposed to the usual two-quasiparticle
representation. This new thermodynamic Bethe ansatz system leads to a new
dilogarithmic formula for the central charge of that model.


  We prove that if an infinite, discrete semigroup has the property that every
right syndetic set is left syndetic, then the semigroup has a left invariant
mean. We prove that the weak*-closed convex hull of the two-sided translates of
every bounded function on an infinite discrete semigroup contains a constant
function. Our proofs use the algebraic properties of the Stone-Cech
compactification.


  Recent advances in conditional recurrent language modelling have mainly
focused on network architectures (e.g., attention mechanism), learning
algorithms (e.g., scheduled sampling and sequence-level training) and novel
applications (e.g., image/video description generation, speech recognition,
etc.) On the other hand, we notice that decoding algorithms/strategies have not
been investigated as much, and it has become standard to use greedy or beam
search. In this paper, we propose a novel decoding strategy motivated by an
earlier observation that nonlinear hidden layers of a deep neural network
stretch the data manifold. The proposed strategy is embarrassingly
parallelizable without any communication overhead, while improving an existing
decoding algorithm. We extensively evaluate it with attention-based neural
machine translation on the task of En->Cz translation.


  With the planned turn-on of the PIP-II 800 MeV superconducting proton linac,
Fermilab will potentially become the world's best laboratory at which to carry
out fundamental muon measurements, sensitive searches for symmetry violation,
and precision tests of theory. In preparation, we propose to develop the
techniques that will be needed. An R&D and physics program is proposed at the
Fermilab MeV Test Area to use the existing 400 MeV Linac to demonstrate the
efficient production of a slow muonium beam using $\mu^+$ stopped in a
~100-$\mu$m-thick layer of superfluid helium, and to use that beam to measure
muonium gravity.


  Hybrid machine learning based on Hamiltonian formulations has recently been
successfully demonstrated for simple mechanical systems, both energy conserving
and not energy conserving. We introduce a pseudo-Hamiltonian formulation that
is a generalization of the Hamiltonian formulation via the port-Hamiltonian
formulation, and show that pseudo-Hamiltonian neural network models can be used
to learn external forces acting on a system. We argue that this property is
particularly useful when the external forces are state dependent, in which case
it is the pseudo-Hamiltonian structure that facilitates the separation of
internal and external forces. Numerical results are provided for a forced and
damped mass-spring system and a tank system of higher complexity, and a
symmetric fourth-order integration scheme is introduced for improved training
on sparse and noisy data.


  Generalized quons interpolating between Bose, Fermi, para-Bose, para-Fermi,
and anyonic statistics are proposed. They follow from the R-matrix approach to
deformed associative algebras. It is proved that generalized quons have the
same main properties as quons. A new result for the number operator is
presented and some physical features of generalized quons are discussed in the
limit $|q_{ij}^{2}| \rightarrow 1$.


  Dense distributions of string-like objects in material media are considered
in terms of continuum field theory. The strings are assumed to carry a
quantized abelian topological charge, such as the Burgers vector of
dislocations in solids or magnetic flux of supercurrent vortices in type-II
supercondoctors. Within this common framework the facts known from dislocation
theory can be extended, in appropriately modified forms, to other physical
contexts. In particular, the concept of incompatible distortions is
transplanted into the theory of type-II superconductivity. The compatibility
law for type-II superconductors is derived in terms of differential forms. As a
result, one obtains an appropriate generalization of the classic Londons'
equation.


  We introduce MTT, a dependent type theory which supports multiple modalities.
MTT is parametrized by a mode theory which specifies a collection of modes,
modalities, and transformations between them. We show that different choices of
mode theory allow us to use the same type theory to compute and reason in many
modal situations, including guarded recursion, axiomatic cohesion, and
parametric quantification. We reproduce examples from prior work in guarded
recursion and axiomatic cohesion, thereby demonstrating that MTT constitutes a
simple and usable syntax whose instantiations intuitively correspond to
previous handcrafted modal type theories. In some cases, instantiating MTT to a
particular situation unearths a previously unknown type theory that improves
upon prior systems. Finally, we investigate the metatheory of MTT. We prove the
consistency of MTT and establish canonicity through an extension of recent
type-theoretic gluing techniques. These results hold irrespective of the choice
of mode theory, and thus apply to a wide variety of modal situations.


  MDPCT1 is a four-layer cos-theta Nb3Sn dipole demonstrator developed and
tested at FNAL in the framework of the U.S. Magnet Development Program. The
magnet reached record fields for accelerator magnets of 14.1 T at 4.5 K in the
first test and 14.5 T at 1.9 K in the second test and then showed large
degradation. While its inner coils performed exceptionally well with only two
quenches up to 14.5 T and no evidence of degradation, the outer coils degraded
over the course of testing. By adopting new measurement and analysis techniques
at FNAL we are discussing in detail what happened. Both success and failure in
our diagnostics are discussed. The evolution of techniques over the course of
two tests (and three thermal cycles) shows the path to address challenges
brought by the first four-layer magnet tested at FNAL. This paper presents the
analysis of quench data along with diagnostic features and complementary
measurements taken in support of the magnet performance analysis.


  We propose to learn deep undirected graphical models (i.e., MRFs) with a
non-ELBO objective for which we can calculate exact gradients. In particular,
we optimize a saddle-point objective deriving from the Bethe free energy
approximation to the partition function. Unlike much recent work in approximate
inference, the derived objective requires no sampling, and can be efficiently
computed even for very expressive MRFs. We furthermore amortize this
optimization with trained inference networks. Experimentally, we find that the
proposed approach compares favorably with loopy belief propagation, but is
faster, and it allows for attaining better held out log likelihood than other
recent approximate inference schemes.


  Motivated by the recent indications for a 750 GeV resonance in the di-photon
final state at the LHC, in this work we analyse the compatibility of the excess
with the broad photon excess detected at the Galactic Centre. Intriguingly, by
analysing the parameter space of an effective models where a 750 GeV
pseudoscalar particles mediates the interaction between the Standard Model and
a scalar dark sector, we prove the compatibility of the two signals. We show,
however, that the LHC mono-jet searches and the Fermi LAT measurements strongly
limit the viable parameter space. We comment on the possible impact of cosmic
antiproton flux measurement by the AMS-02 experiment.


  When a quantum system undergoes unitary evolution in accordance with a
prescribed Hamiltonian, there is a class of states |psi> such that, after the
passage of a certain time, |psi> is transformed into a state orthogonal to
itself. The shortest time for which this can occur, for a given system, is
called the passage time. We provide an elementary derivation of the passage
time, and demonstrate that the known lower bound, due to Fleming, is typically
attained, except for special cases in which the energy spectra have
particularly simple structures. It is also shown, using a geodesic argument,
that the passage times for these exceptional cases are necessarily larger than
the Fleming bound. The analysis is extended to passage times for initially
mixed states.


  A mass function of small-scale dark matter clumps is calculated in the
standard cosmological scenario with an inflationary-produced primordial
fluctuation spectrum and with a hierarchical clustering. We take into account
the tidal destruction of clumps at early stages of structure formation starting
from a time of clump detachment from the Universe expansion. Only a small
fraction of these clumps, ~0.1-0.5%, in each logarithmic mass interval
$\Delta\log M\sim1$ survives the stage of hierarchical clustering. The
surviving clumps can be disrupted further in the galaxies by tidal interactions
with stars. We performed the detailed calculations of the tidal destruction of
clumps by stars in the Galactic bulge and halo and by the Galactic disk itself.
It is shown that the Galactic disc provides the dominant contribution to the
tidal destruction of small-scale clumps outside the bulge. The results obtained
are crucial for calculations of the dark matter annihilation signal in the
Galaxy.


  The rebrightening phenomenon is an interesting feature in some X-ray,
optical, and radio afterglows of gamma-ray bursts (GRBs). Here, we propose a
possible energy-supply assumption to explain the rebrightenings of radio
afterglows, in which the central engine with multiple active phases can supply
at least two GRB pulses in a typical GRB duration time. Considering the case of
double pulses supplied by the central engine, the double pulses have separate
physical parameters, except for the number density of the surrounding
interstellar medium (ISM). Their independent radio afterglows are integrated by
the ground detectors to form the rebrightening phenomenon. In this work, we
firstly simulate diverse rebrightening light curves under consideration of
different and independent physical parameters. Using this assumption, we also
give our best fit to the radio afterglow of GRB 970508 at three frequencies of
1.43, 4.86, and 8.46 GHz. We suggest that the central engine may be active
continuously at a timescale longer than that of a typical GRB duration time as
many authors have suggested, and that it may supply enough energy to cause the
long-lasting rebrightenings observed in some GRB afterglows.


  In high-energy hadronic collisions, hard parton scatterings with large
momentum transfers are prerequisites for the formation of hard and rare probes.
In heavy-ion collisions, these probes---final state particles related to the
early hard-parton scatterings---serve as a powerful tool to explore the whole
evolution of the medium including the quark--gluon plasma (QGP) stage. Hard
probes in proton-proton (pp) collisions test perturbative quantum
chromodynamics (pQCD) processes and hadronization, and provide a reference for
the nuclear collision systems. High-multiplicity pp collisions provide a bridge
to heavy-ion collisions, due to their large event activity.
  Heavy-flavor hadrons containing at least one charm or beauty quark belong to
the hard and rare probes. Recently, ALICE has measured a broad palette of
heavy-flavour baryons allowing to shed more light on charm fragmentation.
Measurements of charmonium production as a function of the event multiplicity
can provide insight into the interplay between charmonium-production processes
and soft processes driving the multiplicity. ALICE has investigated the
multiplicity dependence of J/$\psi$ production at midrapidity and the ratio of
$\psi \rm (2S)$ to J/$\psi$ yields at forward rapidity. The charm and beauty
cross sections can be constrained by fits of Monte-Carlo generators to the
measured dielectron continuum.


  Accurate tracking in urban environments necessitates target birth, survival,
and detection models that quantify the impact of terrain and building geometry
on the sequential estimation procedure. Current efforts assume that target
trajectories are limited to fixed paths, such as road networks. In these
settings a single airborne platform with a downward-facing camera is capable of
fully observing a target, outside of a few obstructed regions that can be
determined a priori (e.g. tunnels). However, many practical target types are
not necessarily restricted to road networks and thus require knowledge of
azimuthal shadowed regions to the sensor. In this paper, we propose the
integration of geospatial data for an urban environment into a particle filter
realization of a random finite set target tracking algorithm. Specifically, we
use 3D building polygons to compute the azimuthal shadowed regions with respect
to deployed sensor location. The particle filter predict and update steps are
modified such that (1) target births are assumed to occur in line-of-sight
(LOS) regions, (2) targets do not move into obstructions, (3) true target
detections only occur in LOS regions. The localization error performance
improvement for a single target Bernoulli filter under these modifications is
presented using freely available building vector data of New York City.


  We continue the systematic investigation of probabilistic and quantum finite
automata (PFAs and QFAs) on promise problems by focusing on unary languages. We
show that bounded-error QFAs are more powerful than PFAs. But, in contrary to
the binary problems, the computational powers of Las-Vegas QFAs and
bounded-error PFAs are equivalent to deterministic finite automata (DFAs).
Lastly, we present a new family of unary promise problems with two parameters
such that when fixing one parameter QFAs can be exponentially more succinct
than PFAs and when fixing the other parameter PFAs can be exponentially more
succinct than DFAs.


  We show that in many cases, the automorphism group of a curve and the
permutation automorphism group of a corresponding AG code are the same. This
generalizes a result of Wesemeyer beyond the case of planar curves.


  Although accumulation of molecular damage is suggested to be an important
molecular mechanism of aging, a quantitative link between the dynamics of
damage accumulation and mortality of species has so far remained elusive. To
address this question, we examine stability properties of a generic gene
regulatory network (GRN) and demonstrate that many characteristics of aging and
the associated population mortality rate emerge as inherent properties of the
critical dynamics of gene regulation and metabolic levels. Based on the
analysis of age-dependent changes in gene-expression and metabolic profiles in
Drosophila melanogaster, we explicitly show that the underlying GRNs are nearly
critical and inherently unstable. This instability manifests itself as aging in
the form of distortion of gene expression and metabolic profiles with age, and
causes the characteristic increase in mortality rate with age as described by a
form of the Gompertz law. In addition, we explain late-life mortality
deceleration observed at very late ages for large populations. We show that
aging contains a stochastic component, related to accumulation of regulatory
errors in transcription/translation/metabolic pathways due to imperfection of
signaling cascades in the network and of responses to environmental factors. We
also establish that there is a strong deterministic component, suggesting
genetic control. Since mortality in humans, where it is characterized best, is
strongly associated with the incidence of age-related diseases, our findings
support the idea that aging is the driving force behind the development of
chronic human diseases.


  We demonstrate the critical need to identify social situation and instability
factors by acquiring public social satisfaction in this research. However,
subject to the large amount of manual work cost in subject recruitment and data
processing, conventional self-reported method cannot be implemented in real
time or applied in large scale investigation. To solve the problem, this paper
proposed an approach to predict users' social satisfaction, especially for the
economy-related satisfaction based on users' social media records. We recruited
2,018 Cantonese active participants from each city in Guangdong province
according to the population distribution. Both behavioral and linguistic
features of the participants are extracted from the online records of social
media, i.e., Sina Weibo. Regression models are used to predict Sina Weibo
users' social satisfaction. Furthermore, we consult the economic indexes of
Guangdong in 2012, and calculate the correlations between these indexes and the
predicted social satisfaction. Results indicate that social satisfaction can be
significantly expressed by specific social media features; local economy
satisfaction has significant positive correlations with several local economy
indexes, which supports that it is reliable to predict social satisfaction from
social media.


  Following the trends of index modulated (IM) techniques for optical
communications, in the last few years several new waveform proposals have been
made, aiming at conveying a higher density of information by driving different
signal properties. One of these proposals mixes multi-pulse pulse-position
modulation (MPPM) and quadrature amplitude modulation (QAM) in a system called
QAM-MPPM. We present here a new way to demodulate its compound waveform, and,
for the non-turbulent free space optical (FSO) channel, we provide accurate
analytical expressions for its error probabilities, both in the case of the
traditional and the new detector. Based on these analytical derivations, we
also provide simplified expressions for the estimation of the error
probabilities. We show that the new detector offers a gain of some tenths of dB
in signal-to-noise ratio with respect to the previously defined one without an
increase in complexity, and that our error probability estimations are more
accurate than previously published results. To the best of our knowledge, this
work is the first to provide simulation results validating the study of the
error probability performance of QAM-MPPM.


  In this note, we prove that the centralizer lattice ${\mathfrak C}(G)$ of a
group $G$ cannot be written as a union of two proper intervals. In particular,
it follows that ${\mathfrak C}(G)$ has no breaking point. As an application, we
show that the generalized quaternion $2$-groups are not capable.


  The difference of quantum mutual information for bipartite system of qubits
and minimum taken with respect to local unitary transformation group is
introduced as a characteristic of quantum correlations.The two qubits example
(and specifically the two qubits X state) is studied in some details.


  The $H~\mathrm{mod}~K$ theorem gives all possible periodic solutions in a
$\Gamma-$equivariant dynamical system, based on the group-theoretical aspects.
In addition, it classifies the spatio temporal symmetries that are possible. By
the contrary, the equivariant Hopf theorem guarantees the existence of families
of small-amplitude periodic solutions bifurcating from the origin for each
$\mathbf{C}-$axial subgroup of $\Gamma\times\mathbb{S}^1.$ In this paper we
identify which periodic solution types, whose existence is guaranteed by the
$H~\mathrm{mod}~K$ theorem, are obtainable by Hopf bifurcation, when the group
$\Gamma$ is finite cyclic.


  Deep learning has been widely used for inferring robust grasps. Although
human-labeled RGB-D datasets were initially used to learn grasp configurations,
preparation of this kind of large dataset is expensive. To address this
problem, images were generated by a physical simulator, and a physically
inspired model (e.g., a contact model between a suction vacuum cup and object)
was used as a grasp quality evaluation metric to annotate the synthesized
images. However, this kind of contact model is complicated and requires
parameter identification by experiments to ensure real world performance. In
addition, previous studies have not considered manipulator reachability such as
when a grasp configuration with high grasp quality is unable to reach the
target due to collisions or the physical limitations of the robot. In this
study, we propose an intuitive geometric analytic-based grasp quality
evaluation metric. We further incorporate a reachability evaluation metric. We
annotate the pixel-wise grasp quality and reachability by the proposed
evaluation metric on synthesized images in a simulator to train an
auto-encoder--decoder called suction graspability U-Net++ (SG-U-Net++).
Experiment results show that our intuitive grasp quality evaluation metric is
competitive with a physically-inspired metric. Learning the reachability helps
to reduce motion planning computation time by removing obviously unreachable
candidates. The system achieves an overall picking speed of 560 PPH (pieces per
hour).


  The collection of individually resolvable gravitational wave (GW) events
makes up a tiny fraction of all GW signals which reach our detectors, while
most lie below the confusion limit and go undetected. Like voices in a crowded
room, the collection of unresolved signals gives rise to a background which is
well-described via stochastic variables, and hence referred to as the
stochastic GW background (SGWB). In this review, we provide an overview of
stochastic GW signals, and characterise them based on features of interest such
as generation processes and observational properties. We then review the
current detection strategies for stochastic backgrounds, offering a
ready-to-use manual for stochastic GW searches in real data. In the process, we
distinguish between interferometric measurements of GWs, either by ground-based
or space-based laser interferometers, and timing-residuals analyses with pulsar
timing arrays (PTAs). These detection methods have been applied to real data
both by the large GW collaborations and smaller research groups, and the most
recent and instructive results are reported here. We close this review with an
outlook on future observations with third generation detectors, space-based
interferometers, and potential non-interferometric detection methods proposed
in the literature.


  We present a strong lens analysis of SDSS J1004+4112, a unique quasar lens
produced by a massive cluster of galaxies at z=0.68, using a newly developed
software for gravitational lensing. We find that our parametric mass model well
reproduces all observations including the positions of quasar images as well as
those of multiply imaged galaxies with measured spectroscopic redshifts, time
delays between quasar images, and the positions of faint central images. The
predicted large total magnification of \mu ~ 70 suggests that the lens system
is indeed a useful site for studying the fine structure of a distant quasar and
its host galaxy. The dark halo component is found to be unimodal centered on
the brightest cluster galaxy and the Chandra X-ray surface brightness profile.
In addition, the orientation of the halo component is quite consistent with
those of the brightest cluster galaxy and member galaxy distribution, implying
that the lensing cluster is a relaxed system. The radial profile of the
best-fit mass model is in good agreement with a mass profile inferred from the
X-ray observation. While the inner radial slope of the dark halo component is
consistent with being -1, a clear dependence of the predicted A-D time delay on
the slope indicates that an additional time delay measurement will improve
constraints on the mass model.


  We study the airplane refueling problem which was introduced by the
physicists Gamow and Stern in their classical book Puzzle-Math (1958). Sticking
to the original story behind this problem, suppose we have to deliver a bomb in
some distant point of the globe, the distance being much greater than the range
of any individual airplane at our disposal. Therefore, the only feasible option
to carry out this mission is to better utilize our fleet via mid-air refueling.
Starting with several airplanes that can refuel one another, and gradually drop
out of the flight until the single plane carrying the bomb reaches the target,
how would you plan the refueling policy?
  The main contribution of Gamow and Stern was to provide a complete
characterization of the optimal refueling policy for the special case of
identical airplanes. In spite of their elegant and easy-to-analyze solution,
the computational complexity of the general airplane refueling problem, with
arbitrary tank volumes and consumption rates, has remained widely open ever
since, as recently pointed out by Woeginger (Open Problems in Scheduling,
Dagstuhl 2010, page 24). To our knowledge, other than a logarithmic
approximation, which can be attributed to folklore, it is not entirely obvious
even if constant-factor performance guarantees are within reach.
  In this paper, we propose a polynomial-time approximation scheme for the
airplane refueling problem in its utmost generality. Our approach builds on a
novel combination of ideas related to parametric pruning, efficient guessing
tricks, reductions to well-structured instances of generalized assignment, and
additional insight into how LP-rounding algorithms in this context actually
work. We complement this result by presenting a fast and easy-to-implement
algorithm that approximates the optimal refueling policy to within a constant
factor.


  The aim of our present work here is to present few results in the theory of
Mellin transforms using the method that S. Ramanujan used in proving his Master
Theorem. Further applications of our results for some number-theoretic
functions such as the prime counting function and the zeta function are
established.


  We investigate the transport properties of an anharmonic oscillator, modeled
by a single-site Bose-Hubbard model, coupled to two different thermal baths
using the numerically exact thermofield based chain-mapping matrix product
states (TCMPS) approach. We compare the effectiveness of TCMPS to probe the
nonequilibrium dynamics of strongly interacting system irrespective of the
system-bath coupling against the global master equation approach in
Gorini-Kossakowski-Sudarshan-Lindblad form. We discuss the effect of on-site
interactions, temperature bias as well as the system-bath couplings on the
steady state transport properties. Last we also show evidence of non-Markovian
dynamics by studying the non-monotonicity of the time evolution of the trace
distance between two different initial states.


  Biologically inspired recurrent neural networks, such as reservoir computers
are of interest in designing spatio-temporal data processors from a hardware
point of view due to the simple learning scheme and deep connections to Kalman
filters. In this work we discuss using in-depth simulation studies a way to
construct hardware reservoir computers using an analog stochastic neuron cell
built from a low energy-barrier magnet based magnetic tunnel junction and a few
transistors. This allows us to implement a physical embodiment of the
mathematical model of reservoir computers. Compact implementation of reservoir
computers using such devices may enable building compact, energy-efficient
signal processors for standalone or in-situ machine cognition in edge devices.


  Layered materials enable the assembly of a new class of heterostructures
where lattice-matching is no longer a requirement. Interfaces in these
heterostructures therefore become a fertile ground for unexplored physics as
dissimilar phenomena can be coupled via proximity effects. In this article we
identify an unexpected photoluminescence (PL) peak when MoSe$_2$ interacts with
TiSe$_2$. A series of temperature-dependent and spatially-resolved PL
measurements reveal this peak is unique to the TiSe$_2$-MoSe$_2$ interface,
higher in energy compared to the neutral exciton, and exhibits exciton-like
characteristics. The feature disappears at the TiSe$_2$ charge density wave
transition, suggesting that the density wave plays an important role in the
formation of this new exciton. We present several plausible scenarios regarding
the origin of this peak that individually capture some aspects of our
observations, but cannot fully explain this feature. These results therefore
represent a fresh challenge for the theoretical community and provide a
fascinating way to engineer excitons through interactions with charge density
waves.


  In this paper we study the second Hochschild cohomology group of the
preprojective algebra of type $D_4$ over an algebraically closed field $K$ of
characteristic 2. We also calculate the second Hochschild cohomology group of a
non-standard algebra which arises as a socle deformation of this preprojective
algebra and so show that the two algebras are not derived equivalent. This
answers a question raised by Holm and Skowro\'nski.


  Quantum mechanics and relativity in the continuum imply the well known
spin-statistics connection. However for particles hopping on a lattice, there
is no such constraint. If a lattice model yields a relativistic field theory in
a continuum limit, this constraint must "emerge" for physical excitations. We
discuss a few models where a spin-less fermion hopping on a lattice gives
excitations which satisfy the continuum Dirac equation. This includes such well
known systems such as graphene and staggered fermions.


  It is shown that kinetic freeze-out in relativistic heavy-ion collisions
invariably entails a non-trivial dependence of the freeze-out temperature on
the collision centrality. The centrality independence of the chemical
freeze-out temperature observed in Au+Au collisions at RHIC is therefore
inconsistent with the hypothesis that hadron abundances decouple kinetically
from inelastic hadron-hadron interactions. On the other hand, it is consistent
with the hypothesis that chemical decoupling is driven by the quark-hadron
phase transition, and that the observed universal chemical freeze-out reflects
its critical temperature, independent of the dynamical state of the collision
fireball as it passes through the phase transition.


  Virtualization allows the simulation of automotive ECUs on a Windows PC
executing in closed-loop with a vehicle simulation model. This approach enables
to move certain development tasks from road or test rigs and HiL (Hardware in
the loop) to PCs, where they can often be performed faster and cheaper. Renault
has recently established such a virtualization process for powertrain control
software based on Simulink models. If the number of runnables exceeds a
threshold (about 1500) the execution of the virtual ECU is no longer straight
forward and specific techniques are required. This paper describes the
motivation behind a Simulink model based process, the virtualization process
and applications of the resulting virtual ECUs. Domain: Critical Transportation
Systems Topic: Processes, methods and tools, in particular: virtual engineering
and simulation 1. Motivation Since 2010, Renault has established a framework to
develop engine control software for Diesel and Gasoline engines [6]. The
framework is heavily based on MATLAB/Simulink and the idea of model-based
development, which facilitates the carry-over and carry-across of application
software between software projects. In the Renault EMS architecture software is
composed in to about 20 functions, such as Air System, Combustion etc. A
function consists of modules. A module is the smallest testable software unit
and contains runnables to be scheduled and executed by the Operating System
(Os) of the ECU. The Renault EMS development process includes basically the
following steps [5]. 1. Specification of about 200 generic configurable modules
per ECU using MATLAB/Simulink. 2. Generation of C code (EMS application
software) from all module specifications using MATLAB/Simulink Embedded Coder.
3. MiL (Model in the Loop) test and validation of the resulting executable
specifications at module level in a simulated system environment, considering
only essential interactions with other modules and system environment. This is
essentially a back-to-back test to make sure that the Simulink model of a
module and the corresponding production C code show equivalent and intended
behaviour. To insure software quality, this step is repeatedly performed with
steps 1 and 2, based on the simulation capabilities of MATLAB/Simulink. 4.
Configuration of modules to fit to the specific needs of a software project,
such as absence or presence of certain components. 5. Integration of generated
configured C code and hand-coded platform software (basic software) on supplied
target hardware, a real ECU that communicates with other controllers via CAN
and other busses. 6. Validation and test of all modules on system level using
the real ECU. In contrast to step 3, the interactions of all modules and
interactions with the system environment are visible then and subject to
testing. For example, the Os runs all scheduled runnables then, not just those
of the modules considered to be 'essential' for a module under test. Critical
assessment of the above process shows that there is a considerable delay
between delivery of a set of specifications to the software project team (at
the end of step 3) and system-level tests based on an ECU that runs entire
software (step 6). Typical delays are weeks or months.


  We explore the hypothesis of having an approximate lepton number conservation
as a way to achieve a successful leptogenesis in low-scale seesaw mechanisms.
The smallness of the active neutrino masses, as well as a strong degeneracy in
the mass spectrum of the heavy sterile states, are both consequence of the
assumed approximate symmetry. We propose a minimal extension of the Standard
Model in order to implement the idea, and perform an analytical and numerical
study to determine the viable solutions in the model and the testability of
this leptogenesis scenario in future experiments.


  We study reductions of the Volterra lattice corresponding to stationary
equations for the additional, noncommutative subalgebra of symmetries. It is
shown that, in the case of general position, such a reduction is equivalent to
the stationary equation for a sum of the scaling symmetry and the negative
flows, and is written as $(m+1)$-component difference equations of the
Painlev\'e type generalizing the dP$_1$ and dP$_{34}$ equations. For these
reductions, we present the isomonodromic Lax pairs and derive the B\"acklund
transformations which form the $\mathbb{Z}^m$ lattice.


  While the presence of discs around classical Be stars is well established,
their origin is still uncertain. To understand what processes result in the
creation of these discs and how angular momentum is transported within them,
their physical properties must be constrained. This requires comparing high
spatial and spectral resolution data with detailed radiative transfer
modelling. We present a high spectral resolution, R~80,000, sub milli-arcsecond
precision, spectroastrometric study of the circumstellar disc around the Be
star beta CMi. The data are confronted with three-dimensional, NLTE radiative
transfer calculations to directly constrain the properties of the disc.
Furthermore, we compare the data to disc models featuring two velocity laws;
Keperian, the prediction of the viscous disc model, and angular momentum
conserving rotation. It is shown that the observations of beta CMi can only be
reproduced using Keplerian rotation. The agreement between the model and the
observed SED, polarisation and spectroastrometric signature of beta CMi
confirms that the discs around Be stars are well modelled as viscous decretion
discs.


  A theory is proposed, in which the basic elements of reality are assumed to
be something called modes. Particles are interpreted as composites of modes,
corresponding to eigenstates of the interaction Hamiltonian of modes. At the
fundamental level of the proposed theory, there are two basic modes only,whose
spinor spaces are the two smallest nontrivial representation spaces of the
SL(2,C) group, one being the complex conjugate of the other. All other modes
are constructed from the two basic modes, making use of the operations of
direct sum and direct product for related spinor spaces. Accompanying the
construction of direct-product modes, interactions among modes are introduced
in a natural way, with the interaction Hamiltonian given from mappings between
the corresponding state spaces. The interaction Hamiltonian thus obtained turn
out to possess a form, which is similar to a major part of the interaction
Hamiltonian in the Glashow-Weinberg-Salam electroweak theory. In the proposed
theory, it is possible for the second-order perturbation expansion of energy to
be free from ultraviolet divergence. This expansion is used to derive some
approximate relations for neutrino masses; in particular, a rough estimate is
obtained for the ratio of mass differences of neutrinos, which gives the
correct order of magnitude compared with the experimental result.


  We study the dynamics of a scalar inflaton field with a symmetric
double--well potential and prove rigorously the existence of a limit cycle in
its phase space. By using analytical and numerical arguments we show that the
limit cycle is stable and give an analytical formula for its period.


  Under hydrostatic pressure, the ground state of a two-dimensional electron
gas at $\nu=5/2$ changes from a fractional quantum Hall state to the stripe
phase. By measuring the energy gap of the fractional quantum Hall state and of
the onset temperature of the stripe phase we mapped out a phase diagram of
these competing phases in the pressure-temperature plane. Our data highlight
the dichotomy of two descriptions of the half-filled Landau level near the
quantum critical point: one based on electrons and another on composite
fermions.


  Profile likelihood confidence intervals are a robust alternative to Wald's
method if the asymptotic properties of the maximum likelihood estimator are not
met. However, the constrained optimization problem defining profile likelihood
confidence intervals can be difficult to solve in these situations, because the
likelihood function may exhibit unfavorable properties. As a result, existing
methods may be inefficient and yield misleading results. In this paper, we
address this problem by computing profile likelihood confidence intervals via a
trust-region approach, where steps computed based on local approximations are
constrained to regions where these approximations are sufficiently precise. As
our algorithm also accounts for numerical issues arising if the likelihood
function is strongly non-linear or parameters are not estimable, the method is
applicable in many scenarios where earlier approaches are shown to be
unreliable. To demonstrate its potential in applications, we apply our
algorithm to benchmark problems and compare it with 6 existing approaches to
compute profile likelihood confidence intervals. Our algorithm consistently
achieved higher success rates than any competitor while also being among the
quickest methods. As our algorithm can be applied to compute both confidence
intervals of parameters and model predictions, it is useful in a wide range of
scenarios.


  Supersymmetry is used to derive conditions on higher derivative terms in the
effective action of type IIB supergravity. Using these conditions, we are able
to prove earlier conjectures that certain modular invariant interactions of
order alpha' **3 relative to the Einstein-Hilbert term are proportional to
eigenfunctions of the Laplace operator on the fundamental domain of SL(2,Z). We
also discuss how these arguments generalize to terms of higher order in alpha',
as well as to compactifications of supergravity.


  We present studies of quantum algorithms exploiting machine learning to
classify events of interest from background events, one of the most
representative machine learning applications in high-energy physics. We focus
on variational quantum approach to learn the properties of input data and
evaluate the performance of the event classification using both simulators and
quantum computing devices. Comparison of the performance with standard
multi-variate classification techniques based on a boosted-decision tree and a
deep neural network using classical computers shows that the quantum algorithm
has comparable performance with the standard techniques at the considered
ranges of the number of input variables and the size of training samples. The
variational quantum algorithm is tested with quantum computers, demonstrating
that the discrimination of interesting events from background is feasible.
Characteristic behaviors observed during a learning process using quantum
circuits with extended gate structures are discussed, as well as the
implications of the current performance to the application in high-energy
physics experiments.


  We compare classical and Bayesian methods for fitting the poisson
distribution to the number of hurricanes making landfall on sections of the US
coastline.


  As models continue to grow in size, the development of memory optimization
methods (MOMs) has emerged as a solution to address the memory bottleneck
encountered when training large models. To comprehensively examine the
practical value of various MOMs, we have conducted a thorough analysis of
existing literature from a systems perspective. Our analysis has revealed a
notable challenge within the research community: the absence of standardized
metrics for effectively evaluating the efficacy of MOMs. The scarcity of
informative evaluation metrics hinders the ability of researchers and
practitioners to compare and benchmark different approaches reliably.
Consequently, drawing definitive conclusions and making informed decisions
regarding the selection and application of MOMs becomes a challenging endeavor.
To address the challenge, this paper summarizes the scenarios in which MOMs
prove advantageous for model training. We propose the use of distinct
evaluation metrics under different scenarios. By employing these metrics, we
evaluate the prevailing MOMs and find that their benefits are not universal. We
present insights derived from experiments and discuss the circumstances in
which they can be advantageous.


  Over the last two decades, frameworks for distributed-memory parallel
computation, such as MapReduce, Hadoop, Spark and Dryad, have gained
significant popularity with the growing prevalence of large network datasets.
The Massively Parallel Computation (MPC) model is the de-facto standard for
studying graph algorithms in these frameworks theoretically. Subgraph counting
is one such fundamental problem in analyzing massive graphs, with the main
algorithmic challenges centering on designing methods which are both scalable
and accurate.
  Given a graph $G=(V, E)$ with $n$ vertices, $m$ edges and $T$ triangles, our
first result is an algorithm that outputs a $(1+\varepsilon)$-approximation to
$T$, with asymptotically \emph{optimal round and total space complexity}
provided any $S \geq \max{(\sqrt m, n^2/m)}$ space per machine and assuming
$T=\Omega(\sqrt{m/n})$. Our result gives a quadratic improvement on the bound
on $T$ over previous works. We also provide a simple extension of our result to
counting \emph{any} subgraph of $k$ size for constant $k \geq 1$. Our second
result is an $O_{\varepsilon}(\log \log n)$-round algorithm for exactly
counting the number of triangles, whose total space usage is parametrized by
the \emph{arboricity} $\alpha$ of the input graph. We extend this result to
exactly counting $k$-cliques for any constant $k$. Finally, we prove that a
recent result of Bera, Pashanasangi and Seshadhri (ITCS 2020) for exactly
counting all subgraphs of size at most $5$ can be implemented in the MPC model
in total space.


  Strong consistency of the quasi-maximum likelihood estimator is given for a
general class of multidimensional causal processes based on asyMmetric
laplacian innovation.


  We report the discovery of KMT-2018-BLG-1292Lb, a super-Jovian $M_{\rm
planet} = 4.5\pm 1.3\,M_J$ planet orbiting an F or G dwarf $M_{\rm host} =
1.5\pm 0.4\,M_\odot$, which lies physically within ${\cal O}(10\,\pc)$ of the
Galactic plane. The source star is a heavily extincted $A_I\sim 5.2$ luminous
giant that has the lowest Galactic latitude, $b=-0.28^\circ$, of any planetary
microlensing event. The relatively blue blended light is almost certainly
either the host or its binary companion, with the first explanation being
substantially more likely. This blend dominates the light at $I$ band and
completely dominates at $R$ and $V$ bands. Hence, the lens system can be probed
by follow-up observations immediately, i.e., long before the lens system and
the source separate due to their relative proper motion. The system is well
characterized despite the low cadence $\Gamma=0.15$--$0.20\,{\rm hr^{-1}}$ of
observations and short viewing windows near the end of the bulge season. This
suggests that optical microlensing planet searches can be extended to the
Galactic plane at relatively modest cost.


  We present a construction of genuinely entangled multipartite quantum states
based on the group theory. Analyzed states resemble the Dicke states, whereas
the interactions occur only between specific subsystems related by the action
of the selected group. The states constructed by this technique exhibit desired
symmetry properties and form a natural resource for less-symmetric quantum
informational tasks. We propose quantum circuits efficiently generating such
states, which in general have smaller complexity than the circuits necessary to
create fully symmetric entangled states.


  The analysis of the distribution of stars in open clusters may yield
important information on the star formation process and early dynamical
evolution of stellar clusters. Here we address this issue by systematically
characterizing the internal spatial structure of 16 open clusters in the Milky
Way spanning a wide range of ages. Cluster stars have been selected from a
membership probability analysis based on a non-parametric method that uses both
positions and proper motions and does not make any a priori assumption on the
underlying distributions. The internal structure is then characterized by means
of the minimum spanning tree method (Q parameter), King profile fitting, and
the correlation dimension (Dc) for those clusters with fractal patterns. On
average, clusters with fractal-like structure are younger than those exhibiting
radial star density profiles and an apparent trend between Q and age is
observed in agreement with previous ideas about the dynamical evolution of the
internal spatial structure of stellar clusters. However, some new results are
obtained from a more detailed analysis: (a) a clear correlation between Q and
the concentration parameter of the King model for those cluster with radial
density profiles, (b) the presence of spatial substructure in clusters as old
as 100 Myr, and (c) a significant correlation between fractal dimension and age
for those clusters with internal substructure. Moreover, the lowest fractal
dimensions seem to be considerably smaller than the average value measured in
galactic molecular cloud complexes.


  Predicting how distributions over discrete variables vary over time is a
common task in time series forecasting. But whereas most approaches focus on
merely predicting the distribution at subsequent time steps, a crucial piece of
information in many settings is to determine how this probability mass flows
between the different elements over time. We propose a new approach to
predicting such mass flow over time using optimal transport. Specifically, we
propose a generic approach to predicting transport matrices in end-to-end deep
learning systems, replacing the standard softmax operation with Sinkhorn
iterations. We apply our approach to the task of predicting how communities
will evolve over time in social network settings, and show that the approach
improves substantially over alternative prediction methods. We specifically
highlight results on the task of predicting faction evolution in Ukrainian
parliamentary voting.


  In this paper, we address the problem of registering multiple point clouds
corrupted with high anisotropic localization noise. Our approach follows the
widely used framework of Gaussian mixture model (GMM) reconstruction with an
expectation-maximization (EM) algorithm. Existing methods are based on an
implicit assumption of space-invariant isotropic Gaussian noise. However, this
assumption is violated in practice in applications such as single molecule
localization microscopy (SMLM). To address this issue, we propose to introduce
an explicit localization noise model that decouples shape modeling with the GMM
from noise handling. We design a stochastic EM algorithm that considers
noise-free data as a latent variable, with closed-form solutions at each EM
step. The first advantage of our approach is to handle space-variant and
anisotropic Gaussian noise with arbitrary covariances. The second advantage is
to leverage the explicit noise model to impose prior knowledge about the noise
that may be available from physical sensors. We show on various simulated data
that our noise handling strategy improves significantly the robustness to high
levels of anisotropic noise. We also demonstrate the performance of our method
on real SMLM data.


  A pair of circularly polarized laser pulses of opposite helicities are shown
to control the route of spin reorientation phase transition in rare-earth
antiferromagnetic orthoferrite (Sm$_{0.55}$Tb$_{0.45}$)FeO$_3$. The route can
be efficiently controlled by the delay between the pulses and the sample
temperature. Simulations employing previously published models of
\mbox{laser-induced} spin dynamics in orthoferrites failed to reproduce the
experimental results. We suggest that the failure is due to neglected
temperature dependence of the antiferromagnetic resonance damping in the
material. Taking into account the experimentally deduced temperature dependence
of the damping, we obtained good agreement between the simulations and the
experiment.