  A continuous approximation framework for non-linear stochastic as well as
deterministic discrete maps is developed. For the stochastic map with
uncorelated Gaussian noise, by successively applying the It\^o lemma, we obtain
a Langevin type of equation. Specifically, we show how non-linear maps give
rise to a Langevin description that involves multiplicative noise. The
multiplicative nature of the noise induces an additional effective force, not
present in the absence of noise. We further exploit the continuum description
and provide an explicit formula for the stable distribution of the stochastic
map and conditions for its existence. Our results are in good agreement with
numerical simulations of several maps.


  The main feature of the Fission-Track Thermochronology is its ability to
infer the thermal histories of mineral samples in regions of interest for
geological studies. The ingredients that make the thermal history inference
possible are the annealing models, which capture the annealing kinetics of
fission tracks for isothermal heating experiments, and the Principle of
Equivalent Time (PET), which allows the application of the annealing models to
variable temperatures. It turns out that the PET only applies to specific types
of annealing models describing single activation energy annealing mechanisms
(parallel models). However, the PET has been extensively applied to models
related to multiple activation energy mechanisms (fanning models). This
procedure is an approximation that has been overlooked due to the lack of a
suitable alternative. To deal with this difficult, a formalism, based on
physicochemical techniques, that allows to quantify the effects of annealing on
the fission tracks for variable temperatures, is developed. It is independent
of the annealing mechanism and, therefore, is applicable to any annealing
model. In the cases in which the PET is valid, parallel models, the proposed
method and the PET predict the same degrees of annealing. However, deviations
appear when the methods are applied to the fanning models, with the PET
underestimating annealing effects. The consequences for the inference of
thermal histories are discussed.


  Branching bisimilarity on normed Basic Process Algebra (BPA) was claimed to
be EXPTIME-hard in previous papers without any explicit proof. Recently it is
reminded by Jan\v{c}ar that the claim is not so dependable. In this paper, we
develop a new complete proof for EXPTIME-hardness of branching bisimilarity on
normed BPA. We also prove the associate regularity problem on normed BPA is
PSPACE-hard and in EXPTIME. This improves previous P-hard and NEXPTIME result.


  In Fermilab we are build and tested several superconducting Single Spoke
Resonators (SSR1, \beta=0.22) which can be used for acceleration of low beta
ions. Fist two cavities performed very well during cold test in Vertical Test
Station at FNAL. One dressed cavity was also tested successfully in Horizontal
Test Station. Currently we are building 8 cavity cryomodule for PIXIE project.
Additional 10 cavities were manufactured in the industry and on-going cold test
results will be presented in this poster.


  We derive a continuum field theory for the Majumdar-Ghosh model in the
large-$S$ limit, where the field takes values in the manifold of the $SO(3)$
group. No topological term is induced in the action and the cases for integer
spin and half-integer spin appear to be indistinguishable. A one-loop $\beta
-$function calculation indicates that the theory flows towards a strong
coupling (disordered) phase at long distances. This is verified in the
large-$N$ limit, where all excitations are shown to be massive. (Three figures
not included)


  Let M be a real analytic manifold modeled on a locally convex space and K be
a non-empty compact subset of M. We show that if an open neighborhood of K in M
admits a complexification which is a regular topological space, then the germ
of the latter (as a complex manifold) is uniquely determined. If M is regular
and the complexified modeling space of M is normal, then a regular
complexification exists for some neighborhood of K. For each (real or complex)
analytic regular manifold M modeled on a metrizable locally convex space and
Banach-Lie group H, this allows the group Germ(K,H) of germs of H-valued
analytic maps around K in M to be turned into an analytic Lie group which is
regular in Milnor's sense. A special case is a regular real analytic Lie group
structure on the group of real analytic H-valued maps on a compact real
analytic manifold M (which, previously, had only been treated in the convenient
setting of analysis). Combining our results concerning groups of germs with an
idea by Neeb and Wagemann, one can also obtain a regular Lie group structure on
the group of all real analytic H-valued mappings on the real line.


  The presence of spectroscopically confirmed Balmer breaks in galaxy spectral
energy distributions (SEDs) at $z>9$ provides one of the best probes of the
assembly history of the first generations of stars in our Universe. Recent
observations of the gravitationally lensed source, MACS 1149_JD1 (JD1),
indicate that significant amounts of star formation likely occurred at
redshifts as high as $z\simeq15$. The inferred stellar mass, dust mass, and
assembly history of JD1, or any other galaxy at these redshifts that exhibits a
strong Balmer break, can provide a strong test of our best theoretical models
from high-resolution cosmological simulations. In this work, we present the
results from a cosmological radiation-hydrodynamics simulation of the region
surrounding a massive Lyman-break galaxy. For two of our most massive systems,
we show that dust preferentially resides in the vicinity of the young stars
thereby increasing the strength of the measured Balmer break such that the
simulated SEDs are consistent with the photometry of JD1 and two other $z>9$
systems (GN-z10-3 and GN-z9-1) that have proposed Balmer breaks at high
redshift. We find strong variations in the shape and luminosity of the SEDs of
galaxies with nearly identical stellar and halo masses, indicating the
importance of morphology, assembly history, and dust distribution in making
inferences on the properties of individual galaxies at high redshifts. Our
results stress the importance that dust may play in modulating the observable
properties of galaxies, even at the extreme redshifts of $z>9$.


  Consider a rooted Galton-Watson tree $T$, to each of whose edges we assign,
independently, a weight that equals $+1$ with probability $p_{1}$, $0$ with
probability $p_{0}$ and $-1$ with probability $p_{-1}=1-p_{1}-p_{0}$. We play a
game on this rooted, edge-weighted Galton-Watson tree, involving two players
and a token. The token is allowed to be moved from where it is currently
located, say a vertex $u$ of $T$, to any child $v$ of $u$. The players begin
with initial capitals that amount to $i$ and $j$ units respectively, and a
player wins if either she is the first to amass a capital worth $\kappa$ units,
where $\kappa$ is a pre-specified positive integer, or her opponent is the
first to have her capital dwindle to $0$, or she is able to move the token to a
leaf vertex, from where her opponent cannot move it any farther. This paper is
concerned with studying the probabilities of the three possible outcomes (i.e.
win for the first player, loss for the first player, and draw for both players)
of this game, as well as finding conditions under which the expected duration
of this game is finite. The theory we develop in this paper for the analysis of
this game is further supported by observations obtained via computer
simulations, and these observations provide a deeper insight into how the
above-mentioned probabilities behave as the underlying parameters and / or
offspring distributions are allowed to vary. We conclude the paper with a
couple of conjectures, one of which suggests the occurrence of a phase
transition phenomenon whereby the probability of draw in this game goes from
being $0$ to being strictly positive as the parameter-pair $(p_{0},p_{1})$ is
varied suitably while keeping the underlying offspring distribution of $T$
fixed.


  We consider 4D quantum-dilaton gravity with the most general coupling in a
homogeneous and isotropic universe, especially an inflationary one, which is
essentially characterized by an exponentially expanding scale factor with time.
We show that on the inflationary background this theory can be miraculously
renormalized, at least at the one-loop level, which must be an effective theory
during the inflation of the un-constructed complete quantum theory of gravity.


  Block diagonalization (BD) based precoding techniques are well-known linear
transmit strategies for multiuser MIMO (MU-MIMO) systems. By employing BD-type
precoding algorithms at the transmit side, the MU-MIMO broadcast channel is
decomposed into multiple independent parallel single user MIMO (SU-MIMO)
channels and achieves the maximum diversity order at high data rates. The main
computational complexity of BD-type precoding algorithms comes from two
singular value decomposition (SVD) operations, which depend on the number of
users and the dimensions of each user's channel matrix. In this work,
low-complexity precoding algorithms are proposed to reduce the computational
complexity and improve the performance of BD-type precoding algorithms. We
devise a strategy based on a common channel inversion technique, QR
decompositions, and lattice reductions to decouple the MU-MIMO channel into
equivalent SU-MIMO channels. Analytical and simulation results show that the
proposed precoding algorithms can achieve a comparable sum-rate performance as
BD-type precoding algorithms, substantial bit error rate (BER) performance
gains, and a simplified receiver structure, while requiring a much lower
complexity.


  We performed a study of the perturbative instabilities in
Einstein-Maxwell-Chern-Simons theory with a gravitational Chern-Simons term,
which is dual to a strongly coupled field theory with both chiral and mixed
gauge-gravitational anomaly. With an analysis of the fluctuations in the near
horizon regime at zero temperature, we found that there might be two possible
sources of instabilities. The first one corresponds to a real mass-squared
which is below the BF bound of AdS$_2$, and it leads to the bell-curve phase
diagram at finite temperature. The effect of mixed gauge-gravitational anomaly
is emphasised. Another source of instability is independent of gauge
Chern-Simons coupling and exists for any finite gravitational Chern-Simons
coupling. There is a singular momentum close to which unstable mode appears.
The possible implications of this singular momentum are discussed. Our analysis
suggests that the theory with a gravitational Chern-Simons term around
Reissner-Nordstr\"om black hole is unreliable unless the gravitational
Chern-Simons coupling is treated as a small perturbative parameter.


  Through the theoretical study of electron spin lifetime in the 2DEG of doped
Si, we highlight a dominant spin relaxation mechanism induced by the impurity
central-cell potential near an interface via intervalley electron scattering.
At low temperatures and with modest doping, this Yafet spin flip mechanism can
become much more important than the Dyakonov-Perel spin relaxation indcued by
the structural Rashba spin-orbit coupling field. As the leading-order
impurity-induced spin flip happens only between two non-opposite valleys in Si,
two-dimensional electron gas (2DEG) systems in Si MOSFETs or SiGe
heterostructures are a natural platform to test and utilize this spin
relaxation mechanism due to the valley splitting near the interface and its
tunability by electrical gating or applied stress. Our proposed new spin
relaxation mechanism may explain a part of the spin relaxation contribution to
Si-based 2DEG systems.


  We propose a new architecture for adapting a sentence-level
sequence-to-sequence transformer by incorporating multiple pretrained document
context signals and assess the impact on translation performance of (1)
different pretraining approaches for generating these signals, (2) the quantity
of parallel data for which document context is available, and (3) conditioning
on source, target, or source and target contexts. Experiments on the NIST
Chinese-English, and IWSLT and WMT English-German tasks support four general
conclusions: that using pretrained context representations markedly improves
sample efficiency, that adequate parallel data resources are crucial for
learning to use document context, that jointly conditioning on multiple context
representations outperforms any single representation, and that source context
is more valuable for translation performance than target side context. Our best
multi-context model consistently outperforms the best existing context-aware
transformers.


  We describe the evolution of hot interstellar gas in a family of low
luminosity elliptical galaxies all having $M_B = -20$ but with different
degrees of flattening (E0, E2, and E6) caused by rotation. The interstellar gas
is furnished by stellar mass loss. The soft X-ray luminosity Lx of the hot
interstellar gas after 15 Gyrs decreases dramatically with galactic rotation.
The hot gas cools onto a large disk having a size that depends inversely on the
assumed supernova rate. Although Lx of the hot, rotating interstellar gas may
be difficult to observe, the photoionized part of the cooled gaseous disk gas
can be observed in optical line emission. The mass of HII gas ($\sim 10^8$
$M_{\odot}$) may be much greater than previously realized since large regions
of rotationally supported, low density HII are optically faint. We interpret
the stellar disks that are common in low luminosity ellipticals as stars that
have formed in the non-ionized part of the cold disk gas. The total mass and
distribution of cold disk gas available for star formation are similar to those
of stellar disks observed. The high stellar H$\beta$ photometric index observed
in disky ellipticals can be understood by combining the light of young disk
stellar populations with that of the old bulge population.


  We classify all primitive embeddings of the lattice of numerical equivalence
classes of divisors of an Enriques surface with the intersection form
multiplied by 2 into an even unimodular hyperbolic lattice of rank 26. These
embeddings have a property that facilitates the computation of the automorphism
group of an Enriques surface by Borcherds' method.


  Decay constants of $D$ and $B$ mesons are estimated within the framework of a
heavy-quark approach using measured isospin mass splittings in the $D$, $D^*$,
and $B$ states to isolate the electromagnetic hyperfine interaction between
quarks. The values $f_D = (262 \pm 29)$ MeV and $f_B = (160 \pm 17)$ MeV are
obtained. Only experimental errors are given; possible theoretical ambiguities,
and suggestions for reducing them, are noted.


  In this paper, we determine the type numbers of the pseudo-hyperbolic Gauss
maps of all oriented Lorentzian surfaces of constant mean and Gaussian
curvatures and non-diagonalizable shape operator in the $3$-dimensional anti-de
Sitter space. Also, we investigate the behavior of type numbers of the
pseudo-hyperbolic Gauss map along the parallel family of such oriented
Lorentzian surfaces in the $3$-dimensional anti-de Sitter space. Furthermore,
we investigate the type number of the pseudo-hyperbolic Gauss map of one of
Lorentzian hypersurfaces of B-scroll type in a general dimensional anti-de
Sitter space.


  Measurements on 'free-standing' single crystal barium titanate capacitors
with thicknesses down to 75nm show a dielectric response typical of large
single crystals rather than conventional thin films. There is a notable absence
of any broadening or temperature shift of the dielectric peak or loss tangent.
Peak dielectric constants of ca. 25,000 are obtained, and Curie-Weiss analysis
demonstrates 1st order transformation behavior. This is in surprising contrast
to results on conventionally deposited thin film heterostructures, which show
large dielectric peak broadening and temperature shifts [e.g. C. B. Parker,
J-P. Maria and A. I. Kingon, Appl. Phys. Lett., 81, 340 (2002)], as well as an
apparent change in the nature of the paraelectric-ferroelectric transition from
1st to 2nd order. Our data are compatible with the recent model by Bratkovsky
and Levanyuk, which attributes dielectric peak broadening to gradient terms
that will exist in any thin film capacitor heterostructure, either through
defect profiles introduced during growth, or through subtle asymmetry between
top and bottom electrodes. The observed recovery of 1st order transformation
behavior is consistent with the absence of significant substrate clamping in
our experiment, as modeled by Pertsev et al. Phys. Rev. Lett., 80, 1988 (1998),
and illustrates that the 2nd order behaviour seen in conventionally deposited
thin films cannot be attributed to the effects of reduced dimensionality in the
system, nor to the influence of an intrinsic universal interfacial capacitance
associated with the electrode-ferroelectric interface.


  Observations of Markarian 231 at 1.1 microns taken with NICMOS on the Hubble
Space Telescope are described. The brightness of the object in the near
infrared and the inherent short-term stability of the NICMOS optical and
instrumental system enables application of special observational and analysis
techniques that effectively increase high spatial resolution. By these means,
we set an upper limit on the size of the core of the AGN nucleus at 8 mas
corresponding to a radial projected distance from the center of MArkarian 231
of ~ 3pc.


  Complex query answering (CQA) is an essential task for multi-hop and logical
reasoning on knowledge graphs (KGs). Currently, most approaches are limited to
queries among binary relational facts and pay less attention to n-ary facts
(n>=2) containing more than two entities, which are more prevalent in the real
world. Moreover, previous CQA methods can only make predictions for a few given
types of queries and cannot be flexibly extended to more complex logical
queries, which significantly limits their applications. To overcome these
challenges, in this work, we propose a novel N-ary Query Embedding (NQE) model
for CQA over hyper-relational knowledge graphs (HKGs), which include massive
n-ary facts. The NQE utilizes a dual-heterogeneous Transformer encoder and
fuzzy logic theory to satisfy all n-ary FOL queries, including existential
quantifiers, conjunction, disjunction, and negation. We also propose a parallel
processing algorithm that can train or predict arbitrary n-ary FOL queries in a
single batch, regardless of the kind of each query, with good flexibility and
extensibility. In addition, we generate a new CQA dataset WD50K-NFOL, including
diverse n-ary FOL queries over WD50K. Experimental results on WD50K-NFOL and
other standard CQA datasets show that NQE is the state-of-the-art CQA method
over HKGs with good generalization capability. Our code and dataset are
publicly available.


  Moral values play a fundamental role in how we evaluate information, make
decisions, and form judgements around important social issues. Controversial
topics, including vaccination, abortion, racism, and sexual orientation, often
elicit opinions and attitudes that are not solely based on evidence but rather
reflect moral worldviews. Recent advances in Natural Language Processing (NLP)
show that moral values can be gauged in human-generated textual content.
Building on the Moral Foundations Theory (MFT), this paper introduces
MoralBERT, a range of language representation models fine-tuned to capture
moral sentiment in social discourse. We describe a framework for both
aggregated and domain-adversarial training on multiple heterogeneous MFT
human-annotated datasets sourced from Twitter (now X), Reddit, and Facebook
that broaden textual content diversity in terms of social media audience
interests, content presentation and style, and spreading patterns. We show that
the proposed framework achieves an average F1 score that is between 11% and 32%
higher than lexicon-based approaches, Word2Vec embeddings, and zero-shot
classification with large language models such as GPT-4 for in-domain
inference. Domain-adversarial training yields better out-of domain predictions
than aggregate training while achieving comparable performance to zero-shot
learning. Our approach contributes to annotation-free and effective morality
learning, and provides useful insights towards a more comprehensive
understanding of moral narratives in controversial social debates using NLP.


  The fast marching method is well-known for its worst-case optimal
computational complexity in solving the Eikonal equation, and has been employed
in numerous scientific and engineering fields. However, it has barely benefited
from fast-advancing multi-core and many-core architectures, due to the
challenges presented by its apparent sequential nature. In this paper, we
present a straightforward block-based approach for a highly scalable
parallelization of the fast marching method on shard-memory computers. Central
to our new algorithm is a simplified restarted narrow band strategy, with which
the global bound for terminating the front marching is replaced by an
incremental one, increasing by a given stride in each restart. It greatly
reduces load imbalance among blocks through a synchronized exchanging step
after the marching step. Furthermore, simple activation mechanisms are
introduced to skip blocks not involved in either step. Thus the new algorithm
mainly consists of two loops, each for performing one step on a group of
blocks. Notably, it does not contain any data race conditions at all, ideal for
a direct loop level parallelization using multiple threads. A systematic
performance study is carried out for several point source problems with various
speed functions on four grids with up to $1024^3$ points using two different
computers. Substantial parallel speedups, e.g., up to 3--5 times the number of
cores on a 16-core/32-thread computer and up to two orders of magnitude on a
64-core/256-thread computer, are demonstrated with all cases. As an extra
bonus, our new algorithm also gives improved sequential performance in most
scenarios. Detailed pseudo-codes are provided to illustrate the modification
procedure from the single-block sequential algorithm to the multi-block one in
a step-by-step manner.


  In this paper, new class of bi-univalent functions are introduced. Upper
bound of the second Hankel determinant $|H_2(2)|$ of subclass of bi-univalant
functions class $\Sigma$, which defined by subordination, investigated.
Furthermore, some results concluded as a special case of our main results and
corrected some previous researchers results which investigated by
miscalculation.


  The jets of compact accreting objects are composed of electrons and a mixture
of positrons and ions. These outflows impinge on the interstellar or
intergalactic medium and both plasmas interact via collisionless processes.
Filamentation (beam-Weibel) instabilities give rise to the growth of strong
electromagnetic fields. These fields thermalize the interpenetrating plasmas.
Hitherto, the effects imposed by a spatial non-uniformity on filamentation
instabilities have remained unexplored. We examine the interaction between
spatially uniform background electrons and a minuscule cloud of electrons and
positrons. A square micro-cloud of equally dense electrons and positrons
impinges in our particle-in-cell (PIC) simulation on a spatially uniform plasma
at rest. The mean speed of the micro-cloud corresponds to a relativistic factor
of 15, which is relevant for laboratory experiments and for relativistic
astrophysical outflows. The spatial distributions of the leptons and of the
electromagnetic fields are examined at several times. A filamentation
instability develops between the magnetic field carried by the micro-cloud and
the background electrons. The electromagnetic fields, which grow from noise
levels, redistribute the electrons and positrons within the cloud, which boosts
the peak magnetic field amplitude. The current density and the moduli of the
electromagnetic fields grow aperiodically in time and steadily along the
direction that is anti-parallel to the cloud's velocity vector. The micro-cloud
remains conjoined during the simulation. The instability induces an
electrostatic wakefield in the background plasma.


  In spinel-type nickelate NiRh$_2$O$_4$, magnetic ordering is observed upon
the sample synthesized via kinetically controlled low-temperature solid-state
metathesis, as opposed to previously-reported samples obtained through
conventional solid-state reaction. Our findings are based on a combination of
bulk susceptibility and specific heat measurements that disclose a N$\'e$el
transition temperature of $T_N$ = 45 K in this material, which might feature
spin-orbit entanglement in the tetragonally-coordinated $d^8$ Mott insulators.
The emergence of magnetic ordering upon alteration of the synthesis route
indicates that the suppression of magnetic ordering in the previous sample was
rooted in the cation-mixing assisted by the entropy gain that results from
high-temperature reactions. Furthermore, the $J_{\rm eff}$ = 0 physics, instead
of solely the spin-only $S = 1$, describes the observed enhancement of
effective magnetic moment well. Overseeing all observations and speculations,
we propose that the possible mechanism responsible for the emergent magnetic
orderings in NiRh$_2$O$_4$ is the condensation of $J_{\rm eff}$ = 0 exciton,
driven by the interplay of the tetragonal crystal field and superexchange
interactions.


  For transportation hubs, leveraging pedestrian flows for commercial
activities presents an effective strategy for funding maintenance and
infrastructure improvements. However, this introduces new challenges, as
consumer behaviors can disrupt pedestrian flow and efficiency. To optimize both
retail potential and pedestrian efficiency, careful strategic planning in store
layout and facility dimensions was done by expert judgement due to the
complexity in pedestrian dynamics in the retail areas of transportation hubs.
This paper introduces an attention-based movement model to simulate these
dynamics. By simulating retail potential of an area through the duration of
visual attention it receives, and pedestrian efficiency via speed loss in
pedestrian walking behaviors, the study further explores how design features
can influence the retail potential and pedestrian efficiency in a
bi-directional corridor inside a transportation hub. Project webpage:
https://danruili.github.io/AttentionMove


  This Letter describes the current most precise measurement of the $W$ boson
pair production cross section and most sensitive test of anomalous $WW\gamma$
and $WWZ$ couplings in $p \bar p$ collisions at a center-of-mass energy of 1.96
TeV. The $WW$ candidates are reconstructed from decays containing two charged
leptons and two neutrinos, where the charged leptons are either electrons or
muons. Using data collected by the CDF II detector from 3.6 fb$^{-1}$ of
integrated luminosity, a total of 654 candidate events are observed with an
expected background contribution of $320 \pm 47$ events. The measured total
cross section is $\sigma (p \bar p \to W^+ W^- + X) = 12.1 \pm 0.9
\textrm{(stat)} ^{+1.6}_{-1.4} \textrm{(syst)}$ pb, which is in good agreement
with the standard model prediction. The same data sample is used to place
constraints on anomalous $WW\gamma$ and $WWZ$ couplings.


  We propose a description of G-fluxes that induce chirality in 4-dimensional
F-theory GUT spectra that is intrinsic to F-theory and does not rely on
Heterotic/F-theory duality. Using this, we describe how to globally extend
fluxes that have been constructed in a semi-local setting and obtain an
F-theoretic formula for computing the chiral spectrum that they induce.
Chirality computations agree with those from the semi-local Higgs bundle
analysis for matter fields that are charged under the GUT-group, and hence with
the standard Heterotic formulae where applicable. Finally, the relation of
G-fluxes to SU(5)_{perp} bundles on the F-theory 4-fold is discussed and used
to motivate a quantization rule that is consistent both with the Higgs bundle
one as well as the Heterotic one when a Heterotic dual exists.


  The recently discovered binary LB-1 has been reported to contain a
$\sim$\,$70\,M_{\odot}$ black hole (BH). The evidence for the unprecedentedly
high mass of the unseen companion comes from reported radial velocity (RV)
variability of the H$\alpha$ emission line, which has been proposed to
originate from an accretion disk around a BH. We show that there is in fact no
evidence for RV variability of the H$\alpha$ emission line, and that its
apparent shifts instead originate from shifts in the luminous star's H$\alpha$
absorption line. If not accounted for, such shifts will cause a stationary
emission line to appear to shift in anti-phase with the luminous star. We show
that once the template spectrum of a B star is subtracted from the observed
Keck/HIRES spectra of LB-1, evidence for RV variability vanishes. Indeed, the
data rule out periodic variability of the line with velocity semi-amplitude
$K_{\rm H\alpha} > 1.3\,\rm km\,s^{-1}$. This strongly suggests that the
observed H$\alpha$ emission does not originate primarily from an accretion disk
around a BH, and thus that the mass ratio cannot be constrained from the
relative velocity amplitudes of the emission and absorption lines. The nature
of the unseen companion remains uncertain, but a "normal" stellar-mass BH with
mass $5\lesssim M/M_{\odot}\lesssim 20 $ seems most plausible. The H$\alpha$
emission likely originates primarily from circumbinary material, not from
either component of the binary.


  In this paper we study the suitability of a new generation of CAPTCHA methods
based on smartphone interactions. The heterogeneous flow of data generated
during the interaction with the smartphones can be used to model human behavior
when interacting with the technology and improve bot detection algorithms. For
this, we propose BeCAPTCHA, a CAPTCHA method based on the analysis of the
touchscreen information obtained during a single drag and drop task in
combination with the accelerometer data. The goal of BeCAPTCHA is to determine
whether the drag and drop task was realized by a human or a bot. We evaluate
the method by generating fake samples synthesized with Generative Adversarial
Neural Networks and handcrafted methods. Our results suggest the potential of
mobile sensors to characterize the human behavior and develop a new generation
of CAPTCHAs. The experiments are evaluated with HuMIdb (Human Mobile
Interaction database), a novel multimodal mobile database that comprises 14
mobile sensors acquired from 600 users. HuMIdb is freely available to the
research community.


  Let $H^{\infty}(\Omega,X)$ be the space of bounded analytic functions
$f(z)=\sum_{n=0}^{\infty} x_{n}z^{n}$ from a proper simply connected domain
$\Omega$ containing the unit disk $\mathbb{D}:=\{z\in \mathbb{C}:|z|<1\}$ into
a complex Banach space $X$ with $\norm{f}_{H^{\infty}(\Omega,X)} \leq 1$. Let
$\phi=\{\phi_{n}(r)\}_{n=0}^{\infty}$ with $\phi_{0}(r)\leq 1$ such that
$\sum_{n=0}^{\infty} \phi_{n}(r)$ converges locally uniformly with respect to
$r \in [0,1)$. For $1\leq p,q<\infty$, we denote
  \begin{equation*}
  R_{p,q,\phi}(f,\Omega,X)= \sup \left\{r \geq 0: \norm{x_{0}}^p \phi_{0}(r) +
\left(\sum_{n=1}^{\infty} \norm{x_{n}}\phi_{n}(r)\right)^q \leq
\phi_{0}(r)\right\}
  \end{equation*}
  and define the Bohr radius associated with $\phi$ by
$$R_{p,q,\phi}(\Omega,X)=\inf \left\{R_{p,q,\phi}(f,\Omega,X):
\norm{f}_{H^{\infty}(\Omega,X)} \leq 1\right\}.$$
  In this article, we extensively study the Bohr radius
$R_{p,q,\phi}(\Omega,X)$, when $X$ is an arbitrary Banach space and $X$ is
certain Hilbert space. Furthermore, we establish the Bohr inequality for the
operator-valued Ces\'{a}ro operator and Bernardi operator.


  The Allais and Ellsberg paradoxes show that the expected utility hypothesis
and Savage's Sure-Thing Principle are violated in real life decisions. The
popular explanation in terms of 'ambiguity aversion' is not completely
accepted. On the other hand, we have recently introduced a notion of
'contextual risk' to mathematically capture what is known as 'ambiguity' in the
economics literature. Situations in which contextual risk occurs cannot be
modeled by Kolmogorovian classical probabilistic structures, but a
non-Kolmogorovian framework with a quantum-like structure is needed. We prove
in this paper that the contextual risk approach can be applied to the Ellsberg
paradox, and elaborate a 'sphere model' within our 'hidden measurement
formalism' which reveals that it is the overall conceptual landscape that is
responsible of the disagreement between actual human decisions and the
predictions of expected utility theory, which generates the paradox. This
result points to the presence of a 'quantum conceptual layer' in human thought
which is superposed to the usually assumed 'classical logical layer'.


  We point out that there is a generalization to higher dimensions $d=2h>2$ of
the two-dimensional Dotsenko-Fateev formula \DF\ for particular Coulomb gas
conformal invariant integrals. These expressions represent structure constants
of 3-point functions of vertex operators related to a higher dimensional
generalization of the Liouville theory. The Coulomb gas formulae admit two
different analytic continuations generalizing the DOZZ formula, i.e., the
theory is not selfdual for $d>2$.


  A key challenge for reinforcement learning (RL) consists of learning in
environments with sparse extrinsic rewards. In contrast to current RL methods,
humans are able to learn new skills with little or no reward by using various
forms of intrinsic motivation. We propose AMIGo, a novel agent incorporating --
as form of meta-learning -- a goal-generating teacher that proposes
Adversarially Motivated Intrinsic Goals to train a goal-conditioned "student"
policy in the absence of (or alongside) environment reward. Specifically,
through a simple but effective "constructively adversarial" objective, the
teacher learns to propose increasingly challenging -- yet achievable -- goals
that allow the student to learn general skills for acting in a new environment,
independent of the task to be solved. We show that our method generates a
natural curriculum of self-proposed goals which ultimately allows the agent to
solve challenging procedurally-generated tasks where other forms of intrinsic
motivation and state-of-the-art RL methods fail.


  We present results of near infrared imaging of the disk-galaxy-merger NGC
6240 using adaptive optics on the Keck II Telescope and reprocessed archival
data from NICMOS on the Hubble Space Telescope. Both the North and South nuclei
of NGC 6240 are clearly elongated, with considerable sub-structure within each
nucleus. In K' band there are at least two point-sources within the North
nucleus; we tentatively identify the south-western point-source within the
North nucleus as the position of one of the two AGNs. Within the South nucleus,
the northern sub-nucleus is more highly reddened. Based upon the nuclear
separation measured at 5 GHz, we suggest that the AGN in the South nucleus is
still enshrouded in dust at K' band, and is located slightly to the north of
the brightest point in K' band. Within the South nucleus there is strong H2 1-0
S(1) line emission from the northern sub-nucleus, contrary to the conclusions
of previous seeing-limited observations. Narrowband H2 emission-line images
show that a streamer or ribbon of excited molecular hydrogen connects the North
and South nuclei. We suggest that this linear feature corresponds to a bridge
of gas connecting the two nuclei, as seen in computer simulations of mergers.
Many point-like regions are seen around the two nuclei. These are most
prominent at 1.1 microns with NICMOS, and in K'-band with Keck adaptive optics.
We suggest that these point-sources represent young star clusters formed in the
course of the merger.


  A considerable effort has recently gone into the study of Gaussianity of
cosmic microwave background (CMB) data. Among such attempts, there is one with
two non-Gaussianity indicators, proposed by the authors, and used in a search
for significant deviation from Gaussianity in the WMAP internal linear
combination (ILC) and in the single frequency WMAP maps with the KQ75 mask.
Here we extend and complement these results by performing a similar analysis
for the de Oliveira-Costa and Tegmark (OT) WMAP three-year $KQ75$ masked map,
in which the foreground is reduced through a different statistical cleaning
procedure.


  This paper proposes a canonical-correlation-based filter method for feature
selection. The sum of squared canonical correlation coefficients is adopted as
the feature ranking criterion. The proposed method boosts the computational
speed of the ranking criterion in greedy search. The supporting theorems
developed for the feature selection method are fundamental to the understanding
of the canonical correlation analysis. In empirical studies, a synthetic
dataset is used to demonstrate the speed advantage of the proposed method, and
eight real datasets are applied to show the effectiveness of the proposed
feature ranking criterion in both classification and regression. The results
show that the proposed method is considerably faster than the definition-based
method, and the proposed ranking criterion is competitive compared with the
seven mutual-information-based criteria.


  We explore the usage of the Levenberg-Marquardt (LM) algorithm for regression
(non-linear least squares) and classification (generalized Gauss-Newton
methods) tasks in neural networks. We compare the performance of the LM method
with other popular first-order algorithms such as SGD and Adam, as well as
other second-order algorithms such as L-BFGS , Hessian-Free and KFAC. We
further speed up the LM method by using adaptive momentum, learning rate line
search, and uphill step acceptance.


  This is my PhD thesis on four-dimensional simplicial quantum gravity using
the dynamical triangulation model. Most of the results we have published in
separate papers are collected here for your convenience. Some new results have
been added as well. Besides these results this thesis also contains an
introduction to simplicial quantum gravity and a detailed description of my
dynamical triangulation program for arbitrary dimension. Some small formal
parts are in Dutch.


  Hybrid optimization algorithms have gained popularity as it has become
apparent there cannot be a universal optimization strategy which is globally
more beneficial than any other. Despite their popularity, hybridization
frameworks require more detailed categorization regarding: the nature of the
problem domain, the constituent algorithms, the coupling schema and the
intended area of application. This report proposes a hybrid algorithm for
solving small to large-scale continuous global optimization problems. It
comprises evolutionary computation (EC) algorithms and a sequential quadratic
programming (SQP) algorithm; combined in a collaborative portfolio. The SQP is
a gradient based local search method. To optimize the individual contributions
of the EC and SQP algorithms for the overall success of the proposed hybrid
system, improvements were made in key features of these algorithms. The report
proposes enhancements in: i) the evolutionary algorithm, ii) a new convergence
detection mechanism was proposed; and iii) in the methods for evaluating the
search directions and step sizes for the SQP local search algorithm. The
proposed hybrid design aim was to ensure that the two algorithms complement
each other by exploring and exploiting the problem search space. Preliminary
results justify that an adept hybridization of evolutionary algorithms with a
suitable local search method, could yield a robust and efficient means of
solving wide range of global optimization problems. Finally, a discussion of
the outcomes of the initial investigation and a review of the associated
challenges and inherent limitations of the proposed method is presented to
complete the investigation. The report highlights extensive research,
particularly, some potential case studies and application areas.


  We present results from two Herschel observing programs using the
Photodetector Array Camera and Spectrometer. During three separate campaigns,
we obtained Herschel data for 24 stars at 70, 100, and 160 microns. We chose
stars that were already known or suspected to have circumstellar dust based on
excess infrared emission previously measured with IRAS or Spitzer, and used
Herschel to examine long-wavelength properties of the dust. Fifteen stars were
found to be uncontaminated by background sources, and possess infrared emission
most likely due to a circumstellar debris disk. We analyzed the properties of
these debris disks to better understand the physical mechanisms responsible for
dust production and removal. Seven targets were spatially resolved in the
Herschel images. Based on fits to their spectral energy distributions, nine
disks appear to have two temperature components. Of these nine, in three cases,
the warmer dust component is likely the result of a transient process rather
than a steady state collisional cascade. The dust belts at four stars are
likely stirred by an unseen planet, and merit further investigation.


  Large-scale cosmological simulations are an indispensable tool for modern
cosmology. To enable model-space exploration, fast and accurate predictions are
critical. In this paper, we show that the performance of such simulations can
be further improved with time-stepping schemes that use input from cosmological
perturbation theory. Specifically, we introduce a class of time-stepping
schemes derived by matching the particle trajectories in a single
leapfrog/Verlet drift-kick-drift step to those predicted by Lagrangian
perturbation theory (LPT). As a corollary, these schemes exactly yield the
analytic Zel'dovich solution in 1D in the pre-shell-crossing regime (i.e.
before particle trajectories cross). One representative of this class is the
popular FastPM scheme by Feng et al. 2016, which we take as our baseline. We
then construct more powerful LPT-inspired integrators and show that they
outperform FastPM and standard integrators in fast simulations in two and three
dimensions with $\mathcal{O}(1 - 100)$ timesteps, requiring less steps to
accurately reproduce the power spectrum and bispectrum of the density field.
Furthermore, we demonstrate analytically and numerically that, for any
integrator, convergence is limited in the post-shell-crossing regime (to order
3/2 for planar wave collapse), owing to the lacking regularity of the
acceleration field, which makes the use of high-order integrators in this
regime futile. Also, we study the impact of the timestep spacing and of a
decaying mode present in the initial conditions. Importantly, we find that
symplecticity of the integrator plays a minor role for fast approximate
simulations with a small number of timesteps.


  We consider the estimation of a dynamic distribution regression panel data
model with heterogeneous coefficients across units. The objects of primary
interest are specific functionals of these coefficients. These include
predicted actual and stationary distributions of the outcome variable and
quantile treatment effects. Coefficients and their functionals are estimated
via fixed effect methods. We investigate how these functionals vary in response
to changes in initial conditions or covariate values. We also identify a
uniformity issue related to the robustness of inference to the unknown degree
of heterogeneity, and propose a cross-sectional bootstrap method for uniformly
valid inference on function-valued objects. Employing PSID annual labor income
data we illustrate some important empirical issues we can address. We first
quantify the impact of a negative labor income shock on the distribution of
future labor income. We also examine the impact on the distribution of labor
income from increasing the education level of a chosen group of workers.
Finally, we demonstrate the existence of heterogeneity in income mobility, and
how this leads to substantial variation in individuals' incidences to be
trapped in poverty. We also provide simulation evidence confirming that our
procedures work well.


  We show there is an upper bound on the diameter of a closed, hyperbolic
3-manifold in terms of the length of any presentation of its fundamental group.


  High Dynamic Range (HDR) images are generated using multiple exposures of a
scene. When a hand-held camera is used to capture a static scene, these images
need to be aligned by globally shifting each image in both dimensions. For a
fast and robust alignment, the shift amount is commonly calculated using Median
Threshold Bitmaps (MTB) and creating an image pyramid. In this study, we
optimize these computations using a parallel processing approach utilizing GPU.
Experimental evaluation shows that the proposed implementation achieves a
speed-up of up to 6.24 times over the baseline multi-threaded CPU
implementation on the alignment of one image pair. The source code is available
at https://github.com/kadircenk/WardMTBCuda


  Let $F$ be a finitely generated free group, and let $H\le F$ be a finitely
generated subgroup. An equation for an element $g\in F$ with coefficients in
$H$ is an element $w(x)\in H*\langle x \rangle$ such that $w(g)=1$ in $F$; the
degree of the equation is the number of occurrences of $x$ and $x^{-1}$ in the
cyclic reduction of $w(x)$. Given an element $g\in F$, we consider the ideal
$\mathfrak{I}_g\subseteq H*\langle x \rangle$ of equations for $g$ with
coefficients in $H$; we study the structure of $\mathfrak{I}_g$ using
context-free languages.
  We describe a new algorithm that determines whether $\mathfrak{I}_g$ is
trivial or not; the algorithm runs in polynomial time. We also describe a
polynomial-time algorithm that, given $d\in\mathbb{N}$, decides whether or not
the subset $\mathfrak{I}_{g,d}\subseteq\mathfrak{I}_g$ of all degree-$d$
equations is empty. We provide a polynomial-time algorithm that computes the
minimum degree $d_{\min}$ of a non-trivial equation in $\mathfrak{I}_g$. We
provide a sharp upper bound on $d_{\min}$. Finally, we study the growth of the
number of (cyclically reduced) equations in $\mathfrak{I}_g$ and in
$\mathfrak{I}_{g,d}$ as a function of their length. We prove that this growth
is either polynomial or exponential, and we provide a polynomial-time algorithm
that computes the type of growth (including the degree of the growth if it's
polynomial).


  R-matrix with time-dependence theory is applied to electron-impact ionisation
processes for He in the S-wave model. Cross sections for electron-impact
excitation, ionisation and ionisation with excitation for impact energies
between 25 and 225 eV are in excellent agreement with benchmark cross sections.
Ultra-fast dynamics induced by a scattering event is observed through
time-dependent signatures associated with autoionisation from doubly excited
states. Further insight into dynamics can be obtained through examination of
the spin components of the time-dependent wavefunction.


  Molecular dynamics simulations of biomolecules have been widely adopted in
biomedical studies. As classical point-charge models continue to be used in
routine biomolecular applications, there have been growing demands on
developing polarizable force fields for handling more complicated biomolecular
processes. Here we focus on a recently proposed polarizable Gaussian Multipole
(pGM) model for biomolecular simulations. A key benefit of pGM is its screening
of all short-range electrostatic interactions in a physically consistent
manner, which is critical for stable charge-fitting and is needed to reproduce
molecular anisotropy. Another advantage of pGM is that each atom's multipoles
are represented by a single Gaussian function or its derivatives, allowing for
more efficient electrostatics than other Gaussian-based models. In this study
we present an efficient formulation for the pGM model defined with respect to a
local frame formed with a set of covalent basis vectors. The covalent basis
vectors are chosen to be along each atom's covalent bonding directions. The new
local frame allows molecular flexibility during molecular simulations and
facilitates an efficient formulation of analytical electrostatic forces without
explicit torque computation. Subsequent numerical tests show that analytical
atomic forces agree excellently with numerical finite-difference forces for the
tested system. Finally, the new pGM electrostatics algorithm is interfaced with
the PME implementation in Amber for molecular simulations under the periodic
boundary conditions. To validate the overall pGM/PME electrostatics, we
conducted an NVE simulation for a small water box of 512 water molecules. Our
results show that, to achieve energy conservation in the polarizable model, it
is important to ensure enough accuracy on both PME and induction iteration.


  We introduce a novel framework for adversarial training where the target
distribution is annealed between the uniform distribution and the data
distribution. We posited a conjecture that learning under continuous annealing
in the nonparametric regime is stable irrespective of the divergence measures
in the objective function and proposed an algorithm, dubbed {\ss}-GAN, in
corollary. In this framework, the fact that the initial support of the
generative network is the whole ambient space combined with annealing are key
to balancing the minimax game. In our experiments on synthetic data, MNIST, and
CelebA, {\ss}-GAN with a fixed annealing schedule was stable and did not suffer
from mode collapse.


  Let $\Gamma$ be the random bipartite graph, a countable graph with two
infinite sides, edges randomly distributed between the sides, but no edges
within a side. In this paper, we investigate the reducts of $\Gamma$ that
preserve sides. We classify the closed permutation subgroups containing the
group $Aut(\Gamma)^*$, where $Aut(\Gamma)^*$ is the group of all isomorphisms
and anti-isomorphisms of $\Gamma$ preserving the two sides. Our results rely on
a combinatorial theorem of Ne\v{s}et\v{r}il-R\"{o}dl and a strong finite
submodel property for $\Gamma$.


  Byte-addressable non-volatile memory (NVRAM) supports persistent storage with
low latency and high bandwidth. Complex data structures in it ought to be
updated transactionally, so that they remain recoverable at all times.
Traditional database technologies such as keeping a separate log, a journal, or
shadow data work on a coarse-grained level, where the whole transaction is made
visible using a final atomic update operation. These methods typically need
significant additional space overhead and induce non-trivial overhead for log
pruning, state maintenance, and resource (de-)allocation. Thus, they are not
necessarily the best choice for NVRAM, which supports fine-grained,
byte-addressable access.
  We present a generic transaction mechanism to update dynamic complex data
structures `in-place' with a constant memory overhead. It is independent of the
size of the data structure. We demonstrate and evaluate our approach on
Red-Black Trees and AVL Trees with a redo log of constant size (4 resp. 2 cache
lines). The redo log guarantees that each accepted (started) transaction is
executed eventually despite arbitrary many system crashes and recoveries in the
meantime. We update complex data structures in local and remote NVRAM providing
exactly once semantics and durable linearizability for multi-reader
single-writer access. To persist data, we use the available processor
instructions for NVRAM in the local case and remote direct memory access (RDMA)
combined with a software agent in the remote case.


  We study Kontsevich's deformation quantization for the dual of a
finite-dimensional real Lie algebra (or superalgebra) g. In this case the
Kontsevich star-product defines a new convolution on S(g), regarded as the
space of distributions supported at 0 in g. For p in S(g), we show that the
convolution operator f->f*p is a differential operator with analytic germ. We
use this fact to prove a conjecture of Kashiwara and Vergne on invariant
distributions on a Lie group. This yields a new proof of Duflo's result on
local solvability of bi-invariant differential operators on a Lie group.
Moreover, this new proof extends to Lie supergroups.


  Federated Averaging (FedAvg) remains the most popular algorithm for Federated
Learning (FL) optimization due to its simple implementation, stateless nature,
and privacy guarantees combined with secure aggregation. Recent work has sought
to generalize the vanilla averaging in FedAvg to a generalized gradient descent
step by treating client updates as pseudo-gradients and using a server step
size. While the use of a server step size has been shown to provide performance
improvement theoretically, the practical benefit of the server step size has
not been seen in most existing works. In this work, we present FedExP, a method
to adaptively determine the server step size in FL based on dynamically varying
pseudo-gradients throughout the FL process. We begin by considering the
overparameterized convex regime, where we reveal an interesting similarity
between FedAvg and the Projection Onto Convex Sets (POCS) algorithm. We then
show how FedExP can be motivated as a novel extension to the extrapolation
mechanism that is used to speed up POCS. Our theoretical analysis later also
discusses the implications of FedExP in underparameterized and non-convex
settings. Experimental results show that FedExP consistently converges faster
than FedAvg and competing baselines on a range of realistic FL datasets.


  STAR observes a complex picture of RHIC collisions where correlation effects
of different origins -- initial state geometry, semi-hard scattering,
hadronization, as well as final state interactions such as quantum intensity
interference -- coexist. Presenting the measurements of flow, mini-jet
deformation, modified hadronization, and the Hanbury Brown and Twiss effect, we
trace the history of the system from the initial to the final state. The
resulting picture is discussed in the context of identifying the relevant
degrees of freedom and the likely equilibration mechanism.


  Concept of high efficiency photon storage based on adiabatic confinement
between concave mirrors is presented and experimentally investigated. The
approach is insensitive to typical for Fabri-Perot cells requirements on
quality of accumulated radiation, tolerance of resonator elements and their
stability. Experiments have been carried out with the trap, which consists from
opposed concave cylindrical mirrors and conjugated with them spherical mirrors.
In result, high efficiency for accumulation of radiation with large angular
spread and spectrum width has been confirmed. As radiation source a commercial
fiber laser has been used.


  We study the late-time behaviour of a dynamically perturbed rapidly rotating
black hole. Considering an extreme Kerr black hole, we show that the large
number of virtually undamped quasinormal modes (that exist for nonzero values
of the azimuthal eigenvalue m) combine in such a way that the field (as
observed at infinity) oscillates with an amplitude that decays as 1/t at late
times. This is in clear contrast with the standard late time power-law fall-off
familiar from studies of non-rotating black holes. This long-lived oscillating
``tail'' will, however, not be present for non-extreme (presumably more
astrophysically relevant) black holes, for which we find that many quasinormal
modes (individually excited to a very small amplitude) combine to give rise to
an exponentially decaying field. This result could have implications for the
detection of gravitational-wave signals from rapidly spinning black holes,
since the required theoretical templates need to be constructed from linear
combinations of many modes. Our main results are obtained analytically, but we
support the conclusions with numerical time-evolutions of the Teukolsky
equation. These time-evolutions provide an interesting insight into the notion
that the quasinormal modes can be viewed as waves trapped in the spacetime
region outside the horizon. They also suggest that a plausible mechanism for
the behaviour we observe for extreme black holes is the presence of a
``superradiance resonance cavity'' immediately outside the black hole.


  In call-by-value languages, some mutually-recursive value definitions can be
safely evaluated to build recursive functions or cyclic data structures, but
some definitions (let rec x = x + 1) contain vicious circles and their
evaluation fails at runtime. We propose a new static analysis to check the
absence of such runtime failures.
  We present a set of declarative inference rules, prove its soundness with
respect to the reference source-level semantics of Nordlander, Carlsson, and
Gill (2008), and show that it can be (right-to-left) directed into an
algorithmic check in a surprisingly simple way.
  Our implementation of this new check replaced the existing check used by the
OCaml programming language, a fragile syntactic/grammatical criterion which let
several subtle bugs slip through as the language kept evolving. We document
some issues that arise when advanced features of a real-world functional
language (exceptions in first-class modules, GADTs, etc.) interact with safety
checking for recursive definitions.


  We have obtained optical (BVR, [OIII]5007 and Halpha), near infrared (JHK)
imaging and long-slit optical spectroscopy for the Blue Compact Dwarf galaxy
Mrk86 (NGC2537). In this paper, the first of two, we present optical-near-
infrared colors and emission-line fluxes for the currently star-forming
regions, intemediate aged starburst and underlying stellar population. We also
describe the evolutionary synthesis models used in Paper II. The R and Halpha
luminosity distributions of the galaxy star-forming regions show maxima at
M_R=-9.5 and L_Halpha=10^37.3 erg s^-1. The underlying stellar population shows
an exponential surface brigthness profile with central value, mu_E,0=21.5 mag
arcsec^-2, and scale, alpha=0.88 kpc, both measured in the R-band image. In the
galaxy outer regions, dominated by this component, no significant color
gradients are observed. Finally, a set of evolutionary synthesis models have
been developed, covering a wide range in metallicity and burst strength.


  The magic wavelength for an optical lattice for hydrogen atoms that cancels
the lowest order AC Stark shift of the 1S-2S transition is calculated to be 513
nm. The magnitude of AC Stark shift $\Delta E=-1.19$ kHz/(10kW/cm$^2$) and the
slope $d\Delta E/d\nu = -27.7$ Hz/(GHz $\cdot$ 10 kW/cm$^2$) at the magic
wavelength suggests that a stable and narrow linewidth trapping laser is
necessary to achieve a deep enough optical lattice to confine hydrogen atoms in
a way that gives a small enough light shift for the precision spectroscopy of
the 1S-2S transition.


  The general BRST-BFV analysis of anomaly in the string theory coupled to
background fields is carried out. An exact equation for c-valued symbol of
anomaly operator is found and structure of its solutions is studied.


  The purpose of this short paper dedicated to the 60th anniversary of
Prof.Constantin Tsallis is to show how the use of mathematical tools and
physical concepts introduced by Burr, L\.{e}vy and Tsallis open a new line of
analysis of the old problem of non-Debye decay and universality of relaxation.
We also show how a finite characteristic time scale can be expressed in terms
of a $q$-expectation using the concept of $q$- escort probability.The
comparison with the Weron et al. probabilistic theory of relaxation leads to a
better understanding of the stochastic properties underlying the Tsallis
entropy concept.


  Utilizing four archival X-ray datasets taken with the Hard X-ray Detector
onboard Suzaku, timing studies were performed on three magnetars, 1E 1841-045
(observed in 2006), SGR 0501+4516 (2008), and 1RXS J170849.0-400910 (2009 and
2010). Their pulsations were reconfirmed, typically in an energy range of 12-50
keV. The 11.783 s pulses of 1E 1841-045, and those of SGR 0501+4516 with 5.762
s were periodically phase modulated, with a long period of about 23.4 ks and
about 16.4 ks, respectively. The pulse-phase modulation was also observed, at
46.5 ks, from two datasets of 1RXS J170849.0-400910. In all these cases, the
modulation amplitude was 6 to 16 percent of the pulse cycle. Including
previously confirmed four objects, this characteristic timing behavior is now
detected from seven magnetars in total, and interpreted as a result of free
precession of neutron stars that are deformed to an asphericity of ~10^{-4}.
Assuming that the deformation is due to magnetic stress, these magnetars are
inferred to harbor toroidal magnetic fields of Bt~10^{16} G. By comparing the
estimated Bt of these objects with their poloidal dipole field Bd, the Bt/Bd
ratio is found to increase with their characteristic age. Therefore, the
toroidal fields of magnetars are likely to last longer than their dipole
fields. This explains the presence of some classes of neutron stars that have
relatively weak Bd but are suspected to hide strong Bt inside them.


  We prove that the relative homological dimension of a Kleinian group G does
not exceed 1 + the critical exponent of G. As an application of this result we
show that for a geometrically finite Kleinian group G, if the topological
dimension of the limit set of G equals its Hausdorff dimension, then the limit
set is a round sphere.


  We prove a formula for the multiplicities of the index of an equivariant
transversally elliptic operator on a $G$-manifold. The formula is a sum of
integrals over blowups of the strata of the group action and also involves eta
invariants of associated elliptic operators. Among the applications, we obtain
an index formula for basic Dirac operators on Riemannian foliations, a problem
that was open for many years.


  Existing Object Pose Estimation (OPE) methods for stacked scenarios are not
robust to changes in object scale. This paper proposes a new 6DoF OPE network
(NormNet) for different scale objects in stacked scenarios. Specifically, each
object's scale is first learned with point-wise regression. Then, all objects
in the stacked scenario are normalized into the same scale through semantic
segmentation and affine transformation. Finally, they are fed into a shared
pose estimator to recover their 6D poses. In addition, we introduce a new
Sim-to-Real transfer pipeline, combining style transfer and domain
randomization. This improves the NormNet's performance on real data even if we
only train it on synthetic data. Extensive experiments demonstrate that the
proposed method achieves state-of-the-art performance on public benchmarks and
the MultiScale dataset we constructed. The real-world experiments show that our
method can robustly estimate the 6D pose of objects at different scales.


  The testing of web forms is an essential activity for ensuring the quality of
web applications, which mainly involves evaluating the interactions between
users and forms. Automated test-case generation remains a challenge for
web-form testing: Due to the complex, multi-level structure of web pages, it
can be difficult to automatically capture their inherent contextual information
for inclusion in the tests. Large Language Models (LLMs) have great potential
for contextual text generation. OpenAI's GPT LLMs have been receiving a lot of
attention in software testing, however, they may fail to be applied in practice
because of information security concerns. To the best of our knowledge, no
comparative study examining different LLMs has yet been reported for
web-form-test generation. To address this gap in the literature, we conducted a
comprehensive empirical study investigating the effectiveness of 11 LLMs on 146
web forms from 30 open-source Java web applications. According to the
experimental results, different LLMs can achieve different testing
effectiveness. Notably, the GPT-4, GLM-4, and Baichuan2 LLMs can generate
better web-form tests than the others. Compared with GPT-4, other LLMs find it
difficult to generate appropriate tests for web forms, resulting in decreased
successfully-submitted rates (SSRs, measured by the proportions of the
LLMs-generated web-form tests that can be successfully inserted into the web
forms and submitted) ranging from 9.10% to 74.15%. Nevertheless, some LLMs
achieve higher SSRs than GPT-3.5, indicating a better ability to generate
appropriate tests for web forms. Our findings also show that, for all LLMs,
when the designed prompts include complete and clear contextual information
about the web forms, more effective web-form tests were generated. Finally, we
offer some insights for using LLMs to guide automated web-form testing.


  We give the stratification by the symmetric tensor rank of all degree $d \ge
9$ homogeneous polynomials with border rank $5$ and which depend essentially on
at least 5 variables, extending previous works (A. Bernardi, A. Gimigliano, M.
Id\`{a}, E. Ballico) on lower border ranks. For the polynomials which depend on
at least 5 variables only 5 ranks are possible: $5$, $d+3$, $2d+1$, $3d-1$,
$4d-3$, but each of the ranks $3d-1$ and $2d+1$ is achieved in two
geometrically different situations. These ranks are uniquely determined by a
certain degree 5 zero-dimensional scheme $A$ associated to the polynomial. The
polynomial $f$ depends essentially on at least 5 variables if and only if $A$
is linearly independent (in all cases $f$ essentially depends on exactly 5
variables). The polynomial has rank $4d-3$ (resp $3d-1$, resp. $2d+1$, resp.
$d+3$, resp. $5$) if $A$ has $1$ (resp. $2$, resp. $3$, resp. $4$, resp. $5$)
connected components. The assumption $d\ge 9$ guarantees that each polynomial
has a uniquely determined associated scheme $A$. In each case we describe the
dimension of the families of the polynomials with prescribed rank, each
irreducible family being determined by the degrees of the connected components
of the associated scheme $A$.


  We start with a small paradigm shift about group representations, namely the
observation that restriction to a subgroup can be understood as an
extension-of-scalars. We deduce that, given a group $G$, the derived and the
stable categories of representations of a subgroup $H$ can be constructed out
of the corresponding category for $G$ by a purely triangulated-categorical
construction, analogous to \'etale extension in algebraic geometry.
  In the case of finite groups, we then use descent methods to investigate when
modular representations of the subgroup $H$ can be extended to $G$. We show
that the presheaves of plain, derived and stable representations all form
stacks on the category of finite $G$-sets (or the orbit category of $G$), with
respect to a suitable Grothendieck topology that we call the sipp topology.
  When $H$ contains a Sylow subgroup of $G$, we use sipp Cech cohomology to
describe the kernel and the image of the homomorphism $T(G)\to T(H)$, where
$T(-)$ denotes the group of endotrivial representations.


  This note gives a generalization of spherical twists, and describe the
autoequivalences associated to certain non-spherical objects. Typically these
are obtained by deforming the structure sheaves of (0,-2)-curves on threefolds,
or deforming $\mathbb{P}$-objects introduced by D.Huybrecht and R.Thomas


  I show that quantum corrections due to a massive particle generates a
non-local term in the gravitational effective action which is of zeroth order
in the derivative expansion, much like the cosmological constant. It carries a
fixed coefficient which is very much larger than the cosmological constant, and
which cannot be fine-tuned. The interaction is active at scales above the
particle's mass. This is of the form $m^4 (\frac1{\Box}R)_x "<x|\log (\Box +m^2
)|y >" (\frac1{\Box}R)_y$, and I discuss the meaning of $ "<x|\log (\Box +m^2)
|y >" $ and other aspects of its interpretation.


  Two-particle correlations have been used to study property of a produced
medium called Quark-Gluon Plasma (QGP) in relativistic heavy-ion collisions,
and a long-range correlation among produced particles has been considered as a
strong evidence of strongly interacting QGP. Strikingly, clear long-range
correlations have been also observed in small collision systems like $pp$ and
$p$+$A$ at a wide range of collision energies. A model introducing a repulsive
force between flux tubes called string shoving can qualitatively describe the
long-range near-side correlations in high multiplicity $pp$ collisions. This
model implemented in the PYTHIA Monte Carlo event generator allows us to
perform detailed study. In this work, a full data analysis to calculate
associated yields and flow coefficients is performed with PYTHIA events, and
the results are compared with experimental results. We find that the string
shoving model overestimates long-range near-side correlations particularly in
low multiplicity events. We also introduce a method to subtract such
overestimated correlations in low multiplicity to have a more relevant
comparison with the data.


  Stealth addresses represent an approach to enhancing privacy within public
and distributed blockchains, such as Ethereum and Bitcoin. Stealth address
protocols generate a distinct, randomly generated address for the recipient,
thereby concealing interactions between entities. In this study, we introduce
BaseSAP, an autonomous base-layer protocol for embedding stealth addresses
within the application layer of programmable blockchains. BaseSAP expands upon
previous research to develop a modular protocol for executing unlikable
transactions on public blockchains. BaseSAP allows for developing additional
stealth address layers using different cryptographic algorithms on top of the
primary implementation, capitalizing on its modularity. To demonstrate the
effectiveness of our proposed protocol, we present simulations of an advanced
Secp256k1-based dual-key stealth address protocol. This protocol is designed on
top of BaseSAP and is deployed on the Goerli and Sepolia test networks as the
first prototype implementation. Furthermore, we provide cost analyses and
underscore potential security ramifications and attack vectors that could
affect the privacy of stealth addresses. Our study reveals the flexibility of
the BaseSAP protocol and offers insight into the broader implications of
stealth address technology.


  The dwarf satellites of `giant' Milky Way (MW)-mass galaxies are our primary
probes of low-mass dark matter halos. The number and velocities of the
satellite galaxies of the MW and M31 initially puzzled galaxy formation
theorists, but are now reproduced well by many models. Yet, are the MW's and
M31's satellites representative? Were galaxy formation models `overfit'? These
questions motivate deep searches for satellite galaxies outside the Local
Group. We present a deep survey of the `classical' satellites
($M_{\star}$$\geqslant$4$\times$10$^5 M_{\odot}$) of the MW-mass galaxy M94 out
to 150 kpc projected distance. We find $only\ two$ satellites, each with
$M_{\star}{\sim}10^6 M_{\odot}$, compared with 6-12 such satellites in the four
other MW-mass systems with comparable data (MW, M31, M81, M101). Using a
`standard' prescription for occupying dark matter halos (taken from the fully
hydrodynamical EAGLE simulation) with galaxies, we find that such a sparse
satellite population occurs in $<$0.2% of MW-mass systems $-$ a $<$1%
probability among a sample of five (known systems + M94). In order to produce
an M94-like system more frequently we make satellite galaxy formation much more
stochastic than is currently predicted by dramatically increasing the slope and
scatter of the stellar mass-halo mass (SMHM) relation. Surprisingly, the SMHM
relation must be altered even for halos masses up to 10$^{11}M_{\odot} -$
significantly above the mass scales predicted to have increased scatter from
current hydrodynamical models. The sparse satellite population of this `lonely
giant' thus advocates for an important modification to ideas of how the
satellites around MW-mass galaxies form.


  We prove that the polar decomposition of the singular part of a vector
measure depends on its conditional expectations computed with respect to the
$q$-regular filtration. This dependency is governed by a martingale analog of
the so-called wave cone, which naturally corresponds to the result of De
Philippis and Rindler about fine properties of PDE-constrained vector measures.
As a corollary we obtain a martingale version of Alberti's rank-one theorem.


  It can be insightful to extend qualitative studies with a secondary
quantitative analysis (where the former suggests insightful questions that the
latter can answer). Documenting developer beliefs should be the start, not the
end, of Software Engineering research. Once prevalent beliefs are found, they
should be checked against real-world data. For example, this paper finds
several notable discrepancies between empirical evidence and the developer
beliefs documented in Wan et al.'s recent TSE paper "Perceptions, expectations,
and challenges in defect prediction". By reporting these discrepancies we can
stop developers (a) wasting time on inconsequential matters or (b) ignoring
important effects. For the future, we would encourage more "extension studies"
of prior qualitative results with quantitative empirical evidence.


  Groups of animals often tend to arrange themselves in flocks that have
characteristic spatial attributes and temporal dynamics. Using a dynamic
continuum model for a flock of individuals, we find equilibria of finite
spatial extent where the density goes continuously to zero at a well-defined
flock edge, and we discuss conditions on the model that allow for such
solutions. We also demonstrate conditions under which, as the flock size
increases, the interior density in our equilibria tends to an approximately
uniform value. Motivated by observations of starling flocks that are relatively
thin in a direction transverse to the direction of flight, we investigate the
stability of infinite, planar-sheet flock equilibria. We find that long-
wavelength perturbations along the sheet are unstable for the class of models
that we investigate. This has the conjectured consequence that sheet-like
flocks of arbitrarily large transverse extent relative to their thickness do
not occur. However, we also show that our model admits approximately
sheet-like, 'pancake-shaped', three-dimensional ellipsoidal equilibria with
definite aspect ratios (transverse length- scale to flock thickness) determined
by anisotropic perceptual/response characteristics of the flocking individuals,
and we argue that these pancake-like equilibria are stable to the previously
mentioned sheet instability.


  We consider the two-dimensional sorted range reporting problem. Our data
structure requires O(n lglg n) words of space and O(lglg n + k lglg n) query
time, where k is the number of points in the query range. This data structure
improves a recent result of Nekrich and Navarro [8] by a factor of O(lglg n) in
query time, and matches the state of the art for unsorted range reporting [1].


  We discuss shape coexistence in the neutron-deficient Kr72-Kr78 isotopes in
the framework of configuration mixing calculations of particle-number and
angular-momentum projected axial mean-field states obtained from
self-consistent calculations with the Skyrme interaction SLy6 and a
density-dependent pairing interaction. While our calculation reproduces
qualitatively and quantitatively many of the global features of these nuclei,
such as coexistence of prolate and oblate shapes, their strong mixing at low
angular momentum, and the deformation of collective bands, the ordering of our
calculated low-lying levels is at variance with experiment. We analyse the role
of the single-particle spectrum of the underlying mean-field for the spectrum
of collective excitations.


  The concurrent rise of artificial intelligence and quantum information poses
opportunity for creating interdisciplinary technologies like quantum neural
networks. Quantum reservoir processing, introduced here, is a platform for
quantum information processing developed on the principle of reservoir
computing that is a form of artificial neural network. A quantum reservoir
processor can perform qualitative tasks like recognizing quantum states that
are entangled as well as quantitative tasks like estimating a non-linear
function of an input quantum state (e.g. entropy, purity or logarithmic
negativity). In this way experimental schemes that require measurements of
multiple observables can be simplified to measurement of one observable on a
trained quantum reservoir processor.


  We consider selfish sources that send updates to a monitor over a shared
wireless access. The sources would like to minimize the age of their
information at the monitor. Our goal is to devise strategies that incentivize
such sources to use the shared spectrum cooperatively. Earlier work has modeled
such a setting using a non-cooperative one-shot game, played over a single
access slot, and has shown that under certain access settings the dominant
strategy of each source is to transmit in any slot, resulting in packet
collisions between the sources' transmissions and causing all of them to be
decoded in error at the monitor.
  We capture the interaction of the sources over an infinitely many medium
access slots using infinitely repeated games. We investigate strategies that
enable cooperation resulting in an efficient use of the wireless access, while
disincentivizing any source from unilaterally deviating from the strategy.
Formally, we are interested in strategies that are a subgame perfect Nash
equilibrium (SPNE). We begin by investigating the properties of the one-stage
(slot) optimal and access-fair correlated strategies. We then consider their
many-slot variants, the age-fair and access-fair strategies, in the infinitely
repeated game model. We prove that the access-fair and age-fair strategies are
SPNEs for when collision slots are longer than successful transmission slots.
Otherwise, neither is a SPNE. We end with simulations that shed light on a
possible SPNE for the latter case.


  We compared the properties of 56 elliptical galaxies selected from three
clusters at $1.2<z<1.4$ with those of field galaxies in the GOODS-S (~30),
COSMOS (~180) and CANDELS (~220) fields. We studied the relationships among
effective radius, surface brightness, stellar mass, stellar mass density
$\Sigma_{Re}$ and central mass density $\Sigma_{1kpc}$ within 1 kpc radius. We
find that cluster ellipticals do not differ from field ellipticals: they share
the same structural parameters at fixed mass and the same scaling relations. On
the other hand, the population of field ellipticals at $z\sim1.3$ shows a
significant lack of massive ($M_*> 2\times 10^{11}$ M$_\odot$) and large (R$_e
> 4-5$ kpc) ellipticals with respect to the cluster. Nonetheless, at
$M*<2\times 10^{11}$ M$_\odot$, the two populations are similar. The size-mass
relation of ellipticals at z~1.3 defines two different regimes, above and below
a transition mass $m_t\sim 2-3\times10^{10}$ M$_\odot$: at lower masses the
relation is nearly flat (R$_e\propto M_*^{-0.1\pm 0.2}$), the mean radius is
constant at ~1 kpc and $\Sigma_{Re}\sim \Sigma_{1kpc}$ while, at larger masses,
the relation is R$_e\propto M*^{0.64\pm0.09}$. The transition mass marks the
mass at which galaxies reach the maximum $\Sigma_{Re}$. Also the
$\Sigma_{1kpc}$-mass relation follows two different regimes,
$\Sigma_{1kpc}\propto M*^{0.64\ >m_t}_{1.07\ <m_t}$, defining a transition mass
density $\Sigma_{1kpc}\sim 2-3\times10^3$ M$_\odot$ pc$^{-2}$. The mass density
$\Sigma_{Re}$ does not correlate with mass, dense/compact galaxies can be
assembled over a wide mass regime, independently of the environment. The
central mass density, $\Sigma_{1kpc}$, besides to be correlated with the mass,
is correlated to the age of the stellar population: the higher the central
stellar mass density, the higher the mass, the older the age of the stellar
population. [Abridged]


  Proton beam dumps are prolific sources of mesons enabling a powerful
technique to search for vector mediator coupling of dark matter to neutral pion
and higher mass meson decays. By the end of the decade the PIP-II linac will be
delivering up to 1 MW of proton power to the FNAL campus. This includes a
significant increase of power to the Booster Neutrino Beamline (BNB) which
delivers 8 GeV protons to the Short Baseline Neutrino (SBN) detectors. By
building a new dedicated beam dump target station, and using the SBN detectors,
a greater than an order of magnitude increase in search sensitivity for dark
matter relative to the recent MiniBooNE beam dump search can be achieved. This
modest cost upgrade to the BNB would begin testing models of the highly
motivated relic density limit predictions and provide novel ways to test
explanations of the anomalous excess of low energy events seen by MiniBooNE.


  We report on an initial user study, which explores how players of an
augmented mirror game, self-style or self-present themselves when they are
allowed to see themselves in the mirror compared to when they do not see
themselves. To this end, we customized an open source fruit slicing game into
an interactive installation for an architecture museum and conducted with 36
visitors a field study. Based on an analysis of video recordings of
participants we identified, for example significant differences in how often
participants smile. Ultimately, presenting a self-image to gamers in a social
setting resulted in behavior change, which we argue could be utilized carefully
from a Somaesthetics perspective as an experience design feature in future
games.


  The ability to grasp ordinary and potentially never-seen objects is an
important feature in both domestic and industrial robotics. For a system to
accomplish this, it must autonomously identify grasping locations by using
information from various sensors, such as Microsoft Kinect 3D camera. Despite
numerous progress, significant work still remains to be done in this field. To
this effect, we propose a dictionary learning and sparse representation (DLSR)
framework for representing RGBD images from 3D sensors in the context of
determining such good grasping locations. In contrast to previously proposed
approaches that relied on sophisticated regularization or very large datasets,
the derived perception system has a fast training phase and can work with small
datasets. It is also theoretically founded for dealing with masked-out entries,
which are common with 3D sensors. We contribute by presenting a comparative
study of several DLSR approach combinations for recognizing and detecting grasp
candidates on the standard Cornell dataset. Importantly, experimental results
show a performance improvement of 1.69% in detection and 3.16% in recognition
over current state-of-the-art convolutional neural network (CNN). Even though
nowadays most popular vision-based approach is CNN, this suggests that DLSR is
also a viable alternative with interesting advantages that CNN has not.


  The recently developed discrete diffusion models perform extraordinarily well
in the text-to-image task, showing significant promise for handling the
multi-modality signals. In this work, we harness these traits and present a
unified multimodal generation model that can conduct both the "modality
translation" and "multi-modality generation" tasks using a single model,
performing text-based, image-based, and even vision-language simultaneous
generation. Specifically, we unify the discrete diffusion process for
multimodal signals by proposing a unified transition matrix. Moreover, we
design a mutual attention module with fused embedding layer and a unified
objective function to emphasise the inter-modal linkages, which are vital for
multi-modality generation. Extensive experiments indicate that our proposed
method can perform comparably to the state-of-the-art solutions in various
generation tasks.


  In this paper, a new precoder for a coherent optical filter bank multicarrier
with offset quadrature amplitude modulation (FBMC/OQAM) system is proposed. The
precoder is designed based on an iterative polynomial eigenvalue decomposition
(PEVD) algorithm to jointly mitigate the inter-symbol interference (ISI) and
inter-carrier interference (ICI). The PEVD algorithm is used to decompose a
polynomial channel matrix into polynomial eigenvectors and eigenvalues
matrices, then a precoder is designed based on the decomposed matrices. The
precoder acts as a filter applied to each subcarrier and to its adjacent
subcarriers. In addition, a new adaptive optimum energy algorithm is proposed
to truncate the insignificant precoder filter coefficients produced by the PEVD
algorithm and consequently reduce the computational complexity. A mathematical
model and algorithm for implementing the precoder are also presented.
Robustness of the proposed precoder has been analyzed and compared to existing
precoder in optical channel with different dispersion effects. Numerical
results demonstrate that the new precoder significantly outperforms the
existing precoder in terms of error vector magnitude (EVM), bit error rate
(BER), Frobenius norm of the error matrix, and computational complexity.


  In this work we explore degree assortativity in complex networks, and extend
its usual definition beyond that of nearest neighbours. We apply this
definition to model networks, and describe a rewiring algorithm that induces
assortativity. We compare these results to real networks. Social networks in
particular tend to be assortatively mixed by degree in contrast to many other
types of complex networks. However, we show here that these positive
correlations diminish after one step and in most of the empirical networks
analysed. Properties besides degree support this, such as the number of papers
in scientific coauthorship networks, with no correlations beyond nearest
neighbours. Beyond next-nearest neighbours we also observe a diasassortative
tendency for nodes three steps away indicating that nodes at that distance are
more likely different than similar.


  We introduce the class of synchronous subsequential relations, a subclass of
the synchronous relations which embodies some properties of subsequential
relations. If we take relations of this class as forming the possible
transitions of an infinite automaton, then most decision problems (apart from
membership) still remain undecidable (as they are for synchronous and
subsequential rational relations), but on the positive side, they can be
approximated in a meaningful way we make precise in this paper. This might make
the class useful for some applications, and might serve to establish an
intermediate position in the trade-off between issues of expressivity and
(un)decidability.


  For a Weyl group W, we give a simple closed formula (valid on elliptic
conjugacy classes) for the character of the representation of W in each
A-isotypic component of the full homology of a Springer fiber. We also give a
formula (valid again on elliptic conjugacy classes) of the W-character of an
irreducible discrete series representation with real central character of a
graded affine Hecke algebra with arbitrary parameters. In both cases, the Pin
double cover of W and the Dirac operator for graded affine Hecke algebras play
key roles.


  Kurepa's hypothesis asserts that for each integer $n\ge 2$ the greatest
common divisor of $!n:=\sum_{k=0}^{n-1}k!$ and $n!$ is $2$. Motivated by an
equivalent formulation of this hypothesis involving derangement numbers, here
we give a formulation of Kurepa's hypothesis in terms of divisibility of any
Kurepa's determinant $K_p$ of order $p-4$
  by a prime $p\ge 7$. In the previous version of this article we have proposed
the strong Kurepa's hypothesis involving a general Kurepa's determinant $K_n$
with any integer $n\ge 7$. We prove the ``even part'' of this hypothesis which
can be considered as a generalization of Kurepa's hypothesis. However, by using
a congruence for $K_n$ involving the derangement number $S_{n-1}$ with an odd
integer $n\ge 9$, we find that the integer $11563=31\times 373$ is a
counterexample to the ``odd composite part'' of strong Kurepa's hypothesis.
  We also present some remarks, divisibility properties and computational
results closely related to the questions on Kurepa's hypothesis involving
derangement numbers and Bell numbers.


  Analysis of repeated measurements for a sample of subjects has been
intensively studied with several important branches developed, including
longitudinal/panel/functional data analysis, while nonparametric regression of
the mean function serves as a cornerstone that many statistical models are
built upon. In this work, we investigate this problem using fully connected
deep neural network (DNN) estimators with flexible shapes. A comprehensive
theoretical framework is established by adopting empirical process techniques
to tackle clustered dependence. We then derive the nearly optimal convergence
rate of the DNN estimators in H\"older smoothness space, and illustrate the
phase transition phenomenon inherent to repeated measurements and its
connection to the curse of dimensionality. Furthermore, we study the function
spaces with low intrinsic dimensions, including the hierarchical composition
model, anisotropic H\"older smoothness and low-dimensional support set, and
also obtain new approximation results and matching lower bounds to demonstrate
the adaptivity of the DNN estimators for circumventing the curse of
dimensionality.


  The path probability of a particle undergoing stochastic motion is studied by
the use of functional technique, and the general formula is derived for the
path probability distribution functional. The probability of finding paths
inside a tube/band, the center of which is stipulated by a given path, is
analytically evaluated in a way analogous to continuous measurements in quantum
mechanics. Then, the formalism developed here is applied to the stochastic
dynamics of stock price in finance.


  Graph structure expression plays a vital role in distinguishing various
graphs. In this work, we propose a Structure-Sensitive Graph Dictionary
Embedding (SS-GDE) framework to transform input graphs into the embedding space
of a graph dictionary for the graph classification task. Instead of a plain use
of a base graph dictionary, we propose the variational graph dictionary
adaptation (VGDA) to generate a personalized dictionary (named adapted graph
dictionary) for catering to each input graph. In particular, for the
adaptation, the Bernoulli sampling is introduced to adjust substructures of
base graph keys according to each input, which increases the expression
capacity of the base dictionary tremendously. To make cross-graph measurement
sensitive as well as stable, multi-sensitivity Wasserstein encoding is proposed
to produce the embeddings by designing multi-scale attention on optimal
transport. To optimize the framework, we introduce mutual information as the
objective, which further deduces to variational inference of the adapted graph
dictionary. We perform our SS-GDE on multiple datasets of graph classification,
and the experimental results demonstrate the effectiveness and superiority over
the state-of-the-art methods.


  An automorphism of a spherical building is called \textit{domestic} if it
maps no chamber onto an opposite chamber. This paper forms a significant part
of a large project classifying domestic automorphisms of spherical buildings of
exceptional type. In previous work the classifications for $\mathsf{G}_2$,
$\mathsf{F}_4$ and $\mathsf{E}_6$ have been completed, and the present work
provides the classification for buildings of type $\mathsf{E}_7$. In many
respects this case is the richest amongst all exceptional types.


  A modification to the Friedmann Robertson Walker equation is proposed in
which the universe is flat, matter dominated, and accelerating. An additional
term, which contains only matter or radiation (no vacuum contribution), becomes
the dominant driver of expansion at a late epoch of the universe. During the
epoch when the new term dominates, the universe accelerates; we call this
period of acceleration the Cardassian era. The universe can be flat and yet
consist of only matter and radiation, and still be compatible with
observations. The energy density required to close the universe is much smaller
than in a standard cosmology, so that matter can be sufficient to provide a
flat geometry. The new term required may arise, e.g., as a consequence of our
observable universe living as a 3-dimensional brane in a higher dimensional
universe. The Cardassian model survives several observational tests, including
the cosmic background radiation, the age of the universe, the cluster baryon
fraction, and structure formation.


  We present synchrotron x-ray diffraction, neutron powder diffraction and
time-of-flight inelastic neutron scattering measurements on the rare earth
pyrochlore oxide Nd2Zr2O7 to study the ordered state magnetic structure and
cystal field states. The structural characterization by high-resolution
synchrotron x-ray diffraction confirms that the pyrochlore structure has no
detectable O vacancies or Nd/Zr site mixing. The neutron diffraction reveals
long range all-in/all-out antiferromagnetic order below T_N ~ 0.4 K with
propagation vector k = (0 0 0) and an ordered moment of 1.26(2) \mu_B/Nd at 0.1
K. The ordered moment is much smaller than the estimated moment of 2.65
\mu_B/Nd for the local <111> Ising ground state of Nd3+ (J=9/2) suggesting that
the ordering is partially suppressed by quantum fluctuations. The strong Ising
anisotropy is further confirmed by the inelastic neutron scattering data which
reveals a well-isolated dipolar-octupolar type Kramers doublet ground state.
The crystal field level scheme and ground state wavefunction have been
determined.


  We investigate quantum correlations in microwave radiation produced by the
dynamical Casimir effect in a superconducting waveguide terminated and
modulated by a superconducting quantum interference device. We apply
nonclassicality tests and evaluate the entanglement for the predicted field
states. For realistic circuit parameters, including thermal background noise,
the results indicate that the produced radiation can be strictly nonclassical
and can have a measurable amount of intermode entanglement. If measured
experimentally, these nonclassicalilty indicators could give further evidence
of the quantum nature of the dynamical Casimir radiation in these circuits.


  We introduce a monoidal category of corings using two different notions of
corings morphisms. The first one is the (right) coring extensions recently
introduced by T. Brzezi\'nski in [2], and the anther is the usual notion of
morphisms defined in [5] by J. G\'omez-Torrecillas.


  Large language models (LLMs) such as those embedded in 'chatbots' are
accelerating and democratizing research by providing comprehensible information
and expertise from many different fields. However, these models may also confer
easy access to dual-use technologies capable of inflicting great harm. To
evaluate this risk, the 'Safeguarding the Future' course at MIT tasked
non-scientist students with investigating whether LLM chatbots could be
prompted to assist non-experts in causing a pandemic. In one hour, the chatbots
suggested four potential pandemic pathogens, explained how they can be
generated from synthetic DNA using reverse genetics, supplied the names of DNA
synthesis companies unlikely to screen orders, identified detailed protocols
and how to troubleshoot them, and recommended that anyone lacking the skills to
perform reverse genetics engage a core facility or contract research
organization. Collectively, these results suggest that LLMs will make
pandemic-class agents widely accessible as soon as they are credibly
identified, even to people with little or no laboratory training. Promising
nonproliferation measures include pre-release evaluations of LLMs by third
parties, curating training datasets to remove harmful concepts, and verifiably
screening all DNA generated by synthesis providers or used by contract research
organizations and robotic cloud laboratories to engineer organisms or viruses.


  In three dimensional Maxwell-Chern-Simons massless scalar electrodynamics
with $ \phi^6$ coupling, the $U(1)$ symmetry is spontaneously broken at two
loop order regardless of the presence or absence of the Maxwell term.
Dimensional transmutation takes place in pure Chern-Simons scalar
electrodynamics. The beta function for the $\phi^6$ coupling is independent of
gauge couplings.


  By employing powerful edge servers for data processing, mobile edge computing
(MEC) has been recognized as a promising technology to support emerging
computation-intensive applications. Besides, non-orthogonal multiple access
(NOMA)-aided MEC system can further enhance the spectral-efficiency with
massive tasks offloading. However, with more dynamic devices brought online and
the uncontrollable stochastic channel environment, it is even desirable to
deploy appealing technique, i.e., intelligent reflecting surfaces (IRS), in the
MEC system to flexibly tune the communication environment and improve the
system energy efficiency. In this paper, we investigate the joint offloading,
communication and computation resource allocation for IRS-assisted NOMA MEC
system. We firstly formulate a mixed integer energy efficiency maximization
problem with system queue stability constraint. We then propose the
Lyapunov-function-based Mixed Integer Deep Deterministic Policy Gradient
(LMIDDPG) algorithm which is based on the centralized reinforcement learning
(RL) framework. To be specific, we design the mixed integer action space
mapping which contains both continuous mapping and integer mapping. Moreover,
the award function is defined as the upper-bound of the Lyapunov
drift-plus-penalty function. To enable end devices (EDs) to choose actions
independently at the execution stage, we further propose the Heterogeneous
Multi-agent LMIDDPG (HMA-LMIDDPG) algorithm based on distributed RL framework
with homogeneous EDs and heterogeneous base station (BS) as heterogeneous
multi-agent. Numerical results show that our proposed algorithms can achieve
superior energy efficiency performance to the benchmark algorithms while
maintaining the queue stability. Specially, the distributed structure
HMA-LMIDDPG can acquire more energy efficiency gain than centralized structure
LMIDDPG.