  This paper deals with the inverse problem of recovering an arbitrary number
of fractional damping terms in a wave equation. We develop several approaches
on uniqueness and reconstruction, some of them relying on Tauberian theorems on
the relation between the asymptotics of solutions in time and Laplace domain.
Also the possibility of additionally recovering space dependent coefficients or
initial data is discussed. The resulting methods for reconstructing
coefficients and fractional orders in these terms are tested numerically.
Additionally, we provide an analysis of the forward problem, a multiterm
fractional wave equation.


  Scientific laboratories are among the most challenging course components to
integrate into online instruction. Available technology restricts the design
and nature of experiments and it can be hard to replicate the collaborative lab
environment where frequent and immediate instructor feedback is the norm. Here
we report on technological and pedagogical aspects of newly developed labs for
online courses using the Interactive Online Lab (iOLab) device. We argue that
this technology, coupled with an online course design emphasizing teamwork,
targeted feedbacks, and self-regulation skills, provides a robust framework for
students to do reliable, engaging, inquiry-based and hands-on labs outside the
classroom. After describing the implementation and technology, we explain our
lab objectives and how the labs were integrated into two introductory physics
courses. We conclude with an example lab on kinematics.


  Persistence phenomena in colonization processes could explain the negative
results of SETI search preserving the possibility of a galactic civilization.
However, persistence phenomena also indicates that search of technological
civilizations in stars in the neighbourhood of Sun is a misdirected SETI
strategy. This last conclusion is also suggested by a weaker form of the Fermi
paradox. A simple model of a branching colonization which includes emergence,
decay and branching of civilizations is proposed. The model could also be used
in the context of ant nests diffusion.


  We reveal and address the frequently overlooked yet important issue of
disguised procedural unfairness, namely, the potentially inadvertent
alterations on the behavior of neutral (i.e., not problematic) aspects of data
generating process, and/or the lack of procedural assurance of the greatest
benefit of the least advantaged individuals. Inspired by John Rawls's advocacy
for pure procedural justice, we view automated decision-making as a microcosm
of social institutions, and consider how the data generating process itself can
satisfy the requirements of procedural fairness. We propose a framework that
decouples the objectionable data generating components from the neutral ones by
utilizing reference points and the associated value instantiation rule. Our
findings highlight the necessity of preventing disguised procedural unfairness,
drawing attention not only to the objectionable data generating components that
we aim to mitigate, but also more importantly, to the neutral components that
we intend to keep unaffected.


  We review recent findings on spin glass models. Both the equilibrium
properties and the dynamic properties are covered. We focus on progress in
theoretical, in particular numerical, studies, while its relationship to real
magnetic materials is also mentioned.


  Suppose $\pi:W\to S$ is a smooth, proper morphism over a variety $S$
contained as a Zariski open subset in a smooth, complex variety $\bar S$. The
goal of this note is to consider the question of when $\pi$ admits a regular,
flat compactification. In other words, when does there exists a flat, proper
morphism $\bar\pi:\overline{W}\to\bar S$ extending $\pi$ with $\overline{W}$
regular? One interesting recent example of this occurs in the preprint
arXiv:1602.05534 of Laza, Sacca and Voisin where $\pi$ is a family of abelian
$5$-folds over a Zariski open subset $S$ of $\bar S=\mathbb{P}^5$. In that
paper, the authors construct $\overline{W}$ using the theory of compactified
Prym varieties and show that it is a holomorphic symplectic manifold
(deformation equivalent to O'Grady's $10$-dimensional example).
  In this note I observe that non-vanishing of the local intersection
cohomology of $R^1\pi_*\mathbb{Q}$ in degree at least $2$ provides an
obstruction to finding a $\bar\pi$. Moreover, non-vanishing in degree $1$
provides an obstruction to finding a $\bar\pi$ with irreducible fibers. Then I
observe that, in some cases of interest, results of Brylinski, Beilinson and
Schnell can be used to compute the intersection cohomology. I also give
examples involving cubic $4$-folds, and ask a question about palindromicity of
hyperplane sections.


  Robust, accurate and efficient quantum tomography is key for future quantum
technologies. Traditional methods are impractical for even medium sized systems
and are not robust against noise and errors. Here we report on an experimental
demonstration of self-guided quantum tomography; an autonomous, fast, robust
and precise technique for measuring quantum states with significantly less
computational resources than standard techniques. The quantum state is
iteratively learned by treating tomography as a projection measurement
optimization problem. We experimentally demonstrate robustness against both
statistical noise and experimental errors on both single qubit and entangled
two-qubit states. Our demonstration provides a method of full quantum state
characterization in current and near-future experiments where standard
techniques are unfeasible.


  We consider the problem of reconstructing a compact 3-manifold (with
boundary) embedded in $\mathbb{R}^3$ from its cross-sections $\mathcal S$ with
a given set of cutting planes $\mathcal P$ having arbitrary orientations. Using
the obvious fact that a point $x \in \mathcal P$ belongs to the original object
if and only if it belongs to $\mathcal S$, we follow a very natural
reconstruction strategy: we say that a point $x \in \mathbb{R}^3$ belongs to
the reconstructed object if (at least one of) its nearest point(s) in $\mathcal
P$ belongs to $\mathcal S$. This coincides with the algorithm presented by Liu
et al. in \cite{LB+08}. In the present paper, we prove that under appropriate
sampling conditions, the output of this algorithm preserves the homotopy type
of the original object. Using the homotopy equivalence, we also show that the
reconstructed object is homeomorphic (and isotopic) to the original object.
This is the first time that 3-dimensional shape reconstruction from
cross-sections comes with theoretical guarantees.


  Intersection of a random fractal or self-affine set with a linear manifold or
another fractal set is studied, assuming that one of the sets is in a
translational motion with respect to the other. It is shown that the mass of
such an intersection is a self-affine function of the relative position of the
two sets. The corresponding Hurst exponent h is a function of the scaling
exponents of the intersecting sets. A generic expression for h is provided, and
its proof is offered for two cases --- intersection of a self-affine curve with
a line, and of two fractal sets. The analytical results are tested using
Monte-Carlo simulations.


  In this paper we propose two new subclasses of Petri nets with resets, for
which the reachability and coverability problems become tractable. Namely, we
add an acyclicity condition that only applies to the consumptions and
productions, not the resets. The first class is acyclic Petri nets with resets,
and we show that coverability is PSPACE-complete for them. This contrasts the
known Ackermann-hardness for coverability in (not necessarily acyclic) Petri
nets with resets. We prove that the reachability problem remains undecidable
for acyclic Petri nets with resets. The second class concerns workflow nets, a
practically motivated and natural subclass of Petri nets. Here, we show that
both coverability and reachability in acyclic workflow nets with resets are
PSPACE-complete. Without the acyclicity condition, reachability and
coverability in workflow nets with resets are known to be equally hard as for
Petri nets with resets, that being Ackermann-hard and undecidable,
respectively.


  We present injectivity and microlocal analyses of a new generalized Radon
transform, $\mathcal{R}$, which has applications to a novel scanner design in
three-dimensional Compton Scattering Tomography (CST), which we also introduce
here. Using Fourier decomposition and Volterra equation theory, we prove that
$\mathcal{R}$ is injective and show that the image solution is unique. Using
microlocal analysis, we prove that $\mathcal{R}$ satisfies the Bolker
condition, and we investigate the edge detection capabilities of $\mathcal{R}$.
This has important implications regarding the stability of inversion and the
amplification of measurement noise. In addition, we present simulated 3-D image
reconstructions from $\mathcal{R}f$ data, where $f$ is a 3-D density, with
varying levels of added Gaussian noise. This paper provides the theoretical
groundwork for 3-D CST using the proposed scanner design.


  We present a short complete proof of the existence of the normal cycle of a
compact subanalytic set. The approach is inspired by some old ides of Joseph
Fu, uses Morse theoretic techniques and $o$-minimal topology.


  In this paper, we investigate steady states of shallow water moment equations
including bottom topographies. We derive a new hyperbolic shallow water moment
model based on linearized moment equations that allows for a simple assessment
of the steady states. After proving hyperbolicity of the new model, the steady
states are fully identified. A well-balanced scheme is adopted to the specific
structure of the new model and allows to preserve the steady states in
numerical simulations.


  Nuclear theory and experiments, alongside astrophysical observations,
constrain the equation of state (EOS) of supranuclear-dense matter. Conversely,
knowledge of the EOS allows an improved interpretation of nuclear or
astrophysical data. In this article, we use several established constraints on
the EOS and the new NICER measurement of PSR J0437-4715 to comment on the
nature of the primary companion in GW230529 and the companion of PSR
J0514-4002E. We find that, with a probability of $\gtrsim 84\%$ and $\gtrsim
68\%$, respectively, both objects are black holes. These likelihoods increase
to above $95\%$ when one uses GW170817's remnant as an upper limit on the TOV
mass. We also demonstrate that the current knowledge of the EOS substantially
disfavors high masses and radii for PSR J0030+0451, inferred recently when
combining NICER with XMM-Newton background data and using particular hot-spot
models. Finally, we also use our obtained EOS knowledge to comment on
measurements of the nuclear symmetry energy, finding that the large value
predicted by the PREX-II measurement displays some mild tension with other
constraints on the EOS.


  L.A. Shemetkov posed a Problem 9.74 in Kourovka Notebook to find all local
formations $\mathfrak{F}$ of finite groups such that every finite minimal
non-$\mathfrak{F}$-group is either a Schmidt group or a group of prime order.
All known solutions to this problem are obtained under the assumption that
every minimal non-$\mathfrak{F}$-group is soluble. Using the above mentioned
solutions we present a polynomial in $n$ time check for a local formation
$\mathfrak{F}$ with bounded $\pi(\mathfrak{F})$ to be a formation of soluble
groups with the Shemtkov property where $n=\max \pi(\mathfrak{F})$.


  The recent implementation of the high-speed burst mode at the ISAAC
instrument on UT1, and its propagation to other ESO instruments, has opened the
door to observational capabilities which hold the potential for a wealth of
novel results. In the ELT era, when the accent will likely be on lengthy
programs aimed at the best sensitivity and angular resolution, the VLT
telescopes could continue to play a significant and largely unique role by
performing routinely observations of transient events at high temporal
resolution. In our contribution, we provide details on two such kinds of
observations, namely lunar occultations of stars and of asteroids. For the
first ones, we report on two passages of the Moon in regions with high stellar
density as the Galactic Center. The VLT-UT1 telescope was used for the first
time to record successfully 53 and 71 occultations on March 22 and August 6,
2006, with an angular resolution of 0.5-1 milliarcsecond and $K\sim12.5$
limiting magnitude. We note that the angular resolution is superior to that
achieved at present by Adaptive Optics on any telescope, and also superior to
that foreseen for the ELT at the same wavelength. LO are also very efficient in
terms of telescope time. We present some of the results, including the
discovery of close binaries, and the detection and study of compact
circumstellar components of cool giants, AGB stars and embedded IR sources.
  Rest of the abstract follows at the paper


  We consider random walks on discrete state spaces, such as general undirected
graphs, where the random walkers are designed to approximate a target quantity
over the network topology via sampling and neighborhood exploration in the form
of Markov chain Monte Carlo (MCMC) procedures. Given any Markov chain
corresponding to a target probability distribution, we design a self-repellent
random walk (SRRW) which is less likely to transition to nodes that were highly
visited in the past, and more likely to transition to seldom visited nodes. For
a class of SRRWs parameterized by a positive real {\alpha}, we prove that the
empirical distribution of the process converges almost surely to the the target
(stationary) distribution of the underlying Markov chain kernel. We then
provide a central limit theorem and derive the exact form of the arising
asymptotic co-variance matrix, which allows us to show that the SRRW with a
stronger repellence (larger {\alpha}) always achieves a smaller asymptotic
covariance, in the sense of Loewner ordering of co-variance matrices.
Especially for SRRW-driven MCMC algorithms, we show that the decrease in the
asymptotic sampling variance is of the order O(1/{\alpha}), eventually going
down to zero. Finally, we provide numerical simulations complimentary to our
theoretical results, also empirically testing a version of SRRW with {\alpha}
increasing in time to combine the benefits of smaller asymptotic variance due
to large {\alpha}, with empirically observed faster mixing properties of SRRW
with smaller {\alpha}.


  Integrating the brain structural and functional connectivity features is of
great significance in both exploring brain science and analyzing cognitive
impairment clinically. However, it remains a challenge to effectively fuse
structural and functional features in exploring the brain network. In this
paper, a novel brain structure-function fusing-representation learning (BSFL)
model is proposed to effectively learn fused representation from diffusion
tensor imaging (DTI) and resting-state functional magnetic resonance imaging
(fMRI) for mild cognitive impairment (MCI) analysis. Specifically, the
decomposition-fusion framework is developed to first decompose the feature
space into the union of the uniform and the unique spaces for each modality,
and then adaptively fuse the decomposed features to learn MCI-related
representation. Moreover, a knowledge-aware transformer module is designed to
automatically capture local and global connectivity features throughout the
brain. Also, a uniform-unique contrastive loss is further devised to make the
decomposition more effective and enhance the complementarity of structural and
functional features. The extensive experiments demonstrate that the proposed
model achieves better performance than other competitive methods in predicting
and analyzing MCI. More importantly, the proposed model could be a potential
tool for reconstructing unified brain networks and predicting abnormal
connections during the degenerative processes in MCI.


  Let $R\to A$ be a homomorphism of associative rings, and let $(\mathcal
F,\mathcal C)$ be a hereditary complete cotorsion pair in $R\mathsf{-Mod}$. Let
$(\mathcal F_A,\mathcal C_A)$ be the cotorsion pair in $A\mathsf{-Mod}$ in
which $\mathcal F_A$ is the class of all left $A$-modules whose underlying
$R$-modules belong to $\mathcal F$. Assuming that the $\mathcal F$-resolution
dimension of every left $R$-module is finite and the class $\mathcal F$ is
preserved by the coinduction functor $\operatorname{Hom}_R(A,-)$, we show that
$\mathcal C_A$ is the class of all direct summands of left $A$-modules finitely
(co)filtered by $A$-modules coinduced from $R$-modules from $\mathcal C$.
Assuming that the class $\mathcal F$ is closed under countable products and
preserved by the functor $\operatorname{Hom}_R(A,-)$, we prove that $\mathcal
C_A$ is the class of all direct summands of left $A$-modules cofiltered by
$A$-modules coinduced from $R$-modules from $\mathcal C$, with the decreasing
filtration indexed by the natural numbers. A combined result, based on the
assumption that countable products of modules from $\mathcal F$ have finite
$\mathcal F$-resolution dimension bounded by $k$, involves cofiltrations
indexed by the ordinal $\omega+k$. The dual results also hold, provable by the
same technique going back to the author's monograph on semi-infinite
homological algebra arXiv:0708.3398. In addition, we discuss the $n$-cotilting
and $n$-tilting cotorsion pairs, for which we obtain better results using a
suitable version of a classical Bongartz-Ringel lemma. As an illustration of
the main results of the paper, we consider certain cotorsion pairs related to
the contraderived and coderived categories of curved DG-modules.


  This paper considers the geometry of $E_8$ from a Clifford point of view in
three complementary ways. Firstly, in earlier work, I had shown how to
construct the four-dimensional exceptional root systems from the 3D root
systems using Clifford techniques, by constructing them in the 4D even
subalgebra of the 3D Clifford algebra; for instance the icosahedral root system
$H_3$ gives rise to the largest (and therefore exceptional)
non-crystallographic root system $H_4$. Arnold's trinities and the McKay
correspondence then hint that there might be an indirect connection between the
icosahedron and $E_8$. Secondly, in a related construction, I have now made
this connection explicit for the first time: in the 8D Clifford algebra of 3D
space the $120$ elements of the icosahedral group $H_3$ are doubly covered by
$240$ 8-component objects, which endowed with a `reduced inner product' are
exactly the $E_8$ root system. It was previously known that $E_8$ splits into
$H_4$-invariant subspaces, and we discuss the folding construction relating the
two pictures. This folding is a partial version of the one used for the
construction of the Coxeter plane, so thirdly we discuss the geometry of the
Coxeter plane in a Clifford algebra framework. We advocate the complete
factorisation of the Coxeter versor in the Clifford algebra into exponentials
of bivectors describing rotations in orthogonal planes with the rotation angle
giving the correct exponents, which gives much more geometric insight than the
usual approach of complexification and search for complex eigenvalues. In
particular, we explicitly find these factorisations for the 2D, 3D and 4D root
systems, $D_6$ as well as $E_8$, whose Coxeter versor factorises as
$W=\exp(\frac{\pi}{30}B_C)\exp(\frac{11\pi}{30}B_2)\exp(\frac{7\pi}{30}B_3)\exp(\frac{13\pi}{30}B_4)$.


  Single Co atoms, which exhibit a Kondo effect on Cu(111), are contacted with
Cu and Fe tips in a low-temperature scanning tunneling microscope. With Fe
tips, the Kondo effect persists with the Abrikosov-Suhl resonance significantly
broadened. In contrast, for Cu-covered W tips, the resonance width remains
almost constant throughout the tunneling and contact ranges. The distinct
changes of the line width are interpreted in terms of modifications of the Co d
state occupation owing to hybridization with the tip apex atoms.


  We report on the first cross section measurements for charged current
coherent pion production by neutrinos and antineutrinos on argon. These
measurements are performed using the ArgoNeuT detector exposed to the NuMI beam
at Fermilab. The cross sections are measured to be
$2.6^{+1.2}_{-1.0}(stat)^{+0.3}_{-0.4}(syst) \times 10^{-38}
\textrm{cm}^{2}/\textrm{Ar}$ for neutrinos at a mean energy of $9.6$ GeV and
$5.5^{+2.6}_{-2.1}(stat)^{+0.6}_{-0.7}(syst) \times 10^{-39}
\textrm{cm}^{2}/\textrm{Ar}$ for antineutrinos at a mean energy of $3.6$ GeV.


  We consider trends resulting from two formation mechanisms for short-period
super-Earths: planet-planet scattering and migration. We model scenarios where
these planets originate near the snow line in ``cold finger'' circumstellar
disks. Low-mass planet-planet scattering excites planets to low periastron
orbits only for lower mass stars. With long circularisation times, these
planets reside on long-period eccentric orbits. Closer formation regions mean
planets that reach short-period orbits by migration are most common around
low-mass stars. Above ~1 Solar mass, planets massive enough to migrate to
close-in orbits before the gas disk dissipates are above the critical mass for
gas giant formation. Thus, there is an upper stellar mass limit for
short-period super-Earths that form by migration. If disk masses are
distributed as a power law, planet frequency increases with metallicity because
most disks have low masses. For disk masses distributed around a relatively
high mass, planet frequency decreases with increasing metallicity. As icy
planets migrate, they shepherd interior objects toward the star, which grow to
~1 Earth mass. In contrast to icy migrators, surviving shepherded planets are
rocky. Upon reaching short-period orbits, planets are subject to evaporation
processes. The closest planets may be reduced to rocky or icy cores. Low-mass
stars have lower EUV luminosities, so the level of evaporation decreases with
decreasing stellar mass.


  Let $p(\cdot):\ \mathbb{R}^n\to(0,\infty]$ be a variable exponent function
satisfying the globally log-H\"{o}lder continuous condition and $A$ a general
expansive matrix on $\mathbb{R}^n$. Let $H_A^{p(\cdot)}(\mathbb{R}^n)$ be the
variable anisotropic Hardy space associated with $A$ defined via the
non-tangential grand maximal function. In this article, via the known atomic
characterization of $H_A^{p(\cdot)}(\mathbb{R}^n)$, the author establishes its
molecular characterization with the known best possible decay of molecules. As
an application, the author obtains a criterion on the boundedness of linear
operators on $H_A^{p(\cdot)}(\mathbb{R}^n)$, which is used to prove the
boundedness of anisotropic Calder\'on-Zygmund operators on
$H_A^{p(\cdot)}(\mathbb{R}^n)$. In addition, the boundedness of anisotropic
Calder\'on-Zygmund operators from $H_A^{p(\cdot)}(\mathbb{R}^n)$ to the
variable Lebesgue space $L^{p(\cdot)}(\mathbb{R}^n)$ is also presented. All
these results are new even in the classical isotropic setting.


  We propose a computational method that simplifies drastically the inclusion
of spin-orbit interaction in density functional theory implemented on localised
atomic orbital basis sets. Our method is based on a well-known procedure for
obtaining pseudopotentials from atomic relativistic 'ab initio' calculations
and on an on-site approximation for the spin-orbit matrix elements. We have
implemented the technique in the SIESTA code, and we show that it provides
accurate results for the overall band structure and splittings of group IV and
III-IV semiconductors as well as for 5d metals.


  Bethe Ansatz solutions of the open spin-1/2 integrable XXZ quantum spin chain
at roots of unity with nondiagonal boundary terms containing two free boundary
parameters have recently been proposed. We use these solutions to compute the
boundary energy (surface energy) in the thermodynamic limit.


  In approximate nearest neighbor search (ANNS) methods based on approximate
proximity graphs, DiskANN achieves good recall-speed balance for large-scale
datasets using both of RAM and storage. Despite it claims to save memory usage
by loading compressed vectors by product quantization (PQ), its memory usage
increases in proportion to the scale of datasets. In this paper, we propose
All-in-Storage ANNS with Product Quantization (AiSAQ), which offloads the
compressed vectors to storage. Our method achieves $\sim$10 MB memory usage in
query search even with billion-scale datasets with minor performance
degradation. AiSAQ also reduces the index load time before query search, which
enables the index switch between muitiple billion-scale datasets and
significantly enhances the flexibility of retrieval-augmented generation (RAG).
This method is applicable to all graph-based ANNS algorithms and can be
combined with higher-spec ANNS methods in the future.


  We develop a framework for learning properties of quantum states beyond the
assumption of independent and identically distributed (i.i.d.) input states. We
prove that, given any learning problem (under reasonable assumptions), an
algorithm designed for i.i.d. input states can be adapted to handle input
states of any nature, albeit at the expense of a polynomial increase in copy
complexity. Furthermore, we establish that algorithms which perform
non-adaptive incoherent measurements can be extended to encompass non-i.i.d.
input states while maintaining comparable error probabilities. This allows us,
among others applications, to generalize the classical shadows of Huang, Kueng,
and Preskill to the non-i.i.d. setting at the cost of a small loss in
efficiency. Additionally, we can efficiently verify any pure state using
Clifford measurements, in a way that is independent of the ideal state. Our
main techniques are based on de Finetti-style theorems supported by tools from
information theory. In particular, we prove a new randomized local de Finetti
theorem that can be of independent interest.


  A wide range of reinforcement learning (RL) problems - including robustness,
transfer learning, unsupervised RL, and emergent complexity - require
specifying a distribution of tasks or environments in which a policy will be
trained. However, creating a useful distribution of environments is error
prone, and takes a significant amount of developer time and effort. We propose
Unsupervised Environment Design (UED) as an alternative paradigm, where
developers provide environments with unknown parameters, and these parameters
are used to automatically produce a distribution over valid, solvable
environments. Existing approaches to automatically generating environments
suffer from common failure modes: domain randomization cannot generate
structure or adapt the difficulty of the environment to the agent's learning
progress, and minimax adversarial training leads to worst-case environments
that are often unsolvable. To generate structured, solvable environments for
our protagonist agent, we introduce a second, antagonist agent that is allied
with the environment-generating adversary. The adversary is motivated to
generate environments which maximize regret, defined as the difference between
the protagonist and antagonist agent's return. We call our technique
Protagonist Antagonist Induced Regret Environment Design (PAIRED). Our
experiments demonstrate that PAIRED produces a natural curriculum of
increasingly complex environments, and PAIRED agents achieve higher zero-shot
transfer performance when tested in highly novel environments.


  In this paper we study the Neumann system, which describes the harmonic
oscillator (of arbitrary dimension) constrained to the sphere. In particular we
will consider the confluent case where two eigenvalues of the potential
coincide, which implies that the system has S^{1} symmetry. We will prove
complete algebraic integrability of confluent Neumann system and show that its
flow can be linearized on the generalized Jacobian torus of some singular
algebraic curve. The symplectic reduction of S^{1} action will be described and
we will show that the general Rosochatius system is a symplectic quotient of
the confluent Neumann system, where all the eigenvalues of the potential are
double. This will give a new mechanical interpretation of the Rosochatius
system.


  We discuss the use of the Gilbert algorithm to tailor entanglement witnesses
for unextendibleproduct basis bound entangled states (UPB BE states). The
method relies on the fact that an optimalentanglement witness is given by a
plane perpendicular to a line between the reference state, entanglementof which
is to be witnessed, and its closest separable state (CSS). The Gilbert
algorithm finds anapproximation of CSS. In this article, we investigate if this
approximation can be good enough toyield a valid entanglement witness. We
compare witnesses found with Gilbert algorithm and those givenby
Bandyopadhyay-Ghosh-Roychowdhury (BGR) construction. This comparison allows us
to learnabout the amount of entanglement and we find a relationship between it
and a feature of the constructionof UPB BE states, namely the size of their
central tile. We show that in most studied cases, witnessesfound with the
Gilbert algorithm in this work are more optimal than ones obtained by
Bandyopadhyay,Ghosh, and Roychowdhury. This result implies the increased
tolerance to experimental imperfections ina realization of the state.


  We show by using a Discrete Element Method that a bilayer of vibrated
granular bidisperse spheres exhibits the striking feature that the horizontal
velocity distribution of the top layer particles has a quasi-Gaussian shape,
whereas that of the bottom layer is far from Gaussian. We examine in detail the
relevance of all physical parameters (acceleration of the bottom plate, mass
ratio, layer coverage). Moreover, a microscopic analysis of the trajectories
and the collision statistics reveal how the mechanism of randomization.


  There is great interest in "saliency methods" (also called "attribution
methods"), which give "explanations" for a deep net's decision, by assigning a
"score" to each feature/pixel in the input. Their design usually involves
credit-assignment via the gradient of the output with respect to input.
Recently Adebayo et al. [arXiv:1810.03292] questioned the validity of many of
these methods since they do not pass simple *sanity checks* which test whether
the scores shift/vanish when layers of the trained net are randomized, or when
the net is retrained using random labels for inputs.
  We propose a simple fix to existing saliency methods that helps them pass
sanity checks, which we call "competition for pixels". This involves computing
saliency maps for all possible labels in the classification task, and using a
simple competition among them to identify and remove less relevant pixels from
the map. The simplest variant of this is "Competitive Gradient $\odot$ Input
(CGI)": it is efficient, requires no additional training, and uses only the
input and gradient. Some theoretical justification is provided for it
(especially for ReLU networks) and its performance is empirically demonstrated.


  Following numerous earlier studies, extensive simulations and analyses were
made on the continuous interaction distribution Gaussian model and the discrete
bimodal interaction distribution Ising Spin Glass (ISG) models in dimension two
(P.H. Lundow and I.A. Campbell, Phys. Rev. E {\bf 93}, 022119 (2016)). Here we
further analyse the bimodal and Gaussian data together with data on two other
continuous interaction distribution 2D ISG models, the uniform and the
Laplacian models, and three other discrete interaction distribution models, a
diluted bimodal model, an "anti-diluted" model, and a more exotic symmetric
Poisson model. Comparisons between the three continuous distribution models
show that not only do they share the same exponent $\eta \equiv 0$ but that to
within the present numerical precision they share the same critical exponent
$\nu$ also, and so lie in a single universality class. On the other hand the
critical exponents of the four discrete distribution models are not the same as
those of the continuous distributions, and differ from one discrete
distribution model to another. Discrete distribution ISG models in dimension
two have non-zero values of the critical exponent $\eta$; they do not lie in a
single universality class.


  Split-complex fields usually appear in the context of Euclidean
supersymmetry. In this paper, we propose that this can be generalized to the
non-Euclidean case and that, in fact, the split-complex representation may be
the most natural way to formulate the scalar fields of the five dimensional
universal hypermultiplet. We supplement earlier evidence of this by studying a
specific class of solutions and explicitly showing that it seems to favor this
formulation. We also argue that this is directly related to the symplectic
structure of the general hypermultiplet fields arising from non-trivial
Calabi-Yau moduli. As part of the argument, we find new explicit instanton and
3-brane solutions coupled to the four scalar fields of the universal
hypermultiplet.


  Foundation models (FMs) have revolutionized computer vision, enabling
effective learning across different domains. However, their performance under
domain shift is yet underexplored. This paper investigates the zero-shot domain
adaptation potential of FMs by comparing different backbone architectures and
introducing novel domain-aware components that leverage domain related textual
embeddings. We propose domain adaptive normalization, termed as Domino, which
explicitly leverages domain embeddings during fine-tuning, thus making the
model domain aware. Ultimately, Domino enables more robust computer vision
models that can adapt effectively to various unseen domains.


  By applying Slater's transformation formulas for the bilateral basic
hypergeometric series ${}_2\psi_{2}$, we derive three type translation formulas
for the generalized Zwegers' $\mu$-function (``continuous $q$-Hermite
function'') which was introduced by Shibukawa--Tsuchimi (SIGMA, 2023). From
some Bailey's transformation formula of ${}_2\psi_{2}$, we also give a formula
for the expression of the generalized Zwegers' $\mu$-function by some
very-well-poised bilateral basic hypergeometric series ${}_4\psi_{8}$. As an
application of this new expression formula for the generalized Zwegers'
$\mu$-function, we obtain some new Fourier expansions for the Weierstrass and
Jacobi elliptic functions.


  In this paper, we continue to explore the consistence and usability of
Probability Bracket Notation (PBN) proposed in our previous articles. After a
brief review of PBN with dimensional analysis, we investigate probability
spaces in terms of PBN by introducing probability spaces associated with random
variables (R.V) or associated with stochastic processes (S.P). Next, we express
several important properties of conditional expectation (CE) and some their
proofs in PBN. Then, we introduce martingales based on sequence of R.V or based
on filtration in PBN. In the process, we see PBN can be used to investigate
some probability problems, which otherwise might need explicit usage of Measure
theory. Whenever applicable, we use dimensional analysis to validate our
formulas and use graphs for visualization of concepts in PBN. We hope this
study shows that PBN, stimulated by and adapted from Dirac notation in Quantum
Mechanics (QM), may have the potential to be a useful tool in probability
modeling, at least for those who are already familiar with Dirac notation in
QM.


  Using VLT/SINFONI, we have obtained repeated AO-assisted, NIR spectroscopy of
the three central WN6ha stars in the core of the very young (~1 Myr), massive
and dense Galactic cluster NGC3603. One of these stars, NGC3603-A1, is a known
3.77-day, double-eclipsing binary, while another one, NGC3603-C, is one of the
brightest X-ray sources among all known Galactic WR stars, which usually is a
strong indication for binarity. Our study reveals that star C is indeed an
8.9-day binary, although only the WN6ha component is visible in our spectra;
therefore we temporarily classify star C as an SB1 system. A1, on the other
hand, is found to consist of two emission-line stars of similar, but not
necessarily of identical spectral type, which can be followed over most the
orbit. Using radial velocities for both components and the previously known
inclination angle of the system, we are able to derive absolute masses for both
stars in A1. We find M_1 = (116 \pm 31) Mo for the primary and M_2 = (89 \pm
16) Mo for the secondary component of A1. While uncertainties are large, A1 is
intrinsically half a magnitude brighter than WR20a, the current record holder
with 83 and 82 Mo, respectively; therefore, it is likely that the primary in A1
is indeed the most massive star weighed so far.


  Electron microdiffraction study of phase transition in La2/3Ca1/3MnO3
revealed temperature dependent (h+1/2,0,l) diffraction spots. Their intensity
peaks at Tc. Quantitative electron diffraction intensity analysis shows that
they come from nanometer-sized domains with modulated transverse atomic
displacements in the orthorhombic a-c plane, which has two types of Mn ions and
thus charge ordering. The average domain is ~3.6 nm in diameter and ~1.5 nm in
height (along the b-axis). The number of domains increases and then decreases,
as the sample is cooled through Tc.


  75As NMR measurements were performed as a function of temperature and doping
in (Eu1-xKx)Fe2As2 (x=0,0.38,0.5,0.7) samples. The large Eu2+ moments and their
fluctuations are found to dominate the 75As NMR properties. The 75As nuclei
close to the Eu2+ moments likely have a very short spin-spin relaxation time
(T2) and are wiped out of our measurement window. The 75As nuclei relatively
far from Eu2+ moments are probed in this study. Increasing the Eu content
progressively decreases the signal intensity with no signal found for the
full-Eu sample (x=0). The large 75As NMR linewidth arises from an inhomogeneous
magnetic environment around them. The spin lattice relaxation rate (1/T1) for
x=0.5 and 0.7 samples is nearly independent of temperature above 100K and
results from a coupling to paramagnetic fluctuations of the Eu2+ moments. The
behavior of 1/T1 at lower temperatures has contributions from the
antiferromagnetic fluctuations of the Eu2+ moments as also the fluctuations
intrinsic to the FeAs planes and from superconductivity.


  A photonics-assisted microwave pulse detection and frequency measurement
scheme is proposed. The unknown microwave pulse is converted to the optical
domain and then injected into a fiber loop for pulse replication, which makes
it easier to identify the microwave pulse with large pulse repetition interval
(PRI), whereas stimulated Brillouin scattering-based frequency-to-time mapping
(FTTM) is utilized to measure the carrier frequency of the microwave pulse. A
sweep optical carrier is generated and modulated by the unknown microwave pulse
and a continuous-wave single-frequency reference, generating two different
frequency sweep optical signals, which are combined and used as the probe wave
to detect a fixed Brillouin gain spectrum. When the optical signal is detected
in a photodetector, FTTM is realized and the frequency of the microwave pulse
can be determined. An experiment is performed. For a fiber loop containing a
210-m fiber, pulse replication and FTTM of the pulses with a PRI of 20 {\mu}s
and pulse width of 1.20, 1.00, 0.85, and 0.65 {\mu}s are realized. Under a
certain sweep frequency chirp rate of 0.978 THz/s, the measurement errors are
below {\pm}12 and {\pm}5 MHz by using one pair of pulses and multiple pairs of
pulses, respectively. The influence of the sweep frequency chirp rate and pulse
width on the measurement error has also been studied. To a certain extent, the
faster the frequency sweep, the greater the frequency measurement error. For a
specific sweep frequency chirp rate, the measurement error is almost unaffected
by the pulse width to be measured.


  We study the time evolution of ranking and spectral properties of the Google
matrix of English Wikipedia hyperlink network during years 2003 - 2011. The
statistical properties of ranking of Wikipedia articles via PageRank and
CheiRank probabilities, as well as the matrix spectrum, are shown to be
stabilized for 2007 - 2011. A special emphasis is done on ranking of Wikipedia
personalities and universities. We show that PageRank selection is dominated by
politicians while 2DRank, which combines PageRank and CheiRank, gives more
accent on personalities of arts. The Wikipedia PageRank of universities
recovers 80 percents of top universities of Shanghai ranking during the
considered time period.


  Generative AI has ushered in the ability to generate content that closely
mimics human contributions, introducing an unprecedented threat: Deployed en
masse, these models can be used to manipulate public opinion and distort
perceptions, resulting in a decline in trust towards digital platforms. This
study contributes to marketing literature and practice in three ways. First, it
demonstrates the proficiency of AI in fabricating disinformative user-generated
content (UGC) that mimics the form of authentic content. Second, it quantifies
the disruptive impact of such UGC on marketing research, highlighting the
susceptibility of analytics frameworks to even minimal levels of
disinformation. Third, it proposes and evaluates advanced detection frameworks,
revealing that standard techniques are insufficient for filtering out
AI-generated disinformation. We advocate for a comprehensive approach to
safeguarding marketing research that integrates advanced algorithmic solutions,
enhanced human oversight, and a reevaluation of regulatory and ethical
frameworks. Our study seeks to serve as a catalyst, providing a foundation for
future research and policy-making aimed at navigating the intricate challenges
at the nexus of technology, ethics, and marketing.


  With the increase in adoption of Electric Vehicles (EVs), proper utilization
of the charging infrastructure is an emerging challenge for service providers.
Overstaying of an EV after a charging event is a key contributor to low
utilization. Since overstaying is easily detectable by monitoring the power
drawn from the charger, managing this problem primarily involves designing an
appropriate "penalty" during the overstaying period. Higher penalties do
discourage overstaying; however, due to uncertainty in parking duration, less
people would find such penalties acceptable, leading to decreased utilization
(and revenue). To analyze this central trade-off, we develop a novel framework
that integrates models for realistic user behavior into queueing dynamics to
locate the optimal penalty from the points of view of utilization and revenue,
for different values of the external charging demand. Next, when the model
parameters are unknown, we show how an online learning algorithm, such as UCB,
can be adapted to learn the optimal penalty. Our experimental validation, based
on charging data from London, shows that an appropriate penalty can increase
both utilization and revenue while significantly reducing overstaying.


  We obtain a closed form expression of the universal T-matrix encapsulating
the duality of the quantum superalgebra U_q[osp(1/2)] and the corresponding
supergroup OSp_q(1/2). The classical q-->1 limit of this universal T-matrix
yields the group element of the undeformed OSp(1/2) supergroup. The finite
dimensional representations of the quantum supergroup OSp_q(1/2) are readily
constructed employing the said universal T-matrix and the known finite
dimensional representations of the dually related deformed U_q[osp(1/2)]
superalgebra. Proceeding further, we derive the product law, the recurrence
relations and the orthogonality of the representations of the quantum
supergroup OSp_q(1/2). It is shown that the entries of these representation
matrices are expressed in terms of the little Q-Jacobi polynomials with Q = -q.
Two mutually complementary singular maps of the universal T-matrix on the
universal R-matrix are also presented.


  In this paper, we undertake a systematic model and valuation theoretic study
of the class of ordered fields which are dense in their real closure. We apply
this study to determine definable henselian valuations on ordered fields, in
the language of ordered rings. In light of our results, we re-examine the
Shelah-Hasson Conjecture (specialised to ordered fields) and provide an example
limiting its valuation theoretic conclusions.


  In special relativity, spacetime algebra (STA) provides a powerful and
insightful approach to an invariant formulation of physics. However, in this
geometric algebra of spacetime, relativistic physics is usually considered a
misnomer: STA provides us with an invariant (coordinate-free) formulation and
hence it seems that (passive) Lorentz transformations are misplaced. However,
in order to interpret experimental results, it is important to relate invariant
physical quantities to some reference frame. In this paper, passive Lorentz
transformations are derived using STA but without the second postulate on the
speed of light used by Einstein. This derivation sheds light on the physical
background of STA and, at the same time, clarifies Lorentz transformations in
the proper setting of (Minkowski) four-dimensional spacetime.


  We search for Milky Way-like galaxies among a sample of approximately 500
galaxies. The characteristics we considered of the candidate galaxies are the
following: stellar mass M_star, optical radius R_25, rotation velocity V_rot,
central oxygen abundance (O/H)_0, and abundance at the optical radius
(O/H)_R25. If the values of R_25 and M_star of the galaxy were close to that of
the Milky Way, then the galaxy was referred to as a structural Milky Way
analogue (sMWA). The oxygen abundance at a given radius of a galaxy is defined
by the evolution of that region, and we then assumed that the similarity of
(O/H)_0 and (O/H)_R25 in two galaxies suggests a similarity in their evolution.
If the values of (O/H)_0 and (O/H)_R25 in the galaxy were close to that of the
Milky Way, then the galaxy was referred to as an evolutionary Milky Way
analogue (eMWA). If the galaxy was simultaneously an eMWA and sMWA, then the
galaxy was considered a Milky Way twin. We find that the position of the Milky
Way on the (O/H)_0 - (O/H)_R25 diagram shows a large deviation from the general
trend in the sense that the (O/H)_R25 in the Milky Way is appreciably lower
than in other galaxies of similar (O/H)_0. This feature of the Milky Way
evidences that its (chemical) evolution is not typical. We identify four
galaxies (NGC~3521, NGC~4651, NGC~2903, and MaNGA galaxy M-8341-09101) that are
simultaneously sMWA and eMWA and can therefore be considered as Milky Way
twins. In previous studies, Milky Way-like galaxies were selected using
structural and morphological characteristics, that is, sMWAs were selected. We
find that the abundances at the centre and at the optical radius (evolutionary
characteristics) provide a stricter criterion for selecting real Milky Way
twins


  We describe a construction of preimages for the Shimura map on Hilbert
modular forms using generalized theta series, and give an explicit Waldspurger
type formula relating their Fourier coefficients to central values of twisted
$L$-functions. This formula extends our previous work, allowing to compute
these central values when the main central value vanishes.


  We present the fundamentals of a measure transport approach to sampling. The
idea is to construct a deterministic coupling---i.e., a transport map---between
a complex "target" probability measure of interest and a simpler reference
measure. Given a transport map, one can generate arbitrarily many independent
and unweighted samples from the target simply by pushing forward reference
samples through the map. We consider two different and complementary scenarios:
first, when only evaluations of the unnormalized target density are available,
and second, when the target distribution is known only through a finite
collection of samples. We show that in both settings the desired transports can
be characterized as the solutions of variational problems. We then address
practical issues associated with the optimization--based construction of
transports: choosing finite-dimensional parameterizations of the map, enforcing
monotonicity, quantifying the error of approximate transports, and refining
approximate transports by enriching the corresponding approximation spaces.
Approximate transports can also be used to "Gaussianize" complex distributions
and thus precondition conventional asymptotically exact sampling schemes. We
place the measure transport approach in broader context, describing connections
with other optimization--based samplers, with inference and density estimation
schemes using optimal transport, and with alternative transformation--based
approaches to simulation. We also sketch current work aimed at the construction
of transport maps in high dimensions, exploiting essential features of the
target distribution (e.g., conditional independence, low-rank structure). The
approaches and algorithms presented here have direct applications to Bayesian
computation and to broader problems of stochastic simulation.


  There is no denying the fact that with the widespread usage of computers and
the Internet in our daily lives, security of information and data has gained
increased attention. Information stored in electronic form is more susceptible
to being leaked to unauthorized individuals intentionally or without intent.
One of the major reasons for this breach of security has been attributed to
proprietary software whose source is available only to the company which made
it. Thus you have no surety that the proprietary and pre-compiled software has
no hole to help an individual break security of your computer or network.
Philosophy of free and open source software as against this provides everyone
an opportunity to view the source code for any possible vulnerabilities and
compile and change it according to ones need. This paper discusses this
philosophy in length with some examples and also some open source tools that
help maintain computer and Internet security.


  Quantum information contained in single-particle states can be masked by
mapping them to entangled states. In this paper, we consider entanglement
swapping under the masking of quantum information. Our work can pave the way
for developing the applications of quantum information masking schemes in
entanglement-swappingbased quantum cryptography.


  Supersymmetry, a new symmetry that relates bosons and fermions in particle
physics, still escapes observation. Search for SUSY is one of the main aims of
the recently launched Large Hadron Collider. The other possible manifestation
of SUSY is the Dark Matter in the Universe. The present lectures contain a
brief introduction to supersymmetry in particle physics. The main notions of
supersymmetry are introduced. The supersymmetric extension of the Standard
Model - the Minimal Supersymmetric Standard Model - is considered in more
detail. Phenomenological features of the MSSM as well as possible experimental
signatures of SUSY at the LHC are described. The DM problem and its possible
SUSY solution is presented.


  Using the strain-dependent effective Hamiltonian and the geometric phase,
Droth et al. [Phys. Rev. B 94, 075404 (2016)] obtain an analytical expression
for the electronic contribution to the piezoelectricity of planar hexagonal
boron nitride (h -BN). Their analytical results of piezoelectric constants for
h -BN are invalid because of the mistakes in constructing the adiabatic process
of the piezoelectricity. In this comment, we reconstruct a proper adiabatic
process for piezoelectricity and formulate a general Berry phase expression for
the piezoelectric coefficients of two-dimensional piezoelectric crystals by
means of the modern theory of polarization. The corrected analytical results of
the piezoelectric constants are in complete consistency with the
first-principles calculations and hence manifest the validity and generality of
the Berry phase expression of piezoelectric coefficients.


  SrTiO$_3$, although a wide gap insulator, has long been known to become
metallic and superconducting at extremely low doping levels. This has given
rise to questions concerning the coexistence or interdependence of metallicity,
superconductivity, and the material's polar properties. This issue becomes
especially intriguing in conjunction with the observation that filamentary
metallicity can be induced by means of resistive switching at conditions well
below relevant doping levels for homogeneous metallicity. In this study, we
demonstrate that resistive switching can also be employed to generate
superconductivity at the superconducting transition temperature of $T_c$
$\approx$ 0.2 K in SrTiO$_3$. By combining local characterization of the
conductivity with theoretical analysis, we propose that the superconducting
properties are associated with the electro-formation of columnar-like bundles
with a diameter of 40-50 nm, consisting of metallic filaments surrounded by
polar regions. We provide a theoretical model identifying the coexistence of
metallic and polar regions as a prerequisite for the filamentary-like
superconductivity observed.


  Recent monocular human performance capture approaches have shown compelling
dense tracking results of the full body from a single RGB camera. However,
existing methods either do not estimate clothing at all or model cloth
deformation with simple geometric priors instead of taking into account the
underlying physical principles. This leads to noticeable artifacts in their
reconstructions, e.g. baked-in wrinkles, implausible deformations that
seemingly defy gravity, and intersections between cloth and body. To address
these problems, we propose a person-specific, learning-based method that
integrates a simulation layer into the training process to provide for the
first time physics supervision in the context of weakly supervised deep
monocular human performance capture. We show how integrating physics into the
training process improves the learned cloth deformations, allows modeling
clothing as a separate piece of geometry, and largely reduces cloth-body
intersections. Relying only on weak 2D multi-view supervision during training,
our approach leads to a significant improvement over current state-of-the-art
methods and is thus a clear step towards realistic monocular capture of the
entire deforming surface of a clothed human.


  In this paper, we address the segmentation of tumor subtypes in whole slide
images (WSI) by utilizing incomplete label proportions. Specifically, we
utilize `partial' label proportions, which give the proportions among tumor
subtypes but do not give the proportion between tumor and non-tumor. Partial
label proportions are recorded as the standard diagnostic information by
pathologists, and we, therefore, want to use them for realizing the
segmentation model that can classify each WSI patch into one of the tumor
subtypes or non-tumor. We call this problem ``learning from partial label
proportions (LPLP)'' and formulate the problem as a weakly supervised learning
problem. Then, we propose an efficient algorithm for this challenging problem
by decomposing it into two weakly supervised learning subproblems: multiple
instance learning (MIL) and learning from label proportions (LLP). These
subproblems are optimized efficiently in the end-to-end manner. The
effectiveness of our algorithm is demonstrated through experiments conducted on
two WSI datasets.


  Let $F_m$ be a free group with $m$ generators and let $R$ be its normal
subgroup such that $F_m/R$ projects onto $\zz$. We give a lower bound for the
growth rate of the group $F_m/R'$ (where $R'$ is the derived subgroup of $R$)
in terms of the length $\rho=\rho(R)$ of the shortest nontrivial relation in
$R$. It follows that the growth rate of $F_m/R'$ approaches $2m-1$ as $\rho$
approaches infinity. This implies that the growth rate of an $m$-generated
amenable group can be arbitrarily close to the maximum value $2m-1$. This
answers an open question by P. de la Harpe. In fact we prove that such groups
can be found already in the class of abelian-by-nilpotent groups as well as in
the class of finite extensions of metabelian groups.


  Since Benjamini and Hochberg introduced false discovery rate (FDR) in their
seminal paper, this has become a very popular approach to the multiple
comparisons problem. An increasingly popular topic within functional data
analysis is local inference, i.e., the continuous statistical testing of a null
hypothesis along the domain. The principal issue in this topic is the infinite
amount of tested hypotheses, which can be seen as an extreme case of the
multiple comparisons problem. In this paper we define and discuss the notion of
false discovery rate in a very general functional data setting. Moreover, a
continuous version of the Benjamini-Hochberg procedure is introduced along with
a definition of adjusted p-value function. Some general conditions are stated,
under which the functional Benjamini-Hochberg procedure provides control of the
functional FDR. Two different simulation studies are presented; the first study
has a one-dimensional domain and a comparison with another state of the art
method, and the second study has a planar two-dimensional domain. Finally, the
proposed method is applied to satellite measurements of Earth temperature. In
detail, we aim at identifying the regions of the planet where temperature has
significantly increased in the last decades. After adjustment, large areas are
still significant.


  Detecting undesired process behavior is one of the main tasks of process
mining and various conformance-checking techniques have been developed to this
end. These techniques typically require a normative process model as input,
specifically designed for the processes to be analyzed. Such models are rarely
available, though, and their creation involves considerable manual
effort.However, reference process models serve as best-practice templates for
organizational processes in a plethora of domains, containing valuable
knowledge about general behavioral relations in well-engineered processes.
These general models can thus mitigate the need for dedicated models by
providing a basis to check for undesired behavior. Still, finding a perfectly
matching reference model for a real-life event log is unrealistic because
organizational needs can vary, despite similarities in process execution.
Furthermore, event logs may encompass behavior related to different reference
models, making traditional conformance checking impractical as it requires
aligning process executions to individual models. To still use reference models
for conformance checking, we propose a framework for mining declarative
best-practice constraints from a reference model collection, automatically
selecting constraints that are relevant for a given event log, and checking for
best-practice violations. We demonstrate the capability of our framework to
detect best-practice violations through an evaluation based on real-world
process model collections and event logs.


  We perform a sudden quench on the Haldane model with long range interactions,
more specifically generalising to the next to next nearest neighbour hopping,
referred to as the $N3$ model in our work. Such a model possesses both
isotropic and multiple anisotropic (satellite) Dirac points which lead to a
rich topological phase diagram consisting of phases with higher Chern number
($C$). Quenches between the topological and the non-topological phases of such
an infinite system probe the effect of the presence of the anisotropic Dirac
points on the non-equilibrium response of the topological system.
Interestingly, the Chern number remains the same before and after the quench
for both the quenching protocols, even when the quench of the system is carried
out between two different topological phases. {However, for a finite system, we
establish that the initial edge current asymptotically decays to zero when the
system is quenched to the non-topological phase although the Chern number for
the corresponding periodically wrapped system remains unaltered; what is
remarkable is that when the Hamiltonian is quenched from $|C|=2$ phase to the
non-topological phase the edge current associated with the inner channel decays
at a faster rate than the outer channel resembling a situation in which the
system passes through the phase with $|C|=1$ before ending up in the phase
$C=0$.


  We present an interrogation laser system for a transportable strontium
lattice clock operating at 698 nm, which is based on an ultra-low-expansion
glass reference cavity. Transportability is achieved by implementing a rigid,
compact, and vibration insensitive mounting of the 12 cm-long reference cavity,
sustaining shocks of up to 50 g. The cavity is mounted at optimized support
points that independently constrain all degrees of freedom. This mounting
concept is especially beneficial for cavities with a ratio of length $L$ over
diameter $D$ $L/D>1$. Generally large $L$ helps to reduce thermal noise-induced
laser frequency instability while small $D$ leads to small cavity volume. The
frequency instability was evaluated, reaching its thermal noise floor of
$\mathrm{mod}\,\sigma_{\rm y} \approx 3 \times 10^{-16}$ for averaging times
between 0.5 s and 10 s. The laser system was successfully operated during
several field studies.


  Inspired by traditional handmade crafts, where a person improvises assemblies
based on the available objects, we formally introduce the Craft Assembly Task.
It is a robotic assembly task that involves building an accurate representation
of a given target object using the available objects, which do not directly
correspond to its parts. In this work, we focus on selecting the subset of
available objects for the final craft, when the given input is an RGB image of
the target in the wild. We use a mask segmentation neural network to identify
visible parts, followed by retrieving labelled template meshes. These meshes
undergo pose optimization to determine the most suitable template. Then, we
propose to simplify the parts of the transformed template mesh to primitive
shapes like cuboids or cylinders. Finally, we design a search algorithm to find
correspondences in the scene based on local and global proportions. We develop
baselines for comparison that consider all possible combinations, and choose
the highest scoring combination for common metrics used in foreground maps and
mask accuracy. Our approach achieves comparable results to the baselines for
two different scenes, and we show qualitative results for an implementation in
a real-world scenario.


  Specialized computational chemistry packages have permanently reshaped the
landscape of chemical and materials science by providing tools to support and
guide experimental efforts and for the prediction of atomistic and electronic
properties. In this regard, electronic structure packages have played a special
role by using first-principledriven methodologies to model complex chemical and
materials processes. Over the last few decades, the rapid development of
computing technologies and the tremendous increase in computational power have
offered a unique chance to study complex transformations using sophisticated
and predictive many-body techniques that describe correlated behavior of
electrons in molecular and condensed phase systems at different levels of
theory. In enabling these simulations, novel parallel algorithms have been able
to take advantage of computational resources to address the polynomial scaling
of electronic structure methods. In this paper, we briefly review the NWChem
computational chemistry suite, including its history, design principles,
parallel tools, current capabilities, outreach and outlook.


  Migration of animal cells is based on the interplay between actin
polymerization at the front, adhesion along the cell-substrate interface, and
actomyosin contractility at the back. Active gel theory has been used before to
demonstrate that actomyosin contractility is sufficient for polarization and
self-sustained cell migration in the absence of external cues, but did not
consider the dynamics of adhesion. Likewise, migration models based on the
mechanosensitive dynamics of adhesion receptors usually do not include the
global dynamics of intracellular flow. Here we show that both aspects can be
combined in a minimal active gel model for one-dimensional cell migration with
dynamic adhesion. This model demonstrates that load sharing between the
adhesion receptors leads to symmetry breaking, with stronger adhesion at the
front, and that bistability of migration arises for intermediate adhesiveness.
Local variations in adhesiveness are sufficient to switch between sessile and
motile states, in qualitative agreement with experiments.


  For closed odd-dimensional manifolds with sectional curvature less or equal
than -1, we define the minimal surface entropy that counts the number of
surface subgroups. It attains the minimum if and only if the metric is
hyperbolic. Moreover, we compute the entropy associated with other locally
symmetric spaces and cusped hyperbolic 3-manifolds.


  While age of Information (AoI) has gained importance as a metric
characterizing the fresh-ness of information in information-update systems and
time-critical applications, most previous studies on AoI have been theoretical.
In this chapter, we compile a set of recent works reporting API measurements in
real-life networks and experimental testbeds, and investigating practical
issues such as synchronization, the role of various transport layer protocols,
congestion control mechanisms, application of machine learning for adaptation
to network conditions, and device related bottlenecks such as limited
processing power.


  In this study, we have comprehensively investigated the scaling law for
elastic properties of three-dimensional honeycomb-like graphenes (3D-graphenes)
using hybrid neural network potential based molecular dynamics simulations and
theoretical analyses. The elastic constants as functions of honeycomb hole
size, denoted by the graphene wall length $L$, were provided. All five
independent elastic constants in the large $L$ limit are proportional to
$L^{-1}$. The associated coefficients are combinations of two-dimensional
graphene's elastic constants. High-order terms including $L^{-2}$ and $L^{-3}$
emerge for finite $L$ values. They have three origins, the distorted areas
close to the joint lines of 3D-graphenes, the variation of solid angles between
graphene plates, and the bending distortion of graphene plates. Significantly,
the chirality becomes essential with the decreasing of $L$, because the joint
line structures are different between the armchair and zigzag type
3D-graphenes. Our findings provide insights into the elastic properties of
graphene-based superstructures and can be used for further studies on
graphene-based materials.


  Deep learning has played a major role in the interpretation of dermoscopic
images for detecting skin defects and abnormalities. However, current deep
learning solutions for dermatological lesion analysis are typically limited in
providing probabilistic predictions which highlights the importance of
concerning uncertainties. This concept of uncertainty can provide a confidence
level for each feature which prevents overconfident predictions with poor
generalization on unseen data. In this paper, we propose an overall framework
that jointly considers dermatological classification and uncertainty estimation
together. The estimated confidence of each feature to avoid uncertain feature
and undesirable shift, which are caused by environmental difference of input
image, in the latent space is pooled from confidence network. Our qualitative
results show that modeling uncertainties not only helps to quantify model
confidence for each prediction but also helps classification layers to focus on
confident features, therefore, improving the accuracy for dermatological lesion
classification. We demonstrate the potential of the proposed approach in two
state-of-the-art dermoscopic datasets (ISIC 2018 and ISIC 2019).


  Feature attribution explains neural network outputs by identifying relevant
input features. The attribution has to be faithful, meaning that the attributed
features must mirror the input features that influence the output. One recent
trend to test faithfulness is to fit a model on designed data with known
relevant features and then compare attributions with ground truth input
features.This idea assumes that the model learns to use all and only these
designed features, for which there is no guarantee. In this paper, we solve
this issue by designing the network and manually setting its weights, along
with designing data. The setup, AttributionLab, serves as a sanity check for
faithfulness: If an attribution method is not faithful in a controlled
environment, it can be unreliable in the wild. The environment is also a
laboratory for controlled experiments by which we can analyze attribution
methods and suggest improvements.


  Zero-shot learning, the task of learning to recognize new classes not seen
during training, has received considerable attention in the case of 2D image
classification. However despite the increasing ubiquity of 3D sensors, the
corresponding 3D point cloud classification problem has not been meaningfully
explored and introduces new challenges. This paper extends, for the first time,
transductive Zero-Shot Learning (ZSL) and Generalized Zero-Shot Learning (GZSL)
approaches to the domain of 3D point cloud classification. To this end, a novel
triplet loss is developed that takes advantage of unlabeled test data. While
designed for the task of 3D point cloud classification, the method is also
shown to be applicable to the more common use-case of 2D image classification.
An extensive set of experiments is carried out, establishing state-of-the-art
for ZSL and GZSL in the 3D point cloud domain, as well as demonstrating the
applicability of the approach to the image domain.


  Blockchain is challenging the status quo of the central trust infrastructure
currently prevalent in the Internet towards a design principle that is
underscored by decentralization, transparency, and trusted auditability. In
ideal terms, blockchain advocates a decentralized, transparent, and more
democratic version of the Internet. Essentially being a trusted and
decentralized database, blockchain finds its applications in fields as varied
as the energy sector, forestry, fisheries, mining, material recycling, air
pollution monitoring, supply chain management, and their associated operations.
In this paper, we present a survey of blockchain-based network applications.
Our goal is to cover the evolution of blockchain-based systems that are trying
to bring in a renaissance in the existing, mostly centralized, space of network
applications. While re-imagining the space with blockchain, we highlight
various common challenges, pitfalls, and shortcomings that can occur. Our aim
is to make this work as a guiding reference manual for someone interested in
shifting towards a blockchain-based solution for one's existing use case or
automating one from the ground up.


  Let $G=SO(3,C)$, $\Gamma=SO(3,Z[i])$, $K=SO(3)$, and let $X$ be the locally
symmetric space $\Gamma\backslash G/K$. In this paper, we write down explicit
equations defining a fundamental domain for the action of $\Gamma$ on $G/K$.
The fundamental domain is well-adapted for studying the theory of
$\Gamma$-invariant functions on $G/K$. We write down equations defining a
fundamental domain for the subgroup $\Gamma_Z=SO(2,1)_Z$ of $\Gamma$ acting on
the symmetric space $G_{R}/K_R$, where $G_R$ is the split real form SO(2,1) of
$G$ and $K_R$ is its maximal compact subgroup SO(2). We formulate a simple
geometric relation between the fundamental domain of $\Gamma$ and $\Gamma_Z$ so
described. These fundamental domains are geared towards the detailed study of
the spectral theory of $X$ and the embedded subspace $X_R=\Gamma_Z\backslash
G_R/K_R$.}


  The grains immersed in plasma get eroded by the ions falling onto them. As a
consequence, they exhibit self-consistent mass fluctuations due to
perturbations in the plasma charging currents. The grain mass is then a
dynamical variable. The modifications in the plasma dielectric properties are
investigated and new ultra-low frequency modes are shown to exist in the
plasma.


  Quantum phase transitions are sudden changes in the ground-state wavefunction
of a many-body system that can occur as a control parameter such as a
concentration or a field strength is varied. They are driven purely by the
competition between quantum fluctuations and mutual interactions among
constituents of the system, not by thermal fluctuations; hence they can occur
even at zero temperature. Examples of quantum phase transitions in many-body
physics may be found in systems ranging from high-temperature superconductors
to topological insulators. A quantum phase transition usually can be
characterized by nonanalyticity/discontinuity in certain order parameters or
divergence of the ground state energy eigenvalue and/or its derivatives with
respect to certain physical quantities. Here in a circular one-dimensional spin
model with Heisenberg XY interaction and no magnetic field, we observe critical
phenomena for the $n_0=1/N\rightarrow0$ Mott insulator caused by a qualitative
change of the boundary condition. We demonstrate in the vicinity of the
transition point a sudden change in ground-state properties accompanied by an
avoided level-crossing between the ground and the first excited states.
Notably, our result links conventional quantum phase transitions to microscopic
boundary conditions, with significant implications for quantum information,
quantum control, and quantum computing.


  A power partial isometry (PPI) is an element $v$ of a $C^*$-algebra with the
property that every power $v^n$ is a partial isometry. The goal of this paper
is to identify the universal $C^*$-algebra generated by a PPI with (a slight
modification of) the algebra of the finite sections method for Toeplitz
operators with continuous generating function, as first described by Albrecht
B\"ottcher and Bernd Silbermann in 1983.


  Minimalist theories of complex systems are broadly of two kinds: mean-field
and axiomatic. So far all theories of complex properties absent from simple
systems and intrinsic to glasses are axiomatic. Stretched Exponential
Relaxation (SER) is the prototypical complex temporal property of glasses,
discovered by Kohlrausch 150 years ago, and now observed almost universally in
microscopically homogeneous, complex non-equilibrium materials, including
luminescent electronic (Coulomb) glasses. Critical comparison of alternative
axiomatic theories with both numerical simulations and experiments strongly
favors dynamical trap models over static percolative or energy landscape
models.
  PACS: 61.20.Lc; 67.40.Fd


  Pre-training a language model and then fine-tuning it for downstream tasks
has demonstrated state-of-the-art results for various NLP tasks. Pre-training
is usually independent of the downstream task, and previous works have shown
that this pre-training alone might not be sufficient to capture the
task-specific nuances. We propose a way to tailor a pre-trained BERT model for
the downstream task via task-specific masking before the standard supervised
fine-tuning. For this, a word list is first collected specific to the task. For
example, if the task is sentiment classification, we collect a small sample of
words representing both positive and negative sentiments. Next, a word's
importance for the task, called the word's task score, is measured using the
word list. Each word is then assigned a probability of masking based on its
task score. We experiment with different masking functions that assign the
probability of masking based on the word's task score. The BERT model is
further trained on MLM objective, where masking is done using the above
strategy. Following this standard supervised fine-tuning is done for different
downstream tasks. Results on these tasks show that the selective masking
strategy outperforms random masking, indicating its effectiveness.


  It is well known that charged particles stored in a Paul trap, one of the
most versatile tools in atomic and molecular physics, may undergo a phase
transition from a disordered cloud state to a geometrically well-ordered
crystalline state (the Wigner crystal). In this paper we show that the average
lifetime $\bar\tau_m$ of the metastable cloud state preceding the cloud
$\rightarrow$ crystal phase transition follows a powerlaw, $\bar\tau_m \sim
(\gamma-\gamma_c)^{-\beta}$, $\gamma>\gamma_c$, where $\gamma_c$ is the
critical value of the damping constant $\gamma$ at which the cloud
$\rightarrow$ crystal phase transition occurs. The critical exponent $\beta$
depends on the trap control parameter $q$, but is independent of the number of
particles $N$ stored in the trap and the trap control parameter $a$, which
determines the shape (oblate, prolate, or spherical) of the cloud. For
$q=0.15,0.20$, and $0.25$, we find $\beta=1.20\pm 0.03$, $\beta=1.61\pm 0.09$,
and $\beta=2.38\pm 0.12$, respectively. In addition we find that for given $a$
and $q$, the critical value $\gamma_c$ of the damping scales approximately like
$\gamma_c=C \ln [ \ln (N)] + D$ as a function of $N$, where $C$ and $D$ are
constants. Beyond their relevance for Wigner crystallization of nonneutral
plasmas in Paul traps and mini storage rings, we conjecture that our results
are also of relevance for the field of crystalline beams.


  Light scattered by amorphous thin-film optical coatings limits the
sensitivity of interferometric gravitational-wave detectors. We describe an
imaging scatterometer to assess the role that crystal growth during annealing
plays in this scatter.


  Inhomogeneous recombination can give rise to perturbations in the electron
number density which can be a factor of five larger than the perturbations in
baryon density. We do a thorough analysis of the second order anisotropies
generated in the cosmic microwave background (CMB) due to perturbations in the
electron number density. We show that solving the second order Boltzmann
equation for photons is equivalent to solving the first + second order
Boltzmann equations and then taking the second order part of the solution. We
find the approximate solution to the photon Boltzmann hierarchy in l modes and
show that the contributions from inhomogeneous recombination to the second
order monopole, dipole and quadrupole are numerically small. We also point out
that perturbing the electron number density in the first order tight coupling
and damping solutions for the monopole, dipole and quadrupole is not equivalent
to solving the second order Boltzmann equations for inhomogeneous
recombination. Finally we confirm our result in a previous paper that
inhomogeneous recombination gives rise to a local type non-Gaussianity
parameter f_{NL}~ -1. The signal to noise for the detection of the temperature
bispectrum generated by inhomogeneous recombination is ~ 1 for an ideal full
sky experiment measuring modes up to l_{max}=2500.


  We illustrate the use of the statistical method of moments for determining
the position and momentum distributions of a quantum object from the statistics
of a single measurement. The method is used for three different, though
related, models; the sequential measurement model, the Arthurs-Kelly model and
the eight-port homodyne detection model. In each case, the method of moments
gives the position and momentum distribution for a large class of initial
states, the relevant condition being the exponential boundedness of the
distributions.


  We study the time evolution of the one-loop diagram in Sen's rolling tachyon
background. We find that at least in the long cylinder case they grow rapidly
at late time, due to the exponential growth of the timelike oscillator terms in
the boundary state. This can also be interpreted as the virtual open string
pair creation in the decaying brane. This behavior indicates a breakdown of
this rolling tachyon solution at some point during the evolution. We also
discuss the closed string emission from this one-loop diagram, and the
evolution of a one-loop diagram connecting a decaying brane to a stable brane,
which is responsible for the physical open string creation on the stable brane.


  In this work, we propose a learning framework for identifying synapses using
a deep and wide multi-scale recursive (DAWMR) network, previously considered in
image segmentation applications. We apply this approach on electron microscopy
data from invertebrate fly brain tissue. By learning features directly from the
data, we are able to achieve considerable improvements over existing techniques
that rely on a small set of hand-designed features. We show that this system
can reduce the amount of manual annotation required, in both acquisition of
training data as well as verification of inferred detections.


  For a family X of k-subsets of the set 1,...,n, let |X| be the cardinality of
X and let Gamma(X,mu) be the expected maximum weight of a subset from X when
the weights of 1,...,n are chosen independently at random from a symmetric
probability distribution mu on R. We consider the inverse isoperimetric problem
of finding mu for which Gamma(X,mu) gives the best estimate of ln|X|. We prove
that the optimal choice of mu is the logistic distribution, in which case
Gamma(X,mu) provides an asymptotically tight estimate of ln|X| as k^{-1}ln|X|
grows. Since in many important cases Gamma(X,mu) can be easily computed, we
obtain computationally efficient approximation algorithms for a variety of
counting problems. Given mu, we describe families X of a given cardinality with
the minimum value of Gamma(X,mu), thus extending and sharpening various
isoperimetric inequalities in the Boolean cube.


  Several large classes of homogeneous spaces are known to be formal---in the
sense of Rational Homotopy Theory. However, it seems that far fewer examples of
non-formal homogeneous spaces are known.
  In this article we provide several construction principles and
characterisations for non-formal homogeneous spaces, which will yield a lot of
examples. This will enable us to prove that, from dimension 72 on, such a space
can be found in each dimension.


  Binscatter is a popular method for visualizing bivariate relationships and
conducting informal specification testing. We study the properties of this
method formally and develop enhanced visualization and econometric binscatter
tools. These include estimating conditional means with optimal binning and
quantifying uncertainty. We also highlight a methodological problem related to
covariate adjustment that can yield incorrect conclusions. We revisit two
applications using our methodology and find substantially different results
relative to those obtained using prior informal binscatter methods. General
purpose software in Python, R, and Stata is provided. Our technical work is of
independent interest for the nonparametric partition-based estimation
literature.


  In this work, we present Dyna-5G, a dynamic, self-organizing 5G New Radio
(5G-NR) network designed for massive Machine-to-Machine (M2M) networks.
Traditional 5G NR networks, characterized by their centralized architecture,
face challenges in supporting applications that require dynamic, decentralized
communication, such as autonomous vehicles and drone swarms for emergency
responses. These scenarios often suffer from the centralized model's single
point of failure, undermining the reliability required in critical and fully
autonomous applications. Dyna-5G addresses these challenges by allowing each
device in the network to function as either part of the Radio Access Network
(RAN) and Core Network, or as User Equipment (UE), thus maintaining network
functionality even when conventional infrastructure components are compromised.
Dyna-5G has built-in mechanisms carefully designed specifically for M2M
networks, such as failure-recovery and ad-hoc entry and exit. We demonstrate
the performance and feasibility of Dyna-5G using a custom-built testbed that
simulates real-world missions, demonstrating our network's robustness,
adaptability, and failure recovery capabilities. The results indicate that our
entire 5G network model can fully re-organize in 6 seconds at maximum, without
compromising the mission.


  A decomposition of a simple graph $G$ is a pair $(G,P)$ where $P$ is a set of
subgraphs of $G$, which partitions the edges of $G$ in the sense that every
edge of $G$ belongs to exactly one subgraph in $P$. If the elements of $P$ are
induced subgraphs then the decomposition is denoted by $[G,P]$.
  A $k$-$P$-coloring of a decomposition $(G,P)$ is a surjective function that
assigns to the edges of $G$ a color from a $k$-set of colors, such that all
edges of $H\in P$ have the same color, and, if $H_1,H_2\in P$ with $V(H_1)\cap
V(H_2)\neq\emptyset$ then $E(H_1)$ and $E(H_2)$ have different colors. The
\emph{chromatic index} $\chi'((G,P))$ of a decomposition $(G,P)$ is the
smallest number $k$ for which there exists a $k$-$P$-coloring of $(G,P)$.
  The well-known Erd\"os-Faber-Lov\'asz Conjecture states that any
decomposition $[K_n,P]$ satisfies $\chi'([K_n,P])\leq n$. We use quasigroups
and complete digraphs to give a new family of decompositions that satisfy the
conjecture.


  The idea that all life on earth traces back to a common beginning dates back
at least to Charles Darwin's {\em Origin of Species}. Ever since, biologists
have tried to piece together parts of this `tree of life' based on what we can
observe today: fossils, and the evolutionary signal that is present in the
genomes and phenotypes of different organisms. Mathematics has played a key
role in helping transform genetic data into phylogenetic (evolutionary) trees
and networks. Here, I will explain some of the central concepts and basic
results in phylogenetics, which benefit from several branches of mathematics,
including combinatorics, probability and algebra.


  In this paper, we prove that if the area functional of a surface $\Sigma^2$
in a symplectic manifold $(M^{2n},\bar{\omega})$ has a critical point or has a
compatible stable point in the same cohomology class, then it must be
$J$-holomorphic. Inspired by a classical result of Lawson-Simons, we show how
various restrictions of the stability assumption to variations of metrics in
the space "projectively induced" metrics are enough to give the desired
conclusion.


  In this paper, we propose SUGAMAN (Supervised and Unified framework using
Grammar and Annotation Model for Access and Navigation). SUGAMAN is a Hindi
word meaning "easy passage from one place to another". SUGAMAN synthesizes
textual description from a given floor plan image for the visually impaired. A
visually impaired person can navigate in an indoor environment using the
textual description generated by SUGAMAN. With the help of a text reader
software, the target user can understand the rooms within the building and
arrangement of furniture to navigate. SUGAMAN is the first framework for
describing a floor plan and giving direction for obstacle-free movement within
a building. We learn $5$ classes of room categories from $1355$ room image
samples under a supervised learning paradigm. These learned annotations are fed
into a description synthesis framework to yield a holistic description of a
floor plan image. We demonstrate the performance of various supervised
classifiers on room learning. We also provide a comparative analysis of system
generated and human written descriptions. SUGAMAN gives state of the art
performance on challenging, real-world floor plan images. This work can be
applied to areas like understanding floor plans of historical monuments,
stability analysis of buildings, and retrieval.


  We study the p(e,e' pi+)n reaction in the framework of an effective
Lagrangian approach including nucleon, pi and rho meson degrees of freedom and
show the importance of the rho-meson t-pole contribution to sigmaT, the
transverse part of cross section. We test two different field representations
of the rho meson, vector and tensor, and find that the tensor representation of
the rho meson is more reliable in the description of the existing data. In
particular, we show that the rho-meson t-pole contribution, including the
interference with an effective non-local contact term, sufficiently improves
the description of the recent JLab data at invariant mass W less 2.2 GeV and Q2
less 2.5 GeV2/c2. A ``soft'' variant of the strong piNN and rhoNN form factors
is also found to be compatible with these data. On the basis of the successful
description of both the sigmaL and sigmaT parts of the cross section we discuss
the importance of taking into account the sigmaT data when extracting the
charge pion form factor Fpi from sigmaL.


  We present preliminary results of a bayesian fit to the Wilson coefficients
of the Standard Model gauge invariant dimension-6 operators involving one or
more Higgs fields, using data on electroweak precision observables and Higgs
boson signal strengths.


  Venus' mass and radius are similar to those of Earth. However,
dissimilarities in atmospheric properties, geophysical activity and magnetic
field generation could hint towards significant differences in the chemical
composition and interior evolution of the two planets. Although various
explanations for the differences between Venus and Earth have been proposed,
the currently available data are insufficient to discriminate among the
different solutions. Here we investigate the possible range of Venus structure
models. We assume that core segregation happened as a single-stage event. The
mantle composition is inferred from the core composition using a prescription
for metal-silicate partitioning. We consider three different cases for the
composition of Venus defined via the bulk Si and Mg content, and the core's S
content. Permissible ranges for the core size, mantle and core composition as
well as the normalized moment of inertia (MoI) are presented for these
compositions. A solid inner core could exist for all compositions. We estimate
that Venus' MoI is 0.317-0.351 and its core size 2930-4350 km for all assumed
compositions. Higher MoI values correspond to more oxidizing conditions during
core segregation. A determination of the abundance of FeO in Venus' mantle by
future missions could further constrain its composition and internal structure.
This can reveal important information on Venus' formation and evolution, and
possibly, the reasons for the differences between Venus and our home planet.


  We show that the form of the chiral condition found by Abanov et al., in the
quantum hydrodyamics of the Sutherland model arises because there are two
distinct inner products with respect to which the chiral Hamitonian hermitian,
but only one with respect to which the full, non-chiral, Hamiltonian is
hermitian.


  As the current initialization method in the state-of-the-art Stereo
Visual-Inertial SLAM framework, ORB-SLAM3 has limitations. Its success depends
on the performance of the pure stereo SLAM system and is based on the
underlying assumption that pure visual SLAM can accurately estimate the camera
trajectory, which is essential for inertial parameter estimation. Meanwhile,
the further improved initialization method for ORB-SLAM3, known as Stereo-NEC,
is time-consuming due to applying keypoint tracking to estimate gyroscope bias
with normal epipolar constraints. To address the limitations of previous
methods, this paper proposes a method aimed at enhancing translation accuracy
during the initialization stage. The fundamental concept of our method is to
improve the translation estimate with a 3 Degree-of-Freedom (DoF) Bundle
Adjustment (BA), independently, while the rotation estimate is fixed, instead
of using ORB-SLAM3's 6-DoF BA. Additionally, the rotation estimate will be
updated by considering IMU measurements and gyroscope bias, unlike ORB-SLAM3's
rotation, which is directly obtained from stereo visual odometry and may yield
inferior results when operating in challenging scenarios. We also conduct
extensive evaluations on the public benchmark, the EuRoC dataset, demonstrating
that our method excels in accuracy.


  We report the performance of a silicon wafer beamsplitter for use for low
$\Delta\nu>0.3 cm^{-1}$ resolution Fourier transform spectroscopy at far
infrared frequencies. We characterize the Si beamsplitter by comparing
throughput spectra measured with it to those measured with the standard Mylar
beamsplitters commonly used in that range. We find that the throughput of the
silicon beamsplitter is substantially greater than that of the Mylar
beamsplitters over most of the IR spectrum, and that they are comparable in
some limited ranges. The 2 mm silicon beamsplitter has an etalon spacing of
about 0.7 cm^{-1}, which interferes with its use for $0.1 cm^{-1}<\Delta\nu <
0.3cm^{-1}$. The average efficiency of the Si beamsplitter is 0.37 compared
with a maximum efficiency of 0.35 for Mylar. The Si is particularly more
efficient in the 100 to 400 cm^{-1} range because of absorption in Mylar.


  The Bell nonlocality and entanglement are two kinds of quantum correlations
in quantum systems. Due to the recent upgrade in Beijing Spectrometer III
(BESIII) experiment, it is possible to explore the nonlocality and entanglement
in hyperon-antihyperon systems produced in electron-positron annihilation with
high precision data. We provide a systematic method for studying quantum
correlations in spin-1/2 hyperon-antihyperon systems through the measures for
the nonlocality and entanglement. We find that with nonvanishing polarizations
of the hyperon and its antihyperon, the kinematic region of nonlocality in the
hyperon-antihyperon system is more restricted than the $\tau^{+}\tau^{-}$
system in which polarizations of $\tau$ leptons are vanishing. We also present
an experimental proposal to probe the nonlocality and entanglement in
hyperon-antihyperon systems at BSEIII.


  We prove new inequalities for the essential generalized and the essential
joint spectral radius of Hadamard (Schur) weighted geometric means of bounded
sets of infinite nonnegative matrices that define operators on suitable Banach
sequence spaces and of bounded sets of positive kernel operators on $L^2$. To
our knowledge the obtained inequalities are new even in the case of singelton
sets.


  We report on the 2.5 arcsec (400 pc) resolution CO (J = 1 -> 0) observations
covering the whole length of the bar in the strongly barred late-type spiral
galaxy NGC 7479. CO emission is detected only along a dust lane that traverses
the whole length of the bar, including the nucleus. The emission is strongest
in the nucleus. The distribution of emission is clumpy along the bar outside
the nucleus, and consists of gas complexes that are unlikely to be
gravitationally bound. The CO kinematics within the bar consist of two separate
components. A kinematically distinct circumnuclear disk, < 500 pc in diameter,
is undergoing predominantly circular motion with a maximum rotational velocity
of 245 km/s at a radius of 1 arcsec (160 pc). The CO-emitting gas in the bar
outside the circumnuclear disk has substantial noncircular motions which are
consistent with a large radial velocity component, directed inwards. The CO
emission has a large velocity gradient across the bar dust lane, ranging from
0.5 to 1.9 km/s/pc after correcting for inclination, and the projected velocity
change across the dust lane is as high as 200 km/s. This sharp velocity
gradient is consistent with a shock front at the location of the bar dust lane.
A comparison of H-alpha and CO kinematics across the dust lane shows that
although the H-alpha emission is often observed both upstream and downstream
from the dust lane, the CO emission is observed only where the velocity
gradient is large. We also compare the observations with hydrodynamic models
and discuss star formation along the bar.


  This paper is the second part of a work devoted to the modelling of thin
elastic plates with small, periodically distributed piezoelectric inclusions.
We consider the equations of linear elasticity coupled with the electrostatic
equation, with various kinds of electric boundary conditions. We derive the
corresponding effective models when the thickness $a$ of the plate and the
characteristic dimension $\varepsilon $ of the inclusions tend\ together to
zero, in the two following situations: first when $a \simeq \varepsilon$,
second when $a/\varepsilon$ tends to zero.


  Two very similar proposals have been made recently for witnessing
nonclassical features of gravity, by Bose et al. and by Marletto and Vedral.
However, while these proposals are asserted to be very general, they are in
fact based on a very strong claim: that quantum systems cannot become entangled
via a classical intermediary. We point out that the support provided for this
claim is only applicable to a very limited class of quantum-classical
interaction models, corresponding to Koopman-type dynamics. We show that the
claim is also valid for mean-field models, but that it is contradicted by
explicit counterexamples based on the configuration-ensemble model. Thus,
neither proposal provides a definitive test of nonclassical gravity.


  Suppose that $X\_{1}$ and $X\_{2}$ are two selfadjoint random variables that
are freely independent over an operator algebra $\mathcal{B}$. We describe the
possible operator atoms of the distribution of $X\_{1}+X\_{2}$ and, using
linearization, we determine the possible eigenvalues of an arbitrary polynomial
$p(X\_{1},X\_{2})$ in case $\mathcal{B}=\mathbb{C}$.