  In this paper, we analyse the rate of convergence of a system of $N$
interacting particles with mean-field rank based interaction in the drift
coefficient and constant diffusion coefficient. We first adapt arguments by
Kolli and Shkolnikhov to check trajectorial propagation of chaos with optimal
rate $N^{-1/2}$ to the associated stochastic differential equations nonlinear
in the sense of McKean. We next relax the assumptions needed by Bossy to check
convergence in $L^1(\mathbb{R})$ with rate ${\mathcal O}(\frac{1}{\sqrt N} +
h)$ of the empirical cumulative distribution function of the Euler
discretization with step $h$ of the particle system to the solution of a one
dimensional viscous scalar conservation law. Last, we prove that the bias of
this stochastic particle method behaves in ${\mathcal O}(\frac{1}{N} + h)$. We
provide numerical results which confirm our theoretical estimates.


  Quantitative theory of the Josephson effect in SFIFS junctions (S denotes
bulk superconductor, F - metallic ferromagnet, I - insulating barrier) is
presented in the dirty limit. Fully self-consistent numerical procedure is
employed to solve the Usadel equations at arbitrary values of the F-layers
thicknesses, magnetizations, and interface parameters. In the case of
antiparallel ferromagnets' magnetizations the effect of the critical current
enhancement by the exchange field is observed, while in the case of parallel
magnetizations the junction exhibits the transition to the pi-state. In the
limit of thin F layers, we study these peculiarities of the critical current
analytically and explain them qualitatively; the scenario of the 0-pi
transition in our case differs from those studied before. The effect of
switching between 0 and pi states by changing the F-layers' mutual orientation
is demonstrated.


  We investigated thermoelectric power $S(T)$ of MgB$_{2-x}$Be$_{x}$ ($x=0$,
0.2, 0.3, 0.4, and 0.6). $S(T)$ decreases systematically with $x$, suggesting
that the hole density increases. Our band calculation shows that the increase
occurs in the $\sigma $-band. With the hole-doping, $T_{c}$ decreases.
Implication of this phenomenon is discussed within the BCS framework. While the
Mott formula explains only the linear part of $S(T)$ at low temperature,
incorporation of electron-phonon interaction enables us to explain $S(T)$ over
wide temperature range including the anomalous behavior at high temperature.


  Consider a primitive polynomial $f$ in two variables, thought of as a map
from the affine plane to the affine line. We study the minimimal
compactification of $f$; from our result one deduces in particular that if one
of the fibers of $f$ has only one fiber at infinity, then all the fibers of $f$
have a simultaneous resolution of singularities at infinity. From this one gets
a very simple proof of the Suzuki-Abhyankar-Moh theorem on the embeddings of
the affine line in the plane.


  We construct a $15$-dimensional affine variety $\Pi_{\mathbb{A}}^{15}$ with a
${\rm GL}_{2}$- and $(\mathbb{C}^{*})^{4}$-actions. We denote by
$\Pi_{\mathbb{A}}^{14}$ the affine variety obtained from
$\Pi_{\mathbb{A}}^{15}$ by setting one specified variable to $1$ (we refer the
precise definition to Definition 1.1 of the paper). Let $\Pi_{\mathbb{P}}^{13}$
be several weighted projectivizations of $\Pi_{\mathbb{A}}^{14}$, and
$\Pi_{\mathbb{P}}^{14}$ the weighted cone over $\Pi_{\mathbb{P}}^{13}$ with a
weight one coordinate added. We show that $\Pi_{\mathbb{P}}^{13}$ or
$\Pi_{\mathbb{P}}^{14}$ produce, as weighted complete intersections, examples
of prime $\mathbb{Q}$-Fano threefolds of codimension four belonging to the
eight classes No.308, 501, 512, 550, 577, 872, 878, and 1766 of the graded ring
database. The construction of $\Pi_{\mathbb{A}}^{15}$ is based on a certain
type of unprojection and is inspired by R.Taylor's thesis submitted to
University of Warwick. We also show that a partial projectivization of
$\Pi_{\mathbb{A}}^{15}$ has a $\mathbb{P}^{2}\times\mathbb{P}^{2}$-fibration
over the affine space $\mathbb{A}^{10}$. To show this, we introduce another
$13$-dimensional affine variety $H_{\mathbb{A}}^{13}$ whose product with an
open subset of $\mathbb{A}^{2}$ is isomorphic to a sextic cover of an open
subset of $\Pi_{\mathbb{A}}^{15}$.


  We present two related Stata modules, r_ml_stata and c_ml_stata, for fitting
popular Machine Learning (ML) methods both in regression and classification
settings. Using the recent Stata/Python integration platform (sfi) of Stata 16,
these commands provide hyper-parameters' optimal tuning via K-fold
cross-validation using greed search. More specifically, they make use of the
Python Scikit-learn API to carry out both cross-validation and outcome/label
prediction.


  We prove that for every digraph $D$ and every choice of positive integers
$k$, $\ell$ there exists a digraph $D^*$ with girth at least $\ell$ together
with a surjective acyclic homomorphism $\psi\colon D^*\to D$ such that: (i) for
every digraph $C$ of order at most $k$, there exists an acyclic homomorphism
$D^*\to C$ if and only if there exists an acyclic homomorphism $D\to C$; and
(ii) for every $D$-pointed digraph $C$ of order at most $k$ and every acyclic
homomorphism $\varphi\colon D^*\to C$ there exists a unique acyclic
homomorphism $f\colon D\to C$ such that $\varphi=f\circ\psi$. This implies the
main results in [A. Harutyunyan et al., Uniquely $D$-colourable digraphs with
large girth, Canad. J. Math., 64(6) (2012), 1310-1328; MR2994666] analogously
with how the work [J. Ne\v{s}et\v{r}il and X. Zhu, On sparse graphs with given
colorings and homomorphisms, J. Combin. Theory Ser. B, 90(1) (2004), 161-172;
MR2041324] generalizes and extends [X. Zhu, Uniquely $H$-colorable graphs with
large girth, J. Graph Theory, 23(1) (1996), 33-41; MR1402136].


  Stars of late-M and L spectral types, collectively known as Ultracool Dwarfs
(UCDs), may be excellent targets for searches for extrasolar planets. Owing to
their small radii, the signal from an Earth-size planet transiting a UCD is, in
principle, readily detectable. We present results from a study designed to
evaluate the feasibility of using precise near infrared (NIR) photometry to
detect terrestrial extrasolar planets orbiting UCDs. We used the Peters
Automated InfRared Imaging TELescope (PAIRITEL) to observe a sample of 13 UCDs
over a period of 10 months. We consider several important systematic effects in
NIR differential photometry and develop techniques for generating photometry
with a precision of 0.01 mag and long-term stability. We simulate the planet
detection efficiency of an extended campaign to monitor a large sample of UCDs
with PAIRITEL. We find that both a targeted campaign with a single telescope
lasting several years and a campaign making use of a network of telescopes
distributed in longitude could provide significant sensitivity to terrestrial
planets orbiting UCDs, potentially in the habitable zone.


  The Fujita phenomenon for nonlinear parabolic problems dtu = \deltau + up in
an exterior domain of RN under the Robin boundary conditions is investigated in
the superlinear case. As in the case of Dirichlet boundary conditions, it turns
out that there exists a critical exponent p = 1+2/N such that blow-up of
positive solutions always occurs for subcritical exponents, whereas in the
supercritical case global existence can occur for small non-negative initial
data.


  We have investigated the single-pole nature of the detectable Lambda(1405) in
detail, by employing a chiral model having double poles of a KbarN-piSigma
coupled channel T-matrix. The effects of the 1st pole and the 2nd pole on the
observed piSigma mass spectrum in the Lambda(1405) region were analyzed
separately by means of the Generalized Optical Potential. It is concluded that
the 1st pole is responsible for both peak structures seen in the T(piSigma
leftarrow KbarN)(T(21)) and T(piSigma leftarrow piSigma)(T(22)) invariant-mass
spectra, and the 2nd pole due to an energy-dependent chiral interaction
provides continuum amplitudes affecting the shape of peak structures in
experimentally observable spectrum of the Lambda(1405).


  We present the analysis of two recently proposed noise reduction techniques,
Hutch++ and XTrace, both based on inexact deflation. These methods were proven
to have a better asymptotic convergence to the solution than the classical
Girard-Hutchinson stochastic method. We applied these methods to the
computation of the trace of the inverse of the Dirac operator with $O(a)$
improved Wilson fermions on the QCD ensemble generated by the RC$^{\star}$
collaboration with $m_{\pi}\approx 400$ MeV and $V = 64\times 32^3$.
Unfortunately, we see no noise reduction with a moderate number of sources, and
we attempt an explanation of why this is the case. This study was part of the
effort to evaluate isospin-breaking effects using the RM123 with C$^{\star}$
boundary conditions in an unquenched set-up.


  Chiral active fluids are known to have anomalous transport properties such as
the so-called odd viscosity. In this paper, we provide a microscopic mechanism
for how such anomalous transport coefficients can emerge. We construct an
Irving-Kirkwood-type stress tensor for chiral liquids and express the transport
coefficients in terms of orientation-averaged intermolecular forces and
distortions of the pair correlation function induced by a flow field. We then
show how anomalous transport properties can be expected naturally due to the
presence of a transverse component in the orientation-averaged intermolecular
forces and anomalous distortion modes of the pair correlation function between
chiral active particles. We anticipate that our work can provide a microscopic
framework to explain the transport properties of non-equilibrium chiral
systems.


  Large language models (LLMs) present a valuable technology for various
applications in healthcare, but their tendency to hallucinate introduces
unacceptable uncertainty in critical decision-making situations. Human-AI
collaboration (HAIC) can mitigate this uncertainty by combining human and AI
strengths for better outcomes. This paper presents a novel guided deferral
system that provides intelligent guidance when AI defers cases to human
decision-makers. We leverage LLMs' verbalisation capabilities and internal
states to create this system, demonstrating that fine-tuning small-scale LLMs
with data from large-scale LLMs greatly enhances performance while maintaining
computational efficiency and data privacy. A pilot study showcases the
effectiveness of our proposed deferral system.


  The dynamics of five dimensional Wilson line phases at finite temperature is
studied in the one-loop approximation. We show that at temperatures of order T
\sim 1/L, where L is the length of the compact space, the gauge symmetry is
always restored and the electroweak phase transition appears to be of first
order.
  Particular attention is devoted to the study of a recently proposed five
dimensional orbifold model (on S1/Z2) where the Wilson line phase is identified
with the Higgs field (gauge-Higgs unification). Interestingly enough, an
estimate of the leading higher-loop ``daisy'' (or ``ring'') diagram
contributions to the effective potential in a simple five dimensional model,
seems to suggest that the electroweak phase transition can be studied in
perturbation theory even for Higgs masses above the current experimental limit
of 114 GeV. The transition is still of first order for such values of the Higgs
mass. If large localized gauge kinetic terms are present, the transition might
be strong enough to give baryogenesis at the electroweak transition.


  Machine vision and image processing are often used with sensors for situation
awareness in autonomous systems, from industrial robots to self-driving cars.
The 3D depth sensors, such as LiDAR (Light Detection and Ranging), Radar, are
great invention for autonomous systems. Due to the complexity of the setup,
LiDAR may not be suitable for some operational environments, for example, a
space environment. This study was motivated by a desire to get real-time
volumetric and change information with multiple 2D cameras instead of a depth
camera. Two cameras were used to measure the dimensions of a rectangular object
in real-time. The R-C-P (row-column-pixel) method is developed using image
processing and edge detection. In addition to the surface areas, the R-C-P
method also detects discontinuous edges or volumes. Lastly, experimental work
is presented for illustration of the R-C-P method, which provides the equations
for calculating surface area dimensions. Using the equations with given
distance information between the object and the camera, the vision system
provides the dimensions of actual objects.


  Transport sector is in the process of being rapidly and fundamentally
reshaped by autonomous and collaborative driving technologies. This reshaping
promises huge economic and social benefits as well as challenges in terms of
developing and deploying secure and safe transportations systems, their smooth
integration to social fabric. We have employed Policy Scan and Technology
Strategy Design methodology in order to identify concrete societal expectations
and problems and map them with mitigating technological availabilities in the
domain of autonomous driving and smart mobility.
  Event Data Recorder for Autonomous Driving (EDR/AD) is an envisioned
subsystem of a vehicular Controller Area Network which ensures the
confidentiality, integrity and availability of data related to operation of a
vehicle in order to permit recovery of exact situation following the occurrence
of an event or on demand. The exact technical and regulatory requirements for
the device are still in the development internationally, but it is clear that
it will be included into vehicle type-approval requirements at UNECE level. We
present an analysis of the context of the usage of the EDR/AD in collaborative
intelligent transport systems, related security, data provenance and privacy,
other regulatory and technical issues considering many interest groups and
stakeholders involved. We present a concrete proposal for developing a EDR/AD
proof of the concept prototype with clear market deployment potential and urge
security researchers, vehicle manufacturers, and component suppliers to form a
collaboration towards implementing important technology for making future
autonomous vehicles more socially acceptable and legally compliant.
Furthermore, EDR/AD technology, apart from its immediate use in autonomous
driving and smart mobility domain has a potential to be extended to general
autonomous robot and AI applications.


  Compliance is a useful parametrization of tactile information that humans
often utilize in manipulation tasks. It can be used to inform low-level
contact-rich actions or characterize objects at a high-level. In robotic
manipulation, existing approaches to estimate compliance have struggled to
generalize across object shape and material. Using camera-based tactile
sensors, we present a novel approach to parametrize compliance through Young's
modulus E. We evaluate our method over a novel dataset of 285 common objects,
including a wide array of shapes and materials with Young's moduli ranging from
5.0 kPa to 250 GPa. Data is collected over automated parallel grasps of each
object. Combining analytical and data-driven approaches, we develop a hybrid
system using a multi-tower neural network to analyze a sequence of tactile
images from grasping. This system is shown to estimate the Young's modulus of
unseen objects within an order of magnitude at 74.2% accuracy across our
dataset. This is a drastic improvement over a purely analytical baseline, which
exhibits only 28.9% accuracy. Importantly, this estimation system performs
irrespective of object geometry and demonstrates robustness across object
materials. Thus, it could be applied in a general robotic manipulation setting
to characterize unknown objects and inform decision-making, for instance to
sort produce by ripeness.


  In cell-free massive multiple-input multiple-output (MIMO) the fluctuations
of the channel gain from the access points to a user are large due to the
distributed topology of the system. Because of these fluctuations, data
decoding schemes that treat the channel as deterministic perform inefficiently.
A way to reduce the channel fluctuations is to design a precoding scheme that
equalizes the effective channel gain seen by the users. Conjugate beamforming
(CB) poorly contributes to harden the effective channel at the users. In this
work, we propose a variant of CB dubbed enhanced normalized CB (ECB), in that
the precoding vector consists of the conjugate of the channel estimate
normalized by its squared norm. For this scheme, we derive an exact closed-form
expression for an achievable downlink spectral efficiency (SE), accounting for
channel estimation errors, pilot reuse and user's lack of channel state
information (CSI), assuming independent Rayleigh fading channels. We also
devise an optimal max-min fairness power allocation based only on large-scale
fading quantities. ECB greatly boosts the channel hardening enabling the users
to reliably decode data relying only on statistical CSI. As the provided
effective channel is nearly deterministic, acquiring CSI at the users does not
yield a significant gain.


  In this article, we evaluate determinants of block hook matrices, which are
block matrices consist of hook matrices. In particular, we deduce that the
determinant of a block hook matrix factorizes nicely. In addition we give a
combinatorial interpretation of the aforesaid factorization property by
counting weighted paths in a suitable weighted digraph.


  The supersymmetric SO(10) GUT based on the ${\bf{210\oplus 10\oplus 120\oplus
126\oplus {\bar {126}}}}$ Higgs system provides a minimal framework for the
emergence of the R-parity exact MSSM at low energies and a viable
supersymmetric seesaw explanation for the observed neutrino masses and mixing
angles. We present formulae for MSSM decomposition of the superpotential
invariants, tree level light charged fermion effective Yukawa couplings,
Weinberg neutrino mass generation operator, and the $d=5,\Delta B=\Delta L \neq
0$ effective superpotential in terms of GUT parameters. We use them to
determine fits of the 18 available fermion mass-mixing data in terms of the
superpotential parameters of the NMSGUT and SUGRY(NUHM) type soft supersymmetry
breaking parameters ($\{m_{\tilde f},m_{1/2},A_0,M^2_{H,\bar H}\} $) specified
at the MSSM one loop unification scale $M_X^0=10^{16.33} $ GeV. Our fits are
compatible with electroweak symmetry breaking and Unification constraints and
yield right-handed neutrino masses in the leptogenesis relevant range :
$10^8-10^{13} $ GeV. Matching the SM data requires lowering the strange and
down quark Yukawas in the MSSM via large $\tan\beta$ driven threshold
corrections and characteristic soft Susy breaking spectra. The Susy spectra
have light pure Bino LSP, heavy exotic Higgs(inos) and large $
\mu,A_0,M_{H,\bar{H}}$ parameters $\sim 100$ TeV. Typically third generation
sfermions are much \emph{heavier} than the first two generations. The smuon is
often the lightest charged sfermion thus offering a Bino-CDM co-annihilation
channel. The parameter sets obtained are used to calculate B violation rates
which are found to be generically much faster($\sim 10^{-28}\, yr^{-1}$) than
the current experimental limits. Improvements which may allow acceptable B
violation rates are identified.


  The rise of e-hailing taxis has significantly altered urban transportation
and resulted in a competitive taxi market with both traditional street-hailing
and e-hailing taxis. The new mobility services provide similar door-to-door
rides as the traditional one and there is competition across these various
services. In this study, we propose an innovative queueing network model for
the competitive taxi market and capture the interactions not only within the
taxi market but also between the taxi market and urban road system.
  An example is designed based on data from New York City. Numerical results
show that the proposed modeling structure, together with the corresponding
stationary limits, can capture dynamics within high demand areas using multiple
data sources. Overall, this study shows how the queueing network approach can
measure both the taxi and urban road system performance at an aggregate level.
The model can be used to estimate not only the waiting/searching time during
passenger-vehicle matching but also the delays in the urban road network.
Furthermore, the model can be generalized to study the control and management
of taxi markets.


  We study two standard multi-unit auction formats for allocating multiple
units of a single good to multi-demand bidders. The first one is the
Discriminatory Auction, which charges every winner his winning bids. The second
is the Uniform Price Auction, which determines a uniform price to be paid per
unit. Variants of both formats find applications ranging from the allocation of
state bonds to investors, to online sales over the internet, facilitated by
popular online brokers. For these formats, we consider two bidding interfaces:
(i) standard bidding, which is most prevalent in the scientific literature, and
(ii) uniform bidding, which is more popular in practice. In this work, we
evaluate the economic inefficiency of both multi-unit auction formats for both
bidding interfaces, by means of upper and lower bounds on the Price of Anarchy
for pure Nash equilibria and mixed Bayes-Nash equilibria. Our developments
improve significantly upon bounds that have been obtained recently in
[Markakis, Telelis, ToCS 2014] and [Syrgkanis, Tardos, STOC 2013] for
submodular valuation functions. Moreover, we consider for the first time
bidders with subadditive valuation functions for these auction formats. Our
results signify that these auctions are nearly efficient, which provides
further justification for their use in practice.


  Maximal $(k+1)$-crossing-free graphs on a planar point set in convex
position, that is, $k$-triangulations, have received attention in recent
literature, with motivation coming from several interpretations of them.
  We introduce a new way of looking at $k$-triangulations, namely as complexes
of star polygons. With this tool we give new, direct, proofs of the fundamental
properties of $k$-triangulations, as well as some new results. This
interpretation also opens-up new avenues of research, that we briefly explore
in the last section.


  We investigate the sensitivity to new physics of the process e+e- -> t bar{t}
when the top polarization is analyzed using leptonic final states e+e- -> t
\bar{t} -> l+l- b \bar{b} nu_l \bar{nu}_l. We first show that the kinematical
reconstruction of the complete kinematics is experimentally tractable for this
process. Then we apply the matrix element method to study the sensitivity to
the Vt\bar{t} coupling (V being a vector gauge boson), at the tree level and in
the narrow width approximation. Assuming the ILC baseline configuration,
sqrt{S}=500 GeV, and a luminosity of 500 fb^{-1}, we conclude that this optimal
analysis allows to determine simultaneously the ten form factors that
parameterize the Vt\bar{t} coupling, below the percent level. We also discuss
the effects of the next leading order (NLO) electroweak corrections using the
GRACE program with polarized beams. It is found that the NLO corrections to
different beam polarization lead to significantly different patterns of
contributions.


  Image2Speech is the relatively new task of generating a spoken description of
an image. This paper presents an investigation into the evaluation of this
task. For this, first an Image2Speech system was implemented which generates
image captions consisting of phoneme sequences. This system outperformed the
original Image2Speech system on the Flickr8k corpus. Subsequently, these
phoneme captions were converted into sentences of words. The captions were
rated by human evaluators for their goodness of describing the image. Finally,
several objective metric scores of the results were correlated with these human
ratings. Although BLEU4 does not perfectly correlate with human ratings, it
obtained the highest correlation among the investigated metrics, and is the
best currently existing metric for the Image2Speech task. Current metrics are
limited by the fact that they assume their input to be words. A more
appropriate metric for the Image2Speech task should assume its input to be
parts of words, i.e. phonemes, instead.


  We analyze the finite temperature phase diagram of fermion mixtures in
one-dimensional optical lattices as a function of interaction strength. At low
temperatures, the system evolves from an anisotropic three-dimensional
Bardeen-Cooper-Schrieffer (BCS) superfluid to an effectively two-dimensional
Berezinskii-Kosterlitz-Thouless (BKT) superfluid as the interaction strength
increases. We calculate the critical temperature as a function of interaction
strength, and identify the region where the dimensional crossover occurs for a
specified optical lattice potential. Finally, we show that the dominant vortex
excitations near the critical temperature evolve from multiplane elliptical
vortex loops in the three-dimensional regime to planar vortex-antivortex pairs
in the two-dimensional regime, and we propose a detection scheme for these
excitations.


  The study of networks has received increased attention recently not only from
the social sciences and statistics but also from physicists, computer
scientists and mathematicians. One of the principal problem in networks is
community detection. Many algorithms have been proposed for community finding
but most of them do not have have theoretical guarantee for sparse networks and
networks close to the phase transition boundary proposed by physicists. There
are some exceptions but all have some incomplete theoretical basis. Here we
propose an algorithm based on the graph distance of vertices in the network. We
give theoretical guarantees that our method works in identifying communities
for block models and can be extended for degree-corrected block models and
block models with the number of communities growing with number of vertices.
Despite favorable simulation results, we are not yet able to conclude that our
method is satisfactory for worst possible case. We illustrate on a network of
political blogs, Facebook networks and some other networks.


  We theoretically investigate the Carlson-Goldman (CG) mode in two-dimensional
clean d-wave superconductors using the effective ``phase only'' action
formalism. In conventional s-wave superconductors, it is known that the CG mode
is observed as a peak in the structure factor of the pair susceptibility
$S(\Omega, \mathbf{K})$ only just below the transition temperature T_c and only
in dirty systems. On the other hand, our analytical results support the
statement by Y.Ohashi and S.Takada, Phys.Rev.B {\bf 62}, 5971 (2000) that in
d-wave superconductors the CG mode can exist in clean systems down to the much
lower temperatures, $T \approx 0.1 T_c$. We also consider the manifestations of
the CG mode in the density-density and current-current correlators and discuss
the gauge independence of the obtained results.


  We prove the solvability of the parabolic $L^p$ Dirichlet boundary value
problem for $1 < p \leq \infty$ for a PDE of the form $u_t = \mbox{div} (A
\nabla u) + B \cdot \nabla u$ on time-varying domains where the coefficients
$A= [a_{ij}(X, t)]$ and $B=[b_i]$ satisfy a certain natural small Carleson
condition.
  This result brings the state of affairs in the parabolic setting up to the
elliptic standard.
  Furthermore, we establish that if the coefficients of the operator $A,\,B$
satisfy a vanishing Carleson condition and the time-varying domain is of VMO
type then the parabolic $L^p$ Dirichlet boundary value problem is solvable for
all $1 < p \leq \infty$.
  This result is related to results in papers by Maz\'ya, Mitrea and
Shaposhnikova, and Hofmann, Mitrea and Taylor where the fact that boundary of
domain has normal in VMO or near VMO implies invertibility of certain boundary
operators in $L^p$ for all $1 < p \leq \infty$ which then (using the method of
layer potentials) implies solvability of the $L^p$ boundary value problem in
the same range for certain elliptic PDEs.
  Our result does not use the method of layer potentials, since the
coefficients we consider are too rough to use this technique but remarkably we
recover $L^p$ solvability in the full range of $p$'s as the two papers
mentioned above.


  We have performed shell-model calculations of the half-lives and
neutron-branching probabilities of the r-process waiting point nuclei at the
magic neutron number N=82. These new calculations use a larger model space than
previous shell model studies and an improved residual interaction which is
adjusted to recent spectroscopic data around A=130. Our shell-model results
give a good account of all experimentally known half-lives and $Q_\beta$-values
for the N=82 r-process waiting point nuclei. Our half-life predictions for the
N=82 nuclei with Z=42--46 agree well with recent estimates based in the
energy-density functional method.


  The use of a band offset between the two leads of an electron pump driven by
a local oscillating voltage is shown to increase the pump current dramatically.
The structure of the electron transmission suggests the existence of dominant
inelastic channels which we call pipelines. This permits the formulation of a
simple model that gives a physical account of the numerical results for a
realistic device. A spectral analysis reveals the pump current to be carried by
scattering states with initial energy deep within the Fermi sea and not at its
surface, thereby rendering the effect insensitive to temperature. We show this
is compatible with the current flowing near the Fermi surface in the leads.


  A well-known result of R\"odl and Ruci\'nski states that for any graph $H$
there exists a constant $C$ such that if $p \geq C n^{- 1/m_2(H)}$, then the
random graph $G_{n,p}$ is a.a.s. $H$-Ramsey, that is, any $2$-colouring of its
edges contains a monochromatic copy of $H$. Aside from a few simple exceptions,
the corresponding $0$-statement also holds, that is, there exists $c>0$ such
that whenever $p\leq cn^{-1/m_2(H)}$ the random graph $G_{n,p}$ is a.a.s. not
$H$-Ramsey.
  We show that near this threshold, even when $G_{n,p}$ is not $H$-Ramsey, it
is often extremely close to being $H$-Ramsey. More precisely, we prove that for
any constant $c > 0$ and any strictly $2$-balanced graph $H$, if $p \geq c
n^{-1/m_2(H)}$, then the random graph $G_{n,p}$ a.a.s. has the property that
every $2$-edge-colouring without monochromatic copies of $H$ cannot be extended
to an $H$-free colouring after $\omega(1)$ extra random edges are added. This
generalises a result by Friedgut, Kohayakawa, R\"odl, Ruci\'nski and Tetali,
who in 2002 proved the same statement for triangles, and addresses a question
raised by those authors. We also extend a result of theirs on the three-colour
case and show that these theorems need not hold when $H$ is not strictly
$2$-balanced.


  Scientific Natural Language Inference (NLI) is the task of predicting the
semantic relation between a pair of sentences extracted from research articles.
The automatic annotation method based on distant supervision for the training
set of SciNLI (Sadat and Caragea, 2022b), the first and most popular dataset
for this task, results in label noise which inevitably degenerates the
performance of classifiers. In this paper, we propose a novel co-training
method that assigns weights based on the training dynamics of the classifiers
to the distantly supervised labels, reflective of the manner they are used in
the subsequent training epochs. That is, unlike the existing semi-supervised
learning (SSL) approaches, we consider the historical behavior of the
classifiers to evaluate the quality of the automatically annotated labels.
Furthermore, by assigning importance weights instead of filtering out examples
based on an arbitrary threshold on the predicted confidence, we maximize the
usage of automatically labeled data, while ensuring that the noisy labels have
a minimal impact on model training. The proposed method obtains an improvement
of 1.5% in Macro F1 over the distant supervision baseline, and substantial
improvements over several other strong SSL baselines. We make our code and data
available on Github.


  We derive the explicit form of the polar decomposition of the Wiener measure,
and obtain the equation connecting functional integrals in conformal quantum
mechanics to those in the Schwarzian theory. Using this connection we evaluate
some nontrivial functional integrals in the Schwarzian theory and also find the
fundamental solution of the Schroedinger equation in imaginary time in the
model of conformal quantum mechanics.


  We provide evidence that gallium purity is the primary impediment to
attainment of ultra-high mobility in a two-dimensional electron gas (2DEG) in
AlGaAs/GaAs heterostructures grown by molecular beam epitaxy (MBE). The purity
of gallium can be enhanced dramatically by in-situ high temperature outgassing
within an operating MBE. Based on analysis of data from an initial growth
campaign in a new MBE system and modifications employed for a 2nd growth
campaign, we have produced 2DEGs with low temperature mobility in excess of
35x10^6cm2/Vs at density n=3.0x10^11/cm2 and mobility 18x10^6cm2/Vs at
n=1.1x1011/cm2. Our 2nd campaign data indicate that gallium purity remains the
factor currently limiting mobility <40x10^6cm2/Vs. We describe strategies to
overcome this limitation.


  The computational modelling of DNA is becoming crucial in light of new
advances in DNA nanotechnology, single-molecule experiments and in vivo DNA
tampering. Here we present a mesoscopic model for double stranded DNA (dsDNA)
at the single nucleotide level which retains the characteristic helical
structure, while being able to simulate large molecules -- up to a million base
pairs -- for time-scales which are relevant to physiological processes. This is
made possible by an efficient and highly-parallelised implementation of the
model which we discuss here. We compare the behaviour of our model with single
molecule experiments where dsDNA is manipulated by external forces or torques.
We also present some results on the kinetics of denaturation of linear DNA.


  We present an efficient and realistic geometric acoustic simulation approach
for generating and augmenting training data in speech-related machine learning
tasks. Our physically-based acoustic simulation method is capable of modeling
occlusion, specular and diffuse reflections of sound in complicated acoustic
environments, whereas the classical image method can only model specular
reflections in simple room settings. We show that by using our synthetic
training data, the same neural networks gain significant performance
improvement on real test sets in far-field speech recognition by 1.58% and
keyword spotting by 21%, without fine-tuning using real impulse responses.


  This technical report presents our solution to the HACS Temporal Action
Localization Challenge 2021, Weakly-Supervised Learning Track. The goal of
weakly-supervised temporal action localization is to temporally locate and
classify action of interest in untrimmed videos given only video-level labels.
We adopt the two-stream consensus network (TSCN) as the main framework in this
challenge. The TSCN consists of a two-stream base model training procedure and
a pseudo ground truth learning procedure. The base model training encourages
the model to predict reliable predictions based on single modality (i.e., RGB
or optical flow), based on the fusion of which a pseudo ground truth is
generated and in turn used as supervision to train the base models. On the HACS
v1.1.1 dataset, without fine-tuning the feature-extraction I3D models, our
method achieves 22.20% on the validation set and 21.68% on the testing set in
terms of average mAP. Our solution ranked the 2nd in this challenge, and we
hope our method can serve as a baseline for future academic research.


  Transformer-based pre-training models like BERT have achieved remarkable
performance in many natural language processing tasks.However, these models are
both computation and memory expensive, hindering their deployment to
resource-constrained devices. In this work, we propose TernaryBERT, which
ternarizes the weights in a fine-tuned BERT model. Specifically, we use both
approximation-based and loss-aware ternarization methods and empirically
investigate the ternarization granularity of different parts of BERT. Moreover,
to reduce the accuracy degradation caused by the lower capacity of low bits, we
leverage the knowledge distillation technique in the training process.
Experiments on the GLUE benchmark and SQuAD show that our proposed TernaryBERT
outperforms the other BERT quantization methods, and even achieves comparable
performance as the full-precision model while being 14.9x smaller.


  Spectral measurements of the 21 cm monopole background have the promise of
revealing the bulk energetic properties and ionization state of our universe
from z ~ 6-30. Synchrotron foregrounds are orders of magnitude larger than the
cosmological signal, and are the principal challenge faced by these
experiments. While synchrotron radiation is thought to be spectrally smooth and
described by relatively few degrees of freedom, the instrumental response to
bright foregrounds may be much more complex. To deal with such complexities, we
develop an approach that discovers contaminated spectral modes using spatial
fluctuations of the measured data. This approach exploits the fact that
foregrounds vary across the sky while the signal does not. The discovered modes
are projected out of each line-of-sight of a data cube. An angular weighting
then optimizes the cosmological signal amplitude estimate by giving preference
to lower-noise regions. Using this method, we show that it is essential for the
passband to be stable to at least ~10^{-4}. In contrast, the constraints on the
spectral smoothness of the absolute calibration are mainly aesthetic if one is
able to take advantage of spatial information. To the extent it is understood,
controlling polarization to intensity leakage at the ~10^{-2} level will also
be essential to rejecting Faraday rotation of the polarized synchrotron
emission.


  We studied dipole excitations in $^{10}$Be based on an extended version of
the antisymmetrized molecular dynamics, which can describe 1p-1h excitations
and large amplitude cluster modes. Toroidal and compressive dipole operators
are found to be good proves to separate the low-energy and high-energy parts of
the isoscalar dipole excitations, respectively. Two low-energy $1^-$ states,
the toroidal dominant $1^-_1$ state at $E\sim 8$ MeV and the $E1$ dominant
$1^-_2$ state at $E\sim 16$ MeV, were obtained. By analysis of transition
current densities, the $1^-_1$ states is understood as a toroidal dipole mode
with exotic toroidal neutron flow caused by rotation of a deformed
$^6\textrm{He}$ cluster, whereas the $1^-_2$ state is regarded as a
neutron-skin oscillation mode, which are characterized by surface neutron flow
with inner isoscalar flow caused by the surface neutron oscillation against the
$2\alpha$ core.


  The lack of structure greater than 10 Gpc/h in Wilkinson Microwave Anisotropy
Probe (WMAP) observations of the cosmic microwave background (CMB) favours
compact Friedmann-Lemaitre-Robertson-Walker (FLRW) models of the Universe. The
present best candidates based on observations are the Poincare dodecahedral
space S^3/I^* and the 3-torus T^3. The residual gravity effect favours the
Poincare space, while a measure space argument where the density parameter is a
derived parameter favours flat spaces almost surely.


  It is shown that exactly 7 distance-transitive cubic graphs among the
existing 12 possess a particular ultrahomogeneous property with respect to
oriented cycles realizing the girth that allows the construction of a related
Cayley digraph with similar ultrahomogeneous properties in which those oriented
cycles appear minimally "pulled apart", or "separated" and whose description is
truly beautiful and insightful. This work is proposed as the initiation of a
study of similar ultrahomogeneous properties for distance-transitive graphs in
general with the aim of generalizing to constructions of similar related
"separator" Cayley digraphs.


  Quantum computing is among the most far-reaching technologies of the 21st
century, tackling challenges at the cutting edge of physics. This new paradigm
in computer science harnesses quantum entanglement, one striking non-intuitive
feature of quantum mechanics and a cornerstone of quantum information, to
provide computation with a quantum speed-up over the best-known classical
algorithms and to enable encrypted data communication against eavesdropping.
The bulk of this article is focused on providing a deep and abiding
understanding of non-relativistic matrix mechanics by demonstrating the
fundamental mathematical identities of the contemporary postulatory approach of
quantum mechanics within the state vector and density operator formalism in
multipartite systems. In addition to that, we derive and analyze the respective
1-qubit, 1-qutrit, 2-qubit, and 2-qudit coherent and incoherent density
operators using Bloch's parametrization for generalized $d$-dimensional
$N$-qudit states embedded in the $SU(d)$ Lie group with associate generalized
Gell Mann's matrices spanning the $\mathfrak{su}(d)$ Lie algebra. We also
address the fundamental concepts of quantum nondemolition measurements, quantum
decoherence and, particularly, quantum entanglement providing for the latter a
systematic view on its historical development and mathematical description in
multipartite systems. We conclude our review by introducing some of the
ubiquitous quantum quantifiers required to measure degrees of quantum
entanglement and quantum coherence, deriving the $p$-norm quantum coherence
measure for a 1-qubit state.


  We study the hydrodynamics of relativistic fluids with several conserved
global charges (i.e., several species of particles) by performing a
Kaluza-Klein dimensional reduction of a neutral fluid on a N-torus. Via
fluid/gravity correspondence, this allows us to describe the long-wavelength
dynamics of black branes with several Kaluza-Klein charges. We obtain the
equation of state and transport coefficients of the charged fluid directly from
those of the higher-dimensional neutral fluid. We specialize these results for
the fluids dual to Kaluza-Klein black branes.


  The purpose of these notes is to discuss the advances in the theory of
Lyapunov exponents of linear $\text{SL}_2(\mathbb{R})$ cocycles over hyperbolic
maps. The main focus is around results regarding the positivity of the Lyapunov
exponent and the regularity of this function with respect to the underlying
data.


  Within the effective Lagrangian framework, we explicitly evaluate the
partition function of two-dimensional ideal ferromagnets up to three loops at
low temperatures and in the presence of a weak external magnetic field. The
low-temperature series for the free energy density, energy density, heat
capacity, entropy density, as well as the magnetization are given and their
range of validity is critically examined in view of the Mermin-Wagner theorem.
The calculation involves the renormalization and numerical evaluation of a
particular three-loop graph which is discussed in detail. Interestingly, in the
low-temperature series for the two-dimensional ideal ferromagnet, the spin-wave
interaction manifests itself in the form of logarithmic terms. In the free
energy density the leading such term is of order $T^4 \ln T$ -- remarkably, in
the case of the three-dimensional ideal ferromagnet no logarithmic terms arise
in the low-temperature series. While the present study demonstrates that it is
straightforward to consider effects up to three-loop order in the effective
field theory framework, this precision seems to be far beyond the reach of
microscopic methods such as modified spin-wave theory.


  We give a combinatorial proof of a theorem first proved by Souto which says
the following. Let M_1 and M_2 be simple 3-manifolds with connected boundary of
genus g>0. If M_1 and M_2 are glued via a complicated map, then every minimal
Heegaard splitting of the resulting closed 3-manifold is an amalgamation. This
proof also provides an algorithm to find a bound on the complexity of the
gluing map.


  A recently explored interesting quantity in AdS/CFT, dubbed 'residual
entropy', characterizes the amount of collective ignorance associated with
either boundary observers restricted to finite time duration, or bulk observers
who lack access to a certain spacetime region. However, the previously-proposed
expression for this quantity involving variation of boundary entanglement
entropy (subsequently renamed to 'differential entropy') works only in a
severely restrictive context. We explain the key limitations, arguing that in
general, differential entropy does not correspond to residual entropy. Given
that the concept of residual entropy as collective ignorance transcends these
limitations, we identify two correspondingly robust, covariantly-defined
constructs: a 'strip wedge' associated with boundary observers and a 'rim
wedge' associated with bulk observers. These causal sets are well-defined in
arbitrary time-dependent asymptotically AdS spacetimes in any number of
dimensions. We discuss their relation, specifying a criterion for when these
two constructs coincide, and prove an inclusion relation for a general case. We
also speculate about the implications for residual entropy. Curiously, despite
each construct admitting a well-defined finite quantity related to the areas of
associated bulk surfaces, these quantities are not in one-to-one correspondence
with the defining regions of unknown. This has nontrivial implications about
holographic measures of quantum information.


  We provide a general treatment for the temporal coupled-mode theory with
arbitrary numbers of modes and ports, and derive tight bounds for the coupling
phases in addition to coupling strengths under time-reversal symmetry. We
report trade-offs between the cardinalities of the reciprocal regions of the
resonant coupling strengths versus phases. We discover that time-reversal
symmetry enforces projected generalized reflections in the background to cancel
out completely. In double-port systems, the reciprocal regions of the coupling
phases span a quarter of the nonreciprocal regions for any non-hidden mode.


  A C++ code for the solution of the relativistic Hartree-Bogoliubov theory in
coordinate space is presented. The theory describes a nucleus as a relativistic
system of baryons and mesons. The RHB model is applied in the self-consistent
mean-field approximation to the description of ground state properties of
spherical nuclei. Finite range interactions are included to describe pairing
correlations and the coupling to particle continuum states. Finite element
methods are used in the coordinate space discretization of the coupled system
of Dirac-Hartree-Bogoliubov integro-differential eigenvalue equations, and
Klein-Gordon equations for the meson fields. The bisection method is used in
the solution of the resulting generalized algebraic eigenvalue problem, and the
biconjugate gradient method for the systems of linear and nonlinear algebraic
equations, respectively.


  Face morphing attack detection is emerging as an increasingly challenging
problem owing to advancements in high-quality and realistic morphing attack
generation. Reliable detection of morphing attacks is essential because these
attacks are targeted for border control applications. This paper presents a
multispectral framework for differential morphing-attack detection (D-MAD). The
D-MAD methods are based on using two facial images that are captured from the
ePassport (also called the reference image) and the trusted device (for
example, Automatic Border Control (ABC) gates) to detect whether the face image
presented in ePassport is morphed. The proposed multispectral D-MAD framework
introduce a multispectral image captured as a trusted capture to acquire seven
different spectral bands to detect morphing attacks. Extensive experiments were
conducted on the newly created Multispectral Morphed Datasets (MSMD) with 143
unique data subjects that were captured using both visible and multispectral
cameras in multiple sessions. The results indicate the superior performance of
the proposed multispectral framework compared to visible images.


  A systematic study is made of the data dependence of the parameter
$A_{\rm{b}}$, that, since 1995, has shown a deviation from the Standard Model
prediction of between 2.4 and 3.1 standard deviations. Issues addressed
include: the effect of particular measurements, values found by individual
experiments, LEP/SLD comparison, and the treatment of systematic errors. The
effect, currently at the 2.4$\sigma$ level, is found to vary in the range from
1.7$\sigma$ to 2.9$\sigma$ by excluding marginal or particularly sensitive
data. Since essentially the full LEP and SLD Z decay data sets are now analysed
the meaning of the deviation, (new physics, or marginal statistical
fluctuation) is unlikely to be given by the present generation of colliders.


  The integration of topological concepts into electronic energy band theory
has been a transformative development in condensed matter physics. Since then,
this paradigm has broadened its reach, extending to a variety of physical
systems, including open ones. In this study, we employ analogues of the
generalized $n$-dimensional Su-Schrieffer-Heeger model, a cornerstone in
understanding topological insulators and higher-order topological states, to
unveil a dimensional hierarchy of topological states within thermal diffusive
networks. Unlike their electronic counterparts, the topological states in these
networks are characterized by confined temperature profiles of dimension
$(n-d)$ with constant diffusive rates, where $n$ represents the system's
dimension and $d$ is the order of the topological state. Our findings
demonstrate the existence of topological corner states in thermal diffusive
systems up to $n=3$, along with surface and hinge states. We also identify and
discuss an intermediate-order topological phase in the case $n=3$,
characterized by the presence of hinge states but the absence of corner states.
Furthermore, our work delves into the influence of chiral symmetry in these
thermal networks, particularly focusing on topological thermal states with a
near-zero diffusion rate. This research lays the foundation for advanced
thermal management strategies that utilize topological states in multiple
dimensions.


  The compression of highly repetitive strings (i.e., strings with many
repetitions) has been a central research topic in string processing, and quite
a few compression methods for these strings have been proposed thus far. Among
them, an efficient compression format gathering increasing attention is the
run-length Burrows--Wheeler transform (RLBWT), which is a run-length encoded
BWT as a reversible permutation of an input string on the lexicographical order
of suffixes. State-of-the-art construction algorithms of RLBWT have a serious
issue with respect to (i) non-optimal computation time or (ii) a working space
that is linearly proportional to the length of an input string. In this paper,
we present \emph{r-comp}, the first optimal-time construction algorithm of
RLBWT in BWT-runs bounded space. That is, the computational complexity of
r-comp is $O(n + r \log{r})$ time and $O(r\log{n})$ bits of working space for
the length $n$ of an input string and the number $r$ of equal-letter runs in
BWT. The computation time is optimal (i.e., $O(n)$) for strings with the
property $r=O(n/\log{n})$, which holds for most highly repetitive strings.
Experiments using a real-world dataset of highly repetitive strings show the
effectiveness of r-comp with respect to computation time and space.


  We present a theoretical analysis of the performance of transformer with
softmax attention in in-context learning with linear regression tasks. While
the existing literature predominantly focuses on the convergence of
transformers with single-/multi-head attention, our research centers on
comparing their performance. We conduct an exact theoretical analysis to
demonstrate that multi-head attention with a substantial embedding dimension
performs better than single-head attention. When the number of in-context
examples D increases, the prediction loss using single-/multi-head attention is
in O(1/D), and the one for multi-head attention has a smaller multiplicative
constant. In addition to the simplest data distribution setting, we consider
more scenarios, e.g., noisy labels, local examples, correlated features, and
prior knowledge. We observe that, in general, multi-head attention is preferred
over single-head attention. Our results verify the effectiveness of the design
of multi-head attention in the transformer architecture.


  We discuss the non-thermal phase structure of a chirally invariant
Higgs-Yukawa model on the lattice in the presence of a higher dimensional
$\Phi^6$-term. For the exploration of the phase diagram we use analytical,
lattice perturbative calculations of the constraint effectice potential as well
as numerical simulations. We also present first results of the effects of the
$\Phi^6$-term on the lower Higgs boson mass bounds.


  A subpopulation of neutron stars (NSs), known as central compact objects
(CCOs) in supernova remnants, are suspected to be low-field objects basing on
$P$-$\dot P$ measurements for three of them. The birth rate of low-field NSs is
probably comparable with the birth rate of normal radio pulsars. However, among
compact objects in High-Mass X-ray Binaries (HMXBs) we do not see robust
candidates for low-field NSs. We propose that this contradiction can be solved
if magnetic fields of CCOs was buried due to strong fall-back, and then the
field emerges on the time scale $10^4$-$10^5$ yrs.


  We survey a sample of 32 M5-M8 stars with distance < 40pc for companions with
separations between 0.1 arcsec and 1.5 arcsec and with Delta m_i <5. We find
five new VLM binaries with separations between 0.15 arcsec and 1.1 arcsec,
including a candidate brown dwarf companion. The raw binary fraction is 16%
+8/-4% and the distance bias corrected fraction is 7% +7/-3%, for companions
within the surveyed range. No systems with contrast ratio Delta m_i>1 were
found, even though our survey is sensitive to up to Delta m=5 (well into the
brown dwarf regime). The distribution of orbital radii is in broad agreement
with previous results, with most systems at 1-5AU, but one detected binary is
very wide at 46.8+/-5.0AU. We also serendipitously imaged for the first time a
companion to Ross 530, a metal-poor single-lined spectroscopic binary. We used
the new Lucky Imaging system LuckyCam on the 2.5m Nordic Optical Telescope to
complete the 32 very low mass star i' and z' survey in only 5 hours of
telescope time.


  Robotic systems are multi-dimensional entities, combining both hardware and
software, that are heavily dependent on, and influenced by, interactions with
the real world. They can be variously categorised as embedded, cyberphysical,
real-time, hybrid, adaptive and even autonomous systems, with a typical robotic
system being likely to contain all of these aspects. The techniques for
developing and verifying each of these system varieties are often quite
distinct. This, together with the sheer complexity of robotic systems, leads us
to argue that diverse formal techniques must be integrated in order to develop,
verify, and provide certification evidence for, robotic systems. Furthermore,
we propose the fast evolving field of robotics as an ideal catalyst for the
advancement of integrated formal methods research, helping to drive the field
in new and exciting directions and shedding light on the development of
large-scale, dynamic, complex systems.


  From a logical point of view, Stone duality for Boolean algebras relates
theories in classical propositional logic and their collections of models. The
theories can be seen as presentations of Boolean algebras, and the collections
of models can be topologized in such a way that the theory can be recovered
from its space of models. The situation can be cast as a formal duality
relating two categories of syntax and semantics, mediated by homming into a
common dualizing object, in this case 2. In the present work, we generalize the
entire arrangement from propositional to first-order logic. Boolean algebras
are replaced by Boolean categories presented by theories in first-order logic,
and spaces of models are replaced by topological groupoids of models and their
isomorphisms. A duality between the resulting categories of syntax and
semantics, expressed first in the form of a contravariant adjunction, is
established by homming into a common dualizing object, now $\Sets$, regarded
once as a boolean category, and once as a groupoid equipped with an intrinsic
topology. The overall framework of our investigation is provided by topos
theory. Direct proofs of the main results are given, but the specialist will
recognize toposophical ideas in the background. Indeed, the duality between
syntax and semantics is really a manifestation of that between algebra and
geometry in the two directions of the geometric morphisms that lurk behind our
formal theory. Along the way, we construct the classifying topos of a decidable
coherent theory out of its groupoid of models via a simplified covering theorem
for coherent toposes.


  Preference elicitation frameworks feature heavily in the research on
participatory ethical AI tools and provide a viable mechanism to enquire and
incorporate the moral values of various stakeholders. As part of the
elicitation process, surveys about moral preferences, opinions, and judgments
are typically administered only once to each participant. This methodological
practice is reasonable if participants' responses are stable over time such
that, all other relevant factors being held constant, their responses today
will be the same as their responses to the same questions at a later time.
However, we do not know how often that is the case. It is possible that
participants' true moral preferences change, are subject to temporary moods or
whims, or are influenced by environmental factors we don't track. If
participants' moral responses are unstable in such ways, it would raise
important methodological and theoretical issues for how participants' true
moral preferences, opinions, and judgments can be ascertained. We address this
possibility here by asking the same survey participants the same moral
questions about which patient should receive a kidney when only one is
available ten times in ten different sessions over two weeks, varying only
presentation order across sessions. We measured how often participants gave
different responses to simple (Study One) and more complicated (Study Two)
repeated scenarios. On average, the fraction of times participants changed
their responses to controversial scenarios was around 10-18% across studies,
and this instability is observed to have positive associations with response
time and decision-making difficulty. We discuss the implications of these
results for the efficacy of moral preference elicitation, highlighting the role
of response instability in causing value misalignment between stakeholders and
AI tools trained on their moral judgments.


  We present exact formulas for the entanglement and R\'{e}nyi entropies
generated at a quantum point contact (QPC) in terms of the statistics of charge
fluctuations, which we illustrate with examples from both equilibrium and
non-equilibrium transport. The formulas are also applicable to groundstate
entanglement in systems described by non-interacting fermions in any dimension,
which in one dimension includes the critical spin-1/2 XX and Ising models where
conformal field theory predictions for the entanglement and R\'{e}nyi entropies
are reproduced from the full counting statistics. These results may play a
crucial role in the experimental detection of many-body entanglement in
mesoscopic structures and cold atoms in optical lattices.


  We use the Bellman function method to give an elementary proof of a sharp
weighted estimate for the Haar shifts, which is linear in the $A_2$ norm of the
weight and in the complexity of the shift. Together with the representation of
a general Calder\'{o}n--Zygmund operator as a weighted average (over all dyadic
lattices) of Haar shifts, (cf. arXiv:1010.0755v2[math.CA],
arXiv:1007.4330v1[math.CA]) it gives a significantly simpler proof of the
so-called the $A_2$ conjecture.
  The main estimate is a very general fact about concave functions, which can
be very useful in other problems of martingale Harmonic Analysis. Concave
functions of such type appear as the Bellman functions for bounds on the
bilinear form of martingale multipliers, thus the main estimate allows for the
transference of the results for simplest possible martingale multipliers to
more general martingale transforms.
  Note that (although this is not important for the $A_2$ conjecture for
general Calder\'{o}n--Zygmund operators) this elementary proof gives the best
known (linear) growth in the complexity of the shift.


  An efficient 3D point cloud learning architecture, named EfficientLO-Net, for
LiDAR odometry is first proposed in this paper. In this architecture, the
projection-aware representation of the 3D point cloud is proposed to organize
the raw 3D point cloud into an ordered data form to achieve efficiency. The
Pyramid, Warping, and Cost volume (PWC) structure for the LiDAR odometry task
is built to estimate and refine the pose in a coarse-to-fine approach. A
projection-aware attentive cost volume is built to directly associate two
discrete point clouds and obtain embedding motion patterns. Then, a trainable
embedding mask is proposed to weigh the local motion patterns to regress the
overall pose and filter outlier points. The trainable pose warp-refinement
module is iteratively used with embedding mask optimized hierarchically to make
the pose estimation more robust for outliers. The entire architecture is
holistically optimized end-to-end to achieve adaptive learning of cost volume
and mask, and all operations involving point cloud sampling and grouping are
accelerated by projection-aware 3D feature learning methods. The superior
performance and effectiveness of our LiDAR odometry architecture are
demonstrated on KITTI, M2DGR, and Argoverse datasets. Our method outperforms
all recent learning-based methods and even the geometry-based approach, LOAM
with mapping optimization, on most sequences of KITTI odometry dataset. We open
sourced our codes at: https://github.com/IRMVLab/EfficientLO-Net.


  In this paper, we investigate the relationships among hypergeometric series,
truncated hypergeometric series, and Gaussian hypergeometric functions through
some families of `hypergeometric' algebraic varieties that are higher
dimensional analogues of Legendre curves.


  We investigate transmission protocols for relay-assisted free-space optical
(FSO) systems, when multiple parallel relays are employed and there is no
direct link between the source and the destination. As alternatives to
all-active FSO relaying, where all the available relays transmit concurrently,
we propose schemes that select only a single relay to participate in the
communication between the source and the destination in each transmission slot.
This selection is based on the channel state information (CSI) obtained either
from all or from some of the FSO links. Thus, the need for synchronizing the
relays' transmissions is avoided and the slowly varying nature of the
atmospheric channel is exploited. For both relay selection and all-active
relaying, novel closed-form expressions for their outage performance are
derived, assuming the versatile Gamma-Gamma channel model. Furthermore, based
on the derived analytical results, the problem of allocating the optical power
resources to the FSO links is addressed, and optimum and suboptimum solutions
are proposed. Numerical results are provided for equal and non-equal length FSO
links, which illustrate the outage behavior of the considered relaying
protocols and demonstrate the significant performance gains offered by the
proposed power allocation schemes.


  Valley lines on total-energy surfaces for the zone-center distortions of
free-standing and in-plane strained SrTiO3 are investigated with a newly
developed first-principles structure optimization technique [Jpn. J. Appl.
Phys. vol.43 (2004), p.6785]. The results of numerical calculations confirmed
that the ferroelectricity is induced, and the Curie temperature is increased,
by applying biaxial compressive or tensile strains. Along the distortion,
strong nonlinear coupling between the soft- and hard-modes is demonstrated.


  We find that the spin susceptibility of a two-dimensional electron system
with valley degeneracy does not grow critically at low densities, at variance
with experimental results [A. Shashkin et al., Phys. Rev. Lett. 96, 036403
(2006)]. We ascribe this apparent discrepancy to the weak disorder present in
experimental samples. Our prediction is obtained from accurate correlation
energies computed with state of-the-art diffusion Monte Carlo simulations and
fitted with an analytical expression which also provides a local spin density
functional for the system under investigation.


  We construct six-dimensional (1,0) superconformal models with non-abelian
gauge couplings for multiple tensor multiplets. A crucial ingredient in the
construction is the introduction of three-form gauge potentials which
communicate degrees of freedom between the tensor multiplets and the Yang-Mills
multiplet, but do not introduce additional degrees of freedom. Generically
these models provide only equations of motions. For a subclass also a
Lagrangian formulation exists, however it appears to exhibit indefinite metrics
in the kinetic sector. We discuss several examples and analyze the excitation
spectra in their supersymmetric vacua. In general, the models are
perturbatively defined only in the spontaneously broken phase with the vev of
the tensor multiplet scalars serving as the inverse coupling constants of the
Yang-Mills multiplet. We briefly discuss the inclusion of hypermultiplets which
complete the field content to that of superconformal (2,0) theories.


  We report on an imaging survey with the Spitzer Space Telescope of 62
brightest cluster galaxies with optical line emission. These galaxies are
located in the cores of X-ray luminous clusters selected from the ROSAT All-Sky
Survey. We find that about half of these sources have a sign of excess infrared
emission; 22 objects out of 62 are detected at 70 microns, 18 have 8 to 5.8
micron flux ratios above 1.0 and 28 have 24 to 8 micron flux ratios above 1.0.
Altogether 35 of 62 objects in our survey exhibit at least one of these signs
of infrared excess. Four galaxies with infrared excesses have a 4.5/3.6 micron
flux ratio indicating the presence of hot dust, and/or an unresolved nucleus at
8 microns. Three of these have high measured [OIII](5007A)/Hbeta flux ratios
suggesting that these four, Abell 1068, Abell 2146, and Zwicky 2089, and
R0821+07, host dusty active galactic nuclei (AGNs). 9 objects (including the
four hosting dusty AGNs) have infrared luminosities greater than 10^11 L_sol
and so can be classified as luminous infrared galaxies (LIRGs). Excluding the
four systems hosting dusty AGNs, the excess mid-infrared emission in the
remaining brightest cluster galaxies is likely related to star formation.


  It is well known that given two probability measures $\mu$ and $\nu$ on
$\mathbb{R}$ in convex order there exists a discrete-time martingale with these
marginals. Several solutions are known (for example from the literature on the
Skorokhod embedding problem in Brownian motion). But, if we add a requirement
that the martingale should minimise the expected value of some functional of
its starting and finishing positions then the problem becomes more difficult.
Beiglb\"{o}ck and Juillet (Ann. Probab. 44 (2016) 42-106) introduced the shadow
measure which induces a family of martingale couplings, and solves the optimal
martingale transport problem for a class of bivariate objective functions. In
this article we extend their (existence and uniqueness) results by providing an
explicit construction of the shadow measure and, as an application, give a
simple proof of its associativity.


  Attention layers, as commonly used in transformers, form the backbone of
modern deep learning, yet there is no mathematical description of their
benefits and deficiencies as compared with other architectures. In this work we
establish both positive and negative results on the representation power of
attention layers, with a focus on intrinsic complexity parameters such as
width, depth, and embedding dimension. On the positive side, we present a
sparse averaging task, where recurrent networks and feedforward networks all
have complexity scaling polynomially in the input size, whereas transformers
scale merely logarithmically in the input size; furthermore, we use the same
construction to show the necessity and role of a large embedding dimension in a
transformer. On the negative side, we present a triple detection task, where
attention layers in turn have complexity scaling linearly in the input size; as
this scenario seems rare in practice, we also present natural variants that can
be efficiently solved by attention layers. The proof techniques emphasize the
value of communication complexity in the analysis of transformers and related
models, and the role of sparse averaging as a prototypical attention task,
which even finds use in the analysis of triple detection.


  The COVID-19 pandemic has impacted the national systems of population
movement around the world. Existing work has focused on countries of the Global
North and restricted to the immediate effects of COVID-19 data during 2020.
Data have represented a major limitation to monitor change in mobility patterns
in countries in the Global South. Drawing on aggregate anonymised mobile phone
location data from Meta-Facebook users, we aim to analyse the extent and
persistence of changes in the levels (or intensity) and spatial patterns of
internal population movement across the rural-urban continuum in Argentina,
Chile and Mexico over a 26-month period from March 2020 to May 2022. We reveal
an overall systematic decline in the level of short- and long-distance movement
during the enactment of nonpharmaceutical interventions in 2020, with the
largest reductions occurred in the most dense areas. We also show that these
levels bounced back closer to pre-pandemic levels in 2022 following the
relaxation of COVID-19 stringency measures. However, the intensity of these
movements has remained below pre-pandemic levels in many areas in 2022.
Additionally our findings lend some support to the idea of an urban exodus.
They reveal a continuing negative net balances of short-distance movements in
the most dense areas of capital cities in Argentina and Mexico, reflecting a
pattern of suburbanisation. Chile displays limited changes in the net balance
of short-distance movements but reports a net loss of long-distance movements.
These losses were, however, temporary, moving to neutral and positive balances
in 2021 and 2022.


  After more than five years of development, we present a new version of Dark
Sage, a semi-analytic model (SAM) of galaxy formation that breaks the mould for
models of its kind. Included among the major changes is an overhauled treatment
of stellar feedback that is derived from energy conservation, operates on local
scales, affects gas gradually over time rather than instantaneously, and
predicts a mass-loading factor for every galaxy. Building on the model's
resolved angular-momentum structure of galaxies, we now consider the heating of
stellar discs, delivering predictions for disc structure both radially and
vertically. We add a further dimension to stellar discs by tracking the
distribution of stellar ages in each annulus. Each annulus--age bin has its own
velocity dispersion and metallicity evolved in the model. This allows Dark Sage
to make structural predictions for galaxies that previously only hydrodynamic
simulations could. We present the model as run on the merger trees of the
highest-resolution gravity-only simulation of the MillenniumTNG suite. Despite
its additional complexity relative to other SAMs, Dark Sage only has three free
parameters, the least of any SAM, which we calibrate exclusively against the
cosmic star formation history and the $z=0$ stellar and HI mass functions using
a particle-swarm optimisation method. The Dark Sage codebase, written in C and
Python, is publicly available at https://github.com/arhstevens/DarkSage


  The convergent iterative procedure for solving the groundstate Schroedinger
equation is extended to derive the excitation energy and the wave function of
the low-lying excited states. The method is applied to the one-dimensional
quartic potential problem. The results show that the iterative solution
converges rapidly when the coupling $g$ is not too small.


  The remaining theoretical uncertainties from unknown higher-order corrections
in the prediction for the light Higgs-boson mass of the MSSM are estimated. The
uncertainties associated with three different approaches that are implemented
in the publicly available code FeynHiggs are compared: the fixed-order
diagrammatic approach, suitable for low SUSY scales, the effective field theory
(EFT) approach, suitable for high SUSY scales, and the hybrid approach which
combines the fixed-order and the EFT approaches. It is demonstrated for a
simple single-scale scenario that the result based on the hybrid approach
yields a precise prediction for low, intermediate and high SUSY scales with a
theoretical uncertainty of up to $\sim 1.5$ GeV for large stop mixing and $\sim
0.5$ GeV for small stop mixing. The uncertainty estimate of the hybrid
calculation approaches the uncertainty estimate of the fixed-order result for
low SUSY scales and the uncertainty estimate of the EFT approach for high SUSY
scales, while for intermediate scales it is reduced compared to both of the
individual results. The estimate of the theoretical uncertainty is also
investigated in scenarios with more than one mass scale. A significantly
enhanced uncertainty is found in scenarios where the gluino is substantially
heavier than the scalar top quarks. The uncertainty estimate presented in this
paper will be part of the public code FeynHiggs.


  We consider a process $X_t$, which is observed on a finite time interval
$[0,T]$, at discrete times $0,\Delta_n,2\Delta_n,\ldots.$ This process is an
It\^{o} semimartingale with stochastic volatility $\sigma_t^2$. Assuming that
$X$ has jumps on $[0,T]$, we derive tests to decide whether the volatility
process has jumps occurring simultaneously with the jumps of $X_t$. There are
two different families of tests for the two possible null hypotheses (common
jumps or disjoint jumps). They have a prescribed asymptotic level as the mesh
$\Delta_n$ goes to $0$. We show on some simulations that these tests perform
reasonably well even in the finite sample case, and we also put them in use on
S&P 500 index data.


  Recent ALMA observations may indicate a surprising abundance of sub-Jovian
planets on very wide orbits in protoplanetary discs that are only a few million
years old. These planets are too young and distant to have been formed via the
Core Accretion (CA) scenario, and are much less massive than the gas clumps
born in the classical Gravitational Instability (GI) theory. It was recently
suggested that such planets may form by the partial destruction of GI
protoplanets: energy output due to the growth of a massive core may unbind all
or most of the surrounding pre-collapse protoplanet. Here we present the first
3D global disc simulations that simultaneously resolve grain dynamics in the
disc and within the protoplanet. We confirm that massive GI protoplanets may
self-destruct at arbitrarily large separations from the host star provided that
solid cores of mass around 10-20 Earth masses are able to grow inside them
during their pre-collapse phase. In addition, we find that the heating force
recently analysed by Masset and Velasco Romero (2017) perturbs these cores away
from the centre of their gaseous protoplanets. This leads to very complicated
dust dynamics in the protoplanet centre, potentially resulting in the formation
of multiple cores, planetary satellites, and other debris such as planetesimals
within the same protoplanet. A unique prediction of this planet formation
scenario is the presence of sub-Jovian planets at wide orbits in Class 0/I
protoplanetary discs.


  The most prominent class of integrable quantum field theories in 1+1
dimensions is affine Toda theory. Distinguished by a rich underlying Lie
algebraic structure these models have in recent years attracted much attention
not only as test laboratories for non-perturbative methods in quantum field
theory but also in the context of off-critical models. After a short
introduction the mathematical preliminaries such as root systems, Coxeter
geometry, dual algebras, q-deformed Coxeter elements and q-deformed Cartan
matrices are introduced. Using this mathematical framework the bootstrap
analysis of the affine Toda S-matrices with real coupling is performed and
several universal Lie algebraic formulae proved. The Lie algebraic methods are
then extended to define a new class of colour valued S-matrices and also here
universal expressions are derived. The second part of the thesis presents a
detailed analysis of the high-energy regime of the integrable models discussed
in the first part. By means of the thermodynamic Bethe ansatz the central
charges of the ultraviolet conformal field theories are calculated and in case
of affine Toda theories also the first order term in the scaling function is
analytically obtained. For the colour valued S-matrices the connection to WZNW
coset models is discussed. A particular subclass of them, the so-called
Homogeneous Sine-Gordon models, is investigated in some detail and it is found
that the presence of unstable particles in these theories gives rise to a
staircase pattern in the corresponding scaling function. This thesis summarizes
the results of previously published articles listed in the introduction.


  It has long been recognized that it is not enough for a Recommender System
(RS) to provide recommendations based only on their relevance to users. Among
many other criteria, the set of recommendations may need to be diverse.
Diversity is one way of handling recommendation uncertainty and ensuring that
recommendations offer users a meaningful choice. The literature reports many
ways of measuring diversity and improving the diversity of a set of
recommendations, most notably by re-ranking and selecting from a larger set of
candidate recommendations. Driven by promising insights from the literature on
how to incorporate versatile Large Language Models (LLMs) into the RS pipeline,
in this paper we show how LLMs can be used for diversity re-ranking.
  We begin with an informal study that verifies that LLMs can be used for
re-ranking tasks and do have some understanding of the concept of item
diversity. Then, we design a more rigorous methodology where LLMs are prompted
to generate a diverse ranking from a candidate ranking using various prompt
templates with different re-ranking instructions in a zero-shot fashion. We
conduct comprehensive experiments testing state-of-the-art LLMs from the GPT
and Llama families. We compare their re-ranking capabilities with random
re-ranking and various traditional re-ranking methods from the literature. We
open-source the code of our experiments for reproducibility. Our findings
suggest that the trade-offs (in terms of performance and costs, among others)
of LLM-based re-rankers are superior to those of random re-rankers but, as yet,
inferior to the ones of traditional re-rankers. However, the LLM approach is
promising. LLMs exhibit improved performance on many natural language
processing and recommendation tasks and lower inference costs. Given these
trends, we can expect LLM-based re-ranking to become more competitive soon.


  The paper aims at reconsidering the famous Le Cam LAN theory. The main
features of the approach which make it different from the classical one are as
follows: (1) the study is nonasymptotic, that is, the sample size is fixed and
does not tend to infinity; (2) the parametric assumption is possibly
misspecified and the underlying data distribution can lie beyond the given
parametric family. These two features enable to bridge the gap between
parametric and nonparametric theory and to build a unified framework for
statistical estimation. The main results include large deviation bounds for the
(quasi) maximum likelihood and the local quadratic bracketing of the
log-likelihood process. The latter yields a number of important corollaries for
statistical inference: concentration, confidence and risk bounds, expansion of
the maximum likelihood estimate, etc. All these corollaries are stated in a
nonclassical way admitting a model misspecification and finite samples.
However, the classical asymptotic results including the efficiency bounds can
be easily derived as corollaries of the obtained nonasymptotic statements. At
the same time, the new bracketing device works well in the situations with
large or growing parameter dimension in which the classical parametric theory
fails. The general results are illustrated for the i.i.d. setup as well as for
generalized linear and median estimation. The results apply for any dimension
of the parameter space and provide a quantitative lower bound on the sample
size yielding the root-n accuracy.


  JEM--EUSO is an international program for the development of space-based
Ultra-High Energy Cosmic Ray observatories. The program consists of a series of
missions which are either under development or in the data analysis phase. All
instruments are based on a wide-field-of-view telescope, which operates in the
near-UV range, designed to detect the fluorescence light emitted by extensive
air showers in the atmosphere. We describe the simulation software ESAFin the
framework of the JEM--EUSO program and explain the physical assumptions used.
We present here the implementation of the JEM--EUSO, POEMMA, K--EUSO, TUS,
Mini--EUSO, EUSO--SPB1 and EUSO--TA configurations in ESAF. For the first time
ESAF simulation outputs are compared with experimental data.


  A natural family of quantized matrix algebras is introduced. It includes the
two best studied such. Located inside ${\s U}_q(A_{2n-1})$, it consists of
quadratic algebras with the same Hilbert series as polynomials in $n^2$
variables. We discuss their general properties and investigate some members of
the family in great detail with respect to associated varieties, degrees,
centers, and symplectic leaves. Finally, the space of rank r matrices becomes a
Poisson submanifold, and there is an associated tensor category of $\rank\leq
r$ matrices.


  A comparative analysis of two bridges constructed with the most commonly used
girder types in Florida is carried out. The girder types that the bridges are
employed for this study are AASHTO Type III (American Association of State
Highway and Transportation Officials) and Florida I-Beam. Two bridges that have
exactly the same specifications but with different girder type are analyzed
under baseline state and different prestress loss cases. Finite element models
of these bridges are utilized and the FE models are subjected to two types of
virtual load tests of Florida legal loads namely C5 and SU4. Florida I-Beam
tends to have higher load carrying capacity, higher lateral stiffness, cost
efficiency and better element level reliability when compared to AASHTO Type
girders.


  Neural models of Knowledge Base data have typically employed compositional
representations of graph objects: entity and relation embeddings are
systematically combined to evaluate the truth of a candidate Knowedge Base
entry. Using a model inspired by Harmonic Grammar, we propose to tokenize
triplet embeddings by subjecting them to a process of optimization with respect
to learned well-formedness conditions on Knowledge Base triplets. The resulting
model, known as Gradient Graphs, leads to sizable improvements when implemented
as a companion to compositional models. Also, we show that the
"supracompositional" triplet token embeddings it produces have interpretable
properties that prove helpful in performing inference on the resulting triplet
representations.


  Measurements of black hole spin made using the continuum-fitting method rely
on the assumption that the inclination of the black hole's spin axis to our
line of sight is the same as the orbital inclination angle of the host binary
system. The X=ray and radio jet data available for the microquasar XTE
J1550-564 offer a rare opportunity to test this assumption. Following the work
of others, we have modeled these data and thereby determined the inclination
angle of the jet axis, which is presumed to be aligned with the black hole's
spin axis. We find a jet inclination angle of approximately 71 degrees and
place an upper limit on the difference between the spin and orbital
inclinations of < 12 degrees (90% confidence). Our measurement tests for
misalignment along the line of sight while providing no constraint
perpendicular to this plane. Our constraint on the misalignment angle supports
the prediction that the spinning black hole in XTE J1550-564 has aligned itself
with the orbital plane and provides support for the measurement of its spin via
the continuum-fitting method. Our conclusions are based on a simple and
reasonable model of a pair of symmetric jets propagating into a low density
cavity whose western wall is approximately 20% closer to XTE J1550-564 than its
eastern wall.


  In this paper, we propose a game between an exogenous adversary and a network
of agents connected via a multigraph. The multigraph is composed of (1) a
global graph structure, capturing the virtual interactions among the agents,
and (2) a local graph structure, capturing physical/local interactions among
the agents. The aim of each agent is to achieve consensus with the other agents
in a decentralized manner by minimizing a local cost associated with its local
graph and a global cost associated with the global graph. The exogenous
adversary, on the other hand, aims to maximize the average cost incurred by all
agents in the multigraph. We derive Nash equilibrium policies for the agents
and the adversary in the Mean-Field Game setting, when the agent population in
the global graph is arbitrarily large and the ``homogeneous mixing" hypothesis
holds on local graphs. This equilibrium is shown to be unique and the
equilibrium Markov policies for each agent depend on the local state of the
agent, as well as the influences on the agent by the local and global mean
fields.


  Principal Component Analysis (PCA) and Kernel Principal Component Analysis
(KPCA) are fundamental methods in machine learning for dimensionality
reduction. The former is a technique for finding this approximation in finite
dimensions and the latter is often in an infinite dimensional Reproducing
Kernel Hilbert-space (RKHS). In this paper, we present a geometric framework
for computing the principal linear subspaces in both situations as well as for
the robust PCA case, that amounts to computing the intrinsic average on the
space of all subspaces: the Grassmann manifold. Points on this manifold are
defined as the subspaces spanned by $K$-tuples of observations. The intrinsic
Grassmann average of these subspaces are shown to coincide with the principal
components of the observations when they are drawn from a Gaussian
distribution. We show similar results in the RKHS case and provide an efficient
algorithm for computing the projection onto the this average subspace. The
result is a method akin to KPCA which is substantially faster. Further, we
present a novel online version of the KPCA using our geometric framework.
Competitive performance of all our algorithms are demonstrated on a variety of
real and synthetic data sets.


  The notion of a finite pairing interaction energy range suggested by Nam,
results in some states at the Fermi level not participating in pairings when
there are scattering centers such as impurities. The fact that not all states
at the Fermi level participate in pairing is shown to suppress $T_c$ in an
isotropic superconductor and destroy superconductivity. We have presented
quantitative calculations of $T_c$ reduced via spinless impurities, in good
agreements with data of Zn-doped YBCO and LSCO, respectively. It is not
necessary to have the anisotropic order parameter, to account for the
destruction of superconductivity via non-magnetic impurities.


  There is currently a great deal of interest in the invisibility cloaks
recently proposed by Pendry et al. that are based in the transformation
approach. They obtained their results using first order transformations. In
recent papers Hendi et al. and Cai et al. considered invisibility cloaks with
high order transformations. In this paper we study high order electromagnetic
invisibility cloaks in transformation media obtained by high order
transformations from general anisotropic media. We consider the case where
there is a finite number of spherical cloaks located in different points in
space. We prove that for any incident plane wave, at any frequency, the
scattered wave is identically zero. We also consider the scattering of finite
energy wave packets. We prove that the scattering matrix is the identity, i.e.,
that for any incoming wave packet the outgoing wave packet is the same as the
incoming one. This proves that the invisibility cloaks can not be detected in
any scattering experiment with electromagnetic waves in high order
transformation media, and in particular in the first order transformation media
of Pendry et al. We also prove that the high order invisibility cloaks, as well
as the first order ones, cloak passive and active devices. The cloaked objects
completely decouple from the exterior. Actually, the cloaking outside is
independent of what is inside the cloaked objects. The electromagnetic waves
inside the cloaked objects can not leave the concealed regions and viceversa,
the electromagnetic waves outside the cloaked objects can not go inside the
concealed regions. As we prove our results for media that are obtained by
transformation from general anisotropic materials, we prove that it is possible
to cloak objects inside general crystals.


  Given a universe of discourse X-a domain of possible outcomes-an experiment
may consist of selecting one of its elements, subject to the operation of
chance, or of observing the elements, subject to imprecision. A priori
uncertainty about the actual result of the experiment may be quantified,
representing either the likelihood of the choice of :r_X or the degree to which
any such X would be suitable as a description of the outcome. The former case
corresponds to a probability distribution, while the latter gives a possibility
assignment on X. The study of such assignments and their properties falls
within the purview of possibility theory [DP88, Y80, Z783. It, like probability
theory, assigns values between 0 and 1 to express likelihoods of outcomes.
Here, however, the similarity ends. Possibility theory uses the maximum and
minimum functions to combine uncertainties, whereas probability theory uses the
plus and times operations. This leads to very dissimilar theories in terms of
analytical framework, even though they share several semantic concepts. One of
the shared concepts consists of expressing quantitatively the uncertainty
associated with a given distribution. In probability theory its value
corresponds to the gain of information that would result from conducting an
experiment and ascertaining an actual result. This gain of information can
equally well be viewed as a decrease in uncertainty about the outcome of an
experiment. In this case the standard measure of information, and thus
uncertainty, is Shannon entropy [AD75, G77]. It enjoys several advantages-it is
characterized uniquely by a few, very natural properties, and it can be
conveniently used in decision processes. This application is based on the
principle of maximum entropy; it has become a popular method of relating
decisions to uncertainty. This paper demonstrates that an equally integrated
theory can be built on the foundation of possibility theory. We first show how
to define measures of in formation and uncertainty for possibility assignments.
Next we construct an information-based metric on the space of all possibility
distributions defined on a given domain. It allows us to capture the notion of
proximity in information content among the distributions. Lastly, we show that
all the above constructions can be carried out for continuous
distributions-possibility assignments on arbitrary measurable domains. We
consider this step very significant-finite domains of discourse are but
approximations of the real-life infinite domains. If possibility theory is to
represent real world situations, it must handle continuous distributions both
directly and through finite approximations. In the last section we discuss a
principle of maximum uncertainty for possibility distributions. We show how
such a principle could be formalized as an inference rule. We also suggest it
could be derived as a consequence of simple assumptions about combining
information. We would like to mention that possibility assignments can be
viewed as fuzzy sets and that every fuzzy set gives rise to an assignment of
possibilities. This correspondence has far reaching consequences in logic and
in control theory. Our treatment here is independent of any special
interpretation; in particular we speak of possibility distributions and
possibility measures, defining them as measurable mappings into the interval
[0, 1]. Our presentation is intended as a self-contained, albeit terse summary.
Topics discussed were selected with care, to demonstrate both the completeness
and a certain elegance of the theory. Proofs are not included; we only offer
illustrative examples.


  The average density of zeros for monic generalized polynomials,
$P_n(z)=\phi(z)+\sum_{k=1}^nc_kf_k(z)$, with real holomorphic $\phi ,f_k$ and
real Gaussian coefficients is expressed in terms of correlation functions of
the values of the polynomial and its derivative. We obtain compact expressions
for both the regular component (generated by the complex roots) and the
singular one (real roots) of the average density of roots. The density of the
regular component goes to zero in the vicinity of the real axis like
$|\hbox{\rm Im}\,z|$. We present the low and high disorder asymptotic
behaviors. Then we particularize to the large $n$ limit of the average density
of complex roots of monic algebraic polynomials of the form $P_n(z) = z^n
+\sum_{k=1}^{n}c_kz^{n-k}$ with real independent, identically distributed
Gaussian coefficients having zero mean and dispersion $\delta = \frac
1{\sqrt{n\lambda}}$. The average density tends to a simple, {\em universal}
function of $\xi={2n}{\log |z|}$ and $\lambda$ in the domain $\xi\coth
\frac{\xi}{2}\ll n|\sin \arg (z)|$ where nearly all the roots are located for
large $n$.


  Studying the spatial distribution of extragalactic source populations is
vital in understanding the matter distribution in the Universe. It also enables
understanding the cosmological evolution of dark matter density fields and the
relationship between dark matter and luminous matter. Clustering studies are
also required for EoR foreground studies since it affects the relevant angular
scales. This paper investigates the angular and spatial clustering properties
and the bias parameter of radio-selected sources in the Lockman Hole field at
325 MHz. The data probes sources with fluxes $\gtrsim$0.3 mJy within a radius
of 1.8$^\circ$ around the phase center of a $6^\circ \times 6^\circ$ mosaic.
Based on their radio luminosity, the sources are classified into Active
Galactic Nuclei (AGNs) and Star-Forming Galaxies (SFGs). Clustering and bias
parameters are determined for the combined populations and the classified
sources. The spatial correlation length and the bias of AGNs are greater than
SFGs -- indicating that more massive haloes host the former. This study is the
first reported estimate of the clustering property of sources at 325 MHz,
intermediate between the preexisting studies at high and low-frequency bands.
It also probes a well-studied deep field at an unexplored frequency with
moderate depth and area. Clustering studies require such observations along
different lines of sight, with various fields and data sets across frequencies
to avoid cosmic variance and systematics. Thus, an extragalactic deep field has
been studied in this work to contribute to this knowledge.


  Data Grids have been adopted as the platform for scientific communities that
need to share, access, transport, process and manage large data collections
distributed worldwide. They combine high-end computing technologies with
high-performance networking and wide-area storage management techniques. In
this paper, we discuss the key concepts behind Data Grids and compare them with
other data sharing and distribution paradigms such as content delivery
networks, peer-to-peer networks and distributed databases. We then provide
comprehensive taxonomies that cover various aspects of architecture, data
transportation, data replication and resource allocation and scheduling.
Finally, we map the proposed taxonomy to various Data Grid systems not only to
validate the taxonomy but also to identify areas for future exploration.
Through this taxonomy, we aim to categorise existing systems to better
understand their goals and their methodology. This would help evaluate their
applicability for solving similar problems. This taxonomy also provides a "gap
analysis" of this area through which researchers can potentially identify new
issues for investigation. Finally, we hope that the proposed taxonomy and
mapping also helps to provide an easy way for new practitioners to understand
this complex area of research.