  We develop a general approach for the characterization of atom-array
platforms as light-matter interfaces, focusing on their application in quantum
memory and photonic entanglement generation. Our approach is based on the
mapping of atom-array problems to a generic 1D model of light interacting with
a collective dipole. We find that the efficiency of light-matter coupling,
which in turn determines those of quantum memory and entanglement, is given by
the on-resonance reflectivity of the 1D scattering problem, $r_0=C/(1+C)$,
where $C$ is a cooperativity parameter of the model. For 2D and 3D atomic
arrays in free space, we derive the mapping parameter $C$ and hence $r_0$,
while accounting for realistic effects such as the finite sizes of the array
and illuminating beam and weak disorder in atomic positions. Our analytical
results are verified numerically and reveal a key idea: efficiencies of quantum
tasks are reduced by our approach to the classical calculation of a
reflectivity. This provides a unified framework for the analysis of collective
light-matter coupling in various relevant platforms such as optical lattices
and tweezer arrays. Generalization to collective systems beyond arrays is
discussed.


  By quantum Monte Carlo simulations of bosons in gapped honeycomb lattices, we
show the existence of bosonic edge states. For single layer honeycomb lattice,
bosonic edge states can be controlled to appear, cross the gap and merge into
bulk states by an on-site potential applied on the outmost sites of the
boundary. On bilayer honeycomb lattice, bosonic edge state traversing the gap
at half filling is demonstrated. The topological origin of the bosonic edge
states is discussed with pseudo Berry curvature. The results will simulate
experimental studies of these exotic bosonic edge states with ultracold bosons
trapped in honeycomb optical lattices.


  We construct Green's functions for elliptic operators of the form
$\mathcal{L}u=-\text{div}(A\nabla u+bu)+c\nabla u+du$ in domains
$\Omega\subseteq\mathbb R^n$, under the assumption $d\geq\text{div}b$, or
$d\geq\text{div}c$. We show that, in the setting of Lorentz spaces, the
assumption $b-c\in L^{n,1}(\Omega)$ is both necessary and optimal to obtain
pointwise bounds for Green's functions. We also show weak type bounds for
Green's functions and their gradients. Our estimates are scale invariant and
hold for general domains $\Omega\subseteq\mathbb R^n$. Moreover, there is no
smallness assumption on the norms of the lower order coefficients. As
applications we obtain scale invariant global and local boundedness estimates
for subsolutions to $\mathcal{L}u\leq -\text{div}f+g$ in the case
$d\geq\text{div}c$.


  The existence problem for holomorphic structures on vector bundles over
non-algebraic surfaces is in general still open. We solve this problem in the
case of rank 2 vector bundles over K3 surfaces and in the case of vector
bundles of arbitrary rank over all known surfaces of class VII. Our methods,
which are based on Donaldson theory and deformation theory, can be used to
solve the existence problem of holomorphic vector bundles on further classes of
non-algebraic surfaces.


  We look at the generalisation of topologically massive gravity (TMG) to
higher spins, specifically spin-3. We find a special "chiral" point for the
spin-three, analogous to the spin-two example, which actually coincides with
the usual spin-two chiral point. But in contrast to usual TMG, there is the
presence of a non-trivial trace and its logarithmic partner at the chiral
point. The trace modes carry energy opposite in sign to the traceless modes.
The logarithmic partner of the traceless mode carries negative energy
indicating an instability at the chiral point. We make several comments on the
asymptotic symmetry and its possible deformations at this chiral point and
speculate on the higher spin generalisation of LCFT2 dual to the spin-3 massive
gravity at the chiral point.


  Simulating laser wakefield acceleration (LWFA) in a Lorentz boosted frame in
which the plasma drifts towards the laser with $v_b$ can speedup the simulation
by factors of $\gamma^2_b=(1-v^2_b/c^2)^{-1}$. In these simulations the
relativistic drifting plasma inevitably induces a high frequency numerical
instability that contaminates the interested physics. Various approaches have
been proposed to mitigate this instability. One approach is to solve Maxwell
equations in Fourier space (a spectral solver) as this has been shown to
suppress the fastest growing modes of this instability in simple test problems
using a simple low pass, ring (in two dimensions), or shell (in three
dimensions) filter in Fourier space. We describe the development of a fully
parallelized, multi-dimensional, particle-in-cell code that uses a spectral
solver to solve Maxwell's equations and that includes the ability to launch a
laser using a moving antenna. This new EM-PIC code is called UPIC-EMMA and it
is based on the components of the UCLA PIC framework (UPIC). We show that by
using UPIC-EMMA, LWFA simulations in the boosted frames with arbitrary
$\gamma_b$ can be conducted without the presence of the numerical instability.
We also compare the results of a few LWFA cases for several values of
$\gamma_b$, including lab frame simulations using OSIRIS, a EM-PIC code with a
finite difference time domain (FDTD) Maxwell solver. These comparisons include
cases in both linear, and nonlinear regimes. We also investigate some issues
associated with numerical dispersion in lab and boosted frame simulations and
between FDTD and spectral solvers.


  We study various aspects on nontrivial logarithmic co-Higgs structure
associated to unstable bundles on algebraic curves. We check several criteria
for (non-)existence of nontrivial logarithmic co-Higgs structures and describe
their parameter spaces. We also investigate the Segre invariants of these
structures and see their non-simplicity. In the end we also study the higher
dimensional case, specially when the tangent bundle is not semistable.


  We calculate some non-perturbative (D-instanton) quantum corrections to the
moduli space metric of several (n>1) identical matter hypermultiplets for the
type-IIA superstrings compactified on a Calabi-Yau threefold, near conifold
singularities. We find a non-trivial deformation of the (real) 4n-dimensional
hypermultiplet moduli space metric due to the infinite number of D-instantons,
under the assumption of n tri-holomorphic commuting isometries of the metric,
in the hyper-K"ahler limit (i.e. in the absence of gravitational corrections).


  Using the embedding of the moduli space of generalized GL(n) Hitchin's
spectral covers to the moduli space of meromorphic abelian differentials we
study the variational formulae of the period matrix, the canonical
bidifferential, the prime form and the Bergman tau function. This leads to
residue formulae which generalize the Donagi-Markman formula for variations of
the period matrix. Computation of second derivatives of the period matrix
reproduces the formula derived by Baraglia and Zhenxi Huang using the framework
of topological recursion.


  We demonstrated a pressure-induced phase transition from a low-Tc phase (3.5
K) to a high-Tc phase (8.7 K) in single crystalline PrO0.5F0.5BiS2. The high-Tc
phase is easily observed even at 0.7 GPa by uniaxial pressure obtained from a
geometric effect of a single crystal with an extremely-thin thickness. For this
phase transition, superconducting anisotropy and the coherence length along the
c axis change from {\gamma} = 20 to 9.3 and from {\xi}c = 0.56 to 0.71 nm
respectively. It is suggested that a shrinkage in the c lattice constant by
applied uniaxial pressure enhances the three dimensionality in the
superconducting state.


  We estimate the magnitude of Lepton Flavour Violation (LFV) from the phase of
the neutrino Yukawa matrix. In the minimal supersymmetric standard model with
right-handed neutrinos, the LFV processes l_i \to l_j \gamma can appear through
the slepton mixing, which comes from the renormalization group effect on the
right-handed neutrino Yukawa interaction between the Grand Unified Theory scale
and the heavy right-handed neutrino mass scale. Two types of phases exist in
the neutrino Yukawa matrix. One is the Majorana phase, which can change the
magnitude of the LFV branching ratios by a few factor. The other phases relate
for the size of the Yukawa hierarchy and its phase effect can change the LFV
branching ratios by several orders of magnitude.


  Topologically non-trivial Hamiltonians with periodic boundary conditions are
characterized by strictly quantized invariants. Open questions and fundamental
challenges concern their existence, and the possibility of measuring them in
systems with open boundary conditions and limited spatial extension. Here, we
consider transport in Hofstadter strips, that is, two-dimensional lattices
pierced by a uniform magnetic flux which extend over few sites in one of the
spatial dimensions. As we show, an atomic wavepacket exhibits a transverse
displacement under the action of a weak constant force. After one Bloch
oscillation, this displacement approaches the quantized Chern number of the
periodic system in the limit of vanishing tunneling along the transverse
direction. We further demonstrate that this scheme is able to map out the Chern
number of ground and excited bands, and we investigate the robustness of the
method in presence of both disorder and harmonic trapping. Our results prove
that topological invariants can be measured in Hofstadter strips with open
boundary conditions and as few as three sites along one direction.


  Wirelessly powered backscatter communication (WPBC) has been identified as a
promising technology for low-power communication systems, which can reap the
benefits of energy beamforming to improve energy transfer efficiency. Existing
studies on energy beamforming fail to simultaneously take energy supply and
information transfer in WPBC into account. This paper takes the first step to
fill this gap, by considering the trade-off between the energy harvesting rate
and achievable rate using estimated backscatter channel state information
(BS-CSI). To ensure reliable communication and user fairness, we formulate the
energy beamforming design as a max-min optimization problem by maximizing the
minimum achievable rate for all tags subject to the energy constraint. We
derive the closed-form expression of the energy harvesting rate, as well as the
lower bound of the ergodic achievable rate. Our numerical results indicate that
our scheme can significantly outperform state-of-the-art energy beamforming
schemes. Additionally, the proposed scheme achieves performance comparable to
that obtained via beamforming with perfect CSI.


  In this article I propose a new method for reducing a co-oriented contact
manifold M equipped with an action of a Lie group G by contact transformations.
  With a certain regularity and integrality assumption the contact quotient
$M_\mu$ at $\mu \in \fg^*$ is a naturally a co-oriented contact orbifold which
is independent of the contact form used to represent the given contact
structure. Removing the regularity and integrality assumptions and replacing
them with one concerning the existence of a slice, which is satisfied for
compact symmetry groups, results in a contact stratified space; i.e, a
stratified space equipped with a line bundle which, when restricted to each
stratum, defines a co-oriented contact structure. This extends the previous
work of the author and E. Lerman [LW].


  We determine dynamical response functions of the S=1/2 Heisenberg quantum
antiferromagnet on the kagome lattice based on large-scale exact
diagonalizations combined with a continued fraction technique. The dynamical
spin structure factor has important spectral weight predominantly along the
boundary of the extended Brillouin zone and energy scans reveal broad response
extending over a range of 2 \sim 3J concomitant with pronounced intensity at
lowest available energies. Dispersive features are largely absent. Dynamical
singlet correlations -- which are relevant for inelastic light probes -- reveal
a similar broad response, with a high intensity at low frequencies omega/J
\lesssim 0.2J. These low energy singlet excitations do however not seem to
favor a specific valence bond crystal, but instead spread over many symmetry
allowed eigenstates.


  Occlusion is a major challenge for LiDAR-based object detection methods. This
challenge becomes safety-critical in urban traffic where the ego vehicle must
have reliable object detection to avoid collision while its field of view is
severely reduced due to the obstruction posed by a large number of road users.
Collaborative perception via Vehicle-to-Everything (V2X) communication, which
leverages the diverse perspective thanks to the presence at multiple locations
of connected agents to form a complete scene representation, is an appealing
solution. State-of-the-art V2X methods resolve the performance-bandwidth
tradeoff using a mid-collaboration approach where the Bird-Eye View images of
point clouds are exchanged so that the bandwidth consumption is lower than
communicating point clouds as in early collaboration, and the detection
performance is higher than late collaboration, which fuses agents' output,
thanks to a deeper interaction among connected agents. While achieving strong
performance, the real-world deployment of most mid-collaboration approaches is
hindered by their overly complicated architectures, involving learnable
collaboration graphs and autoencoder-based compressor/ decompressor, and
unrealistic assumptions about inter-agent synchronization. In this work, we
devise a simple yet effective collaboration method that achieves a better
bandwidth-performance tradeoff than prior state-of-the-art methods while
minimizing changes made to the single-vehicle detection models and relaxing
unrealistic assumptions on inter-agent synchronization. Experiments on the
V2X-Sim dataset show that our collaboration method achieves 98\% of the
performance of an early-collaboration method, while only consuming the
equivalent bandwidth of a late-collaboration method.


  Many important problems in the real world don't have unique solutions. It is
thus important for machine learning models to be capable of proposing different
plausible solutions with meaningful probability measures. In this work we
introduce such a deep learning framework that learns the one-to-many mappings
between the inputs and outputs, together with faithful uncertainty measures. We
call our framework {\it modal uncertainty estimation} since we model the
one-to-many mappings to be generated through a set of discrete latent
variables, each representing a latent mode hypothesis that explains the
corresponding type of input-output relationship. The discrete nature of the
latent representations thus allows us to estimate for any input the conditional
probability distribution of the outputs very effectively. Both the discrete
latent space and its uncertainty estimation are jointly learned during
training. We motivate our use of discrete latent space through the multi-modal
posterior collapse problem in current conditional generative models, then
develop the theoretical background, and extensively validate our method on both
synthetic and realistic tasks. Our framework demonstrates significantly more
accurate uncertainty estimation than the current state-of-the-art methods, and
is informative and convenient for practical use.


  We revisit Gersten's $\ell^\infty$-cohomology of groups and spaces, removing
the finiteness assumptions required by the original definition while retaining
its geometric nature. Mirroring the corresponding results in bounded
cohomology, we provide a characterization of amenable groups using
$\ell^\infty$-cohomology, and generalize Mineyev's characterization of
hyperbolic groups via $\ell^\infty$-cohomology to the relative setting. We then
describe how $\ell^\infty$-cohomology is related to isoperimetric inequalities.
We also consider some algorithmic problems concerning $\ell^\infty$-cohomology
and show that they are undecidable. In an appendix, we prove a version of the
de Rham's theorem in the context of $\ell^\infty$-cohomology.


  This survey summarizes and illustrates the main qualitative properties of
hydrodynamics models for collective behavior. These models include a velocity
consensus term together with attractive-repulsive potentials leading to
non-trivial flock profiles. The connection between the underlying particle
systems to the swarming hydrodynamic equations is performed through kinetic
theory modelling arguments. We focus on Lagrangian schemes for the hydrodynamic
systems showing the different qualitative behavior of the systems and its
capability of keeping properties of the original particle models. We illustrate
known results concerning large time profiles and blow-up in finite time of the
hydrodynamic systems to validate the numerical scheme. We finally explore
unknown situations making use of the numerical scheme showcasing a number of
conjectures based on the numerical results.


  Single Image Super-Resolution (SISR) aims to generate a high-resolution (HR)
image of a given low-resolution (LR) image. The most of existing convolutional
neural network (CNN) based SISR methods usually take an assumption that a LR
image is only bicubicly down-sampled version of an HR image. However, the true
degradation (i.e. the LR image is a bicubicly downsampled, blurred and noisy
version of an HR image) of a LR image goes beyond the widely used bicubic
assumption, which makes the SISR problem highly ill-posed nature of inverse
problems. To address this issue, we propose a deep SISR network that works for
blur kernels of different sizes, and different noise levels in an unified
residual CNN-based denoiser network, which significantly improves a practical
CNN-based super-resolver for real applications. Extensive experimental results
on synthetic LR datasets and real images demonstrate that our proposed method
not only can produce better results on more realistic degradation but also
computational efficient to practical SISR applications.


  Vortex dynamics in a bilayer thin film superconductor are studied through a
Josephson-coupled double layer XY model. A renormalization group analysis shows
that there are three possible states associated with the relative phase of the
layers: a free vortex phase, a logarithmically confined vortex-antivortex pair
phase, and a linearly confined phase. The phases may be distinguished by
measuring the resistance to counterflow current. For a geometry in which
current is injected and removed from the two layers at the same edge by an
ideal (dissipationless) lead, we argue that the three phases yield distinct
behaviors: metallic conductivity in the free vortex phase, a power law I-V in
the logarithmically confined phase, and true dissipationless superconductivity
in the linearly confined phase. Numerical simulations of a resistively shunted
Josephson junction model reveal size dependences for the resistance of this
system that support these expectations.


  The timescale over which planets may form in the circumstellar disks of young
stars is one of the main issues of current planetary formation models. We
present here new constraints on planet formation timescales derived from the
rotational evolution of exoplanet host stars.


  The pinwheel tiling is the paradigm for a substitution tiling with circular
symmetry, in the sense that the corresponding autocorrelation is circularly
symmetric. As a consequence, its diffraction measure is also circularly
symmetric, so the pinwheel diffraction consists of sharp rings and, possibly, a
continuous component with circular symmetry. We consider some combinatorial
properties of the tiles and their orientations, and a numerical approach to the
diffraction of weighted pinwheel point sets.


  Various phenomena related to inhomogeneous magnetoelectric interaction are
considered. The interrelation between spatial modulation of order parameter and
electric polarization, known as flexoelectric effect in liquid crystals, in the
case of magnetic media appears in a form of electric polarization induced by
spin modulation and vice versa. This flexomagnetoelectric interaction is also
related to the influence of ferroelectric domain structure on antiferromagnetic
vector distribution, and to the magnetoelectric properties of micromagnetic
structures. The influence of inhomogeneous magnetoelectric interaction on
dynamic properties of multiferroics, particularly magnon spectra is also
considered.


  We review a number of old and new concepts in quantum gauge theories, some of
which are well established but not widely appreciated, some are most recent.
Such concepts involve non-commutative gauge theories and their relation to the
large-N limit, loop equations and the change to the anti-selfdual variables
also known as Nicolai map, topological field theory (TFT) and its relation to
localization and Morse-Smale-Floer homology, with an emphasis both on the
mathematical aspects and the physical meaning. These concepts, assembled in a
new way, enter a line of attack to the problem of the mass gap in large-N SU(N)
YM, that is reviewed as well. In the large-N limit of pure SU(N) YM the ambient
algebra of Wilson loops is known to be a type II_1 non-hyperfinite factor.
Nevertheless, for the mass gap problem at the leading 1/N order, only the
subalgebra of local gauge-invariant single-trace operators matters. The
connected two-point correlators in this subalgebra must be an infinite sum of
propagators of free massive fields, a vast simplification. It is an open
problem, determined by the grow of the degeneracy of the spectrum, whether the
aforementioned local subalgebra is in fact hyperfinite. For the mass-gap
problem, in the search of a hyperfinite subalgebra containing the scalar sector
of large-N YM, a major role is played by the existence of a TFT underlying the
large-N limit of YM, with twisted boundary conditions on a torus or, what is
the same by Morita duality, on a non-commutative torus.


  We consider cumulative merging percolation (CMP), a long-range percolation
process describing the iterative merging of clusters in networks, depending on
their mass and mutual distance. For a specific class of CMP processes, which
represents a generalization of degree-ordered percolation, we derive a scaling
solution on uncorrelated complex networks, unveiling the existence of diverse
mechanisms leading to the formation of a percolating cluster. The scaling
solution accurately reproduces universal properties of the transition. This
finding is used to infer the critical properties of the
Susceptible-Infected-Susceptible (SIS) model for epidemics in infinite and
finite power-law distributed networks. Here discrepancies between analytical
approaches and numerical results regarding the finite size scaling of the
epidemic threshold are a crucial open issue in the literature. We find that the
scaling exponent assumes a nontrivial value during a long preasymptotic regime.
We calculate this value, finding good agreement with numerical evidence. We
also show that the crossover to the true asymptotic regime occurs for sizes
much beyond currently feasible simulations. Our findings allow us to
rationalize and reconcile all previously published results (both analytical and
numerical), thus ending a long-standing debate.


  Random Dirac fermions in a two-dimensional space are studied numerically. We
realize them on a square lattice using the $\pi$-flux model with random
hopping. The system preserves two symmetries, the time-reversal symmetry and
the symmetry denoted by ${{\cal H},\gamma}=0$ with a $4\times 4$ matrix $\gamma
$ in an effective field theory. Although it belongs to the orthogonal ensemble,
the zero-energy states do not localize and become critical. The density of
states vanishes at zero energy as $\sim E^{\alpha}$ and the exponent $\alpha$
changes with strength of the randomness, which implies the existence of the
critical line. Rapid growth of the localization length near zero energy is
suggested and the eigenstates near zero energy exhibit anomalous behaviour
which can be interpreted as a critical slowing down in the available
finite-size system. The level-spacing distributions close to zero energy
deviate from both the Wigner surmise and the Poissonian, and exhibit critical
behaviour which reflects the existence of critical states at zero energy.


  Interplanetary Filesystem (IPFS) is one of the largest peer-to-peer
filesystems in operation. The network is the default storage layer for Web3 and
is being presented as a solution to the centralization of the web. In this
paper, we present a large-scale, multi-modal measurement study of the IPFS
network. We analyze the topology, the traffic, the content providers and the
entry points from the classical Internet.
  Our measurements show significant centralization in the IPFS network and a
high share of nodes hosted in the cloud. We also shed light on the main
stakeholders in the ecosystem. We discuss key challenges that might disrupt
continuing efforts to decentralize the Web and highlight multiple properties
that are creating pressures toward centralization.


  Understanding how social situations unfold in people's daily lives is
relevant to designing mobile systems that can support users in their personal
goals, well-being, and activities. As an alternative to questionnaires, some
studies have used passively collected smartphone sensor data to infer social
context (i.e., being alone or not) with machine learning models. However, the
few existing studies have focused on specific daily life occasions and limited
geographic cohorts in one or two countries. This limits the understanding of
how inference models work in terms of generalization to everyday life occasions
and multiple countries. In this paper, we used a novel, large-scale, and
multimodal smartphone sensing dataset with over 216K self-reports collected
from 581 young adults in five countries (Mongolia, Italy, Denmark, UK,
Paraguay), first to understand whether social context inference is feasible
with sensor data, and then, to know how behavioral and country-level diversity
affects inferences. We found that several sensors are informative of social
context, that partially personalized multi-country models (trained and tested
with data from all countries) and country-specific models (trained and tested
within countries) can achieve similar performance above 90% AUC, and that
models do not generalize well to unseen countries regardless of geographic
proximity. These findings confirm the importance of the diversity of mobile
data, to better understand social context inference models in different
countries.


  The Spectrometer/Telescope for Imaging X-rays (STIX) is a hard X-ray imaging
spectrometer on board the ESA and NASA heliospheric mission Solar Orbiter. STIX
has been operational for three years and has observed X-ray emission from
~35,000 solar flares. Throughout its lifetime, Solar Orbiter has been
frequently struck by a high flux of energetic particles usually of flare
origin, or from coronal mass ejection shocks. These Solar Energetic Particles
(SEPs) are detected on board by the purpose-built energetic particle detector
instrument suite. During SEP events, the X-ray signal is also contaminated in
STIX. This work investigates the effect of these particles on the STIX
instrument for two events. The first event occurred during an interplanetary
shock crossing and the second event occurred when Solar Orbiter passed through
Earth's radiation belts while performing a gravity assist maneuver. The induced
spectra consist of tungsten fluorescence emission lines and secondary
Bremsstrahlung emission produced by incident particles interacting with
spacecraft components. For these two events, we identify > 100 keV electrons as
significant contributors to the contamination via Bremsstrahlung emission and
tungsten fluorescence.


  The paper develops a logical understanding of processes for signature of
legal contracts, motivated by applications to legal recognition of smart
contracts on blockchain platforms. A number of axioms and rules of inference
are developed that can be used to justify a ``meeting of the minds''
precondition for contract formation from the fact that certain content has been
signed. In addition to an ``offer and acceptance'' process, the paper considers
``signature in counterparts'', a legal process that permits a contract between
two or more parties to be brought into force by having the parties
independently (possibly, remotely) sign different copies of the contract,
rather than placing their signatures on a common copy at a physical meeting. It
is argued that a satisfactory account of signature in counterparts benefits
from a logic with syntactic self-reference. The axioms used are supported by a
formal semantics, and a number of further properties of the logic are
investigated. In particular, it is shown that the logic implies that when a
contract has been signed, the parties do not just agree, but are in mutual
agreement (a common-knowledge-like notion) about the terms of the contract.


  We have derived a fractional Fokker-Planck equation for subdiffusion in a
general space-and- time-dependent force field from power law waiting time
continuous time random walks biased by Boltzmann weights. The governing
equation is derived from a generalized master equation and is shown to be
equivalent to a subordinated stochastic Langevin equation.


  We propose a new string model by adding a higher-order gradient term to the
rigid string, so that the stiffness can be positive or negative without loosing
stability. In the large-D approximation, the model has three phases, one of
which with a new type of generalized "antiferromagnetic" orientational
correlations. We find an infrared-stable fixed point describing world-sheets
with vanishing tension and Hausdorff dimension D_H=2. Crumpling is prevented by
the new term which suppresses configurations with rapidly changing extrinsic
curvature.


  Majority of theoretical results regarding turbulent mixing are based on the
model of ideal flows with zero correlation time. We discuss the reasons why
such results may fail for real flows and develop a scheme which makes it
possible to match real flows to ideal flows. In particular we introduce the
concept of mixing dimension of flows which can take fractional values. For real
incompressible flows, the mixing dimension exceeds the topological dimension;
this leads to a local inhomogeneity of mixing --- a phenomenon which is not
observed for ideal flows and has profound implications, for instance impacting
the rate of bimolecular reactions in turbulent flows. Finally, we build a model
of compressible flows which reproduces the anomalous Lyapunov exponent values
observed for time-correlated flows by Boffetta et al (2004), and provide a
qualitative explanation of this phenomenon.


  Voting is a general method for preference aggregation in multiagent settings,
but seminal results have shown that all (nondictatorial) voting protocols are
manipulable. One could try to avoid manipulation by using voting protocols
where determining a beneficial manipulation is hard computationally. A number
of recent papers study the complexity of manipulating existing protocols. This
paper is the first work to take the next step of designing new protocols that
are especially hard to manipulate. Rather than designing these new protocols
from scratch, we instead show how to tweak existing protocols to make
manipulation hard, while leaving much of the original nature of the protocol
intact. The tweak studied consists of adding one elimination preround to the
election. Surprisingly, this extremely simple and universal tweak makes typical
protocols hard to manipulate! The protocols become NP-hard, #P-hard, or
PSPACE-hard to manipulate, depending on whether the schedule of the preround is
determined before the votes are collected, after the votes are collected, or
the scheduling and the vote collecting are interleaved, respectively. We prove
general sufficient conditions on the protocols for this tweak to introduce the
hardness, and show that the most common voting protocols satisfy those
conditions. These are the first results in voting settings where manipulation
is in a higher complexity class than NP (presuming PSPACE $\neq$ NP).


  In recent years, spammers are now trying to obfuscate their intents by
introducing hybrid spam e-mail combining both image and text parts, which is
more challenging to detect in comparison to e-mails containing text or image
only. The motivation behind this research is to design an effective approach
filtering out hybrid spam e-mails to avoid situations where traditional
text-based or image-baesd only filters fail to detect hybrid spam e-mails. To
the best of our knowledge, a few studies have been conducted with the goal of
detecting hybrid spam e-mails. Ordinarily, Optical Character Recognition (OCR)
technology is used to eliminate the image parts of spam by transforming images
into text. However, the research questions are that although OCR scanning is a
very successful technique in processing text-and-image hybrid spam, it is not
an effective solution for dealing with huge quantities due to the CPU power
required and the execution time it takes to scan e-mail files. And the OCR
techniques are not always reliable in the transformation processes. To address
such problems, we propose new late multi-modal fusion training frameworks for a
text-and-image hybrid spam e-mail filtering system compared to the classical
early fusion detection frameworks based on the OCR method. Convolutional Neural
Network (CNN) and Continuous Bag of Words were implemented to extract features
from image and text parts of hybrid spam respectively, whereas generated
features were fed to sigmoid layer and Machine Learning based classifiers
including Random Forest (RF), Decision Tree (DT), Naive Bayes (NB) and Support
Vector Machine (SVM) to determine the e-mail ham or spam.


  The notion of polytopal map between two polytopal complexes is defined.
Surprisingly, this definition is quite simple and extends naturally those of
simplicial and cubical maps. It is then possible to define an induced chain map
between the associated chain complexes. Finally, we use this new tool to give
the first combinatorial proof of the splitting necklace theorem of Alon. The
paper ends with open questions, such as the existence of Sperner's lemma for a
polytopal complex or the existence of a cubical approximation theorem.


  The Kocinac alpha_i properties, i=1,2,3,4, are generalizations of
Arhangel'skii's alpha_i local properties. We give a complete classification of
these properties when applied to the standard families of open covers of
topological spaces or to the standard families of open covers of topological
groups. One of the latter properties characterizes totally bounded groups. We
also answer a question of Kocinac.


  The revolution of helio- and asteroseismology provides access to the detailed
properties of stellar interiors by studying the star's oscillation modes. Among
them, gravity (g) modes are formed by constructive interferences between
progressive internal gravity waves (IGWs), propagating in stellar radiative
zones. Our new 3D nonlinear simulations of the interior of a solar-like star
allows us to study the excitation, propagation, and dissipation of these waves.
The aim of this article is to clarify our understanding of the behavior of IGWs
in a 3D radiative zone and to provide a clear overview of their properties. We
use a method of frequency filtering that reveals the path of {individual}
gravity waves of different frequencies in the radiative zone. We are able to
identify the region of propagation of different waves in 2D and 3D, to compare
them to the linear raytracing theory and to distinguish between propagative and
standing waves (g modes). We also show that the energy carried by waves is
distributed in different planes in the sphere, depending on their azimuthal
wave number. We are able to isolate individual IGWs from a complex spectrum and
to study their propagation in space and time. In particular, we highlight in
this paper the necessity of studying the propagation of waves in 3D spherical
geometry, since the distribution of their energy is not equipartitioned in the
sphere.


  Contextual Text Block Detection (CTBD) is the task of identifying coherent
text blocks within the complexity of natural scenes. Previous methodologies
have treated CTBD as either a visual relation extraction challenge within
computer vision or as a sequence modeling problem from the perspective of
natural language processing. We introduce a new framework that frames CTBD as a
graph generation problem. This methodology consists of two essential
procedures: identifying individual text units as graph nodes and discerning the
sequential reading order relationships among these units as graph edges.
Leveraging the cutting-edge capabilities of DQ-DETR for node detection, our
framework innovates further by integrating a novel mechanism, a Dynamic
Relation Transformer (DRFormer), dedicated to edge generation. DRFormer
incorporates a dual interactive transformer decoder that deftly manages a
dynamic graph structure refinement process. Through this iterative process, the
model systematically enhances the graph's fidelity, ultimately resulting in
improved precision in detecting contextual text blocks. Comprehensive
experimental evaluations conducted on both SCUT-CTW-Context and ReCTS-Context
datasets substantiate that our method achieves state-of-the-art results,
underscoring the effectiveness and potential of our graph generation framework
in advancing the field of CTBD.


  We prove a general comparison result for homotopic finite $p$-energy $C^{1}$
$p$-harmonic maps $u,v:M\to N$ between Riemannian manifolds, assuming that $M$
is $p$-parabolic and $N$ is complete and non-positively curved. In particular,
we construct a homotopy through constant $p$-energy maps, which turn out to be
$p$-harmonic when $N$ is compact. Moreover, we obtain uniqueness in the case of
negatively curved $N$. This generalizes a well known result in the harmonic
setting due to R. Schoen and S.T. Yau.


  We present a multi-epoch spectroscopic study of LkCa 4, a heavily spotted
non-accreting T Tauri star. Using SpeX at NASA's Infrared Telescope Facility
(IRTF), 12 spectra were collected over five consecutive nights, spanning
$\approx$ 1.5 stellar rotations. Using the IRTF SpeX Spectral Library, we
constructed empirical composite models of spotted stars by combining a warmer
(photosphere) standard star spectrum with a cooler (spot) standard weighted by
the spot filling factor, $f_{spot}$. The best-fit models spanned two
photospheric component temperatures, $T_{phot}$ = 4100 K (K7V) and 4400 K
(K5V), and one spot component temperature, $T_{spot}$ = 3060 K (M5V) with an
$A_V$ of 0.3. We find values of $f_{spot}$ to vary between 0.77 and 0.94 with
an average uncertainty of $\sim$0.04. The variability of $f_{spot}$ is periodic
and correlates with its 3.374 day rotational period. Using a mean value for
$f^{mean}_{spot}$ to represent the total spot coverage, we calculated spot
corrected values for $T_{eff}$ and $L_\star$. Placing these values alongside
evolutionary models developed for heavily spotted young stars, we infer mass
and age ranges of 0.45-0.6 $M_\odot$ and 0.50-1.25 Myr, respectively. These
inferred values represent a twofold increase in the mass and a twofold decrease
in the age as compared to standard evolutionary models. Such a result
highlights the need for constraining the contributions of cool and warm regions
of young stellar atmospheres when estimating $T_{eff}$ and $L_\star$ to infer
masses and ages as well as the necessity for models to account for the effects
of these regions on the early evolution of low-mass stars.


  The paper discusses a model of Van der Waals crystals in which band-gap
structures do not form. An effect of strong and chaotic electron-electron
repulsion, which was excluded from consideration in the traditional approach,
is taken into account. A condensate exists as a result of a dynamic equilibrium
among atoms acted upon by constant Van der Waals forces and periodically
forming and disappearing covalent bonding. One part of atoms is, on the
average, in the ground, and the other, in excited state, to form diatomic
virtual molecules. Treated in terms of this pseudoclassical model, the
interatomic distances, binding energies, volumes, and pressures at which
metallization, for instance, of inert gases and hydrogen, sets in is described
by simple relations involving only two spectroscopic parameters of atoms
(molecules). Applying pressure to a VdW crystals transfers it from the
insulator first to a Bose superconductor, and after that, to a Fermi metal. An
empirical relation $T_c \sim N^{2/3}$ between the superconductivity transition
temperature $T_c$ and the particles concentration $N$ in chalcogens under
pressure is considered as an example of such situation.


  In this paper, we introduce a new class of bivariate distributions called the
bivariate exponentiated extended Weibull distributions. The model introduced
here is of Marshall-Olkin type. This new class of bivariate distributions
contains several bivariate lifetime models. Some mathematical properties of the
new class of distributions are studied. We provide the joint and conditional
density functions, the joint cumulative distribution function and the joint
survival function. Special bivariate distributions are investigated in some
detail. The maximum likelihood estimators are obtained using the EM algorithm.
We illustrate the usefulness of the new class by means of application to two
real data sets.


  In this work we calculate the partition functions of $\mathcal{N}=1$ type 0A
and 0B JT supergravity (SJT) on 2D surfaces of arbitrary genus with multiple
finite cut-off boundaries, based on the $T\bar{T}$ deformed super-Schwarzian
theories. In terms of SJT/matrix model duality, we compute the corresponding
correlation functions in the $T\bar{T}$ deformed matrix model side by using
topological recursion relations as well as the transformation properties of
topological recursion relations under $T\bar{T}$ deformation. We check that the
partition functions finite cut-off 0A and 0B SJT on generic 2D surfaces match
the associated correlation functions in $T\bar{T}$ deformed matrix models
respectively.


  To approach a more reliable observational signature of a high-spin Kerr black
hole, one should take into account the effects of its surroundings. To this end
we study in this paper the influence of a surrounding plasma. We consider its
refractive and dispersive effects on photon trajectories and ignore the
gravitational effects of plasma particles as well as the absorption or
scattering processes of photons. With two specific plasma models, we obtain
analytical formulae for the black hole shadow and for the observational
quantities of an orbiting "hot spot" seen by an observer located far away from
the black hole. We find that the plasma has a frequency-dependent dispersive
effect on the size and shape of the black hole shadow and on the image position
and redshift of the hot spot. These results may be tested by the Event Horizon
Telescope in the future.


  We present the first results using the STAR detector from the Beam Energy
Scan (BES) program at the Relativistic Heavy-Ion Collider (RHIC). In this
program, Au ion collisions at center of mass energies (\sqrt{s_{NN}}) of 7.7,
11.5 and 39 GeV allowed RHIC to extend the study of the QCD phase diagram from
baryonic chemical potential values of 20 MeV to about 400 MeV. For the high
net-baryon density matter at midrapidity, formed in these collisions, we report
several interesting measurements. These include the observation of difference
between anti-particle and particle elliptic flow, disappearance of the
difference in dynamical azimuthal correlations with respect to event plane
between same and opposite signed charged particles, change in slope of
eccentricity at freeze-out and directed flow of protons as a function of
\sqrt{s_{NN}} and the deviation of higher order fluctuations from hadron
resonance gas and Poissonian expectations. Possible interpretations of these
observations are also discussed.


  We prove that, in dimensions greater than 2, the generic metric is not a
Hessian metric and find a curvature condition on Hessian metrics in dimensions
greater than 3. In particular we prove that the forms used to define the
Pontryagin classes in terms of the curvature vanish on a Hessian manifold. By
contrast all analytic Riemannian 2-metrics are Hessian metrics.


  Closed generic quantum many-body systems may fail to thermalize under certain
conditions even after long times, a phenomenon called many-body localization
(MBL). Numerous studies support the stability of the MBL phase in strongly
disordered one-dimensional systems. However, the situation is much less clear
when a small part of the system is ergodic, a scenario which also has important
implications for the existence of many-body localization in higher dimensions.
Here we address this question experimentally using a large-scale quantum
simulator of ultracold bosons in a two-dimensional optical lattice. We prepare
two-component mixtures of varying relative population and implement a disorder
potential which is only experienced by one of the components. The second
non-disordered ''clean'' component plays the role of a bath of adjustable size
that is collisionally coupled to the ''dirty'' component. Our experiments show
how the dynamics of the dirty component, which, when on its own, show strong
evidence of localization, become affected by the coupling to the clean
component. For a high clean population, the clean component appears to behave
as an effective bath for the system which leads to its delocalization, while
for a smaller clean population, the ability of the bath to destabilize the
system becomes strongly reduced. Our results reveal how a finite-sized quantum
system can bring another one towards thermalization, in a regime of complex
interplay between disorder, tunneling and intercomponent interactions. They
provide a new benchmark for effective theories aiming to capture the complex
physics of MBL in the weakly localized regime.


  We provide mathematicaly rigorous justification of using term "probability"
in connection to the so called non-signalling theories,known also as Popescu's
and Rohrlich's box worlds. No only do we prove correctness of these models (in
the sense that they describe composite system of two independent subsystems)
but we obtain new properties of non-signalling boxes and expose new tools for
further investigation. Moreover, it allows strightforward generalization to
more complicated systems.


  We prove dispersive estimates for two models~: the adjacency matrix on a
discrete regular tree, and the Schr\"odinger equation on a metric regular tree
with the same potential on each edge/vertex. The latter model can be thought of
as an extension of the case of periodic Schr\"odinger operators on the real
line. We establish a $t^{-3/2}$-decay for both models which is sharp, as we
give the first-order asymptotics.


  The energy dependence of the local ${\cal P}$ and ${\cal CP}$ violation in
Au+Au and Cu+Cu collisions in a large energy range is estimated within a simple
phenomenological model. It is expected that at LHC the chiral magnetic effect
will be about 20 times weaker than at RHIC. At lower energy range, covered by
the low-energy scan at RHIC and future NICA/FAIR facilities, the created
magnetic field strength and energy density of deconfined matter are rather high
providing necessary conditions for the chiral magnetic effect. However, the
particular model for the chiral magnetic effect predicts that this effect
should vanish sharply at energy somewhere above the top SPS one. To elucidate
CME background effects the Hadron-String-Dynamics (HSD) transport model
including electromagnetic fields is put forward. Importance of new planning
experiments at LHC and for the low-energy RHIC scan program is emphasized.


  We revisit Sakurai's remark on the regularities of lepton-pair widths for
mesons, extending the panorama to radiative $X \to \gamma \gamma$ and total
decays. The regularities persist, and somehow surprisingly some of them seem to
relate with Fermi's constant -or $Z^0$-.


  Isolated pulsars are rotating neutron stars with accurately measured angular
velocities $\Omega$, and their time derivatives which show unambiguously that
the pulsars are slowing down. Although the exact mechanism of the spin-down is
a question of debate, the commonly accepted view is that it arises either
through emission of magnetic dipole radiation (MDR) from a rotating magnetized
body, through emission of a relativistic particle wind, or via higher order
magnetic multipole or gravitational quadrupole radiation. The calculated energy
loss by a rotating pulsar is model dependent and leads to the power law
$\dot{\Omega}$ = -K $\Omega^{\rm n}$ where $n$ is called the braking index. The
theoretical value for braking index is $n = 1, 3, 5$ for wind, MDR, quadrupole
radiation respectively. The accepted view is that pulsar braking is strongly
dominated by MDR. Highly precise observations of isolated pulsars yield braking
index values in the range $1 < n < 2.8$ which are consistently less than the
value predicted from the MDR model. We discuss possible ways to bring theory
closer to observation for the MDR, and also consider how the other mechanisms
may play a role in future study of the braking index problem.


  We propose a mathematical model for the spread of Japanese encephalitis, with
emphasis on environmental effects on the aquatic phase of mosquitoes. The model
is shown to be biologically well-posed and to have a biologically and
ecologically meaningful disease free equilibrium point. Local stability is
analyzed in terms of the basic reproduction number and numerical simulations
presented and discussed.


  Multireference effects are associated with degeneracies and near-degeneracies
of the ground state and are critical to a variety of systems. Most approximate
functionals of density functional theory (DFT) fail to properly describe these
effects. A number of diagnostics have been proposed that allow to estimate the
reliability of a given single-reference solution in this respect. Some of these
diagnostics however lack size-consistency, while remaining computationally
expensive. In this work we use the DFT method of determining atomic populations
of effectively localized electrons (APELE) as a novel diagnostic in this vein.
It is compared with several existing diagnostics of nondynamic correlation on
select exemplary systems. We show that the APELE method is on average in good
agreement with the existing diagnostics, while being both size-consistent and
less costly. It becomes particularly informative in cases involving bond
stretching or bond breaking. The APELE method is applied next to organic
diradicals like the bis-acridine dimer and the p-quinodimethane molecule which
possess unusually high nonlinear optical response, and to the reaction of
ethylene addition to Ni dithiolene, where our results shed some more light on
how the oxidation state of the Ni center may change when going from the initial
reactant to the product.


  We give sufficient and necessary conditions on the Lebesgue exponents for the
Weyl product to be bounded on modulation spaces. The sufficient conditions are
obtained as the restriction to $N=2$ of a result valid for the $N$-fold Weyl
product. As a byproduct, we obtain sharp conditions for the twisted convolution
to be bounded on Wiener amalgam spaces.


  - Like consumer electronic products, medical devices are becoming more
complicated, with performance doubling every two years. With multiple commands
and systems to negotiate, cognitive load can make it difficult for users to
execute commands effectively. In the case of medical devices, which use
advanced technology and require multidisciplinary inputs for design and
development, cognitive workload is a significant factor. As these devices are
very expensive and operators require specialized training, effective and
economical methods are needed to evaluate the user experience. Heuristic
evaluation is an effective method of identifying major usability problems and
related issues. This study used heuristic evaluation to assess the usability of
a CT scan and associated physical and mental loads for Saudi Arabian users. The
findings indicate a gender difference in terms of consistency, flexibility, and
document attributes, with a statistically significant gender difference in
mental load.


  The quantum neural network is one of the promising applications for near-term
noisy intermediate-scale quantum computers. A quantum neural network distills
the information from the input wavefunction into the output qubits. In this
Letter, we show that this process can also be viewed from the opposite
direction: the quantum information in the output qubits is scrambled into the
input. This observation motivates us to use the tripartite information, a
quantity recently developed to characterize information scrambling, to diagnose
the training dynamics of quantum neural networks. We empirically find strong
correlation between the dynamical behavior of the tripartite information and
the loss function in the training process, from which we identify that the
training process has two stages for randomly initialized networks. In the early
stage, the network performance improves rapidly and the tripartite information
increases linearly with a universal slope, meaning that the neural network
becomes less scrambled than the random unitary. In the latter stage, the
network performance improves slowly while the tripartite information decreases.
We present evidences that the network constructs local correlations in the
early stage and learns large-scale structures in the latter stage. We believe
this two-stage training dynamics is universal and is applicable to a wide range
of problems. Our work builds bridges between two research subjects of quantum
neural networks and information scrambling, which opens up a new perspective to
understand quantum neural networks.


  The existence of supermassive black holes as early as z ~ 7 is one of the
great unsolved problems in cosmological structure formation. One leading theory
argues that they are born during catastrophic baryon collapse in z ~ 15
protogalaxies in strong Lyman-Werner UV backgrounds. Atomic line cooling in
such galaxies fragments baryons into massive clumps that are thought to
directly collapse to 10^4 - 10^5 solar-mass black holes. We have now discovered
that some of these fragments can instead become supermassive stars that
eventually explode as pair-instability supernovae with energies of ~ 10^55 erg,
the most energetic explosions in the universe. We have calculated light curves
and spectra for supermassive Pop III PI SNe with the Los Alamos RAGE and
SPECTRUM codes. We find that they will be visible in NIR all-sky surveys by
Euclid out to z ~ 10 - 15 and by WFIRST and WISH out to z ~ 15 - 20, perhaps
revealing the birthplaces of the first quasars.


  We present a method to determine the decay of multiparticle quantum
correlations as quantified by the geometric measure of entanglement under the
influence of decoherence. With this, we compare the robustness of entanglement
in GHZ-, cluster-, W- and Dicke states of four qubits and show that the Dicke
state is most robust. Finally, we determine the geometric measure analytically
for decaying GHZ and cluster states of an arbitrary number of qubits.


  We investigate the effects of spin-orbit interaction (SOI) and valley mixing
on the transport and dynamical properties of a carbon nanotube (CNT) quantum
dot in the Kondo regime. As these perturbations break the pseudo-spin symmetry
in the CNT spectrum but preserve time-reversal symmetry, they induce a finite
splitting $\Delta$ between formerly degenerate Kramers pairs. Correspondingly,
a crossover from the SU(4) to the SU(2)-Kondo effect occurs as the strength of
these symmetry breaking parameters is varied. Clear signatures of the crossover
are discussed both at the level of the spectral function as well as of the
conductance. In particular, we demonstrate numerically and support with scaling
arguments, that the Kondo temperature scales inversely with the splitting
$\Delta$ in the crossover regime. In presence of a finite magnetic field, time
reversal symmetry is also broken. We investigate the effects of both parallel
and perpendicular fields (with respect to the tube's axis), and discuss the
conditions under which Kondo revivals may be achieved.


  In Part 1 of this paper, we study gravitational descendents of Gromov-Witten
invariants for general projective manifolds, applying the Behrend-Fantechi
construction of the virtual fundamental classes.
  In Part 2, we calculate the topological recursion relations in genus 2. There
are two of these, one for the second descendent of a field, and one for the
first descendents of two fields. The proof uses the results of Part 1 together
with a thorough study of intersection theory on the moduli space
$\bar{M}_{2,2}$.


  We report an extensive study of the phase diagram of a simple model for
ortho-terphenyl, focusing on the limits of stability of the liquid state.
Reported data extend previous studies of the same model to both lower and
higher densities and to higher temperatures. We estimate the location of the
homogeneous liquid-gas nucleation line and of the spinodal locus. Within the
potential energy landscape formalism, we calculate the distributions of depth,
number, and shape of the potential energy minima and show that the statistical
properties of the landscape are consistent with a Gaussian distribution of
minima over a wide range of volumes. We report the volume dependence of the
parameters entering in the Gaussian distribution (amplitude, average energy,
variance). We finally evaluate the locus where the configurational entropy
vanishes, the so-called Kauzmann line, and discuss the relative location of the
spinodal and Kauzmann loci.


  The multinomial probit model is often used to analyze choice behaviour.
However, estimation with existing Markov chain Monte Carlo (MCMC) methods is
computationally costly, which limits its applicability to large choice data
sets. This paper proposes a variational Bayes method that is accurate and fast,
even when a large number of choice alternatives and observations are
considered. Variational methods usually require an analytical expression for
the unnormalized posterior density and an adequate choice of variational
family. Both are challenging to specify in a multinomial probit, which has a
posterior that requires identifying restrictions and is augmented with a large
set of latent utilities. We employ a spherical transformation on the covariance
matrix of the latent utilities to construct an unnormalized augmented posterior
that identifies the parameters, and use the conditional posterior of the latent
utilities as part of the variational family. The proposed method is faster than
MCMC, and can be made scalable to both a large number of choice alternatives
and a large number of observations. The accuracy and scalability of our method
is illustrated in numerical experiments and real purchase data with one million
observations.


  The scaled boundary finite element method (SBFEM) is capable of generating
polyhedral elements with an arbitrary number of surfaces. This salient feature
significantly alleviates the meshing burden being a bottleneck in the analysis
pipeline in the standard finite element method (FEM). In this paper, we
implement polyhedral elements based on the SBFEM into the commercial finite
element software ABAQUS. To this end, user elements are provided through the
user subroutine UEL. Detailed explanations regarding the data structures and
implementational aspects of the procedures are given. The focus of the current
implementation is on interfacial problems and therefore, element-based surfaces
are created on polyhedral user elements to establish interactions. This is
achieved by an overlay of standard finite elements with negligible stiffness,
provided in the ABAQUS element library, with polyhedral user elements. By means
of several numerical examples, the advantages of polyhedral elements regarding
the treatment of non-matching interfaces and automatic mesh generation are
clearly demonstrated. Thus, the performance of ABAQUS for problems involving
interfaces is augmented based on the availability of polyhedral meshes. Due to
the implementation of polyhedral user elements, ABAQUS can directly handle
complex geometries given in the form of digital images or stereolithography
(STL) files. In order to facilitate the use of the proposed approach, the code
of the UEL is published open-source and can be downloaded from
https://github.com/ShukaiYa/SBFEM-UEL.


  We introduce the first comprehensive approach to determine the uncertainty in
volumetric Particle Tracking Velocimetry (PTV) measurements. Volumetric PTV is
a state-of-the-art non-invasive flow measurement technique, which measures the
velocity field by recording successive snapshots of the tracer particle motion
using a multi-camera set-up. The measurement chain involves reconstructing the
three-dimensional particle positions by a triangulation process using the
calibrated camera mapping functions. The non-linear combination of the
elemental error sources during the iterative self-calibration correction and
particle reconstruction steps increases the complexity of the task. Here, we
first estimate the uncertainty in the particle image location, which we model
as a combination of the particle position estimation uncertainty and the
reprojection error uncertainty. The latter is obtained by a gaussian fit to the
histogram of disparity estimates within a sub-volume. Next, we determine the
uncertainty in the camera calibration coefficients. As a final step the
previous two uncertainties are combined using an uncertainty propagation
through the volumetric reconstruction process. The uncertainty in the velocity
vector is directly obtained as a function of the reconstructed particle
position uncertainty. The framework is tested with synthetic vortex ring
images. The results show good agreement between the predicted and the expected
RMS uncertainty values. The prediction is consistent for seeding densities
tested in the range of 0.01 to 0.1 particles per pixel. Finally, the
methodology is also successfully validated for an experimental test case of
laminar pipe flow velocity profile measurement where the predicted uncertainty
is within 17% of the RMS error value.


  Learning from preference-based feedback has recently gained considerable
traction as a promising approach to align generative models with human
interests. Instead of relying on numerical rewards, the generative models are
trained using reinforcement learning with human feedback (RLHF). These
approaches first solicit feedback from human labelers typically in the form of
pairwise comparisons between two possible actions, then estimate a reward model
using these comparisons, and finally employ a policy based on the estimated
reward model. An adversarial attack in any step of the above pipeline might
reveal private and sensitive information of human labelers. In this work, we
adopt the notion of label differential privacy (DP) and focus on the problem of
reward estimation from preference-based feedback while protecting privacy of
each individual labelers. Specifically, we consider the parametric
Bradley-Terry-Luce (BTL) model for such pairwise comparison feedback involving
a latent reward parameter $\theta^* \in \mathbb{R}^d$. Within a standard
minimax estimation framework, we provide tight upper and lower bounds on the
error in estimating $\theta^*$ under both local and central models of DP. We
show, for a given privacy budget $\epsilon$ and number of samples $n$, that the
additional cost to ensure label-DP under local model is $\Theta \big(\frac{1}{
e^\epsilon-1}\sqrt{\frac{d}{n}}\big)$, while it is
$\Theta\big(\frac{\text{poly}(d)}{\epsilon n} \big)$ under the weaker central
model. We perform simulations on synthetic data that corroborate these
theoretical results.


  Bloom Filter is an important probabilistic data structure to reduce memory
consumption for membership filters. It is applied in diverse domains such as
Computer Networking, Network Security and Privacy, IoT, Edge Computing, Cloud
Computing, Big Data, and Biometrics. But Bloom Filter has an issue of the false
positive probability. To address this issue, we propose a novel robust Bloom
Filter, robustBF for short. robustBF is a 2D Bloom Filter, capable of filtering
millions of data with high accuracy without compromising the performance. Our
proposed system is presented in two-fold. Firstly, we modify the murmur hash
function, and test all modified hash functions for improvements and select the
best-modified hash function experimentally. Secondly, we embed the modified
hash functions in 2D Bloom Filter. Our experimental results show that robustBF
is better than standard Bloom Filter and counting Bloom Filter in every aspect.
robustBF exhibits nearly zero false positive probability with more than
$10\times$ and $44\times$ lower memory consumption than standard Bloom filter
and counting Bloom Filter, respectively.


  We investigate analytically the fermionic fluctuation determinant at finite
temperatures in the minimal standard model, including all operators up to
dimension 6 and all contributions to the effective potential to all orders in
the high $T$ expansion, to 1 loop. We apply the results to find corrections to
the Sphaleron erasure rate in the broken phase. We conclude that the analytic
treatment of fermions is very reliable and that there is a great deal of baryon
erasure after the phase transition for any physical Higgs mass.


  By keeping nonlinear Boltzmann factor in electron density dependence on
electrostatic potential it is demonstrated that large plasma density blobs,
often seen in experiment inside separatrix, can exist within the framework of
drift wave dynamics. The estimates show that plasma density in a blob can be ~3
times higher that average plasma density, but hardly exceeds this limit, which
in a ball park is in agreement with experimental observations.


  There has been increased interest in missing sensor data imputation, which is
ubiquitous in the field of structural health monitoring (SHM) due to
discontinuous sensing caused by sensor malfunction. To address this fundamental
issue, this paper presents an incremental Bayesian tensor learning method for
reconstruction of spatiotemporal missing data in SHM and forecasting of
structural response. In particular, a spatiotemporal tensor is first
constructed followed by Bayesian tensor factorization that extracts latent
features for missing data imputation. To enable structural response forecasting
based on incomplete sensing data, the tensor decomposition is further
integrated with vector autoregression in an incremental learning scheme. The
performance of the proposed approach is validated on continuous field-sensing
data (including strain and temperature records) of a concrete bridge, based on
the assumption that strain time histories are highly correlated to temperature
recordings. The results indicate that the proposed probabilistic tensor
learning approach is accurate and robust even in the presence of large rates of
random missing, structured missing and their combination. The effect of rank
selection on the imputation and prediction performance is also investigated.
The results show that a better estimation accuracy can be achieved with a
higher rank for random missing whereas a lower rank for structured missing.


  Differential rotation is one of the basic characteristics of the Sun, and it
plays an important role in generating the magnetic fields and its activities.
We investigated rotation rate using chromospheric features such as plages,
enhanced network, active network, and quiet network separately (for the first
time). The digitized Ca-K images from Kodaikanal Observatory for 1907-1996 are
used to study rotation over 0-80 degrees latitudes at an interval of
10$^{\circ}$ . We find that plages and all types of networks exhibit the
differential rotation of the chromosphere. Furthermore, the rotation rate shows
a decreasing pattern as one move from the equator to the higher polar latitudes
for all the features used in the study. By analyzing how the area of
chromospheric features varies over time, we can effectively map the Sun's
rotation rate at all latitudes, including the polar regions. Interestingly,
both plages and small-scale networks exhibit similar differential rotation
rate. This suggests these features likely rooted at the same layer below the
visible surface of the Sun. Therefore, the long-term Ca-K data is very useful
to study the solar rotation rate at all latitudes including the polar regions.


  We investigate the ac transport of magnetization in non-itinerant quantum
systems such as spin chains described by the XXZ Hamiltonian. Using linear
response theory, we calculate the ac magnetization current and the power
absorption of such magnetic systems. Remarkably, the difference in the exchange
interaction of the spin chain itself and the bulk magnets (i.e. the
magnetization reservoirs), to which the spin chain is coupled, strongly
influences the absorbed power of the system. This feature can be used in future
spintronic devices to control power dissipation. Our analysis allows to make
quantitative predictions about the power absorption and we show that magnetic
systems are superior to their electronic counter parts.


  In this paper we extend our previously discovered exact solution for an SU(2)
gauge theory coupled to a massless, non-interacting scalar field, to the
general group SU(N+1). Using the first-order formalism of Bogomolny, an exact,
spherically symmetric solution for the gauge and scalar fields is found. This
solution is similiar to the Schwarzschild solution of general relativity, in
that the gauge and scalar fields become infinite at a radius, $r_0 = K$, from
the origin. It is speculated that this may be the confinement mechanism that
has long been sought for in non-Abelian gauge theories, since any particle
which carries the SU(N+1) charge would become permanently trapped once it
entered the region $r < r_0$. The energy of the field configuration of this
solution is calculated.


  A general quantum network for implementing non-local control-unitary gates,
between remote parties at minimal entanglement cost, is shown to be a
rooted-tree structure. Starting from a five party scenario, we demonstrate the
local implementation of simultaneous control-Hermitian and multiparty
control-unitary gates in an arbitrary n-party network. Previously established
networks are shown to be special cases of this general construct.


  The critical behavior of a model colloid-polymer mixture, the so-called AO
model, is studied using computer simulations and finite size scaling
techniques. Investigated are the interfacial tension, the order parameter, the
susceptibility and the coexistence diameter. Our results clearly show that the
interfacial tension vanishes at the critical point with exponent 2\nu ~ 1.26.
This is in good agreement with the 3D Ising exponent. Also calculated are
critical amplitude ratios, which are shown to be compatible with the
corresponding 3D Ising values. We additionally identify a number of subtleties
that are encountered when finite size scaling is applied to the AO model. In
particular, we find that the finite size extrapolation of the interfacial
tension is most consistent when logarithmic size dependences are ignored. This
finding is in agreement with the work of Berg et al.[Phys. Rev. B, V47 P497
(1993)]


  We give a bound of $k$ for a very ample lattice polytope to be $k$-normal.
Equivalently, we give a new combinatorial bound for the Castelnuovo-Mumford
regularity of normal projective toric varieties.


  CeAu2Si2 is a newly discovered pressure-induced heavy fermion superconductor
which shows very unusual interplay between superconductivity and magnetism
under pressure. Here we compare the results of high-pressure measurements on
single crystalline CeAu2Si2 samples with different levels of disorder. It is
found that while the magnetic properties are essentially sample independent,
superconductivity is rapidly suppressed when the residual resistivity of the
sample increases. We show that the depression of bulk Tc can be well understood
in terms of pair breaking by nonmagnetic disorder, which strongly suggests an
unconventional pairing state in pressurized CeAu2Si2. Furthermore, increasing
the level of disorder leads to the emergence of another phase transition at T*
within the magnetic phase, which might be in competition with
superconductivity.


  Gibbs' thermodynamic entropy is given by the logarithm of the phase volume,
which itself responds to heat transfer to and from thermal reservoirs. We
compare the thermodynamic dissipation described by phase-volume loss with
heat-transfer entropy production. Their equivalence is documented for computer
simulations of the response of an ergodic harmonic oscillator to thermostated
temperature gradients. In the simulations one or two thermostat variables
control the kinetic energy or the kinetic energy and its fluctuation. All of
the motion equations are time-reversible. We consider both strong and weak
control variables. In every case the time-averaged dissipative loss of
phase-space volume coincides with the entropy produced by heat transfer. Linear
response theory nicely reproduces the small-gradient results obtained by
computer simulation. The thermostats considered here are ergodic and provide
simple dynamical models, some of them with as few as three ordinary
differential equations, while remaining capable of reproducing Gibbs' canonical
phase-space distribution and precisely consistent with irreversible
thermodynamics.


  We give sufficient conditions for the existence of Kaehler-Einstein and
constant scalar curvature Kaehler (cscK) metrics on finite ramified Galois
coverings of a cscK manifold in terms of cohomological conditions on the
Kaehler classes and the branching divisor. This result generalizes previous
work on Kaehler-Einstein metrics by Li-Sun [Comm. Math. Phys. 2014], and
extends Chen-Cheng's existence results for cscK metrics in [J. Amer. Math. Soc.
2021].


  The distortion of corner-sharing octahedra in isovalent perovskite
transition-metal oxide interfaces is proven to be an excellent way to tailor
the electronic and magnetic properties of their heterostructures. Combining
depth-dependent magnetic characterization technique; (polarized neutron
reflectivity, PNR); and theoretical calculation (density functional theory), we
report interface-driven magnetic exchange interactions due to a modification in
the octahedral rotations at the interfaces in an isovalent La0.67Ca0.33MnO3
(LCMO)/La0.67Sr0.33MnO3 (LSMO) heterostructures. PNR results determined a
length scale of ~ 8 unit cells at the interface, which demonstrated a
modification in magnetic properties. The results also predicted a
low-temperature exchange bias for these ferromagnetic heterostructures with a
maximum exchange bias for the heterostructure, which showed an enhanced
antiferromagnetic coupling at the interfaces.


  We perform a complete analysis of the supersymmetric particle spectrum in the
Minimal Supergravity (mSUGRA) model. We show that present constraints on the
Higgs boson and superparticle masses from collider searches and precision
measurements still allow for large regions of the mSUGRA parameter space where
some sparticles as well as the heavier Higgs particles, are light enough to be
produced at the next generation of $e^+e^-$ linear colliders. An important part
of this parameter space remains even when we require that the density of the
lightest neutralinos left over from the Big Bang falls in the range favored by
current determinations of the Dark Matter density in the Universe.


  This paper defines the Arrwwid number of a recursive tiling (or space-filling
curve) as the smallest number w such that any ball Q can be covered by w tiles
(or curve sections) with total volume O(vol(Q)). Recursive tilings and
space-filling curves with low Arrwwid numbers can be applied to optimise disk,
memory or server access patterns when processing sets of points in
d-dimensional space. This paper presents recursive tilings and space-filling
curves with optimal Arrwwid numbers. For d >= 3, we see that regular cube
tilings and space-filling curves cannot have optimal Arrwwid number, and we see
how to construct alternatives with better Arrwwid numbers.


  Markov decision processes (MDP) are useful to model optimisation problems in
concurrent systems. To verify MDPs with efficient Monte Carlo techniques
requires that their nondeterminism be resolved by a scheduler. Recent work has
introduced the elements of lightweight techniques to sample directly from
scheduler space, but finding optimal schedulers by simple sampling may be
inefficient. Here we describe "smart" sampling algorithms that can make
substantial improvements in performance.


  The last proton bound calcium isotope $^{35}$Ca has been studied for the
first time, using the $^{37}$Ca($p, t$)$^{35}$Ca two neutron transfer reaction.
The radioactive $^{37}$Ca nuclei, produced by the LISE spectrometer at GANIL,
interacted with the protons of the liquid hydrogen target CRYPTA, to produce
tritons $t$ that were detected in the MUST2 detector array, in coincidence with
the heavy residues Ca or Ar. The atomic mass of $^{35}$Ca and the energy of its
first 3/2$^+$ state are reported. A large $N=16$ gap of 4.61(11) MeV is deduced
from the mass measurement, which together with other measured properties, makes
$^{36}$Ca a doubly-magic nucleus. The $N = 16$ shell gaps in $^{36}$Ca and
$^{24}$O are of similar amplitude, at both edges of the valley of stability.
This feature is discussed in terms of nuclear forces involved, within
state-of-the-art shell model calculations. Even though the global agreement
with data is quite convincing, the calculations underestimate the size of the
$N = 16$ gap in 36Ca by 840(110) keV.


  Transition metal dichalcogenides (TMDs) are layered materials that have a
semiconducting phase with many advantageous optoelectronic properties,
including tightly bound excitons and spin-valley locking. In Tungsten-based
TMDs, spin and momentum forbidden transitions give rise to dark excitons that
typically are optically inaccessible but represent the lowest excitonic states
of the system. Dark excitons can deeply affect transport, dynamics and
coherence of bright excitons, hampering device performance. Therefore, it is
crucial to create conditions in which these excitonic states can be visualized
and controlled. Here, we show that compressive strain in WS2 enables phonon
scattering of photoexcited electrons between momentum valleys, enhancing the
formation of dark intervalley excitons. We show that the emission and spectral
properties of momentum-forbidden excitons are accessible and strongly depend on
the local strain environment that modifies the band alignment. This mechanism
is further exploited for strain sensing in two-dimensional semiconductors
revealing a gauge factor exceeding 10^4.


  The analysis of the end-to-end behavior of novel mobile communication methods
in concrete evaluation scenarios frequently results in a methodological
dilemma: Real world measurement campaigns are highly time-consuming and lack of
a controllable environment, the derivation of analytical models is often not
possible due to the immense system complexity, system-level network simulations
imply simplifications that result in significant derivations to the real world
observations. In this paper, we present a hybrid simulation approach which
brings together model-based mobility simulation, multi-dimensional Radio
Environmental Maps (REMs) for efficient maintenance of radio propagation data,
and Data-driven Network Simulation (DDNS) for fast and accurate analysis of the
end-to-end behavior of mobile networks. For the validation, we analyze an
opportunistic vehicular data transfer use-case and compare the proposed method
to real world measurements and a corresponding simulation setup in Network
Simulator 3 (ns-3). In comparison to the latter, the proposed method is not
only able to better mimic the real world behavior, it also achieves a 300 times
higher computational efficiency.


  For a sequence of immersed connected closed Hamiltonian stationary Lagrangian
submaniolds in $\mathbb{C}^{n}$ with uniform bounds on their volumes and the
total extrinsic curvatures, we prove that a subsequence converges either to a
point or to a Hamiltonian stationary Lagrangian $n$-varifold locally uniformly
in $C^{k}$ for any nonnegative integer $k$ away from a finite set of points,
and the limit is Hamiltonian stationary in ${\mathbb{C}}^{n}$. We also obtain a
theorem on extending Hamiltonian stationary Lagrangian submanifolds $L$ across
a compact set $N$ of Hausdorff codimension at least 2 that is locally
noncollapsing in volumes matching its Hausdorff dimension, provided the mean
curvature of $L$ is in $L^{n}$ and a condition on local volume of $L$ near $N$
is satisfied.


  Deducing the 3D face from a skull is an essential but challenging task in
forensic science and archaeology. Existing methods for automated facial
reconstruction yield inaccurate results, suffering from the non-determinative
nature of the problem that a skull with a sparse set of tissue depth cannot
fully determine the skinned face. Additionally, their texture-less results
require further post-processing stages to achieve a photo-realistic appearance.
This paper proposes an end-to-end 3D face reconstruction and exploration tool,
providing textured 3D faces for reference. With the help of state-of-the-art
text-to-image diffusion models and image-based facial reconstruction
techniques, we generate an initial reference 3D face, whose biological profile
aligns with the given skull. We then adapt these initial faces to meet the
statistical expectations of extruded anatomical landmarks on the skull through
an optimization process. The joint statistical distribution of tissue depths is
learned on a small set of anatomical landmarks on the skull. To support further
adjustment, we propose an efficient face adaptation tool to assist users in
tuning tissue depths, either globally or at local regions, while observing
plausible visual feedback. Experiments conducted on a real skull-face dataset
demonstrated the effectiveness of our proposed pipeline in terms of
reconstruction accuracy, diversity, and stability.


  A new functional calculus, developed recently for a fully non-perturbative
treatment of quantum gravity, is used to begin a systematic construction of a
quantum theory of geometry. Regulated operators corresponding to areas of
2-surfaces are introduced and shown to be self-adjoint on the underlying
(kinematical) Hilbert space of states. It is shown that their spectra are {\it
purely} discrete indicating that the underlying quantum geometry is far from
what the continuum picture might suggest. Indeed, the fundamental excitations
of quantum geometry are 1-dimensional, rather like polymers, and the
3-dimensional continuum geometry emerges only on coarse graining. The full
Hilbert space admits an orthonormal decomposition into finite dimensional
sub-spaces which can be interpreted as the spaces of states of spin systems.
Using this property, the complete spectrum of the area operators is evaluated.
The general framework constructed here will be used in a subsequent paper to
discuss 3-dimensional geometric operators, e.g., the ones corresponding to
volumes of regions.


  Optimal transport is a foundational problem in optimization, that allows to
compare probability distributions while taking into account geometric aspects.
Its optimal objective value, the Wasserstein distance, provides an important
loss between distributions that has been used in many applications throughout
machine learning and statistics. Recent algorithmic progress on this problem
and its regularized versions have made these tools increasingly popular.
However, existing techniques require solving an optimization problem to obtain
a single gradient of the loss, thus slowing down first-order methods to
minimize the sum of losses, that require many such gradient computations. In
this work, we introduce an algorithm to solve a regularized version of this
problem of Wasserstein estimators, with a time per step which is sublinear in
the natural dimensions of the problem. We introduce a dual formulation, and
optimize it with stochastic gradient steps that can be computed directly from
samples, without solving additional optimization problems at each step. Doing
so, the estimation and computation tasks are performed jointly. We show that
this algorithm can be extended to other tasks, including estimation of
Wasserstein barycenters. We provide theoretical guarantees and illustrate the
performance of our algorithm with experiments on synthetic data.


  Physics-based simulation for fluid flow in porous media is a computational
technology to predict the temporal-spatial evolution of state variables (e.g.
pressure) in porous media, and usually requires high computational expense due
to its nonlinearity and the scale of the study domain. This letter describes a
deep learning (DL) workflow to predict the pressure evolution as fluid flows in
large-scale 3D heterogeneous porous media. In particular, we apply feature
coarsening technique to extract the most representative information and perform
the training and prediction of DL at the coarse scale, and further recover the
resolution at the fine scale by 2D piecewise cubic interpolation. We validate
the DL approach that is trained from physics-based simulation data to predict
pressure field in a field-scale 3D geologic CO_2 storage reservoir. We evaluate
the impact of feature coarsening on DL performance, and observe that the
feature coarsening can not only decrease training time by >74% and reduce
memory consumption by >75%, but also maintains temporal error <1.5%. Besides,
the DL workflow provides predictive efficiency with ~1400 times speedup
compared to physics-based simulation.


  We discuss a new technique for studying astrophysical turbulence that
utilizes the statistics of Doppler-broadened spectral lines. The technique
relates the power Velocity Coordinate Spectrum (VCS), i.e. the spectrum of
fluctuations measured along the velocity axis in Position-Position-Velocity
(PPV) data cubes available from observations, to the underlying power spectra
of the velocity/density fluctuations. Unlike the standard spatial spectra, that
are function of angular wavenumber, the VCS is a function of the velocity wave
number k_v ~ 1/v. We show that absorption affects the VCS to a higher degree
for small k_v and obtain the criteria for disregarding the absorption effects
for turbulence studies at large k_v. We consider the retrieval of turbulence
spectra from observations for high and low spatial resolution observations and
find that the VCS allows one to study turbulence even when the emitting
turbulent volume is not spatially resolved. This opens interesting prospects
for using the technique for extragalactic research. We show that, while thermal
broadening interferes with the turbulence studies using the VCS, it is possible
to separate thermal and non-thermal contributions. This allows a new way of
determining the temperature of the interstellar gas using emission and
absorption spectral lines.


  We will prove an identity involving refined $q$-trinomial coefficients. We
then extend this identity to two infinite families of doubly bounded polynomial
identities using transformation properties of the refined $q$-trinomials in an
iterative fashion in the spirit of Bailey chains. One of these two hierarchies
contains an identity which is equivalent to Capparelli's first Partition
Theorem.


  Commercial Cloud computing is becoming mainstream, with funding agencies
moving beyond prototyping and starting to fund production campaigns, too. An
important aspect of any scientific computing production campaign is data
movement, both incoming and outgoing. And while the performance and cost of VMs
is relatively well understood, the network performance and cost is not. This
paper provides a characterization of networking in various regions of Amazon
Web Services, Microsoft Azure and Google Cloud Platform, both between Cloud
resources and major DTNs in the Pacific Research Platform, including OSG data
federation caches in the network backbone, and inside the clouds themselves.
The paper contains both a qualitative analysis of the results as well as
latency and throughput measurements. It also includes an analysis of the costs
involved with Cloud-based networking.


  Results from various searches for new physical phenomena performed by the
four LEP experiments are summarised. Topics presented include the search for
contact interactions, a Z' boson, leptoquarks, excited leptons, technicolour
and gravity in extra dimensions.


  In this paper, we consider simultaneous wireless information and power
transfer (SWIPT) in orthogonal frequency division multiple access (OFDMA)
systems with the coexistence of information receivers (IRs) and energy
receivers (ERs). The IRs are served with best-effort secrecy data and the ERs
harvest energy with minimum required harvested power. To enhance physical-layer
security and yet satisfy energy harvesting requirements, we introduce a new
frequency-domain artificial noise based approach. We study the optimal resource
allocation for the weighted sum secrecy rate maximization via transmit power
and subcarrier allocation. The considered problem is non-convex, while we
propose an efficient algorithm for solving it based on Lagrange duality method.
Simulation results illustrate the effectiveness of the proposed algorithm as
compared against other heuristic schemes.


  In 1998, Bird introduced Meertens numbers as numbers that are invariant under
a map similar to the Godel encoding. In base 10, the only known Meertens number
is 81312000. We look at some properties of Meertens numbers and consider
variations of this concept. In particular, we consider variations where there
is a finite time algorithm to decide whether such numbers exist.


  Motivated by the question of whether the recently introduced Reduced Cutset
Coding (RCC) offers rate-complexity performance benefits over conventional
context-based conditional coding for sources with two-dimensional Markov
structure, this paper compares several row-centric coding strategies that vary
in the amount of conditioning as well as whether a model or an empirical table
is used in the encoding of blocks of rows. The conclusion is that, at least for
sources exhibiting low-order correlations, 1-sided model-based conditional
coding is superior to the method of RCC for a given constraint on complexity,
and conventional context-based conditional coding is nearly as good as the
1-sided model-based coding.


  It is shown that twist-3 fragmentation functions in the large-$N_c$ limit of
QCD obey the DGLAP evolution equations. The anomalous dimensions are found
explicitly. The Gribov-Lipatov reciprocity is violated at the twist-3 level in
the leading logarithmic approximation.


  We report on the results of a de Haas-van Alphen (dHvA) measurement performed
on the recently discovered antiferromagnet URhIn$_5$ ($T_N$ = 98 K), a
5\textit{f}-analogue of the well studied heavy fermion antiferromagnet
CeRhIn$_5$. The Fermi surface is found to consist of four surfaces: a roughly
spherical pocket $\beta$, with $F_\beta \simeq 0.3$ kT; a pillow-shaped closed
surface, $\alpha$, with $F_\alpha \simeq 1.1$ kT; and two higher frequencies
$\gamma_1$ with $F_{\gamma_1} \simeq 3.2$ kT and $\gamma_2$ with $F_{\gamma_2}
\simeq 3.5$ kT that are seen only near the \textit{c}-axis, and that may arise
on cylindrical Fermi surfaces. The measured cyclotron masses range from 1.9
$m_e$ to 4.3 $m_e$. A simple LDA+SO calculation performed for the paramagnetic
ground state shows a very different Fermi surface topology, demonstrating a
need for more advanced electronic structure calculations.


  A version of the $J$-matrix method for solving numerically the three-body
Faddeev-Merkuriev differential equations is proposed. This version allows to
take into account the full spectrum of the two-body Coulomb subsystem. As a
result, a discrete analog of the Lippmann-Schwinger equation is obtained which
allows to interpret correctly the three-body wave function in two-body domains.
The scheme is applied to calculations of the fully resolved absolute
differential cross sections for the He$(e,2e)$He$^+$ and He$(e,3e)$He$^{++}$
reactions at small energy and momentum transfers. The results are in good
agreement with the experiment both in shape and in absolute value.


  The non-equilibrium cation site occupancy in nanosized zinc ferrites (6-13
nm) with different degree of inversion (0.2 to 0.4) was investigated using Fe
and Zn K-edge x-ray absorption spectroscopy XANES and EXAFS, and magnetic
measurements. The very good agreement between experimental and ab-initio
calculations on the Zn K-edge XANES region clearly show the large
Zn2+(A)--Zn2+[B] transference that takes place in addition to the
well-identified Fe3+[B]--Fe3+(A) one, without altering the long-range
structural order. XANES spectra features as a function of the spinel inversion
were shown to depend on the configuration of the ligand shells surrounding the
absorbing atom. This XANES approach provides a direct way to sense cationic
inversion in these spinel compounds. We also demonstrated that a mechanical
crystallization takes place on nanocrystalline spinel that causes an increase
of both grain and magnetic sizes and, simultaneously, generates a significant
augment of the inversion.


  The construction of mirror symmetry in the heterotic string is reviewed in
the context of Calabi-Yau and Landau-Ginzburg compactifications. This framework
has the virtue of providing a large subspace of the configuration space of the
heterotic string, probing its structure far beyond the present reaches of
solvable models. The construction proceeds in two stages: First all
singularities/catastrophes which lead to ground states of the heterotic string
are found. It is then shown that not all ground states described in this way
are independent but that certain classes of these LG/CY string vacua can be
related to other, simpler, theories via a process involving fractional
transformations of the order parameters as well as orbifolding. This
construction has far reaching consequences. Firstly it allows for a systematic
identification of mirror pairs that appear abundantly in this class of string
vacua, thereby showing that the emerging mirror symmetry is not accidental.
This is important because models with mirror flipped spectra are a priori
independent theories, described by distinct CY/LG models. It also shows that
mirror symmetry is not restricted to the space of string vacua described by
theories based on Fermat potentials (corresponding to minimal tensor models).
Furthermore it shows the need for a better set of coordinates of the
configuration space or else the structure of this space will remain obscure.
While the space of LG vacua is {\it not} completely mirror symmetric, results
described in the last part suggest that the space of Landau--Ginburg {\it
orbifolds} possesses this symmetry.


  In a sequence of two papers, S. Capparelli, A. Meurman, A. Primc, M. Primc
(CMPP) and then M. Primc put forth three remarkable sets of conjectures,
stating that the generating functions of coloured integer partition in which
the parts satisfy restrictions on the multiplicities admit simple infinite
product forms. While CMPP related one set of conjectures to the principally
specialised characters of standard modules for the affine Lie algebra
$\mathrm{C}_n^{(1)}$, finding a Lie-algebraic interpretation for the remaining
two sets remained an open problem. In this paper, we use the work of Griffin,
Ono and the fourth author on Rogers-Ramanujan identities for affine Lie
algebras to solve this problem, relating the remaining two sets of conjectures
to non-standard specialisations of standard modules for $\mathrm{A}_{2n}^{(2)}$
and $\mathrm{D}_{n+1}^{(2)}$. We also use their work to formulate conjectures
for the bivariate generating function of one-parameter families of CMPP
partitions in terms of Hall-Littlewood symmetric functions. We make a detailed
study of several further aspects of CMPP partitions, obtaining (i) functional
equations for bivariate generating functions which generalise the well-known
Rogers-Selberg equations, (ii) a partial level-rank duality in the
$\mathrm{A}_{2n}^{(2)}$ case, and (iii) (conjectural) identities of the
Rogers-Ramanujan type for $\mathrm{D}_3^{(2)}$.


  The resonance energy and the transition rate of atoms, molecules and solids
were understood as their intrinsic properties in classical electromagnetism.
With the development of quantum electrodynamics, it is realized that these
quantities are linked to the coupling of the transition dipole and the quantum
vacuum. Such effects can be greatly amplified in macroscopic many-body systems
from virtual photon exchange between dipoles, but are often masked by
inhomogeneity and pure dephasing, especially in solids. Here, we observe an
exceptionally large renormalization of exciton resonance and radiative decay
rate in transition metal dichalcogenides monolayers due to interactions with
the vacuum in both absorption and emission spectroscopy. Tuning the vacuum
energy density near the monolayer, we demonstrate control of cooperative Lamb
shift, radiative decay, and valley polarization as well as control of the
charged exciton emission. Our work establishes a simple and robust experimental
system for vacuum engineering of cooperative matter-light interactions.