  In this study, we delve into an emerging optimization challenge involving a
black-box objective function that can only be gauged via a ranking oracle-a
situation frequently encountered in real-world scenarios, especially when the
function is evaluated by human judges. Such challenge is inspired from
Reinforcement Learning with Human Feedback (RLHF), an approach recently
employed to enhance the performance of Large Language Models (LLMs) using human
guidance. We introduce ZO-RankSGD, an innovative zeroth-order optimization
algorithm designed to tackle this optimization problem, accompanied by
theoretical assurances. Our algorithm utilizes a novel rank-based random
estimator to determine the descent direction and guarantees convergence to a
stationary point. Moreover, ZO-RankSGD is readily applicable to policy
optimization problems in Reinforcement Learning (RL), particularly when only
ranking oracles for the episode reward are available. Last but not least, we
demonstrate the effectiveness of ZO-RankSGD in a novel application: improving
the quality of images generated by a diffusion generative model with human
ranking feedback. Throughout experiments, we found that ZO-RankSGD can
significantly enhance the detail of generated images with only a few rounds of
human feedback. Overall, our work advances the field of zeroth-order
optimization by addressing the problem of optimizing functions with only
ranking feedback, and offers a new and effective approach for aligning
Artificial Intelligence (AI) with human intentions.


  Functional principal component analysis (FPCA) has been widely used to
capture major modes of variation and reduce dimensions in functional data
analysis. However, standard FPCA based on the sample covariance estimator does
not work well in the presence of outliers. To address this challenge, a new
robust functional principal component analysis approach based on the functional
pairwise spatial sign (PASS) operator, termed PASS FPCA, is introduced where we
propose estimation procedures for both eigenfunctions and eigenvalues with and
without measurement error. Compared to existing robust FPCA methods, the
proposed one requires weaker distributional assumptions to conserve the
eigenspace of the covariance function. In particular, a class of distributions
called the weakly functional coordinate symmetric (weakly FCS) is introduced
that allows for severe asymmetry and is strictly larger than the functional
elliptical distribution class, the latter of which has been well used in the
robust statistics literature. The robustness of the PASS FPCA is demonstrated
via simulation studies and analyses of accelerometry data from a large-scale
epidemiological study of physical activity on older women that partly motivates
this work.


  Exponential growth in data collection is creating significant challenges for
data storage and analytics latency.Approximate Query Processing (AQP) has long
been touted as a solution for accelerating analytics on large datasets,
however, there is still room for improvement across all key performance
criteria. In this paper, we propose a novel histogram-based data synopsis
called PairwiseHist that uses recursive hypothesis testing to ensure accurate
histograms and can be built on top of data compressed using Generalized
Deduplication (GD). We thus show that GD data compression can contribute to
AQP. Compared to state-of-the-art AQP approaches, PairwiseHist achieves better
performance across all key metrics, including 2.6$ \times $ higher accuracy,
3.5$ \times $ lower latency, 24$ \times $ smaller synopses and 1.5--4$ \times $
faster construction time.


  Metastable, supersymmetry-breaking configurations can be created in flux
geometries by placing antibranes in warped throats. Via gauge/gravity duality,
such configurations should have an interpretation as supersymmetry-breaking
states in the dual field theory. In this paper, we perturbatively determine the
asymptotic supergravity solutions corresponding to anti-D3-brane probes placed
at the tip of the cascading warped deformed conifold geometry, which is dual to
an SU(N+M) x SU(N) gauge theory. The backreaction of the antibranes has the
effect of introducing imaginary anti-self-dual flux, squashing the compact part
of the space and forcing the dilaton to run. Using the generalization of
holographic renormalization to cascading geometries, we determine the
expectation values of operators in the dual field theory in terms of the
asymptotic values of the supergravity fields.


  Exploration of topology protected by a certain symmetry is central in
condensed matter physics. A recent idea of sub-symmetry-protected (SSP)
topology--remains of a broken symmetry can still protect specific topological
boundary states--has been developed and demonstrated in an optical system [Nat.
Phys. 19, 992-998 (2023)]. Here, we extend this idea further by applying
sub-symmetry-protecting perturbation (SSPP) to one-dimensional topological
insulating and superconducting systems using the Su-Schrieffer-Hegger (SSH) and
Kitaev models. Using the tight-binding and low-energy effective theory, we show
that the SSP boundary states retain topological properties while the SSPP
results in the asymmetry of boundary states. For the SSH model, an SSP
zero-energy edge state localized on one edge possesses quantized polarization.
In contrast, the other edge state is perturbed to have non-zero energy, and its
polarization is not quantized. For topological superconductors, zero-energy SSP
Majorana boundary states for spinful Kitaev models emerge on only one edge,
contrary to the conventional belief that Majorana fermions emerge at opposite
edges. Our findings can be used as a platform to expand our understanding of
topological materials as they broaden our understanding of the symmetry in a
topological system and a method to engineer Majorana fermions.


  This paper is a study of ``topological'' lower bounds for the chromatic
number of a graph. Such a lower bound was first introduced by Lov\'asz in 1978,
in his famous proof of the \emph{Kneser conjecture} via Algebraic Topology.
This conjecture stated that the \emph{Kneser graph} $\KG_{m,n}$, the graph with
all $k$-element subsets of $\{1,2,...,n\}$ as vertices and all pairs of
disjoint sets as edges, has chromatic number $n-2k+2$. Several other proofs
have since been published (by B\'ar\'any, Schrijver, Dolnikov, Sarkaria, Kriz,
Greene, and others), all of them based on some version of the Borsuk--Ulam
theorem, but otherwise quite different. Each can be extended to yield some
lower bound on the chromatic number of an arbitrary graph. (Indeed, we observe
that \emph{every} finite graph may be represented as a generalized Kneser
graph, to which the above bounds apply.)
  We show that these bounds are almost linearly ordered by strength, the
strongest one being essentially Lov\'asz' original bound in terms of a
neighborhood complex. We also present and compare various definitions of a
\emph{box complex} of a graph (developing ideas of Alon, Frankl, and Lov\'asz
and of \kriz). A suitable box complex is equivalent to Lov\'asz' complex, but
the construction is simpler and functorial, mapping graphs with homomorphisms
to $\Z_2$-spaces with $\Z_2$-maps.


  We study the Cauchy problem with periodic initial data for the
forward-backward heat equation defined by the J-self-adjoint linear operator L
depending on a small parameter. The problem has been originated from the
lubrication approximation of a viscous fluid film on the inner surface of the
rotating cylinder. For a certain range of the parameter we rigorously prove the
conjecture, based on the numerical evidence, that the set of eigenvectors of
the operator $L$ does not form a Riesz basis in $\L^2 (-\pi,\pi)$. Our method
can be applied to a wide range of the evolutional problems given by
$PT-$symmetric operators.


  We start by a review of the chronology of mathematical results on the
Dirichlet-to-Neumann map which paved the way towards the physics of
transformational acoustics. We then rederive the expression for the
(anisotropic) density and bulk modulus appearing in the pressure wave equation
written in the transformed coordinates. A spherical acoustic cloak consisting
of an alternation of homogeneous isotropic concentric layers is further
proposed based on the effective medium theory. This cloak is characterised by a
low reflection and good efficiency over a large bandwidth for both near and far
fields, which approximates the ideal cloak with a inhomogeneous and anisotropic
distribution of material parameters. The latter suffers from singular material
parameters on its inner surface. This singularity depends upon the sharpness of
corners, if the cloak has an irregular boundary, e.g. a polyhedron cloak
becomes more and more singular when the number of vertices increases if it is
star shaped. We thus analyse the acoustic response of a non-singular spherical
cloak designed by blowing up a small ball instead of a point, as proposed in
[Kohn, Shen, Vogelius, Weinstein, Inverse Problems 24, 015016, 2008]. The
multilayered approximation of this cloak requires less extreme densities
(especially for the lowest bound). Finally, we investigate another type of
non-singular cloaks, known as invisibility carpets [Li and Pendry, Phys. Rev.
Lett. 101, 203901, 2008], which mimic the reflection by a flat ground.


  Statistical properties of random cross-correlated sequences constructed by
the convolution method (likewise referred to as the Rice's or the inverse
Fourier transformation) are examined. Algorithms for their generation are
discussed. They are frequently reduced to solving the problem for decomposition
of the Fourier transform of the correlation matrix into a product of two
mutually conjugate matrices; different decompositions of the correlation matrix
are considered. The limits of weak and strong correlations for the one-point
probability and pair correlation functions of the sequences are studied.
Special cases of heavy-tailed distributions resulting from the convolution
generation are analyzed. Anisotropic properties of statistically homogeneous
random sequences related to asymmetry of a filtering function are discussed.


  In recent years, the tendency of the number of financial institutions
including cryptocurrencies in their portfolios has accelerated.
Cryptocurrencies are the first pure digital assets to be included by asset
managers. Although they have some commonalities with more traditional assets,
they have their own separate nature and their behaviour as an asset is still in
the process of being understood. It is therefore important to summarise
existing research papers and results on cryptocurrency trading, including
available trading platforms, trading signals, trading strategy research and
risk management. This paper provides a comprehensive survey of cryptocurrency
trading research, by covering 146 research papers on various aspects of
cryptocurrency trading (e.g., cryptocurrency trading systems, bubble and
extreme conditions, prediction of volatility and return, crypto-assets
portfolio construction and crypto-assets, technical trading and others). This
paper also analyses datasets, research trends and distribution among research
objects(contents/properties) and technologies, concluding with some promising
opportunities that remain open in cryptocurrency trading.


  The impossibility of experiencing the molecular world with our senses hampers
teaching and understanding chemistry because very abstract concepts (such as
atoms, chemical bonds, molecular structure, reactivity) are required for this
process. Virtual reality, especially when based on explicit physical modeling
(potentially in real time), offers a solution to this dilemma. Chemistry
teaching can make use of advanced technologies such as virtual-reality
frameworks and haptic devices. We show how an immersive learning setting could
be applied to help students understand the core concepts of typical chemical
reactions by offering a much more intuitive approach than traditional learning
settings. Our setting relies on an interactive exploration and manipulation of
a chemical system; this system is simulated in real-time with quantum chemical
methods, and therefore, behaves in a physically meaningful way.


  Two important classes of spatio-temporal patterns, namely, spatio-temporal
chaos and self-replicating patterns, for a representative three variable
autocatalytic reaction mechanism coupled with diffusion has been studied. The
characterization of these patterns has been carried out in terms of Lyapunov
exponents and dimension density. The results show a linear scaling as a
function of sub-system size for the Lyapunov dimension and entropy while the
Lyapunov dimension density was found to rapidly saturate. The possibility of
synchronizing the spatio-temporal dynamics by analyzing the conditional
Lyapunov exponents of sub-systems was also observed.


  We compare analytic predictions for real and Fourier space two-point
statistics for biased tracers from a variety of Lagrangian Perturbation Theory
approaches against those from state of the art N-body simulations in $f(R)$
Hu-Sawicki and the nDGP braneworld modified gravity theories.
  We show that the novel physics of gravitational collapse in scalar tensor
theories with the chameleon or the Vainshtein screening mechanism can be
effectively factored in with bias parameters analytically predicted using the
Peak-Background Split formalism when updated to include the environmental
sensitivity of modified gravity theories as well as changes to the halo mass
function.
  We demonstrate that Convolution Lagrangian Perturbation Theory (CLPT) and
Standard Perturbation Theory (SPT) approaches provide accurate analytic methods
to predict the correlation function and power spectra, respectively, for biased
tracers in modified gravity models and are able to characterize both the BAO,
power-law and small scale regimes needed for upcoming galaxy surveys such as
DESI, Euclid, LSST and WFIRST.


  The question of thermalisation in closed quantum many-body systems has
received a lot of attention in the past few years. An intimately related
question is whether a closed quantum system shows irreversible dynamics.
However, irreversibility and what we actually mean by this in a quantum
many-body system with unitary dynamics has been explored very little. In this
work we investigate the dynamics of the Ising model in a transverse magnetic
field involving an imperfect effective time reversal. We propose a definition
of irreversibility based on the echo peak decay of observables. Inducing the
effective time reversal by different protocols we find algebraic decay of the
echo peak heights or an ever persisting echo peak indicating that the dynamics
in this model is well reversible.


  This Letter investigates the physics that is responsible for creating the
current system that supports the outgoing Poynting flux emanating from the
ergosphere of a rotating black hole in the limit that the magnetic energy
density greatly exceeds the plasma rest mass density (magnetically dominated
limit). The underlying physics is derived from published three-dimensional
simulations that obey the general relativistic equations of perfect
magnetohydrodynamics (MHD). It is found that the majority of the Poynting flux
emitted from the magnetically dominated regions of the ergosphere has a source
associated with inertial effects outside of the event horizon.


  Extremization of the Boltzmann-Gibbs (BG) entropy under appropriate norm and
width constraints yields the Gaussian distribution. Also, the basic solutions
of the standard Fokker-Planck (FP) equation (related to the Langevin equation
with additive noise), as well as the Central Limit Theorem attractors, are
Gaussians. The simplest stochastic model with such features is N to infinity
independent binary random variables, as first proved by de Moivre and Laplace.
What happens for strongly correlated random variables? Such correlations are
often present in physical situations as e.g. systems with long range
interactions or memory. Frequently q-Gaussians become observed. This is
typically so if the Langevin equation includes multiplicative noise, or the FP
equation to be nonlinear. Scale-invariance, i.e. exchangeable binary stochastic
processes, allow a systematical analysis of the relation between correlations
and non-Gaussian distributions. In particular, a generalized stochastic model
yielding q-Gaussians for all q (including q>1) was missing. This is achieved
here by using the Laplace-de Finetti representation theorem, which embodies
strict scale-invariance of interchangeable random variables. We demonstrate
that strict scale invariance together with q-Gaussianity mandates the
associated extensive entropy to be BG.


  Friedman test is a nonparametric method that proposed for analyzing data from
a randomized complete block design as a robust alternative to parametric method
and widely applied in many fields such as agriculture, biology, business,
education, and medicine. After the null hypothesis of no treatment effects is
rejected, the post-hoc pairwise comparisons must be applied to identify where
the differences occur. As the number of groups increases, the number of
required comparisons becomes large and this may increase the type I error. The
aim of this study is twofold. The main aim is to suggest expression that
facilitates the plotting Friedman test by gathering the test and pairwise
comparisons in one simple step. The second aim is to derive the sampling
distribution of the suggested expression by utilizing method of moments that
helps in obtaining the decision limit. An application and simulation study are
carried out to show the advantage of the suggested method and to compute the
empirical type I error. The results are of great value where the proposed
method makes huge reduction in the number of required tests to show where the
discrepancies occur, holds the type I error close to the nominal value and
provides visual, deep insight and understanding where the treatment effects
occur.


  Video Object Segmentation (VOS) is a vital task in computer vision, focusing
on distinguishing foreground objects from the background across video frames.
Our work draws inspiration from the Cutie model, and we investigate the effects
of object memory, the total number of memory frames, and input resolution on
segmentation performance. This report validates the effectiveness of our
inference method on the coMplex video Object SEgmentation (MOSE) dataset, which
features complex occlusions. Our experimental results demonstrate that our
approach achieves a J\&F score of 0.8139 on the test set, securing the third
position in the final ranking. These findings highlight the robustness and
accuracy of our method in handling challenging VOS scenarios.


  The two-loop massive operator matrix elements for the fermionic local
twist--2 operators with external massive fermion lines in Quantum
Electrodynamics (QED) are calculated up to the constant terms in the
dimensional parameter $\epsilon = D - 4$. We investigate the hypothesis of Ref.
\cite{BBN} that the 2--loop QED initial state corrections to $e^+e^-$
annihilation into a virtual neutral gauge boson, except power corrections of
$O((m_f^2/s)^k), k \geq 1$, can be represented in terms of these matrix
elements and the massless 2-loop Wilson coefficients of the Drell-Yan process.


  Contact reduction is very closely related to symplectic reduction, but it
allows symmetries that are not manifest in Hamiltonian mechanics and moreover,
solution of the reduced problems yields solution of the original problem
without further integration.


  We study the amplitude of deeply virtual Compton scattering in
next-to-leading order of perturbation theory including the two-loop evolution
effects for different sets of skewed parton distributions (SPDs). It turns out
that in the minimal subtraction scheme the relative radiative corrections are
of order 20-50%. We analyze the dependence of our predictions on the choice of
SPD, that will allow to discriminate between possible models of SPDs from
future high precision experimental data, and discuss shortly theoretical
uncertainties induced by the radiative corrections.


  We investigate several boundedness properties of function spaces considered
as uniform spaces.


  We have probed the superconducting proximity effect through long high-quality
monocrystalline Ag nanowires, by realizing Josephson junctions of different
lengths, with different superconducting materials. Thanks to the high number of
junctions probed, both the contact resistance and electron diffusion constant
could be determined, enabling a comparison of the measured critical current to
theoretical expectation, over the entire regime from short to long diffusive
junction. Although the length dependence of the critical current is as
expected, the amplitude of the $R_{N}I_c$ product is smaller than predicted by
theory. We also address the magnetic field dependence of the critical current.
The quasi-gaussian decay of the critical current with field expected of a long
narrow junction is observed for all superconducting contacts we used except for
aluminum. We present the striking non-monotonous effect of field on the
critical current of junctions with aluminum contacts, and analyze it in terms
of improved quasiparticle thermalization by a magnetic field.


  We investigate the validity of fluctuation theorems for an asymmetric rotor
experiment in a granular gas. A first state, with a Gaussian distribution of
the angular velocity, is found to be well described by a first order Langevin
equation. We show that fluctuation theorems are valid for the injected work and
for the total entropy production. In a second state the angular velocity
distribution is double-peaked due to a spontaneous symmetry breaking: A
convection roll develops in the granular gas, which strongly couples to the
rotor. Surprisingly, in this case similar symmetry relations hold, which lead
to a good prediction for the height ratio of the two peaks.


  Customization is a general trend in software engineering, demanding systems
that support variable stakeholder requirements. Two opposing strategies are
commonly used to create variants: software clone & own and software
configuration with an integrated platform. Organizations often start with the
former, which is cheap, agile, and supports quick innovation, but does not
scale. The latter scales by establishing an integrated platform that shares
software assets between variants, but requires high up-front investments or
risky migration processes. So, could we have a method that allows an easy
transition or even combine the benefits of both strategies? We propose a method
and tool that supports a truly incremental development of variant-rich systems,
exploiting a spectrum between both opposing strategies. We design, formalize,
and prototype the variability-management framework virtual platform. It bridges
clone & own and platform-oriented development. Relying on
programming-language-independent conceptual structures representing software
assets, it offers operators for engineering and evolving a system, comprising:
traditional, asset-oriented operators and novel, feature-oriented operators for
incrementally adopting concepts of an integrated platform. The operators record
meta-data that is exploited by other operators to support the transition. Among
others, they eliminate expensive feature-location effort or the need to trace
clones. Our evaluation simulates the evolution of a real-world, clone-based
system, measuring its costs and benefits.


  End-to-end (E2E) systems for automatic speech recognition (ASR), such as RNN
Transducer (RNN-T) and Listen-Attend-Spell (LAS) blend the individual
components of a traditional hybrid ASR system - acoustic model, language model,
pronunciation model - into a single neural network. While this has some nice
advantages, it limits the system to be trained using only paired audio and
text. Because of this, E2E models tend to have difficulties with correctly
recognizing rare words that are not frequently seen during training, such as
entity names. In this paper, we propose modifications to the RNN-T model that
allow the model to utilize additional metadata text with the objective of
improving performance on these named entity words. We evaluate our approach on
an in-house dataset sampled from de-identified public social media videos,
which represent an open domain ASR task. By using an attention model and a
biasing model to leverage the contextual metadata that accompanies a video, we
observe a relative improvement of about 16% in Word Error Rate on Named
Entities (WER-NE) for videos with related metadata.


  $A$ set is called $IP$-set in a semigroup $\left(S,\cdot \right)$ if it
contains finite products of a sequence. A set that intersects with all
$IP$-sets is called $IP^\star$-set. It is a well known and established result
by Bergelson and Hindman that if $A$ is an $IP^{\star}$-set, then for any
sequence $\langle x_{n}\rangle_{n=1}^{\infty}$, there exists a sum subsystem
$\langle y_{n}\rangle_{n=1}^{\infty}$ such that $FS\left(\langle
y_{n}\rangle_{n=1}^{\infty}\right)\cup FP\left(\langle
y_{n}\rangle_{n=1}^{\infty}\right)\subset A$. In \cite[Question 3]{G}, S.
Goswami posed the question: if we replace the single sequence by $l$-sequences,
then is it possible to obtain a sum subsystem such that all of its zigzag
finite sums and products will be in $A$. Goswami has given affirmative answers
only for dynamical $IP^{\star}$-sets which are not equivalent to those of
$IP^{\star}$-sets, but are rather significantly stronger. In this article, we
will give the answer to Goswami's question that was unknown until now.


  Existing RGB-D salient object detection (SOD) models usually treat RGB and
depth as independent information and design separate networks for feature
extraction from each. Such schemes can easily be constrained by a limited
amount of training data or over-reliance on an elaborately designed training
process. Inspired by the observation that RGB and depth modalities actually
present certain commonality in distinguishing salient objects, a novel joint
learning and densely cooperative fusion (JL-DCF) architecture is designed to
learn from both RGB and depth inputs through a shared network backbone, known
as the Siamese architecture. In this paper, we propose two effective
components: joint learning (JL), and densely cooperative fusion (DCF). The JL
module provides robust saliency feature learning by exploiting cross-modal
commonality via a Siamese network, while the DCF module is introduced for
complementary feature discovery. Comprehensive experiments using five popular
metrics show that the designed framework yields a robust RGB-D saliency
detector with good generalization. As a result, JL-DCF significantly advances
the state-of-the-art models by an average of ~2.0% (max F-measure) across seven
challenging datasets. In addition, we show that JL-DCF is readily applicable to
other related multi-modal detection tasks, including RGB-T (thermal infrared)
SOD and video SOD, achieving comparable or even better performance against
state-of-the-art methods. We also link JL-DCF to the RGB-D semantic
segmentation field, showing its capability of outperforming several semantic
segmentation models on the task of RGB-D SOD. These facts further confirm that
the proposed framework could offer a potential solution for various
applications and provide more insight into the cross-modal complementarity
task.


  The assessment of bidirectional heuristic search has been incorrect since it
was first published more than a quarter of a century ago. For quite a long
time, this search strategy did not achieve the expected results, and there was
a major misunderstanding about the reasons behind it. Although there is still
wide-spread belief that bidirectional heuristic search is afflicted by the
problem of search frontiers passing each other, we demonstrate that this
conjecture is wrong. Based on this finding, we present both a new generic
approach to bidirectional heuristic search and a new approach to dynamically
improving heuristic values that is feasible in bidirectional search only. These
approaches are put into perspective with both the traditional and more recently
proposed approaches in order to facilitate a better overall understanding.
Empirical results of experiments with our new approaches show that
bidirectional heuristic search can be performed very efficiently and also with
limited memory. These results suggest that bidirectional heuristic search
appears to be better for solving certain difficult problems than corresponding
unidirectional search. This provides some evidence for the usefulness of a
search strategy that was long neglected. In summary, we show that bidirectional
heuristic search is viable and consequently propose that it be reconsidered.


  This paper presents some basic facts about the so-called connectivity spaces.
In particular, it studies the generation of connectivity structures, the
existence of limits and colimits in the main categories of connectivity spaces,
the closed monoidal category structure given by the so-called tensor product on
integral connectivity spaces; it defines homotopy for connectivity spaces and
mention briefly related difficulties; it defines smash product of pointed
integral connectivity spaces and shows that this operation results in a closed
monoidal category with such spaces as objects. Then, it studies finite
connectivity spaces, associating a directed acyclic graph with each such space
and then defining a new numerical invariant for links: the connectivity order.
Finally, it mentions the not very wellknown Brunn-Debrunner-Kanenobu theorem
which asserts that every finite integral connectivity space can be represented
by a link.


  We propose alternative discriminant measures for selecting the best basis
among a large collection of orthonormal bases for classification purposes. A
generalization of the Local Discriminant Basis Algorithm of Saito and Coifman
is constructed. The success of these new methods is evaluated and compared to
earlier methods in experiments.


  Gromov-Wasserstein distance has found many applications in machine learning
due to its ability to compare measures across metric spaces and its invariance
to isometric transformations. However, in certain applications, this invariance
property can be too flexible, thus undesirable. Moreover, the
Gromov-Wasserstein distance solely considers pairwise sample similarities in
input datasets, disregarding the raw feature representations. We propose a new
optimal transport-based distance, called Augmented Gromov-Wasserstein, that
allows for some control over the level of rigidity to transformations. It also
incorporates feature alignments, enabling us to better leverage prior knowledge
on the input data for improved performance. We present theoretical insights
into the proposed metric. We then demonstrate its usefulness for single-cell
multi-omic alignment tasks and a transfer learning scenario in machine
learning.


  We present lattice results for spin-1/2 fermions at unitarity, where the
effective range of the interaction is zero and the scattering length is
infinite. We measure the spatial coherence of difermion pairs for a system of
6, 10, 14, 18, 22, 26 particles with equal numbers of up and down spins in a
periodic cube. Using Euclidean time projection, we analyze ground state
properties and transient behavior due to low-energy excitations. At
asymptotically large values of t we see long-range order consistent with
spontaneously broken U(1) fermion-number symmetry and a superfluid ground
state. At intermediate times we see exponential decay in the t-dependent signal
due to an unknown low-energy excitation. We probe this low-energy excitation
further by calculating two-particle correlation functions. We find that the
excitation has the properties of a chain of particles extending across the
periodic lattice.


  This study analyzes heat waves (HWs), air pollution (AP) episodes, and
compound HW and AP events (CE) in the urban environment and provides a
comparison between events in urban areas (UAs) and rural areas (RAs). A 1-km
gridded daily minimum temperature dataset and a 1-km gridded daily PM2.5
concentration dataset were used along with geospatial data to characterize
events by their frequency, intensity in heat, intensity in pollution, and
duration. The greatest differences between UAs and RAs in frequency, heat
intensity, pollution intensity, and duration for all events were seen in the
West and Southwest regions. For both UAs and RAs, it was found that HWs were
the most frequent, intense, and longest lasting in the West and Southwest
regions, AP episodes were the most frequent and longest lasting in the
Northeast, Ohio Valley, and Southeast regions, and AP episodes were the most
intense in the Northern Rockies and Plains and Upper Midwest regions. It was
concluded that HWs (AP episodes) had a greater impact on CEs than AP episodes
(HWs) in regions with more prominent HWs (AP episodes).


  Electrochemical capacitors are a class of energy devices in which complex
mechanisms of accumulation and dissipation of electric energy take place when
connected to a charging or discharging power system. Reliably modeling their
frequency-domain and time-domain behaviors is crucial for their proper design
and integration in engineering applications, knowing that electrochemical
capacitors in general exhibit anomalous tendency that cannot be adequately
captured with traditional integer-order-based models. In this study we first
review some of the widely used fractional-oder models for the description of
impedance and relaxation functions of dissipative resistive-capacitive system,
namely the Cole-Cole, Davidson-Cole, and Havriliak-Negami models. We then
propose and derive new q-deformed models based on modified evolution equations
for the charge or voltage when the device is discharged into a parallel
resistive load. We verify our results on anomalous spectral impedance response
and time-domain relaxation data for voltage and charge obtained from a
commercial supercapacitor.


  This note contains some examples of hyperk\"ahler varieties $X$ having a
group $G$ of non-symplectic automorphisms, and such that the action of $G$ on
certain Chow groups of $X$ is as predicted by Bloch's conjecture. The examples
range in dimension from $6$ to $132$. For each example, the quotient $Y=X/G$ is
a Calabi-Yau variety which has interesting Chow-theoretic properties; in
particular, the variety $Y$ satisfies (part of) a strong version of the
Beauville-Voisin conjecture.


  We propose a simple geometrical mechanism for the flattening of galactic
rotation curves, the local compression of field lines around their planes
induced either by the presence of thin string-like objects at the centers of
galaxies or by elongated dark-matter halos, and elaborate on its possible role
in Nature. We fit 83 rotation curves from the SPARC database with logarithmic
potentials produced by a thin "wire" at the origin and then, after selecting 2
galaxies that yield the most interesting fits, analyze them with an alternative
model, deformed versions of two popular models of dark-matter halos. Our
conclusion is that the presence of a filament clearly improves the fit quality
in a number of cases, while bulged dark matter profiles have a lesser effect.
If taken at face value, these results would imply the presence of elongated
mass distributions away from the galactic plane in a number of galaxies, and
may also have some indirect impact on the controversy between cold dark matter
(CDM), self-interacting dark matter (SiDM), and modified Newtonian dynamics
(MOND).


  We investigate the role of Hund's coupling in the spin-wave excitations of
the ($\pi, 0$) ordered magnetic state within a five-orbital tight-binding model
for iron pnictides. To differentiate between the roles of intraorbital Coulomb
interaction and Hund's coupling, we focus on the self-consistently obtained
mean-field SDW state with a fixed magnetic moment obtained by using different
sets of interaction parameters. We find that the Hund's coupling is crucial for
the description of various experimentally observed characteristics of the
spin-wave excitations including the anisotropy, energy-dependent behavior, and
spin-wave spectral weight distribution.


  Causal decomposition analysis provides a way to identify mediators that
contribute to health disparities between marginalized and non-marginalized
groups. In particular, the degree to which a disparity would be reduced or
remain after intervening on a mediator is of interest. Yet, estimating
disparity reduction and remaining might be challenging for many researchers,
possibly because there is a lack of understanding of how each estimation method
differs from other methods. In addition, there is no appropriate estimation
method available for a certain setting (i.e., a regression-based approach with
a categorical mediator). Therefore, we review the merits and limitations of the
existing three estimation methods (i.e., regression, weighting, and imputation)
and provide two new extensions that are useful in practical settings. A
flexible new method uses an extended imputation approach to address a
categorical and continuous mediator or outcome while incorporating any
nonlinear relationships. A new regression method provides a simple estimator
that performs well in terms of bias and variance but at the cost of assuming
linearity, except for exposure and mediator interactions. Recommendations are
given for choosing methods based on a review of different methods and
simulation studies. We demonstrate the practice of choosing an optimal method
by identifying mediators that reduce race and gender disparity in
cardiovascular health, using data from the Midlife Development in the US study.


  For a finite Galois extension of fields L/k with Galois group G, we study a
functor from the G-equivariant stable homotopy category to the stable motivic
homotopy category over k induced by the classical Galois correspondence. We
show that after completing at a prime and eta (the motivic Hopf map) this
results in a full and faithful embedding whenever k is real closed and L =
k[i]. It is a full and faithful embedding after eta-completion if a motivic
version of Serre's finiteness theorem is valid. We produce strong necessary
conditions on the field extension L/k for this functor to be full and faithful.
Along the way, we produce several results on the stable C_2-equivariant Betti
realization functor and prove convergence theorems for the p-primary
C_2-equivariant Adams spectral sequence.


  Spectrum reservation is emerging as one of the potential solutions to cater
for the communication needs of massive number of wireless Internet of Things
(IoT) devices with reliability constraints particularly in mission-critical
scenarios. In most mission-critical systems, the true utility of a reservation
may not be completely known ahead of time as the unforseen events might not be
completely predictable. In this paper, we present a dynamic contract approach
where an advance payment is made at the time of reservation based on partial
information about spectrum reservation utility. Once the complete information
is obtained, a rebate on the payment is made if the reservation is released. In
this paper, we present a contract theoretic approach to design an incentivized
mechanism that coerces the applications to reveal their true application type
resulting in greater profitability of the IoT network operator. The operator
offers a menu of contracts with advanced payments and rebate to the IoT
applications without having knowledge about the types of applications. The
decision of the applications in selecting a contract leads to a revelation of
their true type to the operator which allows it to generate higher profits than
a traditional spectrum auction mechanism. Under some assumptions on
distribution of the utility of the applications, closed form solutions for the
optimal dynamic spectrum reservation contract are provided and the sensitivity
against system parameters is analyzed.


  We devised a first order time stepping ensemble hybridizable discontinuous
Galerkin (HDG) method for a group of parameterized convection diffusion PDEs
with different initial conditions, body forces, boundary conditions and
coefficients in our earlier work [3]. We obtained an optimal convergence rate
for the ensemble solutions in $L^\infty(0,T;L^2(\Omega))$ on a simplex mesh;
and obtained a superconvergent rate for the ensemble solutions in
$L^2(0,T;L^2(\Omega))$ after an element-by-element postprocessing if
polynomials degree $k\ge 1$ and the coefficients of the PDEs are independent of
time. In this work, we propose a new second order time stepping ensemble HDG
method to revisit the problem. We obtain a superconvergent rate for the
ensemble solutions in $L^\infty(0,T;L^2(\Omega))$ without an element-by-element
postprocessing for all polynomials degree $k\ge 0$. Furthermore, our mesh can
be any polyhedron, no need to be simplex; and the coefficients of the PDEs can
dependent on time. Finally, we present numerical experiments to confirm our
theoretical results.


  Modelling, analysing and inferring triggering mechanisms in population
reproduction is fundamental in many biological applications. It is also an
active and growing research domain in mathematical biology. In this chapter, we
review the main results developed over the last decade for the estimation of
the division rate in growing and dividing populations in a steady environment.
These methods combine tools borrowed from PDE's and stochastic processes, with
a certain view that emerges from mathematical statistics. A focus on the
application to the bacterial cell division cycle provides a concrete
presentation, and may help the reader to identify major new challenges in the
field.


  Increasing evidence suggests that the presence of mobile ions in perovskite
solar cells can cause a current-voltage curve hysteresis. Steady state and
transient current-voltage characteristics of a planar metal halide
CH$_3$NH$_3$PbI$_3$ perovskite solar cell are analysed with a drift-diffusion
model that accounts for both charge transport and ion vacancy motion. The high
ion vacancy density within the perovskite layer gives rise to narrow Debye
layers (typical width $\sim$2nm), adjacent to the interfaces with the transport
layers, over which large drops in the electric potential occur and in which
significant charge is stored. Large disparities between (I) the width of the
Debye layers and that of the perovskite layer ($\sim$600nm) and (II) the ion
vacancy density and the charge carrier densities motivate an asymptotic
approach to solving the model, while the stiffness of the equations renders
standard solution methods unreliable. We derive a simplified surface
polarisation model in which the slow ion dynamic are replaced by interfacial
(nonlinear) capacitances at the perovskite interfaces. Favourable comparison is
made between the results of the asymptotic approach and numerical solutions for
a realistic cell over a wide range of operating conditions of practical
interest.


  In the context of the complex-analytic structure within the unit disk
centered at the origin of the complex plane, that was presented in a previous
paper, we show that the complete Fourier theory of integrable real functions is
contained within that structure, that is, within the structure of the space of
inner analytic functions on the open unit disk. We then extend the Fourier
theory beyond the realm of integrable real functions, to include for example
singular Schwartz distributions, and possibly other objects.


  Large-$S$ and large-$N$ theories (spin value $S$ and spinor component number
$N$) are complementary, and sometimes conflicting, approaches to quantum
magnetism. While large-$S$ spin-wave theory captures the correct semiclassical
behavior, large-$N$ theories, on the other hand, emphasize the quantumness of
spin fluctuations. In order to evaluate the possibility of the non-trivial
recovery of the semiclassical magnetic excitations within a large-$N$ approach,
we compute the large-$S$ limit of the dynamic spin structure of the triangular
lattice Heisenberg antiferromagnet within a Schwinger boson spin
representation. We demonstrate that, only after the incorporation of Gaussian
($1/N$) corrections to the saddle-point ($N=\infty$) approximation, we are able
to exactly reproduce the linear spin wave theory results in the large-$S$
limit. The key observation is that the effect of $1/N$ corrections is to cancel
out exactly the main contribution of the saddle-point solution; while the
collective modes (magnons) consist of two spinon bound states arising from the
poles of the RPA propagator. This result implies that it is essential to
consider the interaction of the spinons with the emergent gauge fields and that
the magnon dispersion relation should not be identified with that of the
saddle-point spinons.


  This paper introduces a new approach to cost-effective, high-throughput
hardware designs for Low Density Parity Check (LDPC) decoders. The proposed
approach, called Non-Surjective Finite Alphabet Iterative Decoders (NS-FAIDs),
exploits the robustness of message-passing LDPC decoders to inaccuracies in the
calculation of exchanged messages, and it is shown to provide a unified
framework for several designs previously proposed in the literature. NS-FAIDs
are optimized by density evolution for regular and irregular LDPC codes, and
are shown to provide different trade-offs between hardware complexity and
decoding performance. Two hardware architectures targeting high-throughput
applications are also proposed, integrating both Min-Sum (MS) and NS-FAID
decoding kernels. ASIC post synthesis implementation results on 65nm CMOS
technology show that NS-FAIDs yield significant improvements in the throughput
to area ratio, by up to 58.75% with respect to the MS decoder, with even better
or only slightly degraded error correction performance.


  We propose algorithms based on a multi-level Thompson sampling scheme, for
the stochastic multi-armed bandit and its contextual variant with linear
expected rewards, in the setting where arms are clustered. We show, both
theoretically and empirically, how exploiting a given cluster structure can
significantly improve the regret and computational cost compared to using
standard Thompson sampling. In the case of the stochastic multi-armed bandit we
give upper bounds on the expected cumulative regret showing how it depends on
the quality of the clustering. Finally, we perform an empirical evaluation
showing that our algorithms perform well compared to previously proposed
algorithms for bandits with clustered arms.


  We analyse the subring of the Chow ring with support generated by the
irreducible components of the special fibre of the Gross-Schoen
desingularization of a d-fold self product of a semi-stable curve over the
spectrum of a discrete valuation ring. For this purpose we develop a calculus
which allows to determine intersection numbers in the special fibre explicitly.
As input our simplicial calculus needs only combinatorial data of the special
fibre. It yields a practical procedure for calculating even self intersections
in the special fibre. The first ingredient of our simplicial calculus is a
localization formula, which reduces the problem of calculating intersection
numbers to a special situation. In order to illustrate how our simplicial
calculus works, we calculate all intersection numbers between divisors with
support in the special fibre in dimension three and four. The localization
formula and the general idea were already presented for d=2 in a paper of
Shou-Wu Zhang. In our present work we achieve a generalisation to arbitrary d.


  The quantum phase transition in the ground state of the Extended spin S=1/2
XY model is studied in detail. Using the exact solution of the model the low
temperature thermodynamics, as well as the ground state phase diagram of the
model in the presence of applied uniform and/or staggered magnetic field are
discussed.


  The solution of the Muskhelishvili-Omnes Integral Equation is ambiguous by a
real polynomial. The coefficients of this polynomial can be fixed either by the
knowledge of the low energy parameters or by the asymptotic behavior of the
form factor. The role of the contact terms of the low energy effective
Lagrangian is explicitly analysed.


  Stirling permutations were introduced by Gessel and Stanley, who used their
enumeration by the number of descents to give a combinatorial interpretation of
certain polynomials related to Stirling numbers.
  Quasi-Stirling permutations, which can be viewed as labeled noncrossing
matchings, were introduced by Archer et al. as a natural extension of Stirling
permutations. Janson's correspondence between Stirling permutations and labeled
increasing plane trees extends to a bijection between quasi-Stirling
permutations and the same set of trees without the increasing restriction.
  Archer et al. posed the problem of enumerating quasi-Stirling permutations by
the number of descents, and conjectured that there are $(n+1)^{n-1}$ such
permutations of size $n$ having the maximum number of descents. In this paper
we prove their conjecture, and we give the generating function for
quasi-Stirling permutations by the number of descents, expressed as a
compositional inverse of the generating function of Eulerian polynomials. We
also find the analogue for quasi-Stirling permutations of the main result from
Gessel and Stanley's paper. We prove that the distribution of descents on these
permutations is asymptotically normal, and that the roots of the corresponding
quasi-Stirling polynomials are all real, in analogy to B\'ona's results for
Stirling permutations.
  Finally, we generalize our results to a one-parameter family of permutations
that extends $k$-Stirling permutations, and we refine them by also keeping
track of the number of ascents and the number of plateaus.


  We calculate electromagnetic production from highly excited hadronic matter
created in heavy ion collisions. The rates include the usual lowest order
processes in quark-gluon plasma plus the usual reactions in the hadronic phase,
related with rho,a_1 mesons. The space-time integration is done using a
hydrodynamical model. We have found that dilepton mass spectrum agrees with
results of other previous works, but *disagrees* with the CERES dilepton data.
In order to explain these data, some "unconventional" production mechanism need
to be incorporated: we discuss especially the notion of modified rho,a_1
masses, which indeed may explain the data. Other suggestions (e.g. the
longer-lived fireball) to increase the production of low mass dileptons seem to
be insufficient for the task. The results for direct photon production are
below the current WA80 experimental bounds, for all variants considered.


  The previous constructions of quadrature amplitude modulation (QAM) Golay
complementary sequences (GCSs) were generalized as $4^q $-QAM GCSs of length
$2^{m}$ by Li \textsl{et al.} (the generalized cases I-III for $q\ge 2$) in
2010 and Liu \textsl{et al.} (the generalized cases IV-V for $q\ge 3$) in 2013
respectively. Those sequences are presented as the combination of the
quaternary standard GCSs and compatible offsets. By providing new compatible
offsets based on the factorization of the integer $q$, we proposed two new
constructions of $4^q $-QAM GCSs, which have the generalized cases I-V as
special cases. The numbers of the proposed GCSs (including the generalized
cases IV-V) are equal to the product of the number of the quaternary standard
GCSs and the number of the compatible offsets. For $q=q_{1}\times q_{2}\times
\dots\times q_{t}$ ($q_k>1$), the number of new offsets in our first
construction is lower bounded by a polynomial of $m$ with degree $t$, while the
numbers of offsets in the generalized cases I-III and IV-V are a linear
polynomial of $m$ and a quadratic polynomial of $m$, respectively. In
particular, the numbers of new offsets in our first construction is seven times
more than that in the generalized cases IV-V for $q=4$. We also show that the
numbers of new offsets in our two constructions is lower bounded by a cubic
polynomial of $m$ for $q=6$. Moreover, our proof implies that all the mentioned
GCSs over QAM in this paper can be regarded as projections of Golay
complementary arrays of size $2\times2\times\cdots\times2$.


  We study a three-player variation of the impartial avoidance game introduced
by Anderson and Harary. Three players take turns selecting
previously-unselected elements of a finite group. The losing player is the one
who selects an element that causes the set of jointly-selected elements to be a
generating set for the group, with the previous player winning and the
remaining player coming in second place. We describe the winning strategy for
these games on cyclic, dihedral, and nilpotent groups.


  We report the discovery of a new spin glass ground state in the transition
metal monosilicides with the B20 crystallographic structure. Magnetic,
transport, neutron and muon investigation of the solid solution
Mn$_{1-x}$Co$_{x}$Si have revealed a new dome in the phase diagram with
evidence of antiferromagnetic interactions. For Mn rich compounds, a sharp
decrease of the Curie temperature is observed upon Co doping and neutron
elastic scattering shows that helimagnetic order of MnSi persists up to
$x=0.05$ with a shortening of the helix period. For higher Co ($0.05<x<0.90$)
concentrations, the Curie-Weiss temperature changes sign and the system enters
a spin glass state upon cooling ($T_g=9$ K for $x_{Co}=0.50$), due to chemical
disorder. In this doping range, a minimum appears in the resistivity,
attributed to scattering of conduction electron by localized magnetic moments.


  We introduce and analyze various Regularized Combined Field Integral
Equations (CFIER) formulations of time-harmonic Navier equations in media with
piece-wise constant material properties. These formulations can be derived
systematically starting from suitable coercive approximations of
Dirichlet-to-Neumann operators (DtN), and we present a periodic
pseudodifferential calculus framework within which the well posedness of CIER
formulations can be established. We also use the DtN approximations to derive
and analyze Optimized Schwarz (OS) methods for the solution of elastodynamics
transmission problems. The pseudodifferential calculus we develop in this paper
relies on careful singularity splittings of the kernels of Navier boundary
integral operators which is also the basis of high-order Nystr\"om quadratures
for their discretizations. Based on these high-order discretizations we
investigate the rate of convergence of iterative solvers applied to CFIER and
OS formulations of scattering and transmission problems. We present a variety
of numerical results that illustrate that the CFIER methodology leads to
important computational savings over the classical CFIE one, whenever iterative
solvers are used for the solution of the ensuing discretized boundary integral
equations. Finally, we show that the OS methods are competitive in the
high-frequency high-contrast regime.


  We have conducted a model independent analysis of the $K^+ \bar{K}^0$ pair
correlation function obtained from ultra high energy $pp$ collisions, with the
aim of extracting the information encoded in it related to the $K\bar{K}$
interaction and the coupled channel $\pi^+ \eta$. With the present large errors
at small relative $K^+\bar{K}^0$ momenta, we find that the information obtained
about the scattering matrix suffers from large uncertainties. Even then, we are
able to show that the data imply the existence of the $a_0$ resonance,
$a_0(980)$, showing as a strong cusp close to the $K\bar{K}$ threshold. We also
mention that the measurement of the $\pi^+ \eta$ correlation function will be
essential in order to constrain more the information on $K\bar{K}$ dynamics
that can be obtained from correlation functions.


  A search for Lorentz violation in electrodynamics was performed by measuring
the resonant frequency difference between two counterpropagating directions of
an optical ring cavity. Our cavity contains a dielectric element, which makes
our cavity sensitive to the violation. The laser frequency is stabilized to the
counterclockwise resonance of the cavity, and the transmitted light is
reflected back into the cavity for resonant frequency comparison with the
clockwise resonance. This double-pass configuration enables a null experiment
and gives high common mode rejection of environmental disturbances. We found no
evidence for odd-parity anisotropy at the level of $\delta c /c \lesssim
10^{-14}$. Within the framework of the Standard Model Extension, our result put
more than 5 times better limits on three odd-parity parameters
$\tilde{\kappa}^{JK}_{o+}$ and a 12 times better limit on the scalar parameter
$\tilde{\kappa}_{\tr}$ compared with the previous best limits.


  We discuss the possibility to use a high energy neutrino beam from a muon
storage ring to provide one way communication with a submerged submarine.
Neutrino interactions produce muons which can be detected either, directly when
they pass through the submarine or by their emission of Cerenkov light in sea
water, which, in turn, can be exploited with sensitive photo detectors. Due to
the very high neutrino flux from a muon storage ring, it is sufficient to mount
either detection system directly onto the hull of the submersible. The
achievable data transfer rates compare favorable with existing technologies and
do allow for a communication at the usual speed and depth of submarines.


  Halpern and Yamron have given a Lorentz, conformal, and Diff S$_2$-invariant
world-sheet action for the generic irrational conformal field theory, but the
action is highly non-linear. In this paper, we introduce auxiliary fields to
find an equivalent linearized form of the action, which shows in a very clear
way that the generic affine-Virasoro action is a Diff S$_2$-gauged WZW model.
In particular, the auxiliary fields transform under Diff S$_2$ as local Lie $g$
$\times$ Lie $g$ connections, so that the linearized affine-Virasoro action
bears an intriguing resemblance to the usual (Lie algebra) gauged WZW model.


  We prove that every wandering Julia component of cubic rational maps
eventually has at most two complementary components.


  We consider a continuous-time random walk which is the generalization, by
means of the introduction of waiting periods on sites, of the one-dimensional
nonhomogeneous random walk with a position-dependent drift known in the
mathematical literature as Gillis random walk. This modified stochastic process
allows to significantly change local, non-local and transport properties in the
presence of heavy-tailed waiting-time distributions lacking the first moment:
we provide here exact results concerning hitting times, first-time events,
survival probabilities, occupation times, the moments spectrum and the
statistics of records. Specifically, normal diffusion gives way to subdiffusion
and we are witnessing the breaking of ergodicity. Furthermore we also test our
theoretical predictions with numerical simulations.


  If the Higgs mass m_H is as low as suggested by present experimental
information, the Standard Model ground state might not be absolutely stable. We
present a detailed analysis of the lower bounds on m_H imposed by the
requirement that the electroweak vacuum be sufficiently long-lived. We perform
a complete one-loop calculation of the tunnelling probability at zero
temperature, and we improve it by means of two-loop renormalization-group
equations. We find that, for m_H=115 GeV, the Higgs potential develops an
instability below the Planck scale for m_t>(166\pm 2) GeV, but the electroweak
vacuum is sufficiently long-lived for m_t < (175\pm 2) \GeV.


  Let $a \geq 2$ be an integer. We prove that for every periodic sequence
$(s_n)_{n \geq 1}$ in $\{-1, +1\}$ there exists an effectively computable
rational number $C_\mathbf{s} > 0$ such that \begin{equation*}
\log\operatorname{lcm}(a + s_1, a^2 + s_2, \dots, a^n + s_n) \sim C_\mathbf{s}
\cdot \frac{\log a}{\pi^2} \cdot n^2 , \end{equation*} as $n \to +\infty$,
where $\operatorname{lcm}$ denotes the least common multiple.
  Furthermore, we show that if $(s_n)_{n \geq 1}$ is a sequence of independent
and uniformly distributed random variables in $\{-1, +1\}$ then
\begin{equation*} \log\operatorname{lcm}(a + s_1, a^2 + s_2, \dots, a^n + s_n)
\sim 6 \operatorname{Li}_2\!\big(\tfrac1{2}\big) \cdot \frac{\log a}{\pi^2}
\cdot n^2 , \end{equation*} with probability $1 - o(1)$, as $n \to +\infty$,
where $\operatorname{Li}_2$ is the dilogarithm function.


  We discuss the Palatini formulation of modified gravity including a
Yukawa-like term. It is shown that in this formulation, the Yukawa term offers
an explanation for the current exponential accelerated expansion of the
universe and reduces to the standard Friedmann cosmology in the appropriate
limit. We then discuss the scalar-tensor formulation of the model as a metric
theory and show that the Yukawa term predicts a power-law acceleration at
late-times. The Newtonian limit of the theory is also discussed in context of
the Palatini formalism.


  We describe an FPGA-based, 96-channel, time-to-digital converter (TDC)
intended for use with the Central Outer Tracker (COT) in the CDF Experiment at
the Fermilab Tevatron. The COT system is digitized and read out by 315 TDC
cards, each serving 96 wires of the chamber. The TDC is physically configured
as a 9U VME card. The functionality is almost entirely programmed in firmware
in two Altera Stratix FPGA's. The special capabilities of this device are the
availability of 840 MHz LVDS inputs, multiple phase-locked clock modules, and
abundant memory. The TDC system operates with an input resolution of 1.2 ns.
Each input can accept up to 7 hits per collision. The time-to-digital
conversion is done by first sampling each of the 96 inputs in 1.2-ns bins and
filling a circular memory; the memory addresses of logical transitions (edges)
in the input data are then translated into the time of arrival and width of the
COT pulses. Memory pipelines with a depth of 5.5 $\mu$s allow deadtime-less
operation in the first-level trigger. The TDC VME interface allows a 64-bit
Chain Block Transfer of multiple boards in a crate with transfer-rates up to 47
Mbytes/sec. The TDC also contains a separately-programmed data path that
produces prompt trigger data every Tevatron crossing. The full TDC design and
multi-card test results are described. The physical simplicity ensures
low-maintenance; the functionality being in firmware allows reprogramming for
other applications.


  This is an introduction to the special issue Genome organization: experiments
and simulations, published in Chromosome Research, volume 25, issue 1 (2017).


  For odd dimensional Poincar\'e-Einstein manifolds $(X^{n+1},g)$, we study the
set of harmonic $k$-forms (for $k<\ndemi$) which are $C^m$ (with $m\in\nn$) on
the conformal compactification $\bar{X}$ of $X$. This is infinite dimensional
for small $m$ but it becomes finite dimensional if $m$ is large enough, and in
one-to-one correspondence with the direct sum of the relative cohomology
$H^k(\bar{X},\pl\bar{X})$ and the kernel of the Branson-Gover \cite{BG}
differential operators $(L_k,G_k)$ on the conformal infinity
$(\pl\bar{X},[h_0])$. In a second time we relate the set of
$C^{n-2k+1}(\Lambda^k(\bar{X}))$ forms in the kernel of $d+\delta_g$ to the
conformal harmonics on the boundary in the sense of \cite{BG}, providing some
sort of long exact sequence adapted to this setting. This study also provides
another construction of Branson-Gover differential operators, including a
parallel construction of the generalization of $Q$ curvature for forms.


  We call a multivariable polynomial an Agler denominator if it is the
denominator of a rational inner function in the Schur-Agler class, an important
subclass of the bounded analytic functions on the polydisk. We give a necessary
and sufficient condition for a multi-affine, symmetric, and stable polynomial
to be an Agler denominator and prove several consequences. We also sharpen a
result due to Kummert related to three variable, multi-affine, stable
polynomials.


  Uplink scheduling/resource allocation under the single-carrier FDMA
constraint is investigated, taking into account the queuing dynamics at the
transmitters. Under the single-carrier constraint, the problem of MaxWeight
scheduling, as well as that of determining if a given number of packets can be
served from all the users, are shown to be NP-complete. Finally, a
matching-based scheduling algorithm is presented that requires only a
polynomial number of computations per timeslot, and in the case of a system
with large bandwidth and user population, provably provides a good delay
(small-queue) performance, even under the single-carrier constraint.
  In summary, the results in first part of the paper support the recent push to
remove SCFDMA from the Standards, whereas those in the second part present a
way of working around the single-carrier constraint if it remains in the
Standards.


  We introduce and study covariance fields of distributions on a Riemannian
manifold. At each point on the manifold, covariance is defined to be a
symmetric and positive definite (2,0)-tensor. Its product with the metric
tensor specifies a linear operator on the respected tangent space.
Collectively, these operators form a covariance operator field. We show that,
in most circumstances, covariance fields are continuous. We also solve the
inverse problem: recovering distribution from a covariance field. Surprisingly,
this is not possible on Euclidean spaces. On non-Euclidean manifolds however,
covariance fields are true distribution representations.


  Here we explore the possibility of precise time-keeping in quantum systems
using athermal resources. We show that quantum measurement engineered
reservoirs can be used as athermal resources to drive the ticks of a quantum
clock. Two and three level quantum systems act as transducers in our model,
converting the quantum measurement induced noise to produce a series of ticks.
The ticking rate of the clock is maximized when the measured observable
maximally non-commutes with the clock's Hamiltonian. We use the large deviation
principle to characterize the statistics of observed ticks within a given
time-period and show that it can be sub-Poissonian -- quantified by Mandel's Q
parameter -- alluding to the quantum nature of the clock. We discuss the
accuracy and efficiency of the clock, and extend our framework to include
hybrid quantum clocks fueled by both measurements, and thermal resources. We
make comparisons to relatable recent proposals for quantum clocks, and discuss
alternate device implementations harvesting the quantum measurement engineered
non-equilibrium conditions, beyond the clock realization.


  Relativistic calculations of the second- and third-order contributions in
magnetic field to the Zeeman splitting in boronlike ions are presented for the
wide range of nuclear charge numbers $Z=6$--$92$. The
interelectronic-interaction correction of the first order in $1/Z$ is evaluated
to all orders in $\alpha Z$. The higher-order corrections in $1/Z$ are taken
into account approximately by means of effective screening potentials. The
obtained results are important for interpretation of experimental data on the
Zeeman splitting in boronlike ions, in particular, for the ARTEMIS experiment
presently implemented at GSI.


  The electronic spectra of light one-electron quasi-molecular compounds
H-H$^+$, He$^+$-He$^2+$ and He$^+$-H$^+$ are analyzed. To this end, the
two-center Dirac equation is solved by the dual-kinetically balanced
finite-basis-set method for axially symmetric systems termed as A-DKB. This
method allows a complete relativistic consideration of these systems at fixed
internuclear distances. A comparison of the obtained results with the
nonrelativistic and relativistic calculations presented in the literature is
performed. The advantages and disadvantages of the approach are discussed in
details.


  Let $\nu_\lambda^p$ be the distribution of the random series
$\sum_{n=1}^\infty i_n \lambda^n$, where $i_n$ is a sequence of i.i.d. random
variables taking the values 0,1 with probabilities $p,1-p$. These measures are
the well-known (biased) Bernoulli convolutions.
  In this paper we study the multifractal spectrum of $\nu_\lambda^p$ for
typical $\lambda$. Namely, we investigate the size of the sets
  \[ \Delta_{\lambda,p}(\alpha) = \left\{x\in\R: \lim_{r\searrow 0} \frac{\log
\nu_\lambda^p(B(x,r))}{\log r} =\alpha\right\}. \]
  Our main results highlight the fact that for almost all, and in some cases
all, $\lambda$ in an appropriate range, $\Delta_{\lambda,p}(\alpha)$ is
nonempty and, moreover, has positive Hausdorff dimension, for many values of
$\alpha$. This happens even in parameter regions for which $\nu_\lambda^p$ is
typically absolutely continuous.


  Many current Internet services rely on inferences from models trained on user
data. Commonly, both the training and inference tasks are carried out using
cloud resources fed by personal data collected at scale from users. Holding and
using such large collections of personal data in the cloud creates privacy
risks to the data subjects, but is currently required for users to benefit from
such services. We explore how to provide for model training and inference in a
system where computation is pushed to the data in preference to moving data to
the cloud, obviating many current privacy risks. Specifically, we take an
initial model learnt from a small set of users and retrain it locally using
data from a single user. We evaluate on two tasks: one supervised learning
task, using a neural network to recognise users' current activity from
accelerometer traces; and one unsupervised learning task, identifying topics in
a large set of documents. In both cases the accuracy is improved. We also
analyse the robustness of our approach against adversarial attacks, as well as
its feasibility by presenting a performance evaluation on a representative
resource-constrained device (a Raspberry Pi).


  We introduce volume forms on mapping stacks in derived algebraic geometry
using a parametrized version of the Reidemeister-Turaev torsion. In the case of
derived loop stacks we describe this volume form in terms of the Todd class. In
the case of mapping stacks from surfaces, we compare it to the symplectic
volume form. As an application of these ideas, we construct canonical
orientation data for cohomological DT invariants of closed oriented
3-manifolds.


  Molecular dynamics simulations of sorbates of different sizes confined to the
interior of carbon nanotubes are reported. The mean squared displacement shows
gradual change from diffusive for small sorbates to superdiffusive for
intermediate sized-sorbates to ballistic for sizes comparable to the channel
diameter. We show that this crossover behaviour can be understood on the basis
of a gradual decrease of the x-y component of the force with the levitation
parameter. The analysis can also help to rationalize some recently published
results.


  Large Vision-Language Models (LVLMs) excel in integrating visual and
linguistic contexts to produce detailed content, facilitating applications such
as image captioning. However, using LVLMs to generate descriptions often faces
the challenge of object hallucination (OH), where the output text misrepresents
actual objects in the input image. While previous studies attribute the
occurrence of OH to the inclusion of more details, our study finds technical
flaws in existing metrics, leading to unreliable evaluations of models and
conclusions about OH. This has sparked a debate on the question: Do more
details always introduce more hallucinations in LVLM-based image captioning?
  In this paper, we address this debate by proposing a novel decoding strategy,
Differentiated Beam Decoding (DBD), along with a reliable new set of evaluation
metrics: CLIP-Precision, CLIP-Recall, and CLIP-F1. DBD decodes the wealth of
information hidden in visual input into distinct language representations
called unit facts in parallel. This decoding is achieved via a well-designed
differential score that guides the parallel search and candidate screening. The
selected unit facts are then aggregated to generate the final caption. Our
proposed metrics evaluate the comprehensiveness and accuracy of image captions
by comparing the embedding groups of ground-truth image regions and generated
text partitions. Extensive experiments on the Visual Genome dataset validate
the effectiveness of our approach, demonstrating that it produces detailed
descriptions while maintaining low hallucination levels.


  Anonymous Veto (AV) and Dining cryptographers (DC) are two basic primitives
for the cryptographic problems where the main aim is to hide the identity of
the senders of the messages. These can be achieved by classical methods where
the security is based either on computational hardness or on shared private
keys. In this regard, we present a secure quantum protocol for both DC and AV
by exploiting the GHZ correlations. We first solve a generalized version of the
DC problem with the help of multiparty GHZ state. This allow us to provide a
secure quantum protocol for the AV. Securities for both the protocols rely on
some novel and fundamental features of GHZ correlations related to quantum
nonlocality.


  The ground state energy shifts and excitation spectra of charged
buckminsterfullerene C$_{60}^{n-}$, $n=1,\ldots 5$ are calculated. The
electron--vibron Hamiltonian of Part I is extended to include all $A_g$ and
$H_g$ modes with experimentally determined frequencies and theoretically
estimated coupling constants. Complex splitting patterns of $H_g$ vibrational
levels are found. Our results are relevant to EPR measurements of spin
splittings in C$_{60}^{2-}$ and C$_{60}^{3-}$ in solution. Spectroscopic
gas-phase experiments will be of interest for further testing of this theory.
As found in Part I, degeneracies in the electron and vibron Hamiltonians give
rise to a dynamical Jahn Teller effect, and to a considerable enhancement of
the electronic pairing interaction. This helps to overcome repulsive Coulomb
interactions and has important implications for superconductivity in
K$_3$C$_{60}$ and the insulating state in K$_4$C$_{60}$.


  As cross-chain technologies make the interactions among different blockchains
(hereinafter "chains") possible, multi-chains consensus is becoming more and
more important in blockchain networks. However, more attention has been paid to
the single-chain consensus schemes. The multi-chains consensus with trusted
miners participation has been not considered, thus offering opportunities for
malicious users to launch Diverse Miners Behaviors (DMB) attacks on different
chains. DMB attackers can be friendly in the consensus process of some chains
called mask-chains to enhance trust value, while on other chains called
kill-chains they engage in destructive behaviors of network. In this paper, we
propose a multi-chains consensus scheme named as Proof-of-DiscTrust (PoDT) to
defend against DMB attacks. Distinctive trust idea (DiscTrust) is introduced to
evaluate the trust value of each user concerning different chains. A dynamic
behaviors prediction scheme is designed to strengthen DiscTrust to prevent
intensive DMB attackers who maintain high trust by alternately creating true or
false blocks on kill-chains. On this basis, a trusted miners selection
algorithm for multi-chains can be achieved at a round of block creation.
Experimental results show that PoDT is secure against DMB attacks and more
effective than traditional consensus schemes in multi-chains environments.


  This paper proposes the use of Eukaryotic cells, namely astrocytes, to
develop logic gates. The logic gates are achieved by manipulating the threshold
of Ca$^{2+}$ ion flows between the cells, based on the input signals. Through
wet-lab experiments that engineer the astrocytes cells with pcDNA3.1-hGPR17
genes, we show that both AND and OR gates can be implemented by controlling
Ca$^{2+}$ signals that flow through the population. A reinforced learning
platform is also presented in the paper to optimize two main parameters, which
are the Ca$^{2+}$ activation threshold and time slot of input signals $T_b$
into the gate. This design platform caters for any size and connectivity of the
cell population, by taking into consideration the delay and noise produced from
the signalling between the cells, in order to fine-tune the activation
threshold and input signal time slot parameters. To validate the effectiveness
of the reinforced learning platform, a Ca$^{2+}$ Signalling-based Molecular
Communications Simulator was used to simulate the signalling between the
astrocyte cells. The results from the simulation showed that an optimum value
for both the Ca$^{2+}$ activation threshold and time slot of input signals
$T_b$ is required to achieve optimal computation accuracy, where up to 90\%
accuracy for both the AND and OR gates can be achieved with the right
combination of values. The reinforced learning platform for the engineered
astrocytes to create digital logic gates can be used for future
Neural-Molecular Computing chip, which can revolutionize brain implants that
are constructed from engineered biological cells.


  A unique pattern selection in the absolutely unstable regime of a driven,
nonlinear, open-flow system is analyzed: The spatiotemporal structures of
rotationally symmetric vortices that propagate downstream in the annulus of the
rotating Taylor-Couette system due to an externally imposed axial through-flow
are investigated for two different axial boundary conditions at the in- and
outlet. Unlike the stationary patterns in systems without through-flow the
spatiotemporal structures of propagating vortices are independent of parameter
history, initial conditions, and system's length. They do, however, depend on
the axial boundary conditions, the driving rate of the inner cylinder and the
through-flow rate. Our analysis of the amplitude equation shows that the
pattern selection can be described by a nonlinear eigenvalue problem with the
frequency being the eigenvalue. Approaching the border between absolute and
convective instability the eigenvalue problem becomes effectively linear and
the selection mechanism approaches that one of linear front propagation.
PACS:47.54.+r,47.20.Ky,47.32.-y,47.20.Ft


  Lemaitre-Tolman-Bondi inhomogeneous spacetimes can be used as a cosmological
model to account for the type Ia supernova data. However, such models also give
rise to large velocities of galaxy clusters with respect to the cosmic
microwave background. Those velocities can be measured using the kinematic
Sunyaev-Zeldovich effect. This paper presents a calculation of galaxy cluster
velocities as a function of redshift for such a model.


  We present a lattice study of the phase transitions at zero and nonzero
temperature for the $SU(3)$ gauge theory with a varying number of flavours
$N_f$ in the fundamental representation of the gauge group. We show that all
results are consistent with a lower edge of the conformal window between
$N_f=8$ and $N_f=6$. A lower edge in this interval is in remarkable agreement
with perturbation theory and recent large-$N$ arguments. .


  The energy gap of correlated Hubbard clusters is well studied for
one-dimensional systems using analytical methods and
density-matrix-renormalization-group (DMRG) simulations. Beyond 1D, however,
exact results are available only for small systems by quantum Monte Carlo. For
this reason and, due to the problems of DMRG in simulating 2D and 3D systems,
alternative methods such as Green functions combined with many-body
approximations (GFMBA), that do not have this restriction, are highly
important. However, it has remained open whether the approximate character of
GFMBA simulations prevents the computation of the Hubbard gap. Here we present
new GFMBA results that demonstrate that GFMBA simulations are capable of
producing reliable data for the gap which agrees well with the DMRG benchmarks
in 1D. An interesting observation is that the accuracy of the gap can be
significantly increased when the simulations give up certain symmetry
restriction of the exact system, such as spin symmetry and spatial homogeneity.
This is seen as manifestation and generalization of the "symmetry dilemma"
introduced by L\"owdin for Hartree--Fock wave function calculations.


  The era of "data deluge" has sparked renewed interest in graph-based learning
methods and their widespread applications ranging from sociology and biology to
transportation and communications. In this context of graph-aware methods, the
present paper introduces a tensor-graph convolutional network (TGCN) for
scalable semi-supervised learning (SSL) from data associated with a collection
of graphs, that are represented by a tensor. Key aspects of the novel TGCN
architecture are the dynamic adaptation to different relations in the tensor
graph via learnable weights, and the consideration of graph-based regularizers
to promote smoothness and alleviate over-parameterization. The ultimate goal is
to design a powerful learning architecture able to: discover complex and highly
nonlinear data associations, combine (and select) multiple types of relations,
scale gracefully with the graph size, and remain robust to perturbations on the
graph edges. The proposed architecture is relevant not only in applications
where the nodes are naturally involved in different relations (e.g., a
multi-relational graph capturing family, friendship and work relations in a
social network), but also in robust learning setups where the graph entails a
certain level of uncertainty, and the different tensor slabs correspond to
different versions (realizations) of the nominal graph. Numerical tests
showcase that the proposed architecture achieves markedly improved performance
relative to standard GCNs, copes with state-of-the-art adversarial attacks, and
leads to remarkable SSL performance over protein-to-protein interaction
networks.


  When tensioned, ordinary materials expand along the direction of the applied
force. Here, we explore network concepts to design metamaterials exhibiting
negative compressibility transitions, during which a material undergoes
contraction when tensioned (or expansion when pressured). Continuous
contraction of a material in the same direction of an applied tension, and in
response to this tension, is inherently unstable. The conceptually similar
effect we demonstrate can be achieved, however, through destabilisations of
(meta)stable equilibria of the constituents. These destabilisations give rise
to a stress-induced solid-solid phase transition associated with a twisted
hysteresis curve for the stress-strain relationship. The strain-driven
counterpart of negative compressibility transitions is a force amplification
phenomenon, where an increase in deformation induces a discontinuous increase
in response force. We suggest that the proposed materials could be useful for
the design of actuators, force amplifiers, micro-mechanical controls, and
protective devices.


  Thermal entanglement, magnetic and quadrupole moments properties of the mixed
spin-1/2 and spin-1 Ising-Heisenberg model on a diamond chain are considered.
Magnetization and quadrupole moment plateaus are observed for the
antiferromagnetic couplings. Thermal negativity as a measure of quantum
entanglement of the mixed spin system is calculated. Different behavior for the
negativity is obtained for the various values of Heisenberg dipolar and
quadrupole couplings. The intermediate plateau of the negativity has been
observed at absence of the single-ion anisotropy and quadrupole interaction
term. When dipolar and quadrupole couplings are equal there is a similar
behavior of negativity and quadrupole moment.


  Biological oscillators coordinate individual cellular components so that they
function coherently and collectively. They are typically composed of multiple
feedback loops, and period mismatch is unavoidable in biological
implementations. We investigated the advantageous effect of this period
mismatch in terms of a synchronization response to external stimuli.
Specifically, we considered two fundamental models of genetic circuits: smooth-
and relaxation oscillators. Using phase reduction and Floquet multipliers, we
numerically analyzed their entrainability under different coupling strengths
and period ratios. We found that a period mismatch induces better entrainment
in both types of oscillator; the enhancement occurs in the vicinity of the
bifurcation on their limit cycles. In the smooth oscillator, the optimal period
ratio for the enhancement coincides with the experimentally observed ratio,
which suggests biological exploitation of the period mismatch. Although the
origin of multiple feedback loops is often explained as a passive mechanism to
ensure robustness against perturbation, we study the active benefits of the
period mismatch, which include increasing the efficiency of the genetic
oscillators. Our findings show a qualitatively different perspective for both
the inherent advantages of multiple loops and their essentiality.


  We provide new characterizations of Sobolev ad BV spaces in doubling and
Poincare metric spaces in the spirit of the Bourgain-Brezis-Mironescu and
Nguyen limit formulas holding in domains of R^N.


  A parton produced with a high transverse momentum in a hard collision is
regenerating its color field, intensively radiating gluons and losing energy.
This process cannot last long, if it ends up with production of a leading
hadron carrying the main fraction z_h of the initial parton momentum. So energy
conservation imposes severe constraints on the length scale of production of a
single hadron with high pT. As a result, the main reason for hadron quenching
observed in heavy ion collisions, is not energy loss, but attenuation of the
produced colorless dipole in the created dense medium. The latter mechanism,
calculated with the path-integral method, explains well the observed
suppression of light hadrons and the elliptic flow in a wide range of energies,
from the lowest energy of RHIC up to LHC, and in a wide range of transverse
momenta. The values of the transport coefficient extracted from data range
within 1-2 GeV^2/fm, dependent on energy, and agree well with the theoretical
expectations.


  In this paper we go deep into the connection between duality and fields
redefinition for general bilinear models involving the 1-form gauge field $A$.
A duality operator is fixed based on "gauge embedding" procedure. Dual models
are shown to fit in equivalence classes of models with same fields
redefinitions.


  We study vortex matter in layered superconductors in the limit of zero
Josephson coupling. The long range of the interaction between pancake vortices
in the c-direction allows us to employ a mean-field method: all attractive
inter-layer interactions are reduced to an effective substrate potential, which
pancakes experience in addition to the same-layer pancake repulsion. We perform
numerical simulations of this mean-field model using two independent numerical
implementations with different simulation methods (Monte-Carlo sampling and
Langevin molecular dynamics). The substrate potential is updated
self-consistently from the averaged pancake density. Depending on temperature,
this potential converges to a periodic profile (crystal) or vanishes (liquid).
We compute thermodynamic properties of the system, such as the melting line,
the instability line of the crystal, and the entropy jump across the melting
transition. The simulation results are in good agreement with approximate
analytical calculations.


  In this work the modeling and calibration method of reciprocity error in a
coherent TDD coordinated multi-point (CoMP) joint transmission (JT) system are
addressed. The modeling includes parameters such as amplitude gains and phase
differences of RF chains between the eNBs. The calibration method used for
inter-cell antenna calibration is based on precoding matrix indicator (PMI)
feedback by UE. Furthermore, we provide some simulation results for evaluating
the performance of the calibration method in different cases such as varying
estimation-period, cell-specific reference signals (CRS) ports configuration,
signal to noise ratio (SNR), phase difference, etc. The main conclusion is that
the proposed method for intercell antenna calibration has good performance for
estimating the residual phase difference. Keywords-LTE-Advanced; TDD; CoMP; JT;
reciprocity error; phase difference; inter-cell antenna calibration


  In this work, we aim to understand the mechanisms driving academic
collaboration. We begin by building a model for how researchers split their
effort between multiple papers, and how collaboration affects the number of
citations a paper receives, supported by observations from a large real-world
publication and citation dataset, which we call the h-Reinvestment model. Using
tools from the field of Game Theory, we study researchers' collaborative
behavior over time under this model, with the premise that each researcher
wants to maximize his or her academic success. We find analytically that there
is a strong incentive to collaborate rather than work in isolation, and that
studying collaborative behavior through a game-theoretic lens is a promising
approach to help us better understand the nature and dynamics of academic
collaboration.


  We introduce a categorical approach to classifying actions of C$^*$-tensor
categories $\mathcal{C}$ on C$^*$-algebras up to cocycle conjugacy. We show
that, in this category, inductive limits exist and there is a natural notion of
approximate unitary equivalence. Then, we generalise classical Elliott
intertwining results to the $\mathcal{C}$-equivariant case, in the same fashion
as done by Szab\'o for the group equivariant case in [39].


  It is shown that the Coulomb drag between two identical layers in the
Anderson insulting state indicates a striking difference between the Mott and
Efros-Shklovskii (ES) insulators. In the former, the trans-resistance $\rho_t$
is monotonically increasing with the localization length $\xi$; in the latter,
the presence of a Coulomb gap leads to an opposite result: $\rho_t$ is enhanced
with a decreasing $\xi$, with the same exponential factor as the single layer
resistivity. This distinction reflects the relatively pronounced role of
excited density fluctuations in the ES state, implied by the enhancement in the
rate of hopping processes at low frequencies. The magnitude of drag is
estimated for typical experimental parameters in the different cases. It is
concluded that a measurement of drag can be used to distinguish between
interacting and non-interacting insulating state.


  Tracking scripts can use the sourceURL directive to mask their origin from
developer tools and tools that use the same JS call stack and network stack
information. Firefox and Chromium appear to be affected. Firefox 78 now
includes a preference to disable this behavior. This short paper describes the
effect when using the OpenWPM measurement platform along with details of
discovery.


  The energy-spectrum of two point-like particles interacting in a 3-D
isotropic Harmonic Oscillator (H.O.) trap is related to the free scattering
phase-shifts $\delta$ of the particles by a formula first published by Busch et
al. It is here used to find an expression for the \it shift \rm of the energy
levels, caused by the interaction, rather than the perturbed spectrum itself.
In the limit of high energy (large quantum number $n$ of the H.O.) this shift
is shown to be given by $-2\frac{\delta}{\pi}$, also valid in the limit of
infinite as well as zero scattering length at all H.O. energies.
  Numerical investigation shows that the shifts differ from the exact result of
Busch et al, by less than $<\frac{1}{2}\%$ except for $n=0$ when it can be as
large as $\approx 2.5\%$.
  This approximation for the energy-shift is well known from another exactly
solvable model, namely that of two particles interacting in a spherical
infinite square-well trap (or box) of radius $R$ in the limit $R\rightarrow
\infty$, and/or in the limit of large energy. It is in this context referred to
as the \it phase-shift approximation \rm.
  It can be (and has been) used in (infinite) nuclear matter calculations to
calculate the two-body effective interaction in situations where in-medium
effects can be neglected. It has also been used in expressing the energy of
free electrons in a metal.


  In this work, we first develop a general mesoscopic multiple-relaxation-time
lattice Boltzmann (MRT-LB) model for the two-dimensional diffusion equation
with the constant diffusion coefficient and source term, where the D2Q5 (five
discrete velocities in two-dimensional space) lattice structure is considered.
Then we exactly derive the equivalent macroscopic finite-difference scheme of
the MRT-LB model. Additionally, we also propose a proper MRT-LB model for the
diffusion equation with a linear source term, and obtain an equivalent
macroscopic six-level finite-difference scheme. After that, we conduct the
accuracy and stability analysis of the finite-difference scheme and the
mesoscopic MRT-LB model. It is found that at the diffusive scaling, both of
them can achieve a fourth-order accuracy in space based on the Taylor
expansion. The stability analysis also shows that they are both unconditionally
stable. Finally, some numerical experiments are conducted, and the numerical
results are also consistent with our theoretical analysis.


  The two state molecular orbital (2-MO) model of the phenyl based
semiconductors is used to calculate the low-lying spectra of the Ag and Bu
states of poly(para-phenylene) (PPP). The model parameters are determined by
fitting its predictions to exact Pariser-Parr-Pople model calculations of
benzene and biphenyl, and it is solved using the density matrix renormalisation
group method. It is shown that there exists a band of Bu (s-wave) excitons
below the band states. In the long chain limit the lowest exciton is situated
3.3 eV above the ground state, consistent with experimental data. The
calculated particle-hole separation of these excitons indicates that they are
tightly bound, extending over only a few repeat units. The lowest band state is
found to be a covalent 2Ag state, whose energy almost coincides with the charge
gap Eg. Lying just above the 2Ag state is a band Bu state (the nBu state). The
particle-hole separation of the band states scales linearly with oligomer size.
The binding energy of the 1Bu exciton is determined rigorously as 0.74 eV. The
dipole matrix elements and oscillator strengths for the transitions between the
lowest Ag and Bu states are calculated and the NLO properties of PPP, such as
electroabsorption (EA) and third harmonic generation, are investigated. A
comparison of the EA spectrum with the experimental data shows that the main
features of the experimental spectrum are well described by the 2-MO
Hamiltonian. Only five states account for most of the calculated EA. These are
the 1Ag, 1Bu, 2Ag, nBu and another band Ag state, the kAg, thus confirming the
essential states model. An analysis of the particle excitation weight of these
states indicates that they are predominately single particle in character.


  Recurrent neural networks (RNNs) have fast inference and scale efficiently on
long sequences, but they are difficult to train and hard to scale. We propose
Hawk, an RNN with gated linear recurrences, and Griffin, a hybrid model that
mixes gated linear recurrences with local attention. Hawk exceeds the reported
performance of Mamba on downstream tasks, while Griffin matches the performance
of Llama-2 despite being trained on over 6 times fewer tokens. We also show
that Griffin can extrapolate on sequences significantly longer than those seen
during training. Our models match the hardware efficiency of Transformers
during training, and during inference they have lower latency and significantly
higher throughput. We scale Griffin up to 14B parameters, and explain how to
shard our models for efficient distributed training.


  Considering matter coupled supersymmetric Chern-Simons theories in three
dimensions we extend the Gaiotto-Witten mechanism of supersymmetry enhancement
$\mathcal{N}_3=3\to \mathcal{N}_3=4$ from the case where the hypermultiplets
span a flat HyperK\"ahler manifold to that where they live on a curved one. We
derive the precise conditions of this enhancement in terms of generalized
Gaiotto-Witten identities to be satisfied by the tri-holomorphic moment maps.
An infinite class of HyperK\"ahler metrics compatible with the enhancement
condition is provided by the Calabi metrics on $T^\star \mathbb{P}^{n}$. In
this list we find, for $n=2$ the resolution of the metric cone on
$\mathrm{N}^{0,1,0}$ which is the unique homogeneous Sasaki Einstein 7-manifold
leading to an $\mathcal{N}_4=3$ compactification of M-theory. This leads to
challenging perspectives for the discovery of new relations between the
enhancement mechanism in $D=3$, the geometry of M2-brane solutions and also for
the dual description of super Chern Simons theories on curved HyperK\"ahler
manifolds in terms of gauged fixed supergroup Chern Simons theories. The
relevant supergroup is in this case $\mathrm{SU(3|N)}$ where $\mathrm{SU(3)}$
is the flavor group and $\mathrm{U(N)}$ is the color group.


  Deep learning (DL) enables deep neural networks (DNNs) to automatically learn
complex tasks or rules from given examples without instructions or guiding
principles. As we do not engineer DNNs' functions, it is extremely difficult to
diagnose their decisions, and multiple lines of studies proposed to explain
principles of DNNs/DL operations. Notably, one line of studies suggests that
DNNs may learn concepts, the high level features recognizable to humans. Thus,
we hypothesized that DNNs develop abstract codes, not necessarily recognizable
to humans, which can be used to augment DNNs' decision-making. To address this
hypothesis, we combined foundation segmentation models and unsupervised
learning to extract internal codes and identify potential use of abstract codes
to make DL's decision-making more reliable and safer.