title:
Tight-Binding non-magnetic disorder DOS and residual DOS revisited for
  Unconventional Superconductors

abstract:
  In this paper, we present the calculation of the density of states (DOS) and
the residual density of states (RDOS) for two unconventional superconductors
strontium-doped lanthanum cuprate $La_{2-x}Sr_xCuO_4$, which is a
high-temperature superconductor (HTSC) with singlet pairing, and strontium
ruthenate $Sr_2RuO_4$, with a triplet pairing in the Fermi surface
$\gamma$-sheet. The calculations were carried out in the framework of the
tight-binding (TB) approach with first neighbors interaction in the presence of
nonmagnetic pair breaking disorder, using the experimental values for
$\Delta_0$ and other TB parameters taken from ARPES data. For the case of the
singlet HTSC such as $La_{2-x}Sr_xCuO_4$, DOS and residual RDOS in Born and
Unitary limits can be treated numerically with a dimensionless disorder
parameter $\zeta_{singlet}$ which happens to be one order of magnitude smaller
as to compare with a $\zeta_{triplet}$ in the case of quasi-nodal pairing in
the FS $\gamma$-sheet for the triplet $Sr_2RuO_4$. We demonstrate that the
unitary limit persists in the calculation of both DOS and residual RDOS for the
$\gamma$-sheet of triplet $Sr_2RuO_4$, showing the formalism for the
calculation of the residual RDOS in the TB case for both symmetry groups of the
order parameter (OP) and compare our theoretical results with several
experimental data and theoretical reports found in the scientific literature.
Finally, we show that for the highest values of dimensionless disorder
parameter $\zeta_{singlet}$ and the majority values of $\zeta_{triplet}$ both
compounds are mostly dwelling in the unitary limit.


title: Information geometry of warped product spaces

abstract:
  Information geometry is an important tool to study statistical models. There
are some important examples in statistical models which are regarded as warped
products. In this paper, we study information geometry of warped products. We
consider the case where the warped product and its fiber space are equipped
with dually flat connections and, in the particular case of a cone,
characterize the connections on the base space $\mathbb{R}_{>0}$. The resulting
connections turn out to be the $\alpha$-connections with $\alpha = \pm{1}$.


title: Riemannian Score-Based Generative Modeling

abstract:
  Score-based generative models (SGMs) are a novel class of generative models
demonstrating remarkable empirical performance. One uses a diffusion to add
progressively Gaussian noise to the data, while the generative model is a
"denoising" process obtained by approximating the time-reversal of this
"noising" diffusion. However, current SGMs make the underlying assumption that
the data is supported on a Euclidean manifold with flat geometry. This prevents
the use of these models for applications in robotics, geoscience or protein
modeling which rely on distributions defined on Riemannian manifolds. To
overcome this issue, we introduce Riemannian Score-based Generative Models
(RSGMs) which extend current SGMs to the setting of compact Riemannian
manifolds. We illustrate our approach with earth and climate science data and
show how RSGMs can be accelerated by solving a Schr\"odinger bridge problem on
manifolds.


title:
On Smart Gaze based Annotation of Histopathology Images for Training of
  Deep Convolutional Neural Networks

abstract:
  Unavailability of large training datasets is a bottleneck that needs to be
overcome to realize the true potential of deep learning in histopathology
applications. Although slide digitization via whole slide imaging scanners has
increased the speed of data acquisition, labeling of virtual slides requires a
substantial time investment from pathologists. Eye gaze annotations have the
potential to speed up the slide labeling process. This work explores the
viability and timing comparisons of eye gaze labeling compared to conventional
manual labeling for training object detectors. Challenges associated with gaze
based labeling and methods to refine the coarse data annotations for subsequent
object detection are also discussed. Results demonstrate that gaze tracking
based labeling can save valuable pathologist time and delivers good performance
when employed for training a deep object detector. Using the task of
localization of Keratin Pearls in cases of oral squamous cell carcinoma as a
test case, we compare the performance gap between deep object detectors trained
using hand-labelled and gaze-labelled data. On average, compared to
`Bounding-box' based hand-labeling, gaze-labeling required $57.6\%$ less time
per label and compared to `Freehand' labeling, gaze-labeling required on
average $85\%$ less time per label.


title:
Pushing the Efficiency-Regret Pareto Frontier for Online Learning of
  Portfolios and Quantum States

abstract:
  We revisit the classical online portfolio selection problem. It is widely
assumed that a trade-off between computational complexity and regret is
unavoidable, with Cover's Universal Portfolios algorithm, SOFT-BAYES and
ADA-BARRONS currently constituting its state-of-the-art Pareto frontier. In
this paper, we present the first efficient algorithm, BISONS, that obtains
polylogarithmic regret with memory and per-step running time requirements that
are polynomial in the dimension, displacing ADA-BARRONS from the Pareto
frontier. Additionally, we resolve a COLT 2020 open problem by showing that a
certain Follow-The-Regularized-Leader algorithm with log-barrier regularization
suffers an exponentially larger dependence on the dimension than previously
conjectured. Thus, we rule out this algorithm as a candidate for the Pareto
frontier. We also extend our algorithm and analysis to a more general problem
than online portfolio selection, viz. online learning of quantum states with
log loss. This algorithm, called SCHRODINGER'S BISONS, is the first efficient
algorithm with polylogarithmic regret for this more general problem.


title:
Functional Central Limit Theorems for Local Statistics of Spatial
  Birth-Death Processes in the Thermodynamic Regime

abstract:
  We present normal approximation results at the process level for local
functionals defined on dynamic Poisson processes in $\mathbb{R}^d$. The
dynamics we study here are those of a Markov birth-death process. We prove
functional limit theorems in the so-called thermodynamic regime. Our results
are applicable to several functionals of interest in the stochastic geometry
literature, including subgraph and component counts in the random geometric
graphs.


title:
Numerical convergence of 2D solar convection in implicit large-eddy
  simulations

abstract:
  Large-eddy simulations (LES) and implicit LES (ILES) are wise and affordable
alternatives to the unfeasible direct numerical simulations (DNS) of turbulent
flows at high Reynolds numbers (Re). However, for systems with few
observational constraints, it is a formidable challenge to determine if these
strategies adequately capture the physics of the system. Here we address this
problem by analyzing numerical convergence of ILES of turbulent convection in
2D, with resolutions between $64^2$ and $2048^2$ grid points, along with the
estimation of their effective viscosities, resulting in effective Reynolds
numbers between $1$ and $\sim10^4$. The thermodynamic structure of our model
resembles the solar interior, including a fraction of the radiative zone and
the convection zone. In the convective layer, the ILES solutions converge for
the simulations with $\ge 512^2$ grid points, as evidenced by the integral
properties of the flow and its power spectra. Most importantly, we found that
even a resolution of $128^2$ grid points, Re$\sim10$, is sufficient to capture
the dynamics of the large scales accurately. This is a consequence of the ILES
method allowing that the energy contained in these scales is the same in
simulations with low and high resolution. Special attention is needed in
regions with a small density scale height driving the formation of fine
structures unresolved by the numerical grid. In the stable layer we found the
excitation of internal gravity waves, yet high resolution is needed to capture
their development and interaction.


title: Norm-ideal perturbations of one-parameter semigroups and applications

abstract:
  The notion of equivalence classes of generators of one-parameter semigroups
based on the convergence of the Dyson expansion can be traced back to the
seminal work of Hille and Phillips, who in Chapter XIII of the 1957 edition of
their Functional Analysis monograph, developed the theory in minute detail.
Following their approach of regarding the Dyson expansion as a central object,
in the first part of this paper we examine a general framework for perturbation
of generators relative to the Schatten-von Neumann ideals on Hilbert spaces.
This allows us to develop a graded family of equivalence relations on
generators, which refine the classical notion and provide
stronger-than-expected properties of convergence for the tail of the
perturbation series. We then show how this framework realises in the context of
non-self-adjoint Schrodinger operators.


title:
Asymptotics near extinction for nonlinear fast diffusion on a bounded
  domain

abstract:
  On a smooth bounded Euclidean domain, Sobolev-subcritical fast diffusion with
vanishing boundary trace is known to lead to finite-time extinction, with a
vanishing profile selected by the initial datum. In rescaled variables, we
quantify the rate of convergence to this profile uniformly in relative error,
showing the rate is either exponentially fast (with a rate constant predicted
by the spectral gap), or algebraically slow (which is only possible in the
presence of non-integrable zero modes). In the first case, the nonlinear
dynamics are well-approximated by exponentially decaying eigenmodes up to at
least twice the gap; this refines and confirms a 1980 conjecture of Berryman
and Holland. We also improve on a result of Bonforte and Figalli, by providing
a new and simpler approach which is able to accommodate the presence of zero
modes, such as those that occur when the vanishing profile fails to be isolated
(and possibly belongs to a continuum of such profiles).


title: Hypergraph incidence coloring

abstract:
  An incidence of a hypergraph $\mathcal{H}=(X,S)$ is a pair $(x,s)$ with $x\in
X$, $s\in S$ and $x\in s$. Two incidences $(x,s)$ and $(x',s')$ are adjacent if
(i) $x=x'$, or (ii) $\{x,x'\}\subseteq s$ or $\{x,x'\}\subseteq s'$. A proper
incidence $k$-coloring of a hypergraph $\mathcal{H}$ is a mapping $\varphi$
from the set of incidences of $\mathcal{H}$ to $\{1,2,\ldots,k\}$ so that
$\varphi(x,s)\neq \varphi(x',s')$ for any two adjacent incidences $(x,s)$ and
$(x',s')$ of $\mathcal{H}$. The incidence chromatic number
$\chi_I(\mathcal{H})$ of $\mathcal{H}$ is the minimum integer $k$ such that
$\mathcal{H}$ has a proper incidence $k$-coloring. In this paper we prove
$\chi_I(\mathcal{H})\leq (4/3+o(1))r(\mathcal{H})\Delta(\mathcal{H})$ for every
$t$-quasi-linear hypergraph with $t<<r(\mathcal{H})$ and sufficiently large
$\Delta(\mathcal{H})$, where $r(\mathcal{H})$ is the maximum of the
cardinalities of the edges in $\mathcal{H}$. It is also proved that
$\chi_I(\mathcal{H})\leq \Delta(\mathcal{H})+r(\mathcal{H})-1$ if $\mathcal{H}$
is an $\alpha$-acyclic linear hypergraph, and this bound is sharp.


title: Optimal Algorithms for Decentralized Stochastic Variational Inequalities

abstract:
  Variational inequalities are a formalism that includes games, minimization,
saddle point, and equilibrium problems as special cases. Methods for
variational inequalities are therefore universal approaches for many applied
tasks, including machine learning problems. This work concentrates on the
decentralized setting, which is increasingly important but not well understood.
In particular, we consider decentralized stochastic (sum-type) variational
inequalities over fixed and time-varying networks. We present lower complexity
bounds for both communication and local iterations and construct optimal
algorithms that match these lower bounds. Our algorithms are the best among the
available literature not only in the decentralized stochastic case, but also in
the decentralized deterministic and non-distributed stochastic cases.
Experimental results confirm the effectiveness of the presented algorithms.


title: Missing Mass Estimation from Sticky Channels

abstract:
  Distribution estimation under error-prone or non-ideal sampling modelled as
"sticky" channels have been studied recently motivated by applications such as
DNA computing. Missing mass, the sum of probabilities of missing letters, is an
important quantity that plays a crucial role in distribution estimation,
particularly in the large alphabet regime. In this work, we consider the
problem of estimation of missing mass, which has been well-studied under
independent and identically distributed (i.i.d) sampling, in the case when
sampling is "sticky". Precisely, we consider the scenario where each sample
from an unknown distribution gets repeated a geometrically-distributed number
of times. We characterise the minimax rate of Mean Squared Error (MSE) of
estimating missing mass from such sticky sampling channels. An upper bound on
the minimax rate is obtained by bounding the risk of a modified Good-Turing
estimator. We derive a matching lower bound on the minimax rate by extending
the Le Cam method.


title:
Probing Cosmic Inflation with the LiteBIRD Cosmic Microwave Background
  Polarization Survey

abstract:
  LiteBIRD, the Lite (Light) satellite for the study of B-mode polarization and
Inflation from cosmic background Radiation Detection, is a space mission for
primordial cosmology and fundamental physics. The Japan Aerospace Exploration
Agency (JAXA) selected LiteBIRD in May 2019 as a strategic large-class
(L-class) mission, with an expected launch in the late 2020s using JAXA's H3
rocket. LiteBIRD is planned to orbit the Sun-Earth Lagrangian point L2, where
it will map the cosmic microwave background (CMB) polarization over the entire
sky for three years, with three telescopes in 15 frequency bands between 34 and
448 GHz, to achieve an unprecedented total sensitivity of 2.2$\mu$K-arcmin,
with a typical angular resolution of 0.5$^\circ$ at 100 GHz. The primary
scientific objective of LiteBIRD is to search for the signal from cosmic
inflation, either making a discovery or ruling out well-motivated inflationary
models. The measurements of LiteBIRD will also provide us with insight into the
quantum nature of gravity and other new physics beyond the standard models of
particle physics and cosmology. We provide an overview of the LiteBIRD project,
including scientific objectives, mission and system requirements, operation
concept, spacecraft and payload module design, expected scientific outcomes,
potential design extensions and synergies with other projects.


title:
Optimization on Large Interconnected Graphs and Networks Using Adiabatic
  Quantum Computation

abstract:
  In this paper, we demonstrate that it is possible to create an adiabatic
quantum computing algorithm that solves the shortest path between any two
vertices on an undirected graph with at most 3V qubits, where V is the number
of vertices of the graph. We do so without relying on any classical algorithms,
aside from creating a (V x V) adjacency matrix. The objective of this paper is
to demonstrate the fact that it is possible to model large graphs on an
adiabatic quantum computer using the maximum number of qubits available and
random graph generators such as the Barabasi-Albert and the Erdos-Renyi methods
which can scale based on a power law.


title: NSI effects on the generation of microscopic black hole events

abstract:
  If the universe has more than 4-dimensions, the TeV scale gravity theories
predict formation of microscopic black holes due to interaction of ultra high
energy neutrinos coming from some extragalactic origin with the nucleons
present in the Earth's atmosphere. The decay of these black holes can generate
high multiplicity events which can be detected through neutrino telescopes.
Ultra high energy neutrinos can also produce events without the formation of
black holes which can be distinguished from the black hole events depending on
their topological structure. In this work we study the effects of non-standard
interaction on the production of these shower events. We find that new physics
has inconsequential impact on the number of events produced through the
generation of black holes. For events produced without the formation of black
holes, new physics can only provide a marginal deviation. Therefore a large
enhancement in the number of shower events over the standard model prediction
can provide unambiguous signatures of TeV scale gravity in the form of
microscopic black hole production.


title:
Human rights, democracy, and the rule of law assurance framework for AI
  systems: A proposal

abstract:
  Following on from the publication of its Feasibility Study in December 2020,
the Council of Europe's Ad Hoc Committee on Artificial Intelligence (CAHAI) and
its subgroups initiated efforts to formulate and draft its Possible Elements of
a Legal Framework on Artificial Intelligence, based on the Council of Europe's
standards on human rights, democracy, and the rule of law. This document was
ultimately adopted by the CAHAI plenary in December 2021. To support this
effort, The Alan Turing Institute undertook a programme of research that
explored the governance processes and practical tools needed to operationalise
the integration of human right due diligence with the assurance of trustworthy
AI innovation practices.
  The resulting framework was completed and submitted to the Council of Europe
in September 2021. It presents an end-to-end approach to the assurance of AI
project lifecycles that integrates context-based risk analysis and appropriate
stakeholder engagement with comprehensive impact assessment, and transparent
risk management, impact mitigation, and innovation assurance practices. Taken
together, these interlocking processes constitute a Human Rights, Democracy and
the Rule of Law Assurance Framework (HUDERAF). The HUDERAF combines the
procedural requirements for principles-based human rights due diligence with
the governance mechanisms needed to set up technical and socio-technical
guardrails for responsible and trustworthy AI innovation practices. Its purpose
is to provide an accessible and user-friendly set of mechanisms for
facilitating compliance with a binding legal framework on artificial
intelligence, based on the Council of Europe's standards on human rights,
democracy, and the rule of law, and to ensure that AI innovation projects are
carried out with appropriate levels of public accountability, transparency, and
democratic governance.


title: Learning Features with Parameter-Free Layers

abstract:
  Trainable layers such as convolutional building blocks are the standard
network design choices by learning parameters to capture the global context
through successive spatial operations. When designing an efficient network,
trainable layers such as the depthwise convolution is the source of efficiency
in the number of parameters and FLOPs, but there was little improvement to the
model speed in practice. This paper argues that simple built-in parameter-free
operations can be a favorable alternative to the efficient trainable layers
replacing spatial operations in a network architecture. We aim to break the
stereotype of organizing the spatial operations of building blocks into
trainable layers. Extensive experimental analyses based on layer-level studies
with fully-trained models and neural architecture searches are provided to
investigate whether parameter-free operations such as the max-pool are
functional. The studies eventually give us a simple yet effective idea for
redesigning network architectures, where the parameter-free operations are
heavily used as the main building block without sacrificing the model accuracy
as much. Experimental results on the ImageNet dataset demonstrate that the
network architectures with parameter-free operations could enjoy the advantages
of further efficiency in terms of model speed, the number of the parameters,
and FLOPs. Code and ImageNet pretrained models are available at
https://github.com/naver-ai/PfLayer.


title: An effective model for boundary vortices in thin-film micromagnetics

abstract:
  Ferromagnetic materials are governed by a variational principle which is
nonlocal, nonconvex and multiscale. The main object is given by a unit-length
three-dimensional vector field, the magnetization, that corresponds to the
stable states of the micromagnetic energy. Our aim is to analyze a thin film
regime that captures the asymptotic behavior of boundary vortices generated by
the magnetization and their interaction energy. This study is based on the
notion of "global Jacobian" detecting the topological defects that a priori
could be located in the interior and at the boundary of the film. A major
difficulty consists in estimating the nonlocal part of the micromagnetic energy
in order to isolate the exact terms corresponding to the topological defects.
We prove the concentration of the energy around boundary vortices via a
$\Gamma$-convergence expansion at the second order. The second order term is
the renormalized energy that represents the interaction between the boundary
vortices and governs their optimal position. We compute the expression of the
renormalized energy for which we prove the existence of minimizers having two
boundary vortices of multiplicity $1$. Compactness results are also shown for
the magnetization and the corresponding global Jacobian.


title:
Multi-domain Unsupervised Image-to-Image Translation with Appearance
  Adaptive Convolution

abstract:
  Over the past few years, image-to-image (I2I) translation methods have been
proposed to translate a given image into diverse outputs. Despite the
impressive results, they mainly focus on the I2I translation between two
domains, so the multi-domain I2I translation still remains a challenge. To
address this problem, we propose a novel multi-domain unsupervised
image-to-image translation (MDUIT) framework that leverages the decomposed
content feature and appearance adaptive convolution to translate an image into
a target appearance while preserving the given geometric content. We also
exploit a contrast learning objective, which improves the disentanglement
ability and effectively utilizes multi-domain image data in the training
process by pairing the semantically similar images. This allows our method to
learn the diverse mappings between multiple visual domains with only a single
framework. We show that the proposed method produces visually diverse and
plausible results in multiple domains compared to the state-of-the-art methods.


title: A conjecture of S\'ark\"ozy on quadratic residues, II

abstract:
  Denote by $\mathcal{R}_p$ the set of all quadratic residues in $\mathbf{F}_p$
for each prime $p$. A conjecture of A. S\'ark\"ozy asserts, for all
sufficiently large $p$, that no subsets
$\mathcal{A},\mathcal{B}\subseteq\mathbf{F}_p$ with
$|\mathcal{A}|,|\mathcal{B}|\geqslant2$ satisfy
$\mathcal{A}+\mathcal{B}=\mathcal{R}_p$. In this paper, we show that if such
subsets $\mathcal{A},\mathcal{B}$ do exist, then there are at least $(\log
2)^{-1}\sqrt p-1.6$ elements in $\mathcal{A}+\mathcal{B}$ that have unique
representations and one should have \begin{align*} \frac{1}{4}\sqrt{p}<
|\mathcal{A}|,|\mathcal{B}|< 2\sqrt{p}-1. \end{align*} This refines previous
bounds obtained by I.E. Shparlinski, I.D. Shkredov, and Y.-G. Chen and X.-H.
Yan. Moreover, we also establish bounds for $|\mathcal{A}|,|\mathcal{B}|$ and
the additive energy $E(\mathcal{A},\mathcal{B})$ if few elements in
$\mathcal{A}+\mathcal{B}$ have unique representations.


title: Topological Corner States in Graphene by Bulk and Edge Engineering

abstract:
  Two-dimensional higher-order topology is usually studied in (nearly)
particle-hole symmetric models, so that an edge gap can be opened within the
bulk one. But more often deviates the edge anticrossing even into the bulk,
where corner states are difficult to pinpoint. We address this problem in a
graphene-based $\mathbb{Z}_2$ topological insulator with spin-orbit coupling
and in-plane magnetization both originating from substrates through a
Slater-Koster multi-orbital model. The gapless helical edge modes cross inside
the bulk, where is also located the magnetization-induced edge gap. After
demonstrating its second-order nontriviality in bulk topology by a series of
evidence, we show that a difference in bulk-edge onsite energy can
adiabatically tune the position of the crossing/anticrossing of the edge modes
to be inside the bulk gap. This can help unambiguously identify two pairs of
topological corner states with nonvanishing energy degeneracy for a rhombic
flake. We further find that the obtuse-angle pair is more stable than the
acute-angle one. These results not only suggest an accessible way to "find"
topological corner states, but also provide a higher-order topological version
of "bulk-boundary correspondence".


title: The Exponential-Time Complexity of the complex weighted #CSP

abstract:
  In this paper, I consider a fine-grained dichotomy of Boolean counting
constraint satisfaction problem (#CSP), under the exponential time hypothesis
of counting version (#ETH). Suppose $\mathscr{F}$ is a finite set of algebraic
complex-valued functions defined on Boolean domain. When $\mathscr{F}$ is a
subset of either two special function sets, I prove that #CSP($\mathscr{F}$) is
polynomial-time solvable, otherwise it can not be computed in sub-exponential
time unless #ETH fails. I also improve the result by proving the same dichotomy
holds for #CSP with bounded degree (every variable appears at most constant
constraints), even for #R$_3$-CSP.
  An important preparation before proving the result is to argue that pinning
(two special unary functions $[1,0]$ and $[0,1]$ are used to reduce arity) can
also keep the sub-exponential lower bound of a Boolean #CSP problem. I discuss
this issue by utilizing some common methods in proving #P-hardness of counting
problems. The proof illustrates the internal correlation among these commonly
used methods.


title: Energy awareness in low precision neural networks

abstract:
  Power consumption is a major obstacle in the deployment of deep neural
networks (DNNs) on end devices. Existing approaches for reducing power
consumption rely on quite general principles, including avoidance of
multiplication operations and aggressive quantization of weights and
activations. However, these methods do not take into account the precise power
consumed by each module in the network, and are therefore not optimal. In this
paper we develop accurate power consumption models for all arithmetic
operations in the DNN, under various working conditions. We reveal several
important factors that have been overlooked to date. Based on our analysis, we
present PANN (power-aware neural network), a simple approach for approximating
any full-precision network by a low-power fixed-precision variant. Our method
can be applied to a pre-trained network, and can also be used during training
to achieve improved performance. In contrast to previous methods, PANN incurs
only a minor degradation in accuracy w.r.t. the full-precision version of the
network, even when working at the power-budget of a 2-bit quantized variant. In
addition, our scheme enables to seamlessly traverse the power-accuracy
trade-off at deployment time, which is a major advantage over existing
quantization methods that are constrained to specific bit widths.


title:
Bone tumor suppression in rabbits by hyperthermia below the clinical
  safety limit using aligned magnetic bone cement

abstract:
  Demonstrating highly efficient alternating current (AC) magnetic field
heating of nanoparticles in physiological environments under clinically safe
field parameters has remained a great challenge, hindering clinical
applications of magnetic hyperthermia. In this work, we report exceptionally
high loss power of magnetic bone cement under clinical safety limit of AC field
parameters, incorporating DC field-aligned soft magnetic Zn0.3Fe2.7O4
nanoparticles with low concentration. Under an AC field of 4 kA/m at 430 kHz,
the aligned bone cement with 0.2 wt% nanoparticles achieved a temperature
increase of 30 C in 180 s. This amounts to a specific loss power value of 327
W/gmetal and an intrinsic loss power of 47 nHm^2/kg, which is enhanced by
50-fold compared to randomly oriented samples. The high-performance magnetic
bone cement allows for the demonstration of effective hyperthermia suppression
of tumor growth in the bone marrow cavity of New Zealand White Rabbits
subjecting to rapid cooling due to blood circulation, and significant
enhancement of survival rate.


title:
Magnetic transition in the $J_\textrm{eff} = 1/2$ Kagom\'{e} system
  Sm$_3$Sb$_3$Zn$_2$O$_{14}$

abstract:
  We present a study of Sm$_3$Sb$_3$Zn$_2$O$_{14}$ (SSZO) through magnetization
and specific heat capacity $C_p(T)$ measurements. SSZO contains well separated
planes of Sm$^{3+}$ magnetic ions on a Kagom\'{e} lattice. Though our magnetic
susceptibility (where the data are limited down to 2\,K) does not show any
anomaly, the $C_p(T)$ data which have been taken down to 0.35 K reveal a broad
maximum at $T\sim1.5$\,K followed by a sharp peak at $T\sim0.5$\,K indicative
of short-range correlations and long-range order, respectively.


title:
Proving Information Inequalities and Identities with Symbolic
  Computation

abstract:
  Proving linear inequalities and identities of Shannon's information measures,
possibly with linear constraints on the information measures, is an important
problem in information theory. For this purpose, ITIP and other variant
algorithms have been developed and implemented, which are all based on solving
a linear program (LP). In particular, an identity $f = 0$ is verified by
solving two LPs, one for $f \ge 0$ and one for $f \le 0$. In this paper, we
develop a set of algorithms that can be implemented by symbolic computation.
Based on these algorithms, procedures for verifying linear information
inequalities and identities are devised. Compared with LP-based algorithms, our
procedures can produce analytical proofs that are both human-verifiable and
free of numerical errors. Our procedures are also more efficient
computationally. For constrained inequalities, by taking advantage of the
algebraic structure of the problem, the size of the LP that needs to be solved
can be significantly reduced. For identities, instead of solving two LPs, the
identity can be verified directly with very little computation.


title: Stable cooperation emerges in stochastic multiplicative growth

abstract:
  Understanding the evolutionary stability of cooperation is a central problem
in biology, sociology, and economics. There exist only a few known mechanisms
that guarantee the existence of cooperation and its robustness to cheating.
Here, we introduce a new mechanism for the emergence of cooperation in the
presence of fluctuations. We consider agents whose wealth change stochastically
in a multiplicative fashion. Each agent can share part of her wealth as public
good, which is equally distributed among all the agents. We show that, when
agents operate with long time-horizons, cooperation produce an advantage at the
individual level, as it effectively screens agents from the deleterious effect
of environmental fluctuations.

categories: q-bio.PE cond-mat.stat-mech econ.TH physics.bio-ph q-fin.GN


title: Vertex-coloring graphs with 4-edge-weightings

abstract:
  An edge-weighting of a graph is called vertex-coloring if the weighted
degrees yield a proper vertex coloring of the graph. It is conjectured that for
every graph without isolated edge, a vertex-coloring edge-weighting with the
set {1,2,3} exists. In this note, we show that the statement is true for the
weight set {1,2,3,4}.


title:
Gravity, Quantum Fields and Quantum Information: Problems with classical
  channel and stochastic theories

abstract:
  In recent years an increasing number of papers attempt to mimic or supplant
quantum field theory in discussions of issues related to gravity by the tools
and through the perspective of quantum information theory, often in the context
of alternative quantum theories. In this essay, we point out three common
problems in such treatments. First, we show that the notion of interactions
mediated by an information channel is not, in general, equivalent to the
treatment of interactions by quantum field theory. When used to describe
gravity, this notion may lead to inconsistencies with general relativity.
Second, we point out that in general one cannot replace a quantum field by that
of classical stochastic sources, or mock up the effects of quantum fluctuations
by classical noises, because in so doing important quantum features such as
coherence and entanglement will be left out. Third, we explain how under
specific conditions semi-classical and stochastic theories indeed can be
formulated from their quantum origins and play a role at certain regimes of
interest.


title:
Learning Synthetic Environments and Reward Networks for Reinforcement
  Learning

abstract:
  We introduce Synthetic Environments (SEs) and Reward Networks (RNs),
represented by neural networks, as proxy environment models for training
Reinforcement Learning (RL) agents. We show that an agent, after being trained
exclusively on the SE, is able to solve the corresponding real environment.
While an SE acts as a full proxy to a real environment by learning about its
state dynamics and rewards, an RN is a partial proxy that learns to augment or
replace rewards. We use bi-level optimization to evolve SEs and RNs: the inner
loop trains the RL agent, and the outer loop trains the parameters of the SE /
RN via an evolution strategy. We evaluate our proposed new concept on a broad
range of RL algorithms and classic control environments. In a one-to-one
comparison, learning an SE proxy requires more interactions with the real
environment than training agents only on the real environment. However, once
such an SE has been learned, we do not need any interactions with the real
environment to train new agents. Moreover, the learned SE proxies allow us to
train agents with fewer interactions while maintaining the original task
performance. Our empirical results suggest that SEs achieve this result by
learning informed representations that bias the agents towards relevant states.
Moreover, we find that these proxies are robust against hyperparameter
variation and can also transfer to unseen agents.


title:
SFMGNet: A Physics-based Neural Network To Predict Pedestrian
  Trajectories

abstract:
  Autonomous robots and vehicles are expected to soon become an integral part
of our environment. Unsatisfactory issues regarding interaction with existing
road users, performance in mixed-traffic areas and lack of interpretable
behavior remain key obstacles. To address these, we present a physics-based
neural network, based on a hybrid approach combining a social force model
extended by group force (SFMG) with Multi-Layer Perceptron (MLP) to predict
pedestrian trajectories considering its interaction with static obstacles,
other pedestrians and pedestrian groups. We quantitatively and qualitatively
evaluate the model with respect to realistic prediction, prediction performance
and prediction "interpretability". Initial results suggest, the model even when
solely trained on a synthetic dataset, can predict realistic and interpretable
trajectories with better than state-of-the-art accuracy.


title:
A semi-empirical analysis of the paramagnetic susceptibility of solid
  state magnetic clusters

abstract:
  Recent developments in the synthesis of new magnetic materials lead to the
discovery of new quantum paramagnets. Many of these materials, such as the
perovskites Ba$_{4}$LnMn$_{4}$O$_{12}$ (Ln = Sc or Nb),
Ba$_{3}$Mn$_{2}$O$_{8}$, and Sr$_{3}$Cr$_{2}$O$_{8}$ present isolated magnetic
clusters with strong intracluster interactions but weak intercluster
interactions, which delays the onset of order to lower temperatures ($T$). This
offset between the local energy scale and the magnetic ordering temperature is
the hallmark of magnetic frustration. At sufficient high-$T$, the paramagnetic
susceptibility ($\chi$) of frustrated cluster magnets can be fit to a
Curie-Weiss law, but the derived microscopic parameters cannot in general be
reconciled with those obtained from other methods. In this work, we present an
analytical microscopic theory to obtain $\chi$ of dimer and trimer cluster
magnets, the two most commonly found in literature, making use of suitable
Heisenberg-type Hamiltonians. We also add intercluster interactions in a
mean-field level, thus obtaining an expression to the critical temperature of
the system and defining a new effective frustration parameter $f_{\text{eff}}$.
Our method is exemplified by treating the $\chi$ data of some selected
materials.


title:
On The Algebras $U_q^{\pm}(A_N)$: From A Constructive-Computational
  Viewpoint

abstract:
  Let $U_q^+(A_N)$ (resp. $U_q^-(A_N)$) be the $(+)$-part (resp. $(-)$-part) of
the Drinfeld-Jimbo quantum group of type $A_N$ over a field $K$. With respect
to Jimbo relations and the PBW $K$-basis ${\cal B}$ of $U_q^+(A_N)$ (resp.
$U_q^-(A_N)$) established by Yamane, it is shown, by constructing an
appropriate monomial ordering $\prec$ on ${\cal B}$, that $U_q^+(A_N)$ (resp.
$U_q^-(A_N)$) is a solvable polynomial algebra. Consequently, further
structural properties of $U_q^+(A_N)$ (resp. $U_q^-(A_N)$) and their modules
may be established and realized in a constructive-computational way.


title:
Active Learning on a Budget: Opposite Strategies Suit High and Low
  Budgets

abstract:
  Investigating active learning, we focus on the relation between the number of
labeled examples (budget size), and suitable corresponding querying strategies.
Our theoretical analysis shows a behavior reminiscent of phase transition:
typical points should best be queried in the low budget regime, while atypical
(or uncertain) points are best queried when the budget is large. Combined
evidence from our theoretical and empirical studies shows that a similar
phenomenon occurs in simple classification models. Accordingly, we propose
TypiClust -- a deep active learning strategy suited for low budgets. In a
comparative empirical investigation using a variety of architectures and image
datasets, we report that in the low budget regime, TypiClust outperforms all
other active learning strategies. Using TypiClust in a semi-supervised
framework, the performance of competitive semi-supervised methods gets a
significant boost, surpassing the state of the art.


title:
Rigid and Aeroelastic Analysis of Wind Induced Flow Behavior Around
  Unscaled Tall Buildings using Numerical Techniques

abstract:
  The study focuses on the wind loads acting on the standard Commonwealth
Advisory Aeronautical Council (CAARC) building model. Numerical modeling has
been used instead of employing wind tunnel experiments due to the requirement
of high physical space. This is mainly due to the superiority of CFD codes
included in turbulence models such as RANS and more precise LES. However, the
shortcoming arising through basing the result on numerical investigations is
compensated by direct comparison to experimental data available in literature.
The study extends beyond the typical rigid building structure giving account to
the minor deformations resulting from the impact of the wind force on an
aeroelastic structure through coupled two-way fluid structure interaction,
while designing the building to have its natural fundamental frequency of 0.2
Hz. An improved Smagorinsky-Lily model was used for all LES models and the
results were compared with available wind tunnel experimental data. It was
found that coupled LES analysis provided better correlation to wind tunnel data
compared to rigid fluid domains with respect to pressure distribution and wake
formation despite the additional computation time taken. However, all these
readings were dependent on the boundary conditions which needs to be estimated
concisely fur future use.


title: GLPanoDepth: Global-to-Local Panoramic Depth Estimation

abstract:
  In this paper, we propose a learning-based method for predicting dense depth
values of a scene from a monocular omnidirectional image. An omnidirectional
image has a full field-of-view, providing much more complete descriptions of
the scene than perspective images. However, fully-convolutional networks that
most current solutions rely on fail to capture rich global contexts from the
panorama. To address this issue and also the distortion of equirectangular
projection in the panorama, we propose Cubemap Vision Transformers (CViT), a
new transformer-based architecture that can model long-range dependencies and
extract distortion-free global features from the panorama. We show that cubemap
vision transformers have a global receptive field at every stage and can
provide globally coherent predictions for spherical signals. To preserve
important local features, we further design a convolution-based branch in our
pipeline (dubbed GLPanoDepth) and fuse global features from cubemap vision
transformers at multiple scales. This global-to-local strategy allows us to
fully exploit useful global and local features in the panorama, achieving
state-of-the-art performance in panoramic depth estimation.


title: SIGMA: A Structural Inconsistency Reducing Graph Matching Algorithm

abstract:
  Graph matching finds the correspondence of nodes across two correlated graphs
and lies at the core of many applications. When graph side information is not
available, the node correspondence is estimated on the sole basis of network
topologies. In this paper, we propose a novel criterion to measure the graph
matching accuracy, structural inconsistency (SI), which is defined based on the
network topological structure. Specifically, SI incorporates the heat diffusion
wavelet to accommodate the multi-hop structure of the graphs. Based on SI, we
propose a Structural Inconsistency reducing Graph Matching Algorithm (SIGMA),
which improves the alignment scores of node pairs that have low SI values in
each iteration. Under suitable assumptions, SIGMA can reduce SI values of true
counterparts. Furthermore, we demonstrate that SIGMA can be derived by using a
mirror descent method to solve the Gromov-Wasserstein distance with a novel
K-hop-structure-based matching costs. Extensive experiments show that our
method outperforms state-of-the-art methods.


title: Direct observation of vortices in an electron fluid

abstract:
  Vortices are the hallmarks of hydrodynamic flow. Recent studies indicate that
strongly-interacting electrons in ultrapure conductors can display signatures
of hydrodynamic behavior including negative nonlocal resistance, Poiseuille
flow in narrow channels, and a violation of the Wiedemann-Franz law. Here we
provide the first visualization of whirlpools in an electron fluid. By
utilizing a nanoscale scanning superconducting quantum interference device on a
tip (SQUID-on-tip) we image the current distribution in a circular chamber
connected through a small aperture to an adjacent narrow current carrying strip
in high-purity type-II Weyl semimetal WTe2. In this geometry, the Gurzhi
momentum diffusion length and the size of the aperture determine the vortex
stability phase diagram. We find that the vortices are present only for small
apertures, whereas the flow is laminar (non-vortical) for larger apertures,
consistent with the theoretical analysis of the hydrodynamic regime and in
contrast to the expectations of ballistic transport in WTe2 at low
temperatures. Moreover, near the vortical-to-laminar transition, we observe a
single vortex in the chamber splitting into two vortices, a behavior that can
occur only in the hydrodynamic regime and cannot be sustained by ballistic
transport. These findings suggest a novel mechanism of hydrodynamic flow:
instead of the commonly considered electron-electron scattering at the bulk,
which becomes extremely weak at low temperatures, the spatial diffusion of
charge carriers' momenta is enabled by small-angle scattering at the planar
surfaces of thin pure crystals. This surface-induced para-hydrodynamics opens
new avenues for exploring and utilizing electron fluidics in high-mobility
electron systems.


title: Combining heuristics and Exact Algorithms: A Review

abstract:
  Several different ways exist for approaching hard optimization problems.
Mathematical programming techniques, including (integer) linear
programming-based methods and metaheuristic approaches, are two highly
successful streams for combinatorial problems. These two have been established
by different communities more or less in isolation from each other. Only over
several years ago, a larger number of researchers recognized the advantages and
huge potentials of building hybrids of mathematical programming methods and
metaheuristics.


title:
Learning to be a Statistician: Learned Estimator for Number of Distinct
  Values

abstract:
  Estimating the number of distinct values (NDV) in a column is useful for many
tasks in database systems, such as columnstore compression and data profiling.
In this work, we focus on how to derive accurate NDV estimations from random
(online/offline) samples. Such efficient estimation is critical for tasks where
it is prohibitive to scan the data even once. Existing sample-based estimators
typically rely on heuristics or assumptions and do not have robust performance
across different datasets as the assumptions on data can easily break. On the
other hand, deriving an estimator from a principled formulation such as maximum
likelihood estimation is very challenging due to the complex structure of the
formulation. We propose to formulate the NDV estimation task in a supervised
learning framework, and aim to learn a model as the estimator. To this end, we
need to answer several questions: i) how to make the learned model workload
agnostic; ii) how to obtain training data; iii) how to perform model training.
We derive conditions of the learning framework under which the learned model is
workload agnostic, in the sense that the model/estimator can be trained with
synthetically generated training data, and then deployed into any data
warehouse simply as, e.g., user-defined functions (UDFs), to offer efficient
(within microseconds on CPU) and accurate NDV estimations for unseen tables and
workloads. We compare the learned estimator with the state-of-the-art
sample-based estimators on nine real-world datasets to demonstrate its superior
estimation accuracy. We publish our code for training data generation, model
training, and the learned estimator online for reproducibility.


title:
Magnetic monopole relaxation effects probed by modulation calorimetry in
  small spin-ice samples

abstract:
  We use modulation calorimetry to study the heat capacity of small samples (30
nano gram-10 micro gram) of the classical spin-ice compounds Dy2Ti2O7 and
Ho2Ti2O7 at low temperature (0.5-3 K). Using modulation frequencies of 0.1-200
Hz we find a strong frequency dependence in the measured heat capacity and are
able to study thermal relaxation effects on the corresponding timescales.
Performing dynamic Monte Carlo simulations we verify that the specific heat
frequency response has its origin in the slow magnetic monopole dynamics
indigenous to spin ice. We find a timescale of 20ms per Monte Carlo step at 4K
in contrast to 2.5ms mentioned in previous studies by other 1 techniques. Our
study establishes modulation calorimetry as a versatile experimental probe of
dynamic processes in frustrated magnetic materials.


title: Low-confidence Samples Matter for Domain Adaptation

abstract:
  Domain adaptation (DA) aims to transfer knowledge from a label-rich source
domain to a related but label-scarce target domain. The conventional DA
strategy is to align the feature distributions of the two domains. Recently,
increasing researches have focused on self-training or other semi-supervised
algorithms to explore the data structure of the target domain. However, the
bulk of them depend largely on confident samples in order to build reliable
pseudo labels, prototypes or cluster centers. Representing the target data
structure in such a way would overlook the huge low-confidence samples,
resulting in sub-optimal transferability that is biased towards the samples
similar to the source domain. To overcome this issue, we propose a novel
contrastive learning method by processing low-confidence samples, which
encourages the model to make use of the target data structure through the
instance discrimination process. To be specific, we create positive and
negative pairs only using low-confidence samples, and then re-represent the
original features with the classifier weights rather than directly utilizing
them, which can better encode the task-specific semantic information.
Furthermore, we combine cross-domain mixup to augment the proposed contrastive
loss. Consequently, the domain gap can be well bridged through contrastive
learning of intermediate representations across domains. We evaluate the
proposed method in both unsupervised and semi-supervised DA settings, and
extensive experimental results on benchmarks reveal that our method is
effective and achieves state-of-the-art performance. The code can be found in
https://github.com/zhyx12/MixLRCo.


title: Continuous Evolution Algebras

abstract:
  We formulate the notion of continuous evolution algebra in terms of
differentiable matrix-valued functions, to then study those such algebras
arising as solutions of ODE problems. Given their dependence on natural bases,
matrix Lie groups provide a suitable framework where considering time-variant
evolution algebras. We conclude by broadening our approach by considering
continuous evolution algebras stemming as flow lines on matrix Lie groups.


title:
The effect of ultra-violet photon pumping of H$_2$ in dust-deficient
  protoplanetary disks

abstract:
  We perform radiation hydrodynamics simulations to study the structure and
evolution of a protoplanetary disk. Ultraviolet and X-ray radiation from the
host star heats the disk surface, where H$_2$ pumping also operates
efficiently. We run a set of simulations with varying the amount of dust
grains, or the dust-to-gas mass ratio, which determines the relative importance
between photoelectric heating and H$_2$ pumping. We show that H$_2$ pumping and
X-ray heating contributes stronger to the mass-loss of the disk if the
dust-to-gas mass ratio is $\mathcal{D}\leq10^{-3}$. In such dust-deficient
disks, H$_2$ pumping enhances photoevaporation from the inner disk region and
shapes the disk mass-loss profile. The long-term disk dispersal process may be
affected by the ultra-violet H$_2$ pumping effect.


title:
Formulating Connectedness in Security-Constrained Optimal Transmission
  Switching Problems

abstract:
  This paper focuses on the issue of network connectedness (NC) in
security-constrained optimal transmission switching problems, which is
complicated by branch contingencies and corrective line switching. Two criteria
are firstly proposed with the principle of preserving NC as much as possible
within reasonable limits. By extending the electrical flow based NC
constraints, a proposition is derived to associate different cases of NC with
the optimum of a linear program, yielding the mathematical formulation of the
NC criteria. By Karush-Kuhn-Tucker conditions, this formulation is further
transformed into a tractable version which can be incorporated with existing
SCOTS models without affecting the applicability of original solution
approaches. Finally, case studies on various networks and SCOTS models
demonstrate the efficacy of the proposed approach.


title:
Multi-component separation, inpainting and denoising with recovery
  guarantees

abstract:
  In image processing, problems of separation and reconstruction of missing
pixels from incomplete digital images have been far more advanced in past
decades. Many empirical results have produced very good results, however,
providing a theoretical analysis for the success of algorithms is not an easy
task, especially, for inpainting and separating multi-component signals. In
this paper, we propose two main algorithms based on $l_1$ constrained and
unconstrained minimization for separating $N$ distinct geometric components and
simultaneously filling-in the missing part of the observed image. We then
present a theoretical guarantee for these algorithms using compressed sensing
technique, which is based on a principle that each component can be sparsely
represented by a suitably chosen dictionary. Those sparsifying systems are
extended to the case of general frames instead of Parseval frames which have
been typically used in the past. We finally prove that the method does indeed
succeed in separating point singularities from curvilinear singularities and
texture as well as inpainting the missing band contained in curvilinear
singularities and texture.


title: Heart-Based Biometric Protocols: A look back over almost two decades

abstract:
  This article surveys the literature over the period 2003-2021 on heart-based
biometric protocols. In particular, we focus on how the heart signal is
transformed from a continuous wave to discrete values to be used afterwards in
authentication protocols. We explain and classify the surveyed proposals
according to three main parameters: i) the dataset they use for testing their
results; ii) the delineation algorithms they use to extract the fiducial
points, and; iii) the cryptographic tests they run (if any) to validate how
random the extracted token is.


title: Minkowski problem arising from sub-linear elliptic equations

abstract:
  For any bounded convex domain \Omega in R^N, we assign a positive finite
Borel measure associated with the solution to a su-blinear elliptic equation in
\Omega. We prove that this measure is weakly continuous in the sense of measure
with respect Hausdorff metric, and the Minkowski problem associated with this
measure is uniquely solvable.


title:
An evaluation of the data space dimension in phase retrieval: results in
  Fresnel zone

abstract:
  In this paper, we address the problem of computing the dimension of data
space in phase retrieval problem. Starting from the quadratic formulation of
the phase retrieval,the analysis is performed in two steps. First, we exploit
the lifting technique to obtain a linear representation of the data. Later, we
evaluate the dimension of data space by computing analytically the number of
relevant singular values of the linear operator that represents the data. The
study is done with reference to a 2D scalar geometry consisting of an electric
current strip whose square amplitude of the electric radiated field is observed
on a twodimensional extended domain in Fresnel zone.


title:
Theoretical Study on Anisotropic Magnetoresistance Effects of Arbitrary
  Directions of Current and Magnetization for Ferromagnets: Application to
  Transverse Anisotropic Magnetoresistance Effect

abstract:
  We develop a theory of the anisotropic magnetoresistance (AMR) effects of
arbitrary directions of current and magnetization for ferromagnets. Here, we
use the electron scattering theory with the $s$--$s$ and $s$--$d$ scattering
processes, where $s$ is the conduction electron state and $d$ is the localized
d states. The resistivity due to electron scattering is expressed by the
probability density of the d states of the current direction. The d states are
numerically obtained by applying the exact diagonalization method to the
Hamiltonian of the d states with the exchange field, crystal field, and
spin--orbit interaction. Using the theory, we investigate the transverse AMR
(TAMR) effect for strong ferromagnets with a crystal field of cubic or
tetragonal symmetry. The cubic systems exhibit the fourfold symmetric TAMR
effect, whereas the tetragonal systems show the twofold and fourfold symmetric
TAMR effect. On the basis of the above results, we also comment on the
experimental results of the TAMR effect for Fe$_4$N.


title: Construction of polynomial preserving cochain extensions by blending

abstract:
  A classical technique to construct polynomial preserving extensions of scalar
functions defined on the boundary of an $n$ simplex to the interior is to use
so-called rational blending functions. The purpose of this paper is to
generalize the construction by blending to the de Rham complex. More precisely,
we define polynomial preserving extensions which map traces of $k$ forms
defined on the boundary of the simplex to $k$ forms defined in the interior.
Furthermore, the extensions are cochain maps, i.e., they commute with the
exterior derivative.


title: Lossy Gradient Compression: How Much Accuracy Can One Bit Buy?

abstract:
  In federated learning (FL), a global model is trained at a Parameter Server
(PS) by aggregating model updates obtained from multiple remote learners.
Critically, the communication between the remote users and the PS is limited by
the available power for transmission, while the transmission from the PS to the
remote users can be considered unbounded. This gives rise to the distributed
learning scenario in which the updates from the remote learners have to be
compressed so as to meet communication rate constraints in the uplink
transmission toward the PS. For this problem, one would like to compress the
model updates so as to minimize the resulting loss in accuracy. In this paper,
we take a rate-distortion approach to answer this question for the distributed
training of a deep neural network (DNN). In particular, we define a measure of
the compression performance, the \emph{per-bit accuracy}, which addresses the
ultimate model accuracy that a bit of communication brings to the centralized
model. In order to maximize the per-bit accuracy, we consider modeling the
gradient updates at remote learners as a generalized normal distribution. Under
this assumption on the model update distribution, we propose a class of
distortion measures for the design of quantizer for the compression of the
model updates. We argue that this family of distortion measures, which we refer
to as "$M$-magnitude weighted $L_2$" norm, capture the practitioner intuition
in the choice of gradient compressor. Numerical simulations are provided to
validate the proposed approach.


title: A Coding Framework and Benchmark towards Compressed Video Understanding

abstract:
  Most video understanding methods are learned on high-quality videos. However,
in real-world scenarios, the videos are first compressed before the
transportation and then decompressed for understanding. The decompressed videos
may have lost the critical information to the downstream tasks. To address this
issue, we propose the first coding framework for compressed video
understanding, where another learnable analytic bitstream is simultaneously
transported with the original video bitstream. With the dedicatedly designed
self-supervised optimization target and dynamic network architectures, this new
stream largely boosts the downstream tasks yet with a small bit cost. By only
one-time training, our framework can be deployed for multiple downstream tasks.
Our framework also enjoys the best of both two worlds, (1) high efficiency of
industrial video codec and (2) flexible coding capability of neural networks
(NNs). Finally, we build a rigorous benchmark for compressed video
understanding on three popular tasks over seven large-scale datasets and four
different compression levels. The proposed Understanding oriented Video Coding
framework UVC consistently demonstrates significantly stronger performances
than the baseline industrial codec.


title:
Wave-Encoded Model-based Deep Learning for Highly Accelerated Imaging
  with Joint Reconstruction

abstract:
  Purpose: To propose a wave-encoded model-based deep learning (wave-MoDL)
strategy for highly accelerated 3D imaging and joint multi-contrast image
reconstruction, and further extend this to enable rapid quantitative imaging
using an interleaved look-locker acquisition sequence with T2 preparation pulse
(3D-QALAS).
  Method: Recently introduced MoDL technique successfully incorporates
convolutional neural network (CNN)-based regularizers into physics-based
parallel imaging reconstruction using a small number of network parameters.
Wave-CAIPI is an emerging parallel imaging method that accelerates the imaging
speed by employing sinusoidal gradients in the phase- and slice-encoding
directions during the readout to take better advantage of 3D coil sensitivity
profiles. In wave-MoDL, we propose to combine the wave-encoding strategy with
unrolled network constraints to accelerate the acquisition speed while
enforcing wave-encoded data consistency. We further extend wave-MoDL to
reconstruct multi-contrast data with controlled aliasing in parallel imaging
(CAIPI) sampling patterns to leverage similarity between multiple images to
improve the reconstruction quality.
  Result: Wave-MoDL enables a 47-second MPRAGE acquisition at 1 mm resolution
at 16-fold acceleration. For quantitative imaging, wave-MoDL permits a 2-minute
acquisition for T1, T2, and proton density mapping at 1 mm resolution at
12-fold acceleration, from which contrast weighted images can be synthesized as
well.
  Conclusion: Wave-MoDL allows rapid MR acquisition and high-fidelity image
reconstruction and may facilitate clinical and neuroscientific applications by
incorporating unrolled neural networks into wave-CAIPI reconstruction.


title:
Learning Sparse Graphs via Majorization-Minimization for Smooth Node
  Signals

abstract:
  In this letter, we propose an algorithm for learning a sparse weighted graph
by estimating its adjacency matrix under the assumption that the observed
signals vary smoothly over the nodes of the graph. The proposed algorithm is
based on the principle of majorization-minimization (MM), wherein we first
obtain a tight surrogate function for the graph learning objective and then
solve the resultant surrogate problem which has a simple closed form solution.
The proposed algorithm does not require tuning of any hyperparameter and it has
the desirable feature of eliminating the inactive variables in the course of
the iterations - which can help speeding up the algorithm. The numerical
simulations conducted using both synthetic and real world (brain-network) data
show that the proposed algorithm converges faster, in terms of the average
number of iterations, than several existing methods in the literature.


title: On base sizes for primitive groups of product type

abstract:
  Let $G \leqslant {\rm Sym}(\Omega)$ be a finite permutation group and recall
that the base size of $G$ is the minimal size of a subset of $\Omega$ with
trivial pointwise stabiliser. There is an extensive literature on base sizes
for primitive groups, but there are very few results for primitive groups of
product type. In this paper, we initiate a systematic study of bases in this
setting. Our first main result determines the base size of every product type
primitive group of the form $L \wr P \leqslant {\rm Sym}(\Omega)$ with soluble
point stabilisers, where $\Omega = \Gamma^k$, $L \leqslant {\rm Sym}(\Gamma)$
and $P \leqslant S_k$ is transitive. This extends recent work of Burness on
almost simple primitive groups. We also obtain an expression for the number of
regular suborbits of any product type group of the form $L \wr P$ and we
classify the groups with a unique regular suborbit under the assumption that
$P$ is primitive, which involves extending earlier results due to Seress and
Dolfi. We present applications on the Saxl graphs of base-two product type
groups and we conclude by establishing several new results on base sizes for
general product type primitive groups.


title:
BEAS: Blockchain Enabled Asynchronous & Secure Federated Machine
  Learning

abstract:
  Federated Learning (FL) enables multiple parties to distributively train a ML
model without revealing their private datasets. However, it assumes trust in
the centralized aggregator which stores and aggregates model updates. This
makes it prone to gradient tampering and privacy leakage by a malicious
aggregator. Malicious parties can also introduce backdoors into the joint model
by poisoning the training data or model gradients. To address these issues, we
present BEAS, the first blockchain-based framework for N-party FL that provides
strict privacy guarantees of training data using gradient pruning (showing
improved differential privacy compared to existing noise and clipping based
techniques). Anomaly detection protocols are used to minimize the risk of
data-poisoning attacks, along with gradient pruning that is further used to
limit the efficacy of model-poisoning attacks. We also define a novel protocol
to prevent premature convergence in heterogeneous learning environments. We
perform extensive experiments on multiple datasets with promising results: BEAS
successfully prevents privacy leakage from dataset reconstruction attacks, and
minimizes the efficacy of poisoning attacks. Moreover, it achieves an accuracy
similar to centralized frameworks, and its communication and computation
overheads scale linearly with the number of participants.


title: Formal Certification Methods for Automated Vehicle Safety Assessment

abstract:
  Challenges related to automated driving are no longer focused on just the
construction of such automated vehicles (AVs), but in assuring the safety of
their operation. Recent advances in Level 3 and Level 4 autonomous driving have
motivated more extensive study in safety guarantees of complicated AV
maneuvers, which aligns with the goal of ISO 21448 (Safety of the Intended
Functions, or SOTIF), i.e. minimizing unsafe scenarios both known and unknown,
as well as Vision Zero -- eliminating highway fatalities by 2050. A majority of
approaches used in providing safety guarantees for AV motion control originate
from formal methods, especially reachability analysis (RA), which relies on
mathematical models for the dynamic evolution of the system to provide
guarantees. However, to the best of the authors' knowledge, there have been no
review papers dedicated to describing and interpreting state-of-the-art of
formal methods in the context of AVs. In this work, we provide both an overview
of the safety verification, validation and certification process, as well as
review formal safety techniques that are best suited to AV applications. We
also propose a unified scenario coverage framework that can provide either a
formal or sample-based estimate of safety verification for full AVs. Finally,
remaining challenges and future opportunities beyond the scope of current
published research for assured AV safety are presented.


title: Block shuffling learning for Deepfake Detection

abstract:
  Although the deepfake detection based on convolutional neural network has
achieved good results, the detection results show that these detectors show
obvious performance degradation when the input images undergo some common
transformations (like resizing, blurring), which indicates that the
generalization ability of the detector is insufficient. In this paper, we
propose a novel block shuffling learning method to solve this problem.
Specifically, we divide the images into blocks and then introduce the random
shuffling to intra-block and inter-block. Intra-block shuffling increases the
robustness of the detector and we also propose an adversarial loss algorithm to
overcome the over-fitting problem brought by the noise introduced by shuffling.
Moreover, we encourage the detector to focus on finding differences among the
local features through inter-block shuffling, and reconstruct the spatial
layout of the blocks to model the semantic associations between them.
Especially, our method can be easily integrated with various CNN models.
Extensive experiments show that our proposed method achieves state-of-the-art
performance in forgery face detection, including good generalization ability in
the face of common image transformations.


title: Control of dynamical localization in atom-optics kicked rotor

abstract:
  Atom-optics kicked rotor represents an experimentally realizable version of
the paradigmatic quantum kicked rotor system. After a short initial diffusive
phase the cloud settles down to a stationary state due to the onset of
dynamical localization. In this work we realise an enhancement of localization
by modification of the kick sequence. We experimentally implement the
modification to this system in which the sign of the kick sequence is flipped
by allowing for a free evolution of the wavepackets for half the Talbot time
after every $M$ kicks. Depending on the value of $M$, this modified system
displays a combination of enhanced diffusion followed by asymptotic
localization. This is explained as resulting from two competing processes --
localization induced by standard kicked rotor type kicks, and diffusion induced
by half Talbot time evolution. The evolving states display a localized but
non-exponential wave function profiles. This provides another route to quantum
control in kicked rotor class of systems. The numerical simulations agree well
with the experimental results.


title: Eigenvalues and Critical Groups of Adinkras

abstract:
  Adinkras are signed graphs used to study supersymmetry in physics. We provide
an introduction to these objects, and study the properties of their signed
adjacency and signed Laplacian matrices. These matrices each have exactly two
distinct eigenvalues (of equal multiplicity), making Adinkras closely related
to the notions of strongly regular graphs. We also study the critical groups of
Adinkras, and in particular determine their odd components. A novel technique
of independent interest is used which considers critical groups over polynomial
rings.


title:
Phase space consideration of low energy electron injection for Direct
  Laser Acceleration

abstract:
  Feasibility of ionization injection for Direct Laser Acceleration (DLA) of
electrons up to hundreds of MeV was studied analytically. Criteria for
effective injection determining range of background and in-channel plasma
parameters, laser intensity, etc. were found using phase portraits of the
system deduced from the simplified analytical model. The found optimal
trajectory in the phase space corresponds to the electron with low (few eV)
initial energy experiencing $\sim$10$^9$ times energy gain. For this to occur,
electron density should be a few percent of the critical density, while the
in-channel electron density should be $\sim$3 times lower. The analytically
obtained dependence of the energy gain on the initial electron longitudinal and
transverse momenta corresponds well to the results of exact numerical
simulations of an electron motion in the plasma channel. Developed approach can
form the basis for further studies of electron injection in DLA varying plasma
and laser parameters as well as initial electron energies.


title:
Radial and non-radial multiple solutions to a general mixed dispersion
  NLS equation

abstract:
  We study the following nonlinear Schr\"odinger equation with a forth order
dispersion term \[ \Delta^2u-\beta\Delta u=g(u) \quad \text{in } \mathbb{R}^N
\] in the positive and zero mass regimes: in the former, $N\geq 2$ and $\beta >
-2\sqrt{m}$, where $m>0$ depends on $g$; in the latter, $N\geq 3$ and
$\beta>0$. In either regimes, we find an infinite sequence of solutions under
rather generic assumptions about $g$; if $N=2$ in the positive mass case, or
$N=4$ in the zero mass case, we need to strengthen such assumptions. Our
approach is variational.


title: A Summary of COVID-19 Datasets

abstract:
  This research presents a review of main datasets that are developed for
COVID-19 research. We hope this collection will continue to bring together
members of the computing community, biomedical experts, and policymakers in the
pursuit of effective COVID-19 treatments and management policies. Many
organizations, such as the World Health Organization (WHO), John Hopkins,
National Institute of Health (NIH), COVID-19 open science table4 and such, in
the world, have made numerous datasets available to the public. However, these
datasets originate from a variety of different sources and initiatives. The
purpose of this research is to summarize the open COVID-19 datasets to make
them more accessible to the research community for health systems design and
analysis.


title: On the behavior of Kodaira dimension under smooth morphisms

abstract:
  We prove several results on the additivity of Kodaira dimension under smooth
morphisms of smooth projective varieties.


title:
Post Quantum Cryptography: Techniques, Challenges, Standardization, and
  Directions for Future Research

abstract:
  The development of large quantum computers will have dire consequences for
cryptography. Most of the symmetric and asymmetric cryptographic algorithms are
vulnerable to quantum algorithms. Grover's search algorithm gives a square root
time boost for the searching of the key in symmetric schemes like AES and 3DES.
The security of asymmetric algorithms like RSA, Diffie Hellman, and ECC is
based on the mathematical hardness of prime factorization and discrete
logarithm. The best classical algorithms available take exponential time.
Shor's factoring algorithm can solve the problems in polynomial time. Major
breakthroughs in quantum computing will render all the present-day widely used
asymmetric cryptosystems insecure. This paper analyzes the vulnerability of the
classical cryptosystems in the context of quantum computers discusses various
post-quantum cryptosystem families, discusses the status of the NIST
post-quantum cryptography standardization process, and finally provides a
couple of future research directions in this field.


title: Adhesive wear with a coarse-grained discrete element model

abstract:
  The use of molecular dynamics (MD) simulations has led to promising results
to unravel the atomistic origins of adhesive wear, and in particular for the
onset of wear at nanoscale surface asperities. However, MD simulations come
with a high computational cost and offer access to only a narrow window of time
and length scales. We propose here to resort to the discrete element method
(DEM) to mitigate the computational cost. Using DEM particles with contact and
cohesive forces, we reproduce the key mechanisms observed with MD, while having
particle diameters and system sizes an order of magnitude higher than with MD.
The pairwise forces are tuned to obtain a solid with reasonably approximated
elastic and fracture properties. The simulations of single asperity wear
performed with MD are successfully reproduced with DEM using a range particle
sizes, validating the coarse-graining procedure. More complex simulations
should allow the study of wear particles and the evolution of worn surfaces in
an adhesive wear context, while reaching scales inaccessible to MD.


title:
Consistency and Convergence of a High Order Accurate Meshless Method for
  Solution of Incompressible Fluid Flows

abstract:
  Computations of incompressible flows with velocity boundary conditions
require solution of a Poisson equation for pressure with all Neumann boundary
conditions. Discretization of such a Poisson equation results in a
rank-deficient matrix of coefficients. When a non-conservative discretization
method such as finite difference, finite element, or spectral scheme is used,
such a matrix also generates an inconsistency which makes the residuals in the
iterative solution to saturate at a threshold level that depends on the spatial
resolution and order of the discretization scheme. In this paper, we examine
inconsistency for a high-order meshless discretization scheme suitable for
solving the equations on a complex domain. The high order meshless method uses
polyharmonic spline radial basis functions (PHS-RBF) with appended polynomials
to interpolate scattered data and constructs the discrete equations by
collocation. The PHS-RBF provides the flexibility to vary the order of
discretization by increasing the degree of the appended polynomial. In this
study, we examine the convergence of the inconsistency for different spatial
resolutions and for different degrees of the appended polynomials by solving
the Poisson equation for a manufactured solution as well as the Navier-Stokes
equations for several fluid flows. We observe that the inconsistency decreases
faster than the error in the final solution, and eventually becomes vanishing
small at sufficient spatial resolution. The rate of convergence of the
inconsistency is observed to be similar or better than the rate of convergence
of the discretization errors. This beneficial observation makes it unnecessary
to regularize the Poisson equation by fixing either the mean pressure or
pressure at an arbitrary point. A simple point solver such as the SOR is seen
to be well-convergent, although it can be further accelerated using multilevel
methods.


title: BDDs Strike Back: Efficient Analysis of Static and Dynamic Fault Trees

abstract:
  Fault trees are a key model in reliability analysis. Classical static fault
trees (SFT) can best be analysed using binary decision diagrams (BDD).
State-based techniques are favorable for the more expressive dynamic fault
trees (DFT). This paper combines the best of both worlds by following Dugan's
approach: dynamic sub-trees are analysed via model checking Markov models and
replaced by basic events capturing the obtained failure probabilities. The
resulting SFT is then analysed via BDDs. We implemented this approach in the
Storm model checker. Extensive experiments (a) compare our pure BDD-based
analysis of SFTs to various existing SFT analysis tools, (b) indicate the
benefits of our efficient calculations for multiple time points and the
assessment of the mean-time-to-failure, and (c) show that our implementation of
Dugan's approach significantly outperforms pure Markovian analysis of DFTs. Our
implementation Storm-dft is currently the only tool supporting efficient
analysis for both SFTs and DFTs.


title:
Discovering Personalized Semantics for Soft Attributes in Recommender
  Systems using Concept Activation Vectors

abstract:
  Interactive recommender systems (RSs) allow users to express intent,
preferences and contexts in a rich fashion, often using natural language. One
challenge in using such feedback is inferring a user's semantic intent from the
open-ended terms used to describe an item, and using it to refine
recommendation results. Leveraging concept activation vectors (CAVs) [21], we
develop a framework to learn a representation that captures the semantics of
such attributes and connects them to user preferences and behaviors in RSs. A
novel feature of our approach is its ability to distinguish objective and
subjective attributes and associate different senses with different users.
Using synthetic and real-world datasets, we show that our CAV representation
accurately interprets users' subjective semantics, and can improve
recommendations via interactive critiquing


title: Anticorrelated Noise Injection for Improved Generalization

abstract:
  Injecting artificial noise into gradient descent (GD) is commonly employed to
improve the performance of machine learning models. Usually, uncorrelated noise
is used in such perturbed gradient descent (PGD) methods. It is, however, not
known if this is optimal or whether other types of noise could provide better
generalization performance. In this paper, we zoom in on the problem of
correlating the perturbations of consecutive PGD steps. We consider a variety
of objective functions for which we find that GD with anticorrelated
perturbations ("Anti-PGD") generalizes significantly better than GD and
standard (uncorrelated) PGD. To support these experimental findings, we also
derive a theoretical analysis that demonstrates that Anti-PGD moves to wider
minima, while GD and PGD remain stuck in suboptimal regions or even diverge.
This new connection between anticorrelated noise and generalization opens the
field to novel ways to exploit noise for training machine learning models.


title:
Detecting Melanoma Fairly: Skin Tone Detection and Debiasing for Skin
  Lesion Classification

abstract:
  Convolutional Neural Networks have demonstrated human-level performance in
the classification of melanoma and other skin lesions, but evident performance
disparities between differing skin tones should be addressed before widespread
deployment. In this work, we utilise a modified variational autoencoder to
uncover skin tone bias in datasets commonly used as benchmarks. We propose an
efficient yet effective algorithm for automatically labelling the skin tone of
lesion images, and use this to annotate the benchmark ISIC dataset. We
subsequently use two leading bias unlearning techniques to mitigate skin tone
bias. Our experimental results provide evidence that our skin tone detection
algorithm outperforms existing solutions and that unlearning skin tone improves
generalisation and can reduce the performance disparity between melanoma
detection in lighter and darker skin tones.


title:
CheXstray: Real-time Multi-Modal Data Concordance for Drift Detection in
  Medical Imaging AI

abstract:
  Clinical Artificial lntelligence (AI) applications are rapidly expanding
worldwide, and have the potential to impact to all areas of medical practice.
Medical imaging applications constitute a vast majority of approved clinical AI
applications. Though healthcare systems are eager to adopt AI solutions a
fundamental question remains: \textit{what happens after the AI model goes into
production?} We use the CheXpert and PadChest public datasets to build and test
a medical imaging AI drift monitoring workflow to track data and model drift
without contemporaneous ground truth. We simulate drift in multiple experiments
to compare model performance with our novel multi-modal drift metric, which
uses DICOM metadata, image appearance representation from a variational
autoencoder (VAE), and model output probabilities as input. Through
experimentation, we demonstrate a strong proxy for ground truth performance
using unsupervised distributional shifts in relevant metadata, predicted
probabilities, and VAE latent representation. Our key contributions include (1)
proof-of-concept for medical imaging drift detection that includes the use of
VAE and domain specific statistical methods, (2) a multi-modal methodology to
measure and unify drift metrics, (3) new insights into the challenges and
solutions to observe deployed medical imaging AI, and (4) creation of
open-source tools that enable others to easily run their own workflows and
scenarios. This work has important implications. It addresses the concerning
translation gap found in continuous medical imaging AI model monitoring common
in dynamic healthcare environments.


title:
Enhancing Perpendicular Magnetic Anisotropy in Garnet Ferrimagnet by
  Interfacing with Few-Layer WTe2

abstract:
  Engineering magnetic anisotropy in a ferro- or ferrimagnetic (FM) thin film
is crucial in spintronic device. One way to modify the magnetic anisotropy is
through the surface of the FM thin film. Here, we report the emergence of a
perpendicular magnetic anisotropy (PMA) induced by interfacial interactions in
a heterostructure comprised of a garnet ferrimagnet, Y3Fe5O12 (YIG), and the
low-symmetry, high spin orbit coupling (SOC) transition metal dichalcogenide,
WTe2. At the same time, we also observed an enhancement in Gilbert damping in
the WTe2 covered YIG area. Both the magnitude of interface-induced PMA and the
Gilbert damping enhancement have no observable WTe2 thickness dependence down
to single quadruple-layer, indicating that the interfacial interaction plays a
critical role. The ability of WTe2 to enhance the PMA in FM thin film, combined
with its previously reported capability to generate out-of-plane damping like
spin torque, makes it desirable for magnetic memory applications.


title:
Electron-phonon interaction and longitudinal-transverse phonon splitting
  in doped semiconductors

abstract:
  We study the effect of doping on the electron-phonon interaction and on the
phonon frequencies in 3-dimensional semiconductors, taking into account the
screening in presence of free carriers at finite temperature. We study the
impact of screening on the Fr\"ohlich-like vertex and on the long-range
non-analytical part of the dynamical matrix, going beyond the state-of-the-art
description for undoped crystals, thanks to the development of a
computationally fast method employing interpolation based on maximally
localized Wannier functions. We apply our approach to cubic silicon carbide,
where we find that in presence of doping the Fr\"ohlich coupling and the
longitudinal-transverse phonon splitting are strongly reduced, thereby
influencing observable properties such as the electronic lifetime.


title: Long lines in subsets of large measure in high dimension

abstract:
  We show that for any set $A\subseteq [0,1]^n$ with $\text{Vol}(A)\ge 1/2$
there exists a line $\ell $ such that the one-dimensional Lebesgue measure of
$\ell \cap A$ is at least $\Omega ( n^{1/4} )$. The exponent $1/4$ is tight.
More generally, for a probability measure $\mu $ on $\mathbb R ^n$ and $0<a<1$
define \begin{equation*} L(\mu ,a):= \inf_{A ; \mu(A) = a} \sup _{\ell \text{
line}} \big| \ell \cap A\big| \end{equation*} where $|\cdot | $ stands for the
one-dimensional Lebesgue measure. We study the asymptotic behavior of $L(\mu
,a)$ when $\mu $ is a product measure and when $\mu $ is the uniform measure on
the $\ell _p$ ball. We observe a rather unified behavior in a large class of
product measures. On the other hand, for $\ell_p$ balls with $1 \leq p \leq
\infty$ we find that there are phase transitions of different types.


title:
A new similarity measure for covariate shift with applications to
  nonparametric regression

abstract:
  We study covariate shift in the context of nonparametric regression. We
introduce a new measure of distribution mismatch between the source and target
distributions that is based on the integrated ratio of probabilities of balls
at a given radius. We use the scaling of this measure with respect to the
radius to characterize the minimax rate of estimation over a family of H\"older
continuous functions under covariate shift. In comparison to the recently
proposed notion of transfer exponent, this measure leads to a sharper rate of
convergence and is more fine-grained. We accompany our theory with concrete
instances of covariate shift that illustrate this sharp difference.


title:
Aligning Eyes between Humans and Deep Neural Network through Interactive
  Attention Alignment

abstract:
  While Deep Neural Networks (DNNs) are deriving the major innovations in
nearly every field through their powerful automation, we are also witnessing
the peril behind automation as a form of bias, such as automated racism, gender
bias, and adversarial bias. As the societal impact of DNNs grows, finding an
effective way to steer DNNs to align their behavior with the human mental model
has become indispensable in realizing fair and accountable models. We propose a
novel framework of Interactive Attention Alignment (IAA) that aims at realizing
human-steerable Deep Neural Networks (DNNs). IAA leverages DNN model
explanation method as an interactive medium that humans can use to unveil the
cases of biased model attention and directly adjust the attention. In improving
the DNN using human-generated adjusted attention, we introduce GRADIA, a novel
computational pipeline that jointly maximizes attention quality and prediction
accuracy. We evaluated IAA framework in Study 1 and GRADIA in Study 2 in a
gender classification problem. Study 1 found applying IAA can significantly
improve the perceived quality of model attention from human eyes. In Study 2,
we found using GRADIA can (1) significantly improve the perceived quality of
model attention and (2) significantly improve model performance in scenarios
where the training samples are limited. We present implications for future
interactive user interfaces design towards human-alignable AI.


title: The chromatic number of triangle-free hypergraphs

abstract:
  A triangle in a hypergraph $\mathcal{H}$ is a set of three distinct edges $e,
f, g\in\mathcal{H}$ and three distinct vertices $u, v, w\in V(\mathcal{H})$
such that $\{u, v\}\subseteq e$, $\{v, w\}\subseteq f$, $\{w, u\}\subseteq g$
and $\{u, v, w\}\cap e\cap f\cap g=\emptyset$. Johansson proved in 1996 that
$\chi(G)=\mathcal{O}(\Delta/\log\Delta)$ for any triangle-free graph $G$ with
maximum degree $\Delta$. Cooper and Mubayi later generalized the Johansson's
theorem to all rank $3$ hypergraphs. In this paper we provide a common
generalization of both these results for all hypergraphs, showing that if
$\mathcal{H}$ is a rank $k$, triangle-free hypergraph, then the list chromatic
number \[ \chi_{\ell}(\mathcal{H})\leq \mathcal{O}\left(\max_{2\leq \ell \leq
k} \left\{\left( \frac{\Delta_{\ell}}{\log \Delta_{\ell}}
\right)^{\frac{1}{\ell-1}} \right\}\right), \] where $\Delta_{\ell}$ is the
maximum $\ell$-degree of $\mathcal{H}$. The result is sharp apart from the
constant. Moreover, our result implies, generalizes and improves several
earlier results on the chromatic number and also independence number of
hypergraphs, while its proof is based on a different approach than prior works
in hypergraphs (and therefore provides alternative proofs to them). In
particular, as an application, we establish a bound on chromatic number of
sparse hypergraphs in which each vertex is contained in few triangles, and thus
extend results of Alon, Krivelevich and Sudakov, and Cooper and Mubayi from
hypergraphs of rank 2 and 3, respectively, to all hypergraphs.


title: Simulating Hydrodynamics in Cosmology with CRK-HACC

abstract:
  We introduce CRK-HACC, an extension of the Hardware/Hybrid Accelerated
Cosmology Code (HACC), to resolve gas hydrodynamics in large-scale structure
formation simulations of the universe. The new framework couples the HACC
gravitational N-body solver with a modern smoothed particle hydrodynamics (SPH)
approach called CRKSPH. $\underline{\text{C}}$onservative
$\underline{\text{R}}$eproducing $\underline{\text{K}}$ernel
$\underline{\text{SPH}}$ utilizes smoothing functions that exactly interpolate
linear fields while manifestly preserving conservation laws (momentum, mass,
and energy). The CRKSPH method has been incorporated to accurately model
baryonic effects in cosmology simulations - an important addition targeting the
generation of precise synthetic sky predictions for upcoming observational
surveys. CRK-HACC inherits the performance design specifications of HACC and is
optimized to run effectively on modern GPU-accelerated supercomputers. In this
work, we summarize the primary solver components and present a number of
standard validation tests to demonstrate efficacy, including idealized
hydrodynamic and cosmological setups, as well as self-similarity measurements.


title:
An Asymptotically Optimal Two-Part Coding Scheme for Networked Control
  under Fixed-Rate Constraints

abstract:
  It is known that fixed rate adaptive quantizers can be used to stabilize an
open-loop-unstable linear system driven by unbounded noise. These quantizers
can be designed so that they have near-optimal rate, and the resulting system
will be stable in the sense of having an invariant probability measure, or
ergodicity, as well as the boundedness of the state second moment. However,
results on the minimization of the state second moment for such quantizers, an
important goal in practice, do not seem to be available. In this paper, we
construct a two-part adaptive coding scheme that is asymptotically optimal in
terms of the second moments. The first part, as in prior work, leads to
ergodicity (via positive Harris recurrence) and the second part attains order
optimality of the invariant second moment, resulting in near optimal
performance at high rates.


title:
Evaluating natural language processing models with generalization
  metrics that do not need access to any training or testing data

abstract:
  The search for effective and robust generalization metrics has been the focus
of recent theoretical and empirical work.
  In this paper, we discuss the performance of natural language processing
(NLP) models, and we evaluate various existing and novel generalization
metrics.
  Compared to prior studies, we
  (i) focus on NLP instead of computer vision (CV),
  (ii) focus on generalization metrics that predict test error instead of the
generalization gap,
  (iii) focus on generalization metrics that do not need the access to data,
and
  (iv) focus on the heavy-tail (HT) phenomenon that has received comparatively
less attention in the study of deep neural networks (NNs).
  We extend recent HT-based work which focuses on power law (PL) distributions,
and we study exponential (EXP) and exponentially truncated power law (E-TPL)
fitting to the empirical spectral densities (ESDs) of weight matrices.
  Our detailed empirical studies show that
  (i) \emph{shape metrics}, or the metrics obtained from fitting the shape of
the ESDs, perform uniformly better at predicting generalization performance
than \emph{scale metrics} commonly studied in the literature, as measured by
the \emph{average} rank correlations with the generalization performance for
all of our experiments;
  (ii) among forty generalization metrics studied in our paper, the
\RANDDISTANCE metric, a new shape metric invented in this paper that measures
the distance between empirical eigenvalues of weight matrices and those of
randomly initialized weight matrices, achieves the highest worst-case rank
correlation with generalization performance under a variety of training
settings; and
  (iii) among the three HT distributions considered in our paper, the E-TPL
fitting of ESDs performs the most robustly.


title: Galois LCD codes over mixed alphabets

abstract:
  We study (Galois) linear complementary dual codes over mixed alphabets
arising from finite chain rings. We give a characterization of when a given
code is of We study (Galois) linear complementary dual codes over mixed
alphabets arising from finite chain rings. We give a characterization of when a
given code is of this type and when it is Galois invariant. Finally, this leads
to a study of the Gray image of $\mathbb{F}_p\mathbb{F}_p[\theta]$-linear
codes, where $p\in\{2; 3\}$ and $\theta\neq\theta^2=0$, that provides
$\mathbb{F}_p$-linear complementary dual codes.


title:
Greenberg's conjecture for real quadratic fields and the cyclotomic
  $\mathbb{Z}_2$-extensions

abstract:
  Let $\mathcal{A}_n$ be the $2$-part of the ideal class group of the $n$-th
layer of the cyclotomic $\mathbb{Z}_2$-extension of a real quadratic number
field $F$. The cardinality of $\mathcal{A}_n$ is related to the index of
cyclotomic units in the full group of units. We present a method to study the
latter index. As an application we show that the sequence of the
$\mathcal{A}_n$'s stabilizes for the real fields $F=\mathbb{Q}(\sqrt{f})$ for
any integer $0<f<10000$. Equivalently Greenberg's conjecture holds for those
fields.


title:
A Novel Micro-service Based Platform for Composition, Deployment and
  Execution of BDA Applications

abstract:
  Big Data are growing at an exponential rate and it becomes necessary the use
of tools and technologies to manage, process and visualize them in order to
extract value. In this paper a micro-service based platform is presented for
the composition, deployment and execution of Big Data Analytics (BDA)
application workflows in several domains and scenarios is presented. ALIDA is a
result coming from previous research activities by ENGINEERING. It aims to
achieve a unified platform that allows both BDA application developers and data
analysts to interact with it. Developers will be able to register new BDA
applications through the exposed API and/or through the web user interface.
Data analysts will be able to use the BDA applications provided to create
batch/stream workflows through a dashboard user interface to manipulate and
subsequently visualize results from one or more sources. The platform also
supports the auto-tuning of Big Data frameworks deployment properties to
improve metrics for analytics application. ALIDA has been properly extended and
integrated into a software solution for the analysis of large amounts of data
from the avionic industries. A use case within this context is then presented.


title:
Melnikov analysis for planar piecewise linear vector fields with
  algebraic switching curve $y^n-x^m=0$

abstract:
  This paper is devoted to the study of the maximum number of limit cycles,
$H(m,n)$, of a planar piecewise linear differential system with two zones
separated by the curve $y^n-x^m=0$, with $n,m$ being positive integers. More
precisely, we provide a lower estimate of $ H(m,n)$. for all $m,n\in
\mathbb{N}$, for piecewise linear perturbations of the linear center using some
recent results about Chebyshev systems with positive accuracy and Melnikov
Theory


title:
Solidfmm: A highly optimised library of operations on the solid
  harmonics for use in fast multipole methods

abstract:
  We present solidfmm, a highly optimised C++ library for the solid harmonics
as they are needed in fast multipole methods. The library provides efficient,
vectorised implementations of the translation operations M2M, M2L, and L2L, and
is available as free software. While asymptotically of complexity $O(P^3)$, for
all practically relevant expansion orders, the translation operators display an
empirical complexity of $O(P^2)$, outperforming the na\"ive implementation by
orders of magnitude.