title: Efficient Generation of Spin Cat States

abstract:
  Spin cat states are promising candidates for achieving Heisenberg-limited
quantum metrology. It is suggested that spin cat states can be generated by
adiabatic evolution. However, due to the limited coherence time, the adiabatic
process may be too slow to be practical. To speed up the state generation, we
propose to use machine optimization to generate desired spin cat states. Our
proposed scheme relies only on experimentally demonstrated one-axis twisting
interactions with piecewise time-modulation of rotations designed via machine
optimization. The required evolution time is much shorter than the one with
adiabatic evolution and it does not make large modification to the existing
experimental setups. Our protocol with machine optimization is efficient and
easy to be implemented in state-of-the-art experiments.


title:
Cuscuta-Galileon Cosmology: Dynamics, Gravitational "Constant"s and
  Hubble Constant

abstract:
  We discuss cosmology based on a cuscuta-galileon gravity theory, which
preserves just two degrees of freedom. Although there exists no additional
degrees of freedom, introduction of a potential of a scalar field changes the
dynamics. The scalar field is completely determined by matter fields. Giving an
exponential potential as an example, we discuss the cosmological dynamics. The
gravitational "constant" $G_{\rm F}$ appeared in the effective Friedmann
equation becomes time dependent. We also present how to construct a potential
when we know the evolution of the Hubble parameter. When we assume the
$\Lambda$CDM cosmology for the background evolution, we find the potential
form.
  We then analyze the density perturbations, which equation is characterized
only by a change of the gravitational "constant"$G_{\rm eff}$, which also
becomes time dependent. From the observational constraints such as the
constraint from the big-bang nucleosynthesis and the constraint on
time-variation of gravitational constant, we restrict the parameters in our
models.
  The time dependence of the gravitational constant in the effective Friedmann
equation, we may have a chance to explain the Hubble tension problem.


title:
Multiple exciton generation and giant external quantum efficiency in
  VO$_2$

abstract:
  Multiple exciton generation (MEG) is a widely studied phenomenon in
semiconductor nanocrystals and quantum dots wherein photo-excited carriers
relax by generating additional electron-hole pairs. Here, we present the first
experimental observation of MEG and the same leading to giant external quantum
efficiency (EQE) in VO$_2$, a prototype strongly correlated material. By
employing a photoexcitation (lamda ~ 488 nm) of ~ 4.2 times the bandgap, EQE in
VO$_2$ is enhanced up to ~ 170 % at room temperature. Temperature dependent
experiments exhibit the direct relation between MEG and strength of electron
correlation and suggest that such a phenomenon could be exploited in large
number of strongly correlated materials for high performance solar cell
research in near future.


title: Instance-wise algorithm configuration with graph neural networks

abstract:
  We present our submission for the configuration task of the Machine Learning
for Combinatorial Optimization (ML4CO) NeurIPS 2021 competition. The
configuration task is to predict a good configuration of the open-source solver
SCIP to solve a mixed integer linear program (MILP) efficiently. We pose this
task as a supervised learning problem: First, we compile a large dataset of the
solver performance for various configurations and all provided MILP instances.
Second, we use this data to train a graph neural network that learns to predict
a good configuration for a specific instance. The submission was tested on the
three problem benchmarks of the competition and improved solver performance
over the default by 12% and 35% and 8% across the hidden test instances. We
ranked 3rd out of 15 on the global leaderboard and won the student leaderboard.
We make our code publicly available at
\url{https://github.com/RomeoV/ml4co-competition} .


title:
The group of quasi-isometries of the real line cannot act effectively on
  the line

abstract:
  We prove that the group $\mathrm{QI}^{+}(\mathbb{R})$ of
orientation-preserving quasi-isometries of the real line is a left-orderable,
non-simple group, which cannot act effectively on the real line $\mathbb{R}.$


title:
Random Forests Weighted Local Fr\'echet Regression with Theoretical
  Guarantee

abstract:
  Statistical analysis is increasingly confronted with complex data from
general metric spaces, such as symmetric positive definite matrix-valued data
and probability distribution functions. [47] and [17] establish a general
paradigm of Fr\'echet regression with complex metric space valued responses and
Euclidean predictors. However, their proposed local Fr\'echet regression
approach involves nonparametric kernel smoothing and suffers from the curse of
dimensionality. To address this issue, we in this paper propose a novel random
forests weighted local Fr\'echet regression paradigm. The main mechanism of our
approach relies on the adaptive kernels generated by random forests. Our first
method utilizes these weights as the local average to solve the Fr\'echet mean,
while the second method performs local linear Fr\'echet regression, making both
methods locally adaptive. Our proposals significantly improve existing
Fr\'echet regression methods. Based on the theory of infinite order U-processes
and infinite order Mmn-estimator, we establish the consistency, rate of
convergence, and asymptotic normality for our proposed random forests weighted
Fr\'echet regression estimator, which covers the current large sample theory of
random forests with Euclidean responses as a special case. Numerical studies
show the superiority of our proposed two methods for Fr\'echet regression with
several commonly encountered types of responses such as probability
distribution functions, symmetric positive definite matrices, and sphere data.
The practical merits of our proposals are also demonstrated through the
application to the human mortality distribution data.


title:
Far-ultraviolet investigation into the galactic globular cluster M30
  (NGC 7099): I. Photometry and radial distributions

abstract:
  We present a far-ultraviolet (FUV) study of the globular cluster M30 (NGC
7099). The images were obtained using the Advanced Camera for Surveys (ACS/SBC,
F150LP, FUV) and the Wide Field Planetary Camera 2 (WFPC2, F300W, UV) which
were both on board the Hubble Space Telescope (HST). The FUV-UV
colour-magnitude diagram (CMD) shows a main sequence (MS) turnoff at FUV
$\approx$ 22 mag and FUV-UV $\approx$ 3 mag. The MS extends 4 mag below the
turnoff, and a prominent horizontal branch (HB) and blue straggler (BS)
sequence can be seen. A total of 1218 MS stars, 185 red giant branch stars, 47
BS stars and 41 HB stars are identified, along with 78 sources blueward of the
MS which consist of white dwarfs (WDs) and objects in the gap between the WDs
and the MS that include potential cataclysmic variable (CV) candidates. The
radial distribution of the BS population is concentrated towards the cluster
centre, indicating that mass segregation has occurred. The blue and red
sub-populations of the double BS sequence appear mixed in the ultraviolet CMD,
and no significant central concentration of CV candidates is seen in this
cluster.


title: Random-Matrix Approach to Transition-State Theory

abstract:
  To model a complex system intrinsically separated by a barrier, we use two
random Hamiltonians, coupled to each other either by a tunneling matrix element
or by an intermediate transition state. We study that model in the universal
limit of large matrix dimension. We calculate the average probability for
transition from scattering channel coupled to the first Hamiltonian to a
scattering channel coupled to the second Hamiltonian. Using only the assumption
that the sum of transmission coefficients of channels coupled to the second
Hamiltonian is large we retrieve transition-state theory in its general form.
For tunneling through a very thick barrier independence of formation and decay
of the tunneling process hold more generally.


title:
Quantum advantage using high-dimensional twisted photons as quantum
  finite automata

abstract:
  Quantum finite automata (QFA) are basic computational devices that make
binary decisions using quantum operations. They are known to be exponentially
memory efficient compared to their classical counterparts. Here, we demonstrate
an experimental implementation of multi-qubit QFAs using the orbital angular
momentum (OAM) of single photons. We implement different high-dimensional QFAs
encoded on a single photon, where multiple qubits operate in parallel without
the need for complicated multi-partite operations. Using two to eight OAM
quantum states to implement up to four parallel qubits, we show that a
high-dimensional QFA is able to detect the prime numbers 5 and 11 while
outperforming classical finite automata in terms of the required memory. Our
work benefits from the ease of encoding, manipulating, and deciphering
multi-qubit states encoded in the OAM degree of freedom of single photons,
demonstrating the advantages structured photons provide for complex quantum
information tasks.


title: Discovering plasticity models without stress data

abstract:
  We propose a new approach for data-driven automated discovery of material
laws, which we call EUCLID (Efficient Unsupervised Constitutive Law
Identification and Discovery), and we apply it here to the discovery of
plasticity models, including arbitrarily shaped yield surfaces and isotropic
and/or kinematic hardening laws. The approach is unsupervised, i.e., it
requires no stress data but only full-field displacement and global force data;
it delivers interpretable models, i.e., models that are embodied by
parsimonious mathematical expressions discovered through sparse regression of a
potentially large catalogue of candidate functions; it is one-shot, i.e.,
discovery only needs one experiment. The material model library is constructed
by expanding the yield function with a Fourier series, whereas isotropic and
kinematic hardening are introduced by assuming a yield function dependency on
internal history variables that evolve with the plastic deformation. For
selecting the most relevant Fourier modes and identifying the hardening
behavior, EUCLID employs physics knowledge, i.e., the optimization problem that
governs the discovery enforces the equilibrium constraints in the bulk and at
the loaded boundary of the domain. Sparsity promoting regularization is
deployed to generate a set of solutions out of which a solution with low cost
and high parsimony is automatically selected. Through virtual experiments, we
demonstrate the ability of EUCLID to accurately discover several plastic yield
surfaces and hardening mechanisms of different complexity.


title:
Study of COVID-19 epidemiological evolution in India with a multi-wave
  SIR model

abstract:
  The global pandemic due to the outbreak of COVID-19 ravages the whole world
for more than two years in which all the countries are suffering a lot since
December 2019. In order to control this ongoing waves of epidemiological
infections, attempts have been made to understand the dynamics of this pandemic
in deterministic approach with the help of several mathematical models. In this
article characteristics of a multi-wave SIR model have been studied which
successfully explains the features of this pandemic waves in India. Stability
of this model has been studied by identifying the equilibrium points as well as
by finding the eigen values of the corresponding Jacobian matrices. Complex
eigen values are found which ultimately give rise to the oscillatory solutions
for the three categories of populations, say, susceptible, infected and
removed. In this model, a finite probability of the recovered people for
becoming susceptible again is introduced which eventually lead to the
oscillatory solution in other words. The set of differential equations has been
solved numerically in order to obtain the variation for numbers of susceptible,
infected and removed people with time. In this phenomenological study, finally
an additional modification is made in order to explain the aperiodic
oscillation which is found necessary to capture the feature of epidemiological
waves particularly in India.


title:
QCD axial anomaly enhances the $\eta \eta^\prime$ decay of the hybrid
  candidate $\eta_1(1855)$

abstract:
  We study the hybrid mesons with the exotic quantum number $I^GJ^{PC} =
0^+1^{-+}$ and investigate their decays into the $\eta \eta^\prime$, $a_1(1260)
\pi$, $f_1(1285) \eta$, $f_1(1420) \eta$, $K^*(892) \bar K$, $K_1(1270) \bar
K$, and $K_1(1400) \bar K$ channels. We find that the QCD axial anomaly
enhances the decay width of the $\eta \eta^\prime$ channel although this mode
is strongly suppressed by the small $P$-wave phase space. Our results support
the interpretation of the $\eta_1(1855)$ recently observed by BESIII as the
$\bar s s g$ hybrid meson of $I^GJ^{PC}=0^+1^{-+}$. The QCD axial anomaly
ensures the $\eta \eta^\prime$ decay mode to be a characteristic signal of the
hybrid nature of the $\eta_1(1855)$.


title: Initial data on big bang singularities

abstract:
  The goal of this article is to parametrise solutions to Einstein's equations
with big bang singularities and quiescent asymptotics. To this end, we
introduce a notion of initial data on big bang singularities and conjecture
that it can be used to parametrise quiescent solutions. A mathematical
statement of the conjecture presupposes a precise definition of the class of
quiescent solutions as well as a proof of existence and uniqueness of
developments corresponding to initial data on a big bang singularity. We
provide one definition of quiescence here. We also appeal to existing results
in order to illustrate that, in certain cases, there are unique developments
corresponding to initial data on the singularity. However, our perspective
leads to a large class of open problems corresponding to the general
conjecture. An additional benefit of the notion of initial data developed here
is that it can be used to give a unified perspective on the existing results
concerning quiescent singularities. In fact, we provide several examples of how
existing results can be considered to be special cases of the framework
developed here. A second, potential, application is to oscillatory and
spatially inhomogeneous big bang singularities. Considering the existing
arguments in the spatially homogeneous setting, a crucial first step in the
study of oscillatory behaviour is to understand how solutions approach the
Kasner circle along a stable manifold, and then depart via an unstable
manifold. In order to carry out a similar analysis in the spatially
inhomogeneous setting, it is of central importance to first identify the stable
manifold. Building on the work of Fournodavlos and Luk, we here propose such an
identification.


title:
Collaborative Filtering with Attribution Alignment for Review-based
  Non-overlapped Cross Domain Recommendation

abstract:
  Cross-Domain Recommendation (CDR) has been popularly studied to utilize
different domain knowledge to solve the data sparsity and cold-start problem in
recommender systems. In this paper, we focus on the Review-based Non-overlapped
Recommendation (RNCDR) problem. The problem is commonly-existed and challenging
due to two main aspects, i.e, there are only positive user-item ratings on the
target domain and there is no overlapped user across different domains. Most
previous CDR approaches cannot solve the RNCDR problem well, since (1) they
cannot effectively combine review with other information (e.g., ID or ratings)
to obtain expressive user or item embedding, (2) they cannot reduce the domain
discrepancy on users and items. To fill this gap, we propose Collaborative
Filtering with Attribution Alignment model (CFAA), a cross-domain
recommendation framework for the RNCDR problem. CFAA includes two main modules,
i.e., rating prediction module and embedding attribution alignment module. The
former aims to jointly mine review, one-hot ID, and multi-hot historical
ratings to generate expressive user and item embeddings. The later includes
vertical attribution alignment and horizontal attribution alignment, tending to
reduce the discrepancy based on multiple perspectives. Our empirical study on
Douban and Amazon datasets demonstrates that CFAA significantly outperforms the
state-of-the-art models under the RNCDR setting.


title: The $m$-bipartite Ramsey number $BR_m(H_1,H_2)$

abstract:
  In a $(G^1,G^2)$ coloring of a graph $G$, every edge of $G$ is in $G^1$ or
$G^2$. For two bipartite graphs $H_1$ and $H_2$, the bipartite Ramsey number
$BR(H_1, H_2)$ is the least integer $b\geq 1$, such that for every $(G^1, G^2)$
coloring of the complete bipartite graph $K_{b,b}$, results in either
$H_1\subseteq G^1$ or $H_2\subseteq G^2$. As another view, for bipartite graphs
$H_1$ and $H_2$ and a positive integer $m$, the $m$-bipartite Ramsey number
$BR_m(H_1, H_2)$ of $H_1$ and $H_2$ is the least integer $n$, such that every
subgraph $G$ of $K_{m,n}$ results in $H_1\subseteq G$ or $H_2\subseteq
\overline{G}$. The size of $m$-bipartite Ramsey number $BR_m(K_{2,2},
K_{2,2})$, the size of $m$-bipartite Ramsey number $BR_m(K_{2,2}, K_{3,3})$ and
the size of $m$-bipartite Ramsey number $BR_m(K_{3,3}, K_{3,3})$ have been
computed in several articles up to now. In this paper we determine the exact
value of $BR_m(K_{2,2}, K_{4,4})$ for each $m\geq 2$.


title: The analogue of the BRZ exact sequence for Tate-Shafarevich Groups

abstract:
  We find an exact sequence in term of Tate-Shafarevich groups (assuming being
finite) $\Sha(E/K)$ and $\Sha(E/L)$ of elliptic curve $E$ over a finite Galois
extension $L/K$ of number fields. This is the analogue of the "BRZ exact
sequence" \cite{SRM} for the relative P\'olya group $\Po(L/K)$ \cite{MR2} and
the Ostrowski quotient $\Ost(L/K)$ \cite{SRM}.


title:
On the containment $I^{(3)} \subseteq I^2$ and configurations of triple
  points in B\"{o}r\"{o}czky line arrangements

abstract:
  We study sets of triple points of B\"{o}r\"{o}czky's arrangements of lines in
the context of the containment problem proposed by Harbourne and Huneke. We
show that in the class of those arrangements, the smallest counterexample to
the containment $I^{(3)} \subseteq I^2$ is obtained when the number of lines is
equal to 12.


title: $D(4)$-triples with two largest elements in common

abstract:
  In this paper we consider two new conjectures concerning $D(4)$-quadruples
and prove some special cases which support their validity. The main result is a
proof that $\{a,b,c\}$ and $\{a+1,b,c\}$ cannot both be $D(4)$-triples.


title: Decomposing neural networks as mappings of correlation functions

abstract:
  Understanding the functional principles of information processing in deep
neural networks continues to be a challenge, in particular for networks with
trained and thus non-random weights. To address this issue, we study the
mapping between probability distributions implemented by a deep feed-forward
network. We characterize this mapping as an iterated transformation of
distributions, where the non-linearity in each layer transfers information
between different orders of correlation functions. This allows us to identify
essential statistics in the data, as well as different information
representations that can be used by neural networks. Applied to an XOR task and
to MNIST, we show that correlations up to second order predominantly capture
the information processing in the internal layers, while the input layer also
extracts higher-order correlations from the data. This analysis provides a
quantitative and explainable perspective on classification.


title: Dynamics of Multi-Domains in Ferroelectric Tunnel Junction

abstract:
  The Discovery of giant tunnel electroresistance (TER) in Ferroelectric Tunnel
Junction (FTJ) paves a futuristic possibility of utilizing the FTJ as a
bistable resistive device with an enormously high ON/OFF ratio. In the last 20
years, numerous studies have reported that the formation of multidomain in
ferroelectric material is an inevitable process to minimize the total system
energy. Recent studies based on phase-field simulations have demonstrated that
domain nucleation/motion substantially alters the electrostatics of a
ferroelectric material. However, the impact of domain dynamics on quantum
transport in FTJ remains elusive. This paper presents a comprehensive study of
multidomain dynamics in a ferroelectric tunnel junction. Analysis of this
article is twofold; firstly, we study the impact of domain dynamics on
electrostatics in an FTJ. Subsequently, the obtained electrostatics is used to
study the variations in tunneling current, and TER originated from multidomain
dynamics. We show that ON/OFF current density and TER vary locally in the
ferroelectric region. Furthermore, the device's electrostatics and quantum
transport exhibit an oscillatory nature due to periodic domain texture. ON/OFF
current density shows a sine/cosine distribution in ferroelectric, and
approximately one-decade local variation in current density is observed. These
local fluctuations in current density cause oscillations in the device's ON/OFF
ratio. Optimization techniques to achieve a uniform and maximum TER are also
discussed. A 2D analytical and explicit model is derived by solving coupled 2D
Poisson's equation and Landau-Ginzburg equation. The model incorporates the
switching and nucleation of domains by minimizing net ferroelectric energy
(depolarization+free+gradient energy density). Furthermore, the impact of the
bottom insulator layer on ferroelectric's gradient energy is also studied.


title:
A non-local gradient based approach of infinity Laplacian with
  $\Gamma$-convergence

abstract:
  We propose an infinity Laplacian method to address the problem of
interpolation on an unstructured point cloud. In doing so, we find the labeling
function with the smallest infinity norm of its gradient. By introducing the
non-local gradient, the continuous functional is approximated with a discrete
form. The discrete problem is convex and can be solved efficiently with the
split Bregman method. Experimental results indicate that our approach provides
consistent interpolations and the labeling functions obtained are globally
smooth, even in the case of extreme low sampling rate. More importantly,
convergence of the discrete minimizer to the optimal continuous labeling
function is proved using $\Gamma$-convergence and compactness, which guarantees
the reliability of the infinity Laplacian method in various potential
applications.


title:
Global boundedness and Allee effect for a nonlocal time fractional
  p-Laplacian reaction-diffusion equation

abstract:
  The global boundedness and asymptotic behavior are investigated for the
solutions of a nonlocal time fractional p-Laplacian reaction-diffusion equation
(NTFPLRDE) $$ \frac{\partial^{\alpha }u}{\partial t^{\alpha }}=\Delta_{p} u+\mu
u^{2}(1-kJ*u) -\gamma u, \qquad(x,t)\in\mathbb{R}^{N}\times(0,+\infty)$$ with
$0<\alpha <1,\beta, \mu ,k>0,N\leq 2$ and $\Delta_{p}u =div(\left|
\bigtriangledown u \right|^{p-2}\bigtriangledown u)$. Under appropriate
assumptions on $J$ and the conditions of $1<p<2$, it is proved that for any
nonnegative and bounded initial conditions, the problem has a global bounded
classical solution if $k^{*}=0$ for $N=1$ or $k^{*}=(\mu
C^{2}_{GN}+1)\eta^{-1}$ for $N=2$, where $C_{GN}$ is the constant in
Gagliardo-Nirenberg inequality. With further assumptions on the initial datum,
for small $\mu$ values, the solution is shown to converge to $0$ exponentially
or locally uniformly as $t \rightarrow \infty$, which is referred as the Allee
effect in sense of Caputo derivative. Moreover, under the condition of $J
\equiv 1$, it is proved that the nonlinear NTFPLRDE has a global bounded
solution in any dimensional space with the nonlinear p-Laplacian diffusion
terms $\Delta_{p} u^{m}\, (2-\frac{2}{N}< m\leq 3)$.


title: Study of exotic hadrons with machine learning

abstract:
  We analyzed the invariant mass spectrum of near-threshold exotic states for
one-channel candidates with a deep neural network. It can extract the
scattering length and effective range, which would shed light on the nature of
given states, from the experimental mass spectrum. As an application, the mass
spectrum of the $X(3872)$ and the $T_{cc}^+$ are studied. The obtained
scattering lengths, effective ranges, and most relevant thresholds are
consistent with those from fitting to the experimental data. The advantage of
the neural network is that it is more stable than the fitting, especially for
low-statistic data. The network, which provides another way to analyze the
experimental data, can also be applied to other one-channel near-threshold
exotic candidates.


title:
Level-Set modeling of grain growth in 316L stainless steel under
  different assumptions regarding grain boundary properties

abstract:
  Two finite element level-set (FE-LS) formulations are compared for the
modeling of grain growth of 316L stainless steel in terms of grain size, mean
values and histograms. Two kinds of microstructures are considered, some are
generated statistically from EBSD maps and the others are generated by
immersion of EBSD data in the FE formulation. Grain boundary (GB) mobility is
heterogeneously defined as a function of the GB disorientation. On the other
hand, GB energy is considered as heterogeneous or anisotropic, respectively
defined as a function of the disorientation and both the GB misorientation and
the GB inclination. In terms of mean grain size value and grain size
distribution (GSD), both formulations provide similar responses. However, the
anisotropic formulation better respects the experimental disorientation
distribution function (DDF) and predicts more realistic grain morphologies. It
was also found that the heterogeneous GB mobility described with a sigmoidal
function only affects the DDF and the morphology of grains. Thus, a slower
evolution of twin boundaries (TBs) is perceived.


title: Vaccination nudges

abstract:
  A nudge changes people's actions without removing their options or altering
their incentives.During the COVID-19 vaccine rollout, the Swedish Region of
Uppsala sent letters with pre-booked appointments to inhabitants aged 16-17
instead of opening up manual appointment booking. Using regional and mu-nicipal
vaccination data, we document a higher vaccine uptake among 16- to 17-year-olds
in Uppsala compared to untreated control regions (constructed using the
synthetic control method as well as neighboring municipalities). The results
highlight pre-booked appointments as a strategy for increasing vaccination
rates in populations with low perceived risk.


title: Robust Sylvester-Gallai type theorem for quadratic polynomials

abstract:
  In this work, we extend the robust version of the Sylvester-Gallai theorem,
obtained by Barak, Dvir, Wigderson and Yehudayoff, and by Dvir, Saraf and
Wigderson, to the case of quadratic polynomials. Specifically, we prove that if
$\mathcal{Q}\subset \mathbb{C}[x_1.\ldots,x_n]$ is a finite set,
$|\mathcal{Q}|=m$, of irreducible quadratic polynomials that satisfy the
following condition:
  There is $\delta>0$ such that for every $Q\in\mathcal{Q}$ there are at least
$\delta m$ polynomials $P\in \mathcal{Q}$ such that whenever $Q$ and $P$ vanish
then so does a third polynomial in $\mathcal{Q}\setminus\{Q,P\}$, then
$\dim(\text{span}({\mathcal{Q}}))=\text{poly}(1/\delta)$.
  The work of Barak et al. and Dvir et al. studied the case of linear
polynomials and proved an upper bound of $O(1/\delta)$ on the dimension (in the
first work an upper bound of $O(1/\delta^2)$ was given, which was improved to
$O(1/\delta)$ in the second work).


title: Energy-Based Contrastive Learning of Visual Representations

abstract:
  Contrastive learning is a method of learning visual representations by
training Deep Neural Networks (DNNs) to increase the similarity between
representations of positive pairs and reduce the similarity between
representations of negative pairs. However, contrastive methods usually require
large datasets with significant number of negative pairs per iteration to
achieve reasonable performance on downstream tasks. To address this problem,
here we propose Energy-Based Contrastive Learning (EBCLR) that combines
contrastive learning with Energy-Based Models (EBMs) and can be theoretically
interpreted as learning the joint distribution of positive pairs. Using a novel
variant of Stochastic Gradient Langevin Dynamics (SGLD) to accelerate the
training of EBCLR, we show that EBCLR is far more sample-efficient than
previous self-supervised learning methods. Specifically, EBCLR shows from X4 up
to X20 acceleration compared to SimCLR and MoCo v2 in terms of training epochs.
Furthermore, in contrast to SimCLR, EBCLR achieves nearly the same performance
with 254 negative pairs (batch size 128) and 30 negative pairs (batch size 16)
per positive pair, demonstrating the robustness of EBCLR to small number of
negative pairs.


title: Two-mirror aplanatic telescopes with a flat field

abstract:
  A complete description is given of two-mirror telescopes with a flat medial
focal surface, on which the images of stars are circles of least confusion.
Particular attention is paid to aplanats, since their field of view is
noticeably larger than that of classical systems. Two sets of appropriate
solutions correspond to Schwarzschild and Gregorian telescopes. As a result, it
becomes possible to use flat light detectors with wide-field two-mirror
telescopes. New designs are of particular interest when as few reflective
surfaces as possible are required, which is typical for space exploration and
non-optical observations.


title:
Symmetries of systems of first order ODEs: Symbolic symmetry
  computations, mechanistic model construction and applications in biology

abstract:
  We discuss the role and merits of symmetry methods for the analysis of
biological systems. In particular, we consider systems of first order ordinary
differential equations and provide a comprehensive review of the geometrical
foundations pertinent to symmetries of such systems. Subsequently, we present
an algorithm for finding infinitesimal generators of symmetries for systems
with rational reaction terms, and an open-source implementation of the
algorithm using symbolic computations. We discuss two complementary
perspectives on symmetries in mechanistic modelling; as tools for the analysis
of a given model or as a geometrical principle for incorporating biological
properties in the construction of new models. Through numerous examples of
relevance to modelling in biology we demonstrate the different uses of symmetry
methods, and also discuss how to infer symmetries from experimental data.


title: Graph Neural Network for Local Corruption Recovery

abstract:
  Graph neural networks (GNNs) have seen a surge of development for exploiting
the relational information of input graphs. Nevertheless, messages propagating
through a graph contain both interpretable patterns and small perturbations.
Despite global noise could be distributed over the entire graph data, it is not
uncommon that corruptions appear well-concealed and merely pollute local
regions while still having a vital influence on the GNN learning and prediction
performance. This work tackles the graph recovery problem from local poisons by
a robustness representation learning. Our developed strategy identifies
regional graph perturbations and formulates a robust hidden feature
representation for GNNs. A mask function pinpointed the anomalies without prior
knowledge, and an $\ell_{p,q}$ regularizer defends local poisonings through
pursuing sparsity in the framelet domain while maintaining a conditional
closeness between the observation and new representation. The proposed robust
computational unit alleviates the inertial alternating direction method of
multipliers to achieve an efficient solution. Extensive experiments show that
our new model recovers graph representations from local pollution and achieves
excellent performance.


title:
SDSS-IV MaNGA : spatial resolved properties of kinematically misaligned
  galaxies

abstract:
  We select 456 galaxies with kinematically misaligned gas and stellar
components from 9546 parent galaxies in MaNGA, and classify them into 72
star-forming galaxies, 142 green-valley galaxies and 242 quiescent galaxies.
Comparing the spatial resolved properties of the misaligned galaxies with
control samples closely match in the D$_n$4000 and stellar velocity dispersion,
we find that: (1) the misaligned galaxies have lower values in $V_{\rm
gas}/{\sigma}_{\rm gas}$ and $V_{\rm star}/{\sigma}_{\rm star}$ (the ratio
between ordered to random motion of gas and stellar components) across the
entire galaxies than their control samples; (2) the star-forming and
green-valley misaligned galaxies have enhanced central concentrated star
formation than their control galaxies. The difference in stellar population
between quiescent misaligned galaxies and control samples is small; (3)
gas-phase metallicity of the green valley and quiescent misaligned galaxies are
lower than the control samples. For the star forming misaligned galaxies, the
difference in metallicity between the misaligned galaxies and their control
samples strongly depends on how we select the control samples. All these
observational results suggest external gas accretion influences the evolution
of star forming and green valley galaxies, not only in kinematics/morphologies,
but also in stellar populations. However, the quiescent misaligned galaxies
have survived from different formation mechanisms.


title: A full characterization of Bertrand numeration systems

abstract:
  Among all positional numeration systems, the widely studied Bertrand
numeration systems are defined by a simple criterion in terms of their
numeration languages. In 1989, Bertrand-Mathis characterized them via
representations in a real base $\beta$. However, the given condition turns to
be not necessary. Hence, the goal of this paper is to provide a correction of
Bertrand-Mathis' result. The main difference arises when $\beta$ is a Parry
number, in which case are derived two associated Bertrand numeration systems.
Along the way, we define a non-canonical $\beta$-shift and study its properties
analogously to those of the usual canonical one.


title:
Positron sources: from conventional to advanced accelerator
  concepts-based colliders

abstract:
  Positron sources are the key elements for the future and current lepton
collider projects such as ILC, CLIC, SuperKEKB, FCC-ee, Muon Collider/LEMMA,
etc., introducing challenging critical requirements for high intensity and low
emittance beams in order to achieve high luminosity. In fact, due to their
large production emittance and constraints given by the target thermal load,
the main collider parameters such as the peak and average current, the
emittances, the damping time, the repetition frequency and consequently the
luminosity are determined by the positron beam characteristics. In this paper,
the conventional positron sources and their main properties are explored for
giving an indication to the challenges that apply during the design of the
advanced accelerator concepts. The photon-driven positron sources as the novel
approach proposed, primarily for the future linear colliders, are described
highlighting their variety and problematic.


title:
One dimensional reflected BSDEs with two barriers under logarithmic
  growth and applications

abstract:
  In this paper we deal with the problem of the existence and the uniqueness of
a solution for one dimensional reflected backward stochastic differential
equations with two strictly separated barriers when the generator is allowing a
logarithmic growth $(|y||\ln|y||+|z|\sqrt{|\ln|z||})$ in the state variables
$y$ and $z$. The terminal value $\xi$ and the obstacle processes $(L_t)_{0\leq
t\leq T}$ and $(U_t)_{0\leq t\leq T}$ are $L^p$-integrable for a suitable $p >
2$. The main idea is to use the concept of local solution to construct the
global one. As applications, we broaden the class of functions for which mixed
zero-sum stochastic differential games admit an optimal strategy and the
related double obstacle partial differential equation problem has a unique
viscosity solution.


title: The Steklov problem on triangle-tiling graphs in hyperbolic space

abstract:
  We introduce a graph $\Gamma$ which is roughly isometric to the hyperbolic
plane and we study the Steklov eigenvalues of a subgraph with boundary
$(\Omega, B)$ of $\Gamma$. For $(\Omega_l, B_l)_{l\geq 1}$ a sequence of
subraph of $\Gamma$ such that $|\Omega_l| \longrightarrow \infty$, we prove
that for each $k \in \mathbb{N}$, the $k^{\mbox{th}}$ eigenvalue tends to $0$
proportionally to $1/|B_l|$. The idea of this proof consists in finding a
bounded domain $(N, \Sigma)$ of the hyperbolic plane which is roughly isometric
to $(\Omega, B)$, giving an upper bound for the Steklov eigenvalues of $(N,
\Sigma)$ and transferring this bound to $(\Omega, B)$ via a process called
discretization.


title: Spherical Transformer

abstract:
  Using convolutional neural networks for 360images can induce sub-optimal
performance due to distortions entailed by a planar projection. The distortion
gets deteriorated when a rotation is applied to the 360image. Thus, many
researches based on convolutions attempt to reduce the distortions to learn
accurate representation. In contrast, we leverage the transformer architecture
to solve image classification problems for 360images. Using the proposed
transformer for 360images has two advantages. First, our method does not
require the erroneous planar projection process by sampling pixels from the
sphere surface. Second, our sampling method based on regular polyhedrons makes
low rotation equivariance errors, because specific rotations can be reduced to
permutations of faces. In experiments, we validate our network on two aspects,
as follows. First, we show that using a transformer with highly uniform
sampling methods can help reduce the distortion. Second, we demonstrate that
the transformer architecture can achieve rotation equivariance on specific
rotations. We compare our method to other state-of-the-art algorithms using the
SPH-MNIST, SPH-CIFAR, and SUN360 datasets and show that our method is
competitive with other methods.


title:
Interpretable pipelines with evolutionarily optimized modules for RL
  tasks with visual inputs

abstract:
  The importance of explainability in AI has become a pressing concern, for
which several explainable AI (XAI) approaches have been recently proposed.
However, most of the available XAI techniques are post-hoc methods, which
however may be only partially reliable, as they do not reflect exactly the
state of the original models. Thus, a more direct way for achieving XAI is
through interpretable (also called glass-box) models. These models have been
shown to obtain comparable (and, in some cases, better) performance with
respect to black-boxes models in various tasks such as classification and
reinforcement learning. However, they struggle when working with raw data,
especially when the input dimensionality increases and the raw inputs alone do
not give valuable insights on the decision-making process. Here, we propose to
use end-to-end pipelines composed of multiple interpretable models co-optimized
by means of evolutionary algorithms, that allows us to decompose the
decision-making process into two parts: computing high-level features from raw
data, and reasoning on the extracted high-level features. We test our approach
in reinforcement learning environments from the Atari benchmark, where we
obtain comparable results (with respect to black-box approaches) in settings
without stochastic frame-skipping, while performance degrades in frame-skipping
settings.


title:
Supervised machine learning to estimate instabilities in chaotic
  systems: estimation of local Lyapunov exponents

abstract:
  In chaotic dynamical systems such as the weather, prediction errors grow
faster in some situations than in others. Real-time knowledge about the error
growth could enable strategies to adjust the modelling and forecasting
infrastructure on-the-fly to increase accuracy and/or reduce computation time.
For example one could change the spatio-temporal resolution of the numerical
model, locally increase the data availability, etc. Local Lyapunov exponents
are known indicators of the rate at which very small prediction errors grow
over a finite time interval. However, their computation is very expensive: it
requires maintaining and evolving a tangent linear model and orthogonalisation
algorithms. In this study, we investigate the capability of supervised machine
learning to estimate the imminent local Lyapunov exponents, from input of
current and recent time steps of the system trajectory. Thus machine learning
is not used here to emulate a physical model or some of its components, but
"non intrusively" as a complementary tool. Specifically, we test the accuracy
of four popular supervised learning algorithms: regression trees, multilayer
perceptrons, convolutional neural networks and long short-term memory networks.
Experiments are conducted on two low-dimensional chaotic systems of ordinary
differential equations, the Lorenz 63 and the R\"ossler models. We find that on
average the machine learning algorithms predict the stable local Lyapunov
exponent accurately, the unstable exponent reasonably accurately, and the
neutral exponent only somewhat accurately. We show that greater prediction
accuracy is associated with local homogeneity of the local Lyapunov exponents
on the system attractor. Importantly, the situations in which (forecast) errors
grow fastest are not necessarily the same as those where it is more difficult
to predict local Lyapunov exponents with machine learning.


title: Computability of finite simplicial complexes

abstract:
  The topological properties of a set have a strong impact on its computability
properties. A striking illustration of this idea is given by spheres and closed
manifolds: if a set $X$ is homeomorphic to a sphere or a closed manifold, then
any algorithm that semicomputes $X$ in some sense can be converted into an
algorithm that fully computes $X$. In other words, the topological properties
of $X$ enable one to derive full information about $X$ from partial information
about $X$. In that case, we say that $X$ has computable type. Those results
have been obtained by Miller, Iljazovi\'c, Su\v{s}i\'c and others in the recent
years. A similar notion of computable type was also defined for pairs $(X,A)$
in order to cover more spaces, such as compact manifolds with boundary and
finite graphs with endpoints.
  We investigate the higher dimensional analog of graphs, namely the pairs
$(X,A)$ where $X$ is a finite simplicial complex and $A$ is a subcomplex of
$X$. We give two topological characterizations of the pairs having computable
type. The first one uses a global property of the pair, that we call the
$\epsilon$-surjection property. The second one uses a local property of
neighborhoods of vertices, called the surjection property. We give a further
characterization for $2$-dimensional simplicial complexes, by identifying which
local neighborhoods have the surjection property.
  Using these characterizations, we give non-trivial applications to two famous
sets: we prove that the dunce hat does not have computable type whereas Bing's
house does. Important concepts from topology, such as absolute neighborhood
retracts and topological cones, play a key role in our proofs.


title:
Introducing screening in one-body density matrix functionals: impact on
  the Extended Koopmans' Theorem's charged excitations of model systems

abstract:
  In this work we get insight into the impact of reduced density matrix
functionals on the quality of removal/addition energies obtained using the
Extended Koopmans' Theorem (EKT). Within reduced density matrix functional
theory (RDMFT) the EKT approach reduces to a matrix diagonalization, whose
ingredients are the one- and two-body reduced density matrices. A striking
feature of the EKT within RDMFT is that it opens a band gap, although too
large, in strongly correlated materials, which are a challenge for
state-of-the-art methods such as GW . Using the one-dimensional Hubbard model
and the homogeneous electron gas as test cases, we find that: i) with exact or
very accurate density matrices the EKT systematically overestimates the band
gap in the Hubbard model and the bandwidth in the homogeneous electron gas; ii)
with approximate density matrices, instead, the EKT can benefit from error
cancellation. In particular we test a new approximation which combines RPA
screening with the Power functional (PF) approximation to the two-body reduced
density matrix introduced by Sharma et al. [Phys. Rev. B 78, 201103(R) (2008)].
An important feature of this approximation is that it reduces the EKT band gap
in the studied models; it can hence be a promising approximation for correcting
the EKT band-gap overestimation in strongly correlated materials.


title:
OWL (Observe, Watch, Listen): Localizing Actions in Egocentric Video via
  Audiovisual Temporal Context

abstract:
  Temporal action localization (TAL) is an important task extensively explored
and improved for third-person videos in recent years. Recent efforts have been
made to perform fine-grained temporal localization on first-person videos.
However, current TAL methods only use visual signals, neglecting the audio
modality that exists in most videos and that shows meaningful action
information in egocentric videos. In this work, we take a deep look into the
effectiveness of audio in detecting actions in egocentric videos and introduce
a simple-yet-effective approach via Observing, Watching, and Listening (OWL) to
leverage audio-visual information and context for egocentric TAL. For doing
that, we: 1) compare and study different strategies for where and how to fuse
the two modalities; 2) propose a transformer-based model to incorporate
temporal audio-visual context. Our experiments show that our approach achieves
state-of-the-art performance on EPIC-KITCHENS-100.


title: Many-body localization in a tilted potential in two dimensions

abstract:
  Thermalization in many-body systems can be inhibited by the application of a
linearly increasing potential, which is known as Stark many-body localization.
Here we investigate the fate of this phenomenon on a two-dimensional
disorder-free lattice with up to $24 \times 6$ sites. Similar to the
one-dimensional case, "density-polarized" regions can act as bottlenecks for
transport and thermalization on laboratory timescales. However, compared to the
one-dimensional case, a substantially stronger potential gradient is needed to
prevent thermalization when an extra spatial dimension is involved. The origin
of this difference and implications for experiments are discussed. We argue
that delocalization is generally favored for typical states in two-dimensional
Stark many-body systems, although nonergodicity can still be observed for a
specific choice of initial states, such as those probed in experiments.


title: A Hot Subdwarf Model for the 18.18 Minute Pulsar GLEAM-X

abstract:
  We suggest that the recently discovered, enigmatic pulsar with a period of
18.18 minutes, GLEAM-X J162759.5-523504.3, is most likely a hot subdwarf (proto
white dwarf). A magnetic dipole model explains the observed period and
period-derivative for a highly magnetized ($\sim 10^8$G), hot subdwarf of
typical mass $\sim 0.5M_\odot$ and radius $\sim 0.3R_\odot$, and an age of
$\sim 3\times 10^4$yr. The subdwarf spin is close to its breakup speed and its
spindown luminosity is near its Eddington limit, likely as a result of
accretion from a companion.


title:
Work-from-home and its implication for project management, resilience
  and innovation -- a global survey on software companies

abstract:
  [Context] The COVID-19 pandemic has had a disruptive impact on how people
work and collaborate across all global economic sectors, including the software
business. While remote working is not new for software engineers, forced
Work-from-home situations to come with both constraints, limitations, and
opportunities for individuals, software teams and software companies. As the
"new normal" for working might be based on the current state of Work From Home
(WFH), it is useful to understand what has happened and learn from that.
[Objective] The goal of this study is to gain insights on how their WFH
environment impacts software projects and software companies. We are also
interested in understanding if the impact differs between software startups and
established companies. [Method] We conducted a global-scale, cross-sectional
survey during spring and summer 2021. Our results are based on quantitative and
qualitative analysis of 297 valid responses. [Results] We observed a mixed
perception of the impact of WFH on software project management, resilience, and
innovation. Certain patterns on WFH, control and coordination mechanisms and
collaborative tools are observed globally. We find that team, agility and
leadership are the three most important factors for achieving resilience during
the pandemic. Although startups do not perceive the impact of WFH differently,
there is a difference between engineers who work in a small team context and
those who work in a large team context. [Conclusion] The result suggests a
contingency approach in studying and improving WFH practices and environment in
the future software industry.


title:
Exact uniform approximation and Dirichlet spectrum in dimension at least
  two

abstract:
  For $m\geq 2$, we determine the Dirichlet spectrum in $\Rm$ with respect to
simultaneous approximation and the maximum norm as the entire interval $[0,1]$.
This complements previous work of several authors, especially Akhunzhanov and
Moshchevitin, who considered $m=2$ and Euclidean norm. We construct explicit
examples of real Liouville vectors realizing any value in the unit interval. In
particular, for positive values, they are neither badly approximable nor
singular. Thereby we obtain a constructive proof of the main claim in a recent
paper by Beresnevich, Guan, Marnat, Ram\'irez and Velani, who obtained a
countable partition of $[0,1]$ into intervals with each having non-empty
intersection with the Dirichlet spectrum. Our construction is flexible enough
to show that the according set of vectors with prescribed Dirichlet exponent
has large packing dimension and rather large Hausdorff dimension as well. We
establish a more general result on exact uniform approximation, applicable to a
wide class of approximating functions. Our constructive proofs are considerably
shorter and less involved than previous work on the topic. By minor twists of
our proof, we infer similar, slightly weaker results when restricting to a
certain class of classical fractal sets or other norms. In an Appendix we
address the situation of a linear form.


title:
Ergodicity and long-time behavior of the Random Batch Method for
  interacting particle systems

abstract:
  We study the geometric ergodicity and the long time behavior of the Random
Batch Method for interacting particle systems, which exhibits superior
numerical performance in recent large-scale scientific computing experiments.
We show that for both the interacting particle system (IPS) and the random
batch interacting particle system (RB-IPS), the distribution laws converge to
their respective invariant distributions exponentially, and the convergence
rate does not depend on the number of particles $N$, the time step $\tau$ for
batch divisions or the batch size $p$. Moreover, the Wasserstein distance
between the invariant distributions of the IPS and the RB-IPS is bounded by
$O(\sqrt{\tau})$, showing that the RB-IPS can be used to sample the invariant
distribution of the IPS accurately with greatly reduced computational cost.


title:
Evaluation of indirect damage and damage saturation effects in
  dose-response curves of hypofractionated radiotherapy of early-stage NSCLC
  and brain metastases

abstract:
  Background and purpose: To investigate the possible contribution of indirect
damage and damage saturation to tumour control obtained with SBRT/SRS
treatments for early-stage NSCLC and brain metastases. Methods and Materials:
We have constructed a dataset of early-stage NSCLC and brain metastases
dose-response. These data were fitted to models based on the linear-quadratic
(LQ), the linear-quadratic-linear (LQL), and phenomenological modifications of
the LQ-model to account for indirect cell damage. We use the
Akaike-Information-Criterion formalism to compare performance, and studied the
stability of the results with changes in fitting parameters and perturbations
on dose/TCP values.
  Results: In NSCLC, a modified LQ-model with a beta-term increasing with dose
yields the best-fits for $\alpha$/$\beta$=10 Gy. Only the inclusion of very
fast accelerated proliferation or low $\alpha$/$\beta$ values can eliminate
such superiority. In brain, the LQL model yields the best-fits, and the ranking
is not affected by variations of fitting parameters or dose/TCP perturbations.
  Conclusions: For $\alpha$/$\beta$=10 Gy, a modified LQ-model with a beta-term
increasing with dose provides better fits to NSCLC dose-response curves. For
brain metastases, the LQL provides the best fit. This might be interpreted as a
hint of indirect damage in NSCLC, and damage saturation in brain metastases.
The results for NSCLC are strongly dependent on the value of $\alpha$/$\beta$
and may require further investigation, while those for brain seem to be clearly
significant. Our results can assist in the design of improved radiotherapy for
NSCLC and brain metastases, aiming at avoiding over/under-treatment.


title:
D2A-BSP: Distilled Data Association Belief Space Planning with
  Performance Guarantees Under Budget Constraints

abstract:
  Unresolved data association in ambiguous and perceptually aliased
environments leads to multi-modal hypotheses on both the robot's and the
environment state. To avoid catastrophic results, when operating in such
ambiguous environments, it is crucial to reason about data association within
Belief Space Planning (BSP). However, explicitly considering all possible data
associations, the number of hypotheses grows exponentially with the planning
horizon and determining the optimal action sequence quickly becomes
intractable. Moreover, with hard budget constraints where some non-negligible
hypotheses must be pruned, achieving performance guarantees is crucial. In this
work we present a computationally efficient novel approach that utilizes only a
distilled subset of hypotheses to solve BSP problems while reasoning about data
association. Furthermore, to provide performance guarantees, we derive error
bounds with respect to the optimal solution. We then demonstrate our approach
in an extremely aliased environment, where we manage to significantly reduce
computation time without compromising on the quality of the solution.


title:
Water flow in single-wall nanotubes: Oxygen makes it slip, hydrogen
  makes it stick

abstract:
  Experimental measurements have reported ultra-fast and radius-dependent water
transport in carbon nanotubes which are absent in boron nitride nanotubes.
Despite considerable effort, the origin of this contrasting (and fascinating)
behaviour is not understood. Here, with the aid of machine learning-based
molecular dynamics simulations that deliver first-principles accuracy, we
investigate water transport in single-wall carbon and boron nitride nanotubes.
Our simulations reveal a large, radius-dependent hydrodynamic slippage on both
materials with water experiencing indeed a $\approx 5$ times lower friction on
carbon surfaces compared to boron nitride. Analysis of the diffusion mechanisms
across the two materials reveals that the fast water transport on carbon is
governed by facile oxygen motion, whereas the higher friction on boron nitride
arises from specific hydrogen-nitrogen interactions. This work not only
delivers a clear reference of unprecedented accuracy for water flow in
single-wall nanotubes, but also provides detailed mechanistic insight into its
radius and material dependence for future technological application.


title: Loss-guided Stability Selection

abstract:
  In modern data analysis, sparse model selection becomes inevitable once the
number of predictors variables is very high. It is well-known that model
selection procedures like the Lasso or Boosting tend to overfit on real data.
The celebrated Stability Selection overcomes these weaknesses by aggregating
models, based on subsamples of the training data, followed by choosing a stable
predictor set which is usually much sparser than the predictor sets from the
raw models. The standard Stability Selection is based on a global criterion,
namely the per-family error rate, while additionally requiring expert knowledge
to suitably configure the hyperparameters. Since model selection depends on the
loss function, i.e., predictor sets selected w.r.t. some particular loss
function differ from those selected w.r.t. some other loss function, we propose
a Stability Selection variant which respects the chosen loss function via an
additional validation step based on out-of-sample validation data, optionally
enhanced with an exhaustive search strategy. Our Stability Selection variants
are widely applicable and user-friendly. Moreover, our Stability Selection
variants can avoid the issue of severe underfitting which affects the original
Stability Selection for noisy high-dimensional data, so our priority is not to
avoid false positives at all costs but to result in a sparse stable model with
which one can make predictions. Experiments where we consider both regression
and binary classification and where we use Boosting as model selection
algorithm reveal a significant precision improvement compared to raw Boosting
models while not suffering from any of the mentioned issues of the original
Stability Selection.


title:
Constructing graphs having Laplacian pair state transfer by an edge
  perturbation

abstract:
  In this paper, we give some sufficient conditions for graphs with an edge
perturbation between twin vertices to have Laplacian perfect pair state
transfer as well as Laplacian pretty good pair state transfer. By those
sufficient conditions, we also construct many new graphs having Laplacian
perfect pair state transfer as well as Laplacian pretty good pair state
transfer.


title:
Sound masking degrades perception of self-location during stepping: A
  case for sound-transparent spacesuits for Mars

abstract:
  Most efforts to improve spacesuits have been directed towards adding haptic
feedback. However, sound transparency can also improve situational awareness at
a relatively low cost. The extent of the improvement is unknown. We use the
Fukuda-Unterberger stepping test to measure the accuracy of one's perception of
self-location. We compare accuracy outcomes in two scenarios: one where hearing
is impaired with sound masking with white noise and one where it is not. These
scenarios are acoustic proxies for a sound muffling space suit and a sound
transparent space suit respectively. The results show that when sound masking
is applied, the error in self-location increases by 14.5cm, 95% CI [4.04
28.22]. Suggestions to apply the findings to Mars spacesuit designs are
discussed. A cost-benefit analysis is also provided.


title: Nonlocal effects in temporal metamaterials

abstract:
  Nonlocality is a fundamental concept in photonics. For instance, nonlocal
wave-matter interactions in spatially modulated metamaterials enable novel
effects, such as giant electromagnetic chirality, artificial magnetism, and
negative refraction. Here, we investigate the effects induced by spatial
nonlocality in {\em temporal} metamaterials, i.e., media with a dielectric
permittivity rapidly modulated in time. Via a rigorous multiscale approach, we
introduce a general and compact formalism for the nonlocal effective medium
theory of temporally periodic metamaterials. In particular, we study two
scenarios: {\em i)} a periodic temporal modulation, and {{\em ii)}} a temporal
boundary where the permittivity is abruptly changed in time and subject to
periodic modulation. We show that these configurations can give rise to
peculiar nonlocal effects, and we highlight the similarities and differences
with respect to the spatial-metamaterial counterparts. Interestingly, by
tailoring the effective boundary wave-matter interactions, we also identify an
intriguing configuration for which a temporal metamaterial can perform the
first-order derivative of an incident wavepacket. Our theoretical results,
backed by full-wave numerical simulations, introduce key physical ingredients
that may pave the way for novel applications. By fully exploiting the
time-reversal symmetry breaking, nonlocal temporal metamaterials promise a
great potential for efficient, tunable optical computing devices.


title: Extension of the result by Han J. K., Lee H. Y. and Lee W. Y

abstract:
  We extend well known result of Han J. K., Lee H. Y. and Lee W. Y.
\cite[Theorem 5.2]{HAN} related to invertibility of operator matrices to case
of $3\times3$ upper triangular operator matrices. We provide necessary and
sufficient conditions for invertibility in the framework of arbitrary Banach
spaces, and explain under which additional assumption these conditions become
equivalent. At the end, we construct an illustrating example to show that
without additional assumption equivalence does not hold even in separable
Hilbert spaces. Our main tools are ghost of an index theorem due to Harte
\cite{HARTE}, \cite{HARTE2} and technique of Banach space embeddings introduced
by the first author \cite{OPERATORTHEORY}.


title: Monotonically Convergent Regularization by Denoising

abstract:
  Regularization by denoising (RED) is a widely-used framework for solving
inverse problems by leveraging image denoisers as image priors. Recent work has
reported the state-of-the-art performance of RED in a number of imaging
applications using pre-trained deep neural nets as denoisers. Despite the
recent progress, the stable convergence of RED algorithms remains an open
problem. The existing RED theory only guarantees stability for convex
data-fidelity terms and nonexpansive denoisers. This work addresses this issue
by developing a new monotone RED (MRED) algorithm, whose convergence does not
require nonexpansiveness of the deep denoising prior. Simulations on image
deblurring and compressive sensing recovery from random matrices show the
stability of MRED even when the traditional RED algorithm diverges.


title:
Feasible Low-thrust Trajectory Identification via a Deep Neural Network
  Classifier

abstract:
  In recent years, deep learning techniques have been introduced into the field
of trajectory optimization to improve convergence and speed. Training such
models requires large trajectory datasets. However, the convergence of low
thrust (LT) optimizations is unpredictable before the optimization process
ends. For randomly initialized low thrust transfer data generation, most of the
computation power will be wasted on optimizing infeasible low thrust transfers,
which leads to an inefficient data generation process. This work proposes a
deep neural network (DNN) classifier to accurately identify feasible LT
transfer prior to the optimization process. The DNN-classifier achieves an
overall accuracy of 97.9%, which has the best performance among the tested
algorithms. The accurate low-thrust trajectory feasibility identification can
avoid optimization on undesired samples, so that the majority of the optimized
samples are LT trajectories that converge. This technique enables efficient
dataset generation for different mission scenarios with different spacecraft
configurations.


title:
The Noise Covariances of Linear Gaussian Systems with Unknown Inputs Are
  Not Uniquely Identifiable Using Autocovariance Least-squares

abstract:
  Existing works in optimal filtering for linear Gaussian systems with
arbitrary unknown inputs assume perfect knowledge of the noise covariances in
the filter design. This is impractical and raises the question of whether and
under what conditions one can identify the noise covariances of linear Gaussian
systems with arbitrary unknown inputs. This paper considers the above
identifiability question using the correlation-based autocovariance
least-squares (ALS) approach. In particular, for the ALS framework, we prove
that (i) the process noise covariance Q and the measurement noise covariance R
cannot be uniquely jointly identified; (ii) neither Q nor R is uniquely
identifiable, when the other is known. This not only helps us to have a better
understanding of the applicability of existing filtering frameworks under
unknown inputs (since almost all of them require perfect knowledge of the noise
covariances) but also calls for further investigation of alternative and more
viable noise covariance methods under unknown inputs. Especially, it remains to
be explored whether the noise covariances are uniquely identifiable using other
correlation-based methods. We are also interested to use regularization for
noise covariance estimation under unknown inputs, and investigate the relevant
property guarantees for the covariance estimates. The above topics are the main
subject of our current and future work.


title:
Forecasting large-scale circulation regimes using deformable
  convolutional neural networks and global spatiotemporal climate data

abstract:
  Classifying the state of the atmosphere into a finite number of large-scale
circulation regimes is a popular way of investigating teleconnections, the
predictability of severe weather events, and climate change. Here, we
investigate a supervised machine learning approach based on deformable
convolutional neural networks (deCNNs) and transfer learning to forecast the
North Atlantic-European weather regimes during extended boreal winter for 1 to
15 days into the future. We apply state-of-the-art interpretation techniques
from the machine learning literature to attribute particular regions of
interest or potential teleconnections relevant for any given weather cluster
prediction or regime transition. We demonstrate superior forecasting
performance relative to several classical meteorological benchmarks, as well as
logistic regression and random forests. Due to its wider field of view, we also
observe deCNN achieving considerably better performance than regular
convolutional neural networks at lead times beyond 5-6 days. Finally, we find
transfer learning to be of paramount importance, similar to previous
data-driven atmospheric forecasting studies.


title:
$\Gamma$-Convergence of an Ambrosio-Tortorelli approximation scheme for
  image segmentation

abstract:
  Given an image $u_0$, the aim of minimising the Mumford-Shah functional is to
find a decomposition of the image domain into sub-domains and a piecewise
smooth approximation $u$ of $u_0$ such that $u$ varies smoothly within each
sub-domain. Since the Mumford-Shah functional is highly non-smooth,
regularizations such as the Ambrosio-Tortorelli approximation can be considered
which is one of the most computationally efficient approximations of the
Mumford-Shah functional for image segmentation. Our main result is the
$\Gamma$-convergence of the Ambrosio-Tortorelli approximation of the
Mumford-Shah functional for piecewise smooth approximations. This requires the
introduction of an appropriate function space. As a consequence of our
$\Gamma$-convergence result, we can infer the convergence of minimizers of the
respective functionals.


title: Real-Time Siamese Multiple Object Tracker with Enhanced Proposals

abstract:
  Maintaining the identity of multiple objects in real-time video is a
challenging task, as it is not always possible to run a detector on every
frame. Thus, motion estimation systems are often employed, which either do not
scale well with the number of targets or produce features with limited semantic
information. To solve the aforementioned problems and allow the tracking of
dozens of arbitrary objects in real-time, we propose SiamMOTION. SiamMOTION
includes a novel proposal engine that produces quality features through an
attention mechanism and a region-of-interest extractor fed by an inertia module
and powered by a feature pyramid network. Finally, the extracted tensors enter
a comparison head that efficiently matches pairs of exemplars and search areas,
generating quality predictions via a pairwise depthwise region proposal network
and a multi-object penalization module. SiamMOTION has been validated on five
public benchmarks, achieving leading performance against current
state-of-the-art trackers.


title: First-principles molecular dynamics simulation of liquid indium

abstract:
  We report an ab-initio simulation of liquid Indium in a wide range of
pressures and temperatures. We calculate equation of state, thermal expansion
and compressibility coefficients. The structure of the system is analyzed by
radial distribution functions and structure factors. The results are compared
with available experimental data.


title: Quantum Corrections to the Stochastic Gravitational Wave Background

abstract:
  We study 1-loop corrections to the primordial stochastic background of
gravitational waves produced during inflation. While in single-clock, at the
leading order in slow-roll, quantum corrections keep the amplitude scale-free
this is not the case when the pattern of symmetry breaking is different. In
particular, when spatial diffeomorphisms are also broken during inflation as
for solid inflation, a log-running in the external momentum is generated. We
relate the appearance of a log-running to the spontaneous breaking of
dilatation invariance. The running could be instrumental to distinguish
single-clock from alternative models of inflation in future high sensitivity
CMB polarisation and GWs experiments.


title: A model for boundary dynamics of Baker domains

abstract:
  We consider the transcendental entire function $ f(z)=z+e^{-z} $, which has a
doubly parabolic Baker domain $U$ of degree two, i.e. an invariant stable
component for which all iterates converge locally uniformly to infity, and for
which the hyperbolic distance between successive iterates converges to zero. It
is known from general results that the dynamics on the boundary is ergodic and
recurrent and that the set of points in $\partial U$ whose orbit escapes to
infity has zero harmonic measure. For this model we show that stronger results
hold, namely that this escaping set is non-empty, it is organized in curves
encoded by some symbolic dynamics, whose closure is precisely $\partial U$. We
also prove that nevertheless, all escaping points in $\partial U$ are
non-accessible from $U$, as opposed to points in $\partial U$ having a bounded
orbit, which are all accessible. Moreover, repelling periodic points are shown
to be dense in @U, answering a question posted Baranski, Fagella, Jarque and
Karpinska. None of these features are known to occur for a general doubly
parabolic Baker domain.


title:
Off-Policy Fitted Q-Evaluation with Differentiable Function
  Approximators: Z-Estimation and Inference Theory

abstract:
  Off-Policy Evaluation (OPE) serves as one of the cornerstones in
Reinforcement Learning (RL). Fitted Q Evaluation (FQE) with various function
approximators, especially deep neural networks, has gained practical success.
While statistical analysis has proved FQE to be minimax-optimal with tabular,
linear and several nonparametric function families, its practical performance
with more general function approximator is less theoretically understood. We
focus on FQE with general differentiable function approximators, making our
theory applicable to neural function approximations. We approach this problem
using the Z-estimation theory and establish the following results: The FQE
estimation error is asymptotically normal with explicit variance determined
jointly by the tangent space of the function class at the ground truth, the
reward structure, and the distribution shift due to off-policy learning; The
finite-sample FQE error bound is dominated by the same variance term, and it
can also be bounded by function class-dependent divergence, which measures how
the off-policy distribution shift intertwines with the function approximator.
In addition, we study bootstrapping FQE estimators for error distribution
inference and estimating confidence intervals, accompanied by a Cramer-Rao
lower bound that matches our upper bounds. The Z-estimation analysis provides a
generalizable theoretical framework for studying off-policy estimation in RL
and provides sharp statistical theory for FQE with differentiable function
approximators.


title:
ASRPU: A Programmable Accelerator for Low-Power Automatic Speech
  Recognition

abstract:
  The outstanding accuracy achieved by modern Automatic Speech Recognition
(ASR) systems is enabling them to quickly become a mainstream technology. ASR
is essential for many applications, such as speech-based assistants, dictation
systems and real-time language translation. However, highly accurate ASR
systems are computationally expensive, requiring on the order of billions of
arithmetic operations to decode each second of audio, which conflicts with a
growing interest in deploying ASR on edge devices. On these devices, hardware
acceleration is key for achieving acceptable performance. However, ASR is a
rich and fast-changing field, and thus, any overly specialized hardware
accelerator may quickly become obsolete.
  In this paper, we tackle those challenges by proposing ASRPU, a programmable
accelerator for on-edge ASR. ASRPU contains a pool of general-purpose cores
that execute small pieces of parallel code. Each of these programs computes one
part of the overall decoder (e.g. a layer in a neural network). The accelerator
automates some carefully chosen parts of the decoder to simplify the
programming without sacrificing generality. We provide an analysis of a modern
ASR system implemented on ASRPU and show that this architecture can achieve
real-time decoding with a very low power budget.


title:
IHGNN: Interactive Hypergraph Neural Network for Personalized Product
  Search

abstract:
  A good personalized product search (PPS) system should not only focus on
retrieving relevant products, but also consider user personalized preference.
Recent work on PPS mainly adopts the representation learning paradigm, e.g.,
learning representations for each entity (including user, product and query)
from historical user behaviors (aka. user-product-query interactions). However,
we argue that existing methods do not sufficiently exploit the crucial
collaborative signal, which is latent in historical interactions to reveal the
affinity between the entities. Collaborative signal is quite helpful for
generating high-quality representation, exploiting which would benefit the
representation learning of one node from its connected nodes.
  To tackle this limitation, in this work, we propose a new model IHGNN for
personalized product search. IHGNN resorts to a hypergraph constructed from the
historical user-product-query interactions, which could completely preserve
ternary relations and express collaborative signal based on the topological
structure. On this basis, we develop a specific interactive hypergraph neural
network to explicitly encode the structure information (i.e., collaborative
signal) into the embedding process. It collects the information from the
hypergraph neighbors and explicitly models neighbor feature interaction to
enhance the representation of the target entity. Extensive experiments on three
real-world datasets validate the superiority of our proposal over the
state-of-the-arts.


title:
Floquet-Landau-Zener interferometry: Usefulness of the Floquet theory in
  pulse-laser-driven systems

abstract:
  We develop the Landau-Zener transfer matrix theory for the instantaneous
Floquet states (IFSs) for quantum systems driven by strong pulse lasers.
Applying this theory to the pulse excitation probability in two-level quantum
systems, we show unexpectedly good quantitative agreements for few-cycle
pulses. This approach enables us to qualitatively understand the probability's
peculiar behaviors as quantum path interference between IFSs. We also study the
pulse-width dependence, finding that this Floquet-state interpretation remains
useful for shorter pulses down to 2-cycle ones in the present model. These
results imply that the Floquet theory is meaningful in experimental few-cycle
lasers if applied appropriately in the sense of IFSs.

categories: cond-mat.mes-hall cond-mat.quant-gas cond-mat.stat-mech physics.optics quant-ph


title: Scattering of plane-wave and twisted photons by helical media

abstract:
  By using quantum electrodynamics in a dispersive medium, we describe
scattering of plane-wave and twisted photons by a slab made of a helical
medium, the helix axis being normal to the slab plane and the medium being not
translation invariant in this plane, in general. In the particular cases, the
permittivity tensor of a helical medium corresponds to cholesteric liquid
crystals, $C^*$-smectics, biaxial chiral nematics and smectics, $q$-plates,
chiral sculptured thin films, and helical dislocations. Both perturbative and
nonperturbative approaches are considered. The explicit expressions for
scattering amplitudes, probabilities, and Stokes parameters of photons are
found taking into account the form of the photon wave packet. The selection
rules are established showing that the helical medium transfers the momentum
and the angular momentum to scattered photons. This property can be employed
for production of twisted photons with large projection of the total angular
momentum. We describe the device for shifting the projection of the total
angular momentum of a photon and the principal scheme for signal coding in
terms of twisted photons.


title:
FedAttack: Effective and Covert Poisoning Attack on Federated
  Recommendation via Hard Sampling

abstract:
  Federated learning (FL) is a feasible technique to learn personalized
recommendation models from decentralized user data. Unfortunately, federated
recommender systems are vulnerable to poisoning attacks by malicious clients.
Existing recommender system poisoning methods mainly focus on promoting the
recommendation chances of target items due to financial incentives. In fact, in
real-world scenarios, the attacker may also attempt to degrade the overall
performance of recommender systems. However, existing general FL poisoning
methods for degrading model performance are either ineffective or not concealed
in poisoning federated recommender systems. In this paper, we propose a simple
yet effective and covert poisoning attack method on federated recommendation,
named FedAttack. Its core idea is using globally hardest samples to subvert
model training. More specifically, the malicious clients first infer user
embeddings based on local user profiles. Next, they choose the candidate items
that are most relevant to the user embeddings as hardest negative samples, and
find the candidates farthest from the user embeddings as hardest positive
samples. The model gradients inferred from these poisoned samples are then
uploaded to the server for aggregation and model update. Since the behaviors of
malicious clients are somewhat similar to users with diverse interests, they
cannot be effectively distinguished from normal clients by the server.
Extensive experiments on two benchmark datasets show that FedAttack can
effectively degrade the performance of various federated recommender systems,
meanwhile cannot be effectively detected nor defended by many existing methods.


title: Fast Muon Tracking with Machine Learning Implemented in FPGA

abstract:
  In this work, we present a new approach for fast tracking on multiwire
proportional chambers with neural networks. The tracking networks are developed
and adapted for the first-level trigger at hadron collider experiments. We use
Monte-Carlo samples generated by Geant4 with a custom muon chamber, which
resembles part of the Thin Gap Chambers from the ATLAS experiment, for training
and performance evaluations. The chamber has in total seven layers, where the
first and the last layers are displaced by about 1.5 m. Each layer has 50
channels with a size of 18-20 mm. Two neural network models are developed and
presented: a convolutional neural network and a neural network optimised for
the detector configuration of this study. In the latter network, a
convolutional layer is provided for each of three groups formed from 2-3 layers
of the chamber, and the outputs are fed into multilayer perceptrons in
sequence. Both networks are transformed into hardware description language and
implemented in Virtex UltraScale+ FPGA. The angular resolution is 2 mrad, which
is comparable to the maximum resolution of the detector estimated by a minimum
chi2 method. The latency achieved by the implemented firmware is less than 100
ns, and the throughput rate is 160 MHz.


title: Needs-aware Artificial Intelligence: AI that 'serves [human] needs'

abstract:
  Many boundaries are, and will continue to, shape the future of Artificial
Intelligence (AI). We push on these boundaries in order to make progress, but
they are both pliable and resilient--always creating new boundaries of what AI
can (or should) achieve. Among these are technical boundaries (such as
processing capacity), psychological boundaries (such as human trust in AI
systems), ethical boundaries (such as with AI weapons), and conceptual
boundaries (such as the AI people can imagine). It is within this final
category while it can play a fundamental role in all other boundaries} that we
find the construct of needs and the limitations that our current concept of
need places on the future AI.


title:
Towards Assessing and Characterizing the Semantic Robustness of Face
  Recognition

abstract:
  Deep Neural Networks (DNNs) lack robustness against imperceptible
perturbations to their input. Face Recognition Models (FRMs) based on DNNs
inherit this vulnerability. We propose a methodology for assessing and
characterizing the robustness of FRMs against semantic perturbations to their
input. Our methodology causes FRMs to malfunction by designing adversarial
attacks that search for identity-preserving modifications to faces. In
particular, given a face, our attacks find identity-preserving variants of the
face such that an FRM fails to recognize the images belonging to the same
identity. We model these identity-preserving semantic modifications via
direction- and magnitude-constrained perturbations in the latent space of
StyleGAN. We further propose to characterize the semantic robustness of an FRM
by statistically describing the perturbations that induce the FRM to
malfunction. Finally, we combine our methodology with a certification
technique, thus providing (i) theoretical guarantees on the performance of an
FRM, and (ii) a formal description of how an FRM may model the notion of face
identity.


title: Observability of triple top quark signal at Future Hadron Colliders

abstract:
  This paper is devoted to the Standard Model cross-sections for the production
of single top, top quark in pairs, triple-top quarks, and four top-quarks at
three different centre of mass-energies e.g., $\sqrt{s}=$7, 10 and 14 TeV at
existing particle colliders as well as at Future Hadron Colliders. A fully
kinemtaic analysis with the optimized pre-selection cuts along with invariant
mass reconstruction of top quarks is performed for triple-top production
processes pp$\rightarrow $tttW, tttd,tttb in the presence of Standard Model
background. The three signal processes are forced to decay in fully hadronic
mode and their significance is computed in High Luminosity Large Hadron
Collider (HL$-$LHC) at $\sqrt{s}=$14 TeV and also in High-Energy LHC (HE$-$LHC)
at $\sqrt{s}=$27 TeV. It is found that the observability at HL$-$LHC will would
not be so easy task and chances are much lower but there are higher chances to
observe the signal events at HE$-$LHC. The signal to background ratio and
signal significance of all signal and background processes are estimated for
both the HL$-$LHC and the HE$-$LHC at $\sqrt{s}$ =14 TeV and $\sqrt{s}$ =27 TeV
respectively.


title:
The Magidor Iteration and Restrictions of Ultrapowers to the Ground
  Model

abstract:
  We study the Magidor iteration of Prikry forcings below a measurable limit of
measurables $ \kappa $. We first characterize all the normal measures $ \kappa
$ carries in the generic extension, building on and extending the main result
of \cite{ben2014forcing}. Then, for every such normal measure, we prove that
the restriction of its ultrapower, from the generic extension to the ground
model, is an iterated ultrapower of $ V $ by normal measures. This is done
without core model theoretic assumptions; $ \mbox{GCH}_{\leq \kappa} $ in the
ground model suffices.


title: Barwise Compression Schemes for Audio-Based Music Structure Analysis

abstract:
  Music Structure Analysis (MSA) consists in segmenting a music piece in
several distinct sections. We approach MSA within a compression framework,
under the hypothesis that the structure is more easily revealed by a simplified
representation of the original content of the song. More specifically, under
the hypothesis that MSA is correlated with similarities occurring at the bar
scale, this article introduces the use of linear and non-linear compression
schemes on barwise audio signals. Compressed representations capture the most
salient components of the different bars in the song and are then used to infer
the song structure using a dynamic programming algorithm. This work explores
both low-rank approximation models such as Principal Component Analysis or
Nonnegative Matrix Factorization and "piece-specific" Auto-Encoding Neural
Networks, with the objective to learn latent representations specific to a
given song. Such approaches do not rely on supervision nor annotations, which
are well-known to be tedious to collect and possibly ambiguous in MSA
description. In our experiments, several unsupervised compression schemes
achieve a level of performance comparable to that of state-of-the-art
supervised methods (for 3s tolerance) on the RWC-Pop dataset, showcasing the
importance of the barwise compression processing for MSA.


title: A Robust Version of Heged\H{u}s's Lemma, with Applications

abstract:
  Heged\H{u}s's lemma is the following combinatorial statement regarding
polynomials over finite fields. Over a field $\F$ of characteristic $p > 0$ and
for $q$ a power of $p$, the lemma says that any multilinear polynomial $P\in
\F[x_1,\ldots,x_n]$ of degree less than $q$ that vanishes at all points in
$\{0,1\}^n$ of Hamming weight $k\in [q,n-q]$ must also vanish at all points in
$\{0,1\}^n$ of weight $k + q$. This lemma was used by Heged\H{u}s (2009) to
give a solution to \emph{Galvin's problem}, an extremal problem about set
systems; by Alon, Kumar and Volk (2018) to improve the best-known multilinear
circuit lower bounds; and by Hrube\v{s}, Ramamoorthy, Rao and Yehudayoff (2019)
to prove optimal lower bounds against depth-$2$ threshold circuits for
computing some symmetric functions.
  In this paper, we formulate a robust version of Heged\H{u}s's lemma.
Informally, this version says that if a polynomial of degree $o(q)$ vanishes at
most points of weight $k$, then it vanishes at many points of weight $k+q$. We
prove this lemma and give three different applications.


title:
Magnetic phase diagram and cluster glass-like properties of stage-1
  graphite intercalated FeCl$_3$

abstract:
  We present a comprehensive investigation of the magnetic properties of
stage-1 graphite intercalated FeCl$_3$ using a combination of DC and AC
magnetic susceptibility, thermoremanent magnetization and field dependent
magnetization measurements. This van der Waals system, with a centrosymmetric
honeycomb lattice, combines frustration and disorder, due to intercalation, and
may be hosting topologically non-trivial magnetic phases. Our study identifies
two magnetic phase transitions at $T_{f1} \approx $ 4.2 K and at $T_{f2}
\approx $ 2.7 K. We find that the paramagnetic state, for $T > T_{f1}$, is
dominated by short-range ferromagnetic correlations. These build up well above
$T_{f1}$ and lead to a significant change in magnetic entropy, which reaches
$\Delta S_M^{Pk} = $ -5.52 J kg$^{-1}$ K$^{-1}$ at 7 T. Between $T_{f1}$ and
$T_{f2}$ we observe slow spin dynamics characteristic of a cluster glass-like
state, whereas for $T$ $ < $ $T_{f2}$ our results indicate the onset of a low
temperature long range ordered state. The analysis of the experimental results
leads to a complex phase diagram, which may serve as a reference for future
investigations searching for topological non-trivial phases in this system.


title: Strong density of spherical characters attached to unipotent subgroups

abstract:
  We prove the following result in relative representation theory of a
reductive p-adic group $G$:
  Let $U$ be the unipotent radical of a minimal parabolic subgroup of $G$, and
let $\psi$ be an arbitrary smooth character of $U$. Let $S \subset Irr(G)$ be a
Zariski dense collection of irreducible representations of $G$. Then the span
of the Bessel distributions $B_{\pi}$ attached to representations $\pi$ from
$S$ is dense in the space $\mathcal S^*(G)^{U\times U,\psi \times \psi}$ of all
$(U\times U,\psi \times \psi)$-equivariant distributions on $G.$
  We base our proof on the following results:
  1. The category of smooth representations $\mathcal M(G)$ is Cohen-Macaulay.
  2. The module $ind_U^G(\psi)$ is a projective module.


title: Generalization Bounds via Convex Analysis

abstract:
  Since the celebrated works of Russo and Zou (2016,2019) and Xu and Raginsky
(2017), it has been well known that the generalization error of supervised
learning algorithms can be bounded in terms of the mutual information between
their input and the output, given that the loss of any fixed hypothesis has a
subgaussian tail. In this work, we generalize this result beyond the standard
choice of Shannon's mutual information to measure the dependence between the
input and the output. Our main result shows that it is indeed possible to
replace the mutual information by any strongly convex function of the joint
input-output distribution, with the subgaussianity condition on the losses
replaced by a bound on an appropriately chosen norm capturing the geometry of
the dependence measure. This allows us to derive a range of generalization
bounds that are either entirely new or strengthen previously known ones.
Examples include bounds stated in terms of $p$-norm divergences and the
Wasserstein-2 distance, which are respectively applicable for heavy-tailed loss
distributions and highly smooth loss functions. Our analysis is entirely based
on elementary tools from convex analysis by tracking the growth of a potential
function associated with the dependence measure and the loss function.


title: Enhanced Digital Halftoning via Weighted Sigma-Delta Modulation

abstract:
  In this paper, we study error diffusion techniques for digital halftoning
from the perspective of 1-bit Sigma-Delta quantization. We introduce a method
to generate Sigma-Delta schemes for two-dimensional signals as a weighted
combination of its one-dimensional counterparts and show that various error
diffusion schemes proposed in the literature can be represented in this
framework via Sigma-Delta schemes of first order. Under the model of
two-dimensional bandlimited signals, which is motivated by a mathematical model
of human visual perception, we derive quantitative error bounds for such
weighted Sigma-Delta schemes. We see these bounds as a step towards a
mathematical understanding of the good empirical performance of error
diffusion, even though they are formulated in the supremum norm, which is known
to not fully capture the visual similarity of images.
  Motivated by the correspondence between existing error diffusion algorithms
and first-order Sigma-Delta schemes, we study the performance of the analogous
weighted combinations of second-order Sigma-Delta schemes and show that they
exhibit a superior performance in terms of guaranteed error decay for
two-dimensional bandlimited signals. In extensive numerical simulations for
real world images, we demonstrate that with some modifications to enhance
stability this superior performance also translates to the problem of digital
halftoning.
  More concretely, we find that certain second-order weighted Sigma-Delta
schemes exhibit competitive performance for digital halftoning of real world
images in terms of the Feature Similarity Index (FSIM), a state-of-the-art
measure for image quality assessment.


title:
Ignition limit and shock-to-detonation transition mode of n-heptane/air
  mixture in high-speed wedge flows

abstract:
  In this work, oblique detonation of n-heptane/air mixture in high-speed wedge
flows is simulated by solving the reactive Euler equations with a
two-dimensional (2D) configuration. This is a first attempt to model
complicated hydrocarbon fuel ODWs with a detailed chemistry (44 species and 112
reactions). Effects of freestream equivalence ratios and velocities are
considered, and the abrupt and smooth transition from oblique shock to
detonation are predicted. Ignition limit, ODW characteristics, and
predictability of the transition mode are discussed. Firstly, homogeneous
constant-volume ignition calculations are performed for both fuel-lean and
stoichiometric mixtures. The results show that the ignition delay generally
increases with the wedge angle. However, a negative wedge angle dependence is
observed, due to the negative temperature coefficient effects. The wedge angle
range for successful ignition of n-heptane/air mixtures decreases when the
wedge length is reduced. From 2D simulations of stationary ODWs, the initiation
length generally decreases with the freestream equivalence ratio, but the
transition length exhibits weakly non-monotonic dependence. Smooth ODW
typically occurs for lean conditions (equivalence ratio < 0.4). The
interactions between shock / compression waves and chemical reaction inside the
induction zone are also studied with the chemical explosive mode analysis.
Moreover, the predictability of the shock-to-detonation transition mode is
explored through quantifying the relation between ignition delay and chemical
excitation time. It is demonstrated that the ignition delay (excitation time)
increases (decreases) with the freestream equivalence ratio for the three
studied oncoming flow velocities. Smaller excitation time corresponds to
stronger pressure waves from the ignition location behind OSW.


title: Group Testing on General Set-Systems

abstract:
  Group testing is one of the fundamental problems in coding theory and
combinatorics in which one is to identify a subset of contaminated items from a
given ground set. There has been renewed interest in group testing recently due
to its applications in diagnostic virology, including pool testing for the
novel coronavirus. The majority of existing works on group testing focus on the
\emph{uniform} setting in which any subset of size $d$ from a ground set $V$ of
size $n$ is potentially contaminated. In this work, we consider a {\em
generalized} version of group testing with an arbitrary set-system of
potentially contaminated sets. The generalized problem is characterized by a
hypergraph $H=(V,E)$, where $V$ represents the ground set and edges $e\in E$
represent potentially contaminated sets. The problem of generalized group
testing is motivated by practical settings in which not all subsets of a given
size $d$ may be potentially contaminated, rather, due to social dynamics,
geographical limitations, or other considerations, there exist subsets that can
be readily ruled out. For example, in the context of pool testing, the edge set
$E$ may consist of families, work teams, or students in a classroom, i.e.,
subsets likely to be mutually contaminated. The goal in studying the
generalized setting is to leverage the additional knowledge characterized by
$H=(V,E)$ to significantly reduce the number of required tests. The paper
considers both adaptive and non-adaptive group testing and makes the following
contributions. First, for the non-adaptive setting, we show that finding an
optimal solution for the generalized version of group testing is NP-hard. For
this setting, we present a solution that requires $O(d\log{|E|})$ tests, where
$d$ is the maximum size of a set $e \in E$. Our solutions generalize those
given for the traditional setting and are shown to be of order-optimal size
$O(\log{|E|})$ for hypergraphs with edges that have ``large'' symmetric
differences. For the adaptive setting, when edges in $E$ are of size exactly
$d$, we present a solution of size $O(\log{|E|}+d\log^2{d})$ that comes close
to the lower bound of $\Omega(\log{|E|} + d)$.


title: Semi-Supervised Convolutive NMF for Automatic Piano Transcription

abstract:
  Automatic Music Transcription, which consists in transforming an audio
recording of a musical performance into symbolic format, remains a difficult
Music Information Retrieval task. In this work, which focuses on piano
transcription, we propose a semi-supervised approach using low-rank matrix
factorization techniques, in particular Convolutive Nonnegative Matrix
Factorization. In the semi-supervised setting, only a single recording of each
individual notes is required. We show on the MAPS dataset that the proposed
semi-supervised CNMF method performs better than state-of-the-art low-rank
factorization techniques and a little worse than supervised deep learning
state-of-the-art methods, while however suffering from generalization issues.