  In order to improve the understanding of damage evolution in mechanically
heterogeneous microstructures, like the ones of dual-phase steels, the
influence of the applied stress state is a key element. In this work, we
studied the influence of the globally applied stress state on the evolution of
damage in such a microstructure. Classical damage models allow predictions of
damage during deformation based on considerations of the material as an
isotropic continuum. Here, we investigate their validity in a dual phase
microstructure that is locally dominated by its microstructural morphological
complexity based on a statistical ensemble of thousands of individual voids
formed under different stress states. For this purpose, we combined a
calibrated material model incorporating damage formation to assess the local
stress state in samples with different notch geometries and high-resolution
electron microscopy of large areas using a deep learning-based automated
micrograph analysis to detect and classify microstructural voids according to
their source of origin. This allowed us to obtain both the continuum stress
state during deformation and statistically relevant data of individual void
formation. We found that the applied plastic strain is the major influence on
the overall number, and therefore the nucleation of new voids, while
triaxiality correlates with the median void size, supporting its proposed
influence on void growth. In contrast, coalescence of voids leading to failure
appears related to local instabilities in the form of shear band formation and
is therefore only indirectly determined by the global stress state in that it
determines the global distribution, density and size of voids.


  To explore the nature of the metallic state near the transition to a Mott
insulator we investigate the t-J model with random exchange interaction in
d=infinity dimensions. A numerically exact solution is obtained by an extension
of the continuous-time quantum Monte Carlo (CT-QMC) method to the case of a
vector bosonic field coupled to a local spin. We show that the paramagnetic
solution near the Mott insulator describes an incoherent metal with a residual
moment, and that single-particle excitations produce an additional band, which
is separated from the Mott-Hubbard band.


  The supernova remnant (SNR) RX J1713.7$-$3946 is one of the best-studied
accelerators of cosmic rays because of its strong nonthermal X-ray and
gamma-ray radiation. We have analyzed accumulated \chandra\ observations with a
total exposure time of $\sim$266 ks in the northwest rim of RX J1713.7$-$3946.
We detect a substantially large number of point-like sources, referred to as
``hotspots'', which are likely associated with the remnant. The spectra of the
hotspots are well described by an absorbed power-law model. The spectral
properties ($10^{21}\ \mathrm{cm^{-2}}\lesssim N_H \lesssim 10^{23}\
\mathrm{cm^{-2}}$ and $ 0.5\lesssim \Gamma \lesssim 6$) are different from
diffuse X-ray emission in RX J1713.7$-$3946, and the harder hotspot tends to
have the larger $N_H$. We also confirm yearly and monthly variabilities of flux
for some hotspots. We propose that RX J1713.7$-$3946 is embedded in a complex
surroundings where some dense molecular clumps and cores exist inside a
wind-blown cavity, and that the hotspot traces synchrotron emission caused by
an interaction of shock waves of the SNR and dense molecular cores with a
number density of $10^{5}-10^{7}~ \mathrm{cm}^{-3}$. The X-ray radiation of the
hotspot might be emitted from both primary electrons accelerated at the shocks
and secondary electrons produced by the interaction of accelerated protons with
the cores.


  The study of the possibility of existence of the non-propagating, trapped
continental shelf waves (CSWs)along curved coasts reduces mathematically to a
spectral problem for a self-adjoint operator pencil in a curved strip. Using
the methods developed in the setting of the waveguide trapped mode problem, we
show that such CSWs exist for a wide class of coast curvature and depth
profiles.


  Egocentric interaction recognition aims to recognize the camera wearer's
interactions with the interactor who faces the camera wearer in egocentric
videos. In such a human-human interaction analysis problem, it is crucial to
explore the relations between the camera wearer and the interactor. However,
most existing works directly model the interactions as a whole and lack
modeling the relations between the two interacting persons. To exploit the
strong relations for egocentric interaction recognition, we introduce a dual
relation modeling framework which learns to model the relations between the
camera wearer and the interactor based on the individual action representations
of the two persons. Specifically, we develop a novel interactive LSTM module,
the key component of our framework, to explicitly model the relations between
the two interacting persons based on their individual action representations,
which are collaboratively learned with an interactor attention module and a
global-local motion module. Experimental results on three egocentric
interaction datasets show the effectiveness of our method and advantage over
state-of-the-arts.


  It is known that a Bloch domain wall in an anisotropic ferromagnet is
transparent to spin waves. This result is derived by approximating the dipolar
interaction between magnetic moments by an effective anisotropy interaction. In
this paper we study the the scattering of spin waves by a domain wall taking
into account the full complexity of the dipolar interaction, treating it
perturbatively in the distorted wave Born approximation. Due to the
peculiarities of the dipolar interaction, the implementation of this
approximation is not straightforward. The difficulties are circumvented here by
realizing that the contribution of the dipolar interaction to the spin wave
operator can be split into two terms: i) an operator that commutes with the
spin wave operator in absence of dipolar interaction, and ii) a local operator
suitable to be treated as a perturbation in the distorted wave Born
approximaton. We analyze the scattering parameters obtained within this
approach. It turns out that the reflection coefficient does not vanish in
general, and that the transmitted waves suffer a lateral shift even at normal
incidence. This lateral shift can be greatlty enhanced by making the spin wave
go through an array of well separated domain walls. The outgoing spin wave will
no be attenuated by the scattering at the domain walls since the reflection
coefficient vanishes at normal incidence. This effect may be very useful to
control the spin waves in magnonic devices.


  We introduce SupercheQ, a family of quantum protocols that achieves
asymptotic advantage over classical protocols for checking the equivalence of
files, a task also known as fingerprinting. The first variant, SupercheQ-EE
(Efficient Encoding), uses n qubits to verify files with 2^O(n) bits -- an
exponential advantage in communication complexity (i.e. bandwidth, often the
limiting factor in networked applications) over the best possible classical
protocol in the simultaneous message passing setting. Moreover, SupercheQ-EE
can be gracefully scaled down for implementation on circuits with poly(n^l)
depth to enable verification for files with O(n^l) bits for arbitrary constant
l. The quantum advantage is achieved by random circuit sampling, thereby
endowing circuits from recent quantum supremacy and quantum volume experiments
with a practical application. We validate SupercheQ-EE's performance at scale
through GPU simulation. The second variant, SupercheQ-IE (Incremental
Encoding), uses n qubits to verify files with O(n^2) bits while supporting
constant-time incremental updates to the fingerprint. Moreover, SupercheQ-IE
only requires Clifford gates, ensuring relatively modest overheads for
error-corrected implementation. We experimentally demonstrate proof-of-concepts
through Qiskit Runtime on IBM quantum hardware. We envision SupercheQ could be
deployed in distributed data settings, accompanying replicas of important
databases.


  The Auger Engineering Radio Array (AERA), at the Pierre Auger Observatory in
Argentina, measures the radio emission of extensive air showers in the 30-80
MHz frequency range. AERA consists of more than 150 antenna stations
distributed over 17 km$^2$. Together with the Auger surface detector, the
fluorescence detector and the under-ground muon detector (AMIGA), AERA is able
to measure cosmic rays with energies above 10$^{17}$ eV in a hybrid detection
mode. AERA is optimized for the detection of air showers up to 60$^{\circ}$
zenith angle, however, using the reconstruction of horizontal air showers with
the Auger surface array, very inclined showers can also be measured. In this
contribution an analysis of the AERA data in the zenith angle range from
62$^{\circ}$ to 80$^{\circ}$ will be presented. CoREAS simulations predict
radio emission footprints of several km$^2$ for horizontal air showers, which
are now confirmed by AERA measurements. This can lead to radio-based
composition measurements and energy determination of horizontal showers in the
future and the radio detection of neutrino induced showers is possible.


  We establish a combination theorem for parafree groups. These groups were
introduced by Baumslag in the sixties. One of the current motivations for a
better understanding of their structure is that they show up naturally in
connection with Remeslennikov's conjecture on the profinite rigidity of free
groups. In this article, we determine when the fundamental group of a finite
graph of groups with cyclic edge groups is parafree.


  This paper studies a recent proposal to use randomized value functions to
drive exploration in reinforcement learning. These randomized value functions
are generated by injecting random noise into the training data, making the
approach compatible with many popular methods for estimating parameterized
value functions. By providing a worst-case regret bound for tabular
finite-horizon Markov decision processes, we show that planning with respect to
these randomized value functions can induce provably efficient exploration.


  This work presents an embodied agent that can adapt its semantic segmentation
network to new indoor environments in a fully autonomous way. Because semantic
segmentation networks fail to generalize well to unseen environments, the agent
collects images of the new environment which are then used for self-supervised
domain adaptation. We formulate this as an informative path planning problem,
and present a novel information gain that leverages uncertainty extracted from
the semantic model to safely collect relevant data. As domain adaptation
progresses, these uncertainties change over time and the rapid learning
feedback of our system drives the agent to collect different data. Experiments
show that our method adapts to new environments faster and with higher final
performance compared to an exploration objective, and can successfully be
deployed to real-world environments on physical robots.


  The field just West of the galactic supernova remnant W28
  (l=6.4\degr, b=-0.2\degr) harbors 3 of 5 newly-discovered 1720 OH maser spots
and two recently-discovered candidate supernova candidates (one of which is a
$\gamma$-ray source), as well as several compact and classical HII regions.
Here, we analyze a datacube of CO J=1-0 emission having 1\arcmin and 1 \kms
resolution, made with on-the-fly mapping over the region $5\degr \le l \le
6\degr, -1\degr \le b \le 0.5\degr$}. {Extended and often very bright CO
emission was detected at the velocities of the 1720 MHz OH masers and around
the supernova remnant G5.55+0.32 which lacks a maser. A new bipolar outflow
which is marginally resolved at 1\arcmin resolution and strong in CO (12K) was
detected at the periphery of G5.55+0.32, coincident with an MSX source; there
is also a bright rim of CO just beyond the periphery of the radio remnant. The
OH maser near G5.71-0.08 lies on a shell of strongly-emitting molecular gas (up
to 20K) . At the -21 \kms velocity of G5.4-1.2, CO covers much of the field but
is weak (3 K) and undisturbed near the remnant. The extended molecular gas
around the compact H II region and outflow in G5.89-0.39 (W28A2) is shown for
the first time.}


  We study small-scale and high-frequency turbulent fluctuations in
three-dimensional flows under Fourier-mode reduction. The Navier-Stokes
equations are evolved on a restricted set of modes, obtained as a projection on
a fractal or homogeneous Fourier set. We find a strong sensitivity (reduction)
of the high-frequency variability of the Lagrangian velocity fluctuations on
the degree of mode decimation, similarly to what is already reported for
Eulerian statistics. This is quantified by a tendency towards a quasi-Gaussian
statistics, i.e., to a reduction of intermittency, at all scales and
frequencies. This can be attributed to a strong depletion of vortex filaments
and of the vortex stretching mechanism. Nevertheless, we found that Eulerian
and Lagrangian ensembles are still connected by a dimensional bridge-relation
which is independent of the degree of Fourier-mode decimation.


  We consider the problem of minimising an inhomogeneous anisotropic elliptic
functional in a class of closed $m$ dimensional subsets of $\mathbf{R}^n$ which
is stable under taking smooth deformations homotopic to the identity and under
local Hausdorff limits. We prove that the minimiser exists inside the class and
is an $(\mathscr{H}^m,m)$~rectifiable set in the sense of Federer. The class of
competitors encodes a notion of spanning a boundary. We admit unrectifiable and
non-compact competitors and boundaries, and we make no restrictions on the
dimension $m$ and the co-dimension $n-m$ other than $1 \le m < n$. An important
tool for the proof is a novel smooth deformation theorem. The skeleton of the
proof and the main ideas follow Almgren's 1968 paper. In the end we show that
classes of sets spanning some closed set $B$ in homological and cohomological
sense satisfy our axioms.


  Fundamental experimental measurements of quantities such as ignition delay
times, laminar flame speeds, and species profiles (among others) serve
important roles in understanding fuel chemistry and validating chemical kinetic
models. However, despite both the importance and abundance of such information
in the literature, the community lacks a widely adopted standard format for
this data. This impedes both sharing and wide use by the community. Here we
introduce a new chemical kinetics experimental data format, ChemKED, and the
related Python-based package for validating and working with ChemKED-formatted
files called PyKED. We also review past and related efforts, and motivate the
need for a new solution. ChemKED currently supports the representation of
autoignition delay time measurements from shock tubes and rapid compression
machines. ChemKED-formatted files contain all of the information needed to
simulate experimental data points, including the uncertainty of the data.
ChemKED is based on the YAML data serialization language, and is intended as a
human- and machine-readable standard for easy creation and automated use.
Development of ChemKED and PyKED occurs openly on GitHub under the BSD 3-clause
license, and contributions from the community are welcome. Plans for future
development include support for experimental data from laminar flame, jet
stirred reactor, and speciation measurements.


  We recently proposed a new ensemble clustering algorithm for graphs (ECG)
based on the concept of consensus clustering. We validated our approach by
replicating a study comparing graph clustering algorithms over benchmark
graphs, showing that ECG outperforms the leading algorithms. In this paper, we
extend our comparison by considering a wider range of parameters for the
benchmark, generating graphs with different properties. We provide new
experimental results showing that the ECG algorithm alleviates the well-known
resolution limit issue, and that it leads to better stability of the
partitions. We also illustrate how the ensemble obtained with ECG can be used
to quantify the presence of community structure in the graph, and to zoom in on
the sub-graph most closely associated with seed vertices. Finally, we
illustrate further applications of ECG by comparing it to previous results for
community detection on weighted graphs, and community-aware anomaly detection.


  Although redistribution of red blood cells at bifurcated vessels is highly
dependent on flow rate, it is still challenging to quantitatively express the
dependency of flow rate in plasma skimming due to nonlinear cellular
interactions. We suggest a plasma skimming model that can involve the effect of
fractional blood flow at each bifurcation point. For validating the new model,
it is compared with \textit{in vivo} data at single bifurcation points, as well
as microvascular network systems. In the simulation results, the exponential
decay of plasma skimming parameter, $M$, along fractional flow rate shows the
best performance in both cases.


  The process of data interpretation is always based on the implicit
introduction of equivalence relations on the set of walks over the database.
Every equivalence relation on the set of walks specifies a Markov chain
describing the transitions of a discrete time random walk. In order to
geometrize and interpret the data, we propose the new distance between data
units defined as a "Feynman path integral", in which all possible paths between
any two nodes in a graph model of the data are taken into account, although
some paths are more preferable than others. Such a path integral distance
approach to the analysis of databases has proven its efficiency and success,
especially on multivariate strongly correlated data where other methods fail to
detect structural components (urban planning, historical language phylogenies,
music, street fashion traits analysis, etc. ). We believe that it would become
an invaluable tool for the intelligent complexity reduction and big data
interpretation.


  Measures of discordance between datasets have become an essential part of
cosmological analyses. It is important to accurately evaluate the significance
of such discordances when present. We propose here a Bayesian interpretation of
inconsistency measures that can extract information about physical
inconsistencies in the presence of data scatter. The new framework is based on
the conditional probability distribution of the level of physical inconsistency
given the obtained value of the measure. We use the index of inconsistency as a
case study to illustrate the new interpretation framework, but this can be
generalized to other metrics. Importantly, there are two aspects in the
quantification of inconsistency that behave differently as the number of model
parameters increases. The first is the probability for the level of physical
inconsistency to reach a threshold which drops with the increase of the number
of parameters under consideration. Then the second is the actual level of
physical inconsistency which remains rather insensitive to such an increase in
parameters. This often-overlooked ambiguity leads to an underestimation of the
physical inconsistency by the commonly adopted significance level when used,
but is resolved by the Bayesian interpretation because the conditional
probability distribution includes all the statistical information of the level
of physical inconsistency. Finally, we apply the Bayesian interpretation to
examine the (in)consistency between Planck versus the Cepheid-based local
measurement, the Dark Energy Survey (DES), the Atacama Cosmology Telescope
(ACT) and WMAP. We confirm and revisit the degrees of previous physical
inconsistencies and show the stability of the new interpretation to the number
of cosmological parameters compared to the commonly used n-$\sigma$
interpretation when applied to cosmological tensions in multi-parameter spaces.


  We study risk-sensitive imitation learning where the agent's goal is to
perform at least as well as the expert in terms of a risk profile. We first
formulate our risk-sensitive imitation learning setting. We consider the
generative adversarial approach to imitation learning (GAIL) and derive an
optimization problem for our formulation, which we call it risk-sensitive GAIL
(RS-GAIL). We then derive two different versions of our RS-GAIL optimization
problem that aim at matching the risk profiles of the agent and the expert
w.r.t. Jensen-Shannon (JS) divergence and Wasserstein distance, and develop
risk-sensitive generative adversarial imitation learning algorithms based on
these optimization problems. We evaluate the performance of our algorithms and
compare them with GAIL and the risk-averse imitation learning (RAIL) algorithms
in two MuJoCo and two OpenAI classical control tasks.


  We show that, for a natural notion of quasirandomness in $k$-uniform
hypergraphs, any quasirandom $k$-uniform hypergraph on $n$ vertices with
constant edge density and minimum vertex degree $\Omega(n^{k-1})$ contains a
loose Hamilton cycle. We also give a construction to show that a $k$-uniform
hypergraph satisfying these conditions need not contain a Hamilton $\ell$-cycle
if $k-\ell$ divides $k$. The remaining values of $\ell$ form an interesting
open question.


  We prove that if $G$ is a finitely generated RFRS group of cohomological
dimension $2$, then $G$ is virtually free-by-cyclic if and only if
$b_2^{(2)}(G) = 0$. This answers a question of Wise and generalises and gives a
new proof of a recent theorem of Kielak and Linton, where the same result is
obtained under the additional hypotheses that $G$ is virtually compact special
and hyperbolic. More generally, we show that if $G$ is a RFRS group of
cohomological dimension $n$ and of type $\mathrm{FP}_{n-1}$, then $G$ admits a
virtual map to $\mathbb Z$ with kernel of rational cohomological dimension
$n-1$ if and only if $b_n^{(2)}(G) = 0$.


  As we showed in [3], a geometric inequality can be regarded as an
optimization problem. In this paper we find another proof for a Chen's
inequality,regarding the Ricci curvature [2] and we improve this inequality in
the Lagrangian case.


  We propose a new kernel for Metropolis Hastings called Directional Metropolis
Hastings (DMH) with multivariate update where the proposal kernel has state
dependent covariance matrix. We use the derivative of the target distribution
at the current state to change the orientation of the proposal distribution,
therefore producing a more plausible proposal. We study the conditions for
geometric ergodicity of our algorithm and provide necessary and sufficient
conditions for convergence. We also suggest a scheme for adaptively update the
variance parameter and study the conditions of ergodicity of the adaptive
algorithm. We demonstrate the performance of our algorithm in a Bayesian
generalized linear model problem.


  The electronic anomalous Hall effect (AHE), where charge carriers acquire a
velocity component orthogonal to an applied electric field, is one of the most
fundamental and widely studied phenomena in physics. There are several
different AHE mechanisms known, and material examples are highly sought after,
however in the highly conductive (skew scattering) regime the focus has
centered around ferromagnetic metals. Here we report the observation of a giant
extrinsic AHE in KV$_3$Sb$_5$, an exfoliable, Dirac semimetal with a Kagome
layer of Vanadium atoms. Although there has been no reports of magnetic
ordering down to 0.25 K, the anomalous Hall conductivity (AHC) reaches
$\approx$ 15,507 $\Omega^{-1}$cm$^{-1}$ with an anomalous Hall ratio (AHR) of
$\approx$ 1.8$ \%$; an order of magnitude larger than Fe. Defying expectations
from skew scattering theory, KV$_3$Sb$_5$ shows an enhanced skew scattering
effect that scales quadratically, not linearly, with the longitudinal
conductivity ($\sigma_{xx}$), opening the possibility of reaching an anomalous
Hall angle (AHA) of 90$^{\circ}$ in metals; an effect thought reserved for
quantum anomalous Hall insulators. This observation raises fundamental
questions about the AHE and opens a new frontier for AHE (and correspondingly
SHE) exploration, stimulating investigation in a new direction of materials,
including metallic geometrically frustrated magnets, spin-liquid candidates,
and cluster magnets.


  In the phased-array radar (PAR) signals from each antenna are transmitted at
the same carrier frequency, which yields narrowly focused only angle dependent
beampattern. In contrast, in the frequency-diverse-array (FDA) radar signals
from antenna array are generally transmitted at linearly increasing frequencies
that yields range, time, and angle dependent beampattern. Reported literature
on FDA radar missed the contribution of path-differences in the signal model
due to the antenna array elements, which may lead to misleading results. In
this work, incorporating missed path-differences, the signal model of FDA radar
is corrected. Using the corrected signal model, it is shown that the
instantaneous beampattern depends on the number of transmit antenna and average
beampattern depends on the product of frequency-offset and pulse-duration.
Moreover, to illuminate the desired region-of-interest for longer dwell time,
discrete-Fourier-transform based low-complexity algorithm is proposed. In
contrast to the conventional FDA radar's 'S' shaped beampattern, the
beampattern of the proposed algorithm changes linearly with range. Simulation
results compare the performance of our proposed algorithm with the existing
ones and show the superiority of our proposed algorithm.


  This work presents indirect searches for dark matter (DM) as WIMPs (Weakly
Interacting Massive Particles) using neutrino data recorded by the
Super-Kamiokande detector from 1996 to 2014. The results of the search for
WIMP-induced neutrinos from the Sun and the Milky Way are discussed. We looked
for an excess of neutrinos from the Sun/Milky Way direction compared to the
expected atmospheric neutrino background. Event samples including both electron
and muon neutrinos covering a wide range of neutrino energies (GeV to TeV) were
used, with sensitivity to WIMP masses down to tens of GeV. Various WIMP
annihilation modes were taken into account in the analyses.


  We develop the Ostrogradsky-Hamilton formalism for geodetic brane gravity,
described by the Regge-Teitelboim geometric model in higher codimension. We
treat this gravity theory as a second-order derivative theory, based on the
extrinsic geometric structure of the model. As opposed to previous treatments
of geodetic brane gravity, our Lagrangian is linearly dependent on second-order
time derivatives of the field variables, the embedding functions. The
difference resides in a boundary term in the action, usually discarded.
Certainly, this suggests applying an appropriate Ostrogradsky-Hamiltonian
approach to this type of theories. The price to pay for this choice is the
appearance of second class constraints. We determine the full set of phase
space constraints, as well as the gauge transformations they generate in the
reduced phase space. Additionally, we compute the algebra of constraints and
explain its physical content. In the same spirit, we deduce the counting of the
physical degrees of freedom. We comment briefly on the naive formal canonical
quantization emerging from our development.


  Not all quantum protocols require entanglement to outperform their classical
alternatives. The nonclassical correlations that lead to this quantum advantage
are conjectured to be captured by quantum discord. Here we demonstrate that
discord can be explicitly used as a resource: certifying untrusted entangling
gates without generating entanglement at any stage. We implement our protocol
in the single-photon regime, and show its success in the presence of high
levels of noise and imperfect gate operations. Our technique offers a practical
method for benchmarking entangling gates in physical architectures in which
only highly-mixed states are available.


  This work presents CascadeCNN, an automated toolflow that pushes the
quantisation limits of any given CNN model, to perform high-throughput
inference by exploiting the computation time-accuracy trade-off. Without the
need for retraining, a two-stage architecture tailored for any given FPGA
device is generated, consisting of a low- and a high-precision unit. A
confidence evaluation unit is employed between them to identify misclassified
cases at run time and forward them to the high-precision unit or terminate
computation. Experiments demonstrate that CascadeCNN achieves a performance
boost of up to 55% for VGG-16 and 48% for AlexNet over the baseline design for
the same resource budget and accuracy.


  We present the new results for the generalised double-logarithmic equation,
obtained from the analytical continuation of the seven-loop anomalous dimension
of twist-2 operators in the planar N=4 SYM theory. The double-logarithmic
equation is related to the special asymptotic of the scattering amplitudes,
when the large logarithms of the energy of scattering particles are appeared
and should be summed in all order of perturbative theory. These large
logarithms correspond to the poles of the analytically continued anomalous
dimension. The generalised double-logarithmic equation includes the subleading
logarithms. We have found, that the expansion of the generalised
double-logarithmic equation can be ressumed in the form of rational functions
with simple denominator. The solution of the generalised double-logarithmic
equation provides a lot of information about the poles of the analytically
continued anomalous dimension in all orders of perturbative theory. We have
found also the generalised double-logarithmic equation for the analytically
continued anomalous dimension near the value, which is related with
BFKL-equation.


  Large information sizes in samples and features can be encoded to speed up
the learning of statistical models based on linear algebra and remove unwanted
signals. Encoding information can reduce both sample and feature dimension to a
smaller representational set. Here two examples are shown on linear mixed
models and mixture models speeding up the run time for parameter estimation by
a factor defined by the user's choice on dimension reduction (can be linear,
quadratic or beyond based on dimension specification).


  For a discrete group G, we consider the minimal C*-subalgebra of
$\ell^\infty(G)$ that arises as the image of a unital positive G-equivariant
projection. This algebra always exists and is unique up to isomorphism. It is
trivial if and only if G is amenable. We prove that, more generally, it can be
identified with the algebra $C(\partial_F G)$ of continuous functions on
Furstenberg's universal G-boundary $\partial_F G$.
  This operator-algebraic construction of the Furstenberg boundary has a number
of interesting consequences. We prove that G is exact precisely when the
G-action on $\partial_F G$ is amenable, and use this fact to prove Ozawa's
conjecture that if G is exact, then there is an embedding of the reduced
C*-algebra $\mathrm{C}_r^*(G)$ of G into a nuclear C*-algebra which is
contained in the injective envelope of $\mathrm{C}_r^*(G)$.
  It is a longstanding open problem to determine which groups are C*-simple, in
the sense that the algebra $\mathrm{C}_r^*(G)$ is simple. We prove that this
problem can be reformulated as a problem about the structure of the G-action on
the Furstenberg boundary. Specifically, we prove that a discrete group G is
C*-simple if and only if the G-action on the Furstenberg boundary is
topologically free. We apply this result to prove that Tarski monster groups
are C*-simple. This provides another solution to a problem of de la Harpe
(recently answered by Olshanskii and Osin) about the existence of C*-simple
groups with no free subgroups.


  We consider a stack of parallel sheets composed of conducting planes with
tensorial conductivities. Using the scattering matrix approach, we derive
explicit formulas for the Casimir energy of two, three, and four planes, as
well as a recurrence relation for arbitrary planes. Specifically, for a stack
of graphene, we solve the recurrence relations and obtain formulas for the
Casimir energy and force acting on the planes within the stack. Moreover, we
calculate the binding energy in the graphene stack with graphite interplane
separation, which amounts to $E_{ib} = 9.9$ meV/atom. Notably, the Casimir
force on graphene sheets decreases rapidly for planes beyond the first one. In
particular, for the second graphene layer in the stack, the force is $35$ times
smaller than that experienced by the first layer.


  Starting from 2003, the discovery of a large amount of the so-called exotic
hadronic states, i.e., the $XYZ$ states, the pentaquark states as well as the
tetraquark states, have not only revived studies of hadron spectroscopy, but
also hinted at the existence of new multi-hadron states made of hadrons other
than nucleons and hyperons. We briefly comment on some of the latest studies on
multi-hadron molecules in the light and heavy flavor sectors and highlight what
should be done in the future.


  Sulfur and nitrogen dual doped graphene have been extensively investigated in
the field of oxygen reduction reaction, supercapacitors and batteries, but
their magnetic and absorption performance have not been explored. Besides, the
effects of doping sequence of sulfur and nitrogen atoms on the morphology,
structural property and the corresponding microwave absorption performance of
the dual doped graphene remain unexplored. In this work, nitrogen and sulfur
dual doped graphene with different doping sequence were successfully prepared
using a controllable two steps facile thermal treatment method. The first
doping process played a decisive role on the morphology, crystal size,
interlayer distance, doping degree and ultimately magnetic and microwave
absorption properties of the dual doped graphene samples. Meanwhile, the second
doping step affected the doping sites and further had a repairing or damaging
effect on the final doped graphene. The dual doped graphene samples exhibited
two pronounced absorption peaks which intensity was decided by the order of the
doping elements. This nitrogen and sulfur dual doped graphene with controlled
doping order provides a strategy for understanding of the interaction between
nitrogen and sulfur as dual dopants in graphene and further acquiring microwave
absorbing materials with tunable absorption bands by varying the doping
sequence.


  This contribution is the chapter 2 of the book "geodetic time series
analysis" (10.1007/978-3-030-21718-1). The book is dedicated to the art of
fitting a trajectory model to those geodetic time series in order to extract
accurate geophysical information with realistic error bars in geodymanics and
environmental geodesy related studies. In the vast amount of the literature
published on this topic in the past 25 years, we are specifically interested in
parametric algorithms which are estimating both functional and stochastic
models using various Bayesian statistical tools (maximum likelihood, Monte
Carlo Markov chain, Kalman filter, least squares variance component estimation,
information criteria). This chapter will focus on how the parameters of the
trajectory model can be estimated. It is meant to give researchers new to this
topic an easy introduction to the theory with references to key books and
articles where more details can be found. In addition, we hope that it
refreshes some of the details for the more experienced readers. We pay special
attention to the modelling of the noise which has received much attention in
the literature in the last years and highlight some of the numerical aspects.


  This paper gives a brief review on the recent work on fractional Klein-Gordon
fields, in particular on the Casimir effect associated to fractional
Klein-Gordon fields in various geometries and boundary conditions. New results
on Casimir piston due to a fractional Klein-Gordon massive field are given.


  We consider the problem of estimating the difference between two functional
undirected graphical models with shared structures. In many applications, data
are naturally regarded as high-dimensional random function vectors rather than
multivariate scalars. For example, electroencephalography (EEG) data are more
appropriately treated as functions of time. In these problems, not only can the
number of functions measured per sample be large, but each function is itself
an infinite dimensional object, making estimation of model parameters
challenging. We develop a method that directly estimates the difference of
graphs, avoiding separate estimation of each graph, and show it is consistent
in certain high-dimensional settings. We illustrate finite sample properties of
our method through simulation studies. Finally, we apply our method to EEG data
to uncover differences in functional brain connectivity between alcoholics and
control subjects.


  We present the Arcminute Microkelvin Imager (AMI) Large Array catalogue of
139 gamma-ray bursts (GRBs). AMI observes at a central frequency of 15.7 GHz
and is equipped with a fully automated rapid-response mode, which enables the
telescope to respond to high-energy transients detected by Swift. On receiving
a transient alert, AMI can be on-target within two minutes, scheduling later
start times if the source is below the horizon. Further AMI observations are
manually scheduled for several days following the trigger. The AMI GRB
programme probes the early-time (< 1 day) radio properties of GRBs, and has
obtained some of the earliest radio detections (GRB 130427A at 0.36 and GRB
130907A at 0.51 days post-burst). As all Swift GRBs visible to AMI are
observed, this catalogue provides the first representative sample of GRB radio
properties, unbiased by multi-wavelength selection criteria. We report the
detection of six GRB radio afterglows that were not previously detected by
other radio telescopes, increasing the rate of radio detections by 50% over an
18-month period. The AMI catalogue implies a Swift GRB radio detection rate of
>15%, down to ~0.2 mJy/beam. However, scaling this by the fraction of GRBs AMI
would have detected in the Chandra & Frail sample (all radio-observed GRBs
between 1997 - 2011), it is possible ~44 - 56% of Swift GRBs are radio-bright,
down to ~0.1 - 0.15 mJy/beam. This increase from the Chandra & Frail rate
(~30%) is likely due to the AMI rapid-response mode, which allows observations
to begin while the reverse-shock is contributing to the radio afterglow.


  There are some existence problems of Jenkins-Strebel differentials on a
Riemann surface. The one of them is to find a Jenkins-Strebel differential
whose characteristic ring domains have given positive numbers as their
circumferences, for any fixed underlying Riemann surface and core curves of the
ring domains. However, the solution may not exist for some given underlying
surface, core curves, and positive numbers. In this paper, we investigate the
existence of such the solutions. Our method is to use the surface of
circumferences, which is determined by the extremal problem for Jenkins-Strebel
differentials. We can see degenerations of the characteristic ring domains of
Jenkins-Strebel differentials by the surface. Moreover, we also consider the
behavior of the surface when the underlying Riemann surface varies.


  Continuous time Bayesian networks are investigated with a special focus on
their ability to express causality. A framework is presented for doing
inference in these networks. The central contributions are a representation of
the intensity matrices for the networks and the introduction of a causality
measure. A new model for high-frequency financial data is presented. It is
calibrated to market data and by the new causality measure it performs better
than older models.


  Let G be a simple graph on $n$ vertices and $e(G)$ edges. Consider $Q(G) = D
+ A$ as the signless Laplacian of $G$, where $A$ is the adjacency matrix and
$D$ is the diagonal matrix of the vertices degree of $G$. Let $q_1(G)$ and
$q_2(G)$ be the first and the second largest eigenvalues of $Q(G),$
respectively, and denote by $S_{n}^{+}$ the star graph plus one edge. In this
paper, we prove that inequality $q_1(G)+ q_2(G) <= e(G)+3$ is tighter for the
graph $S_{n}^{+}$ among all firefly graphs and also tighter to $S_{n}^{+}$ than
to the graphs $K_{k} \vee \overline{K_{n-k}}$ recently presented by Ashraf,
Omidi and Tayfeh-Rezaie. Also, we conjecture that the same inequality is
tighter to $S_{n}^{+}$ than any other graph on $n$ vertices.


  In the next few years, the first detections of gravity-wave signals using
Earth-based interferometric detectors will begin to provide precious new
information about the structure and dynamics of compact bodies such as neutron
stars. The intrinsic weakness of gravity-wave signals requires a proactive
approach to modeling the prospective sources and anticipating the shape of the
signals that we seek to detect. Full-blown 3-D numerical simulations of the
sources are playing and will play an important role in planning the
gravity-wave data-analysis effort. I review some recent analytical and
numerical work on neutron stars as sources of gravity waves.


  We study spherical scalar collapse toward a black hole formation and examine
the asymptotic dynamics near the central singularity of the formed black hole.
It is found that, in the vicinity of the singularity, due to the strong
backreaction of a scalar field on the geometry, the mass function inflates and
the Kretschmann scalar grows faster than in the Schwarzschild geometry. In
collapse, the Misner-Sharp mass is a locally conserved quantity, not providing
information on the black hole mass that is measured at asymptotically flat
regions.


  We present a proof of the explicit formula for the asymptotically free
eigenfunctions of the $B_N$ $q$-Toda operator which was conjectured by the
first and third authors. This formula can be regarded as a branching formula
from the $B_N$ $q$-Toda eigenfunction restricted to the $A_{N-1}$ $q$-Toda
eigenfunctions. The proof is given by a contigulation relation of the $A_{N-1}$
Toda eigenfunctions and a recursion relation of the branching coefficients.


  We study bordism groups and bordism homology theories based on
pseudomanifolds and stratified pseudomanifolds. The main seam of the paper
demonstrates that when we uses classes of spaces determined by local link
properties, the stratified and unstratified bordism theories are identical;
this includes the known examples of pseudomanifold bordism theories, such as
bordism of Witt spaces and IP spaces. Along the way, we relate the stratified
and unstratified points of view for describing various (stratified)
pseudomanifold classes.


  We construct solutions of an infinite Toda system and an analogue of the
Painlev'e II equation over noncommutative differential division rings in terms
of quasideterminants of Hankel matrices.


  Cell image analysis is crucial in Alzheimer's research to detect the presence
of A$\beta$ protein inhibiting cell function. Deep learning speeds up the
process by making only low-level data sufficient for fruitful inspection. We
first found Unet is most suitable in augmented microscopy by comparing
performance in multi-class semantics segmentation. We develop the augmented
microscopy method to capture nuclei in a brightfield image and the transformer
using Unet model to convert an input image into a sequence of topological
information. The performance regarding Intersection-over-Union is consistent
concerning the choice of image preprocessing and ground-truth generation.
Training model with data of a specific cell type demonstrates transfer learning
applies to some extent.
  The topological transformer aims to extract persistence silhouettes or
landscape signatures containing geometric information of a given image of
cells. This feature extraction facilitates studying an image as a collection of
one-dimensional data, substantially reducing computational costs. Using the
transformer, we attempt grouping cell images by their cell type relying solely
on topological features. Performances of the transformers followed by SVM,
XGBoost, LGBM, and simple convolutional neural network classifiers are inferior
to the conventional image classification. However, since this research
initiates a new perspective in biomedical research by combining deep learning
and topology for image analysis, we speculate follow-up investigation will
reinforce our genuine regime.


  High-order parametric models that include terms for feature interactions are
applied to various data mining tasks, where ground truth depends on
interactions of features. However, with sparse data, the high- dimensional
parameters for feature interactions often face three issues: expensive
computation, difficulty in parameter estimation and lack of structure. Previous
work has proposed approaches which can partially re- solve the three issues. In
particular, models with factorized parameters (e.g. Factorization Machines) and
sparse learning algorithms (e.g. FTRL-Proximal) can tackle the first two issues
but fail to address the third. Regarding to unstructured parameters,
constraints or complicated regularization terms are applied such that
hierarchical structures can be imposed. However, these methods make the
optimization problem more challenging. In this work, we propose Strongly
Hierarchical Factorization Machines and ANOVA kernel regression where all the
three issues can be addressed without making the optimization problem more
difficult. Experimental results show the proposed models significantly
outperform the state-of-the-art in two data mining tasks: cold-start user
response time prediction and stock volatility prediction.


  A 45 deg2 radio continuum imaging campaign of the nearest radio galaxy,
Centaurus A, is reported. Using the Australia Telescope Compact Array and the
Parkes 64m radio telescope at 1.4 GHz, the spatial resolution of the resultant
image is ~600 pc, resolving the ~500 kpc giant radio lobes with approximately
five times better physical resolution compared to any previous image, and
making this the most detailed radio continuum image of any radio galaxy to
date. In this paper, we present these new data and discuss briefly some of the
most interesting morphological features that we have discovered in the
images... abstract truncated.


  We present results from long-term optical photometric observations of the
Pre-Main Sequence (PMS) stars, located in the star formation region around the
bright nebula NGC 7129. Using the long-term light curves and spectroscopic
data, we tried to classify the PMS objects in the field and to define the
reasons for the observed brightness variations. Our main goal is to explore the
known PMS stars and discover new, young, variable stars. The new variable PMS
star 2MASS J21403576+6635000 exhibits unusual brightness variations for very
short time intervals (few minutes or hours) with comparatively large amplitudes
(Delta I = 2.65 mag).


  Alzheimer's disease (AD) is an incurable neurodegenerative condition leading
to cognitive and functional deterioration. Given the lack of a cure, prompt and
precise AD diagnosis is vital, a complex process dependent on multiple factors
and multi-modal data. While successful efforts have been made to integrate
multi-modal representation learning into medical datasets, scant attention has
been given to 3D medical images. In this paper, we propose Contrastive Masked
Vim Autoencoder (CMViM), the first efficient representation learning method
tailored for 3D multi-modal data. Our proposed framework is built on a masked
Vim autoencoder to learn a unified multi-modal representation and
long-dependencies contained in 3D medical images. We also introduce an
intra-modal contrastive learning module to enhance the capability of the
multi-modal Vim encoder for modeling the discriminative features in the same
modality, and an inter-modal contrastive learning module to alleviate
misaligned representation among modalities. Our framework consists of two main
steps: 1) incorporate the Vision Mamba (Vim) into the mask autoencoder to
reconstruct 3D masked multi-modal data efficiently. 2) align the multi-modal
representations with contrastive learning mechanisms from both intra-modal and
inter-modal aspects. Our framework is pre-trained and validated ADNI2 dataset
and validated on the downstream task for AD classification. The proposed CMViM
yields 2.7\% AUC performance improvement compared with other state-of-the-art
methods.


  In this essay written with my students and collaborators in mind, I share
simple recipes that are easy and often fun to put in practice and that make a
big difference in one's life. The seven guiding principles are: (1) sleep, (2)
love and sex, (3) deep breathing and daily exercises, (4) water and chewing,
(5) fruits, unrefined products, food combination, vitamin D and no meat, (6)
power foods, (7) play, intrinsic motivation, positive psychology and will.
These simple laws are based on an integration of evolutionary thinking,
personal experimentation, and evidence from experiments reported in the
scientific literature. I develop their rationality, expected consequences and
describe briefly how to put them in practice. I hope that professionals and the
broader public may also find some use for it, as I have seen already the
positive impacts on some of my students.


  We study both static and dynamic properties of a weakly interacting
Bose-Einstein condensate (BEC) in a quasi one-dimensional gravito-optical
surface trap, where the downward pull of gravity is compensated by the
exponentially decaying potential of an evanescent wave. First, we work out
approximate solutions of the Gross-Pitaevskii equation for both a small number
of atoms using a Gaussian ansatz and a larger number of atoms using the
Thomas-Fermi limit. Then we confirm the accuracy of these analytical solutions
by comparing them to numerical results. From there, we numerically analyze how
the BEC cloud expands non-ballistically, when the confining evanescent laser
beam is shut off, showing agreement between our theoretical and previous
experimental results. Furthermore, we analyze how the BEC cloud expands
non-ballistically due to gravity after switching off the evanescent laser field
in the presence of a hard-wall mirror. There we find that the BEC shows
significant self-interference patterns for a large number of atoms, whereas for
a small number of atoms, a revival of the BEC wave packet with few matter-wave
interference patterns is observed.


  The effect of background dynamics of the universe on formation of large scale
structures in the framework of Modified Newtonian Dynamics (MOND) is
investigated. A spherical collapse model is used for modeling the formation of
the structures. This study is done in two extreme cases: ({\it i}) assuming a
universe with a low-density baryonic matter without any cold dark matter and
dark energy; ({\it ii}) a dark energy dominated universe with baryonic matter,
without cold dark matter. We show that for the case ({\it ii}) the structures
virialize at lower redshifts with larger radii compared to the low-density
background universe. The dark energy slow downs the collapse of the structures.
We show that our results are compatible with recent simulations of the
structure formation in MOND.


  A novel model, devised to describe spontaneous chirality synchronization in
complex liquids and liquid crystals, is proposed and studied. Segments of
ribbon-like molecular columns with left- or right-handed 180degree twist lie on
the bonds of a honeycomb lattice so that three ribbons meet in a vertex of the
hexagonal honeycomb. The energy of each vertex is a minimum if the three
ribbons have the same chirality, -E, and is +E otherwise, and the ground state
is homochiral, i.e. all ribbons have the same hand. The energy levels for two
vertices linked by a single ribbon are either -2E, 0 and +2 E in this vertex
model. Monte Carlo simulations demonstrate that this model is identical to an
Ising spin model on a Kagome lattice, for which the site energy structure is
quite different. The equivalence of the ordering of the vertex and Ising spin
models is also shown analytically. The energy difference between the disordered
and ground states, 4J in the spin model, is related to the transition
temperature for the Kagome lattice using the exact result, Tc=2.14J. The
ordering energy difference for a single site is 50% higher for the vertex
model. The thermodynamic energy for the vertex model is corrected by a factor
of 1/3 due to double counting and this makes the specific heat of the vertex
model also equal to that of the spin model as expected. Other similar models
where there is an unusual relation between the site and thermodynamic energies
are discussed briefly.


  We study a one-dimensional extended Hubbard model with longer-range Coulomb
interactions at quarter-filling in the strong coupling limit. We find two
different charge-ordered (CO) ground states as the strength of the longer range
interactions is varied. At lower energies, these CO states drive two different
spin-ordered ground states. A variety of response functions computed here bear
a remarkable resemblance to recent experimental observations for organic TMTSF
systems, and so we propose that these systems are proximate to a QCP associated
with T=0 charge order. For a ladder system relevant to $Sr_{14}Cu_{24}O_{41}$,
we find in-chain CO, rung-dimer, and orbital antiferromagnetic ordered phases
with varying interchain couplings and superconductivity with hole-doping. RPA
studies of many chains (ladders) coupled reveal a phase diagram with the
ordered phase extended to finite temperatures and a phase boundary ending at a
quantum critical point (QCP). Critical quantum fluctuations at the QCP are
found to enhance the transverse dispersion, leading to a dimensional crossover
and a T=0 decofinement transition.


  In 2003, Cohn and Umans described a framework for proving upper bounds on the
exponent $\omega$ of matrix multiplication by reducing matrix multiplication to
group algebra multiplication, and in 2005 Cohn, Kleinberg, Szegedy, and Umans
proposed specific conjectures for how to obtain $\omega=2$. In this paper we
rule out obtaining $\omega=2$ in this framework from abelian groups of bounded
exponent. To do this we bound the size of tricolored sum-free sets in such
groups, extending the breakthrough results of Croot, Lev, Pach, Ellenberg, and
Gijswijt on cap sets. As a byproduct of our proof, we show that a variant of
tensor rank due to Tao gives a quantitative understanding of the notion of
unstable tensor from geometric invariant theory.


  We present a database of 908 spectra of 709 stars obtained with the ELODIE
spectrograph at Observatoire de Haute-Provence. 52 orders of the echelle
spectra have been carefully fitted together to provide continuous,
high-resolution spectra in the wavelength range 410 nm - 680 nm. The archive
provides a large coverage of the space of atmospheric parameters : Teff from
3700 K to 13600 K, logg from 0.03 to 5.86 and [Fe/H] from -2.8 to +0.7. At the
nominal resolution, R=42000, the mean signal-to-noise ratio is 150 per pixel.
The spectra given at this resolution are normalized to their pseudo-continuum
and are intended to serve for abundance studies, spectral classification and
tests of stellar atmosphere models. A lower resolution version of the archive,
at R=10000, is calibrated in physical flux with a broad-band photometric
precision of 2.5% and narrow-band precision of 0.5%. It is scoped for stellar
population synthesis of galaxies and clusters, and for kinematical
investigations of stellar systems.


  In this paper we present a method to derive an exact master equation for a
bosonic system coupled to a set of other bosonic systems, which plays the role
of the reservoir, under the strong coupling regime, i.e., without resorting to
either the rotating-wave or secular approximations. Working with phase-space
distribution functions, we verify that the dynamics are separated in the
evolution of its center, which follows classical mechanics, and its shape,
which becomes distorted. This is the generalization of a result by Glauber, who
stated that coherent states remain coherent under certain circumstances,
specifically when the rotating-wave approximation and a zero-temperature
reservoir are used. We show that the counter-rotating terms generate
fluctuations that distort the vacuum state, much the same as thermal
fluctuations.Finally, we discuss conditions for non-Markovian dynamics.


  We propose a physical scheme to generate entangled light at high temperatures
through the excitation of vacuum fluctuations of the electromagnetic field
using periodic modulations of a refractive index of a ring resonator. We
consider the processes of dissipation and decoherence resulting from the
coupling of the system with an environment at finite temperature and show that
the total amount of entanglement generated does not depend on the temperature,
which only affects the time necessary for the system to produce such an amount
of entanglement.


  Molecular chaperones are vital proteins that maintain protein homeostasis by
assisting in protein folding, activation, degradation, and stress protection.
Among them, heat-shock protein 90 (Hsp90) stands out as an essential
proteostasis hub in eukaryotes, chaperoning hundreds of "clients" (substrates).
After decades of research, several "known unknowns" about the molecular
function of Hsp90 remain unanswered, hampering rational drug design for the
treatment of cancers, neurodegenerative and other diseases. We highlight three
fundamental open questions, reviewing the current state of the field for each,
and discuss new opportunities, including single-molecule technologies, to
answer the known unknowns of the Hsp90 chaperone.


  Hate speech, quite common in the age of social media, at times harmless but
can also cause mental trauma to someone or even riots in communities. Image of
a religious symbol with derogatory comment or video of a man abusing a
particular community, all become hate speech with its every modality (such as
text, image, and audio) contributing towards it. Models based on a particular
modality of hate speech post on social media are not useful, rather, we need
models like multi-modal fusion models that consider both image and text while
classifying hate speech. Text-image fusion models are heavily parameterized,
hence we propose a quaternion neural network-based model having additional
fusion components for each pair of modalities. The model is tested on the
MMHS150K twitter dataset for hate speech classification. The model shows an
almost 75% reduction in parameters and also benefits us in terms of storage
space and training time while being at par in terms of performance as compared
to its real counterpart.


  Taking advantage of a semirelativistic and a full relativistic representation
of the quark propagator in an external field we present an unified derivation
of the semirelativistic potential and of a Bethe-Salpeter like equation for the
quark-antiquark system. We consider three different models for the evaluation
of the Wilson loop: the Modified Area Law model (MAL), the Stochastic Vacuum
Model (SVM) and the Dual QCD (DQCD). We compare the corresponding potentials
and show that they all agree at the short and the long distances. In the case
of the Bethe-Salpeter equation we treat explicitly only the MAL model and give
an expression for the kernel. Then we show that an effective mass operator can
be obtained which agrees with the MAL potential in the semirelativistic limit.
In the light quark mass limit this mass operator produces straight Regge
trajectories with Nambu-Goto slope in agreement with the data. Finally we
briefly discuss the mass independence of the hyperfine splitting in the
heavy-light case.


  We investigate a magnetic hysteresis loop with a remanent moment that couples
to electric polarization to create coupled hysteretic multiferroic behavior in
Lu2MnCoO6. Measurements of elastic neutron diffraction, muon spin relaxation,
and micro-Hall magnetometry demonstrate an unusual mechanism for the magnetic
hysteresis, namely the hysteretic evolution of a microscopic magnetic order,
and not classic ferromagnetic domain effects. We show how the frustrated spin
system evolves from antiferromagnetism with an incommensurate long-wavelength
modulation and strong fluctuations towards a net magnetism. We also clarify the
different temperature scales for the onset of ordering, dynamics, and
hysteresis.


  Composites of flexible and rigid polymers are ubiquitous in biology and
industry alike, yet the physical principles determining their mechanical
properties are far from understood. Here, we couple force spectroscopy with
large-scale Brownian Dynamics simulations to elucidate the unique viscoelastic
properties of custom-engineered blends of entangled flexible DNA molecules and
semiflexible actin filaments. We show that composites exhibit enhanced
stress-stiffening and prolonged mechano-memory compared to systems of actin or
DNA alone, and that these nonlinear features display a surprising non-monotonic
dependence on the fraction of actin in the composite. Simulations reveal that
these counterintuitive results arise from synergistic microscale interactions
between the two biopolymers. Namely, DNA entropically drives actin filaments to
form bundles that stiffen the network but reduce the entanglement density,
while a percolating actin network is required to reinforce the DNA network
against yielding and flow. The competition between bundling and percolation
triggers an unexpected stress response that leads equal mass actin-DNA
composites to exhibit the most pronounced stress-stiffening and the most
long-lived entanglements.


  We conjecture that the confinement- deconfinement phase transition in QCD at
large number of colors $N$ and $N_f\ll N$ at $T\neq 0$ and $\mu\neq 0$ is
triggered by the drastic change in $\theta$ behavior. The conjecture is
motivated by the holographic model of QCD where confinement -deconfinement
phase transition indeed happens precisely at $T=T_c$ where $\theta$ dependence
experiences a sudden change in behavior. The conjecture is also supported by
quantum field theory arguments when the instanton calculations (which trigger
the $\theta$ dependence) are under complete theoretical control for $T>T_c$,
suddenly break down immediately below $T<T_c$ with sharp changes in the
$\theta$ dependence. Finally, the conjecture is supported by a number of
numerical lattice results. We employ this conjecture to study confinement
-deconfinement phase transition of hot and dense QCD in large $N$ limit by
analyzing the $\theta$ dependence. We estimate the critical values for $T_c$
and $\mu_c$ where the phase transition happens by approaching the critical
values from the hot and/or dense regions where the instanton calculations are
under complete theoretical control. We also describe some defects of various
codimensions within a holographic model of QCD by focusing on their role around
the phase transition point.


  We obtain nonasymptotic bounds on the spectral norm of random matrices with
independent entries that improve significantly on earlier results. If $X$ is
the $n\times n$ symmetric matrix with $X_{ij}\sim N(0,b_{ij}^2)$, we show that
\[\mathbf{E}\Vert X\Vert \lesssim\max_i\sqrt{\sum_jb_{ij}^2}+\max _{ij}\vert
b_{ij}\vert \sqrt{\log n}.\] This bound is optimal in the sense that a matching
lower bound holds under mild assumptions, and the constants are sufficiently
sharp that we can often capture the precise edge of the spectrum. Analogous
results are obtained for rectangular matrices and for more general sub-Gaussian
or heavy-tailed distributions of the entries, and we derive tail bounds in
addition to bounds on the expected norm. The proofs are based on a combination
of the moment method and geometric functional analysis techniques. As an
application, we show that our bounds immediately yield the correct phase
transition behavior of the spectral edge of random band matrices and of sparse
Wigner matrices. We also recover a result of Seginer on the norm of Rademacher
matrices.


  Publishing and sharing data is crucial for the data mining community,
allowing collaboration and driving open innovation. However, many researchers
cannot release their data due to privacy regulations or fear of leaking
confidential business information. To alleviate such issues, we propose the
Time Series Synthesis Using the Matrix Profile (TSSUMP) method, where
synthesized time series can be released in lieu of the original data. The
TSSUMP method synthesizes time series by preserving similarity join information
(i.e., Matrix Profile) while reducing the correlation between the synthesized
and the original time series. As a result, neither the values for the
individual time steps nor the local patterns (or shapes) from the original data
can be recovered, yet the resulting data can be used for downstream tasks that
data analysts are interested in. We concentrate on similarity joins because
they are one of the most widely applied time series data mining routines across
different data mining tasks. We test our method on a case study of ECG and
gender masking prediction. In this case study, the gender information is not
only removed from the synthesized time series, but the synthesized time series
also preserves enough information from the original time series. As a result,
unmodified data mining tools can obtain near-identical performance on the
synthesized time series as on the original time series.


  Consider a complex classical semi-simple Lie group along with the set of its
nilpotent coadjoint orbits. When the group is of type A, the set of orbital
varieties contained in a given nilpotent orbit is described a set of standard
Young tableaux. We parameterize both, the orbital varieties and the irreducible
components of unipotent varieties in the other classical groups by sets of
standard domino tableaux. The main tools are Spaltenstein's results on signed
domino tableaux together with Garfinkle's operations on standard domino
tableaux.


  We present a very concise summary of the status of our knowledge and
understanding of neutrino masses and mixing.


  Beyond the choice of wavefront control systems or coronographs, advanced data
processing methods play a crucial role in disentangling potential planetary
signals from bright quasi-static speckles. Among these methods, angular
differential imaging (ADI) for data sets obtained in pupil tracking mode (ADI
sequences) is one of the foremost research avenues, considering the many
observing programs performed with ADI-based techniques and the associated
discoveries. Inspired by the field of econometrics, here we propose a new
detection algorithm for ADI sequences, deriving from the regime-switching model
first proposed in the 1980s. The proposed model is very versatile as it allows
the use of PSF-subtracted data sets (residual cubes) provided by various
ADI-based techniques, separately or together, to provide a single detection
map. The temporal structure of the residual cubes is used for the detection as
the model is fed with a concatenated series of pixel-wise time sequences. The
algorithm provides a detection probability map by considering two possible
regimes for concentric annuli, the first one accounting for the residual noise
and the second one for the planetary signal in addition to the residual noise.
The algorithm performance is tested on data sets from two instruments, VLT/NACO
and VLT/SPHERE. The results show an overall better performance in the receiver
operating characteristic space when compared with standard
signal-to-noise-ratio maps for several state-of-the-art ADI-based
post-processing algorithms.


  Current network models assume one type of links to define the relations
between the network entities. However, many real networks can only be correctly
described using two different types of relations. Connectivity links that
enable the nodes to function cooperatively as a network and dependency links
that bind the failure of one network element to the failure of other network
elements. Here we present for the first time an analytical framework for
studying the robustness of networks that include both connectivity and
dependency links. We show that the synergy between the two types of failures
leads to an iterative process of cascading failures that has a devastating
effect on the network stability and completely alters the known assumptions
regarding the robustness of networks. We present exact analytical results for
the dramatic change in the network behavior when introducing dependency links.
For a high density of dependency links the network disintegrates in a form of a
first order phase transition while for a low density of dependency links the
network disintegrates in a second order transition. Moreover, opposed to
networks containing only connectivity links where a broader degree distribution
results in a more robust network, when both types of links are present a broad
degree distribution leads to higher vulnerability.


  In the present article we consider a natural generalization of Hammersley's
Last Passage Percolation (LPP) called Entropy-controlled Last Passage
Percolation (E-LPP), where points can be collected by paths with a global
(entropy) constraint which takes in account the whole structure of the path,
instead of a local ($1$-Lipschitz) constraint as in Hammersley's LPP. The E-LPP
turns out to be a key ingredient in the context of the directed polymer model
when the environment is heavy-tailed, which we consider in the related paper
[Berger and Torri, 2018]. We prove several estimates on the E-LPP in continuous
and in discrete settings, which are of interest on their own. We give
applications in the context of polymers in heavy-tail environment which are
essentials tools in [Berger and Torri, 2018]: we show that the limiting
variational problem conjectured by [Dey and Zygouras, 2016] (Conjecture 1.7) is
finite, and we prove that the discrete variational problem converges to the
continuous one, generalizing techniques used by [Auffinger-Louidor, 2011] and
[Hambly and Martin, 2007].


  The paper faces the problem of scheduling from a new perspective, trying to
bridge the gap between classical heuristic approaches and system identification
and control strategies. To this aim, a complete mathematical formulation of a
general scheduling process is derived, beginning from very broad assumptions.
This allows a greater freedom of manipulation and guarantee the resolution of
the identification (and control) techniques. Both an adaptive and a switching
strategies are presented in relation to the performances of a simple Round
Robin algorithm.


  We study a lower bound for the constant of the Szemer\'edi-Trotter theorem.
In particular, we show that a recent infinite family of point-line
configurations satisfies $I({\mathcal P},{\mathcal L})\ge (c+o(1)) |{\mathcal
P}|^{2/3}|{\mathcal L}|^{2/3}$, with $c\approx 1.27$. Our technique is based on
studying a variety of properties of Euler's totient function. We also improve
the current best constant for Elekes's construction from 1 to about 1.27. From
an expository perspective, this is the first full analysis of the constant of
Erd\H os's construction.


  We report mixed lag synchronization in coupled counter-rotating oscillators.
The trajectories of counter-rotating oscillators has opposite directions of
rotation in uncoupled state. Under diffusive coupling via a scalar variable, a
mixed lag synchronization emerges when a parameter mismatch is induced in two
counter-rotating oscillators. In the state of mixed lag synchronization, one
pair of state variables achieve synchronization shifted in time while another
pair of state variables are in antisynchronization, however, they are too
shifted by the same time. Numerical example of the paradigmatic R{\"o}ssler
oscillator is presented and supported by electronic experiment.


  We present the results of an experiment on measuring the gradient of the
Casimir force between an Au-coated hollow glass microsphere and graphene-coated
fused silica plate by means of a modified atomic force microscope cantilever
based technique operated in the dynamic regime. These measurements were
performed in high vacuum at room temperature. The energy gap and the
concentration of impurities in the graphene sample used have been measured
utilizing scanning tunnelling spectroscopy and Raman spectroscopy,
respectively. The measurement results for the gradients of the Casimir force
are found to be in a very good agreement with theory using the polarization
tensor of graphene at nonzero temperature depending on the energy gap and
chemical potential with no fitting parameters. The theoretical predictions of
the same theory at zero temperature are experimentally excluded over the
measurement region from 250 to 517 nm. We have also investigated a dependence
of the thermal correction to the Casimir force gradient on the values of the
energy gap, chemical potential, and on the presence of a substrate supporting
the graphene sheet. It is shown that the observed thermal effect is consistent
in size with that arising for pristine graphene sheets if the impact of real
conditions such as nonzero values of the energy gap, chemical potential, and
the presence of a substrate is included. Implications of the obtained results
to the resolution of the long-standing problems in Casimir physics are
discussed. In addition to the paper published previously [M. Liu {\it et al}.,
Phys. Rev. Lett. {\bf 126}, 206802 (2021)], we present measurement results for
the energy gap of the graphene sample, double the experimental data for the
Casimir force, and perform a more complete theoretical analysis.


  We derive an expression that allows for the unambiguous evaluation of the
overlap between two arbitrary quasiparticle vacua, including its sign. Our
expression is based on the Pfaffian of a skew-symmetric matrix, extending the
formula recently proposed by [L. M. Robledo, Phys. Rev. C 79, 021302(R) (2009)]
to the most general case, including the one of the overlap between two
different blocked n-quasiparticle states for either even or odd systems. The
powerfulness of the method is illustrated for a few typical matrix elements
that appear in realistic angular-momentum-restored Generator-Coordinate Method
calculations when breaking time-reversal invariance and using the full model
space of occupied single-particle states.


  The recognition and clustering of coins which have been struck by the same
die is of interest for archeological studies. Nowadays, this work can only be
performed by experts and is very tedious. In this paper, we propose a method to
automatically cluster dies, based on 3D scans of coins. It is based on three
steps: registration, comparison and graph-based clustering. Experimental
results on 90 coins coming from a Celtic treasury from the II-Ith century BC
show a clustering quality equivalent to expert's work.


  The long-range quadrupole-quadrupole ($\sim R^{-5}$) and leading dispersion
($\sim R^{-6}$) interactions between all pairs of excited Hg($6s6p$) $^3P_0$,
$^3P_1$, $^3P_2$, and $^1P_1$ atoms are determined. The quadrupole moments are
calculated using the {\it ab initio} relativistic configuration-interaction
method coupled with many-body perturbation theory. The van der Waals
coefficients are approximated using previously calculated static
polarizabilities and expressions for the dispersion energy that are validated
with similar systems. The long-range interactions are critical for associative
ionization in thermal and cold collisions, and are found to be quite different
for different pairs of interacting states. Based on this knowledge and the
short-range parts of previously calculated potential curves, improved estimates
of the chemi-ionization cross sections are obtained.


  In this work, we show that modulating the fractal dimension of nanoporous
gold allows its effective dielectric response to be tailored over a wide
spectral range of infrared wavelengths. In particular, the plasma edge and
effective plasma frequency depend linearly on the fractal dimension, which can
be controlled by varying the pore and ligament sizes. Importantly, the fractal
porous metal exhibits superior plasmonic properties compared to its bulk
counterpart. These properties, combined with a longer skin depth on the order
of 100-200 nm, enables the penetration of optical energy deep into the
nanopores where molecules can be loaded, thus achieving more effective
light-matter coupling. These findings may open new pathways to engineering the
optical response of fractal-like or self-similar metamaterials without the need
for sophisticated lithographic patterning.


  We report on recent progress towards quantitative phenomenology of small x
resummation of deep-inelastic structure functions. We compute small x resummed
K-factors with realistic PDFs and estimate their impact in the HERA kinematical
region. These K-factors, which match smoothly to the fixed order NLO results,
approximately reproduce the effect of a small x resummed PDF analysis. Typical
corrections are found to be of the same order as the NNLO ones, that is, a few
percent, but with opposite sign. These results imply that resummation
corrections could be relevant for a global PDF analysis, especially with the
very precise combined HERA dataset.


  The singularities associated with QCD factorization in the collinear limit
are key ingredients for high-precision theoretical predictions in particle
physics. They govern the collinear behaviour of scattering amplitudes, as well
as the perturbative energy evolution of parton densities (PDFs) and
fragmentation functions (FFs). In this talk, we present the computation of
multiple collinear and higher-order QCD splittings with massive partons. Our
results are highly-relevant for the consistent introduction of mass effects in
the subtraction formalism and PDF/FF evolution.


  Variational minimization of the ground-state energy as a function of the
two-electron reduced density matrix (2-RDM), constrained by necessary
$N$-representability conditions, provides a polynomial-scaling approach to
studying strongly correlated molecules without computing the many-electron
wavefunction. Here we introduce a new route to enhancing necessary conditions
for $N$-representability through rank restriction of the 2-RDM. Rather than
adding computationally more expensive $N$-representability conditions, we
directly enhance the accuracy of two-particle (2-positivity) conditions through
rank restriction, which removes degrees of freedom in the 2-RDM that are not
sufficiently constrained. We select the rank of the particle-hole 2-RDM by
deriving the ranks associated with model wavefunctions including both
mean-field and antisymmetrized geminal power (AGP) wave functions. Because the
2-positivity conditions are exact for quantum systems with AGP ground states,
the rank of the particle-hole 2-RDM from the AGP ansatz provides a minimum for
its value in variational 2-RDM calculations of general quantum systems. To
implement the rank-restricted conditions, we extend a first-order algorithm for
large-scale semidefinite programming. The rank-restricted conditions
significantly improve the accuracy of the energies; for example, the
percentages of correlation energies recovered for HF, CO, and N$_{2}$ improve
from 115.2%, 121.7%, and 121.5% without rank restriction to 97.8%, 101.1%, and
100.0% with rank restriction. Similar results are found at both equilibrium and
non-equilibrium geometries. While more accurate, the rank-restricted
$N$-representability conditions are less expensive computationally than the
full-rank conditions.


  We study the dynamical behavior of the dilaton in the background of
three-dimensional Kerr-de Sitter space which is inspired from the low-energy
string effective action. The Kerr-de Sitter space describes the gravitational
background of a point particle whose mass and spin are given by $1-M$ and $J$
and its curvature radius is given by $\ell$. In order to study the propagation
of metric, dilaton, and Kalb-Ramond two-form, we perform the perturbation
analysis in the southern diamond of Kerr-de Sitter space including a conical
singularity. It reveals a mixing between the dilaton and other unphysical
fields. Introducing a gauge-fixing, we can disentangle this mixing completely
and obtain one decoupled dilaton equation. However it turns out to be a tachyon
with $m^2=-8/\ell^2$. We compute the absorption cross section for the dilatonic
tachyon to extract information on the cosmological horizon of Kerr-de Sitter
space. It is found that there is no absorption of the dilatonic tachyon in the
presence of the cosmological horizon of Kerr-de Sitter space.


  This paper develops a unified finite-time theory for the ordinary least
squares estimation of possibly unstable and even slightly explosive vector
autoregressive models under linear restrictions, with the applicable region
$\rho(A)\leq 1+c/n$, where $\rho(A)$ is the spectral radius of the transition
matrix $A$ in the \VAR(1) representation, $n$ is the time horizon and $c>0$ is
a universal constant. The linear restriction framework encompasses various
existing models such as banded/network vector autoregressive models. We show
that the restrictions reduce the error bounds via not only the reduced
dimensionality but also a scale factor resembling the asymptotic covariance
matrix of the estimator in the fixed-dimensional setup: as long as the model is
correctly specified, this scale factor is decreasing in the number of
restrictions. It is revealed that the phase transition from slow to fast error
rate regimes is determined by the smallest singular value of $A$, a measure of
the least excitable mode of the system. The minimax lower bounds are derived
across different regimes. The developed non-asymptotic theory not only bridges
the theoretical gap between stable and unstable regimes but precisely
characterizes the effect of restrictions and its interplay with model
parameters. Simulations support our theoretical results.


  In this paper, we aimed at reviewing present literature on employing
nonlinear analysis in combination with machine learning methods, in depression
detection or prediction task. We are focusing on an affordable data-driven
approach, applicable for everyday clinical practice, and in particular, those
based on electroencephalographic (EEG) recordings. Among those studies
utilizing EEG, we are discussing a group of applications used for detecting the
depression based on the resting state EEG (detection studies) and
interventional studies (using stimulus in their protocols or aiming to predict
the outcome of therapy). We conclude with a discussion and review of guidelines
to improve the reliability of developed models that could serve the improvement
of diagnostic and more accurate treatment of depression.


  Human--robot co-carrying tasks demonstrate their potential in both industrial
and everyday applications by leveraging the strengths of both parties.
Effective control of robots in these tasks requires minimizing position and
velocity errors to complete the shared tasks while also managing the energy
level within the closed-loop systems to prevent potential dangers such as
instability and unintended force exertion. However, this collaboration scenario
poses numerous challenges due to varied human intentions in adapting to
workspace characteristics, leading to human--robot conflicts and safety
incidents. In this paper, we develop a robot controller that enables the robot
partner to re-plan its path leveraging conflict information, follow co-carrying
motions accurately, ensure passivity, and regular the energy of the closed-loop
system. A cooperation control framework for human--robot co-carrying tasks is
constructed by utilizing admittance control and time-varying Passive Velocity
Field Control with a fractional exponent energy compensation control term. By
measuring the interaction force, the desired trajectory of co-carrying tasks
for the robot partner is first generated using admittance control. Thereafter,
the new Passive Velocity Field Control with the energy compensation feature is
designed to track the desired time-varying trajectory and guarantee passivity.
Furthermore, the proposed approach ensures that the system's kinetic energy
converges to the desired level within a finite time interval, which is critical
for time-critical applications. Numerical simulation demonstrates the
efficiency of the proposed cooperation control method through four
collaborative transportation scenarios.


  Understanding the sources of lunar water is crucial for studying the history
of lunar evolution, and also the solar wind interaction with the Moon and other
airless bodies. Recent observations revealed lunar hydration is very likely a
surficial dynamic process driven by solar wind. Solar wind is shielded over a
period of 3-5 days as the Moon passes through the Earth's magnetosphere, during
which a significant loss of hydration is expected from previous works.Here we
study lunar hydration inside the magnetosphere using orbital spectral data,
which unexpectedly found that the polar surficial OH/H2O abundance remains at
the same level when in the solar wind and in the magnetosphere. We suggest that
particles from the magnetosphere (Earth wind, naturally different from solar
wind) contribute to lunar hydration. From lunar orbital plasma observations, we
find the existence of optimal energy ranges, other than 1 keV as previously
thought, for surface hydration formation. These optimal energy ranges deduced
from space observations may provide strong implications for laboratory
experiments simulating lunar hydration processes.


  We present the generic Dijkstra shortest path algorithm: an efficient
algorithm for finding a shortest path in an optical network, both in a
wavelength-division multiplexed network, and an elastic optical network (EON).
The proposed algorithm is an enabler of real-time softwarized control of
large-scale networks, and is not limited to optical networks. The Dijkstra
algorithm is a generalization of the breadth-first search, and we generalize
the Dijkstra algorithm further to resolve the continuity and contiguity
constraints of the frequency slot units required in EONs. Specifically, we
generalize the notion of a label, change what we iterate with, and reformulate
the edge relaxation so that vertices are revisited, loops avoided, and worse
labels discarded. We also used the typical constriction during edge relaxation
to take care of the signal modulation constraints. The algorithm can be used
with various spectrum allocation policies. We motivate and discuss the
algorithm design, and provide our free, reliable, and generic implementation
using the Boost Graph Library. We carried out 85000 simulation runs for
realistic and random networks (Gabriel graphs) of 75 vertices with about a
billion shortest-path searches, and found that the proposed algorithm
outperforms considerably three other competing optimal algorithms that are
frequently used.


  We compute the spectra of the adjacency matrices of the semi-regular
polytopes. A few different techniques are employed: the most sophisticated,
which relates the 1-skeleton of the polytope to a Cayley graph, is based on
methods akin to those of Lov\'asz and Babai ([L], [B]). It turns out that the
algebraic degree of the eigenvalues is at most 5, achieved at two 3-dimensional
solids.


  Dust emission is the main foreground for cosmic microwave background (CMB)
polarization. Its statistical characterization must be derived from the
analysis of observational data because the precision required for a reliable
component separation is far greater than what is currently achievable with
physical models of the turbulent magnetized interstellar medium. This letter
takes a significant step toward this goal by proposing a method that retrieves
non-Gaussian statistical characteristics of dust emission from noisy Planck
polarization observations at 353 GHz. We devised a statistical denoising method
based on wavelet phase harmonics (WPH) statistics, which characterize the
coherent structures in non-Gaussian random fields and define a generative model
of the data. The method was validated on mock data combining a dust map from a
magnetohydrodynamic simulation and Planck noise maps. The denoised map
reproduces the true power spectrum down to scales where the noise power is an
order of magnitude larger than that of the signal. It remains highly correlated
to the true emission and retrieves some of its non-Gaussian properties. Applied
to Planck data, the method provides a new approach to building a generative
model of dust polarization that will characterize the full complexity of the
dust emission. We also release PyWPH, a public Python package, to perform
GPU-accelerated WPH analyses on images.


  We present a new high-sensitivity HI observation toward nearby spiral galaxy
M101 and its adjacent 2$^{\circ}\times$ 2$^{\circ}$ region using the
Five-hundred-meter Aperture Spherical radio Telescope (FAST). From the
observation, we detect a more extended and asymmetric HI disk around M101.
While the HI velocity field within the M101's optical disk region is regular,
indicating that the relatively strong disturbance occurs in its outer disk.
Moreover, we identify three new HI clouds located on the southern edge of the
M101's HI disk. The masses of the three HI clouds are 1.3$\times$10$^{7}$
$M_{\odot}$, 2.4$\times$10$^{7}$ $M_{\odot}$, and 2.0$\times$10$^{7}$
$M_{\odot}$, respectively. The HI clouds similar to dwarf companion NGC 5477
rotate with the HI disk of M101. Unlike the NGC 5477, they have no optical
counterparts. Furthermore, we detect a new HI tail in the extended HI disk of
M101. The HI tail detected gives a reliable evidence for M101 interaction with
the dwarf companion NGC 5474. We argue that the extra-planar gas (three HI
clouds) and the HI tail detected in the M101's disk may origin from a minor
interaction with NGC 5474.


  In this paper we wish to prove some results related to the growth rates of
entire and meromorphic functions on the basis of relative (p,q) th order and
relative (p,q) th type of a meromorphic function with respect to an entire
function for any two positive integers p and q.


  We report single crystal growth and physical properties characterization of
YbFe$_2$Al$_{10}$ compounds. The measurements of resistivity, magnetic
susceptibility, and specific heat show different behaviors from previous
studies on polycrystal samples. A mixed valent characteristic with moderate
mass enhancement is indicated. In particular, the optical spectroscopy
measurement reveals formation of multiple hybridization energy gaps which
become progressively pronounced at low temperature. The multiple hybridization
energy gaps are likely caused by the hybridizations between the flat band from
Yb 4$f$ electrons and different bands of conduction electrons.


  The one-century-old Stern-Gerlach setup is paradigmatic for a quantum
measurement. We visualize the electron trajectories following the Bohmian
zig-zag dynamics. This dynamics was developed in order to deal with the
fundamentally massless nature of particles (with mass emerging from the
Brout-Englert-Higgs mechanism). The corresponding trajectories exhibit a
stochastic zig-zagging, as the result of the coupling between left- and
right-handed chiral Weyl states. This zig-zagging persists in the
nonrelativistic limit, which will be considered here, and which is described by
the Pauli equation for a nonuniform external magnetic field. Our results
clarify the different meanings of ``spin'' as a property of the wave function
and as a random variable in the Stern-Gerlach setup, and they illustrate the
notion of effective collapse. We also examine the case of an EPR-pair. By
letting one of the entangled particles pass through a Stern-Gerlach device, the
nonlocal influence (action-at-a-distance) on the other particle is manifest in
its trajectory, e.g. by initiating its zig-zagging.


  Surfaces serve as highly efficient catalysts for a vast variety of chemical
reactions. Typically, such surface reactions involve billions of molecules
which diffuse and react over macroscopic areas. Therefore, stochastic
fluctuations are negligible and the reaction rates can be evaluated using rate
equations, which are based on the mean-field approximation. However, in case
that the surface is partitioned into a large number of disconnected microscopic
domains, the number of reactants in each domain becomes small and it strongly
fluctuates. This is, in fact, the situation in the interstellar medium, where
some crucial reactions take place on the surfaces of microscopic dust grains.
In this case rate equations fail and the simulation of surface reactions
requires stochastic methods such as the master equation. However, in the case
of complex reaction networks, the master equation becomes infeasible because
the number of equations proliferates exponentially. To solve this problem, we
introduce a stochastic method based on moment equations. In this method the
number of equations is dramatically reduced to just one equation for each
reactive species and one equation for each reaction. Moreover, the equations
can be easily constructed using a diagrammatic approach. We demonstrate the
method for a set of astrophysically relevant networks of increasing complexity.
It is expected to be applicable in many other contexts in which problems that
exhibit analogous structure appear, such as surface catalysis in nanoscale
systems, aerosol chemistry in stratospheric clouds and genetic networks in
cells.


  An explicit solution for the generating functional of n-point functions in
the planar approximation is given in terms of two sets of free-algebraic
annihilation and creation operators.


  While the planet-metallicity correlation for FGK main-sequence stars hosting
giant planets is well established, the results are not so clear for M-dwarf
stars, for which precise metallicity measurements are not straightforward.
However, new techniques using near infrared spectra show promising results.
Using these, we determine stellar parameters and metallicities for a sample of
16 M-dwarf stars, 11 of which host planets, with near-infrared spectra from the
Gemini Near-Infrared Spectrograph (GNIRS). We find that M-dwarfs with planets
are preferentially metal-rich compared to those without planets. This result,
based on GNIRS spectra, is supported by the analysis of a relatively larger
sample of M stars with planets (18 in total) and a control sample of 213 M
stars without known planets, obtained from the catalogue of Terrien et al.
(2015). This, on the one hand, coincides with the trend (not only for M- but
also for solar-type stars) reported in the literature and, on the other hand,
demonstrates the utility of GNIRS spectra to obtain reliable stellar parameters
of M stars. We also find that M dwarfs that harbor giant planets are
preferentially more metallic than those associated with low-mass planets
(Neptune or super-Earth type). This trend also agrees with that previously
reported for solar-type stars. These results would favor the core accretion
model for planetary formation.


  We give the Fuchsian linear differential equation satisfied by $\chi^{(4)}$,
the ``four-particle'' contribution to the susceptibility of the isotropic
square lattice Ising model. This Fuchsian differential equation is deduced from
a series expansion method introduced in two previous papers and is applied with
some symmetries and tricks specific to $\chi^{(4)}$. The corresponding order
ten linear differential operator exhibits a large set of factorization
properties. Among these factorizations one is highly remarkable: it corresponds
to the fact that the two-particle contribution $\chi^{(2)}$ is actually a
solution of this order ten linear differential operator. This result, together
with a similar one for the order seven differential operator corresponding to
the three-particle contribution, $\chi^{(3)}$, leads us to a conjecture on the
structure of all the $ n$-particle contributions $ \chi^{(n)}$.


  KITTI-CARLA is a dataset built from the CARLA v0.9.10 simulator using a
vehicle with sensors identical to the KITTI dataset. The vehicle thus has a
Velodyne HDL64 LiDAR positioned in the middle of the roof and two color cameras
similar to Point Grey Flea 2. The positions of the LiDAR and cameras are the
same as the setup used in KITTI. The objective of this dataset is to test
approaches of semantic segmentation LiDAR and/or images, odometry LiDAR and/or
image in synthetic data and to compare with the results obtained on real data
like KITTI. This dataset thus makes it possible to improve transfer learning
methods from a synthetic dataset to a real dataset. We created 7 sequences with
5000 frames in each sequence in the 7 maps of CARLA providing different
environments (city, suburban area, mountain, rural area, highway...). The
dataset is available at: http://npm3d.fr


  We present precise measurements of the upper critical field (Hc2) in the
recently discovered cobalt oxide superconductor. We have found that the
critical field has an unusual temperature dependence; namely, there is an
abrupt change of the slope of Hc2(T) in a weak field regime. In order to
explain this result we have derived and solved Gor'kov equations on a
triangular lattice. Our experimental results may be interpreted in terms of the
field-induced transition from singlet to triplet superconductivity.


  We find the best possible constant $C$ in the inequality
$$\|\varphi\|_{L^r}^{\phantom{\frac{p}{r}}}\leq
C\|\varphi\|_{L^p}^{\frac{p}{r}}\|\varphi\|_{\mathrm{BMO}}^{1-\frac{p}{r}}$$
for all possible values of parameters $p$ and $r$ such that $1 \le p < r <
+\infty$. We employ the Bellman function technique to solve this problem. The
Bellman function of three variables corresponding to this problem has a rather
complicated structure, however, we managed to provide the explicit formulas for
this function. First, we solve the problem on an interval and then transfer our
results to the circle and the line. We also obtain explicit estimates in
multi-dimensional cases.