  We consider the coherent stimulated Raman process developing in an optically
dense disordered atomic medium, which can also incoherently scatter the light
over all outward directions. The Raman process is discussed in the context of a
quantum memory scheme and we point out the difference in its physical nature
from a similar but not identical protocol based on the effect of
electromagnetically induced transparency (EIT). We show that the Raman and EIT
memory schemes do not compete but complement one another and each of them has
certain advantages in the area of its applicability. We include in our
consideration an analysis of the transient processes associated with switching
the control pulse off or on and follow how they modify the probe pulse dynamics
on the retrieval stage of the memory protocol.


  We define an elliptic deformation of the Virasoro algebra. We argue that the
$\mathbb{R}^4\times \mathbb{T}^2$ Nekrasov partition function reproduces the
chiral blocks of this algebra. We support this proposal by showing that at
special points in the moduli space the 6d Nekrasov partition function reduces
to the partition function of a 4d vortex theory supported on
$\mathbb{R}^2\times \mathbb{T}^2$, which is in turn captured by a free field
correlator of vertex operators and screening charges of the elliptic Virasoro
algebra.


  As the Lyman-alpha (Lya) line of neutral hydrogen is the brightest emission
line in the solar spectrum, detecting increases in irradiance due to solar
flares at this wavelength can be challenging due to the very high background.
Previous studies that have focused on the largest flares have shown that even
these extreme cases generate enhancements in Lya of only a few percent above
the background. In this study, a superposed-epoch analysis was performed on
~8500 flares greater than B1 class to determine the contribution that flares
make to changes in the solar EUV irradiance. Using the peak of the 1-8A X-ray
emission as a fiducial time, the corresponding time series of 3123 B- and 4972
C-class flares observed in Lya emission by the EUV Sensor on GOES-15 were
averaged to reduce background fluctuations and improve the flare signal. The
summation of these weaker events showed that they produced a 0.1-0.3%
enhancement to the solar Lya irradiance. For comparison on average, the same
technique was applied to 453 M- and 31 X-class flares, which resulted in a 1-4%
increase in Lya emission. Flares were also averaged with respect to their
heliographic angle to investigate any potential center-to-limb variation. For
each GOES class, the relative enhancement in Lya at the flare peak was found to
diminish for flares that occurred closer to the solar limb due to the opacity
of the line, and/or foreshortening of the footpoints. One modest event included
in the study, a C6.6 flare, exhibited an unusually high increase in Lya of 7%
that may have been attributed to a failed filament eruption. Increases of this
magnitude have hitherto only been associated with a small number of X-class
flares.


  Let $A=(a_1, a_2, \ldots, a_n)$ be a sequence of relative prime integers,
each greater than or equal to 2. The Frobenius number $g(A)$ represents the
largest integer that cannot be expressed as a nonnegative linear combination of
the elements in $A$. Our recent work has introduced a combinatorial method for
calculating $g(A)$ in the specific form $A=(a, a+B)=(a, a+b_1, \ldots, a+b_k)$.
This method reduces the problem to a simpler optimization problem, denoted as
$O_B(M)$. In this paper, we apply this method to solve the open problem of
characterizing $g(A)$ for the square sequence $A=(a,a+1,a+2^2,\ldots, a+k^2)$.
We demonstrate that the Frobenius number $g(a, a+1^2, a+2^2, \ldots)$ for the
infinite square sequence admits a simpler solution. This is because the
corresponding optimization problem, $O_B(M)$, can be solved by applying
number-theoretic principles, specifically Lagrange's Four-Square Theorem and
related results. Consequently, we are able to resolve the open problem by
utilizing Lagrange's Four-Square Theorem in conjunction with generating
functions.


  The existence of the Nagaoka ferromagnetism is examined in the context of the
one-dimensional $U=\infty$ Hubbard model. We construct the exact quantum
partition function to describe the physics of such a regime. Our calculation
reveals that, while the ground state in an open chain is always
spin-degenerate, in a finite size closed chain with at least one vacancy, the
ground state can only be ferromagnetic when the number of electrons is less or
equal to three. Our results shed more light on a very recent experimental
verification of Nagaoka ferromagnetism in a quantum dot set up.


  We study deviation probabilities for the number of high positioned particles
in branching Brownian motion, and confirm a conjecture of Derrida and Shi
(2016). We also solve the corresponding problem for the two-dimensional
discrete Gaussian free field. Our method relies on an elementary inequality for
inhomogeneous Galton-Watson processes.


  It is shown that recent experimental data on electronic transport through Pt
nanocontacts in the presence of hydrogen admit an explanation in terms of
topological and electron-electron correlation grounds. A model Hamiltonian,
which incorporates two orbitals on Pt atoms, a single orbital on hydrogens, and
the on-site Coulomb repulsion on the H atoms, is solved exactly, and connected
to Pt leads described by a Bethe lattice. When two weakly coupled H atoms are
placed between the Pt electrodes transversally to the transport direction (as
recently suggested) a Kondo effect related to the symmetry of the Pt-H
couplings, stabilizes the conductance around one quantum with a single channel
contributing to the current, in agreement with the experiments.


  We present a detailed account and extension of our claim in arXiv:1610.01490.
We test the gauge/gravity duality between the ${\cal N} = 6$ mass-deformed ABJM
theory with U$_k(N)\times$U$_{-k}(N)$ gauge symmetry and the 11-dimensional
supergravity on LLM geometries with SO(4)/${\mathbb Z}_k$
$\times$SO(4)/${\mathbb Z}_k$ isometry, in the large $N$ limit. Our analysis is
based on the evaluation of vacuum expectation values of chiral primary
operators from the supersymmetric vacua of mass-deformed ABJM theory and from
the implementation of Kaluza-Klein holography to the LLM geometries. We focus
on the chiral primary operator with conformal dimension $\Delta = 1$. We show
that $\langle {\cal O}^{(\Delta=1)}\rangle= N^{\frac32} \, f_{(\Delta=1)}$ for
all supersymmetric vacuum solutions and LLM geometries with $k=1$, where the
factor $f_{(\Delta)}$ is independent of $N$. We also confirm that the vacuum
expectation value of the the energy momentum tensor is vanishing as expected by
the supersymmetry. We extend our results to the case of $k\ne 1$ for LLM
geometries represented by rectangular-shaped Young-diagrams. In analogy with
the Coulomb branch of the ${\cal N} = 4$ super Yang-Mills theory, we argue that
the discrete Higgs vacua of the mABJM theory as well as the corresponding LLM
geometries are parametrized by the vevs of the chiral primary operators.


  The predominant centralized paradigm in educational data management currently
suffers from several critical issues such as vulnerability to malicious
tampering, a high prevalence of diploma counterfeiting, and the onerous cost of
certificate authentication. Decentralized blockchain technology, with its
cutting-edge capabilities, presents a viable solution to these pervasive
problems. In this paper, we illuminate the inherent limitations of existing
centralized systems and introduce EduChain, a novel heterogeneous
blockchain-based system for managing educational data. EduChain uniquely
harnesses the strengths of both private and consortium blockchains, offering an
unprecedented level of security and efficiency. In addition, we propose a
robust mechanism for performing database consistency checks and error tracing.
This is achieved through the implementation of a secondary consensus, employing
the pt-table-checksum tool. This approach effectively addresses the prevalent
issue of database mismatches. Our system demonstrates superior performance in
key areas such as information verification, error traceback, and data security,
thereby significantly improving the integrity and trustworthiness of
educational data management. Through EduChain, we offer a powerful solution for
future advancements in secure and efficient educational data management.


  This paper provides a quantum-mechanical analysis of an artwork, `Wigner's
friends,' by Diemut Strebe. The work consists of two telescopes, one on earth,
one launched into space, and explores ideas of quantum correlations and quantum
measurement. This paper examines the scientific basis of the work and analyzes
the form of quantum correlation between the two telescope systems.


  We consider boundary value problems of the first and third kind for the
diffusionwave equation. By using the method of energy inequalities, we find a
priori estimates for the solutions of these boundary value problems.


  Pearl opened the door to formally defining actual causation using causal
models. His approach rests on two strategies: first, capturing the widespread
intuition that X=x causes Y=y iff X=x is a Necessary Element of a Sufficient
Set for Y=y, and second, showing that his definition gives intuitive answers on
a wide set of problem cases. This inspired dozens of variations of his
definition of actual causation, the most prominent of which are due to Halpern
& Pearl. Yet all of them ignore Pearl's first strategy, and the second strategy
taken by itself is unable to deliver a consensus. This paper offers a way out
by going back to the first strategy: it offers six formal definitions of causal
sufficiency and two interpretations of necessity. Combining the two gives
twelve new definitions of actual causation. Several interesting results about
these definitions and their relation to the various Halpern & Pearl definitions
are presented. Afterwards the second strategy is evaluated as well. In order to
maximize neutrality, the paper relies mostly on the examples and intuitions of
Halpern & Pearl. One definition comes out as being superior to all others, and
is therefore suggested as a new definition of actual causation.


  We investigate the relativistic Fermi motion effect in the case of $J/\psi$
production in various hadron colliders. A light-cone wave function is adopted
to represent the $J/\psi$ final state. The change in the confinement parameter
which sets a scale for the size of the final state, allows one to see the
effect in an explicit manner. While the effect has considerable influence on
the fragmentation probabilities and the differential cross sections, the total
cross sections are essentially left unchanged. such a feature is in agreement
with the momentum sum rule which the fragmentation functions should satisfy.


  The time decay of the thermo-remanent magnetization (TRM) in Fe-Cr giant
magnetoresistive (GMR) multilayers has been investigated. The magnetization in
these multilayers relaxes as a function of time after being cooled in a small
magnetic field of 100 Oe to a low temperature and then the magnetic field is
switched off. Low-field ($<$ 500 Oe) magnetization studies of these samples
have shown hysteresis. This spin-glass-like behavior may originate from
structural imperfections at the interfaces and in the bulk. We find that the
magnetization relaxation is logarithmic. Here the magnetic viscosity is found
to increase first with increasing temperature, then it reaches a maximum around
T$_g$, and then it decreases with increasing temperature. This behavior is
different from that of conventional spin glasses where the logarithmic creep
rate is observed to increase with temperature. Power law also gives good fits
and it is better than the logarithmic fit at higher temperatures. The dynamical
effects of these multilayers are related to the relaxation of thermally blocked
superparamagnetic grains and magnetic domains in the film layers.


  The statistical tests - done by the authors - are surveyed, which verify the
null-hypothesis of the intrinsic randomness in the angular distribution of
gamma-ray bursts collected at BATSE Catalog. The tests use the counts-in-cells
method, an analysis of spherical harmonics, a test based on the two-point
correlation function and a method based on multiscale methods. The tests
suggest that the intermediate subclass of gamma-ray bursts are distributed
anisotropically.


  The intense UV radiation from a highly luminous QSO should excite fluorescent
Ly-alpha emission from any nearby neutral hydrogen clouds. We present a very
deep narrow-band search for such emission near the z=2.168 quasar PKS 0424-131,
obtained with the Taurus Tunable Filter on the Anglo-Australian Telescope. By
working in the UV, at high spectral resolution and by using charge shuffling,
we have been able to reach surface brightness limits as faint as 4.7E-19
erg/cm^2/s/arcsec^2.
  No fluorescent Ly-alpha emission is seen, whereas QSO absorption-line
statistics suggest that we should have seen ~6 clouds, unless the clouds are
larger than ~ 100 kpc in size. Furthermore, we do not even see the normal
population of Ly-alpha emitting galaxies found by other surveys at this
redshift. This is very different fromobservations of high redshift radio
galaxies, which seem to be surrounded by clusters of Ly-alpha emitters. We
tentatively conclude that there is a deficit of neutral hydrogen close to this
quasar, perhaps due to the photo-evaporation of nearby dwarf galaxies.


  Open research data are heralded as having the potential to increase
effectiveness, productivity, and reproducibility in science, but little is
known about the actual practices involved in data search. The socio-technical
problem of locating data for reuse is often reduced to the technological
dimension of designing data search systems. We combine a bibliometric study of
the current academic discourse around data search with interviews with data
seekers. In this article, we explore how adopting a contextual, socio-technical
perspective can help to understand user practices and behavior and ultimately
help to improve the design of data discovery systems.


  We give a Matsumoto-type presentation of $K_2$-groups over rings of
non-commutative Laurent polynomials, which is a non-commutative version of M.
Tomie's result for loop groups. Our main idea is due to U. Rehmann's approach
in case of division rings.


  These are the notes of a talk that I gave at the Weihnachtsworkshop 2017 in
Saarbr\"ucken. It answered a question by Hooper and Trevi\~no on the Veech
group of the golden ladder, a translation surface of infinite type.


  Chemistry has a key role in the evolution of the interstellar medium (ISM),
so it is highly desirable to follow its evolution in numerical simulations.
However, it may easily dominate the computational cost when applied to large
systems. In this paper we discuss two approaches to reduce these costs: (i)
based on computational strategies, and (ii) based on the properties and on the
topology of the chemical network. The first methods are more robust, while the
second are meant to be giving important information on the structure of large,
complex networks. To this aim we first discuss the numerical solvers for
integrating the system of ordinary differential equations (ODE) associated with
the chemical network. We then propose a buffer method that decreases the
computational time spent in solving the ODE system. We further discuss a
flux-based method that allows one to determine and then cut on the fly the less
active reactions. In addition we also present a topological approach for
selecting the most probable species that will be active during the chemical
evolution, thus gaining information on the chemical network that otherwise
would be difficult to retrieve. This topological technique can also be used as
an a priori reduction method for any size network. We implemented these methods
into a 1D Lagrangian hydrodynamical code to test their effects: both classes
lead to large computational speed-ups, ranging from x2 to x5. We have also
tested some hybrid approaches finding that coupling the flux method with a
buffer strategy gives the best trade-off between robustness and speed-up of
calculations.


  Let R be an associative ring with unity and let M be an R-module. We call M
(ample) Rad-supplementing if M has a (ample) Rad-supplement in every extension.
If M is Rad-supplementing, then every direct summand of M is Rad-supplementing,
but not each factor module of M. Every module with composition series is
(Rad-)supplementing. M has a Rad-supplement in its injective envelope if and
only if M has a Rad-supplement in every essential extension. R is left perfect
if and only if R is semilocal and reduced, and the direct sum of countably many
copies of R is Rad-supplementing if and only if R is reduced and the direct sum
of countably many copies of R is ample Rad-supplementing. M is ample
Rad-supplementing if and only if every submodule of M is Rad-supplementing.
Every left R-module is (ample) Rad-supplementing if and only if R/P(R) is a
left perfect ring, where P(R) is the sum of all left ideals of R such that Rad
I=I.


  Warped string compactifications, characterized by non-singular behavior of
the metric in the infrared (IR), feature departures from the usual anti-de
Sitter warped extra dimensions. We study the implications of the smooth IR
cutoff for Randall-Sundrum (RS) type models. We find that the phenomenology of
the KK gravitons (including their masses and couplings) depends sensitively on
the precise shape of the warp factor in the IR. In particular, we analyze the
warped deformed conifold and find that the spectrum differs significantly from
that of RS, and present a simple prescription (a mass gap ansatz) which can be
used to study the phenomenology of IR modifications to 5-d warped extra
dimensions.


  The branching fractions of $\tau \to \pi^+ \pi^-\pi^- \nu_\tau$ and $\tau \to
\pi^- 2\pi^0\nu_\tau$ are calculated within the chiral NJL model. Features of
the axial-vector $a_1$ meson which plays an important role in describing the
$\tau$ decays are discussed. Permissible values for the mass and width of the
$a_1$ meson are considered in accordance with the latest experiments.


  Let (R,m) be a local ring with prime ideals p and q such that p+q is an
m-primary ideal. If R is regular and contains a field, and
dim(R/p)+dim(R/q)=dim(R), we prove that p^{(r)}\cap q^{(n)}\subseteq m^{m+n}
for all positive integers r and s. This is proved using a generalization of
Serre's Intersection Theorem which we apply to a hypersurface R/fR. The
generalization gives conditions that guarantee that Serre's bound on the
intersection dimension dim(R/p)+dim(R/q) \leq dim(R) holds when R is
nonregular.


  In a basic related-key attack against a block cipher, the adversary has
access to encryptions under keys that differ from the target key by bit-flips.
In this short note we show that for a quantum adversary such attacks are quite
powerful: if the secret key is (i) uniquely determined by a small number of
plaintext-ciphertext pairs, (ii) the block cipher can be evaluated efficiently,
and (iii) a superposition of related keys can be queried, then the key can be
extracted efficiently.


  Recent studies of the $\Lambda(1520)$ resonance within chiral unitary theory
with coupled channels find the resonance as a dynamically generated state from
the interaction of the decuplet of baryons and the octet of mesons, essentially
a quasibound state of $\pi \Sigma^*(1385)$ in this case, although the coupling
of the $\Lambda(1520)$ to the $\bar{K}N$ and $\pi \Sigma$ makes this picture
only approximate. The $\pi \Sigma^*(1385)$ decay channel of the $\Lambda(1520)$
is forbidden in free space for the nominal mass of the $\Sigma^*(1385)$, but
the coupling of the $\pi$ to $ph$ components in the nuclear medium opens new
decay channels of the $\Lambda(1520)$ in the nucleus and produces a much larger
width. Together with medium modifications of the $\bar{K}N$ and $\pi \Sigma$
decay channels, the final width of the $\Lambda(1520)$ at nuclear matter
density is more than five times bigger than the free one. We perform the
calculations by dressing simultaneously the $\Lambda(1520)$ and the
$\Sigma^*(1385)$ resonances, finding moderate changes in the mass but
substantial ones in the width of both resonances.


  Let G be a reductive algebraic group over a field of prime characteristic.
One can associate to G (or subgroups thereof) its Lie algebra, its Frobenius
kernels, and the finite Chevalley group of points over a finite field. The
representation theories of these structures are highly interconnected. This
expository article will focus specifically on the cohomology theories of these
structures and the relationships between them with the aim of highlighting a
few key developments over the past 20 years and related open questions.


  We derive the effective action for a one dimensional electron island formed
between a double barrier in a single channel quantum wire including the
electron spin. Current and energy addition terms corresponding to charge and
spin are identified. The influence of the range and the strength of the
electron interaction and other system parameters on the charge and spin
addition energies, and on the excitation spectra of the modes confined within
the island is studied. We find by comparison with experiment that spin
excitations in addition to non-zero range of the interaction and inhomogeneity
effects are important for understanding the electron transport through one
dimensional quantum islands in cleaved-edge-overgrowth systems.


  We must recognize that natural language is a way of information encoding, and
it encodes not only the information but also the procedures for how information
is processed. To understand natural language, the same as we conceive and
design computer languages, the first step is to separate information (or data)
and the processing procedures of information (or data). In natural language,
some processing procedures of data are encoded directly as the structure chunk
and the pointer chunk (this paper has reclassified lexical chunks as the data
chunk, structure chunk, and the pointer chunk); some processing procedures of
data imply in sentences structures; some requests of processing procedures are
expressed by information senders and processed by information receivers. For
the data parts, the classification encoding system of attribute information and
the information organization architecture (including constitutional structures
of information sets and the hierarchy between the information sets) were
discussed. In section 2, the theoretical part elaborated in section 2 has been
verified in examples and proofed that the studies in this paper have achieved
the goal of enabling machines to understand the information conveyed in the
dialogue. In section 4, the author summarizes the basic conditions of
"Understanding", rethinks what "Understanding" is and how to proceed. The study
in this paper provides a practical, theoretical basis and research methods for
NLU. It also can be applied in large-scale and multi-type information
processing in the artificial intelligence (AI) area.


  In this paper we introduce the study of quantum boolean functions, which are
unitary operators f whose square is the identity: f^2 = I. We describe several
generalisations of well-known results in the theory of boolean functions,
including quantum property testing; a quantum version of the Goldreich-Levin
algorithm for finding the large Fourier coefficients of boolean functions; and
two quantum versions of a theorem of Friedgut, Kalai and Naor on the Fourier
spectra of boolean functions. In order to obtain one of these generalisations,
we prove a quantum extension of the hypercontractive inequality of Bonami,
Gross and Beckner.


  In the spirit of multi-scale modelling magnetization dynamics at elevated
temperature is often simulated in terms of a spin model where the model
parameters are derived from first principles. While these parameters are mostly
assumed temperature-independent and thermal properties arise from spin
fluctuations only, other scenarios are also possible. Choosing bcc Fe as an
example, we investigate the influence of different kinds of model assumptions
on ultra-fast spin dynamics, where following a femtosecond laser pulse a sample
is demagnetized due to a sudden rise of the electron temperature. While
different model assumptions do not affect the simulational results
qualitatively, their details do depend on the nature of the modelling.


  We present a simultaneous analysis of 10 galaxy lenses having time-delay
measurements. For each lens we derive a detailed free-form mass map, with
uncertainties, and with the additional requirement of a shared value of the
Hubble parameter across all the lenses. We test the prior involved in the lens
reconstruction against a galaxy-formation simulation. Assuming a concordance
cosmology, we obtain 1/H_0 = 13.5 (+2.5/-1.3) Gyr


  The structure of the Baxter adhesive hard sphere fluid is examined using
computer simulation. The radial distribution function (which exhibits unusual
discontinuities due to the particle adhesion) and static structure factor are
calculated with high accuracy over a range of conditions and compared with the
predictions of Percus--Yevick theory. We comment on rigidity in percolating
clusters and discuss the role of the model in the context of experiments on
colloidal systems with short-range attractive forces.


  In this work we show that the incidence angle of group-III elements fluxes
plays a significant role on the diffusion-controlled growth of III-V nanowires
(NWs) by molecular beam epitaxy (MBE). We present a thorough experimental study
on the self-assisted growth of GaAs NWs by using a MBE reactor equipped with
two Ga cells located at different incidence angles with respect to the surface
normal of the substrate, so as to ascertain the impact of such a parameter on
the NW growth kinetics. The as-obtained results show a dramatic influence of
the Ga flux incidence angle on the NW length and diameter, as well as on the
shape and size of the Ga droplets acting as catalysts. In order to interpret
the results we developed a semi-empirical analytic model inspired by those
already developed for MBE-grown Au-catalyzed GaAs NWs. Numerical simulations
performed with the model allow to reproduce thoroughly the experimental results
(in terms of NW length and diameter and of droplet size and wetting angle),
putting in evidence that under formally the same experimental conditions the
incidence angle of the Ga flux is a key parameter which can drastically affect
the growth kinetics of the NWs grown by MBE.


  We present results from a search for an exotic Higgs boson in the channel
H$^{++}$ $\rightarrow ~\ell^{+}\ell^{+}$ with the CMS detector using data
accumulated in the 2010 & 2011 running of the LHC at $\sqrt{s}$ = 7 TeV. We
also present results from a search for a charged Higgs boson in $t\bar{t}$
decays in the channel H$^{+}$ $\rightarrow$ $\tau\nu$


  We describe a novel technique for solving the Plateau problem for constant
curvature hypersurfaces based on recent work of Harvey and Lawson. This is
illustrated by an existence theorem for hypersurfaces of constant Gaussian
curvature in $\Bbb{R}^{n+1}$.


  Using Bloch's parametrization for qudits ($d$-level quantum systems), we
write the Hilbert-Schmidt distance (HSD) between two generic $n$-qudit states
as an Euclidean distance between two vectors of observables mean values in
$\mathbb{R}^{\Pi_{s=1}^{n}d_{s}^{2}-1}$, where $d_{s}$ is the dimension for
qudit $s$. Then, applying the generalized Gell Mann's matrices to generate
$SU(d_{s})$, we use that result to obtain the Hilbert-Schmidt quantum coherence
(HSC) of $n$-qudit systems. As examples, we consider in details one-qubit,
one-qutrit, two-qubit, and two copies of one-qubit states. In this last case,
the possibility for controlling local and non-local coherences by tuning local
populations is studied and the contrasting behaviors of HSC, $l_{1}$-norm
coherence, and relative entropy of coherence in this regard are noticed. We
also investigate the decoherent dynamics of these coherence functions under the
action of qutrit dephasing and dissipation channels. At last, we analyze the
non-monotonicity of HSD under tensor products and report the first instance of
a consequence (for coherence quantification) of this kind of property of a
quantum distance measure.


  We study a new class of matrix models, the simplest of which is based on an
Sp(2) symmetry and has a compactification which is equivalent to Chern-Simons
theory on the three-torus. By replacing Sp(2) with the super-algebra Osp(1|32),
which has been conjectured to be the full symmetry group of M theory, we arrive
at a supercovariant matrix model which appears to contain within it the
previously proposed M theory matrix models. There is no background spacetime so
that time and dynamics are introduced via compactifications which break the
full covariance of the model. Three compactifications are studied corresponding
to a hamiltonian quantization in D=10+1, a Lorentz invariant quantization in
D=9+1 and a light cone gauge quantization in D=11=9+1+1. In all cases
constraints arise which eliminate certain higher spin fields in terms of lower
spin dynamical fields. In the SO(9,1) invariant compactification we argue that
the one loop effective action reduces to the IKKT covariant matrix model. In
the light cone gauge compactification the theory contains the standard M theory
light cone gauge matrix model, but there appears an additional transverse five
form field.


  We consider nuclear spin dynamics in a two-electron double dot system near
the intersection of the electron spin singlet $S$ and the lower energy
component $T_{+}$ of the spin triplet. The electron spin interacts with nuclear
spins and is influenced by the spin-orbit coupling. Our approach is based on a
quantum description of the electron spin in combination with the coherent
semiclassical dynamics of nuclear spins. We consider single and double
Landau-Zener passages across the $S$-$T_{+}$ anticrossings. For linear sweeps,
the electron dynamics is expressed in terms of parabolic cylinder functions.
The dynamical nuclear polarization is described by two complex conjugate
functions $\Lambda ^{\pm}$ related to the integrals of the products of the
singlet and triplet amplitudes ${\tilde{c}}_{S}^{\ast}{\tilde{c}}_{T_{+}}$
along the sweep. The real part $P$ of $\Lambda ^{\pm}$ is related to the
$S$-$T_{+}$ spin-transition probability, accumulates in the vicinity of the
anticrossing, and for long linear passages coincides with the Landau-Zener
probability $P_{LZ}=1-e^{-2\pi \gamma}$, where $\gamma $ is the Landau-Zener
parameter. The imaginary part $Q$ of $\Lambda^{+}$ is specific for the nuclear
spin dynamics, accumulates during the whole sweep, and for $\gamma \gtrsim 1$
is typically an order of magnitude larger than $P$. $Q$ has a profound effect
on the nuclear spin dynamics, by (i) causing intensive shake-up processes among
the nuclear spins and (ii) producing a high nuclear spin generation rate when
the hyperfine and spin-orbit interactions are comparable in magnitude. We find
analytical expressions for the back-action of the nuclear reservoir represented
via the change in the Overhauser fields the electron subsystem experiences.


  We employ an exact solution of the simplest model for pump-probe
time-resolved photoemission spectroscopy in charge-density-wave systems to show
how, in nonequilibrium the gap in the density of states disappears while the
charge density remains modulated, and then the gap reforms after the pulse has
passed. This nonequilibrium scenario qualitatively describes the common
short-time experimental features in TaS2 and TbTe3 indicating a
quasiuniversality for nonequilibrium "melting" with qualitative features that
can be easily understood within a simple picture.


  A Mackey type decomposition for group actions on abelian categories is
described. This allows us to define new Mackey functors which associates to any
subgroup the $K$-theory of the corresponding equivariantized abelian category.
In the case of an action by tensor autoequivalences the Mackey functor at the
level of Grothendieck rings has a Green functor structure. As an application we
give a description of the Grothendieck rings of equivariantized fusion
categories under group actions by tensor autoequivalences on graded fusion
categories.


  It is shown that perfect imaging of a point source both in near- and
far-field regions contradicts electrodynamics although ``superlensing'' is
impossible only in the far-field region. These general statements are
illustrated by detailed study of evanescent wave propagation in a photonic
crystal that is known to be a left-handed medium. An analytical expression for
the intensity distribution near the far-field focus is obtained. This
distribution contains some novel features and establishes a new ``diffraction
limit'' for flat lenses. It is generalized for multiple sources located at
different points. The distribution is in very good agreement with computer
simulation.


  Current and future neutrino experiments can be used to discover dark matter,
not only in searches for dark matter annihilating to neutrinos, but also in
scenarios where dark matter itself scatters off Standard Model particles in the
detector. In this work, we study the sensitivity of different neutrino
detectors to a class of models called boosted dark matter, in which a
subdominant component of a dark sector acquires a large Lorentz boost today
through annihilation of a dominant component in a dark matter-dense region,
such as the galactic center or dwarf spheroidal galaxies. This analysis focuses
on the sensitivity of different neutrino detectors, specifically the
Cherenkov-based Super-K and the future argon-based DUNE to boosted dark matter
that scatters off electrons. We study the dependence of the expected limits on
the experimental features, such as energy threshold, volume and exposure in the
limit of constant scattering amplitude. We highlight experiment-specific
features that enable current and future neutrino experiments to be a powerful
tool in finding signatures of boosted dark matter.


  This paper is concerned with a compositional approach for constructing
abstractions of interconnected discrete-time stochastic control systems. The
abstraction framework is based on new notions of so-called stochastic
simulation functions, using which one can quantify the distance between
original interconnected stochastic control systems and their abstractions in
the probabilistic setting. Accordingly, one can leverage the proposed results
to perform analysis and synthesis over abstract interconnected systems, and
then carry the results over concrete ones. In the first part of the paper, we
derive sufficient small-gain type conditions for the compositional
quantification of the distance in probability between the interconnection of
stochastic control subsystems and that of their abstractions. In the second
part of the paper, we focus on the class of discrete-time linear stochastic
control systems with independent noises in the abstract and concrete
subsystems. For this class of systems, we propose a computational scheme to
construct abstractions together with their corresponding stochastic simulation
functions. We demonstrate the effectiveness of the proposed results by
constructing an abstraction (totally 4 dimensions) of the interconnection of
four discrete-time linear stochastic control subsystems (together 100
dimensions) in a compositional fashion.


  The flavor symmetry-breaking scale in the Froggatt-Nielsen (FN) mechanism is
very weakly constrained by present experiments, and can lie anywhere from a few
TeV to the Planck scale. We construct two minimal, non-supersymmetric,
ultraviolet (UV) complete models that generate the FN mechanism, with a global
$U(1)_{\rm{FN}}$ flavor symmetry and a single flavon field. Using the one-loop
finite temperature effective potential, we explore the possibility of a strong
first order phase transition (SFOPT) induced by the flavon. We show that if the
flavor symmetry-breaking occurs at intermediate scales $\sim 10^4-10^7$ GeV,
then in certain regions of the parameter space, the associated stochastic
gravitational wave (GW) background is strong enough to be detected by second
generation GW observatories such as the Big Bang Observer (BBO), the Deci-hertz
interferometer Gravitational Observatory (DECIGO), the Cosmic Explorer (CE) and
the Einstein Telescope (ET). We identify viable regions of the parameter space
for the best detection prospects. While both models of flavor can produce a
detectable GW background, the GW signature cannot be used to discriminate
between them.


  By direct numerical simulation of the time-dependent Gross-Pitaevskii
equation using the split-step Fourier spectral method we study the
double-humped localization of a cigar-shaped Bose-Einstein condensate (BEC) in
a one-dimensional bichromatic quasi-periodic optical-lattice potential, as used
in a recent experiment on the localization of a BEC [Roati et al., Nature 453,
895 (2008)]. Such states are spatially antisymmetric and are excited modes of
Anderson localization. Where possible, we have compared the numerical results
with a variational analysis. We also demonstrate the stability of the localized
double-humped BEC states under small perturbation.


  We present a new scheme to include the van der Waals (vdW) interactions in
approximated Density Functional Theory (DFT) by combining the Quantum Harmonic
Oscillator model with the Maximally Localized Wannier Function technique. With
respect to the recently developed DFT/vdW-WF2 method, also based on Wannier
Functions, the new approach is more general, being no longer restricted to the
case of well separated interacting fragments. Moreover, it includes higher than
pairwise energy contributions, coming from the dipole--dipole coupling among
quantum oscillators. The method is successfully applied to the popular S22
molecular database, and also to extended systems, namely graphite and H$_2$
adsorbed on the Cu(111) metal surface (in this case metal screening effects are
taken into account). The results are also compared with those obtained by other
vdW-corrected DFT schemes.


  Unconventional fermions with high degeneracies in three dimensions beyond
Weyl and Dirac fermions have sparked tremendous interest in condensed matter
physics. Here, we study quantum Hall effects (QHEs) in a two-dimensional (2D)
unconventional fermion system with a pair of gapped spin-1 fermions. We find
that the original unlimited number of zero energy Landau levels (LLs) in the
gapless case develop into a series of bands, leading to a novel QHE phenomenon
that the Hall conductance first decreases (or increases) to zero and then
revives as an infinite ladder of fine staircase when the Fermi surface is moved
toward zero energy, and it suddenly reverses with its sign being flipped due to
a Van Hove singularity when the Fermi surface is moved across zero. We further
investigate the peculiar QHEs in a dice model with a pair of spin-1 fermions,
which agree well with the results of the continuous model.


  We present a new proof of the Willmore inequality for an arbitrary bounded
domain $\Omega\subset\mathbb{R}^{n}$ with smooth boundary. Our proof is based
on a parametric geometric inequality involving the electrostatic potential for
the domain $\Omega$; this geometric inequality is derived from a geometric
differential inequality in divergence form. Our parametric geometric inequality
also allows us to give new proofs of the quantitative Willmore-type and the
weighted Minkowski inequalities by Agostiniani and Mazzieri.


  Bilinear models has been shown to achieve impressive performance on a wide
range of visual tasks, such as semantic segmentation, fine grained recognition
and face recognition. However, bilinear features are high dimensional,
typically on the order of hundreds of thousands to a few million, which makes
them impractical for subsequent analysis. We propose two compact bilinear
representations with the same discriminative power as the full bilinear
representation but with only a few thousand dimensions. Our compact
representations allow back-propagation of classification errors enabling an
end-to-end optimization of the visual recognition system. The compact bilinear
representations are derived through a novel kernelized analysis of bilinear
pooling which provide insights into the discriminative power of bilinear
pooling, and a platform for further research in compact pooling methods.
Experimentation illustrate the utility of the proposed representations for
image classification and few-shot learning across several datasets.


  We consider the problem of on-line prediction of real-valued labels, assumed
bounded in absolute value by a known constant, of new objects from known
labeled objects. The prediction algorithm's performance is measured by the
squared deviation of the predictions from the actual labels. No stochastic
assumptions are made about the way the labels and objects are generated.
Instead, we are given a benchmark class of prediction rules some of which are
hoped to produce good predictions. We show that for a wide range of
infinite-dimensional benchmark classes one can construct a prediction algorithm
whose cumulative loss over the first N examples does not exceed the cumulative
loss of any prediction rule in the class plus O(sqrt(N)); the main differences
from the known results are that we do not impose any upper bound on the norm of
the considered prediction rules and that we achieve an optimal leading term in
the excess loss of our algorithm. If the benchmark class is "universal" (dense
in the class of continuous functions on each compact set), this provides an
on-line non-stochastic analogue of universally consistent prediction in
non-parametric statistics. We use two proof techniques: one is based on the
Aggregating Algorithm and the other on the recently developed method of
defensive forecasting.


  Using a nonlinear electrodynamics coupled to teleparallel theory of gravity,
three regular charged spherically symmetric solutions are obtained. The
nonlinear theory reduces to the Maxwell one in the weak limit and the solutions
correspond to charged spacetimes. The third solution contains an arbitrary
function from which we can generate the other two solutions. The metric
associated with these spacetimes is the same, i.e., a regular charged static
spherically symmetric black hole. In calculating the energy content of the
third solution using the gravitational energy-momentum given by M{\o}ller,
within the framework of the teleparallel geometry, we find that the resulting
form depends on the arbitrary function. Using the regularized expression of the
gravitational energy-momentum we get the value of energy.


  A high-fidelity finite volume scheme based on the BVD (boundary variation
diminishing) concept is proposed in this study to solve the ideal
magnetohydrodynamics (MHD) equations. A hybrid spatial reconstruction profile,
consisting of a quadratic polynomial and a steepness-adjustable hyperbolic
tangent function, is adopted to reproduce the accurate solutions of the complex
magnetohydrodynamics flows. The BVD principle is used to find a optimal
combination of these two types of spatial reconstructions by comparing the
variations of the interface values interpolated in two adjacent cells, aiming
to remove the non-physical oscillations around discontinuities by switching the
quadratic polynomial to a step-shaped function. Additionally, a constrained
transport (CT) method is applied in this study to assure the non-divergent
solution of the magnetic field. The widely used numerical tests in one and two
dimensional cases were checked in this study. The numerical results can
retrieve the accuracy of a $3^{rd}$-order linear scheme in the convergence test
for both advection and MHD equations and capture the strong shock waves in MHD
flows without spurious oscillations. In comparison with the results of a
$3^{rd}$-order WENO (weighted essentially non-oscillatory) scheme, the proposed
scheme gains more accurate solutions not only for the strong discontinuities
but also the smooth structures across scales. To our knowledge, this is the
first attempt to build a high-fidelity model for ideal MHD equations by a BVD
algorithm. Numerical results are competitive to those of existing advanced
models and thus the BVD algorithm has promising potentials to build practical
models for various MHD flows.


  In recent years, we have observed a significant trend towards filling the gap
between social network analysis and control. This trend was enabled by the
introduction of new mathematical models describing dynamics of social groups,
the advancement in complex networks theory and multi-agent systems, and the
development of modern computational tools for big data analysis. The aim of
this tutorial is to highlight a novel chapter of control theory, dealing with
applications to social systems, to the attention of the broad research
community. This paper is the first part of the tutorial, and it is focused on
the most classical models of social dynamics and on their relations to the
recent achievements in multi-agent systems.


  Wolf-Rayet (WR) galaxies are a rare population of galaxies that host living
high-mass stars during their WR phase (i.e. WR stars) and are thus expected to
provide interesting constraints on the stellar Initial Mass Function, massive
star formation, stellar evolution models, etc. Spatially resolved spectroscopy
should in principle provide a more efficient way of identifying WR galaxies
than single-fiber surveys of galactic centers such as SDSS-I & II, as WR stars
should be more preferentially found in discs. Using IFU data from the ongoing
SDSS-IV MaNGA survey, we have performed a thorough search for WR galaxies. We
first identify H II regions in each datacube and carry out full spectral
fitting to the stacked spectra. We then visually inspect the residual spectrum
of each H II region and identify WR regions that present a significant "blue
bump" at 4600-4750 A. The resulting WR catalog includes 267 WR regions of
~500pc (radius) sizes, distributed in 90 galaxies from the current sample of
MaNGA (MaNGA Product Launch 7). We find WR regions are exclusively found in
galaxies that show bluest colors and highest star formation rates for their
mass. Most WR galaxies have late-type morphologies and show relatively large
asymmetry in their images, implying that WR regions are more preferentially
found in interacting/merging galaxies. We estimate the stellar mass function of
WR galaxies and the mass-dependent detection rate. The detection rate of WR
galaxies is typically ~2%, with weak dependence on stellar mass. This detection
rate is about 40 times higher than previous studies with SDSS single fiber
data, and by a factor of 2 lower than the CALIFA-based WR catalog. We make
comparisons with SDSS and CALIFA studies, and conclude that different detection
rates can be explained mainly by three factors: spatial coverage, spectral
signal-to-noise ratio, and redshift ranges of the parent sample.


  The high resolution spectrograph ESPRESSO on the VLT allows measurements of
fundamental constants at unprecedented precision and hence enables tests for
spacetime variations predicted by some theories. In a series of recent papers,
we developed optimal analysis procedures that both exposes and eliminates the
subjectivity and bias in previous quasar absorption system measurements. In
this paper we analyse the ESPRESSO spectrum of the absorption system at
z_{abs}=1.15 towards the quasar HE0515-4414. Our goal here is not to provide a
new unbiased measurement of fine structure constant, alpha, in this system
(that will be done separately). Rather, it is to carefully examine the impact
of blinding procedures applied in the recent analysis of the same data by
Murphy (2022) and prior to that, in several other analyses. To do this we use
supercomputer Monte Carlo AI calculations to generate a large number of
independently constructed models of the absorption complex. Each model is
obtained using AI-VPFIT, with alpha fixed until a "final" model is obtained, at
which point alpha is then released as a free parameter for one final
optimisation. The results show that the "measured" value of alpha is
systematically biased towards the initially-fixed value i.e. this process
produces meaningless measurements. The implication is straightforward: to avoid
bias, all future measurements must include alpha as a free parameter from the
beginning of the modelling process.


  We investigate the evolution of particle ensembles in open chaotic
hydrodynamical flows. Active processes of the type A+B --> 2B and A+B --> 2C
are considered in the limit of weak diffusion. As an illustrative advection
dynamics we consider a model of the von K\'arm\'an vortex street, a time
periodic two-dimensional flow of a viscous fluid around a cylinder. We show
that a fractal unstable manifold acts as a catalyst for the process, and the
products cover fattened-up copies of this manifold. This may account for the
observed filamental intensification of activity in environmental flows. The
reaction equations valid in the wake are derived either in the form of
dissipative maps or differential equations depending on the regime under
consideration. They contain terms that are not present in the traditional
reaction equations of the same active process: the decay of the products is
slower while the productivity is much faster than in homogeneous flows. Both
effects appear as a consequence of underlying fractal structures. In the long
time limit, the system locks itself in a dynamic equilibrium state synchronized
to the flow for both types of reactions. For particles of finite size an
emptying transition might also occur leading to no products left in the wake.


  Renewal theorems are developed for point processes with interarrival times
$W_n=\xi(X_{n+1}X_n\cdots)$, where $(X_n)_{n\in\mathbb Z}$ is a stochastic
process with finite state space $\Sigma$ and $\xi\colon\Sigma_A\to\mathbb R$ is
a H\"older continuous function on a subset $\Sigma_A\subset\Sigma^{\mathbb N}$.
The theorems developed here unify and generalise the key renewal theorem for
discrete measures and Lalley's renewal theorem for counting measures in
symbolic dynamics. Moreover, they capture aspects of Markov renewal theory. The
new renewal theorems allow for direct applications to problems in fractal and
hyperbolic geometry; for instance, results on the Minkowski measurability of
self-conformal sets are deduced. Indeed, these geometric problems motivated the
development of the renewal theorems.


  We employ ab-initio electronic structure calculations to investigate the
charge-density waves and periodic lattice distortions in bilayer 2H-NbSe$_2$.
We demonstrate that the vertical stacking can give rise to a variety of
patterns that may lower the symmetry of the CDW exhibited separately by the two
composing 1H-NbSe$_2$ monolayers. The general tendency to a spontaneous
symmetry breaking observed in the ground state and the first excited states is
shown to originate from a non-negligible inter-layer coupling. Simulated images
for scanning tunnelling microscopy (STM) as well as diffraction/scattering
patterns show signatures of the different stacking orders. This may not only be
useful to reinterpret past experiments on surfaces and thin films, but may also
be exploited to devise ad-hoc experiments for the investigation of the stacking
order in 2H-NbSe$_2$. We anticipate that our analysis does not only apply to
the 2H-NbSe$_2$ bilayer, but is also relevant for thin films and bulk, whose
smallest centro-symmetric component is indeed the bilayer. Finally, our results
illustrate clearly that the vertical stacking is not only important for 1T
structures, as exemplified by the metal-to-insulator transition observed in
1T-TaS$_2$, but seems to be a general feature of metallic layered transition
metal dichalcogenides as well.


  We propose an alternative approach on the existence of affine realizations
for HJM interest rate models. It is applicable to a wide class of models, and
simultaneously it is conceptually rather comprehensible. We also supplement
some known existence results for particular volatility structures and provide
further insights into the geometry of term structure models.


  Measure homology was introduced by Thurston in his notes about the geometry
and topology of 3-manifolds, where it was exploited in the computation of the
simplicial volume of hyperbolic manifolds. Zastrow and Hansen independently
proved that there exists a canonical isomorphism between measure homology and
singular homology (on the category of CW-complexes), and it was then shown by
Loeh that, in the absolute case, such isomorphism is in fact an isometry with
respect to the L^1-seminorm on singular homology and the total variation
seminorm on measure homology. Loeh's result plays a fundamental role in the use
of measure homology as a tool for computing the simplicial volume of Riemannian
manifolds.
  This paper deals with an extension of Loeh's result to the relative case. We
prove that relative singular homology and relative measure homology are
isometrically isomorphic for a wide class of topological pairs. Our results can
be applied for instance in computing the simplicial volume of Riemannian
manifolds with boundary.
  Our arguments are based on new results about continuous (bounded) cohomology
of topological pairs, which are probably of independent interest.


  The transmission of a vertex $v$ of a (chemical) graph $G$ is the sum of
distances from $v$ to other vertices in $G$. If any two vertices of $G$ have
different transmissions, then $G$ is a transmission irregular graph. It is
shown that for any odd number $n\geq 7$ there exists a transmission irregular
chemical tree of order $n$. A construction is provided which generates new
transmission irregular (chemical) trees. Two additional families of chemical
graphs are characterized by property of transmission irregularity and two
sufficient condition provided which guarantee that the transmission
irregularity is preserved upon adding a new edge.


  A new technique for obtaining switched wave packets using spectrally
truncated chirped laser pulses is demonstrated experimentally and numerically
by one-dimensional alignment of both linear and asymmetric top molecules. Using
a simple long-pass transmission filter, a pulse with a slow turn on and a rapid
turn off is produced. The degree of alignment, characterized by
$\langle\cos^2\theta_\text{2D}\rangle$ rises along with the pulse intensity and
reaches a maximum at the peak of the pulse. After truncation
$\langle\cos^2\theta_\text{2D}\rangle$ drops sharply but exhibits pronounced
half and full revivals. The experimental alignment dynamics trace agrees very
well with a numerically calculated trace based on solution of the
time-dependent Schr\"odinger equation. However, the extended periods of
field-free alignment of asymmetric tops following pulse truncation reported
previously is not reproduced in our work.


  In this paper, we advocate CPN-FedSL, a novel and flexible Federated Split
Learning (FedSL) framework over Computing Power Network (CPN). We build a
dedicated model to capture the basic settings and learning characteristics
(e.g., training flow, latency and convergence). Based on this model, we
introduce Resource Usage Effectiveness (RUE), a novel performance metric
integrating training utility with system cost, and formulate a multivariate
scheduling problem that maxi?mizes RUE by comprehensively taking client
admission, model partition, server selection, routing and bandwidth allocation
into account (i.e., mixed-integer fractional programming). We design Refinery,
an efficient approach that first linearizes the fractional objective and
non-convex constraints, and then solves the transformed problem via a greedy
based rounding algorithm in multiple iterations. Extensive evaluations
corroborate that CPN-FedSL is superior to the standard and state-of-the-art
learning frameworks (e.g., FedAvg and SplitFed), and besides Refinery is
lightweight and significantly outperforms its variants and de facto heuristic
methods under a variety of settings.


  This work investigates a method for generating medium fidelity reactor model
cross sections. The methodology used here couples a neutron transport code with
a depletion calculator. Together the two can be used to generate time dependent
group cross sections for medium fidelity reactor models in fuel cycle
simulation. This work analyzes XSgen, a software that performs the functions
mentioned above. Addtionally, it is shown that XSgen is capable of creating
datasets for a medium fidelity reactor model known as Bright-lite. The results
of this work show that XSgen produces datasets that match NEA benchmarks for
both uranium based LWR, and MOX reactors.


  Using the definition of entropy of a family of increasing distances on a
compact metric set given in [10] we introduce a notion of Finsler entropy for
smooth distributions and Stefan-Sussmann foliations. This concept generalizes
most of classical topological entropy on a compact Riemannian manifold : the
entropy of a flow ([9]), of a regular foliation ([11]), of a regular
distribution ([5]) and of a geometrical structure ([22]). The essential results
of this paper is the nullity of the Finsler entropy for a controllable
distribution and for a singular Riemannian foliation.


  After some historical remarks we discuss different criteria of dynamical
stability of stars, and properties of the critical states where dynamical
stability is lost, leading to collapse with formation of the neutron star or a
black hole. At the end some observational and theoretical problems related to
quark stars are discussed.


  Spectra of the brightest blazars detected by the Fermi Gamma-ray Space
Telescope Large Area Telescope cannot be described by a simple power law model.
A much better description is obtained with a broken power law, with the break
energies of a few GeV. We show here that the sharpness and the position of the
breaks can be well reproduced by absorption of gamma-rays via photon--photon
pair production on HeII Lyman recombination continuum and lines. This implies
that the blazar zone lies inside the region of the highest ionization of the
broad-line region (BLR) within a light-year from a super-massive black hole.
The observations of gamma-ray spectral breaks open a way of studying the BLR
photon field in the extreme-UV/soft X-rays, which are otherwise hidden from our
view.


  We study the many-body effects in a two-subband quasi-two-dimensional
electron system in a quantizing magnetic field at filling factor three. A
manifestation of these effects in the phonon absorption spectroscopy is
discussed. The electron system is mapped onto a two-level system with the
separation between levels determined by the intersubband splitting and the
cyclotron energy. The electron-electron interaction enhances the excitation
gap, which exists at all values of the interlevel splitting. This results in a
single-peak structure of the phonon absorption rate as a function of magnetic
field, instead of the double-peak structure for non-interacting electrons.


  We construct mass models of 28 S0-Sb galaxies. The models have an
axisymmetric stellar component and a NFW dark halo and are constrained by
observed Ks-band photometry and stellar kinematics. The median dark halo virial
mass is 10^12.8 Msun, and the median dark/total mass fraction is 20% within a
sphere of radius r_1/2, the intrinsic half-light radius, and 50% within R_25.
We compare the Tully-Fisher relations of the spirals and S0s in the sample and
find that S0s are 0.5 mag fainter than spirals at Ks-band and 0.2 dex less
massive for a given rotational velocity. We use this result to rule out
scenarios in which spirals are transformed into S0s by processes which truncate
star formation without affecting galaxy dynamics or structure, and raise the
possibility of a break in homology between spirals and S0s.


  We study local analytical integrability in a neighborhood of $p:-q$ resonant
singular point of a two-dimensional vector field and its connection to
time-reversibility with respect to the non-smooth involution $
\varphi(x,y)=(y^{p/q},x^{q/p}). $ Some generalizations of the theory developed
by K.~S.~Sibirsky for $1:-1$ resonant case to the $p:-q$ resonant case are
presented.


  The bumblebee gravity model is a vector-tensor theory of gravitation where
the vector field nonminimally couples to the Ricci tensor. By investigating the
vacuum field equations with spherical symmetry, we find two families of
black-hole (BH) solutions in this model: one has a vanishing radial component
of the vector field and the other has a vanishing radial component of the Ricci
tensor. When the coupling between the vector field and the Ricci tensor is set
to zero, the first family becomes the Reissner-Nordstr\"om solution while the
second family degenerates to the Schwarzschild solution with the vector field
being zero. General numerical solutions in both families are obtained for
nonzero coupling between the vector field and the Ricci tensor. Besides BH
solutions, we also reveal the existence of solutions that have a nonvanishing
$tt$-component of the metric on the supposed event horizon where the
$rr$-component of the metric diverges while the curvature scalars are finite.
These solutions are not supported by existing observations but present certain
properties that are of academic interests. We conclude the study by putting the
BH solutions into tests against the Solar-system observations and the images of
supermassive BHs.


  We construct a basis for effective operators responsible for interactions
between the Standard Model and a dark sector composed of particles with spin
less or equal to 1. Redundant operators are eliminated using dim-4 equations of
motion. We consider simple scenarios where the dark matter components are
stabilized against decay by Z2 symmetries. We determine operators which are
loop-generated within an underlying theory and those that are potentially
tree-level generated.


  Adaptive wave model for financial option pricing is proposed, as a
high-complexity alternative to the standard Black--Scholes model. The new
option-pricing model, representing a controlled Brownian motion, includes two
wave-type approaches: nonlinear and quantum, both based on (adaptive form of)
the Schr\"odinger equation. The nonlinear approach comes in two flavors: (i)
for the case of constant volatility, it is defined by a single adaptive
nonlinear Schr\"odinger (NLS) equation, while for the case of stochastic
volatility, it is defined by an adaptive Manakov system of two coupled NLS
equations. The linear quantum approach is defined in terms of de Broglie's
plane waves and free-particle Schr\"odinger equation. In this approach,
financial variables have quantum-mechanical interpretation and satisfy the
Heisenberg-type uncertainty relations. Both models are capable of successful
fitting of the Black--Scholes data, as well as defining Greeks.
  Keywords: Black--Scholes option pricing, adaptive nonlinear Schr\"odinger
equation, adaptive Manakov system, quantum-mechanical option pricing,
market-heat potential
  PACS: 89.65.Gh, 05.45.Yv, 03.65.Ge


  High resolution ultrasonic velocity measurements have been used to determine
the temperature -- magnetic-field phase diagram of the monoclinic multiferroic
CuO. A new transition at TN3 = 230 K, corresponding to an intermediate state
between the antiferromagnetic non-collinear spiral phase observed below TN2 =
229.3 K and the paramagnetic phase, is revealed. Anomalies associated with a
first order transition to the commensurate collinear phase are also observed at
TN1 = 213 K. For fields with B along the b axis, a spin-flop transition is
detected between 11 T - 13 T at lower temperatures. Moreover, our analysis
using a Landau-type free energy clearly reveals the necessity for an
incommensurate collinear phase between the spiral and the paramagnetic phase.
This model is also relevant to the phase diagrams of other monoclinic
multiferroic systems.


  Human knowledge is subject to uncertainties, imprecision, incompleteness and
inconsistencies. Moreover, the meaning of many everyday terms is dependent on
the context. That poses a huge challenge for the Semantic Web. This paper
introduces work on an intuitive notation and model for defeasible reasoning
with imperfect knowledge, and relates it to previous work on argumentation
theory. PKN is to N3 as defeasible reasoning is to deductive logic. Further
work is needed on an intuitive syntax for describing reasoning strategies and
tactics in declarative terms, drawing upon the AIF ontology for inspiration.
The paper closes with observations on symbolic approaches in the era of large
language models.


  Risk limiting dispatch (RLD) has been proposed as an approach that
effectively trades off economic costs with operational risks for power dispatch
under uncertainty. However, how to solve the RLD problem with provably
near-optimal performance still remains an open problem. This paper presents a
learning-based solution to this challenge. We first design a data-driven
formulation for the RLD problem, which aims to construct a decision rule that
directly maps day-ahead observable information to cost-effective dispatch
decisions for the future delivery interval. Unlike most existing works that
follow a predict-then-optimize paradigm, this end-to-end rule bypasses the
additional suboptimality introduced by separately handling prediction and
optimization. We then propose neural RLD, a novel solution method to the
data-driven formulation. This method leverages an L2-regularized neural network
to learn the decision rule, thereby transforming the data-driven formulation
into a neural network training task that can be efficiently completed by
stochastic gradient descent. A theoretical performance guarantee is further
established to bound the suboptimality of our method, which implies that its
suboptimality approaches to zero with high probability as more samples are
utilized. Simulation tests across various systems demonstrate our method's
superior performance in convergence, suboptimality, and computational
efficiency compared with benchmarks.


  Use of knowledge-based planning tools can help alleviate the challenges of
planning a complex operation by a coalition of diverse parties in an
adversarial environment. We explore these challenges and potential
contributions of knowledge-based tools using as an example the CADET system, a
knowledge-based tool capable of producing automatically (or with human
guidance) battle plans with realistic degree of detail and complexity. In
ongoing experiments, it compared favorably with human planners. Interleaved
planning, scheduling, routing, attrition and consumption processes comprise the
computational approach of this tool. From the coalition operations perspective,
such tools offer an important aid in rapid synchronization of assets and
actions of heterogeneous assets belonging to multiple organizations,
potentially with distinct doctrine and rules of engagement. In this paper, we
discuss the functionality of the tool, provide a brief overview of the
technical approach and experimental results, and outline the potential value of
such tools.


  Recently, the authors have demonstrated large-scale integrated systems with
several million transistors and hundreds of photonic elements. Yielding such
large-scale integrated systems requires a design-for-manufacture rigour that is
embodied in the 10 000 to 50 000 design rules that these designs must comply
within advanced complementary metal-oxide semiconductor manufacturing. Here,
the authors present a photonic design automation tool which allows automatic
generation of layouts without design-rule violations. This tool is written in
SKILL, the native language of the mainstream electric design automation
software, Cadence. This allows seamless integration of photonic and electronic
design in a single environment. The tool leverages intuitive photonic layer
definitions, allowing the designer to focus on the physical properties rather
than on technology-dependent details. For the first time the authors present an
algorithm for removal of design-rule violations from photonic layouts based on
Manhattan discretisation, Boolean and sizing operations. This algorithm is not
limited to the implementation in SKILL, and can in principle be implemented in
any scripting language. Connectivity is achieved with software-defined
waveguide ports and low-level procedures that enable auto-routing of waveguide
connections.


  Spontaneous branching of discharge channels is frequently observed, but not
well understood. We recently proposed a new branching mechanism based on
simulations of a simple continuous discharge model in high fields. We here
present analytical results for such streamers in the Lozansky-Firsov limit
where they can be modelled as moving equipotential ionization fronts. This
model can be analyzed by conformal mapping techniques which allow the reduction
of the dynamical problem to finite sets of nonlinear ordinary differential
equations. The solutions illustrate that branching is generic for the intricate
head dynamics of streamers in the Lozansky-Firsov-limit.


  We investigate an energy-harvesting wireless sensor transmitting
latency-sensitive data over a fading channel. The sensor injects captured data
packets into its transmission queue and relies on ambient energy harvested from
the environment to transmit them. We aim to find the optimal scheduling policy
that decides whether or not to transmit the queue's head-of-line packet at each
transmission opportunity such that the expected packet queuing delay is
minimized given the available harvested energy. No prior knowledge of the
stochastic processes that govern the channel, captured data, or harvested
energy dynamics are assumed, thereby necessitating the use of online learning
to optimize the scheduling policy. We formulate this scheduling problem as a
Markov decision process (MDP) and analyze the structural properties of its
optimal value function. In particular, we show that it is non-decreasing and
has increasing differences in the queue backlog and that it is non-increasing
and has increasing differences in the battery state. We exploit this structure
to formulate a novel accelerated reinforcement learning (RL) algorithm to solve
the scheduling problem online at a much faster learning rate, while limiting
the induced computational complexity. Our experiments demonstrate that the
proposed algorithm closely approximates the performance of an optimal offline
solution that requires a priori knowledge of the channel, captured data, and
harvested energy dynamics. Simultaneously, by leveraging the value function's
structure, our approach achieves competitive performance relative to a
state-of-the-art RL algorithm, at potentially orders of magnitude lower
complexity. Finally, considerable performance gains are demonstrated over the
well-known and widely used Q-learning algorithm.


  Radio continuum emission has been detected from a planetary nebula in the
Large Magellanic Cloud: this is the first radio continuum detection for any
planetary nebula outside our galaxy. The radio flux density is a factor of two
lower than predicted from the \hbeta\ flux. This could be due either to a
two-component morphology or to a stellar contribution to the \hbeta\ emission.
We have modeled the optical and infrared spectrum using the photo-ionisation
code Cloudy: a very good fit is obtained if we assume the nebula is carbon
rich. The derived diameter implies an evolutionary age of the nebula of
$<1000\yr$, similar to what is derived from the IRAS colours alone. The central
star, which is of [WC] type, has a much higher stellar temperature than
Galactic [WC] stars showing similar circumstellar IRAS colours. An explanation
could be that the expansion velocity of the nebula is lower than those of its
galactic counterparts. This radio detection indicates that accurate nebular
luminosities could be determined from their radio emission for many LMC
planetary nebulae.


  The problem is that of sequential probability forecasting for finite-valued
time series. The data is generated by an unknown probability distribution over
the space of all one-way infinite sequences. It is known that this measure
belongs to a given set C, but the latter is completely arbitrary (uncountably
infinite, without any structure given). The performance is measured with
asymptotic average log loss. In this work it is shown that the minimax
asymptotic performance is always attainable, and it is attained by a convex
combination of a countably many measures from the set C (a Bayesian mixture).
This was previously only known for the case when the best achievable asymptotic
error is 0. This also contrasts previous results that show that in the
non-realizable case all Bayesian mixtures may be suboptimal, while there is a
predictor that achieves the optimal performance.


  A new Chase-type soft-decision decoding algorithm for Reed-Solomon codes is
proposed, referred to as tree-based Chase-type algorithm}. The proposed
tree-based Chase-type algorithm takes the set of all vectors as the set of
testing patterns, and hence definitely delivers the most-likely codeword
provided that the computational resources are allowed. All the testing patterns
are arranged in an ordered rooted tree according to the likelihood bounds of
the possibly generated codewords, which is an extension of Wu and Pados' method
from binary into $q$-ary linear block codes. While performing the algorithm,
the ordered rooted tree is constructed progressively by adding at most two
leafs at each trial. The ordered tree naturally induces a sufficient condition
for the most-likely codeword. That is, whenever the tree-based Chase-type
algorithm exits before a preset maximum number of trials is reached, the output
codeword must be the most-likely one. But, in fact, the algorithm can be
terminated by setting a discrepancy threshold instead of a maximum number of
trials. When the tree-based Chase-type algorithm is combined with
Guruswami-Sudan (GS) algorithm, each trial can be implement in an extremely
simple way by removing from the gradually updated Grobner basis one old point
and interpolating one new point. Simulation results show that the tree-based
Chase-type algorithm performs better than the recently proposed Chase-type
algorithm by Bellorado et al with less trials (on average) given that the
maximum number of trials is the same.


  Electrons living in a two-dimensional world under a strong magnetic field -
the so-called fractional quantum Hall effect (FQHE) - often manifest themselves
as fractionally charged quasiparticles (anyons). Moreover, being under special
conditions they are expected to be immune to the environment, thus may serve as
building blocks for future quantum computers. Interference of such anyons is
the very first step towards understanding their anyonic statistics. However,
the complex edge-modes structure of the fractional quantum Hall states,
combined with upstream neutral modes, have been suspected to prevent an
observation of the much sought after interference of anyons. Here, we report of
finding a direct correlation between the appearance of neutral modes and the
gradual disappearance of interference in a Mach-Zehnder interferometer (MZI),
as the bulk filling factor is lowered towards Landau filling {\nu}_B =1;
followed by a complete interference quench at {\nu}_B=1. Specifically, the
interference was found to start diminishing at {\nu}_B~1.5 with a growing
upstream neutral mode, which was detected by a born upstream shot noise in the
input quantum point contact (QPC) to the MZI. Moreover, at the same time a
{\nu}_QPC =1/3 conductance plateau, carrying shot-noise, appeared in the
transmission of the QPC - persisting until bulk filling {\nu}_B =1/2. We
identified this conductance plateau to result from edge reconstruction, which
leads to an upstream neutral mode. Here, we also show that even the
particle-like quasiparticles are accompanied by upstream neutral modes,
therefore suppressing interference in the FQHE regime.


  We examine the suggestion that half of the HST Key Project- and
Sandage/Saha-observed galaxies have had their distances systematically
underestimated, by 0.1-0.3 mag in the distance modulus, due to the
underappreciated influence of stellar profile blending on the WFC chips. The
signature of such an effect would be a systematic trend in (i) the Type Ia
supernovae corrected peak luminosity and (ii) the Tully-Fisher residuals, with
increasing calibrator distance, and (iii) a differential offset between PC and
WFC distance moduli, within the same galaxy. The absence of a trend would be
expected if blending were negligible (as has been inherently assumed in the
analyses of the aforementioned teams). We adopt a functional form for the
predicted influence of blending that is consistent with the models of Mochejska
et al. and Stanek & Udalski, and demonstrate that the expected correlation with
distance predicted by these studies is not supported by the data. We conclude
that the Cepheid-based extragalactic distance scale has not been severely
compromised by the neglect of blending.


  Discrete scale invariance (DSI) is a phenomenon featuring intriguing
log-periodicity which can be rarely observed in quantum systems. Here we report
the log-periodic quantum oscillations in the magnetoresistance (MR) and the
Hall traces of HfTe5 crystals, which reveals the appearance of DSI. The
oscillations show the same logB-periodicity in the behavior of MR and Hall,
indicating an overall effect of the DSI on the transport properties. Moreover,
the DSI feature in the Hall resistance signals its close relation to the
carriers. Combined with theoretical simulations, we further clarify the origin
of the log-periodic oscillations and the DSI in the topological materials. Our
work evidences the universality of the DSI in the Dirac materials and paves way
for the full understanding of the novel phenomenon.


  We generalize the surface growth model of Gates and Westcott to arbitrary
inclination. The exact steady growth velocity is of saddle type with principal
curvatures of opposite sign. According to Wolf this implies logarithmic height
correlations, which we prove by mapping the steady state of the surface to
world lines of free fermions with chiral boundary conditions.


  For any flag simplicial complex $\Theta$ obtained by stellar subdividing the
boundary of the cross polytope in edges, we define a flag simplicial complex
$\Gamma(\Theta)$ (dependent on the sequence of subdivisions) whose $f$-vector
is the $\gamma$-vector of $\Theta$. This proves that the $\gamma$-vector of any
such simplicial complex satisfies the Frankl-F\"{u}redi-Kalai inequalities,
partially solving a conjecture by Nevo and Petersen \cite{np}. We show that
when $\Theta$ is the dual simplicial complex to a nestohedron, and the sequence
of subdivisions corresponds to a flag ordering as defined in \cite{ai}, that
$\Gamma(\Theta)$ is equal to the flag simplical complex defined there.


  Federated Learning (FL) is a way for machines to learn from data that is kept
locally, in order to protect the privacy of clients. This is typically done
using local SGD, which helps to improve communication efficiency. However, such
a scheme is currently constrained by slow and unstable convergence due to the
variety of data on different clients' devices. In this work, we identify three
under-explored phenomena of biased local learning that may explain these
challenges caused by local updates in supervised FL. As a remedy, we propose
FedBR, a novel unified algorithm that reduces the local learning bias on
features and classifiers to tackle these challenges. FedBR has two components.
The first component helps to reduce bias in local classifiers by balancing the
output of the models. The second component helps to learn local features that
are similar to global features, but different from those learned from other
data sources. We conducted several experiments to test \algopt and found that
it consistently outperforms other SOTA FL methods. Both of its components also
individually show performance gains. Our code is available at
https://github.com/lins-lab/fedbr.


  Effect of external periodic force on an oscillatory order in a reaction
diffusion system (Gierer Meinhardt model) has been investigated. The 2:1
resonance situation is found susceptible for the generation of a band of phase
instabilities. These phase instabilities, captured on multiple time scales,
produces a mismatch between the oscillation frequency of reacting species.


  Doped Mott insulators are the starting point for interesting physics such as
high temperature superconductivity and quantum spin liquids. For multi-band
Mott insulators, orbital selective ground states have been envisioned. However,
orbital selective metals and Mott insulators have been difficult to realize
experimentally. Here we demonstrate by photoemission spectroscopy how
Ca$_2$RuO$_4$, upon alkali-metal surface doping, develops a single-band metal
skin. Our dynamical mean field theory calculations reveal that homogeneous
electron doping of Ca$_2$RuO$_4$ results in a multi-band metal. All together,
our results provide compelling evidence for an orbital-selective Mott insulator
breakdown, which is unachievable via simple electron doping. Supported by a
cluster model and cluster perturbation theory calculations, we demonstrate a
novel type of skin metal-insulator transition induced by surface dopants that
orbital-selectively hybridize with the bulk Mott state and in turn produce
coherent in-gap states.


  The completion time for the dissemination (or alternatively, aggregation) of
information from all nodes in a network plays a critical role in the design and
analysis of communication systems, especially in real time applications for
which delay is critical. In this work, we analyse the completion time of data
dissemination in a shared loss (i.e., unreliable links) multicast tree, at the
limit of large number of nodes. Specifically, analytic expressions for upper
and lower bounds on the expected completion time are provided, and, in
particular, it is shown that both these bounds scale as $\alpha \log n$. For
example, on a full binary tree with $n$ end users, and packet loss probability
of $0.1$, we bound the expected completion time for disseminating one packet
from below by $1.41 \log_2 n+o \left( \log n \right)$ and from above by $1.78
\log_2 n+o \left( \log n \right)$.
  Clearly, the completion time is determined by the last end user who receives
the message, that is, a maximum over all arrival times. Hence, Extreme Value
Theory (EVT) is an appropriate tool to explore this problem. However, since
arrival times are correlated, non-stationary, and furthermore, time slots are
discrete, a thorough study of EVT for Non-Stationary Integer Valued (NSIV)
sequences is required. To the best of our knowledge, such processes were not
studied before in the framework of EVT. Consequently, we derive the asymptotic
distribution of the maxima of NSIV sequences satisfying certain conditions, and
give EVT results which are applicable also beyond the scope of this work. These
result are then used to derive tight bounds on the completion time. Finally,
the results are validated by extensive simulations and numerical analysis.


  We study upper bounds on Weierstrass primary factors and discuss their
application in spectral theory. One of the main aims of this note is to draw
attention to works of Blumenthal and Denjoy from 1910, but we also provide some
new results and some numerical computations of our own.


  Given a graph of C*-algebras, we prove a long exact sequence in KK-theory for
both the maximal and the vertex-reduced fundamental C*-algebras in the presence
of possibly non GNS-faithful conditional expectations. We deduce from it the
KK-equivalence between the full fundamental C*-algebra and the vertex-reduced
fundamental C*-algebra even for non GNS-faithful conditional expectations. Our
results unify, simplify and generalize all the previous results obtained before
by Cuntz, Pimsner, Germain and Thomsen. It also generalizes the previous
results of the authors on amalgamated free products.


  We analyse abstract data types that model numerical structures with a concept
of error. Specifically, we focus on arithmetic data types that contain an error
value $\bot$ whose main purpose is to always return a value for division. To
rings and fields, we add a division operator $x/y$ and study a class of
algebras called common meadows wherein $x/0 = \bot$. The set of equations true
in all common meadows is named the equational theory of common meadows. We give
a finite equational axiomatisation of the equational theory of common meadows
and prove that it is complete and that the equational theory is decidable.


  The heating, ventilation and air-conditioning (HVAC) system accounts for
substantial energy use in buildings, whereas a large group of occupants are
still not actually feeling comfortable staying inside. This poses the issue of
developing energy-efficient HVAC control, i.e., reduce energy use (cost) while
simultaneously enhancing human comfort. This paper pursues the objective and
studies the stochastic optimal HVAC control subject to uncertain thermal demand
(i.e., the weather and occupancy etc). Particularly, we involve the elaborate
predicted mean vote (PMV) thermal comfort model in the optimization. The
problem is computationally challenging due to the non-linear and non-analytical
constraints imposed by the system dynamics and PMV model. We make the following
contributions to address it. First, we formulate the problem as a Markov
decision process (MDP) which is a desirable modeling technique capable of
handling the complexities. Second, we propose a gradient-based learning (GB-L)
method for progressively learning a stochastic control policy off-line and
store it for on-line execution. Third, we prove the learning method converge to
the optimal policies theoretically, and its performance (i.e., energy cost,
thermal comfort and on-line computation) for HVAC control via simulations. The
comparisons with the existing model predictive control based relaxation (MPC-R)
method which is assumed with accurate future information and supposed to
provide the near-optimal bounds, show that though there exists some performance
loss in energy cost reduction (i.e., 6.5%), the proposed method can enable
efficient on-line implementation (less than 1 second) and provide high
probability of thermal comfort under uncertainties.


  The computational complexity of neural networks for large scale or real-time
applications necessitates hardware acceleration. Most approaches assume that
the network architecture and parameters are unknown at design time, permitting
usage in a large number of applications. This paper demonstrates, for the case
where the neural network architecture and ternary weight values are known a
priori, that extremely high throughput implementations of neural network
inference can be made by customising the datapath and routing to remove
unnecessary computations and data movement. This approach is ideally suited to
FPGA implementations as a specialized implementation of a trained network
improves efficiency while still retaining generality with the reconfigurability
of an FPGA. A VGG style network with ternary weights and fixed point
activations is implemented for the CIFAR10 dataset on Amazon's AWS F1 instance.
This paper demonstrates how to remove 90% of the operations in convolutional
layers by exploiting sparsity and compile-time optimizations. The
implementation in hardware achieves 90.9 +/- 0.1% accuracy and 122 k frames per
second, with a latency of only 29 us, which is the fastest CNN inference
implementation reported so far on an FPGA.


  We consider a free Dirac field in flat spacetime and we derive the
representation of the Minkowski vacuum as an element of the Rindler-Fock space.
We also compute the statistical operator obtained by tracing away the left
wedge. We detail the resulting thermal state for fermionic particles.


  The behavior of polyatomic molecules around their equilibrium positions can
be regarded as quantum coupled anharmonic oscillators. Solving the
corresponding Schr\"odinger equations can interpret or predict experimental
spectra of molecules. In this study, we develop a novel approach to solve
excited states of anharmonic vibrational systems. The normal coordinates of
molecules are transformed into new coordinates through a normalizing flow
parameterized by a neural network, facilitating the construction of a set of
orthogonal many-body variational wavefunctions. Our methodology has been
validated on an exactly solvable $64$-dimensional coupled harmonic oscillator,
yielding numerical results with a relative error on the order of $10^{-6}$.
Furthermore, the neural canonical transformations are also applied to calculate
the energy levels of two specific molecules, acetonitrile
($\text{C}\text{H}_3\text{CN}$) and ethylene oxide
($\text{C}_2\text{H}_4\text{O}$) involving $12$ and $15$ vibrational modes
respectively, which are in agreement with experimental findings. One of the key
advantages of our approach is its flexibility concerning the potential energy
surface, requiring no specific form for its application. Moreover, this method
can be easily implemented on large-scale distributed computing platforms,
making it particularly suitable for investigating more complex vibrational
structures.


  We show how to adjust the coefficient of determination ($R^2$) when used for
measuring predictive accuracy via leave-one-out cross-validation.


  We prove that a normal vector field along a curve in R3 is rotation
minimizing (RM) if and only if it is parallel respect to the normal connection.
This allows us to generalize all the results of RM vectors and frames to curves
immersed in Riemannian manifolds.


  In this paper we present a new GPU-oriented mesh optimization method based on
high-order finite elements. Our approach relies on node movement with fixed
topology, through the Target-Matrix Optimization Paradigm (TMOP) and uses a
global nonlinear solve over the whole computational mesh, i.e., all mesh nodes
are moved together. A key property of the method is that the mesh optimization
process is recast in terms of finite element operations, which allows us to
utilize recent advances in the field of GPU-accelerated high-order finite
element algorithms. For example, we reduce data motion by using tensor
factorization and matrix-free methods, which have superior performance
characteristics compared to traditional full finite element matrix assembly and
offer advantages for GPU-based HPC hardware. We describe the major mathematical
components of the method along with their efficient GPU-oriented
implementation. In addition, we propose an easily reproducible mesh
optimization test that can serve as a performance benchmark for the mesh
optimization community.


  Topological data analyses are rapidly turning into key tools for quantifying
large volumes of neurobiological data, e.g., for organizing the spiking outputs
of large neuronal ensembles and thus gaining insights into the information
produced by various networks. Below we discuss a case in which several
convergent topological analyses not only provide a description of the data
structure, but also produce insights into how these data may be processed in
the hippocampus---a brain part that plays a key role in learning and memory.
The resulting functional model provides a unifying framework for integrating
spiking information at different timescales and understanding the course of
spatial learning at different levels of spatiotemporal granularity. In
particular, the model allows quantifying contributions of various physiological
phenomena---brain waves, synaptic strengths, synaptic architectures, etc., into
spatial cognition.


  We prove that the arboreal Galois representation attached to a large class of
quadratic polynomials defined over a field of rational functions in
characteristic zero has finite index in the full automorphism group of the
associated preimage tree. Moreover, we show that the index is bounded, in most
cases, independently of the polynomial.


  The potential impact of automation on the labor market is a topic that has
generated significant interest and concern amongst scholars, policymakers, and
the broader public. A number of studies have estimated occupation-specific risk
profiles by examining the automatability of associated skills and tasks.
However, relatively little work has sought to take a more holistic view on the
process of labor reallocation and how employment prospects are impacted as
displaced workers transition into new jobs. In this paper, we develop a new
data-driven model to analyze how workers move through an empirically derived
occupational mobility network in response to automation scenarios which
increase labor demand for some occupations and decrease it for others. At the
macro level, our model reproduces a key stylized fact in the labor market known
as the Beveridge curve and provides new insights for explaining the curve's
counter-clockwise cyclicality. At the micro level, our model provides
occupation-specific estimates of changes in short and long-term unemployment
corresponding to a given automation shock. We find that the network structure
plays an important role in determining unemployment levels, with occupations in
particular areas of the network having very few job transition opportunities.
Such insights could be fruitfully applied to help design more efficient and
effective policies aimed at helping workers adapt to the changing nature of the
labor market.


  Pattern classification systems are commonly used in adversarial applications,
like biometric authentication, network intrusion detection, and spam filtering,
in which data can be purposely manipulated by humans to undermine their
operation. As this adversarial scenario is not taken into account by classical
design methods, pattern classification systems may exhibit vulnerabilities,
whose exploitation may severely affect their performance, and consequently
limit their practical utility. Extending pattern classification theory and
design methods to adversarial settings is thus a novel and very relevant
research direction, which has not yet been pursued in a systematic way. In this
paper, we address one of the main open issues: evaluating at design phase the
security of pattern classifiers, namely, the performance degradation under
potential attacks they may incur during operation. We propose a framework for
empirical evaluation of classifier security that formalizes and generalizes the
main ideas proposed in the literature, and give examples of its use in three
real applications. Reported results show that security evaluation can provide a
more complete understanding of the classifier's behavior in adversarial
environments, and lead to better design choices.


  The pseudorapidity density of charged particles,
$\rm{d}\it{N}_\rm{ch}/\rm{d}\it{\eta}$, in p-Pb collisions has been measured at
a centre-of-mass energy per nucleon-nucleon pair of $\sqrt{s_{\rm{NN}}}$ = 8.16
TeV at mid-pseudorapidity for non-single-diffractive events. The results cover
3.6 units of pseudorapidity, $|\eta|<1.8$. The
$\rm{d}\it{N}_\rm{ch}/\rm{d}\it{\eta}$ value is $19.1\pm0.7$ at $|\eta|<0.5$.
This quantity divided by $\langle N_\rm{part} \rangle/2$, is $4.73\pm0.20$,
which is 9.5% higher than the corresponding value for p-Pb collisions at
$\sqrt{s_{\rm{NN}}}$ = 5.02 TeV. Measurements are compared with models based on
different mechanisms for particle production. All models agree within
uncertainties with data in the Pb-going side, while HIJING overestimates,
showing a symmetric behaviour, and EPOS underestimates the p-going side of the
$\rm{d}\it{N}_\rm{ch}/\rm{d}\it{\eta}$ distribution. Saturation-based models
reproduce the distributions well for $\eta>-1.3$. The
$\rm{d}\it{N}_\rm{ch}/\rm{d}\it{\eta}$ is also measured for different
centrality estimators, based both on the charged-particle multiplicity and on
the energy deposited in the Zero-Degree Calorimeters. A study of the
implications of the large multiplicity fluctuations due to the small number of
participants for systems like p-Pb in the centrality calculation for
multiplicity-based estimators is discussed, demonstrating the advantages of
determining the centrality with energy deposited near beam rapidity.


  We consider multiple time scales systems of stochastic differential equations
with small noise in random environments. We prove a quenched large deviations
principle with explicit characterization of the action functional. The random
medium is assumed to be stationary and ergodic. In the course of the proof we
also prove related quenched ergodic theorems for controlled diffusion processes
in random environments that are of independent interest. The proof relies
entirely on probabilistic arguments, allowing to obtain detailed information on
how the rare event occurs. We derive a control, equivalently a change of
measure, that leads to the large deviations lower bound. This information on
the change of measure can motivate the design of asymptotically efficient Monte
Carlo importance sampling schemes for multiscale systems in random
environments.


  In this paper, we discuss the flocking phenomenon for the Cucker-Smale and
Motsch-Tadmor models in continuous time on a general oriented and weighted
graph with a general communication function. We present a new approach for
studying this problem based on a probabilistic interpretation of the solutions.
We provide flocking results under four assumptions on the interaction matrix
and we highlight how they relate to the convergence in total variation of a
certain Markov jump process. Indeed, we refine previous results on the minimal
case where the graph admits a unique closed communication class. Considering
the two particular cases where the adjacency matrix is scrambling or where it
admits a positive reversible measure, we improve the flocking condition
obtained for the minimal case. In the last case, we characterise the asymptotic
speed. We also study the hierarchical leadership case where we give a new
general flocking condition which allows to deal with the case
$\psi(r)\propto(1+r^2)^{-\beta/2}$ and $\beta\geq1$. For the Motsch-Tadmor
model under the hierarchical leadership assumption, we exhibit a case where the
flocking phenomenon occurs regardless of the initial conditions and the
communication function, in particular even if $\beta\geq1$.