  Supervised learning aims to train a classifier under the assumption that
training and test data are from the same distribution. To ease the above
assumption, researchers have studied a more realistic setting:
out-of-distribution (OOD) detection, where test data may come from classes that
are unknown during training (i.e., OOD data). Due to the unavailability and
diversity of OOD data, good generalization ability is crucial for effective OOD
detection algorithms. To study the generalization of OOD detection, in this
paper, we investigate the probably approximately correct (PAC) learning theory
of OOD detection, which is proposed by researchers as an open problem. First,
we find a necessary condition for the learnability of OOD detection. Then,
using this condition, we prove several impossibility theorems for the
learnability of OOD detection under some scenarios. Although the impossibility
theorems are frustrating, we find that some conditions of these impossibility
theorems may not hold in some practical scenarios. Based on this observation,
we next give several necessary and sufficient conditions to characterize the
learnability of OOD detection in some practical scenarios. Lastly, we also
offer theoretical supports for several representative OOD detection works based
on our OOD theory.


  Recently there has been interest in the physical properties of dark matter
axion condensates. Due to gravitational attraction and self-interactions, they
can organize into spatial localized clumps, whose properties were examined by
us in Refs. [1, 2]. Since the axion condensate is coherently oscillating, it
can conceivably lead to parametric resonance of photons, leading to exponential
growth in photon occupancy number and subsequent radio wave emission. We show
that while resonance always exists for spatially homogeneous condensates, its
existence for a spatially localized clump condensate depends sensitively on the
size of clump, strength of axion-photon coupling, and field amplitude. By
decomposing the electromagnetic field into vector spherical harmonics, we are
able to numerically compute the resonance from clumps for arbitrary parameters.
We find that for spherically symmetric clumps, which are the true BEC ground
states, the resonance is absent for conventional values of the QCD axion-photon
coupling, but it is present for axions with moderately large couplings, or into
hidden sector photons, or from scalar dark matter with repulsive interactions.
We extend these results to non-spherically symmetric clumps, organized by
finite angular momentum, and find that even QCD axion clumps with conventional
couplings can undergo resonant decay for sufficiently large angular momentum.
We discuss possible astrophysical consequences of these results, including the
idea of a pile-up of clump masses and rapid electromagnetic emission in the sky
from mergers.


  $\alpha$-FeSe, a prototype iron-chalcogenide superconductor, shows clear
signatures of a strange incoherent normal state. Motivated thereby, we use
LDA+DMFT to show how strong multi-band correlations generate a low-energy
pseudogap in the normal state, giving an incoherent metal in very good
semi-quantitative agreement with observations. We interpret our results in
terms of $\alpha$-FeSe being close to Mottness. A wide range of anomalous
responses in the "normal" state are consistently explained, lending strong
support for this view. Implications for superconductivity arising from such an
anomalous state are touched upon.


  We present an elementary review of some aspects of Chern-Simons theory with
complex gauge group SL(N,C). We discuss some of the challenges in defining the
theory as a full-fledged TQFT, as well as some successes inspired by the 3d-3d
correspondence. The 3d-3d correspondence relates partition functions (and other
aspects) of complex Chern-Simons theory on a 3-manifold M to supersymmetric
partition functions (and other observables) in an associated 3d theory T[M].
Many of these observables may be computed by supersymmetric localization. We
present several prominent applications to 3-manifold topology and number theory
in light of the 3d-3d correspondence.


  Mechanism - collections of rigid elements coupled by perfect hinges which
exhibit a zero-energy motion -- motivate the design of a variety of mechanical
metamaterials. We significantly enlarge this design space by considering
pseudo-mechanisms, collections of elastically coupled elements that exhibit
motions with very low energy costs. We show that their geometric design
generally is distinct from those of true mechanisms, thus opening up a large
and virtually unexplored design space. We further extend this space by
designing building blocks with bistable and tristable energy landscapes,
realize these by 3D printing, and show how these form unit cells for
multistable metamaterials.


  We provide a complete study of existence and uniqueness of solutions to the
Lichnerowicz equation in general relativity with arbitrary mean curvature.


  A graph is 1-planar if it has a drawing where each edge is crossed at most
once. A drawing is RAC (Right Angle Crossing) if the edges cross only at right
angles. The relationships between 1-planar graphs and RAC drawings have been
partially studied in the literature. It is known that there are both 1-planar
graphs that are not straight-line RAC drawable and graphs that have a
straight-line RAC drawing but that are not 1-planar. Also, straight-line RAC
drawings always exist for IC-planar graphs, a subclass of 1-planar graphs. One
of the main questions still open is whether every 1-planar graph has a RAC
drawing with at most one bend per edge. We positively answer this question.


  On strictly starshaped domains of second kind we find natural sufficient
conditions which allow the solution of two long standing open problems closely
related to the mean field equation $\prl$ below. On one side we catch the
global behaviour of the Entropy for the mean field Microcanonical Variational
Principle ((MVP) for short) arising in the Onsager description of
two-dimensional turbulence. This is the completion of well known results first
established in Caglioti et al. Comm.Math.Phys. (1995). Among other things we
find a full unbounded interval of strict convexity of the Entropy. On the other
side, to achieve this goal, we have to provide a detailed qualitative
description of the global branch of solutions of $\prl$ emanating from $\lm=0$
and crossing $\lm=8\pi$. This is the completion of well known results first
established in Suzuki A.I.H.P. (1992) and Chang et al. New Stud. Adv. Math.
(2003) for $\lm\leq 8\pi$, and it has an independent mathematical interest,
since global branches of semilinear elliptic equations, with very few well
known exceptions, are poorly understood. The (MVP) suggests the right variable
(which is the energy) to be used to obtain a global parametrization of
solutions of $\prl$. A crucial spectral simplification is obtained by using the
fact that, by definition, solutions of the (MVP) maximize the entropy at fixed
energy and total vorticity.


  Block-based programming environments are increasingly used to introduce
computing concepts to beginners. However, novice students often struggle in
these environments, given the conceptual and open-ended nature of programming
tasks. To effectively support a student struggling to solve a given task, it is
important to provide adaptive scaffolding that guides the student towards a
solution. We introduce a scaffolding framework based on pop quizzes presented
as multi-choice programming tasks. To automatically generate these pop quizzes,
we propose a novel algorithm, PQuizSyn. More formally, given a reference task
with a solution code and the student's current attempt, PQuizSyn synthesizes
new tasks for pop quizzes with the following features: (a) Adaptive (i.e.,
individualized to the student's current attempt), (b) Comprehensible (i.e.,
easy to comprehend and solve), and (c) Concealing (i.e., do not reveal the
solution code). Our algorithm synthesizes these tasks using techniques based on
symbolic reasoning and graph-based code representations. We show that our
algorithm can generate hundreds of pop quizzes for different student attempts
on reference tasks from Hour of Code: Maze Challenge and Karel. We assess the
quality of these pop quizzes through expert ratings using an evaluation rubric.
Further, we have built an online platform for practicing block-based
programming tasks empowered via pop quiz based feedback, and report results
from an initial user study.


  Open quantum systems can display periodic dynamics at the classical level
either due to external periodic modulations or to self-pulsing phenomena
typically following a Hopf bifurcation. In both cases, the quantum fluctuations
around classical solutions do not reach a quantum-statistical stationary state,
which prevents adopting the simple and reliable methods used for stationary
quantum systems. Here we put forward a general and efficient method to compute
two-time correlations and corresponding spectral densities of time-periodic
open quantum systems within the usual linearized (Gaussian) approximation for
their dynamics. Using Floquet theory we show how the quantum Langevin equations
for the fluctuations can be efficiently integrated by partitioning the time
domain into one-period duration intervals, and relating the properties of each
period to the first one. Spectral densities, like squeezing spectra, are
computed similarly, now in a two-dimensional temporal domain that is treated as
a chessboard with one-period x one-period cells. This technique avoids
cumulative numerical errors as well as efficiently saves computational time. As
an illustration of the method, we analyze the quantum fluctuations of a damped
parametrically-driven oscillator (degenerate parametric oscillator) below
threshold and far away from rotating-wave approximation conditions, which is a
relevant scenario for modern low-frequency quantum oscillators. Our method
reveals that the squeezing properties of such devices are quite robust against
the amplitude of the modulation or the low quality of the oscillator, although
optimal squeezing can appear for parameters that are far from the ones
predicted within the rotating-wave approximation.


  Cobordism categories have played an important role in classical geometry and
more recently in mathematical treatments of quantum field theory. Here we will
compute localisations of two-dimensional discrete cobordism categories. This
allows us, up to equivalence, to determine the category of invertible
two-dimensional topological field theories in the sense of Atiyah. We are able
to treat the orientable, non-orientable, closed and open cases.


  We compute the entanglement entropy and Renyi entropies of arbitrary pure
states in pure Jackiw-Teitelboim gravity in Lorentz signature. We apply the
quantum Hubeny-Rangamani-Ryu-Takayanagi formula by computing the quantum
corrected area term and the bulk entropy term. The sum of these two terms for
the Hartle-Hawking state agrees with the black hole entropy above extremality
computed from the Euclidean disk path integral. We interpret the area term as
the universal contribution of a defect operator that plays a crucial role in
our Lorentzian interpretation of the Euclidean replica trick in gravity.


  Recent advances in artificial intelligence and machine learning have created
a step change in how to measure human development indicators, in particular
asset based poverty. The combination of satellite imagery and machine learning
has the capability to estimate poverty at a level similar to what is achieved
with workhorse methods such as face-to-face interviews and household surveys.
An increasingly important issue beyond static estimations is whether this
technology can contribute to scientific discovery and consequently new
knowledge in the poverty and welfare domain. A foundation for achieving
scientific insights is domain knowledge, which in turn translates into
explainability and scientific consistency. We review the literature focusing on
three core elements relevant in this context: transparency, interpretability,
and explainability and investigate how they relates to the poverty, machine
learning and satellite imagery nexus. Our review of the field shows that the
status of the three core elements of explainable machine learning
(transparency, interpretability and domain knowledge) is varied and does not
completely fulfill the requirements set up for scientific insights and
discoveries. We argue that explainability is essential to support wider
dissemination and acceptance of this research, and explainability means more
than just interpretability.


  The dynamics of two coupled generators of quasiperiodic oscillations is
studied. The opportunity of complete and phase synchronization of generators in
the regime of quasiperiodic oscillations is obtained. The features of structure
of parameter plane is researched using charts of dynamical regimes and charts
of Lyapunov exponents, in which typical structures as resonance Arnold web were
revealed. The possible quasiperiodic bifurctions in the system are discussed.


  Iterative detection and decoding (IDD) is known to achieve near-capacity
performance in multi-antenna wireless systems. We propose deep-unfolded
interleaved detection and decoding (DUIDD), a new paradigm that reduces the
complexity of IDD while achieving even lower error rates. DUIDD interleaves the
inner stages of the data detector and channel decoder, which expedites
convergence and reduces complexity. Furthermore, DUIDD applies deep unfolding
to automatically optimize algorithmic hyperparameters, soft-information
exchange, message damping, and state forwarding. We demonstrate the efficacy of
DUIDD using NVIDIA's Sionna link-level simulator in a 5G-near multi-user
MIMO-OFDM wireless system with a novel low-complexity soft-input soft-output
data detector, an optimized low-density parity-check decoder, and channel
vectors from a commercial ray-tracer. Our results show that DUIDD outperforms
classical IDD both in terms of block error rate and computational complexity.


  We report on multicolour photometry of the short period dwarf nova
CSS130418:174033+414756 during the 2013 superoutburst. The system showed an
unusually short superhump period with 0.046346(67) d during stage A, which is
one of the shortest periods among dwarf novae below the period minimum. We
found that the bluest peaks in $g' - I_{\rm c}$ colour variations tend to
coincide with the brightness minima of the superhump modulations. We also
studied nightly-averaged superhump amplitudes in $g'$, $R_{\rm c}$, and $I_{\rm
c}$ bands and found that they have less dependence on wavelength. These
properties are likely to be in common with dwarf novae exhibiting superhumps.
We successfully obtained $g' - R_{\rm c}$ and $R_{\rm c} - I_{\rm c}$ colours
during the temporal dip. The colour indices were significantly bluer compared
with other dips of WZ Sge-type dwarf novae. By using the period of the growing
superhumps, we estimated the mass ratio to be $q$ = 0.077(5), which is much
larger than the previous study.


  We study the geometry of germs of definable (semialgebraic or subanalytic)
sets over a $p$-adic field from the metric, differential and measure geometric
point of view. We prove that the local density of such sets at each of their
points does exist. We then introduce the notion of distinguished tangent cone
with respect to some open subgroup with finite index in the multiplicative
group of our field and show, as it is the case in the real setting, that, up to
some multiplicities, the local density may be computed on this distinguished
tangent cone.We also prove that these distinguished tangent cones stabilize for
small enough subgroups. We finally obtain the $p$-adic counterpart of the
Cauchy-Crofton formula for the density. To prove these results we use the
Lipschitz decomposition of definable $p$-adic sets of arXiv:0904.3853v1 and
prove here the genericity of the regularity conditions for stratification such
as $(w_f)$, $(w)$, $(a_f)$, $(b)$ and $(a)$ conditions.


  A properly calibrated longitudinal magnetograph is an instrument that
measures circular polarization and gives an estimation of the magnetic flux
density in each observed resolution element. This usually constitutes a lower
bound of the field strength in the resolution element, given that it can be
made arbitrarily large as long as it occupies a proportionally smaller area of
the resolution element and/or becomes more transversal to the observer and
still produce the same magnetic signal. Yet, we know that arbitrarily stronger
fields are less likely --hG fields are more probable than kG fields, with
fields above several kG virtually absent-- and we may even have partial
information about its angular distribution. Based on a set of sensible
considerations, we derive simple formulae based on a Bayesian analysis to give
an improved estimation of the magnetic field strength for magnetographs.


  We calculate the rates for the charged lepton flavour violating decays l_i ->
l_j gamma, tau -> l pi, tau -> l eta, tau -> l eta', mu^- -> e^- e^+ e^-, the
six three body leptonic decays tau^- -> l_i^- l_j^+ l_k^- and the rate for mu-e
conversion in nuclei in the Littlest Higgs model with T-Parity (LHT). We also
calculate the rates for K_{L,S} -> mu e, K_{L,S} -> pi^0 mu e and B_{d,s} ->
l_i l_j. We find that the relative effects of mirror leptons in these
transitions are by many orders of magnitude larger than analogous mirror quark
effects in rare K and B decays analyzed recently. In particular, in order to
suppress the mu -> e gamma and mu^- -> e^- e^+ e^- decay rates and the mu-e
conversion rate below the experimental upper bounds, the relevant mixing matrix
in the mirror lepton sector V_Hl must be rather hierarchical, unless the
spectrum of mirror leptons is quasi-degenerate. We find that the pattern of the
LFV branching ratios in the LHT model differs significantly from the one
encountered in the MSSM, allowing in a transparent manner to distinguish these
two models with the help of LFV processes. We also calculate (g-2)_mu and find
the new contributions to a_mu below 10^{-10} and consequently negligible. We
compare our results with those present in the literature.


  We model tri-bimaximal lepton mixing from first principles in a way that
avoids the problem of the vacuum alignment characteristic of such models. This
is achieved by using a softly broken A4 symmetry realized with an isotriplet
fermion, also triplet under A4. No scalar A4-triplet is introduced. This
represents one possible realization of general schemes characterized by the
minimal set of either three or five physical parameters. In the three parameter
versions mee vanishes, while in the five parameter schemes the absolute scale
of neutrino mass, although not predicted, is related to the two Majorana
phases. The model realization we discuss is potentially testable at the LHC
through the peculiar leptonic decay patterns of the fermionic and scalar
triplets.


  Infectious diseases typically spread over a contact network with millions of
individuals, whose sheer size is a tremendous challenge to analysing and
controlling an epidemic outbreak. For some contact networks, it is possible to
group individuals into clusters. A high-level description of the epidemic
between a few clusters is considerably simpler than on an individual level.
However, to cluster individuals, most studies rely on equitable partitions, a
rather restrictive structural property of the contact network. In this work, we
focus on Susceptible-Infected-Susceptible (SIS) epidemics, and our contribution
is threefold. First, we propose a geometric approach to specify all networks
for which an epidemic outbreak simplifies to the interaction of only a few
clusters. Second, for the complete graph and any initial viral state vectors,
we derive the closed-form solution of the nonlinear differential equations of
the N-Intertwined Mean-Field Approximation (NIMFA) of the SIS process. Third,
by relaxing the notion of equitable partitions, we derive low-complexity
approximations and bounds for epidemics on arbitrary contact networks. Our
results are an important step towards understanding and controlling epidemics
on large networks.


  We have carried out a dedicated transient survey of 300 deg$^2$ of the SDSS
Stripe 82 region using the Giant Meterwavelength Radio Telescope (GMRT) at 150
MHz. Our multi-epoch observations, together with the TGSS survey, allow us to
probe variability and transient activity on four different timescales,
beginning with 4 hours, and up to 4 years. Data calibration, RFI flagging,
source finding and transient search were carried out in a semi-automated
pipeline incorporating the SPAM recipe. This has enabled us to produce
superior-quality images and carry out reliable transient search over the entire
survey region in under 48 hours post-observation. Among the few thousand unique
point sources found in our 5$\sigma$ single-epoch catalogs (flux density
thresholds of about 24 mJy, 20 mJy, 16 mJy and 18 mJy on the respective
timescales), we find $<$0.08%, 0.01%, $<$0.06% and 0.05% to be variable (beyond
a significance of 4$\sigma$ and fractional variability of 30%) on timescales of
4 hours, 1 day, 1 month and 4 years respectively. This is substantially lower
than that in the GHz sky, where $\sim$1% of the persistent point sources are
found to be variable. Although our survey was designed to probe a superior part
of the transient phase space, our transient sources did not yield any
significant candidates. The transient (preferentially extragalactic) rate at
150 MHz is therefore $<$0.005 on timescales of 1 month and 4 years, and
$<$0.002 on timescales of 1 day and 4 hours, beyond 7$\sigma$ detection
threshold. We put these results in the perspective with the previous studies
and give recommendations for future low-frequency transient surveys.


  In this paper, we deal with the problem of marginalization over and
conditioning on two disjoint subsets of the node set of chain graphs (CGs) with
the LWF Markov property. For this purpose, we define the class of chain mixed
graphs (CMGs) with three types of edges and, for this class, provide a
separation criterion under which the class of CMGs is stable under
marginalization and conditioning and contains the class of LWF CGs as its
subclass. We provide a method for generating such graphs after marginalization
and conditioning for a given CMG or a given LWF CG. We then define and study
the class of anterial graphs, which is also stable under marginalization and
conditioning and contains LWF CGs, but has a simpler structure than CMGs.


  In the present work, a novel and the robust computational investigation is
carried out to estimate solubility of different acids in supercritical carbon
dioxide. Four different algorithms such as radial basis function artificial
neural network, Multi-layer Perceptron (MLP) artificial neural network (ANN),
Least squares support vector machine (LSSVM) and adaptive neuro-fuzzy inference
system (ANFIS) are developed to predict the solubility of different acids in
carbon dioxide based on the temperature, pressure, hydrogen number, carbon
number, molecular weight, and acid dissociation constant of acid. In the
purpose of best evaluation of proposed models, different graphical and
statistical analyses and also a novel sensitivity analysis are carried out. The
present study proposed the great manners for best acid solubility estimation in
supercritical carbon dioxide, which can be helpful for engineers and chemists
to predict operational conditions in industries.


  The analysis of public affairs documents is crucial for citizens as it
promotes transparency, accountability, and informed decision-making. It allows
citizens to understand government policies, participate in public discourse,
and hold representatives accountable. This is crucial, and sometimes a matter
of life or death, for companies whose operation depend on certain regulations.
Large Language Models (LLMs) have the potential to greatly enhance the analysis
of public affairs documents by effectively processing and understanding the
complex language used in such documents. In this work, we analyze the
performance of LLMs in classifying public affairs documents. As a natural
multi-label task, the classification of these documents presents important
challenges. In this work, we use a regex-powered tool to collect a database of
public affairs documents with more than 33K samples and 22.5M tokens. Our
experiments assess the performance of 4 different Spanish LLMs to classify up
to 30 different topics in the data in different configurations. The results
shows that LLMs can be of great use to process domain-specific documents, such
as those in the domain of public affairs.


  Pulsar winds shocked in the ambient medium produce spectacular nebulae
observable from the radio through gamma-rays. The shape and the spectrum of a
pulsar wind nebula (PWN) depend on the angular distribution, magnetization and
energy spectrum of the wind streaming from the pulsar magnetosphere, as well as
on the pulsar velocity and the properties of the ambient medium. The advent of
Chandra, with its unprecedented angular resolution and high sensitivity, has
allowed us not only to detect many new PWNe, but also study their spatial and
spectral structure and dynamics, which has significantly advanced our
understanding of these objects. Here we overview recent observational results
on PWNe, with emphasis on Chandra observations.


  We construct Drinfeld realisations for the quantum affine superalgebras
associated with the osp(1|2n)^{(1)}, Sl(1|2n)^{(2)} and osp(2|2n)^{(2)} series
of affine Lie superalgebras.


  We demonstrate that the Faithfulness property that is assumed in much causal
analysis is robustly violated for a large class of systems of a type that
occurs throughout the life and social sciences: control systems. These systems
exhibit correlations indistinguishable from zero between variables that are
strongly causally connected, and can show very high correlations between
variables that have no direct causal connection, only a connection via causal
links between uncorrelated variables. Their patterns of correlation are robust,
in that they remain unchanged when their parameters are varied. The violation
of Faithfulness is fundamental to what a control system does: hold some
variable constant despite the disturbing influences on it. No method of causal
analysis that requires Faithfulness is applicable to such systems.


  The investigations of the reactive magnetron depositing of the stoichiometric
coatings metal-metalloid were done. The dependences between sputtering
parameters of a target and processes of plasmochemical formation on the surface
of sample metal-metalloid and formations of coatings of the appropriate
structure were investigated. Experimental data on stoichiometric coatings AlN,
Al2O3, TiN, TiO2 is given. Features of reactive magnetron deposition and
investigation results for obtaining of coatings with pregiven properties in
particular for providing stability and controllability of coating deposition
processes in time. Keywords: reactive magnetron sputtering, coatings, oxide,
nitride compositions.


  We construct a manifestly gauge invariant Lagrangian in 3+1 dimensions for N
Kaluza-Klein modes of an SU(m) gauge theory in the bulk. For example, if the
bulk is 4+1, the effective theory is \Pi_{i=1}^{N+1} SU(m)_i with N chiral
(\bar{m},m) fields connecting the groups sequentially. This can be viewed as a
Wilson action for a transverse lattice in x^5, and is shown explicitly to match
the continuum 4+1 compactifed Lagrangian truncated in momentum space. Scale
dependence of the gauge couplings is described by the standard renormalization
group technique with threshold matching, leading to effective power law
running. We also discuss the unitarity constraints, and chiral fermions.


  In the first part of the paper, we develop a theory of crossed products of a
$C^*$-algebra $A$ by an arbitrary (not necessarily extendible) endomorphism
$\alpha:A\to A$. We consider relative crossed products $C^*(A,\alpha;J)$ where
$J$ is an ideal in $A$, and describe up to Morita-Rieffel equivalence all gauge
invariant ideals in $C^*(A,\alpha;J)$ and give six term exact sequences
determining their $K$-theory. We also obtain certain criteria implying that all
ideals in $C^*(A,\alpha;J)$ are gauge invariant, and that $C^*(A,\alpha;J)$ is
purely infinite.
  In the second part, we consider a situation where $A$ is a $C_0(X)$-algebra
and $\alpha$ is such that $\alpha(f a)=\Phi(f)\alpha(a)$, $a\in A$, $f\in
C_0(X)$ where $\Phi$ is an endomorphism of $C_0(X)$. Pictorially speaking,
$\alpha$ is a mixture of a topological dynamical system $(X,\varphi)$ dual to
$(C_0(X),\Phi)$ and a continuous field of homomorphisms $\alpha_x$ between the
fibers $A(x)$, $x\in X$, of the corresponding $C^*$-bundle.
  For systems described above, we establish efficient conditions for the
uniqueness property, gauge-invariance of all ideals, and pure infiniteness of
$C^*(A,\alpha;J)$. We apply these results to the case when $X=$Prim$(A)$ is a
Hausdorff space. In particular, if the associated $C^*$-bundle is trivial, we
obtain formulas for $K$-groups of all ideals in $C^*(A,\alpha;J)$. In this way,
we constitute a large class of crossed products whose ideal structure and
$K$-theory is completely described in terms of $(X,\varphi,\{\alpha_{x}\}_{x\in
X};Y)$ where $Y$ is a closed subset of $X$.


  Recently, it has been argued that application of the Weak Gravity Conjecture
(WGC) to spin-2 fields implies a universal upper bound on the cutoff of the
effective theory for a single spin-2 field. We point out here that these
arguments are largely spurious, because of the absence of states carrying
spin-2 Stuckelberg $U(1)$ charge, and because of incorrect scaling assumptions.
Known examples such as Kaluza-Klein theory that respect the usual WGC do so
because of the existence of a genuine $U(1)$ field under which states are
charged, as in the case of the Stuckelberg formulation of spin-1 theories, for
which there is an unambiguously defined $U(1)$ charge. Theories of bigravity
naturally satisfy a naive formulation of the WGC, $M_W< M_{\rm Pl}$, since the
force of the massless graviton is always weaker than the massive spin-2 modes.
It also follows that theories of massive gravity trivially satisfies this form
of the WGC. We also point out that the identification of a massive spin-2 state
in a truncated higher derivative theory, such as Einstein-Weyl-squared or its
supergravity extension, bears no relationship with massive spin-2 states in the
UV completion, contrary to previous statements in the literature. We also
discuss the conjecture from a swampland perspective and show how the emergence
of a universal upper bound on the cutoff relies on strong assumptions on the
scale of the couplings between the spin-2 and other fields, an assumption which
is known to be violated in explicit examples.


  We report on a computation of holomorphic cuspidal modular forms of weight
one and small level (currently level at most $1500$) and classification of them
according to the projective image of their attached Artin representations. The
data we have gathered, such as Fourier expansions and projective images of
Hecke newforms and dimensions of space of forms, is available in both Magma and
\texttt{Sage} readable formats on a webpage created in support of this ongoing
project. We explain some of the novel aspects of these computations and what
they have uncovered.


  Advances in imaging technologies, combined with inexpensive storage, have led
to an explosion in the volume of publicly available neuroimaging datasets.
Effective analyses of these images hold the potential for uncovering mechanisms
that govern functioning of the human brain, and understanding various
neurological diseases and disorders. The potential significance of these
studies notwithstanding, a growing concern relates to the protection of privacy
and confidentiality of subjects who participate in these studies. In this
paper, we present a de-anonymization attack rooted in the innate uniqueness of
the structure and function of the human brain. We show that the attack reveals
not only the identity of an individual, but also the task they are performing,
and their efficacy in performing the tasks. Our attack relies on novel matrix
analyses techniques that are used to extract discriminating features in
neuroimages. These features correspond to individual-specific signatures that
can be matched across datasets to yield highly accurate identification. We
present data preprocessing, signature extraction, and matching techniques that
are computationally inexpensive, and can scale to large datasets. We discuss
implications of the attack and challenges associated with defending against
such attacks.


  Certain alternative theories of gravity predict that gravitational waves will
disperse as they travel from the source to the observer. The recent binary
black hole observations by Advanced-LIGO have set limits on a modified
dispersion relation from the constraints on their effects on gravitational-wave
propagation. Using an identical modified dispersion, of the form
$E^2=p^2c^2+{\mathbb A}\; p^{\alpha} c^{\alpha}$, where ${\mathbb A}$ denotes
the magnitude of dispersion and $E$ and $p$ are the energy and momentum of the
gravitational wave, we estimate the projected constraints on the modified
dispersion from observations of compact binary mergers by third- generation
ground-based detectors such as the Einstein Telescope and Cosmic Explorer as
well as the space-based detector Laser Interferometer Space Antenna. We find
that third-generation detectors would bound dispersion of gravitational waves
much better than their second-generation counterparts. The Laser Interferometer
Space Antenna, with its extremely good low-frequency sensitivity, would place
stronger constraints than the ground-based detectors for $\alpha \leq 1$,
whereas for $\alpha > 1$, the bounds are weaker. We also study the effect of
the spins of the compact binary constituents on the bounds.


  We extend the halo-based group finder developed by \citet[][]{Yang2005a} to
use data {\it simultaneously} with either photometric or spectroscopic
redshifts. A mock galaxy redshift survey constructed from a high-resolution
N-body simulation is used to evaluate the performance of this extended group
finder. For galaxies with magnitude ${\rm z\le 21}$ and redshift $0<z\le 1.0$
in the DESI legacy imaging surveys (the Legacy Surveys), our group finder
successfully identifies more than 60\% of the members in about $90\%$ of halos
with mass $\ga 10^{12.5}\msunh$. Detected groups with mass $\ga
10^{12.0}\msunh$ have a purity (the fraction of true groups) greater than 90\%.
The halo mass assigned to each group has an uncertainty of about 0.2 dex at the
high mass end $\ga 10^{13.5}\msunh$ and 0.40 dex at the low mass end. Groups
with more than 10 members have a redshift accuracy of $\sim 0.008$. We apply
this group finder to the Legacy Surveys DR8 and find 5.2 Million groups with at
least 3 members. About 387,000 of these groups have at least 10 members. The
resulting catalog containing 3D coordinates, richness, halo masses, and total
group luminosities, is made publicly available.


  We investigate the dynamics of a relativistic electron in a strongly
nonlinear plasma wave in terms of classical mechanics by taking into account
the action of the radiative reaction force. The two limiting cases are
considered. In the first case where the energy of the accelerated electrons is
low, the electron makes many betatron oscillations during the acceleration. In
the second case where the energy of the accelerated electrons is high, the
betatron oscillation period is longer than the electron residence time in the
accelerating phase. We show that the force of radiative friction can severely
limit the rate of electron acceleration in a plasma accelerator.


  The calculation of angular-momentum coupling transformation matrices can be
very time consuming and alternative methods, even if they apply only in special
cases, are helpful. We present a recursion relation for the calculation of
particular 9j symbols used in the quantum theory of angular momentum.


  We critically examine the Roberts homothetic solution for the spherically
symmetric Einstein-scalar field equations in double null coordinates, and show
that the Roberts solution indeed solves the field equations only for one
non-trivial case. We generalize this solution and discuss its relations with
other known exact solutions.


  We investigate stochastic processes possessing scale invariance properties
which we refer to as multifractal processes. The examples of such processes
known so far do not go much beyond the original cascade construction of
Mandelbrot. We provide a new definition of the multifractal process by
generalizing the definition of the self-similar process. We establish general
properties of these processes and show how existing examples fit into our
setting. Finally, we define a new class of examples inspired by the idea of
Lamperti transformation. Namely, for any pair of infinitely divisible
distribution and a stationary process one can construct a multifractal process.


  The capacity region of the Finite-State Multiple Access Channel (FS-MAC) with
feedback that may be an arbitrary time-invariant function of the channel output
samples is considered. We provided a sequence of inner and outer bounds for
this region. These bounds are shown to coincide, and hence yield the capacity
region, of FS-MACs where the state process is stationary and ergodic and not
affected by the inputs, and for indecomposable FS-MAC when feedback is not
allowed.
  Though the capacity region is `multi-letter' in general, our results yield
explicit conclusions when applied to specific scenarios of interest.


  In large-eddy simulations of atmospheric boundary layer turbulence, the
lumped coefficient in the eddy-diffusion subgrid-scale (SGS) model is known to
depend on scale for the case of inert scalars. This scale dependence is
predominant near the surface. In this paper, a scale-dependent dynamic SGS
model for the turbulent transport of reacting scalars is implemented in
large-eddy simulations of a neutral boundary layer. Since the model coefficient
is computed dynamically from the dynamics of the resolved scales, the
simulations are free from any parameter tuning. A set of chemical cases
representative of various turbulent reacting flow regimes is examined. The
reactants are involved in a first-order reaction and are injected in the
atmospheric boundary layer with a constant and uniform surface flux. Emphasis
is placed on studying the combined effects of resolution and chemical regime on
the performance of the SGS model. Simulations with the scale-dependent dynamic
model yield the expected trends of the coefficients as function of resolution,
position in the flow and chemical regime, leading to resolution-independent
turbulent reactant fluxes.


  We analyze two distinct samples of GRBs, with and without radio afterglow
emission. We use a sample of 211 GRBs which is an update of the previous sample
from arXiv:1902.01974, and find, in agreement with previous results (although
with a sample that is almost twice as large) as the intrinsic gamma-ray
duration (Tint) and isotropic equivalent energy (Eiso) distributions between
these two populations appear to differ significantly. The redshift (z)
distributions of the two samples are not statistically different. We analyze
several correlations between variables (Eiso, Tint, jet opening angle, and z),
accounting for selection effects and redshift evolution using the
Efron-Petrosian method. We find a statistically significant anti-correlation
between the jet opening angle and redshift, as well as between Tint and
redshift, for both radio-bright and radio-dark GRBs. Finally, in agreement with
previous work, we find that very high energy (0.1 - 100 GeV) extended emission
is present in the radio-bright GRB sample only. Our work supports the
possibility that the radio-bright and the radio-dark GRBs originate from
different progenitors.


  Motivated by recent experiments on nonlocal transport through multiterminal
superconducting hybrid structures, we present self-consistent calculations
based on quasiclassical Green's functions for the order parameter, currents and
voltages in a system consisting of a diffusive superconductor connected to two
normal and one superconducting electrodes. We investigate non-equilibrium
effects for different biasing conditions corresponding to measurements of the
nonlocal conductance and of the nonlocal resistance. It is shown that while the
nonlocal conductance does not change its sign, this change might be observed in
a nonlocal resistance measurement for certain parameter range. The change of
sign of the nonlocal signal takes places at a voltage of the order of the
self-consistent gap of the superconducting region. We show that this is not
related to the nonlocal Andreev processes but rather to non-equilibrium
effects. We finally discuss the case of four terminal measurements and
demonstrate that a change of sign in the nonlocal resistance appears when the
current injected into the superconductor exceeds a critical value. The
connection to the existing experiments is discussed.


  We present a detailed high spectral resolution (R $\sim$ 40000) study of five
high-z damped Lyman $\alpha$ systems (DLAs) and one sub-DLA detected along four
QSO sightlines. Four of these DLAs are very metal-poor with [Fe/H] $\le$ $-$2.
One of them, at z$_{abs}$ = 4.20287 towards J0953$-$0504, is the most
metal-poor DLA at z $>$ 4 known till date. This system shows no enhancement of
C over Fe and O, and standard Population II star yields can explain its
relative abundance pattern. The DLA at z$_{abs}$ = 2.34006 towards J0035$-$0918
has been claimed to be the most carbon-enhanced metal-poor DLA. However, we
show that thermal broadening is dominant in this system and, when this effect
is taken into account, the measured carbon enhancement ([C/Fe] = 0.45 $\pm$
0.19) becomes $\sim$ 10 times less than what was reported previously. The gas
temperature in this DLA is estimated to be in the range of 5000 $-$ 8000 K,
consistent with a warm neutral medium phase. From photoionization modelling of
two of the DLAs showing C II* absorption, we find that the metagalactic
background radiation alone is not sufficient to explain the observed C II*
cooling rate, and local heating sources, probably produced by in-situ star
formation, are needed. Cosmic ray heating is found to contribute $\gtrsim$ 60%
to the total heating in these systems. Using a sample of metal-poor DLAs with C
II* measurements, we conclude that the cosmic ray ionization rate is equal to
or greater than that seen in the Milky Way in $\sim$ 33% of the systems with C
II* detections.


  We study superconductivity in the Hubbard model on various
quasi-one-dimensional lattices with coexisting wide and narrow bands
originating from multiple sites within a unit cell, where each site corresponds
to a single orbital. The systems studied are the 2-leg and 3-leg ladders, the
diamond chain, and the criss-cross ladder. These one-dimensional lattices are
weakly coupled to form two-dimensional (quasi-one-dimensional) ones, and the
fluctuation exchange approximation is adopted to study
spin-fluctuation-mediated superconductivity. When one of the bands is perfectly
flat, and the Fermi level, intersecting the wide band, is placed in the
vicinity of the flat band, superconductivity arising from the interband
scattering processes is found to be strongly enhanced owing to the combination
of the light electron mass of the wide band and the strong pairing interaction
due to the large density of states of the flat band. Even when the narrow band
has finite band width, the pairing mechanism still works since the edge of the
narrow band, due to its large density of states, plays the role of the flat
band. The results indicate the generality of the high $T_c$ pairing mechanism
due to coexisting wide and "incipient" narrow bands in quasi-one-dimensional
systems.


  Quantum gravity is expected to be necessary in order to understand situations
where classical general relativity breaks down. In particular in cosmology one
has to deal with initial singularities, i.e. the fact that the backward
evolution of a classical space-time inevitably comes to an end after a finite
amount of proper time. This presents a breakdown of the classical picture and
requires an extended theory for a meaningful description. Since small length
scales and high curvatures are involved, quantum effects must play a role. Not
only the singularity itself but also the surrounding space-time is then
modified. One particular realization is loop quantum cosmology, an application
of loop quantum gravity to homogeneous systems, which removes classical
singularities. Its implications can be studied at different levels. Main
effects are introduced into effective classical equations which allow to avoid
interpretational problems of quantum theory. They give rise to new kinds of
early universe phenomenology with applications to inflation and cyclic models.
To resolve classical singularities and to understand the structure of geometry
around them, the quantum description is necessary. Classical evolution is then
replaced by a difference equation for a wave function which allows to extend
space-time beyond classical singularities. One main question is how these
homogeneous scenarios are related to full loop quantum gravity, which can be
dealt with at the level of distributional symmetric states. Finally, the new
structure of space-time arising in loop quantum gravity and its application to
cosmology sheds new light on more general issues such as time.


  When interacting, the solar wind and the ionised atmosphere of a comet
exchange energy and momentum. Our aim is to understand the influence of the
average Parker spiral configuration of the solar wind magnetic field on this
interaction. We compare the theoretical expectations of an analytical
generalised gyromotion with Rosetta observations at comet
67P/Churyumov-Gerasimenko. A statistical approach allows one to overcome the
lack of upstream solar wind measurement. We find that additionally to their
acceleration along (for cometary pick-up ions) or against (for solar wind ions)
the upstream electric field orientation and sense, the cometary pick-up ions
are drifting towards the dawn side of the coma, while the solar wind ions are
drifting towards the dusk side of the coma, independent of the heliocentric
distance. The dynamics of the interaction is not taking place in a plane, as
often assumed in previous works.


  We study the range of a planar random walk on a randomly oriented lattice,
already known to be transient. We prove that the expectation of the range grows
linearly, in both the quenched (for a.e. orientation) and annealed ("averaged")
cases. We also express the rate of growth in terms of the quenched Green
function and eventually prove a weak law of large numbers in the
(non-Markovian) annealed case.


  Experiments in particle physics produce enormous quantities of data that must
be analyzed and interpreted by teams of physicists. This analysis is often
exploratory, where scientists are unable to enumerate the possible types of
signal prior to performing the experiment. Thus, tools for summarizing,
clustering, visualizing and classifying high-dimensional data are essential. In
this work, we show that meaningful physical content can be revealed by
transforming the raw data into a learned high-level representation using deep
neural networks, with measurements taken at the Daya Bay Neutrino Experiment as
a case study. We further show how convolutional deep neural networks can
provide an effective classification filter with greater than 97% accuracy
across different classes of physics events, significantly better than other
machine learning approaches.


  The recent development of decentralised and interoperable social networks
(such as the "fediverse") creates new challenges for content moderators. This
is because millions of posts generated on one server can easily "spread" to
another, even if the recipient server has very different moderation policies.
An obvious solution would be to leverage moderation tools to automatically tag
(and filter) posts that contravene moderation policies, e.g. related to toxic
speech. Recent work has exploited the conversational context of a post to
improve this automatic tagging, e.g. using the replies to a post to help
classify if it contains toxic speech. This has shown particular potential in
environments with large training sets that contain complete conversations.
This, however, creates challenges in a decentralised context, as a single
conversation may be fragmented across multiple servers. Thus, each server only
has a partial view of an entire conversation because conversations are often
federated across servers in a non-synchronized fashion. To address this, we
propose a decentralised conversation-aware content moderation approach suitable
for the fediverse. Our approach employs a graph deep learning model (GraphNLI)
trained locally on each server. The model exploits local data to train a model
that combines post and conversational information captured through random walks
to detect toxicity. We evaluate our approach with data from Pleroma, a major
decentralised and interoperable micro-blogging network containing 2 million
conversations. Our model effectively detects toxicity on larger instances,
exclusively trained using their local post information (0.8837 macro-F1). Our
approach has considerable scope to improve moderation in decentralised and
interoperable social networks such as Pleroma or Mastodon.


  Physics-informed neural networks (PINNs) have shown promise in solving
various partial differential equations (PDEs). However, training pathologies
have negatively affected the convergence and prediction accuracy of PINNs,
which further limits their practical applications. In this paper, we propose to
use condition number as a metric to diagnose and mitigate the pathologies in
PINNs. Inspired by classical numerical analysis, where the condition number
measures sensitivity and stability, we highlight its pivotal role in the
training dynamics of PINNs. We prove theorems to reveal how condition number is
related to both the error control and convergence of PINNs. Subsequently, we
present an algorithm that leverages preconditioning to improve the condition
number. Evaluations of 18 PDE problems showcase the superior performance of our
method. Significantly, in 7 of these problems, our method reduces errors by an
order of magnitude. These empirical findings verify the critical role of the
condition number in PINNs' training.


  Disordered solids often change their elastic response as they slowly age.
Using experiments and simulations, we study how aging disordered planar
networks under an applied stress affects their nonlinear elastic response. We
are able to modify dramatically the elastic properties of our systems in the
non-linear regime. Using simulations, we study two models for the microscopic
evolution of properties of such a material; the first considers changes in the
material strength while the second considers distortions in the microscopic
geometry. Both models capture different aspects of the experiments including
the encoding of memories of the aging history of the system and the dramatic
effects on the material's nonlinear elastic properties. Our results demonstrate
how aging can be used to create complex elastic behavior in the nonlinear
regime.


  In a pilot-wave theory, an individual closed system is described by a
wavefunction $\psi(q)$ and configuration $q$. The evolution of the wavefunction
and configuration are respectively determined by the Schr\"odinger and guidance
equations. The guidance equation states that the velocity field for the
configuration is given by the quantum current divided by the density
$|\psi(q)|^2$. We present the currents and associated guidance equations for
any Hamiltonian given by a differential operator. These are derived directly
from the Schr\"odinger equation, and also as Noether currents arising from a
global phase symmetry associated with the wavefunction in configuration space.


  We show in the Skyrme-Hartree-Fock approach that unambiguous correlations
exist between observables of finite nuclei and nuclear matter properties. Using
this correlation analysis to existing data on the neutron skin thickness of Sn
isotopes, we find important constraints on the value E_{sym}(rho_0) and density
slope L of the nuclear symmetry energy at saturation density. Combining these
constraints with those from recent analyses of isospin diffusion and double
neutron/proton ratio in heavy ion collisions leads to a value of L=58\pm 18 MeV
approximately independent of E_{sym}(\rho_0).


  An era has started in which gas and dust can be observed independently in
protoplanetary disks, thanks to the recent surveys with ALMA. The first
near-complete high-resolution disk survey in both dust and gas in a single
star-forming region has been carried out in Lupus, finding surprisingly low
gas/dust ratios. The goal of this work is to fully exploit CO isotopologues
observations in Lupus, comparing them with physical-chemical model results, in
order to obtain gas masses for a large number of disks. We have employed
physical-chemical models to analyze continuum and CO isotopologues observations
of Lupus disks, including isotope-selective processes and freeze-out. Employing
also the ALMA 13CO-only detections, disk gas masses have been calculated for a
total of 34 sources, expanding the sample of 10 disks studied by Ansdell et al.
(2016), where also C18O was detected. We confirm that overall gas-masses are
very low, often smaller than 1 $M_{\rm J}$, if volatile carbon is not depleted.
Accordingly, global gas/dust ratios predominantly between 1 and 10. Low
CO-based gas masses and gas/dust ratios may indicate rapid loss of gas, or
alternatively chemical evolution, e.g. via sequestering of carbon from CO to
more complex molecules, or carbon locked up in larger bodies. Current ALMA
observations cannot distinguish between these two hypotheses. We have simulated
both scenarios, but chemical model results do not allow us to rule out one of
the two. Assuming that all Lupus disks have evolved mainly due to viscous
processes over the past few Myr, the observed correlation between the current
mass accretion rate and dust mass found by Manara et al. (2016) implies a
constant gas-to-dust ratio, which is close to 100 based on the observed $M_{\rm
disk}/\dot{M}_{\rm acc}$ ratio. This in turn points to a scenario in which
carbon depletion is responsible for the low CO isotopologue line luminosities.


  Given a finite group scheme $G$ over a field and a $G$-variety $X$, we obtain
a criterion for $X$ to be $G$-normal in the sense of \cite{Br24}. When $G$ is
diagonalizable, we describe the local structure of $G$-normal varieties in
codimension $1$ and their dualizing sheaf. As an application, we obtain a
version of the Hurwitz formula for $G$-normal varieties, where $G$ is linearly
reductive.


  Atomic and molecular samples reduced to temperatures below 1 microkelvin, yet
still in the gas phase, afford unprecedented energy resolution in probing and
manipulating how their constituent particles interact with one another. For
simple atoms, such as alkalis, scattering resonances are extremely
well-characterized. However, ultracold physics is now poised to enter a new
regime, where far more complex species can be cooled and studied, including
magnetic lanthanide atoms and even molecules. For molecules, it has been
speculated that a dense forest of resonances in ultracold collision cross
sections will likely express essentially random fluctuations, much as the
observed energy spectra of nuclear scattering do. According to the
Bohigas-Giannoni-Schmit conjecture, these fluctuations would imply chaotic
dynamics of the underlying classical motion driving the collision. This would
provide a paradigm shift in ultracold atomic and molecular physics,
necessitating new ways of looking at the fundamental interactions of atoms in
this regime, as well as perhaps new chaos-driven states of ultracold matter. In
this report we provide the first experimental demonstration that random spectra
are indeed found at ultralow temperatures. In the experiment, an ultracold gas
of erbium atoms is shown to exhibit many Fano-Feshbach resonances, for bosons
on the order of 3 per gauss. Analysis of their statistics verifies that their
distribution of nearest-neighbor spacings is what one would expect from random
matrix theory. The density and statistics of these resonances are explained by
fully-quantum mechanical scattering calculations that locate their origin in
the anisotropy of the atoms' potential energy surface. Our results therefore
reveal for the first time chaotic behavior in the native interaction between
ultracold atoms.


  We present the Cosmic Sands suite of cosmological zoom-in simulations based
on the Simba galaxy formation model in order to study the build up of the first
massive and dusty galaxies in the early Universe. Residing in the most massive
halos, we find that the compact proto-massive galaxies undergo nearly
continuous mergers with smaller subhalos, boosting star formation rates (SFRs)
and the build up of stellar mass. The galaxies are already appreciably
chemically evolved by z=10, with modeled dust masses comparable to those
inferred from observations in the same epoch. We track gas accretion onto the
galaxies to understand how extreme SFRs can be sustained by these early
systems. We find that smooth gas accretion can maintain SFRs above 250
M$_{\odot}$ / yr but to achieve SFRs that boost galaxies well above the main
sequence, a larger perturbation like a gas-rich major merger is necessary to
trigger a starburst episode. Post-processing the Cosmic Sands simulations with
dust radiative transfer, we find that while the infrared luminosities of the
most dust rich galaxies are comparable to local ULIRGs, they are substantially
dimmer than classical z=2 sub-millimeter galaxies. We end with a discussion on
the possible reasons for this discrepancy at the highest masses and the future
work we intend to carry out to study the chemical enrichment of the earliest
dusty galaxies.


  It is noted that the CKM matrix elements for both quarks and leptons as
conceived in the Dualized Standard Model (DSM) can be interpreted as direction
cosines obtained by moving the Darboux trihedron (a 3-frame) along a trajectory
on a sphere traced out through changing energy scales by a 3-vector factorized
from the mass matrix. From the `Darboux' analogues of the well-known
Serret--Frenet formulae for space curves, it is seen that the corner elements
($V_{ub}, V_{td}$ for quarks, and $U_{e3}, U_{\tau 1}$ for leptons) are
associated with the (geodesic) torsion, while the other off-diagonal elements
($V_{us}, V_{cd}$ and $V_{cb}, V_{ts}$ for quarks, and $U_{e2}, U_{\mu 1}$ and
$U_{\mu 3}, U_{\tau 2}$ for leptons) with the (respectively geodesic and
normal) curvatures of the trajectory. From this it follows that (i) the corner
elements in both matrices are much smaller than the other elements, (ii) the
$U_{\mu 3}, U_{\tau 2}$ elements for the lepton CKM matrix are much larger than
their counterparts in the quark matrix. Both these conclusions are strongly
borne out by experiment, for quarks in hadron decays and for leptons in
neutrino oscillations, and by previous explicit calculations within the DSM
scheme.


  This paper studies the problem of content distribution in wireless
peer-to-peer networks where all nodes are selfish and non-cooperative. We
propose a model that considers both the broadcast nature of wireless channels
and the incentives of nodes, where each node aims to increase its own download
rate and reduces its upload rate through the course of content distribution. We
then propose a protocol for these selfish nodes to exchange contents. Our
protocol is distributed and does not require the exchange of money, reputation,
etc., and hence can be easily implemented without additional infrastructure.
Moreover, we show that our protocol can be easily modified to employ network
coding.
  The performance of our protocol is studied. We derive a closed-form
expression of Nash Equilibriums when there are only two files in the system.
The prices of anarchy, both from each node's perspective and the whole system's
perspective, are also characterized. Moreover, we propose a distributed
mechanism where each node adjusts its strategies only based on local
information and show that the mechanism converges to a Nash Equilibrium. We
also introduce an approach for calculating Nash Equilibriums for systems that
incorporate network coding when there are more than two files.


  Triple-differential cross sections for two-photon double ionization of
molecular hydrogen are presented for a central photon energy of 30 eV. The
calculations are based on a fully {\it ab initio}, nonperturbative, approach to
the time-dependent Schroedinger equation in prolate spheroidal coordinates,
discretized by a finite-element discrete-variable-representation. The wave
function is propagated in time for a few femtoseconds using the short,
iterative Lanczos method to study the correlated response of the two
photoelectrons to short, intense laser radiation. The current results often lie
in between those of Colgan {\it et al} [J. Phys. B {\bf 41} (2008) 121002] and
Morales {\it et al} [J. Phys. B {\bf 41} (2009) 134013]. However, we argue that
these individual predictions should not be compared directly to each other, but
preferably to experimental data generated under well-defined conditions.


  After the pandemic, humanity has been facing different types of challenges.
Social relationships, societal values, and academic and professional behavior
have been hit the most. People are shifting their routines to social media and
gadgets, and getting addicted to their isolation. This sudden change in their
lives has caused an unusual social breakdown and endangered their mental
health. In mid-2021, Pakistan's first Human Library was established under
HelpingMind to overcome these effects. Despite online sessions and webinars,
HelpingMind needs technology to reach the masses. In this work, we customized
the UI or UX of a Go Together Mobile Application (GTMA) to meet the
requirements of the client organization. A very interesting concept of the book
(expert listener or psychologist) and the reader is introduced in GTMA. It
offers separate dashboards, separate reviews or rating systems, booking, and
venue information to engage the human reader with his or her favorite human
book. The loyalty program enables the members to avail discounts through a
mobile application and its membership is global where both the human-reader and
human-books can register under the platform. The minimum viable product has
been approved by our client organization.


  Prices of option contracts on two assets within uncertain volatility models
for worst and best-case scenarios satisfy a two-dimensional
Hamilton-Jacobi-Bellman (HJB) partial differential equation (PDE) with cross
derivatives terms. Traditional methods mainly involve finite differences and
policy iteration. This "discretize, then optimize" paradigm requires complex
rotations of computational stencils for monotonicity.
  This paper presents a novel and more streamlined "decompose and integrate,
then optimize" approach to tackle the aforementioned HJB PDE. Within each
timestep, our strategy employs a piecewise constant control, breaking down the
HJB PDE into independent linear two-dimensional PDEs. Using known closed-form
expressions for the Fourier transforms of the Green's functions associated with
these PDEs, we determine an explicit formula for these functions. Since the
Green's functions are non-negative, the solutions to the PDEs, cast as
two-dimensional convolution integrals, can be conveniently approximated using a
monotone integration method. Such integration methods, including a composite
quadrature rule, are generally available in popular programming languages. To
further enhance efficiency, we propose an implementation of this monotone
integration scheme via Fast Fourier Transforms, exploiting the Toeplitz matrix
structure. Optimal control is subsequently obtained by efficiently synthesizing
the solutions of the individual PDEs.
  The proposed monotone piecewise constant control method is demonstrated to be
both $\ell_{\infty} $-stable and consistent in the viscosity sense, ensuring
its convergence to the viscosity solution of the HJB equation. Numerical
results show remarkable agreement with benchmark solutions obtained by
unconditionally monotone finite differences, tree methods, and Monte Carlo
simulation, underscoring the robustness and effectiveness of our method.


  We study correlations between geometric subfactors living on the
Ryu-Takayanagi surface that bounds the entanglement wedge. Using the
surface-state correspondence and the bit threads program, we are able to
calculate mutual information and conditional mutual information between
subfactors. This enables us to count the shared Bell pairs between subfactors,
and we propose an entanglement distillation procedure over these subsystems via
a SWAP gate protocol. We comment on extending to multipartite entanglement.


  FemTech, a rising trend in mobile apps, empowers women to digitally manage
their health and family planning. However, privacy and security vulnerabilities
in period-tracking and fertility-monitoring apps present significant risks,
such as unintended pregnancies and legal consequences. Our approach involves
manual observations of privacy policies and app permissions, along with dynamic
and static analysis using multiple evaluation frameworks. Our research reveals
that many of these apps gather personally identifiable information (PII) and
sensitive healthcare data. Furthermore, our analysis identifies that 61% of the
code vulnerabilities found in the apps are classified under the top-ten Open
Web Application Security Project (OWASP) vulnerabilities. Our research
emphasizes the significance of tackling the privacy and security
vulnerabilities present in period-tracking and fertility-monitoring mobile
apps. By highlighting these crucial risks, we aim to initiate a vital
discussion and advocate for increased accountability and transparency of
digital tools for women's health. We encourage the industry to prioritize user
privacy and security, ultimately promoting a safer and more secure environment
for women's health management.


  We introduce a framework for reasoning about what meaning is captured by the
neurons in a trained neural network. We provide a strategy for discovering
meaning by training a second model (referred to as an observer model) to
classify the state of the model it observes (an object model) in relation to
attributes of the underlying dataset. We implement and evaluate observer models
in the context of a specific set of classification problems, employ heat maps
for visualizing the relevance of components of an object model in the context
of linear observer models, and use these visualizations to extract insights
about the manner in which neural networks identify salient characteristics of
their inputs. We identify important properties captured decisively in trained
neural networks; some of these properties are denoted by individual neurons.
Finally, we observe that the label proportion of a property denoted by a neuron
is dependent on the depth of a neuron within a network; we analyze these
dependencies, and provide an interpretation of them.


  Nearly three decades ago, the field of mechanics was cautioned of the obscure
nature of cavitation processes in soft materials [Gent, A.N., 1990. Cavitation
in rubber: a cautionary tale. Rubber Chemistry and Technology, 63(3)]. Since
then, the debate on the mechanisms that drive this failure process is ongoing.
Using a high precision volume controlled cavity expansion procedure, this paper
reveals the intimate relationship between cavitation and fracture. Combining a
Griffith inspired formulation for crack propagation, and a Gent inspired
formulation for cavity expansion, we show that despite the apparent complexity
of the fracture patterns, the pressure-volume response follows a predictable
path. In contrast to available studies, both the model and our experiments are
able to track the entire process including the unstable branch, by controlling
the volume of the cavity. Moreover, this minimal theoretical framework is able
to explain the ambiguity in previous experiments by revealing the presence of
metastable states that can lead to first order transitions at onset of
fracture. The agreement between the simple theory and all of the experimental
results conducted in PDMS samples with shear moduli in the range of 25-246
[kPa], confirms that cavitation and fracture work together in driving the
expansion process. Through this study we also determine the fracture energy of
PDMS and show its significant dependence on strain stiffening.


  We characterize Y/T-system type difference equations arising from cluster
algebras by triples of matrices, which we call T-data, that have a certain
symplectic property. We show that all mutation loops are essentially obtained
from T-data, which generalizes the general solution for period 1 quivers given
by Fordy and Marsh. We also show that any T-datum associated with a periodic
Y/T-system has the simultaneous positivity. As an application, we propose a
version of Nahm's conjecture from a viewpoint of cluster algebras. We
conjecture that given a periodic T/Y-system of a certain type, we have a family
of hypergeometric q-series that are also modular functions.


  The Outer Scutum-Centaurus arm (OSC) is the most distant molecular spiral arm
known in the Milky Way. The OSC may be the very distant end of the well-known
Scutum-Centaurus arm, which stretches from the end of the Galactic bar to the
outer Galaxy. At this distance the OSC is seen in the first Galactic quadrant.
The population of star formation tracers in the OSC remains largely
uncharacterized. Extragalactic studies show a strong correlation between
molecular gas and star formation, and carbon monoxide (CO) emission was
recently discovered in the OSC. Here we use the Arizona Radio Observatory (ARO)
12-m telescope to observe the $^{12}$CO J = 1-0 and $^{13}$CO J = 1-0
transitions toward 78 HII region candidates chosen from the WISE Catalog of
Galactic HII Regions. These targets are spatially coincident with the Galactic
longitude-latitude ($\ell, b$) OSC locus as defined by HI emission. We detect
CO emission in $\sim 80$% of our targets. In total, we detect 117 $^{12}$CO and
40 $^{13}$CO emission lines. About 2/3 of our targets have at least one
emission line originating beyond the Solar orbit. Most of the detections beyond
the Solar orbit are associated with the Outer Arm, but there are 17 $^{12}$CO
emission lines and 8 $^{13}$CO emission lines with LSR velocities that are
consistent with the velocities of the OSC. There is no apparent difference
between the physical properties (e.g., molecular column density) of these OSC
molecular clouds and non--OSC molecular clouds within our sample.


  We report on measurements of the Upsilon(1S), Upsilon(2S) and Upsilon(3S)
differential and integrated cross sections in pp(bar) collisions at sqrt(s)=1.8
TeV. The three resonances were reconstructed through the decay
Upsilon-->mu(+)mu(-). The cross section measurements are compared to
theoretical models of direct bottomonium production.


  Systems with long-range interactions, while relaxing towards equilibrium,
sometimes get trapped in long-lived non-Boltzmann quasistationary states (QSS)
which have lifetimes that grow algebraically with the system size. Such states
have been observed in models of globally coupled particles that move under
Hamiltonian dynamics either on a unit circle or on a unit spherical surface.
Here, we address the ubiquity of QSS in long-range systems by considering a
different dynamical setting. Thus, we consider an anisotropic Heisenberg model
consisting of classical Heisenberg spins with mean-field interactions and
evolving under classical spin dynamics. Our analysis of the corresponding
Vlasov equation for time evolution of the phase space distribution shows that
in a certain energy interval, relaxation of a class of initial states occurs
over a timescale which grows algebraically with the system size. We support
these findings by extensive numerical simulations. This work further supports
the generality of occurrence of QSS in long-range systems evolving under
Hamiltonian dynamics.


  This work presents the design of an RS(31,27) Reed Solomon encoder for a 3.2
Gbps serial transmitter in 0.18 um CMOS technology. The proposed encoder is
designed with a novel full parallel structure optimized for high speed and high
stability. One data frame contains 2 interleaved RS(31,27) codes and thus it
can correct at most 20 bits of consecutive errors. A corresponding decoder is
implemented on Xilinx Kintex-7 FPGA.


  In this paper, we propose efficient and accurate numerical methods for
computing the ground state and dynamics of the dipolar Bose-Einstein
condensates utilising a newly developed dipole-dipole interaction (DDI) solver
that is implemented with the non-uniform fast Fourier transform (NUFFT)
algorithm. We begin with the three-dimensional (3D) Gross-Pitaevskii equation
(GPE) with a DDI term and present the corresponding two-dimensional (2D) model
under a strongly anisotropic confining potential. Different from existing
methods, the NUFFT based DDI solver removes the singularity by adopting the
spherical/polar coordinates in Fourier space in 3D/2D, respectively, thus it
can achieve spectral accuracy in space and simultaneously maintain high
efficiency by making full use of FFT and NUFFT whenever it is necessary and/or
needed. Then, we incorporate this solver into existing successful methods for
computing the ground state and dynamics of GPE with a DDI for dipolar BEC.
Extensive numerical comparisons with existing methods are carried out for
computing the DDI, ground states and dynamics of the dipolar BEC. Numerical
results show that our new methods outperform existing methods in terms of both
accuracy and efficiency.


  The M3Y-type semi-realistic interaction is applied to deformed nuclei for the
first time. The constrained Hartree-Fock calculations assuming axial symmetry
are implemented for the $N=20$ isotones $^{30}$Ne, $^{32}$Mg, $^{34}$Si and the
$N=28$ isotones $^{40}$Mg, $^{42}$Si, $^{44}$S with the M3Y-P6 interaction. The
results match the experimental data well. Effects of the realistic tensor force
on the nuclear quadrupole deformation are investigated in relation to the loss
of the $N=20$ and $28$ magic numbers. The tensor force is confirmed to favor
the deformation for the $N=28$ nuclei owing to the closure of the $jj$-shell
(\textit{i.e.}, $n0f_{7/2}$), while favoring the sphericity for the $N=20$
nuclei owing to the $\ell s$-closure of $N=20$.


  Fusion-in-Decoder (FiD) is an effective retrieval-augmented language model
applied across a variety of open-domain tasks, such as question answering, fact
checking, etc. In FiD, supporting passages are first retrieved and then
processed using a generative model (Reader), which can cause a significant
bottleneck in decoding time, particularly with long outputs. In this work, we
analyze the contribution and necessity of all the retrieved passages to the
performance of reader models, and propose eliminating some of the retrieved
information, at the token level, that might not contribute essential
information to the answer generation process. We demonstrate that our method
can reduce run-time by up to 62.2%, with only a 2% reduction in performance,
and in some cases, even improve the performance results.


  We measure the polarization fraction of a sample of $6282$ Galactic cold
clumps at $353 \, \mathrm{GHz} $, consisting of $Planck$ Galactic cold clump
(PGCC) catalogue category 1 objects (flux densities measured with
signal-to-noise ratio $(\mathrm{S/N}) > 4$). We find the mean-squared
polarization fraction at $353 \, \mathrm{GHz} $ to be $ \langle \Pi ^ 2 \rangle
= [ 4.79 \pm 0.44 ] \times 10 ^ {-4} $ equating to an $ 11 \, \sigma $
detection of polarization. We test if the polarization fraction depends on the
clumps' physical properties, including flux density, luminosity, Galactic
latitude and physical distance. We see a trend towards increasing polarization
fraction with increasing Galactic latitude, but find no evidence that
polarization depends on the other tested properties. The Simons Observatory,
with an angular resolution of order $1 \, \mathrm{arcmin } $ and noise levels
between $22$ and $54$ $ \mu \mathrm{ K-arcmin } $ at high frequencies, will
substantially enhance our ability to determine the magnetic field structure in
Galactic cold clumps. At $\ge5\,\sigma$ significance, we predict the Simons
Observatory will detect at least $\sim12,000$ cold clumps in intensity and
$\sim430$ cold clumps in polarization. This number of polarization detections
would represent a two orders of magnitude increase over the current $Planck$
results. We also release software that can be used to mask these Galactic cold
clumps in other analyses.


  We present POD, a smartphone that flies, as a new way to achieve hands-free,
eyes-up mobile computing. Unlike existing drone-carried user interfaces, POD
features a smartphone-sized display and the computing and sensing power of a
modern smartphone. We share our experience in building a prototype of POD,
discuss the technical challenges facing it, and describe early results toward
addressing them.


  The lepton-flavour-violating decay K_L --> e \mu is studied in detail within
the context of SU(2)_R x SU(2)_L x U(1)_(B-L) models, which include heavy
Majorana neutrinos. Particular attention is paid to the gauge independence of
this decay process to one loop. In analogy with earlier studies on the
K^0\bar{K}^0 mixing, it is explicitly shown how restoration of gauge invariance
occurs in the decay amplitude containing the box diagrams, when the relevant
Higgs-dependent self-energy and vertex graphs are taken into account in the
on-shell skeleton renormalization scheme. Based on the analytic expressions so
derived, we find that the branching ratio B(K_L --> e \mu) can be considerably
enhanced due to the presence of left- and right-handed currents in the loop,
and can reach values close to or even larger than the present experimental
limit 3.3 x 10^{-11} in the manifest left-right symmetric model. Constraints on
the parameter space of typical left-right models are derived from the possible
decay K_L --> e \mu and a global analysis of other low-energy data.


  Acute lymphoblastic leukemia (ALL) is a heterogeneous hematologic malignancy
involving the abnormal proliferation of immature lymphocytes, accounting for
most pediatric cancer cases. ALL management in children has seen great
improvement in the last decades thanks to better understanding of the disease
leading to improved treatment strategies evidenced through clinical trials.
Commonly a first course of chemotherapy (induction phase) is administered,
followed by treatment with a combination of anti-leukemia drugs. A measure of
the efficacy early in the course of therapy is minimal residual disease (MRD).
MRD quantifies residual tumor cells and indicates the effectiveness of the
treatment over the course of therapy. MRD positivity is defined for values of
MRD greater than 0.01%, yielding left-censored observations. We propose a
Bayesian model to study the relationship between patient features and MRD
observed at two time points during the induction phase. Specifically, we model
the observed MRD values via an auto-regressive model, accounting for
left-censoring of the data and for the fact that some patients are already in
remission after the induction phase. Patient characteristics are included in
the model via linear regression terms. In particular, patient-specific drug
sensitivity based on ex-vivo assays of patient samples is exploited to identify
groups of subjects with similar profiles. We include this information as a
covariate in the model for MRD. We adopt horseshoe priors for the regression
coefficients to perform variable selection to identify important covariates. We
fit the proposed approach to data from three prospective pediatric ALL clinical
trials carried out at the St. Jude Children's Research Hospital. Our results
highlight that drug sensitivity profiles and leukemic subtypes play an
important role in the response to induction therapy as measured by serial MRD
measures.


  HalftimeHash is a new algorithm for hashing long strings. The goals are few
collisions (different inputs that produce identical output hash values) and
high performance.
  Compared to the fastest universal hash functions on long strings (clhash and
UMASH) HalftimeHash decreases collision probability while also increasing
performance by over 50%, exceeding 16 bytes per cycle. In addition,
HalftimeHash does not use any widening 64-bit multiplications or any finite
field arithmetic that could limit its portability.


  Using the 1-loop reduced 3D action of the Abelian Higgs-model we discuss the
order of its finite temperature phase transition. A two-variable saddle point
approximation is proposed for the evaluation of the effective potential. The
strength of the first order case scales like \sim e^{3-6}. Analytic asymptotic
weak coupling and numerical small coupling solutions are compared with special
emphasis on the cancellation of divergences. (Figures are not included, can be
sent upon request from<EMAIL_ADDRESS>.)


  Valentine's face-space suggests that faces are represented in a psychological
multidimensional space according to their perceived properties. However, the
proposed framework was initially designed as an account of invariant facial
features only, and explanations for dynamic features representation were
neglected. In this paper we propose, develop and evaluate a computational model
for a twofold structure of the face-space, able to unify both identity and
expression representations in a single implemented model. To capture both
invariant and dynamic facial features we introduce the face-space duality
hypothesis and subsequently validate it through a mathematical presentation
using a general approach to dimensionality reduction. Two experiments with real
facial images show that the proposed face-space: (1) supports both identity and
expression recognition, and (2) has a twofold structure anticipated by our
formal argument.


  In this paper, we propose a novel reduced-rank adaptive filtering algorithm
by blending the idea of the Krylov subspace methods with the set-theoretic
adaptive filtering framework. Unlike the existing Krylov-subspace-based
reduced-rank methods, the proposed algorithm tracks the optimal point in the
sense of minimizing the \sinq{true} mean square error (MSE) in the Krylov
subspace, even when the estimated statistics become erroneous (e.g., due to
sudden changes of environments). Therefore, compared with those existing
methods, the proposed algorithm is more suited to adaptive filtering
applications. The algorithm is analyzed based on a modified version of the
adaptive projected subgradient method (APSM). Numerical examples demonstrate
that the proposed algorithm enjoys better tracking performance than the
existing methods for the interference suppression problem in code-division
multiple-access (CDMA) systems as well as for simple system identification
problems.


  The possibility of light dark matter (DM) annihilating through a dark photon
(DP) which kinetically mixes (KM) with the Standard Model (SM) hypercharge
field is a very attractive scenario. For DM in the interesting mass range below
$\sim 1$ GeV, it is well known that bounds from the CMB provide a very strong
model building constraint forcing the DM annihilation cross section to be
roughly 3 orders of magnitude below that needed to reproduce the observed relic
density. Under most circumstances this removes the possibility of an $s$-wave
annihilation process for DM in this mass range as would be the case, e.g., if
the DM were a Dirac fermion. In an extra-dimensional setup explored previously,
it was found that the $s$-channel exchange of multiple gauge bosons could
simultaneously encompass a suppressed annihilation cross section during the CMB
era while also producing a sufficiently large annihilation rate during
freeze-out to recover the DM relic density. In this paper, we analyze more
globally the necessary requirements for this mechanism to work successfully and
then realize them within the context of a simple model with two `dark' gauge
bosons having masses of a similar magnitude and whose contributions to the
annihilation amplitude destructively interfere. We show that if the DM mass
threshold lies appropriately in the saddle region of this destructive
interference between the two resonance humps it then becomes possible to
satisfy these requirements simultaneously provided several ancillary conditions
are met. The multiple constraints on the parameter space of this setup are then
explored in detail to identify the phenomenologically successful regions.


  Experimental series of stratified gas-liquid two-phase flows had been carried
out in a 26 mm i.d. transparent acrylic horizontal pipe. The study was aimed to
determine the interfacial wave characteristics of the flow and to develop a
high quality database of it. The longitudinal section of the pipe was used as
the reference section of image recording. Air and water were used as the test
fluids, flowing co-currently inside the pipe. The flow behavior was recorded by
using a high-speed video camera around 5 m in axial distance from the inlet
pipe to ensure the fully-developed stratified gas-liquid two-phase flow. To
correct the refraction due to the acrylic pipe, a correction box was employed
in the visualization test section. The group of stratified smooth and wavy
two-phase flows were successfully recorded and classified on the basis of the
visualization study from 24 couples of test condition of superficial water and
air velocities. Digital image processing technique was then used to perform
quantitative analysis and the results were used to evaluate the existing data.
In the present study, the image processing technique was performed to obtain
the liquid holdup distribution. The present results show satisfactory agreement
with previous works.


  Mechanical displacement in commonly used piezoelectric materials is typically
restricted to linear or biaxial in nature and to a few percent of the material
dimensions. Here, we show that free-standing BaTiO$_3$ membranes exhibit
non-conventional electromechanical coupling. Under an external electric field,
these superelastic membranes undergo controllable and reversible
'sushi-rolling-like' 180$^\circ$ folding-unfolding cycles. This crease-free
folding is mediated by charged ferroelectric domains, leading to a giant > 3.8
and 4.6 $\mu$m displacements for a 30-nm thick membrane at room temperature and
60$^\circ$C, respectively. Further increasing the electric field above the
coercive value changes the fold curvature, hence augmenting the effective
piezoresponse. Finally, it is found that the membranes fold with increasing
temperature followed by complete immobility of the membrane above the Curie
temperature, allowing us to model the ferroelectric-domain origin of the
effect.


  We construct an example of supersymmetric Chern-Simons-matter theory with a
matter field transforming as a singlet representation of the supersymmetry
algebra, where the bosonic and fermionic degrees of freedom do not match. This
is obtained as a non-relativistic limit of the N=2 Chern-Simons-matter theory
in 1+2 dimensions, where the particle and anti-particle coexist. We also study
the index to investigate the mimatch of bosonic and fermionic degrees of
freedom.


  This is the third in a series of papers which outlines an approach to the
classification of $\mathcal{N}{=}2$ superconformal field theories at rank 2 via
the study of their Coulomb branch geometries. Here we use the fact that the
encoding of a Coulomb branch geometry as a Seiberg-Witten curve and 1-form
enjoys a large reparametrisation invariance. While there is always a unique way
to fix this invariance such that the curve and 1-form are single-valued over
the Coulomb branch -- the "canonical frame" of the curve used in the first two
papers in this series -- there are other useful frames in which the curve is
single-valued but the 1-form is allowed to be multi-valued. In these frames,
which we call "automorphism frames", the 1-form is periodic up to an
automorphism twist. We argue that the multi-valuedness of the automorphism
frame can simplify the computational complexity of finding new consistent scale
invariant solutions. We demonstrate this in an example by using the
automorphism frame to construct for the first time a genus 2 Seiberg-Witten
curve for the $\mathcal{N}{=}4$ SU(3) superYang-Mills theory, a solution that
is hard to find by other approaches.


  Based on the data sample of 33 pb$^{-1}$ collected at and around 3.773 GeV
with the BES-II detector at the BEPC collider, the absolute branching fractions
for the semileptonic decays $D^0\to K^-\mu^+\nu_\mu$ and
$D^0\to\pi^-\mu^+\nu_\mu$ have been measured. In the system recoiling against
$7584\pm198\pm341$ singly tagged $\bar D^0$ mesons, $87.2\pm13.6$ events for
$D^0\to K^-\mu^+\nu_\mu$ and $9.3\pm7.4$ events for $D^0\to\pi^-\mu^+\nu_\mu$
are observed. These yield the absolute branching fractions to be $BF(D^0\to
K^-\mu ^+\nu_\mu)= (3.55\pm0.56\pm0.59)%$ and $BF(D^0\to\pi^-\mu^+\nu_\mu)=
(0.38\pm0.30\pm0.10)%$. The measured branching fraction for $D^0\to K^-\mu
^+\nu_\mu$ was previously used to determine the ratio $\Gamma(D^0\to
K^-\mu^+\nu_\mu)/ \Gamma(D^+\to \bar K^0\mu^+\nu_\mu)$ combining the previously
measured branching fraction for $D^+\to \bar K^0\mu^+\nu_\mu$ by the BES
Collaboration.


  In this paper, we extend the correspondence between Bayes' estimation and
optimal interpolation in a Reproducing Kernel Hilbert Space (RKHS) to the case
of linear inequality constraints such as boundedness, monotonicity or
convexity. In the unconstrained interpolation case, the mean of the posterior
distribution of a Gaussian Process (GP) given data interpolation is known to be
the optimal interpolation function minimizing the norm in the RKHS associated
to the GP. In the constrained case, we prove that the Maximum A Posteriori
(MAP) or Mode of the posterior distribution is the optimal constrained
interpolation function in the RKHS. So, the general correspondence is achieved
with the MAP estimator and not the mean of the posterior distribution. A
numerical example is given to illustrate this last result.


  We extend some results of Gun, Murty, and Rath on elliptic modular forms. We
take ANY Fuchsian triangle group with a cusp and look at power series
expansions in a natural parameter around that cusp. Consider the automorphic
forms for such a triangle group whose power series expansions in the natural
parameter have algebraic coefficients. We show that the zeros of such forms are
either transcendental or are "CM." By "CM," we mean they correspond to abelian
varieties with complex multiplication. This result is the first of its kind in
the case of non-arithmetic groups.


  We study the star formation and the mass assembly process of 0.3<=z<2.5
galaxies using their IR emission from MIPS 24um band. We used an updated
version of the GOODS-MUSIC catalog, extended by the addition of mid-IR fluxes.
We compared two different estimators of the Star Formation Rate: the total
infrared emission derived from 24um, estimated using both synthetic and
empirical IR templates, and the multiwavelength fit to the full galaxy SED. For
both estimates, we computed the SFR Density and the Specific SFR. The two SFR
tracers are roughly consistent, given the uncertainties involved. However, they
show a systematic trend, IR-based estimates exceeding the fit-based ones as the
SFR increases. We show that: a) at z>0.3, the SFR is well correlated with
stellar mass, and this relationship seems to steepen with redshift (using
IR-based SFRs); b) the contribution to the global SFRD by massive galaxies
increases with redshift up to ~2.5, more rapidly than for galaxies of lower
mass, but appears to flatten at higher z; c) despite this increase, the most
important contributors to the SFRD at any z are galaxies of about, or
immediately lower than, the characteristic stellar mass; d) at z~2, massive
galaxies are actively star-forming, with a median SFR 300 Msun/yr. During this
epoch, they assemble a substantial part of their final stellar mass; e) the
SSFR shows a clear bimodal distribution. The analysis of the SFRD and the SSFR
seems to support the downsizing scenario, according to which high mass galaxies
have formed their stars earlier and faster than their low mass counterparts. A
comparison with theoretical models indicates that they follow the global
increase in the SSFR with redshift and predict the existence of quiescent
galaxies even at z>1.5, but they systematically underpredict the average SSFR.


  This paper presents a method to calculate the exact average block error
probability of some random code ensembles under maximum-likelihood decoding.
The proposed method is applicable to various channels and ensembles. The focus
is on both spherical and Gaussian random codes on the additive white Gaussian
noise channel as well as binary random codes on both the binary symmetric
channel and the binary erasure channel.
  While for the uniform spherical ensemble Shannon, in 1959, argued with solid
angles in $N$-dimensional space, the presented approach projects the problem
into two dimensions and applies standard trigonometry. This simplifies the
derivation and also allows for the analysis of the independent identically
distributed (i.i.d.) Gaussian ensemble which turns out to perform better for
short blocklengths and high rates. Moreover, a new lower bound on the average
block error probability of the uniform spherical ensemble is found. For codes
with more than three codewords, it is tighter than the sphere packing bound,
but requires exactly the same computing effort. Furthermore, tight
approximations are proposed to simplify the computation of both the exact
average error probability and the two bounds.
  For the binary symmetric channel and the binary erasure channel, bounds on
the average block error probability for i.i.d.\ random coding are derived and
compared to the exact calculations.


  Event-based cameras are biologically inspired sensors that output events,
i.e., asynchronous pixel-wise brightness changes in the scene. Their high
dynamic range and temporal resolution of a microsecond makes them more reliable
than standard cameras in environments of challenging illumination and in
high-speed scenarios, thus developing odometry algorithms based solely on event
cameras offers exciting new possibilities for autonomous systems and robots. In
this paper, we propose a novel stereo visual odometry method for event cameras
based on feature detection and matching with careful feature management, while
pose estimation is done by reprojection error minimization. We evaluate the
performance of the proposed method on two publicly available datasets: MVSEC
sequences captured by an indoor flying drone and DSEC outdoor driving
sequences. MVSEC offers accurate ground truth from motion capture, while for
DSEC, which does not offer ground truth, in order to obtain a reference
trajectory on the standard camera frames we used our SOFT visual odometry, one
of the highest ranking algorithms on the KITTI scoreboards. We compared our
method to the ESVO method, which is the first and still the only stereo event
odometry method, showing on par performance on the MVSEC sequences, while on
the DSEC dataset ESVO, unlike our method, was unable to handle outdoor driving
scenario with default parameters. Furthermore, two important advantages of our
method over ESVO are that it adapts tracking frequency to the asynchronous
event rate and does not require initialization.


  Strange nonchaotic attractors (SNAs) have been identified and studied in the
literature exclusively in quasiperiodically driven nonlinear dynamical systems.
It is an interesting question to ask whether they can be identified with other
types of forcings as well, which still remains as an open problem. Here, we
show that robust SNAs can be created by a small amount of noise in periodically
driven nonlinear dynamical systems by a single force. The robustness of these
attractors is tested by perturbing the system with logical signals leading to
the emulation of different logical elements in the SNA regions.


  We revisit the physical properties of global and local monopoles and discuss
their implications in the dynamics of monopole networks. In particular, we
review the Velocity-dependent One-Scale (VOS) model for global and local
monopoles and propose physically motivated changes to its equations. We suggest
a new form for the acceleration term of the evolution equation of the
root-mean-squared velocity and show that, with this change, the VOS model is
able to describe the results of radiation and matter era numerical simulations
of global monopole networks with a single value of the acceleration parameter
$k$, thus resolving the tension previously found in the literature. We also
show that the fact that the energy of global monopoles is not localized within
their cores affects their dynamics and, thus, the Hubble damping terms in the
VOS equations. We study the ultra-relativistic linear scaling regime predicted
by the VOS equations and demonstrate that it cannot be attained either on
radiation or matter eras and, thus, cannot arise from the cosmological
evolution of a global monopole network. We also briefly discuss the
implications of our findings for the VOS model for local monopoles.


  Suggestions concerning the generalization of the geometric quantization to
the case of nonlinear field theories are given. Results for the Liouville field
theory are presented.