  We describe the multisymplectic analysis of the constraints of first-order
embedded submanifolds inherited from diffeomorphisms of the ambient manifold.
The ambient diffeomorphism deformations of first-order embedded submanifolds
are examined. We find that the covariant Noether currents, corresponding to the
inherited ambient diffeomorphism symmetry, satisfy a non-Abelian deformation
algebra, the structure functions being the Cartan structure functions on the
ambient manifold. We define the covariant kinematical phase space of
pseudoholomorphic embeddings (the symplectic 2-submanifolds of a symplectic
manifold) explicitly as a subbundle of the covariant kinematical phase space of
embeddings. The induced algebra of Noether currents satisfies the same algebra
as before, the symmetry thus being preserved on this subclass of embeddings.
The graded multisymplectic manifolds of the covariant Hamiltonian BRST
formalism, developed by the author, are explicitly constructed for the symmetry
of embeddings and pseudoholomorphic embedding.The ``(supersymmetry) multiplet
and its dualities'' postulated by Witten arise naturally as the local fibre
coordinates on the graded phase space. The BRST algebra for the
pseudoholomorphic class is computed. The structure functions implicit in
Witten's treatment of the topological sigma model arise as the Cartan structure
functions in a Darboux basis on the ambient symplectic manifold.


  We first consider a non-primitive substitution subshift that is conjugate to
the Chacon map. We then derive spectral estimates for a particular subshift and
the speed of weak mixing for a class of observables with certain regularity
conditions. After, we use these results to find the speed of weak mixing for
the Chacon map on the interval and show that this bound is essentially sharp.


  We developed new concentration inequalities for a quantum state on an
$N$-qudit system or measurement outcomes on it that apply to an adversarial
setup, where an adversary prepares the quantum state. Our one-sided
concentration inequalities for a quantum state require the $N$-qudit system to
be permutation invariant and are thus de-Finetti type, but they are tighter
than the one previously obtained. We show that the bound can further be
tightened if each qudit system has an additional symmetry. Furthermore, our
concentration inequality for the outcomes of independent and identical
measurements on an $N$-qudit quantum system has no assumption on the
adversarial quantum state and is much tighter than the conventional one
obtained through Azuma's inequality. We numerically demonstrate the tightness
of our bounds in simple quantum information processing tasks.


  We propose an improved exponential Generalized Uncertainty Principle (GUP) by
introducing a positive integer $n$ called the suppressing index. Due to the
UV/IR mixing brought by the GUP, the states with momenta smaller than the
critical momentum ($P < P_{\rm Crit}$) are canceled by the states with momenta
larger than the critical momentum ($P > P_{\rm Crit}$) and thus have no
contributions to the energy density of the vacuum. By considering the
contributions just from the states with momenta larger than the critical
momentum ($P > P_{\rm Crit}$) and choosing a suitable suppressing index, $n
\sim 10^{123}$, we calculate the cosmological constant consistent with the
experimentally observed value.


  We provide a contour integral formula for the exact partition function of
${\cal N}=2$ supersymmetric $U(N)$ gauge theories on compact toric
four-manifolds by means of supersymmetric localisation. We perform the explicit
evaluation of the contour integral for $U(2)$ ${\cal N}=2$ theory on
$\mathbb{P}^2$ for all instanton numbers. In the zero mass case, corresponding
to the ${\cal N}=4$ supersymmetric gauge theory, we obtain the generating
function of the Euler characteristics of instanton moduli spaces in terms of
mock-modular forms. In the decoupling limit of infinite mass we find that the
generating function of local and surface observables computes equivariant
Donaldson invariants, thus proving in this case a long-standing conjecture by
N. Nekrasov. In the case of vanishing first Chern class the resulting
equivariant Donaldson polynomials are new.


This paper has been withdrawn by the author due to a crucial error


  The above equation is also called as Euler(6,2,5) system. By computational
aspect these systems are very interesting. And we can also apply these methods
to other Diophantine equations. We give a brief history of these systems and
how we searched for these big solutions on Boinc. Our two Boinc projects ran
from April of 2010 to July of 2011.


  Anomalous cancellation of fractions is a mathematically inaccurate method
where cancelling the common digits of the numerator and denominator correctly
reduces it. While it appears to be accidentally successful, the property of
anomalous cancellation is intricately connected to the number of digits of the
denominator as well as the base in which the fraction is represented. Previous
work have been mostly surrounding three digit solutions or specific properties
of the same. This paper seeks to get general results regarding the structure of
numbers that follow the cancellation property (denoted by $P^*_{\ell; k}$) and
an estimate of the total number of solutions possible in a given base
representation. In particular, interesting properties regarding the saturation
of the number of solutions in general and $p^n$ bases (where $p$ is a prime)
have been studied in detail.


  In an academic landscape where female physicists are still strongly
underrepresented, underlying causes like unconscious gender bias deserve
specific attention. Members of academia are often not aware of their intrinsic,
hence unconscious, biases; this can have negative effects on students and staff
at all career levels. At the Queen's University Belfast, I have developed and
conducted a workshop on unconscious gender bias awareness at the School of
Mathematics and Physics. The first installment of the workshop was attended by
63 members of the School, among them 26 academic staff (lecturer level and
above). Participants attended an informational talk followed by a discussion
session, and then took part in the Harvard Implicit Association Test for
association of gender with science. The participants self-reported their
results and their previous expectations, followed by a group discussion. Here I
present the observed magnitude of unconscious gender bias and summarise the
discussion points of the participants. The outcomes that bias can have on the
success of physics students as well as the careers of physicists in an academic
context will be highlighted. Putting the results into context, I discuss steps
forward to make physics a level playing field for all genders.


  Fourier transform scanning tunneling microscopy on BSCCO subgap resonances
has deciphered an octet of "quasi-particle" states that are consistent with the
Fermi surface and energy gap observed by ARPES, but the origin of the
high-intensity k-space octets and the sharply defined r-space checkerboard is
unexplained. The filamentary ferroelastic nanodomain model that predicted the
r-space checkerboard also explains the k-space octets and the origin of the
apparent anisotropic surface d-wave gap by using strong electron-phonon
interactions outside the CuO2 planes. The topological model identifies the
factors that stabilize high-intensity k-space octets in the presence of a very
high level of irregular r-space checkerboard noise.


  A scalable quantum computer could be built by networking together many simple
processor cells, thus avoiding the need to create a single complex structure.
The difficulty is that realistic quantum links are very error prone. A solution
is for cells to repeatedly communicate with each other and so 'purify' any
imperfections; however prior studies suggest that the cells themselves must
then have prohibitively low internal error rates. Here we describe a method by
which even error-prone cells can perform purification: groups of cells generate
shared resource states, which then enable stabilization of topologically
encoded data. Given a realistically noisy network (>=10% error rate) we find
that our protocol can succeed provided that intra-cell error rates for
initialisation, state manipulation and measurement are below 0.82%. This level
of fidelity is already achievable in several laboratory systems.


  A curvature model (V,A) is a real vector space V which is equipped with a
"curvature operator" A(x,y)z that A has the same symmetries as an affine
curvature operator; A(x,y)z=-A(y,x)z and A(x,y)z+A(y,z)x+A(z,x)y=0. Such a
model is called projective affine Osserman if the spectrum of the Jacobi
operator J(y):x->A(x,y)y, is projectively constant. There are topological
conditions imposed on such a model by Adam's Theorem concerning vector fields
on spheres. In this paper we construct projective affine Osserman curvature
models when the dimension is odd, when the dimension is congruent to 2 mod 4,
and when the dimension is congruent to 4 mod 8 for all the eigenvalue structure
is allowed by Adam's Theorem.


  Latest developments in leptogenesis are reviewed with a particular emphasis
on the proposals to test leptogenesis. We discuss in particular the important
role played by light and heavy flavour effects in the determination of the
final asymmetry and the attractive features of the N_2 dominated scenario.


  We complete the intrinsic characterization of spherically symmetric solutions
partially accomplished in a previous paper [Class.Quant.Grav. (2010) 27
205024]. In this approach we consider every compatible algebraic type of the
Ricci tensor, and we analyze specifically the conformally flat case for perfect
fluid and Einstein-Maxwell solutions. As a direct application we obtain the
{\em ideal} labeling (exclusively involving explicit concomitants of the metric
tensor) of the Schwarzschild interior metric and the Vaidya solution. The
Stephani universes and some significative subfamilies are also characterized.


  We consider the problem of finding one or more desired items out of an
unsorted database. Patel has shown that if the database permits quantum
queries, then mere digitization is sufficient for efficient search for one
desired item. The algorithm, called factorized quantum search algorithm,
presented by him can locate the desired item in an unsorted database using
$O(log_{4}N)$ queries to factorized oracles. But the algorithm requires that
all the property values must be distinct from each other. In this paper, we
discuss how to make a database satisfy the requirements, and present a quantum
search engine based on the algorithm. Our goal is achieved by introducing
auxiliary files for the property values that are not distinct, and converting
every complex query request into a sequence of calls to factorized quantum
search algorithm. The query complexity of our algorithm is $O(P*Q*M*log_{4}N)$,
where P is the number of the potential simple query requests in the complex
query request, Q is the maximum number of calls to the factorized quantum
search algorithm of the simple queries, M is the number of the auxiliary files
for the property on which our algorithm are searching for desired items. This
implies that to manage an unsorted database on an actual quantum computer is
possible and efficient.


  In the article, we study single and pair $J/\psi$ hadroproduction in the
Improved Color Evaporation Model via the Parton Reggeization Approach. The last
one is based on $k_T$-factorization of hard processes in multi-Regge
kinematics, the Kimber-Martin-Ryskin-Watt model for unintegrated parton
distribution functions, and the effective field theory of Reggezied gluons and
quarks, suggested by L.N. Lipatov. We compare contributions from the single and
double parton scattering mechanisms in the pair $J/\psi$ production. The
numerical calculations are realized using the Monte-Carlo event generator
KaTie.


  The complete set of two-loop renormalization group equations in general gauge
field theories is presented. This includes the \beta functions of parameters
with and without a mass dimension.


  Users of automated vehicles will move away from being drivers to passengers,
preferably engaged in other activities such as reading or using laptops and
smartphones, which will strongly increase susceptibility to motion sickness.
Similarly, in driving simulators, the presented visual motion with scaled or
even without any physical motion causes an illusion of passive motion, creating
a conflict between perceived and expected motion, and eliciting motion
sickness. Given the very large differences in sickness susceptibility between
individuals, we need to consider sickness at an individual level. This paper
combines a group-averaged sensory conflict model with an individualized
accumulation model to capture individual differences in motion sickness
susceptibility across various vision conditions. The model framework can be
used to develop personalized models for users of automated vehicles and improve
the design of new motion cueing algorithms for simulators. The feasibility and
accuracy of this model framework are verified using two existing datasets with
sickening. Both datasets involve passive motion, representative of being driven
by an automated vehicle. The model is able to fit an individuals motion
sickness responses using only 2 parameters (gain K1 and time constant T1), as
opposed to the 5 parameters in the original model. This ensures unique
parameters for each individual. Better fits, on average by a factor of 1.7 of
an individuals motion sickness levels, are achieved as compared to using only
the group-averaged model. Thus, we find that models predicting group-averaged
sickness incidence cannot be used to predict sickness at an individual level.
On the other hand, the proposed combined model approach predicts individual
motion sickness levels and thus can be used to control sickness.


  Engineered optical absorbers are of substantial interest for applications
ranging from stray light reduction to energy conversion. We demonstrate a
large-area (centimeter-scale) metamaterial that features near-unity
frequency-selective absorption in the mid-infrared wavelength range. The
metamaterial comprises a self-assembled porous structure known as an inverse
opal, here made of silica. The structure's large volume fraction of voids,
together with the vibrational resonances of silica in the mid-infrared spectral
range, reduce the metamaterial's refractive index to close to that of air and
introduce considerable optical absorption. As a result, the frequency-selective
structure efficiently absorbs incident light of both polarizations even at very
oblique incidence angles. The absorber remains stable at high temperatures
(measured up to ~900 degrees C), enabling its operation as a
frequency-selective thermal emitter. The excellent performance of this
absorber/emitter and ease of fabrication make it a promising surface coating
for passive radiative cooling, laser safety, and other large-area applications.


  The Hilbert transform is essentially the \textit{only} singular operator in
one dimension. This undoubtedly makes it one of the the most important linear
operators in harmonic analysis. The Hilbert transform has had a profound
bearing on several theoretical and physical problems across a wide range of
disciplines; this includes problems in Fourier convergence, complex analysis,
potential theory, modulation theory, wavelet theory, aerofoil design,
dispersion relations and high-energy physics, to name a few.
  In this monograph, we revisit some of the established results concerning the
global behavior of the Hilbert transform, namely that it is is weakly bounded
on $\eL^1(\R)$, and strongly bounded on $\eL^p(\R)$ for $1 < p <\infty$, and
provide a self-contained derivation of the same using real-variable techniques.


  This article is concerned with the question of constructing effcient
multigrid preconditioners for the linear systems arising when applying
semismooth Newton methods to large-scale linear-quadratic optimization problems
constrained by smoothing operators with box-constraints on the controls. It is
shown that, for certain discretizations of the optimization problem, the linear
systems to be solved at each semismooth Newton iteration reduce to inverting
principal minors of the Hessian of the associated unconstrained problem. As in
the case when box-constraints on the controls are absent, the multigrid
preconditioner introduced here is shown to increase in quality as the mesh-size
decreases, resulting in a number of iterations that decreases with mesh-size.
However, unlike the unconstrained case, the spectral distance between the
preconditioners and the Hessian is shown to be of suboptimal order in general.


  In this paper we study spectral properties of Jacobi operators. In
particular, we prove two main results: (1) that perturbing the diagonal
coefficients of Jacobi operator, in an appropriate sense, results in
exponential localization, and purely pure point spectrum with exponentially
decaying eigenfunctions; and (2) we present examples of decaying potentials
$b_n$ such that the corresponding Jacobi operators have purely pure point
spectrum.


  We impose the requirement that the isovector axial vector current for the
soliton sector of the chiral quark model transforms correctly under particle
conjugation. This forces us to choose an otherwise arbitrary ordering of
collective space operators in such a way that the next--to--leading $1/N_C$
correction to $g_A$ vanishes.


  Participatory budgeting is a democratic process for allocating funds to
projects based on the votes of members of the community. However, most input
methods of voters' preferences prevent the voters from expressing complex
relationships among projects, leading to outcomes that do not reflect their
preferences well enough. In this paper, we propose an input method that begins
to address this challenge, by allowing participants to express substitutes over
projects. Then, we extend a known aggregation mechanism from the literature
(Rule X) to handle substitute projects. We prove that our extended rule
preserves proportionality under natural conditions, and show empirically that
it obtains substantially more welfare than the original mechanism on instances
with substitutes.


  A dynamical version of the Bourgain-Fremlin-Talagrand dichotomy shows that
the enveloping semigroup of a dynamical system is either very large and
contains a topological copy of the Stone-Cech compactification of the natural
numbers, or it is a "tame" topological space whose topology is determined by
the convergence of sequences. In the latter case we say that the dynamical
system is tame. We show that (i) a metric distal minimal system is tame iff it
is equicontinuous (ii) for an abelian acting group a tame metric minimal system
is PI (hence a weakly mixing minimal system is never tame), and (iii) a tame
minimal cascade has zero topological entropy. We also show that for minimal
distal-but-not-equicontinuous systems the canonical map from the enveloping
operator semigroup onto the Ellis semigroup is never an isomorphism. This
answers a long standing open question. We give a complete characterization of
minimal systems whose enveloping semigroup is metrizable. In particular it
follows that for abelian acting group such a system is equicontinuous.


  We present the design, manufacturing methods, and characterization of 20
microwave feed horns currently in use on the Microwave Anisotropy Probe (MAP)
satellite. The nature of the cosmic microwave background (CMB) anisotropy
requires a detailed understanding of the properties of every optical component
of a microwave telescope. In particular, the properties of the feeds must be
known so that the forward gain and sidelobe response of the telescope can be
modeled and so that potential systematic effects may be computed. MAP requires
low emissivity, azimuthally symmetric, low-sidelobe feeds in five microwave
bands (K, Ka, Q, V, and W) that fit within a constrained geometry. The beam
pattern of each feed is modeled and compared with measurements; the agreement
is generally excellent to the -60 dB level (80 degrees from the beam peak).
This agreement verifies the beam-predicting software and the manufacturing
process. The feeds also affect the properties and modeling of the microwave
receivers. To this end, we show that the reflection from the feeds is less than
-25 dB over most of each band and that their emissivity is acceptable. The
feeds meet their multiple requirements.


  It is shown that the lattice Wess-Zumino model written in terms of
Ginsparg-Wilson fermions is invariant under a generalized supersymmetry
transformation which is determined by an iterative procedure in the coupling
constant. This transformation is non-linear in the scalar fields and depends on
the superpotential parameters. The implications of this lattice invariance are
discussed.


  The Kardar-Parisi-Zhang (KPZ) class is a paradigmatic example of universality
in nonequilibrium phenomena, but clear experimental evidences of asymptotic
2D-KPZ statistics are still very rare, and far less understanding stems from
its short-time behavior. We tackle such issues by analyzing surface
fluctuations of CdTe films deposited on polymeric substrates, based on a huge
spatio-temporal surface sampling acquired through atomic force microscopy. A
\textit{pseudo}-steady state (where average surface roughness and spatial
correlations stay constant in time) is observed at initial times, persisting up
to deposition of $\sim 10^{4}$ monolayers. This state results from a fine
balance between roughening and smoothening, as supported by a phenomenological
growth model. KPZ statistics arises at long times, thoroughly verified by
universal exponents, spatial covariance and several distributions. Recent
theoretical generalizations of the Family-Vicsek scaling and the emergence of
log-normal distributions during interface growth are experimentally confirmed.
These results confirm that high vacuum vapor deposition of CdTe constitutes a
genuine 2D-KPZ system, and expand our knowledge about possible
substrate-induced short-time behaviors.


  We consider instances of bipartite graphs and a number of asymptotic
performance experiments in three projects: (1) top movie lists, given databases
of movies and viewers, (2) maximum matchings, and (3) minimum set covers.
Experiments are designed to measure the asymptotic runtime performance of
abstract data types (ADTs) in three programming languages: Java, R, and C++.
The outcomes of these experiments may be surprising. In project (1), the best
ADT in R consistently outperforms all ADTs in public domain Java libraries,
including the library from Google. The largest movie list has $2^{20}$ titles.
In project (2), the Ford-Fulkerson algorithm implementation in R significantly
outperforms Java. The hardest instance has 88452 rows and 729 columns. In
project (3), a stochastic version of a greedy algorithm in R can significantly
outperform a state-of-the-art stochastic solver in C++ on instances with
$num\_rows \ge 300$ and $num\_columns \ge 3000$.


  Most self-force calculations rely, in one way or another, on representations
of a particle's Detweiler- Whiting singular field. We present a simple method
of calculating the singular field to high order in a local expansion in powers
of distance from the particle. As a demonstration, we compute the singular
field to 14th order in distance, 10 orders beyond the previous state of the
art, in the simple case of a scalar charge in circular orbit around a
Schwarzschild black hole. We provide the result in both a 4-dimensional form
and a decomposed form suitable for use in an m-mode puncture scheme. Our method
should have applications in overcoming bottlenecks in current self-force
calculations at both first and second order in perturbation theory.


  There is evidence that string theory possesses a large discretuum of stable
and/or metastable ground states, with zero or four supersymmetries in four
dimensions. I discuss critically the nature of this evidence. Assuming this
"landscape" exists, anthropic explanations of some quantities are almost
inevitable. I explain that this landscape is likely to lead to a prediction of
low energy supersymmetry. But we argue that many features of low energy physics
are not anthropic and, as currently understood, the landscape picture will get
them wrong. This indicates that this viewpoint is potentially falsifiable.
Moreover, if it is correct, many questions must be answered through more
conventional scientific explanations. This is based on talks presented at the
conference QTS3 at the University of Cincinnati and at the ITP in 2003.


  Federated learning (FL) is a distributed learning process where the model
(weights and checkpoints) is transferred to the devices that posses data rather
than the classical way of transferring and aggregating the data centrally. In
this way, sensitive data does not leave the user devices. FL uses the FedAvg
algorithm, which is trained in the iterative model averaging way, on the
non-iid and unbalanced distributed data, without depending on the data
quantity. Some issues with the FL are, 1) no scalability, as the model is
iteratively trained over all the devices, which amplifies with device drops; 2)
security and privacy trade-off of the learning process still not robust enough
and 3) overall communication efficiency and the cost are higher. To mitigate
these challenges we present Federated Learning and Privately Scaling (FLaPS)
architecture, which improves scalability as well as the security and privacy of
the system. The devices are grouped into clusters which further gives better
privacy scaled turn around time to finish a round of training. Therefore, even
if a device gets dropped in the middle of training, the whole process can be
started again after a definite amount of time. The data and model both are
communicated using differentially private reports with iterative shuffling
which provides a better privacy-utility trade-off. We evaluated FLaPS on MNIST,
CIFAR10, and TINY-IMAGENET-200 dataset using various CNN models. Experimental
results prove FLaPS to be an improved, time and privacy scaled environment
having better and comparable after-learning-parameters with respect to the
central and FL models.


  We investigate six supernova remnant (SNR) candidates --- G51.21+0.11,
G52.37-0.70, G53.07+0.49, G53.41+0.03, G53.84-0.75, and the possible shell
around G54.1-0.3 --- in the Galactic Plane using newly acquired LOw-Frequency
ARray (LOFAR) High-Band Antenna (HBA) observations, as well as archival
Westerbork Synthesis Radio Telescope (WSRT) and Very Large Array Galactic Plane
Survey (VGPS) mosaics. We find that G52.37-0.70, G53.84-0.75, and the possible
shell around pulsar wind nebula G54.1+0.3 are unlikely to be SNRs, while
G53.07+0.49 remains a candidate SNR. G51.21+0.11 has a spectral index of
$\alpha=-0.7\pm0.21$, but lacks X-ray observations and as such requires further
investigation to confirm its nature. We confirm one candidate, G53.41+0.03, as
a new SNR because it has a shell-like morphology, a radio spectral index of
$\alpha=-0.6\pm0.2$ and it has the X-ray spectral characteristics of a
1000-8000 year old SNR. The X-ray analysis was performed using archival
XMM-Newton observations, which show that G53.41+0.03 has strong emission lines
and is best characterized by a non-equilibrium ionization model, consistent
with an SNR interpretation. Deep Arecibo radio telescope searches for a pulsar
associated with G53.41+0.03 resulted in no detection, but place stringent upper
limits on the flux density of such a source if it is beamed towards Earth.


  Differential privacy (DP) is the state-of-the-art and rigorous notion of
privacy for answering aggregate database queries while preserving the privacy
of sensitive information in the data. In today's era of data analysis, however,
it poses new challenges for users to understand the trends and anomalies
observed in the query results: Is the unexpected answer due to the data itself,
or is it due to the extra noise that must be added to preserve DP? In the
second case, even the observation made by the users on query results may be
wrong. In the first case, can we still mine interesting explanations from the
sensitive data while protecting its privacy? To address these challenges, we
present a three-phase framework DPXPlain, which is the first system to the best
of our knowledge for explaining group-by aggregate query answers with DP. In
its three phases, DPXPlain (a) answers a group-by aggregate query with DP, (b)
allows users to compare aggregate values of two groups and with high
probability assesses whether this comparison holds or is flipped by the DP
noise, and (c) eventually provides an explanation table containing the
approximately `top-k' explanation predicates along with their relative
influences and ranks in the form of confidence intervals, while guaranteeing DP
in all steps. We perform an extensive experimental analysis of DPXPlain with
multiple use-cases on real and synthetic data showing that DPXPlain efficiently
provides insightful explanations with good accuracy and utility.


  We consider a random wave model introduced by Zelditch to study the behavior
of typical quasi-modes on a Riemannian manifold. Using the exponential moment
method, we show that random waves satisfy the quantum unique ergodicity
property with probability one under mild growth assumptions.


  A continuous groupoid homomorphism $c$ on a locally compact second countable
Hausdorff \'etale groupoid $\mathcal{G}$ gives rise to a $C^{*}$-dynamical
system in which every $\beta$-KMS state can be associated to a $e^{-\beta
c}$-quasi-invariant measure $\mu$ on $\mathcal{G}^{(0)}$. Letting
$\Delta_{\mu}$ denote the set of KMS states associated to such a $\mu$, we will
prove that $\Delta_{\mu}$ is a simplex for a large class of groupoids, and we
will show that there is an abelian group that acts transitively and freely on
the extremal points of $\Delta_{\mu}$. This group can be described using the
support of $\mu$, so our theory of symmetries can be used to obtain a
description of all KMS states by describing the $e^{-\beta c}$-quasi-invariant
measures. To illustrate this we will describe the KMS states for the
Cuntz-Krieger algebras of all finite higher rank graphs without sources and a
large class of continuous one-parameter groups.


  In the last year or so and going back many decades there has been extensive
claims by major computational scientists, engineers, and others that AGI,
artificial general intelligence, is five or ten years away, but without a
scintilla of scientific evidence, for a broad body of these claims. Computers
will become conscious, have a theory of mind, think and reason, will become
more intelligent than humans, and so on. But the claims are science fiction,
not science. This article reviews evidence for the following three propositions
using extensive body of scientific research and related sources from the
cognitive and neurosciences, evolutionary evidence, linguistics, data science,
comparative psychology, self-driving cars, robotics. and the learning sciences.
(1) Do computing machines think or reason? (2) Are computing machines sentient
or conscious? (3) Do computing machines have a theory of mind?


  We introduce the categories of quasi-measurable spaces, which are slight
generalizations of the category of quasi-Borel spaces, where we now allow for
general sample spaces and less restrictive random variables, spaces and maps.
We show that each category of quasi-measurable spaces is bi-complete and
cartesian closed. We also introduce several different strong probability
monads. Together these constructions provide convenient categories for higher
probability theory that also support semantics of higher-order probabilistic
programming languages in the same way as the category of quasi-Borel spaces
does.
  An important special case is the category of quasi-universal spaces, where
the sample space is the set of the real numbers together with the sigma-algebra
of all universally measurable subsets. The induced sigma-algebras on those
quasi-universal spaces then have explicit descriptions in terms of
intersections of Lebesgue-complete sigma-algebras. A central role is then
played by countably separated and universal quasi-universal spaces, which
replace the role of standard Borel spaces. We prove in this setting a Fubini
theorem, a disintegration theorem for Markov kernels, a Kolmogorov extension
theorem and a conditional de Finetti theorem. We also translate our findings
into properties of the corresponding Markov category of Markov kernels between
universal quasi-universal spaces.
  Furthermore, we formalize causal Bayesian networks in terms of
quasi-universal spaces and prove a global Markov property. For this we
translate the notion of transitional conditional independence into this setting
and study its (asymmetric) separoid rules. Altogether we are now able to reason
about conditional independence relations between variables and causal
mechanisms on equal footing. Finally, we also highlight how one can use
exponential objects and random functions for counterfactual reasoning.


  We compute the desorption rate of icy mantles on dust grains as a function of
the size and composition of both the grain and the mantle. We combine existing
models of cosmic ray (CR) related desorption phenomena with a model of CR
transport to accurately calculate the desorption rates in dark regions of
molecular clouds. We show that different desorption mechanisms dominate for
grains of different sizes, and in different regions of the cloud. We then use
these calculations to investigate a simple model of the growth of mantles,
given a distribution of grain sizes. We find that modest variations of the
desorption rate with grain size lead to a strong dependence of mantle thickness
on grain size. Furthermore, we show that freeze-out is almost complete in the
absence of an external UV field, even when photodesorption from CR produced UV
is taken into consideration. Even at gas densities of $10^4$ ${\rm cm^{-3}}$,
less than 30\% of the CO remains in the gas phase after $3\times 10^5$ years
for standard values of the CR ionization rate.


  HI observations have revealed large gaseous extensions in interacting and
merging systems. The interstellar gas is obviously dragged out in tidal tails
during an encounter, and the percentage of HI in the tails increases with the
merging stage. However, the opposite is true for the molecular gas, which is
observed highly concentrated towards the nuclei of interacting galaxies,
amounting to a significant fraction of the dynamical mass. Statistically, there
appears to be more gas observed in interacting galaxies than in normal,
isolated ones. As N-body simulations show, the gas is driven inwards in the
interaction process by the strong gravity torques, before being consumed
through star formation in the triggered starbursts. We review here all
observations that could bring more knowledge about the state of the gas in the
outer parts of galaxies, and about accretion processes. The link with the
observations of the Ly$\alpha$ absorbers at low and high redshifts is
discussed.


  In this paper, we consider a two server system serving heterogeneous
customers. One of the server has a FIFO scheduling policy and charges a fixed
admission price to each customer. The second queue follows the
highest-bidder-first (HBF) policy where an arriving customer bids for its
position in the queue. Customers make an individually optimal choice of the
server and for such system, we characterize the equilibrium routing of
customers. We specifically show that this routing is characterized by two
thresholds.


  Large language models (LLMs) have facilitated significant strides in
generating conversational agents, enabling seamless, contextually relevant
dialogues across diverse topics. However, the existing LLM-driven
conversational agents have fixed personalities and functionalities, limiting
their adaptability to individual user needs. Creating personalized agent
personas with distinct expertise or traits can address this issue. Nonetheless,
we lack knowledge of how people customize and interact with agent personas. In
this research, we investigated how users customize agent personas and their
impact on interaction quality, diversity, and dynamics. To this end, we
developed CloChat, an interface supporting easy and accurate customization of
agent personas in LLMs. We conducted a study comparing how participants
interact with CloChat and ChatGPT. The results indicate that participants
formed emotional bonds with the customized agents, engaged in more dynamic
dialogues, and showed interest in sustaining interactions. These findings
contribute to design implications for future systems with conversational agents
using LLMs.


  Surface properties of mixtures of charged platelike colloids and salt in
contact with a charged planar wall are studied within density functional
theory. The particles are modeled by hard cuboids with their edges constrained
to be parallel to the Cartesian axes corresponding to the Zwanzig model and the
charges of the particles are concentrated in their centers. The density
functional applied is an extension of a recently introduced functional for
charged platelike colloids. Analytically and numerically calculated bulk and
surface phase diagrams exhibit first-order wetting for sufficiently small
macroion charges and isotropic bulk order as well as first-order drying for
sufficiently large macroion charges and nematic bulk order. The asymptotic
wetting and drying behavior is investigated by means of effective interface
potentials which turn out to be asymptotically the same as for a suitable
neutral system governed by isotropic nonretarded dispersion forces. Wetting and
drying points as well as predrying lines and the corresponding critical points
have been located numerically. A crossover from monotonic to non-monotonic
electrostatic potential profiles upon varying the surface charge density has
been observed. Due to the presence of both the Coulomb interactions and the
hard-core repulsions, the surface potential and the surface charge do not
vanish simultaneously, i.e., the point of zero charge and the isoelectric point
of the surface do not coincide.


  We study left-invariant foliations $\mathcal{F}$ on Riemannian Lie groups $G$
generated by a subgroup $K$. We are interested in such foliations which are
conformal and with minimal leaves of codimension two. We classify such
foliations $\mathcal{F}$ when the subgroup $K$ is one of the important
$\textbf{SU}(2)\times\textbf{SU}(2)$,
$\textbf{SU}(2)\times\textbf{SL}_2(\mathbb{R})$,
$\textbf{SU}(2)\times\textbf{SO}(2)$ or
$\textbf{SL}_2(\mathbb{R})\times\textbf{SO}(2)$. By this we yield new
multi-dimensional families of Lie groups $G$ carrying such foliations in each
case. These foliations $\mathcal{F}$ produce local complex-valued harmonic
morphisms on the corresponding Lie group $G$.


  In three dimensions, the gluon condensate of pure SU(3) gauge theory has
ultraviolet divergences up to 4-loop level only. By subtracting the
corresponding terms from lattice measurements of the plaquette expectation
value and extrapolating to the continuum limit, we extract the finite part of
the gluon condensate in lattice regularization. Through a change of
regularization scheme to MSbar and (inverse) dimensional reduction, this result
would determine the first non-perturbative coefficient in the weak-coupling
expansion of hot QCD pressure.


  Self-propelled particles possessing permanent magnetic dipole moments occur
naturally in magnetotactic bacteria and in man-made systems like active
colloids or micro-robots. Yet, the interplay between self-propulsion and
anisotropic dipole-dipole interactions on dynamic self-assembly in three
dimensions (3D) remains poorly understood. We conduct Brownian dynamics
simulations of active dipolar particles in 3D, focusing on the low-density
regime, where dipolar hard spheres tend to form chain-like aggregates and
percolated networks with increasing dipolar coupling strength. We find that
strong active forces override dipolar attractions, effectively inhibiting
chain-like aggregation and network formation. Conversely, activating particles
with low to moderate forces results in a fluid composed of active chains and
rings. At strong dipolar coupling strengths, this active fluid transitions into
an active gel, consisting of a percolated network of active chains. Although
the overall structure of the active gel remains interconnected, the network
experiences more frequent configurational rearrangements due to the reduced
bond lifetime of active dipolar particles. Consequently, particles exhibit
enhanced translational and rotational diffusion within the active fluid of
strings and active gels compared to their passive counterparts. We quantify the
influence of activity on aggregates topology, as they transition from branched
structures to unconnected chains and rings. Our findings are summarized in a
state diagram, delineating the impact of dipolar coupling strength and active
force magnitude on the system.


  We theoretically investigate the flow of electromagnetic waves in complex
honeycomb photonic lattices with local PT symmetries. Such PT structure is
introduced via a judicious arrangement of gain or loss across the honeycomb
lattice, characterized by a gain/loss parameter \gamma. We found a new class of
conical diffraction phenomena where the formed cone is brighter and travels
along the lattice with a transverse speed proportional to Sqrt (\gamma).


  Fog computing architectures distribute computational and storage resources
along the continuum from the cloud to things. Therefore, the execution of
services or the storage of files can be closer to the users. The main
objectives of fog computing domains are to reduce the user latency and the
network usage. Availability is also an issue in fog architectures because the
topology of the network does not guarantee redundant links between devices.
Consequently, the definition of placement polices is a key challenge. We
propose a placement policy for data replication to increase data availability
that contrasts with other storage policies that only consider a single replica
of the files. The system is modeled with complex weighted networks and
topological features, such as centrality indices. Graph partition algorithms
are evaluated to select the fog devices that store data replicas. Our approach
is compared with two other placement policies: one that stores only one replica
and FogStore, which also stores file replicas but uses a greedy approach (the
shortest path). We analyze 22 experiments with simulations. The results show
that our approach obtains the shortest latency times, mainly for writing
operations, a smaller network usage increase, and a similar file availability
to FogStore.


  Suspensions of swimming micro-organisms provide examples of coordinated
active dynamics. That has stimulated the study of a phenomenological theory
combining synchronization and polar order in active matter. Here, we consider
another example inspired by the traction forces of migrating cells. The
novelty, in this case, is the global force-free nature of the traction force
field. Such a constraint is absent in the case where the vector field describes
swimming speeds in micro-organisms suspensions. Cell traction is characterized
by means of a complex tensor quantity, that generalizes the nematic orientation
tensor to incorporate the ability of particles to synchronize, and cell
motility depends on this quantity being non-zero. We provide a realization of
migrating cell which comprises an assembly of dipolar elements exerting
traction on a fluid substrate. This model indicates that spontaneous transition
to the motile state is possible but requires (as in the case of
synchronization) non-isochrony of oscillations and involves subtle
synchronization patterns, associated to propagation of waves. Such results are
consistent with recent experimental work relating motility to the
synchronization of actin oscillators at the periphery of migrating cells.


  Over the last few decades power law distributions have been suggested as
forming generative mechanisms in a variety of disparate fields, such as,
astrophysics, criminology and database curation. However, fitting these heavy
tailed distributions requires care, especially since the power law behaviour
may only be present in the distributional tail. Current state of the art
methods for fitting these models rely on estimating the cut-off parameter
$x_{\min}$. This results in the majority of collected data being discarded.
This paper provides an alternative, principled approached for fitting heavy
tailed distributions. By directly modelling the deviation from the power law
distribution, we can fit and compare a variety of competing models in a single
unified framework.


  The primary purpose of this note is to prove two recent conjectures
concerning the $n$ body matrix that arose in recent papers of Escobar-Ruiz,
Miller, and Turbiner on the classical and quantum $n$ body problem in
$d$-dimensional space. First, whenever the positions of the masses are in a
nonsingular configuration, meaning that they do not lie on an affine subspace
of dimension $\leq n-2$, the $n$ body matrix is positive definite and, hence,
defines a Riemannian metric on the space coordinatized by their interpoint
distances. Second, its determinant can be factored into the product of the
order $n$ Cayley--Menger determinant and a mass-dependent factor that is also
of one sign on all nonsingular mass configurations. The factorization of the
$n$ body determinant is shown to be a special case of an intriguing general
result proving the factorization of determinants of a certain form.


  Approximately 75% of energy used in petrochemical and refining industries is
consumed by furnaces. Operating furnaces at optimal conditions results in huge
amounts of savings. In this paper, we model the furnace efficiency optimization
as a multi-objective problem involving multiple interactions among the
controlled variables and propose a cooperative game based formulation for the
factory of future. The controlled variables are Absorbed Duty and Coil Outlet
Temperature. We propose a comprehensive solution to select the best combination
of manipulated variables (fired duty, throughput and coil inlet temperature)
satisfying multiple criteria using a cooperative game theory approach. We
compare this approach with the standard multi-objective optimization using
NSGA-II and RNSGA-II algorithms.


  In robotics, one of the main challenges is that the on-board Artificial
Intelligence (AI) must deal with different or unexpected environments. Such AI
agents may be incompetent there, while the underlying model itself may not be
aware of this (e.g., deep learning models are often overly confident). This
paper proposes two methods for the online assessment of the competence of the
AI model, respectively for situations when nothing is known about competence
beforehand, and when there is prior knowledge about competence (in semantic
form). The proposed method assesses whether the current environment is known.
If not, it asks a human for feedback about its competence. If it knows the
environment, it assesses its competence by generalizing from earlier
experience. Results on real data show the merit of competence assessment for a
robot moving through various environments in which it sometimes is competent
and at other times it is not competent. We discuss the role of the human in
robot's self-assessment of its competence, and the challenges to acquire
complementary information from the human that reinforces the assessments.


  Prior work has established that all problems in NP admit classical
zero-knowledge proof systems, and under reasonable hardness assumptions for
quantum computations, these proof systems can be made secure against quantum
attacks. We prove a result representing a further quantum generalization of
this fact, which is that every problem in the complexity class QMA has a
quantum zero-knowledge proof system. More specifically, assuming the existence
of an unconditionally binding and quantum computationally concealing commitment
scheme, we prove that every problem in the complexity class QMA has a quantum
interactive proof system that is zero-knowledge with respect to efficient
quantum computations.
  Our QMA proof system is sound against arbitrary quantum provers, but only
requires an honest prover to perform polynomial-time quantum computations,
provided that it holds a quantum witness for a given instance of the QMA
problem under consideration. The proof system relies on a new variant of the
QMA-complete local Hamiltonian problem in which the local terms are described
by Clifford operations and standard basis measurements. We believe that the
QMA-completeness of this problem may have other uses in quantum complexity.


  This article pertains to interpolation of Sobolev functions at shrinking
lattices $h\mathbb{Z}^d$ from $L_p$ shift-invariant spaces associated with
cardinal functions related to general multiquadrics,
$\phi_{\alpha,c}(x):=(|x|^2+c^2)^\alpha$. The relation between the
shift-invariant spaces generated by the cardinal functions and those generated
by the multiquadrics themselves is considered. Additionally, $L_p$ error
estimates in terms of the dilation $h$ are considered for the associated
cardinal interpolation scheme. This analysis expands the range of $\alpha$
values which were previously known to give such convergence rates (i.e.
$O(h^k)$ for functions with derivatives of order up to $k$ in $L_p$,
$1<p<\infty$). Additionally, the analysis here demonstrates that some known
best approximation rates for multiquadric approximation are obtained by their
cardinal interpolants.


  The localization of light in flat-band lattices has been recently proposed
and experimentally demonstrated in several configurations, assuming a classical
description of light. Here, we study the problem of light localization in the
quantum regime. We focus on quasi one-dimensional and two-dimensional lattices
which exhibit a perfect flat-band inside their linear spectrum. Localized
quantum states are constructed as eigenstates of the interaction Hamiltonian
with a vanishing eigenvalue and a well defined total photon number. These are
superpositions of Fock states with probability amplitudes given by positive as
well as negative square roots of multinomial coefficients. The classical
picture can be recovered by considering poissonian superpositions of localized
quantum states with different total photon number. We also study the
separability properties of flat band quantum states and apply them to the
transmission of information via multi-core fibers, where these states allow for
the total passive suppression of photon crosstalk and exhibit robustness
against photon losses. At the end, we propose a novel on-chip setup for the
experimental preparation of localized quantum states of light for any number of
photons.


  The Karlqvist approximation signaling the historical beginning of magnetic
recording head theory is reviewed and compared to various approaches
progressing from Green, Fourier, Conformal mapping that obeys the Sommerfeld
edge condition at angular points and leads to exact results.


  This paper details a system for fast visual exploration and search without
prior map information. We leverage frontier based planning with both LiDAR and
visual sensing and augment it with a perception module that contextually labels
points in the surroundings from wide Field of View 2D LiDAR scans. The goal of
the perception module is to recognize surrounding points more likely to be the
search target in order to provide an informed prior on which to plan next best
viewpoints. The robust map-free scan classifier used to label pixels in the
robot's surroundings is trained from expert data collected using a simple cart
platform equipped with a map-based classifier. We propose a novel utility
function that accounts for the contextual data found from the classifier. The
resulting viewpoints encourage the robot to explore points unlikely to be
permanent in the environment, leading the robot to locate objects of interest
faster than several existing baseline algorithms. Our proposed system is
further validated in real-world search experiments for single and multiple
search objects with a Spot robot in two unseen environments. Videos of
experiments, implementation details and open source code can be found at
https://sites.google.com/view/lives-2024/home.


  It is generally believed that a generic system can be reversibly transformed
from one state into another by sufficiently slow change of parameters. A
standard argument favoring this assertion is based on a possibility to expand
the energy or the entropy of the system into the Taylor series in the ramp
speed. Here we show that this argumentation is only valid in high enough
dimensions and can break down in low-dimensional gapless systems. We identify
three generic regimes of a system response to a slow ramp: (A) mean-field, (B)
non-analytic, and (C) non-adiabatic. In the last regime the limits of the ramp
speed going to zero and the system size going to infinity do not commute and
the adiabatic process does not exist in the thermodynamic limit. We support our
results by numerical simulations. Our findings can be relevant to
condensed-matter, atomic physics, quantum computing, quantum optics, cosmology
and others.


  This paper is devoted to problems stated by Z. Zhou and F. Li in 2009. They
concern relations between almost periodic, weakly almost periodic, and
quasi-weakly almost periodic points of a continuous map f and its topological
entropy. The negative answer follows by our recent paper. But for continuous
maps of the interval and other more general one-dimensional spaces we give more
results; in some cases, the answer is positive.


  Recent methods for people detection in overhead, fisheye images either use
radially-aligned bounding boxes to represent people, assuming people always
appear along image radius or require significant pre-/post-processing which
radically increases computational complexity. In this work, we develop an
end-to-end rotation-aware people detection method, named RAPiD, that detects
people using arbitrarily-oriented bounding boxes. Our fully-convolutional
neural network directly regresses the angle of each bounding box using a
periodic loss function, which accounts for angle periodicities. We have also
created a new dataset with spatio-temporal annotations of rotated bounding
boxes, for people detection as well as other vision tasks in overhead fisheye
videos. We show that our simple, yet effective method outperforms
state-of-the-art results on three fisheye-image datasets. Code and dataset are
available at http://vip.bu.edu/rapid .


  We propose SparsePipe, an efficient and asynchronous parallelism approach for
handling 3D point clouds with multi-GPU training. SparsePipe is built to
support 3D sparse data such as point clouds. It achieves this by adopting
generalized convolutions with sparse tensor representation to build expressive
high-dimensional convolutional neural networks. Compared to dense solutions,
the new models can efficiently process irregular point clouds without densely
sliding over the entire space, significantly reducing the memory requirements
and allowing higher resolutions of the underlying 3D volumes for better
performance.
  SparsePipe exploits intra-batch parallelism that partitions input data into
multiple processors and further improves the training throughput with
inter-batch pipelining to overlap communication and computing. Besides, it
suitably partitions the model when the GPUs are heterogeneous such that the
computing is load-balanced with reduced communication overhead.
  Using experimental results on an eight-GPU platform, we show that SparsePipe
can parallelize effectively and obtain better performance on current point
cloud benchmarks for both training and inference, compared to its dense
solutions.


  An important task in quantum generative machine learning is to model the
probability distribution of measurements of many-body quantum systems.
Classical generative models, such as generative adversarial networks (GANs) and
variational autoencoders (VAEs), can model the distributions of product states
with high fidelity, but fail or require an exponential number of parameters to
model entangled states. In this paper, we introduce a quantum-enhanced VAE
(QeVAE), a generative quantum-classical hybrid model that uses quantum
correlations to improve the fidelity over classical VAEs, while requiring only
a linear number of parameters. We provide a closed-form expression for the
output distributions of the QeVAE. We also empirically show that the QeVAE
outperforms classical models on several classes of quantum states, such as
4-qubit and 8-qubit quantum circuit states, haar random states, and quantum
kicked rotor states, with a more than 2x increase in fidelity for some states.
Finally, we find that the trained model outperforms the classical model when
executed on the IBMq Manila quantum computer. Our work paves the way for new
applications of quantum generative learning algorithms and characterizing
measurement distributions of high-dimensional quantum states.


  In this proceeding, we present the 1-dimensional stellar evolution of two
rotating population III (Pop III) star models, each having a mass of 25
M$_{\odot}$ at the zero-age main-sequence (ZAMS). The slowly rotating model has
an initial angular rotational velocity of 10 per cent of the critical angular
rotational velocity. In contrast, the rapidly rotating model has an initial
angular rotational velocity of 70 per cent of the critical angular rotational
velocity. As an effect of rotationally enhanced mixing, we find that the
rapidly rotating model suffers an enormous mass loss due to the deposition of a
significant amount of CNO elements toward the surface after the main-sequence
phase. We also display the simulated light curves as these models explode into
core-collapse supernovae (CCSNe).


  Random walks describe diffusion processes, where movement at every time step
is restricted to only the neighbouring locations. We construct a quantum random
walk algorithm, based on discretisation of the Dirac evolution operator
inspired by staggered lattice fermions. We use it to investigate the spatial
search problem, i.e. finding a marked vertex on a $d$-dimensional hypercubic
lattice. The restriction on movement hardly matters for $d>2$, and scaling
behaviour close to Grover's optimal algorithm (which has no restriction on
movement) can be achieved. Using numerical simulations, we optimise the
proportionality constants of the scaling behaviour, and demonstrate the
approach to that for Grover's algorithm (equivalent to the mean field theory or
the $d\to\infty$ limit). In particular, the scaling behaviour for $d=3$ is only
about 25% higher than the optimal $d\to\infty$ value.


  Reinforcement learning agents often forget details of the past, especially
after delays or distractor tasks. Agents with common memory architectures
struggle to recall and integrate across multiple timesteps of a past event, or
even to recall the details of a single timestep that is followed by distractor
tasks. To address these limitations, we propose a Hierarchical Chunk Attention
Memory (HCAM), which helps agents to remember the past in detail. HCAM stores
memories by dividing the past into chunks, and recalls by first performing
high-level attention over coarse summaries of the chunks, and then performing
detailed attention within only the most relevant chunks. An agent with HCAM can
therefore "mentally time-travel" -- remember past events in detail without
attending to all intervening events. We show that agents with HCAM
substantially outperform agents with other memory architectures at tasks
requiring long-term recall, retention, or reasoning over memory. These include
recalling where an object is hidden in a 3D environment, rapidly learning to
navigate efficiently in a new neighborhood, and rapidly learning and retaining
new object names. Agents with HCAM can extrapolate to task sequences much
longer than they were trained on, and can even generalize zero-shot from a
meta-learning setting to maintaining knowledge across episodes. HCAM improves
agent sample efficiency, generalization, and generality (by solving tasks that
previously required specialized architectures). Our work is a step towards
agents that can learn, interact, and adapt in complex and temporally-extended
environments.


  We show that the very near horizon region of nonextreme black holes, which
can be described by horizon CFTs, are related to $AdS_2$ Rindler spaces. The
latter are $AdS_2$ black holes with specific masses and can be described by
states of either $D=1$ or $D=2$ CFTs. The central charges of these CFTs and the
conformal weights of their states that correspond to the nonextreme black holes
exactly match those predicted by the horizon CFTs, providing supporting
evidence for this description.


  Consider a graph $G$ and a real-valued function $f$ defined on the degree set
of $G$. The sum of the outputs $f(d_v)$ over all vertices $v\in V(G)$ of $G$ is
usually known as the vertex-degree-function indices and is denoted by $H_f(G)$,
where $d_v$ represents the degree of a vertex $v$ of $G$. This paper gives
sharp bounds on the index $H_f(G)$ in terms of order and size of $G$ when $G$
is connected and has the maximum degree at most $4$. All the graphs achieving
the derived bounds are also determined. Bounds involving several existing
indices - including the general zeroth-order Randi\'c index and coindex, the
general multiplicative first/second Zagreb index, the variable sum lodeg index,
and the variable sum exdeg index - are deduced as the special cases of the
obtained ones.


  The study of Ramanujan-type congruences for functions specific to additive
number theory has a long and rich history. Motivated by recent connections
between divisor sums and overpartitions via congruences in arithmetic
progressions, we investigate the existence and classification of Ramanujan-type
congruences for functions in multiplicative number theory.


  The purpose of this paper is to prove that integral Chow rings of toric
stacks are naturally isomorphic to Stanley-Reisner rings.


  We consider the influence of mode - mode coupling in the inflaton field on
the spectrum of primordial fluctuations. To this end, we formulate a
phenomenological model where the inflaton fluctuations are treated as a fluid
undergoing turbulent motion. Under suitable assumptions, it is possible to
estimate the size and scale of fluctuations in velocity, which upon reheating
induce corresponding fluctuations in the radiation energy density. For De
Sitter inflation the resulting spectrum is scale invariant on all scales of
interest. The amplitude of the resulting spectrum is compatible with known
observational limits. This suggests that the hypothesis of a extremely weakly
coupled inflation could be relaxed without affecting the predictions of the
model. Principal PACS No 98.80.Cq; additional PACS nos: 04.62.+v, 11.10.Wx,
47.27


  The analysis of decision-making process in electricity markets is crucial for
understanding and resolving issues related to market manipulation and reduced
social welfare. Traditional Multi-Agent Reinforcement Learning (MARL) method
can model decision-making of generation companies (GENCOs), but faces
challenges due to uncertainties in policy functions, reward functions, and
inter-agent interactions. Quantum computing offers a promising solution to
resolve these uncertainties, and this paper introduces the Quantum Multi-Agent
Deep Q-Network (Q-MADQN) method, which integrates variational quantum circuits
into the traditional MARL framework. The main contributions of the paper are:
identifying the correspondence between market uncertainties and quantum
properties, proposing the Q-MADQN algorithm for simulating electricity market
bidding, and demonstrating that Q-MADQN allows for a more thorough exploration
and simulates more potential bidding strategies of profit-oriented GENCOs,
compared to conventional methods, without compromising computational
efficiency. The proposed method is illustrated on IEEE 30-bus test network,
confirming that it offers a more accurate model for simulating complex market
dynamics.


  In this paper, we consider Vannimenus model with competing nearest-neighbors
and prolonged next-nearest-neighbors interactions on a Cayley tree. For this
model we define Markov random fields with memory of length 2. By using a new
approach, we obtain new sets of Gibbs measures of Ising-Vannimenus model on
Cayley tree of order 2. We construct the recurrence equations corresponding
Ising-Vannimenus model. We prove the Kolmogorov consistency condition. We
investigate the translation-invariant and periodic non transition-invariant
Gibbs measures for the model. We find new sets of Gibbs measures different from
the Gibbs measures given in the references \cite{NHSS,FreeMA}. We show that
some of the measures are extreme Gibbs distributions.


  Considering a family of upper frequently hypercyclic operators we care about
the existence of vectors which are upper frequently hypercyclic for any
operator of this family. We establish sufficient conditions for a family of
operators to have these vectors called common upper frequently hypercyclic
vectors. Using this result, we then give a construction of such vectors.
Finally we derive some applications to families of weighted shifts.


  It is sketched how a monostable rf- or dc-SQUID can mediate an inductive
coupling between two adjacent flux qubits. The nontrivial dependence of the
SQUID's susceptibility on external flux makes it possible to continuously tune
the induced coupling from antiferromagnetic (AF) to ferromagnetic (FM). In
particular, for suitable parameters, the induced FM coupling can be
sufficiently large to overcome any possible direct AF inductive coupling
between the qubits.
  The main features follow from a classical analysis of the multi-qubit
potential. A fully quantum treatment yields similar results, but with a
modified expression for the SQUID susceptibility.
  Since the latter is exact, it can also be used to evaluate the
susceptibility--or, equivalently, energy-level curvature--of an isolated
rf-SQUID for larger shielding and at degenerate flux bias, i.e., a (bistable)
qubit. The result is compared to the standard two-level (pseudospin) treatment
of the anticrossing, and the ensuing conclusions are verified numerically.


  Graph neural networks (GNNs) have emerged as a powerful paradigm for
embedding-based entity alignment due to their capability of identifying
isomorphic subgraphs. However, in real knowledge graphs (KGs), the counterpart
entities usually have non-isomorphic neighborhood structures, which easily
causes GNNs to yield different representations for them. To tackle this
problem, we propose a new KG alignment network, namely AliNet, aiming at
mitigating the non-isomorphism of neighborhood structures in an end-to-end
manner. As the direct neighbors of counterpart entities are usually dissimilar
due to the schema heterogeneity, AliNet introduces distant neighbors to expand
the overlap between their neighborhood structures. It employs an attention
mechanism to highlight helpful distant neighbors and reduce noises. Then, it
controls the aggregation of both direct and distant neighborhood information
using a gating mechanism. We further propose a relation loss to refine entity
representations. We perform thorough experiments with detailed ablation studies
and analyses on five entity alignment datasets, demonstrating the effectiveness
of AliNet.


  Let B denote an arbitrary Banach space, G a compact abelian group with Haar
measure $\mu$ and dual group $\Gamma$. Let E be a Sidon subset of $\Gamma$ with
Sidon constant S(E). Let r_n denote the n-th Rademacher function on [0, 1]. We
show that there is a constant c, depending only on S(E), such that, for all
$\alpha > 0$: c^{-1}P[| \sum_{n=1}^Na_nr_n| >= c \alpha ] <= \mu[|
\sum_{n=1}^Na_n\gamma_n| >= \alpha ] <= cP [|\sum_{n=1}^Na_nr_n| >= c^{-1}
\alpha ]


  This paper deals also with a problem of gas absorption accompanied by an
instantaneous, irreversible reaction in the liquid layer. The well-known
methods for calculating such processes are based usually on the certain
amendments to solutions, which are obtained disregarding the chemical reaction.
Unlike the known work (1. D. Baetens, R. Van Keer, L.H. Hosten. Gas-liquid
reaction: absorption accompanied by an instantaneous, irreversible reaction//
Moving Boundaries IV, Southampton, Boston, 1997) the approach we used takes
into account the influence of reaction resulting product on the arising and
velocity of a moving reaction plane. The known results in the theory of
chemical apparatuses scaling are devoted to apparatuses with non-regular
packings mainly. However how the phases distribution over the regular packings
of chemical columns effects the heat and mass efficiency is studied lesser.
This paper deals with the methods of simulation the scaling effects applying to
chemical towers with regular packings of various types. The models for
describing the influence of initial liquid and gas distribution in chemical
columns with regular packing on the mass transfer efficiency have been
submitted. The sufficiently simple methods for evaluating the influence of
large-scale factor on the efficiency of mass transfer have been obtained. These
methods are suitable for use in engineering calculation techniques.


  We generalize the torsion vanishing results of Caraiani-Scholze and
Koshikawa. Our results apply to the cohomology of general Shimura varieties
$(\mathbf{G},X)$ of PEL type $A$ or $C$, localized at a suitable maximal ideal
$\mathfrak{m}$ in the spherical Hecke algebra at primes $p$ such that
$\mathbf{G}_{\mathbb{Q}_{p}}$ is a group for which we know the Fargues-Scholze
local Langlands correspondence is the semi-simplification of a suitably nice
local Langlands correspondence. This is accomplished by combining Koshikawa's
technique, the theory of geometric Eisenstein series over the Fargues-Fontaine
curve, the work of Santos describing the structure of the fibers of the
minimally and toroidally compactified Hodge-Tate period morphism for general
PEL type Shimura varieties of type $A$ or $C$, and ideas developed by Zhang on
comparing Hecke correspondences on the moduli stack of $G$-bundles with the
cohomology of Shimura varieties. In the process, we also establish a
description of the generic part of the cohomology that bears resemblance to the
work of Xiao-Zhu. Moreover, we also construct a filtration on the compactly
supported cohomology that differs from Manotovan's filtration in the case that
the Shimura variety is non-compact, allowing us to circumvent some of the
circumlocutions taken by Cariani-Scholze. Our method showcases a very general
strategy for proving such torsion vanishing results, and should bear even more
fruit once the inputs are generalized. Motivated by this, we formulate an even
more general torsion vanishing conjecture.


  Naive estimates of the statistics of large scale structure and weak lensing
power spectrum measurements that include only Gaussian errors exaggerate their
scientific impact. Non-linear evolution and finite volume effects are both
significant sources of non-Gaussian covariance that reduce the ability of power
spectrum measurements to constrain cosmological parameters. Using a halo model
formalism, we derive an intuitive understanding of the various contributions to
the covariance and show that our analytical treatment agrees with simulations.
This approach enables an approximate derivation of a joint likelihood for the
cluster number counts, the weak lensing power spectrum and the bispectrum. We
show that this likelihood is a good description of the ray-tracing simulation.
Since all of these observables are sensitive to the same finite volume effects
and contain information about the non-linear evolution, a combined analysis
recovers much of the "lost" information and obviates the non-Gaussian
covariance. For upcoming weak lensing surveys, we estimate that a joint
analysis of power spectrum, number counts and bispectrum will produce an
improvement of about $30-40\%$ in determinations of the matter density and the
scalar amplitude. This improvement is equivalent to doubling the survey area.


  Recent works have shown that deep neural networks benefit from multi-task
learning by learning a shared representation across several related tasks.
However, performance of such systems depend on relative weighting between
various losses involved during training. Prior works on loss weighting schemes
assume that instances are equally easy or hard for all tasks. In order to break
this assumption, we let the training process dictate the optimal weighting of
tasks for every instance in the dataset. More specifically, we equip every
instance in the dataset with a set of learnable parameters (instance-level task
parameters) where the cardinality is equal to the number of tasks learned by
the model. These parameters model the weighting of each task for an instance.
They are updated by gradient descent and do not require hand-crafted rules. We
conduct extensive experiments on SURREAL and CityScapes datasets, for human
shape and pose estimation, depth estimation and semantic segmentation tasks. In
these tasks, our approach outperforms recent dynamic loss weighting approaches,
e.g. reducing surface estimation errors by 8.97% on SURREAL. When applied to
datasets where one or more tasks can have noisy annotations, the proposed
method learns to prioritize learning from clean labels for a given task, e.g.
reducing surface estimation errors by up to 60%. We also show that we can
reliably detect corrupt labels for a given task as a by-product from learned
instance-level task parameters.


  We study the origin of neutrino mass from $SO(10)$ arising from $M$ Theory
compactified on a $G_2$-manifold. This is linked to the problem of the breaking
of the extra $U(1)$ gauge group, in the $SU(5)\times U(1)$ subgroup of
$SO(10)$, which we show can achieved via a (generalised) Kolda-Martin
mechanism. The resulting neutrino masses arise from a combination of the seesaw
mechanism and induced R-parity breaking contributions. The rather complicated
neutrino mass matrix is analysed for one neutrino family and it is shown how
phenomenologically acceptable neutrino masses can emerge.


  In large-area forest inventories a trade-off between the amount of data to be
sampled and the costs of collecting the data is necessary. It is not always
possible to have a very large data sample when dealing with sampling-based
inventories. It is therefore necessary to optimize the sampling design in order
to achieve optimal population parameter estimation. On the contrary, the
availability of remote sensing (RS) data correlated with the forest inventory
variables is usually much higher. The combination of RS and the sampled field
measurement data is often used for improving the forest inventory parameter
estimation. In addition, it is also reasonable to study the utilization of RS
data in inventory sampling, which can further improve the estimation of forest
variables. In this study, we propose a data sampling method based on Bayesian
optimization which uses RS data in forest inventory sample selection. The
presented method applies the learned functional relationship between the RS and
inventory data in new sampling decisions. We evaluate our method by conducting
simulated sampling experiments with both synthetic data and measured data from
the Aland region in Finland. The proposed method is benchmarked against two
baseline methods: simple random sampling and the local pivotal method. The
results of the simulated experiments show the best results in terms of MSE
values for the proposed method when the functional relationship between RS and
inventory data is correctly learned from the available training data.


  In this paper, we prove rigidity results on gradient shrinking Ricci solitons
with weakly harmonic Weyl curvature tensors. Let $(M^n, g)$ be a compact
gradient shrinking Ricci soliton satisfying ${\rm Ric}_g + Ddf = \rho g$ with
$\rho >0$ constant. We show that if $(M,g)$ satisfies $\delta \mathcal W
(\cdot, \cdot, \nabla f) = 0$, then $(M, g)$ is Einstein. Here $\mathcal W$
denotes the Weyl curvature tensor. In the case of noncompact, if $M$ is
complete and satisfies the same condition, then $M$ is rigid in the sense that
$M$ is given by a quotient of product of an Einstein manifold with Euclidean
space. These are generalizations of the previous known results in
  \cite{l-r}, \cite{m-s} and \cite{p-w3}.


  While deep Convolutional Neural Networks (CNNs) have shown extraordinary
capability of modelling specific noise and denoising, they still perform poorly
on real-world noisy images. The main reason is that the real-world noise is
more sophisticated and diverse. To tackle the issue of blind denoising, in this
paper, we propose a novel pyramid real image denoising network (PRIDNet), which
contains three stages. First, the noise estimation stage uses channel attention
mechanism to recalibrate the channel importance of input noise. Second, at the
multi-scale denoising stage, pyramid pooling is utilized to extract multi-scale
features. Third, the stage of feature fusion adopts a kernel selecting
operation to adaptively fuse multi-scale features. Experiments on two datasets
of real noisy photographs demonstrate that our approach can achieve competitive
performance in comparison with state-of-the-art denoisers in terms of both
quantitative measure and visual perception quality. Code is available at
https://github.com/491506870/PRIDNet.


  We extend our recent work on ``two-metric'' theories of gravity by showing
how in such models cosmic defects can produce a spectrum of primordial Gaussian
density perturbations. This will happen when the speed characterising the decay
products of the defect network is much larger than the speed characterising
gravity and all standard model particles. This model will exactly mimic all the
standard predictions of inflationary models, and the only way of distinguishing
the two will be via the detection of the decay products of the network.


  Enstrophy, kinetic energy (KE) fluxes and spectra are estimated in different
parts of the mid-latitudinal oceans via altimetry data. To begin with, using
geostrophic currents derived from sea-surface height anomaly data provided by
AVISO, we confirm the presence of a strong inverse flux of surface KE at scales
larger than approximately 250 km. We then compute enstrophy fluxes to help
develop a clearer picture of the underlying dynamics at smaller scales, i.e.,
250 km to 100 km. Here, we observe a robust enstrophy cascading regime, wherein
the enstrophy shows a large forward flux and the KE spectra follow an
approximate $k^{-3.5}$ power-law. Given the rotational character of the flow,
not only is this large scale inverse KE and smaller scale forward enstrophy
transfer scenario consistent with expectations from idealized studies of
three-dimensional rapidly-rotating and strongly-stratified turbulence, it also
agrees with detailed analyses of spectra and fluxes in the upper level
midlatitude troposphere. Decomposing the currents into components with greater
and less than 100 day variability (referred to as seasonal and eddy,
respectively), we find that, in addition to the eddy-eddy contribution, the
seasonal-eddy and seasonal-seasonal fluxes play a significant role in the
inverse (forward) flux of KE (enstrophy) at scales larger (smaller) than about
250 km. Taken together, we suspect, it is quite possible that, from about 250
km to 100 km, the altimeter is capturing the relatively steep portion of a
surface oceanic counterpart of the upper tropospheric Nastrom-Gage spectrum.


  Generalizing a recent result on lineability of sets of non-injective linear
operators, we prove, for quite general linear spaces $A$ of maps from an
arbitraty set to a sequence space, that, for every $0 \neq f \in A$, the subset
of $A$ of non-injective maps contains an infinite dimensional subspace of $A$
containing $f$. We provide aplications of the main result to spaces of linear
operators between quasi-Banach spaces, to spaces of linear operators belonging
to an operator ideal, and, in the nonlinear setting, to linear spaces of
homogeneous polynomials and to linear spaces of vector-valued Lispshitz
functions on metric spaces.


  A Fermi liquid with weak attractive interaction undergoes a BCS transition to
a superconductor with reducing temperature. With increasing interaction
strength, the thermal transition is progressively modified as the high
temperature `metallic' phase develops a pseudogap due to pairing fluctuations
and the resistivity above T_c shows insulating behaviour. The crossover to
insulating character occurs much before the system can be considered to be in
the BEC regime of preformed fermion pairs. We use a new Monte Carlo tool to map
out the BCS-BEC crossover in the attractive Hubbard model on large two
dimensional lattices and explicitly compute the resistivity to demonstrate how
the metal to superconductor (MS) thermal transition at weak coupling crosses
over to an insulator to superconductor (IS) transition at intermediate
coupling. Our high resolution access to the single particle and optical
spectrum at finite temperature allows us to completely describe the transport
crossover in this longstanding problem.


  We characterize the uniform limits of Dirichlet polynomials on a right half
plane. In the Dirichlet setting, we find approximation results, with respect to
the Euclidean distance and {to} the chordal one as well, analogous to classical
results of Runge, Mergelyan and Vitushkin. We also strengthen the notion of
universal Dirichlet series.


  We derive an exact closed-form analytical expression for the distribution of
the cover time for a random walk over an arbitrary graph. In special case, we
derive simplified exact expressions for the distributions of cover time for a
complete graph, a cycle graph, and a path graph. An accurate approximation for
the cover time distribution, with computational complexity of O(2n), is also
presented. The approximation is numerically tested only for graphs with n<=1000
nodes.


  The investigation of topological properties of the gauge field in a
two-dimensional Higgs model can help in understanding anomalous fermion number
violation.


  In this article we establish $C^{3,\alpha}$-regularity of the reduced
boundary of stationary points of a nonlocal isoperimetric problem in a domain
$\Omega \subset \mathbb{R}^n$. In particular, stationary points satisfy the
corresponding Euler-Lagrange equation classically on the reduced boundary.
Moreover, we show that the singular set has zero $(n-1)$-dimensional Hausdorff
measure. This complements the results in Choksi & Sternberg, in which the
Euler-Lagrange equation was derived under the assumption of $C^2$-regularity of
the topological boundary and the results in Sternberg & Topaloglu in which the
authors assume local minimality. In case $\Omega$ has non-empty boundary, we
show that stationary points meet the boundary of $\Omega$ orthogonally in a
weak sense, unless they have positive distance to it.


  The recent deployment of multi-agent networks has enabled the distributed
solution of learning problems, where agents cooperate to train a global model
without sharing their local, private data. This work specifically targets some
prevalent challenges inherent to distributed learning: (i) online training,
i.e., the local data change over time; (ii) asynchronous agent computations;
(iii) unreliable and limited communications; and (iv) inexact local
computations. To tackle these challenges, we apply the Distributed Operator
Theoretical (DOT) version of the Alternating Direction Method of Multipliers
(ADMM), which we call "DOT-ADMM". We prove that if the DOT-ADMM operator is
metric subregular, then it converges with a linear rate for a large class of
(not necessarily strongly) convex learning problems toward a bounded
neighborhood of the optimal time-varying solution, and characterize how such
neighborhood depends on (i)-(iv). We first derive an easy-to-verify condition
for ensuring the metric subregularity of an operator, followed by tutorial
examples on linear and logistic regression problems. We corroborate the
theoretical analysis with numerical simulations comparing DOT-ADMM with other
state-of-the-art algorithms, showing that only the proposed algorithm exhibits
robustness to (i)-(iv).


  The space of marked n distinct points on the complex projective line up to
projective transformations will be called a configuration space in this paper.
There are two families of complex hyperbolic structures on the configuration
space constructed by Deligne-Mostow and Thurston. We first confirm that these
families are the same. Then in view of the deformation theory for real
hyperbolic cone 3-manifolds, we review the families for small n.


  For this study we have simulated the 28Ni58+28Ni58 and 26Fe58+26Fe58 systems
at incident energies ranging from 45 MeV/nucleon to 105 MeV/nucleon by using
soft equation of state. The geometry of reactions chosen are = b/bmax = 0.2,
0.4, 0.5, 0.6, and 0.7.The Px/A is becoming more positive for neutron - rich
system 26Fi58 as compared to neutron-poor system 28Ni58. This point towards the
higher value of balance energy for 26Fi58 system. Further study in this
direction is ongoing.


  By utilizing global navigation satellite system (GNSS) position and velocity
measurements, the fusion between the GNSS and the inertial navigation system
provides accurate and robust navigation information. When considering land
vehicles,like autonomous ground vehicles,off-road vehicles or mobile robots,a
GNSS-based heading angle measurement can be obtained and used in parallel to
the position measurement to bound the heading angle drift. Yet, at low vehicle
speeds (less than 2m/s) such a model-based heading measurement fails to provide
satisfactory performance. This paper proposes GHNet, a deep-learning framework
capable of accurately regressing the heading angle for vehicles operating at
low speeds. We demonstrate that GHNet outperforms the current model-based
approach for simulation and experimental datasets.


  Diffusion Posterior Sampling(DPS) methodology is a novel framework that
permits nonlinear CT reconstruction by integrating a diffusion prior and an
analytic physical system model, allowing for one-time training for different
applications. However, baseline DPS can struggle with large variability,
hallucinations, and slow reconstruction. This work introduces a number of
strategies designed to enhance the stability and efficiency of DPS CT
reconstruction. Specifically, jumpstart sampling allows one to skip many
reverse time steps, significantly reducing the reconstruction time as well as
the sampling variability. Additionally, the likelihood update is modified to
simplify the Jacobian computation and improve data consistency more
efficiently. Finally, a hyperparameter sweep is conducted to investigate the
effects of parameter tuning and to optimize the overall reconstruction
performance. Simulation studies demonstrated that the proposed DPS technique
achieves up to 46.72% PSNR and 51.50% SSIM enhancement in a low-mAs setting,
and an over 31.43% variability reduction in a sparse-view setting. Moreover,
reconstruction time is sped up from >23.5 s/slice to <1.5 s/slice. In a
physical data study, the proposed DPS exhibits robustness on an anthropomorphic
phantom reconstruction which does not strictly follow the prior distribution.
Quantitative analysis demonstrates that the proposed DPS can accommodate
various dose levels and number of views. With 10% dose, only a 5.60% and 4.84%
reduction of PSNR and SSIM was observed for the proposed approach. Both
simulation and phantom studies demonstrate that the proposed method can
significantly improve reconstruction accuracy and reduce computational costs,
greatly enhancing the practicality of DPS CT reconstruction.


  Triggered by ongoing dark matter searches in the top quark sector at the
Large Hadron Collider we report on the calculation of the next-to-leading order
QCD corrections to the Standard Model process $pp\to t\bar{t}+ Z(\to \nu_\ell
\bar{\nu}_\ell)$. This calculation is based on matrix elements for $e^+\nu_e \,
\mu^- \bar{\nu}_\mu \, b\bar{b} \, \nu_\tau \bar{\nu}_\tau$ production and
includes all non-resonant diagrams, interferences, and off-shell effects of the
top quarks. Non-resonant and off-shell effects due to the finite $W$-boson
width are also consistently taken into account. As it is common for such
studies, we present results for both integrated and differential cross sections
for a few renormalisation and factorisation scale choices and three different
parton distribution functions. Already with the fairly inclusive cut selection
and independently of the scale choice and the parton distribution function
non-flat differential ${\cal K}$-factors are obtained for $p_T^{miss}, \Delta
\phi_{\ell\ell}, \Delta y_{\ell\ell}, \cos\theta_{\ell\ell}, H_T, H^\prime_T$
observables that are relevant for new physics searches. Good theoretical
control over the Standard Model background is a fundamental prerequisite for a
correct interpretation of possible signals of new physics that may arise in
this channel. Thus, these observables need to be carefully reexamined in the
presence of more exclusive cuts before any realistic strategies for the
detection of new physics signal can be further developed.


  We discuss the calculation of one-loop amplitudes in N=8 supergravity using
MHV diagrams. In contrast to MHV amplitudes of gluons in Yang-Mills, tree-level
MHV amplitudes of gravitons are not holomorphic in the spinor variables. In
order to extend these amplitudes off shell, and use them as vertices to build
loops, we introduce certain shifts for the spinor variables associated to the
loop momenta. Using this off-shell prescription, we rederive the four-point MHV
amplitude of gravitons at one loop, in complete agreement with known results.
We also discuss the extension to the case of one-loop MHV amplitudes with an
arbitrary number of gravitons.


  We present the Overlapping Domain Cover (ODC) notion for kernel machines, as
a set of overlapping subsets of the data that covers the entire training set
and optimized to be spatially cohesive as possible. We show how this notion
benefit the speed of local kernel machines for regression in terms of both
speed while achieving while minimizing the prediction error. We propose an
efficient ODC framework, which is applicable to various regression models and
in particular reduces the complexity of Twin Gaussian Processes (TGP)
regression from cubic to quadratic. Our notion is also applicable to several
kernel methods (e.g., Gaussian Process Regression(GPR) and IWTGP regression, as
shown in our experiments). We also theoretically justified the idea behind our
method to improve local prediction by the overlapping cover. We validated and
analyzed our method on three benchmark human pose estimation datasets and
interesting findings are discussed.


  We report results of torsional oscillator (TO) experiments on solid $^4$He at
temperatures above 1K. We have previously found that single crystals, once
disordered, show some mobility (decoupled mass) even at these rather high
temperatures. The decoupled mass fraction with single crystals is typically 20-
30%. In the present work we performed similar measurements on polycrystalline
solid samples. The decoupled mass with polycrystals is much smaller, $\sim$ 1%,
similar to what is observed by other groups. In particular, we compared the
properties of samples grown with the TO's rotation axis at different
orientations with respect to gravity. We found that the decoupled mass fraction
of bcc samples is independent of the angle between the rotation axis and
gravity. In contrast, hcp samples showed a significant difference in the
fraction of decoupled mass as the angle between the rotation axis and gravity
was varied between zero and 85 degrees. Dislocation dynamics in the solid
offers one possible explanation of this anisotropy.


  The ratio of the CKM quark-mixing matrix elements |Vub|/|Vcb| has been
measured using B hadron semileptonic decays. The analysis uses the
reconstructed mass M_X of the secondary hadronic system produced in association
with an identified lepton. Since B -> X_u lepton anti-nu transitions are
characterised by hadronic masses below those of the D mesons produced in B ->
X_c lepton anti-nu transitions, events with a reconstructed value of M_X
significantly below the D mass are selected. Further signal enrichments are
obtained using the topology of reconstructed decays and hadron identification.
A fit to the numbers of decays in the b -> u enriched and depleted samples with
M_X above and below 1.6 GeV/c^2 and to the shapes of the lepton energy
distribution in the B rest frame gives |Vub|/|Vcb|= 0.103^{+0.011}_{-0.012}
(stat.) +/- 0.016 (syst.) +/- 0.010 (model) and, correspondingly, a charmless
semileptonic B decay branching fraction of BR(B -> X_u lepton anti-nu) = (1.57
+/- 0.35 (stat.) +/- 0.48 (syst.) +/- 0.27 (model)) x 10^{-3}.


  We investigate the statistical properties of the polarized emission of
extragalactic radio sources and estimate their contribution to the power
spectrum of polarization fluctuations in the microwave region. The basic
ingredients of our analysis are the NVSS polarization data, the multifrequency
study of polarization properties of the B3-VLA sample (Mack et al. 2002) which
has allowed us to quantify Faraday depolarization effects, and the 15 GHz
survey by Taylor et al. (2001), which has provided strong constraints on the
high-frequency spectral indices of sources. The polarization degree of both
steep- and flat-spectrum at 1.4 GHz is found to be anti-correlated with the
flux density. The median polarization degree at 1.4 GHz of both steep- and
flat-spectrum sources brighter than $S(1.4 \hbox{GHz})=80 $mJy is $\simeq
2.2%$. The data by Mack et al. (2002) indicate a substantial mean Faraday
depolarization at 1.4 GHz for steep spectrum sources, while the depolarization
is undetermined for most flat/inverted-spectrum sources. Exploiting this
complex of information we have estimated the power spectrum of polarization
fluctuations due to extragalactic radio sources at microwave frequencies. We
confirm that extragalactic sources are expected to be the main contaminant of
Cosmic Microwave Background (CMB) polarization maps on small angular scales. At
frequencies $< 30 $GHz the amplitude of their power spectrum is expected to be
comparable to that of the $E$-mode of the CMB. At higher frequencies, however,
the CMB dominates.


  In this paper we determine the number of the meaningful compositions of
higher order of the differential operations and Gateaux directional derivative.


  We propose a radiatively induced quark and lepton mass model in the first and
second generation with extra $U(1)$ gauge symmetry and vector-like fermions.
Then we analyze the allowed regions which simultaneously satisfy the FCNCs for
the quark sector, LFVs including $\mu-e$ conversion, the quark mass and mixing,
and the lepton mass and mixing. Also we estimate the typical value for the
$(g-2)_\mu$ in our model.


  Dense populations of stars surround the nuclear regions of galaxies. In this
work, we study the interaction of a WR star with relativistic jets in active
galactic nuclei. A bow-shaped double-shock structure will form as a consequence
of the interaction of the jet and the wind of the star. Particles can be
accelerated up to relativistic energies in these shocks and emit high-energy
radiation. We compute the produced gamma-ray emission obtaining that this
radiation may be significant. This emission is expected to be particularly
relevant for nearby non-blazar sources.


  Not long after metastable xenon was photoionized in a magneto-optical trap,
groups in Europe and North America found that similar states of ionized gas
evolved spontaneously from state-selected, high principal quantum number
Rydberg gases. Studies of atomic xenon and molecular nitric oxide entrained in
a supersonically cooled molecular beam subsequently showed much the same final
state evolved from a sequence of prompt Penning ionization and electron-impact
avalanche to plasma, well-described by coupled rate-equation simulations. But,
measured over longer times, the molecular ultracold plasma was found to exhibit
an anomalous combination of very long lifetime and very low apparent electron
temperature. This review summarizes early developments in the study of
ultracold plasmas formed by atomic and molecular Rydberg gases, and then
details observations as they combine to characterize properties of the nitric
oxide molecular ultracold plasma that appear to call for an explanation beyond
the realm of conventional plasma physics.


  We use 1-m class telescopes and the Transiting Exoplanet Survey Satellite
(TESS) to explore the photometric variability of all known rapidly rotating
($v\sin{i}\gtrsim30$ km\,s$^{-1}$) ultra-cool ($\geq$M7) dwarfs brighter than
$I\approx17.5$ mag. For a sample of 13 M7--L1.5 dwarfs without prior
photometric periods, we obtained $I$-band light curves with the SMARTS 1.3m and
WIYN 0.9m telescopes and detected rotation-modulated photometric variability in
three of them. Seven of our targets were also observed by TESS and six of them
show significant periodicities compatible with the estimated rotation periods
of the targets. We investigate the potential of TESS to search for
rotation-modulated photometric variability in ultra-cool dwarfs and find that
its long stare enables $<$80~h periodic variations to be retrieved with
$\leq$1\% amplitudes for ultra-cool dwarfs up to a TESS magnitude of 16.5. We
combine these results with the periods of all other known
photometrically-periodic ultra-cool dwarfs from the literature, and find that
the periods of ultra-cool dwarfs range between 1 and 24 h, although the upper
limit is likely an observational bias. We also observe that the minimum
rotation periods follow a lower envelope that runs from $\approx$2 h at
spectral type $\approx$M8 to $\approx$1 h at spectral type T.