  We present an improved version of our original cosmological model to explain
the current phase of cosmological acceleration without resorting to a
cosmological constant or any other mass scale. Like the original, this
phenomenological approach is based on an effective quantum gravitational
action, but now depends on the original nonlocal dimensionless scalar $X =
\square^{-1} R$ only through $Y = \square^{-1} g^{\mu\nu} X_{,\mu} X_{,\nu}$.
Both $X$ and $Y$ are quiescent during the radiation-dominated ($R=0$) era, both
only grow logarithmically during matter dominance, and neither affects the
propagation of gravitational radiation. However, while $X$ has the same sign
for gravitationally bound systems as for cosmology, we show that the sign of
$Y$ differs for the two cases: it is positive for cosmology and negative for
strongly gravitationally bound systems. We can therefore enforce the
$\Lambda$CDM expansion history by making a suitable choice of the nonlocal
distortion function $f(Y)$ for $Y > 0$, while ensuring that there is no change
in the heavily constrained solar system phenomenology simply by making $f$
vanish for $Y < 0$ without discontinuity. The required $f(Y>0)$ is determined
numerically to have a strikingly simple exponential form.


  Abundances and $m_\bot$-spectra of strange and other hadronic particles
emanating from central 158-200 A GeV reactions between nuclei are found to
originate from a thermally equilibrated, deconfined source in chemical
non-equilibrium. Physical freeze-out parameters and physical conditions
(pressure, specific energy, entropy, and strangeness) are evaluated. Five
properties of the source we obtain are as expected for direct hadron emission
(hadronization) from a deconfined quark-gluon plasma phase.


  We give an elementary construction of a time-invertible Markov process which
is discrete except at one instance. The process is one of the quadratic
harnesses studied in our previous papers and can be regarded as a random joint
of two independent Poisson processes.


  Let $M$ be a K\"ahler manifold with complex structure $J$ and K\"ahler metric
$g$. A c-projective vector field is a vector field on $M$ whose flow sends
$J$-planar curves to $J$-planar curves, where $J$-planar curves are analogs of
what (unparametrised) geodesics are for pseudo-Riemannian manifolds (without
complex structure). The c-projective symmetry algebras of K\"ahler surfaces
with essential (i.e., non-affine) c-projective vector fields are computed.


  We present results for Chandra observations of comets, 17P/Holmes (17P) and
8P/Tuttle (8P). 17P was observed for 30 ksec right after its major outburst, on
31 Oct 2007 (10:07 UT) and comet 8P/Tuttle was observed in 2008 January for 47
ksec. During the two Chandra observations, 17P was producing at least 100 times
more water than 8P but was 2.2 times further away from the Sun. Also, 17P is
the first comet observed at high latitude (+19.1 degrees) during solar minimum,
while 8P was observed at a lower solar latitude (3.4 degrees). The X-ray
spectrum of 17P is unusually soft with little significant emission at energies
above 500 eV. Depending on our choice of background, we derive a 300 to 1000 eV
flux of 0.5 to 4.5 x 10^-13 ergs/cm2/sec, with over 90% of the emission in the
300 to 400 eV range. This corresponds to an X-ray luminosity between 0.4 to 3.3
x 10^15 ergs/sec. 17P's lack of X-rays in the 400 to 1000 eV range, in a simple
picture, may be attributed to the polar solar wind, which is depleted in highly
charged ions. 8P/Tuttle was much brighter, with an average count rate of 0.20
counts/s in the 300 to 1000 eV range. We derive an average X-ray flux in this
range of 9.4 x 10^-13 ergs/cm2/sec and an X-ray luminosity for the comet of 1.7
x 10^14 ergs/sec. The light curve showed a dramatic decrease in flux of over
60% between observations on January 1st and 4th. When comparing outer regions
of the coma to inner regions, its spectra showed a decrease in ratios of
CVI/CV, OVIII/OVII, as predicted by recent solar wind charge exchange emission
models. There are remarkable differences between the X-ray emission from these
two comets, further demonstrating the qualities of cometary X-ray observations,
and solar wind charge exchange emission in more general as a means of remote
diagnostics of the interaction of astrophysical plasmas.


  We consider the possibility of extracting the bottom quark mass from LEP
data. The inclusive decay rate for $\zbb +\cdots$ is obtained at order $\as$ by
summing up the one-loop two-parton decay rate to the tree-level three-parton
rate. We calculate the decay width of the $Z$-boson into two and three jets
containing the $b$-quark including complete quark mass effects. In particular,
we give analytic results for a slight modification of the JADE clustering
algorithm. We also study the angular distribution with respect to the angle
formed between the gluon and the quark jets, which has a strong dependence on
the quark mass. The impact of higher order QCD corrections on these observables
is briefly discussed. Finally, we present numerical results for some popular
jet-clustering algorithms and show that, indeed, these three-jet observables
are very sensitive to the $b$-quark mass and well suited for its determination
at LEP.


  We show that gated bilayer graphene hosts a strong topological insulator (TI)
phase in the presence of Rashba spin-orbit (SO) coupling. We find that gated
bilayer graphene under preserved time-reversal symmetry is a quantum valley
Hall insulator for small Rashba SO coupling $\lambda_{\mathrm{R}}$, and
transitions to a strong TI when $\lambda_{\mathrm{R}} > \sqrt{U^2+t_\bot^2}$,
where $U$ and $t_\bot$ are respectively the interlayer potential and tunneling
energy. Different from a conventional quantum spin Hall state, the edge modes
of our strong TI phase exhibit both spin and valley filtering, and thus share
the properties of both quantum spin Hall and quantum valley Hall insulators.
The strong TI phase remains robust in the presence of weak graphene intrinsic
SO coupling.


  In this paper, we review a few known facts on the coordinate Bethe ansatz. We
present a detailed construction of the Bethe ansatz vector $\psi$ and energy
$\Lambda$, which satisfy $V \psi = \Lambda \psi$, where $V$ is the the transfer
matrix of the six-vertex model on a finite square lattice with periodic
boundary conditions for weights $a= b=1$ and $c > 0$. We also show that the
same vector $\psi$ satisfies $H \psi = E \psi$, where $H$ is the Hamiltonian of
the XXZ model (which is the model for which the Bethe ansatz was first
developed), with a value $E$ computed explicitly.
  Variants of this approach have become central techniques for the study of
exactly solvable statistical mechanics models in both the physics and
mathematics communities. Our aim in this paper is to provide a
pedagogically-minded exposition of this construction, aimed at a mathematical
audience. It also provides the opportunity to introduce the notation and
framework which will be used in a subsequent paper by the authors that amounts
to proving that the random cluster model on $\mathbb{Z}^2$ with cluster weight
$q >4$ exhibits a first-order phase transition.


  It is shown that algebra of quantum space of the title of the present paper
may be realized on usual unphysical Minkowskii one. Equations of field theory
and there solutions are discussed. Solution equations of particle motion are
obtained in implicit form from the classical ones.


  $L^p$ boundedness of the circular maximal function $\mathcal
M_{\mathbb{H}^1}$ on the Heisenberg group $\mathbb{H}^1$ has received
considerable attentions. While the problem still remains open, $L^p$
boundedness of $\mathcal M_{\mathbb{H}^1}$ on Heisenberg radial functions was
recently shown for $p>2$ by Beltran, Guo, Hickman, and Seeger [2]. In this
paper we extend their result considering the local maximal operator
$M_{\mathbb{H}^1}$ which is defined by taking supremum over $1<t<2$. We prove
$L^p-L^q$ estimates for $M_{\mathbb{H}^1}$ on Heisenberg radial functions on
the optimal range of $p,q$ modulo the borderline cases. Our argument also
provides a simpler proof of the aforementioned result due to Beltran et al.


  For problems with multiple bodies, the current integral approach needs the
use of auxiliary potential functions in order to have an individual force
formula for each body. While the singularity approach, based on an extension of
the unsteady Lagally theorem, is restricted to multibody and multivortex flows
without bound vortex and vortex production. In this paper, we consider
multibody and multivortex flow and derive force formulas, in both forms of
singularity approach and integral approach but without auxiliary function, that
give individual forces of each body for unsteady two dimensional potential flow
with vortex production on the surface of bodies. A number of problems,
including Karman vortex street, Wagner problem of impulsively starting flow,
interaction of two circular cylinders with circulation, and interaction of an
airfoil with a bound vortex, are used to validate the force formulas.


  We present a method to investigate the CP quantum numbers of the Higgs boson
in the process $e^+ e^- \to Z\phi$ at a future linear collider (LC), where
$\phi$, a generic Higgs boson, is a mixture of CP-even and CP-odd states. The
procedure consist of a comparison of the data with predictions obtained from
Monte Carlo simulations corresponding to the productions of scalar and
pseudoscalar Higgs and the interference term wich constitutes a distinctive
signal of CP violation. We present estimates of the sensitivity of the method
from Monte Carlo studies using hypothetical data samples with a full LC
detector simulation taking into account the background signals.


  Quantum-mechanical PT-symmetric theories associated with complex cubic
potentials such as V=x^2+y^2+igxy^2 and V=x^2+y^2+z^2+igxyz, where g is a real
parameter, are investigated. These theories appear to possess real, positive
spectra. Low-lying energy levels are calculated to very high order in
perturbation theory. The large-order behavior of the perturbation coefficients
is determined using multidimensional WKB tunneling techniques. This approach is
also applied to the complex Henon-Heiles potential V=x^2+y^2+ig(xy^2-x^3/3).


  Zassenhaus conjectured that any unit of finite order in the integral group
ring $\mathbb{Z}G$ of a finite group $G$ is conjugate in the rational group
algebra of $G$ to an element in $\pm G$. We review the known weaker versions of
this conjecture and introduce a new condition, on the partial augmentations of
the powers of a unit of finite order in $\mathbb{Z}G$, which is weaker than the
Zassenhaus Conjecture but stronger than its other weaker versions.
  We prove that this condition is satisfied for units mapping to the identity
modulo a nilpotent normal subgroup of $G$. Moreover, we show that if the
condition holds then the HeLP Method adopts a more friendly form and use this
to prove the Zassenhaus Conjecture for a special class of groups.


  Graphene on ferroelectric structures can be promising candidates for advanced
field effect transistors, modulators and electrical transducers, providing that
research of their electrotransport and electromechanical performances can be
lifted up from mostly empirical to prognostic theoretical level.Recently we
have shown that alternating piezoelectric displacement of the ferroelectric
domain surfaces can lead to the alternate stretching and separation of graphene
areas at the steps between elongated and contracted domains, and the
conductance of graphene channel can be increased essentially at room
temperature, because electrons in the stretched section scatter on acoustic
phonons.The piezoelectric mechanism of graphene conductance control requires
systematic studies of the ambient condition impact on its manifestations. This
theoretical work studies in details the temperature behavior of the graphene
conductance changes induced by piezoelectric effect in a ferroelectric
substrate with domain stripes.We revealed the possibility to control graphene
conductance (that can change up to 100 times for PZT ferroelectric substrate)
by tuning the ambient temperature from low values to the critical one for given
gate voltage and channel length.Also we demonstrate the possibility to control
graphene conductance changes up to one hundred of times by tuning the gate
voltage from 0 to the critical value at a given temperature and channel length.
Obtained results can be open the way towards graphene on ferroelectric
applications in piezoresistive memories operating in a wide temperature range.


  Accurate and interpretable user satisfaction estimation (USE) is critical for
understanding, evaluating, and continuously improving conversational systems.
Users express their satisfaction or dissatisfaction with diverse conversational
patterns in both general-purpose (ChatGPT and Bing Copilot) and task-oriented
(customer service chatbot) conversational systems. Existing approaches based on
featurized ML models or text embeddings fall short in extracting generalizable
patterns and are hard to interpret. In this work, we show that LLMs can extract
interpretable signals of user satisfaction from their natural language
utterances more effectively than embedding-based approaches. Moreover, an LLM
can be tailored for USE via an iterative prompting framework using supervision
from labeled examples. The resulting method, Supervised Prompting for User
satisfaction Rubrics (SPUR), not only has higher accuracy but is more
interpretable as it scores user satisfaction via learned rubrics with a
detailed breakdown.


  Machine learning techniques have achieved impressive results in recent years
and the possibility of harnessing the power of quantum physics opens new
promising avenues to speed up classical learning methods. Rather than viewing
classical and quantum approaches as exclusive alternatives, their integration
into hybrid designs has gathered increasing interest, as seen in variational
quantum algorithms, quantum circuit learning, and kernel methods. Here we
introduce deep hybrid classical-quantum reservoir computing for temporal
processing of quantum states where information about, for instance, the
entanglement or the purity of past input states can be extracted via a
single-step measurement. We find that the hybrid setup cascading two reservoirs
not only inherits the strengths of both of its constituents but is even more
than just the sum of its parts, outperforming comparable non-hybrid
alternatives. The quantum layer is within reach of state-of-the-art multimode
quantum optical platforms while the classical layer can be implemented in
silico.


  Traffic analysis in Multi-hop Wireless Networks can expose the structure of
the network allowing attackers to focus their efforts on critical nodes. For
example, jamming the only data sink in a sensor network can cripple the
network. We propose a new communication protocol that is part of the MAC layer,
but resides conceptually between the routing layer and MAC, that is resilient
to traffic analysis. Each node broadcasts the data that it has to transmit
according to a fixed transmission schedule that is independent of the traffic
being generated, making the network immune to time correlation analysis. The
transmission pattern is identical, with the exception of a possible time shift,
at all nodes, removing spatial correlation of transmissions to network
strucutre. Data for all neighbors resides in the same encrypted packet. Each
neighbor then decides which subset of the data in a packet to forward onwards
using a routing protocol whose details are orthogonal to the proposed scheme.
We analyze the basic scheme, exploring the tradeoffs in terms of frequency of
transmission and packet size. We also explore adaptive and time changing
patterns and analyze their performance under a number of representative
scenarios.


  Using the pseudopotential density functional method, we find that a Be atom
on a nanostructure with H2 molecules forms a Be-dihydrogen complex through the
hybridization of the Be s or p orbits with the H2 sigma orbits and the binding
energy of the H2 molecules is in the range of ~0.3 - 0.8 eV/H2. We also study
Be-dihydrogen complexes on various nanostructures and demonstrate the
feasibility of the application of the complexes to a hydrogen storage medium
that operates near room temperature and ambient pressure.


  Over 2,000 stars were observed for one month with a high enough cadence in
order to look for acoustic modes during the survey phase of the Kepler mission.
Solar-like oscillations have been detected in about 540 stars. The question of
why no oscillations were detected in the remaining stars is still open.
Previous works explained the non-detection of modes with the high level of
magnetic activity. However, the studied stars contained some classical
pulsators and red giants that could have biased the results. In this work, we
revisit this analysis on a cleaner sample of 1,014 main-sequence solar-like
stars. First we compute the predicted amplitude of the modes. We find that the
stars with detected modes have an amplitude to noise ratio larger than 0.94. We
measure reliable rotation periods and the associated photometric magnetic index
for 684 stars and in particular for 323 stars where the mode amplitude is
predicted to be high enough to be detected. We find that among these 323 stars
32% have a magnetic activity level larger than the Sun at maximum activity,
explaining the non-detection of p modes. Interestingly, magnetic activity
cannot be the primary reason responsible for the absence of detectable modes in
the remaining 68% of the stars without p modes detected and with reliable
rotation periods. Thus, we investigate metallicity, inclination angle, and
binarity as possible causes of low mode amplitudes. Using spectroscopic
observations for a subsample, we find that a low metallicity could be the
reason for suppressed modes. No clear correlation with binarity nor inclination
is found. We also derive the lower limit for our photometric activity index (of
20-30 ppm) below which rotation and magnetic activity are not detected. Finally
with our analysis we conclude that stars with a photometric activity index
larger than 2,000 ppm have 98.3% probability of not having oscillations
detected.


  Typical blur from camera shake often deviates from the standard uniform
convolutional script, in part because of problematic rotations which create
greater blurring away from some unknown center point. Consequently, successful
blind deconvolution requires the estimation of a spatially-varying or
non-uniform blur operator. Using ideas from Bayesian inference and convex
analysis, this paper derives a non-uniform blind deblurring algorithm with
several desirable, yet previously-unexplored attributes. The underlying
objective function includes a spatially adaptive penalty which couples the
latent sharp image, non-uniform blur operator, and noise level together. This
coupling allows the penalty to automatically adjust its shape based on the
estimated degree of local blur and image structure such that regions with large
blur or few prominent edges are discounted. Remaining regions with modest blur
and revealing edges therefore dominate the overall estimation process without
explicitly incorporating structure-selection heuristics. The algorithm can be
implemented using a majorization-minimization strategy that is virtually
parameter free. Detailed theoretical analysis and empirical validation on real
images serve to validate the proposed method.


  We study the Tutte polynomial of two infinite families of finite graphs: the
Sierpi\'{n}ski graphs, which are finite approximations of the well-known
Sierpi\'{n}ski gasket, and the Schreier graphs of the Hanoi Towers group
$H^{(3)}$ acting on the rooted ternary tree. For both of them, we recursively
describe the Tutte polynomial and we compute several special evaluations of it,
giving interesting results about the combinatorial structure of these graphs.


  In this note we present a new proof that Killing horizons are equipotential
hypersurfaces for the electric and the magnetic scalar potential, that makes no
use of gravitational field equations or the assumption about the existence of
bifurcation surface.


  A bipartite bilinear program (BBP) is a quadratically constrained quadratic
optimization problem where the variables can be partitioned into two sets such
that fixing the variables in any one of the sets results in a linear program.
We propose a new second order cone representable (SOCP) relaxation for BBP,
which we show is stronger than the standard SDP relaxation intersected with the
boolean quadratic polytope. We then propose a new branching rule inspired by
the construction of the SOCP relaxation. We describe a new application of BBP
called as the finite element model updating problem, which is a fundamental
problem in structural engineering. Our computational experiments on this
problem class show that the new branching rule together with an polyhedral
outer approximation of the SOCP relaxation outperforms a state-of-the-art
commercial global solver in obtaining dual bounds.


  Software repositories contain large amounts of textual data, ranging from
source code comments and issue descriptions to questions, answers, and comments
on Stack Overflow. To make sense of this textual data, topic modelling is
frequently used as a text-mining tool for the discovery of hidden semantic
structures in text bodies. Latent Dirichlet allocation (LDA) is a commonly used
topic model that aims to explain the structure of a corpus by grouping texts.
LDA requires multiple parameters to work well, and there are only rough and
sometimes conflicting guidelines available on how these parameters should be
set. In this paper, we contribute (i) a broad study of parameters to arrive at
good local optima for GitHub and Stack Overflow text corpora, (ii) an
a-posteriori characterisation of text corpora related to eight programming
languages, and (iii) an analysis of corpus feature importance via per-corpus
LDA configuration. We find that (1) popular rules of thumb for topic modelling
parameter configuration are not applicable to the corpora used in our
experiments, (2) corpora sampled from GitHub and Stack Overflow have different
characteristics and require different configurations to achieve good model fit,
and (3) we can predict good configurations for unseen corpora reliably. These
findings support researchers and practitioners in efficiently determining
suitable configurations for topic modelling when analysing textual data
contained in software repositories.


  We present a family of exact black-hole solutions on a static spherically
symmetric background in second-order generalized Proca theories with derivative
vector-field interactions coupled to gravity. We also derive non-exact
solutions in power-law coupling models including vector Galileons and
numerically show the existence of regular black holes with a primary hair
associated with the longitudinal propagation. The intrinsic vector-field
derivative interactions generally give rise to a secondary hair induced by
non-trivial field profiles. The deviation from General Relativity is most
significant around the horizon and hence there is a golden opportunity for
probing the Proca hair by the measurements of gravitational waves (GWs) in the
regime of strong gravity.


  SARRIGUREN, a new complete algorithm for SAT based on counting clauses (which
is valid also for Unique-SAT and #SAT) is described, analyzed and tested.
Although existing complete algorithms for SAT perform slower with clauses with
many literals, that is an advantage for SARRIGUREN, because the more literals
are in the clauses the bigger is the probability of overlapping among clauses,
a property that makes the clause counting process more efficient. Actually, it
provides a $O(m^2 \times n/k)$ time complexity for random $k$-SAT instances of
$n$ variables and $m$ relatively dense clauses, where that density level is
relative to the number of variables $n$, that is, clauses are relatively dense
when $k\geq7\sqrt{n}$. Although theoretically there could be worst-cases with
exponential complexity, the probability of those cases to happen in random
$k$-SAT with relatively dense clauses is practically zero. The algorithm has
been empirically tested and that polynomial time complexity maintains also for
$k$-SAT instances with less dense clauses ($k\geq5\sqrt{n}$). That density
could, for example, be of only 0.049 working with $n=20000$ variables and
$k=989$ literals. In addition, they are presented two more complementary
algorithms that provide the solutions to $k$-SAT instances and valuable
information about number of solutions for each literal. Although this algorithm
does not solve the NP=P problem (it is not a polynomial algorithm for 3-SAT),
it broads the knowledge about that subject, because $k$-SAT with $k>3$ and
dense clauses is not harder than 3-SAT. Moreover, the Python implementation of
the algorithms, and all the input datasets and obtained results in the
experiments are made available.


  Given a manifold M, it is natural to ask in how many ways it fibers
  (we mean fibering in a general way, where the base might be an orbifold --
this could be described as Seifert fibering)There are group-theoretic
obstructions to the existence of even one fibering, and in some cases (such as
Kahler manifolds or three-dimensional manifolds) the question reduces to a
group-theoretic question. In this note we summarize the author's state of
knowledge of the subject.


  First passage under restart with branching is proposed as a generalization of
first passage under restart. Strong motivation to study this generalization
comes from the observation that restart with branching can expedite the
completion of processes that cannot be expedited with simple restart; yet a
sharp and quantitative formulation of this statement is still lacking. We
develop a comprehensive theory of first passage under restart with branching.
This reveals that two widely applied measures of statistical dispersion---the
coefficient of variation and the Gini index---come together to determine how
restart with branching affects the mean completion time of an arbitrary
stochastic process. The universality of this result is demonstrated and its
connection to extreme value theory is also pointed out and explored.


  The relativistic Sunyaev-Zel'dovich (SZ) effect can be used to measure
intracluster gas temperatures independently of X-ray spectroscopy. Here, we use
the large-volume FLAMINGO simulation suite to determine whether SZ $y$-weighted
temperatures lead to more accurate hydrostatic mass estimates in massive
($M_{\rm 500c} > 7.5\times 10^{14}\,{\rm M}_{\odot}$) clusters than when using
X-ray spectroscopic-like temperatures. We find this to be the case, on average.
The median bias in the SZ mass at redshift zero is $\left< b \right> \equiv
1-\left< M_{\rm 500c,hse}/M_{\rm 500c,true} \right> = -0.05 \pm 0.01$, over 4
times smaller in magnitude than the X-ray spectroscopic-like case, $\left< b
\right> = 0.22 \pm 0.01$. However, the scatter in the SZ bias, $\sigma_{b}
\approx 0.2$, is around 40 per cent larger than for the X-ray case. We show
that this difference is strongly affected by clusters with large pressure
fluctuations, as expected from shocks in ongoing mergers. Selecting the
clusters with the best-fitting generalized NFW pressure profiles, the median SZ
bias almost vanishes, $\left< b \right> = -0.009 \pm 0.005$, and the scatter is
halved to $\sigma_{b} \approx 0.1$. We study the origin of the SZ/X-ray
difference and find that, at $R_{\rm 500c}$ and in the outskirts, SZ weighted
gas better reflects the hot, hydrostatic atmosphere than the X-ray weighted
gas. The SZ/X-ray temperature ratio increases with radius, a result we find to
be insensitive to variations in baryonic physics, cosmology and numerical
resolution.


  This is a translation of Harald Cram\'er's article, 'On a new limit theorem
in probability theory', published in French in 1938 and deriving what is
considered by mathematicians to be the first large deviation result. My hope is
that this translation will help disseminate this historically important work,
80 years after its publication.


  In this paper we discuss a space-time having the topology of S^{3}xR but with
different smoothness structure. This space-time is not a global hyperbolic
space-time. Especially we obtain a time line with a topology change of the
space from the 3-sphere to a homology 3-sphere and back but without a
topology-change of the space-time. Among the infinite possible smoothness
structures of this space-time, we choose a homology 3-sphere with hyperbolic
geometry admitting a homogenous metric. Then the topology change can be
described by a time-dependent curvature parameter k changing from k=+1 to k=-1
and back. The solution of the Friedman equation for dust matter (p=0) after
inserting this function shows an exponential growing which is typical for
inflation. In contrast to other inflation models, this process stops after a
finite time.


  We introduce the concept of "negative bubbles" as the mirror image of
standard financial bubbles, in which positive feedback mechanisms may lead to
transient accelerating price falls. To model these negative bubbles, we adapt
the Johansen-Ledoit-Sornette (JLS) model of rational expectation bubbles with a
hazard rate describing the collective buying pressure of noise traders. The
price fall occurring during a transient negative bubble can be interpreted as
an effective random downpayment that rational agents accept to pay in the hope
of profiting from the expected occurrence of a possible rally. We validate the
model by showing that it has significant predictive power in identifying the
times of major market rebounds. This result is obtained by using a general
pattern recognition method which combines the information obtained at multiple
times from a dynamical calibration of the JLS model. Error diagrams, Bayesian
inference and trading strategies suggest that one can extract genuine
information and obtain real skill from the calibration of negative bubbles with
the JLS model. We conclude that negative bubbles are in general predictably
associated with large rebounds or rallies, which are the mirror images of the
crashes terminating standard bubbles.


  We introduce a new class of numerical schemes which allow for low regularity
approximations to the expectation $ \mathbb{E}(|u_{k}(\tau, v^{\eta})|^2)$,
where $u_k$ denotes the $k$-th Fourier coefficient of the solution $u$ of the
dispersive equation and $ v^{\eta}(x) $ the associated random initial data.
This quantity plays an important role in physics, in particular in the study of
wave turbulence where one needs to adopt a statistical approach in order to
obtain deep insight into the generic long-time behaviour of solutions to
dispersive equations. Our new class of schemes is based on Wick's theorem and
Feynman diagrams together with a resonance based discretisation (see
arXiv:2005.01649) set in a more general context: we introduce a novel
combinatorial structure called paired decorated forests which are two decorated
trees whose decorations on the leaves come in pair. The character of the scheme
draws its inspiration from the treatment of singular stochastic partial
differential equations via Regularity Structures. In contrast to classical
approaches, we do not discretize the PDE itself, but rather its expectation.
This allows us to heavily exploit the optimal resonance structure and
underlying gain in regularity on the finite dimensional (discrete) level.


  Cloud computing is an emerging new computing paradigm for delivering
computing services. This computing approach relies on a number of existing
technologies, e.g., the Internet, virtualization, grid computing, Web services,
etc. Cloud Computing aims to provide scalable and inexpensive on-demand
computing infrastructures with good quality of service levels. It represents a
shift away from computing as a product that is purchased, to computing as a
service that is delivered to consumers from the cloud. It helps an organization
in saving costs and creating new business opportunities.This paper provides a
framework, Education Cloud for the e- management of NGO's. The Education Cloud
can transform a nonprofit, or an entire sector of nonprofits, achieves its
mission and creates lasting impact in its communities. This paper also presents
the case study of Kalgidhar trust, Baru Sahib, Himachal Pradesh, NGO which is
using the education as the tool to solve the social issues.


  We consider a simple binary market model containing $N$ competitive agents.
The novel feature of our model is that it incorporates the tendency shown by
traders to look for patterns in past price movements over multiple time scales,
i.e. {\em multiple memory-lengths}. In the regime where these memory-lengths
are all small, the average winnings per agent exceed those obtained for either
(1) a pure population where all agents have equal memory-length, or (2) a mixed
population comprising sub-populations of equal-memory agents with each
sub-population having a different memory-length. Agents who consistently play
strategies of a given memory-length, are found to win more on average --
switching between strategies with different memory lengths incurs an effective
penalty, while switching between strategies of equal memory does not. Agents
employing short-memory strategies can outperform agents using long-memory
strategies, even in the regime where an equal-memory system would have favored
the use of long-memory strategies. Using the many-body `Crowd-Anticrowd'
theory, we obtain analytic expressions which are in good agreement with the
observed numerical results. In the context of financial markets, our results
suggest that multiple-memory agents have a better chance of identifying price
patterns of unknown length and hence will typically have higher winnings.


  Precise descriptions are given for the operator product expansion of generic
primary fields as well as the factorization of four point functions as sum over
intermediate states. The conjecture underlying the recent derivation of the
space-time current algebra for string theory on $ADS_3$ by Kutasov and Seiberg
is thereby verified. The roles of microscopic and macroscopic states are
further clarified. The present work provides the conformal field theory
prerequisites for a future study of factorization of amplitudes for string
theory on $ADS_3$ as well as operator product expansion in the corresponding
conformal field theory on the boundary.


  We propose a phenomenological generalization of the models of large-scale
structure formation in the Universe by gravitational instability in two ways:
we include pressure forces to model multi-streaming, and noise to model
fluctuations due to neglected short-scale physical processes. We show that
pressure gives rise to a viscous-like force of the same character as that one
introduced in the ``adhesion model'', while noise leads to a roughening of the
density field yielding a scaling behavior of its correlations.


  The origin of grain size distribution in the interstellar medium is one of
the most fundamental problems in the interstellar physics. In the Milky Way,
smaller grains are more abundant in number, but their origins are not
necessarily specified and quantified. One of the most efficient drivers of
small grain production is interstellar turbulence, in which dust grains can
acquire relative velocities large enough to be shattered. Applying the
framework of shattering developed in previous papers, we show that small ($a\la
0.01~\micron$) grains reach the abundance level observed in the Milky Way in
$\sim 10^8$ yr (i.e. within the grain lifetime) by shattering in warm neutral
medium. We also show that if part of grains experience additional shattering in
warm ionized medium, carbonaceous grains with $a\sim 0.01~\micron$ are
redistributed into smaller sizes. This could explain the relative enhancement
of very small carbonaceous grains with $a\sim 3$--100 \AA. Our theory also
explains the ubiquitous association between large grains and very small grains
naturally. Some tests for our theory are proposed in terms of the metallicity
dependence.


  We studied the process of decoherence induced by the presence of an
environment in acoustic black holes, using the open quantum system approach,
thus extending previous work. We focused on the ion trap model but the
formalism is general to any experimental implementation. We computed the
decoherence time for that setup. We found that a quantum to classical
transition occurs during the measurement and we proposed improved parameters to
avoid such a feature. We provide analytic estimations for both zero and finite
temperature. We also studied the entanglement between the Hawking-pair phonons
for an acoustic black hole while in contact with a reservoir, through the
quantum correlations, showing that they remain strongly correlated for small
enough times and temperatures. We used the stochastic formalism and the method
of characteristic to solve the field wave equation.


  We propose a new version of the scalar Weak Gravity Conjecture (WGC) which
would apply to any scalar field coupled to quantum gravity. For a single scalar
it is given by the differential constraint $V''\leq
(2V'''^2/V''-V'''')M_{\text{p}}^2$. It corresponds to the statement that
self-interactions of a scalar must be stronger than gravity for any value of
the scalar field. We find that the solutions which saturate the bound
correspond to towers of extremal states with mass
$m^2(\phi)=m_0^2/((R/m)^2+1/(nR)^2)$, with $R^2=e^\phi$, consistent with the
emergence of an extra dimension at large or small $R$ and the existence of
extended objects (strings). These states act as WGC states for the scalar
$\phi$. It is also consistent with the distance swampland conjecture with a
built-in duality symmetry. From this constraint one can derive several
swampland conjectures. In particular one finds that an axion potential is only
consistent if $f\leq M_{\text{p}}$. The conjecture has far reaching
consequences and applies to several interesting physical systems: i) Among
chaotic inflation potentials only those asymptotically linear may survive. ii)
If applied to the radion of the circle compactification of the Standard Model
to 3D, the constraint implies that the 4D cosmological constant scale must be
larger than the mass of the lightest neutrino, which must be Dirac and in
normal hierarchy. iii) It also constraints simplest moduli fixing string
models. The simplest KKLT model is compatible with the constraints but the
latter may be relevant for some choices of parameters.


  A central hyperplane arrangement in C^2 with multiplicity is called a `locus
configuration' if it satisfies a series of `locus equations' on each
hyperplane. Following Chalykh, Feigin and Veselov [CFV99], we demonstrate that
the first locus equation for each hyperplane corresponds to a force-balancing
equation on a related interacting particle system on C^*: the charged
trigonometric Calogero-Moser system. When the particles lie on S^1 in C^*,
there is a unique equilibrium for this system. For certain classes of particle
weight, this is enough to show that all the locus equations are satisfied,
producing explicit examples of real locus configurations. This in turn produces
new examples of Schr\"odinger operators with Baker-Akhiezer functions.


  Let $B_1$ be a ball in $\mathbb{R}^N$ centred at the origin and $B_0$ be a
smaller ball compactly contained in $B_1$. For $p\in(1, \infty)$, using the
shape derivative method, we show that the first eigenvalue of the $p$-Laplacian
in annulus $B_1\setminus \overline{B_0}$ strictly decreases as the inner ball
moves towards the boundary of the outer ball. The analogous results for the
limit cases as $p \to 1$ and $p \to \infty$ are also discussed. Using our main
result, further we prove the nonradiality of the eigenfunctions associated with
the points on the first nontrivial curve of the Fu\v{c}ik spectrum of the
$p$-Laplacian on bounded radial domains.


  We consider a generic curved non-commutative torus extending the notion of
conformally deformed non-commutative torus from \cite{Connes-Tretkoff}. In
general, a curved non-commutative torus is no longer represented by a spectral
triple, not even by a twisted spectral triple. Therefore, the geometry of this
manifold is governed by a positive second order differential operator
(Laplace-Betrami operator) rather than a first order differential operator
(Dirac operator). For this manifold, we prove an asymptotic expansion of the
heat semi-group generated by Laplace-Beltrami operator and provide an algorithm
to compute the local invariants which appear as coefficients in the expansion.
This allows to extend the results of \cite{Connes-Tretkoff},
\cite{Connes-Moscovici}, \cite{FaKh} (beyond conformal case and/or for
multi-dimensional tori).


  In [Wolfram 1982; Wolfram 1983; Wolfram 2002], the backtracking of
one-dimensional cellular automata is to find out which of the 2n possible
initial configurations of width n evolve to a specific configuration. In this
paper, in one-dimensional cellular automata for a specific configuration of
width n, its unique initial configuration can be found by mean of the proposed
quantum algorithm with polynomial quantum gates, polynomial quantum bits and
the successful probability that is the same as that of Shor's quantum
order-finding algorithm in [Shor 1994].


  From the previously obtained solutions of the Fokker - Planck equation for
Rayleigh gas (small impurity of heavy particles in a thermostat of light
particles) with sources and without them, the entropy production was
calculated. In a system without source (isolated system) shown that it holds
theorem of Prigogine, and in a system with sources (open system) implementation
of the principle of Ziegler (MEPP) depends on the relaxation direction. In an
open system entropy production is compensate by a negative production of
entropy, i.e. by a negentropy production. The algebraic sum of entropy and
negentropy productions is called the generalized entropy production. From the
balance of entropy and negentropy productions in an open system formulated a
possible variation of the second law for open systems in a form: "At the
relaxation of an open system to a nonequilibrium steady state, a generalized
entropy production decreases in absolute value and equal to zero in a
nonequilibrium steady state." Keywords: Fokker-Planck equation, Prigogine
theorem, principle of maximum entropy production, the second law, negentropy.


  Using a non-perturbative method developed in a previous article (paper II) we
investigate the tails of the probability distribution $P(\rho_R)$ of the
overdensity within spherical cells. We show that our results for the
low-density tail of the pdf agree with perturbative results when the latter are
finite (up to the first subleading term), that is for power-spectra with
$-3<n<-1$. Over the range $-1<n<1$ some shell-crossing occurs (which leads to
the break-up of perturbative approaches) but this does not invalidate our
approach. In particular, we explain that we can still obtain an approximation
for the low-density tail of the pdf. This feature also clearly shows that
perturbative results should be viewed with caution (even when they are finite).
We point out that our results can be recovered by a simple spherical model but
they cannot be derived from the stable-clustering ansatz in the regime $\sigma
\gg 1$ since they involve underdense regions which are still expanding. Second,
turning to high-density regions we explain that a naive study of the radial
spherical dynamics fails. Indeed, a violent radial-orbit instability leads to a
fast relaxation of collapsed halos (over one dynamical time) towards a roughly
isotropic equilibrium velocity distribution. Then, the transverse velocity
dispersion stabilizes the density profile so that almost spherical halos obey
the stable-clustering ansatz for $-3<n<1$. We again find that our results for
the high-density tail of the pdf agree with a simple spherical model (which
takes into account virialization). Moreover, they are consistent with the
stable-clustering ansatz in the non-linear regime. Besides, our approach
justifies the large-mass cutoff of the Press-Schechter mass function (although
the various normalization parameters should be modified).


  The main purppose this work is to study periodic points of fiber-preserving
maps on fiber bundles with base circle and fiber torus.