  We consider the forces acting on electrons in magnetic field including the
constraints and a condition arising from quantum mechanics. The force is
calculated as the electron mass, $m_e$, multiplied by the total time-derivative
of the velocity field evaluated using the quantum mechanical many-electron wave
function. The velocity field includes a term of the Berry connection from the
many-body wave function; thereby, quantum mechanical effects are included. It
is shown that additional important forces besides the Lorentz force exist; they
include the gradient of the electron velocity field kinetic energy, the
gradient of the chemical potential, and the `force' for producing topologically
protected loop currents. These additional forces are shown to be important in
superconductivity, electric current in metallic wires, and charging of
capacitors.


  Several results on constrained spline smoothing are obtained. In particular,
we establish a general result, showing how one can constructively smooth any
monotone or convex piecewise polynomial function (ppf) (or any $q$-monotone
ppf, $q\geq 3$, with one additional degree of smoothness) to be of minimal
defect while keeping it close to the original function in the ${\mathbb
L}_p$-(quasi)norm. It is well known that approximating a function by ppf's of
minimal defect (splines) avoids introduction of artifacts which may be
unrelated to the original function, thus it is always preferable. On the other
hand, it is usually easier to construct constrained ppf's with as little
requirements on smoothness as possible. Our results allow to obtain
shape-preserving splines of minimal defect with equidistant or Chebyshev knots.
The validity of the corresponding Jackson-type estimates for shape-preserving
spline approximation is summarized, in particular we show, that the ${\mathbb
L}_p$-estimates, $p\ge1$, can be immediately derived from the ${\mathbb
L}_\infty$-estimates.


  The bulk and shear viscosities ($\eta$ and $\zeta$) have been studied for
quark-gluon-plasma produced in relativistic heavy ion collisions within
semi-classical transport theory, in a recently proposed quasi-particle model of
(2+1)-flavor lattice QCD equation of state. These transport parameters have
been found to be highly sensitive to the interactions present in hot QCD.
Contributions to the transport coefficients from both the gluonic sector and
the matter sector have been investigated. The matter sector is found to be
significantly dominating over the gluonic sector, in both the cases of $\eta$
and $\zeta$. The temperature dependences of the quantities, $\zeta/{\mathcal
S}$, and $\zeta/\eta$ indicate a sharply rising trend for the $\zeta$, closer
to the QCD transition temperature. Both $\eta$, and $\zeta$ are shown to be
equally significant for the temperatures that are accessible in the
relativistic heavy ion collision experiments, and hence play crucial role while
investigating the properties of the quark-gluon plasma.


  This paper has been withdrawn by the author due to a serious gap in the proof
of the main theorem.


  Wearable pupil detection systems often separate the analysis of the captured
wearer's eye images for wirelessly-tethered back-end systems. We argue in this
paper that investigating hardware-software co-designs would bring along
opportunities to make such systems smaller and more efficient. We introduce an
open-source embedded system for wearable, non-invasive pupil detection in
real-time, on the wearable, embedded platform itself. Our system consists of a
head-mounted eye tracker prototype, which combines two miniature camera systems
with Raspberry Pi-based embedded system. Apart from the hardware design, we
also contribute a pupil detection pipeline that operates using edge analysis,
natively on the embedded system at 30fps and run-time of 54ms at 480x640 and
23ms at 240x320. Average cumulative error of 5.3368px is found on the LPW
dataset for a detection rate of 51.9\% with our detection pipeline. For
evaluation on our hardware-specific camera frames, we also contribute a dataset
of 35000 images, from 20 participants.


  The effects of a magnetic field ($h$) and a space modulation ($\delta$) on
the magnetic properties of a one dimensional antiferromagnetic-ferromagnetic
Heisenberg spin-1/2 model have been studied by means of numerical exact
diagonalization of finite size systems, nonlinear sigma model and bosonization
approach. The space modulation is considered on the antiferromagnetic
couplings. At $\delta=0$, the model is mapped to a gapless L\"{u}ttinger liquid
phase by increasing the magnetic field. However, the space modulation induces a
new gap in the spectrum of the system and the system experiences different
quantum phases which are separated by four critical fields. By opening the new
gap a magnetization plateau appears at ${1/2}M_{sat}$. The effects of the space
modulation are reflected in the emergence of a plateau in other physical
functions such as the F-dimer and the bond dimer order parameters, and the
pair-wise entanglement.


  Autonomous driving for urban and highway driving applications often requires
High Definition (HD) maps to generate a navigation plan. Nevertheless, various
challenges arise when generating and maintaining HD maps at scale. While recent
online mapping methods have started to emerge, their performance especially for
longer ranges is limited by heavy occlusion in dynamic environments. With these
considerations in mind, our work focuses on leveraging lightweight and scalable
priors-Standard Definition (SD) maps-in the development of online vectorized HD
map representations. We first examine the integration of prototypical
rasterized SD map representations into various online mapping architectures.
Furthermore, to identify lightweight strategies, we extend the OpenLane-V2
dataset with OpenStreetMaps and evaluate the benefits of graphical SD map
representations. A key finding from designing SD map integration components is
that SD map encoders are model agnostic and can be quickly adapted to new
architectures that utilize bird's eye view (BEV) encoders. Our results show
that making use of SD maps as priors for the online mapping task can
significantly speed up convergence and boost the performance of the online
centerline perception task by 30% (mAP). Furthermore, we show that the
introduction of the SD maps leads to a reduction of the number of parameters in
the perception and reasoning task by leveraging SD map graphs while improving
the overall performance. Project Page:
https://henryzhangzhy.github.io/sdhdmap/.


  We propose a novel method for clustering data which is grounded in
information-theoretic principles and requires no parametric assumptions.
Previous attempts to use information theory to define clusters in an
assumption-free way are based on maximizing mutual information between data and
cluster labels. We demonstrate that this intuition suffers from a fundamental
conceptual flaw that causes clustering performance to deteriorate as the amount
of data increases. Instead, we return to the axiomatic foundations of
information theory to define a meaningful clustering measure based on the
notion of consistency under coarse-graining for finite data.


  Recent years have witnessed rapid developments on social recommendation
techniques for improving the performance of recommender systems due to the
growing influence of social networks to our daily life. The majority of
existing social recommendation methods unify user representation for the
user-item interactions (item domain) and user-user connections (social domain).
However, it may restrain user representation learning in each respective
domain, since users behave and interact differently in the two domains, which
makes their representations to be heterogeneous. In addition, most of
traditional recommender systems can not efficiently optimize these objectives,
since they utilize negative sampling technique which is unable to provide
enough informative guidance towards the training during the optimization
process. In this paper, to address the aforementioned challenges, we propose a
novel deep adversarial social recommendation framework DASO. It adopts a
bidirectional mapping method to transfer users' information between social
domain and item domain using adversarial learning. Comprehensive experiments on
two real-world datasets show the effectiveness of the proposed framework.


  We investigate the geometry of approximates in multiplicative Diophantine
approximation. Our main tool is a new multiparameter averaging result for
Siegel transforms on the space of unimodular lattices in ${\mathbb R}^n$ which
is of independent interest.


  We prove a general width duality theorem for combinatorial structures with
well-defined notions of cohesion and separation. These might be graphs and
matroids, but can be much more general or quite different. The theorem asserts
a duality between the existence of high cohesiveness somewhere local and a
global overall tree structure.
  We describe cohesive substructures in a unified way in the format of tangles:
as orientations of low-order separations satisfying certain consistency axioms.
These axioms can be expressed without reference to the underlying structure,
such as a graph or matroid, but just in terms of the poset of the separations
themselves. This makes it possible to identify tangles, and apply our
tangle-tree duality theorem, in very diverse settings.
  Our result implies all the classical duality theorems for width parameters in
graph minor theory, such as path-width, tree-width, branch-width or rank-width.
It yields new, tangle-type, duality theorems for tree-width and path-width. It
implies the existence of width parameters dual to cohesive substructures such
as $k$-blocks, edge-tangles, or given subsets of tangles, for which no width
duality theorems were previously known.
  Abstract separation systems can be found also in structures quite unlike
graphs and matroids. For example, our theorem can be applied to image analysis
by capturing the regions of an image as tangles of separations defined as
natural partitions of its set of pixels. It can be applied in big data contexts
by capturing clusters as tangles. It can be applied in the social sciences,
e.g. by capturing as tangles the few typical mindsets of individuals found by a
survey. It could also be applied in pure mathematics, e.g. to separations of
compact manifolds.


  3-list colouring is an NP-complete decision problem. It is hard even on
planar bipartite graphs. We give a polynomial-time algorithm for solving 3-list
colouring on permutation graphs.


  Electroweak baryogenesis (EWB) and electric dipole moment (EDM) have close
relation with the new physics beyond the standard model (SM), because the SM
CP-violating (CPV) interactions are not sufficient to provide the baryon
asymmetry of the universe by many orders of magnitude, and the theoretical
predictions for the EDM of electron ($d_e$) in the SM are too tiny to be
detected in near future. In this work, we explore the CPV effects on EWB and
the electron EDM in the minimal supersymmetric extension (MSSM) of the SM with
local $B-L$ gauge symmetry (B-LSSM). And the two-step transition via
tree-effects in this model is discussed. Including two-loop corrections to
$d_e$ and considering the constrains from updated experimental data, the
numerical results show that the B-LSSM can account for the observed baryon
asymmetry. In addition, when the cancellation between different contributions
to $d_e$ takes place, the region favored by EWB can be compatible with the
corresponding EDM bound.


  The concordance model of cosmology contains several unknown components such
as dark matter and dark energy. Many proposals have been made to describe them
by choosing an appropriate potential for a scalar field. We study four models
in the realm of loop quantum cosmology (LQC): the Chaplygin gas, an
inflationary and radiation-like potential, quintessence and an anti-Chaplygin
gas. For the latter we show that all trajectories start and end with a type II
singularity and, depending on the inital value, may go through a bounce. On the
other hand the evolution under the influence of the first three scalar fields
behaves classically at times far away from the big bang singularity and bounces
as the energy density approaches the critical density.


  We prove Pohozaev-type identities for smooth solutions of Euler-Lagrange
equations of second and fourth order that arise from functional depending on
homogeneous H\"{o}rmander vector fields. We then exploit such integral
identities to prove non-existence results for the associated boundary value
problems.


  The increase in yields of light nuclei with charged particle multiplicity, as
reported by the ALICE collaboration at CERN in p-p and p-Pb collisions at the
LHC energy is investigated in the thermal hadron resonance gas model. The model
is extended to account for exact baryon number conservation. The focus is on
the production of protons, deuterons, $^3$He, and $^3_\Lambda$H. A very good
description of proton and deuteron yields is obtained as a function of charged
particle multiplicity in the mid-rapidity region using the same fixed
temperature as in central Pb-Pb collisions. The yields of light nuclei $^3$He
and $^3_\Lambda$H though qualitatively explained as a function of multiplicity,
are lower than the model expectation. One of the possible reasons could be that
for $^{3}$He and $^{3}_{\Lambda}$H, the chemical equilibrium is not yet reached
at small multiplicities.


  Many classical social preference (multiwinner social choice) correspondences
are resolute only when two alternatives and an odd number of individuals are
considered. Thus, they generally admit several resolute refinements, each of
them naturally interpreted as a tie-breaking rule. In this paper we find out
conditions which make a social preference (multiwinner social choice)
correspondence admit a resolute refinement fulfilling suitable weak versions of
the anonymity and neutrality principles, as well as reversal symmetry (immunity
to the reversal bias).


  We report the discovery of a brown dwarf on an eccentric orbit and with a
semimajor axis that places it in the brown dwarf desert region around the star
HD191760. The star has a spectral type of G3IV/V and a metallicity ([Fe/H]) of
0.29 dex. HD191760 adds to the small number of metal-rich stars with brown
dwarf companions. The brown dwarf (HD191760b) is found to have an orbital
period of 505.57+/-0.40 days and semimajor axis of 1.35+/-0.01 AU, placing it
firmly in the brown dwarf desert. The eccentricity of HD191760b is found to be
0.63+/-0.01, meaning it reaches as close as 0.5 AU from the host star.
Dynamical simulations indicate that no inner planets could reside at
separations beyond ~0.17 AU due to the disastrous gravity imposed by HD191760b.
In addition to these first results we also refine the orbits found for the
exoplanets around the stars HD48265, HD143361 and HD154672. All 1-planet
solutions are in agreement with those previously published by the Magellan
Planet Search.


  In this paper, we consider the following PDE involving two Sobolev-Hardy
critical exponents, \label{0.1} {& \Delta u +
\lambda\frac{u^{2^*(s_1)-1}}{|x|^{s_1}} + \frac{u^{2^*(s_2)-1}}{|x|^{s_2}} =0
\text{in} \Omega, & u=0 \qquad \text{on} \Omega, where $0 \le s_2 < s_1 \le 2$,
$0 \ne \lambda \in \Bbb R$ and $0 \in \partial \Omega$. The existence (or
nonexistence) for least-energy solutions has been extensively studied when
$s_1=0$ or $s_2=0$. In this paper, we prove that if $0< s_2 < s_1 <2$ and the
mean curvature of $\partial \Omega$ at 0 $H(0)<0$, then \eqref{0.1} has a
least-energy solution. Therefore, this paper has completed the study of
\eqref{0.1} for the least-energy solutions. We also prove existence or
nonexistence of positive entire solutions of \eqref{0.1} with $\Omega =\rn$
under different situations of $s_1, s_2$ and $\lambda$.


  The BaBar online data acquisition (DAQ) system includes approximately fifty
Unix systems that collectively implement the level-three trigger. These systems
all run the same code. Each of these systems has its own state, and this state
is expected to change in response to changes in the overall DAQ system. A
specialized subsystem has been developed to initiate processing on this
collection of systems, and to monitor them both for error conditions and to
ensure that they all follow the same state trajectory within a specifiable
period of time. This subsystem receives start commands from the main DAQ run
control system, and reports major coherent state changes, as well as error
conditions, back to the run control system. This state monitoring subsystem has
the novel feature that it does not know anything about the state machines that
it is monitoring, and hence does not introduce any fundamentally new state
machine into the overall system. This feature makes it trivially applicable to
other multi-node subsystems. Indeed it has already found a second application
beyond the level-three trigger, within the BaBar experiment.


  Although quantum channels underlie the dynamics of quantum states, maps which
are not physical channels -- that is, not completely positive -- can often be
encountered in settings such as entanglement detection, non-Markovian quantum
dynamics, or error mitigation. We introduce an operational approach to the
quantitative study of the non-physicality of linear maps based on different
ways to approximate a given linear map with quantum channels. Our first measure
directly quantifies the cost of simulating a given map using physically
implementable quantum channels, shifting the difficulty in simulating
unphysical dynamics onto the task of simulating linear combinations of quantum
states. Our second measure benchmarks the quantitative advantages that a
non-completely-positive map can provide in discrimination-based quantum games.
Notably, we show that for any trace-preserving map, the quantities both reduce
to a fundamental distance measure: the diamond norm, thus endowing this norm
with new operational meanings in the characterisation of linear maps. We
discuss applications of our results to structural physical approximations of
positive maps, quantification of non-Markovianity, and bounding the cost of
error mitigation.


  In this paper we analyze the photoproduction of heavy quarkonia pairs which
include $b$-quarks, such as $B_{c}^{+}B_{c}^{-}$-mesons or
charmonium-bottomonium pairs. Compared to charmonia pair production, these
channels get contributions only from some subsets of diagrams, and thus allow
for a better theoretical understanding of different production mechanisms. In
contrast to the production of hidden-flavor quarkonia, for the production of
$B_{c}$-meson pairs there are no restrictions on internal quantum numbers in
the suggested mechanisms. Using the Color Glass Condensate approach, we
estimated numerically the production cross-sections in the kinematics of the
forthcoming Electron-Proton collider and in the kinematics of ultraperipheral
collisions at LHC. We found that the production of $J/\psi\,\eta_{c}$ and
$B_{c}^{+}B_{c}^{-}$ meson pairs are the most promising channels for studies of
quarkonia pair production.


  The OPERA experiment is designed to search for $\nu_{\mu} \rightarrow
\nu_{\tau}$ oscillations in appearance mode i.e. through the direct observation
of the $\tau$ lepton in $\nu_{\tau}$ charged current interactions. The
experiment has taken data for five years, since 2008, with the CERN Neutrino to
Gran Sasso beam. Previously, two $\nu_{\tau}$ candidates with a $\tau$ decaying
into hadrons were observed in a sub-sample of data of the 2008-2011 runs. Here
we report the observation of a third $\nu_\tau$ candidate in the
$\tau^-\to\mu^-$ decay channel coming from the analysis of a sub-sample of the
2012 run. Taking into account the estimated background, the absence of
$\nu_{\mu} \rightarrow \nu_{\tau}$ oscillations is excluded at the 3.4 $\sigma$
level.


  We present experiments which show that the partial wetting of droplets capped
by taut elastic films is highly tunable. Adjusting the tension allows the
contact angle and droplet morphology to be controlled. By exploiting these
elastic boundaries, droplets can be made elliptical, with an adjustable aspect
ratio, and can even be transformed into a nearly square shape. This system can
be used to create tunable liquid lenses, and moreover, presents a unique
approach to liquid patterning.


  The aim of this paper is to introduce our idea of Holonomic Quantum
Computation (Computer). Our model is based on both harmonic oscillators and
non-linear quantum optics, not on spins of usual quantum computation and our
method is moreover completely geometrical. We hope that therefore our model may
be strong for decoherence.


  We characterise the strictly closed left invariant C*-subalgebras of the
C*-algebra C_b(G) of bounded continuous functions on a locally compact group G.
On the dual side, we characterise the strictly closed invariant C*-subalgebras
of the multiplier algebra of the reduced group C*-algebra C*_r(G) when G is
amenable. In both cases, these C*-subalgebras correspond to closed subgroups of
G.


  We obtain an explicit two-point function for the Maxwell field in flat
Roberson-Walker spaces, thanks to a new gauge condition which takes the scale
factor into account and assume a simple form. The two-point function is found
to have the short distance Hadamard behavior.


  In this paper, I solve a 60-year old question posed by Cohen's seminal paper
(1960) and offer an agreement measure centered around the chance-expected
agreement while isolating marginally forced agreement and disagreement. To
achieve this, I formulate the minimum feasible agreement given row and column
marginals by devising a new algorithm that minimizes the sum of diagonals in
contingency tables. Based on this result, I also formulate the lower limit of
the most common agreement measure-Cohen's kappa. Finally, I study the lower
limit of maximum feasible agreement and devise two statistics of distribution
similarity for agreement analysis.


  This paper gives an explanatory framework for obsessive-compulsive disorder
(OCD) based on a generative model of cognition. The framework is constructed
using the new concept of a 'formal narrative' which is a sequence of cognitive
states inferred from sense data. First we propose that human cognition uses a
hierarchy of narratives to predict changes in the natural and social
environment. Each layer in the hierarchy represents a distinct 'view of the
world', but it also contributes to a global unitary perspective. Second, the
generative models used for cognitive inference can create new narratives from
those states already experienced by an individual. We hypothesise that when a
threat is recognised, narratives are generated as a cognitive model of possible
threat scenarios. Using this framework, we suggest that OCD arises from a
dysfunction in sub-surface levels of inference while the global unitary
perspective remains intact. The failure of inference is felt as the external
world being 'not just right', and its automatic correction by the perceptual
system is experienced as compulsion. Ordering and symmetry obsessions are the
effects of the perceptual system trying to achieve precise inference. Checking
behaviour arises because the security system attempts to finesse inference as
part of its protection behaviour. Similarly, fear of harm and distressing
thoughts occur because the failure of inference results in an indistinct view
of the past or the future. A wide variety of symptoms in OCD is thus explained
by a single dysfunction.


  We review recent progress in the theoretical predictions of gravitational
waves (GWs) of core-collapse supernovae. Following a brief summary of the
methods in the numerical modeling, we summarize multiple physical elements that
determine the GW signatures which have been considered to be important in
extracting the information of the long-veiled explosion mechanism from the
observation of the GWs. We conclude with a summary of the most urgent tasks to
make the dream come true.


  Using Hubble data, including new grism spectra, Oesch et al. recently
identified GN-z11, an $M_\textrm{UV}$=-21.1 galaxy at $z$=11.1 (just 400Myr
after the big bang). With an estimated stellar mass of $\sim$10$^9$M$_{\odot}$,
this galaxy is surprisingly bright and massive, raising questions as to how
such an extreme object could form so early in the Universe. Using \Meraxes{}, a
semi-analytic galaxy-formation model developed as part of the Dark-ages
Reionization And Galaxy-formation Observables from Numerical Simulations
(DRAGONS) programme, we investigate the potential formation mechanisms and
eventual fate of GN-z11. The volume of our simulation is comparable to that of
the discovery observations and possesses two analogue galaxies of similar
luminosity to this remarkably bright system. Existing in the two most massive
subhaloes at $z$=11.1 ($M_\textrm{vir}$=1.4$\times 10^{11}$M$_{\odot}$ and
6.7$\times 10^{10}$M$_{\odot}$), our model analogues show excellent agreement
with all available observationally derived properties of GN-z11. Although they
are relatively rare outliers from the full galaxy population at high-$z$, they
are no longer the most massive or brightest systems by $z$=5. Furthermore, we
find that both objects possess relatively smooth, but extremely rapid mass
growth histories with consistently high star formation rates and UV
luminosities at $z{>}11$, indicating that their brightness is not a transient,
merger-driven feature. Our model results suggest that future wide-field surveys
with the \textit{James Webb Space Telescope} may be able to detect the
progenitors of GN-z11 analogues out to $z{\sim}$13--14, pushing the frontiers
of galaxy-formation observations to the early phases of cosmic reionization and
providing a valuable glimpse of the first galaxies to reionize the Universe on
large scales.


  We identify stellar structures in the PHANGS sample of 74 nearby galaxies and
construct morphological masks of sub-galactic environments based on Spitzer 3.6
micron images. At the simplest level, we distinguish centres, bars, spiral
arms, interarm and discs without strong spirals. Slightly more sophisticated
masks include rings and lenses, publicly released but not explicitly used in
this paper. We examine trends using PHANGS-ALMA CO(2-1) intensity maps and
tracers of star formation. The interarm regions and discs without strong
spirals dominate in area, whereas molecular gas and star formation are quite
evenly distributed among the five basic environments. We reproduce the
molecular Kennicutt-Schmidt relation with a slope compatible with unity within
the uncertainties, without significant slope differences among environments. In
contrast to early studies, we find that bars are not always deserts devoid of
gas and star formation, but instead they show large diversity. Similarly,
spiral arms do not account for most of the gas and star formation in disc
galaxies, and they do not have shorter depletion times than the interarm
regions. Spiral arms accumulate gas and star formation, without systematically
boosting the star formation efficiency. Centres harbour remarkably high surface
densities and on average shorter depletion times than other environments.
Centres of barred galaxies show higher surface densities and wider
distributions compared to the outer disc; yet, depletion times are similar to
unbarred galaxies, suggesting highly intermittent periods of star formation
when bars episodically drive gas inflow, without enhancing the central star
formation efficiency permanently. In conclusion, we provide quantitative
evidence that stellar structures in galaxies strongly affect the organisation
of molecular gas and star formation, but their impact on star formation
efficiency is more subtle.


  We obtain constraints on cosmological parameters from the spherically
averaged redshift-space correlation function of the CMASS Data Release 9 (DR9)
sample of the Baryonic Oscillation Spectroscopic Survey (BOSS). We combine this
information with additional data from recent CMB, SN and BAO measurements. Our
results show no significant evidence of deviations from the standard
flat-Lambda CDM model, whose basic parameters can be specified by Omega_m =
0.285 +- 0.009, 100 Omega_b = 4.59 +- 0.09, n_s = 0.96 +- 0.009, H_0 = 69.4 +-
0.8 km/s/Mpc and sigma_8 = 0.80 +- 0.02. The CMB+CMASS combination sets tight
constraints on the curvature of the Universe, with Omega_k = -0.0043 +- 0.0049,
and the tensor-to-scalar amplitude ratio, for which we find r < 0.16 at the 95
per cent confidence level (CL). These data show a clear signature of a
deviation from scale-invariance also in the presence of tensor modes, with n_s
<1 at the 99.7 per cent CL. We derive constraints on the fraction of massive
neutrinos of f_nu < 0.049 (95 per cent CL), implying a limit of sum m_nu < 0.51
eV. We find no signature of a deviation from a cosmological constant from the
combination of all datasets, with a constraint of w_DE = -1.033 +- 0.073 when
this parameter is assumed time-independent, and no evidence of a departure from
this value when it is allowed to evolve as w_DE(a) = w_0 + w_a (1 - a). The
achieved accuracy on our cosmological constraints is a clear demonstration of
the constraining power of current cosmological observations.


  We consider quantum theory of fields \phi defined on a D dimensional manifold
(bulk) with an interaction V(\phi) concentrated on a d<D dimensional surface
(brane). Such a quantum field theory can be less singular than the one in d
dimensions with the interaction $V(\phi)$. It is shown that scaling properties
of fields on the brane are different from the ones in the bulk.


  We consider observational constraints on creation of particles induced by
hypothetical trans-Planckian effects during the current stage of the Universe
expansion. We show that compatibility with the diffuse gamma-ray background
measured by the EGRET experiment strongly restricts this creation. In
particular, it rules out the possibility to detect signatures of such short
distance effects in anisotropies of the cosmic microwave background radiation.
On the other hand, a possibility that some part of the ultra-high energy cosmic
rays originates from new trans-Planckian physics remains open.


  We look for algebraic certificates of positivity for functions which are not
necessarily polynomial functions. Similar questions were examined earlier by
Lasserre and Putinar and by Putinar. We explain how these results can be
understood as results on hidden positivity: The required positivity of the
functions implies their positivity when considered as polynomials on the real
variety of the respective algebra of functions. This variety is however not
directly visible in general. We show how algebras and quadratic modules with
this hidden positivity property can be constructed. We can then use known
results, for example Jacobi's representation theorem or the Krivine-Stengle
Positivstellensatz to obtain certificates of positivity relative to a quadratic
module of an algebra of real-valued functions. Our results go beyond the
results of Lasserre and Putinar, for example when dealing with non-continuous
functions. The conditions are also easier to check. We explain the application
of our result to various sorts of real finitely generated algebras of
semialgebraic functions. The emphasis is on the case where the quadratic module
is also finitely generated. Our results also have application to optimization
of real-valued functions, using the semidefinite programming relaxation methods
pioneered by Lasserre.


  In 1971, Graham and Pollak provided a formula for the determinant of the
distance matrix of any tree on $n$ vertices. Yan and Yeh reproved this by
exploiting the fact that pendant vertices can be deleted from trees without
changing the remaining entries of the distance matrix. Considering failures of
their argument to generalize invites the question: which graphs have the
property that deleting any one vertex results in a change to some pairwise
distance? We refer to such worst-case graphs as ``distance critical''. This
work explores the structural properties of distance critical graphs,
preservation of distance-criticality by products, and the nature of extremal
distance critical graphs. We end with a few open questions.


  With recent advancements in the sixth generation (6G) communication
technologies, more vertical industries have encountered diverse network
services. How to reduce energy consumption is critical to meet the expectation
of the quality of diverse network services. In particular, the number of base
stations in 6G is huge with coupled adjustable network parameters. However, the
problem is complex with multiple network objectives and parameters. Network
intents are difficult to map to individual network elements and require
enhanced automation capabilities. In this paper, we present a network intent
decomposition and optimization mechanism in an energy-aware radio access
network scenario. By characterizing the intent ontology with a standard
template, we present a generic network intent representation framework. Then we
propose a novel intent modeling method using Knowledge Acquisition in automated
Specification language, which can model the network ontology. To clarify the
number and types of network objectives and energy-saving operations, we develop
a Softgoal Interdependency Graph-based network intent decomposition model, and
thus, a network intent decomposition algorithm is presented. Simulation results
demonstrate that the proposed algorithm outperforms without conflict analysis
in intent decomposition time. Moreover, we design a deep Q-network-assisted
intent optimization scheme to validate the performance gain.


  We argue that the quantum nature of matter and gravity should lead to a
discretization of the allowed states of the matter confined in the interior of
black holes. To support and illustrate this idea, we consider a quadratic
extension of General Relativity formulated \`{a} la Palatini and show that
nonrotating, electrically charged black holes develop a compact core at the
Planck density which is nonsingular if the mass spectrum satisfies a certain
discreteness condition. We also find that the area of the core is proportional
to the number of charges times the Planck area.


  The microwave induced magnetoresistance in GaAs/AlGaAs heterostructure was
studied at temperatures below 1K and frequencies in the range of 150-400 GHz. A
distinct node in the Shubnikov- de Haas oscillations, induced by the microwave
radiation, is clearly observed. The node position coincides with the position
of the cyclotron resonance on the carriers with effective mass (0.068 +/-
0.005) m0.


  Automatic generation of loop invariants is a fundamental challenge in
software verification. While this task is undecidable in general, it is
decidable for certain restricted classes of programs. This work focuses on
invariant generation for (branching-free) loops with a single linear update.
  Our primary contribution is a polynomial-space algorithm that computes the
strongest algebraic invariant for simple linear loops, generating all
polynomial equations that hold among program variables across all reachable
states. The key to achieving our complexity bounds lies in mitigating the
blowup associated with variable elimination and Gr\"obner basis computation, as
seen in prior works. Our procedure runs in polynomial time when the number of
program variables is fixed.
  We examine various applications of our results on invariant generation,
focusing on invariant verification and loop synthesis. The invariant
verification problem investigates whether a polynomial ideal defining an
algebraic set serves as an invariant for a given linear loop. We show that this
problem is coNP-complete and lies in PSPACE when the input ideal is given in
dense or sparse representations, respectively. In the context of loop
synthesis, we aim to construct a loop with an infinite set of reachable states
that upholds a specified algebraic property as an invariant. The strong
synthesis variant of this problem requires the construction of loops for which
the given property is the strongest invariant. In terms of hardness,
synthesising loops over integers (or rationals) is as hard as Hilbert's Tenth
problem (or its analogue over the rationals). When loop constants are
constrained to bit-bounded rational numbers, we demonstrate that loop synthesis
and its strong variant are both decidable in PSPACE, and in NP when the number
of program variables is fixed.


  The escalating surge in data generation presents formidable challenges to
information technology, necessitating advancements in storage, retrieval, and
utilization. With the proliferation of artificial intelligence and big data,
the "Data Age 2025" report forecasts an exponential increase in global data
production. The escalating data volumes raise concerns about efficient data
processing. The paper addresses the predicament of achieving a lower
compression ratio while maintaining or surpassing the compression performance
of state-of-the-art techniques.
  This paper introduces a lossy compression framework grounded in the
perceptron model for data prediction, striving for high compression quality.
The contributions of this study encompass the introduction of positive and
negative factors within the relative-to-absolute domain transformation
algorithm, the utilization of a three-layer perceptron for improved predictive
accuracy, and data selection rule modifications for parallelized compression
within compression blocks. Comparative experiments with SZ2.1's PW_REL mode
demonstrate a maximum compression ratio reduction of 17.78%.
  The article is structured as follows: the introduction highlights the data
explosion challenge; related work delves into existing solutions; optimization
of mapping algorithms in the relative and absolute domains is expounded in
Section 3,the design of the new compression framework is detailed in Section
4,In Section 5 we describe the whole process and give pseudo-code, and in
Section 6, our solution is evaluated. Finally, in Section 7, we provide an
outlook for future work.


  Electron-neutral scattering cross sections are fundamental quantities in
simulations of low temperature plasmas used for many technological applications
today. From these microscopic cross sections, several macro-scale quantities
(called "swarm" parameters) can be calculated. However, measurements as well as
theoretical calculations of cross sections are challenging. Since the 1960s
researchers have attempted to solve the inverse swarm problem of obtaining
cross sections from swarm data; but the solutions are not necessarily unique.
To address this issues, we examine the use of deep learning models which are
trained using the previous determinations of elastic momentum transfer,
ionization and excitation cross sections for different gases available on the
LXCat website and their corresponding swarm parameters calculated using the
BOLSIG+ solver for the numerical solution of the Boltzmann equation for
electrons in weakly ionized gases. We implement artificial neural network
(ANN), convolutional neural network (CNN) and densely connected convolutional
network (DenseNet) for this investigation. To the best of our knowledge, there
is no study exploring the use of CNN and DenseNet for the inverse swarm
problem. We test the validity of predictions by all these trained networks for
a broad range of gas species and we deduce that DenseNet effectively extracts
both long and short term features from the swarm data and hence, it predicts
cross sections with significantly higher accuracy compared to ANN. Further, we
apply Monte Carlo dropout as Bayesian approximation to estimate the probability
distribution of the cross sections to determine all plausible solutions of this
inverse problem.


  Under the assumption of two fluid kinematics of a nonrelativistic Bose liquid
in the presence of a local velocity field $v(x)$, local Galilei transformations
are used to derive formulas for the spatial distribution of superfluidity. The
local formulation is shown to subsume several descriptions of superfluidity,
from Landau's free quasiparticle picture of the normal fluid to the fully
microscopic winding number formula for superfluid density. We derive the
superfluid distribution of generic pure states of 1-d bosonic systems by using
the continuum analog of matrix product states. With a view toward spatially
structured superfluid-based quantum devices, we consider the limits to local
distillation of superfluidity within the framework of localized resource
theories of quantum coherence.


  In the present article we prove some results about the Morava K-theory. In
particular, we construct an operation from the Morava K-theory to the Chow
theory analogous to the second Chern class for Grothendieck's K0-theory.
Furthermore, we investigate ordinary and equivariant oriented cohomology
theories in the sense of Levine-Morel of projective quadrics, and discuss the
Rost motives.


  Modern language models often exhibit powerful but brittle behavior, leading
to the development of larger and more diverse benchmarks to reliably assess
their behavior. Here, we suggest that model performance can be benchmarked and
elucidated with much smaller evaluation sets. We first show that in six popular
language classification benchmarks, model confidence in the correct class on
many pairs of points is strongly correlated across models. We build upon this
phenomenon to propose Anchor Point Selection, a technique to select small
subsets of datasets that capture model behavior across the entire dataset.
Anchor points reliably rank models: across 87 diverse language model-prompt
pairs, evaluating models using 1-30 anchor points outperforms uniform sampling
and other baselines at accurately ranking models. Moreover, just several anchor
points can be used to estimate model per-class predictions on all other points
in a dataset with low mean absolute error, sufficient for gauging where the
model is likely to fail. Lastly, we present Anchor Point Maps for visualizing
these insights and facilitating comparisons of the performance of different
models on various regions within the dataset distribution.


  We present the first UBV and uvby photometric observations for the short
period variable star HV Ursae Majoris classified as a field RRc variable. The
observed differences between the consecutive minima and the lack of colour
variations disagree with the RRc-classification and suggest the possible binary
nature of HV UMa. In order to reveal the real physical status of this star, we
took medium resolution spectra in the red spectral region centered at 6600 A.
Spectra obtained around the assumed quadratures clearly showed the presence of
the secondary component.
  An improved ephemeris calculated using our and Hipparcos epoch photometry is
Hel. JD_min=2451346.743+/-0.001, P=0.7107523(3) d. A radial velocity curve was
determined by modelling the cores of Halpha profiles with two Gaussian
components. This approximative approach gave a spectroscopic mass ratio of
q_sp=0.19+/-0.03. A modified Lucy model containing a temperature excess of the
secondary was fitted to the V light curve. The obtained set of physical
parameters together with the parallax measurement indicate that this binary
lies far from the galactic plane, and the primary component is an evolved
object, probably a subgiant or giant star. The large temperature excess of the
secondary may suggest a poor thermal contact between the components due to a
relatively recent formation of this contact system.


  Let $\mathcal{A}$ and $\mathcal{B}$ be two prime $C^{*}$-algebras. In this
paper, we investigate the additivity of map $\Phi$ from $\mathcal{A}$ onto
$\mathcal{B}$ that are bijective unital and satisfies $$\Phi(AP+\lambda
PA^{*})=\Phi(A)\Phi(P)+\lambda \Phi(P)\Phi(A)^{*},$$ for all $A\in\mathcal{A}$
and $P\in\{P_{1},I_{\mathcal{A}}-P_{1}\}$ where $P_{1}$ is a nontrivial
projection in $\mathcal{A}$ and $\lambda\in\{-1,+1\}$. Then, $\Phi$ is
$*$-additive.


  Two models of the circumstellar disc around supergiant B[e] stars are
discussed: an equatorial wind model produced by wind bi-stability, and a
Keplerian viscous disc model. Both models are successful in providing a site
for dust formation once they have cooled sufficiently. However, the
optical--infra-red continuum is calculated and it is found that both models
have significant trouble in accounting for observations. In particular the
optical--near-IR emission is accounted for, but the dust emission is
underestimated by at least an order of magnitude. Variations in the structure
of the models (the temperature variation with radius, the density structure and
the dust opacity) are investigated to assess how (in)appropriate the standard
models are for supergiant B[e] star discs. Changing the temperature structure,
and making simple dust opacity changes within the disc has little effect on the
resultant continuum emission. By altering the density structure of the discs,
the continuum may be accounted for by both models: the equatorial wind model
requires a very flat density profile which is impossible to explain with any
accelerating wind, and the viscous disc model's density structure is required
to fall off less steeply with radius than would have been expected, although
this may be explained from consideration of viscous processes in the disc. It
is recognised that both theoretical interpretations have difficulties and
unsolved problems.


  The objective of this study is to correlate the scaling factor of the
Standard Model (SM) like Higgs boson and the cross section ratio of the process
$e^+ e^- \rightarrow hhf\overline{f}$ where $f\neq t$, normalized to SM
predictions in the type I of the Two Higgs Doublet Model. All calculations have
been performed at $\sqrt{s}=500$ GeV and $1 \leq \tan{\beta} \leq 30$ for
masses $m_H = m_A = m_{H^\pm} = 300GeV$ and $m_H=300$ GeV, $m_A=m_{H^\pm}=500$
GeV. The working scenario is by taking without alignment limit, that is
$s_{\beta-\alpha}= 0.98$ and $s_{\beta-\alpha}= 0.99,$ $0.995$, which gives the
enhancement in the cross section, particularly a few times greater than the
predictions of the SM due to resonant-impacts of the additional heavy neutral
Higgs bosons. This shows that enhancement in cross section occurs on leaving
the alignment i.e., $s_{\beta-\alpha}=1$, at which all the higgs that couple to
vector bosons and fermions have the same values as in SM at tree level. A large
value of enhancement factor is obtained at $s_{\beta-\alpha}= 0.98$ compared to
$s_{\beta-\alpha}= 0.99,$ $0 .995$. Furthermore, the decrease in the
enhancement factor is observed for the case when $m_H=300$ GeV,
$m_A=m_{H^\pm}=500$ GeV. The behavior of the scaling factor with $\tan{\beta}$
is also studied, which shows that for large values of $\tan\beta$, the scaling
factor becomes equal to $s_{\beta-\alpha}$. Finally a convincing correlation is
achieved by taking into account, the experimental and theoretical constraints
e.g, perturbative unitarity, vacuum stability and electroweak oblique
parameters.


  The transformation properties of strong penguin operators under the action of
the flavor group change when they are considered as operators in (partially)
quenched QCD instead of the unquenched theory. As a result, additional
operators and new low-energy constants appear in the effective theory
describing non-leptonic kaon decay matrix elements in the partially quenched
setting. These new low-energy constants do not have a counterpart in the
unquenched theory, and should thus be considered as an artifact of the quenched
approximation. Here we consider strong penguin operators consisting of products
of two left-handed flavor currents, and give a complete one-loop analysis in
the effective theory for K^0 to vacuum and K^+ to pi^+ matrix elements. We find
that the new low-energy constants already appear in these matrix elements at
leading order. This implies that (partially) quenched lattice computations of
for instance the Delta I=1/2 rule are affected by ambiguities intrinsic to the
use of the quenched approximation at leading order. The only exception is the
partially quenched case with three light sea quarks, consistent with general
expectations. Our results are also relevant when the charm quark is kept in the
theory.


  Refractive scintillation effects are powerful techniques for discriminating
between different models proposed for the electron density fluctuation spectrum
in the ISM. Data from our long-term scintillation study of 18 pulsars in the DM
range 3-35 pc cm^{-3} (Paper I) are used to investigate two important
observable effects of refractive scintillation: (i) modulations of DISS
observables and flux, and (ii) drifting bands. Our data provide simultaneous
measurements of decorrelation bandwidth, scintillation time scale, flux density
and drift slope of patterns. The observed modulations of the first 3 are
compared with the theoretical predictions, and constraints are placed on the
density spectral form. The measured modulation indices are larger than
predicted by a Kolmogorov form. Measurements of drift slopes and DISS
parameters are used to independently estimate the slope of the density
spectrum, which is found to be consistent with a Kolmogorov form for several
pulsars.The contradictory results from these 2 independent methods are not
reconcilable with the simple theoretical models. Our observations show
anomalous behaviour like persistent drifting bands for some pulsars.This can be
interpreted as an excess power in the low wavenumber range (~10^{-12} -
10^{-13} m^{-1}) compared to the Kolmogorov expectations or the existence of
localized density structures.The results from our observations and those from
the earlier studies are examined for understanding the overall nature of the
density spectrum.The emerging picture is a Kolmogorov-like form in the
wavenumber range ~10^{-6} m^{-1} to ~10^{-11} m^{-1}, which either steepens or
has a bump near ~ 10^{-12} - 10^{-13} m^{-1}. We also discuss possible
implications of our results for the current theoretical models.


  It is well known that the exceptional set in a resolution of a rational
surface singularity is a tree of rational curves. We generalize the
combinatoric part of this statement to higher dimensions and show that the
highest cohomologies of the dual complex associated to a resolution of an
isolated rational singularity vanish. We also prove that the dual complex
associated to a resolution of an isolated hypersurface singularity is simply
connected. As a consequence, we show that the dual complex associated to a
resolution of a 3-dimensional Gorenstein terminal singularity has the homotopy
type of a point.


  We consider the $M$-ary classification problem via crowdsourcing, where crowd
workers respond to simple binary questions and the answers are aggregated via
decision fusion. The workers have a reject option to skip answering a question
when they do not have the expertise, or when the confidence of answering that
question correctly is low. We further consider that there are spammers in the
crowd who respond to the questions with random guesses. Under the payment
mechanism that encourages the reject option, we study the behavior of honest
workers and spammers, whose objectives are to maximize their monetary rewards.
To accurately characterize human behavioral aspects, we employ prospect theory
to model the rationality of the crowd workers, whose perception of costs and
probabilities are distorted based on some value and weight functions,
respectively. Moreover, we estimate the number of spammers and employ a
weighted majority voting decision rule, where we assign an optimal weight for
every worker to maximize the system performance. The probability of correct
classification and asymptotic system performance are derived. We also provide
simulation results to demonstrate the effectiveness of our approach.


  {Abridged} Rapid variations in optical flux are seen in many quasars and all
blazars. The amount of variability in different classes of Active Galactic
Nuclei has been studied extensively but many questions remain unanswered. We
present the results of a long-term programme to investigate the intra-night
optical variability (INOV) of powerful flat spectrum radio core-dominated
quasars (CDQs), with a focus on probing the relationship of INOV to the degree
of optical polarization. We observed a sample of 16 bright CDQs showing strong
broad optical emission lines and consisting of both high and low optical
polarization quasars (HPCDQs and LPCDQs). We employed ARIES, IIA, IGO
telescopes, to carry out {\it R}-band monitoring on a total of 47 nights.
Combining these INOV data with those taken from the literature, we were able to
increase the sample size to 21 CDQs(12 LPCDQs and 9 HPCDQs) monitored on a
total of 73 nights. As the existence of a prominent flat-spectrum radio core
signifies that strong relativistic beaming is present in all these CDQs, the
definitions of the two sets differ primarily in fractional optical
polarization, the LPCDQs showing a very low median$ P_{op} \simeq$ 0.4 per
cent.
  Our study yields an INOV duty cycle (DC) of $\sim$28 per cent for the LPCDQs
and $\sim 68$ percent for HPCDQs.
  If only strong INOV with fractional amplitude above 3 per cent is considered,
the corresponding DCs are $\sim$ 7 per cent and $\sim$ 40 per cent,
respectively.From this strong contrast between the two classes of luminous,
relativistically beamed quasars, it is apparent that relativistic beaming is
normally not a sufficient condition for strong INOV and a high optical
polarization is the other necessary condition.


  We have measured the nonlinear response to the ac magnetic field in the
superconducting weak ferromagnet Ru-1222, at different regimes of sample
cooling which provides unambiguous evidence of the interplay of the domain
structure and the vorticity in the superconducting state. This is {\em direct}
proof of coexistence of ferromagnetic and superconductive order parameters in
high-$T_c$ ruthenocuprates.


  Based on observations from the EUV Imaging Spectrometer (EIS) on board
Hinode, the existence of a broad distribution of blue and red Dopplershift in
active region loops has been revealed; the distribution of Dopplershifts
depends on the peak temperature of formation of the observed spectral lines. To
reproduce those observations, we use a nanoflare heating model for
multi-stranded coronal loops (Sarkar and Walsh 2008, 2009) and a set of
spectral lines covering a broad range of temperature (from 0.25 MK to 5.6 MK).
We first show that red- and blueshifts are ubiquitous in all wavelength ranges;
redshifts/downflows dominating cool spectral lines (from O V to Si VII) and
blueshifts/upflows dominating the hot lines (from Fe XV to Ca XVII). These
Dopplershifts are indicative of plasma condensation and evaporation. By
computing the average Dopplershift, we derive a new temperature diagnostic for
coronal loops: the temperature at which the average Dopplershift vanishes
estimates the mean temperature of the plasma along the coronal loop and at the
footpoints. To compare closely with observations, we model dense and sparse
Hinode/EIS rasters at the instrument resolution. The temperature diagnostic
provides the same temperature estimates as the model whatever the type of
raster or the viewing angle. To conclude, we have developed a robust
temperature diagnostic to measure the plasma temperature of a coronal loop
using a broad range of spectral lines.


  An overview of non-directional direct detection methods is given. The
currently leading experiments for spin independent WIMPs interactions are using
simultaneous measurement of two quantities for event-by-event background
discrimination in cryogenic bolometers and noble gas like xenon. Besides these,
several interesting techniques have been developped, each having a specific
advantage concerning e.g energy threshold lowering or strong immunity to
ionizing radiations background. Technologies used and most recent results about
spin-dependent and spin-independent cases are presented.


  It was recently found that, when linearised in the absence of matter, 58
cases of the general gravitational theory with quadratic curvature and torsion
are (i) free from ghosts and tachyons and (ii) power-counting renormalisable.
We inspect the nonlinear Hamiltonian structure of the eight cases whose primary
constraints do not depend on the curvature tensor. We confirm the particle
spectra and unitarity of all these theories in the linear regime. We uncover
qualitative dynamical changes in the nonlinear regimes of all eight cases,
suggesting at least a broken gauge symmetry, and possibly the activation of
negative kinetic energy spin-parity sectors and acausal behaviour. Two of the
cases propagate a pair of massless modes at the linear level, and were
interesting as candidate theories of gravity. However, we identify these modes
with vector excitations, rather than the tensor polarisations of the graviton.
Moreover, we show that these theories do not support a viable cosmological
background.


  We study a generalization of the Heston model, which consists of two coupled
stochastic differential equations, one for the stock price and the other one
for the volatility. We consider a cubic nonlinearity in the first equation and
a correlation between the two Wiener processes, which model the two white noise
sources. This model can be useful to describe the market dynamics characterized
by different regimes corresponding to normal and extreme days. We analyze the
effect of the noise on the statistical properties of the escape time with
reference to the noise enhanced stability (NES) phenomenon, that is the noise
induced enhancement of the lifetime of a metastable state. We observe NES
effect in our model with stochastic volatility. We investigate the role of the
correlation between the two noise sources on the NES effect.


  By studying the linearization of contour dynamics equation and using implicit
function theorem, we prove the existence of co-rotating and travelling global
solutions for the gSQG equation, which extends the result of Hmidi and Mateu
\cite{HM} to $\alpha\in[1,2)$. Moreover, we prove the $C^\infty$ regularity of
vortices boundary, and show the convexity of each vortices component.


  The (weighted) average treatment effect is commonly used to quantify the main
effect of a binary exposure on an outcome. Extensions to continuous exposures,
however, either quantify the effects of interventions that are rarely relevant
(e.g., applying the same exposure level uniformly in the population), or
consider shift interventions that are rarely intended, raising the question how
large a shift to consider. Average derivative effects (ADEs) instead express
the effect of an infinitesimal shift in each subject's exposure level, making
inference less prone to extrapolation. ADEs, however, are rarely considered in
practice because their estimation usually requires estimation of (a) the
conditional density of exposure given covariates, and (b) the derivative of (a)
w.r.t. exposure. Here, we introduce a class of estimands which can be inferred
without requiring estimates of (a) and (b), but which reduce to ADEs when the
exposure obeys a specific distribution determined by the choice of estimand in
the class. We moreover show that when the exposure does not obey this
distribution, our estimand represents an ADE w.r.t. an `intervention' exposure
distribution. We identify the `optimal' estimand in our class and propose
debiased machine learning estimators, by deriving influence functions under the
nonparametric model.


  Broken spacetime symmetries might emerge from a fundamental physical theory.
The effective low-energy theory might be expected to exhibit violations of
supersymmetry and Lorentz invariance. Some illustrative models which combine
supersymmetry and Lorentz violation are described, and a superspace formulation
is given.


  Recurrent nova CI Aquilae has entered the final decline phase a bit before
May of 2001, about 300 days after the optical maximum, showing the slowest
evolution among recurrent novae. Based on the optically thick wind mass-loss
theory of the thermonuclear runaway model, we have estimated the turn-off time
of the CI Aql 2000 outburst. It is in late March of 2001 after a luminous
supersoft X-ray source phase lasts 150 days (from November of 2000 until March
of 2001). We have also obtained, by fitting our theoretical light curves with
the 1917 and 2000 outbursts, the white dwarf (WD) mass to be M_{WD}= 1.2 \pm
0.05 M_\sun, the helium enrichment of the envelope is He/H = 0.5 by number, the
mass of the hydrogen-rich envelope on the WD at the optical maximum is \Delta
M_{max} = 8.0 x 10^{-6} M_\sun, and the average mass accretion rate is \dot
M_{acc}= 1.0 x 10^{-7} M_\sun/yr during the quiescent phase between the 1917
and 2000 outbursts. Using these obtained values, we have consistently
reproduced the light curve in quiescence as well as of the two outbursts. We
have also discussed the possibility whether or not CI Aql will explode as a
Type Ia supernova in a future.


  A nondestructive method for estimating the amount of carbon stored by
individuals, communities, vegetation types, and coverages, as well as their
volume and aboveground biomass, is presented. This methodology is based on
information on carbon stocks obtained through three-dimensional analysis of
tree architecture and artificial neural networks. This technique accurately
incorporates the diversity of plant forms measured in plots, transects, and
relev\'es. Stored carbon in any vegetation type is usually calculated as half
the biomass of sampled individuals, estimated with allometric formulas. The
most complete of these formulas incorporate diameter, height, and specific
gravity of wood but do not consider the variation in carbon stored in different
organs or different species, nor do they include information on the wide array
of architectures present in different plant communities. To develop these
allometric models, many individuals of different species must be sacrificed to
identify and validate samples and to minimize error. It is common to find
cutting-edge studies that encourage logging to improve estimates of carbon. In
our approach we replace this destructive methodology with a new technique for
quantifying global aboveground carbon. We demonstrate that carbon content in
forest aboveground biomass in the pantropics could rise to 723.97 Pg C. This
study shows that a reevaluation of climatic and ecological models is needed to
move toward a better understanding of the adverse effects of climate change,
deforestation, and degradation of tropical vegetation.


  The influence maximization is the problem of finding a set of social network
users, called influencers, that can trigger a large cascade of propagation.
Influencers are very beneficial to make a marketing campaign goes viral through
social networks for example. In this paper, we propose an influence measure
that combines many influence indicators. Besides, we consider the reliability
of each influence indicator and we present a distance-based process that allows
to estimate the reliability of each indicator. The proposed measure is defined
under the framework of the theory of belief functions. Furthermore, the
reliability-based influence measure is used with an influence maximization
model to select a set of users that are able to maximize the influence in the
network. Finally, we present a set of experiments on a dataset collected from
Twitter. These experiments show the performance of the proposed solution in
detecting social influencers with good quality.


  Gravitational lensing by clusters of galaxies has been detected on scales
ranging from $\sim10^{-1}$ Mpc to $\sim10$ Mpc, namely, arcs/arclets, weak
lensing and quasar-cluster associations. This allows us to derive an overall
radius matter distribution of clusters of galaxies. While the dynamical
analysis of the X-ray observations has yielded a great number of data for the
virial cluster masses, it becomes possible to statistically compare the cluster
mass determinations by these two independent methods. In this letter we show
that as compared with gravitational lensing, the dynamical analysis under the
assumption of isothermal and hydrostatic equilibrium has systematically
underestimated the cluster masses inside the Abell radius by a factor of
$\sim2$ with scatter between $0.7$ and $5$. Because the same correction factor
should be applicable to the gas baryon fraction of clusters of galaxies
obtained from the X-ray data, it is probably too premature to claim a baryon
crisis in today's cosmology.


  This final analysis of hadronic and leptonic cross-sections and of leptonic
forward-backward asymmetries in e+e- collisions with the OPAL detector makes
use of the full LEP1 data sample comprising 161 pb^-1 of integrated luminosity
and 4.5 x 10^6 selected Z decays. An interpretation of the data in terms of
contributions from pure Z exchange and from Z-gamma interference allows the
parameters of the Z resonance to be determined in a model-independent way. Our
results are in good agreement with lepton universality and consistent with the
vector and axial-vector couplings predicted in the Standard Model. A fit to the
complete dataset yields the fundamental Z resonance parameters: mZ = 91.1852 +-
0.0030 GeV, GZ = 2.4948 +- 0.0041 GeV, s0h = 41.501 +- 0.055 nb, Rl = 20.823 +-
0.044, and Afb0l = 0.0145 +- 0.0017. Transforming these parameters gives a
measurement of the ratio between the decay width into invisible particles and
the width to a single species of charged lepton, Ginv/Gl = 5.942 +- 0.027.
Attributing the entire invisible width to neutrino decays and assuming the
Standard Model couplings for neutrinos, this translates into a measurement of
the effective number of light neutrino species, N_nu = 2.984 +- 0.013.
Interpreting the data within the context of the Standard Model allows the mass
of the top quark, mt = 162 +29-16 GeV, to be determined through its influence
on radiative corrections. Alternatively, utilising the direct external
measurement of mt as an additional constraint leads to a measurement of the
strong coupling constant and the mass of the Higgs boson: alfa_s(mZ) = 0.127 +-
0.005 and mH = 390 +750-280 GeV.


  Weighted sampling is a fundamental tool in data analysis and machine learning
pipelines. Samples are used for efficient estimation of statistics or as sparse
representations of the data. When weight distributions are skewed, as is often
the case in practice, without-replacement (WOR) sampling is much more effective
than with-replacement (WR) sampling: it provides a broader representation and
higher accuracy for the same number of samples. We design novel composable
sketches for WOR $\ell_p$ sampling, weighted sampling of keys according to a
power $p\in[0,2]$ of their frequency (or for signed data, sum of updates). Our
sketches have size that grows only linearly with the sample size. Our design is
simple and practical, despite intricate analysis, and based on off-the-shelf
use of widely implemented heavy hitters sketches such as CountSketch. Our
method is the first to provide WOR sampling in the important regime of $p>1$
and the first to handle signed updates for $p>0$.


  While two-dimensional symmetry-enriched topological phases ($\mathsf{SET}$s)
have been studied intensively and systematically, three-dimensional ones are
still open issues. We propose an algorithmic approach of imposing global
symmetry $G_s$ on gauge theories (denoted by $\mathsf{GT}$) with gauge group
$G_g$. The resulting symmetric gauge theories are dubbed "symmetry-enriched
gauge theories" ($\mathsf{SEG}$), which may be served as low-energy effective
theories of three-dimensional symmetric topological quantum spin liquids. We
focus on $\mathsf{SEG}$s with gauge group
$G_g=\mathbb{Z}_{N_1}\times\mathbb{Z}_{N_2}\times\cdots$ and on-site unitary
symmetry group $G_s=\mathbb{Z}_{K_1}\times\mathbb{Z}_{K_2}\times\cdots$ or
$G_s=\mathrm{U(1)}\times \mathbb{Z}_{K_1}\times\cdots$. Each
$\mathsf{SEG}(G_g,G_s)$ is described in the path integral formalism associated
with certain symmetry assignment. From the path-integral expression, we propose
how to physically diagnose the ground state properties (i.e., $\mathsf{SET}$
orders) of $\mathsf{SEG}$s in experiments of charge-loop braidings (patterns of
symmetry fractionalization) and the \emph{mixed} multi-loop braidings among
deconfined loop excitations and confined symmetry fluxes. From these
symmetry-enriched properties, one can obtain the map from $\mathsf{SEG}$s to
$\mathsf{SET}$s. By giving full dynamics to background gauge fields,
$\mathsf{SEG}$s may be eventually promoted to a set of new gauge theories
(denoted by $\mathsf{GT}^*$). Based on their gauge groups, $\mathsf{GT}^*$s may
be further regrouped into different classes each of which is labeled by a gauge
group ${G}^*_g$. Finally, a web of gauge theories involving $\mathsf{GT}$,
$\mathsf{SEG}$, $\mathsf{SET}$ and $\mathsf{GT}^*$ is achieved. We demonstrate
the above symmetry-enrichment physics and the web of gauge theories through
many concrete examples.


  Monte Carlo simulations of a simple lattice model of protein folding show two
distinct regimes depending on the chain length. The first regime well describes
the folding of small protein sequences and its kinetic counterpart appears to
be single exponential in nature, while the second regime is typical of
sequences longer than 80 amino acids and the folding performance achievable is
sensitive to target conformation. The extent to which stability, as measured by
the energy of a sequence in the target, is an essential requirement and affects
the folding dynamics of protein molecules in the first regime is investigated.
The folding dynamics of sequences whose design stage was restricted to a
certain fraction of randomly selected amino acids shows that while some degree
of stability is a necessary and sufficient condition for successful folding,
designing sequences that provide the lowest energy in the target seems to be a
superfluous constraint. By studying the dynamics of under annealed but
otherwise freely designed sequences we explore the relation between stability
and kinetic accessibility. We find that there is no one-to-one correspondence
between having low energy and folding quickly to the target, as only a small
fraction of the most stable sequences were also found to fold relatively
quickly.


  Skeleton-based action recognition has achieved remarkable results in human
action recognition with the development of graph convolutional networks (GCNs).
However, the recent works tend to construct complex learning mechanisms with
redundant training and exist a bottleneck for long time-series. To solve these
problems, we propose the Temporal-Spatio Graph ConvNeXt (TSGCNeXt) to explore
efficient learning mechanism of long temporal skeleton sequences. Firstly, a
new graph learning mechanism with simple structure, Dynamic-Static Separate
Multi-graph Convolution (DS-SMG) is proposed to aggregate features of multiple
independent topological graphs and avoid the node information being ignored
during dynamic convolution. Next, we construct a graph convolution training
acceleration mechanism to optimize the back-propagation computing of dynamic
graph learning with 55.08\% speed-up. Finally, the TSGCNeXt restructure the
overall structure of GCN with three Spatio-temporal learning
modules,efficiently modeling long temporal features. In comparison with
existing previous methods on large-scale datasets NTU RGB+D 60 and 120,
TSGCNeXt outperforms on single-stream networks. In addition, with the ema model
introduced into the multi-stream fusion, TSGCNeXt achieves SOTA levels. On the
cross-subject and cross-set of the NTU 120, accuracies reach 90.22% and 91.74%.


  An $n$-tournament $T$ with vertex set $V$ is simple if there is no subset $M$
of $V$ such that $2\leq \left \vert M\right \vert \leq n-1$ and for every $x\in
V\setminus M$, either $M\rightarrow x$ or $x \rightarrow M$. The simplicity
index of an $n$-tournament $T$ is the minimum number $s(T)$ of arcs whose
reversal yields a non-simple tournament. M\"{u}ller and Pelant (1974) proved
that $s(T)\leq\frac{n-1}{2}$, and that equality holds if and only if $T$ is
doubly regular. As doubly regular tournaments exist only if $n\equiv
3\pmod{4}$, $s(T)<\frac{n-1}{2}$ for $n\not\equiv3\pmod{4}$. In this paper, we
study the class of $n$-tournaments with maximal simplicity index for
$n\not\equiv3\pmod{4}$.


  Ultrafast lasers are becoming increasingly widespread in science and industry
alike. Fiber-based ultrafast laser sources are especially attractive because of
their compactness, alignment-free setups, and potentially low costs. However,
confining short pulses within a fiber core leads to high intensities, which
drive a host of nonlinear effects. While these phenomena and their interactions
greatly complicate the design of such systems, they can also provide
opportunities for engineering new capabilities. Here, we report a new fiber
amplification regime distinguished by the use of a dynamically-evolving gain
spectrum as a degree of freedom: as a pulse experiences nonlinear spectral
broadening, absorption and amplification actively reshape both the pulse and
the gain spectrum itself. The dynamic co-evolution of the field and
excited-state populations supports pulses that can broaden spectrally by almost
two orders of magnitude and well beyond the gain bandwidth, while remaining
cleanly-compressible to their sub-50-fs transform limit. Theory and experiments
provide evidence that a nonlinear attractor underlies the management of the
nonlinearity by the gain. Further research into the mutual, pulse-inversion
propagation dynamics may address open scientific questions and pave the way
toward simple, compact fiber sources that produce high-energy, sub-30-fs
pulses.


  A triangular partition is a partition whose Ferrers diagram can be separated
from its complement (as a subset of $\mathbb{N}^2$) by a straight line. Having
their origins in combinatorial number theory and computer vision, triangular
partitions have been studied from a combinatorial perspective by Onn and
Sturmfels, and by Corteel et al. under the name plane corner cuts, and more
recently by Bergeron and Mazin. In this paper we derive new enumerative,
geometric and algorithmic properties of such partitions.
  We give a new characterization of triangular partitions and the cells that
can be added or removed while preserving the triangular condition, and use it
to describe the M\"obius function of the restriction of Young's lattice to
triangular partitions. We obtain a formula for the number of triangular
partitions whose Young diagram fits inside a square, deriving, as a byproduct,
a new proof of Lipatov's enumeration theorem for balanced words. Finally, we
present an algorithm that generates all the triangular partitions of a given
size, which is significantly more efficient than previous ones and allows us to
compute the number of triangular partitions of size up to $10^5$.


  The probability distribution of the proper delay times during scattering on a
chaotic system is derived in the framework of the random matrix approach and
the supersymmetry method. The result obtained is valid for an arbitrary number
of scattering channels as well as arbitrary coupling to the energy continuum.
The case of statistically equivalent channels is studied in detail. In
particular, the semiclassical limit of infinite number of weak channels is paid
appreciable attention.


  Quantum communications using continuous variables are quite mature
experimental techniques and the relevant theories have been extensively
investigated with various methods. In this paper, we study the continuous
variable quantum channels from a different angle, i.e., by exploring master
equations. And we finally give explicitly the capacity of the channel we are
studying. By the end of this paper, we derive the criterion for the optimal
capacities of the Gaussian channel versus its fidelity.


  Recent theory and experiment in crystals of molecular magnets suggest that
fundamental tests of the decoherence mechanisms of macroscopic quantum
phenomena may be feasible in these systems (which are almost ideal quantum spin
glasses). We review the results, and suggest new experiments.


  The structure of the photospheric vector magnetic field below a dark filament
on the Sun is studied using the observations of the Spectro-Polarimeter
attached to the Solar Optical Telescope onboard Hinode. Special attention is
paid to discriminate the two suggested models, a flux rope or a bent arcade.
"Inverse-polarity" orientation is possible below the filament in a flux rope,
whereas "normal-polarity" can appear in both models. We study a filament in
active region NOAA 10930, which appeared on the solar disk during 2006
December. The transverse field perpendicular to the line of sight has a
direction almost parallel to the filament spine with a shear angle of 30 deg,
whose orientation includes the 180-degree ambiguity. To know whether it is in
the normal orientation or in the inverse one, the center-to-limb variation is
used for the solution under the assumption that the filament does not
drastically change its magnetic structure during the passage. When the filament
is near the east limb, we found that the line-of-site magnetic component below
is positive, while it is negative near the west limb. This change of sign
indicates that the horizontal photospheric field perpendicular to the polarity
inversion line beneath the filament has an "inverse-polarity", which indicates
a flux-rope structure of the filament supporting field.


  The simple 3-3-1 model that contains the minimal lepton and minimal scalar
contents is detailedly studied. The impact of the inert scalars (i.e., the
extra fundamental fields that provide realistic dark matter candidates) on the
model is discussed. All the interactions of the model are derived, in which the
standard model ones are identified. We constrain the standard model like Higgs
particle at the LHC. We search for the new particles including the inert ones,
which contribute to the $B_s$-$\bar{B}_s$ mixing, the rare $B_s\rightarrow
\mu^+\mu^-$ decay, the CKM unitarity violation, as well as producing the
dilepton, dijet, diboson, diphoton, and monojet final states at the LHC.


  The generators $(J_{\pm}, J_0)$ of the algebra $U_q(sl(2))$ is our starting
point. An invertible nonlinear map involving, apart from q, a second arbitrary
complex parameter h, defines a triplet $({\hat X},{\hat Y},{\hat H})$. The
latter set forms a closed algebra under commutation relations. The nonlinear
algebra $U_{q,h}(sl(2))$, thus generated, has two different limits. For $q \to
1$, the Jordanian h-deformation $U_{h}(sl(2))$ is obtained. For $h \to 0$, the
q-deformed algebra $U_{q}(sl(2))$ is reproduced. From the nonlinear map, the
irreducible representations of the doubly-deformed algebra $U_{q,h}(sl(2))$ may
be directly and explicitly obtained form the known representations of the
algebra $U_q(sl(2))$. Here we consider only generic values of q.


  Since the first recordings made of evoked action potentials it has become
apparent that the responses of individual neurons to ongoing physiologically
relevant input, are highly variable. This variability is manifested in
non-stationary behavior of practically every observable neuronal response
feature. Here we introduce the Neuronal Response Clamp, a closed-loop technique
enabling full control over two important single neuron activity variables:
response probability and stimulus-spike latency. The technique is applicable
over extended durations (up to several hours), and is effective even on the
background of ongoing neuronal network activity. The Response Clamp technique
is a powerful tool, extending the voltage-clamp and dynamic-clamp approaches to
the neuron's functional level, namely - its spiking behavior.


  This paper gives a new characterization of geodesic spheres in the hyperbolic
space in terms of a ``weighted'' higher order mean curvature. Precisely, we
show that a compact hypersurface $\Sigma^{n-1}$ embedded in $\H^n$ with $VH_k$
being constant for some $k=1,\cdots,n-1$ is a centered geodesic sphere. Here
$H_k$ is the $k$-th normalized mean curvature of $\Sigma$ induced from $\H^n$
and $V=\cosh r$, where $r$ is a hyperbolic distance to a fixed point in $\H^n$.
Moreover, this result can be generalized to a compact hypersurface $\Sigma$
embedded in $\H^n$ with the ratio
$V\left(\frac{H_k}{H_j}\right)\equiv\mbox{constant},\;0\leq j< k\leq n-1$ and
$H_j$ not vanishing on $\Sigma$.


  Consider the dynamics of a layer of viscous incompressible fluid under the
influence of gravity. The upper boundary is a free boundary with the effect of
surface tension taken into account, and the lower boundary is a fixed boundary
on which the Navier-slip condition is imposed. It is proved that there is a
uniform time interval on which the estimates independent of both viscosity and
surface tension coefficients of the solution can be established. This then
allows one to justify the vanishing viscosity and surface tension limits by the
strong compactness argument. In the presence of surface tension, the main
difficulty lies in the less regularity of the highest temporal derivative of
the mean curvature of the free surface and the pressure. It seems hard to
overcome this difficulty by using the vorticity in viscous boundary layers. One
of the key observations here is to find that there is a crucial cancelation
between the mean curvature and the pressure by using the dynamic boundary
condition.


  We study a natural class of Fermi-Ulam Models that features good
hyperbolicity properties and that we call dispersing Fermi-Ulam models. Using
tools inspired by the theory of hyperbolic billiards we prove, under very mild
complexity assumptions, a Growth Lemma for our systems. This allows us to
obtain ergodicity of dispersing Fermi-Ulam Models. It follows that almost every
orbit of such systems is oscillatory.


  We adapted a multi-species escape model, developed for close-in extrasolar
planets, to calculate the escape rates of CH4 and N2 from Pluto. In the absence
of escape, CH4 should overtake N2 as the dominant species below the exobase.
The CH4 profile depends strongly on the escape rate, however, and the typical
escape rates predicted for Pluto lead to a nearly constant mixing ratio of less
than 1 % below the exobase. In this case the CH4 escape rate is only 5-10 % of
the N2 escape rate. Observations of the CH4 profile by the New Horizons/ALICE
spectrograph can constrain the CH4 escape rate and provide a unique test for
escape models.


  We give a new proof for the $C^\infty$ regularity of $C^2$ smooth conformal
mappings of the sub-Riemannian Heisenberg group. Our proof avoids any use of
nonlinear potential theory and relies only on hypoellipticity of H\"ormander
operators and quasiconformal flows. This approach is inspired by prior work of
Sarvas and Liu.


  In this paper, we investigate estimators for symmetric $\alpha$-stable CARMA
processes sampled equidistantly. Simulation studies suggest that the Whittle
estimator and the estimator presented in Garc\'{\i}a et al. (2011) are
consistent estimators for the parameters of stable CARMA processes. For CARMA
processes with finite second moments it is well-known that the Whittle
estimator is consistent and asymptotically normally distributed. Therefore, in
the light-tailed setting the properties of the Whittle estimator for CARMA
processes are similar to those of the Whittle estimator for ARMA processes.
However, in the present paper we prove that, in general, the Whittle estimator
for symmetric $\alpha$-stable CARMA processes sampled at low frequencies is not
consistent and highlight why simulation studies suggest something else. Thus,
in contrast to the light-tailed setting the properties of the Whittle estimator
for heavy-tailed ARMA processes can not be transferred to heavy-tailed CARMA
processes. We elaborate as well that the estimator presented in Garc\'{\i}a et
al. (2011) faces the same problems. However, the Whittle estimator for stable
CAR(1) processes is consistent.


  Connes has extended Einstein's principle of general relativity to
noncommutative geometry. The new principle implies that the Dirac operator is
covariant with respect to Lorentz and internal gauge transformations and the
Dirac operator must include Yukawa couplings. It further implies that the
action for the metric, the gauge potentials and the Higgs scalar is coded in
the spectrum of the covariant Dirac operator. This ``universal'' action has
been computed by Chamseddine & Connes, it is the coupled Einstein-Hilbert and
Yang-Mills-Higgs action. This result is rederived and we discuss the physical
consequences.


  We study the $N$-point Coon amplitude discovered first by Baker and Coon in
the 1970s and then again independently by Romans in the 1980s. This
Baker-Coon-Romans (BCR) amplitude retains several properties of tree-level
string amplitudes, namely duality and factorization, with a $q$-deformed
version of the string spectrum. Although the formula for the $N$-point BCR
amplitude is only valid for ${q > 1}$, the four-point case admits a
straightforward extension to all ${q \geq 0}$ which reproduces the usual
expression for the four-point Coon amplitude. At five points, there are
inconsistencies with factorization when pushing ${q < 1}$. Despite these
issues, we find a new relation between the five-point BCR amplitude and Cheung
and Remmen's four-point basic hypergeometric amplitude, placing the latter
within the broader family of Coon amplitudes. Finally, we compute the $q \to
\infty$ limit of the $N$-point BCR amplitudes and discover an exact
correspondence between these amplitudes and the field theory amplitudes of a
scalar transforming in the adjoint representation of a global symmetry group
with an infinite set of non-derivative single-trace interaction terms. This
correspondence at $q = \infty$ is the first definitive realization of the Coon
amplitude (in any limit) from a field theory described by an explicit
Lagrangian.


  The realization of FDI and DDI from January to December 2022 reached
Rp1,207.2 trillion. The largest FDI investment realization by sector was led by
the Basic Metal, Metal Goods, Non-Machinery, and Equipment Industry sector,
followed by the Mining sector and the Electricity, Gas, and Water sector. The
uneven amount of FDI investment realization in each industry and the impact of
the COVID-19 pandemic in Indonesia are the main issues addressed in this study.
This study aims to identify the factors that influence the entry of FDI into
industries in Indonesia and measure the extent of these factors' influence on
the entry of FDI. In this study, classical assumption tests and hypothesis
tests are conducted to investigate whether the research model is robust enough
to provide strategic options nationally. Moreover, this study uses the ordinary
least squares (OLS) method. The results show that the electricity factor does
not influence FDI inflows in the three industries. The Human Development Index
(HDI) factor has a significant negative effect on FDI in the Mining Industry
and a significant positive effect on FDI in the Basic Metal, Metal Goods,
Non-Machinery, and Equipment Industries. However, HDI does not influence FDI in
the Electricity, Gas, and Water Industries in Indonesia.


  Several recent empirical studies demonstrate that important machine learning
tasks, e.g., training deep neural networks, exhibit low-rank structure, where
the loss function varies significantly in only a few directions of the input
space. In this paper, we leverage such low-rank structure to reduce the high
computational cost of canonical gradient-based methods such as gradient descent
(GD). Our proposed \emph{Low-Rank Gradient Descent} (LRGD) algorithm finds an
$\epsilon$-approximate stationary point of a $p$-dimensional function by first
identifying $r \leq p$ significant directions, and then estimating the true
$p$-dimensional gradient at every iteration by computing directional
derivatives only along those $r$ directions. We establish that the "directional
oracle complexities" of LRGD for strongly convex and non-convex objective
functions are $\mathcal{O}(r \log(1/\epsilon) + rp)$ and
$\mathcal{O}(r/\epsilon^2 + rp)$, respectively. When $r \ll p$, these
complexities are smaller than the known complexities of $\mathcal{O}(p
\log(1/\epsilon))$ and $\mathcal{O}(p/\epsilon^2)$ of {\gd} in the strongly
convex and non-convex settings, respectively. Thus, LRGD significantly reduces
the computational cost of gradient-based methods for sufficiently low-rank
functions. In the course of our analysis, we also formally define and
characterize the classes of exact and approximately low-rank functions.


  This paper describes the AVA-Kinetics localized human actions video dataset.
The dataset is collected by annotating videos from the Kinetics-700 dataset
using the AVA annotation protocol, and extending the original AVA dataset with
these new AVA annotated Kinetics clips. The dataset contains over 230k clips
annotated with the 80 AVA action classes for each of the humans in key-frames.
We describe the annotation process and provide statistics about the new
dataset. We also include a baseline evaluation using the Video Action
Transformer Network on the AVA-Kinetics dataset, demonstrating improved
performance for action classification on the AVA test set. The dataset can be
downloaded from https://research.google.com/ava/


  We construct the so-called theta vectors on noncommutative T^4, which
correspond to the theta functions on commutative tori with complex structures.
Following the method of Dieng and Schwarz, we first construct holomorphic
connections and then find the functions satisfying the holomorphic conditions,
the theta vectors. The holomorphic structure in the noncommutative T^4 case is
given by a 2x2 complex matrix, and the consistency requires its off-diagonal
elements to be the same. We also construct the tensor product of these
functions satisfying the consistency requirement.


  The interplay between topology and crystalline symmetries in materials can
lead to a variety of topological crystalline insulator (TCI) states. Despite
significant effort towards their experimental realization, so far only
Pb$_{1-x}$Sn$_x$Te has been confirmed as a mirror-symmetry protected TCI. Here,
based on first-principles calculations combined with a symmetry analysis, we
identify a rotational-symmetry protected TCI state in the transition-metal
dipnictide RX$_2$ family, where R = Ta or Nb and X = P, As, or Sb. Taking
TaAs$_2$ as an exemplar system, we show that its low-energy band structure
consists of two types of bulk nodal lines in the absence of spin-orbit coupling
(SOC) effects. Turning on the SOC opens a continuous bandgap in the energy
spectrum and drives the system into a $C_2T$-symmetry-protected TCI state. On
the (010) surface, we show the presence of rotational-symmetry-protected
nontrivial Dirac cone states within a local bulk energy gap of $\sim$ 300 meV.
Interestingly, the Dirac cones have tilted energy dispersion, realizing a
type-II Dirac fermion state in a topological crystalline insulator. Our results
thus indicate that the TaAs$_2$ materials family provides an ideal setting for
exploring the unique physics associated with type-II Dirac fermions in
rotational-symmetry-protected TCIs.


  The $k$-Detour problem is a basic path-finding problem: given a graph $G$ on
$n$ vertices, with specified nodes $s$ and $t$, and a positive integer $k$, the
goal is to determine if $G$ has an $st$-path of length exactly $\text{dist}(s,
t) + k$, where $\text{dist}(s, t)$ is the length of a shortest path from $s$ to
$t$. The $k$-Detour problem is NP-hard when $k$ is part of the input, so
researchers have sought efficient parameterized algorithms for this task,
running in $f(k)\text{poly}(n)$ time, for $f$ as slow-growing as possible.
  We present faster algorithms for $k$-Detour in undirected graphs, running in
$1.853^k \text{poly}(n)$ randomized and $4.082^k \text{poly}(n)$ deterministic
time. The previous fastest algorithms for this problem took $2.746^k
\text{poly}(n)$ randomized and $6.523^k \text{poly}(n)$ deterministic time
[Bez\'akov\'a-Curticapean-Dell-Fomin, ICALP 2017]. Our algorithms use the fact
that detecting a path of a given length in an undirected graph is easier if we
are promised that the path belongs to what we call a "bipartitioned" subgraph,
where the nodes are split into two parts and the path must satisfy constraints
on those parts. Previously, this idea was used to obtain the fastest known
algorithm for finding paths of length $k$ in undirected graphs
[Bj\"orklund-Husfeldt-Kaski-Koivisto, JCSS 2017].
  Our work has direct implications for the $k$-Longest Detour problem: in this
problem, we are given the same input as in $k$-Detour, but are now tasked with
determining if $G$ has an $st$-path of length at least $\text{dist}(s, t) + k.$
Our results for k-Detour imply that we can solve $k$-Longest Detour in $3.432^k
\text{poly}(n)$ randomized and $16.661^k \text{poly}(n)$ deterministic time.
The previous fastest algorithms for this problem took $7.539^k \text{poly}(n)$
randomized and $42.549^k \text{poly}(n)$ deterministic time [Fomin et al.,
STACS 2022].


  We establish some general dynamical properties of lattice many-body systems
that are subject to a high-frequency periodic driving. We prove that such
systems have a quasi-conserved extensive quantity $H_*$, which plays the role
of an effective static Hamiltonian. The dynamics of the system (e.g., evolution
of any local observable) is well-approximated by the evolution with the
Hamiltonian $H_*$ up to time $\tau_*$, which is exponentially long in the
driving frequency. We further show that the energy absorption rate is
exponentially small in the driving frequency. In cases where $H_*$ is ergodic,
the driven system prethermalizes to a thermal state described by $H_*$ at
intermediate times $t\lesssim \tau_*$, eventually heating up to an
infinite-temperature state at times $t\sim \tau_*$. Our results indicate that
rapidly driven many-body systems generically exhibit prethermalization and very
slow heating. We briefly discuss implications for experiments which realize
topological states by periodic driving.


  Predictive constructions are a powerful way of characterizing the probability
law of stochastic processes with certain forms of invariance, such as
exchangeability or Markov exchangeability. When de Finetti-like representation
theorems are available, the predictive characterization implicitly defines the
prior distribution, starting from assumptions on the observables; moreover, it
often helps designing efficient computational strategies. In this paper we give
necessary and sufficient conditions on the sequence of predictive distributions
such that they characterize a Markov exchangeable probability law for a
discrete valued process X. Under recurrence, Markov exchangeable processes are
mixtures of Markov chains. Thus, our results help checking when a predictive
scheme characterizes a prior for Bayesian inference on the unknown transition
matrix of a Markov chain. Our predictive conditions are in some sense minimal
sufficient conditions for Markov exchangeability; we also provide predictive
conditions for recurrence. We illustrate their application in relevant examples
from the literature and in novel constructions.


  We compute the evolution of the space-dependent mass distribution of galaxies
in clusters due to binary aggregations by solving a space-dependent
Smoluchowski equation. We derive the distribution of intergalactic distance for
different ranges of mass (and of corresponding magnitude). We compare the
results with the observed distributions, and find that the different degrees of
luminosity segregation observed in clusters are well accounted for by our
merging model. In addition, the presence of luminosity segregation is related
to dynamical effects which also show up in different but connected observables,
such as galaxy velocity profiles decreasing toward the center and X-ray
measured beta-parameters smaller than 1. We predict both luminosity segregation
and the observables above (being a product of binary aggregations) to be
inversely correlated with the core radius and with the galaxy velocity
dispersion; we discuss how the whole set of predictions compares with
up-to-date observations.


  Anisotropies in the cosmic microwave background radiation due to gravity
waves are investigated. An initial spectrum of gravity waves may have been
induced during an epoch of inflation. We study the propagation of such a
spectrum in a Friedmann background of hot and cold dark matter, radiation and
(possibly) a cosmological constant. We finally calculate its imprint as
anisotropies on the cosmic microwave background. We also take into account that
massless particles can source gravity waves by their anisotropic stresses. We
consider general mixed dark matter models with and without cosmological
constant. For a given, scale invariant input spectrum of gravity we determine
the dependence of the resulting spectrum of CMB anisotropies on the different
model parameters.


  The CRESST-II cryogenic Dark Matter search, aiming at detection of WIMPs via
elastic scattering off nuclei in CaWO$_4$ crystals, completed 730 kg days of
data taking in 2011. We present the data collected with eight detector modules,
each with a two-channel readout; one for a phonon signal and the other for
coincidently produced scintillation light. The former provides a precise
measure of the energy deposited by an interaction, and the ratio of
scintillation light to deposited energy can be used to discriminate different
types of interacting particles and thus to distinguish possible signal events
from the dominant backgrounds. Sixty-seven events are found in the acceptance
region where a WIMP signal in the form of low energy nuclear recoils would be
expected. We estimate background contributions to this observation from four
sources: 1) "leakage" from the e/\gamma-band 2) "leakage" from the
\alpha-particle band 3) neutrons and 4) Pb-206 recoils from Po-210 decay. Using
a maximum likelihood analysis, we find, at a high statistical significance,
that these sources alone are not sufficient to explain the data. The addition
of a signal due to scattering of relatively light WIMPs could account for this
discrepancy, and we determine the associated WIMP parameters.