  Modern robotic systems sense the environment geometrically, through sensors
like cameras, lidar, and sonar, as well as semantically, often through visual
models learned from data, such as object detectors. We aim to develop robots
that can use all of these sources of information for reliable navigation, but
each is corrupted by noise. Rather than assume that object detection will
eventually achieve near perfect performance across the lifetime of a robot, in
this work we represent and cope with the semantic and geometric uncertainty
inherent in methods like object detection. Specifically, we model data
association ambiguity, which is typically non-Gaussian, in a way that is
amenable to solution within the common nonlinear Gaussian formulation of
simultaneous localization and mapping (SLAM). We do so by eliminating data
association variables from the inference process through max-marginalization,
preserving standard Gaussian posterior assumptions. The result is a
max-mixture-type model that accounts for multiple data association hypotheses
as well as incorrect loop closures. We provide experimental results on indoor
and outdoor semantic navigation tasks with noisy odometry and object detection
and find that the ability of the proposed approach to represent multiple
hypotheses, including the "null" hypothesis, gives substantial robustness
advantages in comparison to alternative semantic SLAM approaches.


  The design of advanced nuclear reactors (Gen IV) involves an array of
challenging fluid-flow issues that affect its safety and performance. The
calculated DNS database will be instrumental in understanding the flow behavior
in the downcomer. Ultimately, we aim to evaluate existing heat transfer
correlations and some modifications are proposed.


  We investigate the influence of thermal energy on the current flow and
electron spin states in double quantum dots in series. The quadruplet Pauli
spin blockade, which is caused by the quadruplet and doublet states, occurs at
low temperatures affecting the transport properties. As the temperature
increases, the quadruplet Pauli spin blockade occurs as a result of the thermal
energy, even in regions where it does not occur at low temperatures. This is
because the triplet state is formed in one dot as a result of the gradual
change of the Fermi distribution function of the electrodes with increasing
temperature. Moreover, the thermally assisted Pauli spin blockade results in
coexistence of the Coulomb and Pauli spin blockades. Conversely, for the
standard triplet Pauli spin blockade, which occurs as a result of the triplet
and singlet states, the current through the double dots monotonously smears out
as the temperature increases. Therefore, the thermally assisted Pauli spin
blockade is not clearly observed. However, the coexistence of the Coulomb and
triplet Pauli spin blockades as a result of the thermal energy is clearly
obtained in the calculation of the probability of the spin state in the double
dots.


  Power diagrams, a type of weighted Voronoi diagrams, have many applications
throughout operations research. We study the problem of power diagram
detection: determining whether a given finite partition of $\mathbb{R}^d$ takes
the form of a power diagram. This detection problem is particularly prevalent
in the field of information elicitation, where one wishes to design contracts
to incentivize self-minded agents to provide honest information.
  We devise a simple linear program to decide whether a polyhedral cell
decomposition can be described as a power diagram. Further, we discuss
applications to property elicitation, peer prediction, and mechanism design,
where this question arises. Our model is able to efficiently decide the
question for decompositions of $\mathbb{R}^d$ or of a restricted domain in
$\mathbb{R}^d$. The approach is based on the use of an alternative
representation of power diagrams, and invariance of a power diagram under
uniform scaling of the parameters in this representation.


  The propagation of charged particles through a scattering medium in the
presence of a magnetic field can be described by a Fokker-Planck equation with
Lorentz force. This model is studied both, from a theoretical and a numerical
point of view. A particular trace estimate is derived for the relevant function
spaces to clarify the meaning of boundary values. Existence of a weak solution
is then proven by the Rothe method. In the second step of our investigations, a
fully practicable discretization scheme is proposed based on implicit
time-stepping through the energy levels and a spherical-harmonics
finite-element discretization with respect to the remaining variables. A full
error analysis of the resulting scheme is given, and numerical results are
presented to illustrate the theoretical results and the performance of the
proposed method.


  Qudits, with their state space of dimension d > 2, open fascinating
experimental prospects. The quantum properties of their states provide new
potentialities for quantum information, quantum contextuality, expressions of
geometric phases, facets of quantum entanglement and many other foundational
aspects of the quantum world, which are unapproachable with qubits. We here
experimentally investigate the quantum dynamics of a qudit (d = 4) that
consists of a single 3/2 nuclear spin embedded in a molecular magnet transistor
geometry, coherently driven by a microwave electric field. We propose and
implement three protocols based on a generalization of the Ramsey
interferometry to a multilevel system. First, the standard Ramsey interference
is used to measure the accumulation of geometric phases. Then, two distinct
transitions of the nuclear spin are addressed to measure the phase of an iSWAP
quantum gate. Finally, through a succession of two Hadamard gates, the
coherence time of a 3-state superposition is measured.


  Cellular-connected unmanned aerial vehicles (UAVs) represent a promising
technology for extending the coverage of 5G and 6G networks in a cost-effective
manner. Additionally, Massive multiple-input multiple-output (MIMO) serves as
an effective solution to interference mitigation in cellular-connected UAV
communications. In this letter, we propose a fusion of wireless and sensor data
to enhance beam alignment for cellular-connected UAV massive MIMO
communications. We develop a predictive beamforming framework, including the
frame structure and predictive beamformer. Moreover, we employ an extended
Kalman filter (EKF) to integrate channel and sensor data and provide the
corresponding state-space and observation models. Simulation results
demonstrate that the proposed scheme can improve position/orientation
estimation accuracy significantly, leading to higher spectral efficiency.


  Latent Dirichlet allocation (LDA) is an important hierarchical Bayesian model
for probabilistic topic modeling, which attracts worldwide interests and
touches on many important applications in text mining, computer vision and
computational biology. This paper introduces a topic modeling toolbox (TMBP)
based on the belief propagation (BP) algorithms. TMBP toolbox is implemented by
MEX C++/Matlab/Octave for either Windows 7 or Linux. Compared with existing
topic modeling packages, the novelty of this toolbox lies in the BP algorithms
for learning LDA-based topic models. The current version includes BP algorithms
for latent Dirichlet allocation (LDA), author-topic models (ATM), relational
topic models (RTM), and labeled LDA (LaLDA). This toolbox is an ongoing project
and more BP-based algorithms for various topic models will be added in the near
future. Interested users may also extend BP algorithms for learning more
complicated topic models. The source codes are freely available under the GNU
General Public Licence, Version 1.0 at https://mloss.org/software/view/399/.


  In this work we study the propagations of normal frequency modes for quantum
hydrodynamic (QHD) waves in the linear limit and introduce a new kind of
instability in a double-degenerate plasma. Three different regimes, namely,
low, intermediate and high magnetic field strengths are considered which span
the applicability of the work to a wide variety of environments. Distinct
behavior is observed for different regimes, for instance, in the
laboratory-scale field regime no frequency-mode instability occurs unlike those
of intermediate and high magnetic-field strength regimes. It is also found that
the instability of this kind is due to the heavy-fermions which appear below a
critical effective-mass parameter ($\mu_{cr}=\sqrt{3}$) and that the responses
of the two (lower and upper frequency) modes to fractional effective-mass
change in different effective-mass parameter ranges (below and above the
critical value) are quite opposite to each other. It is shown that, the
heavy-fermion instability due to extremely high magnetic field such as that
encountered for a neutron-star crust can lead to confinement of stable
propagations in both lower and upper frequency modes to the magnetic poles.
Current study can have important implications for linear wave dynamics in both
laboratory and astrophysical environments possessing high magnetic fields.


  Examples of differentiable mappings into real or complex topological vector
spaces with specific properties are given, which illustrate the differences
between differential calculus in the locally convex and the non-locally convex
case. In particular, for a suitable non-locally convex space E, we describe a
smooth injection of R into E whose derivative vanishes identically; we present
a complex C^\infty-map on the complex field C which is not given locally by its
Taylor series, around any point; we present a complex C^1-map into a complete,
non-locally convex topological vector space which is not C^2; and we present a
compactly supported, non-zero, complex C^\infty-map from C to a suitable
non-locally convex space.


  We propose NH-TTC, a general method for fast, anticipatory collision
avoidance for autonomous robots having arbitrary equations of motions. Our
proposed approach exploits implicit differentiation and subgradient descent to
locally optimize the non-convex and non-smooth cost functions that arise from
planning over the anticipated future positions of nearby obstacles. The result
is a flexible framework capable of supporting high-quality, collision-free
navigation with a wide variety of robot motion models in various challenging
scenarios. We show results for different navigating tasks, with our method
controlling various numbers of agents (with and without reciprocity), on both
physical differential drive robots, and simulated robots with different motion
models and kinematic and dynamic constraints, including acceleration-controlled
agents, differential-drive agents, and smooth car-like agents. The resulting
paths are high quality and collision-free, while needing only a few
milliseconds of computation as part of an integrated sense-plan-act navigation
loop.


  Nuclear reactions heat and cool the crust of accreting neutron stars and need
to be understood to interpret observations of X-ray bursts and of long-term
cooling in transiently accreting systems. It was recently suggested that
previously neglected neutron transfer reactions may play a significant role in
the nuclear processes. We present results from full nuclear network
calculations that now include these reactions and determine their impact on
crust composition, crust impurity, heating, and cooling. We find that a large
number of neutron transfer reactions indeed occur and impact crust models. In
particular, we identify a new type of reaction cycle that brings a pair of
nuclei across the nuclear chart into equilibrium via alternating neutron
capture and neutron release, interspersed with a neutron transfer. While
neutron transfer reactions lead to changes in crust model predictions, and need
to be considered in future studies, previous conclusions concerning heating,
cooling, and compositional evolution are remarkably robust.


  In this paper, we study the (in)sensitivity of the Khovanov functor to
four-dimensional linking of surfaces. We prove that if $L$ and $L'$ are split
links, and $C$ is a cobordism between $L$ and $L'$ that is the union of
disjoint (but possibly linked) cobordisms between the components of $L$ and the
components of $L'$, then the map on Khovanov homology induced by $C$ is
completely determined by the maps induced by the individual components of $C$
and does not detect the linking between the components. As a corollary, we
prove that a strongly homotopy-ribbon concordance (i.e., a concordance whose
complement can be built with only 1- and 2-handles) induces an injection on
Khovanov homology, which generalizes a result of the second author and Zemke.
Additionally, we show that a non-split link cannot be ribbon concordant to a
split link.


  We revisit the stability (instability) of the outer (inner) catenoid
connecting two concentric circular rings and give an explicit new construction
of the unstable mode of the inner catenoid by studying the spectrum of an
exactly solvable one-dimensional Schr\"odinger operator with an asymmetric
Darboux-P\"oschl-Teller potential.


  Human veins are important for carrying the blood from the body-parts to the
heart. The improper functioning of the human veins may arise from several
venous diseases. Varicose vein is one such disease wherein back flow of blood
can occur, often resulting in increased venous pressure or restricted blood
flow due to changes in the structure of vein. To examine the functional
characteristics of the varicose vein, it is crucial to study the physical and
bio mechanical properties of the vein. This work proposes a segmentation model
Opto-UNet, for segmenting the venous wall structure. Optical Coherence
Tomography system is used to acquire images of varicose vein. As the extracted
vein is not uniform in shape, hence adequate method of segmentation is required
to segment the venous wall. Opto-UNet model is based on the U-Net architecture
wherein a new block is integrated into the architecture, employing atrous and
separable convolution to extract spatially wide-range and separable features
maps for attaining advanced performance. Furthermore, the depth wise separable
convolution significantly reduces the complexity of the network by optimizing
the number of parameters. The model achieves accuracy of 0.9830, sensitivity of
0.8425 and specificity of 0.9980 using 8.54 million number of parameters. These
results indicate that model is highly adequate in segmenting the varicose vein
wall without deteriorating the segmentation quality along with reduced
complexity


  Neural network has attracted great attention for a long time and many
researchers are devoted to improve the effectiveness of neural network training
algorithms. Though stochastic gradient descent (SGD) and other explicit
gradient-based methods are widely adopted, there are still many challenges such
as gradient vanishing and small step sizes, which leads to slow convergence and
instability of SGD algorithms. Motivated by error back propagation (BP) and
proximal methods, we propose a semi-implicit back propagation method for neural
network training. Similar to BP, the difference on the neurons are propagated
in a backward fashion and the parameters are updated with proximal mapping. The
implicit update for both hidden neurons and parameters allows to choose large
step size in the training algorithm. Finally, we also show that any fixed point
of convergent sequences produced by this algorithm is a stationary point of the
objective loss function. The experiments on both MNIST and CIFAR-10 demonstrate
that the proposed semi-implicit BP algorithm leads to better performance in
terms of both loss decreasing and training/validation accuracy, compared to SGD
and a similar algorithm ProxBP.


  The properties of the Riemann extensions of nonriemannian spaces defined by
the first order systems of differential equations are considered.


  We report on results of finite-size numerical studies of partially filled
lowest Landau level at low electron filling factors. We find convincing
evidence suggesting that electrons form Wigner Crystals at sufficiently low
filling factors, and the critical filling factor is close to 1/7. At nu=1/7 we
find the system undergoes a phase transition from Wigner Crystal to the
incompressible Laughlin state when the short-range part of the Coulomb
interaction is modified slightly. This transition is either continuous or very
weakly first order.


  We introduce a new approach for designing computationally efficient learning
algorithms that are tolerant to noise, and demonstrate its effectiveness by
designing algorithms with improved noise tolerance guarantees for learning
linear separators.
  We consider both the malicious noise model and the adversarial label noise
model. For malicious noise, where the adversary can corrupt both the label and
the features, we provide a polynomial-time algorithm for learning linear
separators in $\Re^d$ under isotropic log-concave distributions that can
tolerate a nearly information-theoretically optimal noise rate of $\eta =
\Omega(\epsilon)$. For the adversarial label noise model, where the
distribution over the feature vectors is unchanged, and the overall probability
of a noisy label is constrained to be at most $\eta$, we also give a
polynomial-time algorithm for learning linear separators in $\Re^d$ under
isotropic log-concave distributions that can handle a noise rate of $\eta =
\Omega\left(\epsilon\right)$.
  We show that, in the active learning model, our algorithms achieve a label
complexity whose dependence on the error parameter $\epsilon$ is
polylogarithmic. This provides the first polynomial-time active learning
algorithm for learning linear separators in the presence of malicious noise or
adversarial label noise.


  As a dual of the Auslander transpose of modules, we introduce and study the
cotranspose of modules with respect to a semidualizing module $C$. Then using
it we introduce $n$-$C$-cotorsionfree modules, and show that
$n$-$C$-cotorsionfree modules possess many dual properties of $n$-torsionfree
modules. In particular, we show that $n$-$C$-cotorsionfree modules are useful
in characterizing the Bass class and investigating the approximation theory for
modules. Moreover, we study $n$-cotorsionfree modules over artin algebras and
answer negatively an open question of Huang and Huang posed in 2012.


  We present an updated catalogue of M31 globular clusters (GCs) based on
images from the Wide Field CAMera (WFCAM) on the UK Infrared Telescope and from
the Sloan Digital Sky Survey (SDSS). Our catalogue includes new,
self-consistent ugriz and K-band photometry of these clusters. We discuss the
difficulty of obtaining accurate photometry of clusters projected against M31
due to small scale background structure in the galaxy. We consider the effect
of this on the accuracy of our photometry and provide realistic photometric
error estimates. We investigate possible contamination in the current M31 GC
catalogues using the excellent spatial resolution of these WFCAM images
combined with the SDSS multicolour photometry. We identify a large population
of clusters with very blue colours. Most of these have recently been proposed
by other work as young clusters. We distinguish between these, and old
clusters, in the final classifications. Our final catalogue includes 416 old
clusters, 156 young clusters and 373 candidate clusters. We also investigate
the structure of M31's old GCs using previously published King model fits to
these WFCAM images. We demonstrate that the structure and colours of M31's old
GC system are similar to those of the Milky Way. One GC (B383) is found to be
significantly brighter in previous observations than observed here. We
investigate all of the previous photometry of this GC and suggest that this
variability appears to be genuine and short lived. We propose that the large
increase in its luminosity my have been due to a classical nova in the GC at
the time of the previous observations in 1989.


  In the case of minimal supersymmetric extension of the Standard Model (MSSM),
when the pseudoscalar Higgs boson mass is less than the supersymmetry energy
scale, the effective theory at the electroweak scale is a two-Higgs-doublet
model. We diagonalize the mass matrix of the general two-Higgs-doublet model,
expressing Higgs boson self-couplings in terms of two mixing angles and four
Higgs boson masses, and derive in a compact form the complete set of Feynman
rules, including quartic couplings in the Higgs sector, for the case of
CP-violating potential. Some processes of double and triple Higgs boson
production at a high-energy linear collider are calculated in the case of
mixing angles and scalar boson masses satisfying the MSSM constraints.


  We report a limit on the ultra-high-energy neutrino flux based on a
non-detection of radio pulses from neutrino-initiated particle cascades in the
Moon, in observations with the Parkes radio telescope undertaken as part of the
LUNASKA project. Due to the improved sensitivity of these observations, which
had an effective duration of 127 hours and a frequency range of 1.2-1.5 GHz,
this limit extends to lower neutrino energies than those from previous lunar
radio experiments, with a detection threshold below 10^20 eV. The calculation
of our limit allows for the possibility of lunar-origin pulses being
misidentified as local radio interference, and includes the effect of
small-scale lunar surface roughness. The targeting strategy of the observations
also allows us to place a directional limit on the neutrino flux from the
nearby radio galaxy Centaurus A.


  We propose a correspondence between vertex operator superalgebras and
families of sigma models in which the two structures are related by symmetry
properties and a certain reflection procedure. The existence of such a
correspondence is motivated by previous work on N=(4,4) supersymmetric
non-linear sigma models on K3 surfaces and on a vertex operator superalgebra
with Conway group symmetry. Here we present an example of the correspondence
for N=(4,4) supersymmetric non-linear sigma models on four-tori, and compare it
to the K3 case.


  The field of time series forecasting has garnered significant attention in
recent years, prompting the development of advanced models like TimeSieve,
which demonstrates impressive performance. However, an analysis reveals certain
unfaithfulness issues, including high sensitivity to random seeds and minute
input noise perturbations. Recognizing these challenges, we embark on a quest
to define the concept of \textbf{\underline{F}aithful
\underline{T}ime\underline{S}ieve \underline{(FTS)}}, a model that consistently
delivers reliable and robust predictions. To address these issues, we propose a
novel framework aimed at identifying and rectifying unfaithfulness in
TimeSieve. Our framework is designed to enhance the model's stability and
resilience, ensuring that its outputs are less susceptible to the
aforementioned factors. Experimentation validates the effectiveness of our
proposed framework, demonstrating improved faithfulness in the model's
behavior. Looking forward, we plan to expand our experimental scope to further
validate and optimize our algorithm, ensuring comprehensive faithfulness across
a wide range of scenarios. Ultimately, we aspire to make this framework can be
applied to enhance the faithfulness of not just TimeSieve but also other
state-of-the-art temporal methods, thereby contributing to the reliability and
robustness of temporal modeling as a whole.


  I rederive the Kerr/CFT correspondence without first taking the near-horizon
extremal Kerr limit. This method extends easily to nonextremal black holes, for
which the temperature and central charge behave poorly at the horizon but the
entropy remains finite. A computation yields one-half of the standard
Bekenstein-Hawking entropy, with hints that the other half may be related to a
conformal field theory at the inner horizon. I then present an alternative
approach, based on a stretched Killing horizon, in which the full entropy is
obtained and the temperature and central charge remain well-behaved even in the
nonextremal case.


  The social demand for email end-to-end encryption is barely supported by
mainstream service providers. Autocrypt is a new community-driven open
specification for e-mail encryption that attempts to respond to this demand. In
Autocrypt the encryption keys are attached directly to messages, and thus the
encryption can be implemented by email clients without any collaboration of the
providers. The decentralized nature of this in-band key distribution, however,
makes it prone to man-in-the-middle attacks and can leak the social graph of
users. To address this problem we introduce ClaimChain, a cryptographic
construction for privacy-preserving authentication of public keys. Users store
claims about their identities and keys, as well as their beliefs about others,
in ClaimChains. These chains form authenticated decentralized repositories that
enable users to prove the authenticity of both their keys and the keys of their
contacts. ClaimChains are encrypted, and therefore protect the stored
information, such as keys and contact identities, from prying eyes. At the same
time, ClaimChain implements mechanisms to provide strong non-equivocation
properties, discouraging malicious actors from distributing conflicting or
inauthentic claims. We implemented ClaimChain and we show that it offers
reasonable performance, low overhead, and authenticity guarantees.


  Generative model-based deep clustering frameworks excel in classifying
complex data, but are limited in handling dynamic and complex features because
they require prior knowledge of the number of clusters. In this paper, we
propose a nonparametric deep clustering framework that employs an infinite
mixture of Gaussians as a prior. Our framework utilizes a memoized online
variational inference method that enables the "birth" and "merge" moves of
clusters, allowing our framework to cluster data in a "dynamic-adaptive"
manner, without requiring prior knowledge of the number of features. We name
the framework as DIVA, a Dirichlet Process-based Incremental deep clustering
framework via Variational Auto-Encoder. Our framework, which outperforms
state-of-the-art baselines, exhibits superior performance in classifying
complex data with dynamically changing features, particularly in the case of
incremental features. We released our source code implementation at:
https://github.com/Ghiara/diva


  A single server retrial queueing system with two-classes of orbiting
customers, and general class dependent service times is considered. If an
arriving customer finds the server unavailable, it enters a virtual queue,
called the orbit, according to its type. The customers from the orbits retry
independently to access the server according to the constant retrial policy. We
derive the generating function of the stationary distribution of the number of
orbiting customers at service completion epochs in terms of the solution of a
Riemann boundary value problem. For the symmetrical system we also derived
explicit expressions for the expected delay in an orbit without solving a
boundary value problem. A simple numerical example is obtained to illustrate
the system's performance.


  We show how to construct the best linear unbiased predictor (BLUP) for the
continuation of a curve in a spline-function model. We assume that the entire
curve is drawn from some smooth random process and that the curve is given up
to some cut point. We demonstrate how to compute the BLUP efficiently.
Confidence bands for the BLUP are discussed. Finally, we apply the proposed
BLUP to real-world call center data. Specifically, we forecast the continuation
of both the call arrival counts and the workload process at the call center of
a commercial bank.


  For nearly a century since Ising model was proposed in 1925, it is agreed
that there is no phase transition with temperature in the one-dimensional based
on no global spontaneous magnetization in whole temperature region. In this
paper, the exact calculation of local spontaneous magnetization shows that a
diffuse phase transition with temperature occurs in one-dimensional Ising
model. In addition, although diffuse phase transition phenomenon is common in
the systems of heterogeneous-components and grains etc., there is no accurate
prediction of corresponding theoretical models so far, so the present works lay
the theoretical foundation of this kind of phase transition.


  We introduce new efficient integral representations and methods for
evaluation of pdfs, cpds and quantiles of stable distributions. For wide
regions in the parameter space, absolute errors of order $10^{-15}$ can be
achieved in 0.005-0.1 msec (Matlab implementation), even when the index of the
distribution is small or close to 1. For the calculation of quantiles in wide
regions in the tails using the Newton or bisection method, it suffices to
precompute several hundred values of the characteristic exponent at points of
an appropriate grid (conformal principal components) and use these values in
formulas for cpdf and pdf, which require a fairly small number of elementary
operations. The methods of the paper are applicable to other classes of
integrals, especially highly oscillatory ones, and are typically faster than
the popular methods.


  This study presents a semi-nonparametric Latent Class Choice Model (LCCM)
with a flexible class membership component. The proposed model formulates the
latent classes using mixture models as an alternative approach to the
traditional random utility specification with the aim of comparing the two
approaches on various measures including prediction accuracy and representation
of heterogeneity in the choice process. Mixture models are parametric
model-based clustering techniques that have been widely used in areas such as
machine learning, data mining and patter recognition for clustering and
classification problems. An Expectation-Maximization (EM) algorithm is derived
for the estimation of the proposed model. Using two different case studies on
travel mode choice behavior, the proposed model is compared to traditional
discrete choice models on the basis of parameter estimates' signs, value of
time, statistical goodness-of-fit measures, and cross-validation tests. Results
show that mixture models improve the overall performance of latent class choice
models by providing better out-of-sample prediction accuracy in addition to
better representations of heterogeneity without weakening the behavioral and
economic interpretability of the choice models.


  We contrast features of simple varying speed of light (VSL) cosmologies with
inflationary universe models. We present new features of VSL cosmologies and
show that they face problems explaining the cosmological isotropy problem. We
also find that if c falls fast enough to solve the flatness and horizon
problems then the quantum wavelengths of massive particle states and the radii
of primordial black holes can grow to exceed the scale of the particle horizon.
This may provide VSL cosmologies with a self-reproduction property. The
constraint of entropy increase is also discussed. The new problems described in
the this letter provide a set of bench tests for more sophisticated VSL
theories to pass.


  We describe a way to construct supergravity models with an arbitrary inflaton
potential V ({\phi}) and show that all other scalar fields in this class of
models can be stabilized at the inflationary trajectory by a proper choice of
the K\"ahler potential.


  During a search for coherent signals in the X-ray archival data of
XMM-Newton, we discovered a modulation at 1.2 s in 3XMM J004301.4+413017 (3X
J0043), a source lying in the direction of an external arm of M 31. This short
period indicates a neutron star (NS). Between 2000 and 2013, the position of 3X
J0043 was imaged by public XMM-Newton observations 35 times. The analysis of
these data allowed us to detect an orbital modulation at 1.27 d and study the
long-term properties of the source. The emission of the pulsar was rather hard
(most spectra are described by a power law with $\Gamma < 1$) and, assuming the
distance to M 31, the 0.3-10 keV luminosity was variable, from
$\sim$$3\times10^{37}$ to $2\times10^{38}$ erg s$^{-1}$. The analysis of
optical data shows that, while 3X J0043 is likely associated to a globular
cluster in M 31, a counterpart with $V\gtrsim22$ outside the cluster cannot be
excluded. Considering our findings, there are two main viable scenarios for 3X
J0043: a peculiar low-mass X-ray binary, similar to 4U 1822-37 or 4U 1626-67,
or an intermediate-mass X-ray binary resembling Her X-1. Regardless of the
exact nature of the system, 3X J0043 is the first accreting NS in M 31 in which
the spin period has been detected.


  The work aims to improve the existing fast load shedding algorithm for
industrial power system to increase performance, reliability, and scalability
for future expansions. The paper illustrates the development of a scalable
algorithm to compute the shedding matrix, and the test performed on a model of
the electric grid of an offshore platform. From this model it is possible to
study the impact on the transients of various parameters, such as spinning
reserve and delay time. Subsequently, the code is converted into Structured
Text and implemented on an ABB PLC. The scalability of the load shedding
algorithm is thus verified, confirming its performance with respect to the
computation of the shedding matrix and the usefulness of the dynamic
simulations during the design phase of the plant.


  The action--Maslov homomorphism $I\co\pi_1(\text{Ham}(X,\omega))\to\R$ is an
important tool for understanding the topology of the Hamiltonian group of
monotone symplectic manifolds. We explore conditions for the vanishing of this
homomorphism, and show that it is identically zero when the Seidel element has
finite order and the homology satisfies property $\mathcal{D}$ (a
generalization of having homology generated by divisor classes). We use these
results to show that $I=0$ for products of projective spaces and the
Grassmannian of $2$ planes in $\C^4$.


  Enhancement of strangeness production has since long been proposed as a
promising signal of quark-gluon plasma production. A convenient indicator for
it is the Wroblewski parameter which has been shown to be about a factor two
higher in heavy ion collisions. Using a method proposed by us earlier, we
obtained lattice QCD results for the Wroblewski parameter from our simulations
of QCD with two light quarks both below and above the chiral transition. Our
first principles based and parameter free result compare well with the A-A
data.


  Identifying user's identity is a key problem in many data mining
applications, such as product recommendation, customized content delivery and
criminal identification. Given a set of accounts from the same or different
social network platforms, user identification attempts to identify all accounts
belonging to the same person. A commonly used solution is to build the
relationship among different accounts by exploring their collective patterns,
e.g., user profile, writing style, similar comments. However, this kind of
method doesn't work well in many practical scenarios, since the information
posted explicitly by users may be false due to various reasons. In this paper,
we re-inspect the user identification problem from a novel perspective, i.e.,
identifying user's identity by matching his/her cameras. The underlying
assumption is that multiple accounts belonging to the same person contain the
same or similar camera fingerprint information. The proposed framework, called
User Camera Identification (UCI), is based on camera fingerprints, which takes
fully into account the problems of multiple cameras and reposting behaviors.


  This note is intended to be a friendly introduction to virtual classes. We
review virtual classes and we give a number of properties and applications. We
also include a new virtual push-forward theorem and many computations of
virtual classes in simple examples.


  We present an LLT-type formula for a general power of the nabla operator
applied to the Cauchy product for the modified Macdonald polynomials, and use
it to deduce a new proof of the generalized shuffle theorem describing
$\nabla^k e_n$, and the Elias-Hogancamp formula for $(\nabla^k p_1^n,e_n)$ as
corollaries. We give a direct proof of the theorem by verifying that the LLT
expansion satisfies the defining properties of $\nabla^k$, such as
triangularity in the dominance order, as well as a geometric proof based on a
method for counting bundles on $\mathbb{P}^1$ due to the second author. These
formulas are related to an affine paving of the type A unramified affine
Springer fiber studied by Goresky, Kottwitz, and MacPherson, and also to
Stanley's chromatic symmetric functions.


  We propose a model for games in which the players have shared access to a
blockchain that allows them to deploy smart contracts to act on their behalf.
This changes fundamental game-theoretic assumptions about rationality since a
contract can commit a player to act irrationally in specific subgames, making
credible otherwise non-credible threats. This is further complicated by
considering the interaction between multiple contracts which can reason about
each other. This changes the nature of the game in a nontrivial way as choosing
which contract to play can itself be considered a move in the game. Our model
generalizes known notions of equilibria, with a single contract being
equivalent to a Stackelberg equilibrium, and two contracts being equivalent to
a reverse Stackelberg equilibrium. We prove a number of bounds on the
complexity of computing SPE in such games with smart contracts. We show that
computing an SPE is $\textsf{PSPACE}$-hard in the general case. Specifically,
in games with $k$ contracts, we show that computing an SPE is
$\Sigma_k^\textsf{P}$-hard for games of imperfect information. We show that
computing an SPE remains $\textsf{PSPACE}$-hard in games of perfect information
if we allow for an unbounded number of contracts. We give an algorithm for
computing an SPE in two-contract games of perfect information that runs in time
$O(m\ell)$ where $m$ is the size of the game tree and $\ell$ is the number of
terminal nodes. Finally, we conjecture the problem to be $\textsf{NP}$-complete
for three contracts.


  In the present work we consider differential rings of the form $(\mathcal
B,D)$ where $\mathcal B$ is a Danielewski surface and $D$ is a locally
nilpotent derivation on $\mathcal B$. Influenced by several recent works, we
describe the isotropy group of a locally nilpotent derivation, $D$, on
Danielewski surfaces, in the cases $xy = \varphi(z)$, $x^ny=\varphi(Z)$, and
$f(x)x = \varphi(z)$.


  We report the discovery of HN Lib b, a sub-Neptunian mass planet orbiting the
nearby ($d \approx$ = 6.25 pc) M4.0 V star HN Lib detected by our CARMENES
radial-velocity (RV) survey. We determined a planetary minimum mass of
$M_\text{b}\sin i = $ 5.46 $\pm$ 0.75 $\text{M}_\oplus$ and an orbital period
of $P_\text{b} = $ 36.116 $\pm$ 0.029 d, using $\sim$5 yr of CARMENES data, as
well as archival RVs from HARPS and HIRES spanning more than 13 years. The flux
received by the planet equals half the instellation on Earth, which places it
in the middle of the conservative habitable zone (HZ) of its host star. The RV
data show evidence for another planet candidate with $M_\text{[c]}\sin i = $
9.7 $\pm$ 1.9 $\text{M}_\oplus$ and $P_\text{[c]} = $ 113.46 $\pm$ 0.20 d. The
long-term stability of the signal and the fact that the best model for our data
is a two-planet model with an independent activity component stand as strong
arguments for establishing a planetary origin. However, we cannot rule out
stellar activity due to its proximity to the rotation period of HN Lib, which
we measured using CARMENES activity indicators and photometric data from a
ground-based multi-site campaign as well as archival data. The discovery adds
HN Lib b to the shortlist of super-Earth planets in the habitable zone of M
dwarfs, but HN Lib [c] probably cannot be inhabited because, if confirmed, it
would most likely be an icy giant.


  The three-cornered hat method and the Groslambert Covariance are very often
used to estimate the frequency stability of each individual oscillator in a set
of three oscillators by comparing them in pairs. However, no rigorous method to
assess the uncertainties over their estimates has yet been formulated. In order
to overcome this lack, this paper will first study the direct problem, i.e. the
calculation of the statistics of the clock stability estimates by assuming
known values of the true clock stabilities and then will propose a first
attempt to solve the inverse problem, i.e. the assessment of a confidence
interval over the true clock stabilities by assuming known values of the clock
stability estimates. We show that this method is reliable from 5 Equivalent
Degrees of Freedom (EDF) and beyond.


  The correlation between the mass of supermassive black holes (SMBHs;
$\mathcal{M}_{\rm BH}$) and their host galaxies ($\mathcal{M}_\star$) in the
reionization epoch provides valuable constraints on their early growth.
High-redshift quasars typically have a $\mathcal{M}_{\rm
BH}$/$\mathcal{M}_\star$ ratio significantly elevated in comparison to the
local value. However, the degree to which this apparent offset is driven by
observational biases is unclear for the most distant quasars. To address this
issue, we model the sample selection and measurement biases for a compilation
of 20 quasars at $z\sim6$ with host properties based on ALMA observations. We
find that the observed distribution of quasars in the $\mathcal{M}_{\rm BH} -
\mathcal{M}_\star$ plane can be reproduced by assuming that the underlying SMBH
population at $z\sim6$ follows the relationship in the local universe. However,
a positive or even a negative evolution in $\mathcal{M}_{\rm
BH}$/$\mathcal{M}_\star$ can also explain the data, depending on whether the
intrinsic scatter evolves and the strength of various systematic uncertainties.
To break these degeneracies, an improvement in the accuracy of mass
measurements and an expansion of the current sample to lower $\mathcal{M}_{\rm
BH}$ limits are needed. Furthermore, assuming a radiative efficiency of 0.1 and
quasar duty cycles estimated from the active SMBH fraction, significant
outliers in $\mathcal{M}_{\rm BH}$/$\mathcal{M}_\star$ tend to move toward the
local relation given their instantaneous BH growth rate and star formation
rate. This may provide evidence for a self-regulated SMBH-galaxy coevolution
scenario that is in place at $z\sim6$, with AGN feedback being a possible
driver.


  Einstein, Podolsky and Rosen (EPR) pointed out that the quantum-mechanical
description of "physical reality" implied an unphysical, instantaneous action
between distant measurements. To avoid such an action at a distance, EPR
concluded that Quantum Mechanics had to be incomplete. However, its extensions
involving additional "hidden variables", allowing for the recovery of
determinism and locality, have been disproved experimentally (Bell's theorem).
Here, I present an opposite solution of the paradox based on the greater
indeterminism of the modern Quantum Field Theory (QFT) description of Particle
Physics, that prevents the preparation of any state having a definite number of
particles. The resulting uncertainty in photons radiation has interesting
consequences in Quantum Information Theory (e.g. cryptography and
teleportation). Moreover, since it allows for less elements of EPR physical
reality than the old non-relativistic Quantum Mechanics, QFT satisfies the EPR
condition of completeness without the need of hidden variables. The residual
physical reality does never violate locality, thus the unique objective proof
of "quantum nonlocality" is removed in an interpretation-independent way. On
the other hand, the supposed nonlocality of the EPR correlations turns out to
be a problem of the interpretation of the theory. If we do not rely on hidden
variables or new physics beyond QFT, the unique viable interpretation is a
minimal statistical one, that preserves locality and Lorentz symmetry.


  Given a representation V of a group G, there are two natural ways of defining
a representation of the group algebra k[G] in the external power V^{\wedge m}.
The set L(V) of elements of k[G] for which these two ways give the same result
is a Lie algebra and a representation of G. For the case when G is a symmetric
group and V = C^n, a permutation representation, these spaces L(C^n) are
naturally embedded into one another. We describe L(C^n) for small n and
formulate some questions and conjectures.
  This is a note on research in progress.


  We experimentally demonstrate simultaneous spatial and temporal compression
in the propagation of light pulses in multimode nonlinear optical fibers. We
reveal that the spatial beam self-cleaning recently discovered in graded-index
multimode fibers is accompanied by significant temporal reshaping and up to
four-fold shortening of the injected sub-nanosecond laser pulses. Since the
nonlinear coupling among the modes strongly depends on the instantaneous power,
we explore the entire range of the nonlinear dynamics with a single optical
pulse, where the optical power is continuously varied across the pulse profile.


  Time dependent perturbations of states in the holographic dual of a 3+1
dimensional confining theory are considered. The perturbations are induced by
varying the coupling to the theory's most relevant operator. The dual
gravitational theory belongs to a class of Einstein-dilaton theories which
exhibit a mass gap at zero temperature and a first order deconfining phase
transition at finite temperature. The perturbation is realized in various
thermal bulk solutions by specifying time dependent boundary conditions on the
scalar, and we solve the fully backreacted Einstein-dilaton equations of motion
subject to these boundary conditions. We compute the characteristic time scale
of many thermalization processes, noting that in every case we examine, this
time scale is determined by the imaginary part of the lowest lying quasi-normal
mode of the final state black brane. We quantify the dependence of this final
state on parameters of the quench, and construct a dynamical phase diagram.
Further support for a universal scaling regime in the abrupt quench limit is
provided.


  Personalized image aesthetics assessment (PIAA) is challenging due to its
highly subjective nature. People's aesthetic tastes depend on diversified
factors, including image characteristics and subject characters. The existing
PIAA databases are limited in terms of annotation diversity, especially the
subject aspect, which can no longer meet the increasing demands of PIAA
research. To solve the dilemma, we conduct so far, the most comprehensive
subjective study of personalized image aesthetics and introduce a new
Personalized image Aesthetics database with Rich Attributes (PARA), which
consists of 31,220 images with annotations by 438 subjects. PARA features
wealthy annotations, including 9 image-oriented objective attributes and 4
human-oriented subjective attributes. In addition, desensitized subject
information, such as personality traits, is also provided to support study of
PIAA and user portraits. A comprehensive analysis of the annotation data is
provided and statistic study indicates that the aesthetic preferences can be
mirrored by proposed subjective attributes. We also propose a conditional PIAA
model by utilizing subject information as conditional prior. Experimental
results indicate that the conditional PIAA model can outperform the control
group, which is also the first attempt to demonstrate how image aesthetics and
subject characters interact to produce the intricate personalized tastes on
image aesthetics. We believe the database and the associated analysis would be
useful for conducting next-generation PIAA study. The project page of PARA can
be found at: https://cv-datasets.institutecv.com/#/data-sets.


  In this paper we briefly discuss the problem of the origin of Ultra High
Energy Cosmic Rays in the framework of Top-Down models. We show that, for high
energy of decays and in a wide range of spectra of injected protons, their
extragalactic flux is consistent with the observed fluxes of cosmic rays in the
energy range 0.1 E_{GZK}< E < 10E_{GZK}. For suitable energy and spectra of
injected protons, the contribution of galactic sources is moderate, in this
energy range, but it dominates at smaller and larger energies. In such models
we can expect that at these energies the anisotropy of cosmic rays distribution
over sky will be especially small.
  Some possible manifestations of decays of super massive particles such as,
for example, primordial black holes with masses M_{pbh} ~ 10^{-5} g, are
considered. In particular, we show that partial conversion of energy released
during these decays at redshifts z ~ 1000 to Ly-alpha photons can delay the
hydrogen recombination and distort the spectrum of fluctuations of the cosmic
microwave background radiation.


  Here we extend the exploration of significantly super-Chandrasekhar
magnetised white dwarfs by numerically computing axisymmetric stationary
equilibria of differentially rotating magnetised polytropic compact stars in
general relativity (GR), within the ideal magnetohydrodynamic regime. We use a
general relativistic magnetohydrodynamic (GRMHD) framework that describes
rotating and magnetised axisymmetric white dwarfs, choosing appropriate
rotation laws and magnetic field profiles (toroidal and poloidal). The
numerical procedure for finding solutions in this framework uses the 3+1
formalism of numerical relativity, implemented in the open source XNS code. We
construct equilibrium sequences by varying different physical quantities in
turn, and highlight the plausible existence of super-Chandrasekhar white
dwarfs, with masses in the range of 2-3 solar mass, with central (deep
interior) magnetic fields of the order of $10^{14}$ Gauss and differential
rotation with surface time periods of about 1-10 seconds. We note that such
white dwarfs are candidates for the progenitors of peculiar, overluminous type
Ia supernovae, to which observational evidence ascribes mass in the range
2.1-2.8 solar mass. We also present some interesting results related to the
structure of such white dwarfs, especially the existence of polar hollows in
special cases.


  The afterglow of GRB$\,$170817A/GW$\,$170817 was very unusual, slowly rising
as $F_\nu\propto{}t_{\rm{}obs}^{0.8}\nu^{-0.6}$, peaking at
$t_{\rm{obs,pk}}\sim\,150\;$days, and sharply decaying as
$\sim{}t_{\rm{}obs}^{-2.2}$. VLBI observations revealed an unresolved radio
afterglow image whose flux centroid moved superluminally with
$v_{\rm{app}}\approx4c$, clearly indicating that the afterglow was dominated by
a relativistic jet's compact core. Different jet angular structures explained
the afterglow lightcurves: Gaussian and steep power-law profiles with narrow
core angles $\theta_c\lesssim5^\circ$ and larger viewing angles
$\theta_{\rm{}obs}/\theta_c\sim3-5$. However, a top-hat jet (with sharp edges
at $\theta=\theta_0$) was ruled out since it appeared to produce an early flux
rise much steeper than observed. Using 2D relativistic hydrodynamic simulations
we show that the initial steep flux rise is an artifact caused by the
simulation's finite start time, $t_0$, missing its flux contributions from
$t<t_0$ and sometimes "compensated" using an analytic top-hat jet. While an
initially top-hat jet is not very physical, such simulations are particularly
useful at $t_{\rm{}obs}\gtrsim{}t_{\rm{obs,pk}}$ when the afterglow emission is
dominated by the jet's core and becomes insensitive to its exact initial
angular profile if it drops off sharply outside of the core. We demonstrate
that an initially top-hat jet fits GW$\,$170817/GRB$\,$170817A's afterglow
lightcurves and flux centroid motion at $t_{\rm{}obs}\gtrsim{}t_{\rm{obs,pk}}$,
for $\theta_{\rm{}obs}/\theta_0\approx3$ and may also fit the earlier
lightcurves for $\Gamma_0=\Gamma(t_0)\gtrsim10^{2.5}$. We analytically express
the degeneracies between the model parameters, and find a minimal jet energy of
$E_{\rm{}min}\approx5.3\times10^{48}\;$erg and circum-burst medium density of
$n_{\min}\approx5.3\times10^{-6}~{\rm cm}^{-3}$.


  The work is devoted to a probably new connection between deformed Virasoro
algebra and quantum $\widehat{\mathfrak{sl}}_2$. We give an explicit
realization of Virasoro current via vertex operators of level 1 integrable
representation of $\widehat{\mathfrak{sl}}_2$. The same is done for a twisted
version of deformed Virasoro algebra.


  A superconducting thin film with uniform properties is the key to realize
nanowire superconducting single-photon detectors (SSPDs) with high performance
and high yield. To investigate the uniformity of NbN films, we introduce and
characterize simple detectors consisting of short nanowires with length ranging
from 100nm to 15{\mu}m. Our nanowires, contrary to meander SSPDs, allow probing
the homogeneity of NbN at the nanoscale. Experimental results, endorsed by a
microscopic model, show the strongly inhomogeneous nature of NbN films on the
sub-100nm scale.


  We discuss the algebra and the interpretation of the anomalous Zeeman effect
and the spin-orbit coupling within the Dirac theory. Whereas the algebra for
the anomalous Zeeman effect is impeccable and therefore in excellent agreement
with experiment, the physical interpretation of that algebra uses images that
are based on macroscopic intuition but do not correspond to the meaning of this
algebra. The interpretation violates the Lorentz symmetry. We give an
alternative intuitive description of the meaning of this effect, which respects
the symmetry and is exact. It can be summarized by stating that a magnetic
field makes any charged particle spin. We show also that the traditional
discussion about magnetic monopoles confuses two issues, viz. the symmetry of
the Maxwell equations and the quantization of charge. These two issues define
each a different concept of magnetic monopole. They cannot be merged together
into a unique all-encompassing issue. We also generalize the minimal
substitution for a charged particle, and provide some intuition for the
magnetic vector potential. We finally explore the algebra of the spin-orbit
coupling, which turns out to be badly wrong. The traditional theory that is
claimed to reproduce the Thomas half is based on a number of errors. An
error-free application of the Dirac theory cannot account for the Thomas
precession, because it only accounts for the instantaneous local boosts, not
for the rotational component of the Lorentz transformation. This runs contrary
to established beliefs, but Thomas precession can be understood in terms of the
Berry phase on a path through the velocity space of the Lorentz group manifold.
These results clearly reveal the limitations of the prevailing working
philosophy to "shut up and calculate".


  In this work we study the cosmological simulations as a tool to understand
the formation of large-scale structure of the universe, for this, we show the
equivalence of Newtonian cosmology with Poisson gauge and we study the solution
of the Einstein's field equations for this gauge. The simulations are essential
for taking account the results of the cosmological model, allowing to compare
the results with observational data. The N-bodies simulations have been used
from systems of few bodies to the evolution and formation of nonlinear large
scale structure as filaments and galactic halos.


  The double Higgs production in the models with isospin-triplet scalars is
studied. It is shown that in the see-saw type II model the mode with an
intermediate heavy scalar, $pp\to H+X\to 2h+X$, may have the cross section
which is compatible with that in the Standard Model. In the Georgi-Machacek
model this cross section could be much larger than in SM since the vacuum
expectation value of the triplet can be large.


  When compared to blocking concurrency, non-blocking concurrency can provide
higher performance in parallel shared-memory contexts, especially in high
contention scenarios. This paper proposes FLeeC, an application-level cache
system based on Memcached, which leverages re-designed data structures and
non-blocking (or lock-free) concurrency to improve performance by allowing any
number of concurrent writes and reads to its main data structures, even in
high-contention scenarios. We discuss and evaluate its new algorithms, which
allow a lock-free eviction policy and lock-free fast lookups. FLeeC can be used
as a plug-in replacement for the original Memcached, and its new algorithms and
concurrency control strategies result in considerable performance improvements
(up to 6x).


  A graph $G$ is terminal-pairable with respect to a demand multigraph $D$ on
the same vertex set as $G$, if there exists edge-disjoint paths joining the end
vertices of every demand edge of $D$. In this short note, we improve the upper
bound on the largest $\Delta(n)$ with the property that the complete graph on
$n$ vertices is terminal-pairable with respect to any demand multigraph of
maximum degree at most $\Delta(n)$. This disproves a conjecture originally
stated by Csaba, Faudree, Gy\'arf\'as, Lehel and Schelp.


  This paper can be an overview on solutions in Wronskian/Casoratian form to
soliton equations with KdV-type bilinear forms. We first investigate properties
of matrices commuting with a Jordan block, by which we derive explicit general
solutions to equations satisfied by Wronskian/Casoratian entry vectors, which
we call condition equations. These solutions are given according to the
coefficient matrix in the condition equations taking diagonal or Jordan block
form. Limit relations between these different solutions are described. We take
the KdV equation and the Toda lattice to serve as two examples for solutions in
Wronskian form and Casoratian form, respectively. We also discuss Wronskian
solutions for the KP equation. Finally, we formulate the Wronskian technique as
four steps.


  An adjoint multiplet of screened monopoles forming a dilute gas fits very
well lattice data at high $T$. There are now seven ratios for k-strings
available, checking within a few percent with the prediction $k(N-k)$. The
diluteness turns out to be a small parameter for SU(N) gluodynamics, to a good
approximation ($1\over N^2$) independent of the value of $N$, and also
independent of $T$. This suggests a dilute Bose-Einstein gas, with a BE
transition at the deconfinement temperature $T_c$.


  Asymptotically flat black holes in $2+1$ dimensions are a rarity. We study
the recently found black flower solutions (asymptotically flat black holes with
deformed horizons), static black holes, rotating black holes and the dynamical
black flowers (black holes with radiative gravitons ) of the purely quadratic
version of new massive gravity. We show how they appear in this theory and we
also show that they are also solutions to the infinite order extended version
of the new massive gravity, that is the Born-Infeld extension of new massive
gravity with an amputated Einsteinian piece. The same metrics also solve the
topologically extended versions of these theories, with modified conserved
charges and the thermodynamical quantities, such as the Wald entropy. Besides
these we find new conformally flat radiating type solutions to these extended
gravity models. We also show that these metrics do not arise in Einstein's
gravity coupled to physical perfect fluids.


  We propose a novel mechanism to suppress the isocurvature perturbations of
the QCD axion. The point is that the QCD interactions become strong at an
intermediate or high energy scale in the very early Universe, if the Higgs
field has a sufficiently large expectation value. The effective QCD scale can
be even higher in the presence of extra colored particles. We show that the QCD
axion then becomes so heavy during inflation that its isocurvature
perturbations are significantly suppressed, thereby relaxing the constraint on
the inflation scale.


  In this survey, we offer an extensive overview of the Online Influence
Maximization (IM) problem by covering both theoretical aspects and practical
applications. For the integrity of the article and because the online algorithm
takes an offline oracle as a subroutine, we first make a clear definition of
the Offline IM problem and summarize those commonly used Offline IM algorithms,
which include traditional approximation or heuristic algorithms and ML-based
algorithms. Then, we give a standard definition of the Online IM problem and a
basic Combinatorial Multi-Armed Bandit (CMAB) framework, CMAB-T. Here, we
summarize three types of feedback in the CMAB model and discuss in detail how
to study the Online IM problem based on the CMAB-T model. This paves the way
for solving the Online IM problem by using online learning methods.
Furthermore, we have covered almost all Online IM algorithms up to now,
focusing on characteristics and theoretical guarantees of online algorithms for
different feedback types. Here, we elaborately explain their working principle
and how to obtain regret bounds. Besides, we also collect plenty of innovative
ideas about problem definition and algorithm designs and pioneering works for
variants of the Online IM problem and their corresponding algorithms. Finally,
we encapsulate current challenges and outline prospective research directions
from four distinct perspectives.


  We present a novel algorithm for anomaly detection on very large datasets and
data streams. The method, named EXPected Similarity Estimation (EXPoSE), is
kernel-based and able to efficiently compute the similarity between new data
points and the distribution of regular data. The estimator is formulated as an
inner product with a reproducing kernel Hilbert space embedding and makes no
assumption about the type or shape of the underlying data distribution. We show
that offline (batch) learning with EXPoSE can be done in linear time and online
(incremental) learning takes constant time per instance and model update.
Furthermore, EXPoSE can make predictions in constant time, while it requires
only constant memory. In addition, we propose different methodologies for
concept drift adaptation on evolving data streams. On several real datasets we
demonstrate that our approach can compete with state of the art algorithms for
anomaly detection while being an order of magnitude faster than most other
approaches.


  The motion of a particle under the influence of a dynamical disorder is
described by the DLD model. One motivation is to understand the motion of an
electron inside a metal; Another is to understand quantal Brownian motion. The
overview is based on a research report for 1996-1998.


  Cancer progresses with a change in the structure of the gene network in
normal cells. We define a measure of organizational hierarchy in gene networks
of affected cells in adult acute myeloid leukemia (AML) patients. With a
retrospective cohort analysis based on the gene expression profiles of 116
acute myeloid leukemia patients, we find that the likelihood of future cancer
relapse and the level of clinical risk are directly correlated with the level
of organization in the cancer related gene network. We also explore the
variation of the level of organization in the gene network with cancer
progression. We find that this variation is non-monotonic, which implies the
fitness landscape in the evolution of AML cancer cells is nontrivial. We
further find that the hierarchy in gene expression at the time of diagnosis may
be a useful biomarker in AML prognosis.


  Models that can predict the occurrence of events ahead of time with low
false-alarm rates are critical to the acceptance of decision support systems in
the medical community. This challenging task is typically treated as a simple
binary classification, ignoring temporal dependencies between samples, whereas
we propose to exploit this structure. We first introduce a common theoretical
framework unifying dynamic survival analysis and early event prediction.
Following an analysis of objectives from both fields, we propose Temporal Label
Smoothing (TLS), a simpler, yet best-performing method that preserves
prediction monotonicity over time. By focusing the objective on areas with a
stronger predictive signal, TLS improves performance over all baselines on two
large-scale benchmark tasks. Gains are particularly notable along clinically
relevant measures, such as event recall at low false-alarm rates. TLS reduces
the number of missed events by up to a factor of two over previously used
approaches in early event prediction.


  Using one of the deepest datasets available, we determine that the red
sequence of the massive cluster MS1054-0321 at z=0.831 is well populated at all
studied magnitudes, showing no deficit of faint (down to M^*+3.5) red galaxies:
the faint end of the colour-magnitude relation is neither empty nor
underpopulated. The effect is quantified by the computation of the luminosity
function (LF) of red galaxies. We found a flat slope, showing that the
abundance of red galaxies is similar at faint and at intermediate magnitudes.
Comparison with present-day and z~0.4 LFs suggests that the slope of the LF is
not changed, within the errors, between z=0.831 and z=0. Therefore, the
analysis of the LF shows no evidence for a decreasing (with magnitude or
redshift) number of faint red galaxies. The presence of faint red galaxies in
high redshift clusters disfavours scenarios where the evolution of red galaxies
is mass-dependent, because the mass dependency should differentially
depauperate the red sequence, while the MS1054-0321 colour-magnitude relation
is populated as in nearby clusters and as in z~0.4 clusters. The presence of
abundant faint red galaxies in the high redshift cluster MS1054-0321 restricts
the room for allocating descendants of Butcher-Oemler galaxies, because they
should change the faint end slope of the LF of red galaxies, while instead the
same faint end slopes are observed in MS1054-0321, at z~0 and at z~0.4. In the
rich MS1054-0321 cluster, the colour-magnitude relation seems to be fully in
place at z=0.831 and therefore red galaxies of all magnitudes were wholly
assembled at higher redshift.


  Despite the extreme diversity of T cell repertoires, many identical T-cell
receptor (TCR) sequences are found in a large number of individual mice and
humans. These widely-shared sequences, often referred to as `public', have been
suggested to be over-represented due to their potential immune functionality or
their ease of generation by V(D)J recombination. Here we show that even for
large cohorts the observed degree of sharing of TCR sequences between
individuals is well predicted by a model accounting for by the known
quantitative statistical biases in the generation process, together with a
simple model of thymic selection. Whether a sequence is shared by many
individuals is predicted to depend on the number of queried individuals and the
sampling depth, as well as on the sequence itself, in agreement with the data.
We introduce the degree of publicness conditional on the queried cohort size
and the size of the sampled repertoires. Based on these observations we propose
a public/private sequence classifier, `PUBLIC' (Public Universal Binary
Likelihood Inference Classifier), based on the generation probability, which
performs very well even for small cohort sizes.


  The development of summarization research has been significantly hampered by
the costly acquisition of reference summaries. This paper proposes an effective
way to automatically collect large scales of news-related multi-document
summaries with reference to social media's reactions. We utilize two types of
social labels in tweets, i.e., hashtags and hyper-links. Hashtags are used to
cluster documents into different topic sets. Also, a tweet with a hyper-link
often highlights certain key points of the corresponding document. We
synthesize a linked document cluster to form a reference summary which can
cover most key points. To this aim, we adopt the ROUGE metrics to measure the
coverage ratio, and develop an Integer Linear Programming solution to discover
the sentence set reaching the upper bound of ROUGE. Since we allow summary
sentences to be selected from both documents and high-quality tweets, the
generated reference summaries could be abstractive. Both informativeness and
readability of the collected summaries are verified by manual judgment. In
addition, we train a Support Vector Regression summarizer on DUC generic
multi-document summarization benchmarks. With the collected data as extra
training resource, the performance of the summarizer improves a lot on all the
test sets. We release this dataset for further research.


  The quality of sleep has a deep impact on people's physical and mental
health. People with insufficient sleep are more likely to report physical and
mental distress, activity limitation, anxiety, and pain. Moreover, in the past
few years, there has been an explosion of applications and devices for activity
monitoring and health tracking. Signals collected from these wearable devices
can be used to study and improve sleep quality. In this paper, we utilize the
relationship between physical activity and sleep quality to find ways of
assisting people improve their sleep using machine learning techniques. People
usually have several behavior modes that their bio-functions can be divided
into. Performing time series clustering on activity data, we find cluster
centers that would correlate to the most evident behavior modes for a specific
subject. Activity recipes are then generated for good sleep quality for each
behavior mode within each cluster. These activity recipes are supplied to an
activity recommendation engine for suggesting a mix of relaxed to intense
activities to subjects during their daily routines. The recommendations are
further personalized based on the subjects' lifestyle constraints, i.e. their
age, gender, body mass index (BMI), resting heart rate, etc, with the objective
of the recommendation being the improvement of that night's quality of sleep.
This would in turn serve a longer-term health objective, like lowering heart
rate, improving the overall quality of sleep, etc.


  This paper concerns the generation and evolution of the cosmological
(large-scale $\sim Mpc$) magnetic fields in an inflationary universe. The
universe during inflation is represented by de Sitter space-time. We started
with the Maxwell equations in spatially flat Friedmann-Robertson-Walker (FRW)
Cosmologies. Then we calculated the wave equations of the magnetic field and
electric field for the evolution. We consider the input current that was
produced from a massless charged scalar complex field. This field minimally
coupled to both gravity and the electromagnetic fields. The Lagrangian for
massless scalar electrodynamics is then
$L=\sqrt{-g}(D_\mu\phi(D^\mu\phi)^*-{1/4}F_{\mu\nu}F^{\mu\nu})$ . The complex
scalar field couples to electromagnetism through the usual gauge covariant
derivative $D_\mu=\partial_\mu-ieA_\mu$ . After the quantum field theoretical
deduction for the current, we put it back into the wave equation of the
magnetic field.
  After solving this wave equation, our result is $a^2B\sim
\frac{eH}{\sqrt{2}k^2}\mid\sin\sqrt{2}k\eta\mid$ . At the time $\eta_{RH}$ we
have $B_{RH}=\frac{e}{k_{phys}}$. This may imply that the breaking of the
conformal invariance due to the minimal coupling of a massless charged scalar
complex field to both gravitational and electromagnetic fields is not
sufficient for the production of seed galactic magnetic fields during
inflation. But since we are interested in the large-scale cosmological magnetic
field, this could be still a candidate, because of the $1/k$ factor.


  Visual reasoning requires multimodal perception and commonsense cognition of
the world. Recently, multiple vision-language models (VLMs) have been proposed
with excellent commonsense reasoning ability in various domains. However, how
to harness the collective power of these complementary VLMs is rarely explored.
Existing methods like ensemble still struggle to aggregate these models with
the desired higher-order communications. In this work, we propose Cola, a novel
paradigm that coordinates multiple VLMs for visual reasoning. Our key insight
is that a large language model (LLM) can efficiently coordinate multiple VLMs
by facilitating natural language communication that leverages their distinct
and complementary capabilities. Extensive experiments demonstrate that our
instruction tuning variant, Cola-FT, achieves state-of-the-art performance on
visual question answering (VQA), outside knowledge VQA, visual entailment, and
visual spatial reasoning tasks. Moreover, we show that our in-context learning
variant, Cola-Zero, exhibits competitive performance in zero and few-shot
settings, without finetuning. Through systematic ablation studies and
visualizations, we validate that a coordinator LLM indeed comprehends the
instruction prompts as well as the separate functionalities of VLMs; it then
coordinates them to enable impressive visual reasoning capabilities.


  Large language models have made significant progress in various language
tasks, yet they still struggle with complex mathematics. In this paper, we
propose ToRA a series of Tool-integrated Reasoning Agents designed to solve
challenging mathematical problems by seamlessly integrating natural language
reasoning with the utilization of external tools (e.g., computation libraries
and symbolic solvers), thereby amalgamating the analytical prowess of language
and the computational efficiency of tools. To train ToRA, we curate interactive
tool-use trajectories on mathematical datasets, apply imitation learning on the
annotations, and propose output space shaping to further refine models'
reasoning behavior. As a result, ToRA models significantly outperform
open-source models on 10 mathematical reasoning datasets across all scales with
13%-19% absolute improvements on average. Notably, ToRA-7B reaches 44.6% on the
competition-level dataset MATH, surpassing the best open-source model
WizardMath-70B by 22% absolute. ToRA-Code-34B is also the first open-source
model that achieves an accuracy exceeding 50% on MATH, which significantly
outperforms GPT-4's CoT result, and is competitive with GPT-4 solving problems
with programs. Additionally, we conduct a comprehensive analysis of the
benefits and remaining challenges of tool interaction for mathematical
reasoning, providing valuable insights for future research.


  We present some simple models to determine whether or not the accretion of
cold dark matter by supermassive black holes is astrophysically important.
Contrary to some claims in the literature, we show that supermassive black
holes cannot significantly alter a power law density cusp via accretion,
whether during mergers or in the steady state.


  F-signature is an important numeric invariant of singularities in positive
characteristic that can be used to detect strong F-regularity. One would like
to have a variant that rather detects F-rationality, and there are two theories
that aim to fill this gap: F-rational signature of Hochster and Yao and dual
F-signature of Sannai. Unfortunately, several important properties of the
original F-signature are unknown for these invariants.
  We give a modification of the Hochster-Yao definition that agrees with
Sannai's dual F-signature and push further the united theory to achieve a
complete generalization of F-signature.


  Manually labeling datasets with object masks is extremely time consuming. In
this work, we follow the idea of Polygon-RNN to produce polygonal annotations
of objects interactively using humans-in-the-loop. We introduce several
important improvements to the model: 1) we design a new CNN encoder
architecture, 2) show how to effectively train the model with Reinforcement
Learning, and 3) significantly increase the output resolution using a Graph
Neural Network, allowing the model to accurately annotate high-resolution
objects in images. Extensive evaluation on the Cityscapes dataset shows that
our model, which we refer to as Polygon-RNN++, significantly outperforms the
original model in both automatic (10% absolute and 16% relative improvement in
mean IoU) and interactive modes (requiring 50% fewer clicks by annotators). We
further analyze the cross-domain scenario in which our model is trained on one
dataset, and used out of the box on datasets from varying domains. The results
show that Polygon-RNN++ exhibits powerful generalization capabilities,
achieving significant improvements over existing pixel-wise methods. Using
simple online fine-tuning we further achieve a high reduction in annotation
time for new datasets, moving a step closer towards an interactive annotation
tool to be used in practice.


  Transient recurring phenomena are ubiquitous in many scientific fields like
neuroscience and meteorology. Time inhomogenous Vector Autoregressive Models
(VAR) may be used to characterize peri-event system dynamics associated with
such phenomena, and can be learned by exploiting multi-dimensional data
gathering samples of the evolution of the system in multiple time windows
comprising, each associated with one occurrence of the transient phenomenon,
that we will call "trial". However, optimal VAR model order selection methods,
commonly relying on the Akaike or Bayesian Information Criteria (AIC/BIC), are
typically not designed for multi-trial data. Here we derive the BIC methods for
multi-trial ensemble data which are gathered after the detection of the events.
We show using simulated bivariate AR models that the multi-trial BIC is able to
recover the real model order. We also demonstrate with simulated transient
events and real data that the multi-trial BIC is able to estimate a
sufficiently small model order for dynamic system modeling.


  We give a geometric derivation of SLE($\kappa,\rho$) in terms of conformally
invariant random growing subsets of polygons. We relate the parameters $\rho_j$
to the exterior angles of the polygons. We also show that SLE($\kappa,\rho$)
can be generated by a metric Brownian motion, where metric and Brownian motion
are coupled and the metric ist the pull-back metric of the Euclidean metric of
an evolving polygon.


  Deep learning-based human activity recognition (HAR) methods have shown great
promise in the applications of smart healthcare systems and wireless body
sensor network (BSN). Despite their demonstrated performance in laboratory
settings, the real-world implementation of such methods is still hindered by
the cross-subject issue when adapting to new users. To solve this issue, we
propose ActiveSelfHAR, a framework that combines active learning's benefit of
sparsely acquiring data with actual labels and self- training's benefit of
effectively utilizing unlabeled data to enable the deep model to adapt to the
target domain, i.e., the new users. In this framework, the model trained in the
last iteration or the source domain is first utilized to generate pseudo labels
of the target-domain samples and construct a self-training set based on the
confidence score. Second, we propose to use the spatio-temporal relationships
among the samples in the non-self-training set to augment the core set selected
by active learning. Finally, we combine the self-training set and the augmented
core set to fine-tune the model. We demonstrate our method by comparing it with
state-of-the-art methods on two IMU-based datasets and an EMG-based dataset.
Our method presents similar HAR accuracies with the upper bound, i.e. fully
supervised fine-tuning with less than 1\% labeled data of the target dataset
and significantly improves data efficiency and time cost. Our work highlights
the potential of implementing user-independent HAR methods into smart
healthcare systems and BSN.


  The disturbance of the transmission of light through a diffusive medium due
to an object hidden in it can be expressed in terms of an effective charge and
dipole moment. In the mesoscopic regime, beyond the diffusion approximation, we
calculate this effective charge and dipole moment. Various objects are
considered: a single point scatterer, a localised density of such scatterers
and a small sphere.


  We introduce the mode area probability density function (MA-PDF) as a
powerful tool to study transverse Anderson localization (TAL), especially for
highly disordered optical fibers. The MA-PDF encompasses all the relevant
statistical information on TAL; it relies solely on the physics of the
disordered system and is independent of the shape of the external excitation.
We explore the scaling of MA-PDF with the transverse dimensions of the system
and show that it converges to a terminal form for structures considerably
smaller than those used in experiments, hence substantially reducing the
computational cost to study TAL.


  We present a case for the use of codes possessing algebraic closure
properties - coset codes - in developing coding techniques and characterizing
achievable rate regions for generic multi-terminal channels. In particular, we
consider three diverse communication scenarios - $3-$user interference channel
(many-to-many), $3-$user broadcast channel (one-to-many), and multiple access
with distributed states (many-to-one) - and identify non-additive examples for
which coset codes are analytically proven to yield strictly larger achievable
rate regions than those achievable using iid codes. On the one hand, our
findings motivate the need for multi-terminal information theory to step beyond
iid codes. On the other, it encourages current research of linear code-based
techniques to go beyond particular additive communication channels. Detailed
proofs of our results are available in [1]-[3].


  We review the state of the art for measuring the X-ray polarization of
neutron stars. We discuss how valuable precision measurements of the degree and
position angle of polarization as a function of energy and, where relevant, of
pulse phase, would provide deeper insight into the details of the emission
mechanisms. We then review the current state of instrumentation and its
potential for obtaining relevant data. Finally, we conclude our discussion with
some opinions as to future directions.


  The training of deep neural networks (DNNs) requires intensive resources both
for computation and for storage performance. Thus, DNNs cannot be efficiently
applied to mobile phones and embedded devices, which seriously limits their
applicability in industry applications. To address this issue, we propose a
novel encoding scheme of using {-1,+1} to decompose quantized neural networks
(QNNs) into multi-branch binary networks, which can be efficiently implemented
by bitwise operations (xnor and bitcount) to achieve model compression,
computational acceleration and resource saving. Based on our method, users can
easily achieve different encoding precisions arbitrarily according to their
requirements and hardware resources. The proposed mechanism is very suitable
for the use of FPGA and ASIC in terms of data storage and computation, which
provides a feasible idea for smart chips. We validate the effectiveness of our
method on both large-scale image classification tasks (e.g., ImageNet) and
object detection tasks. In particular, our method with low-bit encoding can
still achieve almost the same performance as its full-precision counterparts.


  We present a quantum key distribution (QKD) protocol based on long lived
coherent states prepared on superconducting rings with a mesoscopic Josephson
junction (dc-SQUIDs). This enables storage of the prepared states for long
durations before actually performing the key distribution. Our on-demand QKD
protocol is closely related to the coherent state based continuous variable
quantum key distribution protocol. A detailed analysis of preparation,
evolution and different measurement schemes that are required to be implemented
on dc-SQUIDs to carry out the QKD is provided. We present two variants of the
protocol, one requiring time stamping of states and offering a higher key rate
and the other without time stamping and a lower key rate. This is a step
towards having non-photon based QKD protocols which will be eventually
desirable as photon states cannot be stored for long and therefore the key
distribution has to be implemented immediately after photon exchange has
occurred. Our protocol offers an innovative scheme to perform QKD and can be
realized using current experimental techniques.


  The occurrence of a noncollinear magnetic structure at a Mn monolayer grown
epitaxially on Fe(100) is predicted theoretically, using spinor
density-functional theory, and observed experimentally, using x-ray magnetic
circular dichroism (XMCD) and linear dichroism (XMLD) spectroscopies. The
combined use of XMCD and XMLD at the Mn-absorption edge allows us to assess the
existence of ferromagnetic and antiferromagnetic order at the interface, and
also to determine the moment orientations with element specificity. The
experimental results thus obtained are in excellent agreement with the magnetic
structure determined theoretically.


  We present a generalization of the local expression language used in the
Symbolic Probabilistic Inference (SPI) approach to inference in belief nets
[1l, [8]. The local expression language in SPI is the language in which the
dependence of a node on its antecedents is described. The original language
represented the dependence as a single monolithic conditional probability
distribution. The extended language provides a set of operators (*, +, and -)
which can be used to specify methods for combining partial conditional
distributions. As one instance of the utility of this extension, we show how
this extended language can be used to capture the semantics, representational
advantages, and inferential complexity advantages of the "noisy or"
relationship.


  We study a single-species chemostat model with variable nutrient input and
variable dilution rate with delayed (fixed) response in growth. The first goal
of this article is to prove that persistence implies uniform persistence. Then
we concentrate in the particular case with periodic nutrient input and same
periodic dilution with delayed response in growth. We obtain a threshold for
either the (uniform) persistence of the model or that
  the biomass of every solution tends to vanish. Furthermore, we prove that
persistence is equivalent to the existence of a unique non-trivial periodic
solution. We also prove that this solution is attractive. We remark in no case
we need to impose any restrictions on the size of the delay.


  Smooth actions of the multiplicative monoid $(\mathbb{R},\cdot)$ of real
numbers on manifolds lead to an alternative, and for some reasons simpler,
definition of a vector bundle, a double vector bundle and related structures
like a graded bundle [Grabowski and Rotkiewicz, J. Geom. Phys. 2011]. For these
reasons it is natural to study smooth actions of certain monoids closely
related with the monoid $(\mathbb{R},\cdot)$ . Namely, we discuss geometric
structures naturally related with: smooth and holomorphic actions of the monoid
of multiplicative complex numbers, smooth actions of the monoid of second jets
of punctured maps $(\mathbb{R},0)\rightarrow (\mathbb{R},0)$, smooth action of
the monoid of real 2 by 2 matrices and smooth actions of multiplicative reals
on a supermanifold. In particular cases we recover the notions of a holomorphic
vector bundle, a complex vector bundle and a non-negatively graded manifold.


  We address the problem of including Coulomb distortion effects in inclusive
quasielastic (e,e') reactions using an improved version of the effective
momentum approximation. Arguments are given that a simple modification of the
effective momentum approximation, which is no longer applicable in its original
form in the case of highly charged nuclei, leads to very good results. A
comparison of the improved effective momentum method with exact calculations is
given. A critical remark concerns recent experiments with inclusive
quasielastic positron scattering.


  With rapid technological advancements, mobile learning (m-Learning) offers
incredible opportunities, especially in the area of higher education. However,
while interest in this area has been significant and several pilot studies have
been conducted within universities, relatively less is known about how higher
educational institutions can make efficient use of the m-Learning platform to
support teaching and learning. Although there are numerous studies in the area,
the lack of this insight is mostly due to the fact that very little effort has
been made to collate these studies and determine a common set of key success
factors that affect the acceptance of m-Learning within universities. This
study conducts a systematic analysis of several studies conducted in the area
of m-Learning to assess the critical success factors, by making use of the
meta-analysis technique. Our investigation has shown that the most important
perceived advantages of m-Learning, from learner perspectives, are
collaboration during studies, the prospect of ubiquitous learning in space and
time, and user friendly application design.


  The problem of guessing a random string is revisited. A close relation
between guessing and compression is first established. Then it is shown that if
the sequence of distributions of the information spectrum satisfies the large
deviation property with a certain rate function, then the limiting guessing
exponent exists and is a scalar multiple of the Legendre-Fenchel dual of the
rate function. Other sufficient conditions related to certain continuity
properties of the information spectrum are briefly discussed. This approach
highlights the importance of the information spectrum in determining the
limiting guessing exponent. All known prior results are then re-derived as
example applications of our unifying approach.


  A simple mechanism to generate Dirac masses for the neutrinos in SU(5)
supersymmetric grand unified theory is proposed. The tiny Dirac masses are
induced by the small mixing between the Higgs fields and another superheavy
fields. The mixing terms are obtained by the same mechanism as the mu-term
generation of the order of the supersymmetry breaking scale, so that the mixing
of order TeV / M_GUT \sim 10^{-13} is realized. We consider the lepton flavor
violating processes in this model. The branching ratios are directly related to
the neutrino oscillation parameters and we can predict the B(\tau -> \mu
\gamma) / B(\mu -> e \gamma) ratio once the neutrino oscillation parameters are
determined.


  We calculate the ground-state expectation value of scalar observables in the
matrix formulation of the random phase approximation (RPA). Our expression,
derived using the quasiboson approximation, is a straightforward generalization
of the RPA correlation energy. We test the reliability of our expression by
comparing against full diagonalization in 0 h-bar omega shell-model spaces. In
general the RPA values are an improvement over mean-field (Hartree-Fock)
results, but are not always consistent with shell-model results. We also
consider exact symmetries broken in the mean-field state and whether or not
they are restored in RPA.


  We consider the algebra $R$ generated by three elements $A,B,H$ subject to
three relations $[H,A]=A$, $[H,B]=-B$ and $\{A,B\}=f(H)$. When $f(H)=H$ this
coincides with the Lie superalgebra $osp(1/2)$; when $f$ is a polynomial we
speak of polynomial deformations of $osp(1/2)$. Irreducible representations of
$R$ are described, and in the case $\deg(f)\leq 2$ we obtain a complete
classification, showing some similarities but also some interesting differences
with the usual $osp(1/2)$ representations. The relation with deformed
oscillator algebras is discussed, leading to the interpretation of $R$ as a
generalized paraboson algebra.


  Despite the promise of superior performance under challenging conditions,
event-based motion estimation remains a hard problem owing to the difficulty of
extracting and tracking stable features from event streams. In order to
robustify the estimation, it is generally believed that fusion with other
sensors is a requirement. In this work, we demonstrate reliable, purely
event-based visual odometry on planar ground vehicles by employing the
constrained non-holonomic motion model of Ackermann steering platforms. We
extend single feature n-linearities for regular frame-based cameras to the case
of quasi time-continuous event-tracks, and achieve a polynomial form via
variable degree Taylor expansions. Robust averaging over multiple event tracks
is simply achieved via histogram voting. As demonstrated on both simulated and
real data, our algorithm achieves accurate and robust estimates of the
vehicle's instantaneous rotational velocity, and thus results that are
comparable to the delta rotations obtained by frame-based sensors under normal
conditions. We furthermore significantly outperform the more traditional
alternatives in challenging illumination scenarios. The code is available at
\url{https://github.com/gowanting/NHEVO}.


  We propose a novel volume conserving framework for character-water
interaction, using a novel volume-of-fluid solver on a skinned tetrahedral
mesh, enabling the high degree of the spatial adaptivity in order to capture
thin films and hair-water interactions. For efficiency, the bulk of the fluid
volume is simulated with a standard Eulerian solver which is two way coupled to
our skinned arbitrary Lagrangian-Eulerian mesh using a fast, robust, and
straightforward to implement partitioned approach. This allows for a
specialized and efficient treatment of the volume-of-fluid solver, since it is
only required in a subset of the domain. The combination of conservation of
fluid volume and a kinematically deforming skinned mesh allows us to robustly
implement interesting effects such as adhesion, and anisotropic porosity. We
illustrate the efficacy of our method by simulating various water effects with
solid objects and animated characters.


  We consider the deformed Gaussian Ensemble $H_n=M_n+H^{(0)}_n$ in which
$H_n^{(0)}$ is a diagonal Hermitian matrix and $M_n$ is the Gaussian Unitary
Ensemble (GUE) random matrix. Assuming that the Normalized Counting Measure of
$H_n^{(0)}$ (both non-random and random) converges weakly to a measure
$N^{(0)}$ with a bounded support we prove universality of the local eigenvalue
statistics in the bulk of the limiting spectrum of $H_n$.


  Motivated by the disparity between the experimentally observed properties of
superfluid 3He in aerogel and predictions of the Abrikosov and Gorkov theory of
superconducting alloys we consider effect of correlated pair-breaking
impurities on the temperature dependence of the square of magnitude of the
average order parameter and related thermodynamic properties of a Fermi
superfluid. We show that the correlations, increasing the spectral density of
the fluctuations with small wave vectors increase the transition temperature
and enhance a temperature region below Tc where fluctuations of the order
parameter dominate. Outside of this region we treat effect of impurities as a
perturbation and express corrections to thermodynamic properties in terms of
the structure factor of impurities. Assuming a simple model expression for
correlation function of aerogel we find corrections to the temperature
dependence of the NMR frequency shifts for A-like and B-like phases of 3He and
compare these with experimental data.


  Using three different notions of generalized principal eigenvalue of linear
second order elliptic operators in unbounded domains, we derive necessary and
sufficient conditions for the validity of the maximum principle, as well as for
the existence of positive eigenfunctions satisfying Dirichlet boundary
conditions. Relations between these principal eigenvalues, their simplicity and
several other properties are further discussed.


  An idea of reality conditions in the context of spin foams (Barrett-Crane
models) is developed. The square of areas are the most elementary observables
in the case of spin foams. This observation implies that simplest reality
conditions in the context of the Barrett-Crane models is that the all possible
scalar products of the bivectors associated to the triangles of a four simplex
be real. The continuum generalization of this is the area metric reality
constraint: the area metric is real iff a non-degenerate metric is real or
imaginary. Classical real general relativity (all signatures) can be extracted
from complex general relativity by imposing the area metric reality constraint.
The Plebanski theory can be modified by adding a Lagrange multiplier to impose
the area metric reality condition to derive classical real general relativity.
I discuss the SO(4,C) BF model and SO(4,C) Barrett-Crane model. It appears that
the spin foam models in 4D for all the signatures are the projections of the
SO(4,C) spin foam model using the reality constraints on the bivectors.


  With the widespread use of installed cameras, video-based monitoring
approaches have seized considerable attention for different purposes like
assisted living. Temporal redundancy and the sheer size of raw videos are the
two most common problematic issues related to video processing algorithms. Most
of the existing methods mainly focused on increasing accuracy by exploring
consecutive frames, which is laborious and cannot be considered for real-time
applications. Since videos are mostly stored and transmitted in compressed
format, these kinds of videos are available on many devices. Compressed videos
contain a multitude of beneficial information, such as motion vectors and
quantized coefficients. Proper use of this available information can greatly
improve the video understanding methods' performance. This paper presents an
approach for using residual data, available in compressed videos directly,
which can be obtained by a light partially decoding procedure. In addition, a
method for accumulating similar residuals is proposed, which dramatically
reduces the number of processed frames for action recognition. Applying neural
networks exclusively for accumulated residuals in the compressed domain
accelerates performance, while the classification results are highly
competitive with raw video approaches.