  It was shown in literature that speech representations extracted by
self-supervised pre-trained models exhibit similarities with brain activations
of human for speech perception and fine-tuning speech representation models on
downstream tasks can further improve the similarity. However, it still remains
unclear if this similarity can be used to optimize the pre-trained speech
models. In this work, we therefore propose to use the brain activations
recorded by fMRI to refine the often-used wav2vec2.0 model by aligning model
representations toward human neural responses. Experimental results on SUPERB
reveal that this operation is beneficial for several downstream tasks, e.g.,
speaker verification, automatic speech recognition, intent classification.One
can then consider the proposed method as a new alternative to improve
self-supervised speech models.


  High-centrality nodes have disproportionate influence on the behavior of a
network; therefore controlling such nodes can efficiently steer the system to a
desired state. Existing multiplex centrality measures typically rank nodes
assuming the layers are qualitatively similar. Many real systems, however, are
comprised of networks heterogeneous in nature, for example, social networks may
have both agnostic and affiliative layers. Here, we use rank aggregation
methods to identify intervention targets in multiplex networks when the
structure, the dynamics, and our intervention goals are qualitatively different
for each layer. Our approach is to rank the nodes separately in each layer
considering their different function and desired outcome, and then we use Borda
count or Kemeny aggregation to identify a consensus ranking - top nodes in the
consensus ranking are expected to effectively balance the competing goals
simultaneously among all layers. To demonstrate the effectiveness of consensus
ranking, we apply our method to a degree-based node removal procedure such that
we aim to destroy the largest component in some layers, while maintaining
large-scale connectivity in others. For any multi-objective intervention,
optimal targets only exist in the Pareto-sense; we, therefore, use a weighted
generalization of consensus ranking to investigate the trade-off between the
competing objectives. We use a collection of model and real networks to
systematically investigate how this trade-off is affected by multiplex network
structure. We use the copula representation of the multiplex centrality
distributions to generate model multiplex networks with given rank
correlations. This allows use to separately manipulate the marginal centrality
distribution of each layer and the interdependence between the layers and to
independently investigate the role of the two using both analytical and
numerical methods.


  In finite dimensions, controllability of bilinear quantum control systems can
be decided quite easily in terms of the "Lie algebra rank condition" (LARC),
such that only the systems Lie algebra has to be determined from a set of
generators. In this paper we study how this idea can be lifted to infinite
dimensions. To this end we look at control systems on an infinite dimensional
Hilbert space which are given by an unbounded drift Hamiltonian and bounded
control Hamiltonians. The drift is assumed to have empty continuous spectrum.
We use recurrence methods and the theory of Abelian von Neumann algebras to
develop a scheme, which allows us to use an approximate version of LARC, in
order to check approximate controllability of the control system in question.
Its power is demonstrated by looking at some examples. We recover in particular
previous genericity results with a much easier proof. Finally several possible
generalizations are outlined.


  This work investigates the distributed constrained optimization problem under
inter-agent communication delays from the perspective of passivity. First, we
propose a continuous-time algorithm for distributed constrained optimization
with general convex objective functions. The asymptotic stability under general
convexity is guaranteed by the phase lead compensation. The inequality
constraints are handled by adopting a projection-free generalized Lagrangian,
whose primal-dual gradient dynamics preserves passivity and smoothness,
enabling the application of the LaSalle's invariance principle in the presence
of delays. Then, we incorporate the scattering transformation into the proposed
algorithm to enhance the robustness against unknown and heterogeneous
communication delays. Finally, a numerical example of a matching problem is
provided to illustrate the results.


  Pearson's $\rho$ is the most used measure of statistical dependence. It gives
a complete characterization of dependence in the Gaussian case, and it also
works well in some non-Gaussian situations. It is well known, however, that it
has a number of shortcomings; in particular for heavy tailed distributions and
in nonlinear situations, where it may produce misleading, and even disastrous
results. In recent years a number of alternatives have been proposed. In this
paper, we will survey these developments, especially results obtained in the
last couple of decades. Among measures discussed are the copula,
distribution-based measures, the distance covariance, the HSIC measure popular
in machine learning, and finally the local Gaussian correlation, which is a
local version of Pearson's $\rho$. Throughout we put the emphasis on conceptual
developments and a comparison of these. We point out relevant references to
technical details as well as comparative empirical and simulated experiments.
There is a broad selection of references under each topic treated.


  Caching has recently attracted a lot of attention in the wireless
communications community, as a means to cope with the increasing number of
users consuming web content from mobile devices. Caching offers an opportunity
for a win-win scenario: nearby content can improve the video streaming
experience for the user, and free up valuable network resources for the
operator. At the same time, recent works have shown that recommendations of
popular content apps are responsible for a significant percentage of users
requests. As a result, some very recent works have considered how to nudge
recommendations to facilitate the network (e.g., increase cache hit rates). In
this paper, we follow up on this line of work, and consider the problem of
designing cache friendly recommendations for long viewing sessions;
specifically, we attempt to answer two open questions in this context: (i)
given that recommendation position affects user click rates, what is the impact
on the performance of such network-friendly recommender solutions? (ii) can the
resulting optimization problems be solved efficiently, when considering both
sequences of dependent accesses (e.g., YouTube) and position preference? To
this end, we propose a stochastic model that incorporates position-aware
recommendations into a Markovian traversal model of the content catalog, and
derive the average cost of a user session using absorbing Markov chain theory.
We then formulate the optimization problem, and after a careful sequence of
equivalent transformations show that it has a linear program equivalent and
thus can be solved efficiently. Finally, we use a range of real datasets we
collected to investigate the impact of position preference in recommendations
on the proposed optimal algorithm. Our results suggest more than 30\%
improvement with respect to state-of-the-art methods.


  While the modern science is characterized by an exponential growth in
scientific literature, the increase in publication volume clearly does not
reflect the expansion of the cognitive boundaries of science. Nevertheless,
most of the metrics for assessing the vitality of science or for making funding
and policy decisions are based on productivity. Similarly, the increasing level
of knowledge production by large science teams, whose results often enjoy
greater visibility, does not necessarily mean that "big science" leads to
cognitive expansion. Here we present a novel, big-data method to quantify the
extents of cognitive domains of different bodies of scientific literature
independently from publication volume, and apply it to 20 million articles
published over 60-130 years in physics, astronomy, and biomedicine. The method
is based on the lexical diversity of titles of fixed quotas of research
articles. Owing to large size of quotas, the method overcomes the inherent
stochasticity of article titles to achieve <1% precision. We show that the
periods of cognitive growth do not necessarily coincide with the trends in
publication volume. Furthermore, we show that the articles produced by larger
teams cover significantly smaller cognitive territory than (the same quota of)
articles from smaller teams. Our findings provide a new perspective on the role
of small teams and individual researchers in expanding the cognitive boundaries
of science. The proposed method of quantifying the extent of the cognitive
territory can also be applied to study many other aspects of "science of
science."


  In this article, we provide some necessary and sufficient coefficients
conditions for a harmonic mapping to be hereditarily spirallike. Also, we give
growth estimate for certain harmonic hereditarily spirallike mappings.
Moreover, we connect the concept of harmonic hereditarily spirallike mapping to
analytic spirallike mapping and provide some examples in support of our
results.


  We show how the time-continuous coherent state path integral breaks down for
both the single-site Bose-Hubbard model and the spin path integral.
Specifically, when the Hamiltonian is quadratic in a generator of the algebra
used to construct coherent states, the path integral fails to produce correct
results following from an operator approach. As suggested by previous authors,
we note that the problems do not arise in the time-discretized version of the
path integral.


  Pionium lifetime corrections are evaluated in the frameworks of constrained
Bethe-Salpeter equation and chiral perturbation theory. Corrections of order
$O(\alpha)$ are calculated with respect to the conventional lowest-order
formula, in which the strong interaction amplitude has been calculated to
two-loop order with charged pion masses. The total correction is found to be of
the order of $(6.1\pm 2.0)%$.


  In this paper, we present a new methodology to evaluate whether a business
process model is fully compliant with a regulatory framework composed of a set
of conditional obligations. The methodology is based failure delta-constraints
that are evaluated on bottom-up aggregations of a tree-like representation of
business process models. While the generic problem of proving full compliance
is in coNP-complete, we show that verifying full compliance can be done in
polynomial time using our methodology, for an acyclic structured process model
given a regulatory framework composed by a set of conditional obligations,
whose elements are restricted to be represented by propositional literals


  We present an intermediate resolution, high S/N spectrum of the z = 2.7268
galaxy MS 1512-cB58, obtained with LRIS on the Keck I telescope and covering
the rest frame far-UV from 1150 to 1930 A. Gravitational lensing by a
foreground cluster boosts the flux from cB58 by a factor of about 30 and
provides the opportunity for a first quantitative study of the physical
properties of star forming galaxies at high redshift. Our main results are as
follows. The ultraviolet spectral properties of cB58 are remarkably similar to
those of nearby star forming galaxies. The P-Cygni profiles of CIV and NV are
best matched by continuous star formation with a Salpeter IMF extending beyond
50 solar masses---we find no evidence for either a flatter IMF (at the high
mass end), or an IMF deficient in the most massive stars. There are clues in
our data that the metallicity of both the stars and the gas is a few times
below solar. Our best estimate, approximately equal to 1/4 solar, is 3 times
higher than the typical metallicity of damped Lyman alpha systems at the same
redshift, consistent with the proposal that the galaxies which dominate the H I
absorption cross-section are generally forming stars at a slower rate than L*
Lyman break galaxies like cB58. The relative velocities of the stellar lines,
interstellar absorption, and H II emission indicate the existence of
large-scale outflows in the interstellar medium of cB58, with a bulk outward
motion of 200 km/s and a mass loss rate of approximately 60 solar masses per
year, roughly comparable to the star formation rate. Such galactic winds may
well be the mechanism which self-regulates star formation, distributes metals
over large volumes and allows the escape of ionizing photons into the IGM.


  Jailbreak attacks in large language models (LLMs) entail inducing the models
to generate content that breaches ethical and legal norm through the use of
malicious prompts, posing a substantial threat to LLM security. Current
strategies for jailbreak attack and defense often focus on optimizing locally
within specific algorithmic frameworks, resulting in ineffective optimization
and limited scalability. In this paper, we present a systematic analysis of the
dependency relationships in jailbreak attack and defense techniques,
generalizing them to all possible attack surfaces. We employ directed acyclic
graphs (DAGs) to position and analyze existing jailbreak attacks, defenses, and
evaluation methodologies, and propose three comprehensive, automated, and
logical frameworks. \texttt{AutoAttack} investigates dependencies in two lines
of jailbreak optimization strategies: genetic algorithm (GA)-based attacks and
adversarial-generation-based attacks, respectively. We then introduce an
ensemble jailbreak attack to exploit these dependencies. \texttt{AutoDefense}
offers a mixture-of-defenders approach by leveraging the dependency
relationships in pre-generative and post-generative defense strategies.
\texttt{AutoEvaluation} introduces a novel evaluation method that distinguishes
hallucinations, which are often overlooked, from jailbreak attack and defense
responses. Through extensive experiments, we demonstrate that the proposed
ensemble jailbreak attack and defense framework significantly outperforms
existing research.


  Let $q>2$ be an odd integer. For each integer $x$ with $0<x<q$ and $(q,x)=
1$, we know that there exists one and only one $\bar{x}$ with $0<\bar{x}<q$
such that $x\bar{x}\equiv1(\bmod q)$. A Lehmer number is defined to be any
integer $a$ with $2\dagger(a+\bar{a})$. For any nonnegative integer $k$, Let $$
M(x,q,k)=\displaystyle\mathop {\displaystyle\mathop{\sum{'}}_{a=1}^{q}
\displaystyle\mathop{\sum{'}}_{b\leq xq}}_{\mbox{$\tiny\begin{array}{c}
2|a+b+1\\ ab\equiv1(\bmod q)\end{array}$}}(a-b)^{2k}.$$ The main purpose of
this paper is to study the properties of $M(x,q,k)$, and give a sharp
asymptotic formula, by using estimates of Kloosterman's sums and properties of
trigonometric sums.


  Robots that navigate among pedestrians use collision avoidance algorithms to
enable safe and efficient operation. Recent works present deep reinforcement
learning as a framework to model the complex interactions and cooperation.
However, they are implemented using key assumptions about other agents'
behavior that deviate from reality as the number of agents in the environment
increases. This work extends our previous approach to develop an algorithm that
learns collision avoidance among a variety of types of dynamic agents without
assuming they follow any particular behavior rules. This work also introduces a
strategy using LSTM that enables the algorithm to use observations of an
arbitrary number of other agents, instead of previous methods that have a fixed
observation size. The proposed algorithm outperforms our previous approach in
simulation as the number of agents increases, and the algorithm is demonstrated
on a fully autonomous robotic vehicle traveling at human walking speed, without
the use of a 3D Lidar.


  In this paper, the authors investigate the Deep Sea Treasure (DST) problem as
proposed by Vamplew et al. Through a number of proofs, the authors show the
original DST problem to be quite basic, and not always representative of
practical Multi-Objective Optimization problems. In an attempt to bring theory
closer to practice, the authors propose an alternative, improved version of the
DST problem, and prove that some of the properties that simplify the original
DST problem no longer hold. The authors also provide a reference implementation
and perform a comparison between their implementation, and other existing
open-source implementations of the problem. Finally, the authors also provide a
complete Pareto-front for their new DST problem.


  The uncertainty relation formulated by Heisenberg in 1927 describes a
trade-off between the error of a measurement of one observable and the
disturbance caused on another complementary observable so that their product
should be no less than a limit set by Planck's constant. In 1980, Braginsky,
Vorontsov, and Thorne claimed that this relation leads to a sensitivity limit
for gravitational wave detectors. However, in 1988 a model of position
measurement was constructed that breaks both this limit and Heisenberg's
relation. Here, we discuss the problems as to how we reformulate Heisenberg's
relation to be universally valid and how we experimentally quantify the error
and the disturbance to refute the old relation and to confirm the new relation.


  This paper presents a novel application of large language models in user
simulation for task-oriented dialog systems, specifically focusing on an
in-context learning approach. By harnessing the power of these models, the
proposed approach generates diverse utterances based on user goals and limited
dialog examples. Unlike traditional simulators, this method eliminates the need
for labor-intensive rule definition or extensive annotated data, making it more
efficient and accessible. Additionally, an error analysis of the interaction
between the user simulator and dialog system uncovers common mistakes,
providing valuable insights into areas that require improvement. Our
implementation is available at
https://github.com/telepathylabsai/prompt-based-user-simulator.


  We show that the interface effect on the properties of composite media
recently proposed by Torquato and Rintoul (TR) [Phys. Rev. Lett. 75, 4067
(1995)] is in fact elementary, and follows directly from taking the limit in
the dipolar polarizability of a coated sphere: the TR ``critical values'' are
simply those that make the dipolar polarizability vanish. Furthermore, the new
bounds developed by TR either coincide with the Clausius-Mossotti (CM) relation
or provide poor estimates. Finally, we show that the new bounds of TR do not
agree particularly well with the original experimental data that they quote.


  This paper presents meta-homogenization, a spatially varying homogenization
scheme for knitwear simulation. We are motivated by the observation that
macro-scale fabric dynamics is strongly correlated with its underlying knitting
patterns. Therefore, homogenization towards a single material is less effective
when the knitting is complex and non-repetitive. Our method tackles this
challenge by homogenizing the yarn-level material locally at volumetric
elements. Assigning a virtual volume of a knitting structure enables us to
model bending and twisting effects via a simple volume-preserving penalty and
thus effectively alleviates the material nonlinearity. We employ an adjoint
Gauss-Newton formulation to battle the dimensionality challenge of such
per-element material optimization. This intuitive material model makes the
forward simulation GPU-friendly. To this end, our pipeline also equips a novel
domain-decomposed subspace solver crafted for GPU projective dynamics, which
makes our simulator hundreds of times faster than the yarn-level simulator.
Experiments validate the capability and effectiveness of meta-homogenization.
Our method produces realistic animations of knitwear matching the quality of
full-scale yarn-level simulations. It is also orders of magnitude faster than
existing homogenization techniques in both the training and simulation stages.


  We present a model for a class of random binary lattices by introducing a
one-dimensional system where impurities are placed in one sublattice while host
atoms lie on the other sublattice. The source of disorder is the stochastic
fluctuation of the impurity energy from site to site. We study the optical
absorption spectra and the peculiarities of the motional narrowing effect at
the band edges for perturbative and nonperturbative degrees of disorder.
Analytical results agree well with numerical simulations.


  We present a detailed analysis of the stability of synchronized solutions to
the Kuramoto system of oscillators. We derive an analytical expression counting
the dimension of the unstable manifold associated to a given stationary
solution. From this we are able to derive a number of consequences, including:
analytic expressions for the first and last frequency vectors to synchronize,
upper and lower bounds on the probability that a randomly chosen frequency
vector will synchronize, and very sharp results on the large $N$ limit of this
model. One of the surprises in this calculation is that for frequencies that
are Gaussian distributed the correct scaling for full synchrony is not the one
commonly studied in the literature---rather, there is a logarithmic correction
to the scaling which is related to the extremal value statistics of the random
frequency vector.


  We report here, for the first time, an observed instability of a
Kelvin-Helmholtz (KH) nature occurring in a fully three-dimensional (3D)
current-vortex sheet at the fan plane of a 3D magnetic null point. The
current-vortex layer forms self-consistently in response to foot point driving
around the spine lines of the null. The layer first becomes unstable at an
intermediate distance from the null point, with the instability being
characterized by a rippling of the fan surface and a filamentation of the
current density and vorticity in the shear layer. Owing to the 3D geometry of
the shear layer, a branching of the current filaments and vortices is observed.
The instability results in a mixing of plasma between the two topologically
distinct regions of magnetic flux on either side of the fan separatrix surface,
as flux is reconnected across this surface. We make a preliminary investigation
of the scaling of the system with the dissipation parameters. Our results
indicate that the fan plane separatrix surface is an ideal candidate for the
formation of current-vortex sheets in complex magnetic fields and, therefore,
the enhanced heating and connectivity change associated with the instabilities
of such layers.


  This paper presents a systematic method for the selection of the Model
Predictive Control (MPC) stage cost. We match the MPC feedback law to a
proportional-integral (PI) controller, which we efficiently tune by
high-performance Monte Carlo (MC) simulation. The PI tuning offers a wide range
of tuning possibilities that is then inherited by the MPC design. The MC
simulation tuning of the PI controller is based on the minimization of two
different objectives; 1) the 2-norm tracking error, and 2) a bi-objective
consisting of the 2-norm tracking error and a 2-norm input rate of movement
penalty. We apply the method to design MPC for an exothermic chemical reaction
conducted in an adiabatic continuous stirred tank reactor (CSTR). The process
is of interest as the nonlinear dynamics result in a desired operating point
very close to a constraint. Our MPC design includes stage costs automatically
designed to match the tuned PI controllers, hard input constraints, and a soft
output constraint. Stochastic simulation results show that both the PI
controller and the MPC can track the desired operating point. However, the MPC
shows reduced output constraint violation compared to the PI controller. As
such, the MPC design method successfully combines the efficient tuning of the
PI controller with the constraint handling properties of MPC.


  The kinetics of the sorption and the subsequent desorption of 4He by the
starting graphite oxide (GtO) and the thermally reduced graphene oxide samples
(TRGO, Treduction = 200, 300, 500, 700 and 900 C) have been investigated in the
temperature interval 1.5 - 20 K. The effect of the annealing temperature on the
structural characteristics of the samples was examined by the X-ray diffraction
(XRD) technique. On lowering the temperature from 20 K to 11-12 K, the time of
4He sorption increased for all the samples, which is typically observed under
the condition of thermally activated diffusion. Below 5 K the characteristic
times of 4He sorption by the GtO and TRGO-200 samples were only weakly
dependent on temperature, suggesting the dominance of the tunnel mechanism. In
the same region (T<5 K) the characteristic times of the TRGOs reduced at higher
temperatures (300, 500, 700 and 900 C) were growing with lowering temperature,
presumably due to the defects generated in the carbon planes on removing the
oxygen functional groups (oFGs). The estimates of the activation energy (Ea) of
4He diffusion show that in the TRGO-200 sample the Ea value is 2.9 times lower
as compared to the parent GtO, which is accounted for by GtO exfoliation due to
evaporation of the water intercalated in the interlayer space of carbon. The
nonmonotonic dependences Ea vs T for the GtO samples treated above 200 C are
determined by a competition between two processes - the recovery of the
graphite carbon structure, which increases the activation energy, and the
generation of defects, which decreases the activation energy by opening
additional surface areas and ways for sorption. The dependence of the
activation energy on treatment temperature correlates well with the contents of
the crystalline phase in GtO varying with a rise of the annealing temperature.


  We address the challenging problem of jointly inferring the 3D flow and
volumetric densities moving in a fluid from a monocular input video with a deep
neural network. Despite the complexity of this task, we show that it is
possible to train the corresponding networks without requiring any 3D ground
truth for training. In the absence of ground truth data we can train our model
with observations from real-world capture setups instead of relying on
synthetic reconstructions. We make this unsupervised training approach possible
by first generating an initial prototype volume which is then moved and
transported over time without the need for volumetric supervision. Our approach
relies purely on image-based losses, an adversarial discriminator network, and
regularization. Our method can estimate long-term sequences in a stable manner,
while achieving closely matching targets for inputs such as rising smoke
plumes.


  The chiral quark model with a nonet of Goldstone bosons can yield an adequate
description of the observed proton flavor and spin structure. In a previous
publication we have compared the results of a SU(3) symmetric calculation with
the phenomenological findings based on experimental measurements and SU(3)
symmetry relations. In this paper we discuss their SU(3) and axial-U(1)
breaking corrections. With two parameters, we obtain a very satisfactory fit to
the F/D ratios for the octet baryon masses and for their axial vector
couplings, as well as the different quark flavor contributions to the proton
spin. The result also can account for, not only the light u and d quark
asymmetry, but also the strange quark content, of the proton sea. SU(3)
breaking is the key in reconciling the strange quark fraction as measured in
the neutrino charm production and that as deduced from the pion nuleon sigma
term.


  We present a novel form of explanation for Reinforcement Learning, based
around the notion of intended outcome. These explanations describe the outcome
an agent is trying to achieve by its actions. We provide a simple proof that
general methods for post-hoc explanations of this nature are impossible in
traditional reinforcement learning. Rather, the information needed for the
explanations must be collected in conjunction with training the agent. We
derive approaches designed to extract local explanations based on intention for
several variants of Q-function approximation and prove consistency between the
explanations and the Q-values learned. We demonstrate our method on multiple
reinforcement learning problems, and provide code to help researchers
introspecting their RL environments and algorithms.


  The direct linearization structure is presented of a "mild" but significant
generalization of the lattice BSQ system. Some of the equations in this system
were recently discovered in [J. Hietarinta, J. Phys {\bf A}: Math. Theor. {\bf
44} (2011) 165204] through a search of a class of three-component systems
obeying the property of multidimensional consistency. We show that all the
novel equations arising in this class follow from one and the same underlying
structure. Lax pairs for these systems are derived and explicit expressions for
the $N$-soliton solutions are obtained from the given structure.


  In contrast with entanglement, as measured by concurrence, in general,
quantum discord does not possess the property of monogamy, that is, there is no
tradeoff between the quantum discord shared by a pair of subsystems and the
quantum discord that both of them can share with a third party. Here, we show
that, as far as monogamy is considered, quantum discord of pure states is
equivalent to the entanglement of formation. This result allows one to
analytically prove that none of the pure three-qubit states belonging to the
subclass of W states is monogamous. A suitable physical interpretation of the
meaning of the correlation information as a quantifier of monogamy for the
total information is also given. Finally, we prove that, for rank 2 two-qubit
states, discord and classical correlations are bounded from above by
single-qubit von Neumann entropies.


  Within periodic materials and structures, wave scattering and dispersion
occur across constituent material interfaces leading to a banded frequency
response. In an earlier paper, the elastodynamics of one-dimensional periodic
materials and finite structures comprising these materials were examined with
an emphasis on their frequency-dependent characteristics. In this work, a novel
design paradigm is presented whereby periodic unit cells are designed for
desired frequency band properties, and with appropriate scaling, these cells
are used as building blocks for forming fully periodic or partially periodic
structures with related dynamical characteristics. Through this multiscale
dispersive design methodology, which is hierarchical and integrated, structures
can be devised for effective vibration or shock isolation without needing to
employ dissipative damping mechanisms. The speed of energy propagation in a
designed structure can also be dictated through synthesis of the unit cells.
Case studies are presented to demonstrate the effectiveness of the methodology
for several applications. Results are given from sensitivity analyses that
indicate a high level of robustness to geometric variation.


  This study delves into a comprehensive examination of the three-dimensional
$(3D)$ incompressible magneto-hydrodynamic $(MHD)$ equations in
$H^{1}(\R^{3})$. The modification involves incorporating a power term in the
nonlinear convection component, a particularly relevant adjustment in porous
media scenarios, especially when the fluid adheres to the Darcy-Forchheimer law
instead of the conventional Darcy law. Our main contributions include
establishing global existence over time and demonstrating the uniqueness of
solutions. It is important to note that these achievements are obtained with
smallness conditions on the initial data, but under the condition that $\beta
>3$ and $\alpha>0$. However, when $\beta=3$, the problem is limited to the case
$0<\alpha<\frac{1}{2}$ as the above inequality is unsolvable for these values
of $\alpha$ using our method. To support our statement, we will add a "slight
disturbance" of the function f of the type $f(z)=log(e+z^{2})$ or
$\log(\log(e^{e}+z^{2}))$ or even $\log(\log(\log((e^{e})^{e}+z^{2})))$.


  Automatic and periodic recompiling of building databases with up-to-date
high-resolution images has become a critical requirement for rapidly developing
urban environments. However, the architecture of most existing approaches for
change extraction attempts to learn features related to changes but ignores
objectives related to buildings. This inevitably leads to the generation of
significant pseudo-changes, due to factors such as seasonal changes in images
and the inclination of building fa\c{c}ades. To alleviate the above-mentioned
problems, we developed a contrastive learning approach by validating historical
building footprints against single up-to-date remotely sensed images. This
contrastive learning strategy allowed us to inject the semantics of buildings
into a pipeline for the detection of changes, which is achieved by increasing
the distinguishability of features of buildings from those of non-buildings. In
addition, to reduce the effects of inconsistencies between historical building
polygons and buildings in up-to-date images, we employed a deformable
convolutional neural network to learn offsets intuitively. In summary, we
formulated a multi-branch building extraction method that identifies newly
constructed and removed buildings, respectively. To validate our method, we
conducted comparative experiments using the public Wuhan University building
change detection dataset and a more practical dataset named SI-BU that we
established. Our method achieved F1 scores of 93.99% and 70.74% on the above
datasets, respectively. Moreover, when the data of the public dataset were
divided in the same manner as in previous related studies, our method achieved
an F1 score of 94.63%, which surpasses that of the state-of-the-art method.


  Simultaneous strong coherent pumping of the two transitions of a V-level atom
with very differentdecay rates has been predicted to create almost perfect
inversion on the narrower transition. Usingthe example of the blue and red
transitions in Strontium we show that for suitable operatingconditions the
corresponding resonant gain can be used to continuously operate a laser on
thenarrow transition. In particular, for a strong detuning of the pump field
with respect to the narrowtransition, coherent laser emission occurs close to
the bare atomic transition frequency exhibitingonly a negligible contribution
from coherent pump light scattered into the lasing mode.Calculations of the
cavity output spectrum show that the resulting laser linewidth can get
muchsmaller than the bandwidth of the pump light and even the natural linewidth
of the narrow atomictransition. Its frequency is closely tied to the atomic
transition frequency for properly chosen atomnumbers. Simulations including
atomic motionshow Doppler cooling on the strong transitionwith minor motion
heating on the lasing transition, so that continuous laser operation in
thepresence of a magneto-optical trap should be possible with current
experimental technology.


  A quantum memristor is a resistive passive circuit element with memory
engineered in a given quantum platform. It can be represented by a quantum
system coupled to a dissipative environment, in which a system-bath coupling is
mediated through a weak measurement scheme and classical feedback on the
system. In quantum photonics, such a device can be designed from a beam
splitter with tunable reflectivity, which is modified depending on the results
of measurements in one of the outgoing beams. Here, we show that a similar
implementation can be achieved with frequency-entangled optical fields and a
frequency mixer that, working similarly to a beam splitter, produces state
superpositions. We show that the characteristic hysteretic behavior of
memristors can be reproduced when analyzing the response of the system with
respect to the control, for different experimentally-attainable states. Since
memory effects in memristors can be exploited for classical and neuromorphic
computation, the results presented in this work provides the first steps of a
novel route towards constructing quantum neural networks in quantum photonics.


  An arbitrary Lagrangian--Eulerian (ALE) finite element scheme for
computations of soluble surfactant droplet impingement on a horizontal surface
is presented. The numerical scheme solves the time-dependent Navier--Stokes
equations for the fluid flow, scalar convection-diffusion equation for the
surfactant transport in the bulk phase, and simultaneously, surface evolution
equations for the surfactants on the free surface and on the liquid-solid
interface. The effects of surfactants on the flow dynamics are included into
the model through the surfactant-dependent surface tension and dynamic contact
angle. In particular, the dynamic contact angle $(\theta_d)$ of the droplet is
defined in terms of the surfactant concentration at the contact line and the
equilibrium contact angle $(\theta_e^0)$ of the clean surface using the
nonlinear equation of state for surface tension. Further, the surface forces
are included in the model as the surface divergence of the surface stress
tensor that allows to incorporate the Marangoni effects without calculating the
surface gradient of the surfactant concentration on the free surface. In
addition to a mesh convergence study and validation of the numerical results
with experiments, the effects of adsorption and desorption surfactant
coefficients on the flow dynamics in wetting, partially wetting and non-wetting
droplets are studied in detail. It is observed that the effect of surfactants
are more in wetting droplets than in the non-wetting droplets. Further, the
presence of surfactants at the contact line reduces the equilibrium contact
angle further when $ \theta_e^0 $ is less than $90^\circ$, and increases it
further when $ \theta_e^0 $ is greater than $90^\circ$. The presence of
surfactants has no effect on the contact angle, when $\theta_e^0 =90^\circ$.
The numerical study clearly demonstrates that the surfactant-dependent contact
angle ...


  Generative models for text have substantially contributed to tasks like
machine translation and language modeling, using maximum likelihood
optimization (MLE). However, for creative text generation, where multiple
outputs are possible and originality and uniqueness are encouraged, MLE falls
short. Methods optimized for MLE lead to outputs that can be generic,
repetitive and incoherent. In this work, we use a Generative Adversarial
Network framework to alleviate this problem. We evaluate our framework on
poetry, lyrics and metaphor datasets, each with widely different
characteristics, and report better performance of our objective function over
other generative models.


  By using the quantum hydrodynamic and Maxwell equations, we derive nonlinear
electron-magnetohydrodynamic (MHD), Hall-MHD, and dust Hall-MHD equations for
dense quantum magnetoplasmas. The nonlinear equations include the
electromagnetic, the electron pressure gradient, as well as the quantum
electron tunneling and electron spin forces. They are useful for investigating
a number of wave phenomena including linear and nonlinear electromagnetic
waves, as well as three-dimensional electromagnetic wave turbulence spectra
arising from the mode coupling processes in dense magnetoplasmas.


  The proposed RMS-FlowNet is a novel end-to-end learning-based architecture
for accurate and efficient scene flow estimation which can operate on point
clouds of high density. For hierarchical scene flow estimation, the existing
methods depend on either expensive Farthest-Point-Sampling (FPS) or
structure-based scaling which decrease their ability to handle a large number
of points. Unlike these methods, we base our fully supervised architecture on
Random-Sampling (RS) for multiscale scene flow prediction. To this end, we
propose a novel flow embedding design which can predict more robust scene flow
in conjunction with RS. Exhibiting high accuracy, our RMS-FlowNet provides a
faster prediction than state-of-the-art methods and works efficiently on
consecutive dense point clouds of more than 250K points at once. Our
comprehensive experiments verify the accuracy of RMS-FlowNet on the established
FlyingThings3D data set with different point cloud densities and validate our
design choices. Additionally, we show that our model presents a competitive
ability to generalize towards the real-world scenes of KITTI data set without
fine-tuning.


  In this technical note we give a purely geometric understanding of discrete
torsion, as an analogue of orbifold Wilson lines for two-form tensor field
potentials. In order to introduce discrete torsion in this context, we describe
gerbes and the description of certain type II supergravity tensor field
potentials as connections on gerbes. Discrete torsion then naturally appears in
describing the action of the orbifold group on (1-)gerbes, just as orbifold
Wilson lines appear in describing the action of the orbifold group on the gauge
bundle. Our results are not restricted to trivial gerbes -- in other words, our
description of discrete torsion applies equally well to compactifications with
nontrivial H-field strengths. We also describe a speciric program for
rigorously deriving analogues of discrete torsion for many of the other type II
tensor field potentials, and we are able to make specific conjectures for the
results.


  We give necessary and sufficient conditions for the existence of a
generalization of R\'enyi divergence, which is defined in terms of a deformed
exponential function. If the underlying measure $\mu$ is non-atomic, we found
that not all deformed exponential functions can be used in the generalization
of R\'enyi divergence; a condition involving the deformed exponential function
is provided. In the case $\mu$ is purely atomic (the counting measure on the
set of natural numbers), we show that any deformed exponential function can be
used in the generalization.


  Our aim is to estimate the perspective-effected geometric distortion of a
scene from a video feed. In contrast to all previous work we wish to achieve
this using from low-level, spatio-temporally local motion features used in
commercial semi-automatic surveillance systems. We: (i) describe a dense
algorithm which uses motion features to estimate the perspective distortion at
each image locus and then polls all such local estimates to arrive at the
globally best estimate, (ii) present an alternative coarse algorithm which
subdivides the image frame into blocks, and uses motion features to derive
block-specific motion characteristics and constrain the relationships between
these characteristics, with the perspective estimate emerging as a result of a
global optimization scheme, and (iii) report the results of an evaluation using
nine large sets acquired using existing close-circuit television (CCTV)
cameras. Our findings demonstrate that both of the proposed methods are
successful, their accuracy matching that of human labelling using complete
visual data.


  Even though the KdV and modified KdV equations are nonlinear, we show that
suitable linear combinations of known periodic solutions involving Jacobi
elliptic functions yield a large class of additional solutions. This procedure
works by virtue of some remarkable new identities satisfied by the elliptic
functions.


  We consider the problem of the maximum concentration in a fixed measurable
subset $\Omega\subset\mathbb{R}^{2d}$ of the time-frequency space for functions
$f\in L^2(\mathbb{R}^{d})$. The notion of concentration can be made
mathematically precise by considering the $L^p$-norm on $\Omega$ of some
time-frequency distribution of $f$ such as the ambiguity function $A(f)$. We
provide a positive answer to an open maximization problem, by showing that for
every subset $\Omega\subset\mathbb{R}^{2d}$ of finite measure and every $1\leq
p<\infty$, there exists an optimizer for \[
  \sup\{\|A(f)\|_{L^p(\Omega)}:\ f\in L^2(\mathbb{R}^{d}),\ \|f\|_{L^2}=1
  \}.
  \] The lack of weak upper semicontinuity and the invariance under
time-frequency shifts make the problem challenging. The proof is based on
concentration compactness with time-frequency shifts as dislocations, and
certain integral bounds and asymptotic decoupling estimates for the ambiguity
function. We also discuss the case $p=\infty$ and related optimization problems
for the time correlation function, the cross-ambiguity function with a fixed
window, and for functions in the modulation spaces $M^q(\mathbb{R}^{d})$,
$0<q<2$, equipped with continuous or discrete-type (quasi-)norms.


  This paper is devoted to investigate the anisotropic locally rotationally
symmetric (LRS) Bianchi type-I space-time in the context of the recently
proposed $f(Q)$ gravity in which $Q$ is the non-metricity scalar. For this
purpose, we consider a linear form of $f\left( Q\right) $ gravity model,
specifically, $f\left( Q\right) =\alpha Q+\beta $, where $\alpha $ and $% \beta
$ are free parameters and we analyzed the exact solutions of LRS Bianchi type-I
space-time. The modified Friedmann equations are solved by presuming an
expansion scalar $\theta \left( t\right) $ is proportional to the shear scalar
$\sigma \left( t\right) $ which leads to the relation between the metric
potentials as $A=B^{n}$ where $n$ is an arbitrary constant. Then we constrain
our model parameters with the observational Hubble datasets of 57 data points.
Moreover, we discuss the physical behavior of cosmological parameters such as
energy density, pressure, EoS parameter, and deceleration parameter. The
behavior of the deceleration parameter predicts a transition from deceleration
to accelerated phases in an expanding Universe. Finally, the EoS parameter
indicates that the anisotropic fluid behaves like the standard $\Lambda $CDM
model.


  The presence of neutral C60 fullerenes in circumstellar environments has been
firmly established by astronomical observations as well as laboratory
experiments and quantum-chemistry calculations. However, the large variations
observed in the C60 17.4um/18.9um band ratios indicate that either additional
emitters should contribute to the astronomical IR spectra or there exist
unknown physical processes besides thermal and UV excitation. Fullerene-based
molecules such as metallofullerenes and fullerene-adducts are natural candidate
species as potential additional emitters, but no specific species has been
identified to date. Here we report a model based on quantum-chemistry
calculations and IR spectra simulation of neutral and charged endo(exo)hedral
metallofullerenes, showing that they have a significant contribution to the
four strongest IR bands commonly attributed to neutral C60. These simulations
may explain the large range of 17.4um/18.9um band ratios observed in very
different fullerene-rich circumstellar environments like those around planetary
nebulae and chemically peculiar R Coronae Borealis stars. Our proposed model
also reveals that the 17.4um/18.9um band ratio in the metallofullerenes
simulated IR spectra mainly depends on the metal abundances, ionization level,
and endo/exo concentration in the circumstellar envelopes. We conclude that
metallofullerenes are potential emitters contributing to the observed IR
spectra in fullerene-rich circumstellar envelopes. Our simulated IR spectra
indicate also that the James Webb Space Telescope has the potential to confirm
or refute the presence of metallofullerenes (or even other fullerene-based
species) in circumstellar enviroments.


  A static Einstein metric that generalizes the Schwarzschild metric is
considered. The event horizon is not necessarily a sphere and the term $dt\sp2$
is a function on such horizon. That the metric is Einstein establishes a
relation between its terms. One demonstrates that the scalar curvature of the
horizon is constant, and that the term $dt\sp2$ gives rise to (i) the metric of
the horizon being Einstein, or (ii) the scalar curvature of the horizon being
proportional to an eigenvalue of the Laplace operator.


  We discuss the proof of Kazhdan and Lusztig of the equivalence of the
Drinfeld category D(g,h) of g-modules and the category of finite dimensional
Uq(g)-modules, q=exp(\pi ih), for h\in C\Q*. Aiming at operator algebraists the
result is formulated as the existence for each h\in iR of a normalized unitary
2-cochain F on the dual \hat G of a compact simple Lie group G such that the
convolution algebra of G with the coproduct twisted by F is *-isomorphic to the
convolution algebra of the q-deformation G_q of G, while the coboundary of
F^{-1} coincides with Drinfeld's KZ-associator defined via monodromy of the
Knizhnik-Zamolodchikov equations.


  We build on a 1990 paper of Bukovsky and Coplakova-Hartova. First, we remove
the hypothesis of $\textsf{CH}$ from one of their minimality results. Then,
using a measurable cardinal, we show that there is a
$|\aleph_2^V|=\aleph_1$-minimal extension that is not a
$|\aleph_3^V|=\aleph_1$-extension, answering the first of their questions.


  We have implemented the sweep algorithm for the variational optimization of
SU(2) x U(1) (spin and particle number) invariant matrix product states (MPS)
for general spin and particle number invariant fermionic Hamiltonians. This
class includes non-relativistic quantum chemical systems within the
Born-Oppenheimer approximation. High-accuracy ab-initio finite field results of
the longitudinal static polarizabilities and second hyperpolarizabilities of
one-dimensional hydrogen chains are presented. This allows to assess the
performance of other quantum chemical methods. For small basis sets, MPS
calculations in the saturation regime of the optical response properties can be
performed. These results are extrapolated to the thermodynamic limit.


  There are many examples of 3-folds of general type with $\chi(\mathcal
{O})=1$ found by Iano-Fletcher and Reid about twenty years ago. Iano-Fletcher
has ever proved $P_{12}(X)\ge 1$ and $P_{24}(X)\ge 2$ for all minimal 3-folds
$X$ of general type with $\chi(\mathcal {O}_X)=1$. In this paper, we improve on
Fletcher's method. Our main result is that $\phi_m$ is birational onto its
image for all $m\ge 54$. To prove this we establish a general theory on
birationality for general 3-folds which improve known results. Also we will
show $P_m\geq 1$ for all $m\geq 14$ and $P_{18}\geq 3$.


  We present the kpc-scale behaviour of the powerful extragalactic radio source
Hercules A and the behaviour of the intracluster gas in which the radio source
is situated. We have found that Hercules A exhibits a strong Laing-Garrington
effect. The X-ray observations have revealed an extended X-ray emission
elongated along the radio galaxy axis. The estimated temperature of the cluster
is kT = 2.45 keV and the central electron density is no~7.8 x 10^(-3) cm^(-3)
which reveals a hot, dense environment in which Hercules A is situated. From
the combined study of the radio and X-ray data we have estimated a central
value of 3<Bo (muG)<9. We also present the most recent results from the
analysis of the radio data on the pc-scale structure of the radio galaxy,
observed at 18 cm by the EVN-MERLIN array. A faint but compact radio source,
coincident with the optical centre of Hercules A was detected by the EVN at 18
mas resolution. The total flux density of the EVN core is 14.6 mJy. Its angular
size is 18 x 7 mas with a position angle of ~139 degrees. There is also
evidence for extended emission in the NW-SE direction, most probably from the
eastern pc-scale jet. If this is true then there is a misalignment between the
direction of the pc-eastern and the aligned kpc-scale jets of ~35 degrees.


  Explicit answer is given for the HOMFLY polynomial of the figure eight knot
$4_1$ in arbitrary symmetric representation R=[p]. It generalizes the old
answers for p=1 and 2 and the recently derived results for p=3,4, which are
fully consistent with the Ooguri-Vafa conjecture. The answer can be considered
as a quantization of the \sigma_R = \sigma_{[1]}^{|R|} identity for the
"special" polynomials (they define the leading asymptotics of HOMFLY at q=1),
and arises in a form, convenient for comparison with the representation of the
Jones polynomials as sums of dilogarithm ratios. In particular, we construct a
difference equation ("non-commutative A-polynomial") in the representation
variable p. Simple symmetry transformation provides also a formula for
arbitrary antisymmetric (fundamental) representation R=[1^p], which also passes
some obvious checks. Also straightforward is a deformation from HOMFLY to
superpolynomials. Further generalizations seem possible to arbitrary Young
diagrams R, but these expressions are harder to test because of the lack of
alternative results, even partial.


  With the potential of quantum algorithms to solve intractable classical
problems, quantum computing is rapidly evolving and more algorithms are being
developed and optimized. Expressing these quantum algorithms using a high-level
language and making them executable on a quantum processor while abstracting
away hardware details is a challenging task. Firstly, a quantum programming
language should provide an intuitive programming interface to describe those
algorithms. Then a compiler has to transform the program into a quantum
circuit, optimize it and map it to the target quantum processor respecting the
hardware constraints such as the supported quantum operations, the qubit
connectivity, and the control electronics limitations. In this paper, we
propose a quantum programming framework named OpenQL, which includes a
high-level quantum programming language and its associated quantum compiler. We
present the programming interface of OpenQL, we describe the different layers
of the compiler and how we can provide portability over different qubit
technologies. Our experiments show that OpenQL allows the execution of the same
high-level algorithm on two different qubit technologies, namely
superconducting qubits and Si-Spin qubits. Besides the executable code, OpenQL
also produces an intermediate quantum assembly code (cQASM), which is
technology-independent and can be simulated using the QX simulator.


  Automated vehicles (AV) heavily depend on robust perception systems. Current
methods for evaluating vision systems focus mainly on frame-by-frame
performance. Such evaluation methods appear to be inadequate in assessing the
performance of a perception subsystem when used within an AV. In this paper, we
present a logic -- referred to as Spatio-Temporal Perception Logic (STPL) --
which utilizes both spatial and temporal modalities. STPL enables reasoning
over perception data using spatial and temporal operators. One major advantage
of STPL is that it facilitates basic sanity checks on the functional
performance of the perception system, even without ground-truth data in some
cases. We identify a fragment of STPL which is efficiently monitorable offline
in polynomial time. Finally, we present a range of specifications for AV
perception systems to highlight the types of requirements that can be expressed
and analyzed through offline monitoring with STPL.


  We re-examine spontaneous CP violation at the tree level in the context of
the next-to-minimal supersymmetric standard model (NMSSM) with two Higgs
doublets and a gauge singlet field. We analyse the most general Higgs potential
without a discrete Z_3 symmetry, and derive an upper bound on the mass of the
lightest neutral Higgs boson consistent with present experimental data. We
investigate, in particular, its dependence on the admixture and CP-violating
phase of the gauge singlet field, as well as on tan(beta). To assess the
viability of the spontaneous CP violation scenario, we estimate epsilon_K by
applying the mass insertion approximation. We find that a non-trivial flavour
structure in the soft-breaking A terms is required to account for the observed
CP violation in the neutral kaon sector. Furthermore, combining the
minimisation conditions for spontaneous CP violation with the constraints
coming from K0-K0bar mixing, we find that the upper bound on the lightest
Higgs-boson mass becomes stronger. We also point out that the electric dipole
moments of electron and neutron are a serious challenge for SUSY models with
spontaneous CP violation.


  Sectional pseudocomplementation (sp-complementation) on a poset is a partial
operation $*$ which associates with every pair $(x,y)$ of elements, where $x
\ge y$, the pseudocomplement $x*y$ of $x$ in the upper section $[y)$. Any total
extension $\to$ of $*$ is said to be an extended sp-complementation and is
considered as an implication-like operation. Extended sp-complementations have
already be studied on semilattices and lattices. We describe several naturally
arising classes of general posets with extended sp-complementation, present
respective elementary properties of this operation, demonstrate that two other
known attempts to isolate particular such classes are in fact not quite
correct, and suggest suitable improvements.


  We study the alignment of galaxies relative to their local environment in
SDSS-DR8 and, using these data, we discuss evolution scenarios for different
types of galaxies. We defined a vector field of the direction of anisotropy of
the local environment of galaxies. We summed the unit direction vectors of all
close neighbours of a given galaxy in a particular way to estimate this field.
We found the alignment angles between the spin axes of disc galaxies, or the
minor axes of elliptical galaxies, and the direction of anisotropy. The
distributions of cosines of these angles are compared to the random
distributions to analyse the alignment of galaxies. Sab galaxies show
perpendicular alignment relative to the direction of anisotropy in a sparse
environment, for single galaxies and galaxies of low luminosity. Most of the
parallel alignment of Scd galaxies comes from dense regions, from 2...3 member
groups and from galaxies with low luminosity. The perpendicular alignment of S0
galaxies does not depend strongly on environmental density nor luminosity; it
is detected for single and 2...3 member group galaxies, and for main galaxies
of 4...10 member groups. The perpendicular alignment of elliptical galaxies is
clearly detected for single galaxies and for members of < 11 member groups; the
alignment increases with environmental density and luminosity. We confirm the
existence of fossil tidally induced alignment of Sab galaxies at low z. The
alignment of Scd galaxies can be explained via the infall of matter to
filaments. S0 galaxies may have encountered relatively massive mergers along
the direction of anisotropy. Major mergers along this direction can explain the
alignment of elliptical galaxies. Less massive, but repeated mergers are
possibly responsible for the formation of elliptical galaxies in sparser areas
and for less luminous elliptical galaxies.


  This paper presents the Multilingual COVID-19 Analysis Method (CMTA) for
detecting and observing the spread of misinformation about this disease within
texts. CMTA proposes a data science (DS) pipeline that applies machine learning
models for processing, classifying (Dense-CNN) and analyzing (MBERT)
multilingual (micro)-texts. DS pipeline data preparation tasks extract features
from multilingual textual data and categorize it into specific information
classes (i.e., 'false', 'partly false', 'misleading'). The CMTA pipeline has
been experimented with multilingual micro-texts (tweets), showing
misinformation spread across different languages. To assess the performance of
CMTA and put it in perspective, we performed a comparative analysis of CMTA
with eight monolingual models used for detecting misinformation. The comparison
shows that CMTA has surpassed various monolingual models and suggests that it
can be used as a general method for detecting misinformation in multilingual
micro-texts. CMTA experimental results show misinformation trends about
COVID-19 in different languages during the first pandemic months.


  While many dynamical systems of mechanical origin, in particular billiards,
are strongly chaotic -- enjoy exponential mixing, the rates of mixing in many
other models are slow (algebraic, or polynomial). The dynamics in the latter
are intermittent between regular and chaotic, which makes them particularly
interesting in physical studies. However, mathematical methods for the analysis
of systems with slow mixing rates were developed just recently and are still
difficult to apply to realistic models. Here we reduce those methods to a
practical scheme that allows us to obtain a nearly optimal bound on mixing
rates. We demonstrate how the method works by applying it to several classes of
chaotic billiards with slow mixing as well as discuss a few examples where the
method, in its present form, fails.


  We present new constraints on parameters of cosmic dawn and the epoch of
reionization derived from the EDGES High-Band spectrum ($90-190$ MHz). The
parameters are probed by evaluating global $21$ cm signals generated with the
recently developed Global21cm tool. This tool uses neural networks trained and
tested on $\sim 30,000$ spectra produced with semi-numerical simulations that
assume the standard thermal evolution of the cosmic microwave background and
the intergalactic medium. From our analysis, we constrain at $68\%$ (1) the
minimum virial circular velocity of star-forming halos to $V_{\rm c}<19.3$ km
s$^{-1}$, (2) the X-ray heating efficiency of early sources to $f_{\rm
X}>0.0042$, and (3) the low-energy cutoff of the X-ray spectral energy
distribution to $\nu_{\rm min}<2.3$ keV. We also constrain the star-formation
efficiency ($f_*$), the electron scattering optical depth ($\tau_{\rm e}$), and
the mean-free path of ionizing photons ($R_{\rm mfp}$). We re-compute the
constraints after incorporating into the analysis four estimates for the
neutral hydrogen fraction from high-$z$ quasars and galaxies, and a prior on
$\tau_{\rm e}$ from Planck $2018$. The largest impact of the external
observations is on the parameters that most directly characterize reionization.
Specifically, we derive the combined $68\%$ constraints $\tau_{\rm e}<0.063$
and $R_{\rm mfp}>27.5$ Mpc. The external observations also have a significant
effect on $V_{\rm c}$ due to its degeneracy with $\tau_{\rm e}$, while the
constraints on $f_*$, $f_{\rm X}$, and $\nu_{\rm min}$, remain primarily
determined by EDGES.


  The present experimental tests have proved high precisely the validity of the
Pauli exclusion principle (PEP) in usual cases. The future experiments should
be combined widely with various theories of hidden and obvious violation of
PEP. Author think that known experiments and theories seem to imply the
violation at high energy. Some possible tests have been proposed in particle
physics, nuclei at high energy and astrophysics, etc., in particular, the
excited high-n atoms and multi-quark states. Moreover, the violation is
possibly relevant to the nonlinear quantum theory, in which the present linear
superposition principle may not hold. Finally, the possible violation at very
low temperature is discussed. These experiments may be connected with tests of
other basic principles, for example, the present wave property, possible
decrease of entropy due to internal interactions in isolated systems, and PCT
invariance, etc.


  Geometric properties of the set of quantum entangled states are investigated.
We propose an explicit method to compute the dimension of local orbits for any
mixed state of the general K x M problem and characterize the set of
effectively different states (which cannot be related by local
transformations). Thus we generalize earlier results obtained for the simplest
2 x 2 system, which lead to a stratification of the 6D set of N=4 pure states.
We define the concept of absolutely separable states, for which all globally
equivalent states are separable.


  The properties of rotational bands at the limit of angular momentum are
discussed on the example of smooth terminating bands observed in the A~110 mass
region. The effective alignment approach is used for the study of their
relative properties which provides additional insight into the properties of
such bands.


  The influence of confinement on the topological phases of superfluid 3He is
studied using the torsional pendulum method. We focus on the phase transition
between the chiral A-phase and the time-reversal-invariant B-phase, motivated
by the prediction of a spatiallymodulated (stripe) phase at the A-B phase
boundary. We confine superfluid 3He to a single 1.08 {\mu}m thick nanofluidic
cavity incorporated into a high-precision torsion pendulum, and map the phase
diagram between 0.1 and 5.6 bar. We observe only small supercooling of the
A-phase, in comparison to bulk or when confined in aerogel. This has a
non-monotonic pressure dependence, suggesting that a new intrinsic B-phase
nucleation mechanism operates under confinement, mediated by the putative
stripe phase. Both the phase diagram and the relative superfluid fraction of
the A and B phases, show that strong coupling is present at all pressures, with
implications for the stability of the stripe phase.


  We show by direct calculation that the replica and cavity methods are exactly
equivalent for the spectrum of Erdos-Renyi random graph. We introduce a
variational formulation based on the cavity method and use it to find
approximate solutions for the density of eigenvalues. We also use this
variational method for calculating spectra of sparse covariance matrices.


  Resonant Andreev reflection through superconductor-carbon-nanotube devices
was investigated theoretically with a focus on the superconducting proximity
effect. Consistent with a recent experiment, we find that for high transparency
devices on-resonance, the Andreev current is characterized by a large value and
a resistance dip; low-transparency off-resonance devices give the opposite
result. We also give evidence that the observed low-temperature transport
anomaly may be a natural result of Andreev reflection process.


  Direct detection of gravitational waves (GW) on Aug. 17, 2017, propagating
from a binary neutron star merger, opened the era of multimessenger astronomy.
The ejected material from neutron star mergers, or kilonova, is a good
candidate for optical and near infrared follow-up observations after the
detection of GWs. The kilonova from the ejecta of GW1780817 provided the first
evidence for the astrophysical site of the synthesis of heavy nuclei through
the rapid neutron capture process or rprocess. Since properties of the emission
are largely affected by opacities of the ejected material, enhancements in the
available, but limited rprocess atomic data have been motivated recently.
However, given the complexity of the electronic structure of these heavy
elements, considerable efforts are still needed to converge to a reliable set
of atomic structure data. The aim of this work is to alleviate this situation
for low charge state elements in the Os-like isoelectronic sequence. In this
regard, the general purpose relativistic atomic structure packages (GRASP0 and
GRASP2K) were used to obtain energy levels and transition probabilities (E1 and
M1). We provide line lists and expansion opacities for a range of r-process
elements. We focus here on the Os isoelectronic sequence (Os I, Ir II, Pt III,
Au IV, Hg V). The results are benchmarked against existing experimental data
and prior calculations, and predictions of emission spectra relevant to
kilonovae are provided. Finestructure (M1) lines in the infrared potentially
observable by the James Webb Space Telescope are highlighted.


  We emphasize that the group-theoretical considerations leading to SO(10)
unification of electro-weak and strong matter field components naturally extend
to space-time components, providing a truly unified description of all
generation degrees of freedoms in terms of a single chiral spin representation
of one of the groups SO(13,1), SO(9,5), SO(7,7) or SO(3,11). The realization of
these groups as higher dimensional space-time symmetries produces unification
of all fundamental fermions is a single space-time spinor.


  We point out that events associated with large $E_T$ direct photons in
high-energy heavy-ion collisions can be used to study jet energy loss in dense
matter. In such events, the $p_T$ spectrum of charged hadrons from jet
fragmentation in the opposite direction of the tagged photon is estimated to be
well above the background which can be reliably subtracted at moderately large
$p_T$. We demonstrate that comparison between the extracted fragmentation
function in $AA$ and $pp$ collisions can be used to determine the jet energy
loss and the interaction mean-free-path in the dense matter produced in
high-energy heavy-ion collisions.


  We determine the maximum lifetime t_max of 52 FRII radio sources found in 26
central group galaxies from cross correlation of the Berlind SDSS group catalog
with the VLA FIRST survey. Mock catalogs of FRII sources were produced to match
the selection criteria of FIRST and the redshift distribution of our parent
sample, while an analytical model was used to calculate source sizes and
luminosities. The maximum lifetime of FRII sources was then determined via a
comparison of the observed and model projected length distributions. We
estimate the average FRII lifetime is 1.5x10^7 years and the duty cycle is
~8x10^8 years. Degeneracies between t_max and the model parameters: jet power
distribution, axial ratio, energy injection index, and ambient density
introduce at most a factor of two uncertainty in our lifetime estimate. In
addition, we calculate the radio active galactic nuclei (AGN) fraction in
central group galaxies as a function of several group and host galaxy
properties. The lifetime of radio sources recorded here is consistent with the
quasar lifetime, even though these FRIIs have substantially sub-Eddington
accretion. These results suggest a fiducial time frame for energy injection
from AGN in feedback models. If the morphology of a given extended radio source
is set by large-scale environment, while the lifetime is determined by the
details of the accretion physics, this FRII lifetime is relevant for all
extended radio sources.


  We consider a class of Hill equations where the periodic coefficient is the
squared solution of some Duffing equation plus a constant. We study the
stability of the trivial solution of this Hill equation and we show that a
criterion due to Burdina (V.I. Burdina, Boundedness of solutions of a system of
differential equations) is very helpful for this analysis. In some cases, we
are also able to determine exact solutions in terms of Jacobi elliptic
functions. Overall, we obtain a fairly complete picture of the stability and
instability regions. These results are then used to study the stability of
nonlinear modes in some beam equations.


  Quantum computation and quantum information processing are emerging
technologies that have potential to overcome the physical limitation of
traditional computation systems. Present quantum systems based on photons,
atoms and molecules, however, all face challenges such as short coherence time,
requirement of ultralow temperature and/or high vacuum, and lack of
scalability. We report a new type of molecular qubits and nanoparticle
ensembles based on thermally controllable transformation between J-aggregation
and monomeric states of molecular chromophores, using pyrrolopyrrole cyanine
tethered with polymeric chains such as polycaprolactones as an example. Such
supramolecular quantum systems, resembling some feature of light harvesting
complexes in photosynthesis, provide new opportunities for manipulating quantum
in-formation under mild conditions, which do not require complicated
ultra-cooling and/or high vacuum often involved in present superconducting
qubits or Rydberg atoms for quantum computation and information processing.


  Programming languages like P4 enable specifying the behavior of network data
planes in software. However, with increasingly powerful and complex
applications running in the network, the risk of faults also increases. Hence,
there is growing recognition of the need for methods and tools to statically
verify the correctness of P4 code, especially as the language lacks basic
safety guarantees. Type systems are a lightweight and compositional way to
establish program properties, but there is a significant gap between the kinds
of properties that can be proved using simple type systems (e.g., SafeP4) and
those that can be obtained using full-blown verification tools (e.g., p4v). In
this paper, we close this gap by developing $\Pi$4, a dependently-typed version
of P4 based on decidable refinements. We motivate the design of $\Pi$4, prove
the soundness of its type system, develop an SMT-based implementation, and
present case studies that illustrate its applicability to a variety of data
plane programs.


  We study the state-sum models of quantum gravity based on a representation
2-category of the Poincare 2-group. We call them spin-cube models, since they
are categorical generalizations of spin-foam models. A spin-cube state sum can
be considered as a path integral for a constrained 2-BF theory, and depending
on how the constraints are imposed, a spin-cube state sum can be reduced to a
path integral for the area-Regge model with the edge-length constraints, or to
a path integral for the Regge model. We also show that the effective actions
for these spin-cube models have the correct classical limit.


  The Karolyhazy uncertainty relation is the statement that if a device is used
to measure a length $l$, there will be a minimum uncertainty $\delta l$ in the
measurement, given by $(\delta l)^3 \sim L_P^2\; l$. This is a consequence of
combining the principles of quantum mechanics and general relativity. In this
note we show how this relation arises in our approach to quantum gravity, in a
bottom-up fashion, from the matrix dynamics of atoms of space-time-matter. We
use this relation to define a space-time-matter foam at the Planck scale, and
to argue that our theory is holographic. By coarse graining over time scales
larger than Planck time, one obtains the laws of quantum gravity. Quantum
gravity is not a Planck scale phenomenon; rather it comes into play whenever no
classical space-time background is available to describe a quantum system.
Space-time and classical general relativity arise from spontaneous localisation
in a highly entangled quantum gravitational system. The Karolyhazy relation
continues to hold in the emergent theory. An experimental confirmation of this
relation will constitute a definitive test of the quantum nature of gravity.


  Falls have serious consequences and are prevalent in acute hospitals and
nursing homes caring for older people. Most falls occur in bedrooms and near
the bed. Technological interventions to mitigate the risk of falling aim to
automatically monitor bed-exit events and subsequently alert healthcare
personnel to provide timely supervisions. We observe that frequency-domain
information related to patient activities exist predominantly in very low
frequencies. Therefore, we recognise the potential to employ a low resolution
acceleration sensing modality in contrast to powering and sensing with a
conventional MEMS (Micro Electro Mechanical System) accelerometer.
Consequently, we investigate a batteryless sensing modality with low cost
wirelessly powered Radio Frequency Identification (RFID) technology with the
potential for convenient integration into clothing, such as hospital gowns. We
design and build a passive accelerometer-based RFID sensor
embodiment---ID-Sensor---for our study. The sensor design allows deriving ultra
low resolution acceleration data from the rate of change of unique RFID tag
identifiers in accordance with the movement of a patient's upper body. We
investigate two convolutional neural network architectures for learning from
raw RFID-only data streams and compare performance with a traditional shallow
classifier with engineered features. We evaluate performance with 23
hospitalized older patients. We demonstrate, for the first time and to the best
of knowledge, that: i) the low resolution acceleration data embedded in the RF
powered ID-Sensor data stream can provide a practicable method for activity
recognition; and ii) highly discriminative features can be efficiently learned
from the raw RFID-only data stream using a fully convolutional network
architecture.


  Direct numerical simulation of open-channel flow over a bed of spheres
arranged in a regular pattern has been carried out at bulk Reynolds number and
roughness Reynolds number (based on sphere diameter) of approximately 6900 and
120, respectively, for which the flow regime is fully-rough. The open-channel
height was approximately 5.5 times the diameter of the spheres. Extending the
results obtained by Chan-Braun et al. (J. Fluid Mech., vol. 684, 2011, 441) for
an open-channel flow in the transitionally-rough regime, the present purpose is
to show how the flow structure changes as the fully-rough regime is attained
and, for the first time, to enable a direct comparison with experimental
observations. The results indicate that, in the vicinity of the roughness
elements, the average flow field is affected both by Reynolds number effects
and by the geometrical features of the roughness, while at larger
wall-distances this is not the case, and roughness concepts can be applied. The
flow-roughness interaction occurs mostly in the region above the virtual origin
of the velocity profile, and the effect of form-induced velocity fluctuations
is maximum at the level of sphere crests. The spanwise length scale of
turbulent velocity fluctuations in the vicinity of the sphere crests shows the
same dependence on the distance from the wall as that observed over a smooth
wall, and both vary with Reynolds number in a similar fashion. Moreover, the
hydrodynamic force and torque experienced by the roughness elements are
investigated. Finally, the possibility either to adopt an analogy between the
hydrodynamic forces associated with the interaction of turbulent structures
with a flat smooth wall or with the surface of the spheres is also discussed,
distinguishing the skin-friction from the form-drag contributions both in the
transitionally-rough and in the fully-rough regimes.


  Automatic defect recognition is one of the research hotspots in steel
production, but most of the current methods mainly extract features manually
and use machine learning classifiers to recognize defects, which cannot tackle
the situation, where there are few data available to train and confine to a
certain scene. Therefore, in this paper, a new approach is proposed which
consists of part of pretrained VGG16 as a feature extractor and a new CNN
neural network as a classifier to recognize the defect of steel strip surface
based on the feature maps created by the feature extractor. Our method achieves
an accuracy of 99.1% and 96.0% while the dataset contains 150 images each class
and 10 images each class respectively, which is much better than previous
methods.


  Music recommender systems have become an integral part of music streaming
services such as Spotify and Last.fm to assist users navigating the extensive
music collections offered by them. However, while music listeners interested in
mainstream music are traditionally served well by music recommender systems,
users interested in music beyond the mainstream (i.e., non-popular music)
rarely receive relevant recommendations. In this paper, we study the
characteristics of beyond-mainstream music and music listeners and analyze to
what extent these characteristics impact the quality of music recommendations
provided. Therefore, we create a novel dataset consisting of Last.fm listening
histories of several thousand beyond-mainstream music listeners, which we
enrich with additional metadata describing music tracks and music listeners.
Our analysis of this dataset shows four subgroups within the group of
beyond-mainstream music listeners that differ not only with respect to their
preferred music but also with their demographic characteristics. Furthermore,
we evaluate the quality of music recommendations that these subgroups are
provided with four different recommendation algorithms where we find
significant differences between the groups. Specifically, our results show a
positive correlation between a subgroup's openness towards music listened to by
members of other subgroups and recommendation accuracy. We believe that our
findings provide valuable insights for developing improved user models and
recommendation approaches to better serve beyond-mainstream music listeners.


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


  Knowledge graph embedding (KGE) models represent each entity and relation of
a knowledge graph (KG) with low-dimensional embedding vectors. These methods
have recently been applied to KG link prediction and question answering over
incomplete KGs (KGQA). KGEs typically create an embedding for each entity in
the graph, which results in large model sizes on real-world graphs with
millions of entities. For downstream tasks these atomic entity representations
often need to be integrated into a multi stage pipeline, limiting their
utility. We show that an off-the-shelf encoder-decoder Transformer model can
serve as a scalable and versatile KGE model obtaining state-of-the-art results
for KG link prediction and incomplete KG question answering. We achieve this by
posing KG link prediction as a sequence-to-sequence task and exchange the
triple scoring approach taken by prior KGE methods with autoregressive
decoding. Such a simple but powerful method reduces the model size up to 98%
compared to conventional KGE models while keeping inference time tractable.
After finetuning this model on the task of KGQA over incomplete KGs, our
approach outperforms baselines on multiple large-scale datasets without
extensive hyperparameter tuning.


  We compare the mass cooling rates and cumulative cooled-down masses predicted
by several semi-analytical (SA) cooling models with cosmological hydrodynamical
simulations performed using the AREPO code (ignoring processes such as feedback
and chemical enrichment). The SA cooling models are the new GALFORM cooling
model introduced in Hou et al. (2017), along with two earlier GALFORM cooling
models and the L-GALAXIES and MORGANA cooling models. We find that the
predictions of the new GALFORM cooling model are generally in best agreement
with the simulations. For halos with $M_{\rm halo}\lesssim 3\times
10^{11}\,{\rm M}_{\odot}$, the SA models predict that the timescale for
radiative cooling is shorter than or comparable to the gravitational infall
timescale. Even though SA models assume that gas falls onto galaxies from a
spherical gas halo, while the simulations show that the cold gas is accreted
through filaments, both methods predict similar mass cooling rates, because in
both cases the gas accretion occurs on similar timescales. For halos with
$M_{\rm halo}\gtrsim 10^{12}\,{\rm M}_{\odot}$, gas in the simulations
typically cools from a roughly spherical hot gas halo, as assumed in the SA
models, but the halo gas gradually contracts during cooling, leading to
compressional heating. SA models ignore this heating, and so overestimate mass
cooling rates by factors of a few. At low redshifts halo major mergers or a
sequence of successive smaller mergers are seen in the simulations to strongly
heat the halo gas and suppress cooling, while mergers at high redshifts do not
suppress cooling, because the gas filaments are difficult to heat up. The new
SA cooling model best captures these effects.


  There has been a growing need to devise processes that can create
comprehensive datasets in the world of Computer Algebra, both for accurate
benchmarking and for new intersections with machine learning technology. We
present here a method to generate integrands that are guaranteed to be
integrable, dubbed the LIOUVILLE method. It is based on Liouville's theorem and
the Parallel Risch Algorithm for symbolic integration.
  We show that this data generation method retains the best qualities of
previous data generation methods, while overcoming some of the issues built
into that prior work. The LIOUVILLE generator is able to generate sufficiently
complex and realistic integrands, and could be used for benchmarking or machine
learning training tasks related to symbolic integration.


  We present evidence that an interplay of the laws of microphysics and
cosmology renders the Planck momentum unattainable by an elementary particle.
Several categories of accelerators are analyzed and shown to fail.


  Multiflavour gauge theories of matter systems on a three-dimensional lattice
have recently been widely investigated especially in connection with a possible
symmetry enlargement at a continuous phase transition. Abelian models were
studied both with compact gauge fields and in a mixed formulation in which the
coupling with matter fields is in compact form while the gauge fields
Lagrangian is written in terms of non-compact gauge fields, getting quite
different results. Such a mixed formulation is not permissible for non-Abelian
theories, for which however there exists an entirely non-compact formulation
(in which exact gauge invariance is enforced by help of auxiliary fields), that
for SU(2) was shown to yield in the scaling window a larger physical volume
than Wilson's one. The corresponding U(1) non-compact regularization is derived
in the present work. In both Abelian and SU(2) cases there is only one
auxiliary field which for large mass has a linear coupling with the other
fields and it can be integrated out. The coupling with the auxiliary field
might make the inversion of the fermion matrix easier.


  We present a study of the isocyano isomers of the cyanopolyynes HC3N, HC5N,
and HC7N in TMC-1 and IRC+10216 carried out with the Yebes 40m radio telescope.
This study has enabled us to report the detection, for the first time in space,
of HCCCCNC in TMC-1 and to give upper limits for HC6NC in the same source. In
addition, the deuterated isotopologues of HCCNC and HNCCC were detected, along
with all 13C substitutions of HCCNC, also for the first time in space. The
abundance ratios of HC3N and HC5N, with their isomers, are very different in
TMC-1 and IRC+10216, namely, N(HC5N)/N(HC4NC) is 300 and >2100, respectively.
We discuss the chemistry of the metastable isomers of cyanopolyynes in terms of
the most likely formation pathways and by comparing observational abundance
ratios between different sources.


  In this paper we analyze the porous medium equation
\begin{equation}\label{ProblemAbstract} \tag{$\Diamond$} %\begin{cases}
u_t=\Delta u^m + a\io u^p-b u^q -c\lvert\nabla\sqrt{u}\rvert^2 \quad
\textrm{in}\quad \Omega \times I,%\\ %u_\nu-g(u)=0 & \textrm{on}\; \partial
\Omega, t>0,\\ %u({\bf x},0)=u_0({\bf x})&{\bf x} \in \Omega,\\ %\end{cases}
\end{equation} where $\Omega$ is a bounded and smooth domain of $\R^N$, with
$N\geq 1$, and $I= [0,t^*)$ is the maximal interval of existence for $u$. The
constants $a,b,c$ are positive, $m,p,q$ proper real numbers larger than 1 and
the equation is complemented with nonlinear boundary conditions involving the
outward normal derivative of $u$. Under some hypothesis on the data, including
intrinsic relations between $m,p$ and $q$, and assuming that for some positive
and sufficiently regular function $u_0(\nx)$ the Initial Boundary Value Problem
(IBVP) associated to \eqref{ProblemAbstract} possesses a positive classical
solution $u=u(\nx,t)$ on $\Omega \times I$: \begin{itemize} \item
[$\triangleright$] when $p>q$ and in 2- and 3-dimensional domains, we determine
a \textit{lower bound of} $t^*$ for those $u$ becoming unbounded in
$L^{m(p-1)}(\Omega)$ at such $t^*$; \item [$\triangleright$] when $p<q$ and in
$N$-dimensional settings, we establish a \textit{global existence criterion}
for $u$. \end{itemize}


  We study a crystallographic etching process of graphene nanostructures where
zigzag edges can be prepared selectively. The process involves heating
exfoliated single-layer graphene samples with a predefined pattern of antidot
arrays in an argon atmosphere at 820 C, which selectively removes carbon atoms
located on armchair sites. Atomic force microscopy and scanning electron
microscopy cannot resolve the structure on the atomic scale. However, weak
localization and Raman measurements - which both probe intervalley scattering
at armchair edges - indicate that zigzag regions are enhanced compared to
samples prepared with oxygen based reactive ion etching only.


  In this paper, we propose a novel deep learning architecture for multi-label
zero-shot learning (ML-ZSL), which is able to predict multiple unseen class
labels for each input instance. Inspired by the way humans utilize semantic
knowledge between objects of interests, we propose a framework that
incorporates knowledge graphs for describing the relationships between multiple
labels. Our model learns an information propagation mechanism from the semantic
label space, which can be applied to model the interdependencies between seen
and unseen class labels. With such investigation of structured knowledge graphs
for visual reasoning, we show that our model can be applied for solving
multi-label classification and ML-ZSL tasks. Compared to state-of-the-art
approaches, comparable or improved performances can be achieved by our method.


  The theory of Schroedinger bridges for diffusion processes is extended to
classical and quantum discrete-time Markovian evolutions. The solution of the
path space maximum entropy problems is obtained from the a priori model in both
cases via a suitable multiplicative functional transformation. In the quantum
case, nonequilibrium time reversal of quantum channels is discussed and
space-time harmonic processes are introduced.


  In the report the approach to estimation of quality of planned experiments is
considered. This approach is based on the analysis of uncertainty, which will
take place under the future hypotheses testing about the existence of a new
phenomenon in Nature. The probability of making a correct decision in
hypotheses testing is proposed as estimator of quality of planned experiments.
This estimator allows to take into account systematics and statistical
uncertainties in determination of signal and background rates.


  Unsupervised meta-learning approaches rely on synthetic meta-tasks that are
created using techniques such as random selection, clustering and/or
augmentation. Unfortunately, clustering and augmentation are domain-dependent,
and thus they require either manual tweaking or expensive learning. In this
work, we describe an approach that generates meta-tasks using generative
models. A critical component is a novel approach of sampling from the latent
space that generates objects grouped into synthetic classes forming the
training and validation data of a meta-task. We find that the proposed
approach, LAtent Space Interpolation Unsupervised Meta-learning (LASIUM),
outperforms or is competitive with current unsupervised learning baselines on
few-shot classification tasks on the most widely used benchmark datasets. In
addition, the approach promises to be applicable without manual tweaking over a
wider range of domains than previous approaches.


  We apply bulk holographic dark energy in general braneworld models with a
Gauss-Bonnet term in the bulk and an induced gravity term and a perfect fluid
on the brane. Without making any additional assumptions we extract the
Friedmann equation on the physical brane and we show that a
$\rho$-$\rho_\Lambda$ coupling arises naturally by the full 5D dynamics. The
low-energy (late-time) evolution reveals that the effective 4D holographic dark
energy behaves as ``quintom'', that is it crosses the phantom divide $w=-1$
during the evolution. In particular, the Gauss-Bonnet contribution decreases
the present value of $w_\Lambda$, while it increases the growing rate of
$w_\Lambda(z)$ with $z$, in comparison with the case where such a term is
absent.


  We develop a time and space dependent predator-prey model. The predators'
equation is a non local hyperbolic balance law, while the diffusion of prey
obeys a parabolic equation, so that predators "hunt" for prey, while prey
diffuse. A control term allows to describe the use of predators as parasitoids
to limit the growth of prey-parasites. The general well posedness and stability
results here obtained ensure the existence of optimal pest control strategies,
as discussed through some numerical integrations. The specific example we have
in mind is that of Trichopria drosophilae used to fight against the spreading
of Drosophila suzukii.


  This paper is concerned with the existence of conformal metrics of the disk
with prescribed Gaussian and geodesic curvatures. Being more specific, given
nonnegative smooth functions $K: \overline{\mathbb{D}} \to \mathbb{R}$ and $h:
\partial \mathbb{D} \to \mathbb{R}$, we consider the problem of finding a
conformal metric realizing $K$ and $h$ as Gaussian and geodesic curvatures,
respectively. This is the natural analogue of the classical Nirenberg problem
posed on the disk. As we shall see, both curvatures play a role in the
existence of solutions. Indeed we are able to give existence results under
conditions that involve $K$ and $H$, where $H$ denotes the harmonic extension
of $h$. The proof is based on the computation of the Leray-Schauder degree in a
compact setting.


  We study a cofibrant E-infty operad generated by the Fox-Neuwirth cells of
the configuration space of points in the Euclidean space. We show that, below
the `critical dimensions' in which `bad cells' exist, this operad is modeled by
the geometry of the Fulton-MacPherson compactification of this configuration
space. We analyze the Tamarkin bad cell and calculate the differential of the
corresponding generator. We also describe a simpler, four-dimensional bad cell.
We finish the paper by proving an auxiliary result giving a characterization,
over integers, of free Lie algebras.


  We prove that any sufficiently small perturbation of an isosceles triangle
has a periodic billiard path. Our proof involves the analysis of certain
infinite families of Fourier series that arise in connection with triangular
billiards, and reveals some self-similarity phenomena in irrational triangular
billiards. Our analysis illustrates the surprising fact that billiards on a
triangle near a Veech triangle is extremely complicated even though Billiards
on a Veech triangle is very well understood.


  The proposal of increasingly complex and innovative space endeavours poses
growing demands for mission designers. In order to meet the established
requirements and constraints while maintaining a low fuel cost, the use of
low-energy trajectories is particularly interesting. These allow spacecraft to
change orbits and move with little to no fuel, but they are computed using
motion models of a higher fidelity than the commonly used two-body problem
(2BP). For this purpose, perturbation methods that explore the third-body
effect are especially attractive, since they can accurately convey the system
dynamics of a three-body configuration with a lower computational cost, by
employing mapping techniques or exploring analytical approximations.
  The focus of this work is to broaden the knowledge of low-energy trajectories
by developing new mathematical tools to assist in mission design applications.
In particular, novel motion models based on the third-body effect are
conceived. One application of this study focuses on the trajectory design for
missions to near-Earth asteroids. Two different projects are explored: one is
based on the preliminary design of separate rendezvous and capture missions to
the invariant manifolds of libration point $L_2$. This is achieved by studying
two recently discovered asteroids and determining dates, fuel cost and final
control history for each trajectory. The other covers a larger study on
asteroid capture missions, where several bodies are regarded as potential
targets. The candidates are considered using a multi-fidelity design framework
that filters through the trajectory options using models of motion of
increasing accuracy, so that a final refined, low-thrust solution is obtained.
The trajectory design hinges on harnessing Earth's gravity by exploiting
encounters outside its sphere of influence, the named Earth-resonant
encounters.


  `Hypergeometric states', which are a one-parameter generalization of binomial
states of the single-mode quantized radiation field, are introduced and their
nonclassical properties are investigated. Their limits to the binomial states
and to the coherent and number states are studied. The ladder operator
formulation of the hypergeometric states is found and the algebra involved
turns out to be a one-parameter deformation of $su(2)$ algebra. These states
exhibit highly nonclassical properties, like sub-Poissonian character,
antibunching and squeezing effects. The quasiprobability distributions in phase
space, namely the $Q$ and the Wigner functions are studied in detail. These
remarkable properties seem to suggest that the hypergeometric states deserve
further attention from theoretical and applicational sides of quantum optics.