  The aim of this paper is to study the Mannheim partner curves in three
dimensional Galilean space . Some well known theorems are obtained related to
Mannheim curves.


  Finite dimensional Stein spaces admitting a proper holomorphic embedding of
the complex line are characterized, among all complex spaces, by their
holomorphic endomorphism semigroup in the sense that any semigroup isomorphism
induces either a biholomorphic or an antibiholomorphic map between them.


  We present a description of a new kind of the deformed canonical commutation
relations, their representations and generated by them Heisenberg-Weyl algebra.
This deformed algebra allows us to derive operations of the Hopf algebra
structure: comultiplication, counit and antipode. We discuss properties of a
discrete spectrum of the Hamiltonian of the deformed harmonic oscillator
corresponding to this oscillator-like system.


  The ultraviolet-to-radio continuum spectral energy distributions are
presented for all 75 galaxies in the Spitzer Infrared Nearby Galaxies Survey
(SINGS). A principal component analysis of the sample shows that most of the
sample's spectral variations stem from two underlying components, one
representative of a galaxy with a low infrared-to-ultraviolet ratio and one
representative of a galaxy with a high infrared-to-ultraviolet ratio. The
influence of several parameters on the infrared-to-ultraviolet ratio is studied
(e.g., optical morphology, disk inclination, far-infrared color, ultraviolet
spectral slope, and star formation history). Consistent with our understanding
of normal star-forming galaxies, the SINGS sample of galaxies in comparison to
more actively star-forming galaxies exhibits a larger dispersion in the
infrared-to-ultraviolet versus ultraviolet spectral slope correlation. Early
type galaxies, exhibiting low star formation rates and high optical surface
brightnesses, have the most discrepant infrared-to-ultraviolet correlation.
These results suggest that the star formation history may be the dominant
regulator of the broadband spectral variations between galaxies. Finally, a new
discovery shows that the 24 micron morphology can be a useful tool for
parametrizing the global dust temperature and ultraviolet extinction in nearby
galaxies. The dust emission in dwarf/irregular galaxies is clumpy and warm
accompanied by low ultraviolet extinction, while in spiral galaxies there is
typically a much larger diffuse component of cooler dust and average
ultraviolet extinction. For galaxies with nuclear 24 micron emission, the dust
temperature and ultraviolet extinction are relatively high compared to disk
galaxies.


  We give an upper bound on the dimension of the bounded derived category of an
abelian category. We show that if $\CX$ is a sufficiently nice subcategory of
an abelian category, then derived dimension of $\CA$ is at most $\CX$-dim$\CA$,
provided $\CX$-dim$\CA$ is greater than one. We provide some applications.


  Time-dependent spin phenomena in condensed matter are most often either
described in the weakly correlated limit of metallic Stoner/Slater-like
magnetism via band theory or in the strongly correlated limit of
Heisenberg-like interacting spins in an insulator. However many experimental
studies, e.g. of (de)magnetization processes, focus on itinerant local-moment
materials such as transition metals and various of their compounds. We here
present a general theoretical framework that is capable of addressing
correlated spin dynamics, also in the presence of a vanishing charge gap. A
real-space implementation of the time-dependent rotational-invariant slave
boson methodology allows to treat non-equilibrium spins numerically fast and
efficiently beyond linear response as well as beyond the band-theoretical or
Heisenberg limit.


  Multiscale phenomena exhibit complex structure-function relationships, and
predicting their macroscopic behavior requires deducing differential equations
at different scales. The complexity of these equations and the number of
essential parameters make developing effective, predictive models challenging.
To overcome this, researchers explore leveraging advanced numerical techniques
from artificial intelligence and machine learning. Here, we focus on a
fundamental aspect in multiscale phenomena, i.e the recognition of the
hierarchical role of variables. By adopting a Pareto front interpretation, we
aim to deduce simple and accurate relations for material modeling, starting
from experimental multiscale analyses. From a physical point of view, the aim
is to deduce information at higher scales from lower scales data, possibly
respecting their hierarchical order. A crucial aspect of the proposed approach
is the deduction of causality relations among the different variables to be
compared with the available theoretical notions and possibly new
interpretations resulting by the data modelling. This result in a stepwise
approximation going from data modelling to theoretical equations and back to
data modelling. To demonstrate the key advantages of our multiscale numerical
approach, compared to classical, non-physically based data modelling
techniques, we consider the explicit example of spider silk, known for its
exceptional properties and bioinspiration potential. Indeed, it presents a
complex behavior resulting from mesostructures formed by the aggregation of
amino acids at the molecular scale. We argue that, due to the generality of our
results, our approach may represent a proof of concept in many fields where
multiscale, hierarchical differential equations regulate the observed
phenomenon.


  Kernel methods are widely used for probability estimation by measuring the
distribution of low-passed vector distances in reconstructed state spaces.
However, the information conveyed by the vector distances that are greater than
the threshold has received little attention. In this paper, we consider the
probabilistic difference of the kernel transformation in reconstructed state
spaces, and derive a novel nonequilibrium descriptor by measuring the
fluctuations of the vector distance with respect to the tolerance. We verify
the effectiveness of the proposed kernel probabilistic difference using three
chaotic series (logistic, Henon, and Lorenz) and a first-order autoregressive
series according to the surrogate theory, and we use the kernel parameter to
analyze real-world heartbeat data. In the heartbeat analysis, the kernel
probabilistic difference, particularly that based on the Kullback--Leibler
divergence, effectively characterizes the physiological complexity loss related
to reduced cardiac dynamics in the elderly and diseased heartbeat data.
Overall, the kernel probabilistic difference provides a novel method for the
quantification of nonequilibria by characterizing the fluctuation theorem in
reconstructed state spaces, and enables reliable detection of cardiac
physiological and pathological information from heart rates.


  We study transverse fast magnetohydrodynamic waves in a system of two coronal
loops modeled as smoothed, dense plasma cylinders in a uniform magnetic field.
The collective oscillatory properties of the system due to the interaction
between the individual loops are investigated from two points of view. Firstly,
the frequency and spatial structure of the normal modes are studied. The system
supports four trapped normal modes in which the loops move rigidly in the
transverse direction. The direction of the motions is either parallel or
perpendicular to the plane containing the axes of the loops. Two of these modes
correspond to oscillations of the loops in phase, while in the other two they
move in antiphase. Thus, these solutions are the generalization of the kink
mode of a single cylinder to the double cylinder case. Secondly, we analyze the
time-dependent problem of the excitation of the pair of tubes. We find that
depending on the shape and location of the initial disturbance, different
normal modes can be excited. The frequencies of normal modes are accurately
recovered from the numerical simulations. In some cases, because of the
simultaneous excitation of several eigenmodes, the system shows beating and the
phase lag between the loops is $\pi/2$.


  Differential atmospheric dispersion is a wavelength-dependent effect
introduced by the atmosphere. It is one of the instrumental errors that can
affect the position of the target as perceived on the sky and its flux
distribution. This effect will affect the results of astronomical observations
if not corrected by an atmospheric dispersion corrector (ADC). In
high-resolution spectrographs, in order to reach a radial velocity (RV)
precision of 10 cm/s, an ADC is expected to return residuals at only a few tens
of milli-arcseconds (mas). In fact, current state-of-the-art spectrographs
conservatively require this level of residuals, although no work has been done
to quantify the impact of atmospheric dispersion. In this work we test the
effect of atmospheric dispersion on astronomical observations in general, and
in particular on RV precision degradation and flux losses. Our scientific
objective was to quantify the amount of residuals needed to fulfill the
requirements set on an ADC during the design phase. We found that up to a
dispersion of 100 mas, the effect on the RV is negligible. However, on the flux
losses, such a dispersion can create a loss of ~2% at 380 nm, a significant
value when efficiency is critical. The requirements set on ADC residuals should
take into consideration the atmospheric conditions where the ADC will function,
and also all the aspects related with not only the RV precision requirements
but also the guiding camera used, the tolerances on the flux loss, and the
different melt data of the chosen glasses.


  We calculate photon production from a quark-gluon plasma which is anisotropic
in momentum space including the Compton scattering and quark/anti-quark
annihilation processes. We show that for a quark-gluon plasma which has an
oblate momentum-space anisotropy the photon production rate has an angular
dependence which is peaked transverse to the beam line. We propose to use the
angular dependence of high-energy medium photon production to experimentally
determine the degree of momentum-space isotropy of a quark-gluon plasma
produced in relativistic heavy-ion collisions.


  Strange nonchaotic attractors (SNA) arise in quasiperiodically driven systems
in the neighborhood of a saddle node bifurcation whereby a strange attractor is
replaced by a periodic (torus) attractor. This transition is accompanied by
Type-I intermittency. The largest nontrivial Lyapunov exponent $\Lambda$ is a
good order-parameter for this route from chaos to SNA to periodic motion: the
signature is distinctive and unlike that for other routes to SNA. In
particular, $\Lambda$ changes sharply at the SNA to torus transition, as does
the distribution of finite-time or N--step Lyapunov exponents, P(\Lambda_N).


  We developed a modular silicon photomultiplier camera to detect
Earth-skimming PeV to EeV tau neutrinos with the imaging atmospheric Cherenkov
technique. We built two cameras, a 256-pixel camera with S14161-6050HS SiPMs
for the Trinity Demonstrator located on Frisco Peak, Utah, and a 512-pixel
camera with S14521-6050AN SiPMs for the EUSO-SPB2 Cherenkov Telescope. The
front-end electronics are based on the eMUSIC ASIC, and the camera signals are
sampled and digitized with the 100MS/s and 12-bit AGET system. Both cameras are
liquid-cooled. We detail the camera concept and the results from characterizing
the SiPMs, bench testing, and calibrating the two cameras.


  We generalize a result of Paulin on the Gromov boundary of hyperbolic groups
to the Morse boundary of proper, maximal hierarchically hyperbolic spaces
admitting cocompact group actions by isometries. Namely we show that if the
Morse boundaries of two such spaces each contain at least three points, then
the spaces are quasi-isometric if and only if there exists a 2-stable,
quasi-m\"obius homeomorphism between their Morse boundaries. Our result extends
a recent result of Charney-Murray, who prove such a classification for CAT(0)
groups, and is new for mapping class groups and the fundamental groups of
$3$-manifolds without Nil or Sol components.


  We have recently tested the topological phase predicted by He and McKellar
and by Wilkens: this phase appears when an electric dipole propagates in a
transverse magnetic field. In the present paper, we first recall the physical
origin of this phase and its relations to the Aharononov-Bohm and
Aharonov-Casher phases. We then explain possible detection schemes and we
briefly describe the lithium atom interferometer we have used for this purpose.
Finally, we analyze in great detail the phase shifts induced by electric and
magnetic fields acting on such an interferometer, taking into account
experimental defects. The experiment and its results are described in a
companion paper.


  We compile the radio-optical-X-ray spectral energy distributions (SEDs) of 65
knots and 29 hotspots in 41 active galactic nucleus jets to examine their high
energy radiation mechanisms. Their SEDs can be fitted with the single-zone
leptonic models, except for the hotspot of Pictor A and six knots of 3C 273.
The X-ray emission of one hotspot and 22 knots is well explained as synchrotron
radiations under the equipartition condition; they usually have lower X-ray and
radio luminosities than the others, which may be due to a lower beaming factor.
An inverse Compton (IC) process is involved for explaining the X-ray emission
of the other SEDs. Without considering the equipartition condition, their X-ray
emission can be attributed to the synchrotron-self-Compton (SSC) process, but
the derived jet power (P_jet) are not correlated with L_k and most of them are
larger than L_k with more than three orders of magnitude, where L_k is the jet
kinetic power estimated with their radio emission. Under the equipartition
condition, the X-ray emission is well interpreted with the IC process to the
cosmic microwave background photons (IC/CMB). In this scenario, the derived
P_jet of knots and hotspots are correlated with and comparable to L_k. These
results suggest that the IC/CMB model may be the promising interpretation of
their X-ray emission. In addition, a tentative knot-hotspot sequence in the
synchrotron peak-energy--peak-luminosity plane is observed, similar to the
blazar sequence, which may be attributed to their different cooling mechanisms
of electrons.


  An infinite family of quasi-maximally superintegrable Hamiltonians with a
common set of (2N-3) integrals of the motion is introduced. The integrability
properties of all these Hamiltonians are shown to be a consequence of a hidden
non-standard quantum sl(2,R) Poisson coalgebra symmetry. As a concrete
application, one of this Hamiltonians is shown to generate the geodesic motion
on certain manifolds with a non-constant curvature that turns out to be a
function of the deformation parameter z. Moreover, another Hamiltonian in this
family is shown to generate geodesic motions on Riemannian and relativistic
spaces all of whose sectional curvatures are constant and equal to the
deformation parameter z. This approach can be generalized to arbitrary
dimension by making use of coalgebra symmetry.


  Gravitationally redshifted absorption lines of Fe XXVI, Fe XXV, and O VIII
were inferred recently in the X-ray spectrum of the bursting neutron star EXO
0748-676. We place an upper limit on the stellar magnetic field based on the
iron lines. The oxygen absorption feature shows a multiple component profile
that is consistent with Zeeman splitting in a magnetic field of ~(1-2)x10^9
gauss, and for which the corresponding Zeeman components of the iron lines are
expected to be blended together. In other systems, a field strength >5x10^{10}
gauss could induce a blueshift of the line centroids that would counteract
gravitational redshift and complicate the derivation of constraints on the
equation of state of the neutron star.


  We investigate the relationship between stability, adiabaticity and transfer
efficiency in a \Lambda-type atom-molecule coupling system via a nonlinear
stimulated Raman adiabatic passage. We find that only when the pump and control
lasers overlap in time domain, the coherent population trapping (CPT) state
could become unstable. If the overlapping time of the two lasers is short so
that unstable growth of the deviation from the CPT state is negligible, then
good adiabaticity of the CPT state could be maintained even in the unstable
region. In this case, a high atom-molecule transfer efficiency could be
obtained by chirping applied laser pulses to elegantly compensate the frequency
shift induced by intra-atomic collision. Our results could be useful for
efficiently photoassociating ground-state molecules from a cold atomic gas with
strong atom-atom collisional interaction.


  In a recent post on the Seqfan list the third author proposed a conjecture
concerning the summatory function of odious numbers (i.e., of numbers whose sum
of binary digits is odd), and its analog for evil numbers (i.e., of numbers
whose sum of binary digits is even). We prove these conjectures here. We will
also study the sequences of "generalized" odious and evil numbers, and their
iterations, giving in particular a characterization of the sequences of usual
odious and evil numbers in terms of functional equations satisfied by their
compositions.


  We study minimizers of non-autonomous energies with minimal growth and
coercivity assumptions on the energy. We show that the minimizer is
nevertheless the solution of the relevant Euler--Lagrange equation or
inequality. The main tool is an extension result for convex $C^1$-energies,
which is of independent interest.


  In this paper, we study simplicial hyperplane arrangements in real projective
$3$-space. We give a necessary condition for the characteristic polynomial to
have only real roots, valid also for non-simplicial arrangements. As
application, we obtain combinatorial inequalities which are satisfied for
arrangements with splitting polynomial. This allows us to prove that there are
only finitely many different isomorphism classes of simply laced simplicial
arrangements whose characteristic polynomials split over $\mathbb{R}$. We also
provide an updated version of a catalogue published by Gr\"unbaum and Shephard
and review some conjectures of theirs.


  Recently Peter Keevash solved asymptotically the existence question for
Steiner systems by showing that $S(t,k,n)$ exists whenever the necessary
divisibility conditions on the parameters are satisfied and $n$ is sufficiently
large in terms of $k$ and $t$. The purpose of this paper is to make a
conjecture which if true would be a significant extension of Keevash's theorem,
and to give some theoretical and computational evidence for the conjecture.
  We phrase the conjecture in terms of the notions (which we define here) of
synchronization and separation for association schemes. These definitions are
based on those for permutation groups which grow out of the theory of
synchronization in finite automata. In this theory, two classes of permutation
groups (called \emph{synchronizing} and \emph{separating}) lying between
primitive and $2$-homogeneous are defined. A big open question is how the
permutation group induced by $S_n$ on $k$-subsets of $\{1,\ldots,n\}$ fits in
this hierarchy; our conjecture would give a solution to this problem for $n$
large in terms of $k$. We prove the conjecture in the case $k=4$: our result
asserts that $S_n$ acting on $4$-sets is separating for $n\ge10$ (it fails to
be synchronizing for $n=9$).


  Charmonium directed flows are studied based on transport model coupled with
the realistic three dimensional expansions of the bulk medium. The non-central
symmetric nucleus-nucleus collisions can generate the rotating quark-gluon
plasma (QGP) with symmetry-breaking longitudinal distributions. In
$\sqrt{s_{NN}}=200$ GeV Au-Au semi-central collisions, charmonium are
primordially produced in the initial hard process, they are mainly dissociated
by the initial tilted source with high temperatures and then move out of the
bulk medium to keep the early information of the medium. Charmonia are less
affected by the hydrodynamic expansions of QGP where its tilted shape is being
diluted. This biased dissociation can generate directed flows of $J/\psi$ and
$\psi(2S)$ which are much larger than the values of light charged hadrons and
open heavy flavor. They are sensitive and clean to the effect of QGP
rapidity-odd initial energy densities.


  Several techniques for visualization of dynamic graphs are based on different
spatial arrangements of a temporal sequence of node-link diagrams. Many studies
in the literature have investigated the importance of maintaining the user's
mental map across this temporal sequence, but usually each layout is considered
as a static graph drawing and the effect of user interaction is disregarded. We
conducted a task-based controlled experiment to assess the effectiveness of two
basic interaction techniques: the adjustment of the layout stability and the
highlighting of adjacent nodes and edges. We found that generally both
interaction techniques increase accuracy, sometimes at the cost of longer
completion times, and that the highlighting outclasses the stability adjustment
for many tasks except the most complex ones.


  Factors that contribute to the rapid increase in power dissipation as a
function of input bandwidth in high speed electronic Analog-to-Digital
Converters (ADCs) are discussed. We find that the figure of merit (FOM),
defined as the energy required per conversion step, increases linearly with
bandwidth for high-speed ADCs with moderate to high resolution, or
equivalently, the power dissipation increases quadratically. It is shown that
by use of photonic time-stretch technique, it is possible to have ADCs in which
this FOM remains constant for up to 10 GHz input RF frequency. Using this
technique, it is also possible to overcome the barrier to achieving high
resolution caused by clock jitter and speed limitations of electronics in such
ADCs.
  Use of optics is actively being pursued for reducing power dissipation and
achieving higher data-rates for board-level and chip-level serial communication
links. In the same manner, we expect that optics will also help in reducing
power dissipation in high-speed ADCs in addition to providing broader
bandwidths.


  We prove that there exists a one-parameter meromorphic solution $u(\tau)$
vanishing at $\tau=0$ of the degenerate third Painlev\'e equation,
\begin{equation*} u^{\prime \prime}(\tau) \! = \!
\frac{(u^{\prime}(\tau))^{2}}{u(\tau)} \! - \! \frac{u^{\prime}(\tau)}{\tau} \!
+ \! \frac{1}{\tau} \! \left(-8 \varepsilon (u(\tau))^{2} \! + \! 2ab \right)
\! + \! \frac{b^{2}}{u(\tau)},\qquad \varepsilon=\pm1,\quad\varepsilon b>0,
\end{equation*} for formal monodromy parameter $a=\pm i/2$. We study
number-theoretic properties of the coefficients of the Taylor-series expansion
of $u(\tau)$ at $\tau=0$ and its asymptotic behaviour as $\tau\to+\infty$.
These asymptotics are visualized for generic initial data.


  Given a graph $G$ and a graph property $P$ we say that $G$ is minimal with
respect to $P$ if no proper induced subgraph of $G$ has the property $P$. An
HC-obstruction is a minimal 2-connected non-Hamiltonian graph. Given a graph
$H$, a graph $G$ is $H$-free if $G$ has no induced subgraph isomorphic to $H$.
The main motivation for this paper originates from a theorem of Duffus, Gould,
and Jacobson (1981), which characterizes all the minimal connected graphs with
no Hamiltonian path. In 1998, Brousek characterized all the claw-free
HC-obstructions. On a similar note, Chiba and Furuya (2021), characterized all
(not only the minimal) 2-connected non-Hamiltonian $\{K_{1,3},
N_{3,1,1}\}$-free graphs. Recently, Cheriyan, Hajebi, and two of us (2022),
characterized all triangle-free HC-obstructions and all the HC-obstructions
which are split graphs. A wheel is a graph obtained from a cycle by adding a
new vertex with at least three neighbors in the cycle. In this paper we
characterize all the HC-obstructions which are wheel-free graphs.


  The process of designing neural architectures requires expert knowledge and
extensive trial and error. While automated architecture search may simplify
these requirements, the recurrent neural network (RNN) architectures generated
by existing methods are limited in both flexibility and components. We propose
a domain-specific language (DSL) for use in automated architecture search which
can produce novel RNNs of arbitrary depth and width. The DSL is flexible enough
to define standard architectures such as the Gated Recurrent Unit and Long
Short Term Memory and allows the introduction of non-standard RNN components
such as trigonometric curves and layer normalization. Using two different
candidate generation techniques, random search with a ranking function and
reinforcement learning, we explore the novel architectures produced by the RNN
DSL for language modeling and machine translation domains. The resulting
architectures do not follow human intuition yet perform well on their targeted
tasks, suggesting the space of usable RNN architectures is far larger than
previously assumed.


  The detection of semantic relationships between objects represented in an
image is one of the fundamental challenges in image interpretation.
Neural-Symbolic techniques, such as Logic Tensor Networks (LTNs), allow the
combination of semantic knowledge representation and reasoning with the ability
to efficiently learn from examples typical of neural networks. We here propose
Faster-LTN, an object detector composed of a convolutional backbone and an LTN.
To the best of our knowledge, this is the first attempt to combine both
frameworks in an end-to-end training setting. This architecture is trained by
optimizing a grounded theory which combines labelled examples with prior
knowledge, in the form of logical axioms. Experimental comparisons show
competitive performance with respect to the traditional Faster R-CNN
architecture.


  We investigate the zero modes of the Kaluza-Klein monopole in M-theory and
show that the Born-Infeld action and the Chern-Simons term of a D6-brane are
reproduced to quadratic order in the field strength of the U(1) field on the
brane.


  The ability to generate complex and realistic human body animations at scale,
while following specific artistic constraints, has been a fundamental goal for
the game and animation industry for decades. Popular techniques include
key-framing, physics-based simulation, and database methods via motion graphs.
Recently, motion generators based on deep learning have been introduced.
Although these learning models can automatically generate highly intricate
stylized motions of arbitrary length, they still lack user control. To this
end, we introduce the problem of long-term inbetweening, which involves
automatically synthesizing complex motions over a long time interval given very
sparse keyframes by users. We identify a number of challenges related to this
problem, including maintaining biomechanical and keyframe constraints,
preserving natural motions, and designing the entire motion sequence
holistically while considering all constraints. We introduce a biomechanically
constrained generative adversarial network that performs long-term inbetweening
of human motions, conditioned on keyframe constraints. This network uses a
novel two-stage approach where it first predicts local motion in the form of
joint angles, and then predicts global motion, i.e. the global path that the
character follows. Since there are typically a number of possible motions that
could satisfy the given user constraints, we also enable our network to
generate a variety of outputs with a scheme that we call Motion DNA. This
approach allows the user to manipulate and influence the output content by
feeding seed motions (DNA) to the network. Trained with 79 classes of captured
motion data, our network performs robustly on a variety of highly complex
motion styles.


  Research funding agencies routinely use a proportion of their total revenues
to support internal administration and marketing costs. The ratio of
administration to total costs, referred to as the administration ratio, is
highly variable and within any single fund depends on many factors including
the number and average size of projects and the overall efficiency of the
funding agency. In this study, the standard agency activities have been
identified and used to develop a model of administration costs against expected
outcomes. In particular, the model has been designed to estimate the optimum
portfolio success rate and administration ratio as a function of a range of key
input variables including the project size, the complexity of proposal
evaluation and project management, the risk tolerance of the sponsor and the
targeted research domain.


  The paper considers an effect of intensive ultrasound on the suspension of
soot microparticles and nanoparticles in the inert gas, resulting in the
coagulation of relatively large soot particles and leading to the improvement
of the efficiency of production of nanoparticles, as has been observed in
experiments. The effect of the particles charge on the possibility of
coagulation is analyzed.


  We present an algorithm which, given any finite presentation of a group as
input, will terminate with answer yes if and only if the group is large. We use
this to prove that a mapping torus of a finitely generated free group
automorphism is large if it contains the integers times the integers as a
subgroup of infinite index. We then extend this result to mapping tori of
finitely generated free group endomorphisms, as well as showing that such a
group is large if it contains a Baumslag-Solitar group of infinite index and
has a finite index subgroup with first Betti number at least 2. We also show
that if a group possesses a deficiency 1 presentation where one of the relators
is a commutator then it is the integers times the integers, or it is large, or
it is as far as possible from being residually finite.


  We study theoretically the hydrodynamics of a fluid drop containing oriented
filaments endowed with active contractile or extensile stresses and placed on a
solid surface. The active stresses alter qualitatively the wetting properties
of the drop, leading to new spreading laws and novel static drop shapes.
Candidate systems for testing our predictions include cytoskeletal extracts
with motors and ATP, suspensions of bacteria or pulsatile cells, or fluids
laden with artificial self-propelled colloids.


  Two-dimensional almost-Riemannian structures are generalized Riemannian
structures on surfaces for which a local orthonormal frame is given by a Lie
bracket generating pair of vector fields that can become collinear.
Generically, there are three types of points: Riemannian points where the two
vector fields are linearly independent, Grushin points where the two vector
fields are collinear but their Lie bracket is not, and tangency points where
the two vector fields and their Lie bracket are collinear and the missing
direction is obtained with one more bracket. In this paper we consider the
problem of finding normal forms and functional invariants at each type of
point. We also require that functional invariants are "complete" in the sense
that they permit to recognize locally isometric structures. The problem happens
to be equivalent to the one of finding a smooth canonical parameterized curve
passing through the point and being transversal to the distribution. For
Riemannian points such that the gradient of the Gaussian curvature $K$ is
different from zero, we use the level set of $K$ as support of the
parameterized curve. For Riemannian points such that the gradient of the
curvature vanishes (and under additional generic conditions), we use a curve
which is found by looking for crests and valleys of the curvature. For Grushin
points we use the set where the vector fields are parallel. Tangency points are
the most complicated to deal with. The cut locus from the tangency point is not
a good candidate as canonical parameterized curve since it is known to be
non-smooth. Thus, we analyse the cut locus from the singular set and we prove
that it is not smooth either. A good candidate appears to be a curve which is
found by looking for crests and valleys of the Gaussian curvature. We prove
that the support of such a curve is uniquely determined and has a canonical
parametrization.


  We analyse spectroscopic measurements of 122 type Ia supernovae (SNe Ia) with
z<0.09 discovered by the Palomar Transient Factory, focusing on the properties
of the Si II 6355 and Ca II `near-infrared triplet' absorptions. We examine the
velocities of the photospheric Si II 6355, and the velocities and strengths of
the photospheric and high-velocity Ca II, in the context of the stellar mass
(Mstellar) and star-formation rate (SFR) of the SN host galaxies, as well as
the position of the SN within its host. We find that SNe Ia with faster Si II
6355 tend to explode in more massive galaxies, with the highest velocity events
only occuring in galaxies with Mstellar > 3*10^9 solar mass. We also find some
evidence that these highest velocity SNe Ia explode in the inner regions of
their host galaxies, similar to the study of Wang et al. (2013), although the
trend is not as significant in our data. We show that these trends are
consistent with some SN Ia spectral models, if the host galaxy stellar mass is
interpreted as a proxy for host galaxy metallicity. We study the strength of
the high-velocity component of the Ca II near-IR absorption, and show that SNe
Ia with stronger high-velocity components relative to photospheric components
are hosted by galaxies with low stellar mass, blue colour, and a high sSFR.
Such SNe are therefore likely to arise from the youngest progenitor systems.
This argues against a pure orientation effect being responsible for
high-velocity features in SN Ia spectra and, when combined with other studies,
is consistent with a scenario where high-velocity features are related to an
interaction between the SN ejecta and circumstellar medium (CSM) local to the
SN.


  Suppose we choose $N$ points uniformly randomly from a convex body in $d$
dimensions. How large must $N$ be, asymptotically with respect to $d$, so that
the convex hull of the points is nearly as large as the convex body itself? It
was shown by Dyer-F\"uredi-McDiarmid that exponentially many samples suffice
when the convex body is the hypercube, and by Pivovarov that the Euclidean ball
demands roughly $d^{d/2}$ samples. We show that when the convex body is the
simplex, exponentially many samples suffice; this then implies the same result
for any convex simplicial polytope with at most exponentially many faces.


  We consider the realistic case of a superconductor with a nonzero density of
elastic scatterers, so that the normal state conductivity is finite. The
quantum superconductor-metal (QSM) transition can then be tuned by varying
either the attractive electron-electron interaction, the quenched disorder, or
the applied magnetic field. We explore the consistency of the associated
scaling relations, Tc ~ 1/lamda(0) ~ gap(0) ~ 1/gsi(0) ~ Hc2(0)^-0.5 and Tc(H)
~ 1/Lamda(0,H) ~ gap(0,h) ~ (Hc2(0)-H)^ 1/2, valid for all dimensions D > 2,
with experimental data, in Al, C doped MgB2 and overdoped cuprates.


  In this paper we show that with the help of accessible, teaching quality
equipment, some interesting details of the motion of a gyroscope, typically
overlooked in introductory courses, can be measured and compared to theory. We
begin by deriving a simple relation between the asymptotic dip angle of a
gyroscope released from rest and its precession velocity. We then describe an
experiment which measures these parameters. The data gives excellent agreement
with the model. The idea for this project was suggested by the discussion of
gyroscopic motion in The Feynman Lectures on Physics. Feynman's conclusion
(stated in colloquial terms and quoted in the title) is confirmed and, in
addition, conservation of angular momentum, which underlies this effect, is
quantitatively demonstrated.


  The pressure-temperature phase diagram of a one-component system, with
particles interacting through a spherically symmetric pair potential is
studied. It is shown that if the pair potential allows for a discontinuous
reduction of the volume of the system when pressure is increased (at zero
temperature), then the phase diagram obtained has many ``water like''
characteristics. Among these characteristics the negative thermal expansion and
expansion upon freezing in some range of pressure, and the existence of many
different crystaline structures are clearly observable in numerical
simulations. This implies that complex phase diagrams are not necessarily
originated in complex microscopic interactions.


  We present the theory of dielectric spectra allowing for homogeneous and
inhomogeneous broadening mechanisms contributions. The dielectric absorption
line shape for oscillators with memory and Debye type relaxors with
distribution of, respectively, resonant frequencies and relaxation times (due
to random electric fields distribution) has been calculated. The conditions of
hole burning observation are discussed. It is shown that the investigations of
the inhomogeneously broadened line shape and width as well as hole burning can
give valuable information about the distribution of random fields and
relaxation times. The latter seems to be extremely important for the disordered
systems like supercooled liquids and relaxor ferroelectrics.


  The extended Frank elastic energy density is used to investigate the
existence of a stable periodically modulate structure that appears as a ground
state exhibiting a twist-bend molecular arrangement. For an unbounded sample,
we show that the twist-bend nematic phase $N_{TB}$ is characterized by a
heliconical structure with a pitch in the nano-metric range, in agreement with
experimental results. For a sample of finite thickness, we show that the wave
vector of the stable periodic structure depends not only on the elastic
parameters but also on the anchoring energy, easy axis direction, and the
thickness of the sample.


  We consider the spreading of the wave packet in the generalized
Rosenzweig-Porter random matrix ensemble in the region of non-ergodic extended
states $1<\gamma<2$. We show that despite non-trivial fractal dimensions $0 <
D_{q}=2-\gamma<1$ characterize wave function statistics in this region, the
wave packet spreading $\langle r^{2} \rangle \propto t^{\beta}$ is governed by
the "diffusion" exponent $\beta=1$ outside the ballistic regime $t>\tau\sim 1$
and $\langle r^{2}\rangle \propto t^{2}$ in the ballistic regime for
$t<\tau\sim 1$. This demonstrates that the multifractality exhibits itself only
in {\it local} quantities like the wave packet survival probability but not in
the large-distance spreading of the wave packet.


  Extrapolating the coupling strengths to very high energies, one finds that
they do not converge to a single coupling constant, as expected in the simplest
gauge theory of Grand Unification, the SU(5) theory. We find that the coupling
constants do converge, provided that two new intermediate energy scales are
introduced, the energies where the group SU(4), containing the color group, and
the right-isospin gauge group are spontaneously broken down.


  We re-examine and extend a recent analysis which showed that the rho-omega
mixing amplitude cannot be unambiguously extracted from the pion
electromagnetic form-factor in a model independent way. In particular, we focus
on the argument that the extraction is sensitive to the presence of any
intrinsic omega_I -> 2pi coupling. Our extended analysis confirms the original
conclusion, with only minor, quantitative differences. The extracted mixing
amplitude is shown to be sensitive to both the intrinsic coupling omega_I ->
2pi and to the value assumed for the mass of the neutral rho meson.


  We introduce a graphical presentation for the false nearest neighbors (FNN)
method. In the original method only the percentage of false neighbors is
computed without regard to the distribution of neighboring points in the
time-delay coordinates. With this new presentation it is much easier to
distinguish deterministic chaos from noise. The graphical approach also serves
as a tool to determine better conditions for detecting low dimensional chaos,
and to get a better understanding on the applicability of the FNN method.


  We give a complete description of all classical Enriques surfaces with
non-zero global vector fields. In particular we show that there are such
surfaces. The obtained result also applies to supersingular Enriques surfaces
fulfilling a rather special condition. During this classification we study some
properties of genus 1-fibrations special to characteristic as well as make a
close study of the genus 1-fibration on the surfaces that we classify.


  We present spectroscopy from the Keck telescope of three sets of objects in
the Hubble Deep Field which have lens-like morphologies. In the case of
J123641+621204, which is composed of four objects with similar colors and a
mean separation of <= 0.8", we find at least two distinct components at
redshifts of z=3.209 and z=3.220 which are separated by 0.5" spatially. Each of
these components has narrow Ly-alpha emission, and possibly NV emission and
SiIV and CIV in absorption or with a P-Cygni profile. The second case is
J123652+621227, which has an arc-like feature offset by 1.8" to the southwest
of a red elliptical-like galaxy, and a ``counterimage'' offset 1.4" on the
opposite side. We tentatively find a single line at 5301 AA at the spatial
position of the counterimage, and no corresponding emission line at the
position of the arc. The colors of the counterimage are consistent with the
identification of this line as Ly-alpha at z=3.36. The colors of the arc are
different than those of the counterimage, and thus both the colors and spectra
indicate that this object is unlikely to be a gravitational lens. For a third
lensing candidate (J123656+621221), which is a blue arc offset by 0.9" from a
red, elliptical-like galaxy, our spectroscopy does not clearly resolve the
system spatially, complicating the interpretation of the spectrum. We discuss
possible identifications of features in the spectrum, and find that
gravitational lensing remains a possibility in this case. We conclude that the
frequency of strong gravitational lensing by galaxies in the HDF appears to be
very low. This result is difficult to reconcile with the introduction of a
cosmological constant to account for the large number of faint blue galaxies
via a large volume element at high redshift.


  A generic aggregate forming system in two dimensions (2D) is studied using
canonical ensemble constant temperature molecular dynamics simulation. The
aggregates form due to the competition between short range attraction and long
range repulsion of pair-wise interactions. Choosing the appropriate set of
interaction parameters, we focus on characterising the collective dynamics in
two specific morphologies, {\it viz.} compact and string-like aggregates. We
focus on the temporal evolution of the mobility of an individual particle and
the dynamic change in its nearest neighbourhood, measured in terms of the
Debye-Waller factor ($\bar{u}_i^2$) and the non-affine parameter ($\chi$),
respectively (defined in the text), and their interrelation over several
lengths of observation time $\tau_w$. The distribution for both measures are
found to follow the relation: $P(x;\tau_w) \sim \tau_w^{-\gamma}x$ for the
measured quantity $x$. The exponent $\gamma$ is equal to $2$ and $1$
respectively, for the compact and string-like morphologies following the ideal
fractal dimension of these aggregates. A functional dependence between these
two observables is determined from a detailed statistical analysis of their
joint and conditional distributions. The results obtained can readily be used
and verified by experiments on aggregate forming systems such as globular
proteins, nanoparticle self-assembly etc. Further, the insights gained from
this study might be useful to understand the evolution of collective dynamics
in diverse glass-forming systems.


  The analysis of defects and defect dynamics in crystalline materials is
important for fundamental science and for a wide range of applied engineering.
With increasing system size the analysis of molecular-dynamics simulation data
becomes non-trivial. Here, we present a workflow for semi-automatic
identification and classification of defects in crystalline structures,
combining a new approach for defect description with several already existing
open-source software packages. Our approach addresses the key challenges posed
by the often relatively tiny volume fraction of the modified parts of the
sample, thermal motion and the presence of potentially unforeseen atomic
configurations (defect types) after irradiation. The local environment of any
atom is converted into a rotation-invariant descriptive vector ('fingerprint'),
which can be compared to known defect types and also yields a distance metric
suited for classification. Vectors which cannot be associated to known
structures indicate new types of defects. As proof-of-concept we apply our
method on an iron sample to analyze the defects caused by a collision cascade
induced by a 10 keV primary-knock-on-atom. The obtained results are in good
agreement with reported literature values.


  Input-to-state stability (ISS) and $\mathcal{L}_2$-gain are well-known robust
stability properties that continue to find wide application in the analysis and
control of nonlinear dynamical systems and their interconnections. We
investigate the relationship between ISS-type and $\mathcal{L}_2$-gain
properties, demonstrating several qualitative equivalences between these two
approaches. We subsequently present several new sufficient conditions for the
stability of interconnected systems derived by exploiting these qualitative
equivalences.


  We study the reflection of magnons from a D5-brane in the framework of the
AdS/CFT correspondence. We consider two possible orientations of the D5-brane
with respect to the reference vacuum state, namely vacuum states aligned along
"vertical" and "horizontal" directions. We show that the reflections are of the
achiral type. We also show that the reflection matrices satisfy the boundary
Yang-Baxter equations for both orientations. In the horizontal case the
reflection matrix can be interpreted in terms of a bulk S-matrix, S(p, -p), and
factorizability of boundary scattering therefore follows from that of bulk
scattering. Finally, we solve the nested coordinate Bethe ansatz for the system
in the vertical case to find the Bethe equations. In the horizontal case, the
Bethe equations are of the same form as those for the closed string.


  By introducing an integration factor to the differential one-form of contact
dynamics, equations of motion are derived variationally, and contact Poisson
bracket and contact Lagrangian are formulated. Discrete symplectic integrator,
named hybrid leap-frog method, is found to be a numerical solver of equations
of motion for contact dissipative systems.


  Generative models have proven to be an outstanding tool for representing
high-dimensional probability distributions and generating realistic-looking
images. An essential characteristic of generative models is their ability to
produce multi-modal outputs. However, while training, they are often
susceptible to mode collapse, that is models are limited in mapping input noise
to only a few modes of the true data distribution. In this work, we draw
inspiration from Determinantal Point Process (DPP) to propose an unsupervised
penalty loss that alleviates mode collapse while producing higher quality
samples. DPP is an elegant probabilistic measure used to model negative
correlations within a subset and hence quantify its diversity. We use DPP
kernel to model the diversity in real data as well as in synthetic data. Then,
we devise an objective term that encourages generators to synthesize data with
similar diversity to real data. In contrast to previous state-of-the-art
generative models that tend to use additional trainable parameters or complex
training paradigms, our method does not change the original training scheme.
Embedded in an adversarial training and variational autoencoder, our Generative
DPP approach shows a consistent resistance to mode-collapse on a wide variety
of synthetic data and natural image datasets including MNIST, CIFAR10, and
CelebA, while outperforming state-of-the-art methods for data-efficiency,
generation quality, and convergence-time whereas being 5.8x faster than its
closest competitor.


  We consider the problem of calculating the weak and strong topological
indices in noncentrosymmetric time-reversal (T) invariant insulators. In 2D we
use a gauge corresponding to hybrid Wannier functions that are maximally
localized in one dimension. Although this gauge is not smoothly defined on the
two-torus, it respects the T symmetry of the system and allows for a definition
of the Z_2 invariant in terms of time-reversal polarization. In 3D we apply the
2D approach to T-invariant planes. We illustrate the method with
first-principles calculations on GeTe and on HgTe under [001] and [111] strain.
Our approach differs from ones used previously for noncentrosymmetric materials
and should be easier to implement in ab initio code packages.


  We study integrability properties of the non-chiral intermediate long wave
(ncILW) equation with periodic boundary conditions. The ncILW equation was
recently introduced by the authors as a parity-invariant relative of the
intermediate long wave equation. For this new equation we: (a) derive a Lax
pair, (b) derive a Hirota bilinear form, (c) use the Hirota method to construct
the periodic multi-soliton solutions, (d) derive a B\"{a}cklund transformation,
(e) use the B\"{a}cklund transformation to obtain an infinite number of
conservation laws.


  Interoperability is a feature required by the Semantic Web. It is provided by
the ontology matching methods and algorithms. But now ontologies are presented
not only in English, but in other languages as well. It is important to use an
automatic translation for obtaining correct matching pairs in multilingual
ontology matching. The translation into many languages could be based on the
Google Translate API, the Wiktionary database, etc. From the point of view of
the balance of presence of many languages, of manually crafted translations, of
a huge size of a dictionary, the most promising resource is the Wiktionary. It
is a collaborative project working on the same principles as the Wikipedia. The
parser of the Wiktionary was developed and the machine-readable dictionary was
designed. The data of the machine-readable Wiktionary are stored in a
relational database, but with the help of D2R server the database is presented
as an RDF store. Thus, it is possible to get lexicographic information
(definitions, translations, synonyms) from web service using SPARQL requests.
In the case study, the problem entity is a task of multilingual ontology
matching based on Wiktionary data accessible via SPARQL endpoint. Ontology
matching results obtained using Wiktionary were compared with results based on
Google Translate API.


  Experiments on quasi-one-dimensional systems such as quantum wires and
metallic chains on surfaces suggest the existence of electron-electron
interactions of substantial range and hence physics beyond the Hubbard model.
We therefore investigate one-dimensional, quarter-filled chains with a Coulomb
potential with variable screening length by quantum Monte Carlo methods and
exact diagonalization. The Luttinger liquid interaction parameter K_rho
decreases with increasing interaction strength and range. Experimentally
observed values close to 1/4 require strong interactions and/or large screening
lengths. As predicted by bosonization, we find a metal-insulator transition at
K_rho=1/4. Upon increasing the screening length, the charge and spin
correlation functions reveal the crossover from dominant 2k_F spin correlations
to dominant 4k_F charge correlations, and a strong enhancement of the charge
velocity. In the metallic phase, the signatures of spin-charge separation in
the single-particle spectrum, spinon and holon bands, remain robust even for
rather long-ranged interactions. The charge-density-wave state exhibits
backfolded shadow bands.


  Relativistic bubble walls from cosmological phase transitions (PT)
necessarily accumulate expanding shells of particles. We systematically
characterize shell properties, and identify and calculate the processes that
prevent them from free streaming: phase-space saturation effects,
out-of-equilibrium $2\to2$ and $3\to2$ shell-shell and shell-bath interactions,
and shell interactions with bubble walls. We find that shells do not free
stream in scenarios widely studied in the literature, where standard
predictions will need to be reevaluated, including those of bubble wall
velocities, gravitational waves (GW) and particle production. Our results
support the use of bulk-flow GW predictions in all regions where shells free
stream, irrespectively of whether or not the latent heat is mostly converted in
the scalar field gradient.


  Having first performed a Monte Carlo simulation to justify the analysis
technique to be used, we then analyze the Bose-Einstein correlation functions
from CERN experiment NA44 in the context of the core-halo model. Although
experimental resolution and error bar distribution prevents a direct
observation of the halo structure, the values for the core radius and the core
fraction of pions can be obtained in a straight-forward manner. These are found
to be independent of the structure of the correlation function at small
relative momenta of Q < 50 MeV. Hence, the omega meson decay products do not
distort the Gaussian shape of the Bose-Einstein correlation function in S + Pb
-> pi + pi + X reaction at CERN SPS. As we find that the "model-independent"
HBT radii yield results that are quantitatively as well as qualitatively
unreliable for systems with long-lived resonances, we present their corrected
form that applies for correlation functions with lambda(K) < 1.


  Gaseous electronic characteristics due to cosmic ray ionization in the
electrode systems with ZnO and carbon nanostructures have been examined in
atmospheric Ar/N2 and O2/N2 mixtures. The electric conductivity at the quasi
linear stage is measured at the level of 10-11~10-10 S/m, 4~5 orders of
magnitudes higher than that of the samples without nanostructures, which is
construed by the 108~1010 times increment of the cosmic ray ionization
frequency. The results are consistent with the hypothesis that the role of
one-dimensional nanostructures in this gaseous electronic phenomenon is based
on the intensive field gradient effect, rather than the field enhancement
effect.


  Optical control of graphene-based photonic devices and systems has been under
extensive explorations, nevertheless, the requirement of high power pump laser
due to incoherent modulation makes those schemes low efficient. Here, we
demonstrate coherent manipulation of the operating states of partially
mode-locked fiber laser based on coherent population oscillation in reduced
graphene oxide for the first time. We couple a much weaker continuous wave
laser into the resonator operating with parametric instability state, and
observe significant depression/enhancement of the sidebands when the coherent
population oscillation conditions are satisfied. Besides, significant
depression of partially mode-locked fiber laser is achieved. The experimental
results reveal that the coherent population oscillation in reduced graphene
oxide is highly effective in manipulating mode-locked fiber laser system, and
the induced phase variation is highly asymmetrical. The discovery of coherent
population oscillation in reduced graphene oxide facilitates coherent optical
modulation of reduced graphene oxide-based photonic devices and systems with a
much weaker controlling laser.


  A proposal for a calculational program in fluid turbulence is presented. It
is proposed that the fluid probability density functional has an attractor for
its time-evolution, just as the dynamical system itself has. The evolution of
the fluid's statistics can be set up as a space-time path integral. Fluid
space-time configuration sampling techniques naturally suggest a useful way,
using an arbitrary initial statistics functional, to calculate averages.


  We summarize recent observational and theoretical progress aimed at
understanding the origin of the stellar initial mass function (IMF) with
specific focus on galactic star-forming regions. We synthesize data from
various efforts to determine the IMF in very young, partially-embedded stellar
clusters and find: i) no significant variations in the low-mass IMF have been
observed between different star-forming regions; and ii) the mass distributions
of young stars just emerging from molecular clouds are consistent with having
been drawn from the IMF derived from field stars in the solar neighborhood.
These results apply only to gross characterizations of the IMF (e.g. the ratio
of high to low mass stars); present observations do not rule out more subtle
regional differences. Further studies are required in order to assess whether
or not there is evidence for a universal turnover near the hydrogen--burning
limit. We also provide a general framework for discussing theories of the IMF,
and summarize recent work on several physical mechanisms which could play a
role in determining the form of the stellar initial mass function.


  When utilising PAC-Bayes theory for risk certification, it is usually
necessary to estimate and bound the Gibbs risk of the PAC-Bayes posterior. Many
works in the literature employ a method for this which requires a large number
of passes of the dataset, incurring high computational cost. This manuscript
presents a very general alternative which makes computational savings on the
order of the dataset size.


  Paran\'a Ra'anga (the image of Paran\'a, in Guaran\'i) is the name of a
cultural and scientific expedition that traveled the rivers: R\'io de la Plata,
Paran\'a and Paraguay, from Buenos Aires to Asunci\'on, during March 2010. The
project brought together some forty scientists and artists from three countries
in a slow and enriching cruise, putting in active contact actors from different
backgrounds and disciplines -which usually run separately- in the framework of
an unusual space-time experience. The project recovers the historical tradition
of the trip as an instrument of knowledge and collaboration between the arts
and sciences, necessary to build new ways of seeing and understanding the river
and its banks. This article reports on the motivations of this project and its
projection.


  In this short note, we prove that the subspace of radial multipliers is
contractively complemented in the space of Fourier multipliers on the Bochner
space $\mathrm{L}^p(\mathbb{R}^n,X)$ where $X$ is a Banach space and where $1
\leq p <\infty$. Moreover, if $X = \mathbb{C}$, then this complementation
preserves the positivity of multipliers.


  We report the AGILE observations of GRB 220101A, which took place at the
beginning of 1st January 2022 and was recognized as one of the most energetic
gamma-ray bursts (GRBs) ever detected since their discovery. The AGILE
satellite acquired interesting data concerning the prompt phase of this burst,
providing an overall temporal and spectral description of the event in a wide
energy range, from tens of keV to tens of MeV. Dividing the prompt emission
into three main intervals, we notice an interesting spectral evolution,
featuring a notable hardening of the spectrum in the central part of the burst.
The average fluxes encountered in the different time intervals are relatively
moderate, with respect to those of other remarkable bursts, and the overall
fluence exhibits a quite ordinary value among the GRBs detected by MCAL.
However, GRB 220101A is the second farthest event detected by AGILE, and the
burst with the highest isotropic equivalent energy of the whole MCAL GRB
sample, releasing E_iso=2.54x10^54 erg and exhibiting an isotropic luminosity
of L_iso=2.34x10^52 erg/s (both in the 400 keV - 10 MeV energy range).
  We also analyzed the first 10^6 s of the afterglow phase, using the publicly
available Swift XRT data, carrying out a theoretical analysis of the afterglow,
based on the forward shock model. We notice that GRB 220101A is with high
probability surrounded with a wind-like density medium, and that the energy
carried by the initial shock shall be a fraction of the total E_iso, presumably
near 50%.


  Heterostructures made of transition metal oxides are new tailor-made
materials which are attracting much attention. We have constructed a 6-band k.p
Hamiltonian and used it within the envelope function method to calculate the
subband structure of a variety of LaAlO3/SrTiO3 heterostructures. By use of
density functional calculations, we determine the k.p parameters describing the
conduction band edge of SrTiO3: the three effective mass parameters, L=0.6104
eV AA^2, M=9.73 eV AA^2, N=-1.616 eV AA^2, the spin orbit splitting
Delta_SO=28.5 meV and the low temperature tetragonal distortion energy
splitting Delta_T=2.1 meV. For confined systems we find strongly anisotropic
non-parabolic subbands. As an application we calculate bands, density of states
and magnetic energy levels and compare the results to Shubnikov-de Haas quantum
oscillations observed in high magnetic fields. For typical heterostructures we
find that electric field strength at the interface of F = 0.1 meV/AA for a
carrier density of 7.2 10^{12} cm^-2 results in a subband structure that is
similar to experimental results.


  Rocky planets are common around other stars, but their atmospheric properties
remain largely unconstrained. Thanks to a wealth of recent planet discoveries
and upcoming advances in observing capability, we are poised to characterize
the atmospheres of dozens of rocky exoplanets in this decade. Theoretical
understanding of rocky exoplanet atmospheres has advanced considerably in the
last few years, yielding testable predictions of their evolution, chemistry,
dynamics and even possible biosignatures. Here we review key progress in this
field to date and discuss future objectives. Our major conclusions are as
follows:
  1) Many rocky planets may form with initial H$_2$-He envelopes that are later
lost to space, likely due to a combination of stellar UV/X-ray irradiation and
internal heating.
  2) After the early stages of evolution, a wide diversity of atmospheric
compositions is expected, due to variations in host star flux, atmospheric
escape rates, interior exchange and other factors.
  3) Observations have ruled out the presence of hydrogen-dominated atmospheres
on several nearby rocky exoplanets, and the presence of any thick atmosphere on
one target. More detailed atmospheric characterization of these planets and
others will become possible in the near future.
  4) Exoplanet biosphere searches are an exciting future goal. However,
reliable detections for a representative sample of planets will require further
advances in observing capability and improvements in our understanding of
abiotic planetary processes.


  We present Director's Discretionary Time multi-frequency observations
obtained with the Jansky Very Large Array (VLA) and the Very Long Baseline
Array (VLBA) of the blazar PSO J030947.49+271757.31 (hereafter PSO J0309+27) at
$z = 6.10\pm0.03$. The milliarcsecond angular resolution of our VLBA
observations at 1.5, 5 and 8.4 GHz unveils a bright one-sided jet extended for
$\sim500$ parsecs in projection. This high-z radio-loud AGN is resolved into
multiple compact sub-components, embedded in a more diffuse and faint radio
emission, which enshrouds them in a continuous jet structure. We derive limits
on some physical parameters directly from the observable quantities, such as
viewing angle, Lorentz and Doppler factors. If PSO J0309+27 is a genuine
blazar, as suggested by its X-ray properties, then we find that its bulk
Lorentz factor must be relatively low (less than 5). Such value would be in
favour of a scenario currently proposed to reconcile the paucity of high-z
blazars with respect to current predictions. Nevertheless, we cannot exclude
that PSO J0309+27 is seen under a larger viewing angle, which would imply that
the X-ray emission must be enhanced, for example, by inverse Compton with the
Cosmic Microwave Background. More stringent constraints on the bulk Lorentz
factor in PSO J0309+27 and the other high-z blazars are necessary to test
whether their properties are intrinsically different with respect to the low-z
blazar population.


  Life is a nonequilibrium phenomenon: metabolism provides a continuous supply
of energy that drives nearly all cellular processes. However, very little is
known about how much energy different cellular processes use, i.e. their
energetic costs. The most direct experimental measurements of these costs
involve modulating the activity of cellular processes and determining the
resulting changes in energetic fluxes. In this review, we present a flux
balance framework to aid in the design and interpretation of such experiments,
and discuss the challenges associated with measuring the relevant metabolic
fluxes. We then describe selected techniques that enable measurement of these
fluxes. Finally, we review prior experimental and theoretical work that has
employed techniques from biochemistry and nonequilibrium physics to determine
the energetic costs of cellular processes.


  Quantum metrology employs quantum resources to enhance the measurement
sensitivity beyond that can be achieved classically. While multi-photon
entangled NOON states can in principle beat the shot-noise limit and reach the
Heisenberg limit, high NOON states are difficult to prepare and fragile to
photon loss which hinders it from reaching unconditional quantum metrological
advantages. Here, we combine the idea of unconventional nonlinear
interferometers and stimulated emission of squeezed light, previously developed
for photonic quantum computer Jiuzhang, to propose and realize a new scheme
that achieves a scalable, unconditional, and robust quantum metrological
advantage. We observe a 5.8(1)-fold enhancement above the shot-noise limit in
the Fisher information extracted per photon, without discounting for photon
loss and imperfections, which outperforms ideal 5-NOON states. The
Heisenberg-limited scaling, the robustness to external photon loss, and the
ease-to-use of our method make it applicable in practical quantum metrology at
low photon flux regime.


  The symbol length of ${_pBr}(k(\!(\alpha_1)\!)\dots(\!(\alpha_n)\!))$ for an
algebraically closed field $k$ of $\operatorname{char}(k) \neq p$ is known to
be $\lfloor \frac{n}{2} \rfloor$. We prove that the symbol length for the case
of $\operatorname{char}(k) = p$ is rather $n-1$. We also show that pairs of
anisotropic quadratic or bilinear $n$-fold Pfister forms over this field need
not share an $(n-1)$-fold factor.


  We present a proof of concept machine learning model resting on a
convolutional neural network capable to yield accurate scattering s-wave phase
shifts caused by different three-dimensional spherically symmetric potentials
at fixed collision energy thereby bypassing the radial Schr\"{o}dinger
equation. In out work, we discuss how the Hamiltonian can serve as a guiding
principle in the construction of a physically-motivated descriptor. The good
performance, even in presence of bound states in the data sets, exhibited by
our model that accordingly is trained on the Hamiltonian through each
scattering potential, demonstrates the feasibility of this proof of principle.


  Natural language rationales could provide intuitive, higher-level
explanations that are easily understandable by humans, complementing the more
broadly studied lower-level explanations based on gradients or attention
weights. We present the first study focused on generating natural language
rationales across several complex visual reasoning tasks: visual commonsense
reasoning, visual-textual entailment, and visual question answering. The key
challenge of accurate rationalization is comprehensive image understanding at
all levels: not just their explicit content at the pixel level, but their
contextual contents at the semantic and pragmatic levels. We present
Rationale^VT Transformer, an integrated model that learns to generate free-text
rationales by combining pretrained language models with object recognition,
grounded visual semantic frames, and visual commonsense graphs. Our experiments
show that the base pretrained language model benefits from visual adaptation
and that free-text rationalization is a promising research direction to
complement model interpretability for complex visual-textual reasoning tasks.


  We revisit the classical problem of diffusion of a scalar (or heat) released
in a two-dimensional medium with an embedded periodic array of impermeable
obstacles such as perforations. Homogenisation theory provides a coarse-grained
description of the scalar at large times and predicts that it diffuses with a
certain effective diffusivity, so the concentration is approximately Gaussian.
We improve on this by developing a large-deviation approximation which also
captures the non-Gaussian tails of the concentration through a rate function
obtained by solving a family of eigenvalue problems. We focus on cylindrical
obstacles and on the dense limit, when the obstacles occupy a large area
fraction and non-Gaussianity is most marked. We derive an asymptotic
approximation for the rate function in this limit, valid uniformly over a wide
range of distances. We use finite-element implementations to solve the
eigenvalue problems yielding the rate function for arbitrary obstacle area
fractions and an elliptic boundary-value problem arising in the asymptotics
calculation. Comparison between numerical results and asymptotic predictions
confirm the validity of the latter.


  Exploring and editing colors in images is a common task in graphic design and
photography. However, allowing for interactive recoloring while preserving
smooth color blends in the image remains a challenging problem. We present
LayerBuilder, an algorithm that decomposes an image or video into a linear
combination of colored layers to facilitate color-editing applications. These
layers provide an interactive and intuitive means for manipulating individual
colors. Our approach reduces color layer extraction to a fast iterative linear
system. Layer Builder uses locally linear embedding, which represents pixels as
linear combinations of their neighbors, to reduce the number of variables in
the linear solve and extract layers that can better preserve color blending
effects. We demonstrate our algorithm on recoloring a variety of images and
videos, and show its overall effectiveness in recoloring quality and time
complexity compared to previous approaches. We also show how this
representation can benefit other applications, such as automatic recoloring
suggestion, texture synthesis, and color-based filtering.


  The spectral efficiency (SE) of Massive MIMO (MaMIMO) systems is affected by
low quality channel estimates. Rate-Splitting (RS) has recently gained some
interest in multiuser multiple antenna systems as an effective means to
mitigate the multi-user interference due to imperfect channel state
information. This paper investigates the benefits of RS in the downlink of a
single-cell MaMIMO system when all the users use the same pilot sequence for
channel estimation. Novel expressions for the SE achieved in the downlink by a
single-layer RS strategy (that relies on a single successive interference
cancellation at each user side) are derived and used to design precoding
schemes and power allocation strategies for common and private messages.
Numerical results are used to show that the proposed RS solution achieves
higher spectral efficiency that conventional MaMIMO with maximum ratio
precoding.


  Most recently, the path integral molecular dynamics has been successfully
used to consider the thermodynamics of single-component identical bosons and
fermions. In this work, the path integral molecular dynamics is developed to
simulate the thermodynamics, Green's function and momentum distribution of
two-component bosons in three dimensions. As an example of our general method,
we consider the thermodynamics of up to sixteen bosons in a three-dimensional
harmonic trap. For noninteracting spinor bosons, our simulation shows a bump in
the heat capacity. As the repulsive interaction strength increases, however, we
find the gradual disappearance of the bump in the heat capacity. We believe
this simulation result can be tested by ultracold spinor bosons with optical
lattices and magnetic-field Feshbach resonance to tune the inter-particle
interaction. We also calculate Green's function and momentum distribution of
spinor bosons. Our work facilitates the exact numerical simulation of spinor
bosons, whose property is one of the major problems in ultracold Bose gases.


  Semi-supervised learning (SSL) partially circumvents the high cost of
labeling data by augmenting a small labeled dataset with a large and relatively
cheap unlabeled dataset drawn from the same distribution. This paper offers a
novel interpretation of two deep learning-based SSL approaches, ladder networks
and virtual adversarial training (VAT), as applying distributional smoothing to
their respective latent spaces. We propose a class of models that fuse these
approaches. We achieve near-supervised accuracy with high consistency on the
MNIST dataset using just 5 labels per class: our best model, ladder with
layer-wise virtual adversarial noise (LVAN-LW), achieves 1.42% +/- 0.12 average
error rate on the MNIST test set, in comparison with 1.62% +/- 0.65 reported
for the ladder network. On adversarial examples generated with L2-normalized
fast gradient method, LVAN-LW trained with 5 examples per class achieves
average error rate 2.4% +/- 0.3 compared to 68.6% +/- 6.5 for the ladder
network and 9.9% +/- 7.5 for VAT.


  Symbolic reasoning, rule-based symbol manipulation, is a hallmark of human
intelligence. However, rule-based systems have had limited success competing
with learning-based systems outside formalized domains such as automated
theorem proving. We hypothesize that this is due to the manual construction of
rules in past attempts. In this work, we ask how we can build a rule-based
system that can reason with natural language input but without the manual
construction of rules. We propose MetaQNL, a "Quasi-Natural" language that can
express both formal logic and natural language sentences, and MetaInduce, a
learning algorithm that induces MetaQNL rules from training data consisting of
questions and answers, with or without intermediate reasoning steps. Our
approach achieves state-of-the-art accuracy on multiple reasoning benchmarks;
it learns compact models with much less data and produces not only answers but
also checkable proofs. Further, experiments on a real-world morphological
analysis benchmark show that it is possible for our method to handle noise and
ambiguity. Code will be released at https://github.com/princeton-vl/MetaQNL.


  In this article, a feasible switchyard design is proposed for the Shanghai
soft x-ray free electron laser facility. In the proposed scheme, a switchyard
is used to transport the electron beam to different undulator lines.
Three-dimensional start-to-end simulations have been carried out to research
the beam dynamic during transportation. The results show that the emittance of
the electron beam increases less than 10%, at meanwhile, the peak current, the
energy spread and the bunch length are not spoiled as the beam passes through
the switchyard. The microbunching instability of the beam and the jitter of the
linear accelerator (linac) are analyzed as well.


  We study the effect of tensor correlations on single-particle and collective
states within Skyrme Hartree-Fock and RPA model. Firstly, We study the role of
tensor interactions in Skyrme effective interaction on the spin-orbit
splittings of N=82 isotones and Z=50 isotope.
  The isospin dependence of the shell structure is well described as the
results of the tensor interactions without destroying good properties of the
binding energy and the rms charge radii of the heavy nuclei. Secondly, We
performed self-consistent HF+RPA calculations for charge exchange 1$^+$ states
in $^{90}$Zr and $^{208}$Pb to elucidate the role of tensor interactions on
spin dependent excitations. It is pointed out that Gamow-Teller(GT) states can
couple strongly with the spin-quadrupole (SQ) 1$^+$ states in the high energy
region above E$_x$=30 MeV due to the tensor interactions. As the result of this
coupling, more than 10% of the GT strength is shifted to the energy region
above 30 MeV, and the main GT peak is moved 2 MeV downward.


  Five dimensional dilaton models are considered as possible holographic duals
of the pure gauge QCD vacuum. In the framework of these models, the QCD trace
anomaly equation is considered. Each quantity appearing in that equation is
computed by holographic means. Two exact solutions for different dilaton
potentials corresponding to perturbative and non-perturbative beta-functions
are studied. It is shown that in the perturbative case, where the beta-function
is the QCD one at leading order, the resulting space is not asymptotically AdS.
In the non-perturbative case, the model considered presents confinement of
static quarks and leads to a non-vanishing gluon condensate, although it does
not correspond to an asymptotically free theory. In both cases analyses based
on the trace anomaly and on Wilson loops are carried out.


  We present evidence for the decay B0->rho0 K0s. The results are obtained from
a data sample of 227 10^6 Y(4S) -> BBbar decays collected with the BABAR
detector at the PEP-II asymmetric-energy B-Factory at SLAC. From a
maximum-likelihood fit giving a yield of 99+/-19 events and efficiency
estimated from simulation we make a preliminary measurement of the branching
fraction B0->rho0 K0 =(5.1+/-1.0+/-1.2)10^-6 where the first error is
statistical and the second systematic. The hypothesis of zero signal in the
rho0 mass region, 600MeV-930MeV, is excluded at the 6.1sigma level. Allowing a
B0->f_0(600)K0s contribution in the fit allows us to exclude the hypothesis of
zero B0->rho0 K0s at the 3.5sigma level.


  For all nonnegative integers n, the Franel numbers are defined as $$
f_n=\sum_{k=0}^n {n\choose k}^3.$$ We confirm two conjectures of Z.-W. Sun on
congruences for Franel numbers: \sum_{k=0}^{n-1}(3k+2)(-1)^k f_k &\equiv 0
\pmod{2n^2}, \sum_{k=0}^{p-1}(3k+2)(-1)^k f_k &\equiv 2p^2 (2^p-1)^2
\pmod{p^5}, where n is a positive integer and p>3 is a prime.


  Despite numerous studies, the origin of the gamma-ray emission from blazars
is still debated, in particular whether it is produced by leptonic or hadronic
processes. In this study, we are testing the leptonic scenario for the Flat
Spectrum Radio Quasar (FSRQ) 3C 279, assuming that the gamma-ray emission is
generated by inverse Compton scattering of external target photons from Broad
Line Region (IC-BLR scenario). For this purpose we use a 10-year data set of
the source consisting of the optical spectroscopy data from the Steward
Observatory blazar monitoring program and Fermi-LAT gamma-ray data. We search
for a possible correlation between the Compton dominance and the emission line
luminosity using the discrete correlation function (DCF) analysis. As a result,
we find no significant correlation between these two quantities at any time lag
value, while the emission line luminosity displays a moderate correlation with
the gamma-ray flux at a zero time lag. We also reveal that the optical
synchrotron continuum flux shows a pronounced correlation with the gamma-ray
flux, and therefore we interpret these results within the leptonic IC-BLR
scenario where the Compton dominance variations are primarily induced by
changes in the magnetic field, rather than in the emission line luminosity.


  The properties of the vortex and the gradient of divergence operators ( $
\text{rot}$ and $\nabla \text{div}$ ) are studied in the space $ \mathbf {L}_2
(G) $ in a bounded domain $ G \subset \textrm {R}^3 $ with a smooth boundary $
\Gamma$ and in the Sobolev spaces: $ \mathbf{C}(2k, m)(G)\equiv
\mathbf{A}^{2k}(G) \oplus \mathbf{W}^m(G)$. S.L. Sobolev studied boundary value
problems for the scalar polyharmonic equation $\Delta^m\,u=\rho$ in the spaces
$W_2^m(\Omega)$ with a generalized right-hand side and laid the foundation for
the theory of these spaces. Its constructions have matrix analogs, here are
some of them. Analogues of the spaces ${W}_2^{(m)}(G)$ in the classes $
\mathcal {A} $ and $ \mathcal {B} $ are the space $\mathbf{A}^{2k}(G)$ and
$\mathbf{W}^m(G)$ of orders $ 2k> 0 $ and $ m> 0 $, and $ \mathbf {A}^{-2k} (G)
$ and their dual spaces $ \mathbf{W}^{- m}(G) $. Pairs of spaces form a net of
Sobolev spaces, its elements are classes $ \mathbf{C}(2k, m)(G)\equiv
\mathbf{A}^{2k}(G) \oplus \mathbf{W}^m(G)$; the class $ \mathbf{C}(2k,
2k)$coincides with the Sobolev space $\mathbf{H}^{2k}(G)$. They belong to
$\mathbf{L}_{2}(G)$, if $k\geq 0$ and $m\geq 0$. A wide field of problems has
opened up: studying the operators $(\mathrm{rot})^p$, $ (\nabla \,
\mathrm{div})^p$ for $ p = 1,2, ...,$ and others in the network Sobolev spaces.


  We have proved that homeomorphisms of domains of Euclidean space, inverse of
which distort the modulus of families of curves by Poletskii type, have a
continuous extension to isolated boundary point.


  The definition of the Soret coefficient of a binary mixture includes a
concentration prefactor, $x(1-x)$ when mol fraction $x$ is used, or $w(1-w)$
when mass fraction $w$ is used. In this paper the physical reasons behind this
choice are reviewed, emphasizing that the use of these prefactors makes the
Soret coefficient invariant upon change in the reference frame, either mass or
molar. Then, it is shown how this invariance property can be extended to
ternary mixtures by using an appropriate concentration prefactor in matrix
form. The work is completed with some considerations of general non-isothermal
diffusion fluxes, binary limits of the concentration triangle, selection of the
dependent concentration in a ternary mixture, use of molar concentrations and,
finally, extension to multi-component mixtures.


  The dynamics of 3He atoms in solid 4He have been investigated by measuring
the NMR relaxation times T1, T2 in the region where a significant non-classical
rotational inertia fraction (NCRIF) has been reported. For 3He concentrations
x3 = 16 ppm and 24 ppm, changes are observed for both the spin-lattice
relaxation time T1 and the spin-spin relaxation time T2 at the temperatures
corresponding to the onset of NCRIF and, at lower temperatures, to the 3He-4He
phase separation. The magnitudes of T1 and T2 at temperatures above the phase
separation agree roughly with existing theory based on the tunneling of 3He
impurities in the elastic strain field due to isotopic mismatch. However, a
distinct peak in T1 and a less well-resolved feature in T2 are observed near
the reported NCRIF onset temperature, in contrast to the
temperature-independent relaxation times predicted by the tunneling theory.


  We build a multifractal object and use it as a support to study percolation.
  We identify some differences between percolation in a multifractal and in a
regular lattice. We use many samples of finite size lattices and draw the
histogram of percolating lattices against site occupation probability.
Depending on a parameter characterizing the multifractal and the lattice size,
the histogram can have two peaks. The percolation threshold for the
multifractal is lower than for the square lattice.
  The percolation in the multifractal differs from the percolation in the
regular lattice in two points. The first is related with the coordination
number that changes along the multifractal. The second comes from the way the
weight of each cell in the multifractal affects the percolation cluster. We
compute the fractal dimension of the percolating cluster. Despite the
differences, the percolation in a multifractal support is in the universality
class of standard percolation.


  Large-scale problems are nonlinear problems that need metaheuristics, or
global optimization algorithms. This paper reviews nature-inspired
metaheuristics, then it introduces a framework named Competitive Ant Colony
Optimization inspired by the chemical communications among insects. Then a case
study is presented to investigate the proposed framework for large-scale global
optimization.


  We have investigated the room temperature ferromagnetic order that develops
in Al-substituted magnesium oxide, Mg(Al)O, nanoparticles with Al fractions of
up to 5 at.%. All samples, including undoped MgO nanoparticles, exhibit room
temperature ferromagnetism, with the saturation magnetization reaching a
maximum of 0.023 emu/g at 2 at.% of Al. X-ray photoelectron spectroscopy
identifies the presence of oxygen vacancies in both doped and undoped MgO
nanoparticles, with the vacancy concentration increasing upon vacuum annealing
of Mg(Al)O, resulting in two-fold enhancement of the saturation magnetization
for 2 at.% Al-doped MgO. Our results suggest that the oxygen vacancies are
largely responsible for room temperature ferromagnetism in MgO.


  Small changes to the parameters of a system can lead to abrupt qualitative
changes of its behavior, a phenomenon known as bifurcation. Such instabilities
are typically considered problematic, however, we show that their power can be
leveraged to design novel types of mechanisms. Hysteresis mechanisms use
transient changes of system parameters to induce a permanent improvement to its
performance via optimal equilibrium selection. Optimal control mechanisms
induce convergence to states whose performance is better than even the best
equilibrium. We apply these mechanisms in two different settings that
illustrate the versatility of bifurcation mechanism design. In the first one we
explore how introducing flat taxation can improve social welfare, despite
decreasing agent "rationality", by destabilizing inefficient equilibria. From
there we move on to consider a well known game of tumor metabolism and use our
approach to derive novel cancer treatment strategies.


  The absolute (moduli-independent) U-invariants of all N>2 extended
supergravities at D=4 are derived in terms of (moduli-dependent) central and
matter charges. These invariants give a general definition of the
``topological'' Bekenstein-Hawking entropy formula for extremal black-holes and
reduce to the square of the black-hole ADM mass for ``fixed scalars'' which
extremize the black-hole ``potential'' energy. The Hessian matrix of the
black-hole potential at ``fixed scalars'', in contrast to N=2 theories, is
shown to be degenerate, with rank (N-2)(N-3) + 2 n (N being the number of
supersymmetries and n the number of matter multiplets) and semipositive
definite.


  As a challenging problem, few-shot class-incremental learning (FSCIL)
continually learns a sequence of tasks, confronting the dilemma between slow
forgetting of old knowledge and fast adaptation to new knowledge. In this
paper, we concentrate on this "slow vs. fast" (SvF) dilemma to determine which
knowledge components to be updated in a slow fashion or a fast fashion, and
thereby balance old-knowledge preservation and new-knowledge adaptation. We
propose a multi-grained SvF learning strategy to cope with the SvF dilemma from
two different grains: intra-space (within the same feature space) and
inter-space (between two different feature spaces). The proposed strategy
designs a novel frequency-aware regularization to boost the intra-space SvF
capability, and meanwhile develops a new feature space composition operation to
enhance the inter-space SvF learning performance. With the multi-grained SvF
learning strategy, our method outperforms the state-of-the-art approaches by a
large margin.


  Generative adversarial networks (GANs) have many application areas including
image editing, domain translation, missing data imputation, and support for
creative work. However, GANs are considered 'black boxes'. Specifically, the
end-users have little control over how to improve editing directions through
disentanglement. Prior work focused on new GAN architectures to disentangle
editing directions. Alternatively, we propose GANravel a user-driven direction
disentanglement tool that complements the existing GAN architectures and allows
users to improve editing directions iteratively. In two user studies with 16
participants each, GANravel users were able to disentangle directions and
outperformed the state-of-the-art direction discovery baselines in
disentanglement performance. In the second user study, GANravel was used in a
creative task of creating dog memes and was able to create high-quality edited
images and GIFs.


  In this article an idea is presented, which allows for the explanation of
superluminal muon neutrinos. It is based on the introduction of a new
superluminal, massless gauge boson coupling to the neutrino only, but not to
other standard model particles. The model is discussed with regard to the
Supernova 1987 (SN 1987) velocity bound on electron antineutrinos and the
Cohen-Glashow constraint on superluminal neutrino propagation. The latter can
be circumvented if - within the framework of the model - a sterile neutrino
mixing with the active neutrino mass eigenstates is introduced. The suggestion
of a sterile neutrino accounting for superluminal neutrinos has already been
proposed in several papers. It is possible to choose mixing angles with the
sterile neutrino sector such that the model respects both the SN 1987 bound and
the muon neutrino travels superluminally.


  Two suggested models of jet fragmentation in a quark-gluon plasma have been
tested, combined and further developed. This has been done by generating hard
processes in proton-proton collisions at $\sqrt{s}=2.76$ GeV in PYTHIA 8 with a
modified parton shower algorithm. Subsequently, a jet analysis of the final
state hadrons have been performed with the FastJet recombination package. The
results have been compared to unmodified jets in proton-proton collisions at
the same collision energy, and to experimental data obtained by ATLAS. It has
been shown that modifications of the parton splitting kernels alone is an
insufficient modification to reproduce experimental data on dijet energy
asymmetry and azimuthal decorrelation. Additional jet decollimation
qualitatively reproduces the main features of the data provided certain
variables are chosen aptly. We also study other jet characteristics with the
model, such as the jet substructure, that may be observable experimentally in a
near future.


  Voxel-based lesion-symptom mapping (VLSM) is a major method for studying
brain-behavior relationships that leverages modern neuroimaging analysis
techniques to build on the classic approach of examining the relationship
between location of brain damage and cognitive deficits. Testing an association
between deficit severity and lesion status in each voxel involves very many
individual tests and requires statistical correction for multiple comparisons.
Several strategies have been adapted from analysis of functional neuroimaging
data, though VLSM faces a more difficult trade-off between avoiding false
positives and statistical power (missing true effects). One such strategy is
using permutation to non-parametrically determine a null distribution of
cluster sizes, which is then used to establish a minimum cluster size
threshold. This strategy is intuitively appealing because it respects the
necessary spatial contiguity of stroke lesions and connects with the typical
cluster-based interpretation of VLSM results. We evaluated this strategy for
detecting true lesion-symptom relations using simulated deficit scores based on
percent damage to defined brain regions (BA 45 and BA 39) in a sample of 124
individuals with left hemisphere stroke. Even under the most conservative
settings tested here, the region identified by VLSM with cluster size
correction systematically extended well beyond the true region. As a result,
this strategy appears to be effective for ruling out situations with no true
lesion-symptom relations, but the spatial contiguity of stroke lesions may
cause identified lesion-symptom relations to extend beyond their true regions.


  We study canonical decompositions of postcritically finite branched coverings
of the 2-sphere, as defined by K. Pilgrim. We show that every hyperbolic cycle
in the decomposition does not have a Thurston obstruction. It is thus Thurston
equivalent to a rational map.


  We assess the epidemic situation caused by SARS-CoV-2 using Tsallis' proposal
for determining the occurrence of the peak, and also the
Susceptible-Infected-Recovered-Asymptomatic-Symptomatic and Dead
(\textbf{SIRASD}) compartmental model. Using these two models, we determine a
range of probable peak dates and study several social distancing scenarios
during the epidemic. Due to the socioeconomic situation and the conflictive
political climate, we take for our study the case of Bolivia, where a national
election was originally scheduled to occur on September 6th and recently
rescheduled on October 18th. For this, we analyze both electoral scenarios and
show that such an event can largely affect the epidemic's dynamics.


  C points, characterized by circular polarization in momentum space, play
crucial roles in chiral wave manipulations. However, conventional approaches of
achieving intrinsic C points using photonic crystals with broken symmetries
suffer from low Q factor and are highly sensitive to structural geometry,
rendering them fragile and susceptible to perturbations and disorders. In this
letter, we report the realization of magneto-optical (MO) bound states in the
continuum (BICs) using a symmetry-preserved planar photonic crystal, achieving
intrinsic at-{\Gamma} C points that are robust against variation in structural
geometry and external magnetic field. MO coupling between two dipole modes
induces Zeeman splitting of the eigenfrequencies, leading to MO BICs and
quasi-BICs with circular eigenstates for high-Q chiral responses. Furthermore,
switchable C point handedness and circular dichroism are enabled by reversing
the magnetic field. These findings unveil a new type of BICs with circular
eigenstates and on-demand control of C points, paving the way for advanced
chiral wave manipulation with enhanced light-matter interaction.


  Approximate necessary optimality conditions in terms of Fr\'echet
subgradients and normals for a rather general optimization problem with a
potentially non-Lipschitzian objective function are established with the aid of
Ekeland's variational principle, the fuzzy Fr\'echet subdifferential sum rule,
and a novel notion of lower semicontinuity relative to a set-valued mapping or
set. Feasible points satisfying these optimality conditions are referred to as
approximately stationary. As applications, we derive a new general version of
the extremal principle. Furthermore, we study approximate stationarity
conditions for an optimization problem with a composite objective function and
geometric constraints, a qualification condition guaranteeing that
approximately stationary points of such a problem are M-stationary, and a
multiplier-penalty-method which naturally computes approximately stationary
points of the underlying problem. Finally, necessary optimality conditions for
an optimal control problem with a non-Lipschitzian sparsity-promoting term in
the objective function are established.


  The unique Fermi surfaces and their nesting properties of Sr2RuO4 are
considered. The existence of unconventional superconductivity is shown
microscopically, for the first time, from the magnetic interactions (due to
nesting) and the phonon-mediated interactions. The odd-parity superconductivity
is favored in the $\alpha$ and $\beta$ sheets of the Fermi surface, and the
various superconductivities are possible in the $\gamma$ sheet. There are a
number of possible odd-parity gaps, which include the gaps with nodes, the
breaking of time-reversal symmetry and $\vec{d}\parallel \hat{z}$.


  In this paper we prove a version of the Berman-Konsowa principle for
reversible Markov jump processes on Polish spaces. The Berman-Konsowa principle
provides a variational formula for the capacity of a pair of disjoint
measurable sets. There are two versions, one involving a class of probability
measures for random finite paths from one set to the other, the other involving
a class of finite unit flows from one set to the other. The Berman-Konsowa
principle complements the Dirichlet principle and the Thomson principle, and
turns out to be especially useful for obtaining sharp estimates on crossover
times in metastable interacting particle systems.


  The importance of diquarks has been noticed in the context of several
elementary particle processes. In recent years the study of diquarks has become
of considerable interest in highlighting its role in high density physics from
the point of view of astrophysical situations and cosmological conditions. In
the present paper an attempt is made to briefly review the role of diquarks in
conventional physics and in Quantum Chromodynamic phase transition. The
importance of equation of state for point-like scalar diquark (PSD) and
extended scalar diquark (ESD) gas and matter is reviewed. In this regard, the
sensitivity of ESD energy on the effective interaction parameter, within the
frame work of \phi^4 theory, is studied. The role of diquarks in astro-physical
situations and cosmological conditions with reference to the early phases of
the origin of the universe is discussed. The recent discovery of \theta^+
(1540) baryon - a pentaquark, which may be considered as a two highly
correlated ud-diquark pairs and an anti strange quark, is also highlighted.