  Various radio observations have showed that the hot atmospheres of galaxy
clusters are magnetized. However, our understanding of the origin of these
magnetic fields, their implications on structure formation and their interplay
with the dynamics of the cluster atmosphere, especially in the centers of
galaxy clusters is still very limited. In preparation to the upcoming new
generation of radio telescopes (like EVLA, LWA, LOFAR and SKA), a huge effort
is being made to learn more about cosmological magnetic fields from the
observational perspective. Here we present the implementation of magneto
hydrodynamics in the cosmological SPH code GADGET. We discuss the details of
the implementation and various schemes to suppress numerical instabilities as
well as regularization schemes, in the context of cosmological simulations. The
performance of the SPH MHD code is demonstrated in various one and two
dimensional test problems, which we performed if a fully, three dimensional
setup to test the code under realistic circumstances. Comparing with solutions
obtained with ATHENA, we find excellent agreement with our SPH MHD
implementation. Finally we apply our SPH MHD implementation to forming galaxy
clusters within a large, cosmological box. Performing a resolution study we
demonstrate the robustness of the predicted shape of the magnetic field
profiles in galaxy clusters, which is in good agreement with previous studies.


  We present a systematic study of the influence of cell geometry on the
orientational distribution of microtubules (MTs) nucleated from a single
microtubule organizing center (MTOC). For simplicity we consider an elliptical
cell geometry, a setting appropriate to a generic non-spherical animal cell.
Within this context we introduce four models of increasing complexity, in each
case introducing additional mechanisms that govern the interaction of the MTs
with the cell boundary. In order, we consider the cases: MTs that can bind to
the boundary with a fixed mean residence time (M0), force-producing MTs that
can slide on the boundary towards the cell poles (MS), MTs that interact with a
generic polarity factor that is transported and deposited at the boundary, and
which in turn stabilizes the MTs at the boundary (MP), and a final model in
which both sliding and stabilization by polarity factors is taken into account
(MSP). In the baseline model (M0), the exponential length distribution of MTs
causes most of the interactions at the cell boundary to occur along the shorter
transverse direction in the cell, leading to transverse biaxial order. MT
sliding (MS) is able to reorient the main axis of this biaxial order along the
longitudinal axis. The polarization mechanism introduced in MP and MSP
overrules the geometric bias towards bipolar order observed in M0 and MS, and
allows the establishment of unipolar order either along the short- (MP) or the
long cell axis (MSP). The behavior of the latter two models can be
qualitatively reproduced by a very simple toy model with discrete MT
orientations.


  In the present paper, we introduce the concepts of Pr\"{u}fer sheaves and
adic sheaves over a weighted projective line of genus one or an elliptic curve,
show that Pr\"{u}fer sheaves and adic sheaves can classify the category of
coherent sheaves. Moreover, we describe the relationship between Pr\"{u}fer
sheaves and generic sheaves, and provide two methods to construct generic
sheaves by using coherent sheaves and Pr\"{u}fer sheaves.


  A dynamical $r$-matrix is associated with every self-dual Lie algebra $\A$
which is graded by finite-dimensional subspaces as $\A=\oplus_{n \in \cZ}
\A_n$, where $\A_n$ is dual to $\A_{-n}$ with respect to the invariant scalar
product on $\A$, and $\A_0$ admits a nonempty open subset $\check \A_0$ for
which $\ad \kappa$ is invertible on $\A_n$ if $n\neq 0$ and $\kappa \in \check
\A_0$. Examples are furnished by taking $\A$ to be an affine Lie algebra
obtained from the central extension of a twisted loop algebra $\ell(\G,\mu)$ of
a finite-dimensional self-dual Lie algebra $\G$. These $r$-matrices, $R: \check
\A_0 \to \mathrm{End}(\A)$, yield generalizations of the basic trigonometric
dynamical $r$-matrices that, according to Etingof and Varchenko, are associated
with the Coxeter automorphisms of the simple Lie algebras, and are related to
Felder's elliptic $r$-matrices by evaluation homomorphisms of $\ell(\G,\mu)$
into $\G$. The spectral-parameter-dependent dynamical $r$-matrix that
corresponds analogously to an arbitrary scalar-product-preserving finite order
automorphism of a self-dual Lie algebra is here calculated explicitly.


  Understanding generalization in modern machine learning settings has been one
of the major challenges in statistical learning theory. In this context, recent
years have witnessed the development of various generalization bounds
suggesting different complexity notions such as the mutual information between
the data sample and the algorithm output, compressibility of the hypothesis
space, and the fractal dimension of the hypothesis space. While these bounds
have illuminated the problem at hand from different angles, their suggested
complexity notions might appear seemingly unrelated, thereby restricting their
high-level impact. In this study, we prove novel generalization bounds through
the lens of rate-distortion theory, and explicitly relate the concepts of
mutual information, compressibility, and fractal dimensions in a single
mathematical framework. Our approach consists of (i) defining a generalized
notion of compressibility by using source coding concepts, and (ii) showing
that the `compression error rate' can be linked to the generalization error
both in expectation and with high probability. We show that in the `lossless
compression' setting, we recover and improve existing mutual information-based
bounds, whereas a `lossy compression' scheme allows us to link generalization
to the rate-distortion dimension -- a particular notion of fractal dimension.
Our results bring a more unified perspective on generalization and open up
several future research directions.


  Motivated by developing a field-theoretic algebraic approach to the universal
part of the stress-tensor sector of a scalar four-point function in a class of
higher-dimensional CFTs, we construct a mode operator, ${\cal L}_m$, near the
lightcone in $d=4$ CFTs and show that it leads to a Virasoro-like commutator,
including a regularized central-term. As an example, we describe how to
reproduce the $d=4$ single-stress tensor exchange contribution in the lightcone
limit by a mode summation. A general-$d$ extension is included. We comment on
possible generalizations.


  We study periodic solutions of the discrete nonlinear Schr\"{o}dinger
equation (DNLSE) that bifurcate from a symmetric polygonal relative equilibrium
containing $n$ sites. With specialized numerical continuation techniques and a
varying physically relevant parameter we can locate interesting orbits,
including infinitely many choreographies. Many of the orbits that correspond to
choreographies are stable, as indicated by Floquet multipliers that are
extracted as part of the numerical continuation scheme, and as verified
\textit{a posteriori} by simple numerical integration. We discuss the physical
relevance and the implications of our results.


  Acoustic emission (AE) characterization is an effective technique to
indirectly capture the progressive failure process of the brittle rock. In
previous studies, both the experiment and numerical simulation were adopted to
investigate AE characteristics of the brittle rock. However, as the most
popular numerical model, the moment tensor model (MTM) did not reproduce the
monitoring and analyzing manner of AE signals from the physical experiment.
Consequently, its result could not be constrained by the experimental result.
It is thus necessary to evaluate the consistency and compatibility between the
experiment and MTM. To fulfill this, we developed a particle-velocity-based
model (PVBM) which enabled directly monitor and analyze the particle velocity
in the numerical model and had good robustness. The PVBM imitated the actual
experiment and could fill in gaps between the experiment and MTM. AE
experiments of Marine shale under uniaxial compression were carried out, of
which results were simulated by MTM. In general, the variation trend of the
experimental result could be presented by MTM. Nevertheless, magnitudes of AE
parameters by MTM presented notable differences with more than several orders
compared with those by the experiment. We sequentially used PVBM as a proxy to
analyze these discrepancies quantitatively and make a systematical evaluation
on AE characterization of brittle rocks from the experiment to numerical
simulation, considering the influence of wave reflection, energy geometrical
diffusion, viscous attenuation, particle size as well as progressive
deterioration of rock material. It was suggested that only the combination of
MTM and PVBM could reasonably and accurately acquire AE characteristics of the
actual AE experiment of brittle rocks by making full use of their respective
advantages.


  Methicillin-resistant Staphylococcus aureus (MRSA) is a type of bacteria
resistant to certain antibiotics, making it difficult to prevent MRSA
infections. Among decades of efforts to conquer infectious diseases caused by
MRSA, many studies have been proposed to estimate the causal effects of close
contact (treatment) on MRSA infection (outcome) from observational data. In
this problem, the treatment assignment mechanism plays a key role as it
determines the patterns of missing counterfactuals -- the fundamental challenge
of causal effect estimation. Most existing observational studies for causal
effect learning assume that the treatment is assigned individually for each
unit. However, on many occasions, the treatments are pairwisely assigned for
units that are connected in graphs, i.e., the treatments of different units are
entangled. Neglecting the entangled treatments can impede the causal effect
estimation. In this paper, we study the problem of causal effect estimation
with treatment entangled in a graph. Despite a few explorations for entangled
treatments, this problem still remains challenging due to the following
challenges: (1) the entanglement brings difficulties in modeling and leveraging
the unknown treatment assignment mechanism; (2) there may exist hidden
confounders which lead to confounding biases in causal effect estimation; (3)
the observational data is often time-varying. To tackle these challenges, we
propose a novel method NEAT, which explicitly leverages the graph structure to
model the treatment assignment mechanism, and mitigates confounding biases
based on the treatment assignment modeling. We also extend our method into a
dynamic setting to handle time-varying observational data. Experiments on both
synthetic datasets and a real-world MRSA dataset validate the effectiveness of
the proposed method, and provide insights for future applications.


  A recently introduced restricted variant of the multidimensional stable
roommate problem is the roommate diversity problem: each agent belongs to one
of two types (e.g., red and blue), and the agents' preferences over the
coalitions solely depend on the fraction of agents of their own type among
their roommates.
  There are various notions of stability that defines an optimal partitioning
of agents. The notion of popularity has received a lot of attention recently. A
partitioning of agents is popular if there does not exist another partitioning
in which more agents are better off than worse off. Computing a popular
partition in a stable roommate game can be done in polynomial time. When we
allow ties the stable roommate problem becomes NP-complete. Determining the
existence of a popular solution in the multidimensional stable roommate problem
also NP-hard.
  We show that in the roommate diversity problem with the room size fixed to
two, the problem becomes tractable. Particularly, a popular partitioning of
agents is guaranteed to exist and can be computed in polynomial time.
Additionally a mixed popular partitioning of agents is always guaranteed to
exist in any roommate diversity game. By contrast, when there are no
restrictions on the coalition size of a roommate diversity game, a popular
partitioning may fail to exist and the problem becomes intractable. Our results
intractability results are summarized as follows:
  * Determining the existence of a popular partitioning is co-NP-hard, even if
the agents' preferences are trichotomous.
  * Determining the existence of a strictly popular partitioning is co-NP-hard,
even if the agents' preferences are dichotomous.
  * Computing a mixed popular partitioning of agents in polynomial time is
impossible unless P=NP, even if the agents' preferences are dichotomous.


  A robust (deterministic) filtering approach to the problem of optimal sensor
selection is considered herein. For a given system with several sensors, at
each time step the output of one of the sensors must be chosen in order to
obtain the best state estimate. We reformulate this problem in an optimal
control framework which can then be solved using dynamic programming. In order
to tackle the numerical computation of the solution in an efficient manner, we
exploit the preservation of the min-plus structure of the optimal cost function
when acted upon by the dynamic programming operator. This technique yields a
grid free numerical approach to the problem. Simulations on an example problem
serve to highlight the efficacy of this generalizable approach to robust
multi-sensor state estimation.


  In this paper, we revisit large variable asymptotic expansions of tronqu\'ee
solutions of the Painlev\'e I equation, obtained via the Riemann-Hilbert
approach and the method of steepest descent. The explicit construction of an
extra local parametrix around the recessive stationary point of the phase
function, in terms of complementary error functions, makes it possible to give
detailed information about non-perturbative contributions beyond standard
Poincar\'e expansions for tronqu\'ee and tritronqu\'ee solutions.


  We report the observation of $g$-factors of natural paramagnetic impurities
in a pure synthetic quartz crystal at milli-Kelvin temperatures. Measurements
are made by performing spectroscopy using multiple high-$Q$ Whispering Gallery
Modes sustained in the crystal. Extreme sensitivity of the method at low
temperatures allows the determination of natural residual impurities introduced
during the crystal growth. We observe $g$-factors that significantly differ
from integer multiples of the electron $g$-factor in vacuum, and with values of
up to $7.6$, which reveals much stronger coupling between impurities and the
crystal lattice than in previous studies. Both substitutional and interstitial
ions are proposed as candidates for the observed interactions.


  Integrability conditions arising from general irrotational fluid-flow
considerations of a universe dominated by cosmic dark fluids will be
investigated under special assumptions on the nature of the spacetime shear.
Special emphasis will be placed on linearized perturbations of quasi-Newtonian
and anti-Newtonian spacetimes, whereby the conditions for the existence and
consistent evolution of such spacetimes in the presence of the Chaplygin gas
fluid model will be derived and discussed.


  We prove that in the reduced quartic BCS model with an imaginary external
magnetic field a spontaneous U(1)-symmetry breaking (SSB) and an off-diagonal
long range order (ODLRO) occur. The system is defined on a hyper-cubic lattice
with periodic boundary conditions at positive temperature. In the free part of
the Hamiltonian we assume the nearest-neighbor hopping. The chemical potential
is fixed so that the free Fermi surface does not degenerate. The term
representing the interaction between electrons' spin and the imaginary external
magnetic field is the z-component of the spin operator multiplied by a pure
imaginary parameter. The SSB and the ODLRO are shown in the infinite-volume
limit of the thermal average over the full Fermionic Fock space. The magnitude
of the negative coupling constant must be larger than a certain value so that
the gap equation is solvable. The gap equation is different from that of the
conventional mean field BCS model because of the presence of the imaginary
magnetic field. By adjusting the imaginary magnetic field this model shows the
SSB and the ODLRO in high temperature, weak coupling regimes where the
conventional reduced BCS model does not show these phenomena. The proof is
based on Grassmann Gaussian integral formulations and a double-scale
integration scheme to analytically control the formulations.


  We investigate the dynamics of two point-like particles through the third
post-Newtonian (3PN) approximation of general relativity. The infinite
self-field of each point-mass is regularized by means of Hadamard's concept of
``partie finie''. Distributional forms associated with the regularization are
used systematically in the computation. We determine the stress-energy tensor
of point-like particles compatible with the previous regularization. The
Einstein field equations in harmonic coordinates are iterated to the 3PN order.
The 3PN equations of motion are Lorentz-invariant and admit a conserved energy
(neglecting the 2.5PN radiation reaction). They depend on an undetermined
coefficient, in agreement with an earlier result of Jaranowski and Schaefer.
This suggests an incompleteness of the formalism (in this stage of development)
at the 3PN order. In this paper we present the equations of motion in the
center-of-mass frame and in the case of circular orbits.


  Finite-turn pushdown automata (PDA) are investigated concerning their
descriptional complexity. It is known that they accept exactly the class of
ultralinear context-free languages. Furthermore, the increase in size when
converting arbitrary PDAs accepting ultralinear languages to finite-turn PDAs
cannot be bounded by any recursive function. The latter phenomenon is known as
non-recursive trade-off. In this paper, finite-turn PDAs accepting bounded
languages are considered. First, letter-bounded languages are studied. We prove
that in this case the non-recursive trade-off is reduced to a recursive
trade-off, more precisely, to an exponential trade-off. A conversion algorithm
is presented and the optimality of the construction is shown by proving tight
lower bounds. Furthermore, the question of reducing the number of turns of a
given finite-turn PDA is studied. Again, a conversion algorithm is provided
which shows that in this case the trade-off is at most polynomial. Finally, the
more general case of word-bounded languages is investigated. We show how the
results obtained for letter-bounded languages can be extended to word-bounded
languages.


  The ferroelectric semiconductor $\alpha$-SnTe has been regarded as a
topological crystalline insulator and the dispersion of its surface states has
been intensively measured with angle-resolved photoemission spectroscopy
(ARPES) over the last decade. However, much less attention has been given to
the impact of the ferroelectric transition on its electronic structure, and in
particular on its bulk states. Here, we investigate the low-energy electronic
structure of $\alpha$-SnTe with ARPES and follow the evolution of the
bulk-state Rashba splitting as a function of temperature, across its
ferroelectric critical temperature of about $T_c\sim 110$ K. Unexpectedly, we
observe a persistent band splitting up to room temperature, which is consistent
with an order-disorder contribution to the phase transition that requires the
presence of fluctuating local dipoles above $T_c$. We conclude that no
topological surface state can occur at the (111) surface of SnTe, at odds with
recent literature.


  Federated learning (FL) enables distributed participants to collectively
learn a strong global model without sacrificing their individual data privacy.
Mainstream FL approaches require each participant to share a common network
architecture and further assume that data are are sampled IID across
participants. However, in real-world deployments participants may require
heterogeneous network architectures; and the data distribution is almost
certainly non-uniform across participants. To address these issues we introduce
FedH2L, which is agnostic to both the model architecture and robust to
different data distributions across participants. In contrast to approaches
sharing parameters or gradients, FedH2L relies on mutual distillation,
exchanging only posteriors on a shared seed set between participants in a
decentralized manner. This makes it extremely bandwidth efficient, model
agnostic, and crucially produces models capable of performing well on the whole
data distribution when learning from heterogeneous silos.


  For a fixed d-regular graph H, a random n-lift is obtained by replacing each
vertex v of H by a "fibre" containing n vertices, then placing a uniformly
random matching between fibres corresponding to adjacent vertices of H. We show
that with extremely high probability, all eigenvalues of the lift that are not
eigenvalues of H, have order O(sqrt(d)). In particular, if H is Ramanujan then
its n-lift is with high probability nearly Ramanujan. We also show that any
exceptionally large eigenvalues of the n-lift that are not eigenvalues of H,
are overwhelmingly likely to have been caused by a dense subgraph of size
O(|E(H)|).


  We study the relation between the frame-like and metric-like formulation of
higher-spin gauge theories in three space-time dimensions. We concentrate on
the theory that is described by an SL(3) x SL(3) Chern-Simons theory in the
frame-like formulation. The metric-like theory is obtained by eliminating the
generalised spin connection by its equation of motion, and by expressing
everything in terms of the metric and a spin-3 Fronsdal field. We give an exact
map between fields and gauge parameters in both formulations. To work out the
gauge transformations explicitly in terms of metric-like variables, we have to
make a perturbative expansion in the spin-3 field. We describe an algorithm how
to do this systematically, and we work out the gauge transformations to cubic
order in the spin-3 field. We use these results to determine the gauge algebra
to this order, and explain why the commutator of two spin-3 transformations
only closes on-shell.


  This is a working progress report on the attempt by Yuri Dokshitzer, Gavin
Salam and myself to relate the small-$x$ behaviour of the anomalous dimensions
in the time- and space-like cases. This relation is based on a ``reciprocity
respecting equation'' we propose


  We present a new approach to describe the dynamics of an isolated,
gravitationally bound astronomical $N$-body system in the weak field and
slow-motion approximation of the general theory of relativity. Celestial bodies
are described using an arbitrary energy-momentum tensor and assumed to possess
any number of internal multipole moments. The solution of the gravitational
field equations in any reference frame is presented as a sum of three terms: i)
the inertial flat spacetime in that frame, ii) unperturbed solutions for each
body in the system that is covariantly transformed to the coordinates of this
frame, and iii) the gravitational interaction term. We use the harmonic gauge
conditions that allow reconstruction of a significant part of the structure of
the post-Galilean coordinate transformation functions relating global
coordinates of the inertial reference frame to the local coordinates of the
non-inertial frame associated with a particular body. The remaining parts of
these functions are determined from dynamical conditions, obtained by
constructing the relativistic proper reference frame associated with a
particular body. In this frame, the effect of external forces acting on the
body is balanced by the fictitious frame-reaction force that is needed to keep
the body at rest with respect to the frame, conserving its relativistic
three-momentum. The resulting post-Galilean coordinate transformations have an
approximate group structure that extends the Poincar'e group of global
transformations to the case of accelerating observers in a gravitational field
of $N$-body system. We present and discuss the structure of the metric tensors
corresponding to the reference frames involved, the rules for transforming
relativistic gravitational potentials, the coordinate transformations between
frames and the resulting relativistic equations of motion.


  We study the Collins effect in the azimuthal asymmetric distribution of
hadrons inside a high energy jet in the single transverse polarized proton
proton scattering. From the detailed analysis of one-gluon and two-gluon
exchange diagrams contributions, the Collins function is found the same as that
in the semi-inclusive deep inelastic scattering and e^+e^- annihilations. The
eikonal propagators in these diagrams do not contribute to the phase needed for
the Collins-type single spin asymmetry, and the universality is derived as a
result of the Ward identity. We argue that this conclusion depends on the
momentum flow of the exchanged gluon and the kinematic constraints in the
fragmentation process, and is generic and model-independent.


  We discuss a formulation of quantum field theory on quantum space time where
the perturbation expansion of the S-matrix is term by term ultraviolet finite.
  The characteristic feature of our approach is a quantum version of the Wick
product at coinciding points: the differences of coordinates q_j - q_k are not
set equal to zero, which would violate the commutation relation between their
components. We show that the optimal degree of approximate coincidence can be
defined by the evaluation of a conditional expectation which replaces each
function of q_j - q_k by its expectation value in optimally localized states,
while leaving the mean coordinates (q_1 + ... + q_n)/n invariant.
  The resulting procedure is to a large extent unique, and is invariant under
translations and rotations, but violates Lorentz invariance. Indeed, optimal
localization refers to a specific Lorentz frame, where the electric and
magnetic parts of the commutator of the coordinates have to coincide *).
  Employing an adiabatic switching, we show that the S-matrix is term by term
finite. The matrix elements of the transfer matrix are determined, at each
order in the perturbative expansion, by kernels with Gaussian decay in the
Planck scale. The adiabatic limit and the large scale limit of this theory will
be studied elsewhere.
  --
  *) S. Doplicher, K. Fredenhagen, and J.E.Roberts, Commun. Math. Phys. 172,
187 (1995) [arXiv:hep-th/0303037]


  We present an approach to derivative exposure management based on subjective
and implied probabilities. We suggest to maximize the valuation difference
subject to risk constraints and propose a class of risk measures derived from
the subjective distribution. We illustrate this process with specific examples
for the two and three dimensional case. In these cases the optimization can be
performed graphically.


  We calculate diffractive photo- and leptoproduction of $\rho$-, $\rho'$- and
$\rho''$-mesons. The incoming photon dissociates into a $q\bar{q}$-dipole which
scatters on the nucleon and transforms into a vector meson state. The
scattering amplitude is calculated in non-perturbative QCD with the model of
the stochastic vacuum. Assuming that the physical $\rho'$- and $\rho''$-mesons
are mixed states of an active 2S-excitation and some residual hybrid state
which cannot be produced diffractively in lowest order QCD, we obtain good
agreement with the data, especially the markedly different spectrum in the
$\pi^+\pi^-$-invariant mass for photoproduction and $e^+e^-$-annihilation.


  Representation stability is a theory describing a way in which a sequence of
representations of different groups is related, and essentially contains a
finite amount of information. Starting with Church-Ellenberg-Farb's theory of
$FI$-modules describing sequences of representations of the symmetric groups,
we now have good theories for describing representations of other collections
of groups such as finite general linear groups, classical Weyl groups, and
Wreath products $S_n\wr G$ for a fixed finite group $G$. This paper attempts to
uncover the mechanism that makes the various examples work, and offers an
axiomatic approach that generates the essentials of such a theory: character
polynomials and free modules that exhibit stabilization.
  We give sufficient conditions on a category $C$ to admit such structure via
the notion of categories of $FI$ type. This class of categories includes the
examples listed above, and extends further to new types of categories such as
the categorical power $FI^m$, whose modules encode sequences of representations
of $m$-fold products of symmetric groups. The theory is applied in [Ga] to give
homological and arithmetic stability theorems for various moduli spaces, e.g.
the moduli space of degree n rational maps $P^1 \rightarrow P^m$.


  A mixed graph is a set of vertices together with an edge set and an arc set.
An $(m,n)$-mixed graph $G$ is a mixed graph whose edges are each assigned one
of $m$ colours, and whose arcs are each assigned one of $n$ colours. A
\emph{switch} at a vertex $v$ of $G$ permutes the edge colours, the arc
colours, and the arc directions of edges and arcs incident with $v$. The group
of all allowed switches is $\Gamma$.
  Let $k \geq 1$ be a fixed integer and $\Gamma$ a fixed permutation group. We
consider the problem that takes as input an $(m,n)$-mixed graph $G$ and asks if
there a sequence of switches at vertices of $G$ with respect to $\Gamma$ so
that the resulting $(m,n)$-mixed graph admits a homomorphism to an
$(m,n)$-mixed graph on $k$ vertices. Our main result establishes this problem
can be solved in polynomial time for $k \leq 2$, and is NP-hard for $k \geq 3$.
This provides a step towards a general dichotomy theorem for the
$\Gamma$-switchable homomorphism decision problem.


  Particles of the cosmic radiation, electrons and nuclei, transport a dominant
positive electric charge. A tiny fraction of these particles of extremely high
energies in favorable conditions overflow from galaxies. The overflowing of
positively charged cosmic nuclei into the intergalactic space uncovers an equal
amount of negative charge in the parent galaxy. Negative charge is mainly
stored by quiescent electrons. After adequate particle propagation neither the
negative electric charge located in the galaxies nor the positive electric
charge of the overflowed cosmic nuclei can be neutralized due to the enormous
distances. In several ways it is proved that the total electric charge retained
by clusters of galaxies after an appropriate time interval generate a repulsive
force between clusters which overwhelms gravity. After a few billions years of
electrostatic repulsion, peripheral clusters attain relativistic velocities and
their mutual distances increase accordingly. Several facts suggest that the
expansion of the universe, as determined by optical observations since a
century, has been caused by the electrostatic repulsion of the positively
charged cosmic nuclei overflowed from galaxy clusters.


  This paper shows that the fuzzy temporal logic can model figures of thought
to describe decision-making behaviors. In order to exemplify, some economic
behaviors observed experimentally were modeled from problems of choice
containing time, uncertainty and fuzziness. Related to time preference, it is
noted that the subadditive discounting is mandatory in positive rewards
situations and, consequently, results in the magnitude effect and time effect,
where the last has a stronger discounting for earlier delay periods (as in, one
hour, one day), but a weaker discounting for longer delay periods (for
instance, six months, one year, ten years). In addition, it is possible to
explain the preference reversal (change of preference when two rewards proposed
on different dates are shifted in the time). Related to the Prospect Theory, it
is shown that the risk seeking and the risk aversion are magnitude dependents,
where the risk seeking may disappear when the values to be lost are very high.


  We develop a min-max theory for the construction of capillary surfaces in
3-manifolds with smooth boundary. In particular, for a generic set of ambient
metrics, we prove the existence of nontrivial, smooth, almost properly embedded
surfaces with any given constant mean curvature $c$, and with smooth boundary
contacting at any given constant angle $\theta$. Moreover, if $c$ is nonzero
and $\theta$ is not $\frac{\pi}{2}$, then our min-max solution always has
multiplicity one. We also establish a stable Bernstein theorem for minimal
hypersurfaces with certain contact angles in higher dimensions.


  The TeV afterglow of the BOAT GRB 221009A was interpreted as arising from a
narrow jet while the radio to X-ray afterglows were interpreted as arising from
a wide structured jet. However, there is no model explaining the TeV and
lower-energy multi-wavelength afterglows simultaneously. We here investigate a
two-component jet model, including a narrow uniform core with a wide structured
wing, to explain both the multi-wavelength afterglows that last up to 100 days.
We find that to explain the early TeV afterglow with the inverse-Compton
process, we need a circum-burst density higher than $\gtrsim 0.1{\rm cm^{-3}}$,
while the radio afterglow and the H.E.S.S. upper limit combine to constrain the
density to be lower at larger radii. Thus, a decreasing density profile with
radius is favored. Considering that the rising TeV light curve during the
afterglow onset favors a constant-density medium, we invoke a stratified
density profile, including a constant-density profile at small radii and a wind
density profile at large radii. We find that the two-component jet model with
such a stratified density profile can explain the TeV, X-ray and optical
afterglows of GRB 221009A, although the radio fluxes exceed the observed ones
by a factor of two at later epochs. The discrepancy in the radio afterglow
could be resolved by invoking some non-standard assumption about the
microphysics of afterglow shocks. The total kinetic energy of the two
components in our model is $\lesssim 10^{52}{\rm erg}$, significantly smaller
than that in the single structured jet models.


  We construct short retractions of a CAT(1) space to its small convex subsets.
This construction provides an alternative geometric description of an analytic
tool introduced by Wilfrid Kendall.
  Our construction uses a tractrix flow which can be defined as a gradient flow
for a family of functions of certain type. In an appendix we prove a general
existence result for gradient flows of time-dependent locally Lipschitz
semiconcave functions, which is of independent interest.


  The continued observations of Sw J1644+57 in X-ray and radio bands
accumulated a rich data set to study the relativistic jet launched in this
tidal disruption event. We find that the re-brightening feature in the radio
light curve can be naturally explained by the two-component jet model. The
possible origin of this structured jet are the Blandford-Znajek and
Blandford-Payne mechanisms. We also show that this two-component jet model can
interpret the two kinds of quasi-periodic variations in the X-ray light curve:
a 200 second quasi-periodic oscillation (QPO) and a 2.7-day quasi-periodic
variation. The latter is interpreted by a precessing outer jet launched near
the Bardeen-Petterson radius of a warped disk. The $\sim$ 200s QPO could be
associated with a second, narrower jet sweeping the observer line-of-sight
periodically, which is launched from a spinning black hole in the misaligned
direction with respect to the black hole's angular momentum.


  We consider the problem of optimally executing an order involving multiple
crypto-assets, sometimes called tokens, on a network of multiple constant
function market makers (CFMMs). When we ignore the fixed cost associated with
executing an order on a CFMM, this optimal routing problem can be cast as a
convex optimization problem, which is computationally tractable. When we
include the fixed costs, the optimal routing problem is a mixed-integer convex
problem, which can be solved using (sometimes slow) global optimization
methods, or approximately solved using various heuristics based on convex
optimization. The optimal routing problem includes as a special case the
problem of identifying an arbitrage present in a network of CFMMs, or
certifying that none exists.


  The regularized expectation value of the stress-energy tensor for a massless
bosonic or fermionic field in 1+1 dimensions is calculated explicitly for the
instantaneous vacuum relative to any Cauchy surface (here a spacelike curve) in
terms of the length L of the curve (if closed), the local extrinsic curvature K
of the curve, its derivative K' with respect to proper distance x along the
curve, and the scalar curvature R of the spacetime: T_{00} = - epsilon
pi/(6L^2) - K^2/(24 pi), T_{01} = - K'/(12 pi), T_{11} = - epsilon pi/(6L^2) -
K^2/(24 pi) + R/(24 pi), in an orthonormal frame with the spatial vector
parallel to the curve. Here epsilon = 1 for an untwisted (i.e., periodic in x)
one-component massless bosonic field or for a twisted (i.e., antiperiodic in x)
two-component massless fermionic field, epsilon = -1/2 for a twisted
one-component massless bosonic field, and epsilon = - 2 for an untwisted
two-component massless fermionic field. The calculation uses merely the
energy-momentum conservation law and the trace anomaly (for which a very simple
derivation is also given herein, as well as the expression for the Casimir
energy of bosonic and fermionic fields twisted by an arbitrary amount in
R^{D-1} x S^1). The two coordinate and conformal invariants of a quantum state
that are (nonlocally) determined by the stress-energy tensor are given.
Applications to topologically modified deSitter spacetimes, to a flat cylinder,
and to Minkowski spacetime are discussed.


  Many experiments have shown that locality-realism theory is at variance with
quantum mechanics predictions. Although locality and realism, which are two
different conceptions, are given respective definition, the descriptions of the
both are a little of abstract when they are applied to real experimental
situations. The abstract descriptions result in difficulty for one to judge
whether the variance come from locality or realism or both. Here we provide
more detailed descriptions of locality and realism, and show that any system
being in a pure state or a non-maximally mixed state has property of
non-realism. We also present experimental schemes feasible under current
technologies to test the non-locality realsim. The connections between
non-locality and entanglement and correlation are also discussed.


  This paper aims to address a common challenge in deep learning-based image
transformation methods, such as image enhancement and super-resolution, which
heavily rely on precisely aligned paired datasets with pixel-level alignments.
However, creating precisely aligned paired images presents significant
challenges and hinders the advancement of methods trained on such data. To
overcome this challenge, this paper introduces a novel and simple Frequency
Distribution Loss (FDL) for computing distribution distance within the
frequency domain. Specifically, we transform image features into the frequency
domain using Discrete Fourier Transformation (DFT). Subsequently, frequency
components (amplitude and phase) are processed separately to form the FDL loss
function. Our method is empirically proven effective as a training constraint
due to the thoughtful utilization of global information in the frequency
domain. Extensive experimental evaluations, focusing on image enhancement and
super-resolution tasks, demonstrate that FDL outperforms existing
misalignment-robust loss functions. Furthermore, we explore the potential of
our FDL for image style transfer that relies solely on completely misaligned
data. Our code is available at: https://github.com/eezkni/FDL


  Motivated by the observed correlation between black hole masses $\mbh$ and
the velocity dispersion $\sigma$ of host galaxies, we develop a theoretical
model of black hole formation in galactic bulges (this paper generalizes an
earlier ApJ Letter). The model assumes an initial state specified by a a
uniform rotation rate $\Omega$ and a density distribution of the form $\rho =
\aeff^2 / 2 \pi G r^2$ (so that $\aeff$ is an effective transport speed). The
black hole mass is determined when the centrifugal radius of the collapse flow
exceeds the capture radius of the central black hole (for Schwarzschild
geometry). This model reproduces the observed correlation between the estimated
black hole masses and the velocity dispersions of galactic bulges, i.e., $\mbh
\approx 10^8 M_\odot (\sigma/200 {\rm km s^{-1}})^4$, where $\sigma = \sqrt{2}
\aeff$. To obtain this normalization, the rotation rate $\Omega \approx 2
\times 10^{15}$ rad/s. The model also defines a bulge mass scale $M_B$. If we
identify the scale $M_B$ with the bulge mass, the model determines the ratio
$\mrat$ of black hole mass to the host mass: $\mrat$ $\approx$ 0.0024
$(\sigma/200 {\rm km s^{-1}})$, again in reasonable agreement with observed
values. In this scenario, supermassive black holes form quickly (in $\sim10^5$
yr) and are born rapidly rotating (with $a/M \sim 0.9$). This paper also shows
how these results depend on the assumed initial conditions; the most important
quantity is the initial distribution of specific angular momentum in the
pre-collapse state.


  In 2005, Yang, Wang, and Chang proposed an improved timestamp-based password
authentication scheme in an attempt to overcome the flaws of Yang-Shieh_s
legendary timestamp-based remote authentication scheme using smart cards. After
analyzing the improved scheme proposed by Yang-Wang-Chang, we have found that
their scheme is still insecure and vulnerable to four types of forgery attacks.
Hence, in this paper, we prove that, their claim that their scheme is
intractable is incorrect. Also, we show that even an attack based on Sun et
al._s attack could be launched against their scheme which they claimed to
resolve with their proposal.


  The classical Chow form encodes any projective variety by one equation. We
here introduce the Chow-Lam form for subvarieties of a Grassmannian. By
evaluating the Chow-Lam form at twistor coordinates, we obtain universal
projection formulas. These were pioneered by Thomas Lam for positroid varieties
in the study of amplituhedra, and we develop his approach further. Universal
formulas for branch loci are obtained from Hurwitz-Lam forms. Our focus is on
computations and applications in geometry.


  If stiff inclusions are closely located, then the stress, which is the
gradient of the solution, may become arbitrarily large as the distance between
two inclusions tends to zero. In this paper we investigate the asymptotic
behavior of the stress concentration factor, which is the normalized magnitude
of the stress concentration, as the distance between two inclusions tends to
zero. For that purpose we show that the gradient of the solution to the case
when two inclusions are touching decays exponentially fast near the touching
point. We also prove a similar result when two inclusions are closely located
and there is no potential difference on boundaries of two inclusions. We then
use these facts to show that the stress concentration factor converges to a
certain integral of the solution to the touching case as the distance between
two inclusions tends to zero. We then present an efficient way to compute this
integral.


  The profusion of user generated content caused by the rise of social media
platforms has enabled a surge in research relating to fields such as
information retrieval, recommender systems, data mining and machine learning.
However, the lack of comprehensive baseline data sets to allow a thorough
evaluative comparison has become an important issue. In this paper we present a
large data set of news items from well-known aggregators such as Google News
and Yahoo! News, and their respective social feedback on multiple platforms:
Facebook, Google+ and LinkedIn. The data collected relates to a period of 8
months, between November 2015 and July 2016, accounting for about 100,000 news
items on four different topics: economy, microsoft, obama and palestine. This
data set is tailored for evaluative comparisons in predictive analytics tasks,
although allowing for tasks in other research areas such as topic detection and
tracking, sentiment analysis in short text, first story detection or news
recommendation.


  We use cosmological simulations to identify dark matter subhalo host
candidates of the Fornax dwarf spheroidal galaxy using the stellar kinematic
properties of Fornax. We consider cold dark matter (CDM), warm dark matter
(WDM), and decaying dark matter (DDM) simulations for our models of structure
formation. The subhalo candidates in CDM typically have smaller mass and higher
concentrations at z = 0 than the corresponding candidates in WDM and DDM. We
examine the formation histories of the ~ 100 Fornax candidate subhalos
identified in CDM simulations and, using approximate luminosity-mass
relationships for subhalos, we find two of these subhalos that are consistent
with both the Fornax luminosity and kinematics. These two subhalos have a peak
mass over ten times larger than their z = 0 mass. We suggest that in CDM the
dark matter halo hosting Fornax must have been severely stripped of mass and
that it had an infall time into the Milky Way of ~ 9 Gyr ago. In WDM, we find
that candidate subhalos consistent with the properties of Fornax have a similar
infall time and a similar degree of mass loss, while in DDM we find a later
infall time of ~ 3 - 4 Gyr ago and significantly less mass loss. We discuss
these results in the context of the Fornax star formation history, and show
that these predicted subhalo infall times can be linked to different star
formation quenching mechanisms. This emphasizes the links between the
properties of the dark matter and the mechanisms that drive galaxy evolution.


  An undetected eavesdropping attack must produce count rate statistics that
are indistinguishable from those that would arise in the absence of such an
attack. In principle this constraint should force a reduction in the amount of
information available to the eavesdropper. In this paper we illustrate, by
considering a particular class of eavesdropping attacks, how the general
analysis of this problem may proceed.


  Quasars whose broad emission lines show temporal, bulk radial velocity (RV)
shifts have been proposed as candidate sub-parsec (sub-pc), binary supermassive
black holes (BSBHs). We identified a sample of 16 BSBH candidates based on
two-epoch spectroscopy among 52 quasars with significant RV shifts over a few
rest-frame years. The candidates showed consistent velocity shifts
independently measured from two broad lines (H$\beta$ and H$\alpha$ or Mg${\rm
\,II}$) without significant changes in the broad-line profiles. Here in the
third paper of the series, we present further third- and fourth-epoch
spectroscopy for 12 of the 16 candidates for continued RV tests, spanning
$\sim$5--15 yr in the quasars' rest frames. Cross-correlation analysis of the
broad H$\beta$ calibrated against [O${\rm\,III}]\,\lambda 5007$ suggests that 5
of the 12 quasars remain valid as BSBH candidates. They show broad H$\beta$ RV
curves that are consistent with binary orbital motion without significant
changes in the broad line profiles. Their broad H$\alpha$ (or Mg${\rm \,II}$)
lines display RV shifts that are either consistent with or smaller than those
seen in broad H$\beta$. The RV shifts can be explained by a $\sim$0.05--0.1 pc
BSBH with an orbital period of $\sim$40--130 yr, assuming a mass ratio of
0.5--2 and a circular orbit. However, the parameters are not well constrained
given the few epochs that sample only a small portion of the hypothesized
binary orbital cycle. The apparent occurrence rate of sub-pc BSBHs is
$\lesssim$13$\pm$5% among all SDSS quasars, with no significant difference in
the subsets with and without single-epoch broad line velocity offsets.
Dedicated long-term spectroscopic monitoring is still needed to further confirm
or reject these BSBH candidates.


  The problem of characterising the accuracy of, and disturbance caused by a
joint measurement of position and momentum is investigated. In a previous paper
the problem was discussed in the context of the unbiased measurements
considered by Arthurs and Kelly. It is now shown, that suitably modified
versions of these results hold for a much larger class of simultaneous
measurements. The approach is a development of that adopted by Braginsky and
Khalili in the case of a single measurement of position only. A distinction is
made between the errors of retrodiction and the errors of prediction. Two
error-error relationships and four error-disturbance relationships are derived,
supplementing the Uncertainty Principle usually so-called. In the general case
it is necessary to take into account the range of the measuring apparatus. Both
the ideal case, of an instrument having infinite range, and the case of a real
instrument, for which the range is finite, are discussed.


  In this work, we apply the advantage distillation method to improve the
performance of a practical twin-field quantum key distribution system under
collective attack. Compared with the previous analysis result given by Maeda,
Sasaki and Koashi [Nature Communication 10, 3140 (2019)], the maximal
transmission distance obtained by our analysis method will be increased from
420 km to 470 km. By increasing the loss-independent misalignment error to 12%,
the previous analysis method can not overcome the rate-distance bound. However,
our analysis method can still overcome the rate-distance bound when the
misalignment error is 16%. More surprisingly, we prove that twin-field quantum
key distribution can generate positive secure key even if the misalignment
error is close to 50%, thus our analysis method can significantly improve the
performance of a practical twin-field quantum key distribution system.


  A model of space-time foam in the form of an arbitrary distribution of
spherical Euclidean wormholes is considered. A method for constructing the
exact solution of Einstein's Euclidean equations for the metric corresponding
to this model is proposed. In the framework of our model we obtain the
expression for the Euclidean action and its dependence on the parameters of
wormholes in the explicit form. It is shown how the solutions obtained make it
possible to determine all possible correlation functions associated with the
parameters of virtual wormholes in the vacuum state.


  The Long-Range Wide-Area Network (LoRaWAN) specification was released in
2015, primarily to support the Internet-of-Things by facilitating wireless
communication over long distances. Since 2015, the role-out and adoption of
LoRaWAN has seen a steep growth. To the best of our knowledge, we are the first
to have extensively measured, analyzed, and modeled the performance, features,
and use cases of an operational LoRaWAN, namely The Things Network. Our
measurement data, as presented in this paper, cover the early stages up to the
production-level deployment of LoRaWAN. In particular, we analyze packet
payloads, radio-signal quality, and spatio-temporal aspects, to model and
estimate the performance of LoRaWAN. We also use our empirical findings in
simulations to estimate the packet-loss.


  In this work we perform a Green's function analysis of giant-dipole systems.
First we derive the Green's functions of different magnetically field-dressed
systems, in particular of electronically highly excited atomic species in
crossed electric and magnetic fields, so-called giant-dipole states. We
determine the dynamical polarizability of atomic giant-dipole states as well as
the adiabatic potential energy surfaces of giant-dipole molecules in the
framework of the Green's function approach. Furthermore, we perform an
comparative analysis of the latter to and exact diagonalization scheme and show
the general divergence behavior of the widely applied Fermi-pseudopotential
approach. Finally, we derive the giant-dipole's regularized Green's function
representation.


  Pedestal is the key to conventional high performance plasma scenarios in
tokamaks. However, high fidelity simulations of pedestal plasmas are extremely
challenging due to the multiple physical processes and scales that are
encompassed by tokamak pedestals. The leading paradigm for predicting the
pedestal top pressure is encompassed by EPED-like models. However, EPED does
not predict the pedestal top density, $n_\text{e,ped}$, but requires it as an
input. EUROPED employs simplified models, such as log-linear regression, to
constrain $n_\text{e,ped}$ with tokamak machine control parameters in an
EPED-like model. However, these simplified models for $n_\text{e,ped}$ often
show disagreements with experimental observations and do not use all of the
available numerical and categorical machine control information. In this work
it is observed that using the same input parameters, decision tree ensembles
and deep learning models improve the predictive quality of $n_\text{e,ped}$ by
about 23% relative to that obtained with log-linear scaling laws, measured by
root mean square error. Including all of the available tokamak machine control
parameters, both numerical and categorical, leads to further improvement of
about 13%. Finally, predictive quality was tested when including global
normalized plasma pressure and effective charge state as inputs, as these
parameters are known to impact pedestals. Surprisingly, these parameters lead
to only a few percent further improvement of the predictive quality.


  Plasmons are the quantized collective oscillations of electrons in metals and
doped semiconductors. The plasmons of ordinary, massive electrons are since a
long time basic ingredients of research in plasmonics and in optical
metamaterials. Plasmons of massless Dirac electrons were instead recently
observed in a purely two-dimensional electron system (2DEG)like graphene, and
their properties are promising for new tunable plasmonic metamaterials in the
terahertz and the mid-infrared frequency range. Dirac quasi-particles are known
to exist also in the two-dimensional electron gas which forms at the surface of
topological insulators due to a strong spin-orbit interaction. Therefore,one
may look for their collective excitations by using infrared spectroscopy. Here
we first report evidence of plasmonic excitations in a topological insulator
(Bi2Se3), that was engineered in thin micro-ribbon arrays of different width W
and period 2W to select suitable values of the plasmon wavevector k. Their
lineshape was found to be extremely robust vs. temperature between 6 and 300 K,
as one may expect for the excitations of topological carriers. Moreover, by
changing W and measuring in the terahertz range the plasmonic frequency vP vs.
k we could show, without using any fitting parameter, that the dispersion curve
is in quantitative agreement with that predicted for Dirac plasmons.


  We report interferometric schemes to prepare arbitrary states of
four-dimensional qudits (ququarts) based on biphoton states of ultrafast-pumped
frequency-nondegenerate spontaneous parametric down-conversion. Preparation and
tomographic characterization of a few examples of general single-ququart
states, a pure state, a completely mixed state, and a partially-mixed state,
are experimentally demonstrated.


  Mainly motivated by Pirashvili's spectral sequences on a Leibniz algebra, a
cohomological characterization of Leibniz central extensions of Lie algebras is
given based on Corollary 3.3 and Theorem 3.5. In particular, as applications,
we obtain the cohomological version of Gao's main Theorem in \cite{Gao2} for
Kac-Moody algebras and answer a question in \cite{LH}.


  We present two approaches for next step linear prediction of long memory time
series. The first is based on the truncation of the Wiener-Kolmogorov predictor
by restricting the observations to the last $k$ terms, which are the only
available values in practice. Part of the mean squared prediction error comes
from the truncation, and another part comes from the parametric estimation of
the parameters of the predictor. By contrast, the second approach is
non-parametric. An AR($k$) model is fitted to the long memory time series and
we study the error made with this misspecified model.


  We propose a general topology optimization framework for metasurface inverse
design that can automatically discover highly complex multi-layered
meta-structures with increased functionalities. In particular, we present
topology-optimized multi-layered geometries exhibiting angular phase control,
including a single-piece nanophotonic metalens with angular aberration
correction as well as an angle-convergent metalens that focuses light onto the
same focal spot regardless of the angle of incidence.


  In this paper, the application of 5G communication technology in an
industrial environment is discussed. It acts as an enabler for the separation
of sensors/actors and resources, like memory and computational power. 5G offers
characteristics essential for the proposed approach like robustness, ultra-low
latency, high data rates and massive number of devices.
  A demonstrator of a production line was used as an test environment for 5G in
a real-world industrial application. A wide variety of heterogeneous sensor
systems is used by a mobile robot platform. The collected data is transmitted
via a 5G network to various Cloud systems. The product is treated as a
cyber-physical system with a RFID tag in conjunction with the product memory
system.
  The dynamic production flow approach is discussed centered around the robot
which is used for transportation and inspection of products. This inspection is
performed during the transportation and influences the production flow
directly. This is desirable in the scope of Industry 4.0 to have an efficient
production down to batch size 1.


  For a set $R$ of $n$ red points and a set $B$ of $n$ blue points, a
$BR$-matching is a non-crossing geometric perfect matching where each segment
has one endpoint in $B$ and one in $R$. Two $BR$-matchings are compatible if
their union is also non-crossing. We prove that, for any two distinct
$BR$-matchings $M$ and $M'$, there exists a sequence of $BR$-matchings $M =
M_1, ..., M_k = M'$ such that $M_{i-1} $ is compatible with $M_i$. This implies
the connectivity of the compatible bichromatic matching graph containing one
node for each bichromatic matching and an edge joining each pair of compatible
matchings, thereby answering the open problem posed by Aichholzer et al. in
"Compatible matchings for bichromatic plane straight-line graphs"


  We investigate fine global properties of nonnegative, integrable solutions to
the Cauchy problem for the Fast Diffusion Equation with weights (WFDE)
$u_t=|x|^\gamma\mathrm{div}\left(|x|^{-\beta}\nabla u^m\right)$ posed on
$(0,+\infty)\times\mathbb{R}^d$, with $d\ge 3$, in the so-called good fast
diffusion range $m_c<m<1$, within the range of parameters $\gamma, \beta$,
optimal for the validity of the so-called Caffarelli-Kohn-Nirenberg
inequalities. It is a natural question to ask in which sense such solutions
behave like the Barenblatt $\mathfrak{B}$ (fundamental solution): for instance,
asymptotic convergence, i.e. $\|u(t)-\mathfrak{B}(t)\|_{{\rm
L}^p(\mathbb{R}^d)}\xrightarrow[]{t\to\infty}0$, is well known for all $1\le
p\le \infty$, while only few partial results tackle a finer analysis of the
tail behaviour. We characterize the maximal set of data $\mathcal{X}\subset{\rm
L}^1_+(\mathbb{R}^d)$ that produces solutions which are pointwise trapped
between two Barenblatt (Global Harnack Principle), and uniformly converge in
relative error (UREC), i.e. ${\rm
d}_\infty(u(t))=\|u(t)/\mathcal{B}(t)-1\|_{{\rm
L}^\infty(\mathbb{R}^d)}\xrightarrow[]{t\to\infty}0$. Such characterization is
in terms of an integral condition on $u(t=0)$. To the best of our knowledge,
analogous issues for the linear heat equation $m=1$, do not possess such clear
answers. Our characterization is also new for the classical, non-weighted, FDE.
We are able to provide minimal rates of convergence to $\mathcal{B}$ in
different norms. Such rates are almost optimal in the non weighted case, and
become optimal for radial solutions. To complete the panorama, we show that
solutions with data in ${\rm L}^1_+(\mathbb{R}^d)\setminus\mathcal{X}$,
preserve the same "fat" spatial tail for all times, hence UREC fails.


  The discovery of two dimensional (2D) magnetic materials has brought great
research value for spintronics and data storage devices. However, their
air-stability as well as the oxidation mechanism has not been unveiled, which
limits their further applications. Here, by first-principles calculations, we
carried out a detailed study on the oxidation process of monolayer CrSe2 and
biaxial tensile strain effect. We found dissociation process of O2 on pristine
CrSe2 sheet is an endothermic reaction with a reaction energy barrier of 0.53
eV, indicating its thermodynamics stability. However, such a process becomes
exothermic under a biaxial tensile strain reaching 1%, accompanying with a
decreased reaction barrier, leading to reduced stability. These results
manifest that in-plane strain plays a significant role in modifying
air-stability in CrSe2 and shed considerable light on searching appropriate
substrate to stabilize 2D magnetic materials.


  The temporal evolution of the magnetization vector of a single-domain
magnetostrictive nanomagnet, subjected to in-plane stress, is studied by
solving the Landau-Lifshitz-Gilbert equation. The stress is ramped up linearly
in time and the switching delay, which is the time it takes for the
magnetization to flip, is computed as a function of the ramp rate. For high
levels of stress, the delay exhibits a non-monotonic dependence on the ramp
rate, indicating that there is an {\it optimum} ramp rate to achieve the
shortest delay. For constant ramp rate, the delay initially decreases with
increasing stress but then saturates showing that the trade-off between the
delay and the stress (or the energy dissipated in switching) becomes less and
less favorable with increasing stress. All of these features are due to a
complex interplay between the in-plane and out-of-plane dynamics of the
magnetization vector induced by stress.


  Helioseismology is the branch of the Solar Physics which studies the solar
global oscillations, a phenomenon very important in order to understand the
inside of the Sun. We explain here a method for measuring the solar velocity
fields along the line of sight by the VAMOS instrument developed at the
Astronomical Observatory of Capodimonte in Naples, in particular we present the
measures of the so called five-minutes oscillations and of the
Supergranulation.


  We prove a connection between Schmidt-rank and weight of quadratic forms.
This provides a new tool for the classification of graph states based on
entanglement. Our main tool arises from a reformulation of previously known
results concerning the weight of quadratic forms in terms of graph states
properties. As a byproduct, we obtain a straightforward characterization of the
weight of functions associated with pivot-minor of bipartite graphs.


  Knowing accurate Pb abundances of metal-poor stars provides constraints on
the Pb production mechanisms in the early Galaxy. Accurately deriving Th
abundances permits a nucleo-chronometric age determination of the star. We
improve the calculation of the Pb I and Th II lines in stellar atmospheres
based on non-LTE line formation and evaluate the influence of departures from
LTE on Pb and Th abundance determinations through a range of stellar
parameters. Comprehensive model atoms for Pb I and Th II are presented. The
departures from LTE lead to systematically depleted total absorption in the Pb
I lines and positive abundance corrections. Non-LTE removes the discrepancy
between the solar and the meteoritic Pb abundance. With the Holweger & Mueller
(1974) solar model atmosphere, log eps(Pb, non-LTE) = 2.09. We revise the Pb
and Eu abundances of the strongly r-process enhanced (r-II) stars CS 31082-001
and HE 1523-0901 and the Roederer et al. (2010) stellar sample. Our results
provide strong evidence for universal Pb/Eu relative r-process yields during
course of the Galaxy evolution. The stars with -2.3<[Fe/H]< -1.4 have, on
average, 0.51 dex higher Pb/Eu ratios compared with that of the r-II stars
suggesting that the s-process synthesis of Pb started as early as the time when
Galactic metallicity had grown to [Fe/H] = -2.3. The average Pb/Eu ratio of the
-1.4<[Fe/H]< -0.59 stars is close to the solar value, in line with the
predictions of Travaglio et al. (2001) that AGB stars with [Fe/H] ~ -1 provided
the largest contribution to the solar s-nuclei of Pb. Non-LTE leads to weakened
Th II lines. Overall, the abundance correction does not exceed +0.2 dex when
collisions with H I atoms are taken into account in non-LTE calculations.


  A finite size scaling theory, originally developed only for transitions to
absorbing states [Phys. Rev. E {\bf 92}, 062126 (2015)], is extended to
distinct sorts of discontinuous nonequilibrium phase transitions. Expressions
for quantities such as, response functions, reduced cumulants and equal area
probability distributions, are derived from phenomenological arguments.
Irrespective of system details, all these quantities scale with the volume,
establishing the dependence on size. The approach generality is illustrated
through the analysis of different models. The present results are a relevant
step in trying to unify the scaling behavior description of nonequilibrium
transition processes.


  We propose a modified version of the sliver-frame level expansion which gives
a tool for analyzing singularities related to the identity string field. We
apply this formalism to the newly discovered solutions of Masuda, Noumi, and
Takahashi.


  For a compact group $G$ we define the Beurling-Fourier algebra $A_\omega(G)$
on $G$ for weights $\omega$ defined on the dual $\what G$ and taking positive
values. The classical Fourier algebra corresponds to the case $\omega$ is the
constant weight 1. We study the Gelfand spectrum of the algebra realizing it as
a subset of the complexification $G_{\mathbb C}$ defined by McKennon and
Cartwright and McMullen. In many cases, such as for polynomial weights, the
spectrum is simply $G$. We discuss the questions when the algebra $A_\omega(G)$
is symmetric and regular. We also obtain various results concerning spectral
synthesis for $A_\omega(G)$.


  We evaluate cross sections for $\eslt$, 1$\ell$ and various dilepton and
multilepton event topologies that result from the simultaneous production of
all sparticles at the Tevatron collider, both within the minimal model
framework as well as in two different $R$-parity violating scenarios. Our
analysis assumes that these $R$-violating couplings are small, and that their
sole effect is to cause the lightest supersymmetric particle to decay inside
the detector. We reassess future strategies for sparticle searches at the
Tevatron, and quantify by how much the various signals for supersymmetry could
differ from their minimal model expectations, if $R$-parity is not conserved
due to either baryon number or lepton number violating operators. We also
evaluate the Tevatron reach in $m_{\tg}$ for the various models, and find that
rate-limited multilepton signals ultimately provide the largest reach for both
$R$-parity conserving and $R$-parity violating cases.


  We introduce the embedded Nash problem allowing singularities in the ambient
space, and solve it in the case of surfaces, generalizing \cite[Theorem
1.22]{BdlB}.


  Strongly correlated bosons in a lattice are a platform to realize rich
bosonic states of matter and quantum phase transitions. While strongly
correlated bosons in a lattice have been studied in cold-atom experiments,
their realization in a solid-state system has remained challenging. Here we
trap interlayer excitons--bosons composed of bound electron-hole pairs--in a
lattice provided by an angle-aligned WS2/bilayer WSe2/WS2 multilayer; the
heterostructure supports Coulomb-coupled triangular moir\'e lattices of nearly
identical period at the top and bottom interfaces. We observe correlated
insulating states when the combined electron filling factor of the two
lattices, with arbitrary partitions, equals to 1/3,2/3,4/3 and 5/3. These new
states can be interpreted as exciton density waves in a Bose-Fermi mixture of
excitons and holes. Because of the strong repulsive interactions between the
constituents, the holes form robust generalized Wigner crystals , which
restrict the exciton fluid to channels that spontaneously break the
translational symmetry of the lattice. Our results demonstrate that
Coulomb-coupled moir\'e lattices are fertile ground for correlated many-boson
phenomena.


  In this paper, we address the problem of data description using a Bayesian
framework. The goal of data description is to draw a boundary around objects of
a certain class of interest to discriminate that class from the rest of the
feature space. Data description is also known as one-class learning and has a
wide range of applications.
  The proposed approach uses a Bayesian framework to precisely compute the
class boundary and therefore can utilize domain information in form of prior
knowledge in the framework. It can also operate in the kernel space and
therefore recognize arbitrary boundary shapes. Moreover, the proposed method
can utilize unlabeled data in order to improve accuracy of discrimination.
  We evaluate our method using various real-world datasets and compare it with
other state of the art approaches of data description. Experiments show
promising results and improved performance over other data description and
one-class learning algorithms.


  We present a new cubic theory of gravity in five dimensions which has second
order traced field equations, analogous to BHT new massive gravity in three
dimensions. Moreover, for static spherically symmetric spacetimes all the field
equations are of second order, and the theory admits a new asymptotically
locally flat black hole. Furthermore, we prove the uniqueness of this solution,
study its thermodynamical properties, and show the existence of a C-function
for the theory following the arguments of Anber and Kastor (arXiv:0802.1290
[hep-th]) in pure Lovelock theories. Finally, we include the
Einstein-Gauss-Bonnet and cosmological terms and we find new asymptotically AdS
black holes at the point where the three maximally symmetric solutions of the
theory coincide. These black holes may also possess a Cauchy horizon.


  We explore the phenomenon of unidirectional invisibility in two dimensions,
examine its optical realizations, and discuss its three-dimensional
generalization. In particular we construct an infinite class of
unidirectionally invisible optical potentials that describe the scattering of
normally incident transverse electric waves by an infinite planar slab with
refractive-index modulations along both the normal directions to the electric
field. A by-product of this investigation is a demonstration of nonreciprocal
transmission in two dimensions. To elucidate this phenomenon we state and prove
a general reciprocity theorem that applies to quantum scattering theory of real
and complex potentials in two and three dimensions.


  The scattering problems arising when considering the contribution of the
topologically inequivalent configurations of the spinors on
Reissner-Nordstr\"{o}m black holes to the Hawking radiation are correctly
stated. The corresponding $S$-matrices are described and presented in the form
convenient to numerical computations.


  We present a catalogue of 247 photometrically and spectroscopically confirmed
fainter classical Be stars (13 < r < 16) in the direction of the Perseus Arm of
the Milky Way (-1 < b < +4, 120 < l < 140). The catalogue consists of 181
IPHAS-selected new classical Be stars, in addition to 66 objects that were
studied by Raddi et al. (2013) more closely, and 3 stars identified as
classical Be stars in earlier work. This study more than doubles the number
known in the region. Photometry spanning 0.6 to 5 micron, spectral types, and
interstellar reddenings are given for each object. The spectral types were
determined from low-resolution spectra (lambda / Delta-lambda ~ 800-2000), to a
precision of 1-3 subtypes. The interstellar reddenings are derived from the (r
- i) colour, using a method that corrects for circumstellar disc emission. The
colour excesses obtained range from E(B-V) = 0.3 up to 1.6 - a distribution
that modestly extends the range reported in the literature for Perseus-Arm open
clusters. For around half the sample, the reddenings obtained are compatible
with measures of the total sightline Galactic extinction. Many of these are
likely to lie well beyond the Perseus Arm.


  For semantic segmentation in urban scene understanding, RGB cameras alone
often fail to capture a clear holistic topology in challenging lighting
conditions. Thermal signal is an informative additional channel that can bring
to light the contour and fine-grained texture of blurred regions in low-quality
RGB image. Aiming at practical RGB-T (thermal) segmentation, we systematically
propose a Spatial-aware Demand-guided Recursive Meshing (SpiderMesh) framework
that: 1) proactively compensates inadequate contextual semantics in
optically-impaired regions via a demand-guided target masking algorithm; 2)
refines multimodal semantic features with recursive meshing to improve
pixel-level semantic analysis performance. We further introduce an asymmetric
data augmentation technique M-CutOut, and enable semi-supervised learning to
fully utilize RGB-T labels only sparsely available in practical use. Extensive
experiments on MFNet and PST900 datasets demonstrate that SpiderMesh achieves
state-of-the-art performance on standard RGB-T segmentation benchmarks.


  Functional near-infrared spectroscopy (fNIRS) is a non-invasive, low-cost
method used to study the brain's blood flow pattern. Such patterns can enable
us to classify performed by a subject. In recent research, most classification
systems use traditional machine learning algorithms for the classification of
tasks. These methods, which are easier to implement, usually suffer from low
accuracy. Further, a complex pre-processing phase is required for data
preparation before implementing traditional machine learning methods. The
proposed system uses a Bi-Directional LSTM based deep learning architecture for
task classification, including mental arithmetic, motor imagery, and idle state
using fNIRS data. Further, this system will require less pre-processing than
the traditional approach, saving time and computational resources while
obtaining an accuracy of 81.48\%, which is considerably higher than the
accuracy obtained using conventional machine learning algorithms for the same
data set.


  We report on our result for the equation of state (EOS) with a Symanzik
improved gauge action and the asqtad improved staggered fermion action at
$N_t=4$ and 6. In our dynamical simulations with 2+1 flavors we use the inexact
R algorithm and here we estimate the finite step-size systematic error on the
EOS. Finally we discuss the non-zero chemical potential extension of the EOS
and give some preliminary results.


  Reliability assessment of interconnection networks is critical to the design
and maintenance of multiprocessor systems. The (n, k)-enhanced hypercube
Q_{n,k} as a variation of the hypercube Q_{n}, was proposed by Tzeng and Wei in
1991. As an extension of traditional edge-connectivity, h-extra
edge-connectivity of a connected graph G, \lambda_h(G), is an essential
parameter for evaluating the reliability of interconnection networks. This
article intends to study the h-extra edge-connectivity of the (n,2)-enhanced
hypercube Q_{n,2}. Suppose that the link malfunction of an interconnection
network Q_{n,2} does not isolate any subnetwork with no more than h-1
processors, the minimum number of these possible faulty links concentrate on a
constant 2^{n-1} for each integer \lceil\frac{11\times2^{n-1}}{48}\rceil \leq h
\leq 2^{n-1} and n\geq 9. That is, for about 77.083 percent values of
h\leq2^{n-1}, the corresponding h-extra edge-connectivity of Q_{n,2},
\lambda_h(Q_{n,2}), presents a concentration phenomenon. Moreover, the above
lower and upper bounds of h are both tight.


  We give a proof of existence of centre manifolds within large domains for
systems with an integral of motion. The proof is based on a combination of
topological tools, normal forms and rigorous-computer-assisted computations. We
apply our method to obtain an explicit region in which we prove existence of a
center manifold in the planar Restricted Three Body Problem.


  We investigate the dynamics of many interacting bubbles in boiling water by
using a laser scattering experiment. Specifically, we analyze the temporal
variations of a laser intensity signal which passed through a sample of boiling
water. Our empirical results indicate that the return interval distribution of
the laser signal does not follow an exponential distribution; contrariwise, a
heavy-tailed distribution has been found. Additionally, we compare the
experimental results with those obtained from a minimalist phenomenological
model, finding a good agreement.


  Recent years have seen dramatic progress in the study of the core and nuclear
properties of galaxies. The structure of the cores has been shown to vary
methodically with global and nuclear properties, as cores respond to the
mechanisms by which galaxies form/evolve. The dynamical centers of galaxies
have been found capable of hosting two seemingly disparate objects:
supermassive black holes (SBHs) and compact stellar nuclei. In a drastic
departure from previous beliefs, it has been discovered that both structures
are common: galaxies lacking SBHs and/or stellar nuclei are the exception,
rather than the norm. This review explores the connection between cores, SBHs
and stellar nuclei in early-type galaxies, as revealed by the ACS Virgo Cluster
Survey. We find that, from parsec to kiloparsec scales, the surface brightness
profiles of early-type galaxies are well described by a Sersic model -- a
parametrization that is shown to be preferable to the so called `Nuker' model.
Relative to the inward extrapolation of the best fitting Sersic model, the
profiles within the inner few tens of parsecs transition from luminosity
`deficits', in the brightest (M_B < ~-20) galaxies, to luminosity `excesses' in
the faintest. The compact stellar nuclei responsible for such luminosity
excesses comprise approximatively 0.2% of the total galactic mass. Remarkably,
this is the same fraction believed to reside in the SBHs, which are
predominantly found in the brightest galaxies showing luminosity deficits.


  High-level synthesis (HLS) has received significant attention in recent
years, improving programmability for FPGAs. PolyMage is a domain-specific
language (DSL) for image processing pipelines that also has a HLS backend to
translate the input DSL into an equivalent circuit that can be synthesized on
FPGAs, while leveraging an HLS suite. The data at each stage of a pipeline is
stored using a fixed-point data type (alpha,beta) where alpha and beta denote
the number of integral and fractional bits. The power and area savings while
performing arithmetic operations on fixed-point data type is known to be
significant over using floating point. In this paper, we first propose an
interval-arithmetic based range analysis (alpha-analysis) algorithm to estimate
the number of bits required to store the integral part of the data at each
stage of an image processing pipeline. The analysis algorithm uses the
homogeneity of pixel signals at each stage to cluster them and perform a
combined range analysis. Secondly, we propose a software architecture for
easily deploying any kind of interval/affine arithmetic based range analyses in
the DSL compiler. Thirdly, we propose a new range analysis technique using
Satisfiability Modulo Theory (SMT) solvers, and show that the range estimates
obtained through it are very close to the lower bounds obtained through
profile-driven analysis.We evaluated our bitwidth analysis algorithms on four
image processing benchmarks listed in the order of increasing complexity:
Unsharp Mask, Down-Up Sampling, Harris Corner Detection and Horn-Schunck
Optical Flow. For example, on Optical Flow, the interval analysis based
approach showed an 1.4x and 1.14x improvement on area and power metrics over
floating-point representation respectively; whereas the SMT solver based
approach showed 2.49x and 1.58x improvement on area and power metrics when
compared to interval analysis.


  In this talk, I review the status of the calculation of the photon production
rate in a hot quark-gluon plasma. Particular emphasis is given to the
discussion of the various length scales of the problem.


  We consider a system of $N$ particles living on the noncommutative plane in
the presence of a confining potential and study its thermodynamics properties.
Indeed, after calculating the partition function, we determine the
corresponding internal energy and heat capacity where different corrections are
obtained. In analogy with the magnetic field case, we define an effective
magnetization and study its susceptibility in terms of the noncommutative
parameter $\theta$. By introducing the chemical potential, we investigate the
Bose-Einstein condensation for the present system. Different limiting cases
related to the temperature and $\theta$ will be analyzed as well as some
numerical illustration will be presented.


  Strained Fe-Co films have recently been demonstrated to exhibit a large
magnetocrystalline anisotropy (MCA) and thus to be of potential interest as
magnetic storage material. Here, we show by means of density-functional (DF)
calculations, that chemical order can remarkably enhance the MCA. We also
investigate the effect of relaxation perpendicular to the applied strain and
evaluate the strain energy as a function of Co concentration and substrate
lattice parameter. On this basis, favourable preparation routes for films with
a large perpendicular anisotropy are suggested.


  We present a detailed study on the infrared structure of $\mathcal{N}=4$ SYM
and its connection to QCD. Calculation of collinear splitting functions helps
to understand the structure and thus one can get infrared safe cross sections.
We also demonstrate the factorization property that soft plus virtual part of
the cross section satisfies and through factorization, we calculate soft
distribution function up to third order in perturbation theory. We show that
the soft distribution function is process independent that includes operators
as well as external legs. In addition to this we compare our findings against
the known results in QCD through principle of maximum transcendentality (PMT).
We extend our analysis further for the case of three-point form factors
involving stress tensor and find that it violates the PMT while comparing with
the corresponding quantity in the standard model, observed for the first time
at the level of form factor.


  Although traditional symbolic reasoning methods are highly interpretable,
their application in knowledge graphs link prediction has been limited due to
their computational inefficiency. A new RNNNTP method is proposed in this
paper, using a generalized EM-based approach to continuously improve the
computational efficiency of Neural Theorem Provers(NTPs). The RNNNTP is divided
into relation generator and predictor. The relation generator is trained
effectively and interpretably, so that the whole model can be carried out
according to the development of the training, and the computational efficiency
is also greatly improved. In all four data-sets, this method shows competitive
performance on the link prediction task relative to traditional methods as well
as one of the current strong competitive methods.


  Fractional hedonic games are coalition formation games where a player's
utility is determined by the average value they assign to the members of their
coalition. These games are a variation of graph hedonic games, which are a
class of coalition formation games that can be succinctly represented. Due to
their applicability in network clustering and their relationship to graph
hedonic games, fractional hedonic games have been extensively studied from
various perspectives. However, finding welfare-maximizing partitions in
fractional hedonic games is a challenging task due to the nonlinearity of
utilities. In fact, it has been proven to be NP-hard and can be solved in
polynomial time only for a limited number of graph classes, such as trees. This
paper presents (pseudo)polynomial-time algorithms to compute welfare-maximizing
partitions in fractional hedonic games on tree-like graphs. We consider two
types of social welfare measures: utilitarian and egalitarian. Tree-like graphs
refer to graphs with bounded treewidth and block graphs. A hardness result is
provided, demonstrating that the pseudopolynomial-time solvability is the best
possible under the assumption P$\neq$NP.


  In this study, we will discuss recent developments in risk management of the
global financial and insurance business with respect to sustainable
development. So far climate change aspects have been the dominant aspect in
managing sustainability risks and opportunities, accompanied by the development
of several legislative initiatives triggered by supervisory authorities.
However, a sole concentration on these aspects misses out other important
economic and social facets of sustainable development goals formulated by the
UN. Such aspects have very recently come into the focus of the European
Committee concerning the Solvency II project for the European insurance
industry. Clearly the new legislative expectations can be better handled by
larger insurance companies and holdings than by small- and medium-sized mutual
insurance companies which are numerous in central Europe, due to their historic
development starting in the late medieval ages and early modern times. We
therefore also concentrate on strategies within the risk management of such
small- and medium-sized enterprises that can be achieved without much effort,
in particular those that are not directly related to climate change.


  The degeneracy of an $n$-vertex graph $G$ is the smallest number $d$ such
that every subgraph of $G$ contains a vertex of degree at most $d$. We show
that there exists a nearly-optimal fixed-parameter tractable algorithm for
enumerating all maximal cliques, parametrized by degeneracy. To achieve this
result, we modify the classic Bron--Kerbosch algorithm and show that it runs in
time $O(dn3^{d/3})$. We also provide matching upper and lower bounds showing
that the largest possible number of maximal cliques in an $n$-vertex graph with
degeneracy $d$ (when $d$ is a multiple of 3 and $n\ge d+3$) is $(n-d)3^{d/3}$.
Therefore, our algorithm matches the $\Theta(d(n-d)3^{d/3})$ worst-case output
size of the problem whenever $n-d=\Omega(n)$.


  We derive the structure of the Landau-Zener-St\"uckelberg-Majorana (LZSM)
interference pattern for a qubit that experiences quantum dissipation and is
additionally subjected to time-periodic but otherwise general driving. A
spin-boson Hamiltonian serves as model which we treat with a Bloch-Redfield
master equation in Floquet basis. It predicts a peak structure that depends
sensitively on the operator through which the qubit couples to the bath. The
Fourier transforms of the LZSM patterns exhibit arc structures which reflect
the shape of the driving. These features are captured by an effective
time-independent Bloch equation which provides an analytical solution.
Moreover, we determine the decay of these arcs as a function of dissipation
strength and temperature.


  Controlling the bandgap of carbon nanostructures is key to the development
and mainstream application of carbon-based nanoelectronic devices. We report
density functional theory calculations of the effect of silicon impurities on
the electronic properties of carbon nanotubes (CNTs). We have found that Si
adatoms open up a bandgap in intrinsically metallic CNTs even when the linear
density of Si atoms is low enough that they do not create a bonded adatom
chain. The bandgap opened in metallic CNTs can range between 0.10 eV and 0.47
eV, depending on adsorption site, linear density of Si adatoms, and CNT
chirality.


  Interactive recommendation is able to learn from the interactive processes
between users and systems to confront the dynamic interests of users. Recent
advances have convinced that the ability of reinforcement learning to handle
the dynamic process can be effectively applied in the interactive
recommendation. However, the sparsity of interactive data may hamper the
performance of the system. We propose to train a Model-agnostic Counterfactual
Synthesis Policy to generate counterfactual data and address the data sparsity
problem by modelling from observation and counterfactual distribution. The
proposed policy can identify and replace the trivial components for any state
in the training process with other agents, which can be deployed in any
RL-based algorithm. The experimental results demonstrate the effectiveness and
generality of our proposed policy.


  We argue that cold quark matter is a color superconductor. The Cooper pairs
of QCD are spin-isospin zero, color anti-triplet diquarks. In this contribution
we review some of the available information on the quark-quark interaction in
QCD. We show that instantons provide a strongly attractive interaction in the
scalar diquark channel. In the high density phase, this interaction leads to
diquark Bose condensation with a gap on the order of 50 MeV.


  Let $G$ be a finite permutation group on $\Omega$. An ordered sequence
  $(\omega_1\ldots,\omega_\ell)$ of elements of $\Omega$ is an irredundant base
for $G$ if the pointwise stabilizer is trivial and no point is fixed by the
stabilizer of its predecessors. The minimal cardinality of a base is said to be
the base size of $G$. If all irredundant bases of $G$ have the same
cardinality, $G$ is said to be an IBIS group.
  In this paper, we classify the finite almost simple primitive IBIS groups
whose base size is at least $6$.


  Networks are widely used to model objects with interactions and have enabled
various downstream applications. However, in the real world, network mining is
often done on particular query sets of objects, which does not require the
construction and computation of networks including all objects in the datasets.
In this work, for the first time, we propose to address the problem of
query-specific network construction, to break the efficiency bottlenecks of
existing network mining algorithms and facilitate various downstream tasks. To
deal with real-world massive networks with complex attributes, we propose to
leverage the well-developed data cube technology to organize network objects
w.r.t. their essential attributes. An efficient reinforcement learning
algorithm is then developed to automatically explore the data cube structures
and construct the optimal query-specific networks. With extensive experiments
of two classic network mining tasks on different real-world large datasets, we
show that our proposed cube2net pipeline is general, and much more effective
and efficient in query-specific network construction, compared with other
methods without the leverage of data cube or reinforcement learning.


  It is well known that there exist non-isomorphic compact groups with
isomorphic representation rings (fusion rules). Nevertheless, considerable
structural information about the group can be reconstructed from its
representation ring. We review these types of partial reconstruction theorems,
including some recent results. In the Appendix a derivation of the
Clebsch-Gordan series of SU(2) based only on information about the dimensions
of the irreps is presented.


  In recent years, thanks to the rapid development of deep learning (DL),
DL-based multi-task learning (MTL) has made significant progress, and it has
been successfully applied to recommendation systems (RS). However, in a
recommender system, the correlations among the involved tasks are complex.
Therefore, the existing MTL models designed for RS suffer from negative
transfer to different degrees, which will injure optimization in MTL. We find
that the root cause of negative transfer is feature redundancy that features
learned for different tasks interfere with each other. To alleviate the issue
of negative transfer, we propose a novel multi-task learning method termed
Feature Decomposition Network (FDN). The key idea of the proposed FDN is
reducing the phenomenon of feature redundancy by explicitly decomposing
features into task-specific features and task-shared features with carefully
designed constraints. We demonstrate the effectiveness of the proposed method
on two datasets, a synthetic dataset and a public datasets (i.e., Ali-CCP).
Experimental results show that our proposed FDN can outperform the
state-of-the-art (SOTA) methods by a noticeable margin.


  We present a study of environmental effects and preprocessing in a large
galaxy group using a high-resolution, zoom-in simulation run with the GASOLINE2
hydrodynamics code. We categorize galaxies that were always in distinct haloes
as unaccreted, galaxies that were distinct before accretion onto the main group
as single, and galaxies that were in external sub-groups before accretion onto
the main group as grouped.
  The unaccreted galaxy population experiences steady growth in dark matter,
gas and stellar mass. Both single- and group-accreted galaxies begin to lose
dark matter and gas after first accretion onto any host but continue to grow in
stellar mass. Individual trajectories show that galaxies cease mass growth
within roughly three virial radii of the main group. Single galaxies continue
to form stars until the group virial radius is crossed, when they begin to lose
both dark matter and gas. Grouped galaxies peak in mass when joining their
external sub-group, indicating that they experience preprocessing. Most
accreted galaxies retain their accumulated stellar mass. The total mass loss is
dominated by tidal stripping, with evidence for additional gas stripping via
ram pressure. Most accreted galaxies are quenched $\sim$(0.5-2.5) Gyr after
accretion onto any group.
  These differing histories place unaccreted, single and grouped galaxies in
distinct regions of the stellar mass-to-halo mass (SMHM) relation. This
suggests that preprocessed galaxies are a key source of scatter in the SMHM
relation for mixed galaxy populations.


  We study the conformations of a self-avoiding polymer confined to a channel
by computing the cross-sectional distributions of the positions of its
monomers. By means of Monte-Carlo simulations for a self-avoiding,
freely-jointed chain we determine how the cross-sectional distribution for a
given monomer depends on its location in the polymer, and how strongly this
distribution is affected by self avoidance. To this end we analyze how the
frequency of intra-chain collisions between monomers depends on their spatial
position in the channel and on their location within the polymer. We show that
most collisions occur between closely neighboring monomers. As a consequence
the collision probability depends only weakly on the spatial position of the
monomers. Our results explain why the effect of self-avoidance on the monomer
distributions is weaker than predicted by mean-field theory. We discuss the
relevance of our results for studies of DNA conformations in nanofluidic
channels.


  Using the international ground-based network of two-frequency receivers of
the GPS navigation system provides a means of carrying out a global, continuous
and fully-computerized monitoring of phase fluctuations of signals from
satellite-borne radio engineering systems caused by the Earth's inhomogeneous
and nonstationary ionosphere. We found that during major geomagnetic storms,
the errors of determination of the range, frequency Doppler shift and angles of
arrival of transionospheric radio signals exceeds the one for magnetically
quiet days by one order of magnitude as a minimum. This can be the cause of
performance degradation of current satellite radio engineering navigation,
communication and radar systems as well as of superlong-baseline radio
interferometry systems.


  By means of elementary conditions on coefficients, we isolate a large class
of Fermat-like Diophantine equations that are not partition regular, the
simplest examples being $x^n+y^m=z^k$ with $k\notin\{n,m\}$.


  We consider the problem of controlling the spread of harmful items in
networks, such as the contagion proliferation of diseases or the diffusion of
fake news. We assume the linear threshold model of diffusion where each node
has a threshold that measures the node resistance to the contagion. We study
the parameterized complexity of the problem: Given a network, a set of
initially contaminated nodes, and two integers $k$ and $\ell$, is it possible
to limit the diffusion to at most $k$ other nodes of the network by immunizing
at most $\ell$ nodes? We consider several parameters associated to the input,
including: the bounds $k$ and $\ell$, the maximum node degree $\Delta$, the
treewidth, and the neighborhood diversity of the network. We first give $W[1]$
or $W[2]$-hardness results for each of the considered parameters. Then we give
fixed-parameter algorithms for some parameter combinations.