  Experimental results have shown that the quaternary compound Cu2ZnSnSe4 is an
excellent thermoelectric material. This inspires us to seek the other
quaternary compounds with similar chemical formula to Cu2ZnSnSe4 as
thermoelectric materials. In this paper, we use the first-principle method to
systematically explore the electronic and phonon structures, mechanical,
thermal and thermoelectric properties of p- and n-type Ag2XYSe4 (X=Ba, Sr;
Y=Sn, Ge). It is found that the ZT maximum for n-type Ag2SrGeSe4 can reach up
to 1.22 at 900 K, and those for p-type Ag2SrSnSe4, Ag2SrGeSe4 and Ag2BaSnSe4
can reach up to 1.20, 1.13 and 1.12, respectively. Our work not only shows that
Ag2XYSe4 (X=Ba, Sr; Y=Sn, Ge) are a kind of potential thermoelectric materials,
but also can inspire more theoretical and experimental researches on
thermoelectric properties of quaternary compounds.


  Although TLS is used on a daily basis by many critical applications, the
public-key infrastructure that it relies on still lacks an adequate revocation
mechanism. An ideal revocation mechanism should be inexpensive, efficient,
secure, and privacy-preserving. Moreover, rising trends in pervasive encryption
pose new scalability challenges that a modern revocation system should address.
In this paper, we investigate how network nodes can deliver
certificate-validity information to clients. We present RITM, a framework in
which middleboxes (as opposed to clients, servers, or certification
authorities) store revocation-related data. RITM provides a secure
revocation-checking mechanism that preserves user privacy. We also propose to
take advantage of content-delivery networks (CDNs) and argue that they would
constitute a fast and cost-effective way to disseminate revocations.
Additionally, RITM keeps certification authorities accountable for the
revocations that they have issued, and it minimizes overhead at clients and
servers, as they have to neither store nor download any messages. We also
describe feasible deployment models and present an evaluation of RITM to
demonstrate its feasibility and benefits in a real-world deployment.


  We construct several Milky Way-like galaxy models containing a gas halo (as
well as gaseous and stellar disks, a dark matter halo, and a stellar bulge)
following either an isothermal or an NFW density profile with varying mass and
initial spin. In addition, galactic winds associated with star formation are
tested in some of the simulations. We evolve these isolated galaxy models using
the GADGET-3 $N$-body/hydrodynamic simulation code, paying particular attention
to the effects of the gas halo on the evolution. We find that the evolution of
the models is strongly affected by the adopted gas halo component. The model
without a gas halo shows an increasing star formation rate (SFR) at the
beginning of the simulation for some hundreds of millions of years and then a
continuously decreasing rate to the end of the run at 3 Gyr. On the other hand,
the SFRs in the models with a gas halo emerge to be either relatively flat
throughout the simulations or increasing over a gigayear and then decreasing to
the end. The models with the more centrally concentrated NFW gas halo show
overall higher SFRs than those with the isothermal gas halo of the equal mass.
The gas accretion from the halo onto the disk also occurs more in the models
with the NFW gas halo, however, this is shown to take place mostly in the inner
part of the disk and not to contribute significantly to the star formation
unless the gas halo has very high density at the central part. The rotation of
a gas halo is found to make SFR lower in the model. The SFRs in the runs
including galactic winds are found to be lower than the same runs but without
winds. We conclude that the effects of a hot gaseous halo on the evolution of
galaxies are generally too significant to be simply ignored, and expect that
more hydrodynamical processes in galaxies could be understood through numerical
simulations employing both gas disk and gas halo components.


  The equation with the time fractional substantial derivative and space
fractional derivative describes the distribution of the functionals of the
L\'evy flights; and the equation is derived as the macroscopic limit of the
continuous time random walk in unbounded domain and the L\'evy flights have
divergent second order moments. However, in more practical problems, the
physical domain is bounded and the involved observables have finite moments.
Then the modified equation can be derived by tempering the probability of large
jump length of the L\'evy flights and the corresponding tempered space
fractional derivative is introduced. This paper focuses on providing the high
order algorithms for the modified equation, i.e., the equation with the time
fractional substantial derivative and space tempered fractional derivative.
More concretely, the contributions of this paper are as follows: 1. the
detailed numerical stability analysis and error estimates of the schemes with
first order accuracy in time and second order in space are given in
{\textsl{complex}} space, which is necessary since the inverse Fourier
transform needs to be made for getting the distribution of the functionals
after solving the equation; 2. we further propose the schemes with high order
accuracy in both time and space, and the techniques of treating the issue of
keeping the high order accuracy of the schemes for {\textsl{nonhomogeneous}}
boundary/initial conditions are introduced; 3. the multigrid methods are
effectively used to solve the obtained algebraic equations which still have the
Toeplitz structure; 4. we perform extensive numerical experiments, including
verifying the high convergence orders, simulating the physical system which
needs to numerically make the inverse Fourier transform to the numerical
solutions of the equation.


  We solve the existence problem for $F$-designs for arbitrary $r$-uniform
hypergraphs~$F$. This implies that given any $r$-uniform hypergraph~$F$, the
trivially necessary divisibility conditions are sufficient to guarantee a
decomposition of any sufficiently large complete $r$-uniform hypergraph into
edge-disjoint copies of~$F$, which answers a question asked e.g.~by Keevash.
The graph case $r=2$ was proved by Wilson in 1975 and forms one of the
cornerstones of design theory. The case when~$F$ is complete corresponds to the
existence of block designs, a problem going back to the 19th century, which was
recently settled by Keevash. In particular, our argument provides a new proof
of the existence of block designs, based on iterative absorption (which employs
purely probabilistic and combinatorial methods).
  Our main result concerns decompositions of hypergraphs whose clique
distribution fulfills certain regularity constraints. Our argument allows us to
employ a `regularity boosting' process which frequently enables us to satisfy
these constraints even if the clique distribution of the original hypergraph
does not satisfy them. This enables us to go significantly beyond the setting
of quasirandom hypergraphs considered by Keevash. In particular, we obtain a
resilience version and a decomposition result for hypergraphs of large minimum
degree.


  Naturalistic animal behavior exhibits a strikingly complex organization in
the temporal domain, whose variability stems from at least three sources:
hierarchical, contextual, and stochastic. What are the neural mechanisms and
computational principles generating such complex temporal features? In this
review, we provide a critical assessment of the existing behavioral and
neurophysiological evidence for these sources of temporal variability in
naturalistic behavior. We crystallize recent studies which converge on an
emergent mechanistic theory of temporal variability based on attractor neural
networks and metastable dynamics, arising from the coordinated interactions
between mesoscopic neural circuits. We highlight the crucial role played by
structural heterogeneities and by noise arising in mesoscopic circuits. We
assess the shortcomings and missing links in the current theoretical and
experimental literature and propose new directions of investigations to fill
these gaps.


  This paper concerns a diffusive logistic equation with a free boundary and
sign-changing intrinsic growth rate in heterogeneous time-periodic environment,
in which the variable intrinsic growth rate may be "very negative" in a
"suitable large region". Such a model can be used to describe the spreading of
a new or invasive species, with the free boundary representing the expanding
front. In the case of higher space dimensions with radial symmetry and the
intrinsic growth rate has a positive lower bound, this problem has been studied
by Du, Guo and Peng . They established a spreading-vanishing dichotomy, the
sharp criteria for spreading and vanishing and estimate of the asymptotic
spreading speed. In the present paper, we show that the above results are
retained for our problem. This paper has been submitted to Journal of
Functional Analysis in August 5, 2014 (JFA-14-548).


  Calculation of conductivity in the Hubbard model is a challenging task.
Recent years have seen much progress in this respect and numerically exact
solutions are now possible in certain regimes. In this paper we discuss the
calculation of conductivity for the square lattice Hubbard model in the
presence of a perpendicular magnetic field, focusing on orbital effects. We
present the relevant formalism in all detail and in full generality, and then
discuss the simplifications that arise at the level of the dynamical mean field
theory (DMFT). We prove that the Kubo bubble preserves gauge and translational
invariance, and that in the DMFT the vertex corrections cancel regardless of
the magnetic field. We present the DMFT results for the spectral function and
both the longitudinal and Hall conductivity in several regimes of parameters.
We analyze thoroughly the quantum oscillations of the longitudinal conductivity
and identify a high-frequency oscillation component, arising as a combined
effect of scattering and temperature, in line with recent experimental
observations in moir\'e systems.


  Quantum effects on a Landau-type system associated with a moving atom with a
magnetic quadrupole moment subject to confining potentials are analysed. It is
shown that the spectrum of energy of the Landau-type system can be modified,
where the degeneracy of the energy levels can be broken. In three particular
cases, it is shown that the analogue of the cyclotron frequency is modified,
and the possible values of this angular frequency of the system are determined
by the quantum numbers associated with the radial modes and the angular
momentum and by the parameters associated with confining potentials in order
that bound states solutions can be achieved.


  Let F be a locally compact nonarchimedean field with residue characteristic p
and G the group of F-rational points of a connected split reductive group over
F. For k an arbitrary field, we study the homological properties of the
Iwahori-Hecke k-algebra H' and of the pro-p Iwahori-Hecke k-algebra H of G. We
prove that both of these algebras are Gorenstein rings with self-injective
dimension bounded above by the rank of G. If G is semisimple, we also show that
this upper bound is sharp, that both H and H' are Auslander-Gorenstein and that
there is a duality functor on the finitely generated modules of H (respectively
H'). We obtain the analogous Gorenstein and Auslander-Gorenstein properties for
the graded rings associated to H and H'.
  When k has characteristic p, we prove that in most cases H and H' have
infinite global dimension. In particular, we deduce that the category of smooth
k-representations of G=PGL(2,Q_p) generated by their invariant vectors under
the pro-p-Iwahori subgroup has infinite global dimension (at least if k is
algebraically closed).


  The cross section of $e^+e^- \to b \bar{b} u \bar{d} \mu^- \bar{\nu}_\mu$
process with a complete set of tree diagrams, 232 diagrams in the unitary
gauge, was calculated at the energy range of $\sqrt{s}$ = 340 - 500 GeV by
using GRACE system. A main contribution to the cross section comes from
$t\bar{t}$ production, where $t$ and $\bar{t}$ decay into $bu\bar{d}$ and
$\bar{b} \mu^- \bar{\nu}_{\mu}$, respectively. It was found that the
interference between the diagrams with $t\bar{t}$ production and those with
single-$t$ through $ WW $ pair production amounts to 10% at the $t \bar{t}$
threshold energy region. In the energy region above twice of the top quark
mass, more than 95% of the cross section comes from the $t\bar{t}$ diagrams.


  We investigate thermodynamic and electronic properties of group IV (C, Si,
Ge, Sn) and group VI (O, S, Se, Te) impurities as well as P and H in aluminum
antimonide (AlSb) using first-principles calculations. To this end, we compute
the formation energies of a broad range of possible defect configurations
including defect complexes with the most important intrinsic defects. We also
obtain relative scattering cross strengths for these defects to determine their
impact on charge carrier mobility. Furthermore, we employ a self-consistent
charge equilibration scheme to determine the net charge carrier concentrations
for different temperatures and impurity concentrations. Thereby, we are able to
study the effect of impurities incorporated during growth and identify optimal
processing conditions for achieving compensated material. The key findings are
summarized as follows. Among the group IV elements, C, Si, and Ge substitute
for Sb and act as shallow acceptors, while Sn can substitute for either Sb or
Al and displays amphoteric character. Among the group VI elements, S, Se, and
Te substitute for Sb and act as deep donors. In contrast, O is most likely to
be incorporated as an interstitial and predominantly acts as an acceptor. As a
group V element, P substitutes for Sb and is electrically inactive. C and O are
the most detrimental impurities to carrier transport, while Sn, Se, and Te have
a modest to low impact. Therefore, Te can be used to compensate C and O
impurities, which are unintentionally incorporated during the growth process,
with minimal effect on the carrier mobilities.


  We investigate S^3/Z_n partition function of 3d N = 2 supersymmetric field
theories. In a gauge theory the partition function is the sum of the
contributions of sectors specified by holonomies, and we should carefully
choose the relative signs among the contributions. We argue that the
factorization to holomorphic blocks is a useful criterion to determine the
signs and propose a formula for them. We show that the orbifold partition
function of a general non-gauge theory is correctly factorized provided that we
take appropriate relative signs. We also present a few examples of gauge
theories. We point out that the sign factor for the orbifold partition function
is closely related to a similar sign factor in the lens space index and the 3d
index.


  Measurements of differential and double-differential cross sections of top
quark pair ($\text{t}\overline{\text{t}}$) production are presented in the
lepton+jets channels with a single electron or muon and jets in the final
state. The analysis combines for the first time signatures of top quarks with
low transverse momentum $p_\text{T}$, where the top quark decay products can be
identified as separated jets and isolated leptons, and with high $p_\text{T}$,
where the decay products are collimated and overlap. The measurements are based
on proton-proton collision data at $\sqrt{s} = $ 13 TeV collected by the CMS
experiment at the LHC, corresponding to an integrated luminosity of 137
fb$^{-1}$. The cross sections are presented at the parton and particle levels,
where the latter minimizes extrapolations based on theoretical assumptions.
Most of the measured differential cross sections are well described by standard
model predictions with the exception of some double-differential distributions.
The inclusive $\text{t}\overline{\text{t}}$ production cross section is
measured to be $\sigma_{\text{t}\overline{\text{t}}} = $ 791 $\pm$ 25 pb, which
constitutes the most precise measurement in the lepton+jets channel to date.


  The random magnetic field produced by nuclear spins has long been viewed as
the dominating source of decoherence in the quantum-dot based spins. Here we
obtain in both exact and analytical manner the dynamics of spin qubits coupled
to nuclear spin environments via the hyperfine interaction, going beyond the
weak system-bath interaction and Markovian approximation. We predict that the
detailed-balance breaking produced by chemical potential gradient in nuclear
baths leads to the rapid oscillations of populations, quantum coherence and
entanglement, which are absent in the conventional case (i.e., Overhauser
noise). This is attributed to the nonequilibrium feature of the system as shown
in the relation between the oscillation period and the chemical potential
imbalance. Our results reveal the essentiality of nonequilibriumness with
detailed-balance breaking for enhancing the dynamical coherence and
entanglement of spin qubits. Moreover, our exact solution explicitly
demonstrates that the non-Markovian bath comprised by nuclear spins can
preserve the collective quantum state, due to the recovery of coherence.
Finally, we propose an experiment using ultracold trapped ions to observe these
nonequilibrium and memory effects.


  In this paper, we study a boundary control problem associated to the
stationary Rayleigh-B\'enard-Marangoni (RBM) system in presence of controls for
the velocity and the temperature on parts of the boundary. We analyze the
existence, uniqueness and regularity of weak solutions for the stationary RBM
system in polyhedral domains of $\mathbb{R}^3,$ and then, we prove the
existence of the optimal solution. By using the Theorem of Lagrange
multipliers, we derive an optimality system. We also give a second-order
sufficient optimality condition and we establish a result of uniqueness of the
optimal solution.


  We use the coordinate Bethe ansatz approach to derive the nested Bethe
equations corresponding to the recently found S-matrix for strings in AdS5 x
S5, compatible with centrally extended su(2|2) symmetry.


  Previous work has shown that robot navigation systems that employ an
architecture based upon the idiotypic network theory of the immune system have
an advantage over control techniques that rely on reinforcement learning only.
This is thought to be a result of intelligent behaviour selection on the part
of the idiotypic robot. In this paper an attempt is made to imitate idiotypic
dynamics by creating controllers that use reinforcement with a number of
different probabilistic schemes to select robot behaviour. The aims are to show
that the idiotypic system is not merely performing some kind of periodic random
behaviour selection, and to try to gain further insight into the processes that
govern the idiotypic mechanism. Trials are carried out using simulated Pioneer
robots that undertake navigation exercises. Results show that a scheme that
boosts the probability of selecting highly-ranked alternative behaviours to 50%
during stall conditions comes closest to achieving the properties of the
idiotypic system, but remains unable to match it in terms of all round
performance.


  Source code summarization aims to generate natural language summaries from
structured code snippets for better understanding code functionalities.
However, automatic code summarization is challenging due to the complexity of
the source code and the language gap between the source code and natural
language summaries. Most previous approaches either rely on retrieval-based
(which can take advantage of similar examples seen from the retrieval database,
but have low generalization performance) or generation-based methods (which
have better generalization performance, but cannot take advantage of similar
examples). This paper proposes a novel retrieval-augmented mechanism to combine
the benefits of both worlds. Furthermore, to mitigate the limitation of Graph
Neural Networks (GNNs) on capturing global graph structure information of
source code, we propose a novel attention-based dynamic graph to complement the
static graph representation of the source code, and design a hybrid message
passing GNN for capturing both the local and global structural information. To
evaluate the proposed approach, we release a new challenging benchmark, crawled
from diversified large-scale open-source C projects (total 95k+ unique
functions in the dataset). Our method achieves the state-of-the-art
performance, improving existing methods by 1.42, 2.44 and 1.29 in terms of
BLEU-4, ROUGE-L and METEOR.


  The Page-Wootters mechanism questioned the fundamental nature of time in
quantum physics. The mechanism explored the notion that a given physical
quantity is always defined and measured relative to a reference frame, in
general, not explained in the theoretical description of quantum physical
experiments. Recently, the resource theory of asymmetry deals explicitly with
what are the physical conditions for a quantum system to serve as a good
reference frame. Nonetheless, to quantify a quantum reference frame in relation
to another one it is a important task to establish an internal description of
quantum theory, i.e., without the need of a classical reference frame. In this
work we address this issue by the concept of mutual asymmetry and use this
machinery in the Page-Wootters mechanism by identifying the concept of mutual
asymmetry as mutual or internal coherence. To do so, the notion of quantum
coherence in relation of a quantum reference frame is revisited and a
quantifier is proposed in this scenario. Also, this open space to investigate
the link of internal coherence and correlations, as proposed by Page and
Wootters, under a resource theory approach.


  One additional position of the famous Mataveri calendar of Easter Island has
been interpreted. New data on the watchings of Venus and Aldebaran have been
rendered. Some reports about the sun, the moon as well as Sirius are of our
interest, too.


  We present results from CCD observations of comet 2P/Encke acquired at
Steward Observatory's 2.3m Bok Telescope on Kitt Peak obtained in Oct. 2002,
when the comet was near aphelion. Rotational lightcurves in B, V and R-filters
were acquired over two nights of observations, and analysed to study the
physical and color properties of the nucleus. The average apparent R-filter
magnitude across both nights corresponds to a mean effective radius of 3.95 +/-
0.06 km. The rotational lightcurve results in a nucleus axial ratio a/b >= 1.44
+/- 0.06 and semi-axes lengths of [3.60 +/- 0.09] x [5.20 +/- 0.13] km. Our
data includes the first detailed time series multi-color measurements of a
cometary nucleus, and significant color variations were seen. The average color
indices across both nights are: (V-R) = 0.39 +/- 0.06 and (B-V) = 0.73 +/- 0.06
(R_mean = 19.76 +/- 0.03). We linked our data with the September 2002 data from
Fernandez et al. (2005) - taken just 2-3 weeks before the current data set -
and we show that a rotation period of 11.083 +/- 0.003hours works extrememly
well for the combined data set.


  The effect of anti-mirror reflection from a bounded plane optical waveguide
used earlier for observation of slow light in a Bragg waveguide is considered.
A theory of the effect is proposed that allowed us to interpret the observed
spectral (Gaussian lineshape) and angular (Lorentzian angular profile)
properties of the light scattered by the bounded waveguide in the anti-specular
direction.


  In this paper, we generalize 2-trees by replacing triangles by
quadrilaterals, pentagons or $k$-sided polygons ($k$-gons), where $k\geq 3$ is
fixed. This generalization, to $k$-gonal 2-trees, is natural and is closely
related, in the planar case, to some specializations of the cell-growth
problem. Our goal is the labelled and unlabelled enumeration of $k$-gonal
2-trees according to the number $n$ of $k$-gons. We give explicit formulas in
the labelled case, and, in the unlabelled case, recursive and asymptotic
formulas.


  This paper takes a new look at ideals generated by 2x2 minors of 2x3 matrices
whose entries are powers of three elements not necessarily forming a regular
sequence. A special case of this are the ideals determining monomial curves in
three dimensional space, which were already studied by Herzog. In the broader
context studied here, these ideals are identified as Northcott ideals in the
sense of Vasconcelos, and so their liaison properties are displayed. It is
shown that they are set-theoretically complete intersections, revisiting the
work of Bresinsky and of Valla. Even when the three elements are taken to be
variables in a polynomial ring in three variables over a field, this point of
view gives a larger class of ideals than just the defining ideals of monomial
curves. We then characterize when the ideals in this larger class are prime, we
show that they are usually radical and, using the theory of multiplicities, we
give upper bounds on the number of their minimal prime ideals, one of these
primes being a uniquely determined prime ideal of definition of a monomial
curve. Finally, we provide examples of characteristic-dependent minimal prime
and primary structures for these ideals.


  Up to date, inertial migration of particles in microflows has demonstrated a
great potential for a wide range of applications. In particular, this
phenomenon is used to achieve particle separation or sorting in a suspension.
Recent works reported that the focusing mode of particles can be modified in a
polydisperse suspension. Nevertheless, the impact of the particle sizes in a
mixture on their inertial migration has been rarely studied up to now. Thus, we
have investigated in this work the influence of bidispersity on the lateral
migration of the particles towards equilibrium positions and on their
longitudinal ordering into trains. Different changes in the particles behavior
were observed when the ratio between the particle sizes (dp1/dp2) varied from
1.64 to 4.58.


  We show that the accumulation of spin-polarized electrons at a forward-biased
Schottky tunnel barrier between Fe and n-GaAs can be detected electrically. The
spin accumulation leads to an additional voltage drop across the barrier that
is suppressed by a small transverse magnetic field, which depolarizes the spins
in the semiconductor. The dependence of the electrical accumulation signal on
magnetic field, bias current, and temperature is in good agreement with the
predictions of a drift-diffusion model for spin-polarized transport.


  An overview is given of the ongoing measurement at HERA of the parton
structure of the photon, as a function of its virtuality. Preliminary ZEUS
results show disagreement with an NLO QCD calculation.


  Using Monte Carlo methods, we simulated the effects of bias in generation and
elimination of paralogs on the size distribution of paralog groups. It was
found that the function describing the decay of the number of paralog groups
with their size depends on the ratio between the probability of duplications of
genes and their deletions, which corresponds to different selection pressures
on the genome size. Slightly different slopes of curves describing the decay of
the number of paralog groups with their size were also observed when the
threshold of homology between paralogous sequences was changed.


  This work presents the design of nonlinear stabilization techniques for the
finite element discretization of Euler equations in both steady and transient
form. Implicit time integration is used in the case of the transient form. A
differentiable local bounds preserving method has been developed, which
combines a Rusanov artificial diffusion operator and a differentiable shock
detector. Nonlinear stabilization schemes are usually stiff and highly
nonlinear. This issue is mitigated by the differentiability properties of the
proposed method. Moreover, in order to further improve the nonlinear
convergence, we also propose a continuation method for a subset of the
stabilization parameters. The resulting method has been successfully applied to
steady and transient problems with complex shock patterns. Numerical
experiments show that it is able to provide sharp and well resolved shocks. The
importance of the differentiability is assessed by comparing the new scheme
with its non-differentiable counterpart. Numerical experiments suggest that,
for up to moderate nonlinear tolerances, the method exhibits improved
robustness and nonlinear convergence behavior for steady problems. In the case
of transient problem, we also observe a reduction in the computational cost.


  In a recent article the authors obtained a formula which relates explicitly
the tail of risk neutral returns with the wing behavior of the Black Scholes
implied volatility smile. In situations where precise tail asymptotics are
unknown but a moment generating function is available we first establish, under
easy-to-check conditions, tail asymptoics on logarithmic scale as soft
applications of standard Tauberian theorems. Such asymptotics are enough to
make the tail-wing formula work and we so obtain a version of Lee's moment
formula with the novel guarantee that there is indeed a limiting slope when
plotting implied variance against log-strike. We apply these results to
time-changed Levy models and the Heston model. In particular, the
term-structure of the wings can be analytically understood.


  This paper studies the inflationary dynamics of a Non-Local Theory of
gravity. This theory, based around derivatives of the Ricci Scalar in the
Einstein-Hilbert action, was previously found to be Ghost free, and to give
rise to a bouncing cosmology. Perturbation spectra are calculated and found to
be similar to those for chaotic inflation.


  The Hypercube operator determines a variant of the approximate, truncated
perfect fermion action. In this pilot study we are going to report on first
experiences in dynamical QCD simulations with the Hypercube fermions. We apply
this formulation in an investigation of the finite temperature transition for
two flavours. On lattices of size $8^3\times 4$ we explore the phase diagram.
Physical scales are estimated from pseudoscalar and vector meson masses
obtained on $8^3\times 16$ lattices. We observe the presence of a metastability
region but do not find evidence for an Aoki phase. The Hypercube operator
allows us to simulate at ratios of pseudoscalar to vector meson masses at least
as small as 0.8 at the thermal crossover at $N_t=4$, which renders this
formulation cheaper than the Wilson like fermions.


  Relaxation processes following inner-valence ionization of a system can be
modified dramatically by embedding this system in a suitable environment.
Surprisingly, such an environment can be even composed of helium atoms, the
most inert species available. As demonstrated by the examples of Ne and Ca
atoms embedded in He droplets, a fast relaxation process [Interatomic Coulombic
Decay (ICD)] takes place merely due to the presence of the He surroundings. We
have computed ICD widths for both 4He_N and 3He_N droplets doped with Ne and Ca
and discuss the findings in some detail. In the case of Ne, ICD is by far the
dominating relaxation pathway. In Ca, atomic Auger decay is also possible but
ICD becomes a competitive relaxation pathway in the droplets.


  We use a "twisted group algebra" method to constructively adjoin formal
radicals $\sqrt[n]{\alpha}$, for $\alpha$ a unit in a commutative ring spectrum
or an invertible object in a symmetric monoidal $\infty$-category. We show that
this construction is classified by maps from Eilenberg-Mac Lane objects to the
unit spectrum, the Picard spectrum, and the Brauer spectrum.


  Neutrino cross sections are a critical ingredient in experiments that depend
on neutrino scattering to reconstruct event kinematics and infer neutrino
characteristics, like NOvA and T2K. An opportunity exists to reduce the 5-10%
broad uncertainty on neutrino cross sections by producing more measurements of
neutrino scattering from light nuclear targets at the relevant energies. Bubble
chambers with light nuclear targets would be ideal for these measurements but
the most recent device designed for use with an accelerator neutrino source is
at least fifty years old. A new bubble chamber with light nuclear targets could
be designed by observing how the technology has progressed for use in dark
matter experiments and producing smaller modular devices that use more
efficient cooling systems. A smaller modular device could also be designed for
deployment to all functioning neutrino beams, but an investigation of the
proper operating characteristics is necessary to adapt newer detectors to the
structure of contemporary neutrino beams.


  The Einstein equations for one of the hypersurface-homogeneous rotating dust
models are investigated. It is a Bianchi type V model in which one of the
Killing fields is spanned on velocity and rotation (case 1.2.2.2 in the
classification scheme of the earlier papers). A first integral of the field
equations is found, and with a special value of this integral coordinate
transformations are used to eliminate two components of the metric. The k = -1
Friedmann model is shown to be contained among the solutions in the limit of
zero rotation. The field equations for the simplified metric are reduced to 3
second-order ordinary differential equations that determine 3 metric components
plus a first integral that algebraically determines the fourth component. First
derivatives of the metric components are subject to a constraint (a
second-degree polynomial with coefficients depending on the functions). It is
shown that the set does not follow from a Lagrangian of the Hilbert type. The
group of Lie point-symmetries of the set is found, it is two-dimensional
noncommutative. Finally, a method of searching for first integrals (for sets of
differential equations) that are polynomials of degree 1 or 2 in the first
derivatives is applied. No such first integrals exist. The method is used to
find a constraint (of degree 1 in first derivatives) that could be imposed on
the metric, but it leads to a vacuum solution, and so is of no interest for
cosmology.


  In Bayesian inference, the maximum a posteriori (MAP) problem combines the
most probable explanation (MPE) and marginalization (MAR) problems. The
counterpart in propositional logic is the exist-random stochastic
satisfiability (ER-SSAT) problem, which combines the satisfiability (SAT) and
weighted model counting (WMC) problems. Both MAP and ER-SSAT have the form
$\operatorname{argmax}_X \sum_Y f(X, Y)$, where $f$ is a real-valued function
over disjoint sets $X$ and $Y$ of variables. These two optimization problems
request a value assignment for the $X$ variables that maximizes the weighted
sum of $f(X, Y)$ over all value assignments for the $Y$ variables. ER-SSAT has
been shown to be a promising approach to formally verify fairness in supervised
learning. Recently, dynamic programming on graded project-join trees has been
proposed to solve weighted projected model counting (WPMC), a related problem
that has the form $\sum_X \max_Y f(X, Y)$. We extend this WPMC framework to
exactly solve ER-SSAT and implement a dynamic-programming solver named DPER.
Our empirical evaluation indicates that DPER contributes to the portfolio of
state-of-the-art ER-SSAT solvers (DC-SSAT and erSSAT) through competitive
performance on low-width problem instances.


  A superintegrable system is, roughly speaking, a system that allows more
integrals of motion than degrees of freedom. This review is devoted to finite
dimensional classical and quantum superintegrable systems with scalar
potentials and integrals of motion that are polynomials in the momenta. We
present a classification of second-order superintegrable systems in
two-dimensional Riemannian and pseudo-Riemannian spaces. It is based on the
study of the quadratic algebras of the integrals of motion and on the
equivalence of different systems under coupling constant metamorphosis. The
determining equations for the existence of integrals of motion of arbitrary
order in real Euclidean space $E_2$ are presented and partially solved for the
case of third-order integrals. A systematic exposition is given of systems in
two and higher dimensional space that allow integrals of arbitrary order. The
algebras of integrals of motions are not necessarily quadratic but close
polynomially or rationally. The relation between superintegrability and the
classification of orthogonal polynomials is analyzed.


  Atmospheric neutrinos provide a unique avenue to explore the internal
structure of Earth based on weak interactions, which is complementary to
seismic studies and gravitational measurements. In this work, we demonstrate
that the atmospheric neutrino oscillations in the presence of Earth matter can
serve as an important tool to locate the core-mantle boundary (CMB). An
atmospheric neutrino detector like the proposed 50 kt magnetized ICAL at INO
can observe the core-passing neutrinos efficiently. These neutrinos would have
experienced the MSW resonance and the parametric or neutrino oscillation length
resonance. The net effect of these resonances on neutrino flavor conversions
depends upon the location of CMB and the density jump at that radius. We
quantify the capability of ICAL to measure the location of CMB in the context
of multiple three-layered models of Earth. For the model where the density and
the radius of core are kept flexible while the mass and radius of Earth as well
as the densities of outer and inner mantle are fixed, ICAL can determine the
location of CMB with a 1$\sigma$ precision of about 250 km with an exposure of
1000 kt$\cdot$yr. With the 81-layered PREM profile, this $1\sigma$ precision
would be about 350 km. The charge identification capability of ICAL plays an
important role in achieving this precision.


  We present a sequence-to-action parsing approach for the natural language to
SQL task that incrementally fills the slots of a SQL query with feasible
actions from a pre-defined inventory. To account for the fact that typically
there are multiple correct SQL queries with the same or very similar semantics,
we draw inspiration from syntactic parsing techniques and propose to train our
sequence-to-action models with non-deterministic oracles. We evaluate our
models on the WikiSQL dataset and achieve an execution accuracy of 83.7% on the
test set, a 2.1% absolute improvement over the models trained with traditional
static oracles assuming a single correct target SQL query. When further
combined with the execution-guided decoding strategy, our model sets a new
state-of-the-art performance at an execution accuracy of 87.1%.


  We give a universal approach to the deformation-obstruction theory of objects
of the derived category of coherent sheaves over a smooth projective family. We
recover and generalise the obstruction class of Lowen and Lieblich, and prove
that it is a product of Atiyah and Kodaira--Spencer classes. This allows us to
obtain deformation-invariant virtual cycles on moduli spaces of objects of the
derived category on threefolds.


  Fragments of small solar system bodies entering Earth's atmosphere have
possibly been important contributors of organic compounds to the early Earth.
The cyano radical (CN) emission from meteors is considered as potentially one
of the most suitable markers of organic compounds in meteoroids, however, its
detection in meteor spectra has been thus far unsuccessful. With the aim to
improve our abilities to identify CN emission in meteor observations and use
its spectral features to characterize the composition of incoming asteroidal
meteoroids, we present a detailed analysis of CN emission from high-resolution
spectra of 22 laboratory simulated meteors including ordinary, carbonaceous,
and enstatite chondrites, as well as a large diversity of achondrites (i.e.,
ureilite, aubrite, lunar, martian, howardite, eucrite, and diogenite),
mesosiderite, and iron meteorites. We describe the variations of CN emission
from different classes of asteroidal meteor analogues, its correlation and time
evolution relative to other major meteoroid components. We demonstrate that CN
can be used as a diagnostic spectral feature of carbonaceous and carbon-rich
meteoroids, while most ordinary chondrites show no signs of CN. Our results
point out strong correlation between CN and H emission and suggest both
volatile features are suitable to trace contents of organic matter and water
molecules present within meteoroids. For the application in lower resolution
meteor observations, we demonstrate that CN can be best recognized in the early
stages of ablation and for carbon-rich materials by measuring relative
intensity ratio of CN band peak to the nearby Fe I-4 lines.


  We present a specific two-dimensional dilaton gravity model in which a black
hole evaporates leaving a wormhole at the end state. As the black hole formed
by infalling matter in a initially static spacetime evaporates by emitting
Hawking radiation, the black hole singularity that is initially hidden behind a
timelike apparent horizon meets the shrinking horizon. At this intersection
point, we imposed boundary conditions which require disappearance of the black
hole singularity and generation of the exotic matter which is the source of the
wormhole as the end state of the black hole. These, of course, preserve energy
conservation and continuity of the metric.


  We present an optical to near-infrared selected astronomical catalogue
covering 1270 deg.$^2$. This is the first attempt to systematically combine
data from 23 of the premier extragalactic survey fields - the product of a vast
investment of telescope time. The fields are those imaged by the Herschel Space
Observatory which form the Herschel Extragalactic Legacy Project (HELP). Our
catalogue of 170 million objects is constructed by a positional cross match of
51 public surveys. This high resolution optical, near-infrared, and
mid-infrared catalogue is designed for photometric redshift estimation,
extraction of fluxes in lower resolution far-infrared maps, and spectral energy
distribution modelling. It collates, standardises, and provides value added
derived quantities including corrected aperture magnitudes and astrometry
correction over the Herschel extragalactic wide fields for the first time.
$grizy$ fluxes are available on all fields with $g$ band data reaching
$5\sigma$ point-source depths in a 2 arcsec aperture of 23.5, 24.4, and 24.6
(AB) mag at the 25th, 50th, and 75th percentiles, by area covered, across all
HELP fields. It has $K$ or $K_s$ coverage over 1146 deg.$^2$ with depth
percentiles of 20.2, 20.4, and 21.0 mag respectively. The IRAC Ch 1 band is
available over 273 deg.$^2$ with depth percentiles of 17.7, 21.4, and 22.2 mag
respectively. This paper defines the "masterlist" objects for the first data
release (DR1) of HELP. This large sample of standardised total and corrected
aperture fluxes, uniform quality flags, and completeness measures provides
large well understood statistical samples over the full Herschel extragalactic
sky.


  We report calculated dependence of magneto-exciton energy spectrum upon
electron-hole separation $d$ in Fractional Quantum Hall systems. We calculated
the dependence of photoluminescence upon $d$, and we obtained the doublet
structure observed recently. The Raman scattering spectrum around resonance is
calculated: a robust resonance peak at $\nu=1/3$ around gap value is reported.


  A sequence of vertices $(v_1,\, \dots , \,v_k)$ of a graph $G$ is called a
{\it dominating closed neighborhood sequence} if $\{v_1,\, \dots , \,v_k\}$ is
a dominating set of $G$ and $N[v_i]\nsubseteq \cup _{j=1}^{i-1} N[v_j]$ for
every $i$. A graph $G$ is said to be {\it $k-$uniform} if all dominating closed
neighborhood sequences have equal length $k$. Bre{\v s}ar et al. (2014)
characterized $k$-uniform graphs with $k\leq 3$. In this article we extend
their work by giving a complete characterization of all $k$-uniform graphs with
$k\geq 4$.


  Using minimalist assumptions we develop a natural functional decomposition
for the spacetime metric, and explicit tractable formulae for the surface
gravities, in arbitrary stationary circular (PT symmetric) axisymmetric
spacetimes. We relate rigidity results, (the existence of a Killing horizon),
and the zeroth law to the absence of curvature singularities at the would-be
horizons. These observations are of interest to both observational
astrophysicists (modelling the cold, dark, heavy objects at the centre of most
spiral galaxies), and to the analogue spacetime community, (wherein the
presence of naked singularities is not necessarily deprecated, and the
occurrence of non-Killing horizons is relatively common).


  Web-scale search systems learn an encoder to embed a given query which is
then hooked into an approximate nearest neighbor search (ANNS) pipeline to
retrieve similar data points. To accurately capture tail queries and data
points, learned representations typically are rigid, high-dimensional vectors
that are generally used as-is in the entire ANNS pipeline and can lead to
computationally expensive retrieval. In this paper, we argue that instead of
rigid representations, different stages of ANNS can leverage adaptive
representations of varying capacities to achieve significantly better
accuracy-compute trade-offs, i.e., stages of ANNS that can get away with more
approximate computation should use a lower-capacity representation of the same
data point. To this end, we introduce AdANNS, a novel ANNS design framework
that explicitly leverages the flexibility of Matryoshka Representations. We
demonstrate state-of-the-art accuracy-compute trade-offs using novel
AdANNS-based key ANNS building blocks like search data structures (AdANNS-IVF)
and quantization (AdANNS-OPQ). For example on ImageNet retrieval, AdANNS-IVF is
up to 1.5% more accurate than the rigid representations-based IVF at the same
compute budget; and matches accuracy while being up to 90x faster in wall-clock
time. For Natural Questions, 32-byte AdANNS-OPQ matches the accuracy of the
64-byte OPQ baseline constructed using rigid representations -- same accuracy
at half the cost! We further show that the gains from AdANNS translate to
modern-day composite ANNS indices that combine search structures and
quantization. Finally, we demonstrate that AdANNS can enable inference-time
adaptivity for compute-aware search on ANNS indices built non-adaptively on
matryoshka representations. Code is open-sourced at
https://github.com/RAIVNLab/AdANNS.


  Ott, Tomforde, and Willis proposed a useful compactification for one-sided
shifts over infinite alphabets. Building from their idea we develop a notion of
two-sided shift spaces over infinite alphabets, with an eye towards
generalizing a result of Kitchens. As with the one-sided shifts over infinite
alphabets our shift spaces are compact Hausdorff spaces but, in contrast to the
one-sided setting, our shift map is continuous everywhere. We show that many of
the classical results from symbolic dynamics are still true for our two-sided
shift spaces. In particular, while for one-sided shifts the problem about
whether or not any $M$-step shift is conjugate to an edge shift space is open,
for two-sided shifts we can give a positive answer for this question.


  We present the first measurements of the transverse momentum spectra and
mid-rapidity yields of the $\Xi^{0}(1530)$ multi-strange baryon resonance, from
$\sqrt{\mathrm{s_{NN}}}=200$ GeV Au+Au collisions at RHIC from the STAR
experiment. Ratios of the mid-rapidity yield of this long-lived ($c\tau=21$ fm)
resonance to its non-resonance partner (the $\Xi$ baryon) are compared to
predictions from thermal models and to the corresponding ratios for other
resonances previously reported by STAR. Conclusions will be drawn about the
implication of these measurements for the time between chemical and thermal
freeze-out ($\Delta t_{therm-chem}$) and any observed deviations from the
expected mass and width will be discussed.


  Electromagnetic degrees of freedom are instrumental in antenna design,
wireless communications, imaging, and scattering. Larger number of degrees of
freedom enhances control in antenna design, influencing radiation patterns and
directivity, while in communication systems, it links to spatial channels for
increased data rates and reliability, and resolution in imaging. The
correlation between computed degrees of freedom and physical quantities is not
fully understood, prompting a comparison between classical estimates, Weyl's
law, modal expansions, and optimization techniques. In this paper, it is shown
that NDoF for arbitrary shaped radiating structures approaches the shadow area
measured in squared wavelengths.


  Inelastic collisions occur among regolith particles, such as those in the
ejecta curtain from a crater, and may cause clustering or agglomeration of
particles and thus produce discrete patterns of ejecta deposits around a
crater. Previous studies have shown that clusters, and even agglomerates, are
formed via mutual, inelastic collisions of spherical particles due to adhering
forces between particles in granular streams. To investigate the condition of
agglomerate formation in granular streams, we conducted laboratory experiments
of granular streams using both spherical and irregular, non-spherical
particles. Measurements of particle adhesion in this study were performed using
a centrifugal separation method, in contrast to the previous study in which
atomic force microscopy (AFM) was used. This enabled simultaneous measurements
of multiple particles of various shapes for a statistical analysis of the
results. With similar relative velocities and adhesion values, irregular
particles were found to form agglomerates much more easily than spherical
particles. The axial ratio of the agglomerates of spherical particles and
irregular particles was similar and was in accordance with those observed in
previous laboratory studies, whereas the size of the agglomerates of irregular
particles was larger than the size of spherical particles. The degree of
agglomeration and the size of agglomerates can be used as an indicator of the
shape or adhesive force of the particles in granular stream. Our findings on
agglomeration in granular streams could provide new insights into the origin of
rays on airless bodies and grooves on Phobos.


  Multiple initial state parton interactions in p(d)+Au collisions are
calculated in a Glauber-Eikonal formalism. The convolution of perturbative QCD
parton-nucleon cross sections predicts naturally the competing pattern of
low-pT suppression due geometrical shadowing, and a moderate-pT Cronin
enhancement of hadron spectra. The formal equivalence to recent classical
Yang-Mills calculations is demonstrated, but our approach is shown to be more
general in the large x>0.01 domain because it automatically incorporates the
finite kinematic constraints of both quark and gluon processes in the
fragmentation regions, and accounts for the observed spectra in elementary
pp-->\pi+X processes in the RHIC energy range, sqrt{s} = 20-200 GeV. The
Glauber-Eikonal formalism can be used as a baseline to extract the magnitude of
dynamical shadowing effects from the experimental data at differente
centralities and pseudo-rapidities.


  It is illustrated by the fitted Regge trajectories for a large majority of
mesons that both the radial and orbital Regge trajectories for mesons prefer
being concave. The concavity of the meson Regge trajectories is
model-independent. If the convex Regge trajectories or the Regge trajectories
having the inflection points do not exist, the concavity can act as a criterion
to choose a newly observed meson or to assign a particle to the
unwell-established state. The curvature of the meson Regge trajectories can be
taken as a guide in constructing models. The appropriate models should yield
the spectra which can produce the concave Regge trajectories according to the
concavity of the meson Regge trajectories. If the large majority of the meson
Regge trajectories are concave while a few meson Regge trajectories are convex
which neither have been confirmed nor have been completely excluded at present,
many existing models should be corrected or even be reconstructed, which will
lead to the further understanding of the meson dynamics.


  Leveraging class semantic descriptions and examples of known objects,
zero-shot learning makes it possible to train a recognition model for an object
class whose examples are not available. In this paper, we propose a novel
zero-shot learning model that takes advantage of clustering structures in the
semantic embedding space. The key idea is to impose the structural constraint
that semantic representations must be predictive of the locations of their
corresponding visual exemplars. To this end, this reduces to training multiple
kernel-based regressors from semantic representation-exemplar pairs from
labeled data of the seen object categories. Despite its simplicity, our
approach significantly outperforms existing zero-shot learning methods on
standard benchmark datasets, including the ImageNet dataset with more than
20,000 unseen categories.


  We establish monotone bijections between subsequences of the Farey sequences
and the halfsequences of Farey subsequences associated with elements of the
Boolean lattices.


  We present a weighted $L_{q}(L_{p})$-theory ($p,q\in(1,\infty)$) with
Muckenhoupt weights for the equation $$ \partial_{t}^{\alpha}u(t,x)=\Delta
u(t,x) +f(t,x), \quad t>0, x\in \mathbb{R}^d. $$ Here, $\alpha\in (0,2)$ and
$\partial_{t}^{\alpha}$ is the Caputo fractional derivative of order $\alpha$.
In particular we prove that for any $p,q\in (1,\infty)$, $w_{1}(x)\in A_p$ and
$w_{2}(t)\in A_q$, $$ \int^{\infty}_0\left(\int_{\mathbb{R}^d} |u_{xx}|^p
\,w_{1} dx \right)^{q/p}\,w_{2}dt \leq N
\int^{\infty}_0\left(\int_{\mathbb{R}^d} |f|^p \,w_{1} dx
\right)^{q/p}\,w_{2}dt, $$ where $A_p$ is the class of Muckenhoupt $A_p$
weights. Our approach is based on the sharp function estimates of the
derivatives of solutions.


  In Internet of things (IoT), data is continuously recorded from different
data sources and devices can suffer faults in their embedded electronics, thus
leading to a high-dimensional data sets and concept drift events. Therefore,
methods that are capable of high-dimensional non-stationary time series are of
great value in IoT applications. Fuzzy Time Series (FTS) models stand out as
data-driven non-parametric models of easy implementation and high accuracy.
Unfortunately, FTS encounters difficulties when dealing with data sets of many
variables and scenarios with concept drift. We present a new approach to handle
high-dimensional non-stationary time series, by projecting the original
high-dimensional data into a low dimensional embedding space and using FTS
approach. Combining these techniques enables a better representation of the
complex content of non-stationary multivariate time series and accurate
forecasts. Our model is able to explain 98% of the variance and reach 11.52% of
RMSE, 2.68% of MAE and 2.91% of MAPE.


  Araci et al. introduced a $p$-adic $(\rho,q)$-analogue of the Haar
distribution. By means of the distribution, they constructed the $p$-adic
$(\rho,q)$-Volkenborn integral. In this paper, by virtue of the Mahler
expansion of continuous functions, the author gives the Radon-Nikodym theorem
with respect to the $p$-adic $(\rho,q)$-distribution on $\Bbb Z_p$.


  We try to constrain the Equation-of-State (EoS) of supra-nuclear-density
matter in neutron stars (NSs) by observations of nearby NSs. There are seven
thermally emitting NSs known from X-ray and optical observations, the so-called
Magnificent Seven (M7), which are young (up to few Myrs), nearby (within a few
hundred pc), and radio-quiet with blackbody-like X-ray spectra, so that we can
observe their surfaces. As bright X-ray sources, we can determine their
rotational (pulse) period and their period derivative from X-ray timing. From
XMM and/or Chandra X-ray spectra, we can determine their temperature. With
precise astrometric observations using the Hubble Space Telescope, we can
determine their parallax (i.e. distance) and optical flux. From flux, distance,
and temperature, one can derive the emitting area - with assumptions about the
atmosphere and/or temperature distribution on the surface. This was recently
done by us for the two brightest M7 NSs RXJ1856 and RXJ0720. Then, from
identifying absorption lines in X-ray spectra, one can also try to determine
gravitational redshift. Also, from rotational phase-resolved spectroscopy, we
have for the first time determined the compactness (mass/radius) of the M7 NS
RBS1223. If also applied to RXJ1856, radius (from luminosity and temperature)
and compactness (from X-ray data) will yield the mass and radius - for the
first time for an isolated single neutron star. We will present our
observations and recent results.


  L\'{e}vy processes with completely monotone jumps appear frequently in
various applications of probability. For example, all popular stock price
models based on L\'{e}vy processes (such as the Variance Gamma, CGMY/KoBoL and
Normal Inverse Gaussian) belong to this class. In this paper we continue the
work started in [Int. J. Theor. Appl. Finance 13 (2010) 63-91, Quant. Finance
10 (2010) 629-644] and develop a simple yet very efficient method for
approximating processes with completely monotone jumps by processes with
hyperexponential jumps, the latter being the most convenient class for
performing numerical computations. Our approach is based on connecting L\'{e}vy
processes with completely monotone jumps with several areas of classical
analysis, including Pad\'{e} approximations, Gaussian quadrature and orthogonal
polynomials.


  In a recent paper by Rodrigues-Williams \& Hogan (RH94), a correlation
between high-redshift, optically-selected QSOs and Zwicky clusters was reported
at a very high significance level. Due to the fairly bright flux threshold of
the cluster sample, these correlations cannot be interpreted as being due to an
environmental effect of the clusters on the quasar activity. The most likely
interpretation employed in RH94 was the effect of gravitational lensing by the
foreground clusters, though the required magnification to explain the observed
correlations has to be considerably higher than obtained from simple mass
models for the clusters. We have repeated the analysis of RH94 using a
different QSO sample, namely radio quasars and radio galaxies from the 1-Jy
sample. In accordance with RH, we detect a statistically significant
correlation between Zwicky clusters and 1-Jy sources with intermediate redshift
($z\approx 1$), but fail to detect significant effects for higher-redshift
sources. In addition, we detect a highly significant underdensity of
low-redshift radio sources around Zwicky clusters, for which an environmental
interpretation seems to be most reasonable. Our result for the overdensity of
$z\sim 1$ sources is in good agreement with previous results and can possibly
be interpreted as a lensing effect, though we have not tried to quantitatively
investigate a lensing model. Other interpretations, such as patchy dust
obscuration, can not explain the observed effect and its tendency with
redshift.


  We revisit Stasheff's construction of a minimal Lie-Quillen model of a
simply-connected closed manifold $M$ using the language of infinity-algebras.
  This model is then used to construct a graded Lie bracket on the equivariant
homology of the free loop space of $M$ minus a point similar to the
Chas-Sullivan string bracket.


  Multi-output inference tasks, such as multi-label classification, have become
increasingly important in recent years. A popular method for multi-label
classification is classifier chains, in which the predictions of individual
classifiers are cascaded along a chain, thus taking into account inter-label
dependencies and improving the overall performance. Several varieties of
classifier chain methods have been introduced, and many of them perform very
competitively across a wide range of benchmark datasets. However, scalability
limitations become apparent on larger datasets when modeling a fully-cascaded
chain. In particular, the methods' strategies for discovering and modeling a
good chain structure constitutes a mayor computational bottleneck. In this
paper, we present the classifier trellis (CT) method for scalable multi-label
classification. We compare CT with several recently proposed classifier chain
methods to show that it occupies an important niche: it is highly competitive
on standard multi-label problems, yet it can also scale up to thousands or even
tens of thousands of labels.


  We study the hadron-quark phase transition in the interior of neutron stars
(NS's). We calculate the equation of state (EOS) of hadronic matter using the
Brueckner-Bethe-Goldstone formalism with realistic two-body and three-body
forces, as well as a relativistic mean field model. For quark matter we employ
the MIT bag model constraining the bag constant by using the indications coming
from the recent experimental results obtained at the CERN SPS on the formation
of a quark-gluon plasma. We find necessary to introduce a density dependent bag
parameter, and the corresponding consistent thermodynamical formalism. We
calculate the structure of NS interiors with the EOS comprising both phases,
and we find that the NS maximum masses fall in a relatively narrow interval,
$1.4 M_\odot \leq M_{\rm max} \leq 1.7 M_\odot$. The precise value of the
maximum mass turns out to be only weakly correlated with the value of the
energy density at the assumed transition point in nearly symmetric nuclear
matter.


  Three component models of the IMF are made to consider possible origins for
the observed relative variations in the numbers of brown dwarfs,
solar-to-intermediate mass stars, and high mass stars. Three distinct physical
processes are noted. The characteristic mass for most star formation is
identified with the thermal Jeans mass in the molecular cloud core, and this
presumably leads to the middle mass range by the usual collapse and accretion
processes. Pre-stellar condensations (PSCs) observed in mm-wave continuum
studies presumably form at this mass. Significantly smaller self-gravitating
masses require much larger pressures and may arise following dynamical
processes inside these PSCs, including disk formation, tight-cluster ejection,
and photoevaporation as studied elsewhere, but also gravitational collapse of
shocked gas in colliding PSCs. Significantly larger stellar masses form in
relatively low abundance by normal cloud processes, possibly leading to steep
IMFs in low-pressure field regions, but this mass range can be significantly
extended in high pressure cloud cores by gravitationally-focussed gas accretion
onto PSCs and by the coalescence of PSCs. These models suggest that the
observed variations in brown dwarf, solar-to-intermediate mass, and high mass
populations are the result of dynamical effects that depend on environmental
density and velocity dispersion. They accommodate observations ranging from
shallow IMFs in cluster cores to Salpeter IMFs in average clusters and whole
galaxies to steep and even steeper IMFs in field and remote field regions. They
also suggest how the top-heavy IMFs in some starburst clusters may originate
and they explain bottom-heavy IMFs in low surface brightness galaxies.


  Due to their inherent capabilities of capturing non-local dependencies,
Transformer neural networks have quickly been established as the paradigmatic
architecture for large language models and image processing. Next to these
traditional applications, machine learning methods have also been demonstrated
to be versatile tools in the analysis of image-like data of quantum phases of
matter, e.g. given snapshots of many-body wave functions obtained in ultracold
atom experiments. While local correlation structures in image-like data of
physical systems can reliably be detected, identifying phases of matter
characterized by global, non-local structures with interpretable machine
learning methods remains a challenge. Here, we introduce the correlator
Transformer (CoTra), which classifies different phases of matter while at the
same time yielding full interpretability in terms of physical correlation
functions. The network's underlying structure is a tailored attention
mechanism, which learns efficient ways to weigh local and non-local
correlations for a successful classification. We demonstrate the versatility of
the CoTra by detecting local order in the Heisenberg antiferromagnet, and show
that local gauge constraints in one- and two-dimensional lattice gauge theories
can be identified. Furthermore, we establish that the CoTra reliably detects
non-local structures in images of correlated fermions in momentum space (Cooper
pairs) and that it can distinguish percolating from non-percolating images.


  The Vera Rubin Observatory, set to begin observations in mid-2024, will
increase our discovery rate of supernovae to well over one million annually.
There has been a significant push to develop new methodologies to identify,
classify and ultimately understand the millions of supernovae discovered with
the Rubin Observatory. Here, we present the first simulation-based inference
method using normalizing flows, trained to rapidly infer the parameters of toy
supernovae model in multivariate, Rubin-like datastreams. We find that our
method is well-calibrated compared to traditional inference methodologies
(specifically MCMC), requiring only one-ten-thousandth of the CPU hours during
test time.


  Optimization-based 3D object tracking is known to be precise and fast, but
sensitive to large inter-frame displacements. In this paper we propose a fast
and effective non-local 3D tracking method. Based on the observation that
erroneous local minimum are mostly due to the out-of-plane rotation, we propose
a hybrid approach combining non-local and local optimizations for different
parameters, resulting in efficient non-local search in the 6D pose space. In
addition, a precomputed robust contour-based tracking method is proposed for
the pose optimization. By using long search lines with multiple candidate
correspondences, it can adapt to different frame displacements without the need
of coarse-to-fine search. After the pre-computation, pose updates can be
conducted very fast, enabling the non-local optimization to run in real time.
Our method outperforms all previous methods for both small and large
displacements. For large displacements, the accuracy is greatly improved
($81.7\% \;\text{v.s.}\; 19.4\%$). At the same time, real-time speed ($>$50fps)
can be achieved with only CPU. The source code is available at
\url{https://github.com/cvbubbles/nonlocal-3dtracking}.


  The method of waveform cross correlation (WCC) allows remote monitoring of
weak seismic activity induced by underground tests. This type of monitoring is
considered as a principal task of on-site inspection under the Comprehensive
nuclear-test-ban treaty. On September 11, 2016, a seismic event with body wave
magnitude 2.1 was found in automatic processing near the epicenter of the
underground explosion conducted by the DPRK on September 9, 2016. This event
occurred approximately two days after the test. Using the WCC method, two array
stations of the International Monitoring System (IMS), USRK and KSRS, detected
Pn-wave arrivals, which were associated with a unique event. Standard automatic
processing at the International Data Centre (IDC) did not create an event
hypothesis, but in the following interactive processing based on WCC
detections, an IDC analyst was able to create a two-station event . Location
and other characteristics of this small seismic source indicate that it is
likely an aftershock of the preceding explosion. Building on the success of
automatic detection and phase association, we carried out an extended analysis,
which included later phases and closest non-IMS stations. The final cross
correlation solution uses four stations, including MDJ (China) and SEHB
(Republic of Korea), with the epicenter approximately 2 km to north-west from
the epicenter of the Sept. 9 test. We also located the aftershock epicenter by
standard IDC program LocSAT using the arrival times obtained by cross
correlation. The distance between the DPRK and LocSAT aftershock epicenters is
25.5 km, i.e. by an order of magnitude larger than that obtained by the WCC
relative location method.


  Selection of 25 examples from extensive nontrivial families for different
types of nonlinear PDEs and their formal general solutions are given. The main
goal here is to show on examples the types of solvable PDEs and what their
general solutions look like.


  In this work we find analytical solutions to the null geodesics in the
hyperbolic topological black hole spacetime of conformal Weyl gravity in an
invariant $2$-plane given by the orbits of an azimuthal Killing vector. Exact
expressions for the (non-compact) horizons are found, which depend on the
cosmological constant and the coupling constants of conformal Weyl gravity. The
angular motion is examined qualitatively by means of an effective potential;
quantitatively, the equation of motion is solved in terms of the
$\wp$-Weierstra{\ss} elliptic function. Thus, we find the deflection angle for
photons without using any approximation, which is a novel result for this
topology.


  Many success stories involving deep neural networks are instances of
supervised learning, where available labels power gradient-based learning
methods. Creating such labels, however, can be expensive and thus there is
increasing interest in weak labels which only provide coarse information, with
uncertainty regarding time, location or value. Using such labels often leads to
considerable challenges for the learning process. Current methods for
weak-label training often employ standard supervised approaches that
additionally reassign or prune labels during the learning process. The
information gain, however, is often limited as only the importance of labels
where the network already yields reasonable results is boosted. We propose
treating weak-label training as an unsupervised problem and use the labels to
guide the representation learning to induce structure. To this end, we propose
two autoencoder extensions: class activity penalties and structured dropout. We
demonstrate the capabilities of our approach in the context of score-informed
source separation of music.


  In the context of the composite boson interpretation, we construct the exact
general solution of the Dirac--K\"ahler equation for the case of the spherical
Riemann space of constant positive curvature, for which due to the geometry
itself one may expect to have a discrete energy spectrum. In the case of the
minimal value of the total angular momentum, $j=0$, the radial equations are
reduced to second-order ordinary differential equations, which are
straightforwardly solved in terms of the hypergeometric functions. For non-zero
values of the total angular momentum, however, the radial equations are reduced
to a pair of complicated fourth-order differential equations. Employing the
factorization approach, we derive the general solution of these equations
involving four independent fundamental solutions written in terms of
combinations of the hypergeometric functions. The corresponding discrete energy
spectrum is then determined via termination of the involved hypergeometric
series, resulting in quasi-polynomial wave-functions. The constructed solutions
lead to notable observations when compared with those for the ordinary Dirac
particle. The energy spectrum for the Dirac-K\"ahler particle in spherical
space is much more complicated. Its structure substantially differs from that
for the Dirac particle since it consists of two paralleled energy level series
each of which is twofold degenerate. Besides, none of the two separate series
coincides with the series for the Dirac particle. Thus, the Dirac--K\"ahler
field cannot be interpreted as a system of four Dirac fermions. Additional
arguments supporting this conclusion are discussed.


  We study the emissivity properties of a geometrically thin, optically thick,
steady accretion disc about a static boson star. Starting from a numerical
computation of the metric potentials and the rotational velocities of the
particles in the vicinity of the compact object, we obtain the power per unit
area, the temperature of the disc, and the spectrum of the emitted radiation.
In order to see if different central objects could be actually distinguished,
all these results are compared with the case of a central Schwarzschild black
hole of equal mass. We considered different situations both for the boson star,
assumed with and without self-interactions, and the disc, whose internal
commencement can be closer to the center than in the black hole case. We
finally make some considerations about the Eddington luminosity, which becomes
radially dependent for a transparent object. We found that, particularly at
high energies, differences in the emitted spectrum are notorious. Reasons for
that are discussed.


  The Peierls stress of the a/2<110> screw dislocation belonging to the shuffle
set is calculated for silicon using density functional theory. We have checked
the effect of boundary conditions by using two models, the supercell method
where one considers a periodic array of dislocations, and the cluster method
where a single dislocation is embedded in a small cluster. The Peierls stress
is underestimated with the supercell and overestimated with the cluster. These
contributions have been calculated and the Peierls stress is determined in the
range between 2.4 x 10-2 and 2.8 x 10-2 eV {\AA}-3. When moving, the
dislocation follows the {111} plane going through a low energy metastable
configuration and never follows the 100 plane, which includes a higher energy
metastable core configuration.


  As large language models (LLMs) become more powerful and ubiquitous, systems
like ChatGPT are increasingly used by students to help them with writing tasks.
To better understand how these tools are used, we investigate how students
might use an LLM for essay writing, for example, to study the queries asked to
ChatGPT and the responses that ChatGPT gives. To that end, we plan to conduct a
user study that will record the user writing process and present them with the
opportunity to use ChatGPT as an AI assistant. This study's findings will help
us understand how these tools are used and how practitioners -- such as
educators and essay readers -- should consider writing education and evaluation
based on essay writing.


  We develop a computational approach for calculating the optical conductivity
in the augmented plane wave basis set of Wien2K and apply it for thoroughly
comparing the full dipole matrix element calculation and the Peierls
approximation. The results for SrVO3 and V2O3 show that the Peierls
approximation, which is commonly used in model calculations, works well for
optical transitions between the d orbitals. In a typical transition metal
oxide, these transitions are solely responsible for the optical conductivity at
low frequencies. The Peierls approximation does not work, on the other hand,
for optical transitions between p- and d-orbitals which usually became
important at frequencies of a few eVs


  In software development, the predominant emphasis on functionality often
supersedes security concerns, a trend gaining momentum with AI-driven
automation tools like GitHub Copilot. These tools significantly improve
developers' efficiency in functional code development. Nevertheless, it remains
a notable concern that such tools are also responsible for creating insecure
code, predominantly because of pre-training on publicly available repositories
with vulnerable code. Moreover, developers are called the "weakest link in the
chain" since they have very minimal knowledge of code security. Although
existing solutions provide a reasonable solution to vulnerable code, they must
adequately describe and educate the developers on code security to ensure that
the security issues are not repeated. Therefore we introduce a multipurpose
code vulnerability analysis system \texttt{SecRepair}, powered by a large
language model, CodeGen2 assisting the developer in identifying and generating
fixed code along with a complete description of the vulnerability with a code
comment. Our innovative methodology uses a reinforcement learning paradigm to
generate code comments augmented by a semantic reward mechanism. Inspired by
how humans fix code issues, we propose an instruction-based dataset suitable
for vulnerability analysis with LLMs. We further identify zero-day and N-day
vulnerabilities in 6 Open Source IoT Operating Systems on GitHub. Our findings
underscore that incorporating reinforcement learning coupled with semantic
reward augments our model's performance, thereby fortifying its capacity to
address code vulnerabilities with improved efficacy.


  Recently, the concept of dynamical extended charged events has been
introduced, and it has been argued that they should play as central a role as
that played by particles or ordinary branes. In this article we show that in
the presence of a Chern-Simons coupling, a magnetically charged extended event
emits an extended object, which geometrically is just like a Dirac string, but
it is observable, obeys equations of motion, and may be electrically charged.
We write a complete action principle which accounts for this effect. The action
involves two Chern-Simons terms, one integrated over spacetime and the other
integrated over the worldvolume of the submanifold that is the union of the
Dirac world-sheet and the history of the emitted physical object. By demanding
that the total charge emitted by a composite extended magnetic event be
quantized according to Dirac's rule, we find a quantization condition for the
Chern-Simons coupling. For a 1-form electric potential in D=2n+1 spacetime
dimensions, the composite event is formed by n elementary extended magnetic
events separated in time such that the product of their transverse spaces,
together with the time axis, is the entire spacetime. We show that the emitted
electric charge is given by the integral of the (n-1)-th exterior power of the
electromagnetic field strength over the last elementary event, or,
equivalently, over an appropriate closed surface. The extension to more general
p-form potentials and higher dimensions is also discussed. For the case D=11,
p=3, our result for the quantization of the Chern-Simons coupling was obtained
previously in the context of M-theory, a remarkable agreement that makes the
existence of events even more compelling.


  Based on spectroscopic constraints derived from NLTE line formation, we
explore the likely range of stellar parameters (T_eff and log g) for the
hyper-metal-poor (HMP) star HE 1327-2326. Combining the constraints from Balmer
line profiles and the Ca I/II ionization equilibrium, a subgiant stage of
evolution is indicated. This result is further supported by spectrophotometric
observations of the Balmer jump. If a higher T_eff value was used (as favoured
by some photometric calibrations), the spectroscopic analysis would indicate a
turnoff-point stage of evolution. Using a stellar-structure code that treats
the effects of atomic diffusion throughout the star in detail, we evolve a
low-mass model star to reach the HR-diagram position of HE 1327-2326 after
roughly 13 Gyr. While the surface abundances are modified significantly (by
more than 1 dex for the case of uninhibited diffusion), such corrections can
not resolve the discrepancy between the abundance inferred from the
non-detection of the Li I resonance line at 6707 Angstroem and the WMAP-based
primordial lithium abundance. As there are numerous processes that can destroy
lithium, any cosmological interpretation of a lower-than-expected lithium
abundance at the lowest metallicities will have to await sample sizes of
unevolved hyper-metal-poor stars that are one order of magnitude larger. The
situation remains equally inconclusive concerning atomic-diffusion corrections.
Here, attempts have to be made to better constrain internal mixing processes,
both observationally and by means of sophisticated modelling. With constraints
on additional mixing processes taken from a recent globular-cluster study, the
likeliest scenario is that HE 1327-2326's surface abundances have undergone
mild depletion (of order 0.2 dex).


  For propagating and evanescent vector Bessel beams, we study the
singularities of the Poynting vector (Poynting singularities), at which the
energy flux density turns to zero. Poynting singularities include all the phase
singularities and some of polarization ones (L- and C-points). We reveal the
existence conditions and positions of singularities, which are located at
cylindrical surfaces around the beam axis. We mark the special case of the
evanescent Bessel beam in the form of cylindrical standing wave, that is
singular at any spatial point.


  While current systems for autonomous robot navigation can produce safe and
efficient motion plans in static environments, they usually generate suboptimal
behaviors when multiple robots must navigate together in confined spaces. For
example, when two robots meet each other in a narrow hallway, they may either
turn around to find an alternative route or collide with each other. This paper
presents a new approach to navigation that allows two robots to pass each other
in a narrow hallway without colliding, stopping, or waiting. Our approach,
Perceptual Hallucination for Hallway Passing (PHHP), learns to synthetically
generate virtual obstacles (i.e., perceptual hallucination) to facilitate
passing in narrow hallways by multiple robots that utilize otherwise standard
autonomous navigation systems. Our experiments on physical robots in a variety
of hallways show improved performance compared to multiple baselines.


  We present a linear-time algorithm for simplifying flow networks on directed
planar graphs: Given a directed planar graph on $n$ vertices, a source vertex
$s$ and a sink vertex $t$, our algorithm removes all the arcs that do not
participate in any simple $s,t$-path in linear-time. The output graph produced
by our algorithm satisfies the prerequisite needed by the $O(n\log n)$-time
algorithm of Weihe [FOCS'94 \& JCSS'97] for computing maximum $s,t$-flow in
directed planar graphs. Previously, Weihe's algorithm could not run in $O(n\log
n)$-time due to the absence of the preprocessing step; all the preceding
algorithms run in $\tilde{\Omega}(n^2)$-time [Misiolek-Chen, COCOON'05 \&
IPL'06; Biedl, Brejov{\'{a}} and Vinar, MFCS'00]. Consequently, this provides
an alternative $O(n\log n)$-time algorithm for computing maximum $s,t$-flow in
directed planar graphs in addition to the known $O(n\log n)$-time algorithms
[Borradaile-Klein, SODA'06 \& J.ACM'09; Erickson, SODA'10].
  Our algorithm can be seen as a (truly) linear-time $s,t$-flow sparsifier for
directed planar graphs, which runs faster than any maximum $s,t$-flow algorithm
(which can also be seen of as a sparsifier). The simplified structures of the
resulting graph might be useful in future developments of maximum $s,t$-flow
algorithms in both directed and undirected planar graphs.


  Creeping flow of polymeric fluid without inertia exhibits elastic
instabilities and elastic turbulence accompanied by drag enhancement due to
elastic stress produced by flow-stretched polymers. However, in
inertia-dominated flow at high $\mbox{Re}$ and low fluid elasticity $El$, a
reduction in turbulent frictional drag is caused by an intricate competition
between inertial and elastic stresses. Here, we explore the effect of inertia
on the stability of viscoelastic flow in a broad range of control parameters
$El$ and $(\mbox{Re}, \mbox{Wi})$. We present the stability diagram of observed
flow regimes in $\mbox{Wi}-\mbox{Re}$ coordinates and find that instabilities'
onsets show unexpectedly non-monotonic dependence on $El$. Further, three
distinct regions in the diagram are identified based on $El$. Strikingly, for
high elasticity fluids we discover a complete relaminarization of flow at
Reynolds number of the order of unity, different from a well-known turbulent
drag reduction. These counterintuitive effects may be explained by a finite
polymer extensibility and a suppression of vorticity at high $\mbox{Wi}$. Our
results call for further theoretical and numerical development to uncover the
role of inertial effect on elastic turbulence in a viscoelastic flow.


  We show that irradiation induced stellar winds can explain two important
metallicity effects in X-ray binaries - the higher numbers and the softer
spectra of the X-ray binaries in metal rich globular clusters compared to the
metal poor ones. As has been previously noted by Iben, Tutukov and Fedorova,
the winds should be stronger at lower metallicity due to less efficient line
cooling. This will speed up the evolution of the LMXBs in metal poor clusters,
hence reducing their numbers. These winds can also provide extra material near
the accreting object which may create an intrinsic absorber to harden the X-ray
spectra of the metal poor cluster systems relative to the metal rich ones, as
suggested by observations. We outline some additional observational predictions
of the model.


  We propose a global scheme for a controlled Navier-Stokes equation system on
compact smooth Riemannian manifolds.


  It is shown that disjunction of two switch-lists can blow up the
representation size exponentially. Since switch-lists can be negated without
any increase in size, this shows that conjunction of switch-lists also leads to
an exponential blow-up in general.


  We describe a stochastic birth-and-death model of evolution of horizontally
transferred genes in microbial populations. The model is a generalization of
the stochastic model described by Berg and Kurland and includes five
parameters: the rate of mutational inactivation, selection coefficient,
immigration rate (i.e., rate of arrival of a novel sequence from outside of the
recipient population), within-population horizontal transmission rate, and
population size. The model of Berg and Kurland included four parameters,
namely, mutational inactivation, selection coefficient, population size, and
transmission rate. However, the effect of transmission was disregarded in the
interpretation of the results, and the overall conclusion was that horizontally
acquired sequences can be fixed in a population only when they confer a
substantial selective advantage onto the recipient and therefore are subject to
strong positive selection. By contrast, analysis of the present model in
different domains of parameter values shows that, as long as the rate of
within-population horizontal transmission is comparable to the mutational
inactivation rate and there is even a low rate of immigration, horizontally
acquired sequences can be fixed in the population or at least persist for a
long time even when they are neutral or slightly deleterious. The available
biological data strongly suggest that intense within-population and even
between-populations gene flows are realistic for at least some prokaryotic
species and environments. Therefore our modeling results are compatible with
the notion of a pivotal role of horizontal gene transfer in the evolution of
prokaryotes.


  We derive a new equation of state (EoS) for neutron stars (NS) from the outer
crust to the core based on modern microscopic Brueckner-Hartree-Fock (BHF)
calculations using the Argonne $v_{18}$ potential plus three-body forces
computed with the Urbana model. To deal with the inhomogeneous structures of
matter in the NS crust, we use the recent Barcelona-Catania-Paris-Madrid (BCPM)
nuclear energy density functional that is directly based on the same
microscopic BHF calculations, and which is able to reproduce the ground-state
properties of nuclei along the periodic table. The EoS of the outer crust
requires the masses of neutron-rich nuclei, which are obtained through
Hartree-Fock-Bogoliubov calculations with the BCPM functional when they are
unknown experimentally. To compute the inner crust, Thomas-Fermi calculations
in Wigner-Seitz cells are performed with the same functional. Existence of
nuclear pasta is predicted in a range of average baryon densities between
$\simeq$0.067 fm$^{-3}$ and $\simeq$0.0825 fm$^{-3}$, where the transition to
the core takes place. The NS core is computed from the nuclear EoS of the BHF
calculation assuming non-exotic constituents (core of $npe\mu$ matter). In each
region of the star, we discuss the comparison of the new EoS with previous
EoSes for the complete NS structure, in particular, with the Lattimer-Swesty
EoS and with the Shen et al. EoS widely used in astrophysical calculations. The
new microscopically derived EoS fulfills at the same time a NS maximum mass of
2~$M_\odot$ with a radius of 10 km, and a 1.5~$M_\odot$ NS with a radius of
11.7 km.


  We establish curious Lefschetz property for generic character varieties of
Riemann surfaces conjectured by Hausel, Letellier and Rodriguez-Villegas. Our
main tool applies directly in the case when there is at least one puncture
where the local monodromy has distinct eigenvalues. We pass to a vector bundle
over the character variety, which is then decomposed into cells, which look
like vector bundles over varieties associated to braids by
Shende-Treumann-Zaslow. These varieties are in turn decomposed into cells that
look like $(\mathbb{C}^*)^{d-2k}\times \mathbb{C}^k$. The curious Lefschetz
property is shown to hold on each cell, and therefore holds for the character
variety. To deduce the general case, we introduce a fictitious puncture with
trivial monodromy, and show that the cohomology of the character variety where
one puncture has trivial monodromy is isomorphic to the sign component of the
$S_n$ action on the cohomology for the character variety where trivial
monodromy is replaced by regular semisimple monodromy. This involves an
argument with the Grothendieck-Springer sheaf, and analysis of how the
cohomology of the character variety varies when the eigenvalues are moved
around.


  We consider a first-passage percolation model on a Delaunay triangulation of
the plane. In this model each edge is independently equipped with a nonnegative
random variable, with distribution function F, which is interpreted as the time
it takes to traverse the edge. Vahidi-Asl and Wierman have shown that, under a
suitable moment condition on F, the minimum time taken to reach a point x from
the origin 0 is asymptotically \mu(F)|x|, where \mu(F) is a nonnegative finite
constant. However the exact value of the time constant \mu(F) still a
fundamental problem in percolation theory. Here we prove that if F(0)<1-p_c^*
then \mu(F)>0, where p_c^* is a critical probability for bond percolation on
the dual graph (Voronoi tessellation).


  In this work we are interested in the well-posedness issues for the initial
value problem associated with a higher order water wave model posed on a
pe\-rio\-dic domain $\mathbb{T}$. We derive some multilinear estimates and use
them in the contraction mapping argument to prove local well-posedness for
initial data in the periodic Sobolev space $H^s(\mathbb{T})$, $s\geq 1$. With
some restriction on the parameters appeared in the model, we use the conserved
quantity to obtain global well-posedness for given data with Sobolev regularity
$s\geq 2$. Also, we use splitting argument to improve the global well-posedness
result in $H^s(\mathbb{T})$ for $1\leq s< 2$. Well-posedness result obtained in
this work is sharp in the sense that the flow-map that takes initial data to
the solution cannot to be continuous for given data in $H^s(\mathbb{T})$, $s<
1$. Finally, we prove a norm-inflation result by showing that the solution
corresponding to a smooth initial data may have arbitrarily large
$H^s(\mathbb{T})$ norm, with $s<1$, for arbitrarily short time.


  Spatial regression of random fields based on potentially biased sensing
information is proposed in this paper. One major concern in such applications
is that since it is not known a-priori what the accuracy of the collected data
from each sensor is, the performance can be negatively affected if the
collected information is not fused appropriately. For example, the data
collector may measure the phenomenon inappropriately, or alternatively, the
sensors could be out of calibration, thus introducing random gain and bias to
the measurement process. Such readings would be systematically distorted,
leading to incorrect estimation of the spatial field. To combat this
detrimental effect, we develop a robust version of the spatial field model
based on a mixture of Gaussian process experts. We then develop two different
approaches for Bayesian spatial field reconstruction: the first algorithm is
the Spatial Best Linear Unbiased Estimator (S-BLUE), in which one considers the
quadratic loss function and restricts the estimator to the linear family of
transformations; the second algorithm is based on empirical Bayes, which
utilises a two-stage estimation procedure to produce accurate predictive
inference in the presence of "misbehaving" sensors. In addition, we develop the
distributed version of these two approaches to drastically improve the
computational efficiency in large-scale settings. We present extensive
simulation results using both synthetic datasets and semi-synthetic datasets
with real temperature measurements and simulated distortions to draw useful
conclusions regarding the performance of each of the algorithms.


  Non-negative matrix factorization with the generalized Kullback-Leibler
divergence (NMF) and latent Dirichlet allocation (LDA) are two popular
approaches for dimensionality reduction of non-negative data. Here, we show
that NMF with $\ell_1$ normalization constraints on the columns of both
matrices of the decomposition and a Dirichlet prior on the columns of one
matrix is equivalent to LDA. To show this, we demonstrate that explicitly
accounting for the scaling ambiguity of NMF by adding $\ell_1$ normalization
constraints to the optimization problem allows a joint update of both matrices
in the widely used multiplicative updates (MU) algorithm. When both of the
matrices are normalized, the joint MU algorithm leads to probabilistic latent
semantic analysis (PLSA), which is LDA without a Dirichlet prior. Our approach
of deriving joint updates for NMF also reveals that a Lasso penalty on one
matrix together with an $\ell_1$ normalization constraint on the other matrix
is insufficient to induce any sparsity.


  We consider immiscible and incompressible two-phase flow in porous media
under steady-state conditions using a dynamic pore network model. We focus on
the fluctuations in a Representative Elementary Area (REA), with the aim to
demonstrate that the statistical distributions of the volumetric flow rate and
the saturation within the REA become independent of the size of the entire
model when the model is large enough. This independence is a necessary
condition for developing a local statistical theory for the flow, which in turn
opens for the possibility to formulate a description at scales large enough for
the typical pore size to be negligible using differential equations.


  In this article we give an exposition of Toom's proof of Bulgarian Solitaire
that appeared in \emph{Kvant}. We provide more details. We also show how an
application of the Chinese Remainder Theorem allows us to generalize the proof.


  We study the Cauchy problem for the Klein-Gordon-Zakharov system in 3D with
low regularity data. We lower down the regularity to the critical value with
respect to scaling up to the endpoint. The decisive bilinear estimates are
proved by means of methods developed by Bejenaru-Herr for the Zakharov system
and already applied by Kinoshita to the Klein-Gordon-Zakharov system in 2D.


  The random $2$-dimensional simplicial complex process starts with a complete
graph on $n$ vertices, and in every step a new $2$-dimensional face, chosen
uniformly at random, is added. We prove that with probability tending to $1$ as
$n\to\infty$, the first homology group over $\mathbb Z$ vanishes at the very
moment when all the edges are covered by triangular faces.


  This paper is concerned with the asymptotic behavior of solutions of the
two-dimensional Navier-Stokes equations with both non-autonomous deterministic
and stochastic terms defined on unbounded domains. We first introduce a
continuous cocycle for the equations and then prove the existence and
uniqueness of tempered random attractors. We also characterize the structures
of the random attractors by complete solutions. When deterministic forcing
terms are periodic, we show that the tempered random attractors are also
periodic. Since the Sobolev embeddings on unbounded domains are not compact, we
establish the pullback asymptotic compactness of solutions by Ball's idea of
energy equations.


  Cyclic cellular automata (CCA) are models of excitable media. Started from
random initial conditions, they produce several different kinds of spatial
structure, depending on their control parameters. We introduce new tools from
information theory that let us calculate the dynamical information content of
spatial random processes. This complexity measure allows us to quantitatively
determine the rate of self-organization of these cellular automata, and
establish the relationship between parameter values and self-organization in
CCA. The method is very general and can easily be applied to other cellular
automata or even digitized experimental data.


  We use an elementary argument building on group actions to prove that the
selection-free steady state genetic algorithm analyzed by Sutton and Witt
(GECCO 2019) takes an expected number of $\Omega(2^n / \sqrt n)$ iterations to
find any particular target search point. This bound is valid for all population
sizes $\mu$. Our result improves over the previous lower bound of
$\Omega(\exp(n^{\delta/2}))$ valid for population sizes $\mu = O(n^{1/2 -
\delta})$, $0 < \delta < 1/2$.


  We propose a new formula to explain circular velocity profiles of spiral
galaxies obtained from the Starobinsky model in Palatini formalism. It is based
on the assumption that the gravity can be described by two conformally related
metrics: one of them is responsible for the measurement of distances, while the
other so-called dark metric, is responsible for a geodesic equation and
therefore can be used for the description of the velocity profile. The formula
is tested against a subset of galaxies taken from the HI Nearby Galaxy Survey
(THINGS).