  We study absolute continuity of harmonic measure with respect to surface
measure on domains $\Omega$ that have large complements. We show that if
$\Gamma\subset \mathbb{R}^{d+1}$ is $d$-Ahlfors regular and splits $
\mathbb{R}^{d+1}$ into two NTA domains then $\omega_{\Omega}\ll
\mathscr{H}^{d}$ on $\Gamma\cap \partial\Omega$. This result is a natural
generalisation of a result of Wu in [Wu86].
  We also prove that almost every point in $\Gamma\cap\partial\Omega$ is a cone
point if $\Gamma$ is a Lipschitz graph. Combining these results and a result
from [AHMMMTV], we characterize sets of absolute continuity with finite
$\mathscr{H}^{d}$-measure both in terms of the cone point condition and in
terms of the rectifiable structure of the boundary. This generalizes the
results of McMillan in [McM69] and Pommerenke in [Pom86].
  Finally, we also show our first result holds for elliptic measure associated
with real second order divergence form elliptic operators with a mild
assumption on the gradient of the matrix.


  We offer a new proposal for cosmic singularity resolution based upon a
quantum cosmology with a unitary bounce. This proposal is illustrated via a
novel quantization of a mini-superspace model in which there can be
superpositions of the cosmological constant. This possibility leads to a
finite, bouncing unitary cosmology. Whereas the usual Wheeler--DeWitt cosmology
generically displays pathological behaviour in terms of non-finite expectation
values and non-unitary dynamics, the finiteness and unitarity of our model are
formally guaranteed. For classically singular models with a massless scalar
field and cosmological constant, we show that well-behaved quantum observables
can be constructed and generic solutions to the universal Schr\"{o}dinger
equation are singularity-free. Generic solutions of our model displays novel
features including: i) superpositions of values of the cosmological constant;
ii) universal effective physics due to non-trivial self-adjoint extensions of
the Hamiltonian; and iii) bound `Efimov universe' states for negative
cosmological constant. The last feature provides a new platform for quantum
simulation of the early universe. A companion paper provides detailed
interpretation and analysis of particular cosmological solutions that display a
cosmic bounce due to quantum gravitational effects, a well-defined FLRW limit
far from the bounce, and a semi-classical turnaround point in the dynamics of
the scalar field which resembles an effective inflationary epoch.


  We study the dynamics of vortex nucleation and lattice formation in a
Bose--Einstein condensate in a rotating square optical lattice by numerical
simulations of the Gross--Pitaevskii equation. Different dynamical regimes of
vortex nucleation are found, depending on the depth and period of the optical
lattice. We make an extensive comparison with the experiments by Williams {\it
et al.} [Phys. Rev. Lett. {\bf 104}, 050404 (2010)], especially focusing on the
issues of the critical rotation frequency for the first vortex nucleation and
the vortex number as a function of rotation frequency.


  We derive in a straightforward way the spectrum of a hydrogen atom in a
strong magnetic field.


  We consider a financial market with one riskless and one risky asset. The
super-replication theorem states that there is no duality gap in the problem of
super-replicating a contingent claim under transaction costs and the associated
dual problem. We give two versions of this theorem. The first theorem relates a
num\'eraire-based admissibility condition in the primal problem to the notion
of a local martingale in the dual problem. The second theorem relates a
num\'eraire -free admissibility condition in the primal problem to the notion
of a uniformly integrable martingale in the dual problem.


  Various time variant non-stationary signals need to be pre-processed properly
in hydrological time series forecasting in real world, for example, predictions
of water level. Decomposition method is a good candidate and widely used in
such a pre-processing problem. However, decomposition methods with an
inappropriate sampling technique may introduce future data which is not
available in practical applications, and result in incorrect
decomposition-based forecasting models. In this work, a novel Fully Stepwise
Decomposition-Based (FSDB) sampling technique is well designed for the
decomposition-based forecasting model, strictly avoiding introducing future
information. This sampling technique with decomposition methods, such as
Variational Mode Decomposition (VMD) and Singular spectrum analysis (SSA), is
applied to predict water level time series in three different stations of
Guoyang and Chaohu basins in China. Results of VMD-based hybrid model using
FSDB sampling technique show that Nash-Sutcliffe Efficiency (NSE) coefficient
is increased by 6.4%, 28.8% and 7.0% in three stations respectively, compared
with those obtained from the currently most advanced sampling technique. In the
meantime, for series of SSA-based experiments, NSE is increased by 3.2%, 3.1%
and 1.1% respectively. We conclude that the newly developed FSDB sampling
technique can be used to enhance the performance of decomposition-based hybrid
model in water level time series forecasting in real world.


  We present a new version of the CompHEP program (version 4.4). We describe
shortly new issues implemented in this version, namely, simplification of quark
flavor combinatorics for the evaluation of hadronic processes, Les Houches
Accord based CompHEP-PYTHIA interface, processing the color configurations of
events, implementation of MSSM, symbolical and numerical batch modes, etc. We
discuss how the CompHEP program is used for preparing event generators for
various physical processes. We mention a few concrete physics examples for
CompHEP based generators prepared for the LHC and Tevatron.


  We prove that Keimel and Lawson's K-completion Kc of the simple valuation
monad Vs defines a monad Kc o Vs on each K-category A. We also characterize the
Eilenberg-Moore algebras of Kc o Vs as the weakly locally convex K-cones, and
its algebra morphisms as the continuous linear maps. In addition, we explicitly
describe the distributive law of Vs over Kc, which allows us to show that the
K-completion of any locally convex (respectively, weakly locally convex,
locally linear) topological cone is a locally convex (respectively, weakly
locally convex, locally linear) K-cone. We also give an example - the Cantor
tree with a top - that shows the dcpo-completion of the simple valuations is
not the D-completion of the simple valuations in general, where D is the
category of monotone convergence spaces and continuous maps.


  We present an updated version of Lightning, a galaxy spectral energy
distribution (SED) fitting code that can model X-ray to submillimeter
observations. The models in Lightning include the options to contain
contributions from stellar populations, dust attenuation and emission, and
active galactic nuclei (AGN). X-ray emission, when utilized, can be modeled as
originating from stellar compact binary populations with the option to include
emission from AGN. We have also included a variety of algorithms to fit the
models to observations and sample parameter posteriors; these include an
adaptive Markov-Chain Monte-Carlo (MCMC), affine-invariant MCMC, and
Levenberg-Marquardt gradient decent (MPFIT) algorithms. To demonstrate some of
the capabilities of Lightning, we present several examples using a variety of
observational data. These examples include (1) deriving the spatially resolved
stellar properties of the nearby galaxy M81, (2) demonstrating how X-ray
emission can provide constrains on the properties of the supermassive black
hole of a distant AGN, (3) exploring how to rectify the attenuation effects of
inclination on the derived the star formation rate of the edge-on galaxy NGC
4631, (4) comparing the performance of Lightning to similar Bayesian SED
fitting codes when deriving physical properties of the star-forming galaxy NGC
628, and (5) comparing the derived X-ray and UV-to-IR AGN properties from
Lightning and CIGALE for a distant AGN. Lightning is an open-source application
developed in the Interactive Data Language (IDL) and is available at
https://github.com/rafaeleufrasio/lightning.


  Representations of the Abelian-projected SU(2)- and SU(3)-gluodynamics in
terms of the magnetic monopole currents are derived. Besides the quadratic
part, the obtained effective actions contain interactions of these currents
with the world-sheets of electric strings in 4D or electric vortex lines in 3D.
Next, we illustrate that 3D compact QED is a small gauge boson mass limit of 3D
Abelian Higgs model with external monopoles and give a physical interpretation
to the confining string theory as the integral over the monopole densities.
Finally, we derive the bilocal field strength correlator in the weak-field
limit of 3D compact QED, which turns out to be in line with the one predicted
by the Stochastic Vacuum Model.


  We quantify possible differences between turbulent dynamo action in the Sun
and the dynamo action studied in idealized simulations. For this purpose we
compare Fourier-space shell-to-shell energy transfer rates of three
incrementally more complex dynamo simulations: an incompressible, periodic
simulation driven by random flow, a simulation of Boussinesq convection, and a
simulation of fully compressible convection that includes physics relevant to
the near-surface layers of the Sun. For each of the simulations studied, we
find that the dynamo mechanism is universal in the kinematic regime because
energy is transferred from the turbulent flow to the magnetic field from
wavenumbers in the inertial range of the energy spectrum. The addition of
physical effects relevant to the solar near-surface layers, including
stratification, compressibility, partial ionization, and radiative energy
transport, does not appear to affect the nature of the dynamo mechanism. The
role of inertial-range shear stresses in magnetic field amplification is
independent from outer-scale circumstances, including forcing and
stratification. Although the shell-to-shell energy transfer functions have
similar properties to those seen in mean-flow driven dynamos in each simulation
studied, the saturated states of these simulations are not universal because
the flow at the driving wavenumbers is a significant source of energy for the
magnetic field.


  We propose a three-stage load balancing packet switch and its configuration
scheme. The input- and central-stage switches are bufferless crossbars, and the
output-stage switches are buffered crossbars. We call this switch ThRee-stage
Clos-network swItch with queues at the middle stage and DEtermiNisTic
scheduling (TRIDENT), and the switch is cell based. The proposed configuration
scheme uses predetermined and periodic interconnection patterns in the input
and central modules to load-balance and route traffic, therefore; it has low
configuration complexity. The operation of the switch includes a mechanism
applied at input and output modules to forward cells in sequence. TRIDENT
achieves 100% throughput under uniform and nonuniform admissible traffic with
independent and identical distributions (i.i.d.). The switch achieves this high
performance using a low-complexity architecture while performing in-sequence
forwarding and no central-stage expansion or memory speedup. Our discussion
includes throughput analysis, where we describe the operations the
configuration mechanism performs on the traffic traversing the switch, and
proof of in-sequence forwarding. We present a simulation analysis as a
practical demonstration of the switch performance under uniform and nonuniform
i.i.d. traffic.


  The spin--network quantum simulator model, which essentially encodes the
(quantum deformed) SU(2) Racah--Wigner tensor algebra, is particularly suitable
to address problems arising in low dimensional topology and group theory. In
this combinatorial framework we implement families of finite--states and
discrete--time quantum automata capable of accepting the language generated by
the braid group, and whose transition amplitudes are colored Jones polynomials.
The automaton calculation of the polynomial of (the plat closure of) a link L
on 2N strands at any fixed root of unity is shown to be bounded from above by a
linear function of the number of crossings of the link, on the one hand, and
polynomially bounded in terms of the braid index 2N, on the other. The growth
rate of the time complexity function in terms of the integer k appearing in the
root of unity q can be estimated to be (polynomially) bounded by resorting to
the field theoretical background given by the Chern-Simons theory.


  We study the electronic properties of GaV4S8 (GVS) and GaTaSe8 (GTS), two
distant members within the large family of chalcogenides AM4X8, with A={Ga,
Ge}, M={V, Nb, Ta, Mo} and X={S, Se}. While all these compounds are Mott
insulators, their ground state show many types of magnetic order, with GVS
being ferromagnetic and GTS non-magnetic. Based on their bandstructures,
calculated with Density Functional Theory methods, we compute an effective
tight binding Hamiltonian in a localised Wannier basis set, for each one of the
two compounds. The localised orbitals provide a very accurate representation of
the bandstructure, with hopping amplitudes that rapidly decrease with distance.
We estimate the super-exchange interactions and show that the Coulomb repulsion
with the Hund's coupling may account the for the different ground states
observed in GVS and GTS. Our localised Wannier basis provides a starting point
for realistic Dynamical Mean Field Theory studies of strong correlation effects
in this family compounds.


  Accurate programming is a practical approach to producing high quality
programs. It combines ideas from test-automation, test-driven development,
agile programming, and other state of the art software development methods. In
addition to building on approaches that have proven effective in practice, it
emphasizes concepts that help programmers sharpen their understanding of both
the problems they are solving and the solutions they come up with. This is
achieved by encouraging programmers to think about programs in terms of
properties.


  Proton-proton fusion is considered in the effective field theory of Kaplan,
Savage and Wise. Coulomb effects are included systematically in a
non-perturbative way. Including the dimension-eight derivative coupling which
determines the effective ranges of the scattering amplitudes, next-to-leading
order corrections to the fusion rate are calculated. When the renormalization
mass is well above the characteristic energies of the system, this contribution
gives a rate which is eight percent below the standard value. The difference
can be due to an unknown counterterm which comes in at this order.


  A bound resembling Pascal's identity is presented for binary necklaces with
fixed density using Lyndon words with fixed density. The result is generalized
to k-ary necklaces and Lyndon words with fixed content. The bound arises in the
study of Nichols algebras of diagonal type.


  Quantum information processing architectures typically only allow for
nearest-neighbour entanglement creation. In many cases, this prevents the
direct generation of GHZ states, which are commonly used for many communication
and computation tasks. Here, we show how to obtain GHZ states between nodes in
a network that are connected in a straight line, naturally allowing them to
initially share linear cluster states. We prove a strict upper bound of
$\lfloor (n+3)/2 \rfloor$ on the size of the set of nodes sharing a GHZ state
that can be obtained from a linear cluster state of $n$ qubits, using local
Clifford unitaries, local Pauli measurements, and classical communication.
Furthermore, we completely characterize all selections of nodes below this
threshold that can share a GHZ state obtained within this setting. Finally, we
demonstrate these transformations on the IBMQ Montreal quantum device for
linear cluster states of up to $n=19$ qubits.


  We discuss some of the practical considerations that need to be made in the
design of extra-galactic field surveys using FIRST. We investigate the various
limitations that confusion noise imposes on possible FIRST surveys and the
benefits of super resolution or decconvolution techniques. We consider the
possible sizes and depths of survey fields in order to meet many of the
scientific objectives of the FIRST mission. In particular we discuss the
factors that need to be taken into account in selecting the survey fields. The
final choice of fields will be influenced by the location of other surveys that
are currently being planned; so it is vital that the FIRST community begin
debating this issue now. We conclude that a substantial survey of order of 100
square degrees is likely to be sited in the region of the SIRTF Legacy survey,
SWIRE.


  The Miniature X-ray Solar Spectrometer (MinXSS) is a 3 Unit (3U) CubeSat
designed for a 3-month mission to study solar soft X-ray spectral irradiance.
The first of the two flight models was deployed from the International Space
Station in 2016 May and operated for one year before its natural deorbiting.
This was the first flight of the Blue Canyon Technologies XACT 3-axis attitude
determination and control system -- a commercially available, high-precision
pointing system. We characterized the performance of the pointing system on
orbit including performance at low altitudes where drag torque builds up. We
found that the pointing accuracy was 0.0042\degree\ - 0.0117\degree\ (15$''$ -
42$''$, 3$\sigma$, axis dependent) consistently from 190 km - 410 km, slightly
better than the specification sheet states. Peak-to-peak jitter was estimated
to be 0.0073\degree\ (10 s$^{-1}$) - 0.0183\degree\ (10 s$^{-1}$) (26$''$ (10
s$^{-1}$) - 66$''$ (10 s$^{-1}$), 3$\sigma$). The system was capable of dumping
momentum until an altitude of 185 km. We found small amounts of sensor
degradation in the star tracker and coarse sun sensor. Our mission profile did
not require high-agility maneuvers so we are unable to characterize this
metric. Without a GPS receiver, it was necessary to periodically upload
ephemeris information to update the orbit propagation model and maintain
pointing. At 400 km, these uploads were required once every other week. At
$\sim$270 km, they were required every day. We also characterized the power
performance of our electric power system, which includes a novel pseudo-peak
power tracker -- a resistor that limited the current draw from the battery on
the solar panels. With 19 30\% efficient solar cells and an 8 W system load,
the power balance had 65\% of margin on orbit. We present several
recommendations to other CubeSat programs throughout.


  The theory of finitely supported algebraic structures represents a
reformulation of Zermelo-Fraenkel set theory in which every construction is
finitely supported according to the action of a group of permutations of some
basic elements named atoms. In this paper we study the properties of finitely
supported sets that contain infinite uniformly supported subsets, as well as
the properties of finitely supported sets that do not contain infinite
uniformly supported subsets. For classical atomic sets, we study whether they
contain or not infinite uniformly supported subsets.


  We report the parameter-free, density functional theory calculations of
interatomic exchange interactions and Curie temperatures of half-metallic
ferrimagnetic full Heusler alloys Mn2VZ (Z=Al, Ge). To calculate the
interatomic exchange interactions we employ the frozen-magnon approach. The
Curie temperatures are calculated within the mean-field approximation to the
classical Heisenberg Hamiltonian by solving a matrix equation for a
multi-sublattice system. Our calculations show that, although a large magnetic
moment is carried by Mn atoms, competing ferromagnetic (inter sublattice) and
antiferromagnetic (intra sublattice) Mn-Mn interactions in Mn2VAl almost cancel
each other in the mean-field experienced by the Mn atoms. In Mn2VGe the leading
Mn-Mn exchange interaction is antiferromagnetic. In both compounds the
ferromagnetism of the Mn subsystem is favored by strong antiferromagnetic Mn-V
interactions. The obtained value of the Curie temperature of Mn2VAl is in good
agrement with experiment. For Mn2VGe there is no experimental information
available and our calculation is a prediction.


  After one year since the entry into force of the GDPR, all web sites and data
controllers have updated their procedures to store users' data. The GDPR does
not only cover how and what data should be saved by the service providers, but
it also guarantees an easy way to know what data are collected and the freedom
to export them.
  In this paper, we carry out a comprehensive study on the right to access data
provided by Article 15 of the GDPR. We examined more than 300 data controllers,
performing for each of them a request to access personal data. We found that
almost each data controller has a slightly different procedure to fulfill the
request and several ways to provide data back to the user, from a structured
file like CSV to a screenshot of the monitor. We measure the time needed to
complete the access data request and the completeness of the information
provided. After this phase of data gathering, we analyze the authentication
process followed by the data controllers to establish the identity of the
requester. We find that 50.4\% of the data controllers that handled the
request, even if they store the data in compliance with the GDPR, have flaws in
the procedure of identifying the users or in the phase of sending the data,
exposing the users to new threats. With the undesired and surprising result
that the GDPR, in its present deployment, has actually decreased the privacy of
the users of web services.


  Recently, several studies involving open quantum systems which possess a
strong symmetry have observed that every individual trajectory in the Monte
Carlo unravelling of the master equation will dynamically select a specific
symmetry sector to freeze into in the long-time limit. This phenomenon has been
termed dissipative freezing, and in this paper we argue, by presenting several
simple mathematical perspectives on the problem, that it is a general
consequence of the presence of a strong symmetry in an open system with only a
few exceptions. Using a number of example systems we illustrate these
arguments, uncovering an explicit relationship between the spectral properties
of the Liouvillian in off-diagonal symmetry sectors and the time it takes for
freezing to occur. In the limiting case that eigenmodes with purely imaginary
eigenvalues are manifest in these sectors, freezing fails to occur. Such modes
indicate the preservation of information and coherences between symmetry
sectors of the system and can lead to phenomena such as non-stationarity and
synchronisation. The absence of freezing at the level of a single quantum
trajectory provides a simple, computationally efficient way of identifying
these traceless modes.


  The vast majority of world trade is carried by the sea shipping industry and
petroleum is still the major energy source. To reduce greenhouse gas emissions,
it is an urgent need for both industry and government to promote green
shipping. To move shipping towards a more environmentally and financially
sustainable future, we consider to develop an integrated fleet deployment and
bunker management model in this paper. The fleet deployment refers to the
decisions on which ships to operate on which route, at what speed and what
cargos to be transported. The bunker management refers to the decision on which
ships to bunker on which port and at what volume. A more realistic fuel
consumption function with considering not only cruise speed but also freight
tonnage on board is adopted in the proposed optimization model, which can
further improve its effectiveness in practice. An efficient algorithm termed
"Most Promising Area Search" (MPAS) is developed afterwards to solve the
corresponding mixed integer programming problem, which can guarantee to
converge to a local optimal solution. The benefits of the integrated model and
the computational performance of the MPAS are illustrated by numerical examples
and a case study.


  We propose a mechanism of a long-range coherent interaction between two
singlet-triplet qubits dipolarly coupled to a dogbone-shaped ferromagnet. An
effective qubit-qubit interaction Hamiltonian is derived and the coupling
strength is estimated. Furthermore we derive the effective coupling between two
spin-1/2 qubits that are coupled via dipolar interaction to the ferromagnet and
that lie at arbitrary positions and deduce the optimal positioning. We consider
hybrid systems consisting of spin-1/2 and ST qubits and derive the effective
Hamiltonian for this case. We then show that operation times vary between 1MHz
and 100MHz and give explicit estimates for GaAs, Silicon, and NV-center based
spin qubits. Finally, we explicitly construct the required sequences to
implement a CNOT gate. The resulting quantum computing architecture retains all
the single qubit gates and measurement aspects of earlier approaches, but
allows qubit spacing at distances of order 1$\,\mu$m for two-qubit gates,
achievable with current semiconductor technology.


  We show that in supersymmetric extensions of the Standard Model gluino box
diagrams can yield a large Delta(I)=3/2 contribution to s->d+q(bar)+q FCNC
processes, which may induce a sizable CP-violating contribution to the I=2
isospin amplitude in K->pi+pi decays. This contribution only requires moderate
mass splitting between the right-handed up- and down-squarks, and persists for
squark masses of order 1 TeV. Taking into account current bounds on
Im(delta_{sd}^{LL}) from K-K(bar) mixing, the resulting contribution to
epsilon'/epsilon could be an order of magnitude larger than the measured value.


  Fully robust versions of the elastic net estimator are introduced for linear
and logistic regression. The algorithms to compute the estimators are based on
the idea of repeatedly applying the non-robust classical estimators to data
subsets only. It is shown how outlier-free subsets can be identified
efficiently, and how appropriate tuning parameters for the elastic net
penalties can be selected. A final reweighting step improves the efficiency of
the estimators. Simulation studies compare with non-robust and other competing
robust estimators and reveal the superiority of the newly proposed methods.
This is also supported by a reasonable computation time and by good performance
in real data examples.


  To date, most probabilistic reasoning systems have relied on a fixed belief
network constructed at design time. The network is used by an application
program as a representation of (in)dependencies in the domain. Probabilistic
inference algorithms operate over the network to answer queries. Recognizing
the inflexibility of fixed models has led researchers to develop automated
network construction procedures that use an expressive knowledge base to
generate a network that can answer a query. Although more flexible than fixed
model approaches, these construction procedures separate construction and
evaluation into distinct phases. In this paper we develop an approach to
combining incremental construction and evaluation of a partial probability
model. The combined method holds promise for improved methods for control of
model construction based on a trade-off between fidelity of results and cost of
construction.


  We consider the division of a finite number of homogeneous divisible items
among three players. Under the assumption that each player assigns a positive
value to every item, we characterize the optimal allocations and we develop two
exact algorithms for its search. Both the characterization and the algorithm
are based on the tight relationship two geometric objects of fair division: the
Individual Pieces Set (IPS) and the Radon-Nykodim Set (RNS).


  Effective biological utilization of wood biomass is necessary worldwide.
Since several insect larvae can use wood biomass as a nutrient source, studies
on their digestive mechanism are expected to speculate a novel rule in wood
biomass processing. Here, the relationships of inhabitant bacteria involved in
carbon and nitrogen metabolism in the intestine of beetle larvae, an insect
model, are investigated. Bacterial analysis of larval feces showed enrichment
of members of which could include candidates for plant growth promotion,
nitrogen cycle modulation, and/or environmental protection. The abundances of
these bacteria were not necessarily positively correlated with the abundance in
the habitat, suggesting that they might be selectively enriched in the
intestines of larvae. Further association analysis predicted that carbon and
nitrogen metabolism in the intestine was affected by the presence of the other
common bacteria, the populations of which were not remarkably altered in the
habitat and feces. Based on hypotheses targeting these selected bacterial
groups, structural estimation modeling analyses statistically suggested that
their metabolism of carbon and nitrogen and their stable isotopes, {\delta}13C
and {\delta}15N, may be associated with fecal enriched bacteria and other
common bacteria. In addition, other causal inference analyses, such as causal
mediation analysis, linear non-Gaussian acyclic model (LiNGAM), and
BayesLiNGAM, did not necessarily affirm the existence of prominent bacteria
involved in metabolism, implying its importance as the bacterial groups for
metabolism rather than a remarkable bacterium. Thus, these observations
highlight a multifaceted view of symbiotic bacterial groups utilizing carbon
and nitrogen from wood biomass in insect larvae as a cultivator of potentially
environmentally beneficial bacteria.


  Spin-polarized symmetric nuclear matter is studied within the
Dirac-Brueckner-Hartree-Fock approach. We pay particular attention to the
difference between the one-body potentials of upward and downward polarized
nucleons. This is formally analogous to the "Lane potential" for
isospin-asymmetric nuclear matter. We point out the necessity for additional
information on this fundamentally important quantity and suggest ways to
constrain it.


  In recent times, Large Language Models (LLMs) have captured a global
spotlight and revolutionized the field of Natural Language Processing. One of
the factors attributed to the effectiveness of LLMs is the model architecture
used for training, transformers. Transformer models excel at capturing
contextual features in sequential data since time series data are sequential,
transformer models can be leveraged for more efficient time series data
prediction. The field of prognostics is vital to system health management and
proper maintenance planning. A reliable estimation of the remaining useful life
(RUL) of machines holds the potential for substantial cost savings. This
includes avoiding abrupt machine failures, maximizing equipment usage, and
serving as a decision support system (DSS). This work proposed an
encoder-transformer architecture-based framework for multivariate time series
prediction for a prognostics use case. We validated the effectiveness of the
proposed framework on all four sets of the C-MAPPS benchmark dataset for the
remaining useful life prediction task. To effectively transfer the knowledge
and application of transformers from the natural language domain to time
series, three model-specific experiments were conducted. Also, to enable the
model awareness of the initial stages of the machine life and its degradation
path, a novel expanding window method was proposed for the first time in this
work, it was compared with the sliding window method, and it led to a large
improvement in the performance of the encoder transformer model. Finally, the
performance of the proposed encoder-transformer model was evaluated on the test
dataset and compared with the results from 13 other state-of-the-art (SOTA)
models in the literature and it outperformed them all with an average
performance increase of 137.65% over the next best model across all the
datasets.


  The magnetohydrodynamic (MHD) equations of incompressible viscous fluids with
finite electrical conductivity describe the motion of viscous electrically
conducting fluids in a magnetic field. In this paper, we find twelve families
of solutions of these equations by Xu's asymmetric and moving frame methods. A
family of singular solutions may reflect basic characteristics of vortices. The
other solutions are globally analytic with respect to the spacial variables. In
particular, Bernoulli equation and Wronskian determinants play important roles
in our approaches. Our solutions may also help engineers to develop more
effective algorithms to find physical numeric solutions to practical models.


  Proceedings of the Second Croatian Computer Vision Workshop (CCVW 2013,
http://www.fer.unizg.hr/crv/ccvw2013) held September 19, 2013, in Zagreb,
Croatia. Workshop was organized by the Center of Excellence for Computer Vision
of the University of Zagreb.


  We develop Morse theory for manifolds with boundary. Besides standard and
expected facts like the handle cancellation theorem and the Morse lemma for
manifolds with boundary, we prove that, under a topological assumption, a
critical point in the interior of a Morse function can be moved to the
boundary, where it splits into a pair of boundary critical points. As an
application, we prove that every cobordism of manifolds with boundary splits as
a union of left product cobordisms and right product cobordisms.


  We explore the feasibility of estimating primary cosmic ray composition at
ultra high energies from the study of lateral age parameter of Extensive Air
Showers (EAS) at ground level. Using different types of lateral distribution
functions, we fit the particle density of simulated EAS to find the lateral age
parameter. We discuss the chemical composition calculating the merit factor for
each parameter distribution. The analysis considers three different primary
particles (proton, iron and gamma), four different zenith angles (0{\deg},
15{\deg}, 30{\deg} and 45{\deg}) and three primary energies (10^{17.25} eV,
10^{17.50} eV and 10^{17.75} eV).


  Multi-access edge computing (MEC) emerges as an essential part of the
upcoming Fifth Generation (5G) and future beyond-5G mobile communication
systems. It adds computational power towards the edge of cellular networks,
much closer to energy-constrained user devices, and therewith allows the users
to offload tasks to the edge computing nodes for low-latency applications with
very-limited battery consumption. However, due to the high dynamics of user
demand and server load, task congestion may occur at the edge nodes resulting
in long queuing delay. Such delays can significantly degrade the quality of
experience (QoE) of some latency-sensitive applications, raise the risk of
service outage, and cannot be efficiently resolved by conventional queue
management solutions.
  In this article, we study a latency-outage critical scenario, where users
intend to limit the risk of latency outage. We propose an impatience-based
queuing strategy for such users to intelligently choose between MEC offloading
and local computation, allowing them to rationally renege from the task queue.
The proposed approach is demonstrated by numerical simulations to be efficient
for generic service model, when a perfect queue status information is
available. For the practical case where the users obtain only imperfect queue
status information, we design an optimal online learning strategy to enable its
application in Poisson service scenarios.


  Let $G$ be a simple algebraic group of exceptional type over an algebraically
closed field of characteristic $p > 0$. This paper continues a long-standing
effort to classify the connected reductive subgroups of $G$. Having previously
completed the classification when $p$ is sufficiently large, we focus here on
the case that $p$ is bad for $G$. We classify the connected reductive subgroups
of $G$ which are not $G$-completely reducible, whose simple components have
rank at least $3$. For each such subgroup $X$, we determine the action of $X$
on the adjoint module $L(G)$ and on a minimal non-trivial $G$-module, and the
connected centraliser of $X$ in $G$. As corollaries we obtain information on:
subgroups which are maximal among connected reductive subgroups; products of
commuting $G$-completely reducible subgroups; subgroups with trivial connected
centraliser; and subgroups which act indecomposably on an adjoint or minimal
module for $G$.


  Global pointwise estimates are obtained for quasilinear Lane-Emden-type
systems involving measures in the "sublinear growth" rate. We give necessary
and sufficient conditions for existence expressed in terms of Wolff's
potential. Our approach is based on recent advances due to Kilpel\"{a}inen and
Mal\'{y} in the potential theory. This method enables us to treat several
problems, such as equations involving general quasilinear operators and
fractional Laplacian.


  Background Little is known about the population pharmacokinetics (PPK) of
tacrolimus (TAC) in pediatric primary nephrotic syndrome (PNS). This study
aimed to compare the predictive performance between nonlinear and linear PK
models and investigate the significant factors of TAC PK characteristics in
pediatric PNS. Methods Data were obtained from 71 pediatric patients with PNS,
along with 525 TAC trough concentrations at steady state. The demographic,
medical, and treatment details were collected. Genetic polymorphisms were
analyzed. The PPK models were developed using nonlinear mixed effects model
software. Two modeling strategies, linear compartmental and nonlinear Michaelis
Menten (MM) models, were evaluated and compared. Results Body weight, age,
daily dose of TAC, co-therapy drugs (including azole antifungal agents and
diltiazem), and CYP3A5*3 genotype were important factors in the final linear
model (onecompartment model), whereas only body weight, codrugs, and CYP3A5*3
genotype were the important factors in the nonlinear MM model. Apparent
clearance and volume of distribution in the final linear model were 7.13 L/h
and 142 L, respectively. The maximal dose rate (Vmax) of the nonlinear MM model
was 1.92 mg/day and the average concentration at steady state at half-Vmax (Km)
was 1.98 ng/mL. The nonlinear model described the data better than the linear
model. Dosing regimens were proposed based on the nonlinear PK model.Conclusion
Our findings demonstrate that the nonlinear MM model showed better predictive
performance than the linear compartmental model, providing reliable support for
optimizing TAC dosing and adjustment in children with PNS.


  In this paper we characterize the Pr\"ufer v-multiplication domain as a class
of essential domains verifying an additional property on the closure of some
families of prime ideals, with respect to the constructible topology.


  We report results from searches for neutral Higgs bosons produced in p-pbar
collisions recorded by the Dzero experiment at the Fermilab Tevatron Collider.
We study the production of inclusive neutral Higgs boson in the tautau final
state and in association with a b quark in the btautau and bbb final states.
These results are combined to improve the sensitivity to the production of
neutral Higgs bosons in the context of the minimal supersymmetric standard
model (MSSM). The data are found to be consistent with expectation from
background processes. Upper limits on MSSM Higgs boson production are set for
Higgs boson masses ranging from 90 to 300 GeV. We exclude tanBeta>20-30 for
Higgs boson masses below 180 GeV. These are the most stringent constraints on
MSSM Higgs boson production in p-pbar collisions.


  Predicting human trajectories is a challenging task due to the complexity of
pedestrian behavior, which is influenced by external factors such as the
scene's topology and interactions with other pedestrians. A special challenge
arises from the dependence of the behaviour on the density of the scene. In the
literature, deep learning algorithms show the best performance in predicting
pedestrian trajectories, but so far just for situations with low densities. In
this study, we aim to investigate the suitability of these algorithms for
high-density scenarios by evaluating them on different error metrics and
comparing their accuracy to that of knowledge-based models that have been used
since long time in the literature. The findings indicate that deep learning
algorithms provide improved trajectory prediction accuracy in the distance
metrics for all tested densities. Nevertheless, we observe a significant number
of collisions in the predictions, especially in high-density scenarios. This
issue arises partly due to the absence of a collision avoidance mechanism
within the algorithms and partly because the distance-based collision metric is
inadequate for dense situations. To address these limitations, we propose the
introduction of a novel continuous collision metric based on pedestrians'
time-to-collision. Subsequently, we outline how this metric can be utilized to
enhance the training of the algorithms.


  Three-dimensional topological textures have become a topic of intense
interest in recent years. Through analytical calculations, this work determines
the magnetostatic field produced by a Bloch Point (BP) singularity confined in
a magnetic nanosphere. It is observed that BPs hosted in a nanosphere generate
magnetic fields with quadrupolar nature. This finding is interesting because it
shows the possibility of obtaining quadrupole magnetic fields with just one
magnetic particle, unlike other propositions considering arrays of magnetic
elements to generate this kind of field. The obtained magnetostatic field
allows us to determine the interaction between two BPs as a function of the
relative orientation of their polarities and the distance between them. It is
shown that depending on the rotation of one BP related to the other, the
magnetostatic interaction varies in strength and character, being attractive or
repulsive. The obtained results reveal that the BP interaction has a complex
behavior beyond topological charge-mediated interaction.


  A theorem due to Kazhdan and Ziegler implies that, by substituting linear
forms for its variables, a homogeneous polynomial of sufficiently high strength
specialises to any given polynomial of the same degree in a bounded number of
variables. Using entirely different techniques, we extend this theorem to
arbitrary polynomial functors. As a corollary of our work, we show that
specialisation induces a quasi-order on elements in polynomial functors, and
that among the elements with a dense orbit there are unique smallest and
largest equivalence classes in this quasi-order.


  QCD at finite isospin chemical potential mu_I has no fermion sign problem and
can be studied on the lattice. We solve this theory analytically in two limits:
at low mu_I where chiral perturbation theory is applicable, and at
asymptotically high mu_I where perturbative QCD works. At low isospin density
the ground state is a pion condensate, whereas at high density it is a Fermi
liquid with Cooper pairing. The pairs carry the same quantum numbers as the
pion. This leads us to a conjecture that the transition from hadron to quark
matter is smooth, which passes several tests. Our results imply a nontrivial
phase diagram in the space of temperature and chemical potentials of isospin
and baryon number.


  The topology and form finding of tensegrity structures have been studied
extensively since the introduction of the tensegrity concept. However, most of
these studies address topology and form separately, where the former
represented a research focus of rigidity theory and graph theory, while the
latter attracted the attention of structural engineers. In this paper, a
biomimetic approach for the combined topology and form finding of spatial
tensegrity systems is introduced. Tensegrity cells, elementary infinitesimally
rigid self-stressed structures that have been proven to compose any tensegrity,
are used to generate more complex tensegrity structures through the
morphogenesis mechanisms of adhesion and fusion. A methodology for constructing
a basis to describe the self-stress space is also provided. Through the
definition of self-stress, the cellular morphogenesis method can integrate
design considerations, such as a desired shape or number of nodes and members,
providing great flexibility and control over the tensegrity structure
generated.


  We consider dynamics of Bose-Einstein condensates with long-range attractive
interaction proportional to $1/r^b$ and arbitrary angular dependence. It is
shown exactly that collapse of Bose-Einstein condensate without contact
interactions is possible only for $b\ge 2$. Case $b=2$ is critical and requires
number of particles to exceed critical value to allow collapse. Critical
collapse in that case is strong one trapping into collapsing region a finite
number of particles.
  Case $b>2$ is supercritical with expected weak collapse which traps rapidly
decreasing number of particles during approach to collapse. For $b<2$
singularity at $r=0$ is not strong enough to allow collapse but attractive
$1/r^b$ interaction admits stable self-trapping even in absence of external
trapping potential.


  A projective symplectic variety $\mathcal{P}$ of dimension 6, with only
finite quotient singularities, $\pi(\mathcal{P})=0$ and
$h^{(2,0)}(\mathcal{P}_{smooth})=1$, is described as a relative compactified
Prym variety of a family of genus 4 curves with involution. It is a Lagrangian
fibration associated to a K3 surface double cover of a generic cubic surface.
It has no symplectic desingularization.


  Verifying properties and interpreting the behaviour of deep neural networks
(DNN) is an important task given their ubiquitous use in applications,
including safety-critical ones, and their black-box nature. We propose an
automata-theoric approach to tackling problems arising in DNN analysis. We show
that the input-output behaviour of a DNN can be captured precisely by a
(special) weak B\"uchi automaton and we show how these can be used to address
common verification and interpretation tasks of DNN like adversarial robustness
or minimum sufficient reasons.


  For many next-generation high intensity proton accelerator applications
including the Spallation Neutron Source (SNS), superconducting (SC) RF provides
the technology of choice for the linac. In designing the superconducting
cavity, several features, such as peak fields, inter-cell coupling, mechanical
stiffness, field flatness, external Q, manufacturability, shunt impedance,
higher order mode (HOM), etc., should be considered together. A systematic
approach to determine the optimum cavity shape by exploring the entire
geometric space of the cavity has been found. The most efficient use of RF
energy can be accomplished by adjusting the cell shape. A small region in
parameter space satisfying all reasonable design criteria has been found. With
this design procedure, choosing the optimum shape is simplified. In this paper,
the whole design procedure of this optimisation scheme is explained and applied
to the SNS cavity design.


  In the present paper, we define two directed pseudo graphs. Then, we
investigate the adjacency matrices of the defined graphs and show that the
permanents of the adjacency matrices are Jacobsthal and Jacobsthal-Lucas
numbers.


  This is the first paper of a series. We prove an arithmetic Hodge index
theorem for adelic line bundles on projective varieties over number fields. It
extends the arithmetic Hodge index theorem of Faltings, Hriljac and Moriwaki on
arithmetic varieties. As consequences, we obtain the uniqueness part of the
non-archimedean Calabi--Yau theorem, and a rigidity property of the sets of
preperiodic points of polarizable algebraic dynamical systems over number
fields.


  Cross-lingual summarization (CLS) has attracted increasing interest in recent
years due to the availability of large-scale web-mined datasets and the
advancements of multilingual language models. However, given the rareness of
naturally occurring CLS resources, the majority of datasets are forced to rely
on translation which can contain overly literal artifacts. This restricts our
ability to observe naturally occurring CLS pairs that capture organic diction,
including instances of code-switching. This alteration between languages in
mid-message is a common phenomenon in multilingual settings yet has been
largely overlooked in cross-lingual contexts due to data scarcity. To address
this gap, we introduce CroCoSum, a dataset of cross-lingual code-switched
summarization of technology news. It consists of over 24,000 English source
articles and 18,000 human-written Chinese news summaries, with more than 92% of
the summaries containing code-switched phrases. For reference, we evaluate the
performance of existing approaches including pipeline, end-to-end, and
zero-shot methods. We show that leveraging existing CLS resources as a
pretraining step does not improve performance on CroCoSum, indicating the
limited generalizability of current datasets. Finally, we discuss the
challenges of evaluating cross-lingual summarizers on code-switched generation
through qualitative error analyses.


  Fluctuations of non-Abelian gauge fields in a background magnetic flux
contain tachyonic modes and hence the background is unstable. We extend these
results to the cases where the background flux is coupled to Einstein gravity
and show that the corresponding spherically symmetric geometries, which in the
absence of a cosmological constant are of the form of Reissner-Nordstrom
blackholes or the AdS_2xS^2, are also unstable. We discuss the relevance of
these instabilities to several places in string theory including various string
compactifications and the attractor mechanism. Our results for the latter imply
that the attractor mechanism shown to work for the extremal Abelian charged
blackholes, cannot be applied in a straightforward way to the extremal
non-Abelian colored blackholes.


  The video exhibits experimental qualitative and quantitative results of
water/glycerol (50%/50% by mass) droplet impact on two types of micro-patterned
superhydrophobic surfaces. The two types of surfaces used were 80% cavity
fraction ribs and posts with a periodic spacing of 40 {\mu}m and 32 {\mu}m,
respectively. All surfaces were manufactured through photolithography. The
impact Weber number is used as the dynamic parameter to compare splash and
rebound behaviors between the two types of surfaces. While droplets exhibit
similar dynamics at low Weber numbers, rebound jet speed (normalized by droplet
impact speed) is notably higher on posts than ribs for all Weber numbers tested
here (5<We<900). At elevated Weber numbers, droplets splash peripherally. These
side droplets created at splash are referred to as satellite droplets. Top view
videos show the significant difference in splashing behavior for the two
surface types. On ribs, satellite droplet formation consistently prefers a path
60{\deg} from the ribs longitudinal direction. This behavior prevails for Weber
numbers greater than 150, however, distinguished splashing does not occur for
We > 265. On posts, satellite droplets also follow a specific path but in a
different orientation. Satellite droplets form in locations aligned with the
post lattice structure. This behavior is observed for 600 < We < 750. Jet
rebound exhibits an interesting phenomenon on ribs under certain conditions.
Due to the uneven shear distribution on the retracting droplet due to the
surface anisotropy, two jets form at rebound and are referred to as two-pronged
jets. This behavior occurs for 115 < We < 265 on ribs. Two-pronged jets are
also observed on posts but are less coherent and less repetitive. This behavior
was observed at around 500 < We < 600.


  In this paper we consider two sources of enhancement for the meshfree
Lagrangian particle method smoothed particle hydrodynamics (SPH) by improving
the accuracy of the particle approximation. Namely, we will consider shape
functions constructed using: moving least-squares approximation (MLS); radial
basis functions (RBF). Using MLS approximation is appealing because polynomial
consistency of the particle approximation can be enforced. RBFs further appeal
as they allow one to dispense with the smoothing-length -- the parameter in the
SPH method which governs the number of particles within the support of the
shape function. Currently, only ad hoc methods for choosing the
smoothing-length exist. We ensure that any enhancement retains the conservative
and meshfree nature of SPH. In doing so, we derive a new set of
variationally-consistent hydrodynamic equations. Finally, we demonstrate the
performance of the new equations on the Sod shock tube problem.


  We propose a simple approach to study the conductance through an array of $N$
interacting quantum dots, weakly coupled to metallic leads. Using a mapping to
an effective site which describes the low-lying excitations and a slave-boson
representation in the saddle-point approximation, we calculated the conductance
through the system. Explicit results are presented for N=1 and N=3: a linear
array and an isosceles triangle. For N=1 in the Kondo limit, the results are in
very good agreement with previous results obtained with numerical
renormalization group (NRG). In the case of the linear trimer for odd $N$, when
the parameters are such that electron-hole symmetry is induced, we obtain
perfect conductance $G_0=2e^2/h$. The validity of the approach is discussed in
detail.


  Diagnosis-oriented dialogue system queries the patient's health condition and
makes predictions about possible diseases through continuous interaction with
the patient. A few studies use reinforcement learning (RL) to learn the optimal
policy from the joint action space of symptoms and diseases. However, existing
RL (or Non-RL) methods cannot achieve sufficiently good prediction accuracy,
still far from its upper limit. To address the problem, we propose a decoupled
automatic diagnostic framework DxFormer, which divides the diagnosis process
into two steps: symptom inquiry and disease diagnosis, where the transition
from symptom inquiry to disease diagnosis is explicitly determined by the
stopping criteria. In DxFormer, we treat each symptom as a token, and formalize
the symptom inquiry and disease diagnosis to a language generation model and a
sequence classification model respectively. We use the inverted version of
Transformer, i.e., the decoder-encoder structure, to learn the representation
of symptoms by jointly optimizing the reinforce reward and cross entropy loss.
Extensive experiments on three public real-world datasets prove that our
proposed model can effectively learn doctors' clinical experience and achieve
the state-of-the-art results in terms of symptom recall and diagnostic
accuracy.


  This work presents an algorithm for numerically computing Maass forms and
their eigenvalues for Fuchsian groups of infinite covolume. By
Patterson-Sullivan theory, this has the added benefit of computing Hausdorff
dimensions of the limit sets of these groups. To approximate Maass forms, we
consider their Fourier expansions in different coordinate systems. To handle
infinite volume fundamental domains, we make use of the concept of flare
domains. We also develop theory about Fourier expansions in flare domains which
mimics the classical theory on expansions with respect to cusps. Finally, we
present detailed examples of the algorithm applied to symmetric Schottky groups
and infinite volume Hecke groups.


  We present a photometric analysis of the star clusters Lindsay 1, Kron 3,
NGC339, NGC416, Lindsay 38, and NGC419 in the Small Magellanic Cloud (SMC),
observed with the Hubble Space Telescope Advanced Camera for Surveys (ACS) in
the F555W and F814W filters. Our color magnitude diagrams (CMDs) extend ~3.5
mag deeper than the main-sequence turnoff points, deeper than any previous
data. Cluster ages were derived using three different isochrone models: Padova,
Teramo, and Dartmouth, which are all available in the ACS photometric system.
Fitting observed ridgelines for each cluster, we provide a homogeneous and
unique set of low-metallicity, single-age fiducial isochrones. The cluster CMDs
are best approximated by the Dartmouth isochrones for all clusters, except for
NGC419 where the Padova isochrones provided the best fit. The CMD of NGC419
shows several main-sequence turn-offs, which belong to the cluster and to the
SMC field. We thus derive an age range of 1.2-1.6 Gyr for NGC419.
Interestingly, our intermediate-age star clusters have a metallicity spread of
~0.6 dex, which demonstrates that the SMC does not have a smooth, monotonic
age-metallicity relation. We find an indication for centrally concentrated blue
straggler star candidates in NGC416, while for the other clusters these are not
present. Using the red clump magnitudes, we find that the closest cluster,
NGC419 (~50kpc), and the farthest cluster, Lindsay 38 (~67kpc), have a relative
distance of ~17kpc, which confirms the large depth of the SMC.


  Detecting influential features in non-linear and/or high-dimensional data is
a challenging and increasingly important task in machine learning. Variable
selection methods have thus been gaining much attention as well as
post-selection inference. Indeed, the selected features can be significantly
flawed when the selection procedure is not accounted for. We propose a
selective inference procedure using the so-called model-free "HSIC-Lasso" based
on the framework of truncated Gaussians combined with the polyhedral lemma. We
then develop an algorithm, which allows for low computational costs and
provides a selection of the regularisation parameter. The performance of our
method is illustrated by both artificial and real-world data based experiments,
which emphasise a tight control of the type-I error, even for small sample
sizes.


  A more complete understanding of entanglement entropy in a covariant manner
could inform the search for quantum gravity. We build on work in this direction
by extending previous results to disjoint regions in $1+1$D. We investigate the
entanglement entropy of a scalar field in disjoint intervals within the causal
set framework, using the spacetime commutator and correlator,
$i\mathbf{\Delta}$ and $\mathbf{W}$ (or the Pauli-Jordan and Wightman
functions), respectively. A new truncation scheme for disjoint causal diamonds
is presented, which follows from the single diamond truncation scheme. We
investigate setups including two and three disjoint causal diamonds, as well as
a single causal diamond that shares a boundary with a larger global causal
diamond. In all the cases that we study, our results agree with the expected
area laws. In addition, we study the mutual information in the two disjoint
diamonds setup. The ease of our calculations indicate our methods to be a
useful tool for numerically studying such systems. We end with a discussion of
some of the strengths and future applications of the spacetime formulation we
use in our entanglement entropy computations, both in causal set theory and in
the continuum.


  Malicious domains are one of the major resources required for adversaries to
run attacks over the Internet. Due to the important role of the Domain Name
System (DNS), extensive research has been conducted to identify malicious
domains based on their unique behavior reflected in different phases of the
life cycle of DNS queries and responses. Existing approaches differ
significantly in terms of intuitions, data analysis methods as well as
evaluation methodologies. This warrants a thorough systematization of the
approaches and a careful review of the advantages and limitations of every
group.
  In this paper, we perform such an analysis. In order to achieve this goal, we
present the necessary background knowledge on DNS and malicious activities
leveraging DNS. We describe a general framework of malicious domain detection
techniques using DNS data. Applying this framework, we categorize existing
approaches using several orthogonal viewpoints, namely (1) sources of DNS data
and their enrichment, (2) data analysis methods, and (3) evaluation strategies
and metrics. In each aspect, we discuss the important challenges that the
research community should address in order to fully realize the power of DNS
data analysis to fight against attacks leveraging malicious domains.


  In this work, a flexible higher-order space-time adaptive finite element
approximation of convection-dominated transport with coupled fluid flow is
developed and studied. Convection-dominated transport is a challenging
subproblem in poromechanics in which coupled transport with flow, chemical
reaction and mechanical response in porous media is considered. Key ingredients
are the arbitrary degree discontinuous Galerkin time discretization of the
primal and dual problems for the Dual Weighted Residual (DWR) approach, an a
posteriori error estimation for the transport problem coupled with flow and its
implementation in an advanced software architecture. The error estimate allows
the separation of the temporal and spatial discretization error contributions
which facilitates the simultaneous adjustment of the time and space mesh. The
performance of the approach and its software implementation is studied by
numerical convergence examples as well as an example of physical interest for
convection-dominated cases.


  We review the theoretical and experimental progress in the Glauber model of
multiple nucleon and/or parton scatterings, after the last 10--15 years of
operation with proton and nuclear beams at the CERN Large Hadron Collider (LHC)
and with various light and heavy colliding ions at the BNL Relativistic Heavy
Ion Collider (RHIC). The main developments and the state-of-the-art of the
field are summarized. These encompass measurements of the inclusive inelastic
proton and nuclear cross sections, advances in the description of the proton
and nuclear density profiles and their fluctuations, inclusion of subnucleonic
degrees of freedom, experimental procedures and issues related to the
determination of the collision centrality, validation of the binary scaling
prescription for hard scattering cross sections, and constraints on transport
properties of quark-gluon matter from varying initial-state conditions in
relativistic hydrodynamics calculations. These advances confirm the validity
and usefulness of the Glauber formalism for quantitative studies of QCD matter
produced in high-energy collisions of systems, from protons to uranium nuclei,
of vastly different size.


  Learning relations based on evidence from knowledge bases relies on
processing the available relation instances. Many relations, however, have
clear domain and range, which we hypothesize could help learn a better, more
generalizing, model. We include such information in the RESCAL model in the
form of a regularization factor added to the loss function that takes into
account the types (categories) of the entities that appear as arguments to
relations in the knowledge base. We note increased performance compared to the
baseline model in terms of mean reciprocal rank and hits@N, N = 1, 3, 10.
Furthermore, we discover scenarios that significantly impact the effectiveness
of the type regularizer.


  We present a protocol for an atomic interferometer that reaches the
Heisenberg Limit (HL), within a factor of $\sim$ $\sqrt{2}$, via collective
state detection and critical tuning of one-axis twist spin squeezing. It
generates a Schr\"odinger cat (SC) state, as a superposition of two extremal
collective states. When this SC interferometer is used as a gyroscope, the
interference occurs at an ultrahigh Compton frequency, corresponding to a
mesoscopic single object with a mass of $Nm$, where $N$ is the number of
particles in the ensemble, and $m$ is the mass of each particle. For $^{87}$Rb
atoms, with $N=10^{6}$, for example, the intereference would occur at a Compton
frequency of $\sim$ $2 \times 10^{31}$ Hz. Under this scheme, the signal is
found to depend critically on the parity of $N$. We present two variants of the
protocol. Under Protocol A, the fringes are narrowed by a factor of $N$ for one
parity, while for the other parity the signal is zero. Under Protocol B, the
fringes are narrowed by a factor of $N$ for one parity, and by a factor of
$\sqrt{N}$ for the other parity. Both protocols can be modified in a manner
that reverses the behavior of the signals for the two parities. Over repeated
measurements under which the probability of being even or odd is equal, the
averaged sensitivity is smaller than the HL by a factor of $\sim$ $\sqrt{2}$
for both versions of the protocol. We show that when the SC interferometer is
configured as an accelerometer, the effective two-photon wave vector is
enhanced by a factor of $N$, leading to the same degree of enhancement in
sensitivity. We also show that such a mesoscopic single object can be used to
increase the effective base frequency of an atomic clock by a factor of $N$,
with a sensitivity that is equivalent to the HL, within a factor of $\sim$
$\sqrt{2}$.


  Understanding NP-complete problems is a central topic in computer science.
This is why adiabatic quantum optimization has attracted so much attention, as
it provided a new approach to tackle NP-complete problems using a quantum
computer. The efficiency of this approach is limited by small spectral gaps
between the ground and excited states of the quantum computer's Hamiltonian. We
show that the statistics of the gaps can be analyzed in a novel way, borrowed
from the study of quantum disordered systems in statistical mechanics. It turns
out that due to a phenomenon similar to Anderson localization, exponentially
small gaps appear close to the end of the adiabatic algorithm for large random
instances of NP-complete problems. This implies that unfortunately, adiabatic
quantum optimization fails: the system gets trapped in one of the numerous
local minima.


  In the matching problem, each node maintains a pointer to one of its neighbor
or to $null$, and a maximal matching is computed when each node points either
to a neighbor that itself points to it (they are then called married), or to
$null$, in which case no neighbor can also point to $null$. This paper presents
a self-stabilizing distributed algorithm to compute a maximal matching in the
link-register model under read/write atomicity, with complexity
{$O(n\Delta^3)$} moves under the adversarial distributed daemon, where $\Delta$
is the maximum degree of the graph.


  Phenomenological models of the dipole cross section that enters in the
description of for instance deep inelastic scattering at very high energies
have had considerable success in describing the available small-x data in both
the saturation region and the so-called extended geometric scaling (EGS)
region. We investigate to what extent such models are compatible with the
numerical solutions of the Balitsky-Kovchegov (BK) equation which is expected
to describe the nonlinear evolution in x of the dipole cross section in these
momentum regions. We find that in the EGS region the BK equation yields results
that are qualitatively different from those of phenomenological studies. In
particular, geometric scaling around the saturation scale is only obtained at
asymptotic rapidities. We find that in this limit, the anomalous dimension
\gamma(r,x) of phenomenological models approaches a limiting function that is
universal for a large range of initial conditions. At the saturation scale,
this function equals approximately 0.44, in contrast to the value 0.628
commonly used in the models. We further investigate the dependence of these
results on the starting distribution, the small-r limit of the anomalous
dimension for fixed rapidities and the x-dependence of the saturation scale.


  Deep biasing for the Transducer can improve the recognition performance of
rare words or contextual entities, which is essential in practical
applications, especially for streaming Automatic Speech Recognition (ASR).
However, deep biasing with large-scale rare words remains challenging, as the
performance drops significantly when more distractors exist and there are words
with similar grapheme sequences in the bias list. In this paper, we combine the
phoneme and textual information of rare words in Transducers to distinguish
words with similar pronunciation or spelling. Moreover, the introduction of
training with text-only data containing more rare words benefits large-scale
deep biasing. The experiments on the LibriSpeech corpus demonstrate that the
proposed method achieves state-of-the-art performance on rare word error rate
for different scales and levels of bias lists.


  We present a study of six open clusters (Berkeley 67, King 2, NGC 2420, NGC
2477, NGC 2682 and NGC 6940) using the Ultra Violet Imaging Telescope (UVIT)
aboard \textit{ASTROSAT} and \textit{Gaia} EDR3. We used combinations of
astrometric, photometric and systematic parameters to train and supervise a
machine learning algorithm along with a Gaussian mixture model for the
determination of cluster membership. This technique is robust, reproducible and
versatile in various cluster environments. In this study, the \textit{Gaia}
EDR3 membership catalogues are provided along with classification of the stars
as \texttt{members, candidates} and \texttt{field} in the six clusters. We
could detect 200--2500 additional members using our method with respect to
previous studies, which helped estimate mean space velocities, distances,
number of members and core radii. UVIT photometric catalogues, which include
blue stragglers, main-sequence and red giants are also provided. From
UV--Optical colour-magnitude diagrams, we found that majority of the sources in
NGC 2682 and a few in NGC 2420, NGC 2477 and NGC 6940 showed excess UV flux.
NGC 2682 images have ten white dwarf detection in far-UV. The far-UV and
near-UV images of the massive cluster NGC 2477 have 92 and 576 \texttt{members}
respectively, which will be useful to study the UV properties of stars in the
extended turn-off and in various evolutionary stages from main-sequence to red
clump. Future studies will carry out panchromatic and spectroscopic analysis of
noteworthy members detected in this study.


  Consider the following inequalities due to Caffarelli, Kohn and Nirenberg
{\it (Compositio Mathematica,1984):} $$\Big(\int_\Omega
\frac{|u|^r}{|x|^s}dx\Big)^{\frac{1}{r}}\leq
C(p,q,r,\mu,\sigma,s)\Big(\int_\Omega \frac{|\nabla
u|^p}{|x|^\mu}dx\Big)^{\frac{a}{p}}\Big(\int_\Omega
\frac{|u|^q}{|x|^\sigma}dx\Big)^{\frac{1-a}{q}},$$ where $\Omega \subset \R^N
(N\geq 2)$ is an open set; $p, q, r, \mu, \sigma, s, a$ are some parameters
satisfying some balanced conditions. When $\Omega$ is a cone in $\R^N$ (for
example, $\Omega=\R^N)$, we prove the sharp constant $C(p,q,r,\mu,\sigma,s)$
can be achieved for a very large parameter space. Besides, we find some
sufficient conditions which guarantee that the following Sobolev spaces
$$W_{\mu}^{1,p}(\Omega),\; W_{\mu}^{1,p}(\Omega)\cap L^p(\Omega), \;
H^{1,p}(\R^N) $$ are compactly embedded into $L^r(\R^N, \frac{dx}{|x|^s})$ for
some new ranges of parameters, where $\displaystyle W_{\mu}^{1,p}(\Omega)$ is
the completion of $C_0^\infty(\Omega)$ with respect to the norm $\displaystyle
\Big(\int_\Omega \frac{ |\nabla u|^p}{|x|^\mu}dx\Big)^{\frac{1}{p}}. $ As
applications, we also study the equation $$\displaystyle -div\Big(\frac{|\nabla
u|^{p-2}\nabla u}{|x|^\mu}\Big)=\lambda V(x)|u|^{q-2}u, \;\;\; u\in
W_{\mu}^{1,p}(\Omega)$$ under some proper conditions on $V(x)$.


  As a generalization of Dempster-Shafer theory, the theory of D numbers is a
new theoretical framework for uncertainty reasoning. Measuring the uncertainty
of knowledge or information represented by D numbers is an unsolved issue in
that theory. In this paper, inspired by distance based uncertainty measures for
Dempster-Shafer theory, a total uncertainty measure for a D number is proposed
based on its belief intervals. The proposed total uncertainty measure can
simultaneously capture the discord, and non-specificity, and non-exclusiveness
involved in D numbers. And some basic properties of this total uncertainty
measure, including range, monotonicity, generalized set consistency, are also
presented.


  In this note, we prove that if a compact even dimensional manifold $M^{n}$
with negative sectional curvature is homotopic to some compact space-like
manifold $N^{n}$, then the Euler characteristic number of $M^{n}$ satisfies
$(-1)^{\frac{n}{2}}\chi(M^{n})>0$. We also show that the minimal volume
conjecture of Gromov is true for all compact even dimensional space-like
manifolds.


  Dreams of machines rivaling human intelligence have shaped the field of AI
since its inception. Yet, the very meaning of human-level AI or artificial
general intelligence (AGI) remains elusive and contested. Definitions of AGI
embrace a diverse range of incompatible values and assumptions. Contending with
the fractured worldviews of AGI discourse is vital for critiques that pursue
different values and futures. To that end, we provide a taxonomy of AGI
definitions, laying the ground for examining the key social, political, and
ethical assumptions they make. We highlight instances in which these
definitions frame AGI or human-level AI as a technical topic and expose the
value-laden choices being implicitly made. Drawing on feminist, STS, and social
science scholarship on the political and social character of intelligence in
both humans and machines, we propose contextual, democratic, and participatory
paths to imagining future forms of machine intelligence. The development of
future forms of AI must involve explicit attention to the values it encodes,
the people it includes or excludes, and a commitment to epistemic justice.


  ATP-driven microtubule-kinesin bundles can self-assemble into two-dimensional
active liquid crystals (ALCs) that exhibit a rich creation and annihilation
dynamics of topological defects, reminiscent of particle-pair production
processes in quantum systems. This recent discovery has sparked considerable
interest but a quantitative theoretical description is still lacking. We
present and validate a minimal continuum theory for this new class of active
matter systems by generalizing the classical Landau-de Gennes free-energy to
account for the experimentally observed spontaneous buckling of motor-driven
extensile microtubule bundles. The resulting model agrees with recently
published data and predicts a regime of antipolar order. Our analysis implies
that ALCs are governed by the same generic ordering principles that determine
the non-equilibrium dynamics of dense bacterial suspensions and elastic bilayer
materials. Moreover, the theory manifests an energetic analogy with strongly
interacting quantum gases. Generally, our results suggest that complex
non-equilibrium pattern-formation phenomena might be predictable from a few
fundamental symmetry-breaking and scale-selection principles.


  Several methods exist to measure $CP$ violation observables related to the
$C\!K\!M$ angle $\gamma$. These observables are different for every $B$ meson
decay channel. However, the information they contain on $\gamma$ is encoded in
a similar way for all of them. This paper describes a strategy for a
simultaneous measurement including several $B$ meson decay channels, while
taking into account any possible correlations between them.


  In tracking multiple objects, it is often assumed that each observation
(measurement) is originated from one and only one object. However, we may
encounter a situation that each measurement may or may not be associated with
multiple objects at each time step --spawning. Therefore, the association of
each measurement to multiple objects is a crucial task to perform in order to
track multiple objects with birth and death. In this paper, we introduce a
novel Bayesian nonparametric approach that models a scenario where each
observation may be drawn from an unknown number of objects for which it
provides a tractable Markov chain Monte Carlo (MCMC) approach to sample from
the posterior distribution. The number of objects at each time step, itself, is
also assumed to be unknown. We, then, show through experiments the advantage of
nonparametric modeling to scenarios with spawning events. Our experiment
results also demonstrate the advantages of our framework over the existing
methods.


  We consider the problem of determining the maximum number of moves required
to sort a permutation of $[n]$ using cut-and-paste operations, in which a
segment is cut out and then pasted into the remaining string, possibly
reversed. We give short proofs that every permutation of $[n]$ can be
transformed to the identity in at most $\flr{2n/3}$ such moves and that some
permutations require at least $\flr{n/2}$ moves.


  Additional scalar fields from scalar-tensor, modified gravity or higher
dimensional theories beyond general relativity may account for dark energy and
the accelerating expansion of the Universe. These theories have lead to
proposed models of screening mechanisms, such as chameleon and symmetron
fields, to account for the tight experimental bounds on fifth-force searches.
Cold atom systems have been very successfully used to constrain the parameters
of these screening models, and may in future eliminate the interesting
parameter space of some models entirely. In this paper, we show how to
manipulate a Bose-Einstein condensate to simulate the effect of any screened
scalar field model coupled conformally to the metric. We give explicit
expressions for the simulation of various common models. This result may be
useful for investigating the computationally challenging evolution of particles
on a screened scalar field background, as well as for testing the metrology
scheme of an upcoming detector proposal.


  In this study, we analyze the flow filtration process of slightly
compressible fluids in fractured porous media. We model the coupled fractured
porous media system, where the linear Darcy flow is considered in porous media
and the nonlinear Forchheimer equation is used inside the fracture.
  Flow in the fracture is modeled as a reduced low dimensional BVP which is
coupled with an equation in the reservoir. We prove that the solution of the
reduced model can serve very accurately to approximate the solution of the
actual high-dimensional flow in reservoir fracture system, because the
thickness of the fracture is small. In the analysis we consider two types of
Forchhemer flows in the fracture: isotropic and anisotropic, which are
different in their nature.
  Using method of reduction, we developed a formulation for an optimal design
of the fracture, which maximizes the capacity of the fracture in the reservoir
with fixed geometry. Our method, which is based on a set point control
algorithm, explores the coupled impact of the fracture geometry and
beta-Forchheimer coefficient.


  Our work examines the detectability of tidally distorted solid exoplanets in
synchronous rotation. Previous work has shown that tidally distorted shapes of
close-in gas giants can give rise to radius underestimates and subsequently
density overestimates for those planets. We examine the assumption that such an
effect is too minimal for rocky exoplanets and find that for smaller M Class
stars there may be an observationally significant tidal distortion effect at
very close-in orbits. We quantify the effect for different stellar types and
planetary properties using some basic assumptions. Finally, we develop a simple
analytic expression to test if there are detectable bulge signatures in the
photometry of a system. We find that close in for smaller M Class stars there
may be an observationally significant signature that may manifest itself in
both in-transit bulge signatures and ellipsoidal variations.


  In [90] the first-named author gave a working definition of a family of
automorphic L-functions. Since then there have been a number of works [33],
[107], [67] [47], [66] and especially [98] by the second and third-named
authors which make it possible to give a conjectural answer for the symmetry
type of a family and in particular the universality class predicted in [64] for
the distribution of the zeros near s=1/2. In this note we carry this out after
introducing some basic invariants associated to a family.


  Even if not so ancient, the history of the heat engine efficiency at maximum
power expression have been yet turbulent. More than a decade after the
publication of the seminal article by Curzon and Ahlborn in 1975, one's
rediscovered two older works by Chambadal and Novikov, both dating from 1957.
Then, some years ago, the name of Yvon arose from a textual reference to this
famous relation in a conference article published in 1955. Thanks to an
historical study of French written books not anymore published for a long time,
and since never translated in other languages, we bring to light in this paper
that this relation was actually firstly proposed by Henri B. Reitlinger in
1929.


  In this paper, we employ a nonlocal $Q$-curvature flow inspired by
Gursky-Malchiodi's work \cite{gur_mal} to solve the prescribed $Q$-curvature
problem on a class of closed manifolds: For $n \geq 5$, let $(M^n,g_0)$ be a
smooth closed manifold, which is not conformally diffeomorphic to the standard
sphere, satisfying either Gursky-Malchiodi's semipositivity hypotheses: scalar
curvature $R_{g_0}>0$ and $Q_{g_0} \geq 0$ not identically zero or Hang-Yang's:
Yamabe constant $Y(g_0)>0$, Paneitz-Sobolev constant $q(g_0)>0$ and $Q_{g_0}
\geq 0$ not identically zero. Let $f$ be a smooth positive function on $M^n$
and $x_0$ be some maximum point of $f$. Suppose either (a) $n=5,6,7$ or
$(M^n,g_0)$ is locally conformally flat; or (b) $n \geq 8$, Weyl tensor at
$x_0$ is nonzero. In addition, assume all partial derivatives of $f$ vanish at
$x_0$ up to order $n-4$, then there exists a conformal metric $g$ of $g_0$ with
its $Q$-curvature $Q_g$ equal to $f$. This result generalizes Escobar-Schoen's
work [Invent. Math. 1986] on prescribed scalar curvature problem on any locally
conformally flat manifolds of positive scalar curvature.


  Both classical and quantum dynamics of the synchronization between two
nonlinear mechanical modes scattered from Bose-Einstein condensates (BECs) by
the standing-wave laser beam are comparatively investigated. As the ultra-low
dissipations of the momentum modes in the atomic BECs, the synchronized
dynamics are studied in a framework of closed-system theory in order to track
down both the classical and the quantum synchronizations from an angle of
quantum control. The classical synchronization and the relevant dynamics of
measure synchronization, the quantum synchronization and two different types of
measures proposed by Mari and estimated by mutual information based on
$Q$-function are studied respectively in order to reveal both the macroscopic
and the microscopic signatures of synchronized behaviors in a closed quantum
system. The results demonstrate that the "revival and collapse" of the quantum
fluctuations beyond the classical mean-value dynamics due to long-lasting mode
coherence discriminates the quantum synchronization from the classical one,
which not only excludes the possibilities of an exact synchronization and a
perfect density overlap in phase space, but also leads to upper limitations to
Mari measure and large unceasing fluctuations to mutual information between two
scattering modes. We reveal a close dynamic connection between Mari measure and
the mutual information of two nonlinear momentum modes in closed BEC systems by
demonstrating an opposite mean-value behavior but a similar fluctuation
variation with respect to their respective evolutionary scales.


  After recalling the rigorous mathematical representations in Relativity
Theory (\emph{RT}) of (i): observers, (ii): reference frames fields, (iii):
their classifications, (iv) naturally adapted coordinate systems (\emph{nacs}%)
to a given reference frame, (v): synchronization procedure and some other key
concepts, we analyze three problems concerning experiments on rotating frames
which even now (after almost a century from the birth of \emph{RT}) are sources
of misunderstandings and misconceptions. The first problem, which serves to
illustrate the power of rigorous mathematical methods in \emph{RT}is the
explanation of the Sagnac effect (\emph{SE}). This presentation is opportune
because recently there are many non sequitur claims in the literature stating
that the \emph{SE} cannot be explained by \emph{SRT}, even disproving this
theory or that the explanation of the effect requires a new theory of
electrodynamics. The second example has to do with the measurement of the one
way velocity of light in rotating reference frames, a problem for which many
wrong statements appear in recent literature. The third problem has to do with
claims that only Lorentz like type transformations can be used between the
\emph{nacs}associated to a reference frame mathematically moddeling of a
rotating platform and the \emph{nacs} associated with a inertial frame (the
laboratory). Whe show that these claims are equivocated.


  Regular nilpotent Hessenberg varieties form an important family of
subvarieties of the flag variety, which are often singular and sometimes not
normal varieties. Like Schubert varieties, they contain distinguished points
called permutation flags. In this paper, we give a combinatorial
characterization for a permutation flag of a regular nilpotent Hessenberg
variety to be a singular point. We also apply this result to characterize
regular nilpotent Hessenberg varieties which are normal algebraic varieties.


  Recent results in the literature indicate that a residual network (ResNet)
composed of a single residual block outperforms linear predictors, in the sense
that all local minima in its optimization landscape are at least as good as the
best linear predictor. However, these results are limited to a single residual
block (i.e., shallow ResNets), instead of the deep ResNets composed of multiple
residual blocks. We take a step towards extending this result to deep ResNets.
We start by two motivating examples. First, we show that there exist datasets
for which all local minima of a fully-connected ReLU network are no better than
the best linear predictor, whereas a ResNet has strictly better local minima.
Second, we show that even at the global minimum, the representation obtained
from the residual block outputs of a 2-block ResNet do not necessarily improve
monotonically over subsequent blocks, which highlights a fundamental difficulty
in analyzing deep ResNets. Our main theorem on deep ResNets shows under simple
geometric conditions that, any critical point in the optimization landscape is
either (i) at least as good as the best linear predictor; or (ii) the Hessian
at this critical point has a strictly negative eigenvalue. Notably, our theorem
shows that a chain of multiple skip-connections can improve the optimization
landscape, whereas existing results study direct skip-connections to the last
hidden layer or output layer. Finally, we complement our results by showing
benign properties of the "near-identity regions" of deep ResNets, showing
depth-independent upper bounds for the risk attained at critical points as well
as the Rademacher complexity.


  Fine-grained visual classification (FGVC) is much more challenging than
traditional classification tasks due to the inherently subtle intra-class
object variations. Recent works mainly tackle this problem by focusing on how
to locate the most discriminative parts, more complementary parts, and parts of
various granularities. However, less effort has been placed to which
granularities are the most discriminative and how to fuse information cross
multi-granularity. In this work, we propose a novel framework for fine-grained
visual classification to tackle these problems. In particular, we propose: (i)
a progressive training strategy that effectively fuses features from different
granularities, and (ii) a random jigsaw patch generator that encourages the
network to learn features at specific granularities. We obtain state-of-the-art
performances on several standard FGVC benchmark datasets, where the proposed
method consistently outperforms existing methods or delivers competitive
results. The code will be available at
https://github.com/PRIS-CV/PMG-Progressive-Multi-Granularity-Training.


  The vector autoregressive (VAR) model has been used to describe the
dependence within and across multiple time series. This is a model for
stationary time series which can be extended to allow the presence of a
deterministic trend in each series. Detrending the data either parametrically
or nonparametrically before fitting the VAR model gives rise to more errors in
the latter part. In this study, we propose a new approach called DeepVARwT that
employs deep learning methodology for maximum likelihood estimation of the
trend and the dependence structure at the same time. A Long Short-Term Memory
(LSTM) network is used for this purpose. To ensure the stability of the model,
we enforce the causality condition on the autoregressive coefficients using the
transformation of Ansley & Kohn (1986). We provide a simulation study and an
application to real data. In the simulation study, we use realistic trend
functions generated from real data and compare the estimates with true
function/parameter values. In the real data application, we compare the
prediction performance of this model with state-of-the-art models in the
literature.


  We propose a method for finding 2D spatial modes of thermal field through a
direct measurement of the field intensity and an offline analysis of its
spatial fluctuations. Using this method, in a simple and efficient way we
reconstruct the modes of a multimode fiber and the spatial Schmidt modes of
squeezed vacuum generated via high-gain parametric down conversion. The
reconstructed shapes agree with the theoretical results.


  Most recent research about automatic music transcription (AMT) uses
convolutional neural networks and recurrent neural networks to model the
mapping from music signals to symbolic notation. Based on a high-resolution
piano transcription system, we explore the possibility of incorporating another
powerful sequence transformation tool -- the Transformer -- to deal with the
AMT problem. We argue that the properties of the Transformer make it more
suitable for certain AMT subtasks. We confirm the Transformer's superiority on
the velocity detection task by experiments on the MAESTRO dataset and a
cross-dataset evaluation on the MAPS dataset. We observe a performance
improvement on both frame-level and note-level metrics after introducing the
Transformer network.


  The behavior of an adaptive optics (AO) system for ground-based high contrast
imaging (HCI) dictates the achievable contrast of the instrument. In conditions
where the coherence time of the atmosphere is short compared to the speed of
the AO system, the servo-lag error becomes the dominate error term of the AO
system. While the AO system measures the wavefront error and subsequently
applies a correction (taking a total of 1 to 2 milli-seconds), the atmospheric
turbulence above the telescope has changed. In addition to reducing the Strehl
ratio, the servo-lag error causes a build-up of speckles along the direction of
the dominant wind vector in the coronagraphic image, severely limiting the
contrast at small angular separations. One strategy to mitigate this problem is
to predict the evolution of the turbulence over the delay. Our predictive
wavefront control algorithm minimizes the delay in a mean square sense and has
been implemented on the Keck II AO bench. In this paper we report on the latest
results of our algorithm and discuss updates to the algorithm itself. We
explore how to tune various filter parameters on the basis of both daytime
laboratory tests and on-sky tests. We show a reduction in residual-mean-square
wavefront error for the predictor compare to the leaky integrator implemented
on Keck. Finally, we present contrast improvements for both day time and on-sky
tests. Using the L-band vortex coronagraph for Keck's NIRC2 instrument, we find
a contrast gain of 2.03 at separation of 3~$\lambda/D$ and up to 3 for larger
separations (4-6~$\lambda/D$).


  We introduce a generalized thermostatistics based on Kolmogorov-Nagumo
averages and appropriately selected information measures. The formalism
includes Tsallis non-extensive thermostatistics, but also extensive
thermostatistics based on Renyi entropy. The Curie-Weiss model is discussed as
an example.


  We extend the notion of the compressed zero-divisor graph $\varTheta(R)$ to
noncommutative rings in a way that still induces a product preserving functor
$\varTheta$ from the category of finite unital rings to the category of
directed graphs. For a finite field $F$, we investigate the properties of
$\varTheta(M_n(F))$, the graph of the matrix ring over $F$, and give a purely
graph-theoretic characterization of this graph when $n \neq 3$. For $n \neq 2$
we prove that every graph automorphism of $\varTheta(M_n(F))$ is induced by a
ring automorphism of $M_n(F)$. We also show that for finite unital rings $R$
and $S$, where $S$ is semisimple and has no homomorphic image isomorphic to a
field, if $\varTheta(R) \cong \varTheta(S)$, then $R \cong S$. In particular,
this holds if $S=M_n(F)$ with $n \neq 1$.


  Network interpretation as an effort to reveal the features learned by a
network remains largely visualization-based. In this paper, our goal is to
tackle semantic network interpretation at both filter and decision level. For
filter-level interpretation, we represent the concepts a filter encodes with a
probability distribution of visual attributes. The decision-level
interpretation is achieved by textual summarization that generates an
explanatory sentence containing clues behind a network's decision. A Bayesian
inference algorithm is proposed to automatically associate filters and network
decisions with visual attributes. Human study confirms that the semantic
interpretation is a beneficial alternative or complement to visualization
methods. We demonstrate the crucial role that semantic network interpretation
can play in understanding a network's failure patterns. More importantly,
semantic network interpretation enables a better understanding of the
correlation between a model's performance and its distribution metrics like
filter selectivity and concept sparseness.


  We systematically analyze the 6-year {\it Fermi}/LAT data of the
lobe-dominated quasars (LDQs) in the complete LDQ sample from 3CRR survey and
report the discovery of high-energy $\gamma$-ray emission from 3C 275.1. The
$\gamma$-ray emission of 3C 207 is confirmed and significant variability of the
lightcurve is identified. We do not find statistically significant $\gamma$-ray
emission from other LDQs. 3C 275.1 is the known $\gamma$-ray quasar with the
lowest core dominance parameter (i.e., $R=0.11$). We also show that both the
northern radio hotspot and parsec jet models can reasonably reproduce the
$\gamma$-ray data. The parsec jet model, however, is favored by the potential
$\gamma$-ray variability at the timescale of months. We suggest that some
dimmer $\gamma$-ray LDQs will be detected in the future and LDQs could
contribute non-negligibly to the extragalactic $\gamma$-ray background.


  We show that strong parametric driving of a quantum harmonic oscillator
coupled to a thermal bath allows one to distinguish between different
microscopic models for the oscillator-bath coupling. We consider a bath with an
Ohmic spectral density and a model where the system-bath interaction can be
tuned continuously between position and momentum coupling via the coupling
angle $\alpha$. We derive a master equation for the reduced density operator of
the oscillator in Born-Markov approximation and investigate its quasi-steady
state as a function of the driving parameters, the temperature of the bath and
the coupling angle $\alpha$. We find that the time-averaged variance of
position and momentum exhibits a strong dependence on these parameters. In
particular, we identify parameter regimes that maximise the $\alpha$-dependence
and provide an intuitive explanation of our results.


  Using a special ansatz for the metric, by straightforward computation we
prove that gravi-dilaton effective action in higher dimensions is reduced to
the p-brane action. The dual symmetry of the generic type
$%a\longleftrightarrow \frac 1a$ is an important symmetry of the reduced
action.


  The physical origin of the large-scale conformity in the colours and specific
star formation rates of isolated low mass central galaxies and their neighbours
on scales in excess of 1 Mpc is still under debate. One possible scenario is
that gas is heated over large scales by feedback from active galactic nuclei
(AGN), leading to coherent modulation of cooling and star formation between
well-separated galaxies. In this Letter, the metal line absorption catalogue of
Zhu & Menard (2013) is used to probe gas out to large projected radii around a
sample of a million galaxies with stellar masses ~10^{10} M_{sun} and
photometric redshifts in the range 0.4<z<0.8 selected from Sloan Digital Sky
Survey imaging data. This galaxy sample covers an effective volume of 2.2
Gpc^3. A statistically significant excess of MgII absorbers is present around
the red low mass galaxies compared to their blue counterparts out to projected
radii of 10 Mpc. In addition, the equivalent width distribution function of
MgII absorbers around low mass galaxies is shown to be strongly affected by the
presence of a nearby (R_p<2 Mpc) radio-loud AGN out to projected radii of 5
Mpc.