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    We consider stationary axisymmetric solutions of the Euler-Poisson equations, which govern the internal structure of barotropic gaseous stars. The equation of states is supposed to be near to that of the polytropic gaseous stars of the adiabatic exponent $\gamma$ such that $6/5<\gamma <2$ at the vacuum, so that, besides the exact $\gamma$-laws of polytropic stars, as an example, the equation of states for white dwarfs can be treated. A generic condition of the existence of stationary solutions with differential rotation is given, and the existence of slowly rotating configurations near spherically symmetric equilibria is given. The problem is formulated as a nonlinear integral equation, and is solved by application of the infinite dimensional implicit function theorem. Properties of solutions such as physical vacuum boundary condition and oblateness of star surface are clarified.
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    A variety of network modeling problems begin by generating a degree sequence drawn from a given probability distribution. If the randomly generated sequence is not graphic, we give a new approach for generating a graphic approximation of the sequence. This approximation scheme is fast, requiring only one pass through the sequence, and produces small probability distribution distances for large sequences.
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    Purpose: Experimental measurements of bone mineral density distributions (BMDDs) enable a determination of secondary mineralisation kinetics in bone, but the maximum degree of mineralisation and how this maximum is approached remain uncertain. We thus test computationally different hypotheses on late stages of bone mineralisation by simulating BMDDs in low turnover conditions. Materials and Methods: An established computational model of the BMDD that accounts for mineralisation and remodelling processes was extended to limit mineralisation to various maximum calcium capacities of bone. Simulated BMDDs obtained by reducing turnover rate from the reference trabecular BMDD under different assumptions on late stage mineralisation kinetics were compared with experimental BMDDs of low-turnover bone. Results: Simulations show that an abrupt stopping of mineralisation near a maximum calcium capacity induces a pile-up of minerals in the BMDD statistics that is not observed experimentally. With a smooth decrease of mineralisation rate, imposing low maximum calcium capacities helps to match peak location and width of simulated low turnover BMDDs with peak location and width of experimental BMDDs, but results in a distinctive asymmetric peak shape. No tuning of turnover rate and maximum calcium capacity was able to explain the differences found in experimental BMDDs between trabecular bone (high turnover) and femoral cortical bone (low turnover). Conclusions: Secondary mineralisation in human bone does not stop abruptly, but continues slowly up to a calcium content greater than 30 wt% Ca. The similar mineral heterogeneity seen in trabecular and femoral cortical bones at different peak locations was unexplained by turnover differences tested.
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    Viscoelastic subdiffusion governed by a fractional Langevin equation is studied numerically in stationary random Gaussian potentials with decaying spatial correlations. This anomalous diffusion is archetypal for living cells, where cytoplasm is known to be viscoelastic and spatial disorder emerges also naturally. Two type of potential correlations are studied: exponentially-decaying (Ornstein-Uhlenbeck process in space) and algebraically-decaying with an infinite correlation length. It is shown that for a relatively small disorder strength in units of thermal energy (several $k_BT$) viscoelastic subdiffusion in the ensemble sense easily overcomes the potential disorder and asymptotically is not distinguishable from the free-space subdiffusion. However, such subdiffusion on the level of single-tajectory averages still exhibits transiently a characteristic scatter featuring weak ergodicity breaking. With an increase of disorder strength to $5\div 10\; k_BT$, a very long regime of logarithmic Sinai-like diffusion emerges. Long correlations in the potentials fluctuations make such a transient regime essentially longer, but faster in the absolute terms. This nominally ultraslow Sinai diffusion is, however, not dramatically slower than the free-space viscoelastic subdiffusion, in the absolute terms, on the ensemble level. It can transiently be even faster. The explanation of this paradoxical phenomenon is provided. On the level of single-trajectories, such disorder-obstructed persistent viscoelastic subdiffusion is always slower and exhibits a strong scatter in single-trajectory averages.
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    We define what it means for a proper continuous morphism between groupoids to be Haar system preserving, and show that such a morphism induces (via pullback) a *-morphism between the corresponding convolution algebras. We prove that an inverse system of groupoids with Haar system preserving bonding maps has a limit, and that we get a corresponding direct system of groupoid $C^*$-algebras. An explicit construction of an inverse system of groupoids is used to approximate a $\sigma$-compact groupoid $G$ by second countable groupoids; if $G$ is equipped with a Haar system and 2-cocycle then so are the approximation groupoids, and the maps in the inverse system are Haar system preserving. As an application of this construction, we show how to easily extend the Maximal Equivalence Theorem of Jean Renault to $\sigma$-compact groupoids.
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    In many superconducting devices, including qubits, quasiparticle excitations are detrimental. A normal metal ($N$) in contact with a superconductor ($S$) can trap these excitations; therefore such a trap can potentially improve the devices performances. The two materials influence each other, a phenomenon known as proximity effect which has drawn attention since the '60s. Here we study whether this mutual influence places a limitation on the possible performance improvement in superconducting qubits. We first revisit the proximity effect in uniform $NS$ bilayers; despite the long history of this problem, we present novel findings for the density of states. We then extend our results to describe a non-uniform system in the vicinity of a trap edge. Using these results together with a phenomenological model for the suppression of the quasiparticle density due to the trap, we find in a transmon qubit an optimum trap-junction distance at which the qubit relaxation rate is minimized. This optimum distance, of the order of 4 to 20 coherence lengths, originates from the competition between proximity effect and quasiparticle density suppression. We conclude that the harmful influence of the proximity effect can be avoided so long as the trap is farther away from the junction than this optimum.
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    One-loop contributions to the $h\rightarrow Z\gamma$ are evaluated in the one-loop approximation. The unitary gauge gauge is used. The analytic result is expressed in terms of the Passarino-Veltman functions. The calculations are applicable as for the Standard Model as well for a wide class of its gauge extensions. In particular, the decay width of a charged Higgs boson $H^{\pm}\rightarrow W^{\pm}\gamma$ can be derived. The consistence of our formulas and several specific earlier results is shown.
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    In the framework of the $(B-L)$ Supersymmetric Standard Model (BLSSM), we assess the ability of ground and space based experiments to establish the nature of its prevalent Dark Matter (DM) candidate, the sneutrino, which could either be CP-even or -odd. Firstly, by benchmarking this theory construct against the results obtained by the Planck spacecraft, we extract the portions of the BLSSM parameter space compliant with relic density data. Secondly, we show that, based on current sensitivities of the Fermi Large Area Telescope (FermiLAT) and their future projections, the study of high-energy $\gamma$-ray spectra will eventually enable us to extract evidence of this DM candidate through its annihilations into $W^+W^-$ pairs (in turn emitting photons), in the form of both an integrated flux and a differential energy spectrum which cannot be reconciled with the assumption of DM being fermionic (like, e.g., a neutralino), although it should not be possible to distinguish between the scalar and pseudoscalar hypotheses. Thirdly, we show that, while underground direct detection experiments will have little scope in testing sneutrino DM, the Large Hadron Collider (LHC) may be able to do so in a variety of multi-lepton signatures, with and without accompanying jets (plus missing transverse energy), following data collection during Run 2 and 3.
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    Bogoliubov quasiparticles moving in the background of superfluid $\text{He}^3$-A see an apparently curved space-time metric when the background superfluid vacuum is in motion. We study how this curvature couples with the spins of the effiectively massless quasiparticles. First, we set up the problem in null Fermi coordinates for radial as well as circular geodesics and then use it in the context of the analog metric seen by the quasiparticles. We obtain an effective magnetic interaction due to curvature coupling, and provide numerical estimates. Some possible implications of these results are then pointed out.
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    In this work we handle with categorical (ordinal) variables and we focus on the (in)dependence relationship under the marginal, conditional and context-specific perspective. If the first two are well known, the last one concerns independencies holding only in a subspace of the outcome space. We take advantage from the Hierarchical Multinomial Marginal models and provide several original results about the representation of context-specific independencies through these models. By considering the graphical aspect, we take advantage from the chain graphical models. The resultant graphical model is a so-called "stratified" chain graphical model with labelled arcs. New Markov properties are provided. Furthermore, we consider the graphical models under the regression poit of view. Here we provide simplification of the regression parameters due to the context-specific independencies. Finally, an application about the innovation degree of the Italian enterprises is provided.
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    The goal of this work is to improve focusing of high-intensity ultrasound by modifying the geometry of acoustic lenses through shape optimization. The shape optimization problem is formulated by introducing a tracking-type cost functional to match a desired pressure distribution in the focal region. Westervelt's equation, a nonlinear acoustic wave equation, is used to model the pressure field. We apply the optimize first, then discretize approach, where we first rigorously compute the shape derivative of our cost functional. A gradient-based optimization algorithm is then developed within the concept of isogeometric analysis, where the geometry is exactly represented by splines at every gradient step and the same basis is used to approximate the equations. Numerical experiments in a 2D setting illustrate our findings.
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    This paper contains results related to synthesis and presentation of abstract automata by fragments of behaviour and investigates the structure of the classes of finite connected initial output-less automata specified by systems of defining relations considered as fragments, co-fragments, counter-fragments and co-counter-fragments of automata.
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    We have used LOFAR to perform targeted millisecond pulsar surveys of Fermi gamma-ray sources. Operating at a center frequency of 135 MHz, the surveys use a novel semi-coherent dedispersion approach where coherently dedispersed trials at coarsely separated dispersion measures are incoherently dedispersed at finer steps. Three millisecond pulsars have been discovered as part of these surveys. We describe the LOFAR surveys and the properties of the newly discovered pulsars.
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    This paper presents novel insights about the influence of soluble surfactants on bubble flows obtained by Direct Numerical Simulation (DNS). Surfactants are amphiphilic compounds which accumulate at fluid interfaces and significantly modify the respective interfacial properties, influencing also the overall dynamics of the flow. With the aid of DNS local quantities like the surfactant distribution on the bubble surface can be accessed for a better understanding of the physical phenomena occurring close to the interface. The core part of the physical model consists in the description of the surfactant transport in the bulk and on the deformable interface. The solution procedure is based on an Arbitrary Lagrangian-Eulerian (ALE) Interface-Tracking method. The existing methodology was enhanced to describe a wider range of physical phenomena. A subgrid-scale (SGS) model is employed in the cases where a fully resolved DNS for the species transport is not feasible due to high mesh resolution requirements and, therefore, high computational costs. After an exhaustive validation of the latest numerical developments, the DNS of single rising bubbles in contaminated solutions is compared to experimental results. The full velocity transients of the rising bubbles, especially the contaminated ones, are correctly reproduced by the DNS. The simulation results are then studied to gain a better understanding of the local bubble dynamics under the effect of soluble surfactant. One of the main insights is that the quasi-steady state of the rise velocity is reached without ad- and desorption being necessarily in local equilibrium.
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    In this paper, we prove the existence of an initial trace ${\cal T}_u$ of any positive solution $u$ of the semilinear fractional diffusion equation $(H)$ $$\partial_t u + (-∆)^\alpha u+f(t,x,u)=0\quad \rm in\quad \mathbbR^*_+\times\mathbbR^N,$$ where $N\geq1$ where the operator $(-\Delta)^\alpha$ with $\alpha\in(0,1)$ is the fractional Laplacian and $f:\mathbb{R}^+\times\mathbb{R}^N\times \mathbb{R}_+\mapsto\mathbb{R}$ is a Caratheodory function satisfying $f(t,x,u)u\geq 0$ for all $(t,x,u)\in \mathbb{R}^+\times\mathbb{R}^N\times\mathbb{R}_+.$ We define the regular set of the trace ${\cal T}_u$ as an open subset of ${\cal R}_u\subset\mathbb{R}^N$ carrying a nonnegative Radon measive $\nu_u$ such that $$\lim_t\to 0\int_\cal R_uu(t,x)\zeta(x) dx=\int_\cal R_u\zeta d\nu\qquad∀\zeta∈C^2_0(\cal R_u),$$ and the singular set ${\cal S}_u=\mathbb{R}^N\setminus {\cal R}_u$ as the set points $a$ such that $$\limsup_t\to 0\int_B_\rho(a)u(t,x) dx = ∞\qquad ∀\rho>0.$$ We study the reverse problem of constructing a positive solution to $(H)$ with a given initial trace $({\cal S},\nu)$ where ${\cal S}\subset\mathbb{R}^N$ is a closed set and $\nu$ is a positive Radon measure on ${\cal R}=\mathbb{R}^N\setminus{\cal S}$ and develop the case $f(t,x,u)=t^\beta u^p$ where $\beta >-1$ and $p>1$.
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    Symmetry in mathematical programming may lead to a multiplicity of solutions. In nonconvex optimisation, it can negatively affect the performance of the Branch and Bound algorithm. Symmetry may induce large search trees with multiple equivalent solutions, i.e. with the same optimal value. Dealing with symmetry requires detecting and classifying it first. This paper develops several methods for detecting symmetry in quadratically constrained quadratic optimisation problems via adjacency matrices. Using graph theory, we transform these matrices into binary layered graphs and enter them into the software package nauty. Nauty generates important symmetric properties of the original problem.
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    In this paper we use variational methods to establish a Berestycki-Lions type result for a class of generalized Kadomtsev-Petviashvili equation in $\mathbb{R}^2$. The cases positive and zero mass are considered.
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    Fixed two positive integers m and e, some algorithms for computing the minimal Frobenius number and minimal genus of the set of numerical semigroups with multiplicity m and embedding dimension e are provided. Besides, the semigroups where these minimal values are achieved are computed too.
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    Monolayer transition metal dichalcogenides (TMDs) show an optimal surface-to-volume ratio and are thus promising candidates for novel molecule sensor devices. It was recently predicted that a certain class of molecules exhibiting a large dipole moment can be detected through the activation of optically inaccessible (dark) excitonic states in absorption spectra of tungsten-based TMDs. In this work, we investigate the molecule signatures in photoluminescence spectra in dependence of a number of different experimentally accessible quantities, such as excitation density, temperature as well as molecular characteristics including the dipole moment and its orientation, molecule-TMD distance, molecular coverage and distribution. We show that under certain optimal conditions, even room temperature detection of molecules can be achieved.
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    We introduce and study a class of optimization problems we coin replenishment problems with fixed turnover times: a very natural model that has received little attention in the literature. Nodes with capacity for storing a certain commodity are located at various places; at each node the commodity depletes within a certain time, the turnover time, which is constant but can vary between locations. Nodes should never run empty, and to prevent this we may schedule nodes for replenishment every day. The natural feature that makes this problem interesting is that we may schedule a replenishment (well) before a node becomes empty, but then the next replenishment will be due earlier also. This added workload needs to be balanced against the cost of routing vehicles to do the replenishments. In this paper, we focus on the aspect of minimizing routing costs. However, the framework of recurring tasks, in which the next job of a task must be done within a fixed amount of time after the previous one is much more general and gives an adequate model for many practical situations. Note that our problem has an infinite time horizon. However, it can be fully characterized by a compact input, containing only the location of each store and a turnover time. This makes determining its computational complexity highly challenging and indeed it remains essentially unresolved. We study the problem for two objectives: min-avg minimizes the average tour length and min-max minimizes the maximum tour length over all days. For min-max we derive a logarithmic factor approximation for the problem on general metrics and a 6-approximation for the problem on trees, for which we have a proof of NP-hardness. For min-avg we present a logarithmic approximation on general metrics, 2-approximation for trees, and a pseudopolynomial time algorithm for the line. Many intriguing problems remain open.
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    Using high-contrast imaging with the SPHERE instrument at the VLT, we report the first images of a cold brown dwarf companion to the exoplanet host star HD4113A. The brown dwarf HD4113C is part of a complex dynamical system consisting of a giant planet, stellar host and a known wide M-dwarf companion. Its separation of $535\pm3$mas and H-band contrast of $13.35\pm0.10$mag correspond to a projected separation of 22AU and an isochronal mass estimate of $36\pm5$M$_J$ based on COND models. The companion shows strong methane absorption, and through atmospheric model fitting we estimate a surface gravity of $\log g$=5 and an effective temperature of ~500-600K. A comparison of its spectrum with observed T dwarfs indicates a late-T spectral type, with a T9 object providing the best match. By combining the observed astrometry from the imaging data with 27 years of radial velocities, we use orbital fitting to constrain its orbital and physical parameters, as well as update those of the planet HD4113Ab, discovered by previous radial velocity measurements. The data suggest a dynamical mass of $66\pm5$M$_J$ and moderate eccentricity of $0.44\pm0.08$ for the brown dwarf. This mass estimate appears to conflict with the isochronal estimate and that of similar objects, which may be caused by the newly detected object being an unresolved binary brown dwarf system or the presence of an additional object in the system. Through dynamical simulations we show that the planet may undergo strong Lidov-Kozai cycles, raising the possibility that it formed on a quasi-circular orbit and gained its currently observed high eccentricity through interactions with the brown dwarf. Follow-up observations combining radial velocities, direct imaging and Gaia astrometry will be crucial to precisely constrain the dynamical mass of the brown dwarf and allow for in-depth comparison with evolutionary and atmospheric models.
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    We have investigated the in-gap bound states (IGBS) induced by a single nonmagnetic impurity in multiband superconductors with incipient bands. Contrary to the naive expectation, we found that even if the superconducting (SC) order parameter is sign-preserving s-wave on the Fermi surfaces, the incipient bands may still affect the appearance and locations of the IGBS, although the gap between the incipient bands and the Fermi level is much larger than the SC gap. Therefore in scanning tunneling microscopy experiments, the IGBS induced by a single nonmagnetic impurity are not the definitive evidences for the sign-changing order parameter on the Fermi surfaces. Our findings have special implications for the experimental determination of the pairing symmetry in the FeSe-based superconductors.
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    The identification of meaningful reaction coordinates plays a key role in the study of complex molecular systems whose essential dynamics is characterized by rare or slow transition events. In a recent publication, the authors identified a condition under which such reaction coordinates exist - the existence of a so-called transition manifold - and proposed a numerical method for their point-wise computation that relies on short bursts of MD simulations. This article represents an extension of the method towards practical applicability in computational chemistry. It describes an alternative computational scheme that instead relies on more commonly available types of simulation data, such as single long molecular trajectories, or the push-forward of arbitrary canonically-distributed point clouds. It is based on a Galerkin approximation of the transition manifold reaction coordinates, that can be tuned to individual requirements by the choice of the Galerkin ansatz functions. Moreover, we propose a ready-to-implement variant of the new scheme, that computes data-fitted, mesh-free ansatz functions directly from the available simulation data. The efficacy of the new method is demonstrated on a realistic peptide system.
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    We develop a new compact scheme for second-order PDE (parabolic and Schrödinger type) with a variable time-independent coefficient. It has a higher order and smaller error than classic implicit scheme. The Dirichlet and Neumann boundary problems are considered. The relative finite-difference operator is almost self-adjoint.
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    A brief introduction to the statistical hadronization approach to particle production in relativistic heavy-ion collisions is given. In the context of fluid dynamics modeling various aspects of hadron emission at the freeze-out are discussed. Practical applications of the presented concepts are presented within the THERMINATOR Monte-Carlo hadron generator.
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    In this paper we consider a notion of nonmeasurablity with respect to Marczewski and Marczewski-like tree ideals $s_0$, $m_0$, $l_0$, and $cl_0$. We show that there exists a subset $A$ of the Baire space $\omega^\omega$ which is $s$-, $l$-, and $m$-nonmeasurable, that forms dominating m.e.d. family. We introduce and investigate a notion of $\mathbb{T}$-Bernstein sets - sets that intersect but does not containt any body of a tree from a given family of trees $\mathbb{T}$. We also acquire some results on $\mathcal{I}$-Luzin sets, namely we prove that there are no $m_0$-, $l_0$-, and $cl_0$-Luzin sets and that if $\mathfrak{c}$ is a regular cardinal, then the algebraic sum (considered on the real line $\mathbb{R}$) of a generalized Luzin set and a generalized Sierpiński set belongs to $s_0, m_0$, $l_0$ and $cl_0$.
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    We prove a simple equivalence between the virtual count of rational curves in the total space of an anti-nef line bundle and the virtual count of rational curves maximally tangent to a smooth section of the dual line bundle. We conjecture a generalization to direct sums of line bundles.
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    Through the modelling of near-infrared photometry of star plus disk systems with the codes BEDISK/BERAY, we successfully describe the WISE photometric characteristics of Be stars in five young open clusters, NGC 663, NGC 869, NGC 884, NGC 3766 and NGC 4755, broadly studied in the literature. WISE photometry allows previously known Be stars to be detected and to find new Be candidates which could be confirmed spectroscopically. The location of Be stars in the WISE colour-magnitude diagram, separates them in two groups; active (Be stars hosting a developed circumstellar disk) and quiescent objects (Be stars in a diskless phase), and this way, we can explore how often stars are observed in these different stages. The variability observed in most active variable Be stars is compatible with a disk dissipation phase. We find that 50 percent of Be stars in the studied open clusters are in an active phase. We can interpret this as Be stars having a developed circumstellar disk half of the time. The location of Be stars with a developed disk in the CMD require mass loss rates in agreement with values recently reported in the literature. For these objects, we expect to have a tight relation between the equivalent width of the H\alpha line and the mass of the disk, if the inclination is known. Also, near-infrared photometry of Be stars in stellar clusters has the potential of being useful to test whether there is a preferential viewing angle.
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    Binaries in double-lined spectroscopic systems provide a homogeneous set of stars. Differences of parameters, such as age or initial conditions, which otherwise would have strong impact on the stellar evolution, can be neglected. The observed differences are determined by the difference in stellar mass between the two components. The mass ratio can be determined with much higher accuracy than the actual stellar mass. In this work, we aim to study the eccentric binary system KIC9163796, whose two components are very close in mass and both are low-luminosity red-giant stars from four years of Kepler space photometry and high-resolution spectroscopy with Hermes. Mass and radius of the primary were determined through asteroseismology to be 1.39+/-0.06 Mo and 5.35+/-0.09 Ro, resp. From spectral disentangling the mass ratio was found to be 1.015+/-0.005 and that the secondary is ~600K hotter than the primary. Evolutionary models place both components, in the early and advanced stage of the first dredge-up event on the red-giant branch. From theoretical models of the primary, we derived the internal rotational gradient. From a grid of models, the measured difference in lithium abundance is compared with theoretical predictions. The surface rotation of the primary is determined from the Kepler light curve and resembles the orbital period within 10 days. The radial rotational gradient between the surface and core is found to be 6.9+2.0/-1.0. The agreement between the surface rotation with the seismic result indicates that the full convective envelope is rotating quasi-rigidly. The models of the lithium abundance are compatible with a rigid rotation in the radiative zone during the main sequence. Because of the many constraints offered by oscillating stars in binary systems, such objects are important test beds of stellar evolution.
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    Fast digitisers and digital pulse processing have been widely used for spectral application and pulse shape discrimination (PSD) owing to their advantages in terms of compactness, higher trigger rates, offline analysis, etc. Meanwhile, the noise of readout electronics is usually trivial for organic, plastic, or liquid scintillator with PSD ability because of their poor intrinsic energy resolution. However, LaBr3(Ce) has been widely used for its excellent energy resolution and has been proven to have PSD ability for alpha/gamma particles. Therefore, designing a digital acquisition system for such scintillators as LaBr3(Ce) with both optimal energy resolution and promising PSD ability is worthwhile. Several experimental research studies about the choice of digitiser properties for liquid scintillators have already been conducted in terms of the sampling rate and vertical resolution. Quantitative analysis on the influence of waveform digitisers, that is, fast amplifier (optional), sampling rates, and vertical resolution, on both applications is still lacking. The present paper provides quantitative analysis of these factors and, hence, general rules about the optimal design of digitisers for both energy resolution and PSD application according to the noise analysis of time-variant gated charge integration.
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    We consider an optimal control problem for piecewise deterministic Markov processes (PDMPs) on a bounded state space. The control problem under study is very general: a pair of controls acts continuously on the deterministic flow and on the two transition measures (in the interior and from the boundary of the domain) describing the jump dynamics of the process. For this class of control problems, the value function can be characterized as the unique viscosity solution to the corresponding fully-nonlinear Hamilton-Jacobi-Bellman equation with a non-local type boundary condition. By means of the recent control randomization method, we are able to provide a probabilistic representation for the value function in terms of a constrained backward stochastic differential equation (BSDE), known as nonlinear Feynman-Kac formula. This result considerably extends the existing literature, where only the case with no jumps from the boundary is considered. The additional boundary jump mechanism is described in terms of a non quasi-left-continuous random measure and induces predictable jumps in the PDMP's dynamics. The existence and uniqueness results for BSDEs driven by such a random measure are non trivial, even in the unconstrained case, as emphasized in the recent work [2].
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    The algorithm of finding inverse multivector (MV) in a symbolic form is of paramount importance in computational Clifford or geometric algebra (GA) $Cl_{p,q}$. The first attempts of inversion of general MV were based on matrix representation of MV basis elements. However, the complexity of such calculations grows exponentially with the dimension $n=p+q$ of $Cl_{p,q}$ algebra. The breakthrough occurred 10 years later (P. Dadbeh, 2011), after grade-negation operation was introduced. It has allowed to write down explicit and compact inverse MVs as a product of initial MV and its carefully chosen grade-negation counterparts for all GAs up to dimension $n\le5$. In this report we show that the grade-negation self-product method can be extended beyond p+q=5 threshold if, in addition, properly constructed multilinear combinations of such MV products are used. In particular, we write down compact and explicit MV inverse formulas for all $p+q=6$ algebras. For readers convenience we have also presented inverse MVs for lower algebras, $p+q\le 5$, in a form of grade negations.
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    Variations and spatial distributions of bright and dark material on dwarf planet Ceres play a key role for the understanding of the processes that have led to its present surface composition. We define limits for bright and dark material in order to distinguish them consistently, based on the reflectance with respect to the average surface using Dawn Framing Camera data. A systematic classification of four types of bright material is presented based on their spectral properties, composition, spatial distribution, and association with specific geomorphological features. We found obvious correlations of reflectance with spectral shape (slopes) and age; however, this is not unique throughout the bright spots. Although impact features show generally more extreme reflectance variations, several areas can only be understood in terms of inhomogeneous distribution of composition as inferred from Dawn Visible and Infrared Spectrometer data. Additional materials with anomalous composition and spectral properties are rare. The identification of the origin of the dark, and particularly the darkest, material remains to be explored. The spectral properties and the morphology of the dark sites suggest an endogenic origin, but it is not clear whether they are more or less primitive surficial exposures or excavated sub-surface but localized material. The reflectance, spectral properties, inferred composition, and geologic context collectively suggest that the bright and dark materials tend to gradually change towards the average surface over time. This could be because of multiple processes, i.e., impact gardening/space weathering, and lateral mixing, including thermal and aqueous alteration, accompanied with changes in composition and physical properties such as grain size, surface temperature, porosity (compaction).
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    Cellular Automata (CAs) are computational models that can capture the essential features of systems in which global behavior emerges from the collective effect of simple components, which interact locally. During the last decades, CAs have been extensively used for mimicking several natural processes and systems to find fine solutions in many complex hard to solve computer science and engineering problems. Among them, the shortest path problem is one of the most pronounced and highly studied problems that scientists have been trying to tackle by using a plethora of methodologies and even unconventional approaches. The proposed solutions are mainly justified by their ability to provide a correct solution in a better time complexity than the renowned Dijkstra's algorithm. Although there is a wide variety regarding the algorithmic complexity of the algorithms suggested, spanning from simplistic graph traversal algorithms to complex nature inspired and bio-mimicking algorithms, in this chapter we focus on the successful application of CAs to shortest path problem as found in various diverse disciplines like computer science, swarm robotics, computer networks, decision science and biomimicking of biological organisms' behaviour. In particular, an introduction on the first CA-based algorithm tackling the shortest path problem is provided in detail. After the short presentation of shortest path algorithms arriving from the relaxization of the CAs principles, the application of the CA-based shortest path definition on the coordinated motion of swarm robotics is also introduced. Moreover, the CA based application of shortest path finding in computer networks is presented in brief. Finally, a CA that models exactly the behavior of a biological organism, namely the Physarum's behavior, finding the minimum-length path between two points in a labyrinth is given.
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    Nd2Hf2O7, belonging to the family of geometrically frustrated cubic rare earth pyrochlore oxides, was recently identified to order antiferromagnetically below T_N = 0.55 K with an all-in/all-out arrangement of Nd3+ moments, however with a much reduced ordered state moment. Herein we investigate the spin dynamics and crystal field states of Nd2Hf2O7 using muon spin relaxation (muSR) and inelastic neutron scattering (INS) measurements. Our muSR study confirms the long range magnetic ordering and shows evidence for coexisting persistent dynamic spin fluctuations deep inside the ordered state down to 42 mK. The INS data show the crytal electric field (CEF) excitations due to the transitions both within the ground state multiplet and to the first excited state multiplet. The INS data are analyzed by a model based on CEF and crystal field states are determined. Strong Ising-type anisotropy is inferred from the ground state wavefunction. The CEF parameters indicate the CEF-split Kramers doublet ground state of Nd3+ to be consistent with the dipolar-octupolar character.
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    Magnetic resonance imaging (MRI) is an effective imaging modality for identifying and localizing breast lesions in women. Accurate and precise lesion segmentation using a computer-aided-diagnosis (CAD) system, is a crucial step in evaluating tumor volume and in the quantification of tumor characteristics. However, this is a challenging task, since breast lesions have sophisticated shape, topological structure, and high variance in their intensity distribution across patients. In this paper, we propose a novel marker-controlled watershed transformation-based approach, which uses the brightest pixels in a region of interest (determined by experts) as markers to overcome this challenge, and accurately segment lesions in breast MRI. The proposed approach was evaluated on 106 lesions, which includes 64 malignant and 42 benign cases. Segmentation results were quantified by comparison with ground truth labels, using the Dice similarity coefficient (DSC) and Jaccard index (JI) metrics. The proposed method achieved an average Dice coefficient of 0.7808$\pm$0.1729 and Jaccard index of 0.6704$\pm$0.2167. These results illustrate that the proposed method shows promise for future work related to the segmentation and classification of benign and malignant breast lesions.
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    We consider scalar conservation laws with nonlocal diffusion of Riesz-Feller type such as the fractal Burgers equation. The existence of traveling wave solutions with monotone decreasing profile has been established recently (in special cases). We show the local asymptotic stability of these traveling wave solutions in a Sobolev space setting by constructing a Lyapunov functional. Most importantly, we derive the algebraic-in-time decay of the norm of such perturbations with explicit algebraic-in-time decay rates.
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Recent comments

Andrew W Simmons Dec 14 2017 11:40 UTC

Hi Māris, you might well be right! Stabiliser QM with more qubits, I think, is also a good candidate for further investigation to see if we can close the gap a bit more between the analytical upper bound and the example-based lower bound.

Planat Dec 14 2017 08:43 UTC

Interesting work. You don't require that the polar space has to be symplectic. In ordinary quantum mechanics the commutation of n-qudit observables is ruled by a symplectic polar space. For two qubits, it is the generalized quadrangle GQ(2,2). Incidently, in https://arxiv.org/abs/1601.04865 this pro

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Māris Ozols Dec 12 2017 19:41 UTC

$E_7$ also has some nice properties in this regard (in fact, it might be even better than $E_8$). See https://arxiv.org/abs/1009.1195.

Danial Dervovic Dec 10 2017 15:25 UTC

Thank you for the insightful observations, Simon.

In response to the first point, there is a very short comment in the Discussion section to this effect. I felt an explicit dependence on $T$ as opposed to the diameter would make the implications of the result more clear. Namely, lifting can mix

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Simon Apers Dec 09 2017 07:54 UTC

Thanks for the comment, Simone. A couple of observations:

- We noticed that Danial's result can in fact be proved more directly using the theorem that is used from ([arXiv:1705.08253][1]): by choosing the quantum walk Cesaro average as the goal distribution, it can be attained with a lifted Markov

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Simone Severini Dec 07 2017 02:51 UTC

Closely related to

Simon Apers, Alain Sarlette, Francesco Ticozzi, Simulation of Quantum Walks and Fast Mixing with Classical Processes, https://scirate.com/arxiv/1712.01609

In my opinion, lifting is a good opportunity to put on a rigorous footing the relationship between classical and quantu

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Mark Everitt Dec 05 2017 07:50 UTC

Thank you for the helpful feedback.

Yes these are 14 pairs of graphs [This is an edit - I previously mistakenly posted that it was 7 pairs] that share the same equal angle slice. We have only just started looking at the properties of these graphs. Thank you for the link - that is a really useful r

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Simone Severini Dec 05 2017 01:13 UTC

When looking at matrix spectra as graph invariants, it is easy to see that the spectrum of the adjacency matrix or the Laplacian fails for 4 vertices. Also, the spectrum of the adjacency matrix together with the spectrum of the adjacency matrix of the complement fail for 7 vertices. So, the algorith

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Mark Everitt Dec 04 2017 17:52 UTC

Thank you for this - its the sort of feedback we were after.

We have found 14 examples of 8 node graphs (of the possible 12,346) that break our conjecture.

We are looking into this now to get some understanding and see if we can overcome this issue. We will check to see if the failure of our algo

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Dave Bacon Dec 02 2017 00:08 UTC

A couple of comments:

1. To be a complete algorithm I think you need to specify how many of the equal angles you need to sample from (i.e. how many Euler angles)? And also maybe what "experimental accuracy means"? If those are exponential in order to work that's bad (but still very interesting

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