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    The study of time-varying (dynamic) networks (graphs) is of fundamental importance for computer network analytics. Several methods have been proposed to detect the effect of significant structural changes in a time series of graphs. The main contribution of this work is a detailed analysis of a dynamic community graph model. This model is formed by adding new vertices, and randomly attaching them to the existing nodes. It is a dynamic extension of the well-known stochastic blockmodel. The goal of the work is to detect the time at which the graph dynamics switches from a normal evolution -- where balanced communities grow at the same rate -- to an abnormal behavior -- where communities start merging. In order to circumvent the problem of decomposing each graph into communities, we use a metric to quantify changes in the graph topology as a function of time. The detection of anomalies becomes one of testing the hypothesis that the graph is undergoing a significant structural change. In addition the the theoretical analysis of the test statistic, we perform Monte Carlo simulations of our dynamic graph model to demonstrate that our test can detect changes in graph topology.
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    We compute modifications to the jet spectrum in the presence of a dense medium. We show that in the large-$N_c$ approximation and at leading logarithmic accuracy the jet nuclear modification factor factorizes into a quenching factor associated to the total jet color charge and a Sudakov suppression factor which accounts for the energy loss of jet substructure fluctuations. This factor, called the jet collimator, implements the fact that subjets, that are not resolved by the medium, lose energy coherently as a single color charge, whereas resolved large angle fluctuations suffer more quenching. For comparison, we show that neglecting color coherence results in a stronger suppression of the jet nuclear modification factor.
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    In this article, we derive an inequality of Łojasiewicz-Siciak type for certain sets arising in the context of the complex dynamics in dimension 1. More precisely, if we denote by $dist$ the euclidian distance in $\mathbb{C}$, we show that the Green function $G_K$ of the filled Julia set $K$ of a polynomial such that $\mathring{K}\neq \emptyset$ satisfies the so-called ŁS condition $\displaystyle G_A\geq c\cdot dist(\cdot, K)^{c'}$ in a neighborhood of $K$, for some constants $c,c'>0$. Relatively few examples of compact sets satisfying the ŁS condition are known. Our result highlights an interesting class of compact sets fulfilling this condition. The fact that filled Julia sets satisfy the ŁS condition may seem surprising, since they are in general very irregular. In order to prove our main result, we define and study the set of obstruction points to the ŁS condition. We also prove, in dimension $n\geq 1$, that for a polynomially convex and L-regular compact set of non empty interior, these obstruction points are rare, in a sense which will be specified.
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    The resolution of photoacoustic imaging deep inside scattering media is limited by the acoustic diffraction limit. In this work, taking inspiration from super-resolution imaging techniques developed to beat the optical diffraction limit, we demonstrate that the localization of individual optical absorbers can provide super-resolution photoacoustic imaging well beyond the acoustic diffraction limit. As a proof-of-principle experiment, photoacoustic cross-sectional images of microfluidic channels were obtained with a 15 MHz linear CMUT array while absorbing beads were flown through the channels. The localization of individual absorbers allowed to obtain super-resolved cross-sectional image of the channels, by reconstructing both the channel width and position with an accuracy better than $\lambda/10$. Given the discrete nature of endogenous absorbers such as red blood cells, or that of exogenous particular contrast agents, localization is a promising approach to push the current resolution limits of photoacoustic imaging.
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    We study the problem of construction of rationally extended quantum isotonic oscillator systems of a general form and a related issue of finding the complete sets of ladder operators for them. For this we develop the method of the mirror diagrams based on the dual schemes of the Darboux-Crum transformations to generate rational deformations of the isotonic oscillator systems from the quantum harmonic oscillator. We show that unlike the rationally extended quantum harmonic oscillator systems case, one can obtain infinite families of completely isospectral rational extensions of the isotonic oscillator in addition to non-isospectral gapped deformations. For each completely isospectral or gapped deformation of the isotonic oscillator system given by a mirror diagram, we identify the sets of spectrum-generating ladder operators which coherently reflect its peculiarities such as the number of the valence bands, the total number of the energy levels in them, and the spacing between energy levels of the ground state and the lowest state in the infinite equidistant part of the spectrum.
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    By performing 2.5-dimensional general relativistic radiation magnetohydrodynamic simulations, we demonstrate supercritical accretion onto a non-rotating, magnetized neutron star, where the magnetic field strength of dipole fields is $10^{10}$ G on the star surface. We found the supercritical accretion flow consists of two parts; the accretion columns and the truncated accretion disk. The supercritical accretion disk, which appears far from the neutron star, is truncated at around $\sim 3R_*$ ($R_*=10^6$ cm is the neutron star radius), where the magnetic pressure via the dipole magnetic fields balances with the radiation pressure of the disks. The angular momentum of the disk around the truncation radius is effectively transported inward through magnetic torque by dipole fields, inducing the spin up of a neutron star. The evaluated spin up rate, $\sim -10^{-11}$ s s$^{-1}$, is consistent with the recent observations of the ultra luminous X-ray pulsars. Within the truncation radius, the gas falls onto neutron star along dipole fields, which results in a formation of accretion columns onto north and south hemispheres. The net accretion rate and the luminosity of the column are $\sim 66L_{\rm Edd}/c^2$ and $\lesssim 10L_{\rm Edd}$, where $L_{\rm Edd}$ is the Eddington luminosity and c is the light speed. Our simulations support a hypothesis whereby the ultra luminous X-ray pulsars are powered by the supercritical accretion onto the magnetized neutron stars.
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    Non-equilibrium Green's Function (NGF) method is a powerful tool for studying the evolution of quantum many-body systems. Different types of correlations can be systematically incorporated within the formalism. The time evolution of the single-particle Green's functions is described in terms of the Kadanoff-Baym equations. The current work initially focuses on introducing the correlations within infinite nuclear matter in one dimension and then in a finite system in the NGF approach. Starting from the harmonic oscillator Hamiltonian, by switching on adiabatically the mean-field and correlations simultaneously, a correlated state with ground-state characteristics is arrived at within the NGF method. Furthermore the use of cooling to for improving the adiabatic switching is explored.
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    We investigate the robustness of the Araki-Lieb inequality in a two-dimensional (2D) conformal field theory (CFT) on torus. The inequality requires that $\Delta S=S(L)-|S(L-\ell)-S(\ell)|$ is nonnegative, where $S(L)$ is the thermal entropy and $S(L-\ell)$, $S(\ell)$ are the entanglement entropies. Holographically there is an entanglement plateau in the BTZ black hole background, which means that there exists a critical length such that when $\ell \leq \ell_c$ the inequality saturates $\Delta S=0$. In thermal AdS background, the holographic entanglement entropy leads to $\Delta S=0$ for arbitrary $\ell$. We compute the next-to-leading order contributions to $\Delta S$ in the large central charge CFT at both high and low temperatures. In both cases we show that $\Delta S$ is strictly positive except for $\ell = 0$ or $\ell = L$. This turns out to be true for any 2D CFT. In calculating the single interval entanglement entropy in a thermal state, we develop new techniques to simplify the computation. At a high temperature, we ignore the finite size correction such that the problem is related to the entanglement entropy of double intervals on a complex plane. As a result, we show that the leading contribution from a primary module takes a universal form. At a low temperature, we show that the leading thermal correction to the entanglement entropy from a primary module does not take a universal form, depending on the details of the theory.
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    Consider a (possibly big) silting object $U$ in a derived category over a (dg-)algebra $A$. Under some fairly general appropriate hypotheses, we show that it induces derived equivalences between the derived category over $A$ and a localization of the derived category of dg-endomorphism algebra $B$ of $U$. If, in addition, $U$ is small then this localization is the whole derived category over $B$. We also study the way in which these equivalences restrict to some subcategories of module categories, providing a correspondent for the celebrated Tilting Theorem.
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    The optical conductivity of a metal near a quantum critical point (QCP) is expected to depend on frequency not only via the scattering time but also via the effective mass, which acquires a singular frequency dependence near a QCP. We check this assertion by computing diagrammatically the optical conductivity, $\sigma' (\Omega)$, near both nematic and spin-density wave (SDW) quantum critical points (QCPs) in 2D. If renormalization of current vertices is not taken into account, $\sigma' (\Omega)$ is expressed via the quasiparticle residue $Z$ (equal to the ratio of bare and renormalized masses in our approximation) and transport scattering rate $\gamma_{\text{tr}}$ as $\sigma' (\Omega)\propto Z^2 \gamma_{\text{tr}}/\Omega^2$. For a nematic QCP ($\gamma_{\text{tr}}\propto\Omega^{4/3}$ and $Z\propto\Omega^{1/3}$), this formula suggests that $\sigma'(\Omega)$ would tend to a constant at $\Omega \to 0$. We explicitly demonstrate that the actual behavior of $\sigma' (\Omega)$ is different due to strong renormalization of the current vertices, which cancels out a factor of $Z^2$. As a result, $\sigma' (\Omega)$ diverges as $1/\Omega^{2/3}$, as earlier works conjectured. In the SDW case, we consider two contributions to the conductivity: from hot spots and from"lukewarm" regions of the Fermi surface. The hot-spot contribution is not affected by vertex renormalization, but it is subleading to the lukewarm one. For the latter, we argue that a factor of $Z^2$ is again cancelled by vertex corrections. As a result, $\sigma' (\Omega)$ at a SDW QCP scales as $1/\Omega$ down to the lowest frequencies.
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    In part I we considered the problem of convergence to a saddle point of a concave-convex function via gradient dynamics and an exact characterization was given to their asymptotic behaviour. In part II we consider a general class of subgradient dynamics that provide a restriction in an arbitrary convex domain. We show that despite the nonlinear and non-smooth character of these dynamics their $\omega$-limit set is comprised of solutions to only linear ODEs. In particular, we show that the latter are solutions to subgradient dynamics on affine subspaces which is a smooth class of dynamics the asymptotic properties of which have been exactly characterized in part I. Various convergence criteria are formulated using these results and several examples and applications are also discussed throughout the manuscript.
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    We investigate the fluctuations of cumulative density of the asymmetric simple exclusion process with respect to the stationary distribution (also known as the steady state), as a stochastic process indexed by $[0,1]$. In three phases of the model and their boundaries within the fan region, we establish a complete picture of the scaling limits of the fluctuations of the density as the number of sites goes to infinity. In the maximal current phase, the limit fluctuation is the sum of two independent processes, a Brownian motion and a Brownian excursion. This extends an earlier result by Derrida et al. (2004) for totally asymmetric simple exclusion process in the same phase. In the low/high density phases, the limit fluctuations are Brownian motion. Most interestingly, at the boundary of the maximal current phase, the limit fluctuation is the sum of two independent processes, a Brownian motion and a Brownian meander (or a time-reversal of the latter, depending on the side of the boundary). The proof is based on a recently revealed relation between the generating function of asymmetric simple exclusion processes and Askey--Wilson processes.
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    We consider the problem of convergence to a saddle point of a concave-convex function via gradient dynamics. Since first introduced by Arrow, Hurwicz and Uzawa in [1] such dynamics have been extensively used in diverse areas, there are, however, features that render their analysis non trivial. These include the lack of convergence guarantees when the function considered is not strictly concave-convex and also the non-smoothness of subgradient dynamics. Our aim in this two part paper is to provide an explicit characterization to the asymptotic behaviour of general gradient and subgradient dynamics applied to a general concave-convex function. We show that despite the nonlinearity and non-smoothness of these dynamics their $\omega$-limit set is comprised of trajectories that solve only explicit linear ODEs that are characterized within the paper. More precisely, in Part I an exact characterization is provided to the asymptotic behaviour of unconstrained gradient dynamics. We also show that when convergence to a saddle point is not guaranteed then the system behaviour can be problematic, with arbitrarily small noise leading to an unbounded variance. In Part II we consider a general class of subgradient dynamics that restrict trajectories in an arbitrary convex domain, and show that their limiting trajectories are solutions of subgradient dynamics on only affine subspaces. The latter is a smooth class of dynamics with an asymptotic behaviour exactly characterized in Part I, as solutions to explicit linear ODEs. These results are used to formulate corresponding convergence criteria and are demonstrated with several examples and applications presented in Part II.
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    Two common approaches of studying theoretically the property of a superconductor are shown to have significant differences, when they are applied to the Larkin-Ovchinnikov state of Weyl metals. In the first approach the pairing term is restricted by a cutoff energy to the neighborhood of the Fermi surface, whereas in the second approach the pairing term is extended to the whole Brillouin zone. We explore their difference by considering two minimal models for the Weyl metal. For a model giving a single pair of Weyl pockets, both two approaches give a partly-gapped (fully-gapped) bulk spectrum for small (large) pairing amplitude. However, for very small cutoff energy, a portion of the Fermi surface can be completely unaffected by the pairing term in the first approach. For the other model giving two pairs of Weyl pockets, while the bulk spectrum for the first approach can be fully gapped, the one from the second approach has a robust line node, and the surface states are also changed qualitatively by the pairing. We elucidate the above differences by topological arguments and analytical analyses. A factor common to both of the two models is the tilting of the Weyl cones which leads to asymmetric normal state band structure with respect to the Weyl nodes. For the Weyl metal with two pairs of Weyl pockets, the band folding leads to a double degeneracy in the effective model, which distinguishes the pairing of the second approach from all others.
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    We develop a local positivity theory for movable curves on projective varieties similar to the classical Seshadri constants of nef divisors. We give analogues of the Seshadri ampleness criterion, of a characterization of the augmented base locus of a big and nef divisor, and of the interpretation of Seshadri constants as an asymptotic measure of jet separation.
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    Spectral projectors of second order differential operators play an important role in quantum physics and other scientific and engineering applications. In order to resolve local features and to obtain converged results, typically the number of degrees of freedom needed is much larger than the rank of the spectral projector. This leads to significant cost in terms of both computation and storage. In this paper, we develop a method to construct a basis set that is adaptive to the given differential operator. The basis set is systematically improvable, and the local features of the projector is built into the basis set. As a result the required number of degrees of freedom is only a small constant times the rank of the projector. The construction of the basis set uses a randomized procedure, and only requires applying the differential operator to a small number of vectors on the global domain, while each basis function itself is supported on strictly local domains and is discontinuous across the global domain. The spectral projector on the global domain is systematically approximated from such a basis set using the discontinuous Galerkin (DG) method. The global construction procedure is very flexible, and allows a local basis set to be consistently constructed even if the operator contains a nonlocal potential term. We verify the effectiveness of the globally constructed adaptive local basis set using one-, two- and three-dimensional linear problems with local potentials, as well as a one dimensional nonlinear problem with nonlocal potentials resembling the Hartree-Fock problem in quantum physics.
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    We study some mathematical aspects of the Mahjong game. In particular, we use combinatorial theory and write a Python program to study some special features of the game. The results confirm some folklore concerning the game, and expose some unexpected results. Related results and possible future research in connection to artificial intelligence are mentioned.
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    We define a simple dependent type theory and prove that its well-formed types correspond exactly to finite inverse categories.
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    Details of the London pilot of the `Discovery Project' are presented, where university-based astronomers were given the chance to pass on some real and applied knowledge of astronomy to a group of selected secondary school pupils. It was aimed at students in Key Stage 3 of their education, allowing them to be involved in real astronomical research at an early stage of their education, the chance to become the official discoverer of a new variable star, and to be listed in the International Variable Star Index database, all while learning and practising research-level skills. Future plans are discussed.
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    A major topic of investigation in differential geometry is the study of geodesic spheres, which in particular turns the understanding of spherical curves of great importance. In this respect, the consideration of rotation minimizing (RM) frames along curves play a prominent role. Indeed, due to their minimal twist, in many contexts these frames are preferable over the usual Frenet one and, in addition, they allow for a simple and elegant characterization of spherical curves in Euclidean space via a linear equation (a line not passing through the origin) involving the coefficients that dictate the frame motion, in contrast with a differential equation from a Frenet frame approach. In this work, we extend these investigations in order to characterize curves that lie on the (hyper)surface of geodesic spheres in a Riemannian manifold. Using that geodesic spherical curves are normal curves, i.e., the geodesics connecting the curve to a fixed point induce a normal vector field along the curve, we are able to characterize geodesic spherical curves in hyperbolic spaces and spheres through a linear equation (line not passing through the origin) involving the coefficients that dictate the RM frame motion. Finally, we also show that curves on totally geodesic submanifolds, which play the role of planes in Riemannian geometry, should be characterized by a line passing through the origin. In short, our results give interesting and significant similarities between hyperbolic, spherical, and Euclidean geometries.
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    We study which property testing and sublinear time algorithms can be transformed into graph streaming algorithms for random order streams. Our main result is that for bounded degree graphs, any property that is constant-query testable in the adjacency list model can be tested with constant space in a single-pass in random order streams. Our result is obtained by estimating the distribution of local neighborhoods of the vertices on a random order graph stream using constant space. We then show that our approach can also be applied to constant time approximation algorithms for bounded degree graphs in the adjacency list model: As an example, we obtain a constant-space single-pass random order streaming algorithms for approximating the size of a maximum matching with additive error $\epsilon n$ ($n$ is the number of nodes). Our result establishes for the first time that a large class of sublinear algorithms can be simulated in random order streams, while $\Omega(n)$ space is needed for many graph streaming problems for adversarial orders.
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    Recently a consistent non-perturbative quantization of the Schwarzschild interior resulting in a bounce from black hole to white hole geometry has been obtained by loop quantizing the Kantowski-Sachs vacuum spacetime. As in other spacetimes where the singularity is dominated by the Weyl part of the spacetime curvature, the structure of the singularity is highly anisotropic in the Kantowski-Sachs vacuum spacetime. As a result the bounce turns out to be in general asymmetric creating a large mass difference between the parent black hole and the child white hole. In this manuscript, we investigate under what circumstances a symmetric bounce scenario can be constructed in the above quantization. Using the setting of Dirac observables and geometric clocks we obtain a symmetric bounce condition which can be satisfied by a slight modification in the construction of loops over which holonomies are considered in the quantization procedure. These modifications can be viewed as quantization ambiguities, and are demonstrated in three different flavors which all lead to a non-singular black to white hole transition with identical masses. Our results show that quantization ambiguities can mitigate or even qualitatively change some key features of physics of singularity resolution. Further, these results are potentially helpful in motivating and constructing symmetric black to white hole transition scenarios.
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    Preprocessing tools for automated text analysis have become more widely available in major languages, but non-English tools are often still limited in their functionality. When working with Spanish-language text, researchers can easily find tools for tokenization and stemming, but may not have the means to extract more complex word features like verb tense or mood. Yet Spanish is a morphologically rich language in which such features are often identifiable from word form. Conjugation rules are consistent, but many special verbs and nouns take on different rules. While building a complete dictionary of known words and their morphological rules would be labor intensive, resources to do so already exist, in spell checkers designed to generate valid forms of known words. This paper introduces a set of tools for Spanish-language morphological analysis, built using the COES spell checking tools, to label person, mood, tense, gender and number, derive a word's root noun or verb infinitive, and convert verbs to their nominal form.
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    A detailed study of energy dependence of positive kaon to pion, negative kaon to pion and total kaon to pion multiplicity ratio have been carried out in pp collisions at 6.3, 17.3, 62.4, 200 and 900 GeV and also at root s =2.76 TeV and 7 TeV in the framework of UrQMD and DPMJET III model. Energy dependence of positive kaon to pion and negative kaon to pion show different behavior in case of UrQMD and DPMJET III model. The presence of the horn like structure in the variation of positive kaon to pion and negative kaon to pion ratio with energy for the experimental data is supported by the DPMJET III model. Experimentally it has been observed that as energy increases, the total kaon to pion multiplicity ratio increases systematically for pp collisions at lower energies and becomes independent of energy in LHC energy regime. Our analysis on total kaon to pion multiplicity ratio with UrQMD data is well supported by the experimental results obtained by different collaborations in different times. In case of DPMJET III data, the saturation of kaon to pion ratio at LHC region has not been observed.
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    We consider the problem of optimal estimation of the value of a vector parameter $\thetavector=(\theta_0,\ldots,\theta_n)^{\top}$ of the drift term in a fractional Brownian motion represented by the finite sum $\sum_{i=0}^{n}\theta_{i}\varphi_{i}(t)$ over known functions $\varphi_i(t)$, $\alli$. For the value of parameter $\thetavector$, we obtain a maximum likelihood estimate as well as Bayesian estimates for normal and uniform a priori distributions.
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    This paper analyzes sequences generated by infeasible interior point methods. In convex and non-convex settings, we prove that moving the primal feasibility at the same rate as complementarity will ensure that the Lagrange multiplier sequence will remain bounded, provided the limit point of the primal sequence has a Lagrange multiplier, without constraint qualification assumptions. We also show that maximal complementarity holds, which guarantees the algorithm finds a strictly complementary solution, if one exists. Alternatively, in the convex case, if the primal feasibility is reduced too fast and the set of Lagrange multipliers is unbounded, then the Lagrange multiplier sequence generated will be unbounded. Conversely, if the primal feasibility is reduced too slowly, the algorithm will find a minimally complementary solution. We also demonstrate that the dual variables of the interior point solver IPOPT become unnecessarily large on Netlib problems, and we attribute this to the solver reducing the constraint violation too quickly.
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    We review and extend several recent results on the existence of the ground state for the nonlinear Schrödinger (NLS) equation on a metric graph. By ground state we mean a minimizer of the NLS energy functional constrained to the manifold of fixed $L^2$-norm. In the energy functional we allow for the presence of a potential term, of delta-interactions in the vertices of the graph, and of a power-type focusing nonlinear term. We discuss both subcritical and critical nonlinearity. Under general assumptions on the graph and the potential, we prove that a ground state exists for sufficiently small mass, whenever the constrained infimum of the quadratic part of the energy functional is strictly negative.
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    The hidden metric space behind complex network topologies is a fervid topic in current network science and the hyperbolic space is one of the most studied, because it seems associated to the structural organization of many real complex systems. The Popularity-Similarity-Optimization (PSO) model simulates how random geometric graphs grow in the hyperbolic space, reproducing strong clustering and scale-free degree distribution, however it misses to reproduce an important feature of real complex networks, which is the community organization. The Geometrical-Preferential-Attachment (GPA) model was recently developed to confer to the PSO also a community structure, which is obtained by forcing different angular regions of the hyperbolic disk to have variable level of attractiveness. However, the number and size of the communities cannot be explicitly controlled in the GPA, which is a clear limitation for real applications. Here, we introduce the nonuniform PSO (nPSO) model that, differently from GPA, forces heterogeneous angular node attractiveness by sampling the angular coordinates from a tailored nonuniform probability distribution, for instance a mixture of Gaussians. The nPSO differs from GPA in other three aspects: it allows to explicitly fix the number and size of communities; it allows to tune their mixing property through the network temperature; it is efficient to generate networks with high clustering. After several tests we propose the nPSO as a valid and efficient model to generate networks with communities in the hyperbolic space, which can be adopted as a realistic benchmark for different tasks such as community detection and link prediction.
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    Diffusion couple technique is an efficient tool for the estimating the chemical diffusion coefficients. Typical experimental uncertainties of the composition profile measurements complicate a correct determination of the interdiffusion coefficients via the standard Boltzmann-Matano, Sauer-Freise or the den Broeder methods, especially for systems with a strong compositional dependence of the interdiffusion coefficient. A new approach for reliable fitting of the experimental profiles with an improved behavior at both ends of the diffusion couple is proposed and tested against the experimental data on chemical diffusion in the system Fe-Ga
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    Let $\mathbb{F}$ be a finite field, an algebraically closed field, or the field of real numbers. Consider the vector space $V=\mathbb{F}^3 \otimes \mathbb{F}^3$ of $3 \times 3$ matrices over $\mathbb{F}$, and let $G \leq \text{PGL}(V)$ be the setwise stabiliser of the corresponding Segre variety $S_{3,3}(\mathbb{F})$ in the projective space $\text{PG}(V)$. The $G$-orbits of lines in $\text{PG}(V)$ were determined by the first author and Sheekey as part of their classification of tensors in $\mathbb{F}^2 \otimes V$ in the article "Canonical forms of $2 \times 3 \times 3$ tensors over the real field, algebraically closed fields, and finite fields", Linear Algebra Appl. 476 (2015) 133-147. Here we consider the related problem of classifying those line orbits that may be represented by \em symmetric matrices, or equivalently, of classifying the line orbits in the $\mathbb{F}$-span of the Veronese variety $\mathcal{V}_3(\mathbb{F}) \subset S_{3,3}(\mathbb{F})$ under the natural action of $K=\text{PGL}(3,\mathbb{F})$. Interestingly, several of the $G$-orbits that have symmetric representatives split under the action of $K$, and in many cases this splitting depends on the characteristic of $\mathbb{F}$. The corresponding orbit sizes and stabiliser subgroups of $K$ are also determined in the case where $\mathbb{F}$ is a finite field, and connections are drawn with old work of Jordan, Dickson and Campbell on the classification of pencils of conics in $\text{PG}(2,\mathbb{F})$, or equivalently, of pairs of ternary quadratic forms over $\mathbb{F}$.
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    The main of this paper is to introduce a family of risk measures which generalizes the Gini-type measures of risk and variability, by taking into consideration the psychological behavior. Our risk measures family is coherent and catches variability with respect to the decision-maker attitude towards risk.
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    Using a non-Laver modification of Uri Abraham's minimal $\varDelta^1_3$ collapse function, we define a generic extension $L[a]$ by a real $a$, in which, for a given $n\ge3$, $\{a\}$ is a lightface $\varPi^1_n$ singleton, $a$ effectively codes a cofinal map $\omega\to\omega_1^L$ minimal over $L$, while every $\varSigma^1_n$ set $X\subseteq\omega$ is still constructible.
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    We show rational homological stability for the homotopy automorphisms and block diffeomorphims of iterated connected sums of products of spheres. The spheres can have different dimension, but need to satisfy a certain connectivity assumption. The main theorems of this paper extend homological stability results for automorphism spaces of connected sums of products of spheres of the same dimension by Berglund and Madsen.
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    The purpose of this paper is to identify all eight of the basic Cayley-Dickson doubling products. A Cayley-Dickson algebra $\cda{N+1}$ of dimension $2^{N+1}$ consists of all ordered pairs of elements of a Cayley-Dickson algebra $\cda{N}$ of dimension $2^N$ where the product $(a,b)(c,d)$ of elements of $\cda{N+1}$ is defined in terms of a pair of second degree binomials $\left(f(a,b,c,d),g(a,b,c,d)\right)$ satisfying certain properties. The polynomial pair$(f,g)$ is called a `doubling product.' While $\cda{0}$ may denote any ring, here it is taken to be the set $\mathbb{R}$ of real numbers. The binomials $f$ and $g$ should be devised such that $\cda{1}=\mathbb{C}$ the complex numbers, $\cda{2}=\mathbb{H}$ the quaternions, and $\cda{3}=\mathbb{O}$ the octonions. Historically, various researchers have used different yet equivalent doubling products.
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    Let $M$ be a II$_1$ factor with a von Neumann subalgebra $Q\subset M$ that has infinite index under any projection in $Q'\cap M$ (e.g., $Q$ abelian; or $Q$ an irreducible subfactor with infinite Jones index). We prove that given any separable subalgebra $B$ of the ultrapower II$_1$ factor $M^\omega$, for a non-principal ultrafilter $\omega$ on $\Bbb N$, there exists a unitary element $u\in M^\omega$ such that $uBu^*$ is orthogonal to $Q^\omega$.
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    The purpose of this paper is to investigate the asymptotic behavior of automorphism groups of function fields when genus tends to infinity. Motivated by applications in coding and cryptography, we consider the maximum size of abelian subgroups of the automorphism group $\mbox{Aut}(F/\mathbb{F}_q)$ in terms of genus ${g_F}$ for a function field $F$ over a finite field $\mathbb{F}_q$. Although the whole group $\mbox{Aut}(F/\mathbb{F}_q)$ could have size $\Omega({g_F}^4)$, the maximum size $m_F$ of abelian subgroups of the automorphism group $\mbox{Aut}(F/\mathbb{F}_q)$ is upper bounded by $4g_F+4$ for $g_F\ge 2$. In the present paper, we study the asymptotic behavior of $m_F$ by defining $M_q=\limsup_{{g_F}\rightarrow\infty}\frac{m_F \cdot \log_q m_F}{{g_F}}$, where $F$ runs through all function fields over $\mathbb{F}_q$. We show that $M_q$ lies between $2$ and $3$ (or $4$) for odd characteristic (or for even characteristic, respectively). This means that $m_F$ grows much more slowly than genus does asymptotically. The second part of this paper is to study the maximum size $b_F$ of subgroups of $\mbox{Aut}(F/\mathbb{F}_q)$ whose order is coprime to $q$. The Hurwitz bound gives an upper bound $b_F\le 84(g_F-1)$ for every function field $F/\mathbb{F}_q$ of genus $g_F\ge 2$. We investigate the asymptotic behavior of $b_F$ by defining ${B_q}=\limsup_{{g_F}\rightarrow\infty}\frac{b_F}{{g_F}}$, where $F$ runs through all function fields over $\mathbb{F}_q$. Although the Hurwitz bound shows ${B_q}\le 84$, there are no lower bounds on $B_q$ in literature. One does not even know if ${B_q}=0$. For the first time, we show that ${B_q}\ge 2/3$ by explicitly constructing some towers of function fields in this paper.
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    A function field over a finite field is called maximal if it achieves the Hasse-Weil bound. Finding possible genera that maximal function fields achieve has both theoretical interest and practical applications to coding theory and other topics. As a subfield of a maximal function field is also maximal, one way to find maximal function fields is to find all subfields of a maximal function field. Due to the large automorphism group of the Hermitian function field, it is natural to find as many subfields of the Hermitian function field as possible. In literature, most of papers studied subfields fixed by subgroups of the decomposition group at one point (usually the point at infinity). This is because it becomes much more complicated to study the subfield fixed by a subgroup that is not contained in the decomposition group at one point. In this paper, we study subfields of the Hermitian function field fixed by subgroups that are not contained in the decomposition group of any point except the cyclic subgroups. It turns out that some new maximal function fields are found.
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Recent comments

SHUAI ZHANG Jul 26 2017 00:20 UTC

I am still working on improving this survey. If you have any suggestions, questions or find any mistakes, please do not hesitate to contact me: shuai.zhang@student.unsw.edu.au.

gae Jul 25 2017 23:19 UTC

Dear Marco, that representation does not depend on the specific channel as long as the input and output dimensions are fixed (in DV). Said in other words you may always choose the same representation. Let me remark that the only teleportation channels we know in DVs are: 1) Pauli channels (from dime

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Marco Piani Jul 25 2017 22:07 UTC

Thanks gae. I see in Definition 7 of "WH- teleportation channel" in https://arxiv.org/pdf/1706.05384.pdf that

> $V (g)$ is a (generally different) representation of the [Weyl-Heisenberg] group

I take that such a different representation depends on the channel. Thus, I imagine that in general

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Alvaro M. Alhambra Jul 24 2017 16:10 UTC

This paper has just been updated and we thought it would be a good
idea to advertise it here. It was originally submitted a year ago, and
it has now been essentially rewritten, with two new authors added.

We have fixed some of the original results and now we:
-Show how some fundamental theorem

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gae Jul 21 2017 17:58 UTC

Dear Marco, indeed the description in those two papers is very general because they treat both DV and CV channels. However, things become "easier" and more specific if you restrict things to DVs. In this regard, let me point you at this paper https://arxiv.org/pdf/1706.05384.pdf , in particular to

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Marco Piani Jul 21 2017 16:33 UTC

Is it really the case for the general definition of teleportation-covariant channel given in https://arxiv.org/abs/1609.02160 or https://arxiv.org/abs/1510.08863 ? I understand that there special classes of teleportation-covariant channels are considered where what you say holds (that is, for pairs

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gae Jul 21 2017 15:51 UTC

If two channels are teleportation-covariant and between Hilbert spaces with the same dimension, then the correction unitaries are exactly the same. For instance, for any pair of Pauli channels (not just a Pauli and the identity), the corrections are Pauli operators.

Marco Piani Jul 21 2017 15:36 UTC

Is it more precisely that the result holds for any pair of *jointly* teleportation-covariant channels? The definition of teleportation-covariant channel (according to what I see in https://arxiv.org/abs/1609.02160 ) is such that the covariance can be achieved with a unitary at the output that depend

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gae Jul 21 2017 14:01 UTC

Thx Steve for pointing out this paper too, which is relevant as well. Let me just remark that the PRL mentioned in my previous comment [PRL 118, 100502 (2017), https://arxiv.org/abs/1609.02160 ] finds the result for any pair of teleportation-covariant channels (not just between a Pauli channel and t

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Steve Flammia Jul 21 2017 13:43 UTC

Actually, there is even earlier work that shows this result. In [arXiv:1109.6887][1], Magesan, Gambetta, and Emerson showed that for any Pauli channel the diamond distance to the identity is equal to the trace distance between the associated Choi states. They prefer to phrase their results in terms

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