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1601.07671 | Let $(X, C)$ be a germ of a threefold $X$ with terminal singularities along an irreducible reduced complete curve $C$ with a contraction $f: (X, C)\to (Z, o)$ such that $C=f^{-1}(o)_{red}$ and $-K_X$ is ample. Assume that $(X, C)$ contains a point of type (IIA) and that a general member $H\in |O_X|$ containing $C$ is normal. We classify such germs in terms of $H$. | [
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1601.07672 | This note discusses the bijection between the exceptional subcategories of representations of quivers and generalized non-crossing partitions of Weyl groups. We give a new proof of the Ingalls-Thomas-Igusa-Schiffler bijection by using the exchange property of the Weyl groups of the Kac-Moody Lie algebras. | [
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1601.07673 | Boiling is a very efficient way to transfer heat from a heater to the liquid carrier. We discuss the boiling crisis, a transition between two regimes of boiling: nucleate and film boiling. The boiling crisis results in a sharp decrease in the heat transfer rate, which can cause a major accident in industrial heat exchangers. In this communication, we present a physical model of the boiling crisis based on the vapor recoil effect. Under the action of the vapor recoil the gas bubbles begin to spread over the heater thus forming a germ for the vapor film. The vapor recoil force not only causes its spreading, it also creates a strong adhesion to the heater that prevents the bubble departure, thus favoring the further spreading. Near the liquid-gas critical point, the bubble growth is very slow and allows the kinetics of the bubble spreading to be observed. Since the surface tension is very small in this regime, only microgravity conditions can preserve a convex bubble shape. In the experiments both in the Mir space station and in the magnetic levitation facility, we directly observed an increase of the apparent contact angle and spreading of the dry spot under the bubble. Numerical simulations of the thermally controlled bubble growth show this vapor recoil effect too thus confirming our model of the boiling crisis. | [
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1601.07674 | The Degasperis-Procesi equation possesses well-known peaked solitary waves that are called peakons. Their stability has been established by Lin and Liu in [5]. In this paper, we localize the proof (in some suitable sense detailed in Section 3) of the stability of a single peakon. Thanks to this, we extend the result of stability to the sum of N peakons traveling to the right with respective speeds c1, . . . , cN , such that the difference between consecutive locations of peakons is large enough. | [
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1601.07675 | We investigate the Bose-Einstein condensation patterns, the critical and multicritical behaviors of three-dimensional mixtures of bosonic gases with short-range density-density interactions. These systems have a global U(1)+U(1) symmetry, as the system Hamiltonian is invariant under independent U(1) transformations acting on each species. In particular, we consider the three-dimensional Bose-Hubbard model for two lattice bosonic gases coupled by an on-site inter-species density-density interaction. We study the phase diagram and the critical behaviors along the transition lines characterized by the Bose-Einstein condensation of one or both species. We present mean-field calculations and numerical finite-size scaling analyses of quantum Monte Carlo data. We also consider multicritical points, close to which it is possible to observe the condensation of both gas components. We determine the possible multicritical behaviors by using field-theoretical perturbative methods. We consider the U(1)+U(1)-symmetric Landau-Ginzburg-Wilson Phi4 theory and determine the corresponding stable fixed points of the renormalization-group flow. The analysis predicts that, in all cases, the multicritical behavior is analogous to the one that would be observed in systems of two identical gases, with an additional Z_2 exchange symmetry. | [
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1601.07676 | In this paper, we study a conjugate gradient method for electronic structure calculations. We propose a Hessian based step size strategy, which together with three orthogonality approaches yields three algorithms for computing the ground state energy of atomic and molecular systems. Under some mild assumptions, we prove that our algorithms converge locally. It is shown by our numerical experiments that the conjugate gradient method is efficient. | [
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1601.07677 | We study $L^p\to L^r$ estimates for restricted averaging operators related to algebraic varieties $V$ of $d$-dimensional vector spaces over finite fields $\mathbb F_q$ with $q$ elements. We observe properties of both the Fourier restriction operator and the averaging operator over $V\subset \mathbb F_q^d.$ As a consequence, we obtain optimal results on the restricted averaging problems for spheres and paraboloids in dimensions $d\ge2,$ and cones in odd dimensions $d\ge 3.$ In addition, when the variety $V$ is a cone lying in an even dimensional vector space over $\mathbb F_q$ and $-1$ is a square number in $\mathbb F_q$, we also obtain sharp estimates except for two endpoints. | [
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1601.07678 | The paper examines relationships between the Shannon entropy and the $\ell_{\alpha}$-norm for $n$-ary probability vectors, $n \ge 2$. More precisely, we investigate the tight bounds of the $\ell_{\alpha}$-norm with a fixed Shannon entropy, and vice versa. As applications of the results, we derive the tight bounds between the Shannon entropy and several information measures which are determined by the $\ell_{\alpha}$-norm, e.g., R\'{e}nyi entropy, Tsallis entropy, the $R$-norm information, and some diversity indices. Moreover, we apply these results to uniformly focusing channels. Then, we show the tight bounds of Gallager's $E_{0}$ functions with a fixed mutual information under a uniform input distribution. | [
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1601.07679 | Money is central in US politics, and most campaign contributions stem from a tiny, wealthy elite. Like other political acts, campaign donations are known to be socially contagious. We study how campaign donations diffuse through a network of more than 50 000 elites and examine how connectivity among previous donors reinforces contagion. We find that the diffusion of donations is driven by independent reinforcement contagion: people are more likely to donate when exposed to donors from different social groups than when they are exposed to equally many donors from the same group. Counter-intuitively, being exposed to one side may increase donations to the other side. Although the effect is weak, simultaneous cross-cutting exposure makes donation somewhat less likely. Finally, the independence of donors in the beginning of a campaign predicts the amount of money that is raised throughout a campaign. We theorize that people infer population-wide estimates from their local observations, with elites assessing the viability of candidates, possibly opposing candidates in response to local support. Our findings suggest that theories of complex contagions need refinement and that political campaigns should target multiple communities. | [
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1601.07681 | Multi-filter images from the solar corona are used to obtain temperature maps which are analyzed using techniques based on proper orthogonal decomposition (POD) in order to extract dynamical and structural information at various scales. Exploring active regions before and after a solar flare and comparing them with quiet regions we show that the multiscale behavior presents distinct statistical properties for each case that can be used to characterize the level of activity in a region. Information about the nature of heat transport is also be extracted from the analysis. | [
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1601.07682 | Recent developments in high-temperature superconductivity highlight a generic tendency of the cuprates to develop competing electronic (charge) supermodulations. While coupled to the lattice and showing different characteristics in different materials, these supermodulations themselves are generally conceived to be quasi-two-dimensional, residing mainly in individual CuO2 planes, and poorly correlated along the c-axis. Here we observed with resonant elastic x-ray scattering a distinct type of electronic supermodulation in YBa2Cu3O7-x (YBCO) thin films grown epitaxially on La0.7Ca0.3MnO3 (LCMO). This supermodulation has a periodicity nearly commensurate with four lattice constants in-plane, eight out-of-plane, with long correlation lengths in three dimensions. It sets in far above the superconducting transition temperature and competes with superconductivity below this temperature for electronic states predominantly in the CuO2 plane. Our finding sheds new light on the nature of charge ordering in cuprates as well as a reported long-range proximity effect between superconductivity and ferromagnetism in YBCO/LCMO heterostructures. | [
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1601.07683 | Quantum metrology exploits entangled states of particles to improve sensing precision beyond the limit achievable with uncorrelated particles. All previous methods required detection noise levels below this standard quantum limit to realize the benefits of the intrinsic sensitivity provided by these states. Remarkably, a recent proposal has shown that, in principle, such low-noise detection is not a necessary requirement. Here, we experimentally demonstrate a widely applicable method for entanglement-enhanced measurements without low-noise detection. Using an intermediate magnification step, we perform squeezed state metrology 8 dB below the standard quantum limit with a detection system that has a noise floor 10 dB above the standard quantum limit. Beyond its conceptual significance, this method eases implementation complexity and is expected to find application in next generation quantum sensors. | [
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1601.07684 | We present a new method to measure a theoretically well-defined mass of the top quark at the LHC. This method uses lepton energy distribution and has a boost-invariant nature. We perform a simulation analysis of the top mass reconstruction with this method for tt -> lepton+jets channel at the leading order. We estimate several major uncertainties in the top mass determination and find that they are under good control. | [
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1601.07685 | Let $R$ be a unital ring with involution.In this paper, several new necessary and sufficient conditions for the existence of the Moore-Penrose inverse of an element in a ring $R$ are given.In addition, the formulae of the Moore-Penrose inverse of an element in a ring are presented. | [
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1601.07686 | Convergence and density evolution of a low complexity, iterative MIMO detection based on belief propagation (BP) over a ring-type pair-wise graph are presented in this paper. The detection algorithm to be considered is effectively a forward-backward recursion and was originally proposed in [13], where the link level performance and the convergence for Gaussian input were analyzed. Presented here are the convergence proof for discrete alphabet and the density evolution framework for binary input to give an asymptotic performance in terms of average SINR and bit error rate (BER) without channel coding. The BER curve obtained via density evolution shows a good match with simulation results, verifying the effectiveness of the density evolution analysis and the performance of the detection algorithm. | [
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1601.07687 | An electric current in the presence of spin-orbit coupling can generate a spin accumulation that exerts torques on a nearby magnetization. We demonstrate that, even in the absence of materials with strong bulk spin-orbit coupling, a torque can arise solely due to interfacial spin-orbit coupling, namely Rashba-Eldestein effects at metal/insulator interfaces. In magnetically soft NiFe sandwiched between a weak spin-orbit metal (Ti) and insulator (Al$_2$O$_3$), this torque appears as an effective field, which is significantly larger than the Oersted field and sensitive to insertion of an additional layer between NiFe and Al$_2$O$_3$. Our findings point to new routes for tuning spin-orbit torques by engineering interfacial electric dipoles. | [
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1601.07688 | We discuss the well-posedness of the Cauchy problem for hyperbolic operators with double characteristics which changes from non-effectively hyperbolic to effectively hyperbolic, on the double characteristic manifold, across a submanifold of codimension 1. We assume that there is no bicharacteristic tangent to the double characteristic manifold and the spatial dimension is 2. Then we prove the well-posedness of the Cauchy problem in all Gevrey classes assuming, on the double characteristic manifold, that the ratio of the imaginary part of the subprincipal symbol to the real eigenvalue of the Hamilton map is bounded and that the sum of the real part of the subprincipal symbol and the modulus of the imaginary eigenvalue of the Hamilton map is strictly positive. | [
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] |
1601.07689 | We theoretically investigate gap plasmons for two silver nanocubes coupled through a molecular tunnel junction. In absence of tunneling, the red-shift of the bonding mode saturates with decreasing gap distance. Tunneling at small gap distances leads to a damping and slight blue-shift of the bonding mode, but no low-energy charge transfer plasmon mode appears in the spectra. This finding is in stark contrast to recent work of Tan et al. [Science 343, 1496 (2014)]. | [
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1601.07691 | We discuss the potential of the advanced ground-based gravitational-wave detectors such as LIGO, Virgo, and KAGRA to detect generic deviations of gravitational waveforms from the predictions of general relativity. We use the parameterized post-Einsteinian formalism to characterize the deviations, and assess what magnitude of deviations are detectable by using an approximate decision scheme based on Bayesian statistics. We find that there exist detectable regions of the parameterized post-Einsteinian parameters for different binary masses from the observation of a single gravitational wave event. The regions are not excluded by currently existing binary pulsar observations for the parameterized post-Einsteinian parameters at higher post-Newtonian order. We also find that neglect of orbital eccentricity or tidal deformation effects do not cause a significant bias on the detectable region of generic deviations from general relativity. | [
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1601.07692 | We analyze the directed flow of protons and pions in high-energy heavy-ion collisions in the incident energy range from $\sqrt{s_{{\scriptscriptstyle NN}}}=7.7$ to 27 GeV within a microscopic transport model. Standard hadronic transport approaches do not describe the collapse of directed flow below $\sqrt{s_{{\scriptscriptstyle NN}}}\simeq 20$ GeV. By contrast, a model which simulates effects of a softening of the equation of state, well describes the behavior of directed flow data recently obtained by the STAR Collaboration~\cite{STARv1}. We give a detailed analysis of how directed flow is generated. Particularly, we found that softening of effective equation of state at the overlapping region of two nuclei, i.e. the reaction stages where the system reaches high baryon density state, is needed to explain the observed collapse of proton directed flow within a hadronic transport approach. | [
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1601.07693 | Friction is a complicated phenomenon involving nonlinear dynamics at different length and time scales[1, 2]. The microscopic origin of friction is poorly understood, due in part to a lack of methods for measuring the force on a nanometer-scale asperity sliding at velocity of the order of cm/s.[3, 4] Despite enormous advance in experimental techniques[5], this combination of small length scale and high velocity remained illusive. Here we present a technique for rapidly measuring the frictional forces on a single asperity (an AFM tip) over a velocity range from zero to several cm/s. At each image pixel we obtain the velocity dependence of both conservative and dissipative forces, revealing the transition from stick-slip to a smooth sliding friction[1, 6]. We explain measurements on graphite using a modified Prandtl-Tomlinson model that takes into account the damped elastic deformation of the asperity. With its greatly improved force sensitivity and very small sliding amplitude, our method enables rapid and detailed surface mapping of the full velocity-dependence of frictional forces with less than 10~nm spatial resolution. | [
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1601.07694 | Clusters of galaxies are at the intersection of cosmic filaments and are still accreting galaxies and groups along these preferential directions, but, because of their relatively low contrast on the sky, they are difficult to detect (unless a large amount of spectroscopic data are available), and unambiguous detections have been limited until now to relatively low redshifts (z<0.3). We searched for extensions and filaments around the thirty clusters of the DAFT/FADA survey (redshift range 0.4<z<0.9) with deep wide field photometric data. For each cluster, based on a colour-magnitude diagram, we selected galaxies that were likely to belong to the red sequence, and hence to be at the cluster redshift, and built density maps. By computing the background for each map and drawing 3sigma contours, we estimated the elongations of the structures detected in this way. Whenever possible, we identified the other structures detected on the density maps with clusters listed in NED. We found clear elongations in twelve clusters, with sizes reaching up to 7.6 Mpc. Eleven other clusters have neighbouring structures, but the zones linking them are not detected in the density maps at a 3sigma level. Three clusters show no extended structure and no neighbours, and four clusters are of too low contrast to be clearly visible on our density maps. The simple method we have applied appears to work well to show the existence of filaments and/or extensions around a number of clusters in the redshift range 0.4<z<0.9. We plan to apply it to other large cluster samples such as the clusters detected in the CFHTLS and SDSS-Stripe 82 surveys in the near future. | [
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1601.07695 | A complex non-Newtonian fluid models the nematic liquid crystal flows confined in a bounded domain in $\mathbb{R}^3$ is considered. The system is a forced incompressible Navier-Stokes equation coupled with a parabolic type Q-tensor flows. Under suitable condition on the coefficients of the Landau-de Gennes energy functional, global strong solution for small initial data is proved. | [
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1601.07696 | Let $M$ be an $n-$dimensional differentiable manifold equipped with a torsion-free linear connection $\nabla $ and $T^{\ast }M$ its cotangent bundle. The present paper aims to study a metric connection $\widetilde{% \nabla }$ with nonvanishing torsion on $T^{\ast }M$ with modified Riemannian extension ${}\bar{g}_{\nabla ,c}$. First, we give a characterization of fibre-preserving projective vector fields on $(T^{\ast }M,{}\bar{g}%_{\nabla ,c})$ with respect to the metric connection $\widetilde{\nabla }$. Secondly, we study conditions for $(T^{\ast }M,{}\bar{g}_{\nabla ,c})$ to be semi-symmetric, Ricci semi-symmetric, $\widetilde{Z}$ semi-symmetric or locally conharmonically flat with respect to the metric connection $% \widetilde{\nabla }$. Finally, we present some results concerning the Schouten-Van Kampen connection associated to the Levi-Civita connection $% \bar{\nabla }$ of the modified Riemannian extension $\bar{g}%_{\nabla ,c}$. | [
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1601.07697 | In this work we want to simulate with the Lattice-Boltzmann method in 2D the capillary infiltration into porous structures obtained from the packing of particles. The experimental problem motivating our work is the densification of carbon preforms by reactive melt infiltration. The aim is to determine optimization principles for the manufacturing of high-performance ceramics. Simulations are performed for packings with varying structural properties. Our analysis suggests that the observed slow infiltrations can be ascribed to interface dynamics. Pinning represents the primary factor retarding fluid penetration. The mechanism responsible for this phenomenon is analyzed in detail. When surface growth is allowed, it is found that the phenomenon of pinning becomes stronger. Systems trying to reproduce typical experimental conditions are also investigated. It turns out that the standard for accurate simulations is challenging. The primary obstacle to overcome for enhanced accuracy seems to be the over-occurrence of pinning. | [
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1601.07698 | Let $p$ be an odd prime number. In this paper, we are concerned with the behaviour of Fermat curves defined over ${\bf Q}$ given by equations $ax^p+by^p+cz^p=0$, with respect to the local-global Hasse principle. It is conjectured that there exist infinitely many Fermat curves of exponent $p$ which are counterexamples to the Hasse principle. It is a consequence of the abc-conjecture if $p\geq 5$. Using a cyclotomic approach due to H. Cohen and Chebotarev's density theorem, we obtain a partial result towards this conjecture, by proving it for $p\leq 19$. | [
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1601.07699 | Although some work has been done on the metamathematics of Metamath, there has not been a clear definition of a model for a Metamath formal system. We define the collection of models of an arbitrary Metamath formal system, both for tree-based and string-based representations. This definition is demonstrated with examples for propositional calculus, $\textsf{ZFC}$ set theory with classes, and Hofstadter's MIU system, with applications for proving that statements are not provable, showing consistency of the main Metamath database (assuming $\textsf{ZFC}$ has a model), developing new independence proofs, and proving a form of G\"odel's completeness theorem. | [
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1601.07701 | Massive spatial modulation (SM)-MIMO, which employs massive low-cost antennas but few power-hungry transmit radio frequency (RF) chains at the transmitter, is recently proposed to provide both high spectrum efficiency and energy efficiency for future green communications. However, in massive SM-MIMO, the optimal maximum likelihood (ML) detector has the prohibitively high complexity, while state-of-the-art low-complexity detectors for conventional small-scale SM-MIMO suffer from an obvious performance loss. In this paper, by exploiting the structured sparsity of multiple SM signals, we propose a low-complexity signal detector based on structured compressive sensing (SCS) to improve the signal detection performance. Specifically, we first propose the grouped transmission scheme at the transmitter, where multiple SM signals in several continuous time slots are grouped to carry the common spatial constellation symbol to introduce the desired structured sparsity. Accordingly, a structured subspace pursuit (SSP) algorithm is proposed at the receiver to jointly detect multiple SM signals by leveraging the structured sparsity. In addition, we also propose the SM signal interleaving to permute SM signals in the same transmission group, whereby the channel diversity can be exploited to further improve the signal detection performance. Theoretical analysis quantifies the performance gain from SM signal interleaving, and simulation results demonstrate the near-optimal performance of the proposed scheme. | [
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1601.07702 | We study correlated equilibria and coarse equilibria of simple first-price single-item auctions in the simplest auction model of full information. Nash equilibria are known to always yield full efficiency and a revenue that is at least the second-highest value. We prove that the same is true for all correlated equilibria, even those in which agents overbid -- i.e., bid above their values. Coarse equilibria, in contrast, may yield lower efficiency and revenue. We show that the revenue can be as low as 26% of the second-highest value in a coarse equilibrium, even if agents are assumed not to overbid, and this is tight. We also show that when players do not overbid, the worst-case bound on social welfare at coarse equilibrium improves from 63% of the highest value to 81%, and this bound is tight as well. | [
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1601.07703 | It has been clarified that bulk superconductivity in Fe$_{1+y}$Te$_{0.6}$Se$_{0.4}$ can be induced by annealing in an appropriate atmosphere to remove the harmful effects of excess iron. In order to clarify the details of the annealing process, we studied the changes in the physical properties and reaction products of Fe$_{1+y}$Te$_{0.6}$Se$_{0.4}$ annealed in pnictogen (P, As, Sb) atmospheres. Crystals annealed in a pnictogen atmosphere show bulk superconductivity and the values of $T_{c}$ and $J_{c}$ are about $14~$K and 2-4 $\times 10{^5}~$A/cm$^2$ ($2~$K, self-field), respectively. It is also found that the reaction rate increases with the increase in the saturated vapor pressure of the pnictogen. Unexpectedly, the reaction products of Fe$_{1+y}$Te$_{0.6}$Se$_{0.4}$ after annealing in a P atmosphere mainly consist of FeTe$_2$. In addition, the amount of P required to obtain the optimal $T_{c}$ is much smaller than the amount of excess iron, which is similar to the case of oxygen annealing. P, oxygen, and to some extent As could serve as catalysts to form FeTe$_2$ to remove excess iron. | [
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1601.07704 | In this paper we consider the separability problem for bipartite quantum states arising from graphs. Earlier it was proved that the degree criterion is the graph-theoretic counterpart of the familiar positive partial transpose criterion for separability, although there are entangled states with positive partial transpose for which the degree criterion fails. Here we introduce the concept of partially symmetric graphs and degree symmetric graphs by using the well-known concept of partial transposition of a graph and degree criteria, respectively. Thus, we provide classes of bipartite separable states of dimension $m \times n$ arising from partially symmetric graphs. We identify partially asymmetric graphs that lack the property of partial symmetry. We develop a combinatorial procedure to create a partially asymmetric graph from a given partially symmetric graph. We show that this combinatorial operation can act as an entanglement generator for mixed states arising from partially symmetric graphs. | [
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1601.07705 | Based on DFT and Berry curvature calculations, we predict that quantum anomalous hall effect (QAHE) can be realized in two dimensional anti-ferromagnetic (AFM) NiRuCl6 with zero net magnetic moment. By tuning spin-orbits coupling (SOC), we find that the topological properties of NiRuCl6 come from its energy band reversal. The results indicate that NiRuCl6 behaves as AFM Chern insulator and its spin-polarized electronic structure and strong spin-orbits coupling (SOC) are the origin of QAHE. Considering the compatibility between AFM and insulator, AFM Chern insulator is more suitable to realize high temperature QAHE because generally Neel temperature of AFM systems is more easily improved than Curie temperature of ferromagnetic (FM) systems. Due to the different magnetic coupling mechanism between FM and AFM Chern insulator, AFM Chern insulator provides a new way to archive high temperature QAHE in experiments. | [
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1601.07706 | We study the stress response to a step strain of covalently bonded gelatin gels in the temperature range where triple helix reversible crosslink formation is prohibited. We observe slow stress relaxation towards a $T$-dependent finite asymptotic level. We show that this is assignable to the strain-induced coil $\rightarrow$ helix transition, previously evidenced by S. Courty, J.L. Gornall and E.M. Terentjev (PNAS, {\bf 102}, 13453 (2005)), of a fraction of the polymer strands. Relaxation proceeds, in a first stage, according to a stretched exponential dynamics, then crosses over to a terminal simple exponential decay. The respective characteristic times $\tau_{K}$ and $\tau_{f}$ exhibit an Arrhenius-like $T$-dependence with an associated energy $\cal E$ incompatibly larger than the activation barrier height for the isomerisation process which sets the clock for an elementary coil $\to$ helix transformation event. We tentatively assign this glass-like slowing down of the dynamics to the long-range couplings due to the mechanical noise generated by the local elementary events in this random elastic medium. | [
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1601.07707 | We present a plausible micro-founded model for the previously postulated power law finite time singular form of the crash hazard rate in the Johansen-Ledoit-Sornette model of rational expectation bubbles. The model is based on a percolation picture of the network of traders and the concept that clusters of connected traders share the same opinion. The key ingredient is the notion that a shift of position from buyer to seller of a sufficiently large group of traders can trigger a crash. This provides a formula to estimate the crash hazard rate by summation over percolation clusters above a minimum size of a power sa (with a > 1) of the cluster sizes s, similarly to a generalized percolation susceptibility. The power sa of cluster sizes emerges from the super-linear dependence of group activity as a function of group size, previously documented in the literature. The crash hazard rate exhibits explosive finite-time singular behaviors when the control parameter (fraction of occupied sites, or density of traders in the network) approaches the percolation threshold pc. Realistic dynamics are generated by modelling the density of traders on the percolation network by an Ornstein-Uhlenbeck process, whose memory controls the spontaneous excursion of the control parameter close to the critical region of bubble formation. Our numerical simulations recover the main stylized properties of the JLS model with intermittent explosive super-exponential bubbles interrupted by crashes. | [
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1601.07708 | Using ab-initio methods we investigate the possibility of three-terminal graphene "T-junction" devices and show that these all-graphene edge contacts are energetically feasible when the 1D interface itself is free from foreign atoms. We examine the energetics of various junction structures as a function of the atomic scale geometry. Three-terminal equilibrium Green's functions are used to determine the transmission spectrum and contact resistance of the system. We find that the most symmetric structures have a significant binding energy, and we determine the contact resistances in the junction to be in the range of 1-10 kOhm which is comparable to the best contact resistance reported for edge-contacted graphene-metal contacts. We conclude that conducting all-carbon T-junctions should be feasible. | [
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1601.07709 | Categorization is crucial for content description in archiving of music signals. On many occasions, human brain fails to classify the instruments properly just by listening to their sounds which is evident from the human response data collected during our experiment. Some previous attempts to categorize several musical instruments using various linear analysis methods required a number of parameters to be determined. In this work, we attempted to categorize a number of string instruments according to their mode of playing using latest-state-of-the-art robust non-linear methods. For this, 30 second sound signals of 26 different string instruments from all over the world were analyzed with the help of non linear multifractal analysis (MFDFA) technique. The spectral width obtained from the MFDFA method gives an estimate of the complexity of the signal. From the variation of spectral width, we observed distinct clustering among the string instruments according to their mode of playing. Also there is an indication that similarity in the structural configuration of the instruments is playing a major role in the clustering of their spectral width. The observations and implications are discussed in detail. | [
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1601.07711 | Black hole-neutron star mergers are among the promising gravitational-wave sources for ground-based detectors, and gravitational waves from black hole-neutron star mergers are expected to be detected in the next few years. Simultaneous detection of electromagnetic counterparts with gravitational-wave detection provides rich information about the merger events. Among the possible electromagnetic counterparts from the black hole-neutron star merger, the emission powered by the decay of radioactive r-process nuclei, so called kilonova/macronova, is one of the best targets for follow-up observation. We derive fitting formulas for the mass and the velocity of ejecta from a generic black hole-neutron star merger based on recently performed numerical relativity simulations. We combined these fitting formulas with a new semi-analytic model for a black hole-neutron star kilonova/macronova lightcurve which reproduces the results of radiation-transfer simulations. Specifically, the semi-analytic model reproduces the result of each band magnitude obtained by the radiation transfer simulations within ~1 mag. By using this semi-analytic model, we found that, at 400 Mpc, the kilonova/macronova is as bright as 22-24 mag for the cases with a small chirp mass and a high black hole spin, and >28 mag for a large chirp mass and a low black hole spin. We also apply our model to GRB130603B as an illustration, and show that a black hole-neutron star merger with a rapidly spinning black hole and a large neutron star radius is favored. | [
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1601.07712 | A kinetic chemotaxis model with attractive interaction by quasistationary chemical signalling is considered. The special choice of the turning operator, with velocity jumps biased towards the chemical concentration gradient, permits closed ODE systems for moments of the distribution function of arbitrary order. The system for second order moments exhibits a critical mass phenomeneon. The main result is existence of an aggregated steady state for supercritical mass. | [
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1601.07713 | Many car-following models are developed for jam avoidance in highways. Two mechanisms are used to improve the stability: feedback control with autonomous models and increasing of the interaction within cooperative ones. In this paper, we compare the linear autonomous and collective optimal velocity (OV) models. We observe that the stability is significantly increased by adding predecessors in interaction with collective models. Yet autonomous and collective approaches are close when the speed difference term is taking into account. Within the linear OV models tested, the autonomous models including speed difference are sufficient to maximise the stability. | [
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1601.07714 | The ubiquitous proliferation of online social networks has led to the widescale emergence of relational graphs expressing unique patterns in link formation and descriptive user node features. Matrix Factorization and Completion have become popular methods for Link Prediction due to the low rank nature of mutual node friendship information, and the availability of parallel computer architectures for rapid matrix processing. Current Link Prediction literature has demonstrated vast performance improvement through the utilization of sparsity in addition to the low rank matrix assumption. However, the majority of research has introduced sparsity through the limited L1 or Frobenius norms, instead of considering the more detailed distributions which led to the graph formation and relationship evolution. In particular, social networks have been found to express either Pareto, or more recently discovered, Log Normal distributions. Employing the convexity-inducing Lovasz Extension, we demonstrate how incorporating specific degree distribution information can lead to large scale improvements in Matrix Completion based Link prediction. We introduce Log-Normal Matrix Completion (LNMC), and solve the complex optimization problem by employing Alternating Direction Method of Multipliers. Using data from three popular social networks, our experiments yield up to 5% AUC increase over top-performing non-structured sparsity based methods. | [
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1601.07715 | Many models and real complex systems possess critical thresholds at which the systems shift from one sate to another. The discovery of the early warnings of the systems in the vicinity of critical point are of great importance to estimate how far a system is from a critical threshold. Multifractal Detrended Fluctuation analysis (MF-DFA) and visibility graph method have been employed to investigate the fluctuation and geometrical structures of magnetization time series of two-dimensional Ising model around critical point. The Hurst exponent has been confirmed to be a good indicator of phase transition. Increase of the multifractality of the time series have been observed from generalized Hurst exponents and singularity spectrum. Both Long-term correlation and broad probability density function are identified to be the sources of multifractality of time series near critical regime. Heterogeneous nature of the networks constructed from magnetization time series have validated the fractal properties of magnetization time series from complex network perspective. Evolution of the topology quantities such as clustering coefficient, average degree, average shortest path length, density, assortativity and heterogeneity serve as early warnings of phase transition. Those methods and results can provide new insights about analysis of phase transition problems and can be used as early warnings for various complex systems. | [
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1601.07716 | The growing conflicts in and about oil exporting regions and speculations about volatile oil prices during the last decade have renewed the public interest in predictions for the near future oil production and consumption. Unfortunately, studies from only 10 years ago, which tried to forecast the oil production during the next 20-30 years, failed to make accurate predictions for today's global oil production and consumption. Forecasts using economic growth scenarios, overestimated the actual oil production, while models which tried to estimate the maximum future oil production/year, using the official country oil reserve data, predicted a too low production. In this paper, a new approach to model the maximal future regional and thus global oil production (part I) and consumption (part II) during the next decades is proposed. Our analysis of the regional oil production data during past decades shows that, in contrast to periods when production was growing and growth rates varied greatly from one country to another, remarkable similarities are found during the plateau and decline periods of different countries. Following this model, the particular production phase of each major oil producing country and region is determined essentially only from the recent past oil production data. Using these data, the model is then used to predict the production from all major oil producing countries, regions and continents up to the year 2050. The limited regional and global potential to compensate this decline with unconventional oil and oil-equivalents is also presented. | [
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1601.07717 | We revisit the shift technique applied to Quasi-Birth and Death (QBD) processes (He, Meini, Rhee, SIAM J. Matrix Anal. Appl., 2001) by bringing the attention to the existence and properties of canonical factorizations. To this regard, we prove new results concerning the solutions of the quadratic matrix equations associated with the QBD. These results find applications to the solution of the Poisson equation for QBDs. | [
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1601.07718 | We study magnetic field penetration into a thin film made of a superconducting niobium. Imaging of magnetic field is performed by optically detecting magnetic resonances of negatively charged nitrogen-vacancy defects inside a single crystal diamond, which is attached to the niobium film under study. The experimental results are compared with theoretical predictions based on the critical state model, and good agreement is obtained. | [
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1601.07719 | A three species one-dimensional kinetic model is presented for a spatially homogeneous weakly ionized plasma subjected to the action of a time varying electric field. Planar geometry is assumed, which means that the plasma dynamics evolves in the privileged direction of the field. The energy transmitted to the charges is be channelized to the neutrals thanks to collisions and impacting the plasma dynamics. Charge-charge interactions have been designed as a one dimensional collision term equivalent to the Landau operator used for fully ionized plasmas. Charge-neutral collisions are modelled by a conservative drift diffusion operator in the Doughertys form. The resulting set of coupled drift diffusion equations is solved with the stable and robust Propagator Integral Method. This method feasibility accounts for non-linear effects without appealing to linearisation or simplifications, providing conservative physically meaningful solutions. It is found that charge neutral collisions exert a significant effect since a quite different plasma dynamics arises if compared to the collisionless limit. In addition, substantial differences in the system evolution are found for constant and temperature dependent collision frequencies cases. | [
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1601.07721 | We study distributed low rank approximation in which the matrix to be approximated is only implicitly represented across the different servers. For example, each of $s$ servers may have an $n \times d$ matrix $A^t$, and we may be interested in computing a low rank approximation to $A = f(\sum_{t=1}^s A^t)$, where $f$ is a function which is applied entrywise to the matrix $\sum_{t=1}^s A^t$. We show for a wide class of functions $f$ it is possible to efficiently compute a $d \times d$ rank-$k$ projection matrix $P$ for which $\|A - AP\|_F^2 \leq \|A - [A]_k\|_F^2 + \varepsilon \|A\|_F^2$, where $AP$ denotes the projection of $A$ onto the row span of $P$, and $[A]_k$ denotes the best rank-$k$ approximation to $A$ given by the singular value decomposition. The communication cost of our protocols is $d \cdot (sk/\varepsilon)^{O(1)}$, and they succeed with high probability. Our framework allows us to efficiently compute a low rank approximation to an entry-wise softmax, to a Gaussian kernel expansion, and to $M$-Estimators applied entrywise (i.e., forms of robust low rank approximation). We also show that our additive error approximation is best possible, in the sense that any protocol achieving relative error for these problems requires significantly more communication. Finally, we experimentally validate our algorithms on real datasets. | [
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1601.07722 | Time global wellposedness in L^p for the Chern-Simons-Dirac equation in 1+1 dimension is discussed. | [
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1601.07723 | Two matrices are said non-overlapping if one of them can not be put on the other one in a way such that the corresponding entries coincide. We provide a set of non-overlapping binary matrices and a formula to enumerate it which involves the $k$-generalized Fibonacci numbers. Moreover, the generating function for the enumerating sequence is easily seen to be rational. | [
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1601.07724 | Valiant (1975) has developed an algorithm for recognition of context free languages. As of today, it remains the algorithm with the best asymptotic complexity for this purpose. In this paper, we present an algebraic specification, implementation, and proof of correctness of a generalisation of Valiant's algorithm. The generalisation can be used for recognition, parsing or generic calculation of the transitive closure of upper triangular matrices. The proof is certified by the Agda proof assistant. The certification is representative of state-of-the-art methods for specification and proofs in proof assistants based on type-theory. As such, this paper can be read as a tutorial for the Agda system. | [
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1601.07725 | Energy-dependent apparent step heights of two-dimensional ultra-thin Pb islands grown on the Si(111)6$\times$6Au surface have been investigated by a combination of scanning tunneling microscopy, first-principles density functional theory and the particle in a box model calculations. The apparent step height shows the thickness and energy dependent oscillatory behavior, which is directly related to the spilling of electron states into the vacuum exhibiting a quantum size effect. This has been unambiguously proven by extensive first-principles scanning tunneling microscopy and spectroscopy simulations. An electronic contribution to the apparent step height is directly determined. At certain energies it reaches values as high as a half of the atomic contribution. The applicability of the particle in a box model to the spilling of electron states is also discussed. | [
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1601.07726 | Recently a new type of Feshbach resonance, i.e., orbital Feshbach resonance (OFR) was proposed for the ultracold alkali-earth (like) atoms, and experimentally observed in the ultracold gases of $^{{\rm 173}}$Yb atoms. Unlike most of the magnetic Feshbach resonances of ultracold alkali atoms, when the OFR of $^{{\rm 173}}$Yb atoms appears, the energy gap between the thresholds of the open channel (OC) and the closed channel (CC) is much smaller than the characteristic energy of the inter-atomic interaction, i.e., the van der Waals energy. In this paper we study the OFR in the systems with small CC-OC threshold gap. We show that in these systems the OFR can be induced by the coupling between the OC and either an isolated bound state of the CC or the scattering states of the CC. Moreover, we also show that in each case the two-channel Huang-Yang pesudopoential is always applicable for the approximate calculation of the low-energy scattering amplitude. Our results imply that in the theoretical calculations for these systems it is appropriate to take into account the contributions from the scattering states of the CC. | [
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1601.07727 | We consider the relationship between the relative stable category of Benson, Iyengar, and Krause and the usual singularity category for group algebras with coefficients in a commutative noetherian ring. When the coefficient ring is self-injective we show that these categories share a common, relatively large, Verdier quotient. At the other extreme, when the coefficient ring has finite global dimension, there is a semi-orthogonal decomposition, due to Poulton, relating the two categories. We prove that this decomposition is partially compatible with the monoidal structure and study the morphism it induces on spectra. | [
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1601.07728 | We present an efficient implementation of the Bethe-Salpeter equation (BSE) method for obtaining core-level spectra including x-ray absorption (XAS), x-ray emission (XES), and both resonant and non-resonant inelastic x-ray scattering spectra (N/RIXS). Calculations are based on density functional theory (DFT) electronic structures generated either by abinit or Quantumespresso, both plane-wave basis, pseudopotential codes. This electronic structure is improved through the inclusion of a GW self energy. The projector augmented wave technique is used to evaluate transition matrix elements between core-level and band states. Final two-particle scattering states are obtained with the NIST core-level BSE solver (NBSE). We have previously reported this implementation, which we refer to as ocean (Obtaining Core Excitations from Ab initio electronic structure and NBSE) [Phys. Rev. B 83, 115106 (2011)]. Here, we present additional efficiencies that enable us to evaluate spectra for systems ten times larger than previously possible; containing up to a few thousand electrons. These improvements include the implementation of optimal basis functions that reduce the cost of the initial DFT calculations, more complete parallelization of the screening calculation and of the action of the BSE Hamiltonian, and various memory reductions. Scaling is demonstrated on supercells of SrTiO_3 and example spectra for the organic light emitting molecule Tris-(8-hydroxyquinoline)aluminum (Alq_3 ) are presented. The ability to perform large-scale spectral calculations is particularly advantageous for investigating dilute or non-periodic systems such as doped materials, amorphous systems, or complex nano-structures. | [
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1601.07729 | The Ge:Ga detectors used in the PACS spectrograph onboard the Herschel space telescope react to changes of the incident flux with a certain delay. This generates transient effects on the resulting signal which can be important and last for up to an hour. The paper presents a study of the effects of transients on the detected signal and proposes methods to mitigate them especially in the case of the "unchopped" mode. Since transients can arise from a variety of causes, we classified them in three main categories: transients caused by sudden variations of the continuum due to the observational mode used; transients caused by cosmic ray impacts on the detectors; transients caused by a continuous smooth variation of the continuum during a wavelength scan. We propose a method to disentangle these effects and treat them separately. In particular, we show that a linear combination of three exponential functions is needed to fit the response variation of the detectors during a transient. An algorithm to detect, fit, and correct transient effects is presented. The solution proposed to correct the signal for the effects of transients substantially improves the quality of the final reduction with respect to the standard methods used for archival reduction in the case where transient effects are most pronounced. The programs developed to implement the corrections are offered through two new interactive data reduction pipelines in the latest releases of the Herschel Interactive Processing Environment. | [
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1601.07731 | We present a comparative study of the unfilled CoSb3 and FeSb3 skutterudites and report on their compressibility studied by high-pressure synchrotron X-ray diffraction. The equation of state for FeSb3 was received for the first time. The third order Birch- Murnaghan isothermal equations of state were fitted to the experimental data in the pressure ranges atm-34 GPa for CoSb3 and atm-14 GPa for FeSb3. Bulk moduli of 95(5) GPa and 86(4) GPa have been obtained for CoSb3 and FeSb3, respectively. The bulk modulus of FeSb3 is in a contrast by about 30% with literature value obtained indirectly. Anomaly was observed in the diffraction pattern of CoSb3 at the pressures 34.4-39.6 GPa which is most probably reasoned by structure transition. | [
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1601.07732 | The relativistic analogue of the Hall-Vinen-Bekarevich-Khalatnikov (HVBK) hydrodynamics is derived making use of the phenomenological method similar to that used by Bekarevich and Khalatnikov [1] in their derivation of HVBK-hydrodynamics. The resulting equations describe a finite-temperature superfluid liquid with the distributed vorticity. The main dissipative effects, including mutual friction, are taken into account. The proposed hydrodynamics is needed for reliable modeling of the dynamical properties of superfluid neutron stars. | [
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1601.07733 | We consider portal models which are ultraweakly coupled with the Standard Model, and confront them with observational constraints on dark matter abundance and isocurvature perturbations. We assume the hidden sector to contain a real singlet scalar $s$ and a sterile neutrino $\psi$ coupled to $s$ via a pseudoscalar Yukawa term. During inflation, a primordial condensate consisting of the singlet scalar $s$ is generated, and its contribution to the isocurvature perturbations is imprinted onto the dark matter abundance. We compute the total dark matter abundance including the contributions from condensate decay and nonthermal production from the Standard Model sector. We then use the Planck limit on isocurvature perturbations to derive a novel constraint connecting dark matter mass and the singlet self coupling with the scale of inflation: $m_{\rm DM}/{\rm GeV}\lesssim 0.2\lambda_{\rm s}^{\scriptscriptstyle 3/8} \left(H_*/10^{\scriptscriptstyle 11}{\rm GeV}\right)^{\scriptscriptstyle -3/2}$. This constraint is relevant in most portal models ultraweakly coupled with the Standard Model and containing light singlet scalar fields. | [
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1601.07734 | In this paper we prove some results on the covering morphisms of internal groupoids. We also give a result on the coverings of the crossed modules of groups with operations. | [
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1601.07735 | Vela X-1 is among the best studied and most luminous accreting X-ray pulsars. The supergiant optical companion produces a strong radiatively-driven stellar wind, which is accreted onto the neutron star producing highly variable X-ray emission. A complex phenomenology, due to both gravitational and radiative effects, needs to be taken into account in order to reproduce orbital spectral variations. We have investigated the spectral and light curve properties of the X-ray emission from Vela X-1 along the binary orbit. These studies allow to constrain the stellar wind properties and its perturbations induced by the compact object. We took advantage of the All Sky Monitor MAXI/GSC data to analyze Vela X-1 spectra and light curves. By studying the orbital profiles in the $4-10$ and $10-20$ keV energy bands, we extracted a sample of orbital light curves (${\sim}15$% of the total) showing a dip around the inferior conjunction, i.e., a double-peaked shape. We analyzed orbital phase-averaged and phase-resolved spectra of both the double-peaked and the standard sample. The dip in the double-peaked sample needs $N_H\sim2\times10^{24}\,$cm$^{-2}$ to be explained by absorption solely, which is not observed in our analysis. We show how Thomson scattering from an extended and ionized accretion wake can contribute to the observed dip. Fitted by a cutoff power-law model, the two analyzed samples show orbital modulation of the photon index, hardening by ${\sim}0.3$ around the inferior conjunction, compared to earlier and later phases, hinting a likely inadequacy of this model. On the contrary, including a partial covering component at certain orbital phase bins allows a constant photon index along the orbital phases, indicating a highly inhomogeneous environment. We discuss our results in the framework of possible scenarios. | [
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1601.07736 | A square matrix is called stochastic (or row-stochastic) if it is non-negative and has each row sum equal to unity. Here, we constitute an eigenvalue localization theorem for a stochastic matrix, by using its principal submatrices. As an application, we provide a suitable bound for the eigenvalues, other than unity, of the Randi\'c matrix of a connected graph. | [
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1601.07737 | In this paper, we discuss the new hard pole contribution to the $P_{h\perp}$-weighted single-transverse spin asymmetry in semi-inclusive deep inelastic scattering. We perform the complete next-to-leading order calculation of the $P_{h\perp}$-weighted cross section and show that the new hard pole contribution is required in order to obtain the complete evolution equation for the Qiu-Sterman function derived by different approaches. | [
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1601.07738 | Maxwell theory is usually treated in the lab frame under the standard time order (light-signal clock synchronization). Particle tracking in the lab frame usually treats time as an independent variable. Then, the evolution of electron beams is treated according to the absolute time convention (non-standard clock synchronization). This point has never received attention in the accelerator community. There are two ways of coupling fields and particles. The first, Lorentz's way, consists in `translating' Maxwell's electrodynamics to the absolute time world-picture. The second, Einstein's way, consists in `translating' particle tracking results to the electromagnetic world-picture. Conventional particle tracking shows that the electron beam direction changes after a transverse kick, while the orientation of the microbunching fronts stays unvaried. We show that under Einstein's time order, in the ultrarelativistic asymptote the orientation of the planes of simultaneity is always perpendicular to the electron beam velocity. This allows for the production of coherent undulator radiation from a modulated electron beam in the kicked direction without suppression. We hold a recent FEL study at the LCLS as experimental evidence of microbunching wavefront readjusting after a large kick. In a previous paper we quantitatively described this result invoking the aberration of light, corresponding to Lorentz's way of coupling fields and particles. Here we give details of the Lorentz's approach used in that paper. We also demonstrate that an `inverse translation' of particle tracking results to the standard time order resolves puzzles related with the strong qualitative disagreement between simulations and experiments. Previous simulation results in ultrarelativistic electron beam physics should be reexamined in the light of the difference between particle tracking and electromagnetic world-pictures. | [
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1601.07739 | Optimum experimental design theory has recently been extended for parameter estimation in copula models. However, the choice of the correct dependence structure still requires wider analyses. In this work the issue of copula selection is treated by using discrimination design techniques. The new proposed approach consists in the use of $D_s$-optimality following an extension of corresponding equivalence theory. We also present some examples and highlight the strength of such a criterion as a way to discriminate between various classes of dependences. | [
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1601.07741 | Tourism is becoming a significant contributor to medium and long range travels in an increasingly globalized world. Leisure traveling has an important impact on the local and global economy as well as on the environment. The study of touristic trips is thus raising a considerable interest. In this work, we apply a method to assess the attractiveness of 20 of the most popular touristic sites worldwide using geolocated tweets as a proxy for human mobility. We first rank the touristic sites based on the spatial distribution of the visitors' place of residence. The Taj Mahal, the Pisa Tower and the Eiffel Tower appear consistently in the top 5 in these rankings. We then pass to a coarser scale and classify the travelers by country of residence. Touristic site's visiting figures are then studied by country of residence showing that the Eiffel Tower, Times Square and the London Tower welcome the majority of the visitors of each country. Finally, we build a network linking sites whenever a user has been detected in more than one site. This allow us to unveil relations between touristic sites and find which ones are more tightly interconnected. | [
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1601.07742 | Understanding or comprehending source code is one of the core activities of software engineering. Understanding object-oriented source code is essential and required when a programmer maintains, migrates, reuses, documents or enhances source code. The source code that is not comprehended cannot be changed. The comprehension of object-oriented source code is a difficult problem solving process. In order to document object-oriented software system there are needs to understand its source code. To do so, it is necessary to mine source code dependencies in addition to quantitative information in source code such as the number of classes. This paper proposes an automatic approach, which aims to document object-oriented software by visualizing its source code. The design of the object-oriented source code and its main characteristics are represented in the visualization. Package content, class information, relationships between classes, dependencies between methods and software metrics is displayed. The extracted views are very helpful to understand and document the object-oriented software. The novelty of this approach is the exploiting of code dependencies and quantitative information in source code to document object-oriented software efficiently by means of a set of graphs. To validate the approach, it has been applied to several case studies. The results of this evaluation showed that most of the object-oriented software systems have been documented correctly. | [
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1601.07743 | Recurrences for positive definite functions in terms of the space dimension have been used in several fields of applications. Such recurrences typically relate to properties of the system of special functions characterizing the geometry of the underlying space. In the case of the sphere ${\mathbb S}^{d-1} \subset {\mathbb R}^d$ the (strict) positive definiteness of the zonal function $f(\cos \theta)$ is determined by the signs of the coefficients in the expansion of $f$ in terms of the Gegenbauer polynomials $\{C^\lambda_n\}$, with $\lambda=(d-2)/2$. Recent results show that classical differentiation and integration applied to $f$ have positive definiteness preserving properties in this context. However, in these results the space dimension changes in steps of two. This paper develops operators for zonal functions on the sphere which preserve (strict) positive definiteness while moving up and down in the ladder of dimensions by steps of one. These fractional operators are constructed to act appropriately on the Gegenbauer polynomials $\{C^\lambda_n\}$. | [
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1601.07744 | We consider the anomalous localized resonance due to a plasmonic structure for the elastostatic system in R^2. The plasmonic structure takes a general core-shell-matrix form with the metamaterial located in the shell. If there is no core, we show that resonance occurs for a very broad class of sources. If the core is nonempty and of an arbitrary shape, we show that there exists a critical radius such that anomalous localized resonance (ALR) occurs. Our argument is based on a variational technique by making use of the primal and dual variational principles for the elastostatic system, along with the construction of suitable test functions. | [
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1601.07745 | We introduce a model-theoretic characterization of Magidor cardinals, from which we infer that Magidor filters are beyond ZFC-inconsistency | [
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1601.07746 | A gas of ultracold molecules interacting via the long-range dipolar potential offers a highly controlled environment in which to study strongly correlated phases. However, at particle coalescence the divergent $1/r^3$ dipolar potential and associated pathological wavefunction hinder computational analysis. For a dipolar gas constrained to two dimensions we overcome these numerical difficulties by proposing a pseudopotential that is explicitly smooth at particle coalescence, resulting in a 2000-times speedup in diffusion Monte Carlo calculations. The pseudopotential delivers the scattering phase shifts of the dipolar interaction with an accuracy of $10^{-5}$ and predicts the energy of a dipolar gas to an accuracy of $10^{-4}E_\mathrm{F}$ in a diffusion Monte Carlo calculation. | [
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1601.07747 | The Jacobian algebra $\mathsf{A}$ arising from a consistent dimer model is derived equivalent to crepant resolutions of a $3$-dimensional Gorenstein toric singularity $R$, and it is also called a non-commutative crepant resolution of $R$. This algebra $\mathsf{A}$ is a maximal Cohen-Macaulay (= MCM) module over $R$, and it is a finite direct sum of rank one MCM $R$-modules. In this paper, we observe a relationship between properties of a dimer model and those of MCM modules appearing in the decomposition of $\mathsf{A}$ as an $R$-module. More precisely, we take notice of isoradial dimer models and divisorial ideals which are called conic. Especially, we investigate them for the case of $3$-dimensional Gorenstein toric singularities associated with reflexive polygons. | [
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1601.07748 | High contrast imaging and spectroscopy provide unique constraints for exoplanet formation models as well as for planetary atmosphere models. But this can be challenging because of the planet-to-star small angular separation and high flux ratio. Recently, optimized instruments like SPHERE and GPI were installed on 8m-class telescopes. These will probe young gazeous exoplanets at large separations (~1au) but, because of uncalibrated aberrations that induce speckles in the coronagraphic images, they are not able to detect older and fainter planets. There are always aberrations that are slowly evolving in time. They create quasi-static speckles that cannot be calibrated a posteriori with sufficient accuracy. An active correction of these speckles is thus needed to reach very high contrast levels (>1e7). This requires a focal plane wavefront sensor. Our team proposed the SCC, the performance of which was demonstrated in the laboratory. As for all focal plane wavefront sensors, these are sensitive to chromatism and we propose an upgrade that mitigates the chromatism effects. First, we recall the principle of the SCC and we explain its limitations in polychromatic light. Then, we present and numerically study two upgrades to mitigate chromatism effects: the optical path difference method and the multireference self-coherent camera. Finally, we present laboratory tests of the latter solution. We demonstrate in the laboratory that the MRSCC camera can be used as a focal plane wavefront sensor in polychromatic light using an 80 nm bandwidth at 640 nm. We reach a performance that is close to the chromatic limitations of our bench: contrast of 4.5e-8 between 5 and 17 lambda/D. The performance of the MRSCC is promising for future high-contrast imaging instruments that aim to actively minimize the speckle intensity so as to detect and spectrally characterize faint old or light gaseous planets. | [
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1601.07749 | We study the preheating of gauge fields in a simple axion monodromy model and compute the induced entropy perturbations and their effect on the curvature fluctuations. We find that the correction to the spectrum of curvature perturbations has a blue spectrum with index $n_s = 5/2$. Hence, these induced modes are harmless for the observed structure of the universe. Since the spectrum is blue, there is the danger of overproduction of primordial black holes. However, we show that the observational constraints are easily satisfied. | [
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1601.07751 | We consider the generalised Mathieu series \[\sum_{n=1}^\infty \frac{n^\gamma}{(n^\lambda+a^\lambda)^\mu}\qquad (\mu>0)\] when the parameters $\lambda$ ($>0$) and $\gamma$ are even integers for large complex $a$ in the sector $|\arg\,a|<\pi/\lambda$. The asymptotics in this case consist of a {\it finite} algebraic expansion together with an infinite sequence of increasingly subdominant exponentially small expansions. When $\mu$ is also a positive integer it is possible to give closed-form evaluations of this series. Numerical results are given to illustrate the accuracy of the expansion obtained. | [
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1601.07752 | Cardinal's factorization algorithm of 1996 splits a univariate polynomial into two factors with root sets separated by the imaginary axis, which is an important goal itself and a basic step toward root-finding. The novelty of the algorithm and its potential power have been well recognized by experts immediately, but by 2016, that is, two decades later, its practical value still remains nil, particularly because of the high computational cost of performing its final stage by means of computing approximate greatest common divisor of two polynomials. We briefly recall Cardinal's algorithm and its difficulties, amend it based on some works performed since 1996, extend its power to splitting out factors of a more general class, and reduce the final stage of the algorithm to quite manageable computations with structured matrices. Some of our techniques can be of independent interest for matrix computations. | [
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1601.07753 | We extend the relaxation mechanism to the Elementary Goldstone Higgs framework. Besides studying the allowed parameter space of the theory we add the minimal ingredients needed for the framework to be phenomenologically viable. The very nature of the extended Higgs sector allows to consider very flat scalar potential directions along which the relaxation mechanism can be implemented. This fact translates into wider regions of applicability of the relaxation mechanism when compared to the Standard Model Higgs case. Our results show that, if the electroweak scale is not fundamental but radiatively generated, it is possible to generate the observed matter-antimatter asymmetry via the relaxation mechanism. | [
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1601.07754 | We share the implementation details and testing results for video retrieval system based exclusively on features extracted by convolutional neural networks. We show that deep learned features might serve as universal signature for semantic content of video useful in many search and retrieval tasks. We further show that graph-based storage structure for video index allows to efficiently retrieving the content with complicated spatial and temporal search queries. | [
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1601.07755 | Spin-Cherenkov effect enables strong excitations of spin waves (SWs) with nonlinear wave dispersions. The Dzyaloshinskii-Moriya interaction (DMI) results in anisotropy and nonreciprocity of SWs propagation. In this work, we study the effect of the interfacial DMI on SW Cherenkov excitations in permalloy thin-film strips within the framework of micromagnetism. By performing micromagnetic simulations, it is shown that coherent SWs are excited when the velocity of a moving magnetic source exceeds the propagation velocity of the SWs. Moreover, the threshold velocity of the moving magnetic source with finite DMI can be reduced compared to the case of zero DMI. It thereby provides a promising route towards efficient SW generation and propagation, with potential applications in spintronic and magnonic devices. | [
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1601.07756 | We construct the free field representation of irregular vertex operators of arbitrary rank which generates simultaneous eigenstates of positive modes of Virasoro and W symmetry generators. The irregular vertex operators turn out to be the exponentials of combinations of derivatives of Liouville or Toda fields, creating irregular coherent states. We compute examples of correlation functions of these operators and study their operator algebra. | [
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1601.07757 | We study the dissipative Hofstadter model on a triangular lattice, making use of the $O(2,2;R)$ T-dual transformation of string theory. The $O(2,2;R)$ dual transformation transcribes the model in a commutative basis into the model in a non-commutative basis. In the zero temperature limit, the model exhibits an exact duality, which identifies equivalent points on the two dimensional parameter space of the model. The exact duality also defines magic circles on the parameter space, where the model can be mapped onto the boundary sine-Gordon on a triangular lattice. The model describes the junction of three quantum wires in a uniform magnetic field background. An explicit expression of the equivalence condition, which identifies the points on the two dimensional parameter space of the model by the exact duality, is obtained. It may help us to understand the structure of the phase diagram of the model. | [
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1601.07758 | In this note we revisit the SUSY effects in $R_b$ under current experimental constraints including the LHC Higgs data, the $B$-physics measurements, the dark matter relic density and direct detection limits, as well as the precision electroweak data. We first perform a scan to figure out the currently allowed parameter space and then display the SUSY effects in $R_b$. We find that although the SUSY parameter space has been severely restrained by current experimental data, both the general MSSM and the natural-SUSY scenario can still alter $R_b$ with a magnitude sizable enough to be observed at future $Z$-factories (ILC, CEPC, FCC-ee, Super $Z$-factory) which produce $10^9-10^{12}$ $Z$-bosons. To be specific, assuming a precise measurement $\delta R_b = 2.0 \times 10^{-5}$ at FCC-ee, we can probe a right-handed stop up to 530 GeV through chargino-stop loops, probe a sbottom to 850 GeV through neutralino-sbottom loops and a charged Higgs to 770 GeV through the Higgs-top quark loops for a large $\text{tan}\beta$. The full one-loop SUSY correction to $R_b$ can reach $1 \times 10^{-4}$ in natural SUSY and $2 \times 10^{-4}$ in the general MSSM. | [
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1601.07759 | Gravitational Microlensing has been used as a powerful tool for astrophysical studies and exoplanet detections. In the gravitational microlensing, we have two images with negative and positive parities. The negative-parity image is a fainter image and is produced at a closer angular separation with respect to the lens star. In the case of a red-giant lens star and large impact parameter of lensing, this image can be eclipsed by the lens star. The result would be dimming the flux receiving from the combination of the source and the lens stars and the light curve resembles to an eclipsing binary system. In this work, we introduce this phenomenon and propose an observational procedure for detecting this eclipse. The follow-up microlensing telescopes with lucky imaging camera or space-based telescopes can produce high resolution images from the events with reddish sources and confirm the possibility of blending due to the lens star. After conforming a red-giant lens star and source star, we can use the advance photometric methods and detect the relative flux change during the eclipse in the order of $10^{-4}-10^{-3}$. Observation of the eclipse provides the angular size of source star in the unit of Einstein angle and combination of this observation with the parallax observation enable us to calculate the mass of lens star. Finally, we analyzed seven microlensing event and show the feasibility of observation of this effect in future observations. | [
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1601.07761 | Recent large scale surveys of galactic bulge stars allowed to build a detailed map of the bulge kinematics. The bulge exhibits cylindrical rotation consistent with a disky origin which evolved through bar driven secular evolution. However correlations between metallicity and kinematics complicate this picture. In particular a metal-poor component with distinct kinematic signatures has been detected. Its origin, density profile and link with the other Milky Way stellar populations are currently still poorly constrained. | [
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1601.07762 | (Abridged) In the framework of the BinaMicS project, we have begun a study of the magnetic properties of a sample of intermediate-mass and massive short-period binary systems, as a function of binarity properties. We report in this paper the characterisation of the magnetic field of HD 5550, a double-lined spectroscopic binary system of intermediate-mass, using high-resolution spectropolarimetric Narval observations of HD 5550. We first fit the intensity spectra using Zeeman/ATLAS9 LTE synthetic spectra to estimate the effective temperatures, microturbulent velocities, and the abundances of some elements of both components, as well as the light-ratio of the system. We then fit the least-square deconvolved $I$ profiles to determine the radial and projected rotational velocities of both stars. We then analysed the shape and evolution of the LSD $V$ profiles using the oblique rotator model to characterise the magnetic fields of both stars. We confirm the Ap nature of the primary, previously reported in the literature, and find that the secondary displays spectral characteristics typical of an Am star. While a magnetic field is clearly detected in the lines of the primary, no magnetic field is detected in the secondary, in any of our observation. If a dipolar field were present at the surface of the Am star, its polar strength must be below 40 G. The faint variability observed in the Stokes $V$ profiles of the Ap star allowed us to propose a rotation period of $6.84_{-0.39}^{+0.61}$ d, close to the orbital period ($\sim$6.82 d), suggesting that the star is synchronised with its orbit. By fitting the variability of the $V$ profiles, we propose that the Ap component hosts a dipolar field inclined with the rotation axis at an angle $\beta=156\pm17$ $^{\circ}$ and a polar strength $B_{\rm d}=65 \pm 20$ G. The field strength is the weakest known for an Ap star. | [
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1601.07763 | We prove that the existence of a Hurewicz fibration between certain spaces with the homotopy type of a CW-complex implies some topological restrictions on their universal coverings. This result is used to deduce differentiable and metric properties of maps between compact Riemannian manifolds under curvature restrictions. | [
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1601.07764 | We establish a criterion for characterizing superfluidity in interacting, particle-number conserving systems of fermions as topologically trivial or non-trivial. Because our criterion is based on the concept of many-body fermionic parity switches, it is directly associated to the observation of the fractional Josephson effect and indicates the emergence of zero-energy modes that anticommute with fermionic parity. We tested these ideas on the Richardson-Gaudin-Kitaev chain, a particle-number conserving system that is solvable by way of the algebraic Bethe ansatz, and reduces to a long-range Kitaev chain in the mean-field approximation. Guided by its closed-form solution, we introduce a procedure for constructing many-body Majorana zero-energy modes of gapped topological superfluids in terms of coherent superpositions of states with different number of fermions. We discuss their significance and the physical conditions required to enable quantum control in the light of superselection rules. | [
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1601.07765 | Targeted user studies are often employed to measure how well artists can perform specific tasks. But these studies cannot properly describe editing workflows as wholes, since they guide the artists both by choosing the tasks and by using simplified interfaces. In this paper, we investigate digital sculpting workflows used to produce detailed models. In our experiment design, artists can choose freely what and how to model. We recover whole-workflow trends with sophisticated statistical analyzes and validate these trends with goodness-of-fits measures. We record brush strokes and mesh snapshots by instrumenting a sculpting program and analyze the distribution of these properties and their spatial and temporal characteristics. We hired expert artists that can produce relatively sophisticated models in short time, since their workflows are representative of best practices. We analyze 13 meshes corresponding to roughly 25 thousand strokes in total. We found that artists work mainly with short strokes, with average stroke length dependent on model features rather than the artist itself. Temporally, artists do not work coarse-to-fine but rather in bursts. Spatially, artists focus on some selected regions by dedicating different amounts of edits and by applying different techniques. Spatio-temporally, artists return to work on the same area multiple times without any apparent periodicity. We release the entire dataset and all code used for the analyzes as reference for the community. | [
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1601.07766 | Nowadays, the experimental study of emotional learning is commonly based on classical conditioning paradigms and models, which have been thoroughly investigated in the last century. On the contrary, limited attention has been paid to the revaluation of an unconditioned stimulus (UCS), which, as experimentally observed by various researchers in the last four decades, occurs out of classical conditioning. For this reason, no analytical or quantitative theory has been developed for this phenomenon and its dynamics. Unluckily, models based on classical conditioning are unable to explain or predict important psychophysiological phenomena, such as the failure of the extinction of emotional responses in certain circumstances. In this manuscript an analytical representation of UCS revaluation learning is developed; this allows us to identify the conditions determining the "inextinguishability" (or resistant-to-extinction) property of emotional responses and reactions (such as those observed in evaluative conditioning, in the nonreinforcement presentation of a conditioned inhibitor, in post-traumatic stress disorders and in panic attacks). Furthermore, an analysis of the causal relation existing between classical conditioning and UCS revaluation is provided. Starting from this result, a theory of implicit emotional learning and a novel interpretation of classical conditioning are derived. Moreover, we discuss how the proposed theory can lead to the development of new methodologies for the detection and the treatment of undesired or pathological emotional responses, and can inspire animal models for resistant-to-extinction responses and reactions. | [
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1601.07767 | We consider germs of holomorphic vector fields with an isolated singularity at the origin $0\in\mathbb{C}^2$. We introduce a notion of stability, similar to "Lyapunov stability". For such a germ, called $L$-stable singularity, either the corresponding foliation admits a holomorphic first integral, or it is a real logarithmic foliation singularity. A notion of $L$-stability is also naturally introduced for a leaf of a foliation. In the complex codimension one case, for holomorphic foliations, the holonomy groups of $L$-stable leaves are proved to be abelian, of a suitable type. This implies the existence of local closed meromorphic one-forms defining the foliation, in a neighborhood of $L$-stable leaves. | [
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1601.07768 | We consider the effective capacity performance measure of persistent- and truncated-retransmission schemes that can involve any combination of multiple transmissions per packet, multiple communication modes, or multiple packet communication. We present a structured unified analytical approach, based on a random walk model and recurrence relation formulation, and give exact effective capacity expressions for persistent hybrid automatic repeat request (HARQ) and for truncated-retransmission schemes. For the latter, effective capacity expressions are given for systems with finite (infinite) time horizon on an algebraic (spectral radius-based) form of a special block companion matrix. In contrast to prior HARQ models, assuming infinite time horizon, the proposed method does not involve a non-trivial per case modeling step. We give effective capacity expressions for several important cases that have not been addressed before, e.g. persistent-HARQ, truncated-HARQ, network-coded ARQ (NC-ARQ), two-mode-ARQ, and multilayer-ARQ. We propose an alternative QoS parameter (instead of the commonly used moment generating function parameter) that represents explicitly the target delay and the delay violation probability. This also enables closed-form expressions for many of the studied systems. Moreover, we use the recently proposed matrix-exponential distributed (MED) modeling of wireless fading channels to provide the basis for numerous new effective capacity results for HARQ. | [
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1601.07769 | Let $L_0$ be a densely defined minimal linear operator in a Hilbert space $H$. We prove theorem that if there exists at least one correct extension $L_S$ of $L_0$ with the property $D(L_S)=D(L_S^*)$, then we can describe all correct extensions $L$ with the property $D(L)=D(L^*)$. We also prove that if $L_0$ is formally normal and there exists at least one correct normal extension $L_N$, then we can describe all correct normal extensions $L$ of $L_0$. As an example, the Cauchy-Riemann operator is given. | [
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1601.07771 | Whether the total angular momentum of the photon can be separated into spin and orbital parts has been a long-standing problem due to the constraint of transversality condition on its vector wavefunction. A careful analysis shows that the situation arises from a misuse of the constraint in quantum mechanics. To use the constraint properly, we convert the vector representation into a two-component representation in which the wavefunction is not constrained by any conditions. Upon doing so, we not only separate the spin conceptually from the orbital angular momentum but also identify the Berry gauge in which the two-component wavefunction can be canonically quantized. A corollary is that only in one particular Berry gauge can a radiation field be canonically quantized in terms of the plane waves. The degree of freedom to fix the Berry gauge, which reflects a symmetry of the constraint, turns out to have observable quantum effects. | [
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1601.07772 | The possibility of constructing a complete, continuous Wigner function for any quantum system has been a subject of investigation for over 50 years. A key system that has served to illustrate the difficulties of this problem has been an ensemble of spins. Here we present a general and consistent framework for constructing Wigner functions exploiting the underlying symmetries in the physical system at hand. The Wigner function can be used to fully describe any quantum system of arbitrary dimension or ensemble size. | [
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1601.07773 | A strong in-plane magnetic field drastically alters the low-energy spectrum of bilayer graphene by separating the parabolic energy dispersion into two linear Dirac cones. The effect of this dramatic change on the transport properties strongly depends on the orientation of the in-plane magnetic field with respect to the propagation direction of the charge carriers and the angle at which they impinge on the electrostatic potentials. For magnetic fields oriented parallel to the potential boundaries an additional propagating mode that results from the splitting into Dirac cones enhances the transmission probability for charge carriers tunneling through the potentials and increases the corresponding conductance. Our results show that the chiral suppression of transmission at normal incidence is turned into a chiral enhancement when the magnetic field increases, thus indicating a transition from a bilayer to a monolayer-like system at normal incidence. Further, we find that the typical transmission resonances stemming from confinement in a potential barrier are shifted to higher energy and are eventually transformed into anti-resonances with increasing magnetic field. For magnetic fields oriented perpendicular to the potential boundaries we find a very pronounced transition from a bilayer system to two separated monolayer-like systems with Klein tunneling emerging at certain incident angles symmetric around 0, which also leaves a signature in the conductance. For both orientations of the magnetic field, the transmission probability is still correctly described by pseudospin conservation. Finally, to motivate the large in-plane magnetic field, we show that its energy spectrum can be mimicked by specific lattice deformations such as a relative shift of one of the layers. With this equivalence we introduce the notion of an in-plane pseudo-magnetic field. | [
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1601.07774 | We recall that the exclusive production of high mass objects via \gamma\gamma fusion at the LHC is not strongly suppressed in comparison with inclusive \gamma\gamma fusion. Therefore it may be promising to study new objects produced by the \gamma\gamma subprocess in experiments with exclusive kinematics. We list the main advantages of exclusive experiments. We discuss the special advantage of observing $\gamma\gamma \to X \to \gamma Z$ exclusive events. | [
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1601.07775 | Let $D=(V,A)$ be a digraph and consider an arc subset $A'\subseteq A$ and an exhaustive mapping $\phi: A\to A'$ such that $(i)$ the set of heads of $A'$ is $H(A')=V$; $(ii)$ the map fixes the elements of $A'$, that is, $\phi|A'=Id$, and for every vertex $j\in V$, $\phi(\omega^-(j))\subset \omega^-(j)\cap A'$. Then, {\it the partial line digraph} of $D$, denoted by $\mathcal{L}_{(A',\phi)}D $ (for short $\mathcal{L}D$ if the pair $(A', \phi)$ is clear from the context), is the digraph with vertex set $V (\mathcal{L}D)=A'$ and set of arcs $A(\mathcal{L}D) = \{(ij, \phi(j,k)) : (j,k)\in A\}.$ In this paper we prove the following results: Let $k,l$ be two natural numbers such that $1\le l \le k$, and $D$ a digraph with minimum in-degree at least 1. Then the number of $(k,l)$-kernels of $D$ is less than or equal to the number of $(k,l)$-kernels of $\mathcal{L} D$. Moreover, if $l<k$ and the girth of $D$ is at least $l+1$, then these two numbers are equal. The number of semikernels of $D$ is equal to the number of semikernels of $\mathcal{L} D$. Also we introduce the concept of $(k,l)$-Grundy function as a generalization of the concept of Grundy function and we prove that the number of $(k,l)$-Grundy functions of $D$ is equal to the number of $(k,l)$-Grundy functions of any partial line digraph $\mathcal{L} D$. | [
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1601.07776 | The rise in online social networking has brought about a revolution in social relations. However, its effects on offline interactions and its implications for collective well-being are still not clear and are under-investigated. We study the ecology of online and offline interaction in an evolutionary game framework where individuals can adopt different strategies of socialization. Our main result is that the spreading of self-protective behaviors to cope with hostile social environments can lead the economy to non-socially optimal stationary states. | [
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1601.07777 | Within the standard 3nu mass-mixing framework, we present an up-to-date global analysis of neutrino oscillation data (as of January 2016), including the latest available results from experiments with atmospheric neutrinos (Super-Kamiokande and IceCube DeepCore), at accelerators (first T2K anti-nu and NOvA nu runs in both appearance and disappearance mode), and at short-baseline reactors (Daya Bay and RENO far/near spectral ratios), as well as a reanalysis of older KamLAND data in the light of the "bump" feature recently observed in reactor spectra. We discuss improved constraints on the five known oscillation parameters (delta m^2, |Delta m^2|, sin^2theta_12, sin^2theta_13, sin^2theta_23), and the status of the three remaining unknown parameters: the mass hierarchy, the theta_23 octant, and the possible CP-violating phase delta. With respect to previous global fits, we find that the reanalysis of KamLAND data induces a slight decrease of both delta m^2 and sin^2theta_12, while the latest accelerator and atmospheric data induce a slight increase of |Delta m^2|. Concerning the unknown parameters, we confirm the previous intriguing preference for negative values of sin(delta) [with best-fit values around sin(delta) ~ -0.9], but we find no statistically significant indication about the theta_23 octant or the mass hierarchy (normal or inverted). Assuming an alternative (so-called LEM) analysis of NOvA data, some delta ranges can be excluded at >3 sigma, and the normal mass hierarchy appears to be slightly favored at 90% C.L. We also describe in detail the covariances of selected pairs of oscillation parameters. Finally, we briefly discuss the implications of the above results on the three non-oscillation observables sensitive to the (unknown) absolute nu mass scale: the sum of nu masses, the effective nu_e mass, and the effective Majorana mass. | [
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1601.07778 | This article motivates and presents the scale relativistic approach to non-differentiability in mechanics and its relation to quantum mechanics. It stems from the scale relativity proposal to extend the principle of relativity to resolution-scale transformations, which leads to considering non-differentiable dynamical paths. We first define a complex scale-covariant time-differential operator and show that mechanics of non-differentiable paths is implemented in the same way as classical mechanics but with the replacement of the time derivative and velocity with the time-differential operator and associated complex velocity. With this, the generalized form of Newton's fundamental relation of dynamics is shown to take the form of a Langevin equation in the case of stationary motion characterized by a null average classical velocity. The numerical integration of the Langevin equation in the case of a harmonic oscillator taken as an example reveals the same statistics as the stationary solutions of the Schrodinger equation for the same problem. This motivates the rest of the paper, which shows Schrodinger's equation to be a reformulation of Newton's fundamental relation of dynamics as generalized to non-differentiable geometries and leads to an alternative interpretation of the other axioms of standard quantum mechanics in a coherent picture. This exercise validates the scale relativistic approach and, at the same time, it allows to envision macroscopic chaotic systems observed at resolution time-scales exceeding their horizon of predictability as candidates in which to search for quantum-like dynamics and structures. | [
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1601.07779 | In this paper, we investigate a group sparse optimization problem via $\ell_{p,q}$ regularization in three aspects: theory, algorithm and application. In the theoretical aspect, by introducing a notion of group restricted eigenvalue condition, we establish some oracle property and a global recovery bound of order $O(\lambda^\frac{2}{2-q})$ for any point in a level set of the $\ell_{p,q}$ regularization problem, and by virtue of modern variational analysis techniques, we also provide a local analysis of recovery bound of order $O(\lambda^2)$ for a path of local minima. In the algorithmic aspect, we apply the well-known proximal gradient method to solve the $\ell_{p,q}$ regularization problems, either by analytically solving some specific $\ell_{p,q}$ regularization subproblems, or by using the Newton method to solve general $\ell_{p,q}$ regularization subproblems. In particular, we establish the linear convergence rate of the proximal gradient method for solving the $\ell_{1,q}$ regularization problem under some mild conditions. As a consequence, the linear convergence rate of proximal gradient method for solving the usual $\ell_{q}$ regularization problem ($0<q<1$) is obtained. Finally in the aspect of application, we present some numerical results on both the simulated data and the real data in gene transcriptional regulation. | [
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1601.07781 | The anomalous magnetic moment of the muon is an important observable that tests radiative corrections of all three observed local gauge forces: electromagnetic, weak and strong interactions. High precision measurements reveal some discrepancy with the most accurate theoretical evaluations of the anomalous magnetic moment. We show in this note that the UV finite theory cannot resolve this discrepancy. We believe that more reliable estimate of the nonperturbative hadronic contribution and the new measurements can resolve the problem. | [
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