# Top arXiv papers

• Two triangle meshes are conformally equivalent if for any pair of incident triangles the absolute values of the corresponding cross-ratios of the four vertices agree. Such a pair can be considered as preimage and image of a discrete conformal map. In this article we study discrete conformal maps which are defined on parts of a triangular lattice $T$ with strictly acute angles. That is, $T$ is an infinite triangulation of the plane with congruent strictly acute triangles. A smooth conformal map $f$ can be approximated on a compact subset by such discrete conformal maps $f^\varepsilon$, defined on a part of $\varepsilon T$ for $\varepsilon>0$ small enough, see [U. Bücking, Approximation of conformal mappings using conformally equivalent triangular lattices, in "Advances in Discrete Differential Geometry" (A.I. Bobenko ed.), Springer (2016), 133--149]. We improve this result and show that the convergence is in fact in $C^\infty$. Furthermore, we describe how the cross-ratios of the four vertices for pairs of incident triangles are related to the Schwarzian derivative of $f$.
• In this article, a Leslie-Gower Holling type III predator-prey model with disease in predator has been developed from both biological and mathematical point of view. The total population is divided into three classes, namely, prey, susceptible predator and infected predator. The local stability, global stability together with sufficient conditions for persistence of the ecosystem near biologically feasible equilibria is thoroughly investigated. Boundedness and existence of the system are established. All the important analytical findings are numerically verified using program software MATLAB and Maple.
• In this paper we consider a control problem for a Partially Observable Piecewise Deterministic Markov Processes in the following way: After the jump of the process the controller receives a noisy signal about the state and the time point of the jump. The aim is to control the process in such a way that the expected discounted cost of the system is minimized. We solve this optimization problem by reducing it to a discrete-time Markov Decision Process. This includes the derivation of a filter for the unobservable state. Imposing sufficient continuity and compactness assumptions we are able to prove the existence of optimal policies and show that the value function satisfies a fixed point equation. A generic application is given to illustrate the results.
• Recently, a hybrid percolation transitions (HPT) that exhibits both a discontinuous transition and critical behavior at the same transition point has been observed in diverse complex systems. In spite of considerable effort to develop the theory of HPT, it is still incomplete, particularly when the transition is induced by cluster merging dynamics. Here, we aim to develop a theoretical framework of the HPT induced by such dynamics. We find that two correlation-length exponents are necessary for characterizing the giant cluster and finite clusters, respectively. Finite-size scaling method for the HPT is also introduced. The conventional formula of the fractal dimension in terms of the critical exponents is not valid. Neither the giant nor finite clusters are fractals but they have fractal boundaries.
• We obtain new uniform bounds for the symmetric tensor rank of multiplication in finite extensions of any finite field Fp or Fp2 where p denotes a prime number greater or equal than 5. In this aim, we use the symmetric Chudnovsky-type generalized algorithm applied on sufficiently dense families of modular curves defined over Fp2 attaining the Drinfeld-Vladuts bound and on the descent of these families to the definition field Fp. These families are obtained thanks to prime number density theorems of type Hoheisel, in particular a result due to Dudek (2016).
• In this work, the author developed a multiple scattering model for heterogeneous elastic continua with strong property fluctuation and obtained the exact solution to the dispersion equation derived from the Dyson equation under the first-order smoothing approximation. The model establishes accurate quantitative relation between the microstructural properties and the coherent wave propagation parameters and can be used for characterization or inversion of microstructures. As applications of the new model, dispersion and attenuation curves for coherent waves in the Earth lithosphere, the porous and two-phase alloys, and human cortical bone are calculated. Detailed analysis shows the model can capture the major dispersion and attenuation characteristics, such as the longitudinal and transverse wave Q-factors and their ratios, existence of two propagation modes, anomalous negative dispersion, nonlinear attenuation-frequency relation, and even the disappearance of coherent waves. Additionally, it helps gain new insights into a series of longstanding problems, such as the dominant mechanism of seismic attenuation and the existence of the Mohorovicic discontinuity. This work provides a general and accurate theoretical framework for quantitative characterization of microstructures in a broad spectrum of heterogeneous materials and it is anticipated to have vital applications in seismology, ultrasonic nondestructive evaluation and biomedical ultrasound.
• We give a finite analogue of the well-known formula $\mathrm{Li}_{\underbrace{1, \ldots, 1}_n}(t) = \frac{1}{n!}\mathrm{Li}_1(t)^n$ of multiple polylogarithms for any positive integer n by using the shuffle relation of finite multiple polylogarithms of Ono-Yamamoto type. Unlike the usual case, the terms regarded as error terms appear in this formula. As a corollary, we obtain $"t \leftrightarrow 1 - t"$ type new functional equations of finite multiple polylogarithms of Ono-Yamamoto type and Sakugawa-Seki type.
• We study relaxation dynamics of dark soliton, created by a phase-imprinted method, in a two-dimensional trapped Bose-Einstein condensate at non-zero temperatures by using the projected Gross-Pitaevskii equation. At absolute zero temperature, a dark soliton is known to decay with a snake instability. At non-zero temperature, as we expected, we find that this snake instability cannot be clearly seen as in the absolute zero temperature case because of the presence of thermal fluctuations. However, we find that the decay rate, the half width of the overlap integral with respect to the phase-imprinted initial state, shows a power low decay as a function of the energy and finally remains a non-zero value.
• Abramov's algorithm enables us to decide whether a univariate rational function can be written as a difference of another rational function, which has been a fundamental algorithm for rational summation. In 2014, Chen and Singer generalized Abramov's algorithm to the case of rational functions in two ($q$-)discrete variables. In this paper we solve the remaining three mixed cases, which completes our recent project on bivariate extensions of Abramov's algorithm for rational summation.
• In this paper, the behavior of a photovoltaic (PV) system, with maximum power point tracking (MPPT) connected to three-phased grid has been investigated. A voltage source inverter (VSI) has been used to connect the photovoltaic system to the grid. The control strategy applied to control inverter switches is based on voltage mode method. Strategy of this project is that during sunlight the system sends active power to the grid and at the same time compensates the reactive power of the load. In case there is no sunlight, the inverter only compensates the reactive of the load. So the photovoltaic system is operated the whole day. In this paper the behavior of the photovoltaic system to provide active power and compensate reactive power of the load is investigated. The time domain simulation is performed using PSCAD/EMTDC software.
• We study Nash equilibria and the price of anarchy in the classical model of Network Creation Games introduced by Fabrikant et al. In this model every agent (node) buys links at a prefixed price $\alpha>0$ in order to get connected to the network formed by all the $n$ agents. In this setting, the reformulated tree conjecture states that for $\alpha > n$, every Nash equilibrium network is a tree. Since it was shown that the price of anarchy for trees is constant, if the tree conjecture were true, then the price of anarchy would be constant for $\alpha >n$. Moreover, Demaine et al. conjectured that the price of anarchy for this model is constant. Up to now the last conjecture has been proven in (i) the \emphlower range, for $\alpha = O(n^{1-\epsilon})$ with $\epsilon \geq \frac{1}{\log n}$ and (ii) in the \emphupper range, for $\alpha > 65n$. In contrast, the best upper bound known for the price of anarchy for the remaining range is $2^{O(\sqrt{\log n})}$. In this paper we give new insights into the structure of the Nash equilibria for different ranges of $\alpha$ and we enlarge the range for which the price of anarchy is constant. Regarding the upper range, we prove that every Nash equilibrium is a tree for $\alpha > 17n$ and that the price of anarchy is constant even for $\alpha > 9n$. In the lower range, we show that any Nash equilibrium for $\alpha < n/C$ with $C > 4$, induces an $\epsilon-$distance-almost-uniform graph.
• We provide a detailed analysis of the correlation length in the direction parallel to a line of modified coupling constants in the Potts model on Z^d at temperatures T>T_c. We also describe how a line of weakened bonds pins the interface of the Potts model on Z^2 below its critical temperature. These results are obtained by extending the analysis by Friedli, Ioffe and Velenik from Bernoulli percolation to FK-percolation of arbitrary parameter q>1.
• In the framework of the ordinary non-relativistic quantum mechanics, it is known that a quantum particle in a rapidly-oscillating bound potential with vanishing time average can be scattered off or even trapped owing to the phenomenon of dynamical (Kapitza) stabilization. A similar phenomenon occurs for scattering and trapping of optical waves. Such a remarkable result stems from the fact that, even though the particle is not able to follow the rapid external oscillations of the potential, these are still able to affect the average dynamics by means of an effective -albeit small- nonvanishing potential contribution. Here we consider the scattering and dynamical stabilization problem for matter or classical waves by a bound potential with oscillating ac amplitude $f(t)$ in the framework of a non-Hermitian extension of the Schrödinger equation, and predict that for a wide class of imaginary amplitude modulations $f(t)$ possessing a one-sided Fourier spectrum the oscillating potential is effectively canceled, i.e. it does not have any effect to the particle dynamics, contrary to what happens in the Hermitian case
• Time reversal in quantum or classical systems described by an Hermitian Hamiltonian is a physically allowed process, which requires in principle inverting the sign of the Hamiltonian. Here we consider the problem of time reversal of a subsystem of discrete states coupled to an external environment characterized by a continuum of states, into which they generally decay. It is shown that, by flipping the discrete-continuum coupling from an Hermitian to a non-Hermitian interaction, thus resulting in a non unitary dynamics, time reversal of the subsystem of discrete states can be achieved, while the continuum of states is not reversed. Exact time reversal requires frequency degeneracy of the discrete states, or large frequency mismatch among the discrete states as compared to the strength of indirect coupling mediated by the continuum. Interestingly, periodic and frequent switch of the discrete-continuum coupling results in a frozen dynamics of the subsystem of discrete states.
• We consider the Cauchy problem of systems of quasilinear wave equations in 2-dimensional space. We assume that the propagation speeds are distinct and that the nonlinearities contain quadratic and cubic terms of the first and second order derivatives of the solution. We know that if the all quadratic and cubic terms of nonlinearities satisfy $Strong$ $Null$-$condition$, then there exists a global solution for sufficiently small initial data. In this paper, we study about the lifespan of the smooth solution, when the cubic terms in the quasi-linear nonlinearities do not satisfy the Strong null-condition. In the proof of our claim, we use the $ghost$ $weight$ energy method and the $L^{\infty}$-$L^{\infty}$ estimates of the solution, which is slightly improved.
• Time reversal is one of the most intriguing yet elusive wave phenomenon of major interest in different areas of classical and quantum physics. Time reversal requires in principle to flip the sign of the Hamiltonian of the system, leading to a revival of the initial state (Loschmidt echo). Here it is shown that Loschmidt echo of photons can be observed in an optical setting without resorting to reversal of the Hamiltonian. We consider photonic propagation in a binary waveguide lattice and show that, by exchanging the two sublattices after some propagation distance, a Loschmidt echo can be observed. Examples of Loschmidt echoes for single photon and NOON states are given in one- and two-dimensional waveguide lattices.
• Using long-range surface plasmon polaritons light can propagate in metal nano-scale waveguides for ultracompact opto-electronic devices. Gold is an important material for plasmonic waveguides, but although its linear optical properties are fairly well understood, the nonlinear response is still under investigation. We consider propagation of pulses in ultrathin gold strip waveguides, modeled by the nonlinear Schrödinger equation. The nonlinear response of gold is accounted for by the two-temperature model, revealing it as a delayed nonlinearity intrinsic in gold. The consequence is that the measured nonlinearities are strongly dependent on pulse duration. This issue has so far only been addressed phenomenologically, but we provide an accurate estimate of the quantitative connection as well as a phenomenological theory to understand the enhanced nonlinear response as the gold thickness is reduced. In comparison with the previous works, the analytical model for the power-loss equation has been improved, and can be applied now to cases with a high laser peak power. We show new fits to experimental data from literature and provide updated values for the real and imaginary part of the nonlinear susceptibility of gold for various pulse durations and gold layer thicknesses. Our simulations show that the nonlinear loss is inhibiting efficient nonlinear interaction with low-power laser pulses. We therefore propose to design waveguides suitable for the mid-IR, where the ponderomotive instantaneous nonlinearity can dominate over the delayed hot-electron nonlinearity and provide a suitable plasmonics platform for efficient ultrafast nonlinear optics.
• Moore's law officially ends in 2020 giving rise to "Post-Moore" technologies nowadays. Energy efficiency is one of the major challenges in high performance computing which should be answered. Superconductor digital technology is a promising after Moore's alternative for supercomputer development. In this paper we consider operation principles of energy efficient superconductor logic and memory circuits with short retrospective review of their evolution. We analyze their shortcomings in respect to computer circuits design. Possible ways of further researches are outlined.
• Efficient charge separation at the interfaces between the perovskite and with the carrier transport layers is crucial for perovskite solar cells to achieve high power conversion efficiency. We systematically investigate the hole injection dynamics from MAPbI$_3$ perovskite to three typical hole transport materials (HTMs) PEDOT:PSS, PTAA and NiO$_x$ by means of pump-probe transmission measurements. We photoexcite only near the MAPbI$_3$/HTM interface or near the back surface, and measure the differential transient transmission between the two excitation configurations to extract the carrier dynamics directly related to the hole injection. The differential transmission signals directly monitor the hole injections to PTAA and PEDOT:PSS being complete within 1 and 2 ps, respectively, and that to NiO$_x$ exhibiting an additional slow process of 40 ps time scale. The obtained injection dynamics are discussed in comparison with the device performance of the solar cells containing the same MAPbI$_3$/HTM interfaces.
• In this work, we present a highly accurate spectral neighbor analysis potential (SNAP) model for molybdenum (Mo) developed through the rigorous application of machine learning techniques on large materials data sets. Despite Mo's importance as a structural metal, existing force fields for Mo based on the embedded atom and modified embedded atom methods still do not provide satisfactory accuracy on many properties. We will show that by fitting to the energies, forces and stress tensors of a large density functional theory (DFT)-computed dataset on a diverse set of Mo structures, a Mo SNAP model can be developed that achieves close to DFT accuracy in the prediction of a broad range of properties, including energies, forces, stresses, elastic constants, melting point, phonon spectra, surface energies, grain boundary energies, etc. We will outline a systematic model development process, which includes a rigorous approach to structural selection based on principal component analysis, as well as a differential evolution algorithm for optimizing the hyperparameters in the model fitting so that both the model error and the property prediction error can be simultaneously lowered. We expect that this newly developed Mo SNAP model will find broad applications in large-scale, long-time scale simulations.
• A nonadiabatic and robust method of excitation transfer in a non-Hermitian tight-binding linear chain, assisted by an imaginary gauge field, is theoretically proposed. The gauge field undergoes a linear gradient in time, from a negative to a positive value, which results in an effective transfer of excitation between the two edge sites of the chain. An imaginary (gain and loss) gradient of site energy potentials is introduced to exactly cancel nonadiabatic effects, thus providing an effective shortcut to adiabaticity and pseudo-Hermitian dynamics. Numerical simulations indicate that the non-Hermitian excitation transfer method is very robust against disorder in hopping rates and site energy of the chain.
• Automatic lane tracking involves estimating the underlying signal from a sequence of noisy signal observations. Many models and methods have been proposed for lane tracking, and dynamic targets tracking in general. The Kalman Filter is a widely used method that works well on linear Gaussian models. But this paper shows that Kalman Filter is not suitable for lane tracking, because its Gaussian observation model cannot faithfully represent the procured observations. We propose using a Particle Filter on top of a novel multiple mode observation model. Experiments show that our method produces superior performance to a conventional Kalman Filter.
• In this paper we state and prove the statement that tame quivers have finitely many $m$-maximal green sequences using a generalized version of Brüstle-Dupont-Pérotin's argument that tame quivers have finitely many maximal green sequences. Finally we strengthen the property of having finitely many $m$-maximal green sequences to almost morphism finiteness and prove that all path algebras of quivers of finite or tame type are almost morphism finite.
• We investigate the heating of an erupting prominence and loops associated with a coronal mass ejection and X-class flare. The prominence is seen in absorption in EUV at the beginning of its eruption. Later the prominence changes to emission, which indicates heating of the erupting plasma. We find the densities of the erupting prominence using the absorption properties of hydrogen and helium in different passbands. We estimate the temperatures and densities of the erupting prominence and loops seen as emission features using the differential emission measure method, which uses both EUV and X-ray observations from the Atmospheric Imaging Assembly on board Solar Dynamics Observatory and the X-ray Telescope on board Hinode. We consider synthetic spectra using both photospheric and coronal abundances in these calculations. We verify the methods for the estimation of temperatures and densities for the erupting plasmas. Then we estimate the thermal, kinetic, radiative loss, thermal conduction, and heating energies of the erupting prominence and loops. We find that the heating of the erupting prominence and loop occurs strongly at early times in the eruption. This event shows a writhing motion of the erupting prominence, which may indicate a hot flux rope heated by thermal energy release during magnetic reconnection.
• BBR is a new congestion-based congestion control algorithm proposed by Google. A BBR flow, if running alone, delivers the highest throughput with the lowest delay. To this end, each sender constantly measures the bottleneck bandwidth and round-trip propagation time of the network pipe, and uses the results to govern its behavior. However, our deployment in geo-distributed cloud servers reveals an unexpected RTT fairness problem: unlike conventional loss-based congestion control, BBR has an opposite bias towards long RTT flows. In this paper, we analyze the extent and cause of this fairness problem through cluster deployment in a clean network environment. Experimental results suggest that BBR's bias against short RTT is an intrinsic problem of its design, irrespective of the bottleneck bandwidth, AQM deployment, and the number of coexisting flows. A BBR flow with 3x RTT of the other dominates with >90% of bandwidth. Worse, strategic receivers can steal bandwidth by artificially inflating end-to-end delays. To address this problem, we show, through in-depth analysis, that a rapid-growing queue due to flow probing is the root cause of the bias. Based on this observation, we design a simple, yet effective algorithm, BBQ, with better RTT fairness while retaining BBR's promising performance advantages. We have implemented BBQ in Linux kernel and evaluated it through extensive experiments. Our evaluation results show that BBQ improves RTT fairness by up to 6.1x in comparison to BBR. Moreover, BBQ reduces queueing delay by more than 64.5%, while maintaining near-optimal link utilization.
• Monolayer two-dimensional transitional metal dichalcogenides, such as MoS2, WS2 and WSe2, are direct band gap semiconductors with large exciton binding energy. They attract growing attentions for opto-electronic applications including solar cells, photo-detectors, light-emitting diodes and photo-transistors, capacitive energy storage, photodynamic cancer therapy and sensing on flexible platforms. While light-induced luminescence has been widely studied, luminescence induced by injection of free electrons could promise another important applications of these new materials. However, cathodoluminescence is inefficient due to the low cross-section of the electron-hole creating process in the monolayers. Here for the first time we show that cathodoluminescence of monolayer chalcogenide semiconductors can be evidently observed in a van der Waals heterostructure when the monolayer semiconductor is sandwiched between layers of hexagonal boron nitride (hBN) with higher energy gap. The emission intensity shows a strong dependence on the thicknesses of surrounding layers and the enhancement factor is more than 1000 folds. Strain-induced exciton peak shift in the suspended heterostructure is also investigated by the cathodoluminescence spectroscopy. Our results demonstrate that MoS2, WS2 and WSe2 could be promising cathodoluminescent materials for applications in single-photon emitters, high-energy particle detectors, transmission electron microscope displays, surface-conduction electron-emitter and field emission display technologies.
• In this paper we continue the analysis of the two-scale method for the Monge-Ampère equation for dimension $d \geq 2$ introduced in [10]. We prove continuous dependence of discrete solutions on data that in turn hinges on a discrete version of the Alexandroff estimate. They are both instrumental to prove pointwise error estimates for classical solutions with Hölder and Sobolev regularity. We also derive convergence rates for viscosity solutions with bounded Hessians which may be piecewise smooth or degenerate.
• We present $ab$ $initio$ study of the electronic stopping power of protons and helium ions in an insulating material, HfO$_{2}$. The calculations are carried out in channeling conditions with different impact parameters by employing Ehrenfest dynamics and real--time, time--dependent density functional theory. The satisfactory comparison with available experiments demonstrates that this approach provides an accurate description of electronic stopping power. The velocity-proportional stopping power is predicted for protons and helium ions in the low energy region, which conforms the linear response theory. Due to the existence of wide band gap, a threshold effect in extremely low velocity regime below excitation is expected. For protons, the threshold velocity is observable, while it does not appear in helium ions case. This indicates the existence of extra energy loss channels beyond the electron--hole pair excitation when helium ions are moving through the crystal. To analyze it, we checked the charge state of the moving projectiles and an explicit charge exchange behavior between the ions and host atoms is found. The missing threshold effect for helium ions is attributed to the charge transfer, which also contributes to energy loss of the ion.
• We consider the ill-posedness and well-posedness of the Cauchy problem for the third order NLS equation with Raman scattering term on the one dimensional torus. It is regarded as a mathematical model for the photonic crystal fiber oscillator. Regarding the ill-posedness, we show the nonexistence of solutions in the Sobolev space and the norm inflation of the data-solution map at the origin under slightly different conditions, respectively. We also prove the local unique existence of solutions in the analytic function space.
• There is urgent clinical need to improve the clinical outcome of peripheral nerve injury. Many efforts are directed towards the fabrication of bioengineered conduits, which could deliver stem cells to the site of injury to promote and guide peripheral nerve regeneration. The aim of this study is to assess if graphene and related nanomaterials can be useful in the fabrication of such conduits. A comparison is made between GO and reduced GO substrates. Our results show that the graphene substrates are highly biocompatible, and the reduced GO substrates are more effective in ncreasing the gene expression of the biomolecules involved in the regeneration process compared to the other substrates studied.
• In this work, we use the numerical renormalization group (NRG) theory to study the thermodynamics of the two-impurity Anderson model. Two different methods are used to estimate the effect of the Dzyaloshiskii-Moriya (DM) interaction on the variation of the Kondo temperature. When the Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction is vanishing, the two different estimations give different tendency. If we use the peak of the specific heat to identify the variation of the Kondo temperature versus the Dzyaloshiskii-Moriya interaction, we get an almost linear function. However, if we use the low temperature universal curve of the impurity entropy, we get a quadratic function. These results indicate that the previous debates about the influence of the spin-orbit coupling on the Kondo temperature may come from the different definitions of the Kondo temperature. When the RKKY interaction is ferromagnetic, there are two stages of the Kondo screening. Both the two estimations demonstrate that the second stage of the Kondo temperature is exponentially dependent on the DM interaction. There results are dramatically different from those calculated via perturbation theory.
• The aim of this thesis was to perform the drift chamber calibration and charged particles 3d track reconstruction for the P349 antiproton polarization experiment. A dedicated procedures were designed, implemented and tested on the experimental data for the the D1 drift chamber. The calibration consisted of the drift time offsets determination, estimation of the initial drift time - space relations by means of the homogeneous irradiation method and the iterative procedure for the time - space relations optimization. Calibration curves for all wire planes of the detector were determined. The obtained uncertainties of the hit position reconstruction are in the range of 150 - 220 $\rm \mu m$. Furthermore, based on the prepared 3d track reconstruction angular distribution of tracks passing through the drift chamber were determined.
• As an important part of the Internet-of-Things (IoT), machine-to-machine (M2M) communications have attracted great attention. In this paper, we introduce mobile edge computing (MEC) into virtualized cellular networks with M2M communications, to decrease the energy consumption and optimize the computing resource allocation as well as improve computing capability. Moreover, based on different functions and quality of service (QoS) requirements, the physical network can be virtualized into several virtual networks, and then each MTCD selects the corresponding virtual network to access. Meanwhile, the random access process of MTCDs is formulated as a partially observable Markov decision process (POMDP) to minimize the system cost, which consists of both the energy consumption and execution time of computing tasks. Furthermore, to facilitate the network architecture integration, software-defined networking (SDN) is introduced to deal with the diverse protocols and standards in the networks. Extensive simulation results with different system parameters reveal that the proposed scheme could significantly improve the system performance compared to the existing schemes.
• The present article is an exposition of a theory of discrete convex functions on certain graph structures, developed by the author in recent years. This theory is a spin-off of discrete convex analysis by Murota, and is motivated by combinatorial dualities in multiflow problems and the complexity classification of facility location problems on graphs. We outline the theory and algorithmic applications in combinatorial optimization problems.
• The solar activity provides an important impact not only on the intensity of cosmic rays but also on the earth environment. In this paper, a coupled oscillator model is proposed to explain the solar activity. By this model the 89 year Gleissberg cycle can be naturally reduced. Furthermore as an application of the coupled oscillator model we try to apply it to the El Nino-La Nina phenomena (ENSO). The 26 year oscillation of the Pacific Ocean is naturally explained. Finally we search a possible substance of the coupled oscillators in actual solar activities.
• We calculated the magnetic dipole and the electric quadrupole hyperfine interaction constants of 3s3p $^{3,1}P^o_1$ states and the isotope shift, including mass and field shift, factors for transitions from these two states to the ground state 3s$^2~^1S_0$ in Al$^+$ ions using the multiconfiguration Dirac-Hartree-Fock method. The effects of the electron correlations and the Breit interaction on these physical quantities were investigated in detail based on the active space approach. It is found that the CC and the higher-order correlations are considerable for evaluating the uncertainties of the atomic parameters concerned. The uncertainties of the hyperfine interaction constants in this work are less than 1.5\%. Although the isotope shift factors are highly sensitive to the electron correlations, reasonable uncertainties were obtained by exploring the effects of the electron correlations. Moreover, we found that the relativistic nuclear recoil corrections to the mass shift factors are very small and insensitive to the electron correlations for Al$^{+}$. These atomic parameters present in this work are valuable for extracting the nuclear electric quadrupole moments and the mean-square charge radii of Al isotopes.
• We continue studying polynomials generated by the Szegő recursion when a finite number of Verblunsky coefficients lie outside the closed unit disk. We prove some asymptotic results for the corresponding orthogonal polynomials and then translate them to the real line to obtain the Szegő asymptotics for the resulting polynomials. The latter polynomials give rise to a non-symmetric tridiagonal matrix but it is a finite-rank perturbation of a symmetric Jacobi matrix.
• Jun 29 2017 math.NT arXiv:1706.09102v1
In this paper, we develop Furstenberg's proof of infinity of primes, and prove several results about prime divisors of sequences of integers, including the celebrated Schur's theorem. In particular, we give a simple proof of a classical result which says that a non-degenerate linear recurrence sequence of integers of order $k>1$ has infinitely many prime divisors.
• The kagome lattice is a paragon of geometrical frustration, long-studied for its association with novel ground-states including spin liquids (SLs). Many recently synthesized kagome materials feature rare-earth ions, which may be expected to exhibit highly anisotropic exchange interactions. The consequences of this combination of strong exchange anisotropy and extreme geometrical frustration are yet to be fully understood. Here, we establish a general picture of the interactions and resulting ground-states (GSs) arising from nearest neighbour exchange anisotropy on the kagome lattice. We determine a generic anisotropic exchange Hamiltonian from symmetry arguments. In the high-symmetry case where reflection in the kagome plane is a symmetry of the system, the generic nearest-neighbour Hamiltonian can be locally defined as a XYZ model with out-of-plane Dzyaloshinskii-Moriya interactions. We proceed to study its phase diagram in the classical limit, making use of an exact reformulation of the Hamiltonian in terms of irreducible representations (irreps) of the lattice symmetry group. This reformulation in terms of irreps naturally explains the three-fold mapping between SLs recently studied on kagome by the present authors [Nat Commun 7, 10297 (2016)]. In addition, a number of unusual states are stabilised in the regions where different forms of GS order compete, including a stripy phase with a local Z8 symmetry and a classical analogue of a chiral SL. This generic Hamiltonian also turns out to be a fruitful hunting ground for coexistence of different forms of magnetic order, or of order and disorder, which we find is a particular property of the kagome lattice arising from the odd number of spins per frustrated unit. These results are compared and contrasted with those obtained on the pyrochlore lattice, and connection is made with recent progress in understanding quantum models with S = 1/2
• A micrometer-scale elastic shell immersed in a nematic liquid crystal may be deformed by the host if the cost of deformation is comparable to the cost of elastic deformation of the nematic. Moreover, such inclusions interact and form chains due to quadrupolar distortions induced in the host. A continuum theory model using finite elements is developed for this system, using mesh regularization and dynamic refinement to ensure quality of the numerical representation even for large deformations. From this model, we determine the influence of the shell elasticity, nematic elasticity and anchoring condition on the shape of the shell and hence extract parameter values from an experimental realization. Extending the model to multi-body interactions, we predict the alignment angle of the chain with respect to the host nematic as a function of aspect ratio, which is found to be in excellent agreement with experiments and greatly improves upon previous theoretical predictions.
• Starting with the first-order singular Lagrangian describing the dynamical system with 2nd-class constraints, the noncommutative quantum mechanics on a curved space is investigated by the constraint star-product quantization formalism of the projection operator method. Imposing the additional constraints to eliminate the reduntant degrees of freedom, it is shown that the resultant noncommutative quantum system on the curved space is represented with two kinds of the constrained quantum systems, which are equivalent with each other. Then, it is shown that the resultant Hamiltonians contain the quantum corrections caused by the uncertainty relations among the constraint-operators in addition to those due to the projections of operators, which are missed in the usual approaches with the Dirac-bracket quantization formalism.
• There has been tremendous interest in manipulating electron and hole-spin states in low-dimensional structures for electronic and spintronic applications. We study the edge magnetic coupling and anisotropy in zigzag stanene nanoribbons, by first-principles calculations. Taking into account considerable spin-orbit coupling and ferromagnetism at each edge, zigzag stanene nanoribbon is insulating and its band gap depends on the inter-edge magnetic coupling and the magnetization direction. Especially for nanoribbon edges with out-of-plane antiferromagnetic coupling, two non-degenerate valleys of edge states emerge and the spin degeneracy is tunable by a transverse electric field, which give full play to spin and valley degrees of freedom. More importantly, both the magnetic order and anisotropy can be selectively controlled by electron and hole doping, demonstrating a readily accessible gate-induced modulation of magnetism. These intriguing features offer a practical avenue for designing energy-efficient devices based on multiple degrees of freedom of electron and magneto-electric couplings.
• We carefully examine the depolarization feature of blazars in the optical and near-infrared bands using the sample of Mead et al. Magnetohydrodynamics (MHD) turbulence could be one possible reason for the depolarization of optical/infrared blazars when we apply the theoretical analysis of Lazarian and Pogosyan. We further identify in the sample that the depolarization results shown in most blazars roughly obey the form of the three-dimensional anisotropic Kolmogorov scaling. The effective Faraday rotation window length scale is not small enough to resolve the polarization correlation length scale in the blazar sample. The depolarization and the related turbulent features show diversities in different blazar sources. We suggest more simultaneous observations in both the optical/infrared and the high-energy bands for the study of the blazar polarization.
• Jun 29 2017 cs.CY arXiv:1706.09096v1
Education in the digital period in which we live, is reaching challenges never before seen, preceded by phenomena that involve not only traditional social units, but also new virtual communities; Innovating is difficult, it is a challenge, however, we must think of new teaching methods that impact the current generation of students, who arrive with new needs and expectations. The construction of knowledge from the subject and the virtual world that surrounds it, establishes the basis for the development of a new model of teaching, where the classroom is the particular representation of a new physical-cybernetic ecosystem composed of the three large dimensions. Which are part of this new techno-social convergence (human - information - machine); Allowing an interrelation between the student, information, machine and the teacher; Using Biocybernetic methods of influence, control and replication, by means of the massive impact vector (i); In addition, the development of new strategies assisted by cybernetics and the updating of academic content according to the new teaching environment. Hence the importance of this study, which leads us to the need for a new model of transforming academic instruction, which is not based on a conglomerate of technological tools, but establishes a new educational and transformative model, based on "Collaborative Thinking" and the ubiquity of information, thus establishing the relationship between the subject and object of study, thus allowing us to establish the new Biocybernetic educational paradigm in the digital period.
• Disease, opinions, ideas, gossip, etc. all spread on social networks. How these networks are connected (the network structure) influences the dynamics of the spreading processes. By investigating these relationships one gains understanding both of the spreading itself and the structure and function of the contact network. In this chapter, we will summarize the recent literature using simulation of spreading processes on top of empirical contact data. We will mostly focus on disease simulations on temporal proximity networks -- networks recording who is close to whom, at what time -- but also cover other types of networks and spreading processes. We analyze 29 empirical networks to illustrate the methods.
• The traditional humanism of the twentieth century, inspired by the culture of the book, systematically distanced itself from the new society of digital information; the Internet and tools of information processing revolutionized the world, society during this period developed certain adaptive characteristics based on coexistence (Human - Machine), this transformation sets based on the impact of three technology segments: devices, applications and infrastructure of social communication, which are involved in various physical, behavioural and cognitive changes of the human being; and the emergence of new models of influence and social control through the new ubiquitous communication; however in this new process of conviviality new models like the "collaborative thinking" and "InfoSharing" develop; managing social information under three Human ontological dimensions (h) - Information (i) - Machine (m), which is the basis of a new physical-cyber ecosystem, where they coexist and develop new social units called "virtual communities ". This new communication infrastructure and social management of information given discovered areas of vulnerability "social perspective of risk", impacting all social units through massive impact vector (i); The virtual environment "H + i + M"; and its components, as well as the life cycle management of social information allows us to understand the path of integration "Techno - Social" and setting a new contribution to cybernetics, within the convergence of technology with society and the new challenges of coexistence, aimed at a new holistic and not pragmatic vision, as the human component (h) in the virtual environment is the precursor of the future and needs to be studied not as an application, but as the hub of a new society.
• Jun 29 2017 math.CO arXiv:1706.09093v1
While much attention has been directed to the maximum modulus and maximum real part of chromatic roots of graphs of order $n$ (that is, with $n$ vertices), relatively little is known about the maximum imaginary part of such graphs. We prove that the maximum imaginary part can grow linearly in the order of the graph. We also show that for any fixed $p \in (0,1)$, almost every random graph $G$ in the Erdös-Rényi model has a non-real root.
• Objective: Amyotrophic lateral sclerosis (ALS) is a rare disease, but is also one of the most common motor neuron diseases, and people of all races and ethnic backgrounds are affected. There is currently no cure. Brain computer interfaces (BCIs) can establish a communication channel directly between the brain and an external device by recognizing brain activities that reflect user intent. Therefore, this technology could help ALS patients in promoting functional independence through BCI-based speller systems and motor assistive devices. Methods: In this paper, two kinds of ERP-based speller systems were tested on 18 ALS patients to: (1) assess performance when they spelled 42 characters online continuously, without a break; and (2) to compare performance between a matrix-based speller paradigm (MS-P, mean visual angle 6 degree) and a new speller paradigm that used a larger visual angle called the large visual angle speller paradigm (LS-P, mean visual angle 8 degree). Results: Although results showed that there were no significant differences between the two paradigms in accuracy trend over continuous use (p>0.05), the fatigue during the LS-P condition was significantly lower than that of MS-P (p<0.05). Results also showed that continuous use slightly reduced the performance of this ERP-based BCI. Conclusion: 15 subjects obtained higher than 80% feedback accuracy (online output accuracy) and 9 subjects obtained higher than 90% feedback accuracy in one of the two paradigms, thus validating the BCI approaches in this study. Significance: Most ALS subjects in this study could spell effectively after continuous use of an ERP-based BCI. The new LS-P display may be easier for subjects to use, resulting in lower fatigue.
• We study the problem of recovering an $s$-sparse signal $\mathbf{x}^{\star}\in\mathbb{C}^n$ from corrupted measurements $\mathbf{y} = \mathbf{A}\mathbf{x}^{\star}+\mathbf{z}^{\star}+\mathbf{w}$, where $\mathbf{z}^{\star}\in\mathbb{C}^m$ is a $k$-sparse corruption vector whose nonzero entries may be arbitrarily large and $\mathbf{w}\in\mathbb{C}^m$ is a dense noise with bounded energy. We aim to exactly and stably recover the sparse signal with tractable optimization programs. In the literature, the uniform recovery guarantee of this problem has been obtained when the sensing matrix consists of i.i.d. Gaussian entries. However, whether the uniform recovery guarantee can be satisfied by any structured sensing matrix is still open. Here, we address this question by proving the uniform recovery guarantee for two classes of structured sensing matrices. The first class can be expressed as the product of a unit-norm tight frame (UTF), a random diagonal matrix and a bounded columnwise orthonormal matrix (e.g., partial random circulant matrix). When the UTF is bounded (i.e. $\mu(\mathbf{U})\sim1/\sqrt{m}$), we prove that with high probability, one can recover an $s$-sparse signal exactly and stably by $l_1$ minimization programs even if the measurements are corrupted by a sparse vector, provided $m = \mathcal{O}(s \log^2 s \log^2 n)$ and the sparsity level $k$ of the corruption is a constant fraction of the total number of measurements. The second class considers randomly sub-sampled orthogonal matrix (e.g., random Fourier matrix). We prove the uniform recovery guarantee provided that the corruption is sparse on certain sparsifying domain. Numerous simulation results are also presented to verify and complement the theoretical results.

xecehim Jun 27 2017 15:03 UTC

It has been [published][1]

Kenneth Goodenough Jun 21 2017 12:48 UTC

Ah yes I see, thank you for the clarification!

Stefano Pirandola Jun 20 2017 13:26 UTC

Hi Kenneth, more precisely that plot is for a particular "Pauli-damping" channel, i.e., a qubit channel that is decomposable into a Pauli channel (1) and an amplitude damping channel (2). This "Pauli-damping" channel can be simulated by performing noisy teleportation over a resource state that corre

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Kenneth Goodenough Jun 20 2017 12:47 UTC

Interesting work! I was wondering, how do the new upper bounds for the amplitude-damping channel in Fig. 2 compare to previous bounds?

Barbara Terhal Jun 20 2017 07:25 UTC

It would be good if this conflict on assigning priority and credit is peacefully resolved by the parties involved (i have no opinions on the matter).

Stefano Pirandola Jun 15 2017 05:32 UTC

The secret-key capacity of the pure-loss channel -log(1-t) was proven in [9], not in the follow-up work [13] (which appeared 4 months later). Ref. [13] found that this capacity is also a strong converse bound, which is Eq. (1) here. Same story for Eq. (4) that was proven in [9], not in [13]. Again t

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Chris Ferrie Jun 09 2017 10:06 UTC

I have posted an open review of this paper here: https://github.com/csferrie/openreviews/blob/master/arxiv.1703.09835/arxiv.1703.09835.md

Eddie Smolansky May 26 2017 05:23 UTC

Updated summary [here](https://github.com/eddiesmo/papers).

# How they made the dataset
- collect youtube videos
- automated filtering with yolo and landmark detection projects
- crowd source final filtering (AMT - give 50 face images to turks and ask which don't belong)
- quality control through s

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Felix Leditzky May 24 2017 20:43 UTC

Yes, that's right, thanks!

For (5), you use the Cauchy-Schwarz inequality $\left| \operatorname{tr}(X^\dagger Y) \right| \leq \sqrt{\operatorname{tr}(X^\dagger X)} \sqrt{\operatorname{tr}(Y^\dagger Y)}$ for the Hilbert-Schmidt inner product $\langle X,Y\rangle := \operatorname{tr}(X^\dagger Y)$ wi

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Michael Tolan May 24 2017 20:27 UTC

Just reading over Eq (5) on P5 concerning the diamond norm.

Should the last $\sigma_1$ on the 4th line be replaced with a $\sigma_2$? I think I can see how the proof is working but not entirely certain.