Representation Of Moments Research Articles

Iterative approach for the moment representation of the density-density response function

The linear density-density response function χ(r,r′) can be transformed from its Eigensystem representation into a computationally more efficient moment expansion representation using a suitable unitary transformation. Here, we propose an iterative approach for the direct calculation of this moment representation without resorting to either the direct-space or the conventional Eigensystem representation.

The bispectrum and its relationship to phase-amplitude coupling

Most biological signals are non-Gaussian, reflecting their origins in highly nonlinear physiological systems. A versatile set of techniques for studying non-Gaussian signals relies on the spectral representations of higher moments, known as polyspectra, which describe forms of cross-frequency dependence that do not arise in time-invariant Gaussian signals. The most commonly used of these employ the bispectrum. Recently, other measures of cross-frequency dependence have drawn interest in EEG literature, in particular those which address phase-amplitude coupling (PAC). Here we demonstrate a close relationship between the bispectrum and popular measures of PAC, which we relate to smoothings of the signal bispectrum, making them fundamentally bispectral estimators. Viewed this way, however, conventional PAC measures exhibit some unfavorable qualities, including poor bias properties, lack of correct symmetry and artificial constraints on the spectral range and resolution of the estimate. Moreover, information obscured by smoothing in measures of PAC, but preserved in standard bispectral estimators, may be critical for distinguishing nested oscillations from transient signal features and other non-oscillatory causes of “spurious” PAC. We propose guidelines for gauging the nature and origin of cross-frequency coupling with bispectral statistics. Beyond clarifying the relationship between PAC and the bispectrum, the present work lays out a general framework for the interpretation of the bispectrum, which extends to other higher-order spectra. In particular, this framework holds promise for the detailed identification of signal features related to both nested oscillations and transient phenomena. We conclude with a discussion of some broader theoretical implications of this framework and highlight promising directions for future development.

Application of Probabilistic Method on Daehee Sequences

In this paper, we investigate some combinatorial sequences based on Daehee and Changhee numbers and polynomials, then derive their moment representations in use of probabilistic method. We also provide identities related to Daehee numbers, derangement numbers, Cauchy numbers of the second kind, and Stirling numbers of the first kind.

Spectral Compositions in a time of Revolt

In March 2017, Firstsite, a contemporary art gallery in Colchester, UK, hosted #WorldsUpsideDown, an exhibition curated by Stevphen Shukaitis that explored art’s treatment of moments of destabilization, crisis, and renewal. Included were photographs by Cairo-based artist Mosa’ab Elshamy of the 2011-2013 revolt in Egypt; Justseeds’s Celebrate People’s History poster series; and David Mabb’s Long Live the New! Morris & Co, Hand Printed Wallpapers and K. Malevich’s, Suprematism. These works were chosen because each communicates or represents moments of upheaval and provokes questions for audiences about how such moments resonate with each other and about what we can learn from aesthetic representation of such moments. Connecting with the themes of this issue, the exhibit explored how cycles of struggle expand aesthetic possibilities and media communications, from the Russian revolution’s embrace of the avant-garde to more recent utilization of social media. A public seminar with Richard Gilman-Opalsky and Stevphen Shukaitis was organized to explore themes in the exhibition and in their respective writings. What follows is an excerpt from that seminar.

Exploring the electron density localization in MoS2 nanoparticles using a localized-electron detector: Unraveling the origin of the one-dimensional metallic sites on MoS2 catalysts.

The nature of the electron density localization in two MoS2 nanoclusters containing eight rows of Mo atoms, one with 100% sulphur coverage at the Mo edges (n8_100S) and the other with 50% coverage (n8_50S) was studied using a localized-electron detector function defined in the local moment representation. For n8_100S, pairs of neighboring S2 dimers cover the edges and the electron density localization function analysis shows the presence of a local triangular-shaped ring zone of highly delocalized electrons along these edges, which corresponds to a good metallic conductor zone. The optimized geometry analysis shows that the Mo-S2 bond length is much longer than that of the Mo-S bonds inside the cluster. The removal of one S atom from each sulphur dimer to create a cluster with 50% coverage produces a general compressive stress on the cluster optimized geometry, which shortens the Mo-S bond length, particularly at the edge. The electron density location function analysis shows that close to the cluster corners, a zone of highly delocalized electron zones with a characteristic semiconductor pattern and broken one-dimensional metallic ring was generated. These results suggest that the Mo-S2 bond elongation produced by the sulphur dimers is similar to a MoS2 monolayer under tensile strain and is the origin of the one-dimensional metallic sites at the Mo-edges. In general, the present findings show excellent agreement with the key features of the reported ambient pressure X-ray photoemission spectra and the corresponding simulated scanning tunneling microscopy images.

Padé -Type Approximants for Some Classes of Multivariate Functions

We extend Dzyadyk’s method of generalized moment representations to the multidimensional case and, on this basis, construct and investigate the Pade-type approximants for some classes of multivariate functions.

Finite Blaschke products with prescribed critical points, Stieltjes polynomials, and moment problems

The determination of a finite Blaschke product from its critical points is a well-known problem with interrelations to several other topics. Though existence and uniqueness of solutions are established for long, we present new aspects which have not yet been explored to their full extent. In particular, we show that the following three problems are equivalent: (i) determining a finite Blaschke product from its critical points, (ii) finding the equilibrium position of moveable point charges interacting with a special configuration of fixed charges, and (iii) solving a moment problem for the canonical representation of power moments on the real axis. These equivalences are not only of theoretical interest, but also open up new perspectives for the design of algorithms. For instance, the second problem is closely linked to the determination of certain Stieltjes and Van Vleck polynomials for a second order ODE and characterizes solutions as global minimizers of an energy functional.

Existence Theorems for Multidimensional Generalized Moment Representations

We establish the conditions for the existence of multidimensional generalized moment representations.

Griffiths singularities in the random quantum Ising antiferromagnet: A tree tensor network renormalization group study

The antiferromagnetic Ising chain in both transverse and longitudinal magnetic fields is one of the paradigmatic models of a quantum phase transition. The antiferromagnetic system exhibits a zero-temperature critical line separating an antiferromagnetic phase and a paramagnetic phase; the critical line connects an integrable quantum critical point at zero longitudinal field and a classical first-order transition point at zero transverse field. Using a strong-disorder renormalization group method formulated as a tree tensor network, we study the zero-temperature phase of the quantum Ising chain with bond randomness. We introduce a new matrix product operator representation of high-order moments, which provides an efficient and accurate tool for determining quantum phase transitions via the Binder cumulant of the order parameter. Our results demonstrate an infinite-randomness quantum critical point in zero longitudinal field accompanied by pronounced quantum Griffiths singularities, arising from rare ordered regions with anomalously slow fluctuations inside the paramagnetic phase. The strong Griffiths effects are signaled by a large dynamical exponent $z>1$, which characterizes a power-law density of low-energy states of the localized rare regions and becomes infinite at the quantum critical point. Upon application of a longitudinal field, the quantum phase transition between the paramagnetic phase and the antiferromagnetic phase is completely destroyed. Furthermore, quantum Griffiths effects are suppressed, showing $z<1$, when the dynamics of the rare regions is hampered by the longitudinal field.

On the electron density localization in elemental cubic ceramic and FCC transition metals by means of a localized electrons detector.

The electron density localization in insulator and semiconductor elemental cubic materials with diamond structure, carbon, silicon, germanium, and tin, and good metallic conductors with face centered cubic structure such as α-Co, Ni, Cu, Rh, Pd, Ag, Ir, Pt, and Au, was studied using a localized electrons detector defined in the local moment representation. Our results clearly show an opposite pattern of the electron density localization for the cubic ceramic and transition metal materials. It was found that, for the elemental ceramic materials, the zone of low electron localization is very small and is mainly localized on the atomic basin edges. On the contrary, for the transition metals, there are low-valued localized electrons detector isocontours defining a zone of highly delocalized electrons that extends throughout the material. We have found that the best conductors are those in which the electron density at this low-value zone is the lowest.

疾走する馬のイマージュ論・再考 : ベルクソン哲学と瞬間の表象(第五十四回美学会全国大会発表要旨)

疾走する馬のイマージュ論・再考 : ベルクソン哲学と瞬間の表象(第五十四回美学会全国大会発表要旨)

Action recognition from point cloud patches using discrete orthogonal moments

3D sensors such as standoff Light Detection and Ranging (LIDAR) generate partial 3D point clouds that resemble patches of irregularly-shaped, coarse groups of points. 3D modeling of this type of data for human action recognition has been rarely studied. Although 2D---based depth image analysis is an option, its effectiveness on this type of low-resolution data hasn't been well answered. This paper investigates a new multi-scale 3D shape descriptor, based on the discrete orthogonal Tchebichef Moments, for the characterization of 3D action pose shapes made of low-resolution point cloud patches. Our shape descriptor consists of low-order 3D Tchebichef moments computed with respect to a new point cloud voxelization scheme that normalizes translation, scale, and resolution. The action recognition is built on the Naive Bayes classifier using temporal statistics of a `bag of pose shapes'. For performance evaluation, a synthetic LIDAR pose shape baseline was developed with 62 human subjects performing three actions - digging, jogging, and throwing. Our action classification experiments demonstrated that the 3D Tchebichef moment representation of point clouds achieves excellent action and viewing direction predictions with superb consistency across a large range of scale and viewing angle variations.

Statistical average of residual stresses in elastically homogeneous medium with random field of noncanonical inclusions

We consider a linearly elastic composite material (CM), which consists of a homogeneous matrix containing a statistically homogeneous random set of noncanonical (i.e. nonellipsoidal) inclusions. The elastic properties of the matrix and the inclusions are the same, but the stress-free strains are different. One proposes a new exact representation for the first statistical moments of stresses in the phases expressed trough the averaged boundary integrals over the inclusion boundaries. These integrals presenting the perturbations introduced by a single inclusion inside the infinite matrix are evaluated by a meshfree method based on fundamental solutions basis functions for a transmission problem in linear elasticity. Increasing of volume fraction of inclusions can lead to change of a sign of local residual stresses estimated by either the new approach or the classical one. The main properties of the method are analyzed and illustrated with several numerical simulations in 2D infinite domains containing statistically homogeneous random field of inclusions.

A representação social do ser professor de acadêmicos da Licenciatura em Educação Física antes e depois da formação inicial

O objetivo deste estudo foi analisar as representações que os acadêmicos de um curso de licenciatura em Educação Física de uma universidade pública da região sul do Brasil possuem sobre o ser professor antes e depois da formação inicial e se elas mudaram. Caracterizamos a pesquisa como qualitativa descritiva do tipo estudo de caso. O instrumento de coleta de informações foi um questionário com perguntas abertas. A interpretação das informações foi feita por meio da análise de conteúdo. Participaram 10 acadêmicos do 8º semestre do referido curso. Os resultados evidenciam que as representações dos acadêmicos sobre o ser professor de antes e depois da formação inicial não são as mesmas, pois ocorreram mudanças, prevalecendo neste momento representações mais coerentes com as propostas e objetivos almejados pelo curso de licenciatura em Educação Física estudado, sendo que desaparecem as representações do ser professor ligado a uma educação reprodutora da sociedade e aparecem representações ligadas a uma educação transformadora da sociedade.

A note on moments of limit log-infinitely divisible stochastic measures of Bacry and Muzy

A multiple integral representation of single and joint moments of the total mass of the limit log-infinitely divisible stochastic measure of Bacry and Muzy [$\textit{Comm. Math. Phys.}$ ${\bf 236}$: 449-475, 2003] is derived. The covariance structure of the total mass of the measure is shown to be logarithmic. A generalization of the Selberg integral corresponding to single moments of the limit measure is proposed and shown to satisfy a recurrence relation. The joint moments of the limit lognormal measure, classical Selberg integral with $\lambda_1=\lambda_2=0,$ and Morris integral are represented in the form of multiple binomial sums. For application, low moments of the limit log-Poisson measure are computed exactly and low joint moments of the limit lognormal measure are considered in detail.

‘Why Didn’t I Know About This Book When I Started?’: In Memory of Donald Graves and Arthur Applebee

This essay explores Donald Graves’ groundbreaking research of the 1980s. We show how Graves’ approach to the teaching of writing built on his sensitive appreciation of the ways children actually engage in the composing process when they are given the opportunity to produce writing that is meaningful to them. However, the issue for us is not simply the quality of Graves’ research, but how his work slipped from our memories, to be replaced by the dull drills in writing skills that now dominate US classrooms. To try to engage with this second issue, it has seemed best to disrupt the flow of our account of Graves’ work with representations of personal moments in teaching writing that we have each experienced, which we include as interpolations in the text. Only in this way do we feel that we can somehow get close to the nub of the issue with respect to the collective amnesia surrounding Graves’ achievement, in an attempt to bring back – both individually and collectively – his key insights and our students’ re-voicing of them to apply them in our professional practice as teachers of writing. We have also tried to include other voices beyond our own, all in an attempt to challenge the culture of the template, of the uniform response that ignores what ‘I’ have to say.

Exact and Invariant Representation of Nuclear Magnetic Moments and Spins According to Hadronic Mechanics

In order to render this paper minimally self-sufficient, we review and specialize the main structure of the isomathematics to nuclear constituents as extended and deformable charge distributions under linear and non-linear, local and non-local and Hamiltonian as well non-Hamiltonian interactions; we then review and specialize for the nuclear structure the main laws of the isotopic branch of hadronic mechanics known as isomechanics; we review and specialize the method for turning quantum mechanical nuclear models for point-like nucleons into covering isomechanical models for extended and deformable constituents under the most general known realization of strong interactions; we then review and specialize to nuclear structures the consequential notion of isoparticles; we then review the ensuing, first known, numerically exact and time invariant representation of the magnetic moments of stable nuclides; we then review the structure of the neutron as a bound state according to isomechanics of an isoproton and an isoelectron; and we finally review the ensuing three-body structure of the Deuteron. Via the use of the preceding advances. We then present, apparently for the first time, a numerically exact and time invariant representation of the spin of stable nuclides, firstly, via their approximation as isotopic bound states of isodeuterons, isoneutron and isoprotons, and secondly, via their reduction to isobound states of isoprotons and isoelectrons. Some observations on the nuclear configurations so obtained have also been presented in the case of the first model and in view of the second option we have identified in isoelectrons the nuclear glue which tightly holds isonucleons of stable nuclide in the atomic nucleus in the preferred orientation of their intrinsic spins. In Appendix A, we provide a technical review specialized for the first time to nuclear physics of the Lie-Santilli theory and its main application to the notion of isoparticles as isoirreducible isounitary isorepresentations of the Lorentz-Poincare-Santilli isosymmetry.

Entropic multirelaxation lattice Boltzmann models for turbulent flows.

We present three-dimensional realizations of a class of lattice Boltzmann models introduced recently by the authors [I. V. Karlin, F. Bösch, and S. S. Chikatamarla, Phys. Rev. E 90, 031302(R) (2014)] and review the role of the entropic stabilizer. Both coarse- and fine-grid simulations are addressed for the Kida vortex flow benchmark. We show that the outstanding numerical stability and performance is independent of a particular choice of the moment representation for high-Reynolds-number flows. We report accurate results for low-order moments for homogeneous isotropic decaying turbulence and second-order grid convergence for most assessed statistical quantities. It is demonstrated that all the three-dimensional lattice Boltzmann realizations considered herein converge to the familiar lattice Bhatnagar-Gross-Krook model when the resolution is increased. Moreover, thanks to the dynamic nature of the entropic stabilizer, the present model features less compressibility effects and maintains correct energy and enstrophy dissipation. The explicit and efficient nature of the present lattice Boltzmann method renders it a promising candidate for both engineering and scientific purposes for highly turbulent flows.

Analytic properties of complex Hermite polynomials

We study the complex Hermite polynomials { H m , n ( z , z ¯ ) } \{H_{m,n}(z, \bar z)\} in some detail, establish operational formulas for them and prove a Kibble-Slepian type formula, which extends the Poisson kernel for these polynomials. Positivity of the associated kernels is discussed. We also give an infinite family of integral operators whose eigenfunctions are { H m , n ( z , z ¯ ) } \{H_{m,n}(z,\bar z)\} . Some inverse relations are also given. We give a two dimensional moment representation for H m , n ( z , z ¯ ) H_{m,n}(z,\bar z) and evaluate several related integrals. We also introduce bivariate Appell polynomials and prove that { H m , n ( z , z ¯ ) } \{H_{m,n}(z, \bar z)\} are the only bivariate orthogonal polynomials of Appell type.

Model Reconstruction for Moment-Based Stochastic Chemical Kinetics

Based on the theory of stochastic chemical kinetics, the inherent randomness of biochemical reaction networks can be described by discrete-state continuous-time Markov chains. However, the analysis of such processes is computationally expensive and sophisticated numerical methods are required. Here, we propose an analysis framework in which we integrate a number of moments of the process instead of the state probabilities. This results in a very efficient simulation of the time evolution of the process. To regain the state probabilities from the moment representation, we combine the fast moment-based simulation with a maximum entropy approach for the reconstruction of the underlying probability distribution. We investigate the usefulness of this combined approach in the setting of stochastic chemical kinetics and present numerical results for three reaction networks showing its efficiency and accuracy. Besides a simple dimerization system, we study a bistable switch system and a multiattractor network with complex dynamics.