Self-organization of five species in a cyclic competition game

Cyclic competition game models, particularly the “rock–paper–scissors” model, play important roles in exploring the problem of multi-species coexistence in spatially ecological systems. We propose an extended “rock–paper–scissors” game to model cyclic interactions among five species, and find that two of the five can coexistent when biodiversity disappears, which is different from the “rock–paper–scissors” game. As the number of fingers is five, we named the new model the “fingers” game, where the thumb, forefinger, middle finger, ring finger, and little finger cyclically dominate their subsequent species and are dominated by their former species. We investigate the “fingers” model in two ways: direct simulations and nonlinear partial differential equations. An important finding is that the number of species in a cyclic competition game has an influence on the emergence of biodiversity. To be specific, the “rock–paper–scissors” model is in favor of maintaining biodiversity in comparison with the “fingers” model when the variables (population size, reproduction rate, selection rate, and migration rate) are the same. It is also shown that the mobility and reproduction rate can promote or jeopardize biodiversity.     

An analytical discrete-ordinates solution of the S-model kinetic equations for flow in a cylindrical tube

An integro-differential form of the linearized S-model kinetic equations for describing flow in a cylindrical tube is projected in such a way as to yield a pair of coupled transport equations that defines the desired velocity and heat-flow profiles. This system is then solved symbolically to yield a pair of coupled integral equations for the physical quantities required. At this point some transformations are carried out to yield a restatement of the original problem in terms of a “pseudo-problem” defined by plane-geometry variables. An analytical version of the discrete-ordinates method is then used to solve the pseudo-problem, and so, after both MATLAB and FORTRAN versions of the developed algorithm are implemented, results thought to be highly accurate are obtained for the case of diffuse reflection from the walls of a cylindrical tube. In addition to the velocity and heat-flow profiles, for the cases of Poiseuille flow and thermal-creep flow, the velocity slips, the heat-flow profiles evaluated at the wall, the particle-flow rates and the heat-flow rates for these two problems are reported for selected values of the tube radius.     

Study of mutual information multimodality medical image registration based on modified simplex optimization method

Because of a different imaging mechanism and highly complexity of body tissues and structures. Different modality medical images provide non-overlay complementary information. This has very important significance for multimodal medical image registration. Image registration is the first and key part of problem to be solved in the integrations. When the spatial position of two medical images is same, the registration could be achieved. For two CT and PET images, the principal axis method is adopted to achieve the rough registration. The modified simplex algorithm is employed to implement global search using the mutual information as similarity measure. The initial registration parameters are achieved through principal axis Based on the results of test, improved simplex method can adjust reflecting distance. Stepped-up optimization algorithm on the new experimental points through the methods of “reflection”, “enlargement”, “shrinkage” or “global systolic”. A mutual information registration based on modified simplex optimization method is presented in this paper to improve the speed of medical image registration.Results indicate that the proposed registration method prevents the optimizing process from falling into local extremum and improves the convergence speed while keeping the precision. The accurate registration of multimodal image with different resolutions is achieved.     

Comparison of the performance of different tools for fast simulation of ultrasound data

Simulation of ultrasound data is often performed for developing new ultrasound data processing techniques. The spatial impulse response method (as implemented in FieldII) has typically been used as the gold standard due to its excellent accuracy in the linear domain. When scatterer numbers become significant and when 3D volumetric data sets need to be computed, calculation time can become an issue however. In order to solve this problem, two alternative methods have recently been proposed both of which are based on the principle of convolving a set of point scatterers with a point spread function. “FUSK” operates in the frequency domain while “COLE” runs in the spatio-temporal domain. The aim of this study was to directly contrast both methodologies in terms of accuracy and processing speed using FieldII as a reference.     

Effects of misalignments in the optical vortex transformation performed by holograms with embedded phase singularity

Spatial characteristics of diffracted beams produced by a “fork” hologram from an incident circular Laguerre-Gaussian beam whose axis differs from the hologram optical axis are studied theoretically. General analytical representations for the complex amplitude distribution of a diffracted beam are derived in terms of superposition of Kummer beams or hypergeometric-Gaussian beams. The diffracted beam structure is determined by combination of the “proper” topological charge m of the incident vortex beam and the topological charge l of the singularity “imparted” by the hologram. Evolution of the diffracted beam structure is studied in detail for several combinations of m and l and for various incident beam displacements with respect to the optical axis of the hologram. Variations of the intensity and phase distribution due to the incident beam misalignment are investigated and possible applications for the purposeful optical vortex beam generation and optical measurements are discussed.     

Output-only identification and dynamic analysis of time-varying mechanical structures under random excitation: A comparative assessment of parametric methods

This article addresses the problem of parametric time-domain identification and dynamic analysis for time-varying (TV) mechanical structures under unobservable random excitation. The methods presented are based on time-dependent autoregressive moving average (TARMA) models, and are classified according to the mathematical structure imposed on the TV parameter evolution as unstructured parameter evolution, stochastic parameter evolution, and deterministic parameter evolution. The features and relative merits of each class are outlined. A representative method from each is then assessed through its application to the identification and dynamic analysis of a laboratory TV structure consisting of a beam with a mass moving on it. The results are mutually compared and contrasted to those obtained through “frozen-configuration” (multiple experiment) baseline identification.     

Understanding the time dependence of atomic level populations in evolving plasmas

The time dependence of atomic level populations in evolving plasmas is studied using an eigenfunction expansion of the non-LTE rate equations. The work aims to develop understanding without the need for, and as an aid to, numerical solutions. The discussion is mostly limited to linear systems, especially those for optically thin plasmas, but the implicitly non-linear case of non-LTE radiative transfer is briefly discussed. Eigenvalue spectra for typical atomic systems are examined using results compiled by Hearon. Diagonal dominance and sign symmetry of rate matrices show that just one eigenvalue is zero (corresponding to the equilibrium state), that the remaining eigenvalues have negative real parts, and that oscillations, if any, are necessarily damped. Gershgorin's theorems are used to show that many eigenvalues are determined by the radiative lifetimes of certain levels, because of diagonal dominance. With other properties, this demonstrates the existence of both “slow” and “fast” time-scales, where the “slow” evolution is controlled by properties of meta-stable levels. It is shown that, when collisions are present, Rydberg states contribute only “fast” eigenvalues. This justifies use of the quasi-static approximation, in which atoms containing just meta-stable levels can suffice to determine the atomic evolution on time-scales long compared with typical radiative lifetimes. Analytic solutions for two- and three-level atoms are used to examine the basis of earlier intuitive ideas, such as the “ionizing plasma” approximation. The power and limitations of Gershgorin's theorems are examined through examples taken from the solar atmosphere. The methods should help in the planning and interpretation of both experimental and numerical experiments in which atomic evolution is important. While the examples are astrophysical, the methods and results are applicable to plasmas in general.     

A simple algorithm for spectral line deconvolution

The objective of this work is to develop a numerical procedure to subtract the instrumental function from a measured spectral line profile. The measuring device (for example, a Fabry-Perot Interferometer) distorts the spectral line profile and the experimentally measured one is a convolution of this profile and the instrumental function. Restoring the spectral line profile is strongly affected by numerical instabilities and the problem has been overcome by using the Tikhonov regularization method. The approach is very simple and easy for programming and it is particularly useful for “noisy” experimental data.     

Equations of motion of compact binaries at the third post-Newtonian order

The equations of motion of two point masses in harmonic coordinates are derived through the third post-Newtonian (3PN) approximation. The problem of selffield regularization (necessary for removing the divergent self-field of point particles) is dealt with in two separate steps. In the first step the extended Hadamard regularization is applied, resulting in equations of motion which are complete at the 3PN order, except for the occurrence of one and only one unknown parameter. In the second step the dimensional regularization (ind dimensions) is used as a powerful argument for fixing the value of this parameter, thereby completing the 3-dimensional Hadamard-regularization result. The complete equations of motion and associated energy at the 3PN order are given in the case of circular orbits.     

Modified perturbation method for eigenvalues of structure with interval parameters

In overcoming the drawbacks of traditional interval perturbation method due to the unpredictable effect of ignoring higher order terms,a modified parameter perturbation method is presented to predict the eigenvalue intervals of the uncertain structures with interval parameters.In the proposed method,interval variables are used to quantitatively describe all the uncertain parameters.Different order perturbations in both eigenvalues and eigenvectors are fully considered.By retaining higher order terms,the original dynamic eigenvalue equations are transformed into interval linear equations based on the orthogonality and regularization conditions of eigenvectors.The eigenvalue ranges and corresponding eigenvectors can be approximately predicted by the parameter combinatorial approach.Compared with the Monte Carlo method,two numerical examples are given to demonstrate the accuracy and efficiency of the proposed algorithm to solve both the real eigenvalue problem and complex eigenvalue problem.     

Fronts and bumps in spatially extended Kuramoto networks

We consider moving fronts and stationary “bumps” in networks of non-locally coupled phase oscillators. Fronts connect regions of high local synchrony with regions of complete asynchrony, while bumps consist of spatially-localised regions of partially-synchronous oscillators surrounded by complete asynchrony. Using the Ott-Antonsen ansatz we derive non-local differential equations which describe the network dynamics in the continuum limit. Front and bump solutions of these equations are studied by either “freezing” them in a travelling coordinate frame or analysing them as homoclinic or heteroclinic orbits. Numerical continuation is used to determine parameter regions in which such solutions exist and are stable.     

Integrating the original face images and “symmetrical faces” to perform face recognition

Using the original and ‘symmetrical face’ training samples to perform representation based face recognition was first proposed in [1]. It simultaneously used the original and ‘symmetrical face’ training samples to perform a two-step classification and achieved an outstanding classification result. However, in [1] the “symmetrical face” is devised only for one method. In this paper, we do some improvements on the basis of [1] and combine this “symmetrical faces” transformation with several representation based methods. We exploit all original training samples, left “symmetrical face” training samples and right “symmetrical face” training samples for classification and use the score fusion for ultimate face recognition. The symmetry of the face is first used to generate new samples, which is different from original face image but can really reflect some possible appearance of the face. It effectively overcomes the problem of non-sufficient training samples. The experimental results show that the proposed scheme can be used to improve a number of traditional representation based methods including those that are not presented in the paper.     

A heuristic approach to automated molecular line assignment

A first investigation on the feasibility of automated molecular line assignment is presented. Dense rovibrational molecular spectra are normally assigned by strongly interactive computer methods, ranging from commercial spreadsheets to dedicated programs, like Loomis-Wood or Ritz. While a general-purpose, fully automated assignment procedure seems to be out of reach for the near future, we show that a thorough investigation of the problem can lead to new, more efficient and less interactive methods, at least in reasonably favorable conditions. Interesting suggestions are provided by some modern “heuristic” problem-solving algorithms, which mimic natural processes. As a first step, we have developed a “transgenic-evolutionary” algorithm, which has successfully assigned artificial spectra of up to almost 3500 lines. We discuss also its performance on an experimental, but “filtered,” methanol spectrum. Possible future improvements and developments of this method, as well as its limits, are discussed.     

On higher derivatives in 3D gravity and higher-spin gauge theories

The general second-order massive field equations for arbitrary positive integer spin in three spacetime dimensions, and their “self-dual” limit to first-order equations, are shown to be equivalent to gauge-invariant higher-derivative field equations. We recover most known equivalences for spins 1 and 2, and find some new ones. In particular, we find a non-unitary massive 3D gravity theory with a 5th order term obtained by contraction of the Ricci and Cotton tensors; this term is part of an N=2 super-invariant that includes the “extended Chern-Simons” term of 3D electrodynamics. We also find a new unitary 6th order gauge theory for “self-dual” spin 3.     

LIMIT-CYCLE STABILITY REVERSAL NEAR A HOPF BIFURCATION WITH AEROELASTIC APPLICATIONS

The objective of this paper is to present an analytical/numerical analysis of the phenomenon of limit-cycle stability reversal (from unstable to stable, and vice versa). A singular perturbation technique, the method of the normal form (in the asymptotic- expansion version), is utilized. The number of equations is then reduced to a “minimal set”, for which the results are in good agreement with those from the original equations. This minimal set is determined by the amplitude of the λ̂-points (a concept closely related to the small divisors in the KAM theory). This set is larger than that corresponding to the zero real-part eigenvalues (center-manifold theorem). The method is applied to a specific problem: an aeroelastic section with cubic free-play non-linearities where the parameter μ is the flight speed. Numerical studies have been performed to show the dependence of the Hopf bifurcation characteristics upon the structural and geometric properties of the wing section. Plots depicting amplitudes and frequency versus flight speed are presented.     

Relationship between different approaches to derive weighting functions related to atmospheric remote sensing problems

The paper is devoted to the investigation of the relationship between different methods used to derive weighting functions required to solve numerous inverse problems related to the remote sensing of the Earth's atmosphere by means of scattered solar light observations. The first method commonly referred to as the forward-adjoint approach is based on a joint solution of the forward and adjoint radiative transfer equations and the second one requires the linearized forward radiative transfer equation to be solved. In the framework of the forward-adjoint method we consider two approaches commonly used to derive the weighting functions. These approaches are referenced as the “response function” and the “formal solution” techniques, respectively. We demonstrate here that the weighting functions derived employing the formal solution technique can also be obtained substituting the analytical representations for the direct forward and direct adjoint intensities into corresponding expressions obtained in the framework of the response function technique. The advantages and disadvantages of different techniques are discussed.     

Model updating via weighted reference basis with connectivity constraints

The paper considers the problem of updating an analytical model from experimental data using the reference basis approach. In the general framework of the reference basis method, certain quantities, e.g., natural frequencies or modeshapes, are considered to be completely accurate and the others are updated by solving a constrained optimization problem. However, the underlying structure, known as connectivity, existing in the model is not preserved, and the method is not suited for parametric updating. In this paper, a method for introducing connectivity constraints into reference basis, while maintaining its advantages, is presented. It brings the reference basis method closer to a broad class of updating methods that use parametric updating. The notions of “connectivity cost” and “parameterization cost” are defined and used to obtain the best model for a given parameterization and to compare the outcomes of different parameterizations.     

Simulating the dynamics of flexible bodies and vortex sheets

We present a numerical method for the dynamics of a flexible body in an inviscid flow with a free vortex sheet. The formulation is implicit with respect to body variables and explicit with respect to the free vortex sheet. We apply the method to a flexible foil driven periodically in a steady stream. We give numerical evidence that the method is stable and accurate for a relatively small computational cost. A continuous form of the vortex sheet regularization permits continuity of the flow across the body’s trailing edge. Nonlinear behavior arises gradually with respect to driving amplitude, and is attributed to the rolling-up of the vortex sheet. Flow quantities move across the body in traveling waves, and show large gradients at the body edges. We find that in the small-amplitude regime, the phase difference between heaving and pitching which maximizes trailing edge deflection also maximizes power output; the phase difference which minimizes trailing edge deflection maximizes efficiency.