Search

In this paper, we present a new model for deformations of shapes. A pseudolikelihood is based on the statistical distribution of the gradient vector field of the gray level. The prior distribution is based on the Probabilistic Principal Component Analysis (PPCA). We also propose a new model based on mixtures of PPCA that is useful in the case of greater variability in the shape. A criterion of global or local object specificity based on a preliminary color segmentation of the image is included into the model. The localization of a shape in an image is then viewed as minimizing the corresponding Gibbs field. We use the Exploration/Selection (E/S) stochastic algorithm in order to find the optimal deformation. This yields a new unsupervised statistical method for localization of shapes. In order to estimate the statistical parameters for the gradient vector field of the gray level, we use an Iterative Conditional Estimation (ICE) procedure. The color segmentation of the image can be computed with an Exploration/Selection/Estimation (ESE) procedure. [ABSTRACT FROM AUTHOR]

Super- and sub-additive transformations of aggregation functions have been recently introduced by Greco, Mesiar, Rindone and Šipeky [The superadditive and the subadditive transformations of integrals and aggregation functions, Fuzzy Sets and Systems 291 (2016), 40-53]. In th is article we give a survey of the recent development regarding the existence of aggregation functions with a preassigned super- and sub-additive transformation, and address approximation of these transformations. The underpinning feature of the presented results is dependence of global properties of super- and sub-additive transformations on local properties of aggregation functions. [ABSTRACT FROM AUTHOR]

Several existing digital straight line segment (DSS) recognition algorithms can be used to determine the digital straightness of a given one-pixel-thick digital curve. Because of the inherent geometric constraints of digital straightness, these algorithms often produce a large number of segments to cover a given digital curve representing a real-life object/image. Thus, a curve segment, which is not exactly digitally straight but appears to be visually straight, is fragmented into multiple DSS when these algorithms are run. In this paper, a new concept of approximate straightness is introduced by relaxing certain conditions of DSS, and an algorithm is described to extract those segments from a digital curve. The number of such segments required to cover the curve is found to be significantly fewer than that of the exact DSS cover. As a result, the data set required for representing a curve also reduces to a large extent. The extracted set of segments can further be combined to determine a compact polygonal approximation of a digital curve based on certain approximation criteria and a specified error tolerance. The proposed algorithm involves only primitive integer operations and, thus, runs very fast compared to those based on exact DSS. The overall time complexity becomes linear in the number of points present in the representative set. Experimental results on several digital curves demonstrate the speed, elegance, and efficacy of the proposed method. [ABSTRACT FROM AUTHOR]

This paper presents a novel approach for visual scene modeling and classification, investigating the combined use of text modeling methods and local invariant features. Our work attempts to elucidate 1) whether a textlike bag-of-visterms (BOV) representation (histogram of quantized local visual features) is suitable for scene (rather than object) classification, 2) whether some analogies between discrete scene representations and text documents exist, and 3) whether unsupervised, latent space models can be used both as feature extractors for the classification task and to discover patterns of visual co-occurrence. Using several data sets, we validate our approach, presenting and discussing experiments on each of these issues. We first show, with extensive experiments on binary and multiclass scene classification tasks using a 9,500-image data set, that the BOV representation consistently outperforms classical scene classification approaches. In other data sets, we show that our approach competes with or outperforms other recent more complex methods. We also show that Probabilistic Latent Semantic Analysis (PLSA) generates a compact scene representation, is discriminative for accurate classification, and is more robust than the BOV representation when less labeled training data is available. Finally, through aspect-based image ranking experiments, we show the ability of PLSA to automatically extract visually meaningful scene patterns, making such representation useful for browsing image collections. [ABSTRACT FROM AUTHOR]

In this work we study a dynamical system with a complicated nonlinearity, which describes oscillation of a turbine rotor, and give an algorithm to compute Melnikov functions for analysis of its chaotic behavior. We first derive the rotor model whose nonlinear term brings difficulties to investigating the distribution and qualitative properties of its equilibria. This nonlinear model provides a typical example of a system for which the homoclinic and heteroclinic orbits cannot be analytically determined. In order to apply Melnikov's method to make clear the underlying conditions for chaotic motion, we present a generic algorithm that provides a systematic procedure to compute Melnikov functions numerically. Substantial analysis is done so that the numerical approximation precision at each phase of the computation can be guaranteed. Using the algorithm developed in this paper, it is straightforward to obtain a sufficient condition for chaotic motion under damping and periodic external excitation, whenever the rotor parameters are given. [ABSTRACT FROM AUTHOR]

This paper introduces a simple model for solving a system of first-order rate equations using the TLM numerical method. A general algorithm is developed by setting up a matrix of discrete compartments. The rate constants provide the linkage between each compartment and the neighbouring ones. The method is demonstrated by some examples in which saturation conditions are considered. The TLM solution is compared with analytical solutions and the Rung-Kutta method of solving differential equations. [ABSTRACT FROM AUTHOR]

Abstract: In this paper the continuous Verhulst dynamic model is used to synthesize a new distributed power control algorithm (DPCA) for use in direct sequence code division multiple access (DS-CDMA) systems. The Verhulst model was initially designed to describe the population growth of biological species under food and physical space restrictions. The discretization of the corresponding differential equation is accomplished via the Euler numeric integration (ENI) method. Analytical convergence conditions for the proposed DPCA are also established. Several properties of the proposed recursive algorithm, such as Euclidean distance from optimum vector after convergence, convergence speed, normalized mean squared error (NSE), average power consumption per user, performance under dynamics channels, and implementation complexity aspects, are analyzed through simulations. The simulation results are compared with two other DPCAs: the classic algorithm derived by Foschini and Miljanic and the sigmoidal of Uykan and Koivo. Under estimated errors conditions, the proposed DPCA exhibits smaller discrepancy from the optimum power vector solution and better convergence (under fixed and adaptive convergence factor) than the classic and sigmoidal DPCAs. [Copyright &y& Elsevier]

A new method named as Statistical Average Algorithm is developed for solving the structural dynamic compound inverse problem, which means to identify structural parameters with unknown input or to inverse input time history with unknown structural parameters. By taking the mechanical characteristic of the ground motion as an additional condition, an iterative algorithm based on the least-squares technique is developed so that the input process and structural parameters can be correctly determined using only output measurements. The procedure of the proposed method is discussed in detail, and a mathematical proof is presented as well in the appendix. A practical input situation such as earthquake, ambient vibration is considered in the numerical examples to verify the accuracy, reliability and robustness of the proposed algorithm. Considering the background of the practical application, both of the noise-free and noise-included output responses are considered in the numerical examples. In all cases, the proposed method identifies the structural parameters and reconstructs the input process rationally. [ABSTRACT FROM AUTHOR]

Dynamical systems appear in many models in all sciences and in technology. They can be either discrete or continuous, finite or infinite dimensional, deterministic or with random terms. Many theoretical results, the related algorithms and implementations for careful simulations and a wide range of applications have been obtained up to now. But still many key questions remain open. They are mainly related either to global aspects of the dynamics or to the lack of a sufficiently good agreement between qualitative and quantitative results. In these notes a sample of questions, for which the author is not aware of the existence of a good solution, are presented. Of course, it is easy to largely extend the list. [ABSTRACT FROM AUTHOR]

We provide an integral estimate for a non-divergence (non-variational) form second order elliptic equation aijuij = up, u ≥ 0, p ∈ [0,1), with bounded discontinuous coefficients aij having small BMO norm. We consider the simplest discontinuity of the form x * x|x|-2 at the origin. As an application we show that the free boundary corresponding to the obstacle problem (i.e. when p = 0) cannot be smooth at the points of discontinuity of aij (x). To implement our construction, an integral estimate and a scale invariance will provide the homogeneity of the blow-up sequences, which then can be classified using ODE arguments. [ABSTRACT FROM AUTHOR]

The outbreaks of the severe acute respiratory syndrome (SARS) epidemic in 2003 resulted in unprecedented impacts on people's daily life. One of the most significant impacts to people is the fear of contacting the SARS virus while engaging daily routine activity. Here we use data from daily underground ridership in Taipei City and daily reported new SARS cases in Taiwan to model the dynamics of the public fear of the SARS virus during the wax and wane of the SARS period. We found that for each reported new SARS case there is an immediate loss of about 1200 underground ridership (the fresh fear). These daily loss rates dissipate to the following days with an e-folding time of about 28 days, reflecting the public perception on the risk of contacting SARS virus when traveling with the underground system (the residual fear). About 50% of daily ridership was lost during the peak of the 2003 SARS period, compared with the loss of 80% daily ridership during the closure of the underground system after Typhoon Nari, the loss of 50–70% ridership due to the closure of the governmental offices and schools during typhoon periods, and the loss of 60% daily ridership during Chinese New Year holidays. [ABSTRACT FROM AUTHOR]

Biochemical systems involving a high number of components with intricate interactions often lead to complex models containing a large number of parameters. Although a large model could describe in detail the mechanisms that underlie the system, its very large size may hinder us in understanding the key elements of the system. Also in terms of parameter identification, large models are often problematic. Therefore, a reduced model may be preferred to represent the system. Yet, in order to efficaciously replace the large model, the reduced model should have the same ability as the large model to produce reliable predictions for a broad set of testable experimental conditions. We present a novel method to extract an “optimal” reduced model from a large model to represent biochemical systems by combining a reduction method and a model discrimination method. The former assures that the reduced model contains only those components that are important to produce the dynamics observed in given experiments, whereas the latter ensures that the reduced model gives a good prediction for any feasible experimental conditions that are relevant to answer questions at hand. These two techniques are applied iteratively. The method reveals the biological core of a model mathematically, indicating the processes that are likely to be responsible for certain behavior. We demonstrate the algorithm on two realistic model examples. We show that in both cases the core is substantially smaller than the full model. [ABSTRACT FROM AUTHOR]

Mathematical models and numerical algorithms are explored for several technological challenges in physics, chemistry, aerothermodynamics, and evolution of dynamic systems in economics and weather forecast. Various mathematical concepts are examined to evaluate multifold integrals, dynamics of strange attractors, and solutions of differential equations with small parameters at the highest derivatives. [ABSTRACT FROM AUTHOR]

Higher-order finite-volume flux operators for transport algorithms used within Runge-Kutta time integration schemes on irregular Voronoi (hexagonal) meshes are proposed and tested. These operators are generalizations of third- and fourth-order operators currently used in atmospheric models employing regular, orthogonal rectangular meshes. Two-dimensional least squares fit polynomials are used to evaluate the higher-order spatial derivatives needed to cancel the leading-order truncation error terms of the standard second-order centered formulation. Positive definite or monotonic behavior is achieved by applying an appropriate limiter during the final Runge-Kutta stage within a given time step. The third- and fourth-order formulations are evaluated using standard transport tests on the sphere. The new schemes are more accurate and significantly more efficient than the standard second-order scheme and other schemes in the literature examined by the authors. The third-order formulation is equivalent to the fourth-order formulation plus an additional diffusion term that is proportional to the Courant number. An optimal value for the coefficient scaling this diffusion term is chosen based on qualitative evaluation of the test results. Improvements using the higher-order scheme in place of the traditional second-order centered approach are illustrated within 3D unstable baroclinic wave simulations produced using two global nonhydrostatic models employing spherical Voronoi meshes. [ABSTRACT FROM AUTHOR]