LPNN-based approach for LASSO problem via a sequence of regularized minimizations

In compressive sampling theory, the least absolute shrinkage and selection operator (LASSO) is a representative problem. Nevertheless, the non-differentiable constraint impedes the use of Lagrange programming neural networks (LPNNs). We present in this article the -LPNN model, a novel algorithm that tackles the LASSO minimization together with the underlying theory support. First, we design a sequence of smooth constrained optimization problems, by introducing a convenient differentiable approximation to the non-differentiable -norm constraint. Next, we prove that the optimal solutions of the regularized intermediate problems converge to the optimal sparse signal for the LASSO. Then, for every regularized problem from the sequence, the -LPNN dynamic model is derived, and the asymptotic stability of its equilibrium state is established as well. Finally, numerical simulations are carried out to compare the performance of the proposed -LPNN algorithm with both the LASSO-LPNN model and a standard digital method.     

A unified approach to some inequalities of Ostrowski-Grüss type

Based on the Euler-Maclaurin formula in the spirit of [1], we provide a unified approach to some inequalities of Ostrowski-Grüss type, which include some existing results as special cases. Some illustrative examples are also included.     

Application of aeroelastic modes on nonlinear supersonic panel flutter at elevated temperatures

This paper shows that the use of aeroelastic modes, instead of the traditional in vacuo natural modes, can reduce drastically the number of coupled nonlinear modal equations for the large amplitude nonlinear panel flutter analysis at an arbitrary yawed supersonic flow angle and elevated temperatures. All four types of panel behavior can be predicted and they are flat and stable, aerothermally buckled but dynamically stable, limit cycle oscillations, and chaos.     

OPAH a model for optimal design of multipurpose small hydropower plants

The investment in small hydropower plants requires the analysis of hydrological, technical, operational, budgetary, economical and financial aspects. The analysis of each possible configuration demands the joint action of several technicians, consuming substantial time and money. During initial design of the project, simplified procedures are usually adopted which may compromise the quality of the base configuration.In this paper we will present a global overview of the OPAH model, which was developed to surpass these limitations. This global model performs the optimization of project configuration. This model uses non-linear programming optimization to analyze the multipurpose operation of the hydropower plant. It uses a numeric simulation model of unsteady flow under pressure to analyze the hydraulic circuit. It uses an economical and financial simulation model that takes in to account the project risk associated to hydrologic and market variability, the financial capacity of the investor and the fiscal aspects.     

Mathematical framework for Bz-based MREIT model in electrical impedance imaging

Magnetic resonance electrical impedance tomography (MREIT) is a new medical imaging modality visualizing static conductivity images of a subject by injecting electrical currents (Neumann data) and measuring the induced internal magnetic flux density B using an MRI scanner. Taking advantage of the internal information B, MREIT can deal with the ill-posed characteristics of the inverse problem in electrical impedance tomography (EIT However, the MREIT model at its early stage has technical difficulties in clinical applications mainly due to the requirement of subject rotations for acquiring all of the three components of B = (B_z, B_y, B_z). Lately, a new model so called the B_z-based MREIT model has been proposed to eliminate the subject rotation procedure. In this new MREIT model, we need to measure only one component B_z when the z-axis is the direction of the main magnetic field of the MRI scanner. There have been significant advances in reconstruction algorithms based on the B_z-based MREIT model and experimental studies showed that an excellent contrast resolution can be achievable. Although these advance in B_z-based MREIT, we have not dealt with its rigorous mathematical theory yet.The primary purpose of this work is to provide the rigorous mathematical framework for the B_z-based MREIT model. With this mathematical framework, we obtain the uniqueness in a two-dimensional setting of the B_z-based MREIT model. After introducing an example of the B_z-based MREIT algorithm, we present typical numerical and also experimental results.     

Parallel genetic algorithms for optimising cellular automata models of natural complex phenomena: An application to debris flows

Cellular automata models of natural complex phenomena may depend on a set of parameters which can significantly influence the global dynamics of the simulated events. In order to reliably apply such models for predictive purposes, their parameters have to be estimated with the greatest possible accuracy. However, no standardised optimisation techniques exist in this specific research field. Genetic Algorithms (GAs) offer a possible solution: they are parallel algorithms, and can be easily implemented to exploit the simultaneous use of multiple CPUs, thereby greatly reducing the execution time.An application of a parallel GA to the optimisation of a cellular automata model for the simulation of debris flows characterised by strong inertial effects is presented. The May 1998, Curti-Sarno (Italy) debris flow has been selected as a case study for the optimisation of the model. Theoretical considerations on the dynamics of the adopted GA are discussed, with reference to two different fitness functions applied to an idealised case study.Results demonstrated the usefulness of the approach, in terms of both computing time and quality of performed simulations. Moreover, experiments on the idealised case study pointed out that the simplest fitness function (only based on the comparison of affected areas) could conveniently be adopted for calibration purposes.     

Average consensus in networks of dynamic agents with switching topologies and multiple time-varying delays

In this paper, we discuss average consensus problem in undirected networks of dynamic agents with fixed and switching topologies as well as multiple time-varying communication delays. By employing a linear matrix inequality method, we prove that all the nodes in the network achieve average consensus asymptotically for appropriate communication delays if the network topology is connected. Particularly, several feasible linear matrix inequalities are established to determine the maximal allowable upper bound of time-varying communication delays. Numerical examples are given to demonstrate the effectiveness and the sharpness of the theoretical results.     

Generalization of the Wolstenholme cyclic inequality and its application

This paper deals with the generalization and sharp versions of the Wolstenholme cyclic inequality and their applications. The inequalities of this paper improve and unify corresponding known results. Several interesting inequalities including the celebrated Ozeki inequality are obtained. Extensions of the Wolstenholme inequality for a complex polygon and the Wolstenholme inequality for a convex quadrilateral are derived. As example of applications, the well-known Erdös–Mordell inequality is improved in this paper. In addition, several extensions, unifications and refinements of Gueron–Shafrir’s inequalities and Mitrinović–Pecaric’s inequality are established.     

Beliefs, time and incomplete information in multiple encounter negotiations among autonomous agents

In negotiations among autonomous agents over resource allocation, beliefs about opponents, and about opponents’ beliefs, become particularly important when there is incomplete information. This paper considers interactions among self‐motivated, rational, and autonomous agents, each with its own utility function, and each seeking to maximize its expected utility. The paper expands upon previous work and focuses on incomplete information and multiple encounters among the agents. It presents a strategic model that takes into consideration the passage of time during the negotiation and also includes belief systems. The paper provides strategies for a wide range of situations. The framework satisfies the following criteria: symmetrical distribution, simplicity, instantaneously, efficiency and stability. This revised version was published online in June 2006 with corrections to the Cover Date.     

Reinterpreting the basic theorem of flagellar hydrodynamics

Lorentz [1] pioneered the representation of flows at very low Reynolds number by a surface distribution of stokeslets — whose strengths, nowadays, are computed by surface-velocity collocations. That method is here compared with a representation widely used in flagellar hydrodynamics, by a curvilinear distribution of stokeslets and dipoles along the flagellar centreline; with the velocity of each cross-section expressed as a centreline value of the combined fields of singularities beyond a certain cutoff distance. The latter is also a good representation, and offers moreover some computational advantages. This paper establishes the equivalence of the two representations, and identifies those properties of Stokes flows which make both the dipoles and the cutoff essential to that equivalence.