Iterative Algorithms for Nonlinear Equations and Dynamical Behaviors: Applications

Numerical iteration methods for solving the roots of nonlinear transcendental or algebraic model equations (in 1D, 2D or 3D) are useful in most applied sciences (Biology, physics, mathematics, Chemistry…) and in engineering, for example, problems of beam deflections. This article presents new iterative algorithms for finding roots of nonlinear equations applying some fixed point transformation and interpolation. A method for solving nonlinear systems (in higher dimensions, for multi-variables) is also considered. Our main focus is on methods not involving the equation f(x) in problem and or its derivatives. These new algorithm can be considered as the acceleration convergence of several existing methods. For convergence and efficiency proofs and applications, we solve deflection of a beam differential equation and some test experiments in in Matlab.  Different (real & complex) dynamical (convergence plane) analyzes are also shown graphically. Keywords: nonlinear equations, deflection of beam, iterations, dynamical analysis, applications, 2

A review of modelling and verification approaches for computational biology

This paper reviews most frequently used computational modelling approaches and formal verification techniques in computational biology. The paper also compares a number of model checking tools and software suits used in analysing biological systems and biochemical networks and verifiying a wide range of biological properties

The Quaternion-Based Spatial Coordinate and Orientation Frame Alignment Problems

We review the general problem of finding a global rotation that transforms a given set of points and/or coordinate frames (the "test" data) into the best possible alignment with a corresponding set (the "reference" data). For 3D point data, this "orthogonal Procrustes problem" is often phrased in terms of minimizing a root-mean-square deviation or RMSD corresponding to a Euclidean distance measure relating the two sets of matched coordinates. We focus on quaternion eigensystem methods that have been exploited to solve this problem for at least five decades in several different bodies of scientific literature where they were discovered independently. While numerical methods for the eigenvalue solutions dominate much of this literature, it has long been realized that the quaternion-based RMSD optimization problem can also be solved using exact algebraic expressions based on the form of the quartic equation solution published by Cardano in 1545; we focus on these exact solutions to expose the structure of the entire eigensystem for the traditional 3D spatial alignment problem. We then explore the structure of the less-studied orientation data context, investigating how quaternion methods can be extended to solve the corresponding 3D quaternion orientation frame alignment (QFA) problem, noting the interesting equivalence of this problem to the rotation-averaging problem, which also has been the subject of independent literature threads. We conclude with a brief discussion of the combined 3D translation-orientation data alignment problem. Appendices are devoted to a tutorial on quaternion frames, a related quaternion technique for extracting quaternions from rotation matrices, and a review of quaternion rotation-averaging methods relevant to the orientation-frame alignment problem. Supplementary Material covers extensions of quaternion methods to the 4D problem.Comment: This replaces an early draft that lacked a number of important references to previous work. There are also additional graphics elements. The extensions to 4D data and additional details are worked out in the Supplementary Material appended to the main tex

Dynamic Effective Connectivity of Inter-Areal Brain Circuits

Anatomic connections between brain areas affect information flow between neuronal circuits and the synchronization of neuronal activity. However, such structural connectivity does not coincide with effective connectivity (or, more precisely, causal connectivity), related to the elusive question “Which areas cause the present activity of which others?”. Effective connectivity is directed and depends flexibly on contexts and tasks. Here we show that dynamic effective connectivity can emerge from transitions in the collective organization of coherent neural activity. Integrating simulation and semi-analytic approaches, we study mesoscale network motifs of interacting cortical areas, modeled as large random networks of spiking neurons or as simple rate units. Through a causal analysis of time-series of model neural activity, we show that different dynamical states generated by a same structural connectivity motif correspond to distinct effective connectivity motifs. Such effective motifs can display a dominant directionality, due to spontaneous symmetry breaking and effective entrainment between local brain rhythms, although all connections in the considered structural motifs are reciprocal. We show then that transitions between effective connectivity configurations (like, for instance, reversal in the direction of inter-areal interactions) can be triggered reliably by brief perturbation inputs, properly timed with respect to an ongoing local oscillation, without the need for plastic synaptic changes. Finally, we analyze how the information encoded in spiking patterns of a local neuronal population is propagated across a fixed structural connectivity motif, demonstrating that changes in the active effective connectivity regulate both the efficiency and the directionality of information transfer. Previous studies stressed the role played by coherent oscillations in establishing efficient communication between distant areas. Going beyond these early proposals, we advance here that dynamic interactions between brain rhythms provide as well the basis for the self-organized control of this “communication-through-coherence”, making thus possible a fast “on-demand” reconfiguration of global information routing modalities

Fourth Conference on Artificial Intelligence for Space Applications

Proceedings of a conference held in Huntsville, Alabama, on November 15-16, 1988. The Fourth Conference on Artificial Intelligence for Space Applications brings together diverse technical and scientific work in order to help those who employ AI methods in space applications to identify common goals and to address issues of general interest in the AI community. Topics include the following: space applications of expert systems in fault diagnostics, in telemetry monitoring and data collection, in design and systems integration; and in planning and scheduling; knowledge representation, capture, verification, and management; robotics and vision; adaptive learning; and automatic programming

Adomian decomposition method, nonlinear equations and spectral solutions of burgers equation

Tese de doutoramento. Ciências da Engenharia. 2006. Faculdade de Engenharia. Universidade do Porto, Instituto Superior Técnico. Universidade Técnica de Lisbo

A recommendation framework based on automated ranking for selecting negotiation agents. Application to a water market

This thesis presents an approach which relies on automatic learning and data mining techniques in order to search the best group of items from a set, according to the behaviour observed in previous groups. The approach is applied to a framework of a water market system, which aims to develop negotiation processes, where trading tables are built in order to trade water rights from users. Our task will focus on predicting which agents will show the most appropriate behaviour when are invited to participate in a trading table, with the purpose of achieving the most bene cial agreement. This way, a model is developed and learns from past transactions occurred in the market. Then, when a new trading table is opened in order to trade a water right, the model predicts, taking into account the individual features of the trading table, the behaviour of all the agents that can be invited to join the negotiation, and thus, becoming potential buyers of the water right. Once the model has made the predictions for a trading table, the agents are ranked according to their probability (which has been assigned by the model) of becoming a buyer in that negotiation. Two di erent methods are proposed in the thesis for dealing with the ranked participants. Depending on the method used, from this ranking we can select the desired number of participants for making the group, or choose only the top user of the list and rebuild the model adding some aggregate information in order to throw a more detailed prediction.Dura Garcia, EM. (2011). A recommendation framework based on automated ranking for selecting negotiation agents. Application to a water market. http://hdl.handle.net/10251/15875Archivo delegad