Affine Lie algebraic origin of constrained KP hierarchies

An affine sl(n + 1) algebraic construction of the basic constrained KP hierarchy is presented. This hierarchy is analyzed using two approaches, namely linear matrix eigenvalue problem on hermitian symmetric space and constrained KP Lax formulation and it is shown that these approaches are equivalent. The model is recognized to be the generalized non-linear Schrödinger (GNLS) hierarchy and it is used as a building block for a new class of constrained KP hierarchies. These constrained KP hierarchies are connected via similarity-Bäcklund transformations and interpolate between GNLS and multi-boson KP-Toda hierarchies. Our construction uncovers the origin of the Toda lattice structure behind the latter hierarchy. © 1995 American Institute of Physics.

Constrained KP models as integrable matrix hierarchies

We formulate the constrained KP hierarchy (denoted by cKP K+1,M) as an affine sl(M + K+ 1) matrix integrable hierarchy generalizing the Drinfeld-Sokolov hierarchy. Using an algebraic approach, including the graded structure of the generalized Drinfeld-Sokolov hierarchy, we are able to find several new universal results valid for the cKP hierarchy. In particular, our method yields a closed expression for the second bracket obtained through Dirac reduction of any untwisted affine Kac-Moody current algebra. An explicit example is given for the case sl(M + K + 1), for which a closed expression for the general recursion operator is also obtained. We show how isospectral flows are characterized and grouped according to the semisimple non-regular element E of sl(M + K+ 1) and the content of the center of the kernel of E. © 1997 American Institute of Physics.

Insulator-to-metal transition driven by clustering of solitons in polyacetylene

It's believed that the simple Su-Schrieffer-Heeger Hamiltonian can not predict the insulator to metal transition of transpolyacetylene (t-PA). The soliton lattice configuration at a doping level y=6% still has a semiconductor gap. Disordered distributions of solitons close the gap, but the electronic states around the Fermi energy are localized. However, within the same framework, it is possible to show that a cluster of solitons can produce dramatic changes in the electronic structure, allowing an insulator-to-metal transition.

Gluon field strength correlation functions within a constrained instanton model

We suggest a constrained instanton (CI) solution in the physical QCD vacuum which is described by large-scale vacuum field fluctuations. This solution decays exponentially at large distances. It is stable only if the interaction of the instanton with the background vacuum field is small and additional constraints are introduced. The CI solution is explicitly constructed in the ansatz form, and the two-point vacuum correlator of the gluon field strengths is calculated in the framework of the effective instanton vacuum model. At small distances the results are qualitatively similar to the single instanton case; in particular, the D1 invariant structure is small, which is in agreement with the lattice calculations.

A barrier method for constrained nonlinear optimization using a modified Hopfield network

The ability of neural networks to realize some complex nonlinear function makes them attractive for system identification. This paper describes a novel barrier method using artificial neural networks to solve robust parameter estimation problems for nonlinear model with unknown-but-bounded errors and uncertainties. This problem can be represented by a typical constrained optimization problem. More specifically, a modified Hopfield network is developed and its internal parameters are computed using the valid-subspace technique. These parameters guarantee the network convergence to the equilibrium points. A solution for the robust estimation problem with unknown-but-bounded error corresponds to an equilibrium point of the network. Simulation results are presented as an illustration of the proposed approach.

Bound constrained smooth optimization for solving variational inequalities and related problems

Variational inequalities and related problems may be solved via smooth bound constrained optimization. A comprehensive discussion of the important features involved with this strategy is presented. Complementarity problems and mathematical programming problems with equilibrium constraints are included in this report. Numerical experiments are commented. Conclusions and directions of future research are indicated.

Balance of payments constrained growth within a consistent stock-flow framework: an application to the economies of CARICOM

Includes bibliography

Free time and mixed constrained optimal control problems

We consider free time optimal control problems with pointwise set control constraints u(t) ∈ U(t). Here we derive necessary conditions of optimality for those problem where the set U(t) is defined by equality and inequality control constraints. The main ingredients of our analysis are a well known time transformation and recent results on necessary conditions for mixed state-control constraints. ©2010 IEEE.

Market-driven security-constrained transmission network expansion planning

This paper presents a Bi-level Programming (BP) approach to solve the Transmission Network Expansion Planning (TNEP) problem. The proposed model is envisaged under a market environment and considers security constraints. The upper-level of the BP problem corresponds to the transmission planner which procures the minimization of the total investment and load shedding cost. This upper-level problem is constrained by a single lower-level optimization problem which models a market clearing mechanism that includes security constraints. Results on the Garver's 6-bus and IEEE 24-bus RTS test systems are presented and discussed. Finally, some conclusions are drawn. © 2011 IEEE.

Land use image classification through optimum-path forest clustering

Land use classification has been paramount in the last years, since we can identify illegal land use and also to monitor deforesting areas. Although one can find several research works in the literature that address this problem, we propose here the land use recognition by means of Optimum-Path Forest Clustering (OPF), which has never been applied to this context up to date. Experiments among Optimum-Path Forest, Mean Shift and K-Means demonstrated the robustness of OPF for automatic land use classification of images obtained by CBERS-2B and Ikonos-2 satellites. © 2011 IEEE.

Necessary conditions of optimality for state constrained infinite horizon differential inclusions

This article presents and discusses necessary conditions of optimality for infinite horizon dynamic optimization problems with inequality state constraints and set inclusion constraints at both endpoints of the trajectory. The cost functional depends on the state variable at the final time, and the dynamics are given by a differential inclusion. Moreover, the optimization is carried out over asymptotically convergent state trajectories. The novelty of the proposed optimality conditions for this class of problems is that the boundary condition of the adjoint variable is given as a weak directional inclusion at infinity. This improves on the currently available necessary conditions of optimality for infinite horizon problems. © 2011 IEEE.

Spatial clustering applied to health area

The significant volume of work accidents in the cities causes an expressive loss to society. The development of Spatial Data Mining technologies presents a new perspective for the extraction of knowledge from the correlation between conventional and spatial attributes. One of the most important techniques of the Spatial Data Mining is the Spatial Clustering, which clusters similar spatial objects to find a distribution of patterns, taking into account the geographical position of the objects. Applying this technique to the health area, will provide information that can contribute towards the planning of more adequate strategies for the prevention of work accidents. The original contribution of this work is to present an application of tools developed for Spatial Clustering which supply a set of graphic resources that have helped to discover knowledge and support for management in the work accidents area. © 2011 IEEE.

A maximum principle for constrained infinite horizon dynamic control systems

This article presents and discusses a maximum principle for infinite horizon constrained optimal control problems with a cost functional depending on the state at the final time. The main feature of these optimality conditions is that, under reasonably weak assumptions, the multiplier is shown to satisfy a novel transversality condition at infinite time. It is also shown that these conditions can also be obtained for impulsive control problems whose dynamics are given by measure driven differential equations. © 2011 IFAC.

Post-processing association rules with clustering and objective measures

The post-processing of association rules is a difficult task, since a large number of patterns can be obtained. Many approaches have been developed to overcome this problem, as objective measures and clustering, which are respectively used to: (i) highlight the potentially interesting knowledge in domain; (ii) structure the domain, organizing the rules in groups that contain, somehow, similar knowledge. However, objective measures don't reduce nor organize the collection of rules, making the understanding of the domain difficult. On the other hand, clustering doesn't reduce the exploration space nor direct the user to find interesting knowledge, making the search for relevant knowledge not so easy. This work proposes the PAR-COM (Post-processing Association Rules with Clustering and Objective Measures) methodology that, combining clustering and objective measures, reduces the association rule exploration space directing the user to what is potentially interesting. Thereby, PAR-COM minimizes the user's effort during the post-processing process.

Characterization of the temperature, load and damage effects using piezoelectric transducer patches based on fuzzy clustering

Structural Health Monitoring (SHM) denotes a system with the ability to detect and interpret adverse changes in a structure. One of the critical challenges for practical implementation of SHM system is the ability to detect damage under changing environmental conditions. This paper aims to characterize the temperature, load and damage effects in the sensor measurements obtained with piezoelectric transducer (PZT) patches. Data sets are collected on thin aluminum specimens under different environmental conditions and artificially induced damage states. The fuzzy clustering algorithm is used to organize the sensor measurements into a set of clusters, which can attribute the variation in sensor data due to temperature, load or any induced damage.