Exact Solution of the Nonlinear Dynamics of Recurrent Neural Mechanisms for Direction Selectivity

Different theoretical models have tried to investigate the feasibility of recurrent neural mechanisms for achieving direction selectivity in the visual cortex. The mathematical analysis of such models has been restricted so far to the case of purely linear networks. We present an exact analytical solution of the nonlinear dynamics of a class of direction selective recurrent neural models with threshold nonlinearity. Our mathematical analysis shows that such networks have form-stable stimulus-locked traveling pulse solutions that are appropriate for modeling the responses of direction selective cortical neurons. Our analysis shows also that the stability of such solutions can break down giving raise to a different class of solutions ("lurching activity waves") that are characterized by a specific spatio-temporal periodicity. These solutions cannot arise in models for direction selectivity with purely linear spatio-temporal filtering.

An Equivalence Between Sparse Approximation and Support Vector Machines

In the first part of this paper we show a similarity between the principle of Structural Risk Minimization Principle (SRM) (Vapnik, 1982) and the idea of Sparse Approximation, as defined in (Chen, Donoho and Saunders, 1995) and Olshausen and Field (1996). Then we focus on two specific (approximate) implementations of SRM and Sparse Approximation, which have been used to solve the problem of function approximation. For SRM we consider the Support Vector Machine technique proposed by V. Vapnik and his team at AT&T Bell Labs, and for Sparse Approximation we consider a modification of the Basis Pursuit De-Noising algorithm proposed by Chen, Donoho and Saunders (1995). We show that, under certain conditions, these two techniques are equivalent: they give the same solution and they require the solution of the same quadratic programming problem.

Support Vector Machines: Training and Applications

The Support Vector Machine (SVM) is a new and very promising classification technique developed by Vapnik and his group at AT&T Bell Labs. This new learning algorithm can be seen as an alternative training technique for Polynomial, Radial Basis Function and Multi-Layer Perceptron classifiers. An interesting property of this approach is that it is an approximate implementation of the Structural Risk Minimization (SRM) induction principle. The derivation of Support Vector Machines, its relationship with SRM, and its geometrical insight, are discussed in this paper. Training a SVM is equivalent to solve a quadratic programming problem with linear and box constraints in a number of variables equal to the number of data points. When the number of data points exceeds few thousands the problem is very challenging, because the quadratic form is completely dense, so the memory needed to store the problem grows with the square of the number of data points. Therefore, training problems arising in some real applications with large data sets are impossible to load into memory, and cannot be solved using standard non-linear constrained optimization algorithms. We present a decomposition algorithm that can be used to train SVM's over large data sets. The main idea behind the decomposition is the iterative solution of sub-problems and the evaluation of, and also establish the stopping criteria for the algorithm. We present previous approaches, as well as results and important details of our implementation of the algorithm using a second-order variant of the Reduced Gradient Method as the solver of the sub-problems. As an application of SVM's, we present preliminary results we obtained applying SVM to the problem of detecting frontal human faces in real images.

Characterization of ZnO Nanorods Grown on GaN Using Aqueous Solution Method

Uniformly distributed ZnO nanorods with diameter 70-100 nm and 1-2μm long have been successfully grown at low temperatures on GaN by using the inexpensive aqueous solution method. The formation of the ZnO nanorods and the growth parameters are controlled by reactant concentration, temperature and pH. No catalyst is required. The XRD studies show that the ZnO nanorods are single crystals and that they grow along the c axis of the crystal plane. The room temperature photoluminescence measurements have shown ultraviolet peaks at 388nm with high intensity, which are comparable to those found in high quality ZnO films. The mechanism of the nanorod growth in the aqueous solution is proposed. The dependence of the ZnO nanorods on the growth parameters was also investigated. While changing the growth temperature from 60°C to 150°C, the morphology of the ZnO nanorods changed from sharp tip (needle shape) to flat tip (rod shape). These kinds of structure are useful in laser and field emission application.

Growth of ZnO Nanorods on GaN Using Aqueous Solution Method

Uniformly distributed ZnO nanorods with diameter 80-120 nm and 1-2µm long have been successfully grown at low temperatures on GaN by using the inexpensive aqueous solution method. The formation of the ZnO nanorods and the growth parameters are controlled by reactant concentration, temperature and pH. No catalyst is required. The XRD studies show that the ZnO nanorods are single crystals and that they grow along the c axis of the crystal plane. The room temperature photoluminescence measurements have shown ultraviolet peaks at 388nm with high intensity, which are comparable to those found in high quality ZnO films. The mechanism of the nanorod growth in the aqueous solution is proposed. The dependence of the ZnO nanorods on the growth parameters was also investigated. While changing the growth temperature from 60°C to 150°C, the morphology of the ZnO nanorods changed from sharp tip with high aspect ratio to flat tip with smaller aspect ratio. These kinds of structure are useful in laser and field emission application.

Context Interchange as a Scalable Solution to Interoperating Amongst Heterogeneous Dynamic Services

Many online services access a large number of autonomous data sources and at the same time need to meet different user requirements. It is essential for these services to achieve semantic interoperability among these information exchange entities. In the presence of an increasing number of proprietary business processes, heterogeneous data standards, and diverse user requirements, it is critical that the services are implemented using adaptable, extensible, and scalable technology. The COntext INterchange (COIN) approach, inspired by similar goals of the Semantic Web, provides a robust solution. In this paper, we describe how COIN can be used to implement dynamic online services where semantic differences are reconciled on the fly. We show that COIN is flexible and scalable by comparing it with several conventional approaches. With a given ontology, the number of conversions in COIN is quadratic to the semantic aspect that has the largest number of distinctions. These semantic aspects are modeled as modifiers in a conceptual ontology; in most cases the number of conversions is linear with the number of modifiers, which is significantly smaller than traditional hard-wiring middleware approach where the number of conversion programs is quadratic to the number of sources and data receivers. In the example scenario in the paper, the COIN approach needs only 5 conversions to be defined while traditional approaches require 20,000 to 100 million. COIN achieves this scalability by automatically composing all the comprehensive conversions from a small number of declaratively defined sub-conversions.

Exploring Bit-Difference for Approximate KNN Search in High-dimensional Databases

In this paper, we develop a novel index structure to support efficient approximate k-nearest neighbor (KNN) query in high-dimensional databases. In high-dimensional spaces, the computational cost of the distance (e.g., Euclidean distance) between two points contributes a dominant portion of the overall query response time for memory processing. To reduce the distance computation, we first propose a structure (BID) using BIt-Difference to answer approximate KNN query. The BID employs one bit to represent each feature vector of point and the number of bit-difference is used to prune the further points. To facilitate real dataset which is typically skewed, we enhance the BID mechanism with clustering, cluster adapted bitcoder and dimensional weight, named the BID⁺. Extensive experiments are conducted to show that our proposed method yields significant performance advantages over the existing index structures on both real life and synthetic high-dimensional datasets.

Certified Rapid Solution of Parametrized Linear Elliptic Equations: Application to Parameter Estimation

We present a technique for the rapid and reliable evaluation of linear-functional output of elliptic partial differential equations with affine parameter dependence. The essential components are (i) rapidly uniformly convergent reduced-basis approximations — Galerkin projection onto a space WN spanned by solutions of the governing partial differential equation at N (optimally) selected points in parameter space; (ii) a posteriori error estimation — relaxations of the residual equation that provide inexpensive yet sharp and rigorous bounds for the error in the outputs; and (iii) offline/online computational procedures — stratagems that exploit affine parameter dependence to de-couple the generation and projection stages of the approximation process. The operation count for the online stage — in which, given a new parameter value, we calculate the output and associated error bound — depends only on N (typically small) and the parametric complexity of the problem. The method is thus ideally suited to the many-query and real-time contexts. In this paper, based on the technique we develop a robust inverse computational method for very fast solution of inverse problems characterized by parametrized partial differential equations. The essential ideas are in three-fold: first, we apply the technique to the forward problem for the rapid certified evaluation of PDE input-output relations and associated rigorous error bounds; second, we incorporate the reduced-basis approximation and error bounds into the inverse problem formulation; and third, rather than regularize the goodness-of-fit objective, we may instead identify all (or almost all, in the probabilistic sense) system configurations consistent with the available experimental data — well-posedness is reflected in a bounded "possibility region" that furthermore shrinks as the experimental error is decreased.

Preconditioning and iterative solution of symmetric indefinite linear systems arising from interior point methods for linear programming

We study the preconditioning of symmetric indefinite linear systems of equations that arise in interior point solution of linear optimization problems. The preconditioning method that we study exploits the block structure of the augmented matrix to design a similar block structure preconditioner to improve the spectral properties of the resulting preconditioned matrix so as to improve the convergence rate of the iterative solution of the system. We also propose a two-phase algorithm that takes advantage of the spectral properties of the transformed matrix to solve for the Newton directions in the interior-point method. Numerical experiments have been performed on some LP test problems in the NETLIB suite to demonstrate the potential of the preconditioning method discussed.