Qualitative analysis of a recurrent neural network for nonlinear continuously differentiable convex minimization over a nonempty closed convex subset.

We investigate the qualitative properties of a recurrent neural network (RNN) for minimizing a nonlinear continuously differentiable and convex objective function over any given nonempty, closed, and convex subset which may be bounded or unbounded, by exploiting some key inequalities in mathematical programming. The global existence and boundedness of the solution of the RNN are proved when the objective function is convex and has a nonempty constrained minimum set. Under the same assumption, the RNN is shown to be globally convergent in the sense that every trajectory of the RNN converges to some equilibrium point of the RNN.

An algorithm for compression of bilevel images.

This paper presents the block arithmetic coding for image compression (BACIC) algorithm: a new method for lossless bilevel image compression which can replace JBIG, the current standard for bilevel image compression. BACIC uses the block arithmetic coder (BAC): a simple, efficient, easy-to-implement, variable-to-fixed arithmetic coder, to encode images. BACIC models its probability estimates adaptively based on a 12-bit context of previous pixel values; the 12-bit context serves as an index into a probability table whose entries are used to compute p(1) (the probability of a bit equaling one), the probability measure BAC needs to compute a codeword.

Stability of steepest descent with momentum for quadratic functions.

This paper analyzes the effect of momentum on steepest descent training for quadratic performance functions. We demonstrate that there always exists a momentum coefficient that will stabilize the steepest descent algorithm, regardless of the value of the learning rate. We also demonstrate how the value of the momentum coefficient changes the convergence properties of the algorithm.

On the analysis of a recurrent neural network for solving nonlinear monotone variational inequality problems.

We investigate the qualitative properties of a recurrent neural network (RNN) for solving the general monotone variational inequality problems (VIPs), defined over a nonempty closed convex subset, which are assumed to have a nonempty solution set but need not be symmetric. The equilibrium equation of the RNN system simply coincides with the nonlinear projection equation of the VIP to be solved. We prove that the RNN system has a global and bounded solution trajectory starting at any given initial point in the above closed convex subset which is positive invariant for the RNN system.

Effect of transmission delay on the rate of convergence of a class of nonlinear contractive dynamical systems.

We investigate the qualitative properties of a general class of contractive dynamical systems with time delay by using a unified analysis approach for any p-contraction with p in [1,infinity]. It is proved that the delayed contractive dynamical system is always globally exponentially stable no matter how large the time delay is, while the rate of convergence of the delayed system is reduced as the time delay increases. A lower bound on the rate of convergence of the delayed contractive dynamical system is obtained, which is the unique positive solution of a nonlinear equation with three parameters, namely, the time delay, the time constant and the p-contraction constant in the system.

Gravity balancing rehabilitative robot for the human legs.

People with severe muscle weakness from neurological injury, such as hemiparesis from stroke, often have substantial limitations. The focus of rehabilitation after stroke is often on walking function, however, equipment available to facilitate walking function is severely limited. Most devices move patients through predetermined movements rather than allowing the patient to move under their control.

Elements of resilience after the World Trade Center disaster: reconstituting New York City's Emergency Operations Centre.

In this paper we examine the reconstitution of the Emergency Operations Centre (EOC) after its destruction in the World Trade Center attack, using that event to highlight several features of resilience. The paper summarises basic EOC functions, and then presents conceptions of resilience as understood from several disciplinary perspectives, noting that work in these fields has sought to understand how a natural or social system that experiences disturbance sustains its functional processes. We observe that, although the physical EOC facility was destroyed, the organisation that had been established to manage crises in New York City continued, enabling a response that drew on the resources of New York City and neighbouring communities, states and the federal government.

Order statistic filter banks.

Filter banks play a major role in multirate signal processing where these have been successfully used in a variety of applications. In the past, filter banks have been developed within the framework of linear filters. It is well known, however, that linear filters may have less than satisfactory performance whenever the underlying processes are non-Gaussian.

Permutation weighted order statistic filter lattices.

We introduce and analyze a new class of nonlinear filters called permutation weighted order statistic (PWOS) filters. These filters extend the concept of weighted order statistic (WOS) filters, in which filter weights associated with the input samples are used to replicate the corresponding samples, and an order statistic is chosen as the filter output. PWOS filters replicate each input sample according to weights determined by the temporal-order and rank-order of samples within a window.

Switched-capacitor neuromorphs with wide-range variable dynamics.

The use of switched capacitors as wide-range, programmable resistive elements in spatially extensive artificial dendritic trees (ADT's) is described. We show that silicon neuro-morphs with ADT's can produce impulse responses that last millions of times longer than the initiating impulse and that dynamical responses are tunable in both shape and duration over a wide range. The switched-capacitor resistors forming a dendritic tree are shown indirectly to have a useful programmable resistance range between 500 KOmega and 1000 GOmega.