A nonlinear modification to PI control is motivated by a model of a signal transduction pathway active in mammalian blood pressure regulation. This control algorithm, labeled PII (proportional with intermittent integral), is appropriate for plants requiring exact set-point matching and disturbance attenuation in the presence of infrequent step changes in load disturbances or set-point. The proportional aspect of the controller is independently designed to be a disturbance attenuator and set-point matching is achieved by intermittently invoking an integral controller. The mechanisms observed in the Angiotensin 11/ AT1 signaling pathway are used to control the switching of the integral control. Improved performance over PI control is shown on a model of cyc1opentenol production. A sign change in plant gain at the desirable operating point causes traditional PI control to result in an unstable system.

A wavelet basis selection procedure is presented for wavelet regression. Both the basis and threshold are selected using crossvalidation. The method includes the capability of incorporating prior knowledge on the smoothness (or shape of the basis functions) into the basis selection procedure. The results of the method are demonstrated using widely published sampled functions. The results of the method are contrasted with other basis function based methods.

Clustering is importa nt in m any fields including m anufactlll'ing,

One of the simplest methods is to use linear transformations of the observed data.

Despite the fact that mental arithmetic is based on only a few hundred basic facts and some simple algorithms, humans have a difficult time mastering the subject, and even experienced individuals make mistakes. Associative multiplication, the process of doing multiplication by memory without the use of rules or algorithms, is especially problematic.

In this paper, we propose to use recurrent reinforcement learning to directly optimize such trading system performance functions, and we compare two different reinforcement learning methods. The first, Recurrent Reinforcement Learning, uses immediate rewards to train the trading systems, while the second (Q-Learning (Watkins 1989)) approximates discounted future rewards. These methodologies can be applied to optimizing systems designed to trade a single security or to trade portfolios . In addition, we propose a novel value function for risk-adjusted return that enables learning to be done online: the differential Sharpe ratio. Trading system profits depend upon sequences of interdependent decisions, and are thus path-dependent. Optimal trading decisions when the effects of transactions costs, market impact and taxes are included require knowledge of the current system state. In Moody, Wu, Liao & Saffell (1998), we demonstrate that reinforcement learning provides a more elegant and effective means for training trading systems when transaction costs are included, than do more standard supervised approaches.

We present a stochastic clustering algorithm based on pairwise similarity of datapoints. Our method extends existing deterministic methods, including agglomerative algorithms, min-cut graph algorithms, and connected components. Thus it provides a common framework for all these methods. Our graph-based method differs from existing stochastic methods which are based on analogy to physical systems. The stochastic nature of our method makes it more robust against noise, including accidental edges and small spurious clusters. We demonstrate the superiority of our algorithm using an example with 3 spiraling bands and a lot of noise. 1 Introduction Clustering algorithms can be divided into two categories: those that require a vectorial representation of the data, and those which use only pairwise representation. In the former case, every data item must be represented as a vector in a real normed space, while in the second case only pairwise relations of similarity or dissimilarity are used.

As a benchmark task, the spiral problem is well known in neural networks. Unlike previous work that emphasizes learning, we approach the problem from a generic perspective that does not involve learning. We point out that the spiral problem is intrinsically connected to the inside/outside problem. A generic solution to both problems is proposed based on oscillatory correlation using a time delay network. Our simulation results are qualitatively consistent with human performance, and we interpret human limitations in terms of synchrony and time delays, both biologically plausible. As a special case, our network without time delays can always distinguish these figures regardless of shape, position, size, and orientation.

There has been much recent work on measuring image statistics and on learning probability distributions on images. We observe that the mapping from images to statistics is many-to-one and show it can be quantified by a phase space factor. This phase space approach throws light on the Minimax Entropy technique for learning Gibbs distributions on images with potentials derived from image statistics and elucidates the ambiguities that are inherent to determining the potentials. In addition, it shows that if the phase factor can be approximated by an analytic distribution then this approximation yields a swift "Minutemax" algorithm that vastly reduces the computation time for Minimax entropy learning. An illustration of this concept, using a Gaussian to approximate the phase factor, gives a good approximation to the results of Zhu and Mumford (1997) in just seconds of CPU time. The phase space approach also gives insight into the multi-scale potentials found by Zhu and Mumford (1997) and suggests that the forms of the potentials are influenced greatly by phase space considerations. Finally, we prove that probability distributions learned in feature space alone are equivalent to Minimax Entropy learning with a multinomial approximation of the phase factor. 1 Introduction Bayesian probability theory gives a powerful framework for visual perception (Knill and Richards 1996). This approach, however, requires specifying prior probabilities and likelihood functions. Learning these probabilities is difficult because it requires estimating distributions on random variables of very high dimensions (for example, images with 200 x 200 pixels, or shape curves of length 400 pixels).

A binding problem occurs when two different events (or objects) are represented identically. For example, representing "John hit Ted" by activating the units JOHN, HIT, and TED would lead to a binding problem because the same pattern of activation would also be used to represent "Ted hit John". The binding problem is ubiquitous and is a concern whenever internal representations are postulated. In addition to guarding against the binding problem, an effective binding mechanism must construct representations that assist processing. For instance, different states of the world must be represented in a manner that assists in discovering commonalities between disparate states, allowing for category formation and analogical processing.