An Extension to the Tactical Planning Model for a Job Shop: Continuous-Time Control

We develop an extension to the tactical planning model (TPM) for a job shop by the third author. The TPM is a discrete-time model in which all transitions occur at the start of each time period. The time period must be defined appropriately in order for the model to be meaningful. Each period must be short enough so that a job is unlikely to travel through more than one station in one period. At the same time, the time period needs to be long enough to justify the assumptions of continuous workflow and Markovian job movements. We build an extension to the TPM that overcomes this restriction of period sizing by permitting production control over shorter time intervals. We achieve this by deriving a continuous-time linear control rule for a single station. We then determine the first two moments of the production level and queue length for the workstation.

A Theory of How the Brain Might Work

I wish to propose a quite speculative new version of the grandmother cell theory to explain how the brain, or parts of it, may work. In particular, I discuss how the visual system may learn to recognize 3D objects. The model would apply directly to the cortical cells involved in visual face recognition. I will also outline the relation of our theory to existing models of the cerebellum and of motor control. Specific biophysical mechanisms can be readily suggested as part of a basic type of neural circuitry that can learn to approximate multidimensional input-output mappings from sets of examples and that is expected to be replicated in different regions of the brain and across modalities. The main points of the theory are: -the brain uses modules for multivariate function approximation as basic components of several of its information processing subsystems. -these modules are realized as HyperBF networks (Poggio and Girosi, 1990a,b). -HyperBF networks can be implemented in terms of biologically plausible mechanisms and circuitry. The theory predicts a specific type of population coding that represents an extension of schemes such as look-up tables. I will conclude with some speculations about the trade-off between memory and computation and the evolution of intelligence.

A Network Charge-Orineted MOS Transistor Model

The MOS transistor physical model as described in [3] is presented here as a network model. The goal is to obtain an accurate model, suitable for simulation, free from certain problems reported in the literature [13], and conceptually as simple as possible. To achieve this goal the original model had to be extended and modified. The paper presents the derivation of the network model from physical equations, including the corrections which are required for simulation and which compensate for simplifications introduced in the original physical model. Our intrinsic MOS model consists of three nonlinear voltage-controlled capacitors and a dependent current source. The charges of the capacitors and the current of the current source are functions of the voltages $V_{gs}$, $V_{bs}$, and $V_{ds}$. The complete model consists of the intrinsic model plus the parasitics. The apparent simplicity of the model is a result of hiding information in the characteristics of the nonlinear components. The resulted network model has been checked by simulation and analysis. It is shown that the network model is suitable for simulation: It is defined for any value of the voltages; the functions involved are continuous and satisfy Lipschitz conditions with no jumps at region boundaries; Derivatives have been computed symbolically and are available for use by the Newton-Raphson method. The model"s functions can be measured from the terminals. It is also shown that small channel effects can be included in the model. Higher frequency effects can be modeled by using a network consisting of several sections of the basic lumped model. Future plans include a detailed comparison of the network model with models such as SPICE level 3 and a comparison of the multi- section higher frequency model with experiments.

(Semi-)Predictive Discretization During Model Selection

In this paper, we present an approach to discretizing multivariate continuous data while learning the structure of a graphical model. We derive the joint scoring function from the principle of predictive accuracy, which inherently ensures the optimal trade-off between goodness of fit and model complexity (including the number of discretization levels). Using the so-called finest grid implied by the data, our scoring function depends only on the number of data points in the various discretization levels. Not only can it be computed efficiently, but it is also independent of the metric used in the continuous space. Our experiments with gene expression data show that discretization plays a crucial role regarding the resulting network structure.

On the Behavior of the Homogeneous Self-Dual Model for Conic Convex Optimization

There is a natural norm associated with a starting point of the homogeneous self-dual (HSD) embedding model for conic convex optimization. In this norm two measures of the HSD model’s behavior are precisely controlled independent of the problem instance: (i) the sizes of ε-optimal solutions, and (ii) the maximum distance of ε-optimal solutions to the boundary of the cone of the HSD variables. This norm is also useful in developing a stopping-rule theory for HSD-based interior-point methods such as SeDuMi. Under mild assumptions, we show that a standard stopping rule implicitly involves the sum of the sizes of the ε-optimal primal and dual solutions, as well as the size of the initial primal and dual infeasibility residuals. This theory suggests possible criteria for developing starting points for the homogeneous self-dual model that might improve the resulting solution time in practice

AMAR: A Computational Model of Autosegmental Phonology

This report describes a computational system with which phonologists may describe a natural language in terms of autosegmental phonology, currently the most advanced theory pertaining to the sound systems of human languages. This system allows linguists to easily test autosegmental hypotheses against a large corpus of data. The system was designed primarily with tonal systems in mind, but also provides support for tree or feature matrix representation of phonemes (as in The Sound Pattern of English), as well as syllable structures and other aspects of phonological theory. Underspecification is allowed, and trees may be specified before, during, and after rule application. The association convention is automatically applied, and other principles such as the conjunctivity condition are supported. The method of representation was designed such that rules are designated in as close a fashion as possible to the existing conventions of autosegmental theory while adhering to a textual constraint for maximum portability.

Theory of Handwriting

Handwriting production is viewed as a constrained modulation of an underlying oscillatory process. Coupled oscillations in horizontal and vertical directions produce letter forms, and when superimposed on a rightward constant velocity horizontal sweep result in spatially separated letters. Modulation of the vertical oscillation is responsible for control of letter height, either through altering the frequency or altering the acceleration amplitude. Modulation of the horizontal oscillation is responsible for control of corner shape through altering phase or amplitude. The vertical velocity zero crossing in the velocity space diagram is important from the standpoint of control. Changing the horizontal velocity value at this zero crossing controls corner shape, and such changes can be effected through modifying the horizontal oscillation amplitude and phase. Changing the slope at this zero crossing controls writing slant; this slope depends on the horizontal and vertical velocity zero amplitudes and on the relative phase difference. Letter height modulation is also best applied at the vertical velocity zero crossing to preserve an even baseline. The corner shape and slant constraints completely determine the amplitude and phase relations between the two oscillations. Under these constraints interletter separation is not an independent parameter. This theory applies generally to a number of acceleration oscillation patterns such as sinusoidal, rectangular and trapezoidal oscillations. The oscillation theory also provides an explanation for how handwriting might degenerate with speed. An implementation of the theory in the context of the spring muscle model is developed. Here sinusoidal oscillations arise from a purely mechanical sources; orthogonal antagonistic spring pairs generate particular cycloids depending on the initial conditions. Modulating between cycloids can be achieved by changing the spring zero settings at the appropriate times. Frequency can be modulated either by shifting between coactivation and alternating activation of the antagonistic springs or by presuming variable spring constant springs. An acceleration and position measuring apparatus was developed for measurements of human handwriting. Measurements of human writing are consistent with the oscillation theory. It is shown that the minimum energy movement for the spring muscle is bang-coast-bang. For certain parameter values a singular arc solution can be shown to be minimizing. Experimental measurements however indicate that handwriting is not a minimum energy movement.

Switching Between Discrete and Continuous Process Models to Predict Molecular Genetic Activity

Two kinds of process models have been used in programs that reason about change: Discrete and continuous models. We describe the design and implementation of a qualitative simulator, PEPTIDE, which uses both kinds of process models to predict the behavior of molecular energetic systems. The program uses a discrete process model to simulate both situations involving abrupt changes in quantities and the actions of small numbers of molecules. It uses a continuous process model to predict gradual changes in quantities. A novel technique, called aggregation, allows the simulator to switch between theses models through the recognition and summary of cycles. The flexibility of PEPTIDE's aggregator allows the program to detect cycles within cycles and predict the behavior of complex situations.