Distributed Optimization

We demonstrate a new framework for analyzing and controlling distributed systems, by solving constrained optimization problems with an algorithm based on that framework. The framework is ar. information-theoretic extension of conventional full-rationality game theory to allow bounded rational agents. The associated optimization algorithm is a game in which agents control the variables of the optimization problem. They do this by jointly minimizing a Lagrangian of (the probability distribution of) their joint state. The updating of the Lagrange parameters in that Lagrangian is a form of automated annealing, one that focuses the multi-agent system on the optimal pure strategy. We present computer experiments for the k-sat constraint satisfaction problem and for unconstrained minimization of NK functions

Self-dissimilarity as a High Dimensional Complexity Measure

For many systems characterized as "complex" the patterns exhibited on different scales differ markedly from one another. For example the biomass distribution in a human body "looks very different" depending on the scale at which one examines it. Conversely, the patterns at different scales in "simple" systems (e.g., gases, mountains, crystals) vary little from one scale to another. Accordingly, the degrees of self-dissimilarity between the patterns of a system at various scales constitute a complexity "signature" of that system. Here we present a novel quantification of self-dissimilarity. This signature can, if desired, incorporate a novel information-theoretic measure of the distance between probability distributions that we derive here. Whatever distance measure is chosen, our quantification of self-dissimilarity can be measured for many kinds of real-world data. This allows comparisons of the complexity signatures of wholly different kinds of systems (e.g., systems involving information density in a digital computer vs. species densities in a rain-forest vs. capital density in an economy, etc.). Moreover, in contrast to many other suggested complexity measures, evaluating the self-dissimilarity of a system does not require one to already have a model of the system. These facts may allow self-dissimilarity signatures to be used a s the underlying observational variables of an eventual overarching theory relating all complex systems. To illustrate self-dissimilarity we present several numerical experiments. In particular, we show that underlying structure of the logistic map is picked out by the self-dissimilarity signature of time series produced by that ma

Estimating probabilities from experimental frequencies

Estimating the probability distribution 'q' governing the behaviour of a certain variable by sampling its value a finite number of times most typically involves an error. Successive measurements allow the construction of a histogram, or frequency count 'f', of each of the possible outcomes. In this work, the probability that the true distribution be 'q', given that the frequency count 'f' was sampled, is studied. Such a probability may be written as a Gibbs distribution. A thermodynamic potential, which allows an easy evaluation of the mean Kullback-Leibler divergence between the true and measured distribution, is defined. For a large number of samples, the expectation value of any function of 'q' is expanded in powers of the inverse number of samples. As an example, the moments, the entropy and the mutual information are analyzed.Comment: 10 pages, 3 figures, to be published in Physical Review

Television's image of the city : the Jamaica Plain case.

Thesis. 1977. Ph.D.--Massachusetts Institute of Technology. Dept. of Urban Studies and Planning.MICROFICHE COPY AVAILABLE IN ARCHIVES AND ROTCH.Bibliography : leaves 212-215.Ph.D

A Feedback Quenched Oscillator Produces Turing Patterning with One Diffuser

Efforts to engineer synthetic gene networks that spontaneously produce patterning in multicellular ensembles have focused on Turing's original model and the “activator-inhibitor” models of Meinhardt and Gierer. Systems based on this model are notoriously difficult to engineer. We present the first demonstration that Turing pattern formation can arise in a new family of oscillator-driven gene network topologies, specifically when a second feedback loop is introduced which quenches oscillations and incorporates a diffusible molecule. We provide an analysis of the system that predicts the range of kinetic parameters over which patterning should emerge and demonstrate the system's viability using stochastic simulations of a field of cells using realistic parameters. The primary goal of this paper is to provide a circuit architecture which can be implemented with relative ease by practitioners and which could serve as a model system for pattern generation in synthetic multicellular systems. Given the wide range of oscillatory circuits in natural systems, our system supports the tantalizing possibility that Turing pattern formation in natural multicellular systems can arise from oscillator-driven mechanisms

Ageing increases reliance on sensorimotor prediction through structural and functional differences in frontostriatal circuits

This is the author accepted manuscript. It is currently under an indefinite embargo pending publication by Nature Publishing Group.The control of voluntary movement changes markedly with age. A critical component of motor control is the integration of sensory information with predictions of the consequences of action, arising from internal models of movement. This leads to sensorimotor attenuation – a reduction in the perceived intensity of sensations from self-generated compared to external actions. Here we show that sensorimotor attenuation occurs in 98% of adults in a population-based cohort (n=325; 18-88 years; the Cambridge Centre for Ageing and Neuroscience). Importantly, attenuation increases with age, in proportion to reduced sensory sensitivity. This effect is associated with differences in the structure and functional connectivity of the pre-supplementary motor area (pre-SMA), assessed with magnetic resonance imaging. The results suggest that ageing alters the balance between the sensorium and predictive models, mediated by the pre-SMA and its connectivity in frontostriatal circuits. This shift may contribute to the motor and cognitive changes observed with age.Cam-CAN research was supported by the Biotechnology and Biological Sciences Research Council (BB/H008217/1). JBR and NW were supported by the James S. McDonnell Foundation 21st Century Science Initiative, Scholar Award in Understanding Human Cognition. JBR was also supported by Wellcome Trust [103838] and the Medical Research Council [MC-A060-5PQ30]. DMW was supported by the Wellcome Trust [097803], Human Frontier Science Program and the Royal Society Noreen Murray Professorship in Neurobiology. RNH was supported by the Medical Research Council [MC-A060-5PR10]. RAK was supported by a Sir Henry Wellcome Trust Postdoctoral Fellowship [107392]. LG was funded by a Rubicon grant from the Netherlands Organisation for Scientific Research (NWO)

Spatial theory and human behavior

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/45971/1/10110_2005_Article_BF01952731.pd

A Glycemia Risk Index (GRI) of Hypoglycemia and Hyperglycemia for Continuous Glucose Monitoring Validated by Clinician Ratings

BackgroundA composite metric for the quality of glycemia from continuous glucose monitor (CGM) tracings could be useful for assisting with basic clinical interpretation of CGM data.MethodsWe assembled a data set of 14-day CGM tracings from 225 insulin-treated adults with diabetes. Using a balanced incomplete block design, 330 clinicians who were highly experienced with CGM analysis and interpretation ranked the CGM tracings from best to worst quality of glycemia. We used principal component analysis and multiple regressions to develop a model to predict the clinician ranking based on seven standard metrics in an Ambulatory Glucose Profile: very low-glucose and low-glucose hypoglycemia; very high-glucose and high-glucose hyperglycemia; time in range; mean glucose; and coefficient of variation.ResultsThe analysis showed that clinician rankings depend on two components, one related to hypoglycemia that gives more weight to very low-glucose than to low-glucose and the other related to hyperglycemia that likewise gives greater weight to very high-glucose than to high-glucose. These two components should be calculated and displayed separately, but they can also be combined into a single Glycemia Risk Index (GRI) that corresponds closely to the clinician rankings of the overall quality of glycemia (r = 0.95). The GRI can be displayed graphically on a GRI Grid with the hypoglycemia component on the horizontal axis and the hyperglycemia component on the vertical axis. Diagonal lines divide the graph into five zones (quintiles) corresponding to the best (0th to 20th percentile) to worst (81st to 100th percentile) overall quality of glycemia. The GRI Grid enables users to track sequential changes within an individual over time and compare groups of individuals.ConclusionThe GRI is a single-number summary of the quality of glycemia. Its hypoglycemia and hyperglycemia components provide actionable scores and a graphical display (the GRI Grid) that can be used by clinicians and researchers to determine the glycemic effects of prescribed and investigational treatments