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Item Analysis of noise reduction in redundant expansions under distributed processing requirements(2005-03-01) Rozell, Chris; Johnson, Don; Digital Signal Processing (http://dsp.rice.edu/)Show more We considered signal reconstruction with redundant expansions under distributed processing in noisy environments. Redundant expansions have the ability to reduce noise corrupting the coefficients, but distributed processing schemes will not be able to take full advantage of the redundancy present. We apply frame theory and a generalization called â frames of subspacesâ to find conditions when distributed reconstruction suffers no loss in noise reduction ability, and we bound performance loss in more general cases.Show more Item Analyzing Dynamics and Stimulus Feature Dependence in the Information Processing of Crayfish Sustaining Fibers(2002-04-20) Rozell, Chris; Center for Multimedia Communications (http://cmc.rice.edu/); Digital Signal Processing (http://dsp.rice.edu/); CITI (http://citi.rice.edu/)Show more The sustaining fiber (SF) stage of the crayfish visual system converts analog stimulus representations to spike train signals. A recent theory quantifies a system's information processing capabilities and relates to statistical signal processing. To analyze SF responses to light stimuli, we extend a wavelet-based algorithm for separating analog input signals and spike output waveforms in composite intracellular recordings. We also present a time-varying RC circuit model to capture nonstationary membrane noise spectral characteristics. In our SF anlysis, information transfer ratios are generally on the order of (10^{-4}). The SF information processing dynamics show transient peaks followed by decay to steady-state values. A simple theoretical spike generator is analyzed analytically and shows general dynamic and steady-state properties similar to SFs. The information transfer ratios increase with spike rate and dynamic properties are due to direct spike generator dependence on input changes.Show more Item Analyzing the robustness of redundant population codes in sensory and feature extraction systems(2005-07-01) Rozell, Chris; Johnson, DonShow more Sensorineural systems often use groups of redundant neurons to represent stimulus information both during transduction and population coding of features. This redundancy makes the system more robust to corruption in the representation. We approximate neural coding as a projection of the stimulus onto a set of vectors, with the result encoded by spike trains. We use the formalism of frame theory to quantify the inherent noise reduction properties of such population codes. Additionally, computing features from the stimulus signal can also be thought of as projecting the coefficients of a sensory representation onto another set of vectors specific to the feature of interest. The conditions under which a combination of different features form a complete representation for the stimulus signal can be found through a recent extension to frame theory called "frames of subspaces". We extend the frame of subspaces theory to quantify the noise reduction properties of a collection of redundant feature spaces.Show more Item Examining methods for estimating mutual information in spiking neural systems(2005-06-01) Rozell, Chris; Johnson, Don; Center for Multimedia Communications (http://cmc.rice.edu/); Digital Signal Processing (http://dsp.rice.edu/); CITI (http://citi.rice.edu/)Show more Mutual information enjoys wide use in the computational neuroscience community for analyzing spiking neural systems. Its direct calculation is difficult because estimating the joint stimulus-response distribution requires a prohibitive amount of data. Consequently, several techniques have appeared for bounding mutual information that rely on less data. We examine two upper bound techniques and find that they are unreliable and can introduce strong assumptions about the neural code. We also examine two lower bounds, showing that they can be very loose and possibly bear little relation to the mutual information's actual value.Show more Item Information processing during transient responses in the crayfish visual system(2003-06-01) Rozell, Chris; Johnson, Don; Glantz, Raymon; Digital Signal Processing (http://dsp.rice.edu/)Show more We analyzed sustaining fiber responses in the crayfish visual system to light pulses using information processing techniques. The light pulse stimuli elicited a transient and a steady-state component in the EPSP input and in the firing rate of the spike train output. The overall information transfer of the system was very low (10^{-4}), with a sharp increase during the transient portion of the response followed by a steady decrease. The change in the information transfer rate is related to the difference in communication rates possible in spike trains with varying rates. This analysis corroborates the observed light reflex behavior.Show more Item A Markov Chain Analysis of Blackjack Strategy(2004-07-01) Wakin, Michael; Rozell, ChrisShow more Blackjack receives considerable attention from mathematicians and entrepreneurs alike, due to its simple rules, its inherent random nature, and the abundance of "prior" information available to an observant player. Many attempts have been made to propose card-counting systems that exploit such information to the player's advantage. Because blackjack is a complicated game, attempts to actually calculate the expected gain from a particular system often rely on simulation techniques. While such techniques may yield correct results, they may also fail to explore the interesting mathematical properties of the game. Despite the apparent complexity, there is a great deal of structure inherent in both the blackjack rules and the card-counting systems. Exploiting this structure and elementary results from the theory of Markov chains, we present a novel framework for analyzing the expected advantage of a card-counting system entirely without simulation. The method presented here requires only a few, mild simplifying assumptions, can account for many rule variations, and is applicable to a large class of counting systems. As a specific example, we verify the reported advantage provided by one of the earliest systems, the Complete Point-Count System, discussed in Edward Thorp's famous book,*Beat the Dealer*. While verifying this analysis is satisfying, in our opinion the primary value of this work lies in the exposition of an interesting mathematical framework for analyzing a complicated "real-world" problem.Show more Item Modeling wireless sensor and actuator networks using frame theory(2005-11-01) Rozell, Chris; Johnson, Don; Digital Signal Processing (http://dsp.rice.edu/)Show more Wireless sensor networks are often studied with the goal of removing information from the network as efficiently as possible. However, when the application also includes an actuator network, it is advantageous to determine actions in-network. In such settings, optimizing the sensor node behavior with respect to sensor information fidelity will not necessarily translate into optimum behavior in terms of action fidelity. Inspired by neural systems, we present a model of a sensor and actuator network based on the vector space tools of frame theory that applies to applications analogous to reflex behaviors in biological systems. Our analysis yields bounds on both absolute and average actuation error that point directly to strategies for limiting sensor communication based not only on local measurements but also on a measure of how important each sensor-actuator link is to the fidelity of the total actuation output.Show more