Over the past several years I have been working to develop two, two-semester course sequences in Applied Physics and Computational Physics. By covering material traditionally handled in Classical Mechanics and Electricity and Magnetism, the Applied Physics sequence stresses mathematical rigor, physical insight and a project-based paradigm. The Computational Physics sequence also stresses a project-based approach and introduces students to the essentials of Maple, Matlab and JAVA for computational modeling, as well as elements of HTML, JavaScript, LaTeX, and PHP for web-page development and publishing of scientific manuscripts.
I am currently working on a two-volume text - Top-Down Physics: The Nature of the Physical World - for the Computational Physics sequence. Portions of it may be viewed on my download page. I have also given a few talks on the the overall scope of my "Top-Down Physics" approach. These are available below in PDF format:
View SESAPS 2006 Presentation
View SESAPS 2007 Presentation
Projects
I have developed many project/modules for use in both applied and computational physics courses with topics such as, "Realistic Tidal Models",
"Tossing Toothpicks", "The Not-So-Simple Harmonic Oscillator", "MRI of a Pencil", and "The Chaotic Diode."
The goal of these projects is two-fold: First, the projects illustrate how one may apply concepts and techniques stressed in the classroom to solve, "real-world" problems. Secondly, the projects reinforce the increasingly popular viewpoint that through the solution of a specific, multi-faceted problem, a student may glean skills and insights that are not easily transmitted in a lecture-based setting. Ideally the entire curriculum "folds" on itself and upper-level students write applications that may be used by introductory students.
For project examples and complete source code please visit my download page.
I am interested in all things neuro - everything from neurophysiology to neurophilosophy - and in assessing modern approaches to the study of high-order cognitive processes. I have been (and remain) involved in many multi-disciplinary research projects which focus on establishing state correlates that can be used to differentiate between brain states. I am particlularly interested in the analysis and interpretation of evoked reaction scalp potential (ERP) and functional magnetic resonance imaging (fMRI) data as these modalities allow for maximal temporal (via high-density ERP) and spatial (through fMRI) resolution.
Though centered in theoretical, experimental, and computational aspects, my research interests also provide much "food for thought" on the philosophical side - especially regarding the relationship between objective measurements of the brain and the subjective reports of the mind. Many of these thoughts are brought together in my presentation - "A Letter to Doug Hofstadter" which can be downloaded above.
I am interested in how the brain and/or mind (literally) represents objects. Owing to my education as a physicist, I fall somewhere between a functionalist/materialist and naturalists view and tend to "glom" problems first in a mathematical way.
Object States
To begin to see how objects may be represented by the brain I naturally think of how objects may be generated by simple mathematical prescriptions. For example, to produce all the 2-D polygons one can use a simple state incorporating the class of n-sided polygons of radius r and the RGB color palette. I do not of course mean to imply that this is the whole story but it gives us a place to start thinking about the problem.
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Affective State Discrimination
In work on establishing the self-perception of affective states, Doug Wedell and I have begun to map out the Valence-Arousal Space for subjects viewing images from the International Affective Picture System (IAPS).
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Using a generalization of the classic Yerkes-Dodson law governing the relationship between task performance and "arousal" level, we have developed a simple paradigm wherein subjects are exposed to groups of picture sets of parametrically varying arousal and valence values in quick succesion and then asked to assess their state. For example, subjects may view a high arousal and high valence (HP) picture set containing pictures of sky-divers and baloon rides or may see a neutral arousal and low valence (MN) picture set containing pictures of a gray day or someone smoking cigarettes. In all cases the subjects are immediately asked to assess their affective state. i.e., "How happy do you feel?"
Preliminary findings with a limited arousal valence space with five categories (below-left; N=33) show that the valence-arousal space may be mapped out quite consistently; aside from individual differences, likely due to affective style, subjects consistently rate their states. These results indicate that subject are both in and aware of a particular affective state.
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Continuing efforts involving Jen Vendemia and Svetlana Shinkareva include performing the experiement in both EEG and fMRI modalities. One question that I am fascinated by is the possibility of discriminating the affective states using the neural correlates found in these experiments. Indeed, more generally one may consider existing fMRI data from so called "meta-analyses" such as that of Phan et. al., and apply Tegmark's decomposition of subject, object, and environment to establish a model for affective states of the brain.
Co-Clustering of fMRI Category Data
In this work Svetlana Shinkareva and I have investigated object representation (e.g.tools and dwellings) using an exploratory co-clustering approach that associates groups of objects with networks of voxels.
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An information theoretic approach to co-clustering was implemented in C++ (original code from Hyuk Cho) and Matlab and the clustered variables were found iteratively by minimizing the mutual information (Kullback-Leibler divergence) function. The algorithm was run with two object clusters and ten voxel clusters. Rows and columns of the data matrix (below-top) were reordered to reflect co-cluster membership. Objects were successfully clustered in to the two categories - representing perfect category classification!
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The smallest cluster for the representation of the dwellings category (cluster6; below left) contained voxels that were widely distributed throughout the cortex. The smallest cluster shown to be important for the representation of the tools category (cluster9; below right) grouped voxels with similar profiles together. Most voxels in that cluster were located in the left inferior parietal and post central gyri – areas previously associated with activation for tools.
Deception is an excellent example of a complex cognitive-socio construct. As such it provides a fundamental test bed for the robustness of cognitive signatures. With direct applications to homeland security, the work I have been involved in with Dr. Jennifer Vendemia is essentially aimed at determining a consitent cognitive theory of deception and its related processes. We have used EEG/ERP and fMRI correlates of deceptive reponding for subjects participating in various tasks including autobiographical information, mock-crime interrogation and intentional misrepresention.
Among our basic findings to date is a solid verification of the intuitive idea that deceptive responding simply takes longer than truthful responding. Employing a new analysis technique based upon the assessment of the time course of the erp-energy for different tasks, we have shown that this finding is not only behaviorally based but likely has neural underpinnings. Click here for a more in-depth look at this research.
In one study (shown above; N=39) we find that deceptive response load-switching times are twice as great with a ratio of 88 ms to 44 ms. we define the load-switching time as the difference in the maximal posterior attention network (PAN) and minimal anterior attention network (AAN) latency values. fMRI data (below) confirm that activations in the AAN and PAN differ for truthful and deceptive responses.
In a pilot experiment 200 trials of the two-stimulus type were presented to a participant (N=1). On 100 trials he was directed to lie (LIE) and on 100 trials he was directed to tell the truth (TRUE); balanced across these trials were 100 trials in which he told a lie after telling the truth or told the truth after telling a lie (SWITCH), and 100 trials in which lies followed lies or truths followed truths (NO SWITCH).
As an example fo the vast amount of data involved in a particular psychological experiment, consider that in a typical high-density, ERP expriement one samples 128 channels at a frequency of 250 Hz - more than 30K data points in one minute!
Typically one performs a set of pre-processing steps of the data, such as the four steps illustrated above.
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erPlot |
erPeak |
I have developed a suite of software tools to help automate many of the post-processing steps involved in the analysis and modeling of high-density evoked reaction scalp potential (ERP) data. erPlot allows for quick plotting of single or grand-averaged data from a 128-Channel array and can display the voltage, power, energy and cognitive activity measures. erPeak will perform a standard waveform identification analysis on a set of files - providing a topographic display of the peak amplitude and latency values within user specified windows. The software is written in Visual Basic 6 and may be downloaded from my dowload page.