Publications (24)41.86 Total impact
- [Show abstract] [Hide abstract] ABSTRACT: The problem of commodity price determination in a market-based, capitalist economy has a long and contentious history. Neoclassical microeconomic theories are based typically on marginal utility assumptions, while classical macroeconomic theories tend to be value-based. In the current work, I study a simplified meso-scale model of a commodity capitalist economy. The production/exchange model is represented by a network whose nodes are firms, workers, capitalists, and markets, and whose directed edges represent physical or monetary flows. A pair of multivariate linear equations with stochastic input parameters represent physical (supply/demand) and monetary (income/expense) balance. The input parameters yield a non-degenerate profit rate distribution across firms. Labor time and price are found to be eigenvector solutions to the respective balance equations. A simple relation is derived relating the expected value of commodity price to commodity labor content. Results of Monte Carlo simulations are consistent with the stochastic price/labor content relation.
- [Show abstract] [Hide abstract] ABSTRACT: Profit realization is the dominant feature of market-based economic systems, determining their dynamics to a large extent. Rather than attaining an equilibrium, profit rates vary widely across firms, and the variation persists over time. Differing definitions of profit result in differing empirical distributions. To study the statistical properties of profit rates, I used data from a publicly available database for the US Economy for 2009-2010 (Risk Management Association). For each of three profit rate measures, the sample space consists of 771 points. Each point represents aggregate data from a small number of US manufacturing firms of similar size and type (NAICS code of principal product). When comparing the empirical distributions of profit rates, significant 'heavy tails' were observed, corresponding principally to a number of firms with larger profit rates than would be expected from simple models. An apparently novel correlated sum of random variables statistical model was used to model the data. In the case of operating and net profit rates, a number of firms show negative profits (losses), ruling out simple gamma or lognormal distributions as complete models for these data.
- [Show abstract] [Hide abstract] ABSTRACT: Connectivity measures are (typically bivariate) statistical measures that may be used to estimate interactions between brain regions from electrophysiological data. We review both formal and informal descriptions of a range of such measures, suitable for the analysis of human brain electrophysiological data, principally electro- and magnetoencephalography. Methods are described in the space-time, space-frequency, and space-time-frequency domains. Signal processing and information theoretic measures are considered, and linear and nonlinear methods are distinguished. A novel set of cross-time-frequency measures is introduced, including a cross-time-frequency phase synchronization measure.
- [Show abstract] [Hide abstract] ABSTRACT: The characterization of spatial network dynamics is desirable for a better understanding of seizure physiology. The goal of this work is to develop a computational method for identifying transient spatial patterns from intracranial electroencephalographic (iEEG) data. Starting with bivariate synchrony measures, such as phase correlation, a two-step clustering procedure is used to identify statistically significant spatial network patterns, whose temporal evolution can be inferred. We refer to this as the composite synchrony profile (CSP) method. The CSP method was verified with simulated data and evaluated using ictal and interictal recordings from three patients with intractable epilepsy. Application of the CSP method to these clinical iEEG datasets revealed a set of distinct CSPs with topographies consistent with medial temporal/limbic and superior parietal/medial frontal networks thought to be involved in the seizure generation process. By combining relatively straightforward multivariate signal processing techniques, such as phase synchrony, with clustering and statistical hypothesis testing, the methods we describe may prove useful for network definition and identification. The network patterns we observe using the CSP method cannot be inferred from direct visual inspection of the raw time series data, nor are they apparent in voltage-based topographic map sequences.
- [Show abstract] [Hide abstract] ABSTRACT: We extend adaptive beamformers (DICS) and RAP MUSIC to solve the MEG inverse problem in the time-frequency domain for induced and phase-locked components. Using event-related data, we estimate the complex covariances from time-frequency transformed single trials for total power, phase locked, and induced components . We obtain the phase-locked DICS inverse as the difference between the total power and induced solutions. RAP-MUSIC was adapted to constrain the real and imaginary parts of the source space solution. We have verified these methods using simulated data, and validated them with somatosensory and motor MEG data. Keywordsmagnetoencephalography-source estimation-time-frequency-DICS-RAP MUSIC
- [Show abstract] [Hide abstract] ABSTRACT: A method is described that combines linear source estimation (beamformers) with non-parametric statistical significance testing to yield vector time series estimates for brain regions of interest. These source time series are a suitable starting point for functional connectivity analysis.
- [Show abstract] [Hide abstract] ABSTRACT: We studied adaptive and non-adaptive beamformers for source space time series estimation from MEG data, using simulated data and the interference function as a metric. Both filter types show significant interference from non-target locations. We describe a method to obtain additional interference suppression. Modeling error suppression is also discussed.
- [Show abstract] [Hide abstract] ABSTRACT: Linear estimators have been used widely in the bioelectromagnetic inverse problem, but their properties and relationships have not been fully characterized. Here, we show that the most widely used linear estimators may be characterized by a choice of norms on signal space and on source space. These norms depend, in part, on assumptions about the signal space and source space covariances. We demonstrate that two estimator classes (standardized and weight vector normalized) yield unbiased estimators of source location for simple source models (including only the noise-free case) but biased estimators of source magnitude. In the presence of instrumental (white) noise, we show that the nonadaptive standardized estimator is a biased estimator of source location, while the adaptive weight vector normalized estimator remains unbiased. A third class (distortionless) is an unbiased estimator of source magnitude but a biased estimator of source location.
- [Show abstract] [Hide abstract] ABSTRACT: For patients with partial epilepsy, automatic spike detection techniques applied to interictal MEG data often discover several potentially epileptogenic brain regions. An important determination in treatment planning is which of these detected regions are most likely to be the primary sources of epileptogenic activity. Analysis of the patterns of propagation activity between the detected regions may allow for detection of these primary epileptic foci. We describe the use of hidden Markov models (HMM) for estimation of the propagation patterns between several spiking regions from interictal MEG data. Analysis of the estimated transition probability matrix allows us to make inferences regarding the propagation pattern of the abnormal activity and determine the most likely region of its origin. The proposed HMM paradigm allows for a simple incorporation of the spike detector specificity and sensitivity characteristics. We develop bounds on performance for the case of perfect detection. We also apply the technique to simulated data sets in order to study the robustness of the method to the non-ideal specificity-sensitivity characteristics of the event detectors and compare results with the lower bounds. Our study demonstrates robustness of the proposed technique to event detection errors. We conclude with an example of the application of this method to a single patient.
- [Show abstract] [Hide abstract] ABSTRACT: Different modeling frameworks (such as error analyses for dipole localization [Fuchs, 1998] [Huizenga, 2001]; crosstalk and point spread analyses for linear estimators [Liu, 2002]; etc.) have demonstrated improved three-dimensional (3D) resolution for combined MEG/EEG (or EMEG) source estimation. Complementary to these, an empirical analysis of 2D surface data suggested that MEG and EEG information content could be superadditive [Pflieger, 2000]. Taking a hybrid approach in the present study, we made simulations within a regional activity estimation (REGAE, [Pflieger, 2001]) framework, which quantifies the ability of EMEG to discriminate brain activity originating within a 3D region of interest (ROI) from simultaneous non-ROI activity. Two metrics were employed: Kullback-Leibler divergence (KLD) and area under the receiver operator characteristic curve (AUROC). High-density sensor configurations (248 magnetometers, 256 electrodes) were combined with a gray matter source space model (7931 dipole triples, maximum entropy activities), assuming magnetic 3-shell sphere and electric BEM head models. Superadditive KLD was observed frequently across 89 representative brain ROIs and 3 ROI sizes (5, 10, and 15 mm radii), especially for regions already fairly visible to each modality. We also report an observed functional relationship between AUROC and KLD.
- [Show abstract] [Hide abstract] ABSTRACT: Methods are described for non-parametric significance testing from event-related encephalographic data, using randomization tests. These methods may be applied in both signal space and source space. The methods include within-subject between-condition comparisons, paired and unpaired comparisons, and within-group and between-group comparisons. Test statistics are also derived for comparing the spatial or temporal response patterns, independent of specific changes at individual locations. Novel methods for testing peak-height significance, and also for making map-wide comparisons, are described. These methods have been validated using simulated data.
- [Show abstract] [Hide abstract] ABSTRACT: Considerable ambiguity exists about the generators of the scalp recorded P300, despite a vast body of research employing a diverse range of methodologies. Previous investigations employing source localization techniques have been limited largely to equivalent current dipole models, with most studies identifying medial temporal and/or hippocampal sources, but providing little information about the contribution of other cortical regions to the generation of the scalp recorded P3. Event-related potentials (ERPs) were recorded from 5 subjects using a 124-channel sensor array during the performance of a visuo-verbal Oddball task. Cortically constrained, MRI-guided boundary element modeling was used to identify the cortical generators of this target P3 in individual subjects. Cortical generators of the P3 were localized principally to the intraparietal sulcus (IPS) and surrounding superior parietal lobes (SPL) bilaterally in all subjects, though with some variability across subjects. Two subjects also showed activity in the lingual/inferior occipital gyrus and mid-fusiform gyrus. A group cortical surface was calculated by non-linear warping of each subject's segmented cortex followed by averaging and creation of a group mesh. Source activity identified across the group reflected the individual subject activations in the IPS and SPL bilaterally and in the lingual/inferior occipital gyrus primarily on the left. Activation of IPS and SPL is interpreted to reflect the role of this region in working memory and related attention processes and visuo-motor integration. The activity in left lingual/inferior occipital gyrus is taken to reflect activation of regions associated with modality-specific analysis of visual word forms.
- [Show abstract] [Hide abstract] ABSTRACT: This study is an exploratory investigation of the regional timing of cortical activity associated with verbal working memory function. ERP activity was obtained from a single subject using a 124-channel sensor array during a task requiring the monitoring of imageable words for occasional targets. Distributed cortical activity was estimated every 2.5 ms with high spatial resolution using real head, boundary element modelling of non-target activity. High-resolution structural MRI was used for segmentation of tissue boundaries and co-registration to the scalp electrode array. The inverse solution was constrained to the cortical surface. Cortical activity was observed in regions commonly associated with verbal working memory function. This included: the occipital pole (early visual processing); the superior temporal and inferior parietal gyrus bilaterally and the left angular gyrus (visual and phonological word processing); the dorsal lateral occipital gyrus (spatial processing); and aspects of the bilateral superior parietal lobe (imagery and episodic verbal memory). Activity was also observed in lateral and superior prefrontal regions associated with working memory control of sensorimotor processes. The pattern of cortical activity was relatively stable over time, with variations in the extent and amplitude of contributing local source activations. By contrast, the pattern of concomitant scalp topography varied considerably over time, reflecting the linear summation effects of volume conduction that often confound dipolar source modelling.
San Diego State University
San Diego, California, United States
- Computational Science Research Center