Mutual Dependence: A Novel Method for Computing Dependencies Between Random Variables

In data science, it is often required to estimate dependencies between different data sources. These dependencies are typically calculated using Pearson's correlation, distance correlation, and/or mutual information. However, none of these measures satisfy all the Granger's axioms for an "ideal measure". One such ideal measure, proposed by Granger himself, calculates the Bhattacharyya distance between the joint probability density function (pdf) and the product of marginal pdfs. We call this measure the mutual dependence. However, to date this measure has not been directly computable from data. In this paper, we use our recently introduced maximum likelihood non-parametric estimator for band-limited pdfs, to compute the mutual dependence directly from the data. We construct the estimator of mutual dependence and compare its performance to standard measures (Pearson's and distance correlation) for different known pdfs by computing convergence rates, computational complexity, and the ability to capture nonlinear dependencies. Our mutual dependence estimator requires fewer samples to converge to theoretical values, is faster to compute, and captures more complex dependencies than standard measures

Electrical neurostimulation for chronic pain: on selective relay of sensory neural activities in myelinated nerve fibers

Chronic pain affects about 100 million adults in the US. Despite their great need, neuropharmacology and neurostimulation therapies for chronic pain have been associated with suboptimal efficacy and limited long-term success, as their mechanisms of action are unclear. Yet current computational models of pain transmission suffer from several limitations. In particular, dorsal column models do not include the fundamental underlying sensory activity traveling in these nerve fibers. We developed a (simple) simulation test bed of electrical neurostimulation of myelinated nerve fibers with underlying sensory activity. This paper reports our findings so far. Interactions between stimulation-evoked and underlying activities are mainly due to collisions of action potentials and losses of excitability due to the refractory period following an action potential. In addition, intuitively, the reliability of sensory activity decreases as the stimulation frequency increases. This first step opens the door to a better understanding of pain transmission and its modulation by neurostimulation therapies

A segment-based speaker verification system using SUMMIT

Thesis (M.S.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 1997.Includes bibliographical references (p. 75-79).by Sridevi Vedula Sarma.M.S

Finite-rate control : stability and performance

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2006.Includes bibliographical references (leaves 88-91).The classical control paradigm addressed problems where communication between one plant and one controller is essentially perfect, and both have either discrete or continuous dynamics. Today, new problems in control over networks are emerging. A complex network involves an interconnection of numerous computational components where the controllers may be decentralized, and the components can have discrete or continuous dynamics. Communication links can be very noisy, induce delays, and have finite-rate constraints. Applications include remote navigation systems over the internet (eg. telesurgery) or in constrained environments (eg. deep sea/Mars exploration). These complexities demand that control be integrated with the protocols of communication to ensure stability and performance. Control over networks is recent and continues to receive growing interest. Initial work has focused on asymptotic stability under finite-rate feedback control, where the only excitation to the system is an unknown (but bounded) finite-dimensional initial condition vector. Such problems reduce to state-estimation under finite-rate constraints.(cont.) More recently, disturbance rejection limitations were derived for the same setting, assuming stochastic exogenous signals entering the system. Although these studies have contributed greatly to our understanding of such systems, input-output stability, performance analysis, and synthesis of coding schemes and controllers under finite-rate constraints remains largely untapped. In this thesis we address how finiterate control impacts input-output stability and performance, and we also construct computable methods for synthesizing controllers and coding schemes to meet control objectives. We first investigate how finite-rate feedback limits input-output stability and closed-loop performance. We assume that exogenous inputs belong to rich deterministic classes of signals, and perform analyses in a worst case setting. Since our results are derived using a robust control perspective, we are able to translate performance demands into optimization problems that can be solved to obtain quantization strategies and controllers in a streamlined manner. We then study how finite-rate feedforward control impacts finite-horizon tracking and navigation.(cont.) We derive performance limitations for each case, and illustrate time and performance tradeoffs. Finally, we investigate feedforward control over noisy discrete channels, and solve a decentralized distributed design problem involving the simultaneous synthesis of a block coding strategy and a single-input single-output linear time-invariant controller. We also illustrate delay versus accuracy tradeoffs.by Sridevi Vedula Sarma.Ph.D

PMv Neuronal Firing May Be Driven by a Movement Command Trajectory within Multidimensional Gaussian Fields

The premotor cortex (PM) is known to be a site of visuo-somatosensory integration for the production of movement. We sought to better understand the ventral PM (PMv) by modeling its signal encoding in greater detail. Neuronal firing data was obtained from 110 PMv neurons in two male rhesus macaques executing four reach-grasp-manipulate tasks. We found that in the large majority of neurons (∼90%) the firing patterns across the four tasks could be explained by assuming that a high-dimensional position/configuration trajectory-like signal evolving ∼250 ms before movement was encoded within a multidimensional Gaussian field (MGF). Our findings are consistent with the possibility that PMv neurons process a visually specified reference command for the intended arm/hand position trajectory with respect to a proprioceptively or visually sensed initial configuration. The estimated MGF were (hyper) disc-like, such that each neuron's firing modulated strongly only with commands that evolved along a single direction within position/configuration space. Thus, many neurons appeared to be tuned to slices of this input signal space that as a collection appeared to well cover the space. The MGF encoding models appear to be consistent with the arm-referent, bell-shaped, visual target tuning curves and target selectivity patterns observed in PMV visual-motor neurons. These findings suggest that PMv may implement a lookup table-like mechanism that helps translate intended movement trajectory into time-varying patterns of activation in motor cortex and spinal cord. MGFs provide an improved nonlinear framework for potentially decoding visually specified, intended multijoint arm/hand trajectories well in advance of movement

Non-stationary discharge patterns in motor cortex under subthalamic nucleus deep brain stimulation

Deep brain stimulation (DBS) of the subthalamic nucleus (STN) directly modulates the basal ganglia (BG), but how such stimulation impacts the cortex upstream is largely unknown. There is evidence of cortical activation in 6-hydroxydopamine (OHDA)-lesioned rodents and facilitation of motor evoked potentials in Parkinson's disease (PD) patients, but the impact of the DBS settings on the cortical activity in normal vs. Parkinsonian conditions is still debated. We use point process models to analyze non-stationary activation patterns and inter-neuronal dependencies in the motor and sensory cortices of two non-human primates during STN DBS. These features are enhanced after treatment with 1-methyl-4-phenyl-1,2,3,6-tetrahydropyridine (MPTP), which causes a consistent PD-like motor impairment, while high-frequency (HF) DBS (i.e., ≥100 Hz) strongly reduces the short-term patterns (period: 3–7 ms) both before and after MPTP treatment, and elicits a short-latency post-stimulus activation. Low-frequency DBS (i.e., ≤50 Hz), instead, has negligible effects on the non-stationary features. Finally, by using tools from the information theory [i.e., receiver operating characteristic (ROC) curve and information rate (IR)], we show that the predictive power of these models is dependent on the DBS settings, i.e., the probability of spiking of the cortical neurons (which is captured by the point process models) is significantly conditioned on the timely delivery of the DBS input. This dependency increases with the DBS frequency and is significantly larger for high- vs. low-frequency DBS. Overall, the selective suppression of non-stationary features and the increased modulation of the spike probability suggest that HF STN DBS enhances the neuronal activation in motor and sensory cortices, presumably because of reinforcement mechanisms, which perhaps involve the overlap between feedback antidromic and feed-forward orthodromic responses along the BG-thalamo-cortical loop

Winning versus losing during gambling and its neural correlates

Humans often make decisions which maximize an internal utility function. For example, humans often maximize their expected reward when gambling and this is considered as a "rational" decision. However, humans tend to change their betting strategies depending on how they "feel". If someone has experienced a losing streak, they may "feel" that they are more likely to win on the next hand even though the odds of the game have not changed. That is, their decisions are driven by their emotional state. In this paper, we investigate how the human brain responds to wins and losses during gambling. Using a combination of local field potential recordings in human subjects performing a financial decision-making task, spectral analyses, and non-parametric cluster statistics, we investigated whether neural responses in different cognitive and limbic brain areas differ between wins and losses after decisions are made. In eleven subjects, the neural activity modulated significantly between win and loss trials in one brain region: the anterior insula ($p=0.01$). In particular, gamma activity (30-70 Hz) increased in the anterior insula when subjects just realized that they won. Modulation of metabolic activity in the anterior insula has been observed previously in functional magnetic resonance imaging studies during decision making and when emotions are elicited. However, our study is able to characterize temporal dynamics of electrical activity in this brain region at the millisecond resolution while decisions are made and after outcomes are revealed

Tibia Fracture Healing Prediction Using First-Order Mathematical Model

The prediction of healing period of a tibia fracture in humans across limb using first-order mathematical model is demonstrated. At present, fracture healing is diagnosed using X-rays. Recent studies have demonstrated electric stimulation as a diagnostic tool in fracture healing. A DC electric voltage of 0.7 V was applied across the fracture and stabilized with Teflon coated carbon rings and the data was recorded at different time intervals until the fracture heals. The experimental data fitted a first-order plus dead time zero model (FOPDTZ) that coincided with the mathematical model of electrical simulated tibia fracture limb. Fracture healing diagnosis was proposed using model parameter process gain. Current stabilization in terms of process gain parameter becoming constant indicates that the healing of fracture is a new finding in the work. An error analysis was performed and it was observed that the measured data correlated to the FOPDTZ model with an error of less than 2 percent. Prediction of fracture healing period was done by one of the identified model parameters, namely, process gain. Moreover, mathematically, it is justified that once the fracture is completely united there is no capacitance present across the fracture site, which is a novelty of the work

Modeling Responses to Peripheral Nerve Stimulation in the Dorsal Horn

peer reviewe

Model simulation of tide-induced currents in Gauthami-Godavari estuary

Predictive spatial distribution of flow field has been simulated from the time series data on currents and tides during dry season (11-19, February, 2009) in the Gauthami-Godavari Estuary utilizing TIDAL model. A 2D-Tidal Estuarine model has been considered (instead of 3D model) due to well-mixed type system and its circulation is dominated by tides during the observational period. The model forcing functions consist of wind and tidal elevations along the open boundaries and no fresh water inflow from the main stream and no land flood in river system. The bathymetry data of the river basin has been collected and supplemented to the model as one of the rigid boundary conditions to evaluate integration. The bottom roughness length (K) was adjusted to achieve model calibration and verification in model simulations of flow field. The model simulation results are in qualitative agreement with the observational data with calibrated bottom roughness length which is about 0.085 m. Model results reveal that the majority of flow was found to be along the channel axis (i.e. high iso-bath contour). During flood time, flow is south-west direction and it is changed to northeast direction during ebb period which is indicating that the model results resemble flow in the real eastern system