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

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

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

Modeling Responses to Peripheral Nerve Stimulation in the Dorsal Horn

peer reviewe

High Frequency Activity in the Orbital Frontal Cortex Modulates with Mismatched Expectations During Gambling in Humans.

peer reviewedDuring gambling, humans often begin by making decisions based on expected rewards and expected risks. However, expectations may not match actual outcomes. As gamblers keep track of their performance, they may feel more or less lucky, which then influences future betting decisions. Studies have identified the orbitofrontal cortex (OFC) as a brain region that plays a significant role during risky decision making in humans. However, most human studies infer neural activation from functional magnetic resonance imaging (fMRI), which has a poor temporal resolution. In particular, fMRI cannot detect activity from neuronal populations in the OFC, which may encode specific information about how a subject reacts to mismatched outcomes. In this preliminary study, four human subjects participated in a gambling task while local field potentials (LFPs), captured at a millisecond resolution, were recorded from the OFC. We analyzed high-frequency activity (HFA: >70 Hz) in the LFPs, as HFA has been shown to correlate to activation of neuronal populations. In 3 out of 4 subjects, HFA in OFC modulated between matched and mismatched trials as soon as the outcome of each bet was revealed, with modulations occurring at different times and directions depending on the anatomical location within the OFC

Decomposing Executive Function into Distinct Processes Underlying Human Decision Making.

peer reviewedExecutive function (EF) consists of higher level cognitive processes including working memory, cognitive flexibility, and inhibition which together enable goal-directed behaviors. Many neurological disorders are associated with EF dysfunctions which can lead to suboptimal behavior. To assess the roles of these processes, we introduce a novel behavioral task and modeling approach. The gamble-like task, with sub-tasks targeting different EF capabilities, allows for quantitative assessment of the main components of EF. We demonstrate that human participants exhibit dissociable variability in the component processes of EF. These results will allow us to map behavioral outcomes to EEG recordings in future work in order to map brain networks associated with EF deficits. Clinical relevance- This work will allow us to quantify EF deficits and corresponding brain activity in patient populations in future work

Modulations in Oscillatory Activity of Globus Pallidus Internus Neurons During a Directed Hand Movement Task—A Primary Mechanism for Motor Planning

Globus pallidus internus (GPi) neurons in the basal ganglia are traditionally thought to play a significant role in the promotion and suppression of movement via a change in firing rates. Here, we hypothesize that a primary mechanism of movement control by GPi neurons is through specific modulations in their oscillatory patterns. We analyzed neuronal spiking activity of 83 GPi neurons recorded from two healthy nonhuman primates executing a radial center-out motor task. We found that, in directionally tuned neurons, the power in the gamma band is significantly (p < 0.05) greater than that in the beta band (a “cross-over” effect), during the planning stages of movements in their preferred direction. This cross-over effect is not observed in the non-directionally tuned neurons. These data suggest that, during movement planning, information encoding by GPi neurons may be governed by a sudden emergence and suppression of oscillatory activities, rather than simply by a change in average firing rates