Analyzing multiple spike trains with nonparametric granger causality

Simultaneous recordings of spike trains from multiple single neurons are becoming commonplace. Understanding the interaction patterns among these spike trains remains a key research area. A question of interest is the evaluation of information flow between neurons through the analysis of whether one spike train exerts causal influence on another. For continuous-valued time series data, Granger causality has proven an effective method for this purpose. However, the basis for Granger causality estimation is autoregressive data modeling, which is not directly applicable to spike trains. Various filtering options distort the properties of spike trains as point processes. Here we propose a new nonparametric approach to estimate Granger causality directly from the Fourier transforms of spike train data. We validate the method on synthetic spike trains generated by model networks of neurons with known connectivity patterns and then apply it to neurons limultaneously recorded from the thalamus and the primary somatosensory cortex of a squirrel monkey undergoing tactile stimulation.

Statistical significance of sequential firing patterns in multi-neuronal spike trains

Sequential firings with fixed time delays are frequently observed in simultaneous recordings from multiple neurons. Such temporal patterns are potentially indicative of underlying microcircuits and it is important to know when a repeatedly occurring pattern is statistically significant. These sequences are typically identified through correlation counts. In this paper we present a method for assessing the significance of such correlations. We specify the null hypothesis in terms of a bound on the conditional probabilities that characterize the influence of one neuron on another. This method of testing significance is more general than the currently available methods since under our null hypothesis we do not assume that the spiking processes of different neurons are independent. The structure of our null hypothesis also allows us to rank order the detected patterns. We demonstrate our method on simulated spike trains.

Inferring neuronal network connectivity from spike data: A temporal data mining approach

Understanding the functioning of a neural system in terms of its underlying circuitry is an important problem in neuroscience. Recent d evelopments in electrophysiology and imaging allow one to simultaneously record activities of hundreds of neurons. Inferring the underlying neuronal connectivity patterns from such multi-neuronal spike train data streams is a challenging statistical and computational problem. This task involves finding significant temporal patterns from vast amounts of symbolic time series data. In this paper we show that the frequent episode mining methods from the field of temporal data mining can be very useful in this context. In the frequent episode discovery framework, the data is viewed as a sequence of events, each of which is characterized by an event type and its time of occurrence and episodes are certain types of temporal patterns in such data. Here we show that, using the set of discovered frequent episodes from multi-neuronal data, one can infer different types of connectivity patterns in the neural system that generated it. For this purpose, we introduce the notion of mining for frequent episodes under certain temporal constraints; the structure of these temporal constraints is motivated by the application. We present algorithms for discovering serial and parallel episodes under these temporal constraints. Through extensive simulation studies we demonstrate that these methods are useful for unearthing patterns of neuronal network connectivity.

Conditional Probability-Based Significance Tests for Sequential Patterns in Multineuronal Spike Trains

We consider the problem of detecting statistically significant sequential patterns in multineuronal spike trains. These patterns are characterized by ordered sequences of spikes from different neurons with specific delays between spikes. We have previously proposed a data-mining scheme to efficiently discover such patterns, which occur often enough in the data. Here we propose a method to determine the statistical significance of such repeating patterns. The novelty of our approach is that we use a compound null hypothesis that not only includes models of independent neurons but also models where neurons have weak dependencies. The strength of interaction among the neurons is represented in terms of certain pair-wise conditional probabilities. We specify our null hypothesis by putting an upper bound on all such conditional probabilities. We construct a probabilistic model that captures the counting process and use this to derive a test of significance for rejecting such a compound null hypothesis. The structure of our null hypothesis also allows us to rank-order different significant patterns. We illustrate the effectiveness of our approach using spike trains generated with a simulator.

Predicting price-tag for customized goods

We discuss a dynamic pricing model which will aid automobile manufacturer in choosing the right price for customer segment. Though there is oligopoly market structure, the customers get "locked" into a particular technology/company which virtually makes the situation akin to a monopoly. There are associated network externalities and positive feedback. The key idea in monopoly pricing lies in extracting the customer surplus by exploiting the respective elasticities of demand. We present a Walrasian general equilibrium approach to determine the segment price. We compare the prices obtained from optimization model with that from Walrasian dynamics. The results are encouraging and can serve as a critical factor in Customer Relationship Management (CRM) and thereby effectively manage the lock-in.

A Wavelet based Teager Energy Operator for Spike Detection in Microelectrode Array Recordings

Spike detection in neural recordings is the initial step in the creation of brain machine interfaces. The Teager energy operator (TEO) treats a spike as an increase in the `local' energy and detects this increase. The performance of TEO in detecting action potential spikes suffers due to its sensitivity to the frequency of spikes in the presence of noise which is present in microelectrode array (MEA) recordings. The multiresolution TEO (mTEO) method overcomes this shortcoming of the TEO by tuning the parameter k to an optimal value m so as to match to frequency of the spike. In this paper, we present an algorithm for the mTEO using the multiresolution structure of wavelets along with inbuilt lowpass filtering of the subband signals. The algorithm is efficient and can be implemented for real-time processing of neural signals for spike detection. The performance of the algorithm is tested on a simulated neural signal with 10 spike templates obtained from [14]. The background noise is modeled as a colored Gaussian random process. Using the noise standard deviation and autocorrelation functions obtained from recorded data, background noise was simulated by an autoregressive (AR(5)) filter. The simulations show a spike detection accuracy of 90%and above with less than 5% false positives at an SNR of 2.35 dB as compared to 80% accuracy and 10% false positives reported [6] on simulated neural signals.

Learning dynamic prices in multiseller electronic retail markets with price sensitive customers, stochastic demands, and inventory replenishments

In this paper, we use reinforcement learning (RL) as a tool to study price dynamics in an electronic retail market consisting of two competing sellers, and price sensitive and lead time sensitive customers. Sellers, offering identical products, compete on price to satisfy stochastically arriving demands (customers), and follow standard inventory control and replenishment policies to manage their inventories. In such a generalized setting, RL techniques have not previously been applied. We consider two representative cases: 1) no information case, were none of the sellers has any information about customer queue levels, inventory levels, or prices at the competitors; and 2) partial information case, where every seller has information about the customer queue levels and inventory levels of the competitors. Sellers employ automated pricing agents, or pricebots, which use RL-based pricing algorithms to reset the prices at random intervals based on factors such as number of back orders, inventory levels, and replenishment lead times, with the objective of maximizing discounted cumulative profit. In the no information case, we show that a seller who uses Q-learning outperforms a seller who uses derivative following (DF). In the partial information case, we model the problem as a Markovian game and use actor-critic based RL to learn dynamic prices. We believe our approach to solving these problems is a new and promising way of setting dynamic prices in multiseller environments with stochastic demands, price sensitive customers, and inventory replenishments.

Some new results regarding spikes and a heuristic for spike construction

his paper addresses the problem of minimizing the number of columns with superdiagonal nonzeroes (viz., spiked columns) in a square, nonsingular linear system of equations which is to be solved by Gaussian elimination. The exact focus is on a class of min-spike heuristics in which the rows and columns of the coefficient matrix are first permuted to block lower-triangular form. Subsequently, the number of spiked columns in each irreducible block and their heights above the diagonal are minimized heuristically. We show that ifevery column in an irreducible block has exactly two nonzeroes, i.e., is a doubleton, then there is exactly one spiked column. Further, if there is at least one non-doubleton column, there isalways an optimal permutation of rows and columns under whichnone of the doubleton columns are spiked. An analysis of a few benchmark linear programs suggests that singleton and doubleton columns can abound in practice. Hence, it appears that the results of this paper can be practically useful. In the rest of the paper, we develop a polynomial-time min-spike heuristic based on the above results and on a graph-theoretic interpretation of doubleton columns.

Patent Price Dynamics in the Context of Patent Age and Patent Latent Variables

The decision to patent a technology is a difficult one to make for the top management of any organization. The expected value that the patent might deliver in the market is an important factor that impacts this judgement. Earlier researchers have suggested that patent prices are better indicators of value of a patent and that auction prices are the best way of determining value. However, the lack of public data on pricing has prevented research on understanding the dynamics of patent pricing. Our paper uses singleton patent auction price data of Ocean Tomo LLC to study the prices of patents. We describe price characteristics of these patents. The price of these patents was correlated with their age, and a significant correlation was found. A price - age matrix was developed and we describe the price characteristics of patents using four quadrants of the matrix, namely young and old patents with low and high prices. We also found that patents owned by small firms get transacted more often and inventor owned patents attracted a better price than assignee owned patents.

Noise-spike-induced escape in a bistable system driven by colored noise: Noise with long correlation times

An escape mechanism in a bistable system driven by colored noise of large but finite correlation time (tau) is analyzed. It is shown that the fluctuating potential theory [Phys. Rev. A 38, 3749 (1988)] becomes invalid in a region around the inflection points of the bistable potential, resulting in the underestimation of the mean first passage time at finite tau by this theory. It is shown that transitions at large but finite tau are caused by noise spikes, with edges rising and falling exponentially in a time of O(tau). Simulation of the dynamics of the bistable system driven by noise spikes of the above-mentioned nature clearly reveal the physical mechanism behind the transition.

Network Rhythms Influence the Relationship between Spike-Triggered Local Field Potential and Functional Connectivity

Characterizing the functional connectivity between neurons is key for understanding brain function. We recorded spikes and local field potentials (LFPs) from multielectrode arrays implanted in monkey visual cortex to test the hypotheses that spikes generated outward-traveling LFP waves and the strength of functional connectivity depended on stimulus contrast, as described recently. These hypotheses were proposed based on the observation that the latency of the peak negativity of the spike-triggered LFP average (STA) increased with distance between the spike and LFP electrodes, and the magnitude of the STA negativity and the distance over which it was observed decreased with increasing stimulus contrast. Detailed analysis of the shape of the STA, however, revealed contributions from two distinct sources-a transient negativity in the LFP locked to the spike (similar to 0 ms) that attenuated rapidly with distance, and a low-frequency rhythm with peak negativity similar to 25 ms after the spike that attenuated slowly with distance. The overall negative peak of the LFP, which combined both these components, shifted from similar to 0 to similar to 25 ms going from electrodes near the spike to electrodes far from the spike, giving an impression of a traveling wave, although the shift was fully explained by changing contributions from the two fixed components. The low-frequency rhythm was attenuated during stimulus presentations, decreasing the overall magnitude of the STA. These results highlight the importance of accounting for the network activity while using STAs to determine functional connectivity.