Spike Clustering and Neuron Tracking over Successive Time Windows

This paper introduces a new methodology for tracking signals from individual neurons over time in multiunit extracellular recordings. The core of our strategy relies upon an extension of a traditional mixture model approach, with parameter optimization via expectation-maximimization (EM), to incorporate clustering results from the preceding time period in a Bayesian manner. EM initialization is also achieved by utilizing these prior clustering results. After clustering, we match the current and prior clusters to track persisting neurons. Applications of this spike sorting method to recordings from macaque parietal cortex show that it provides significantly more consistent clustering and tracking results

Artificial potential functions for highway driving with collision avoidance

We present a set of potential function components to assist an automated or semi-automated vehicle in navigating a multi-lane, populated highway. The resulting potential field is constructed as a superposition of disparate functions for lane- keeping, road-staying, speed preference, and vehicle avoidance and passing. The construction of the vehicle avoidance potential is of primary importance, incorporating the structure and protocol of laned highway driving. Particularly, the shape and dimensions of the potential field behind each obstacle vehicle can appropriately encourage control vehicle slowing and/or passing, depending on the cars' velocities and surrounding traffic. Hard barriers on roadway edges and soft boundaries between navigable lanes keep the vehicle on the highway, with a preference to travel in a lane center

A Miniature Robot for Isolating and Tracking Neurons in Extracellular Cortical Recordings

This paper presents a miniature robot device and control algorithm that can autonomously position electrodes in cortical tissue for isolation and tracking of extracellular signals of individual neurons. Autonomous electrode positioning can significantly enhance the efficiency and quality of acute electrophysiolgical experiments aimed at basic understanding of the nervous system. Future miniaturized systems of this sort could also overcome some of the inherent difficulties in estabilishing long-lasting neural interfaces that are needed for practical realization of neural prostheses. The paper describes the robot's design and summarizes the overall structure of the control system that governs the electrode positioning process. We present a new sequential clustering algorithm that is key to improving our system's performance, and which may have other applications in robotics. Experimental results in macaque cortex demonstrate the validity of our approach

Multiple hypothesis tracking using clustered measurements

This paper introduces an algorithm for tracking targets whose locations are inferred from clusters of observations. This method, which we call MHTC, expands the traditional multiple hypothesis tracking (MHT) hypothesis tree to include model hypotheses - possible ways the data can be clustered in each time step - as well as ways the measurements can be associated with existing targets across time steps. We present this new hypothesis framework and its probability expressions and demonstrate MHTC's operation in a robotic solution to tracking neural signal sources

Bayesian clustering and tracking of neuronal signals for autonomous neural interfaces

This paper introduces a new, unsupervised method for sorting and tracking the non-stationary spike signals of individual neurons in multi-unit extracellular recordings. While this method may be applied to a variety of problems that arise in the field of neural interfaces, its development is motivated by a new class of autonomous neural recording devices. The core of the proposed strategy relies upon an extension of a traditional expectation-maximization (EM) mixture model optimization to incorporate clustering results from the preceding recording interval in a Bayesian manner. Explicit filtering equations for the case of a Gaussian mixture are derived. Techniques using prior data to seed the EM iterations and to select the appropriate model class are also developed. As a natural byproduct of the sorting method, current and prior signal clusters can be matched over time in order to track persisting neurons. Applications of this signal classification method to recordings from macaque parietal cortex show that it provides significantly more consistent clustering and tracking results than traditional methods

Human detection and tracking via Ultra-Wideband (UWB) radar

This paper presents an algorithm for human presence detection and tracking using an Ultra-Wideband (UWB) impulse-based mono-static radar. UWB radar can complement other human tracking technologies, as it works well in poor visibility conditions. UWB electromagnetic wave scattering from moving humans forms a complex returned signal structure which can be approximated to a specular multi-path scattering model (SMPM). The key technical challenge is to simultaneously track multiple humans (and non-humans) using the complex scattered waveform observations. We develop a multiple-hypothesis tracking (MHT) framework that solves the complicated data association and tracking problem for an SMPM of moving objects/targets. Human presence detection utilizes SMPM signal features, which are tested in a classical likelihood ratio (LR) detector framework. The process of human detection and tracking is a combination of the MHT method and the LR human detector. We present experimental results in which a mono-static UWB radar tracks human and non-human targets, and detects human presence by discerning human from moving non-human objects

Scheduling with Setup Costs and Monotone Penalties

We consider single processor preemptive scheduling with job-dependent setup times. In this model, a job-dependent setup time is incurred when a job is started for the first time, and each time it is restarted after preemption. This model is a common generalization of preemptive scheduling, and actually of non-preemptive scheduling as well. The objective is to minimize the sum of any general non-negative, non-decreasing cost functions of the completion times of the jobs -- this generalizes objectives of minimizing weighted flow time, flow-time squared, tardiness or the number of tardy jobs among many others. Our main result is a randomized polynomial time O(1)-speed O(1)-approximation algorithm for this problem. Without speedup, no polynomial time finite multiplicative approximation is possible unless P=NP. We extend the approach of Bansal et al. (FOCS 2007) of rounding a linear programming relaxation which accounts for costs incurred due to the non-preemptive nature of the schedule. A key new idea used in the rounding is that a point in the intersection polytope of two matroids can be decomposed as a convex combination of incidence vectors of sets that are independent in both matroids. In fact, we use this for the intersection of a partition matroid and a laminar matroid, in which case the decomposition can be found efficiently using network flows. Our approach gives a randomized polynomial time offline O(1)-speed O(1)-approximation algorithm for the broadcast scheduling problem with general cost functions as well

UWB radar-based human target tracking

This paper presents a framework and algorithms for tracking the range of moving humans via a mono-static ultra-wideband (UWB) radar. The approach is based on a specular multi-path model for UWB radar scatters from walking humans. Empirical studies show that multipath time-of-arrival (TOA) can be modeled as a point process whose behavior is governed by a Gamma distribution. Based on this insight, we develop a tracking procedure that combines a Kalman Filter with a point process observation model whose measurements are processed with an Expectation-Maximization (EM) procedure. As a byproduct, the EM procedure solves the multi-target data segmentation and data association problems. We present experimental results in which a monostatic UWB radar tracks both individual and up to two human targets

The Container Selection Problem

We introduce and study a network resource management problem that is a special case of non-metric k-median, naturally arising in cross platform scheduling and cloud computing. In the continuous d-dimensional container selection problem, we are given a set C of input points in d-dimensional Euclidean space, for some d >= 2, and a budget k. An input point p can be assigned to a "container point" c only if c dominates p in every dimension. The assignment cost is then equal to the L1-norm of the container point. The goal is to find k container points in the d-dimensional space, such that the total assignment cost for all input points is minimized. The discrete variant of the problem has one key distinction, namely, the container points must be chosen from a given set F of points. For the continuous version, we obtain a polynomial time approximation scheme for any fixed dimension d>= 2. On the negative side, we show that the problem is NP-hard for any d>=3. We further show that the discrete version is significantly harder, as it is NP-hard to approximate without violating the budget k in any dimension d>=3. Thus, we focus on obtaining bi-approximation algorithms. For d=2, the bi-approximation guarantee is (1+epsilon,3), i.e., for any epsilon>0, our scheme outputs a solution of size 3k and cost at most (1+epsilon) times the optimum. For fixed d>2, we present a (1+epsilon,O((1/epsilon)log k)) bi-approximation algorithm