Todd P. Coleman

Fractal design concepts for stretchable electronics

Stretchable electronics provide a foundation for applications that exceed the scope of conventional wafer and circuit board technologies due to their unique capacity to integrate with soft materials and curvilinear surfaces. The range of possibilities is predicated on the development of device architectures that simultaneously offer advanced electronic function and compliant mechanics. Here we report that thin films of hard electronic materials patterned in deterministic fractal motifs and bonded to elastomers enable unusual mechanics with important implications in stretchable device design. In particular, we demonstrate the utility of Peano, Greek cross, Vicsek and other fractal constructs to yield space-filling structures of electronic materials, including monocrystalline silicon, for electrophysiological sensors, precision monitors and actuators, and radio frequency antennas. These devices support conformal mounting on the skin and have unique properties such as invisibility under magnetic resonance imaging. The results suggest that fractal-based layouts represent important strategies for hard-soft materials integration.

Estimating the directed information to infer causal relationships in ensemble neural spike train recordings

Advances in recording technologies have given neuroscience researchers access to large amounts of data, in particular, simultaneous, individual recordings of large groups of neurons in different parts of the brain. A variety of quantitative techniques have been utilized to analyze the spiking activities of the neurons to elucidate the functional connectivity of the recorded neurons. In the past, researchers have used correlative measures. More recently, to better capture the dynamic, complex relationships present in the data, neuroscientists have employed causal measures—most of which are variants of Granger causality—with limited success. This paper motivates the directed information, an information and control theoretic concept, as a modality-independent embodiment of Granger’s original notion of causality. Key properties include: (a) it is nonzero if and only if one process causally influences another, and (b) its specific value can be interpreted as the strength of a causal relationship. We next describe how the causally conditioned directed information between two processes given knowledge of others provides a network version of causality: it is nonzero if and only if, in the presence of the present and past of other processes, one process causally influences another. This notion is shown to be able to differentiate between true direct causal influences, common inputs, and cascade effects in more two processes. We next describe a procedure to estimate the directed information on neural spike trains using point process generalized linear models, maximum likelihood estimation and information-theoretic model order selection. We demonstrate that on a simulated network of neurons, it (a) correctly identifies all pairwise causal relationships and (b) correctly identifies network causal relationships. This procedure is then used to analyze ensemble spike train recordings in primary motor cortex of an awake monkey while performing target reaching tasks, uncovering causal relationships whose directionality are consistent with predictions made from the wave propagation of simultaneously recorded local field potentials.

Circadian Rhythm of Redox State Regulates Excitability in Suprachiasmatic Nucleus Neurons

Diurnal metabolic changes in circadian clock neurons are coupled to changes in potassium channel activity. Daily rhythms of mammalian physiology, metabolism, and behavior parallel the day-night cycle. They are orchestrated by a central circadian clock in the brain, the suprachiasmatic nucleus (SCN). Transcription of clock genes is sensitive to metabolic changes in reduction and oxidation (redox); however, circadian cycles in protein oxidation have been reported in anucleate cells, where no transcription occurs. We investigated whether the SCN also expresses redox cycles and how such metabolic oscillations might affect neuronal physiology. We detected self-sustained circadian rhythms of SCN redox state that required the molecular clockwork. The redox oscillation could determine the excitability of SCN neurons through nontranscriptional modulation of multiple potassium (K+) channels. Thus, dynamic regulation of SCN excitability appears to be closely tied to metabolism that engages the clockwork machinery.

Capacity of time-slotted ALOHA packetized multiple-access systems over the AWGN channel

We study different notions of capacity for time-slotted ALOHA systems. In these systems, multiple users synchronously send packets in a bursty manner over a common additive white Gaussian noise (AWGN) channel. The users do not coordinate their transmissions, which may collide at the receiver. For such a system, we define both single-slot capacity and multiple-slot capacity. We then construct a coding and decoding scheme for single-slot capacity that achieves any rate within this capacity region. This coding and decoding scheme for a single time slot combines aspects of multiple access rate splitting and of broadcast codes for degraded AWGN channels. This design allows some bits to be reliably received even when collisions occur and more bits to be reliably received in the absence of collisions. The exact number of bits reliably received under both of these scenarios is part of the code design process, which we optimize to maximize the expected rate in each slot. Next, we examine the behavior of the system asymptotically over multiple slots. We show that there exist coding and decoding strategies such that regardless of the burstiness of the traffic, the system is stable as long as the average rate of the users is within the multiple access capacity region of the channel. In other words, we show that bursty traffic does not decrease the Cover-Wyner capacity region of the multiple access channel. A vast family of codes, which includes the type of codes we introduce for the single-slot transmission, achieve the capacity region, in a sense we define, for multiple-slot transmissions. These codes are stabilizing, using only local information at each of the individual queues. The use of information regarding other queues or the use of scheduling does not improve the multiple-slot capacity region.

Grand Challenges in Mapping the Human Brain: NSF Workshop Report

This report summarizes the outcomes of the NSF Workshop on Mapping and Engineering the Brain, held at Arlington, VA, during August 13-14, 2013. Three grand challenges were identified, including high spatiotemporal resolution neuroimaging, perturbation-based neuroimaging, and neuroimaging in naturalistic environments. It was highlighted that each grand challenge requires groundbreaking discoveries, enabling technologies, appropriate knowledge transfer, and multi- and transdisciplinary education and training for success.

Directed Information Graphs

We propose a graphical model for representing networks of stochastic processes, the minimal generative model graph. It is based on reduced factorizations of the joint distribution over time. We show that under appropriate conditions, it is unique and consistent with another type of graphical model, the directed information graph, which is based on a generalization of Granger causality. We demonstrate how directed information quantifies Granger causality in a particular sequential prediction setting. We also develop efficient methods to estimate the topological structure from data that obviate estimating the joint statistics. One algorithm assumes upper bounds on the degrees and uses the minimal dimension statistics necessary. In the event that the upper bounds are not valid, the resulting graph is nonetheless an optimal approximation in terms of Kullback-Leibler (KL) divergence. Another algorithm uses near-minimal dimension statistics when no bounds are known, but the distribution satisfies a certain criterion. Analogous to how structure learning algorithms for undirected graphical models use mutual information estimates, these algorithms use directed information estimates. We characterize the sample-complexity of two plug-in directed information estimators and obtain confidence intervals. For the setting when point estimates are unreliable, we propose an algorithm that uses confidence intervals to identify the best approximation that is robust to estimation error. Last, we demonstrate the effectiveness of the proposed algorithms through the analysis of both synthetic data and real data from the Twitter network. In the latter case, we identify which news sources influence users in the network by merely analyzing tweet times.

A feedback information-theoretic approach to the design of brain-computer interfaces

This article presents a new approach to designing brain–computer interfaces (BCIs) that explicitly accounts for both the uncertainty of neural signals and the important role of sensory feedback. This approach views a BCI as the means by which users communicate intent to an external device and models intent as a string in an ordered symbolic language. This abstraction allows the problem of designing a BCI to be reformulated as the problem of designing a reliable communication protocol using tools from feedback information theory. Here, this protocol is given by a posterior matching scheme. This scheme is not only provably optimal but also easily understood and implemented by a human user. Experimental validation is provided by an interface for text entry and an interface for tracing smooth planar curves, where input is taken in each case from an electroencephalograph during left- and right-hand motor imagery.

Large-scale spatiotemporal spike patterning consistent with wave propagation in motor cortex

Aggregate signals in cortex are known to be spatiotemporally organized as propagating waves across the cortical surface, but it remains unclear whether the same is true for spiking activity in individual neurons. Furthermore, the functional interactions between cortical neurons are well documented but their spatial arrangement on the cortical surface has been largely ignored. Here we use a functional network analysis to demonstrate that a subset of motor cortical neurons in non-human primates spatially coordinate their spiking activity in a manner that closely matches wave propagation measured in the beta oscillatory band of the local field potential. We also demonstrate that sequential spiking of pairs of neuron contains task-relevant information that peaks when the neurons are spatially oriented along the wave axis. We hypothesize that the spatial anisotropy of spike patterning may reflect the underlying organization of motor cortex and may be a general property shared by other cortical areas.

Efficient Methods to Compute Optimal Tree Approximations of Directed Information Graphs

Recently, directed information graphs have been proposed as concise graphical representations of the statistical dynamics among multiple random processes. A directed edge from one node to another indicates that the past of one random process statistically affects the future of another, given the past of all other processes. When the number of processes is large, computing those conditional dependence tests becomes difficult. Also, when the number of interactions becomes too large, the graph no longer facilitates visual extraction of relevant information for decision-making. This work considers approximating the true joint distribution on multiple random processes by another, whose directed information graph has at most one parent for any node. Under a Kullback-Leibler (KL) divergence minimization criterion, we show that the optimal approximate joint distribution can be obtained by maximizing a sum of directed informations. In particular, each directed information calculation only involves statistics among a pair of processes and can be efficiently estimated and given all pairwise directed informations, an efficient minimum weight spanning directed tree algorithm can be solved to find the best tree. We demonstrate the efficacy of this approach using simulated and experimental data. In both, the approximations preserve the relevant information for decision-making.

A stochastic control viewpoint on ‘Posterior Matching’-style feedback communication schemes

This paper re-visits Shayevitz & Feders recent ‘Posterior Matching Scheme’, a deterministic, recursive, capacity-achieving feedback encoding scheme for memoryless channels. We here consider the feedback encoder design problem from a stochastic control perspective. The state of the system is the posterior distribution of the message given current outputs of the channel. The per-trial reward is the average ‘reduction in distance’ of the posterior to the target unit step function. We show that the converse to the channel coding theorem with feedback upper bounds the optimal reward, and that the posterior matching scheme is an optimal policy. We illustrate that this ‘reduction in distance’ symbolism leads to the existence of a Lyapunov function on the Markov chain under this optimal policy, which leads to demonstration of achievability for all rates less than capacity.