Filter Bank Fusion Frames

In this paper we characterize and construct novel oversampled filter banks implementing fusion frames. A fusion frame is a sequence of orthogonal projection operators whose sum can be inverted in a numerically stable way. When properly designed, fusion frames can provide redundant encodings of signals which are optimally robust against certain types of noise and erasures. However, up to this point, few implementable constructions of such frames were known; we show how to construct them using oversampled filter banks. In this work, we first provide polyphase domain characterizations of filter bank fusion frames. We then use these characterizations to construct filter bank fusion frame versions of discrete wavelet and Gabor transforms, emphasizing those specific finite impulse response filters whose frequency responses are well-behaved.Comment: keywords: filter banks, frames, tight, fusion, erasures, polyphas

Unsupervised discovery of temporal sequences in high-dimensional datasets, with applications to neuroscience.

Identifying low-dimensional features that describe large-scale neural recordings is a major challenge in neuroscience. Repeated temporal patterns (sequences) are thought to be a salient feature of neural dynamics, but are not succinctly captured by traditional dimensionality reduction techniques. Here, we describe a software toolbox-called seqNMF-with new methods for extracting informative, non-redundant, sequences from high-dimensional neural data, testing the significance of these extracted patterns, and assessing the prevalence of sequential structure in data. We test these methods on simulated data under multiple noise conditions, and on several real neural and behavioral datas. In hippocampal data, seqNMF identifies neural sequences that match those calculated manually by reference to behavioral events. In songbird data, seqNMF discovers neural sequences in untutored birds that lack stereotyped songs. Thus, by identifying temporal structure directly from neural data, seqNMF enables dissection of complex neural circuits without relying on temporal references from stimuli or behavioral outputs

An information-theoretic approach to understanding the neural coding of relevant tactile features

Objective: Traditional theories in neuroscience state that tactile afferents present in the glabrous skin of the human hand encode tactile information following a submodality segregation strategy, meaning that each modality (eg. motion, vibration, shape, ... ) is encoded by a different afferent class. Modern theories suggest a submodality convergence instead, in which different afferent classes work together to capture information about the environment through tactile sense. Typically, studies involve electrophysiological recordings of tens of afferents. At the same time, the human hand is filled with around 17.000 afferents. In this thesis, we want to tackle the theoretical gap this poses. Specifically, we aim to address whether the peripheral nervous system relies on population coding to represent tactile information and whether such population coding enables us to disambiguate submodality convergence against the classical segregation. Approach: Understanding the encoding and flow of information in the nervous system is one of the main challenges of modern neuroscience. Neural signals are highly variable and may be non-linear. Moreover, there exist several candidate codes compatible with sensory and behavioral events. For example, they can rely on single cells or populations and also on rate or timing precision. Information-theoretic methods can capture non-linearities while being model independent, statistically robust, and mathematically well-grounded, becoming an ideal candidate to design pipelines for analyzing neural data. Despite information-theoretic methods being powerful for our objective, the vast majority of neural signals we can acquire from living systems makes analyses highly problem-specific. This is so because of the rich variety of biological processes that are involved (continuous, discrete, electrical, chemical, optical, ...). Main results: The first step towards solving the aforementioned challenges was to have a solid methodology we could trust and rely on. Consequently, the first deliverable from this thesis is a toolbox that gathers classical and state-of-the-art information-theoretic approaches and blends them with advanced machine learning tools to process and analyze neural data. Moreover, this toolbox also provides specific guidance on calcium imaging and electrophysiology analyses, encompassing both simulated and experimental data. We then designed an information-theoretic pipeline to analyze large-scale simulations of the tactile afferents that overcomes the current limitations of experimental studies in the field of touch and the peripheral nervous system. We dissected the importance of population coding for the different afferent classes, given their spatiotemporal dynamics. We also demonstrated that different afferent classes encode information simultaneously about very simple features, and that combining classes increases information levels, adding support to the submodality convergence theory. Significance: Fundamental knowledge about touch is essential both to design human-like robots exhibiting naturalistic exploration behavior and prostheses that can properly integrate and provide their user with relevant and useful information to interact with their environment. Demonstrating that the peripheral nervous system relies on heterogeneous population coding can change the designing paradigm of artificial systems, both in terms of which sensors to choose and which algorithms to use, especially in neuromorphic implementations

Functional Sensory Representations of Natural Stimuli: the Case of Spatial Hearing

In this thesis I attempt to explain mechanisms of neuronal coding in the auditory system as a form of adaptation to statistics of natural stereo sounds. To this end I analyse recordings of real-world auditory environments and construct novel statistical models of these data. I further compare regularities present in natural stimuli with known, experimentally observed neuronal mechanisms of spatial hearing. In a more general perspective, I use binaural auditory system as a starting point to consider the notion of function implemented by sensory neurons. In particular I argue for two, closely-related tenets: 1. The function of sensory neurons can not be fully elucidated without understanding statistics of natural stimuli they process. 2. Function of sensory representations is determined by redundancies present in the natural sensory environment. I present the evidence in support of the first tenet by describing and analysing marginal statistics of natural binaural sound. I compare observed, empirical distributions with knowledge from reductionist experiments. Such comparison allows to argue that the complexity of the spatial hearing task in the natural environment is much higher than analytic, physics-based predictions. I discuss the possibility that early brain stem circuits such as LSO and MSO do not \"compute sound localization\" as is often being claimed in the experimental literature. I propose that instead they perform a signal transformation, which constitutes the first step of a complex inference process. To support the second tenet I develop a hierarchical statistical model, which learns a joint sparse representation of amplitude and phase information from natural stereo sounds. I demonstrate that learned higher order features reproduce properties of auditory cortical neurons, when probed with spatial sounds. Reproduced aspects were hypothesized to be a manifestation of a fine-tuned computation specific to the sound-localization task. Here it is demonstrated that they rather reflect redundancies present in the natural stimulus. Taken together, results presented in this thesis suggest that efficient coding is a strategy useful for discovering structures (redundancies) in the input data. Their meaning has to be determined by the organism via environmental feedback

Statistical Coding and Decoding of Heartbeat Intervals

The heart integrates neuroregulatory messages into specific bands of frequency, such that the overall amplitude spectrum of the cardiac output reflects the variations of the autonomic nervous system. This modulatory mechanism seems to be well adjusted to the unpredictability of the cardiac demand, maintaining a proper cardiac regulation. A longstanding theory holds that biological organisms facing an ever-changing environment are likely to evolve adaptive mechanisms to extract essential features in order to adjust their behavior. The key question, however, has been to understand how the neural circuitry self-organizes these feature detectors to select behaviorally relevant information. Previous studies in computational perception suggest that a neural population enhances information that is important for survival by minimizing the statistical redundancy of the stimuli. Herein we investigate whether the cardiac system makes use of a redundancy reduction strategy to regulate the cardiac rhythm. Based on a network of neural filters optimized to code heartbeat intervals, we learn a population code that maximizes the information across the neural ensemble. The emerging population code displays filter tuning proprieties whose characteristics explain diverse aspects of the autonomic cardiac regulation, such as the compromise between fast and slow cardiac responses. We show that the filters yield responses that are quantitatively similar to observed heart rate responses during direct sympathetic or parasympathetic nerve stimulation. Our findings suggest that the heart decodes autonomic stimuli according to information theory principles analogous to how perceptual cues are encoded by sensory systems

Developing robust movement decoders for local field potentials

textBrain Computer Interfaces (BCI) are devices that translate acquired neural signals to command and control signals. Applications of BCI include neural rehabilitation and neural prosthesis (thought controlled wheelchair, thought controlled speller etc.) to aid patients with disabilities and to augment human computer interaction. A successful practical BCI requires a faithful acquisition modality to record high quality neural signals; a signal processing system to construct appropriate features from these signals; and an algorithm to translate these features to appropriate outputs. Intracortical recordings like local field potentials provide reliable high SNR signals over long periods and suit BCI applications well. However, the non-stationarity of neural signals poses a challenge in robust decoding of subject behavior. Most BCI research focuses either on developing daily re-calibrated decoders that require exhaustive training sessions; or on providing cross-validation results. Such results ignore the variation of signal characteristics over different sessions and provide an optimistic estimate of BCI performance. Specifically, traditional BCI algorithms fail to perform at the same level on chronological data recordings. Neural signals are susceptible to variations in signal characteristics due to changes in subject behavior and learning, and variability in electrode characteristics due to tissue interactions. While training day-specific BCI overcomes signal variability, BCI re-training causes user frustration and exhaustion. This dissertation presents contributions to solve these challenges in BCI research. Specifically, we developed decoders trained on a single recording session and applied them on subsequently recorded sessions. This strategy evaluates BCI in a practical scenario with a potential to alleviate BCI user frustration without compromising performance. The initial part of the dissertation investigates extracting features that remain robust to changes in neural signal over several days of recordings. It presents a qualitative feature extraction technique based on ranking the instantaneous power of multichannel data. These qualitative features remain robust to outliers and changes in the baseline of neural recordings, while extracting discriminative information. These features form the foundation in developing robust decoders. Next, this dissertation presents a novel algorithm based on the hypothesis that multiple neural spatial patterns describe the variation in behavior. The presented algorithm outperforms the traditional methods in decoding over chronological recordings. Adapting such a decoder over multiple recording sessions (over 6 weeks) provided > 90% accuracy in decoding eight movement directions. In comparison, performance of traditional algorithms like Common Spatial Patterns deteriorates to 16% over the same time. Over time, adaptation reinforces some spatial patterns while diminishing others. Characterizing these spatial patterns reduces model complexity without user input, while retaining the same accuracy levels. Lastly, this dissertation provides an algorithm that overcomes the variation in recording quality. Chronic electrode implantation causes changes in signal-to-noise ratio (SNR) of neural signals. Thus, some signals and their corresponding features available during training become unavailable during testing and vice-versa. The proposed algorithm uses prior knowledge on spatial pattern evolution to estimate unknown neural features. This algorithm overcomes SNR variations and provides up to 93% decoding of eight movement directions over 6 weeks. Since model training requires only one session, this strategy reduces user frustration. In a practical closed-loop BCI, the user learns to produce stable spatial patterns, which improves performance of the proposed algorithms.Electrical and Computer Engineerin

Estimating the Amount of Information Conveyed by a Population of Neurons

Recent advances in electrophysiological recording technology have allowed for the collection of data from large populations of neurons simultaneously. Yet despite these advances, methods for the estimation of the amount of information conveyed by multiple neurons have been stymied by the “curse of dimensionality”–as the number of included neurons increases, so too does the dimensionality of the data necessary for such measurements, leading to an exponential and, therefore, intractible increase in the amounts of data required for valid measurements. Here we put forth a novel method for the estimation of the amount of information transmitted by the discharge of a large population of neurons, a method which exploits the little-known fact that (under certain constraints) the Fourier coefficients of variables such as neural spike trains follow a Gaussian distribution. This fact enables an accurate measure of information even with limited data. The method, which we call the Fourier Method, is presented in detail, tested for robustness, and its application is demonstrated with both simulated and real spike trains. ii

NASA JSC neural network survey results

A survey of Artificial Neural Systems in support of NASA's (Johnson Space Center) Automatic Perception for Mission Planning and Flight Control Research Program was conducted. Several of the world's leading researchers contributed papers containing their most recent results on artificial neural systems. These papers were broken into categories and descriptive accounts of the results make up a large part of this report. Also included is material on sources of information on artificial neural systems such as books, technical reports, software tools, etc

Muscle synergies in neuroscience and robotics: from input-space to task-space perspectives

In this paper we review the works related to muscle synergies that have been carried-out in neuroscience and control engineering. In particular, we refer to the hypothesis that the central nervous system (CNS) generates desired muscle contractions by combining a small number of predefined modules, called muscle synergies. We provide an overview of the methods that have been employed to test the validity of this scheme, and we show how the concept of muscle synergy has been generalized for the control of artificial agents. The comparison between these two lines of research, in particular their different goals and approaches, is instrumental to explain the computational implications of the hypothesized modular organization. Moreover, it clarifies the importance of assessing the functional role of muscle synergies: although these basic modules are defined at the level of muscle activations (input-space), they should result in the effective accomplishment of the desired task. This requirement is not always explicitly considered in experimental neuroscience, as muscle synergies are often estimated solely by analyzing recorded muscle activities. We suggest that synergy extraction methods should explicitly take into account task execution variables, thus moving from a perspective purely based on input-space to one grounded on task-space as well