Minimum Number of Probes for Brain Dynamics Observability

In this paper, we address the problem of placing sensor probes in the brain such that the system dynamics' are generically observable. The system dynamics whose states can encode for instance the fire-rating of the neurons or their ensemble following a neural-topological (structural) approach, and the sensors are assumed to be dedicated, i.e., can only measure a state at each time. Even though the mathematical description of brain dynamics is (yet) to be discovered, we build on its observed fractal characteristics and assume that the model of the brain activity satisfies fractional-order dynamics. Although the sensor placement explored in this paper is particularly considering the observability of brain dynamics, the proposed methodology applies to any fractional-order linear system. Thus, the main contribution of this paper is to show how to place the minimum number of dedicated sensors, i.e., sensors measuring only a state variable, to ensure generic observability in discrete-time fractional-order systems for a specified finite interval of time. Finally, an illustrative example of the main results is provided using electroencephalogram (EEG) data.Comment: arXiv admin note: text overlap with arXiv:1507.0720

An Ontology-Based Recommender System with an Application to the Star Trek Television Franchise

Collaborative filtering based recommender systems have proven to be extremely successful in settings where user preference data on items is abundant. However, collaborative filtering algorithms are hindered by their weakness against the item cold-start problem and general lack of interpretability. Ontology-based recommender systems exploit hierarchical organizations of users and items to enhance browsing, recommendation, and profile construction. While ontology-based approaches address the shortcomings of their collaborative filtering counterparts, ontological organizations of items can be difficult to obtain for items that mostly belong to the same category (e.g., television series episodes). In this paper, we present an ontology-based recommender system that integrates the knowledge represented in a large ontology of literary themes to produce fiction content recommendations. The main novelty of this work is an ontology-based method for computing similarities between items and its integration with the classical Item-KNN (K-nearest neighbors) algorithm. As a study case, we evaluated the proposed method against other approaches by performing the classical rating prediction task on a collection of Star Trek television series episodes in an item cold-start scenario. This transverse evaluation provides insights into the utility of different information resources and methods for the initial stages of recommender system development. We found our proposed method to be a convenient alternative to collaborative filtering approaches for collections of mostly similar items, particularly when other content-based approaches are not applicable or otherwise unavailable. Aside from the new methods, this paper contributes a testbed for future research and an online framework to collaboratively extend the ontology of literary themes to cover other narrative content.Comment: 25 pages, 6 figures, 5 tables, minor revision

On the Limited Communication Analysis and Design for Decentralized Estimation

This paper pertains to the analysis and design of decentralized estimation schemes that make use of limited communication. Briefly, these schemes equip the sensors with scalar states that iteratively merge the measurements and the state of other sensors to be used for state estimation. Contrarily to commonly used distributed estimation schemes, the only information being exchanged are scalars, there is only one common time-scale for communication and estimation, and the retrieval of the state of the system and sensors is achieved in finite-time. We extend previous work to a more general setup and provide necessary and sufficient conditions required for the communication between the sensors that enable the use of limited communication decentralized estimation~schemes. Additionally, we discuss the cases where the sensors are memoryless, and where the sensors might not have the capacity to discern the contributions of other sensors. Based on these conditions and the fact that communication channels incur a cost, we cast the problem of finding the minimum cost communication graph that enables limited communication decentralized estimation schemes as an integer programming problem.Comment: Updates on the paper in CDC 201

Decentralized Observability with Limited Communication between Sensors

In this paper, we study the problem of jointly retrieving the state of a dynamical system, as well as the state of the sensors deployed to estimate it. We assume that the sensors possess a simple computational unit that is capable of performing simple operations, such as retaining the current state and model of the system in its memory. We assume the system to be observable (given all the measurements of the sensors), and we ask whether each sub-collection of sensors can retrieve the state of the underlying physical system, as well as the state of the remaining sensors. To this end, we consider communication between neighboring sensors, whose adjacency is captured by a communication graph. We then propose a linear update strategy that encodes the sensor measurements as states in an augmented state space, with which we provide the solution to the problem of retrieving the system and sensor states. The present paper contains three main contributions. First, we provide necessary and sufficient conditions to ensure observability of the system and sensor states from any sensor. Second, we address the problem of adding communication between sensors when the necessary and sufficient conditions are not satisfied, and devise a strategy to this end. Third, we extend the former case to include different costs of communication between sensors. Finally, the concepts defined and the method proposed are used to assess the state of an example of approximate structural brain dynamics through linearized measurements.Comment: 15 pages, 5 figures, extended version of paper accepted at IEEE Conference on Decision and Control 201

Static Output Feedback: On Essential Feasible Information Patterns

In this paper, for linear time-invariant plants, where a collection of possible inputs and outputs are known a priori, we address the problem of determining the communication between outputs and inputs, i.e., information patterns, such that desired control objectives of the closed-loop system (for instance, stabilizability) through static output feedback may be ensured. We address this problem in the structural system theoretic context. To this end, given a specified structural pattern (locations of zeros/non-zeros) of the plant matrices, we introduce the concept of essential information patterns, i.e., communication patterns between outputs and inputs that satisfy the following conditions: (i) ensure arbitrary spectrum assignment of the closed-loop system, using static output feedback constrained to the information pattern, for almost all possible plant instances with the specified structural pattern; and (ii) any communication failure precludes the resulting information pattern from attaining the pole placement objective in (i). Subsequently, we study the problem of determining essential information patterns. First, we provide several necessary and sufficient conditions to verify whether a specified information pattern is essential or not. Further, we show that such conditions can be verified by resorting to algorithms with polynomial complexity (in the dimensions of the state, input and output). Although such verification can be performed efficiently, it is shown that the problem of determining essential information patterns is in general NP-hard. The main results of the paper are illustrated through examples