Shapley Ratings in Brain Networks

Recent applications of network theory to brain networks as well as the expanding empirical databases of brain architecture spawn an interest in novel techniques for analyzing connectivity patterns in the brain. Treating individual brain structures as nodes in a directed graph model permits the application of graph theoretical concepts to the analysis of these structures within their large-scale connectivity networks. In this paper, we explore the application of concepts from graph and game theory toward this end. Specifically, we utilize the Shapley value principle, which assigns a rank to players in a coalition based upon their individual contributions to the collective profit of that coalition, to assess the contributions of individual brain structures to the graph derived from the global connectivity network. We report Shapley values for variations of a prefrontal network, as well as for a visual cortical network, which had both been extensively investigated previously. This analysis highlights particular nodes as strong or weak contributors to global connectivity. To understand the nature of their contribution, we compare the Shapley values obtained from these networks and appropriate controls to other previously described nodal measures of structural connectivity. We find a strong correlation between Shapley values and both betweenness centrality and connection density. Moreover, a stepwise multiple linear regression analysis indicates that approximately 79% of the variance in Shapley values obtained from random networks can be explained by betweenness centrality alone. Finally, we investigate the effects of local lesions on the Shapley ratings, showing that the present networks have an immense structural resistance to degradation. We discuss our results highlighting the use of such measures for characterizing the organization and functional role of brain networks

A Complete Characterization of Irreducible Cyclic Orbit Codes and their Pl\"ucker Embedding

Constant dimension codes are subsets of the finite Grassmann variety. The study of these codes is a central topic in random linear network coding theory. Orbit codes represent a subclass of constant dimension codes. They are defined as orbits of a subgroup of the general linear group on the Grassmannian. This paper gives a complete characterization of orbit codes that are generated by an irreducible cyclic group, i.e. a group having one generator that has no non-trivial invariant subspace. We show how some of the basic properties of these codes, the cardinality and the minimum distance, can be derived using the isomorphism of the vector space and the extension field. Furthermore, we investigate the Pl\"ucker embedding of these codes and show how the orbit structure is preserved in the embedding.Comment: submitted to Designs, Codes and Cryptograph

Criteria for Optimizing Cortical Hierarchies with Continuous Ranges

In a recent paper (Reid et al., 2009) we introduced a method to calculate optimal hierarchies in the visual network that utilizes continuous, rather than discrete, hierarchical levels, and permits a range of acceptable values rather than attempting to fit fixed hierarchical distances. There, to obtain a hierarchy, the sum of deviations from the constraints that define the hierarchy was minimized using linear optimization. In the short time since publication of that paper we noticed that many colleagues misinterpreted the meaning of the term “optimal hierarchy”. In particular, a majority of them were under the impression that there was perhaps only one optimal hierarchy, but a substantial difficulty in finding that one. However, there is not only more than one optimal hierarchy but also more than one option for defining optimality. Continuing the line of this work we look at additional options for optimizing the visual hierarchy: minimizing the number of violated constraints and minimizing the maximal size of a constraint violation using linear optimization and mixed integer programming. The implementation of both optimization criteria is explained in detail. In addition, using constraint sets based on the data from Felleman and Van Essen (1991), optimal hierarchies for the visual network are calculated for both optimization methods

From Functional Genomics to Functional Immunomics: New Challenges, Old Problems, Big Rewards

The development of DNA microarray technology a decade ago led to the establishment of functional genomics as one of the most active and successful scientific disciplines today. With the ongoing development of immunomic microarray technology—a spatially addressable, large-scale technology for measurement of specific immunological response—the new challenge of functional immunomics is emerging, which bears similarities to but is also significantly different from functional genomics. Immunonic data has been successfully used to identify biological markers involved in autoimmune diseases, allergies, viral infections such as human immunodeficiency virus (HIV), influenza, diabetes, and responses to cancer vaccines. This review intends to provide a coherent vision of this nascent scientific field, and speculate on future research directions. We discuss at some length issues such as epitope prediction, immunomic microarray technology and its applications, and computation and statistical challenges related to functional immunomics. Based on the recent discovery of regulation mechanisms in T cell responses, we envision the use of immunomic microarrays as a tool for advances in systems biology of cellular immune responses, by means of immunomic regulatory network models

Network Analysis: Overview

Non peer reviewe

Discovery of Novel Term Associations in a Document Collection

Non peer reviewe

(Missing) Concept Discovery in Heterogeneous Information Networks

This article proposes a new approach to extract existing (or detect missing) concepts from a loosely integrated collection of information units by means of concept graph detection. Thereby a concept graph defines a concept by a quasi bipartite sub-graph of a bigger network with the members of the concept as the first vertex partition and their shared aspects as the second vertex partition. Once the concepts have been extracted they can be used to create higher level representations of the data. Concept graphs further allow the discovery of missing concepts, which could lead to new insights by connecting seemingly unrelated information units

An Algebraic Approach for Decoding Spread Codes

In this paper we study spread codes: a family of constant-dimension codes for random linear network coding. In other words, the codewords are full-rank matrices of size (k x n) with entries in a finite field F_q. Spread codes are a family of optimal codes with maximal minimum distance. We give a minimum-distance decoding algorithm which requires O((n-k)k^3) operations over an extension field F_{q^k}. Our algorithm is more efficient than the previous ones in the literature, when the dimension k of the codewords is small with respect to n. The decoding algorithm takes advantage of the algebraic structure of the code, and it uses original results on minors of a matrix and on the factorization of polynomials over finite fields

Discovering universal statistical laws of complex networks

Different network models have been suggested for the topology underlying complex interactions in natural systems. These models are aimed at replicating specific statistical features encountered in real-world networks. However, it is rarely considered to which degree the results obtained for one particular network class can be extrapolated to real-world networks. We address this issue by comparing different classical and more recently developed network models with respect to their generalisation power, which we identify with large structural variability and absence of constraints imposed by the construction scheme. After having identified the most variable networks, we address the issue of which constraints are common to all network classes and are thus suitable candidates for being generic statistical laws of complex networks. In fact, we find that generic, not model-related dependencies between different network characteristics do exist. This allows, for instance, to infer global features from local ones using regression models trained on networks with high generalisation power. Our results confirm and extend previous findings regarding the synchronisation properties of neural networks. Our method seems especially relevant for large networks, which are difficult to map completely, like the neural networks in the brain. The structure of such large networks cannot be fully sampled with the present technology. Our approach provides a method to estimate global properties of under-sampled networks with good approximation. Finally, we demonstrate on three different data sets (C. elegans' neuronal network, R. prowazekii's metabolic network, and a network of synonyms extracted from Roget's Thesaurus) that real-world networks have statistical relations compatible with those obtained using regression models