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- Peter A. Robinson, Somwrita Sarkar, Grishma Mehta Pandejee, James Andrew Henderson
- Physical review. E, Statistical, nonlinear, and…
- 2014

Neural field theory insights are used to derive effective brain connectivity matrices from the functional connectivity matrix defined by activity covariances. The symmetric case is exactly solved for a resting state system driven by white noise, in which strengths of connections, often termed effective connectivities, are inferred from functional data;… (More)

This paper presents an approach to making design optimization tools more useful to designers. Design optimization is the selection of the best design solution from alternative solutions to a given problem. Design optimization tools require that all the variables, parameters, goals and constraints be defined prior to the execution of any optimization… (More)

- Somwrita Sarkar, James Andrew Henderson, Peter A. Robinson
- PloS one
- 2013

Many real world networks are reported to have hierarchically modular organization. However, there exists no algorithm-independent metric to characterize hierarchical modularity in a complex system. The main results of the paper are a set of methods to address this problem. First, classical results from random matrix theory are used to derive the spectrum of… (More)

- Somwrita Sarkar, Andy Dong
- Physical review. E, Statistical, nonlinear, and…
- 2011

A spectral algorithm for community detection is presented. The algorithm consists of three stages: (1) matrix factorization of two matrix forms, square signless Laplacian for unipartite graphs and rectangular adjacency matrix for bipartite graphs, using singular value decompostion (SVD); (2) dimensionality reduction using an optimal linear approximation;… (More)

This paper presents a design optimization problem reformulation method based on Singular Value Decomposition (SVD), dimensionality reduction, and unsupervised clustering. The method calculates linear approximations of the associative patterns of symbol co-occurrences in a design problem representation to infer induced interaction/coupling strengths between… (More)

This paper presents a knowledge-lean learning and inference mechanism based on Singular Value Decomposition (SVD) for design optimization problem (re)-formulation at the problem modeling stage. The distinguishing feature of the mechanism is that it requires very few training cases to extract and generalize knowledge for large classes of problems sharing… (More)

- Peter A. Robinson, X. Zhao, Kevin M. Aquino, J. D. Griffiths, Somwrita Sarkar, Grishma Mehta-Pandejee
- NeuroImage
- 2016

Neural field theory of the corticothalamic system is applied to predict and analyze the activity eigenmodes of the bihemispheric brain, focusing particularly on their spatial structure. The eigenmodes of a single brain hemisphere are found to be close analogs of spherical harmonics, which are the natural modes of the sphere. Instead of multiple eigenvalues… (More)

The anatomical structure of the brain can be observed via non-invasive techniques such as diffusion imaging. However, these are imperfect because they miss connections that are actually known to exist, especially long range interhemispheric ones. In this paper we formulate the inverse problem of inferring the structural connectivity of brain networks from… (More)

This paper presents a learning and inference mechanism for unsupervised learning of semantic concepts from purely syntactical examples of design optimization formulation data. Symbolic design formulation is a tough problem from computational and cognitive perspectives, requiring domain and mathematical expertise. By conceptualizing the learning problem as a… (More)

- Grishma Mehta-Pandejee, Peter A. Robinson, James Andrew Henderson, Kevin M. Aquino, Somwrita Sarkar
- Journal of neuroscience methods
- 2017

BACKGROUND
The problem of inferring effective brain connectivity from functional connectivity is under active investigation, and connectivity via multistep paths is poorly understood.
NEW METHOD
A method is presented to calculate the direct effective connection matrix (deCM), which embodies direct connection strengths between brain regions, from… (More)