arXiv subjects

Indika Rajapakse

Publications and source records attributed to Indika Rajapakse.

26 records · Page 2Linked to original sources

arXiv2019

Fast Incremental von Neumann Graph Entropy Computation: Theory, Algorithm, and Applications

The von Neumann graph entropy (VNGE) facilitates measurement of information divergence and distance between graphs in a graph sequence. It has been successfully applied to various learning tasks driven by network-based data. While effective, VNGE is computationally demanding as it requires the full eigenspectrum of the graph Laplacian matrix. In this paper, we propose a new computational framework, Fast Incremental von Neumann Graph EntRopy (FINGER), which approaches VNGE with a performance guarantee. FINGER reduces the cubic complexity of VNGE to linear complexity in the number of nodes and edges, and thus enables online computation based on incremental graph changes. We also show asymptotic equivalence of FINGER to the exact VNGE, and derive its approximation error bounds. Based on FINGER, we propose efficient algorithms for computing Jensen-Shannon distance between graphs. Our experimental results on different random graph models demonstrate the computational efficiency and the asymptotic equivalence of FINGER. In addition, we apply FINGER to two real-world applications and one synthesized anomaly detection dataset, and corroborate its superior performance over seven baseline graph similarity methods.

stat.ML↗

arXiv2019

Multilinear Time Invariant System Theory

In biological and engineering systems, structure, function and dynamics are highly coupled. Such interactions can be naturally and compactly captured via tensor based state space dynamic representations. However, such representations are not amenable to the standard system and controls framework which requires the state to be in the form of a vector. In order to address this limitation, recently a new class of multiway dynamical systems has been introduced in which the states, inputs and outputs are tensors. We propose a new form of multilinear time invariant (MLTI) systems based on the Einstein product and even-order paired tensors. We extend classical linear time invariant (LTI) system notions including stability, reachability and observability for the new MLTI system representation by leveraging recent advances in tensor algebra.

math.OC↗

arXiv2018

First-order bifurcation detection for dynamic complex networks

In this paper, we explore how network centrality and network entropy can be used to identify a bifurcation network event. A bifurcation often occurs when a network undergoes a qualitative change in its structure as a response to internal changes or external signals. In this paper, we show that network centrality allows us to capture important topological properties of dynamic networks. By extracting multiple centrality features from a network for dimensionality reduction, we are able to track the network dynamics underlying an intrinsic low-dimensional manifold. Moreover, we employ von Neumann graph entropy (VNGE) to measure the information divergence between networks over time. In particular, we propose an asymptotically consistent estimator of VNGE so that the cubic complexity of VNGE is reduced to quadratic complexity that scales more gracefully with network size. Finally, the effectiveness of our approaches is demonstrated through a real-life application of cyber intrusion detection.

eess.SP↗

arXiv2017

An Algorithm for Cellular Reprogramming

The day we understand the time evolution of subcellular elements at a level of detail comparable to physical systems governed by Newton's laws of motion seems far away. Even so, quantitative approaches to cellular dynamics add to our understanding of cell biology, providing data-guided frameworks that allow us to develop better predictions about and methods for control over specific biological processes and system-wide cell behavior. In this paper we describe an approach to optimizing the use of transcription factors in the context of cellular reprogramming. We construct an approximate model for the natural evolution of a synchronized population of fibroblasts, based on data obtained by sampling the expression of some 22,083 genes at several times along the cell cycle. (These data are based on a colony of cells that have been cell cycle synchronized) In order to arrive at a model of moderate complexity, we cluster gene expression based on the division of the genome into topologically associating domains (TADs) and then model the dynamics of the expression levels of the TADs. Based on this dynamical model and known bioinformatics, we develop a methodology for identifying the transcription factors that are the most likely to be effective toward a specific cellular reprogramming task. The approach used is based on a device commonly used in optimal control. From this data-guided methodology, we identify a number of validated transcription factors used in reprogramming and/or natural differentiation. Our findings highlight the immense potential of dynamical models models, mathematics, and data guided methodologies for improving methods for control over biological processes.

q-bio.GN↗

arXiv2016

Emergence of Function

This work gives a mathematical study of tissue dynamics. We combine within-cell genome dynamics and diffusion between cells, where the synthesis of the two gives rise to the emergence of function. We introduce a concept of monotonicity and prove that monotonicity together with hardwiring, defined as all cells of the same tissue having the same genome dynamics, is sufficient for the global convergence of the tissue dynamics.

q-bio.OT↗

arXiv2016

The Pitchfork Bifurcation

We give development of a new theory of the Pitchfork bifurcation, which removes the perspective of the third derivative and a requirement of symmetry.

math.DS↗

arXiv2016

Mathematics of the Genome

This work gives a mathematical foundation for bifurcation from a stable equilibrium in the genome. We construct idealized dynamics associated with the genome. For this dynamics we investigate the two main bifurcations from a stable equilibrium. Finally, we give a mathematical framework for the Repressilator and the Toggle gene circuits.

math.DS↗

arXiv2010

Structures and Assumptions: Strategies to Harness Gene $\times$ Gene and Gene $\times$ Environment Interactions in GWAS

Genome-wide association studies, in which as many as a million single nucleotide polymorphisms (SNP) are measured on several thousand samples, are quickly becoming a common type of study for identifying genetic factors associated with many phenotypes. There is a strong assumption that interactions between SNPs or genes and interactions between genes and environmental factors substantially contribute to the genetic risk of a disease. Identification of such interactions could potentially lead to increased understanding about disease mechanisms; drug $\times$ gene interactions could have profound applications for personalized medicine; strong interaction effects could be beneficial for risk prediction models. In this paper we provide an overview of different approaches to model interactions, emphasizing approaches that make specific use of the structure of genetic data, and those that make specific modeling assumptions that may (or may not) be reasonable to make. We conclude that to identify interactions it is often necessary to do some selection of SNPs, for example, based on prior hypothesis or marginal significance, but that to identify SNPs that are marginally associated with a disease it may also be useful to consider larger numbers of interactions.

stat.ME↗