arXiv subjects

Indika Rajapakse

Publications and source records attributed to Indika Rajapakse.

At least 19 recordsLinked to original sources

arXiv2026

Global analysis of the Kuramoto flow

Kuramoto's differential equation describes a synchronization process between several harmonic oscillators. It has been used to model biological phenomena such as the synchronization of heart cells, the circadian rhythm, or brain waves. It is also used in power system control. The simplest possible model assumes that all oscillators are identical and connected to each other with equal pairwise attraction. In this paper, we give a full geometric description of its global dynamics in terms of Morse theory and dynamical systems. Most of this description is stable in the sense that it is topologically preserved under small perturbations of the parameters.

math.DS↗

arXiv2025

Dynamic Sensor Selection for Biomarker Discovery

Advances in methods of biological data collection are driving the rapid growth of comprehensive datasets across clinical and research settings. These datasets provide the opportunity to monitor biological systems in greater depth and at finer time steps than was achievable in the past. Classically, biomarkers are used to represent and track key aspects of a biological system. Biomarkers retain utility even with the availability of large datasets, since monitoring and interpreting changes in a vast number of molecules remains impractical. However, given the large number of molecules in these datasets, a major challenge is identifying the best biomarkers for a particular setting Here, we apply principles of observability theory to establish a general methodology for biomarker selection. We demonstrate that observability measures effectively identify biologically meaningful sensors in a range of time series transcriptomics data. Motivated by the practical considerations of biological systems, we introduce the method of dynamic sensor selection (DSS) to maximize observability over time, thus enabling observability over regimes where system dynamics themselves are subject to change. This observability framework is flexible, capable of modeling gene expression dynamics and using auxiliary data, including chromosome conformation, to select biomarkers. Additionally, we demonstrate the applicability of this approach beyond genomics by evaluating the observability of neural activity These applications demonstrate the utility of observability-guided biomarker selection for across a wide range of biological systems, from agriculture and biomanufacturing to neural applications and beyond.

q-bio.MN↗

arXiv2024

Language Model Powered Digital Biology with BRAD

Recent advancements in Large Language Models (LLMs) are transforming biology, computer science, engineering, and every day life. However, integrating the wide array of computational tools, databases, and scientific literature continues to pose a challenge to biological research. LLMs are well-suited for unstructured integration, efficient information retrieval, and automating standard workflows and actions from these diverse resources. To harness these capabilities in bioinformatics, we present a prototype Bioinformatics Retrieval Augmented Digital assistant (BRAD). BRAD is a chatbot and agentic system that integrates a variety of bioinformatics tools. The Python package implements an AI \texttt{Agent} that is powered by LLMs and connects to a local file system, online databases, and a user's software. The \texttt{Agent} is highly configurable, enabling tasks such as Retrieval-Augmented Generation, searches across bioinformatics databases, and the execution of software pipelines. BRAD's coordinated integration of bioinformatics tools delivers a context-aware and semi-autonomous system that extends beyond the capabilities of conventional LLM-based chatbots. A graphical user interface (GUI) provides an intuitive interface to the system.

cs.AI↗

arXiv2024

Geometric Aspects of Observability of Hypergraphs

In this paper we consider aspects of geometric observability for hypergraphs, extending our earlier work from the uniform to the nonuniform case. Hypergraphs, a generalization of graphs, allow hyperedges to connect multiple nodes and unambiguously represent multi-way relationships which are ubiquitous in many real-world networks including those that arise in biology. We consider polynomial dynamical systems with linear outputs defined according to hypergraph structure, and we propose methods to evaluate local, weak observability.

math.DS↗

arXiv2024

Kronecker Product of Tensors and Hypergraphs: Structure and Dynamics

Hypergraphs and tensors extend classic graph and matrix theory to account for multiway relationships, which are ubiquitous in engineering, biological, and social systems. While the Kronecker product is a potent tool for analyzing the coupling of systems in graph or matrix contexts, its effectiveness in capturing multiway interactions remains elusive. In this article, we present a comprehensive exploration of algebraic, structural, and spectral properties of the tensor Kronecker product. We express Tucker and tensor train decompositions and various tensor eigenvalues in terms of the tensor Kronecker product. Additionally, we utilize the tensor Kronecker product to form Kronecker hypergraphs, a tensor-based hypergraph product, and investigate the structure and stability of polynomial dynamics on Kronecker hypergraphs. Finally, we provide numerical examples to demonstrate the utility of the tensor Kronecker product in computing Z-eigenvectors, various tensor decompositions, and determining the stability of polynomial systems.

math.DS↗

arXiv2023

Observability of Hypergraphs

In this paper we develop a framework to study observability for uniform hypergraphs. Hypergraphs, being extensions of graphs, allow edges to connect multiple nodes and unambiguously represent multi-way relationships which are ubiquitous in many real-world networks. We extend the canonical homogeneous polynomial or multilinear dynamical system on uniform hypergraphs to include linear outputs, and we derive a Kalman-rank-like condition for assessing the local weak observability. We propose an exact techniques for determining the local observability criterion, and we propose a greedy heuristic to determine the minimum set of observable nodes. Numerical experiments demonstrate our approach on several hypergraph topologies and a hypergraph representations of neural networks within the mouse hypothalamus.

math.DS↗

arXiv2022

Hypergraph Analysis Toolbox for Chromosome Conformation

Recent advances in biological technologies, such as multi-way chromosome conformation capture (3C), require development of methods for analysis of multi-way interactions. Hypergraphs are mathematically tractable objects that can be utilized to precisely represent and analyze multi-way interactions. Here we present the Hypergraph Analysis Toolbox (HAT), a software package for visualization and analysis of multi-way interactions in complex systems.

q-bio.QM↗

arXiv2022

ASK: Adversarial Soft k-Nearest Neighbor Attack and Defense

K-Nearest Neighbor (kNN)-based deep learning methods have been applied to many applications due to their simplicity and geometric interpretability. However, the robustness of kNN-based classification models has not been thoroughly explored and kNN attack strategies are underdeveloped. In this paper, we propose an Adversarial Soft kNN (ASK) loss to both design more effective kNN attack strategies and to develop better defenses against them. Our ASK loss approach has two advantages. First, ASK loss can better approximate the kNN's probability of classification error than objectives proposed in previous works. Second, the ASK loss is interpretable: it preserves the mutual information between the perturbed input and the in-class-reference data. We use the ASK loss to generate a novel attack method called the ASK-Attack (ASK-Atk), which shows superior attack efficiency and accuracy degradation relative to previous kNN attacks. Based on the ASK-Atk, we then derive an ASK-\underline{Def}ense (ASK-Def) method that optimizes the worst-case training loss induced by ASK-Atk. Experiments on CIFAR-10 (ImageNet) show that (i) ASK-Atk achieves $\geq 13\%$ ($\geq 13\%$) improvement in attack success rate over previous kNN attacks, and (ii) ASK-Def outperforms the conventional adversarial training method by $\geq 6.9\%$ ($\geq 3.5\%$) in terms of robustness improvement.

cs.LG↗

arXiv2022

RAILS: A Robust Adversarial Immune-inspired Learning System

Adversarial attacks against deep neural networks (DNNs) are continuously evolving, requiring increasingly powerful defense strategies. We develop a novel adversarial defense framework inspired by the adaptive immune system: the Robust Adversarial Immune-inspired Learning System (RAILS). Initializing a population of exemplars that is balanced across classes, RAILS starts from a uniform label distribution that encourages diversity and uses an evolutionary optimization process to adaptively adjust the predictive label distribution in a manner that emulates the way the natural immune system recognizes novel pathogens. RAILS' evolutionary optimization process explicitly captures the tradeoff between robustness (diversity) and accuracy (specificity) of the network, and represents a new immune-inspired perspective on adversarial learning. The benefits of RAILS are empirically demonstrated under eight types of adversarial attacks on a DNN adversarial image classifier for several benchmark datasets, including: MNIST; SVHN; CIFAR-10; and CIFAR-10. We find that PGD is the most damaging attack strategy and that for this attack RAILS is significantly more robust than other methods, achieving improvements in adversarial robustness by $\geq 5.62\%, 12.5\%$, $10.32\%$, and $8.39\%$, on these respective datasets, without appreciable loss of classification accuracy. Codes for the results in this paper are available at https://github.com/wangren09/RAILS.

cs.NE↗

arXiv2021

Immuno-mimetic Deep Neural Networks (Immuno-Net)

Biomimetics has played a key role in the evolution of artificial neural networks. Thus far, in silico metaphors have been dominated by concepts from neuroscience and cognitive psychology. In this paper we introduce a different type of biomimetic model, one that borrows concepts from the immune system, for designing robust deep neural networks. This immuno-mimetic model leads to a new computational biology framework for robustification of deep neural networks against adversarial attacks. Within this Immuno-Net framework we define a robust adaptive immune-inspired learning system (Immuno-Net RAILS) that emulates, in silico, the adaptive biological mechanisms of B-cells that are used to defend a mammalian host against pathogenic attacks. When applied to image classification tasks on benchmark datasets, we demonstrate that Immuno-net RAILS results in improvement of as much as 12.5% in adversarial accuracy of a baseline method, the DkNN-robustified CNN, without appreciable loss of accuracy on clean data.

cs.NE↗

arXiv2021

Understanding Memory B Cell Selection

The mammalian adaptive immune system has evolved over millions of years to become an incredibly effective defense against foreign antigens. The adaptive immune system's humoral response creates plasma B cells and memory B cells, each with their own immunological objectives. The affinity maturation process is widely viewed as a heuristic to solve the global optimization problem of finding B cells with high affinity to the antigen. However, memory B cells appear to be purposely selected earlier in the affinity maturation process and have lower affinity. We propose that this memory B cell selection process may be an approximate solution to two optimization problems: optimizing for affinity to similar antigens in the future despite mutations or other minor differences, and optimizing to warm start the generation of plasma B cells in the future. We use simulations to provide evidence for our hypotheses, taking into account data showing that certain B cell mutations are more likely than others. Our findings are consistent with memory B cells having high-affinity to mutated antigens, but do not provide strong evidence that memory B cells will be more useful than selected naive B cells for seeding the secondary germinal centers.

q-bio.CB↗

arXiv2021

Hypergraph Dissimilarity Measures

In this paper, we propose two novel approaches for hypergraph comparison. The first approach transforms the hypergraph into a graph representation for use of standard graph dissimilarity measures. The second approach exploits the mathematics of tensors to intrinsically capture multi-way relations. For each approach, we present measures that assess hypergraph dissimilarity at a specific scale or provide a more holistic multi-scale comparison. We test these measures on synthetic hypergraphs and apply them to biological datasets.

cs.LG↗

arXiv2021

Controllability of Hypergraphs

In this paper, we develop a notion of controllability for hypergraphs via tensor algebra and polynomial control theory. Inspired by uniform hypergraphs, we propose a new tensor-based multilinear dynamical system representation, and derive a Kalman-rank-like condition to determine the minimum number of control nodes (MCN) needed to achieve controllability of even uniform hypergraphs. We present an efficient heuristic to obtain the MCN. MCN can be used as a measure of robustness, and we show that it is related to the hypergraph degree distribution in simulated examples. Finally, we use MCN to examine robustness in real biological networks.

math.OC↗

arXiv2020

RAILS: A Robust Adversarial Immune-inspired Learning System

Adversarial attacks against deep neural networks are continuously evolving. Without effective defenses, they can lead to catastrophic failure. The long-standing and arguably most powerful natural defense system is the mammalian immune system, which has successfully defended against attacks by novel pathogens for millions of years. In this paper, we propose a new adversarial defense framework, called the Robust Adversarial Immune-inspired Learning System (RAILS). RAILS incorporates an Adaptive Immune System Emulation (AISE), which emulates in silico the biological mechanisms that are used to defend the host against attacks by pathogens. We use RAILS to harden Deep k-Nearest Neighbor (DkNN) architectures against evasion attacks. Evolutionary programming is used to simulate processes in the natural immune system: B-cell flocking, clonal expansion, and affinity maturation. We show that the RAILS learning curve exhibits similar diversity-selection learning phases as observed in our in vitro biological experiments. When applied to adversarial image classification on three different datasets, RAILS delivers an additional 5.62%/12.56%/4.74% robustness improvement as compared to applying DkNN alone, without appreciable loss of accuracy on clean data.

cs.LG↗

arXiv2020

Multilinear Control Systems Theory

In this paper, we provide a system theoretic treatment of a new class of multilinear time-invariant (MLTI) systems in which the states, inputs and outputs are tensors, and the system evolution is governed by multilinear operators. The MLTI system representation is based on the Einstein product and even-order paired tensors. There is a particular tensor unfolding which gives rise to an isomorphism from this tensor space to the general linear group, i.e. the group of invertible matrices. By leveraging this unfolding operation, one can extend classical linear time-invariant (LTI) system notions including stability, reachability and observability to MLTI systems. While the unfolding based formulation is a powerful theoretical construct, the computational advantages of MLTI systems can only be fully realized while working with the tensor form, where hidden patterns/structures can be exploited for efficient representations and computations. Along these lines, we establish new results which enable one to express tensor unfolding based stability, reachability and observability criteria in terms of more standard notions of tensor ranks/decompositions. In addition, we develop a generalized CANDECOMP/PARAFAC decomposition and tensor train decomposition based model reduction framework, which can significantly reduce the number of MLTI system parameters. We demonstrate our framework with numerical examples.

math.OC↗

arXiv2020

Tensor Entropy for Uniform Hypergraphs

In this paper, we develop the notion of entropy for uniform hypergraphs via tensor theory. We employ the probability distribution of the generalized singular values, calculated from the higher-order singular value decomposition of the Laplacian tensors, to fit into the Shannon entropy formula. We show that this tensor entropy is an extension of von Neumann entropy for graphs. In addition, we establish results on the lower and upper bounds of the entropy and demonstrate that it is a measure of regularity for uniform hypergraphs in simulated and experimental data. We exploit the tensor train decomposition in computing the proposed tensor entropy efficiently. Finally, we introduce the notion of robustness for uniform hypergraphs.

cs.LG↗

arXiv2020

Data-Driven Model Reduction for Multilinear Control Systems via Tensor Trains

In this paper, we explore the role of tensor algebra in balanced truncation (BT) based model reduction/identification for high-dimensional multilinear/linear time invariant systems. In particular, we employ tensor train decomposition (TTD), which provides a good compromise between numerical stability and level of compression, and has an associated algebra that facilitates computations. Using TTD, we propose a new BT approach which we refer to as higher-order balanced truncation, and consider different data-driven variations including higher-order empirical gramians, higher-order balanced proper orthogonal decomposition and a higher-order eigensystem realization algorithm. We perform computational and memory complexity analysis for these different flavors of TTD based BT methods, and compare with the corresponding standard BT methods in order to develop insights into where the proposed framework may be beneficial. We provide numerical results on simulated and experimental datasets showing the efficacy of the proposed framework.

eess.SY↗

arXiv2019

Latent heterogeneous multilayer community detection

We propose a method for simultaneously detecting shared and unshared communities in heterogeneous multilayer weighted and undirected networks. The multilayer network is assumed to follow a generative probabilistic model that takes into account the similarities and dissimilarities between the communities. We make use of a variational Bayes approach for jointly inferring the shared and unshared hidden communities from multilayer network observations. We show that our approach outperforms state-of-the-art algorithms in detecting disparate (shared and private) communities on synthetic data as well as on real genome-wide fibroblast proliferation dataset.

cs.SI↗