50 citations · 265 across the 22 of their papers we have counts for
25 papers
Global analysis of the Kuramoto flow
Daniel Burns, Gregorio Malajovich, Charles Pugh +2
Kuramoto's differential equation describes a synchronization process between several harmonic oscillators. It has been used to model biological phenomena such as the synchronizatio…
Language Model Powered Digital Biology with BRAD
Joshua Pickard, Ram Prakash, Marc Andrew Choi +6
Recent advancements in Large Language Models (LLMs) are transforming biology, computer science, engineering, and every day life. However, integrating the wide array of computationa…
Geometric Aspects of Observability of Hypergraphs
Joshua Pickard, Cooper Stansbury, Amit Surana +2
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 g…
Kronecker Product of Tensors and Hypergraphs: Structure and Dynamics
Joshua Pickard, Can Chen, Cooper Stansbury +3
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…
Observability of Hypergraphs
Joshua Pickard, Amit Surana, Anthony Bloch +1
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 unambiguousl…
Hypergraph Analysis Toolbox for Chromosome Conformation
Joshua Pickard, Can Chen, Rahmy Salman +5
Recent advances in biological technologies, such as multi-way chromosome conformation capture (3C), require development of methods for analysis of multi-way interactions. Hypergrap…
RAILS: A Robust Adversarial Immune-inspired Learning System
Ren Wang, Tianqi Chen, Stephen Lindsly +4
Adversarial attacks against deep neural networks (DNNs) are continuously evolving, requiring increasingly powerful defense strategies. We develop a novel adversarial defense framew…
Immuno-mimetic Deep Neural Networks (Immuno-Net)
Ren Wang, Tianqi Chen, Stephen Lindsly +3
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 psyc…
Hypergraph Dissimilarity Measures
Amit Surana, Can Chen, Indika Rajapakse
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 dissimi…
ASK: Adversarial Soft k-Nearest Neighbor Attack and Defense
Ren Wang, Tianqi Chen, Philip Yao +3
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-b…
RAILS: A Robust Adversarial Immune-inspired Learning System
Ren Wang, Tianqi Chen, Stephen Lindsly +3
Adversarial attacks against deep neural networks are continuously evolving. Without effective defenses, they can lead to catastrophic failure. The long-standing and arguably most p…
Understanding Memory B Cell Selection
Stephen Lindsly, Maya Gupta, Cooper Stansbury +1
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 res…
Controllability of Hypergraphs
Can Chen, Amit Surana, Anthony Bloch +1
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-bas…
Data-Driven Model Reduction for Multilinear Control Systems via Tensor Trains
Can Chen, Amit Surana, Anthony Bloch +1
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…
Tensor Entropy for Uniform Hypergraphs
Can Chen, Indika Rajapakse
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 fro…
Multilinear Time Invariant System Theory
Can Chen, Amit Surana, Anthony Bloch +1
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 d…
Multilinear Control Systems Theory
Can Chen, Amit Surana, Anthony Bloch +1
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 syst…
Latent heterogeneous multilayer community detection
Hafiz Tiomoko Ali, Sijia Liu, Yasin Yilmaz +3
We propose a method for simultaneously detecting shared and unshared communities in heterogeneous multilayer weighted and undirected networks. The multilayer network is assumed to…
Fast Incremental von Neumann Graph Entropy Computation: Theory, Algorithm, and Applications
Pin-Yu Chen, Lingfei Wu, Sijia Liu +1
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…
First-order bifurcation detection for dynamic complex networks
Sijia Liu, Pin-Yu Chen, Indika Rajapakse +1
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 qual…
An Algorithm for Cellular Reprogramming
Scott Ronquist, Geoff Patterson, Markus Brown +5
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, qu…
Emergence of Function
Indika Rajapakse, Steve Smale
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 emerge…
The Pitchfork Bifurcation
Indika Rajapakse, Steve Smale
We give development of a new theory of the Pitchfork bifurcation, which removes the perspective of the third derivative and a requirement of symmetry.
Mathematics of the Genome
Indika Rajapakse, Steve Smale
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…