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How can neural networks be trained on large-volume temporal data efficiently? To compute the gradients required to update parameters, backpropagation blocks computations until the forward and backward passes are completed. For temporal…
Understanding how gene regulatory networks (GRNs) give rise to stable and dynamic cellular states remains a central challenge in theoretical biology, particularly when slow epigenetic feedback reshapes the underlying regulatory landscape.…
Embryonic development leads to the reproducible and ordered appearance of complexity from egg to adult. The successive differentiation of different cell types, that elaborates this complexity, result from the activity of gene networks and…
Feed-forward convolutional neural networks (CNNs) are currently state-of-the-art for object classification tasks such as ImageNet. Further, they are quantitatively accurate models of temporally-averaged responses of neurons in the primate…
We describe the construction and theoretical analysis of a framework derived from canonical neurophysiological principles that model the competing dynamics of incident signals into nodes along directed edges in a network. The framework…
In bacterial populations, cells are able to cooperate in order to yield complex collective functionalities. Interest in population-level cellular behaviour is increasing, due to both our expanding knowledge of the underlying biological…
Certain neural network architectures, in the infinite-layer limit, lead to systems of nonlinear differential equations. Motivated by this idea, we develop a framework for analyzing time signals based on non-autonomous dynamical equations.…
The level set approach represents surfaces implicitly, and advects them by evolving a level set function, which is numerically defined on an Eulerian grid. Here we present an approach that augments the level set function values by gradient…
Learning dynamical systems through purely data-driven methods is challenging as they do not learn the underlying conservation laws that enable them to correctly generalize. Existing port-Hamiltonian neural network methods have recently been…
Stochastic dynamics govern many important processes in cellular biology, and an underlying theoretical approach describing these dynamics is desirable to address a wealth of questions in biology and medicine. Mathematical tools exist for…
One of the defining features of living systems is their adaptability to changing environmental conditions. This requires organisms to extract temporal and spatial features of their environment, and use that information to compute the…
Growth patterns generated by filamentous organisms (e.g. actinomycetes and fungi) involve spatial and temporal dynamics at different length scales. Several mathematical models have been proposed in the last thirty years to address these…
Interactions between crawling cells, which are essential for many biological processes, can be quantified by measuring cell-cell collisions. Conventionally, experiments of cell-cell collisions are conducted on two-dimensional flat…
We address the challenging problem of deep representation learning--the efficient adaption of a pre-trained deep network to different tasks. Specifically, we propose to explore gradient-based features. These features are gradients of the…
Large-scale robot learning has made progress on complex manipulation tasks, yet long horizon, contact rich problems, especially those involving deformable objects, remain challenging due to inconsistent demonstration quality. We propose a…
We study the problem of sparse nonlinear model recovery of high dimensional compositional functions. Our study is motivated by emerging opportunities in neuroscience to recover fine-grained models of biological neural circuits using…
Finding an appropriate representation of dynamic activities in the brain is crucial for many downstream applications. Due to its highly dynamic nature, temporally averaged fMRI (functional magnetic resonance imaging) can only provide a…
A deep equilibrium model uses implicit layers, which are implicitly defined through an equilibrium point of an infinite sequence of computation. It avoids any explicit computation of the infinite sequence by finding an equilibrium point…
Skin dynamics contributes to the enriched realism of human body models in rendered scenes. Traditional methods rely on physics-based simulations to accurately reproduce the dynamic behavior of soft tissues. Due to the model complexity and…
Dynamics simulations of constrained particles can greatly aid in understanding the temporal and spatial evolution of biological processes such as lateral transport along membranes and self-assembly of viruses. Most theoretical efforts in…