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The Helmholtz-Hodge decomposition (HHD) is applied to the construction of Lyapunov functions. It is shown that if a stability condition is satisfied, such a decomposition can be chosen so that its potential function is a Lyapunov function.…
To celebrate Hans Frauenfelder's achievements, we examine energy(-like) "landscapes" for complex living systems. Energy landscapes summarize all possible dynamics of some physical systems. Energy(-like) landscapes can explain some…
The morphogenesis of cells and tissues involves an interplay between chemical signals and active forces on their surrounding surface layers. The complex interaction of hydrodynamics and material flows on such active surfaces leads to…
We study topological and geometric properties of a cell growth process in the Euclidean plane, where the cells are regular pentagons. To explore the aesthetic aspects of this model, we employ a laser cutter on various materials to create…
Automatic cell detection in histology images is a challenging task due to varying size, shape and features of cells and stain variations across a large cohort. Conventional deep learning methods regress the probability of each pixel…
DNA-based storage offers unprecedented density and durability, but its scalability is fundamentally limited by the efficiency of parallel strand synthesis. Existing methods either allow unconstrained nucleotide additions to individual…
We present EPR-Net, a novel and effective deep learning approach that tackles a crucial challenge in biophysics: constructing potential landscapes for high-dimensional non-equilibrium steady-state (NESS) systems. EPR-Net leverages a nice…
Designing complex physical systems, including photonic structures, is typically a tedious trial-and-error process that requires extensive simulations with iterative sweeps in multi-dimensional parameter space. To circumvent this…
This chapter will provide an overview of how characterizing free-energy landscapes can provide insights into the biophysical properties of DNA, as well as into the behaviour of the DNA assemblies used in the field of DNA nanotechnology. The…
Solving the wave equation is one of the most (if not the most) fundamental problems we face as we try to illuminate the Earth using recorded seismic data. The Helmholtz equation provides wavefield solutions that are dimensionally reduced,…
A general theoretical framework is put forth to organize and understand various observed phenomena and mathematical relationships in the field of molecular biology. By modeling each cell in eukaryotic organisms as a processor having a…
We introduce a coarse-grained rigid nucleotide model of DNA that reproduces the basic thermodynamics of short strands: duplex hybridization, single-stranded stacking and hairpin formation, and also captures the essential structural…
We introduce a new neural architecture and an unsupervised algorithm for learning invariant representations from temporal sequence of images. The system uses two groups of complex cells whose outputs are combined multiplicatively: one that…
Generative modeling of three-dimensional (3D) molecules is a fundamental yet challenging problem in drug discovery and materials science. Existing approaches typically represent molecules as 3D graphs and co-generate discrete atom types…
The RNA inverse folding problem, a key challenge in RNA design, involves identifying nucleotide sequences that can fold into desired secondary structures, which are critical for ensuring molecular stability and function. The inherent…
The tempo and mode of an adaptive process is strongly determined by the structure of the fitness landscape that underlies it. In order to be able to predict evolutionary outcomes (even on the short term), we must know more about the nature…
Wetlands are important to communities, offering benefits ranging from water purification, and flood protection to recreation and tourism. Therefore, identifying and prioritizing potential wetland areas is a critical decision problem. While…
We devise a theoretical framework and a numerical method to infer trajectories of a stochastic process from samples of its temporal marginals. This problem arises in the analysis of single cell RNA-sequencing data, which provide high…
Evolvability refers to the ability of an individual genotype (solution) to produce offspring with mutually diverse phenotypes. Recent research has demonstrated that divergent search methods, particularly novelty search, promote evolvability…
This paper describes an Artificial Embryology method (called ``Epigenetic Tracking'') to generate predefined arbitrarily shaped 2-dimensional arrays of cells by means of evolutionary techniques. It is based on a model of development, whose…