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Understanding the emergence of biological structures and their changes is a complex problem. On a biochemical level, it is based on gene regulatory networks (GRN) consisting on interactions between the genes responsible for cell…
Energy landscape theory describes how a full-length protein can attain its native fold after sampling only a tiny fraction of all possible structures. Although protein folding is now understood to be concomitant with synthesis on the…
Epigenetics is most often reduced to chromatin marking in the current literature, whereas this notion was initially defined in a more general context. This restricted view ignores that epigenetic memories are in fact more robustly ensured…
DNA hairpin molecules with periodic base sequences can be expected to exhibit a regular coarse-grained free energy landscape (FEL) as function of the number of open base pairs and applied mechanical force. Using a commonly employed model,…
We view the folding of RNA-sequences as a map that assigns a pattern of base pairings to each sequence, known as secondary structure. These preimages can be constructed as random graphs (i.e. the neutral networks associated to the structure…
In the context of intra-cluster medium turbulence, it is essential to be able to split the turbulent velocity field in a compressive and a solenoidal component. We describe and implement a new method for this aim, i.e., performing a…
We present a phase-field model based on the Cahn-Hilliard equation to investigate the properties of phase separation in DNA nanostar systems. Leveraging a realistic free-energy functional derived from Wertheim theory, our model captures the…
Single-cell trajectory analysis aims to reconstruct the biological developmental processes of cells as they evolve over time, leveraging temporal correlations in gene expression. During cellular development, gene expression patterns…
Describing the complex landscape of infinite-dimensional free energy is generally a challenging problem. This difficulty arises from the existence of numerous minimizers and, consequently, a vast number of saddle points. These factors make…
This paper introduces a novel method to extend the Helmholtz Decomposition to n-dimensional sufficiently smooth and fast decaying vector fields. The rotation is described by a superposition of n(n-1)/2 rotations within the coordinate…
We present a novel diffusion-based framework for synthesizing 2D vector fields from sparse, coherent inputs (i.e., streamlines) while maintaining physical plausibility. Our method employs a conditional denoising diffusion probabilistic…
The paper aims at proposing an efficient and stable quasi-interpolation based method for numerically computing the Helmholtz-Hodge decomposition of a vector field. To this end, we first explicitly construct a matrix kernel in a general form…
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.…
In single-cell research, tracing and analyzing high-throughput single-cell differentiation trajectories is crucial for understanding biological processes. Key to this is the robust modeling of hierarchical structures that govern cellular…
Cells can often choose among several stably heritable phenotypes. Examples are the expression of genes in eukaryotic cells where long chromosomal regions can adopt persistent and heritable silenced or active states, that may be associated…
Constructing cell developmental trajectories is a critical task in single-cell RNA sequencing (scRNA-seq) analysis, enabling the inference of potential cellular progression paths. However, current automated methods are limited to…
In this paper, we consider a tree inference problem motivated by the critical problem in single-cell genomics of reconstructing dynamic cellular processes from sequencing data. In particular, given a population of cells sampled from such a…
Trajectory inference is a critical problem in single-cell transcriptomics, which aims to reconstruct the dynamic process underlying a population of cells from sequencing data. Of particular interest is the reconstruction of differentiation…
Many dynamical systems can be described in terms of structured flows combining source/sink behavior, cyclic dynamics, and topology-constrained transport. These features arise across a wide range of domains, including physical, engineered,…
Neural shape representation generally refers to representing 3D geometry using neural networks, e.g., computing a signed distance or occupancy value at a specific spatial position. In this paper we present a neural-network architecture…