Related papers: Hierarchical p-Adic Framework for Gene Regulatory …
The functioning of a living cell is largely determined by the structure of its regulatory network, comprising non-linear interactions between regulatory genes. An important factor for the stability and evolvability of such regulatory…
Existing machine learning frameworks operate over the field of real numbers ($\mathbb{R}$) and learn representations in real (Euclidean or Hilbert) vector spaces (e.g., $\mathbb{R}^d$). Their underlying geometric properties align well with…
We rigorously study the thermodynamic limit of deep neural networks (DNNS) and recurrent neural networks (RNNs), assuming that the activation functions are sigmoids. A thermodynamic limit is a continuous neural network, where the neurons…
We prove that nested canalizing functions are the minimum-sensitivity Boolean functions for any activity ratio and we determine the functional form of this boundary which has a nontrivial fractal structure. We further observe that the…
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…
Modeling gene regulatory networks (GRNs) is an important topic in systems biology. Although there has been much work focusing on various specific systems, the generic behavior of GRNs with continuous variables is still elusive. In…
We define a natural notion of higher order stability and show that subsets of $\mathbb{F}_p^n$ that are tame in this sense can be approximately described by a union of low-complexity quadratic varieties, up to linear error. This generalizes…
Complex dynamical systems are often modeled as networks, with nodes representing dynamical units which interact through the network's links. Gene regulatory networks, responsible for the production of proteins inside a cell, are an example…
Developing and maintaining life requires a lot of computation. This is done by gene regulatory networks. But we have little understanding of how this computation is organized. I show that there is a direct correspondence between the…
Functional networks provide a topological description of activity patterns in the brain, as they stem from the propagation of neural activity on the underlying anatomical or structural network of synaptic connections. This latter is well…
Robustness to mutations and noise has been shown to evolve through stabilizing selection for optimal phenotypes in model gene regulatory networks. The ability to evolve robust mutants is known to depend on the network architecture. How do…
Based on a non-equilibrium mechanism for spatial pattern formation we study how position information can be controlled by locally coupled discrete dynamical networks, similar to gene regulation networks of cells in a developing…
The hierarchical organisation of cell identity is a fundamental feature of animal development with rich and well-characterized experimental phenomenology, yet the mechanisms driving its emergence remain unknown. The regulation of cell…
We introduce simple models of genetic regulatory networks and we proceed to the mathematical analysis of their dynamics. The models are discrete time dynamical systems generated by piecewise affine contracting mappings whose variables…
We develop a geometric framework to study the structure and function of complex networks. We assume that hyperbolic geometry underlies these networks, and we show that with this assumption, heterogeneous degree distributions and strong…
The connection between network topology and stability remains unclear. General approaches that clarify this relationship and allow for more efficient stability analysis would be desirable. Inspired by chemical reaction networks, I…
The structure of interactions in most of animals and human societies can be best represented by complex hierarchical networks. In order to maintain close to optimal functioning both stability and adaptability are necessary. Here we…
The relationship between network topology and system dynamics has significant implications for unifying our understanding of the interplay among metabolic, gene-regulatory, and ecosystem network architecures. Here we analyze the stability…
We study a genetic regulatory network model developed to demonstrate that genetic robustness can evolve through stabilizing selection for optimal phenotypes. We report preliminary results on whether such selection could result in a…
Random boolean networks are a model of genetic regulatory networks that has proven able to describe experimental data in biology. They not only reproduce important phenomena in cell dynamics, but they are also extremely interesting from a…