Related papers: Probabilistic Regulatory Networks: Modeling Geneti…

In this paper we study homomorphisms of Probabilistic Regulatory Gene Networks(PRN) introduced in arXiv:math.DS/0603289 v1 13 Mar 2006. The model PRN is a natural generalization of the Probabilistic Boolean Networks (PBN), introduced by I.…

In this paper we study finite dynamical systems with $n$ functions acting on the same set $X$, and probabilities assigned to these functions, that it is called Probabilistic Regulatory Gene Networks (PRN. his concept is the same or a…

In this paper we made a review of some papers about probabilistic regulatory networks (PRN), in particular we introduce our concept of homomorphisms of PRN with an example of projection of a regulatory network to a smaller one. We apply the…

The reverse engineering problem with probabilities and sequential behavior is introducing here, using the expression of an algorithm. The solution is partially founded, because we solve the problem only if we have a Probabilistic Sequential…

Understanding the complex and stochastic nature of Gene Regulatory Networks (GRNs) remains a central challenge in systems biology. Existing modeling paradigms often struggle to effectively capture the intricate, multi-factor regulatory…

We introduce Graph-Induced Sum-Product Networks (GSPNs), a new probabilistic framework for graph representation learning that can tractably answer probabilistic queries. Inspired by the computational trees induced by vertices in the context…

Reconstruction of gene regulatory networks is the process of identifying gene dependency from gene expression profile through some computation techniques. In our human body, though all cells pose similar genetic material but the activation…

A sum-product network (SPN) is a probabilistic model, based on a rooted acyclic directed graph, in which terminal nodes represent univariate probability distributions and non-terminal nodes represent convex combinations (weighted sums) and…

In this paper, we use the framework of infinitesimal homeostasis to study general design principles for the occurrence of homeostasis in gene regulatory networks. We assume that the dynamics of the genes explicitly includes both…

Random Boolean networks (RBNs) are frequently employed for modelling complex systems driven by information processing, e.g. for gene regulatory networks (GRNs). Here we propose a hierarchical adaptive RBN (HARBN) as a system consisting of…

We consider the problem of symmetrising a neural network along a group homomorphism: given a homomorphism $\varphi : H \to G$, we would like a procedure that converts $H$-equivariant neural networks to $G$-equivariant ones. We formulate…

The projected belief network (PBN) is a layered generative network with tractable likelihood function, and is based on a feed-forward neural network (FF-NN). It can therefore share an embodiment with a discriminative classifier and can…

Connections between integration along hypersufaces, Radon transforms, and neural networks are exploited to highlight an integral geometric mathematical interpretation of neural networks. By analyzing the properties of neural networks as…

A large driver of the complexity of graph learning is the interplay between structure and features. When analyzing the expressivity of graph neural networks, however, existing approaches ignore features in favor of structure, making it…

In recent years many algorithms have been developed for finding patterns in graphs and networks. A disadvantage of these algorithms is that they use subgraph isomorphism to determine the support of a graph pattern; subgraph isomorphism is a…

Neural network design has utilized flexible nonlinear processes which can mimic biological systems, but has suffered from a lack of traceability in the resulting network. Graphical probabilistic models ground network design in probabilistic…

Hidden Markov Chains (HMC) and Recurrent Neural Networks (RNN) are two well known tools for predicting time series. Even though these solutions were developed independently in distinct communities, they share some similarities when…

Biological networks often encapsulate promotion/inhibition as signed edge-weights of a graph. Nodes may correspond to genes assigned expression levels (mass) of respective proteins. The promotion/inhibition nature of co-expression between…

Coregulation of the expression of groups of genes has been extensively demonstrated empirically in bacterial and eukaryotic systems. Such coregulation can arise through the use of shared regulatory motifs, which allow the coordinated…

Sum-product networks (SPNs) represent an emerging class of neural networks with clear probabilistic semantics and superior inference speed over graphical models. This work reveals a strikingly intimate connection between SPNs and tensor…