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Single-Cell-Based Analysis Highlights a Surge in Cell-to-Cell Molecular Variability Preceding Irreversible Commitment in a Differentiation Process
In some recent studies, a view emerged that stochastic dynamics governing the switching of cells from one differentiation state to another could be characterized by a peak in gene expressionExpand
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Inferring gene regulatory networks from single-cell data: a mechanistic approach
TLDR
In this paper, we introduce a general stochastic model for gene regulatory networks, which can describe bursty gene expression as observed in individual cells. Expand
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Estimating the transition matrix of a Markov chain observed at random times
In this paper we develop a statistical estimation technique to recover the transition kernel $P$ of a Markov chain $X=(X_m)_{m \in \mathbb N}$ in presence of censored data. We consider the situationExpand
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A Coupling of the Spectral Measures at a Vertex
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We prove an extension of Obata's Central Limit Theorem in growing star-graphs to the multivariate case and discuss some combinatorial properties using Viennot's heaps of pieces point of view. Expand
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A Combinatorial Approach to a Model of Constrained Random Walkers
TLDR
We study an extended version of this model by conditioning the extremal coordinates to be at some fixed distance at every time. Expand
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Reconstructing undirected graphs from eigenspaces
TLDR
In this paper, we aim at recovering an undirected weighted graph of $N$ vertices from the knowledge of a perturbed version of the eigenspaces of its adjacency matrix $W$. Expand
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Relations Between Connected and Self-Avoiding Hikes in Labelled Complete Digraphs
TLDR
We construct a collection of polynomials of W whose entries enumerate the self-avoiding hikes of a given length from one vertex to another. Expand
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REDUCTION OF A STOCHASTIC MODEL OF GENE EXPRESSION: LAGRANGIAN DYNAMICS GIVES ACCESS TO BASINS OF ATTRACTION AS CELL TYPES AND METASTABILTY
Differentiation is the process whereby a cell acquires a specific phenotype, by differential gene expression as a function of time. This is thought to result from the dynamical functioning of anExpand
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Polynomial regression under shape constraints
Calculating regression under shape constraints is a problem addressed by statisticians since long. This paper shows how to calculate a polynomial regression of any degree and of any number ofExpand
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Relations between connected and self-avoiding walks in a digraph
Walks in a directed graph can be given a partially ordered structure that extends to possibly unconnected objects, called hikes. Studying the incidence algebra on this poset reveals unsuspectedExpand
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