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One of the most interesting scientific challenges nowadays deals with the analysis and the understanding of complex networks' dynamics. A major issue is the definition of new frameworks for the exploration of the dynamics at play in real…
We propose a novel approach to continuum modeling of the dynamics of crystal surfaces. Our model follows the evolution of an ensemble of step configurations, which are consistent with the macroscopic surface profile. Contrary to the usual…
Lineage tracing, the determination and mapping of progeny arising from single cells, is an important approach enabling the elucidation of mechanisms underlying diverse biological processes ranging from development to disease. We developed a…
The myriad microscopic interactions among the individual organisms that constitute an ecological system collectively give rise, at the macroscopic scale, to evolutionary trends. The ability to detect the directionality of such trends is…
The observed architecture of ecological and socio-economic networks differs significantly from that of random networks. From a network science standpoint, non-random structural patterns observed in real networks call for an explanation of…
Evolution has fascinated quantitative and physical scientists for decades: how can the random process of mutation, recombination, and duplication of genetic information generate the diversity of life? What determines the rate of evolution?…
In many practical applications of clustering, the objects to be clustered evolve over time, and a clustering result is desired at each time step. In such applications, evolutionary clustering typically outperforms traditional static…
Measuring gene expression simultaneously in both hosts and symbionts offers a powerful approach to explore the biology underlying species interactions. Such dual or simultaneous RNAseq approaches have primarily been used to gain insight…
The main topic of this thesis is the analysis of evolution equations reflecting issues in ecology and population dynamics. In mathematical modelling, the impact of environmental elements and the interaction between species is read into the…
Lurking is a complex user-behavioral phenomenon that occurs in all large-scale online communities and social networks. It generally refers to the behavior characterizing users that benefit from the information produced by others in the…
The problem of predicting the growth of a system of cracks, each crack influencing the growth of the others, arises in multiple fields. We develop an analytical framework toward this aim, which we apply to the `En-Passant' family of crack…
Artificial intelligence methods are being increasingly applied across various domains, but their often opaque nature has raised concerns about accountability and trust. In response, the field of explainable AI (XAI) has emerged to address…
Multiscale phenomena that evolve on multiple distinct timescales are prevalent throughout the sciences. It is often the case that the governing equations of the persistent and approximately periodic fast scales are prescribed, while the…
We consider the evolution of populations under the joint action of mutation and differential reproduction, or selection. The population is modelled as a finite-type Markov branching process in continuous time, and the associated…
One of the first successes of neutral ecology was to predict realistically-broad distributions of rare and abundant species. However, it has remained an outstanding theoretical challenge to describe how this distribution of abundances…
Determining the trajectories of cells and their lineages or ancestries in live-cell experiments are fundamental to the understanding of how cells behave and divide. This paper proposes novel online algorithms for jointly tracking and…
Most research on predicting community evolution focuses on changes in the states of communities. Instead, we focus on individual nodes and define the novel problem of predicting whether a specific node stays in the same cluster, moves to…
Bayesian hierarchical modeling is a natural framework to effectively integrate data and borrow information across groups. In this paper, we address problems related to density estimation and identifying clusters across related groups, by…
The last decades have not only been characterized by an explosive growth of data, but also an increasing appreciation of data as a valuable resource. Their value comes with the ability to extract meaningful patterns that are of economic,…
We are interested in the evolving genealogy of a birth and death process with trait structure and ecological interactions. Traits are hereditarily transmitted from a parent to its offspring unless a mutation occurs. The dynamics may depend…