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The Log-Gaussian Cox Process is a commonly used model for the analysis of spatial point patterns. Fitting this model is difficult because of its doubly-stochastic property, i.e., it is an hierarchical combination of a Poisson process at the…
Traditionally evolution is seen as a process where from a pool of possible variations of a population (e.g. biological species or industrial goods) a few variations get selected which survive and proliferate, whereas the others vanish.…
We introduce a new approach to constructing analytic solutions of the linear PDEs describing elastodynamics. This approach is illustrated for the case of a homogeneous isotropic half-plane body satisfying arbitrary initial conditions and…
We propose a stochastic model for evolution through mutation and natural selection of a population that evolves on a $\bbT_d^+$ tree. We think of this model as a way of describing the evolution fitness landscape of a population. We obtain…
We study an individual-based model in which two spatially-distributed species, characterized by different diffusivities, compete for resources. We consider three different ecological settings. In the first, diffusing faster has a cost in…
The theory of evolution states that the diversity of species can be explained by descent with modification. Therefore, all living beings are related through a common ancestor. This evolutionary process must have left traces in our molecular…
In a convergence of machine learning and biology, we reveal that diffusion models are evolutionary algorithms. By considering evolution as a denoising process and reversed evolution as diffusion, we mathematically demonstrate that diffusion…
Despite recent molecular technique improvements, biological knowledge remains incomplete. Reasoning on living systems hence implies to integrate heterogeneous and partial informations. Although current investigations successfully focus on…
We introduce a model for stochastic transport on a one-dimensional substrate with particles assuming different conformations during their stepping cycles. These conformations correspond to different footprints on the substrate: in order to…
The theory of lithopanspermia proposes the natural exchange of organisms between solar system bodies through meteorites. The focus of this theory comprises three distinct stages: planetary ejection, interplanetary transit and planetary…
In this paper for the first time, we construct quantum analogs starting from classical stochastic processes, by replacing random which path decisions with superpositions of all paths. This procedure typically leads to non-unitary quantum…
Many theories of physical interest, which admit a Hamiltonian description, exhibit symmetries under a particular class of non - strictly canonical transformation, known as dynamical similarities. The presence of such symmetries allows a…
We use topological data analysis and machine learning to study a seminal model of collective motion in biology [D'Orsogna et al., Phys. Rev. Lett. 96 (2006)]. This model describes agents interacting nonlinearly via attractive-repulsive…
The theory of slow manifolds is an important tool in the study of deterministic dynamical systems, giving a practical method by which to reduce the number of relevant degrees of freedom in a model, thereby often resulting in a considerable…
The co-optimization of a robot's body and brain presents a coupled challenge: the morphology constrains which control strategies are effective, while the control determines how well the morphology performs. To address this, we combine…
Phylogenetic networks extend phylogenetic trees to allow for modeling reticulate evolutionary processes such as hybridization. They take the shape of a rooted, directed, acyclic graph, and when parameterized with evolutionary parameters,…
This paper demonstrates that simple yet important characteristics of coevolution can occur in evolutionary algorithms when only a few conditions are met. We find that interaction-based fitness measurements such as fitness (linear) ranking…
Stochastic systems characterised by a random driving in a form of the general stable noise are considered. The particle experiences long rests due to the traps the density of which is position-dependent and obeys a power-law form attributed…
The value of unknown parameters of multibody systems is crucial for prediction, monitoring, and control, sometimes estimated using a biased physics-based model leading to incorrect outcomes. Discovering motion equations of multibody systems…
Several numerical approximation strategies for the expectation-propagation algorithm are studied in the context of large-scale learning: the Laplace method, a faster variant of it, Gaussian quadrature, and a deterministic version of…