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Since the discovery of the presence of biogenic magnetites in living organisms, there have been speculations on the role that these biomagnetites play in cellular processes. It seems that the formation of biomagnetite crystals is a…
We give a criterion which allows to determine, in terms of the combinatorics of the root system of the general linear group, which p-kernels occur in an isogeny class of p-divisible groups over an algebraically closed field of positive…
The dynamics of recombination in genetics leads to an interesting nonlinear differential equation, which has a natural generalization to a measure valued version. The latter can be solved explicitly under rather general circumstances. It…
We present a modelling framework for the dynamics of cells structured by the concentration of a micromolecule they contain. We derive general equations for the evolution of the cell population and of the extra-cellular concentration of the…
In the paper we obtain an existence criterion for Hall subgroups of finite groups in terms of a composition series.
We investigate the problem of deciding whether a system of linear equations, together with divisibility conditions on the variables, has a solution over holomorphy subrings of global fields. We obtain decidability results when we allow…
Reliability on complex biological networks reconstructions remains a concern. Although observations are getting more and more precise, the data collection process is yet error prone and the proofs display uneven certitude. In the case of…
We prove the main rules of causal calculus (also called do-calculus) for i/o structural causal models (ioSCMs), a generalization of a recently proposed general class of non-/linear structural causal models that allow for cycles, latent…
We introduce a generalized concept of solutions for reaction-diffusion systems and prove their global existence. The only restriction on the reaction function beyond regularity, quasipositivity and mass control is special in that it merely…
Some of the centrality experiments indicate regime change and saturation in the behaviour of characteristics of the secondary particles produced in relativistic nuclear interactions. We discuss that the responsible mechanism to explain the…
We study the ability to maintain information in a population of reacting polymers under the influence of decay, i.e., spontaneous breakdown of large polymers. At a certain decay rate, it becomes impossible to maintain a significant…
We improve a recent result by giving the optimal conclusion possible both to the frequent universality criterion and the frequent hypercyclicity criterion using the notion of A-densities, where A refers to some weighted densities sharper…
We present an algorithm to decide whether a given ideal in the polynomial ring contains a monomial without using Gr\"obner bases, factorization or sub-resultant computations.
Many cellular processes require a polarization axis which generally initially emerges as an inhomogeneous distribution of molecular markers in the cell. We present a simple analytical model of a general mechanism of cell polarization taking…
The T-cell (TCR) repertoire relies on the diversity of receptors composed of two chains, called $\alpha$ and $\beta$, to recognize pathogens. Using results of high throughput sequencing and computational chain-pairing experiments of human…
Reversibility of the Fleming-Viot process with mutation, selection, and recombination is well understood. In this paper, we study the reversibility of a system of Fleming-Viot processes that live on a countable number of colonies…
We review the theory of regenerative processes, which are processes that can be intuitively seen as comprising of i.i.d.\ cycles. Although we focus on the classical definition, we present a more general definition that allows for some form…
We prove that the set of limit groups is recursive, answering a question of Delzant. One ingredient of the proof is the observation that a finitely presented group with local retractions (a la Long and Reid) is coherent and, furthermore,…
One of the main goals of Artificial Life is to research the conditions for the emergence of life, not necessarily as it is, but as it could be. Artificial Chemistries are one of the most important tools for this purpose because they provide…
Define the non-overlapping return time of a random process to be the number of blocks that we wait before a particular block reappears. We prove a Central Limit Theorem based on these return times. This result has applications to entropy…