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We consider the following \emph{model repair problem}: given a finite Kripke structure $M$ and a specification formula $\eta$ in some modal or temporal logic, determine if $M$ contains a substructure $M'$ (with the same initial state) that…
Cells and microorganisms employ dynamic shape changes to enable steering and avoidance for efficient spatial exploration and collective organization. In contrast, active colloids, their synthetic counterparts, currently lack similar…
As for other latent-variable problems, exact Bayesian analysis is typically not practicable for mixture problems and approximate methods have been developed. Variational Bayes tends to produce approximate posterior distributions for…
In this thesis we present few theoretical studies of the models of self-organized criticality. Following a brief introduction of self-organized criticality, we discuss three main problems. The first problem is about growing patterns formed…
A critical issue in the evolution of software models is change propagation: given a primary change that is made to a model in order to meet a new or changed requirement, what additional secondary changes are needed to maintain consistency…
We generalize the well-studied notion of a modular pair of a finite matroid to arbitrary families of sets in infinite matroids, and use it to develop the theory of infinite matroids in several as-yet-unexplored areas. Our results include a…
Many complex systems have been shown to share universal properties of organization, such as scale independence, modularity and self-similarity. We borrow tools from statistical physics in order to study structural preferential attachment…
Non-linear gravitational collapse introduces non-Gaussian statistics into the matter fields of the late Universe. As the large-scale structure is the target of current and future observational campaigns, one would ideally like to have the…
The origin of macroscopic complexity is traced in a wide range of systems (imunology, ecology, finance, marketing, etc) to the discrete and auto-catalytic (i.e. multiplicative) character of their elementary components. Even in the simplest…
We introduce various models for cellulose bio-degradation by micro-organisms. Those models rely on complex chemical mechanisms, involve the structure of the cellulose chains and are allowed to depend on the phenotypical traits of the…
The frozen-perigee behavior of elliptic orbits at the critical inclination is usually displayed after an averaging procedure. However, this singularity in Artificial Satellite Theory manifests also in the presence of short-period effects.…
The cortical microtubule array of dark-grown hypocotyl cells of plant seedlings undergoes a striking, and developmentally significant, reorientation upon exposure to light. This process is driven by the exponential amplification of a…
The lace expansion has been a powerful tool for investigating mean-field behavior for various stochastic-geometrical models, such as self-avoiding walk and percolation, above their respective upper-critical dimension. In this paper, we…
The martingale expansion provides a refined approximation to the marginal distributions of martingales beyond the normal approximation implied by the martingale central limit theorem. We develop a martingale expansion framework specifically…
The state of many physical, biological and socio-technical systems evolves by combining smooth local transitions and abrupt resetting events to a set of reference values. The inclusion of the resetting mechanism not only provides the…
The nuclear many-body problem for medium-mass systems is commonly addressed using wave-function expansion methods that build upon a second-quantized representation of many-body operators with respect to a chosen computational basis. While…
In this work we approach cell migration under a large-scale assumption, so that the system reduces to a particle in motion. Unlike classical particle models, the cell displacement results from its internal activity: the cell velocity is a…
A new class of probabilistic models for cascading failure propagation in interconnected systems is proposed. The models take into account important characteristics of real systems that are not considered in existing generic approaches.…
Growth and folding in one-layered model tissue sheets are studied in a stochastic, lattice-free single cell model which considers the discrete cellular structure of the tissue, and a coarse grained analytical approach. The polarity of the…
Any optical structure possesses resonance modes and its response to an excitation can be decomposed onto the quasinormal and numerical modes of discretized Maxwell's operator. In this paper, we consider a dielectric permittivity that is a…