Related papers: A space-averaged model of branched structures
The thermodynamic, dynamic and structural behavior of a water-like system confined in a matrix is analyzed for increasing confining geometries. The liquid is modeled by a two dimensional associating lattice gas model that exhibits density…
Geometric modeling by constraints, whose applications are of interest to communities from various fields such as mechanical engineering, computer aided design, symbolic computation or molecular chemistry, is now integrated into standard…
Dissipative phenomena manifest in multiple mechanical systems. In this dissertation, different geometric frameworks for modelling non-conservative dynamics are considered. The objective is to generalize several results from conservative…
Complex networks describe a wide range of systems in nature and society, much quoted examples including the cell, a network of chemicals linked by chemical reactions, or the Internet, a network of routers and computers connected by physical…
Tree-ordered weakly sparse models have recently emerged as a robust framework for representing structures in an ``almost sparse'' way, while allowing the structure to be reconstructed through a simple first-order interpretation. A prominent…
Models for the dynamics of congestion control generally involve systems of coupled differential equations. Universally, these models assume that traffic sources saturate the maximum transmissions allowed by the congestion control method.…
The goal of these lectures is to review some mathematical aspects of random tree models used in evolutionary biology to model gene trees or species trees. We start with stochastic models of tree shapes (finite trees without edge lengths),…
Gromov hyperbolicity of a metric space measures the distance of the space from a perfect tree-like structure. The measure has a "worst-case" aspect to it, in the sense that it detects a region in the space which sees the maximum deviation…
We present a unified framework for embedding and analyzing dynamical systems using generalized projection operators rooted in local conservation laws. By representing physical, biological, and engineered systems as graphs with incidence and…
We introduce a biologically natural, mathematically tractable model of random phylogenetic network to describe evolution in the presence of hybridization. One of the features of this model is that the hybridization rate of the lineages…
We propose a model for the growth of weighted networks that couples the establishment of new edges and vertices and the weights' dynamical evolution. The model is based on a simple weight-driven dynamics and generates networks exhibiting…
We define and study complex structures and generalizations on spaces consisting of geodesics or harmonic maps that are compatible with the symmetries of these spaces. The main results are about existence and uniqueness of such structures.
Many physical systems are well described on domains which are relatively large in some directions but relatively thin in other directions. In this scenario we typically expect the system to have emergent structures that vary slowly over the…
The behavior of annealed branched polymers near adsorbing surfaces plays a fundamental role in many biological and industrial processes. Most importantly single stranded RNA in solution tends to fold up and self-bind to form a highly…
We study the compression of bundles of aligned macroscopic fibers with intrinsic shape disorder, as found in human hair and in many other natural and man-made systems. We show by a combination of experiments, numerical simulations and…
Spatio-temporal processes in environmental applications are often assumed to follow a Gaussian model, possibly after some transformation. However, heterogeneity in space and time might have a pattern that will not be accommodated by…
Vertical profiles for mean wind, standard deviations of velocity fluctuations, and wave-induced part of the momentum flux over a wavy fluid surface are calculated in the Cartesian coordinates on the basis of recent numerical results by…
We consider a model of Internet congestion control that represents the randomly varying number of flows present in a network where bandwidth is shared fairly between document transfers. We study critical fluid models obtained as formal…
We investigate the role of generalized symmetries in driving non-equilibrium and non-linear phenomena, specifically focusing on turbulent systems. While conventional turbulence studies have revealed inverse cascades driven by conserved…
We derive a composite centrality measure for general weighted and directed complex networks, based on measure standardisation and invariant statistical inheritance schemes. Different schemes generate different intermediate abstract measures…