arXiv subjects

Ph. Blanchard

Publications and source records attributed to Ph. Blanchard.

At least 19 recordsLinked to original sources

arXiv2020

Dynamics of contact epidemic models for finite populations

We study contact epidemic models for the spread of infective diseases in finite populations. The size dependence enters in the infection rate. The dynamics of such models is then analyzed within the deterministic approximation, as well as in terms of a stochastic formulation. At the level of the deterministic equations, we deduce relations between the parameters of the model for the disease to become endemic. Within the stochastic formulation, it is possible to write recursion relations for the probability distribution, that lead to exact expression for some of its moments and check the validity of the stochastic threshold theorems.

q-bio.PE↗

arXiv2011

Heavy-tailed Distributions In Stochastic Dynamical Models

Heavy-tailed distributions are found throughout many naturally occurring phenomena. We have reviewed the models of stochastic dynamics that lead to heavy-tailed distributions (and power law distributions, in particular) including the multiplicative noise models, the models subjected to the Degree-Mass-Action principle (the generalized preferential attachment principle), the intermittent behavior occurring in complex physical systems near a bifurcation point, queuing systems, and the models of Self-organized criticality. Heavy-tailed distributions appear in them as the emergent phenomena sensitive for coupling rules essential for the entire dynamics.

math-ph↗

arXiv2010

Random Walks Estimate Land Value

Expected urban population doubling calls for a compelling theory of the city. Random walks and diffusions defined on spatial city graphs spot hidden areas of geographical isolation in the urban landscape going downhill. First--passage time to a place correlates with assessed value of land in that. The method accounting the average number of random turns at junctions on the way to reach any particular place in the city from various starting points could be used to identify isolated neighborhoods in big cities with a complex web of roads, walkways and public transport systems.

physics.soc-ph↗

arXiv2009

Hyperbolic angular statistics for globally coupled phase oscillators

We analytically discuss a multiplicative noise generalization of the Kuramoto-Sakaguchi dynamics for an assembly of globally coupled phase oscillators. In the mean field limit, the resulting class of invariant measures coincides with a generalized, two parameter family of angular von Mises probability distributions which is governed by the exit law from the unit disc of a hyperbolic drifted Brownian motion. Our dynamics offers a simple yet analytically tractable generalization of Kuramoto-Sakaguchi dynamics with two control parameters. We derive an exact and very compact relation between the two control parameters at the onset of phase oscillators synchronization.

cond-mat.stat-mech↗

arXiv2008

Probabilistic Embedding Of Discrete Sets As Continuous Metric Spaces

Any symmetric affinity function $w: V\times V \to \mathbb{R}_+$ defined on a discrete set $V$ induces Euclidean space structure on $V$. In particular, an undirected graph specified by an affinity (or adjacency) matrix can be considered as a metric topological space. We have calculated the visual representations of the probabilistic locus for a chain, a polyhedron, and a finite 2-dimensional lattice.

math-ph↗

arXiv2008

Intelligibility and First Passage Times In Complex Urban Networks

Topology of urban environments can be represented by means of graphs. We explore the graph representations of several compact urban patterns by random walks. The expected time of recurrence and the expected first passage time to a node scales apparently linearly in all urban patterns we have studied In space syntax theory, a positive relation between the local property of a node (qualified by connectivity or by the recurrence time) and the global property of the node (estimated in our approach by the first passage time to it) is known as intelligibility. Our approach based on random walks allows to extend the notion of intelligibility onto the entire domain of complex networks and graph theory.

physics.soc-ph↗

arXiv2008

Exploring Urban Environments By Random Walks

A complex web of roads, walkways and public transport systems can hide areas of geographical isolation very difficult to analyze. Random walks are used to spot the structural details of urban fabric.

physics.soc-ph↗

arXiv2007

Scale-free Segregation in Transport Networks

Every route of a transport network approaching equilibrium can be represented by a vector of Euclidean space which length quantifies its segregation from the rest of the graph. We have empirically observed that the distribution of lengths over the edge connectivity in many transport networks exhibits scaling invariance phenomenon. We give an example of the canal network of Veneice to demonstrate our result. The method is applicable to any transport network.

physics.soc-ph↗

arXiv2007

Transport Networks Revisited: Why Dual Graphs?

Deterministic equilibrium flows in transport networks can be investigated by means of Markov's processes defined on the dual graph representations of the network. Sustained movement patterns are generated by a subset of automorphisms of the graph spanning the spatial network of a city naturally interpreted as random walks. Random walks assign absolute scores to all nodes of a graph and embed space syntax into Euclidean space.

physics.soc-ph↗

arXiv2007

Markov Chain Methods For Analyzing Complex Transport Networks

We have developed a steady state theory of complex transport networks used to model the flow of commodity, information, viruses, opinions, or traffic. Our approach is based on the use of the Markov chains defined on the graph representations of transport networks allowing for the effective network design, network performance evaluation, embedding, partitioning, and network fault tolerance analysis. Random walks embed graphs into Euclidean space in which distances and angles acquire a clear statistical interpretation. Being defined on the dual graph representations of transport networks random walks describe the equilibrium configurations of not random commodity flows on primary graphs. This theory unifies many network concepts into one framework and can also be elegantly extended to describe networks represented by directed graphs and multiple interacting networks.

physics.soc-ph↗

arXiv2007

Ghetto of Venice: Access to the Target Node and the Random Target Access Time

Random walks defined on undirected graphs assign the absolute scores to all nodes based on the quality of path they provide for random walkers. In city space syntax, the notion of segregation acquires a statistical interpretation with respect to random walks. We analyze the spatial network of Venetian canals and detect its most segregated part which can be identified with canals adjacent to the Ghetto of Venice.

physics.soc-ph↗

arXiv2007

Sestieri of Venice

We have investigated space syntax of Venice by means of random walks. Random walks being defined on an undirected graph establish the Euclidean space in which distances and angles between nodes acquire the clear statistical interpretation. The properties of nodes with respect to random walks allow partitioning the city canal network into disjoint divisions which may be identified with the traditional divisions of the city (sestieri).

physics.soc-ph↗

arXiv2007

City Space Syntax as a Complex Network

The encoding of cities into non-planar dual graphs reveals their complex structure. We investigate the statistics of the typical space syntax measures for the five different compact urban patterns. Universal statistical behavior of space syntax measures uncovers the universality of the city creation mechanism.

physics.soc-ph↗

arXiv2007

Discovering Important Nodes Through Graph Entropy Encoded in Urban Space Syntax

Potentially influential spaces in the spatial networks of cities can be detected by means of the entropy participation ratios. Local (connectivity) and global (centrality) entropies are considered. While the connectivity entropy has a tendency to increase with the city size, the centrality entropy is decreasing that reflects the global connectedness of cities. In urban networks, the local and global properties of nodes are positively correlated that indicates the intelligibility of cities. Correlations between entropy participation ratios can be used in purpose of intelligibility measurements and city networks comparisons.

physics.soc-ph↗

arXiv2007

Comparative Study of Cities as Complex Networks

Degree distributions of graph representations for compact urban patterns are scale-dependent. Therefore, the degree statistics alone does not give us the enough information to reach a qualified conclusion on the structure of urban spatial networks. We investigate the statistics of far-away neighbors and propose the new method for automatic structural classification of cities.

physics.soc-ph↗

arXiv2007

Scaling and Universality in City Space Syntax: between Zipf and Matthew

We report about universality of rank-integration distributions of open spaces in city space syntax similar to the famous rank-size distributions of cities (Zipf's law). We also demonstrate that the degree of choice an open space represents for other spaces directly linked to it in a city follows a power law statistic. Universal statistical behavior of space syntax measures uncovers the universality of the city creation mechanism. We suggest that the observed universality may help to establish the international definition of a city as a specific land use pattern.

physics.soc-ph↗

arXiv2007

Complex Networks in and beyond Physics

Physicists study a wide variety of phenomena creating new interdisciplinary research fields by applying theories and methods originally developed in physics in order to solve problems in economics, social science, biology, medicine, technology, etc. In their turn, these different branches of science inspire the invention of new concepts in physics. A basic tool of analysis, in such a context, is the mathematical theory of complexity concerned with the study of complex systems including human economies, climate, nervous systems, cells and living things, including human beings, as well as modern energy or communication infrastructures which are all networks of some kind. Recently, complexity has become a natural domain of interest of the real world socio-cognitive systems, linguistics, and emerging systemics research. The phenomena to be studied and understood arise from neither the physical laws nor the abstraction of mathematics. The challenge is to discern and formulate plausible mathematical structures to describe problems that represent vague human goals.

physics.pop-ph↗

arXiv2007

Point Interaction Hamiltonians in Bounded Domains

Making use of recent techniques in the theory of selfadjoint extensions of symmetric operators, we characterize the class of point interaction Hamiltonians in a 3-D bounded domain with regular boundary. In the particular case of one point interaction acting in the center of a ball, we obtain an explicit representation of the point spectrum of the operator togheter with the corresponding related eigenfunctions. These operators are used to build up a model-system where the dynamics of a quantum particle depends on the state of a quantum bit.

math-ph↗