Biomedical subjects

Zoltán Toroczkai

Publications and source records attributed to Zoltán Toroczkai.

10 recordsLinked to original sources

PubMed2006

Congestion-gradient driven transport on complex networks.

We present a study of transport on complex networks with routing based on local information. Particles hop from one node of the network to another according to a set of routing rules with different degrees of congestion awareness, ranging from random diffusion to rigid congestion-gradient driven flow. Each node can be either source or destination for particles and all nodes have the same routing capacity, which are features of ad hoc wireless networks. It is shown that the transport capacity increases when a small amount of congestion awareness is present in the routing rules, and that it then decreases as the routing rules become too rigid when the flow becomes strictly congestion-gradient driven. Therefore, an optimum value of the congestion awareness exists in the routing rules. It is also shown that, in the limit of a large number of nodes, networks using routing based on local information jam at any nonzero load. Finally, we study the correlation between congestion at node level and a betweenness centrality measure.

Journal Article↗

PubMed2004

Modelling disease outbreaks in realistic urban social networks.

Most mathematical models for the spread of disease use differential equations based on uniform mixing assumptions or ad hoc models for the contact process. Here we explore the use of dynamic bipartite graphs to model the physical contact patterns that result from movements of individuals between specific locations. The graphs are generated by large-scale individual-based urban traffic simulations built on actual census, land-use and population-mobility data. We find that the contact network among people is a strongly connected small-world-like graph with a well-defined scale for the degree distribution. However, the locations graph is scale-free, which allows highly efficient outbreak detection by placing sensors in the hubs of the locations network. Within this large-scale simulation framework, we then analyse the relative merits of several proposed mitigation strategies for smallpox spread. Our results suggest that outbreaks can be contained by a strategy of targeted vaccination combined with early detection without resorting to mass vaccination of a population.

Contact Tracing↗

PubMed2004

Network dynamics: jamming is limited in scale-free systems.

A large number of complex networks are scale-free--that is, they follow a power-law degree distribution. Here we propose that the emergence of many scale-free networks is tied to the efficiency of transport and flow processing across these structures. In particular, we show that for large networks on which flows are influenced or generated by gradients of a scalar distributed on the nodes, scale-free structures will ensure efficient processing, whereas structures that are not scale-free, such as random graphs, will become congested.

Journal Article↗

PubMed2004

Competition-driven network dynamics: emergence of a scale-free leadership structure and collective efficiency.

Using the minority game as a model for competition dynamics, we investigate the effects of interagent communications across a network on the global evolution of the game. Agent communication across this network leads to the formation of an influence network, which is dynamically coupled to the evolution of the game, and it is responsible for the information flow driving the agents' actions. We show that the influence network spontaneously develops hubs with a broad distribution of in-degrees, defining a scale-free robust leadership structure. Furthermore, in realistic parameter ranges, facilitated by information exchange on the network, agents can generate a high degree of cooperation making the collective almost maximally efficient.

Competitive Behavior↗

PubMed2004

Universality in active chaos.

Many examples of chemical and biological processes take place in large-scale environmental flows. Such flows generate filamental patterns which are often fractal due to the presence of chaos in the underlying advection dynamics. In such processes, hydrodynamical stirring strongly couples into the reactivity of the advected species and might thus make the traditional treatment of the problem through partial differential equations difficult. Here we present a simple approach for the activity in inhomogeneously stirred flows. We show that the fractal patterns serving as skeletons and catalysts lead to a rate equation with a universal form that is independent of the flow, of the particle properties, and of the details of the active process. One aspect of the universality of our approach is that it also applies to reactions among particles of finite size (so-called inertial particles).

Computer Simulation↗

PubMed2003

Advection of finite-size particles in open flows.

It is known that small, spherical particles with inertia do not follow the local velocity field of the flow. Here we investigate the motion of such particles and particle ensembles immersed in open, unsteady flows which, in the case of ideal pointlike tracers, generate chaotic Lagrangian trajectories. Due to the extra force terms in the equations of motion (such as Stokes drag, added mass) the inertial tracer trajectories become described by a high-dimensional (2d+1, with d being the flow's dimension) chaotic dynamics, which can drastically differ from the (d+1)-dimensional ideal tracer dynamics. As a consequence, we find parameter regimes (in terms of density and size), where long-term tracer trapping can occur for the inertial particle, even for flows in which no ideal, pointlike passive tracers can be trapped. These studies are performed in a model of a two-dimensional channel flow past a cylindrical obstacle. Since the Lagrangian tracer dynamics is sensitive to the particle density and size parameters, a simple geometric setup in such flows could be used as a (low-density) particle mixture segregator.

Journal Article↗

PubMed2003

Competing populations in flows with chaotic mixing.

We investigate the effects of spatial heterogeneity on the coexistence of competing species in the case when the heterogeneity is dynamically generated by environmental flows with chaotic mixing properties. We show that one effect of chaotic advection on the passively advected species (such as phytoplankton, or self-replicating macro-molecules) is the possibility of coexistence of more species than that limited by the number of niches they occupy. We derive a novel set of dynamical equations for competing populations.

Competitive Behavior↗

PubMed2003

Spatial models of prebiotic evolution: soup before pizza?

The problem of information integration and resistance to the invasion of parasitic mutants in prebiotic replicator systems is a notorious issue of research on the origin of life. Almost all theoretical studies published so far have demonstrated that some kind of spatial structure is indispensable for the persistence and/or the parasite resistance of any feasible replicator system. Based on a detailed critical survey of spatial models on prebiotic information integration, we suggest a possible scenario for replicator system evolution leading to the emergence of the first protocells capable of independent life. We show that even the spatial versions of the hypercycle model are vulnerable to selfish parasites in heterogeneous habitats. Contrary, the metabolic system remains persistent and coexistent with its parasites both on heterogeneous surfaces and in chaotically mixing flowing media. Persistent metabolic parasites can be converted to metabolic cooperators, or they can gradually obtain replicase activity. Our simulations show that, once replicase activity emerged, a gradual and simultaneous evolutionary improvement of replicase functionality (speed and fidelity) and template efficiency is possible only on a surface that constrains the mobility of macromolecule replicators. Based on the results of the models reviewed, we suggest that open chaotic flows ('soup') and surface dynamics ('pizza') both played key roles in the sequence of evolutionary events ultimately concluding in the appearance of the first living cell on Earth.

Animals↗

PubMed2002

Finite-size effects on active chaotic advection.

A small (but finite-size) spherical particle advected by fluid flows obeys equations of motion that are inherently dissipative, due to the Stokes drag. The dynamics of the advected particle can be chaotic even with a flow field that is simply time periodic. Similar to the case of ideal tracers, whose dynamics is Hamiltonian, chemical or biological activity involving such particles can be analyzed using the theory of chaotic dynamics. Using the example of an autocatalytic reaction, A+Bright arrow2B, we show that the balance between dissipation in the particle dynamics and production due to reaction leads to a steady state distribution of the reagent. We also show that, in the case of coalescence reaction, B+Bright arrowB, the decay of the particle density obeys a universal scaling law as approximately t(minus sign1) and that the particle distribution becomes restricted to a subset with fractal dimension D2, where D2 is the correlation dimension of the chaotic attractor in the particle dynamics.

Journal Article↗

PubMed2001

Topological classification of binary trees using the Horton-Strahler index.

The Horton-Strahler (HS) index r=max(i,j)+delta(i,j) has been shown to be relevant to a number of physical (such as diffusion limited aggregation) geological (river networks), biological (pulmonary arteries, blood vessels, various species of trees), and computational (use of registers) applications. Here we revisit the enumeration problem of the HS index on the rooted, unlabeled, plane binary set of trees, and enumerate the same index on the ambilateral set of rooted, plane binary set of trees of n leaves. The ambilateral set is a set of trees whose elements cannot be obtained from each other via an arbitrary number of reflections with respect to vertical axes passing through any of the nodes on the tree. For the unlabeled set we give an alternate derivation to the existing exact solution. Extending this technique for the ambilateral set, which is described by an infinite series of nonlinear functional equations, we are able to give a double exponentially converging approximant to the generating functions in a neighborhood of their convergence circle, and derive an explicit asymptotic form for the number of such trees.

Journal Article↗