Panos Argyrakis

Stability and Topology of Scale-Free Networks under Attack and Defense Strategies

We study tolerance and topology of random scale-free networks under attack and defense strategies that depend on the degree k of the nodes. This situation occurs, for example, when the robustness of a node depends on its degree or in an intentional attack with insufficient knowledge of the network. We determine, for all strategies, the critical fraction p(c) of nodes that must be removed for disintegrating the network. We find that, for an intentional attack, little knowledge of the well-connected sites is sufficient to strongly reduce p(c). At criticality, the topology of the network depends on the removal strategy, implying that different strategies may lead to different kinds of percolation transitions.

A Reappraisal of Drug Release Laws Using Monte Carlo Simulations: The Prevalence of the Weibull Function

AbstractPurpose. To verify the Higuchi law and study the drug release from cylindrical and spherical matrices by means of Monte Carlo computer simulation. Methods. A one-dimensional matrix, based on the theoretical assumptions of the derivation of the Higuchi law, was simulated and its time evolution was monitored. Cylindrical and spherical three-dimensional lattices were simulated with sites at the boundary of the lattice having been denoted as leak sites. Particles were allowed to move inside it using the random walk model. Excluded volume interactions between the particles was assumed. We have monitored the system time evolution for different lattice sizes and different initial particle concentrations. Results. The Higuchi law was verified using the Monte Carlo technique in a one-dimensional lattice. It was found that Fickian drug release from cylindrical matrices can be approximated nicely with the Weibull function. A simple linear relation between the Weibull function parameters and the specific surface of the system was found. Conclusions. Drug release from a matrix, as a result of a diffusion process assuming excluded volume interactions between the drug molecules, can be described using a Weibull function. This model, although approximate and semiempirical, has the benefit of providing a simple physical connection between the model parameters and the system geometry, which was something missing from other semiempirical models.

Improving immunization strategies.

We introduce an immunization method where the percentage of required vaccinations for immunity are close to the optimal value of a targeted immunization scheme of highest degree nodes. Our strategy retains the advantage of being purely local, without the need for knowledge on the global network structure or identification of the highest degree nodes. The method consists of selecting a random node and asking for a neighbor that has more links than himself or more than a given threshold and immunizing him. We compare this method to other efficient strategies on three real social networks and on a scale-free network model and find it to be significantly more effective.

Fractal kinetics in drug release from finite fractal matrices

We have re-examined the random release of particles from fractal polymer matrices using Monte Carlo simulations, a problem originally studied by Bunde et al. [J. Chem. Phys. 83, 5909 (1985)]. A certain population of particles diffuses on a fractal structure, and as particles reach the boundaries of the structure they are removed from the system. We find that the number of particles that escape from the matrix as a function of time can be approximated by a Weibull (stretched exponential) function, similar to the case of release from Euclidean matrices. The earlier result that fractal release rates are described by power laws is correct only at the initial stage of the release, but it has to be modified if one is to describe in one picture the entire process for a finite system. These results pertain to the release of drugs, chemicals, agrochemicals, etc., from delivery systems.

Spectroscopic studies of ArF laser photoablation of PMMA

A Spectroscopic study has been made of the emission spectra arising from ArF laser initiated photoablation of PMMA samples. This process leads to direct etching of the polymer. The thermal temperature of the CH fragment species in the plume immediately above the ablated site was found to be ∼ 3200 ±200 K. The translational velocity of this species was found to be ∼4.2×105 cm/s corresponding to a translational temperature of ∼ 11,000 K. These results are consistent with a rapid direct bond scission model for ablation.

Gastrointestinal Drug Absorption: Is It Time to Consider Heterogeneity as Well as Homogeneity?

The current analysis of gastrointestinal absorption phenomena relies on the concept of homogeneity. However, drug dissolution, transit and uptake in the gastrointestinal tract are heterogeneous processes since they take place at interfaces of different phases under variable stirring conditions. Recent advances in physics and chemistry demonstrate that the geometry of the environment is of major importance for the treatment of heterogeneous processes. In this context, the heterogeneous character of in vivo drug dissolution, transit and uptake is discussed in terms of fractal concepts. Based on this analysis, drugs are classified in accordance with their gastrointestinal absorption characteristics into two broad categories i.e. homogeneous and heterogeneous. The former category includes drugs with satisfactory solubility and permeability which ensure the validity of the homogeneous hypothesis. Drugs with low solubility and permeability are termed heterogeneous since they traverse the entire gastrointestinal tract and therefore are more likely to exhibit heterogeneous dissolution, transit and uptake. The high variability of whole bowel transit and the unpredictability of conventional dissolution tests for heterogeneous drugs are interpreted on the basis of the fractal nature of these processes underin vivoconditions. The implications associated with the use of strict statistical criteria in bioequivalence studies for heterogeneous drugs are also pointed out.

Analysis of Case II drug transport with radial and axial release from cylinders

Analysis is presented for Case II drug transport with axial and radial release from cylinders. The previously reported [J. Control Release 5 (1987) 37] relationships for radial release from films and slabs are special cases of the general solution derived in this study. The widely used exponential relation M(t)/M(infinity) = kt(n) describes nicely the first 60% of the fractional release curve when Case II drug transport with axial and radial release from cylinders is operating.

Language evolution and population dynamics in a system of two interacting species

We use Monte Carlo simulations and assumptions from evolutionary game theory in order to study the evolution of words and the population dynamics of a system made of two interacting species which initially speak two different languages. The species are characterized by their identity, vocabulary, and have different initial fitness, i.e. reproduction capability. We investigate how different initial fitness affects the vocabulary of the species or the population dynamics by leading to a permanent populational advantage. We further find that the spatial distributions of the species may cause the system to exhibit pattern formation or segregation. We show that an initial fitness advantage, even though very quickly balanced, leads to better spatial arrangement and enhances survival probabilities of the species. In most cases the system will arrive at a final state where both languages coexist. However, in cases where one species greatly outnumbers the other in population and fitness, then only one species survives with its “final” language having a slightly richer vocabulary than its initial language. Thus, our results offer an explanation for the existence and origin of synonyms in spoken languages.

Diffusive and percolative lattice migration: Excitons

A microscopic transport theory is developed for stochastic and correlated hopping on ordered and random lattices that contain a small fraction of supertraps and a small number of ’’hoppers’’ (i.e., excitons). It includes short‐time (’’transient’’) behavior, which is of interest for both time‐resolved and steady‐state experiments. The relations with diffusion, percolation, random walk, and rate equations are exhibited and applications to energy transport in disordered molecular aggregates illustrate the approach, which is a combination of a rigorous analytical method and simple computer simulations of general validity. Simple analytical results, derived for special (limiting) cases, are compared with other methods, thus emphasizing the roles of time, dimensionality, anisotropy, clusterization, correlation of hops, and the order parameter of the lattice as well as the suitability of various approaches for dealing with these factors.

A Heterogeneous Tube Model of Intestinal Drug Absorption Based on Probabilistic Concepts

AbstractPurpose. To develop an approach based on computer simulations for the study of intestinal drug absorption. Methods. The drug flow in the gastrointestinal tract was simulated with a biased random walk model in the heterogeneous tube model Pharm. Res. 16, 87-91, 1999), while probability concepts were used to describe the dissolution and absorption processes. An amount of drug was placed into the input end of the tube and allowed to flow, dissolve and absorb along the tube. Various drugs with a diversity in dissolution and permeability characteristics were considered. The fraction of dose absorbed (Fabs) was monitored as a function of time measured in Monte Carlo steps (MCS). The absorption number An was calculated from the mean intestinal transit time and the absorption rate constant adhering to each of the drugs examined. Results. A correspondence between the probability factor used to simulate drug absorption and the conventional absorption rate constant derived from the analysis of data was established. For freely soluble drugs, the estimates for Fabs derived from simulations using as an intestinal transit time 24500 MCS (equivalent to 4.5 h) were in accord with the corresponding data obtained from literature. For sparingly soluble drugs, a comparison of the normalized concentration profiles in the tube derived from the heterogeneous tube model and the classical macroscopic mass balance approach enabled the estimation of the dissolution probability factor for five drugs examined. The prediction of Fabs can be accomplished using estimates for the absorption and the dissolution probability factors. Conclusions. A fully computerized approach which describes the flow, dissolution and absorption of drug in the gastrointestinal tract in terms of probability concepts was developed. This approach can be used to predict Fabs for drugs with various solubility and permeability characteristics provided that probability factors for dissolution and absorption are available.