Queues with Simultaneous Arrival of Customers and the Dependence Structure of the Waiting Times

Methodology and Computing in Applied Probability - We consider a queueing system where some customers decide to simultaneously wait in two queues, rather than in a single queue, to receive their...     

Spatially homogeneous random evolutions

Spatially homogeneous random evolutions arise in the study of the growth of a population in a spatially homogeneous random environment. The random evolution is obtained as the solution of a bilinear stochastic evolution equation. The main results are concerned with the asymptotic behavior of the solution for large times. In particular, conditions for the existence of a stationary random field are established. Furthermore space-time renormalization limit theorems are obtained which lead to either Gaussian or non-Gaussian generalized processes depending on the case under consideration.     

Motif structure and cooperation in real-world complex networks

Networks of dynamical nodes serve as generic models for real-world systems in many branches of science ranging from mathematics to physics, technology, sociology and biology. Collective behavior of agents interacting over complex networks is important in many applications. The cooperation between selfish individuals is one of the most interesting collective phenomena. In this paper we address the interplay between the motifs’ cooperation properties and their abundance in a number of real-world networks including yeast protein-protein interaction, human brain, protein structure, email communication, dolphins’ social interaction, Zachary karate club and Net-science coauthorship networks. First, the amount of cooperativity for all possible undirected subgraphs with three to six nodes is calculated. To this end, the evolutionary dynamics of the Prisoner’s Dilemma game is considered and the cooperativity of each subgraph is calculated as the percentage of cooperating agents at the end of the simulation time. Then, the three- to six-node motifs are extracted for each network. The significance of the abundance of a motif, represented by a Z-value, is obtained by comparing them with some properly randomized versions of the original network. We found that there is always a group of motifs showing a significant inverse correlation between their cooperativity amount and Z-value, i.e. the more the Z-value the less the amount of cooperativity. This suggests that networks composed of well-structured units do not have good cooperativity properties.     

Maximum flow problem on dynamic generative network flows with time-varying bounds

This paper considers a new class of network flows, called dynamic generative network flows in which, the flow commodity is dynamically generated at a source node and dynamically consumed at a sink node and the arc-flow bounds are time dependent. Then the maximum dynamic flow problem in such networks for a pre-specified time horizon T is defined and mathematically formulated in both arc flow and path flow presentations. By exploiting the special structure of the problem, an efficient algorithm is developed to solve the general form of the dynamic problem as a minimum cost static flow problem.     

Study of Salinity and pH Effects on Gelation Time of a Polymer Gel Using Central Composite Design Method

Experiments were conducted to investigate the main effects of salinity (NaCl) concentrations and pH factors and their interactions on the gelation time response of a polymer gel used in a water shutoff system in oil field reservoirs. Central composite design (CCD) was used to design experiments and a mathematical model building. The main advantage of CCD was to generate the quadratic mathematical model for the gelation time as functions of salinity and pH factors. Tests were limited and optimized by CCD points including low star (axial), low factorial, central, high factorial, and high star points. The evaluation of the data and the developed model were performed through the examination of graphical trend of residuals and a numerical approach. Analysis of variance (ANOVA) was used to estimate the amount of data variations from the model predictions. It was found that the model was significant at the 99% confidence against test data. The results showed that the gelation time was dependent more on pH than salinity. For low pH, the gelation time increased with increasing of the salinity, while for a high pH (>4) the relationship was inversed. The research shows that CCD can effectively be applied for the modeling of gelation time and finding an optimum condition to achieve maximum or minimum gelation time for different salinity and pH factors.