Novel critical phenomena in optimization driven processes on networks

The work presented in this Ph.D thesis was developed in the context of complex network theory, from a statistical physics standpoint. We examine two distinct problems in this research field, taking a special interest in their respective critical properties. In both cases, the emergence of criticality is driven by a local optimization dynamics. Firstly, a recently introduced class of percolation problems that attracted a significant amount of attention from the scientific community, and was quickly followed up by an abundance of other works. Percolation transitions were believed to be continuous, until, recently, an 'explosive' percolation problem was reported to undergo a discontinuous transition, in [93]. The system's evolution is driven by a metropolis-like algorithm, apparently producing a discontinuous jump on the giant component's size at the percolation threshold. This finding was subsequently supported by number of other experimental studies [96, 97, 98, 99, 100, 101]. However, in [1] we have proved that the explosive percolation transition is actually continuous. The discontinuity which was observed in the evolution of the giant component's relative size is explained by the unusual smallness of the corresponding critical exponent, combined with the finiteness of the systems considered in experiments. Therefore, the size of the jump vanishes as the system's size goes to infinity. Additionally, we provide the complete theoretical description of the critical properties for a generalized version of the explosive percolation model [2], as well as a method [3] for a precise calculation of percolation's critical properties from numerical data (useful when exact results are not available). Secondly, we study a network flow optimization model, where the dynamics consists of consecutive mergings and splittings of currents flowing in the network. The current conservation constraint does not impose any particular criterion for the split of current among channels outgoing nodes, allowing us to introduce an asymmetrical rule, observed in several real systems. We solved analytically the dynamic equations describing this model in the high and low current regimes. The solutions found are compared with numerical results, for the two regimes, showing an excellent agreement. Surprisingly, in the low current regime, this model exhibits some features usually associated with continuous phase transitions.

The impact of communication disability on quality of life of people with aphasia and their caregivers

Aphasia is a chronic acquired communication disorder that may change people with aphasia (PWA) and their caregivers’ lives for ever. Social and emotional changes are frequently reported by both, although the impact of these changes in quality of life (QOL) needs further research. This study identifies predictors and variables that influence PWA’s and their caregivers’ QOL and social relationships (SR). A cross-sectional descriptive, correlational and comparative study was undertaken with 255 individuals from Portuguese general population (mean age 43 years, range 25-84 years; 148 females, 107 males), 25 PWA (mean age 54 years, range 20-71; 12 females and 13 males), and 25 caregivers (mean age 51 years, range 26-73; 17 females and 8 males). All the participants completed the World Health Quality of Life Bref instrument, the SR domain of the World Health Organization Quality of Life – 100 scale, and the Center for Epidemiologic Studies Depression Scale. Participants with aphasia completed the Lisbon Aphasia Assessment Battery, Barthel Index, Frenchay Activities Index, Communication Disability Profile and the Modified Mini-Mental State which evaluated language disability, aphasia coefficient, activities, participation and cognition. In addition, caregivers completed the Carers’ Assessment of Managing Index to assess coping strategies. PWA and their caregivers are less satisfied with their QOL and SR than Portuguese general population; whereas PWA have the worse QOL and SR. Thus, aphasia seems to impact negatively in their QOL and SR. Emotional status has great importance for QOL and SR among the three groups. PWA’s activities and participation have great impact in both PWA’s and caregivers’ QOL and SR. Additionally, emotional status and participation are the best predictors of PWA’s QOL. Along with these two variables, activities of the PWA are the best predictors of caregivers’ QOL. Participation is the best predictor of PWA’s SR; emotional status and number of cohabitants are best predictors for caregivers’ SR. Aphasia assessment and intervention should take into account all the factors that influence PWA’s and caregivers’ QOL and SR so the central goal of enhancing it can be achieved. These results are important for identifying and planning support needs and are useful in the orientation of the activities carried out by the service providers allowing the adjustment of health programs and policies based on people’s real life needs.