Invasion percolation and critical transient in the Barabási Model of human dynamics

We introduce an exact probabilistic description for L=2 of the Barabási model for the dynamics of a list of L tasks. This permits us to study the problem out of the stationary state and to solve explicitly the extremal limit case where a critical behavior for the waiting time distribution is observed. This behavior deviates at any finite time from that of the stationary state. We study also the characteristic relaxation time for finite time deviations from stationarity in all cases showing that it diverges in the extremal limit, confirming that these deviations are important at all time

Amyloid-β, cortical thickness, and subsequent cognitive decline in cognitively normal oldest-old.

OBJECTIVE: To investigate the relationship between amyloid-β (Aβ) deposition and markers of brain structure on cognitive decline in oldest-old individuals with initial normal cognition. METHODS: We studied cognitive functioning in four domains at baseline and change over time in fifty-seven cognitively intact individuals from the EMIF-AD 90+ study. Predictors were Aβ status determined by [18 F]-flutemetamol PET (normal = Aβ - vs. abnormal = Aβ+), cortical thickness in 34 regions and hippocampal volume. Mediation analyses were performed to test whether effects of Aβ on cognitive decline were mediated by atrophy of specific anatomical brain areas. RESULTS: Subjects had a mean age of 92.7 ± 2.9 years, of whom 19 (33%) were Aβ+. Compared to Aβ-, Aβ+ individuals showed steeper decline on memory (β ± SE = -0.26 ± 0.09), and processing speed (β ± SE = -0.18 ± 0.08) performance over 1.5 years (P < 0.05). Furthermore, medial and lateral temporal lobe atrophy was associated with steeper decline in memory and language across individuals. Mediation analyses revealed that part of the memory decline observed in Aβ+ individuals was mediated through parahippocampal atrophy. INTERPRETATION: These results show that Aβ abnormality even in the oldest old with initially normal cognition is not part of normal aging, but is associated with a decline in cognitive functioning. Other pathologies may also contribute to decline in the oldest old as cortical thickness predicted cognitive decline similarly in individuals with and without Aβ pathology

An approximation approach for the deviation matrix of continuous-time Markov processes with application to Markov decision theory

We present an update formula that allows the expression of the deviation matrix of a continuous-time Markov process with denumerable state space having generator matrix Q* through a continuous-time Markov process with generator matrix Q. We show that under suitable stability conditions the algorithm converges at a geometric rate. By applying the concept to three different examples, namely, the M/M/1 queue with vacations, the M/G/1 queue, and a tandem network, we illustrate the broad applicability of our approach. For a problem in admission control, we apply our approximation algorithm toMarkov decision theory for computing the optimal control policy. Numerical examples are presented to highlight the efficiency of the proposed algorithm. © 2010 INFORMS

Epidemic processes in complex networks

In recent years the research community has accumulated overwhelming evidence for the emergence of complex and heterogeneous connectivity patterns in a wide range of biological and sociotechnical systems. The complex properties of real-world networks have a profound impact on the behavior of equilibrium and nonequilibrium phenomena occurring in various systems, and the study of epidemic spreading is central to our understanding of the unfolding of dynamical processes in complex networks. The theoretical analysis of epidemic spreading in heterogeneous networks requires the development of novel analytical frameworks, and it has produced results of conceptual and practical relevance. A coherent and comprehensive review of the vast research activity concerning epidemic processes is presented, detailing the successful theoretical approaches as well as making their limits and assumptions clear. Physicists, mathematicians, epidemiologists, computer, and social scientists share a common interest in studying epidemic spreading and rely on similar models for the description of the diffusion of pathogens, knowledge, and innovation. For this reason, while focusing on the main results and the paradigmatic models in infectious disease modeling, the major results concerning generalized social contagion processes are also presented. Finally, the research activity at the forefront in the study of epidemic spreading in coevolving, coupled, and time-varying networks is reported.Comment: 62 pages, 15 figures, final versio

How Xenopus laevis embryos replicate reliably: investigating the random-completion problem

DNA synthesis in \textit{Xenopus} frog embryos initiates stochastically in time at many sites (origins) along the chromosome. Stochastic initiation implies fluctuations in the time to complete and may lead to cell death if replication takes longer than the cell cycle time ($\approx 25$ min). Surprisingly, although the typical replication time is about 20 min, \textit{in vivo} experiments show that replication fails to complete only about 1 in 300 times. How is replication timing accurately controlled despite the stochasticity? Biologists have proposed two solutions to this "random-completion problem." The first solution uses randomly located origins but increases their rate of initiation as S phase proceeds, while the second uses regularly spaced origins. In this paper, we investigate the random-completion problem using a type of model first developed to describe the kinetics of first-order phase transitions. Using methods from the field of extreme-value statistics, we derive the distribution of replication-completion times for a finite genome. We then argue that the biologists' first solution to the problem is not only consistent with experiment but also nearly optimizes the use of replicative proteins. We also show that spatial regularity in origin placement does not alter significantly the distribution of replication times and, thus, is not needed for the control of replication timing.Comment: 16 pages, 9 figures, submitted to Physical Review

Gray matter networks and cognitive impairment in multiple sclerosis

BACKGROUND: Coordinated patterns of gray matter morphology can be represented as networks, and network disruptions may explain cognitive dysfunction related to multiple sclerosis (MS). OBJECTIVE: To investigate whether single-subject gray matter network properties are related to impaired cognition in MS. METHODS: We studied 148 MS patients (99 female) and 33 healthy controls (HC, 21 female). Seven network parameters were computed and compared within MS between cognitively normal and impaired subjects, and associated with performance on neuropsychological tests in six cognitive domains with regression models. Analyses were controlled for age, gender, whole-brain gray matter volumes, and education level. RESULTS: Compared to MS subjects with normal cognition, MS subjects with cognitive impairment showed a more random network organization as indicated by lower lambda values (all p < 0.05). Worse average cognition and executive function were associated with lower lambda values. Impaired information processing speed, working memory, and attention were associated with lower clustering values. CONCLUSION: Our findings indicate that MS subjects with a more randomly organized gray matter network show worse cognitive functioning, suggesting that single-subject gray matter graphs may capture neurological dysfunction due to MS