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Condensation phase transitions of symmetric conserved-mass aggregation model on complex networks

We investigate condensation phase transitions of symmetric conserved-mass aggregation (SCA) model on random networks (RNs) and scale-free networks (SFNs) with degree distribution $P(k) \sim k^{-\gamma}$. In SCA model, masses diffuse with unite rate, and unit mass chips off from mass with rate $\omega$. The dynamics conserves total mass density $\rho$. In the steady state, on RNs and SFNs with $\gamma>3$ for $\omega \neq \infty$, we numerically show that SCA model undergoes the same type condensation transitions as those on regular lattices. However the critical line $\rho_c (\omega)$ depends on network structures. On SFNs with $\gamma \leq 3$, the fluid phase of exponential mass distribution completely disappears and no phase transitions occurs. Instead, the condensation with exponentially decaying background mass distribution always takes place for any non-zero density. For the existence of the condensed phase for $\gamma \leq 3$ at the zero density limit, we investigate one lamb-lion problem on RNs and SFNs. We numerically show that a lamb survives indefinitely with finite survival probability on RNs and SFNs with $\gamma >3$, and dies out exponentially on SFNs with $\gamma \leq 3$. The finite life time of a lamb on SFNs with $\gamma \leq 3$ ensures the existence of the condensation at the zero density limit on SFNs with $\gamma \leq 3$ at which direct numerical simulations are practically impossible. At $\omega = \infty$, we numerically confirm that complete condensation takes place for any $\rho > 0$ on RNs. Together with the recent study on SFNs, the complete condensation always occurs on both RNs and SFNs in zero range process with constant hopping rate.Comment: 6 pages, 6 figure

An Algorithm to Simplify Tensor Expressions

The problem of simplifying tensor expressions is addressed in two parts. The first part presents an algorithm designed to put tensor expressions into a canonical form, taking into account the symmetries with respect to index permutations and the renaming of dummy indices. The tensor indices are split into classes and a natural place for them is defined. The canonical form is the closest configuration to the natural configuration. In the second part, the Groebner basis method is used to simplify tensor expressions which obey the linear identities that come from cyclic symmetries (or more general tensor identities, including non-linear identities). The algorithm is suitable for implementation in general purpose computer algebra systems. Some timings of an experimental implementation over the Riemann package are shown.Comment: 15 pages, Latex2e, submitted to Computer Physics Communications: Thematic Issue on "Computer Algebra in Physics Research

Format zorgpad Voeding bij kanker

Het zorgpad ‘Voeding bij kanker’ beschrijft het (logistiek) pad dat de oncologische patiënt doorloopt binnen de voedingszorg vanaf het moment dat screening op behoefte aan voedingszorg plaatsvindt en verwijzing naar de diëtist tot en met follow-up of palliatieve fase. Hierbij zijn het format en de indeling aangehouden van de IKNL-formats van (niet-)tumorspecifieke zorgpade

The Parallel Persistent Memory Model

We consider a parallel computational model that consists of $P$ processors, each with a fast local ephemeral memory of limited size, and sharing a large persistent memory. The model allows for each processor to fault with bounded probability, and possibly restart. On faulting all processor state and local ephemeral memory are lost, but the persistent memory remains. This model is motivated by upcoming non-volatile memories that are as fast as existing random access memory, are accessible at the granularity of cache lines, and have the capability of surviving power outages. It is further motivated by the observation that in large parallel systems, failure of processors and their caches is not unusual. Within the model we develop a framework for developing locality efficient parallel algorithms that are resilient to failures. There are several challenges, including the need to recover from failures, the desire to do this in an asynchronous setting (i.e., not blocking other processors when one fails), and the need for synchronization primitives that are robust to failures. We describe approaches to solve these challenges based on breaking computations into what we call capsules, which have certain properties, and developing a work-stealing scheduler that functions properly within the context of failures. The scheduler guarantees a time bound of $O(W/P_A + D(P/P_A) \lceil\log_{1/f} W\rceil)$ in expectation, where $W$ and $D$ are the work and depth of the computation (in the absence of failures), $P_A$ is the average number of processors available during the computation, and $f \le 1/2$ is the probability that a capsule fails. Within the model and using the proposed methods, we develop efficient algorithms for parallel sorting and other primitives.Comment: This paper is the full version of a paper at SPAA 2018 with the same nam

Upper bounds for number of removed edges in the Erased Configuration Model

Models for generating simple graphs are important in the study of real-world complex networks. A well established example of such a model is the erased configuration model, where each node receives a number of half-edges that are connected to half-edges of other nodes at random, and then self-loops are removed and multiple edges are concatenated to make the graph simple. Although asymptotic results for many properties of this model, such as the limiting degree distribution, are known, the exact speed of convergence in terms of the graph sizes remains an open question. We provide a first answer by analyzing the size dependence of the average number of removed edges in the erased configuration model. By combining known upper bounds with a Tauberian Theorem we obtain upper bounds for the number of removed edges, in terms of the size of the graph. Remarkably, when the degree distribution follows a power-law, we observe three scaling regimes, depending on the power law exponent. Our results provide a strong theoretical basis for evaluating finite-size effects in networks