Social Networks and Interactions in Cities

We examine how interaction choices depend on the interplay of social and physical distance, and show that agents who are more central in the social network, or are located closer to the geographic center of interaction, choose higher levels of interactions in equilibrium. As a result, the level of interactivity in the economy as a whole will rise with the density of links in the social network and with the degree to which agents are clustered in physical space. When agents can choose geographic locations, there is a tendency for those who are more central in the social network to locate closer to the interaction center, leading to a form of endogenous geographic separation based on social distance. Finally, we show that the market equilibrium is not optimal because of social externalities. We determine the value of the subsidy to interactions that could support the first-best allocation as an equilibrium and show that interaction effort and the incentives for clustering are higher under the subsidy program.Social networks; urban-land use; Bonacich centrality

Scheduling multiple divisible loads on a linear processor network

Min, Veeravalli, and Barlas have recently proposed strategies to minimize the overall execution time of one or several divisible loads on a heterogeneous linear network, using one or more installments. We show on a very simple example that their approach does not always produce a solution and that, when it does, the solution is often suboptimal. We also show how to find an optimal schedule for any instance, once the number of installments per load is given. Then, we formally state that any optimal schedule has an infinite number of installments under a linear cost model as the one assumed in the original papers. Therefore, such a cost model cannot be used to design practical multi-installment strategies. Finally, through extensive simulations we confirmed that the best solution is always produced by the linear programming approach, while solutions of the original papers can be far away from the optimal

Multi-criteria scheduling of pipeline workflows

Mapping workflow applications onto parallel platforms is a challenging problem, even for simple application patterns such as pipeline graphs. Several antagonist criteria should be optimized, such as throughput and latency (or a combination). In this paper, we study the complexity of the bi-criteria mapping problem for pipeline graphs on communication homogeneous platforms. In particular, we assess the complexity of the well-known chains-to-chains problem for different-speed processors, which turns out to be NP-hard. We provide several efficient polynomial bi-criteria heuristics, and their relative performance is evaluated through extensive simulations

Bayesian computation for statistical models with intractable normalizing constants

This paper deals with some computational aspects in the Bayesian analysis of statistical models with intractable normalizing constants. In the presence of intractable normalizing constants in the likelihood function, traditional MCMC methods cannot be applied. We propose an approach to sample from such posterior distributions. The method can be thought as a Bayesian version of the MCMC-MLE approach of Geyer and Thompson (1992). To the best of our knowledge, this is the first general and asymptotically consistent Monte Carlo method for such problems. We illustrate the method with examples from image segmentation and social network modeling. We study as well the asymptotic behavior of the algorithm and obtain a strong law of large numbers for empirical averages.Comment: 20 pages, 4 figures, submitted for publicatio

Rational extensions of the quantum harmonic oscillator and exceptional Hermite polynomials

We prove that every rational extension of the quantum harmonic oscillator that is exactly solvable by polynomials is monodromy free, and therefore can be obtained by applying a finite number of state-deleting Darboux transformations on the harmonic oscillator. Equivalently, every exceptional orthogonal polynomial system of Hermite type can be obtained by applying a Darboux-Crum transformation to the classical Hermite polynomials. Exceptional Hermite polynomial systems only exist for even codimension 2m, and they are indexed by the partitions \lambda of m. We provide explicit expressions for their corresponding orthogonality weights and differential operators and a separate proof of their completeness. Exceptional Hermite polynomials satisfy a 2l+3 recurrence relation where l is the length of the partition \lambda. Explicit expressions for such recurrence relations are given.Comment: 25 pages, typed in AMSTe

Social Networks and Interactions in Cities

We examine how interaction choices depend on the interplay of social and physical distance, and show that agents who are more central in the social network, or are located closer to the geographic center of interaction, choose higher levels of interactions in equilibrium. As a result, the level of interactivity in the economy as a whole will rise with the density of links in the social network and with the degree to which agents are clustered in physical space. When agents can choose geographic locations, there is a tendency for those who are more central in the social network to locate closer to the interaction center, leading to a form of endogenous geographic separation based on social distance. Finally, we show that the market equilibrium is not optimal because of social externalities. We determine the value of the subsidy to interactions that could support the first-best allocation as an equilibrium and show that interaction effort and the incentives for clustering are higher under the subsidy program.social networks, urban-land use, Bonacich centrality

Checkpointing algorithms and fault prediction

This paper deals with the impact of fault prediction techniques on checkpointing strategies. We extend the classical first-order analysis of Young and Daly in the presence of a fault prediction system, characterized by its recall and its precision. In this framework, we provide an optimal algorithm to decide when to take predictions into account, and we derive the optimal value of the checkpointing period. These results allow to analytically assess the key parameters that impact the performance of fault predictors at very large scale.Comment: Supported in part by ANR Rescue. Published in Journal of Parallel and Distributed Computing. arXiv admin note: text overlap with arXiv:1207.693

Reclaiming the energy of a schedule: models and algorithms

We consider a task graph to be executed on a set of processors. We assume that the mapping is given, say by an ordered list of tasks to execute on each processor, and we aim at optimizing the energy consumption while enforcing a prescribed bound on the execution time. While it is not possible to change the allocation of a task, it is possible to change its speed. Rather than using a local approach such as backfilling, we consider the problem as a whole and study the impact of several speed variation models on its complexity. For continuous speeds, we give a closed-form formula for trees and series-parallel graphs, and we cast the problem into a geometric programming problem for general directed acyclic graphs. We show that the classical dynamic voltage and frequency scaling (DVFS) model with discrete modes leads to a NP-complete problem, even if the modes are regularly distributed (an important particular case in practice, which we analyze as the incremental model). On the contrary, the VDD-hopping model leads to a polynomial solution. Finally, we provide an approximation algorithm for the incremental model, which we extend for the general DVFS model.Comment: A two-page extended abstract of this work appeared as a short presentation in SPAA'2011, while the long version has been accepted for publication in "Concurrency and Computation: Practice and Experience

Tiled QR factorization algorithms

This work revisits existing algorithms for the QR factorization of rectangular matrices composed of p-by-q tiles, where p >= q. Within this framework, we study the critical paths and performance of algorithms such as Sameh and Kuck, Modi and Clarke, Greedy, and those found within PLASMA. Although neither Modi and Clarke nor Greedy is optimal, both are shown to be asymptotically optimal for all matrices of size p = q^2 f(q), where f is any function such that \lim_{+\infty} f= 0. This novel and important complexity result applies to all matrices where p and q are proportional, p = \lambda q, with \lambda >= 1, thereby encompassing many important situations in practice (least squares). We provide an extensive set of experiments that show the superiority of the new algorithms for tall matrices