The Parallel Complexity of Growth Models

This paper investigates the parallel complexity of several non-equilibrium growth models. Invasion percolation, Eden growth, ballistic deposition and solid-on-solid growth are all seemingly highly sequential processes that yield self-similar or self-affine random clusters. Nonetheless, we present fast parallel randomized algorithms for generating these clusters. The running times of the algorithms scale as $O(\log^2 N)$, where $N$ is the system size, and the number of processors required scale as a polynomial in $N$. The algorithms are based on fast parallel procedures for finding minimum weight paths; they illuminate the close connection between growth models and self-avoiding paths in random environments. In addition to their potential practical value, our algorithms serve to classify these growth models as less complex than other growth models, such as diffusion-limited aggregation, for which fast parallel algorithms probably do not exist.Comment: 20 pages, latex, submitted to J. Stat. Phys., UNH-TR94-0

Consensus theories: an oriented survey

This article surveys seven directions of consensus theories: Arrowian results, federation consensus rules, metric consensus rules, tournament solutions, restricted domains, abstract consensus theories, algorithmic and complexity issues. This survey is oriented in the sense that it is mainly – but not exclusively – concentrated on the most significant results obtained, sometimes with other searchers, by a team of French searchers who are or were full or associate members of the Centre d'Analyse et de Mathématique Sociale (CAMS).Consensus theories ; Arrowian results ; aggregation rules ; metric consensus rules ; median ; tournament solutions ; restricted domains ; lower valuations ; median semilattice ; complexity

Demand Forecasting at Low Aggregation Levels using Factored Conditional Restricted Boltzmann Machine.

The electrical demand forecasting problem can be regarded as a non-linear time series prediction problem depending on many complex factors since it is required at various aggregation levels and at high resolution. To solve this challenging problem, various time series and machine learning approaches has been proposed in the literature. As an evolution of neural network-based prediction methods, deep learning techniques are expected to increase the prediction accuracy by being stochastic and allowing bi-directional connections between neurons. In this paper, we investigate a newly developed deep learning model for time series prediction, namely Factored Conditional Restricted Boltzmann Machine (FCRBM), and extend it for demand forecasting. The assessment is made on the EcoGrid EU dataset, consisting of aggregated electric power consumption, price and meteorological data collected from 1900 customers. The households are equipped with local generation and smart appliances capable of responding to real-time pricing signals. The results show that for the energy prediction problem solved here, FCRBM outperforms the benchmark machine learning approach, i.e. Support Vector Machine