The Fermi–Pasta–Ulam Problem and Its Underlying Integrable Dynamics: An Approach Through Lyapunov Exponents

open3noFPU models, in dimension one, are perturbations either of the linear model or of the Toda model; perturbations of the linear model include the usual $eta$-model, perturbations of Toda include the usual $alpha+eta$ model. In this paper we explore and compare two families, or hierarchies, of FPU models, closer and closer to either the linear or the Toda model, by computing numerically, for each model, the maximal Lyapunov exponent $chi$. More precisely, we consider statistically typical trajectories and study the asymptotics of $chi$ for large $N$ (the number of particles) and small $eps$ (the specific energy $E/N$), and find, for all models, asymptotic power laws $chisimeq Ceps^a$, $C$ and $a$ depending on the model. The asymptotics turns out to be, in general, rather slow, and producing accurate results requires a great computational effort. We also revisit and extend the analytic computation of $chi$ introduced by Casetti, Livi and Pettini, originally formulated for the $eta$-model. With great evidence the theory extends successfully to all models of the linear hierarchy, but not to models close to Toda.openBenettin, G.*; Pasquali, S.; Ponno, A.Benettin, G.; Pasquali, S.; Ponno, A

The genetic code for cities – is it simpler than we thought?

September 200

RELEASE: A High-level Paradigm for Reliable Large-scale Server Software

Erlang is a functional language with a much-emulated model for building reliable distributed systems. This paper outlines the RELEASE project, and describes the progress in the first six months. The project aim is to scale the Erlang’s radical concurrency-oriented programming paradigm to build reliable general-purpose software, such as server-based systems, on massively parallel machines. Currently Erlang has inherently scalable computation and reliability models, but in practice scalability is constrained by aspects of the language and virtual machine. We are working at three levels to address these challenges: evolving the Erlang virtual machine so that it can work effectively on large scale multicore systems; evolving the language to Scalable Distributed (SD) Erlang; developing a scalable Erlang infrastructure to integrate multiple, heterogeneous clusters. We are also developing state of the art tools that allow programmers to understand the behaviour of massively parallel SD Erlang programs. We will demonstrate the effectiveness of the RELEASE approach using demonstrators and two large case studies on a Blue Gene

A theory of the city as object: or, how spatial laws mediate the social construction of urban space

A series of recent papers (Hillier et al 1993, Hillier 1996b, Hillier 2000) have outlined a generic process by which spatial configurations, through their effect on movement, first shape, and then are shaped by, land use patterns and densities. The aim of this paper is to make the spatial dimension of this process more precise. The paper begins by examining a large number of axial maps, and finds that although there are strong cultural variations in different regions of the world, there are also powerful invariants. The problem is to understand how both cultural variations and invariants can arise from the spatial processes that generate cities. The answer proposed is that socio-cultural factors generate the differences by imposing a certain local geometry on the local construction of settlement space, while micro-economic factors, coming more and more into play as the settlement expands, generate the invariants

An Unsupervised Deep Learning Approach for Scenario Forecasts

In this paper, we propose a novel scenario forecasts approach which can be applied to a broad range of power system operations (e.g., wind, solar, load) over various forecasts horizons and prediction intervals. This approach is model-free and data-driven, producing a set of scenarios that represent possible future behaviors based only on historical observations and point forecasts. It first applies a newly-developed unsupervised deep learning framework, the generative adversarial networks, to learn the intrinsic patterns in historical renewable generation data. Then by solving an optimization problem, we are able to quickly generate large number of realistic future scenarios. The proposed method has been applied to a wind power generation and forecasting dataset from national renewable energy laboratory. Simulation results indicate our method is able to generate scenarios that capture spatial and temporal correlations. Our code and simulation datasets are freely available online.Comment: Accepted to Power Systems Computation Conference 2018 Code available at https://github.com/chennnnnyize/Scenario-Forecasts-GA