Theorems on existence and global dynamics for the Einstein equations

This article is a guide to theorems on existence and global dynamics of solutions of the Einstein equations. It draws attention to open questions in the field. The local-in-time Cauchy problem, which is relatively well understood, is surveyed. Global results for solutions with various types of symmetry are discussed. A selection of results from Newtonian theory and special relativity that offer useful comparisons is presented. Treatments of global results in the case of small data and results on constructing spacetimes with prescribed singularity structure or late-time asymptotics are given. A conjectural picture of the asymptotic behaviour of general cosmological solutions of the Einstein equations is built up. Some miscellaneous topics connected with the main theme are collected in a separate section.Comment: Submitted to Living Reviews in Relativity, major update of Living Rev. Rel. 5 (2002)

Simultaneous activities in the household and residential electricity demand in Spain

Recent research and policy studies on the low-carbon future highlight the importance of flexible electricity demand. This might be problematic particularly for residential electricity demand, which is related to simultaneous consumers’ practices in the household. This paper analyses issues of simultaneity in residential electricity demand in Spain. It makes use of the 2011 Spanish Time Use Survey data with comparisons from the previous Spanish Time Use Survey and the Harmonised European Time Use Surveys. Findings show that media activities are associated the highest levels of continuity and simultaneity, particularly in the early and late parts of the evening during weekdays

Encoding Odorant Identity by Spiking Packets of Rate-Invariant Neurons in Awake Mice

Background: How do neural networks encode sensory information? Following sensory stimulation, neural coding is commonly assumed to be based on neurons changing their firing rate. In contrast, both theoretical works and experiments in several sensory systems showed that neurons could encode information as coordinated cell assemblies by adjusting their spike timing and without changing their firing rate. Nevertheless, in the olfactory system, there is little experimental evidence supporting such model. Methodology/Principal Findings: To study these issues, we implanted tetrodes in the olfactory bulb of awake mice to record the odorant-evoked activity of mitral/tufted (M/T) cells. We showed that following odorant presentation, most M/T neurons do not significantly change their firing rate over a breathing cycle but rather respond to odorant stimulation by redistributing their firing activity within respiratory cycles. In addition, we showed that sensory information can be encoded by cell assemblies composed of such neurons, thus supporting the idea that coordinated populations of globally rateinvariant neurons could be efficiently used to convey information about the odorant identity. We showed that different coding schemes can convey high amount of odorant information for specific read-out time window. Finally we showed that the optimal readout time window corresponds to the duration of gamma oscillations cycles. Conclusion: We propose that odorant can be encoded by population of cells that exhibit fine temporal tuning of spiking activity while displaying weak or no firing rate change. These cell assemblies may transfer sensory information in spikin

The Einstein-Vlasov System/Kinetic Theory

The main purpose of this article is to provide a guide to theorems on global properties of solutions to the Einstein--Vlasov system. This system couples Einstein's equations to a kinetic matter model. Kinetic theory has been an important field of research during several decades in which the main focus has been on non-relativistic and special relativistic physics, i.e., to model the dynamics of neutral gases, plasmas, and Newtonian self-gravitating systems. In 1990, Rendall and Rein initiated a mathematical study of the Einstein--Vlasov system. Since then many theorems on global properties of solutions to this system have been established.Comment: Published version http://www.livingreviews.org/lrr-2011-