Coordinates and frames from the causal point of view

Lorentzian frames may belong to one of the 199 causal classes. Of these numerous causal classes, people are essentially aware only of two of them. Nevertheless, other causal classes are present in some well-known solutions, or present a strong interest in the physical construction of coordinate systems. Here we show the unusual causal classes to which belong so familiar coordinate systems as those of Lema{\^{\i}}tre, those of Eddington-Finkelstein, or those of Bondi-Sachs. Also the causal classes associated to the Coll light coordinates (four congruences of real geodetic null lines) and to the Coll positioning systems (light signals broadcasted by four clocks) are analyzed. The role that these results play in the comprehension and classification of relativistic coordinate systems is emphasized.Comment: 5 pages, 1 figure, short communication in A Century of Relativity Physics, Proceedings of the XXVIII Spanish Relativity Meeting ERE-2006, 6-10 September - Oviedo - Spain (AIP Conference Proceedings

Which Factors Determine Academic Performance of Undergraduate Students in Economics?: Some Spanish Evidence

This paper analyses the determinants of academic performance of first-year undergraduate students in Economics at Universidad Carlos III de Madrid, over the period 2001-2005. We focus on a few core subjects which differ in their degree of mathematical complexity. Type of school, specialization track at high school, and the grades obtained at the university entry-exam are among the key factors we examine. Our main finding is that those students who completed a technical track at high school tend to do much better in subjects involving mathematics than those who followed a social sciences track (tailor-made for future economics students) and that the latter do not perform significantly better than the former in subjects with less degree of formalism. Moreover, students from public schools are predominant in the lower and upper parts of the grade distribution while females tend to perform better than males.Banco de Santande

Bolivia's Economic Crisis

By any standard, Bolivia's economic crisis in the 1980's has been extraordinary. Like its neighbors. Bolivia suffered from major external shocks, but the extent of economic collapse in the face of these shocks (including a hyperinflation during 1984-85) suggests that internal factors as well as external shocks have been critical to Bolivia's poor economic performance. One major theme of our work is that the recent economic crisis in Bolivia is a reflection of political and economic conflicts in Bolivian society that have undermined the development process throughout this century. While major reforms have been begun by the present government, many of the deepest problems in Bolivian society that contributed to the crisis remain unresolved.

An Integrated Market for Electricity and Natural Gas Systems with Stochastic Power Producers

In energy systems with high shares of weather-driven renewable power sources, gas-fired power plants can serve as a back-up technology to ensure security of supply and provide short-term flexibility. Therefore, a tighter coordination between electricity and natural gas networks is foreseen. In this work, we examine different levels of coordination in terms of system integration and time coupling of trading floors. We propose an integrated operational model for electricity and natural gas systems under uncertain power supply by applying two-stage stochastic programming. This formulation co-optimizes day-ahead and real-time dispatch of both energy systems and aims at minimizing the total expected cost. Additionally, two deterministic models, one of an integrated energy system and one that treats the two systems independently, are presented. We utilize a formulation that considers the linepack of the natural gas system, while it results in a tractable mixed-integer linear programming (MILP) model. Our analysis demonstrates the effectiveness of the proposed model in accommodating high shares of renewables and the importance of proper natural gas system modeling in short-term operations to reveal valuable flexibility of the natural gas system. Moreover, we identify the coordination parameters between the two markets and show their impact on the system's operation and dispatch

Commitment and Dispatch of Heat and Power Units via Affinely Adjustable Robust Optimization

The joint management of heat and power systems is believed to be key to the integration of renewables into energy systems with a large penetration of district heating. Determining the day-ahead unit commitment and production schedules for these systems is an optimization problem subject to uncertainty stemming from the unpredictability of demand and prices for heat and electricity. Furthermore, owing to the dynamic features of production and heat storage units as well as to the length and granularity of the optimization horizon (e.g., one whole day with hourly resolution), this problem is in essence a multi-stage one. We propose a formulation based on robust optimization where recourse decisions are approximated as linear or piecewise-linear functions of the uncertain parameters. This approach allows for a rigorous modeling of the uncertainty in multi-stage decision-making without compromising computational tractability. We perform an extensive numerical study based on data from the Copenhagen area in Denmark, which highlights important features of the proposed model. Firstly, we illustrate commitment and dispatch choices that increase conservativeness in the robust optimization approach. Secondly, we appraise the gain obtained by switching from linear to piecewise-linear decision rules within robust optimization. Furthermore, we give directions for selecting the parameters defining the uncertainty set (size, budget) and assess the resulting trade-off between average profit and conservativeness of the solution. Finally, we perform a thorough comparison with competing models based on deterministic optimization and stochastic programming.Comment: 31 page