Obtaining the Weyl tensor from the Bel-Robinson tensor

The algebraic study of the Bel-Robinson tensor proposed and initiated in a previous work (Gen. Relativ. Gravit. {\bf 41}, see ref [11]) is achieved. The canonical form of the different algebraic types is obtained in terms of Bel-Robinson eigen-tensors. An algorithmic determination of the Weyl tensor from the Bel-Robinson tensor is presented.Comment: 21 page

Dynamical laws of superenergy in General Relativity

The Bel and Bel-Robinson tensors were introduced nearly fifty years ago in an attempt to generalize to gravitation the energy-momentum tensor of electromagnetism. This generalization was successful from the mathematical point of view because these tensors share mathematical properties which are remarkably similar to those of the energy-momentum tensor of electromagnetism. However, the physical role of these tensors in General Relativity has remained obscure and no interpretation has achieved wide acceptance. In principle, they cannot represent {\em energy} and the term {\em superenergy} has been coined for the hypothetical physical magnitude lying behind them. In this work we try to shed light on the true physical meaning of {\em superenergy} by following the same procedure which enables us to give an interpretation of the electromagnetic energy. This procedure consists in performing an orthogonal splitting of the Bel and Bel-Robinson tensors and analysing the different parts resulting from the splitting. In the electromagnetic case such splitting gives rise to the electromagnetic {\em energy density}, the Poynting vector and the electromagnetic stress tensor, each of them having a precise physical interpretation which is deduced from the {\em dynamical laws} of electromagnetism (Poynting theorem). The full orthogonal splitting of the Bel and Bel-Robinson tensors is more complex but, as expected, similarities with electromagnetism are present. Also the covariant divergence of the Bel tensor is analogous to the covariant divergence of the electromagnetic energy-momentum tensor and the orthogonal splitting of the former is found. The ensuing {\em equations} are to the superenergy what the Poynting theorem is to electromagnetism. See paper for full abstract.Comment: 27 pages, no figures. Typos corrected, section 9 suppressed and more acknowledgments added. To appear in Classical and Quantum Gravit

Lieb-Robinson bounds and the speed of light from topological order

We apply the Lieb-Robinson bounds technique to find the maximum speed of interaction in a spin model with topological order whose low-energy effective theory describes light [see X.-G. Wen, \prb {\bf 68}, 115413 (2003)]. The maximum speed of interactions is found in two dimensions is bounded from above less than $\sqrt{2} e$ times the speed of emerging light, giving a strong indication that light is indeed the maximum speed of interactions. This result does not rely on mean field theoretic methods. In higher spatial dimensions, the Lieb-Robinson speed is conjectured to increase linearly with the dimension itself. Implications for the horizon problem in cosmology are discussed.Comment: 4 pages, 1 eps figure. Bound improve

National institutions and subnational development in Africa

Few issues have received more inquiry in the social sciences than “”what are the fundamental determinants of comparative development?”” The institutional view asserts that the ultimate causes of underdevelopment are poorly performing institutional structures, such as lack of constraints on the executive, poor property-rights protection, as well as inefficient legal and court systems (see Acemoglu, Johnson and Robinson 2005 for a review and Acemoglu and Robinson 2012 for an influential popular argument). Other works downplay the role of formal institutions, emphasising instead the importance of geographical features, informal cultural norms, genetic, and epidemiological traits (see Spolaore and Wacziarg 2013 for a review, and Diamond 1997 and Landes 1998 on popular arguments on the importance of geography and culture, respectively)

General entanglement scaling laws from time evolution

We establish a general scaling law for the entanglement of a large class of ground states and dynamically evolving states of quantum spin chains: we show that the geometric entropy of a distinguished block saturates, and hence follows an entanglement-boundary law. These results apply to any ground state of a gapped model resulting from dynamics generated by a local hamiltonian, as well as, dually, to states that are generated via a sudden quench of an interaction as recently studied in the case of dynamics of quantum phase transitions. We achieve these results by exploiting ideas from quantum information theory and making use of the powerful tools provided by Lieb-Robinson bounds. We also show that there exist noncritical fermionic systems and equivalent spin chains with rapidly decaying interactions whose geometric entropy scales logarithmically with block length. Implications for the classical simulatability are outlined.Comment: 4 pages, 1 figure (see also related work by S. Bravyi, M. Hastings, and F. Verstraete, quant-ph/0603121); replaced with final versio

Mount Rushmore: A Tomb for Dead Ideas of American Greatness

The Mount Rushmore National Memorial stands in the Black Hills of South Dakota as a symbol of American greatness. However, the public perceptions of the greatness represented in this memorial do not take into consideration the ideals held by the three main contributors to the development of the mountain, Doane Robinson, Peter Norbeck, and Gutzon Borglum. An exploration into the lives and beliefs of these three men reveals that they possessed a specific definition of America greatness exemplified in the white male farmer of the American West. The four former presidents selected for carving symbolize a general American greatness, but more importantly they epitomize the specific version of greatness championed by the planners of the memorial. Yet, from the earliest perceptions of Mt. Rushmore, the public saw only the representation of a general American greatness that included all members of the nation and eventually the entire world. Visitors to Mount Rushmore do not see the specific ideas of American greatness intended by the planners of the memorial and these ideas of American greatness are now dead

Consolidation, technology, and the changing structure of banks' small business lending

The U.S. banking industry continues to consolidate, with large, complex banking organizations becoming more important. Traditionally, these institutions have not emphasized small business lending. On the other hand, technological advances, particularly credit scoring models, make it easier for banks to extend small business credit. To see what effects these influences might have generated on small business lending, David Ely and Kenneth Robinson explore the small business lending patterns at U.S. banks from 1994 through 1999. They find that larger banks are increasing their market share, most noticeably in the smallest segment of the small business loan market. The authors also present evidence that the size of the average small business loan has declined, especially at larger organizations, and that the gap in lending focus on the smallest small business loans has narrowed between small and large banks. These trends are consistent with increasing use of credit scoring models.Credit ; Credit scoring systems

Nonparametric inference for unbalance time series data

Estimation of heteroskedasticity and autocorrelation consistent covariance matrices (HACs) is a well established problem in time series. Results have been established under a variety of weak conditions on temporal dependence and heterogeneity that allow one to conduct inference on a variety of statistics, see Newey and West (1987), Hansen (1992), de Jong and Davidson (2000), and Robinson (2004). Indeed there is an extensive literature on automating these procedures starting with Andrews (1991). Alternative methods for conducting inference include the bootstrap for which there is also now a very active research program in time series especially, see Lahiri (2003) for an overview. One convenient method for time series is the subsampling approach of Politis, Romano, andWolf (1999). This method was used by Linton, Maasoumi, andWhang (2003) (henceforth LMW) in the context of testing for stochastic dominance. This paper is concerned with the practical problem of conducting inference in a vector time series setting when the data is unbalanced or incomplete. In this case, one can work only with the common sample, to which a standard HAC/bootstrap theory applies, but at the expense of throwing away data and perhaps losing effciency. An alternative is to use some sort of imputation method, but this requires additional modelling assumptions, which we would rather avoid.1 We show how the sampling theory changes and how to modify the resampling algorithms to accommodate the problem of missing data. We also discuss effciency and power. Unbalanced data of the type we consider are quite common in financial panel data, see for example Connor and Korajczyk (1993). These data also occur in cross-country studies.