A construction of 2-cofiltered bilimits of topoi

We show the existence of bilimits of 2-cofiltered diagrams of topoi, generalizing the construction of cofiltered bilimits developed in "SGA 4 Springer LNM 270 (1972)". For any given such diagram, we show that it can be represented by a 2-cofiltered diagram of small sites with finite limits, and we construct a small site for the inverse limit topos. This is done by taking the 2-filtered bicolimit of the underlying categories and inverse image functors. We use the construction of this bicolimit developed in "A construction of 2-filtered bicolimits of categories, Cah. Top. et Geo. Diff. Vol. XLVII-2 (2006)", where it is proved that if the categories in the diagram have finite limits and the transition functors are exact, then the bicolimit category has finite limits and the pseudocone functors are exact. An application of our result here is the fact that every Galois topos has points "2-Filteredness and the point of every Galois topos, Proc. CT2007, App. Cat. St., Vol. 18, 2, (2010)".Comment: 7 page

Geomagnetic effects on cosmic ray propagation under different conditions for Buenos Aires and Marambio, Argentina

The geomagnetic field (Bgeo) sets a lower cutoff rigidity (Rc) to the entry of cosmic particles to Earth which depends on the geomagnetic activity. From numerical simulations of the trajectory of a proton using different models for Bgeo (performed with the MAGCOS code), we use backtracking to analyze particles arriving at the location of two nodes of the net LAGO (Large Aperture Gamma ray burst Observatory) that will be built in the near future: Buenos Aires and Marambio (Antarctica), Argentina. We determine the asymptotic trajectories and the values of Rc for different incidence directions, for each node. Simulations were done using several models for Bgeo that emulate different geomagnetic conditions. The presented results will help to make analysis of future observations of the flux of cosmic rays done at these two LAGO nodes.Comment: 9 page

An out-of-equilibrium model of the distributions of wealth

The distribution of wealth among the members of a society is herein assumed to result from two fundamental mechanisms, trade and investment. An empirical distribution of wealth shows an abrupt change between the low-medium range, that may be fitted by a non-monotonic function with an exponential-like tail such as a Gamma distribution, and the high wealth range, that is well fitted by a Pareto or inverse power-law function. We demonstrate that an appropriate trade-investment model, depending on three adjustable parameters associated with the total wealth of a society, a social differentiation among agents, and economic volatility referred to as investment can successfully reproduce the distribution of empirical wealth data in the low, medium and high ranges. Finally, we provide an economic interpretation of the mechanisms in the model and, in particular, we discuss the difference between Classical and Neoclassical theories regarding the concepts of {\it value} and {\it price}. We consider the importance that out-of-equilibrium trade transactions, where the prices differ from values, have in real economic societies.Comment: 11 pages + 7 figures. in press on Quantitavive Financ

Minimum Number of Probes for Brain Dynamics Observability

In this paper, we address the problem of placing sensor probes in the brain such that the system dynamics' are generically observable. The system dynamics whose states can encode for instance the fire-rating of the neurons or their ensemble following a neural-topological (structural) approach, and the sensors are assumed to be dedicated, i.e., can only measure a state at each time. Even though the mathematical description of brain dynamics is (yet) to be discovered, we build on its observed fractal characteristics and assume that the model of the brain activity satisfies fractional-order dynamics. Although the sensor placement explored in this paper is particularly considering the observability of brain dynamics, the proposed methodology applies to any fractional-order linear system. Thus, the main contribution of this paper is to show how to place the minimum number of dedicated sensors, i.e., sensors measuring only a state variable, to ensure generic observability in discrete-time fractional-order systems for a specified finite interval of time. Finally, an illustrative example of the main results is provided using electroencephalogram (EEG) data.Comment: arXiv admin note: text overlap with arXiv:1507.0720

Educational Performance and Spatial Convergence in Peru

While an enormous and growing literature exists on the topic of regional income convergence, other aspects of socioeconomic well-being and development have attracted much less attention. Social indicators are a valuable complement to economic indicators when analyzing spatial patterns in a given geographic region, and can often yield a more comprehensive view about regional socioeconomic behavior. In poorer nations dominated by many low income areas that exhibit similar economic performance, social indicators may reveal further insight into the differences among regions. This paper explores the issue of educational convergence in Peru over the period 1993 to 2005. Using both exploratory spatial data analysis and spatial econometrics, the study is conducted at province level in order to uncover potential spatial patterns that help explain variation in educational performance over time, among regions, and across different terrain.