Hemeroteca del mes diciembre, 2013

Foundations of statistical inference, revisited

Por • 31 dic, 2013 • Category: Leyes

This is an invited contribution to the discussion on Professor Deborah Mayo’s paper, «On the Birnbaum argument for the strong likelihood principle,» to appear in Statistical Science. Mayo clearly demonstrates that statistical methods violating the likelihood principle need not violate either the sufficiency or conditionality principle, thus refuting Birnbaum’s claim. With the constraints of Birnbaum’s theorem lifted, we revisit issues related to the foundations of statistical inference, focusing on some new foundational principles, the inferential model framework, and connections with sufficiency and conditioning.

Global Inequality in Energy Consumption from 1980 to 2010

Por • 31 dic, 2013 • Category: Economía

We study the global probability distribution of energy consumption per capita around the world using data from the U.S. Energy Information Administration (EIA) for 1980-2010. We find that the Lorenz curves have moved up during this time period, and the Gini coefficient G has decreased from 0.66 in 1980 to 0.55 in 2010, indicating a decrease in inequality. The global probability distribution of energy consumption per capita in 2010 is close to the exponential distribution with G=0.5. We attribute this result to the globalization of the world economy, which mixes the world and brings it closer to the state of maximal entropy. We argue that global energy production is a limited resource that is partitioned among the world population. The most probable partition is the one that maximizes entropy, thus resulting in the exponential distribution function. A consequence of the latter is the law of 1/3: the top 1/3 of the world population consumes 2/3 of produced energy. We also find similar results for the global probability distribution of CO2 emissions per capita.

Arithmetical Foundations – Excerpt

Por • 31 dic, 2013 • Category: Crítica

Recursive maps, nowadays called primitive recursive maps, PR maps, have been introduced by G\»odel in his 1931 article for the arithmetisation, g\»odelisation, of metamathematics. For construction of his undecidable formula he introduces a non-constructive, non-recursive predicate beweisbar, provable. Staying within the area of categorical free-variables theory PR of primitive recursion or appropriate extensions opens the chance to avoid the two (original) G\»odel’s incompleteness theorems: these are stated for Principia Mathematica und verwandte Systeme, «related systems» such as in particular Zermelo-Fraenkel set theory ZF and v. Neumann G\»odel Bernays set theory NGB. On the basis of primitive recursion we consider \mu-recursive maps as partial pr maps. Special terminating general recursive maps considered are complexity controlled iterations. Map code evaluation is then given in terms of such an iteration. We discuss iterative pr map code evaluation versus termination conditioned soundness and based on this decidability of primitive recursive predicates.

Causality and local determinism versus quantum nonlocality

Por • 29 dic, 2013 • Category: Ciencia y tecnología

The entanglement and the violation of Bell and CHSH inequalities in spin polarization correlation experiments (SPCE) is considered to be one of the biggest mysteries of Nature and is called quantum nonlocality. In this paper we show once again that this conclusion is based on imprecise terminology and on the lack of understanding of probabilistic models used in various proofs of Bell and CHSH theorems. These models are inconsistent with experimental protocols used in SPCE. This is the only reason why Bell and CHSH inequalities are violated. A probabilistic non-signalling description of SPCE, consistent with quantum predictions, is possible and it depends explicitly on the context of each experiment. It is also deterministic in the sense that the outcome is determined by supplementary local parameters describing both a physical signals and measuring instruments.

Preguntas al general Miguel Rodríguez Torres

Por • 29 dic, 2013 • Category: Nacionales

Su designación como ministro del Interior no me causó sorpresa. Fue una hábil maniobra de Nicolás Maduro utilizada para disminuir el natural rechazo que causó su escogencia entre la Fuerza Armada. Usted desempeña un cargo político, pero no escapará a su criterio, que en esas funciones representa a la institución armada. Esa es la razón por la cual le hago estas preguntas.

Social Resilience in Online Communities: The Autopsy of Friendster

Por • 29 dic, 2013 • Category: sociologia

We empirically analyze five online communities: Friendster, Livejournal, Facebook, Orkut, Myspace, to identify causes for the decline of social networks. We define social resilience as the ability of a community to withstand changes. We do not argue about the cause of such changes, but concentrate on their impact. Changes may cause users to leave, which may trigger further leaves of others who lost connection to their friends. This may lead to cascades of users leaving. A social network is said to be resilient if the size of such cascades can be limited. To quantify resilience, we use the k-core analysis, to identify subsets of the network in which all users have at least k friends. These connections generate benefits (b) for each user, which have to outweigh the costs (c) of being a member of the network. If this difference is not positive, users leave. After all cascades, the remaining network is the k-core of the original network determined by the cost-to-benefit c/b ratio. By analysing the cumulative distribution of k-cores we are able to calculate the number of users remaining in each community.

The Last 50 Years of General Relativity and Gravitation: From GR3 to GR20 Warsaw Conferences

Por • 28 dic, 2013 • Category: Leyes

This article has a dual purpose: i) to provide a flavor of the scientific highlights of the landmark conference, GR3, held in July 1962 at Jablonna, near Warsaw; and, ii) to present a bird’s eye view of the tremendous advances that have occurred over the half century that separates GR3 and GR20, which was again held in Warsaw in July 2013.

Sharpening independence results for Huntington’s affine geometry

Por • 28 dic, 2013 • Category: Opinion

We improve upon Huntington’s affine geometry by showing that his independence proofs can be, in some cases, simplified. We carry out a systematic investigation of the strict notion of betweenness that Huntington employs (the three arguments are supposed to be distinct) by comparing it to McPhee’s three axiom systems for the same intended class of structures, which employs weak betweenness (the arguments are permitted to be equal). Upon closely inspecting the proof that McPhee’s axiom systems are equivalent to Huntington’s (subject of course to the definition of weak betweenness in terms of strict and vice versa), one finds surprisingly that McPhee’s axiom systems have quite different relations to strict betweenness.

Categories within the Foundation of Mathematics

Por • 27 dic, 2013 • Category: Educacion

The recent trend in mathematics is towards a framework of abstract mathematical objects, rather than the more concrete approach of explicitly defining elements which objects were thought to consist of. A natural question to raise is whether this sort of abstract approach advocated for by Lawvere, among others, is foundational in the sense that it provides a unified, universal, system of first order axioms in which we can define the usual mathematical objects and prove their usual properties. In this way, we view the «foundation» as something without any necessary justification or starting point. Some of the main arguments for categories as such a structure are laid out by MacLane as he argues that the set-theoretic constructions are inappropriate for current mathematics as practices, and that they are inadequate to properly encompass category theory itself and therefore cannot properly encompass all of mathematics, while category theory can be used to describe set theory and all the natural consequences of a given primitive system.
arXiv:1312.6198v1 [math.LO]

Barrio Nuevo, Barrio Tricolor: Transformación integral en una sola misión

Por • 26 dic, 2013 • Category: Nacionales

«Nosotros queremos al pueblo con poder. Nosotros queremos al pueblo con comunidades dignas (…) Tenemos que romper de tajo con el modelo dependiente populista. Barrios de dignidad, donde el pueblo tenga servicios, donde podamos construir y reconstruir», explicó el Jefe de Estado.