Hemeroteca del mes septiembre, 2016

Logical compactness and constraint satisfaction problems

Por • 23 sep, 2016 • Category: Crítica

We investigate a correspondence between the complexity hierarchy of constraint satisfaction problems and a hierarchy of logical compactness hypotheses for finite relational structures. It seems that the harder a constraint satisfaction problem is, the stronger the corresponding compactness hypothesis is. At the top level, the NP-complete constraint satisfaction problems correspond to compactness hypotheses that are equivalent to the ultrafilter axiom in all the cases we have investigated. At the bottom level, the simplest constraint satisfaction problems correspond to compactness hypotheses that are readily provable from the axioms of Zermelo and Fraenkel.

On the class of perfectly null sets and its transitive version

Por • 23 sep, 2016 • Category: Leyes

We introduce two new classes of special subsets of the real line: the class of perfectly null sets and the class of sets which are perfectly null in the transitive sense. These classes may play the role of duals to the corresponding classes on the category side. We investigate their properties and, in particular, we prove that every strongly null set is perfectly null in the transitive sense, and that it is consistent with ZFC that there exists a universally null set which is not perfectly null in the transitive sense. Finally, we state some open questions concerning the above classes. Although the main problem of whether the classes of perfectly null sets and universally null sets are consistently different remains open, we prove some results related to this question.

Indistinguishability

Por • 23 sep, 2016 • Category: Filosofía

This is a systematic review of the concept of indistinguishability in both classical and quantum mechanics, with particular attention to Gibbs’ paradox. Section 1 is on the Gibbs paradox; section 2 is a defense of the concept of classical indistinguishability, that addresses (and refutes) the view that classical particles can always be distinguished by their trajectories so are distinguishable. Section 3 is on the notion of object more generally, and on whether indistinguishables should be thought of as objects at all

Equivalent Theories Redefine Hamiltonian Observables to Exhibit Change in General Relativity

Por • 23 sep, 2016 • Category: Ciencia y tecnología

Change and local spatial variation are missing in canonical GR’s observables as usually defined, part of the problem of time. Definitions can be tested using equivalent formulations, non-gauge and gauge, because they must have equivalent observables and everything is observable in the non-gauge formulation. Taking an observable from the non-gauge formulation and finding the equivalent in the gauge formulation, one requires that the equivalent be an observable, thus constraining definitions. For massive photons, the de Broglie-Proca non-gauge observable A μ is equivalent to the Stueckelberg-Utiyama quantity A μ +∂ μ ϕ. Thus observables must have 0 Poisson bracket not with each first-class constraint, but with the Anderson-Bergmann-Castellani gauge generator G , a tuned sum of first-class constraints, in accord with the Pons-Salisbury-Sundermeyer definition of observables.

On the length of global integrals for GL n

Por • 23 sep, 2016 • Category: Ambiente

In this paper we prove Conjecture ??? for a set of representations of the group GL n (A) . This Conjecture is stated in complete generality as Conjecture 1 in \cite{G2}, and here we prove it for various cases. See Conjecture ??? below. First we prove it in the case when the length of the integral is four, and then we discuss the general case.

Time-dependent rate of convergence for binomial approximations

Por • 23 sep, 2016 • Category: Opinion

Let W be a Brownian motion. Then u(t,x)=E[g(x+σW T−t )] is the solution of the backward heat equation with terminal condition g . Let v n (t,x) denote the according approximation produced by a simple random walk. This paper is concerned with the rate of convergence of v n (t,x) to u(t,x) for functions g of bounded variation and Lipschitz functions, and the behavior of the error v n (t,x)−u(t,x) as t tends to T .

Constructing Sequences One Step at a Time

Por • 23 sep, 2016 • Category: Educacion

We propose a new method for constructing Turing ideals satisfying principles of reverse mathematics below the Chain-Antichain Principle (CAC). Using this method, we are able to prove several new separations in the presence of Weak Konig’s Lemma (WKL), including showing that CAC+WKL does not imply the thin set theorem for pairs, and that the principle “the product of well-quasi-orders is a well-quasi-order” is strictly between CAC and the Ascending/Descending Sequences principle, even in the presence of WKL.

Dificultades y vetas en la interpretación del pensamiento aristotélico, el límite y el no-ser

Por • 20 sep, 2016 • Category: Filosofía

En el presente artículo se abordan algunas de las principales dificultades derivadas de la interpretación del pensamiento aristotélico en el mundo contemporáneo. Se inicia con la consideración de las influencias del contexto de la Academia en el pensamiento aristotélico, incluyendo el vínculo con el referente platónico. Posteriormente, se analizan las distintas vetas de estudio aristotélico de acuerdo a los principales enfoques de sus diversos intérpretes en la historia de la filosofía occidental. En tercer orden, se realiza una revisión del concepto del no‑ser en Aristóteles, aludiendo a nuevas posibilidades de interpretación en función de su idea de límite.

Reconstrucción filogenética usando geometría algebraica

Por • 20 sep, 2016 • Category: Crítica

Una nueva aproximación a la reconstrucción filogenética basada en la geometría algebraica está ganando fuerza en los últimos años. Fijado un modelo evolutivo para un conjunto de especies, las distribuciones teóricas de los nucleótidos de estas especies satisfacen ciertas relaciones algebraicas que llamamos invariantes. Estos invariantes son de interés teórico y práctico dado que se pueden utilizar para inferir filogenias. En este artículo, explicamos cómo usar los invariantes para implementar algoritmos de reconstrucción filogenética y mostramos cómo el uso de técnicas y resultados teóricos procedentes del álgebra conmutativa y la geometría algebraica puede contribuir en la mejora en la eficacia y la eficiencia de estos algoritmos.

Light Will be Thrown: The Emerging Science of Cultural Evolution

Por • 20 sep, 2016 • Category: Leyes

Culture evolves, not just in the trivial sense that cultures change over time, but also in the strong sense that such change is governed by Darwinian principles. Both biological and cultural evolution are essentially cumulative selection processes in which information (whether genetic or cultural) is sieved, retained and then transmitted to the next generation. In both domains such a process will result in recognizable lineages and tree-like phylogenies so characteristic of Darwinian evolution. Because a principle of inheritance (i.e., faithful replication of information) holds in both domains, we may trace back particular transmission histories and identify the forces that influenced them.