This paper is a tour of how the laws of nature can distinguish between the past and the future, or be T-violating. I argue that, in terms of the basic argumentative structure, there are really just three approaches currently being explored. I show how each is characterized by a symmetry principle, which provides a template for detecting T-violating laws even without knowing the laws of physics themselves. Each approach is illustrated with an example, and the prospects of each are considered in extensions of particle physics beyond the standard model.

In contrast to the claim of Motter and Campbell on Chaos at Fifty, done at arXiv:1306.5777, it is pointed out that in 2013 we are at Chaos Fifty Four, if to count correctly and to remember about pioneering results of Boris Chirikov obtained in 1959.

We examine prevailing philosophical and historical views about the origin of infinitesimal mathematics in light of modern infinitesimal theories, and show the works of Fermat, Leibniz, Euler, Cauchy and other giants of infinitesimal mathematics in a new light. We also detail several procedures of the historical infinitesimal calculus that were only clarified and formalized with the advent of modern infinitesimals. These procedures include Fermat’s adequality; Leibniz’s law of continuity and the transcendental law of homogeneity; Euler’s principle of cancellation and infinite integers with the associated infinite products; Cauchy’s infinitesimal-based definition of continuity and «Dirac» delta function. Such procedures were interpreted and formalized in Robinson’s framework in terms of concepts like microcontinuity (S-continuity), the standard part principle, the transfer principle, and hyperfinite products. We evaluate the critiques of historical and modern infinitesimals by their foes from Berkeley and Cantor to Bishop and Connes. We analyze the issue of the consistency, as distinct from the issue of the rigor, of historical infinitesimals, and contrast the methodologies of Leibniz and Nieuwentijt in this connection.

La única manera que existe para hacer desaparecer tan inconveniente percepción es lograr alcanzar algunos éxitos indiscutibles que demuestren la voluntad de Nicolás Maduro de producir un verdadero cambio en la actual situación política.

Dedicado al ilustre Profesor Vladimir Acosta quien, por ser consecuente con los principios que proclama esta Revolución, fue sacado de RNV. Lo que me recuerda aquel eslogan que tanto le gustaba repetir el comandante supremo y que decía: «irreverencia en la crítica y lealtad en la acción». Pero lo que más sorprende es que quienes viven rasgándose las vestiduras en favor de la libertad de expresión, José Vicente Rangel, Roberto Hernández Montoya, Luis Brito García, Earle Herrera, José Sant Roz, no hayan dicho nada en relación con un hecho de tanta entidad como este.

We revisit the classical hard-core model, also known as independent set and dual to vertex cover problem, where one puts particles with a first-neighbor hard-core repulsion on the vertices of a random graph. Although the case of random graphs with small and very large average degrees respectively are quite well understood, they yield qualitatively different results and our aim here is to reconciliate these two cases. We revisit results that can be obtained using the (heuristic) cavity method and show that it provides a closed-form conjecture for the exact density of the densest packing on random regular graphs with degree K>=20, and that for K>16 the nature of the phase transition is the same as for large K. This also shows that the hard-code model is the simplest mean-field lattice model for structural glasses and jamming.

According to ‘t Hooft the combination of quantum mechanics and gravity requires the three dimensional world to be an image of data that can be stored on a two dimensional projection much like a holographic image. The two dimensional description only requires one discrete degree of freedom per Planck area and yet it is rich enough to describe all three dimensional phenomena. After outlining ‘t Hooft’s proposal I give a preliminary informal description of how it may be implemented. One finds a basic requirement that particles must grow in size as their momenta are increased far above the Planck scale. The consequences for high energy particle collisions are described. The phenomena of particle growth with momentum was previously discussed in the context of string theory and was related to information spreading near black hole horizons. The considerations of this paper indicate that the effect is much more rapid at all but the earliest times. In fact the rate of spreading is found to saturate the bound from causality.

We solve the unstructured search problem in constant time by computing with a physically motivated nonlinearity of the Gross–Pitaevskii type. This speedup comes, however, at the novel expense of increasing the time-measurement precision. Jointly optimizing these resource requirements results in an overall scaling of N1/4. This is a significant, but not unreasonable, improvement over the N1/2 scaling of Grover’s algorithm. Since the Gross–Pitaevskii equation approximates the multi-particle (linear) Schrödinger equation, for which Grover’s algorithm is optimal, our result leads to a quantum information-theoretic lower bound on the number of particles needed for this approximation to hold, asymptotically

No cuesta mucho hilar los acontecimientos que se desataron en diferentes ámbitos tras la fatal recaída del Presidente Chávez (luego de entregarse en cuerpo y alma a la campaña electoral que lo llevó a la victoria del 7 de octubre del año 2012). Apareció un prototipo-humano que le importa poco el llamado “país” y que prefiere optar por la ambición desmedida ante las cirustancias sobrevenidas: el raspa olla.

Colombia y la Organización del Tratado del Atlántico del Norte (OTAN) firmaron hoy un acuerdo para el intercambio de información clasificada y buenas prácticas en la lucha antiterrorista y contra el narcotráfico, y otros retos comunes.