Elementary spacetime cycles

Every system in physics is described in terms of interacting elementary particles characterized by modulated spacetime recurrences. These intrinsic periodicities, implicit in undulatory mechanics, imply that every free particle is a reference clock linking time to the particle's mass, and every system is formalizable by means of modulated elementary spacetime cycles. We propose a novel consistent relativistic formalism based on intrinsically cyclic spacetime dimensions, encoding the quantum recurrences of elementary particles into spacetime geometrodynamics. The advantage of the resulting theory is a formal derivation of quantum behaviors from relativistic mechanics, in which the constraint of intrinsic periodicity turns out to quantize the elementary particles; as well as a geometrodynamical description of gauge interaction which, similarly to gravity, turns out to be represented by relativistic modulations of the internal clocks of the elementary particles. The characteristic classical to quantum correspondence of the theory brings novel conceptual and formal elements to address fundamental open questions of modern physics.Comment: 6 pages. Accepted for publication in Europhysics Letters (EPL) 30 April 201

Unification of Relativistic and Quantum Mechanics from Elementary Cycles Theory

In Elementary Cycles theory elementary quantum particles are consistently described as the manifestation of ultra-fast relativistic spacetime cyclic dynamics, classical in the essence. The peculiar relativistic geometrodynamics of Elementary Cycles theory yields de facto a unification of ordinary relativistic and quantum physics. In particular its classical-relativistic cyclic dynamics reproduce exactly from classical physics first principles all the fundamental aspects of Quantum Mechanics, such as all its axioms, the Feynman path integral, the Dirac quantisation prescription (second quantisation), quantum dynamics of statistical systems, non-relativistic quantum mechanics, atomic physics, superconductivity, graphene physics and so on. Furthermore the theory allows for the explicit derivation of gauge interactions, without postulating gauge invariance, directly from relativistic geometrodynamical transformations, in close analogy with the description of gravitational interaction in general relativity. In this paper we summarise some of the major achievements, rigorously proven also in several recent peer-reviewed papers, of this innovative formulation of quantum particle physics.Comment: 35 page

Deterministic Quantization by Dynamical Boundary Conditions

We propose an unexplored quantization method. It is based on the assumption of dynamical space-time intrinsic periodicities for relativistic fields, which in turn can be regarded as dual to extra-dimensional fields. As a consequence we obtain a unified and consistent interpretation of Special Relativity and Quantum Mechanics in terms of Deterministic Geometrodynamics.Comment: 4 pages. Based on the talk given at Frontiers Of Fundamental And Computational Physics: 10th International Symposiu

AdS/CFT as classical to quantum correspondence in a Virtual Extra Dimension

The correspondence between classical extra dimensional geometry and quantum behavior, typical of the AdS/CFT, has a heuristic semiclassical interpretation in terms of undulatory mechanics and relativistic geometrodynamics. We note, in fact, that the quantum recurrence of ordinary particles enters into the equations of motions in formal duality with the extra dimensional dynamics of a Kaluza-Klein theory. The kinematics of the particle in a generic interaction scheme can be described as modulations of the spacetime recurrences and encoded in corresponding geometrodynamics. The quantization can be obtained semiclassically by means of boundary conditions, so that the interference of the classical paths with different windings numbers associated to the resulting recurrences turns out to be described by the ordinary Feynman Path Integral. This description applied to the Quark-Gluon-Plasma freeze-out yields basic aspects of AdS/QCD phenomenology.Comment: 6 pages. 36th International Conference on High Energy Physics - ICHEP 2012, Melbourne, Australia. Minor corrections. Comments welcom

Quantum Mechanics from Periodic Dynamics: the bosonic case

Enforcing the periodicity hypothesis of the "old" formulation of Quantum Mechanics we show the possibility for a new scenario where Special Relativity and Quantum Mechanics are unified in a Deterministic Field Theory [arXiv:0903.3680]. A novel interpretation of the AdS/CFT conjecture is discussed.Comment: 6 pages. Talk given at QTRF5, Vaxjo, Sweden. Updated reference

Joint Clustering and Registration of Functional Data

Curve registration and clustering are fundamental tools in the analysis of functional data. While several methods have been developed and explored for either task individually, limited work has been done to infer functional clusters and register curves simultaneously. We propose a hierarchical model for joint curve clustering and registration. Our proposal combines a Dirichlet process mixture model for clustering of common shapes, with a reproducing kernel representation of phase variability for registration. We show how inference can be carried out applying standard posterior simulation algorithms and compare our method to several alternatives in both engineered data and a benchmark analysis of the Berkeley growth data. We conclude our investigation with an application to time course gene expression