Does quantum mechanics tell an atomistic spacetime?

The canonical answer to the question posed is "Yes." -- tacitly assuming that quantum theory and the concept of spacetime are to be unified by `quantizing' a theory of gravitation. Yet, instead, one may ponder: Could quantum mechanics arise as a coarse-grained reflection of the atomistic nature of spacetime? -- We speculate that this may indeed be the case. We recall the similarity between evolution of classical and quantum mechanical ensembles, according to Liouville and von Neumann equation, respectively. The classical and quantum mechanical equations are indistinguishable for objects which are free or subject to spatially constant but possibly time dependent, or harmonic forces, if represented appropriately. This result suggests a way to incorporate anharmonic interactions, including fluctuations which are tentatively related to the underlying discreteness of spacetime. Being linear and local at the quantum mechanical level, the model offers a decoherence and natural localization mechanism. However, the relation to primordial deterministic degrees of freedom is nonlocal.Comment: Based on invited talks at Fourth International Workshop DICE2008, held at Castello Pasquini / Castiglioncello, Italy, 22-26 September 2008 and at DISCRETE'08 - Symposium on Prospects in the Physics of Discrete Symmetries, held at IFIC, Valencia, Spain, 11-16 December 2008 - to appear in respective volumes of Journal of Physics: Conference Serie

Selective phenotyping, entropy reduction, and the mastermind game.

BACKGROUND: With the advance of genome sequencing technologies, phenotyping, rather than genotyping, is becoming the most expensive task when mapping genetic traits. The need for efficient selective phenotyping strategies, i.e. methods to select a subset of genotyped individuals for phenotyping, therefore increases. Current methods have focused either on improving the detection of causative genetic variants or their precise genomic location separately. RESULTS: Here we recognize selective phenotyping as a Bayesian model discrimination problem and introduce SPARE (Selective Phenotyping Approach by Reduction of Entropy). Unlike previous methods, SPARE can integrate the information of previously phenotyped individuals, thereby enabling an efficient incremental strategy. The effective performance of SPARE is demonstrated on simulated data as well as on an experimental yeast dataset. CONCLUSIONS: Using entropy reduction as an objective criterion gives a natural way to tackle both issues of detection and localization simultaneously and to integrate intermediate phenotypic data. We foresee entropy-based strategies as a fruitful research direction for selective phenotyping

Is there a relativistic nonlinear generalization of quantum mechanics?

Yes, there is. - A new kind of gauge theory is introduced, where the minimal coupling and corresponding covariant derivatives are defined in the space of functions pertaining to the functional Schroedinger picture of a given field theory. While, for simplicity, we study the example of an U(1) symmetry, this kind of gauge theory can accommodate other symmetries as well. We consider the resulting relativistic nonlinear extension of quantum mechanics and show that it incorporates gravity in the (0+1)-dimensional limit, where it leads to the Schroedinger-Newton equations. Gravity is encoded here into a universal nonlinear extension of quantum theory. The probabilistic interpretation, i.e. Born's rule, holds provided the underlying model has only dimensionless parameters.Comment: 10 pages; talk at DICE 2006 (Piombino, September 11-15, 2006); to appear in Journal of Physics: Conference Series (2007

Quantum fields, cosmological constant and symmetry doubling

Energy-parity has been introduced by Kaplan and Sundrum as a protective symmetry that suppresses matter contributions to the cosmological constant [KS05]. It is shown here that this symmetry, schematically Energy --> - Energy, arises in the Hilbert space representation of the classical phase space dynamics of matter. Consistently with energy-parity and gauge symmetry, we generalize the Liouville operator and allow a varying gauge coupling, as in "varying alpha" or dilaton models. In this model, classical matter fields can dynamically turn into quantum fields (Schroedinger picture), accompanied by a gauge symmetry change -- presently, U(1) --> U(1) x U(1). The transition between classical ensemble theory and quantum field theory is governed by the varying coupling, in terms of a one-parameter deformation of either limit. These corrections introduce diffusion and dissipation, leading to decoherence.Comment: Replaced by published version, no change in contents - Int. J. Theor. Phys. (2007

General linear dynamics - quantum, classical or hybrid

We describe our recent proposal of a path integral formulation of classical Hamiltonian dynamics. Which leads us here to a new attempt at hybrid dynamics, which concerns the direct coupling of classical and quantum mechanical degrees of freedom. This is of practical as well as of foundational interest and no fully satisfactory solution of this problem has been established to date. Related aspects will be observed in a general linear ensemble theory, which comprises classical and quantum dynamics in the form of Liouville and von Neumann equations, respectively, as special cases. Considering the simplest object characterized by a two-dimensional state-space, we illustrate how quantum mechanics is special in several respects among possible linear generalizations.Comment: 17 pages; based on invited talks at the conferences DICE2010 (Castiglioncello, Italia, Sept 13-17, 2010) and Quantum Field Theory and Gravity (Regensburg, Germany, Sept 28 - Oct 1, 2010

Wellington : a novel method for the accurate identification of digital genomic footprints from DNase-seq data

The expression of eukaryotic genes is regulated by cis-regulatory elements such as promoters and enhancers, which bind sequence-specific DNA-binding proteins. One of the great challenges in the gene regulation field is to characterise these elements. This involves the identification of transcription factor (TF) binding sites within regulatory elements that are occupied in a defined regulatory context. Digestion with DNase and the subsequent analysis of regions protected from cleavage (DNase footprinting) has for many years been used to identify specific binding sites occupied by TFs at individual cis-elements with high resolution. This methodology has recently been adapted for high-throughput sequencing (DNase-seq). In this study, we describe an imbalance in the DNA strand-specific alignment information of DNase-seq data surrounding protein–DNA interactions that allows accurate prediction of occupied TF binding sites. Our study introduces a novel algorithm, Wellington, which considers the imbalance in this strand-specific information to efficiently identify DNA footprints. This algorithm significantly enhances specificity by reducing the proportion of false positives and requires significantly fewer predictions than previously reported methods to recapitulate an equal amount of ChIP-seq data. We also provide an open-source software package, pyDNase, which implements the Wellington algorithm to interface with DNase-seq data and expedite analyses

The Functional Derivation of Master Equations

Master equations describe the quantum dynamics of open systems interacting with an environment. They play an increasingly important role in understanding the emergence of semiclassical behavior and the generation of entropy, both being related to quantum decoherence. Presently we derive the exact master equation for a homogeneous scalar Higgs or inflaton like field coupled to an environment field represented by an infinite set of harmonic oscillators. Our aim is to demonstrate a derivation directly from the path integral representation of the density matrix propagator. Applications and generalizations of this result are discussed.Comment: 10 pages; LaTex. - Contribution to the workshop Hadron Physics VI, March 1998, Florianopolis (Brazil); proceedings, E. Ferreira et al., eds. (World Scientific). Replaced by slightly modified published versio

Time without time: a stochastic clock model

We study a classical reparametrization-invariant system, in which ``time'' is not a priori defined. It consists of a nonrelativistic particle moving in five dimensions, two of which are compactified to form a torus. There, assuming a suitable potential, the internal motion is ergodic or more strongly irregular. We consider quasi-local observables which measure the system's ``change'' in a coarse-grained way. Based on this, we construct a statistical timelike parameter, particularly with the help of maximum entropy method and Fisher-Rao information metric. The emergent reparametrization-invariant ``time'' does not run smoothly but is simply related to the proper time on the average. For sufficiently low energy, the external motion is then described by a unitary quantum mechanical evolution in accordance with the Schr\"odinger equation.Comment: 18 pages; LaTeX. 4 (.ps) plus 2 (.gif) figure file

Isospin Fluctuations from a Thermally Equilibrated Hadron Gas

Partition functions, multiplicity distributions, and isospin fluctuations are calculated for canonical ensembles in which additive quantum numbers as well as total isospin are strictly conserved. When properly accounting for Bose-Einstein symmetrization, the multiplicity distributions of neutral pions in a pion gas are significantly broader as compared to the non-degenerate case. Inclusion of resonances compensates for this broadening effect. Recursion relations are derived which allow calculation of exact results with modest computer time.Comment: 10 pages, 5 figure