Higher gauge theory -- differential versus integral formulation

The term higher gauge theory refers to the generalization of gauge theory to a theory of connections at two levels, essentially given by 1- and 2-forms. So far, there have been two approaches to this subject. The differential picture uses non-Abelian 1- and 2-forms in order to generalize the connection 1-form of a conventional gauge theory to the next level. The integral picture makes use of curves and surfaces labeled with elements of non-Abelian groups and generalizes the formulation of gauge theory in terms of parallel transports. We recall how to circumvent the classic no-go theorems in order to define non-Abelian surface ordered products in the integral picture. We then derive the differential picture from the integral formulation under the assumption that the curve and surface labels depend smoothly on the position of the curves and surfaces. We show that some aspects of the no-go theorems are still present in the differential (but not in the integral) picture. This implies a substantial structural difference between non-perturbative and perturbative approaches to higher gauge theory. We finally demonstrate that higher gauge theory provides a geometrical explanation for the extended topological symmetry of BF-theory in both pictures.Comment: 26 pages, LaTeX with XYPic diagrams; v2: typos corrected and presentation improve

Holonomic quantum computation in the presence of decoherence

We present a scheme to study non-abelian adiabatic holonomies for open Markovian systems. As an application of our framework, we analyze the robustness of holonomic quantum computation against decoherence. We pinpoint the sources of error that must be corrected to achieve a geometric implementation of quantum computation completely resilient to Markovian decoherence.Comment: I. F-G. Now publishes under name I. Fuentes-Schuller Published versio

An algebraic Birkhoff decomposition for the continuous renormalization group

This paper aims at presenting the first steps towards a formulation of the Exact Renormalization Group Equation in the Hopf algebra setting of Connes and Kreimer. It mostly deals with some algebraic preliminaries allowing to formulate perturbative renormalization within the theory of differential equations. The relation between renormalization, formulated as a change of boundary condition for a differential equation, and an algebraic Birkhoff decomposition for rooted trees is explicited

Spatial frequency equalization does not prevent spatial–numerical associations

There is an intense debate surrounding the origin of spatial–numerical associations (SNAs), according to which small numbers are mapped onto the left side of the space and large numbers onto the right. Despite evidence suggesting that SNAs would emerge as an innate predisposition to map numerical information onto a left-to-right spatially oriented mental representation, alternative accounts have challenged these proposals, maintaining that such a mapping would be the result of a mere spatial frequency (SF) coding of any visual image. That is, any smaller or larger array of objects would naturally contain more low or high SF information and, accordingly, each hemisphere would be preferentially tuned only for one SF range (e.g., right hemisphere tuned for low SF and left hemisphere tuned for high SF). This would determine the typical SNA (e.g., faster RTs for small numerical arrays with the left hand and for large numerical arrays with the right hand). To directly probe the role of SF coding in SNAs, we tested participants in a typical dot-arrays comparison task with two numerical sets: one in which SFs were confounded with numerosity (Experiment 1) and one in which the full SF power spectrum was equalized across all stimuli, keeping this cue uninformative about numerosity (Experiment 2). We found that SNAs emerged in both experiments, independently of whether SF was confounded or not with numerosity. Taken together, these findings suggest that SNAs cannot simply originate from SF power spectrum alone, and, thus, they rule out the brain’s asymmetric SF tuning as a primary cause of such an effect

VERY HIGH-RESOLUTION 3D SURVEYING AND MODELLING EXPERIENCES IN CIVIL ENGINEERING APPLICATIONS

Abstract. In this paper some experiences in 3D modelling of objects with very high-resolution are described, carried out by the DICAM Geomatics group of the University of Bologna in multi-disciplinary contexts within the field of the Civil Engineering. In all the addressed case studies the main aim is the generation of a 3D model of the surface at a sub-millimetric scale, allowing a very accurate characterization of the surface geometry, useful for different purposes. 3D scanning and Structure from Motion photogrammetry have been used to generate the 3D models. In the paper the encountered problems and the adopted solutions in data surveying and processing are underlined, also discussing the added value of very high-resolution 3D modelling in multi-disciplinary activities

VERY HIGH-RESOLUTION 3D SURVEYING AND MODELLING EXPERIENCES IN CIVIL ENGINEERING APPLICATIONS

In this paper some experiences in 3D modelling of objects with very high-resolution are described, carried out by the DICAM Geomatics group of the University of Bologna in multi-disciplinary contexts within the field of the Civil Engineering. In all the addressed case studies the main aim is the generation of a 3D model of the surface at a sub-millimetric scale, allowing a very accurate characterization of the surface geometry, useful for different purposes. 3D scanning and Structure from Motion photogrammetry have been used to generate the 3D models. In the paper the encountered problems and the adopted solutions in data surveying and processing are underlined, also discussing the added value of very high-resolution 3D modelling in multi-disciplinary activities

unconscious priming by illusory figures the role of the salient region

In this study we provide evidence that unconscious priming can be obtained as a result of the processing of the salient region (SR) of illusory figures and without that of illusory contours (ICs). We used a metacontrast masking paradigm where illusory figures were masked by real figures. In Experiment 1 we found a clear priming effect when participants were asked to discriminate between square and diamond masks preceded by congruent or incongruent illusory square or diamond primes. It is likely that metacontrast impairs the processing of ICs but not of the SR; therefore the above result strongly suggests that the priming effect was specifically related to the processing of the SR. In Experiment 2 participants were tested in the same task as in Experiment 1 with additional primes in which the inducers were presented in the same locations but their shapes were changed so as to modify the global configuration. We termed these primes High, Low, and No Salient Region (HSR, LSR, and NSR, respectively). The HSR condition replicated Experiment 1, whereas in the LSR and NSR conditions the priming effect got progressively smaller. The results of Experiment 1 were replicated with the priming effect significantly larger in the HSR than in all other conditions. It was also larger in the HSR than in LSR condition and smallest but still present in the NSR condition. Taken together, these results indicate that the unconscious processing of only the SR yields a priming effect and that a reduction of the saliency of the SR leads to a reduction of the priming effect, while its elimination does not abolish it

Density fluctuations in κ\kappa-deformed inflationary universe

We study the spectrum of metric fluctuation in $\kappa$-deformed inflationary universe. We write the theory of scalar metric fluctuations in the $\kappa-$deformed Robertson-Walker space, which is represented as a non-local theory in the conventional Robertson-Walker space. One important consequence of the deformation is that the mode generation time is naturally determined by the structure of the $\kappa-$deformation. We expand the non-local action in $H^2/\kappa^2$, with $H$ being the Hubble parameter and $\kappa$ the deformation parameter, and then compute the power spectra of scalar metric fluctuations both for the cases of exponential and power law inflations up to the first order in $H^2/\kappa^2$. We show that the power spectra of the metric fluctuation have non-trivial corrections on the time dependence and on the momentum dependence compared to the commutative space results. Especially for the power law inflation case, the power spectrum for UV modes is weakly blue shifted early in the inflation and its strength decreases in time. The power spectrum of far-IR modes has cutoff proportional to $k^3$ which may explain the low CMB quadrupole moment.Comment: final revision; 19 pages, 3 figures; to appear in Phys. Rev.

The Free Particle in Deformed Special Relativity

The phase space of a classical particle in DSR contains de Sitter space as the space of momenta. We start from the standard relativistic particle in five dimensions with an extra constraint and reduce it to four dimensional DSR by imposing appropriate gauge fixing. We analyze some physical properties of the resulting theories like the equations of motion, the form of Lorentz transformations and the issue of velocity. We also address the problem of the origin and interpretation of different bases in DSR.Comment: 15 page

Noncommutative fluid dynamics in the Snyder space-time

In this paper, we construct for the first time the non-commutative fluid with the deformed Poincare invariance. To this end, the realization formalism of the noncommutative spaces is employed and the results are particularized to the Snyder space. The non-commutative fluid generalizes the fluid model in the action functional formulation to the noncommutative space. The fluid equations of motion and the conserved energy-momentum tensor are obtained.Comment: 12 pages. Version published by Phys. Rev.