Berry Phases on Virasoro Orbits

We point out that unitary representations of the Virasoro algebra contain Berry phases obtained by acting on a primary state with conformal transformations that trace a closed path on a Virasoro coadjoint orbit. These phases can be computed exactly thanks to the Maurer-Cartan form on the Virasoro group, and they persist after combining left- and right-moving sectors. Thinking of Virasoro representations as particles in AdS_3 dressed with boundary gravitons, the Berry phases associated with Brown-Henneaux diffeomorphisms provide a gravitational extension of Thomas precession.Comment: 34 pages, 3 figures. v2: examples moved to appendix + minor clarifications. Published in JHE

Seizure-onset mapping based on time-variant multivariate functional connectivity analysis of high-dimensional intracranial EEG : a Kalman filter approach

The visual interpretation of intracranial EEG (iEEG) is the standard method used in complex epilepsy surgery cases to map the regions of seizure onset targeted for resection. Still, visual iEEG analysis is labor-intensive and biased due to interpreter dependency. Multivariate parametric functional connectivity measures using adaptive autoregressive (AR) modeling of the iEEG signals based on the Kalman filter algorithm have been used successfully to localize the electrographic seizure onsets. Due to their high computational cost, these methods have been applied to a limited number of iEEG time-series (< 60). The aim of this study was to test two Kalman filter implementations, a well-known multivariate adaptive AR model (Arnold et al. 1998) and a simplified, computationally efficient derivation of it, for their potential application to connectivity analysis of high-dimensional (up to 192 channels) iEEG data. When used on simulated seizures together with a multivariate connectivity estimator, the partial directed coherence, the two AR models were compared for their ability to reconstitute the designed seizure signal connections from noisy data. Next, focal seizures from iEEG recordings (73-113 channels) in three patients rendered seizure-free after surgery were mapped with the outdegree, a graph-theory index of outward directed connectivity. Simulation results indicated high levels of mapping accuracy for the two models in the presence of low-to-moderate noise cross-correlation. Accordingly, both AR models correctly mapped the real seizure onset to the resection volume. This study supports the possibility of conducting fully data-driven multivariate connectivity estimations on high-dimensional iEEG datasets using the Kalman filter approach

Lorenz-like systems and classical dynamical equations with memory forcing: a new point of view for singling out the origin of chaos

A novel view for the emergence of chaos in Lorenz-like systems is presented. For such purpose, the Lorenz problem is reformulated in a classical mechanical form and it turns out to be equivalent to the problem of a damped and forced one dimensional motion of a particle in a two-well potential, with a forcing term depending on the ``memory'' of the particle past motion. The dynamics of the original Lorenz system in the new particle phase space can then be rewritten in terms of an one-dimensional first-exit-time problem. The emergence of chaos turns out to be due to the discontinuous solutions of the transcendental equation ruling the time for the particle to cross the intermediate potential wall. The whole problem is tackled analytically deriving a piecewise linearized Lorenz-like system which preserves all the essential properties of the original model.Comment: 48 pages, 25 figure

PonyGE2: Grammatical Evolution in Python

Grammatical Evolution (GE) is a population-based evolutionary algorithm, where a formal grammar is used in the genotype to phenotype mapping process. PonyGE2 is an open source implementation of GE in Python, developed at UCD's Natural Computing Research and Applications group. It is intended as an advertisement and a starting-point for those new to GE, a reference for students and researchers, a rapid-prototyping medium for our own experiments, and a Python workout. As well as providing the characteristic genotype to phenotype mapping of GE, a search algorithm engine is also provided. A number of sample problems and tutorials on how to use and adapt PonyGE2 have been developed.Comment: 8 pages, 4 figures, submitted to the 2017 GECCO Workshop on Evolutionary Computation Software Systems (EvoSoft

Encoding and processing of sensory information in neuronal spike trains

Recently, a statistical signal-processing technique has allowed the information carried by single spike trains of sensory neurons on time-varying stimuli to be characterized quantitatively in a variety of preparations. In weakly electric fish, its application to first-order sensory neurons encoding electric field amplitude (P-receptor afferents) showed that they convey accurate information on temporal modulations in a behaviorally relevant frequency range (<80 Hz). At the next stage of the electrosensory pathway (the electrosensory lateral line lobe, ELL), the information sampled by first-order neurons is used to extract upstrokes and downstrokes in the amplitude modulation waveform. By using signal-detection techniques, we determined that these temporal features are explicitly represented by short spike bursts of second-order neurons (ELL pyramidal cells). Our results suggest that the biophysical mechanism underlying this computation is of dendritic origin. We also investigated the accuracy with which upstrokes and downstrokes are encoded across two of the three somatotopic body maps of the ELL (centromedial and lateral). Pyramidal cells of the centromedial map, in particular I-cells, encode up- and downstrokes more reliably than those of the lateral map. This result correlates well with the significance of these temporal features for a particular behavior (the jamming avoidance response) as assessed by lesion experiments of the centromedial map

Structural analyses of features in cultural landscapes based on historical cadastral maps and GIS

A landscape may appear to be ancient and to contain old man-made structures even if this is not the whole truth. Structures are moved, removed, replaced and added over the years. New users introduce new land use and management regimes. In Norway, information from land consolidation processes is crucially important in gaining a better understanding of the history, dynamics and development of farms, identifying older traces of human activity and selecting important areas for protection and management. When cadastral maps are transformed, common points are needed during the transformation process and for testing the accuracy of the final transformation. It is often difficult to find enough common points to satisfy statistical requirements. Paper I presents a simple method using buffers based on linear features to evaluate whether or not the accuracy of the transformation results is better than the known accuracy of the source. Papers II, III and IV show how digitised and geographically referenced historical cadastral maps can be used to reconstruct the situation at various dates back to the 19th century, and for some information back to the 16th century. The digitised cadastral map provides a snapshot of the situation at the time of the land consolidation process, and the information is considered to be very exact. Paper IV also demonstrates how a DEM (digital elevation model) can add significantly to an understanding of the information contained in the land consolidation material. The use of digitised cadastral maps reveals that many man-made structures generally perceived as old, because they are constructed using traditional techniques, in fact date from after the land consolidation process. One aim of the new European Landscape Convention is to promote landscape protection, management and planning. It therefore requires identification of landscapes and analysis of their characteristics and the forces and pressures transforming them. Using land consolidation material in a GIS makes it possible to document changes in a landscape and improve understanding of the pressures behind these changes

Electric-Magnetic Duality And The Geometric Langlands Program

The geometric Langlands program can be described in a natural way by compactifying on a Riemann surface C a twisted version of N=4 super Yang-Mills theory in four dimensions. The key ingredients are electric-magnetic duality of gauge theory, mirror symmetry of sigma-models, branes, Wilson and 't Hooft operators, and topological field theory. Seemingly esoteric notions of the geometric Langlands program, such as Hecke eigensheaves and D-modules, arise naturally from the physics.Comment: 225 pp; further clarification