Symmetric spaces and Lie triple systems in numerical analysis of differential equations

A remarkable number of different numerical algorithms can be understood and analyzed using the concepts of symmetric spaces and Lie triple systems, which are well known in differential geometry from the study of spaces of constant curvature and their tangents. This theory can be used to unify a range of different topics, such as polar-type matrix decompositions, splitting methods for computation of the matrix exponential, composition of selfadjoint numerical integrators and dynamical systems with symmetries and reversing symmetries. The thread of this paper is the following: involutive automorphisms on groups induce a factorization at a group level, and a splitting at the algebra level. In this paper we will give an introduction to the mathematical theory behind these constructions, and review recent results. Furthermore, we present a new Yoshida-like technique, for self-adjoint numerical schemes, that allows to increase the order of preservation of symmetries by two units. Since all the time-steps are positive, the technique is particularly suited to stiff problems, where a negative time-step can cause instabilities

Fingerprint-enhanced capacitive-piezoelectric flexible sensing skin to discriminate static and dynamic tactile stimuli

nspired by the structure and functions of the human skin, a highly sensitive capacitive‐piezoelectric flexible sensing skin with fingerprint‐like patterns to detect and discriminate between spatiotemporal tactile stimuli including static and dynamic pressures and textures is presented. The capacitive‐piezoelectric tandem sensing structure is embedded in the phalange of a 3D‐printed robotic hand, and a tempotron classifier system is used for tactile exploration. The dynamic tactile sensor, interfaced with an extended gate configuration to a common source metal oxide semiconductor field effect transistor (MOSFET), exhibits a sensitivity of 2.28 kPa−1. The capacitive sensing structure has nonlinear characteristics with sensitivity varying from 0.25 kPa−1 in the low‐pressure range (<100 Pa) to 0.002 kPa−1 in high pressure (≈2.5 kPa). The output from the presented sensor under a closed‐loop tactile scan, carried out with an industrial robotic arm, is used as latency‐coded spike trains in a spiking neural network (SNN) tempotron classifier system. With the capability of performing a real‐time binary naturalistic texture classification with a maximum accuracy of 99.45%, the presented bioinspired skin finds applications in robotics, prosthesis, wearable sensors, and medical devices

The effects of long-standing limb loss on anatomical reorganization of the somatosensory afferents in the brainstem and spinal cord,‖ Somatosens

Abstract We examined the terminations of sensory afferents in the brainstem and spinal cord of squirrel monkeys and prosimian galagos 4± 8 years after a therapeutic forelimb or hindlimb amputation within 2 months of birth. In each animal, the distributions of labeled sensory afferent terminations from remaining body parts proximal to the limb stump were much more extensive than in normal animals. These sprouted afferents extended into the portions of the dorsal horn of the spinal cord as well as the cuneate and external cuneate nuclei of the brainstem (forelimb amputees) or spinal Clarke's column (hindlimb amputee) related to the amputated limb. Such reorganization in sensory afferents along with reorganization of the motor efferents to muscles (Wu and Kaas, J Neurosci 19: 7679± 7697, 19997679± 7697, , Neuron 28: 967± 978, 2000 may provide a basis for mislocated phantom sensations of missing forelimb movements accompanying actual shoulder movements during cortical stimulation or movement imagery in patients with amputations

Intrinsic-Signal Optical Imaging Reveals Cryptic Ocular Dominance Columns in Primary Visual Cortex of New World Owl Monkeys

A significant concept in neuroscience is that sensory areas of the neocortex have evolved the remarkable ability to represent a number of stimulus features within the confines of a global map of the sensory periphery. Modularity, the term often used to describe the inhomogeneous nature of the neocortex, is without a doubt an important organizational principle of early sensory areas, such as the primary visual cortex (V1). Ocular dominance columns, one type of module in V1, are found in many primate species as well as in carnivores. Yet, their variable presence in some New World monkey species and complete absence in other species has been enigmatic. Here, we demonstrate that optical imaging reveals the presence of ocular dominance columns in the superficial layers of V1 of owl monkeys (Aotus trivirgatus), even though the geniculate inputs related to each eye are highly overlapping in layer 4. The ocular dominance columns in owl monkeys revealed by optical imaging are circular in appearance. The distance between left eye centers and right eye centers is approximately 650 μm. We find no relationship between ocular dominance centers and other modular organizational features such as orientation pinwheels or the centers of the cytochrome oxidase blobs. These results are significant because they suggest that functional columns may exist in the absence of obvious differences in the distributions of activating inputs and ocular dominance columns may be more widely distributed across mammalian taxa than commonly suggested

Forbedret togbetjening med S-tog til Roskilde

S-togsprojektet indeholder to etaper: Første etape er at etablere mulighed for at køre 2-system S-tog Østerport-Roskilde, anden etape at skabe tilsvarende mulighed Kastrup-Roskilde. Artiklen giver en generel projektstatus på fremlæggelsestidspunktet; herunder hovedmilepæle, myndigheds- og interessentindragelse mm.Kørsel med 2-system S-tog betyder, at der skal etableres systemskiftezoner for togkontrol, radio og kørestrøm ved overgang fra S-bane til fjernbane og vice versa. Indlæggene vil beskrive principperne for systemskiftet, samt gennemgå de planlagte anlægsarbejder på de største lokaliteter. Også konsekvenserne for trafikstyringen vil blive gennemgået, og der vil blive givet en konceptbeskrivelse af mulig sammenbinding af fjernstyring S-bane/fjernbane.Artiklen omfatter endvidere trafikale forhold: Køreplanseksempler, passagertal, muligheden for nye stationer, projektets perspektiver for videreførelse af 2-systemdriften; f eks ad Kystbanen. Der vil blive sat fokus på resultaterne af de gennemførte kapacitetsanalyser

The time delay of the quadruple quasar RX J0911.4+0551

We present optical lightcurves of the gravitationally lensed components A (=A1+A2+A3) and B of the quadruple quasar RX J0911.4+0551 (z = 2.80). The observations were primarily obtained at the Nordic Optical Telescope between 1997 March and 2001 April and consist of 74 I-band data points for each component. The data allow the measurement of a time delay of 146 +- 8 days (2 sigma) between A and B, with B as the leading component. This value is significantly shorter than that predicted from simple models and indicates a very large external shear. Mass models including the main lens galaxy and the surrounding massive cluster of galaxies at z = 0.77, responsible for the external shear, yield H_0 = 71 +- 4 (random, 2 sigma) +- 8 (systematic) km/s/Mpc. The systematic model uncertainty is governed by the surface-mass density (convergence) at the location of the multiple images.Comment: 12 pages, 3 figures, ApJL, in press (June 20, 2002

Spin and Statistics and First Principles

It was shown in the early Seventies that, in Local Quantum Theory (that is the most general formulation of Quantum Field Theory, if we leave out only the unknown scenario of Quantum Gravity) the notion of Statistics can be grounded solely on the local observable quantities (without assuming neither the commutation relations nor even the existence of unobservable charged field operators); one finds that only the well known (para)statistics of Bose/Fermi type are allowed by the key principle of local commutativity of observables. In this frame it was possible to formulate and prove the Spin and Statistics Theorem purely on the basis of First Principles. In a subsequent stage it has been possible to prove the existence of a unique, canonical algebra of local field operators obeying ordinary Bose/Fermi commutation relations at spacelike separations. In this general guise the Spin - Statistics Theorem applies to Theories (on the four dimensional Minkowski space) where only massive particles with finite mass degeneracy can occur. Here we describe the underlying simple basic ideas, and briefly mention the subsequent generalisations; eventually we comment on the possible validity of the Spin - Statistics Theorem in presence of massless particles, or of violations of locality as expected in Quantum Gravity.Comment: Survey based on a talk given at the Meeting on "Theoretical and experimental aspects of the spin - statistics connection and related symmetries", Trieste, Italy - October 21-25, 200