Uniqueness of signature for simple curves

We propose a topological approach to the problem of determining a curve from its iterated integrals. In particular, we prove that a family of terms in the signature series of a two dimensional closed curve with finite p-variation, 1≤p<2, are in fact moments of its winding number. This relation allows us to prove that the signature series of a class of simple non-smooth curves uniquely determine the curves. This implies that outside a Chordal SLEκ null set, where 0<κ≤4, the signature series of curves uniquely determine the curves. Our calculations also enable us to express the Fourier transform of the n-point functions of SLE curves in terms of the expected signature of SLE curves. Although the techniques used in this article are deterministic, the results provide a platform for studying SLE curves through the signatures of their sample paths.

Simple piecewise geodesic interpolation of simple and Jordan curves with applications

We explicitly construct simple, piecewise minimizing geodesic, arbitrarily fine interpolation of simple and Jordan curves on a Riemannian manifold. In particular, a finite sequence of partition points can be specified in advance to be included in our construction. Then we present two applications of our main results: the generalized Green’s theorem and the uniqueness of signature for planar Jordan curves with finite p -variation for 1⩽p<2.

Cell motility and SCAR localisation in axenically growing Dictyostelium cells.

Dictyostelium is a popular experimental organism, in particular for studies of actin dynamics, cell motility and chemotaxis. We find that the motility of axenic cells is unexpectedly different from other strains during growth. In particular, vegetative AX3 cells do not show detectable localisation of SCAR and its regulatory complex to actin-rich protrusions such as filopodia and pseudopodia. Similarly, a range of different mutations, in particular knockouts of members of the SCAR complex and Ras proteins, cause different phenotypes during vegetative growth in different parental strains. Development reverses this unusual behaviour; aggregation-competent AX3 cells localise SCAR in the same way as cells of other strains and species. Studies on cell motility using vegetative cells should therefore be interpreted with caution.

Unusually short tandem repeats appear to reach chromosome ends of Rhynchosciara americana (Diptera: Sciaridae)

The characterisation of sequences at chromosome ends of Rhynchosciara americana was continued with the screening of a genomic library using as a probe a short repeat identified in a previous report (M-22, 22 bp) which was found to be specific for noncentromeric termini of this species. Simple repeats, complex tandem and apparently dispersed repeats were present in the genomic clones analysed. Repetitive sequences do not define individual chromosome tips as they were found in all noncentromeric ends. A novel and unusually short tandem repeat type for dipteran chromosome ends (named M-16) composed of 16 nucleotides and frequently associated with M-22 arrays was characterised in this work. Islands of M-16 and M-22 tandem repeats were found in all the genomic clones analysed. Individual probes representative of each repetitive element hybridised not only to all noncentromeric ends of R. americana chromosomes but also to inter-telomeric bridges. This contrasted with the other repeat types which displayed sub-telomeric localisation as seen by double detection of hybridised probe and telomeric reverse transcriptase. Some stretches composed of M-16 and M-22 tandem repeats localised in different regions of the analysed genomic clones were either identical or showed sequence similarity that was unexpectedly higher than the mean sequence similarity observed among repeats within each of their tandem arrays. The occurrence of segmental duplications, as deduced by sequence analyses involving the two repeats that appeared to reach chromosome ends, might indicate the involvement of this type of duplication process in the chromosome end maintenance in this species.

Effects of intensity and positional predictability of a visual stimulus on simple reaction time

The influence of visual stimuli intensity on manual reaction time (RT) was investigated under two different attentional settings: high (Experiment 1) and low (Experiment 2) stimulus location predictability. These two experiments were also run under both binocular and monocular viewing conditions. We observed that RT decreased as stimulus intensity increased. It also decreased as the viewing condition was changed from monocular to binocular as well as the location predictability shifted from low to high. A significant interaction was found between stimulus intensity and viewing condition, but no interaction was observed between neither of these factors and location predictability. These findings support the idea that the stimulus intensity effect arises from purely sensory, pre-attentive mechanisms rather than deriving from more efficient attentional capture. (C) 2010 Elsevier Ireland Ltd. All rights reserved.

M-deformations of A-simple germs from R(n) to R(n+1)

All A-simple corank-1 germs from R(n) to R(n+1), where n not equal 4, have an M-deformation, that is a deformation in which the maximal numbers of isolated stable singular points are simultaneously present in the image.

Termination of diamond surfaces with hydrogen, oxygen and fluorine using a small, simple plasma gun

We have formed and characterized polycrystalline diamond films with surfaces having hydrogen terminations, oxygen terminations, or fluorine terminations, using a small, simple and novel plasma gun to bombard the diamond surface, formed by plasma assisted CVD in a prior step, with ions of the wanted terminating species. The potential differences between surface regions with different terminations were measured by Kelvin Force Microscopy (KFM). The highest potential occurred for oxygen termination regions and the lowest for fluorine. The potential difference between regions with oxygen terminations and hydrogen terminations was about 80 mV, and between regions with hydrogen terminations and fluorine terminations about 150 mV. Regions with different terminations were identified and imaged using the secondary electron signal provided by scanning electron microscopy (SEM). since this signal presents contrast for surfaces with different electrical properties. The wettability of the surfaces with different terminations was evaluated, measuring contact angles. The sample with oxygen termination was the most hydrophilic, with a contact angle of 75 degrees. hydrogen-terminated regions with 83 degrees, and fluorine regions 93 degrees, the most hydrophobic sample. (C) 2010 Elsevier B.V. All rights reserved.

Tokamak magnetic field lines described by simple maps

The magnetic field line structure in a tokamak can be obtained by direct numerical integration of the field line equations. However, this is a lengthy procedure and the analysis of the solution may be very time-consuming. Otherwise we can use simple two-dimensional, area-preserving maps, obtained either by approximations of the magnetic field line equations, or from dynamical considerations. These maps can be quickly iterated, furnishing solutions that mirror the ones obtained from direct numerical integration, and which are useful when long-term studies of field line behavior are necessary (e.g. in diffusion calculations). In this work we focus on a set of simple tokamak maps for which these advantages are specially pronounced.

GLUON SATURATION AND THE FROISSART BOUND: A SIMPLE APPROACH

At very high energies we expect that the hadronic cross sections satisfy the Froissart bound, which is a well-established property of the strong interactions. In this energy regime we also expect the formation of the Color Glass Condensate, characterized by gluon saturation and a typical momentum scale: the saturation scale Q(s). In this paper we show that if a saturation window exists between the nonperturbative and perturbative regimes of Quantum Chromodynamics (QCD), the total cross sections satisfy the Froissart bound. Furthermore, we show that our approach allows us to described the high energy experimental data on pp/p (p) over bar total cross sections.

The dynamics of cargo driven by molecular motors in the context of asymmetric simple exclusion processes

We consider the dynamics of cargo driven by a collection of interacting molecular motors in the context of ail asymmetric simple exclusion process (ASEP). The model is formulated to account for (i) excluded-volume interactions, (ii) the observed asymmetry of the stochastic movement of individual motors and (iii) interactions between motors and cargo. Items (i) and (ii) form the basis of ASEP models and have already been considered to study the behavior of motor density profile [A. Parmeggiani. T. Franosch, E. Frey, Phase Coexistence in driven one-dimensional transport, Phys. Rev. Lett. 90 (2003) 086601-1-086601-4]. Item (iii) is new. It is introduced here as an attempt to describe explicitly the dependence of cargo movement on the dynamics of motors in this context. The steady-state Solutions Of the model indicate that the system undergoes a phase transition of condensation type as the motor density varies. We study the consequences of this transition to the behavior of the average cargo velocity. (C) 2009 Elsevier B.V. All rights reserved.

A simple relation between the Leimkuhler curve and the mean residual life

In this paper, a simple relation between the Leimkuhler curve and the mean residual life is established. The result is illustrated with several models commonly used in informetrics, such as exponential, Pareto and lognormal. Finally, relationships with some other reliability concepts are also presented. (C) 2010 Elsevier Ltd. All rights reserved.

The smallest simple Moufang loop

We study the simple Moufang loop GLL(F(2)) and give a complete description of its lattice of subloops. (C) 2008 Elsevier Inc. All rights reserved.

Integral group ring of the Suzuki sporadic simple group

Using the Luthar-Passi method, we investigate the classical Zassenhaus conjecture for the normalized unit group of the integral group ring of the Suzuki sporadic simple group Suz. As a consequence, for this group we confirm the Kimmerle`s conjecture on prime graphs.

TAUT REPRESENTATIONS OF COMPACT SIMPLE LIE GROUPS

The concept of taut submanifold of Euclidean space is due to Carter and West, and can be traced back to the work of Chern and Lashof on immersions with minimal total absolute curvature and the subsequent reformulation of that work by Kuiper in terms of critical point theory. In this paper, we classify the reducible representations of compact simple Lie groups, all of whose orbits are tautly embedded in Euclidean space, with respect to Z(2)-coefficients.

Simple components of the center of FG/J(FG)

Let G be a finite group, F a field, FG the group ring of G over F, and J(FG) the Jacobson radical of FG. Using a result of Berman and Witt, we give a method to determine the structure of the center of FG/J(FG), provided that F satisfies a field theoretical condition.