Upper estimate of martingale dimension for self-similar fractals

We study upper estimates of the martingale dimension $d_m$ of diffusion processes associated with strong local Dirichlet forms. By applying a general strategy to self-similar Dirichlet forms on self-similar fractals, we prove that $d_m=1$ for natural diffusions on post-critically finite self-similar sets and that $d_m$ is dominated by the spectral dimension for the Brownian motion on Sierpinski carpets.Comment: 49 pages, 7 figures; minor revision with adding a referenc

A macroscopic multifractal analysis of parabolic stochastic PDEs

It is generally argued that the solution to a stochastic PDE with multiplicative noise---such as $\dot{u}=\frac12 u"+u\xi$, where $\xi$ denotes space-time white noise---routinely produces exceptionally-large peaks that are "macroscopically multifractal." See, for example, Gibbon and Doering (2005), Gibbon and Titi (2005), and Zimmermann et al (2000). A few years ago, we proved that the spatial peaks of the solution to the mentioned stochastic PDE indeed form a random multifractal in the macroscopic sense of Barlow and Taylor (1989; 1992). The main result of the present paper is a proof of a rigorous formulation of the assertion that the spatio-temporal peaks of the solution form infinitely-many different multifractals on infinitely-many different scales, which we sometimes refer to as "stretch factors." A simpler, though still complex, such structure is shown to also exist for the constant-coefficient version of the said stochastic PDE.Comment: 41 page

Relic Abundance of Asymmetric Dark Matter

We investigate the relic abundance of asymmetric Dark Matter particles that were in thermal equilibrium in the early universe. The standard analytic calculation of the symmetric Dark Matter is generalized to the asymmetric case. We calculate the asymmetry required to explain the observed Dark Matter relic abundance as a function of the annihilation cross section. We show that introducing an asymmetry always reduces the indirect detection signal from WIMP annihilation, although it has a larger annihilation cross section than symmetric Dark Matter. This opens new possibilities for the construction of realistic models of MeV Dark Matter.Comment: 20 pages, 11 figures, Accepted by JCA

A Biomimetic steering robot for Minimally invasive surgery application

International audienceMinimally Invasive Surgery represents the future of many types of medical inter- ventions such as keyhole neurosurgey or transluminal endoscopic surgery. These procedures involve insertion of surgical instruments such as needles and endoscopes into human body through small incision/ body cavity for biopsy and drug delivery. However, nearly all surgical instruments for these procedures are inserted manually and there is a long learning curve for surgeons to use them properly. Many research efforts have been made to design active instruments (endoscope, needles) to improve this procedure during last decades. New robot mechanisms have been designed and used to improve the dexterity of current endoscope. Usually these robots are flexible and can pass the constrained space for fine manipulations. In recent years, a con- tinuum robotic mechanism has been investigated and designed for medical surgery. Those robots are characterized by the fact that their mechanical components do not have rigid links and discrete joints in contrast with traditional robot manipula- tors. The design of these robots is inspired by movements of natural animals such as tongues, elephant trunks and tentacles. The unusual compliance and redundant degrees of freedom of these robots provide strong potential to achieve delicate tasks successfully even in cluttered and unstructured environments. This chapter will present a complete application of a continuum robot for Mini- mally Invasive Surgery of colonoscopy. This system is composed of a micro-robotic tip, a set of position sensors and a real-time control system for guiding the explo- ration of colon. Details will be described on the modeling of the used pneumatic actuators, the design of the mechanical component, the kinematic model analysis and the control strategy for automatically guiding the progression of the device inside the human colon. Experimental results will be presented to check the perfor- mances of the whole system within a transparent tube

Comments on the Boundary Scattering Phase

We present a simple solution to the crossing equation for an open string worldsheet reflection matrix, with boundaries preserving a SU(1|2)^2 residual symmetry, which constrains the boundary dressing factor. In addition, we also propose an analogous crossing equation for the dressing factor where extra boundary degrees of freedom preserve a SU(2|2)^2 residual symmetry.Comment: 14 pages, 2 figures; v2: affiliation correcte

Palladacycles bearing tridentate CNS-type benzamidinate ligands as catalysts for cross-coupling reactions

Three pendant benzamidines, [Ph-C(=NC6H5)-{NH(E)}] [E = -(CH2)(2)SMe (1); -(CH2)(2)(SBu)-Bu-t (2); -o-C6H4SMe (3)], are described. Reactions of 1, 2 or 3 with one molar equivalent of Pd(OAc)(2) in CH2Cl2 give the palladacyclic complexes, [Ph-C{-NH(eta(1)-C6H4)} {=N(E)}]Pd(OAc) [E = -(CH2)(2)SMe (4); -(CH2)(2)(SBu)-Bu-t (5); -o-C6H4SMe (6)], as mononuclear palladium complexes respectively. A minor product described as 5', {[Ph-C{-N(C6H5)} {-N(CH2)(2)(SBu)-Bu-t}]Pd(OAc)}(2), was isolated as benzamidinate-bridged dinuclear palladium complex upon recrystallizing from Et2O/hexane solution. Treatment of 1, 2 or 3 with one molar equivalent of PdCl2 in the presence of NEt3 in CH2Cl2 gives the palladacyclic complexes, [Ph-C{-NH(eta(1)-C6H4)}{=N(E)}]PdCl [E = -(CH2)(2)SMe (7); -(CH2)(2)(SBu)-Bu-t (8); -o-C6H4SMe (9)], as mononuclear palladium complexes respectively. The crystal and molecular structures are reported for compounds 5, 5' and 6-8. The application of these palladacyclic complexes to the Suzuki and Heck coupling reactions was examined

Pathogenesis and Treatment of Usher Syndrome Type IIA

Usher syndrome (USH) is the most common form of deaf-blindness, with an estimated prevalence of 4.4 to 16.6 per 100,000 people worldwide. The most common form of USH is type IIA (USH2A), which is caused by homozygous or compound heterozygous mutations in the USH2A gene and accounts for around half of all USH cases. USH2A patients show moderate to severe hearing loss from birth, with diagnosis of retinitis pigmentosa in the second decade of life and variable vestibular involvement. Although hearing aids or cochlear implants can provide some mitigation of hearing deficits, there are currently no treatments aimed at preventing or restoring vision loss in USH2A patients. In this review, we first provide an overview of the molecular biology of the USH2A gene and its protein isoforms, which include a transmembrane protein (TM usherin) and an extracellular protein (EC usherin). The role of these proteins in the inner ear and retina and their impact on the pathogenesis of USH2A is discussed. We review animal cell-derived and patient cell-derived models currently used in USH2A research and conclude with an overview of potential treatment strategies currently in preclinical development and clinical trials

The Zamolodchikov-Faddeev algebra for open strings attached to giant gravitons

We extend the Zamolodchikov-Faddeev algebra for the superstring sigma model on $AdS_{5}\times S^{5}$, which was formulated by Arutyunov, Frolov and Zamaklar, to the case of open strings attached to maximal giant gravitons, which was recently considered by Hofman and Maldacena. We obtain boundary $S$-matrices which satisfy the standard boundary Yang-Baxter equation.Comment: 22 pages, no figure; added a referenc

Constraining the variation of the coupling constants with big bang nucleosynthesis

We consider the possibility of the coupling constants of the $SU(3)\times SU(2)\times U(1)$ gauge interactions at the time of big bang nucleosynthesis having taken different values from what we measure at present, and investigate the allowed difference requiring the shift in the coupling constants not violate the successful calculation of the primordial abundances of the light elements. We vary gauge couplings and Yukawa couplings (fermion masses) using a model in which their relative variations are governed by a single scalar field, dilaton, as found in string theory. The results include a limit on the fine structure constant $-6.0\times10^{-4}<\Delta\alpha_{EM}/\alpha_{EM}<1.5\times10^{-4}$, which is two orders stricter than the limit obtained by considering the variation of $\alpha_{EM}$ alone.Comment: 7 page

Dynamics of high-velocity domain wall motion and spin wave excitation in trilayer structures

Propagation of dipolar-coupled transverse domain walls in a permalloy/non-magnetic/permalloy trilayer was investigated using micromagnetic modeling. Circulating stray fields meant that the walls adopted a composite structure with behavior analogous to walls seen in nanotubes. Wall velocities were sensitive to the chirality of the stray field circulation, with velocities of the most favored chirality enhanced by 32% compared with velocities seen in the individual constituent layers just below their Walker breakdown field. Additionally, Walker breakdown was completely suppressed within the trilayer for both chiralities, despite occurring in the constituent layers when modelled in isolation, leading to a maximum of 317% velocity enhancement. Wall velocity saturated around 1100 m/s due to the Cherenkov-like emission of spin waves, comparable to the magnonic regime of nanotubes. By reproducing the advantageous domain wall dynamics of nanotubes within a planar system, we demonstrate that ultrafast magnetic switching may feasibly be realized within a lithographically produced system