Simulation of Turing machines with analytic discrete ODEs: FPTIME and FPSPACE over the reals characterised with discrete ordinary differential equations

We prove that functions over the reals computable in polynomial time can be characterised using discrete ordinary differential equations (ODE), also known as finite differences. We also provide a characterisation of functions computable in polynomial space over the reals. In particular, this covers space complexity, while existing characterisations were only able to cover time complexity, and were restricted to functions over the integers. We prove furthermore that no artificial sign or test function is needed even for time complexity. At a technical level, this is obtained by proving that Turing machines can be simulated with analytic discrete ordinary differential equations. We believe this result opens the way to many applications, as it opens the possibility of programming with ODEs, with an underlying well-understood time and space complexity.Comment: arXiv admin note: text overlap with arXiv:2209.1340

A Characterisation of Functions Computable in Polynomial Time and Space over the Reals with Discrete Ordinary Differential Equations: Simulation of Turing Machines with Analytic Discrete ODEs

We prove that functions over the reals computable in polynomial time can be characterised using discrete ordinary differential equations (ODE), also known as finite differences. We also provide a characterisation of functions computable in polynomial space over the reals. In particular, this covers space complexity, while existing characterisations were only able to cover time complexity, and were restricted to functions over the integers, and we prove that no artificial sign or test function is needed even for time complexity. At a technical level, this is obtained by proving that Turing machines can be simulated with analytic discrete ordinary differential equations. We believe this result opens the way to many applications, as it opens the possibility of programming with ODEs, with an underlying well-understood time and space complexity

Role of coagulation cascade peptides in the regulation of fibroblast proliferation.

Fibroblast proliferation and extracellular matrix deposition play a critical role in tissue repair and fibrosis. These functions are thought to be modulated by cytokines and growth factors, but these mechanisms are only partially understood. Tissue injury is associated with blood vessel disruption and the activation of coagulation cascade factors VII, IX, X and II (prothrombin) which result in the cleavage of blood fibrinogen into a haemostatic fibrin clot. In addition, increased levels of active coagulation cascade factors and fibrin deposition are associated with fibrotic diseases of the lung, liver, kidney, heart and vasculature. Recently, thrombin has been shown to promote fibroblast chemotaxis, proliferation and procollagen production in vitro and it has been proposed that it may contribute to tissue repair and fibrosis. Little is known about the cellular effects of the other coagulation cascade factors. The aim of this thesis is to study the effects of coagulation factors VIIa, IXa, Xa and fibrinogen cleavage products on fibroblast proliferation in vitro. This thesis shows that factor Xa is mitogenic for fibroblasts and the kinetics of this effect are equivalent to that of thrombin. Studies with specific inhibitors and antibodies demonstrated that this effect is dependent on its catalytic site, but independent of thrombin generation. Furthermore, this is mediated by platelet-derived growth factor production and autocrine stimulation similarly to thrombin. In contrast, factor IXa and fibrinogen-derived peptides have no effects, but factor VIIa and stimulates proliferation at high concentrations. Further studies of receptor expression, activation and intracellular calcium signalling showed that factor Xa stimulates proliferation via binding to effector cell-protease receptor-1 and the proteolytic activation of protease-activated receptor-1. In conclusion, this thesis demonstrated for the first time that coagulation cascade factors Xa and VIIa are mitogenic for fibroblasts, but not all peptides generated during blood coagulation. Furthermore, the mitogenic effect of factor Xa is mediated by a novel dual receptor system involving binding to effector-cell protease receptor-1 and activation of protease-activated receptor-1. These observations suggest that factor Xa may play a role in the regulation of fibroblast proliferation during normal tissue repair and fibrosis

Experimental phase-space-based optical amplification of scar modes

Waves billiard which are chaotic in the geometrical limit are known to support non-generic spatially localized modes called scar modes. The interaction of the scar modes with gain has been recently investigated in optics in micro-cavity lasers and vertically-cavity surface-emitting lasers. Exploiting the localization properties of scar modes in their wave analogous phase space representation, we report experimental results of scar modes selection by gain in a doped D-shaped optical fiber

Local deformations and incommensurability of high quality epitaxial graphene on a weakly interacting transition metal

We investigate the fine structure of graphene on iridium, which is a model for graphene weakly interacting with a transition metal substrate. Even the highest quality epitaxial graphene displays tiny imperfections, i.e. small biaxial strains, ca. 0.3%, rotations, ca. 0.5^{\circ}, and shears over distances of ca. 100 nm, and is found incommensurate, as revealed by X-ray diffraction and scanning tunneling microscopy. These structural variations are mostly induced by the increase of the lattice parameter mismatch when cooling down the sample from the graphene preparation temperature to the measurement temperature. Although graphene weakly interacts with iridium, its thermal expansion is found positive, contrary to free-standing graphene. The structure of graphene and its variations are very sensitive to the preparation conditions. All these effects are consistent with initial growth and subsequent pining of graphene at steps

Modal Decomposition in Goalpost Micro/nano Electro-mechanical Devices

We have studied the first three symmetric out-of-plane flexural resonance modes of a goalpost silicon micro-mechanical device. Measurements have been performed at 4.2K in vacuum, demonstrating high Qs and good linear properties. Numerical simulations have been realized to fit the resonance frequencies and produce the mode shapes. These mode shapes are complex, since they involve distortions of two coupled orthogonal bars. Nonetheless, analytic expressions have been developed to reproduce these numerical results, with no free parameters. Owing to their generality they are extremely helpful, in particular to identify the parameters which may limit the performances of the device. The overall agreement is very good, and has been verified on our nano-mechanical version of the device.Comment: Journal of Low Temperature Physics (2013

Assessing Regional Sustainability with the EPSILON Project

http://www.smia.info/files/eh94g6x4.f1_fr-1254.pdfInternational audienceThe EPSILON project (Environmental Policy via Sustainability Indicators On a European-wide level --2002-2005) is delivering a GIS integrated computerized model for benchmarking European regions through an aggregation of indicators represented on sustainability maps. Assessing sustainability within the EPSILON project has been addressed over four spheres/pillars: the environmental, the economic, the social and the institutional dimension as defined by the UN Commission on Sustainable Development. A coherent objective based structure has been defined relying strongly on the analytical DPSIR framework (Driving-Forces, Pressures, State, Impact and Response model from the European Environmental Agency). Such structure has been defined through a relevant definition of Indicators, sub-themes, themes and pillars for which maps at national level over 15 European countries are provided. Regional maps are also provided at regional levels (NUTS II and NUTS III levels). These results should not be considered as absolute figures but rather as an attempt of a relative sustainability assessment. Such regional sustainability assessment illustrates the interest to move down from a national assessment to a more local level by revealing higher data dispersion and detecting for example specific environmental issues, which would have been levelled otherwise at national scale

An Efficient Network API for in-Kernel Applications in Clusters

International audienceRunning parallel applications on clusters with high-speed local networks requires fast communication between computing nodes but also low latency and high bandwidth file access. However, the application programming interfaces of high-speed local networks were designed for MPI communication and do not always meet the requirements of other applications like distributed file systems. In this paper, we explore several solutions to improve the use of high-speed network for in-kernel applications. Distributed file systems implemented on top of the GM interface of Myrinet are first examined to demonstrate how hard it is to get an efficient interaction between such applications and the network. Then, we propose solutions to simplify and improve this interaction and integrate them into the kernel interface of the new Myrinet. Performance comparisons between MX and GM, and their usage in both a distributed file system and a zero-copy protocol show nice improvements. Moreover, we are able to improve the performance of the flexible kernel API we designed in MX that allows to remove some intermediate copy