Certified Roundoff Error Bounds using Bernstein Expansions and Sparse Krivine-Stengle Representations

Floating point error is an inevitable drawback of embedded systems implementation. Computing rigorous upper bounds of roundoff errors is absolutely necessary to the validation of critical software. This problem is even more challenging when addressing non-linear programs. In this paper, we propose and compare two new methods based on Bernstein expansions and sparse Krivine-Stengle representations, adapted from the field of the global optimization to compute upper bounds of roundoff errors for programs implementing polynomial functions. We release two related software package FPBern and FPKiSten, and compare them with state of the art tools. We show that these two methods achieve competitive performance, while computing accurate upper bounds by comparison with other tools.Comment: 20 pages, 2 table

Ubiquitin Carboxyl-Terminal Hydrolase L1 in Parkinson’s Disease

Ubiquitin plays the crucial roles to maintain the ubiquitin proteasome system (UPS) functions, which were suggested that involved in Parkinson’s diease (PD). Ubiquitin C-terminal hydrolase L1 (UCHL1), which was detected in Lewy bodies of nerve cells in PD brains, plays an important role for maintaining ubiquitin pool in UPS. The first UCHL1 mutation (UCHL1I93M) was found in two siblings of a PD family. By contrast, UCHL1S18Y mutation was recognized to reduce the risk of developing PD by its specific antioxidant protective function. The studies of UCHL1 in mouse models showed that lack of UCHL1 resulted in motor ataxia, degeneration of axons, and instability of free ubiquitin level. Transgenic mice expressing UCHL1I93M mutant exhibited dopaminergic neuron (DA) degeneration in MPTP-treated conditions. In this chapter, we provide a summary on recent findings related to roles of UCH-L1 in PD. Knockdown dUCH, a homolog of human UCHL1, in fly dopaminergic neuron resulted as some Parkinson’s disease—like phenotype such as: (1) the underdevelopment and/or degeneration of DA neurons; (2) the shortage of dopamine in the brain; and (3) the locomotor dysfunctions. Those finding indicated that dUCH (ortholog of human UCH-L1 in Drosophila) plays an important role in Parkinson’s disease

Drosophila Model in the Study Role of UCH-L1

UCH-L1 (ubiquitin carboxyl-terminal hydrolase L1) is a protein, which plays an important role in ubiquitin-proteasome system. Many previous reports showed the relation between UCH-L1 and neurodegenerative diseases, diabetes, as well as cancer. However, the mechanism still remains unclear. In the aim to investigate the functions and regulatory mechanism of UCH-L1 in living organism, Drosophila melanogaster model was utilized to examine the role of UCH-L1. This chapter provides a summary on recent findings related to the roles of UCH-L1 based on the model. First, abnormal expression of Drosophila ubiquitin carboxyl-terminal hydrolase (dUCH) leads to the defects on fly tissue development and function. Gain function of dUCH in the eye imaginal discs induced a rough eye phenotype in the adult, partly resulting from induction of caspase-dependent apoptosis, upset of photoreceptor cell distribution and ommatidium apical mispatterning. Interestingly, the dUCH overexpression of induced rough eye phenotype was completely recused by co-expression either Sevenless or Draf of the mitogen-activated protein kinase pathway. Besides, knockdown dUCH in dopaminergic neurons resulted in some Parkinson’s disease—like phenotypes in fly. Taken together, those findings in Drosophila model contributed a significant dUCH in tissue development and function

Caractérisation du domaine cytoplasmique du récepteur du facteur autocrine de motilité et formation du complexe AMFR/p97/ubiquitine

Mémoire numérisé par la Direction des bibliothèques de l'Université de Montréal

Analysis of parametric biological models with non-linear dynamics

In this paper we present recent results on parametric analysis of biological models. The underlying method is based on the algorithms for computing trajectory sets of hybrid systems with polynomial dynamics. The method is then applied to two case studies of biological systems: one is a cardiac cell model for studying the conditions for cardiac abnormalities, and the second is a model of insect nest-site choice.Comment: In Proceedings HSB 2012, arXiv:1208.315

A study on the effects of plasma spraying parameters on the adhesion strength of Cr3C2-NiCr coating on 16Mn steel

This paper experimentally studied the adhesion strength of Cr3C2-30 %NiCr coating created on 16Mn steel substrate by plasma thermal coating technique in relation to spraying parameters. Experiments were carried out according to the central composite design (CCD) experimental matrix with three parameters: current intensity, powder feeding rate, and spray distance. Samples consisting of an annular disc and a latch made of 16Mn were fabricated according to the JIS H8664-1977 standard. Cr3C2-30 %NiCr coating was then created on the top surface of the disc including end of the latch. Adhesion strength of the coating to the substrate was measured through the tensile test. ANOVA analysis of variance was performed to evaluate the influence of the spraying parameters on adhesion strength and to build an empirical regression function representing the relationship between those parameters and the adhesion. Optimization problem was solved by ANOVA method and genetic algorithm (GA) to determine the value of the spraying parameters at which the coating has the greatest adhesion strength to the substrate. The results showed that the spraying parameters greatly affected the adhesion of the Cr3C2-30 %NiCr coating to the 16Mn substrate. Among them the spray distance has the greatest influence while the powder feeding rate has the least. Secondly, the regression function was well reflected the relationship between the three parameters and adhesion strength of the coating on the substrate. Using the values of spray parameter obtained from the GA optimization to create Cr3C2-30 %NiCr coating on 16Mn steel, the adhesion strength of the coating to the substrate reached a value of 98.4 % compared to the predictio

Reachability computation for polynomial dynamical systems

This paper is concerned with the problem of computing the bounded time reachable set of a polynomial discrete-time dynamical system. The problem is well-known for being difficult when nonlinear systems are considered. In this regard, we propose three reachability methods that differ in the set representation. The proposed algorithms adopt boxes, parallelotopes, and parallelotope bundles to construct flowpipes that contain the actual reachable sets. The latter is a new data structure for the symbolic representation of polytopes. Our methods exploit the Bernstein expansion of polynomials to bound the images of sets. The scalability and precision of the presented methods are analyzed on a number of dynamical systems, in comparison with other existing approaches

Stability Verification of Nearly Periodic Impulsive Linear Systems using Reachability Analysis

International audienceThe paper provides stability analysis to certain classes of hybrid systems, more precisely impulsive linear systems. This analysis is conducted using the notion of reachable set. The main contribution in this work is the derivation of theoretical necessary and sufficient conditions for impulsive linear systems with nearly periodic resets subject to timing contracts. This characterization serves as the basis of a computational method for the stability verification of the considered class of systems. In addition, we show how this work handles the problem of timing contract synthesis for the considered class and we generalize our approach to verify stability of impulsive linear systems with stochastic reset instants. Applications on sampled-data control systems and comparisons with existing results are then discussed, showing the effectiveness of our approach