Liapunov's second method

Stability theorem based on Liapunov function, and using invariance property of limit sets of solutions to differential equation

La Banque de France et la gestion des billets.

Au cours des vingt-cinq dernières années, le rôle de la banque centrale et celui des sociétés de transport de fonds se sont renforcés dans l’organisation de la filière fiduciaire en France.monnaie fiduciaire, billets, cycle fiduciaire, banque centrale, transport de fonds.

Asymptotic Stability for a Class of Metriplectic Systems

Using the framework of metriplectic systems on $\R^n$ we will describe a constructive geometric method to add a dissipation term to a Hamilton-Poisson system such that any solution starting in a neighborhood of a nonlinear stable equilibrium converges towards a certain invariant set. The dissipation term depends only on the Hamiltonian function and the Casimir functions

Advanced Multilevel Node Separator Algorithms

A node separator of a graph is a subset S of the nodes such that removing S and its incident edges divides the graph into two disconnected components of about equal size. In this work, we introduce novel algorithms to find small node separators in large graphs. With focus on solution quality, we introduce novel flow-based local search algorithms which are integrated in a multilevel framework. In addition, we transfer techniques successfully used in the graph partitioning field. This includes the usage of edge ratings tailored to our problem to guide the graph coarsening algorithm as well as highly localized local search and iterated multilevel cycles to improve solution quality even further. Experiments indicate that flow-based local search algorithms on its own in a multilevel framework are already highly competitive in terms of separator quality. Adding additional local search algorithms further improves solution quality. Our strongest configuration almost always outperforms competing systems while on average computing 10% and 62% smaller separators than Metis and Scotch, respectively

Thermodynamics of adiabatic feedback control

We study adaptive control of classical ergodic Hamiltonian systems, where the controlling parameter varies slowly in time and is influenced by system's state (feedback). An effective adiabatic description is obtained for slow variables of the system. A general limit on the feedback induced negative entropy production is uncovered. It relates the quickest negentropy production to fluctuations of the control Hamiltonian. The method deals efficiently with the entropy-information trade off.Comment: 6 pages, 1 figur

Nonlinear effect on quantum control for two-level systems

The traditional quantum control theory focuses on linear quantum system. Here we show the effect of nonlinearity on quantum control of a two-level system, we find that the nonlinearity can change the controllability of quantum system. Furthermore, we demonstrate that the Lyapunov control can be used to overcome this uncontrollability induced by the nonlinear effect.Comment: 4 pages, 5 figure

Phase II Open Label Study of Valproic Acid in Spinal Muscular Atrophy

UNLABELLED:Preliminary in vitro and in vivo studies with valproic acid (VPA) in cell lines and patients with spinal muscular atrophy (SMA) demonstrate increased expression of SMN, supporting the possibility of therapeutic benefit. We performed an open label trial of VPA in 42 subjects with SMA to assess safety and explore potential outcome measures to help guide design of future controlled clinical trials. Subjects included 2 SMA type I ages 2-3 years, 29 SMA type II ages 2-14 years and 11 type III ages 2-31 years, recruited from a natural history study. VPA was well-tolerated and without evident hepatotoxicity. Carnitine depletion was frequent and temporally associated with increased weakness in two subjects. Exploratory outcome measures included assessment of gross motor function via the modified Hammersmith Functional Motor Scale (MHFMS), electrophysiologic measures of innervation including maximum ulnar compound muscle action potential (CMAP) amplitudes and motor unit number estimation (MUNE), body composition and bone density via dual-energy X-ray absorptiometry (DEXA), and quantitative blood SMN mRNA levels. Clear decline in motor function occurred in several subjects in association with weight gain; mean fat mass increased without a corresponding increase in lean mass. We observed an increased mean score on the MHFMS scale in 27 subjects with SMA type II (p<or=0.001); however, significant improvement was almost entirely restricted to participants <5 years of age. Full length SMN levels were unchanged and Delta7SMN levels were significantly reduced for 2 of 3 treatment visits. In contrast, bone mineral density (p<or=0.0036) and maximum ulnar CMAP scores (p<or=0.0001) increased significantly. CONCLUSIONS:While VPA appears safe and well-tolerated in this initial pilot trial, these data suggest that weight gain and carnitine depletion are likely to be significant confounding factors in clinical trials. This study highlights potential strengths and limitations of various candidate outcome measures and underscores the need for additional controlled clinical trials with VPA targeting more restricted cohorts of subjects. TRIAL REGISTRATION:ClinicalTrials.gov

SMA CARNI-VAL Trial Part I: Double-Blind, Randomized, Placebo-Controlled Trial of L-Carnitine and Valproic Acid in Spinal Muscular Atrophy

Valproic acid (VPA) has demonstrated potential as a therapeutic candidate for spinal muscular atrophy (SMA) in vitro and in vivo.Two cohorts of subjects were enrolled in the SMA CARNIVAL TRIAL, a non-ambulatory group of "sitters" (cohort 1) and an ambulatory group of "walkers" (cohort 2). Here, we present results for cohort 1: a multicenter phase II randomized double-blind intention-to-treat protocol in non-ambulatory SMA subjects 2-8 years of age. Sixty-one subjects were randomized 1:1 to placebo or treatment for the first six months; all received active treatment the subsequent six months. The primary outcome was change in the modified Hammersmith Functional Motor Scale (MHFMS) score following six months of treatment. Secondary outcomes included safety and adverse event data, and change in MHFMS score for twelve versus six months of active treatment, body composition, quantitative SMN mRNA levels, maximum ulnar CMAP amplitudes, myometry and PFT measures.At 6 months, there was no difference in change from the baseline MHFMS score between treatment and placebo groups (difference = 0.643, 95% CI = -1.22-2.51). Adverse events occurred in >80% of subjects and were more common in the treatment group. Excessive weight gain was the most frequent drug-related adverse event, and increased fat mass was negatively related to change in MHFMS values (p = 0.0409). Post-hoc analysis found that children ages two to three years that received 12 months treatment, when adjusted for baseline weight, had significantly improved MHFMS scores (p = 0.03) compared to those who received placebo the first six months. A linear regression analysis limited to the influence of age demonstrates young age as a significant factor in improved MHFMS scores (p = 0.007).This study demonstrated no benefit from six months treatment with VPA and L-carnitine in a young non-ambulatory cohort of subjects with SMA. Weight gain, age and treatment duration were significant confounding variables that should be considered in the design of future trials.Clinicaltrials.gov NCT00227266

Understanding the town centre customer experience (TCCE)

This research enhances the understanding of consumer behaviour and customer experience in the context of town centres. First, it defines town centre customer experience (TCCE) as a multifaceted journey that combines interactions with a diverse range of public and private organisations, including retailers and social and community elements; this results in a unique experience co-created with the consumer across a series of functional and experiential touchpoints. Second, combining qualitative and quantitative insights, this research reveals a series of specific functional and experiential TCCE touchpoints, which underpin the consumer internal response (motivation to visit) and outward behaviour (desire to stay and revisit intentions) in the town centre. In addition to enhancing town centre and customer experience knowledge, these findings offer important new insights to those managing town centres and seeking to retain customer loyalty in the high street. Above all, these findings can help identify the touchpoints that need to be reinforced and/or improved to differentiate a town from its competing centres and to create tailored marketing strategies. Taken together, such initiatives have the potential to positively impact the revitalisation of the high street and the town centre economy