Stochastic Formal Correctness of Numerical Algorithms

We provide a framework to bound the probability that accumulated errors were never above a given threshold on numerical algorithms. Such algorithms are used for example in aircraft and nuclear power plants. This report contains simple formulas based on Levy's and Markov's inequalities and it presents a formal theory of random variables with a special focus on producing concrete results. We selected four very common applications that fit in our framework and cover the common practices of systems that evolve for a long time. We compute the number of bits that remain continuously significant in the first two applications with a probability of failure around one out of a billion, where worst case analysis considers that no significant bit remains. We are using PVS as such formal tools force explicit statement of all hypotheses and prevent incorrect uses of theorems

Acute painful diabetic neuropathy: an uncommon, remittent type of acute distal small fibre neuropathy.

INTRODUCTION: Acute painful diabetic neuropathy (APDN) is a distinctive diabetic polyneuropathy and consists of two subtypes: treatment-induced neuropathy (TIN) and diabetic neuropathic cachexia (DNC). The characteristics of APDN are (1.) the small-fibre involvement, (2.) occurrence paradoxically after short-term achievement of good glycaemia control, (3.) intense pain sensation and (4.) eventual recovery. In the face of current recommendations to achieve quickly glycaemic targets, it appears necessary to recognise and understand this neuropathy. METHODS AND RESULTS: Over 2009 to 2012, we reported four cases of APDN. Four patients (three males and one female) were identified and had a mean age at onset of TIN of 47.7 years (±6.99 years). Mean baseline HbA1c was 14.2% (±1.42) and 7.0% (±3.60) after treatment. Mean estimated time to correct HbA1c was 4.5 months (±3.82 months). Three patients presented with a mean time to symptom resolution of 12.7 months (±1.15 months). One patient had an initial normal electroneuromyogram (ENMG) despite the presence of neuropathic symptoms, and a second abnormal ENMG showing axonal and myelin neuropathy. One patient had a peroneal nerve biopsy showing loss of large myelinated fibres as well as unmyelinated fibres, and signs of microangiopathy. CONCLUSIONS: According to the current recommendations of promptly achieving glycaemic targets, it appears necessary to recognise and understand this neuropathy. Based on our observations and data from the literature we propose an algorithmic approach for differential diagnosis and therapeutic management of APDN patients

A clinical study of motor evoked potentials using a triple stimulation technique

Amplitudes of motor evoked potentials (MEPs) are usually much smaller than those of motor responses to maximal peripheral nerve stimulation, and show marked variation between normal subjects and from one stimulus to another. Consequently, amplitude measurements have low sensitivity to detect central motor conduction failures due to the broad range of normal values. Since these characteristics are mostly due to varying desynchronization of the descending action potentials, causing different degrees of phase cancellation, we applied the recently developed triple stimulation technique (TST) to study corticospinal conduction to 489 abductor digiti minimi muscles of 271 unselected patients referred for possible corticospinal dysfunction. The TST allows resynchronization of the MEP, and thereby a quantification of the proportion of motor units activated by the transcranial stimulus. TST results were compared with those of conventional MEPs. In 212 of 489 sides, abnormal TST responses suggested conduction failure of various degrees. By contrast, conventional MEPs detected conduction failures in only 77 of 489 sides. The TST was therefore 2.75 times more sensitive than conventional MEPs in disclosing corticospinal conduction failures. When the results of the TST and conventional MEPs were combined, 225 sides were abnormal: 145 sides showed central conduction failure, 13 sides central conduction slowing and 67 sides both conduction failure and slowing. It is concluded that the TST is a valuable addition to the study of MEPs, since it improves detection and gives quantitative information on central conduction failure, an abnormality which appears to be much more frequent than conduction slowing. This new technique will be useful in following the natural course and the benefit of treatments in disorders affecting central motor conductio

Deep reflection seismic imaging of the internal zone of the South Armorican Hercynian belt (western France) (ARMOR 2/Géofrance 3D Program) Imagerie sismique de la zone interne de la chaîne hercynienne sud-armoricaine (projet Armor 2/programme Géofrance 3D)

International audienceWe present results and interpretation of a 72 km long deep seismic reflection profile acquired across the internal zone of the Hercynian belt of South Brittany. The profile is of excellent quality, most of the crust being highly reflective. The “ARMOR 2 South” profile, is correlated with the “ARMOR 2 North” profile that was published in 2003. Correlation of the main subsurface reflections with surface geological and structural data provides important information about the crustal structure that resulted from thickening during Late Devonian and regional-scale extension during Late Carboniferous. In particular, seismics image shows a very high reflectivity zone, lying flat over more than 40 km at about 10–12 km depth. This zone is interpreted as a major zone of ductile crustal thinning. Nous présentons les résultats et l'interprétation d'un profil de sismique réflexion en écoute longue, de 72 km de long à travers les zones internes de la chaîne hercynienne sud-armoricaine. Le profil est d'excellente qualité, avec une forte réflectivité à travers toute la croûte. Le profil, « ARMOR 2 Sud », est corrélé avec le profil « ARMOR 2 Nord » publié en 2003. Les corrélations des réflexions les plus superficielles avec les données géologiques et structurales de surface fournissent d'importantes informations sur la structure crustale qui résulte d'un épaississement débutant au Dévonien supérieur et d'une extension régionale au Carbonifère supérieur. En particulier, la sismique met en évidence une zone sub-horizontale à très forte réflectivité, de plus de 40 km de long à environ 10–12 km de profondeur. Cette zone est interprétée comme une zone d'amincissement crustal majeur

Slab segmentation controls the interplate slip motion in the SW Hellenic subduction: New insight from the 2008Mw 6.8 Methoni interplate earthquake

We present an integrated approach of the seismic structure and activity along the offshore SW Hellenic subduction from combined observations of marine and land seismic stations. Our imaging of the slab top topography from teleseismic receiver function analysis at ocean bottom seismometers supports a trenchward continuation of the along-dip slab faults beneath the Peloponnesus. We further show that their morphostructural control accounts for the backstepping of the thrust contact of the Mediterranean Ridge accretionary wedge over the upper plate. Local seismic activity offshore SW Peloponnesus constrained by ocean bottom seismometer observations reveals a correlation with specific features of the forearc: the Matapan Troughs. We study the Mw6.8 14.02.2008 interplate earthquake offshore SW Peloponnesus and show that its nucleation, rupture zone, and aftershocks sequence are confined to one slab panel between two adjacent along-dip faults and are thus controlled by not only the offshore slab top segmentation but also the upper plate sea-bottom morphology

Machine Learning on Multiplexed Optical Metrology Pattern Shift Response Targets to Predict Electrical Properties

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Differential control of the scapulothoracic muscles in humans

This article has been made available through the Brunel Open Access Publishing Fund and is available from the specified link - Copyright @ 2007 The Physiological Society.The control of the scapulothoracic muscles trapezius (Tr) and serratus anterior (SA) has been examined in normal human subjects. Electromyographic recordings were made from the SA and Tr muscles (upper trapezius UTr, lower trapezius LTr) using surface electrodes placed bilaterally. Magnetic stimulation of the motor cortex and electrical stimulation of peripheral nerves were used to examine their descending and reflex control. The average optimal site of cortical stimulation was found to be the same for SA, UTr and LTr (an approximate centre of gravity of −0.6 cm, 3.7 cm where the centre of gravity is expressed as the mean anterio-posterior position, the mean medio-lateral position). Some asymmetry in the cortical representation of UTr was found in each individual tested. Magnetic stimulation evoked bilateral MEPs in Tr (latency contralateral (c) UTr 8.5 ± 1.6 ms, ipsilateral (i) UTr 19.0 ± 2.7 ms) but only contralateral responses were evoked in SA (11.2 ± 2.6 ms). Electrical stimulation of the long thoracic nerve at two sites was used to examine homonymous and heteronymous reflexes of SA, while electrical stimulation of cervical nerve of C3/4 was used to examine the heteronymous reflexes of Tr. Ipsilateral SA H reflexes were evoked at a latency of 9.9 ± 0.8 ms (proximal site) and 10.8 ± 1.2 ms (distal site). No group I reflexes were evoked from SA to its contralateral homologue. No group I reflexes were evoked between Tr and SA. Finally, cross-correlation of activity from the Tr muscle pairs and the SA muscle pair revealed that the motoneurones of the Tr muscles share some common presynaptic input whereas there was no detectable common presynaptic input to the SA muscle pair. This study extends and consolidates knowledge regarding the neural control of trapezius and for the first time explores the neural control of SA. The study demonstrates a contrasting bilateral control of Tr and SA. These patterns of connections are discussed in relation to the contrasting bilateral functional roles of these muscles