nth Root extraction: Double iteration process and Newton's method

AbstractA double iteration process already used to find the nth root of a positive real number is analysed and showed to be equivalent to the Newton's method. These methods are of order two and three. Higher-order methods for finding the nth root are also mentioned

Optimal Error Bounds for Quadratic Spline Interpolation

AbstractFour types of quadratic spline interpolants are considered for which we obtain error bounds of the form[formula]Moreover, the optimality of the constantC0is proved

Polynomial and Rational Approximations and the Link between Schröder’s Processes of the First and Second Kind

We show that Schröder’s processes of the first kind and of the second kind to obtain a simple root of a nonlinear equation are related by polynomial and rational approximations

Scalp spindles are associated with widespread intracranial activity with unexpectedly low synchrony

In humans, the knowledge of intracranial correlates of spindles is mainly gathered from noninvasive neurophysiologic and functional imaging studies which provide an indirect estimate of neuronal intracranial activity. This potential limitation can be overcome by intracranial electroencephalography used in presurgical epilepsy evaluation. We investigated the intracranial correlates of scalp spindles using combined scalp and intracerebral depth electrodes covering the frontal, parietal and temporal neocortex, and the scalp and intracranial correlates of hippocampal and insula spindles in 35 pre-surgical epilepsy patients. Spindles in the scalp were accompanied by widespread cortical increases in sigma band energy (10-16. Hz): the highest percentages were observed in the frontoparietal lateral and mesial cortex, whereas in temporal lateral and mesial structures only a low or no simultaneous increase was present. This intracranial involvement during scalp spindles showed no consistent pattern, and exhibited unexpectedly low synchrony across brain regions. Hippocampal spindles were shorter and spatially restricted with a low synchrony even within the temporal lobe. Similar results were found for the insula. We suggest that the generation of spindles is under a high local cortical influence contributing to the concept of sleep as a local phenomenon and challenging the notion of spindles as widespread synchronous oscillations.Instituto de Investigaciones en Electrónica, Control y Procesamiento de Señale

Scalp spindles are associated with widespread intracranial activity with unexpectedly low synchrony

In humans, the knowledge of intracranial correlates of spindles is mainly gathered from noninvasive neurophysiologic and functional imaging studies which provide an indirect estimate of neuronal intracranial activity. This potential limitation can be overcome by intracranial electroencephalography used in presurgical epilepsy evaluation. We investigated the intracranial correlates of scalp spindles using combined scalp and intracerebral depth electrodes covering the frontal, parietal and temporal neocortex, and the scalp and intracranial correlates of hippocampal and insula spindles in 35 pre-surgical epilepsy patients. Spindles in the scalp were accompanied by widespread cortical increases in sigma band energy (10-16. Hz): the highest percentages were observed in the frontoparietal lateral and mesial cortex, whereas in temporal lateral and mesial structures only a low or no simultaneous increase was present. This intracranial involvement during scalp spindles showed no consistent pattern, and exhibited unexpectedly low synchrony across brain regions. Hippocampal spindles were shorter and spatially restricted with a low synchrony even within the temporal lobe. Similar results were found for the insula. We suggest that the generation of spindles is under a high local cortical influence contributing to the concept of sleep as a local phenomenon and challenging the notion of spindles as widespread synchronous oscillations.Instituto de Investigaciones en Electrónica, Control y Procesamiento de Señale

Burkholderia thailandensis harbors two identical rhl gene clusters responsible for the biosynthesis of rhamnolipids

<p>Abstract</p> <p>Background</p> <p>Rhamnolipids are surface active molecules composed of rhamnose and β-hydroxydecanoic acid. These biosurfactants are produced mainly by <it>Pseudomonas aeruginosa </it>and have been thoroughly investigated since their early discovery. Recently, they have attracted renewed attention because of their involvement in various multicellular behaviors. Despite this high interest, only very few studies have focused on the production of rhamnolipids by <it>Burkholderia </it>species.</p> <p>Results</p> <p>Orthologs of <it>rhlA</it>, <it>rhlB </it>and <it>rhlC</it>, which are responsible for the biosynthesis of rhamnolipids in <it>P. aeruginosa</it>, have been found in the non-infectious <it>Burkholderia thailandensis</it>, as well as in the genetically similar important pathogen <it>B. pseudomallei</it>. In contrast to <it>P. aeruginosa</it>, both <it>Burkholderia </it>species contain these three genes necessary for rhamnolipid production within a single gene cluster. Furthermore, two identical, paralogous copies of this gene cluster are found on the second chromosome of these bacteria. Both <it>Burkholderia </it>spp. produce rhamnolipids containing 3-hydroxy fatty acid moieties with longer side chains than those described for <it>P. aeruginosa</it>. Additionally, the rhamnolipids produced by <it>B. thailandensis </it>contain a much larger proportion of dirhamnolipids versus monorhamnolipids when compared to <it>P. aeruginosa</it>. The rhamnolipids produced by <it>B. thailandensis </it>reduce the surface tension of water to 42 mN/m while displaying a critical micelle concentration value of 225 mg/L. Separate mutations in both <it>rhlA </it>alleles, which are responsible for the synthesis of the rhamnolipid precursor 3-(3-hydroxyalkanoyloxy)alkanoic acid, prove that both copies of the <it>rhl </it>gene cluster are functional, but one contributes more to the total production than the other. Finally, a double Δ<it>rhlA </it>mutant that is completely devoid of rhamnolipid production is incapable of swarming motility, showing that both gene clusters contribute to this phenotype.</p> <p>Conclusions</p> <p>Collectively, these results add another <it>Burkholderia </it>species to the list of bacteria able to produce rhamnolipids and this, by the means of two identical functional gene clusters. Our results also demonstrate the very impressive tensio-active properties these long-chain rhamnolipids possess in comparison to the well-studied short-chain ones from <it>P. aeruginosa</it>.</p

RGB-D-E: Event Camera Calibration for Fast 6-DOF Object Tracking

Augmented reality devices require multiple sensors to perform various tasks such as localization and tracking. Currently, popular cameras are mostly frame-based (e.g. RGB and Depth) which impose a high data bandwidth and power usage. With the necessity for low power and more responsive augmented reality systems, using solely frame-based sensors imposes limits to the various algorithms that needs high frequency data from the environement. As such, event-based sensors have become increasingly popular due to their low power, bandwidth and latency, as well as their very high frequency data acquisition capabilities. In this paper, we propose, for the first time, to use an event-based camera to increase the speed of 3D object tracking in 6 degrees of freedom. This application requires handling very high object speed to convey compelling AR experiences. To this end, we propose a new system which combines a recent RGB-D sensor (Kinect Azure) with an event camera (DAVIS346). We develop a deep learning approach, which combines an existing RGB-D network along with a novel event-based network in a cascade fashion, and demonstrate that our approach significantly improves the robustness of a state-of-the-art frame-based 6-DOF object tracker using our RGB-D-E pipeline.Comment: 9 pages, 9 figure

Facilitation of epileptic activity during sleep is mediated by high amplitude slow waves

Epileptic discharges in focal epilepsy are frequently activated during non-rapid eye movement sleep. Sleep slow waves are present during this stage and have been shown to include a deactivated ('down', hyperpolarized) and an activated state ('up', depolarized). The 'up' state enhances physiological rhythms, and we hypothesize that sleep slow waves and particularly the 'up' state are the specific components of non-rapid eye movement sleep that mediate the activation of epileptic activity. We investigated eight patients with pharmaco-resistant focal epilepsies who underwent combined scalp-intracerebral electroencephalography for diagnostic evaluation. We analysed 259 frontal electroencephalographic channels, and manually marked 442 epileptic spikes and 8487 high frequency oscillations during high amplitude widespread slow waves, and during matched control segments with low amplitude widespread slow waves, non-widespread slow waves or no slow waves selected during the same sleep stages (total duration of slow wave and control segments: 49 min each). During the slow waves, spikes and high frequency oscillations were more frequent than during control segments (79% of spikes during slow waves and 65% of high frequency oscillations, both P ~ 0). The spike and high frequency oscillation density also increased for higher amplitude slow waves. We compared the density of spikes and high frequency oscillations between the 'up' and 'down' states. Spike and high frequency oscillation density was highest during the transition from the 'up' to the 'down' state. Interestingly, high frequency oscillations in channels with normal activity expressed a different peak at the transition from the 'down' to the 'up' state. These results show that the apparent activation of epileptic discharges by non-rapid eye movement sleep is not a state-dependent phenomenon but is predominantly associated with specific events, the high amplitude widespread slow waves that are frequent, but not continuous, during this state of sleep. Both epileptic spikes and high frequency oscillations do not predominate, like physiological activity, during the 'up' state but during the transition from the 'up' to the 'down' state of the slow wave, a period of high synchronization. Epileptic discharges appear therefore more associated with synchronization than with excitability. Furthermore, high frequency oscillations in channels devoid of epileptic activity peak differently during the slow wave cycle from those in channels with epileptic activity. This property may allow differentiating physiological from pathological high frequency oscillations, a problem that is unresolved until now.Instituto de Investigaciones en Electrónica, Control y Procesamiento de Señale

Facilitation of epileptic activity during sleep is mediated by high amplitude slow waves

Epileptic discharges in focal epilepsy are frequently activated during non-rapid eye movement sleep. Sleep slow waves are present during this stage and have been shown to include a deactivated ('down', hyperpolarized) and an activated state ('up', depolarized). The 'up' state enhances physiological rhythms, and we hypothesize that sleep slow waves and particularly the 'up' state are the specific components of non-rapid eye movement sleep that mediate the activation of epileptic activity. We investigated eight patients with pharmaco-resistant focal epilepsies who underwent combined scalp-intracerebral electroencephalography for diagnostic evaluation. We analysed 259 frontal electroencephalographic channels, and manually marked 442 epileptic spikes and 8487 high frequency oscillations during high amplitude widespread slow waves, and during matched control segments with low amplitude widespread slow waves, non-widespread slow waves or no slow waves selected during the same sleep stages (total duration of slow wave and control segments: 49 min each). During the slow waves, spikes and high frequency oscillations were more frequent than during control segments (79% of spikes during slow waves and 65% of high frequency oscillations, both P ~ 0). The spike and high frequency oscillation density also increased for higher amplitude slow waves. We compared the density of spikes and high frequency oscillations between the 'up' and 'down' states. Spike and high frequency oscillation density was highest during the transition from the 'up' to the 'down' state. Interestingly, high frequency oscillations in channels with normal activity expressed a different peak at the transition from the 'down' to the 'up' state. These results show that the apparent activation of epileptic discharges by non-rapid eye movement sleep is not a state-dependent phenomenon but is predominantly associated with specific events, the high amplitude widespread slow waves that are frequent, but not continuous, during this state of sleep. Both epileptic spikes and high frequency oscillations do not predominate, like physiological activity, during the 'up' state but during the transition from the 'up' to the 'down' state of the slow wave, a period of high synchronization. Epileptic discharges appear therefore more associated with synchronization than with excitability. Furthermore, high frequency oscillations in channels devoid of epileptic activity peak differently during the slow wave cycle from those in channels with epileptic activity. This property may allow differentiating physiological from pathological high frequency oscillations, a problem that is unresolved until now.Instituto de Investigaciones en Electrónica, Control y Procesamiento de Señale