Simultaneous double transformations of functions depending on space and time

It is shown that performing simultaneously two transformations on functions of space and time (for instance a Fourier transform on the space variable and a Laplace transform on the time variable) can be easier than performing them one after the other when the variables are combined in invariant quantities. This is naturally also true when performing two inverse transforms simultaneously, when the conjugated variables are combined into a propagator. An immediate application is found in the computation of the solutions of partial differential equations. This article contains several general examples of such "simultaneous double transforms" for arbitrary analytic functions of space and time.Comment: 8 pages, 1 table of simultaneous double transformation pair

Local time in diffusive media and applications to imaging

Local time is the measure of how much time a random walk has visited a given position. In multiple scattering media, where waves are diffuse, local time measures the sensitivity of the waves to the local medium's properties. Local variations of absorption, velocity and scattering between two measurements yield variations in the wave field. These variations are proportionnal to the local time of the volume where the change happened and the amplitude of variation. The wave field variations are measured using correlations and can be used as input in a inversion algorithm to produce variation maps. The present article gives the expression of the local time in dimensions one, two and three and an expression of its fluctuations, in order to perform such inversions and estimate their accuracy.Comment: 10 pages, 2 figures and 3 table

The binding of botulinum neurotoxins to different peripheral neurons

Botulinum neurotoxins are the most potent toxins known. The double receptor binding modality represents one of the most significant properties of botulinum neurotoxins and largely accounts for their incredible potency and lethality. Despite the high affinity and the very specific binding, botulinum neurotoxins are versatile and multi-tasking toxins. Indeed they are able to act both at the somatic and at the autonomic nervous system. In spite of the preference for cholinergic nerve terminals botulinum neurotoxins have been shown to inhibit to some extent also the noradrenergic postganglionic sympathetic nerve terminals and the afferent nerve terminals of the sensory neurons inhibiting the release of neuropeptides and glutamate, which are responsible of nociception. Therefore, there is increasing evidence that the therapeutic effect in both motor and autonomic disorders is based on a complex mode of botulinum neurotoxin action modulating the activity of efferent as well as afferent nerve fibres

Web Video in Numbers - An Analysis of Web-Video Metadata

Web video is often used as a source of data in various fields of study. While specialized subsets of web video, mainly earmarked for dedicated purposes, are often analyzed in detail, there is little information available about the properties of web video as a whole. In this paper we present insights gained from the analysis of the metadata associated with more than 120 million videos harvested from two popular web video platforms, vimeo and YouTube, in 2016 and compare their properties with the ones found in commonly used video collections. This comparison has revealed that existing collections do not (or no longer) properly reflect the properties of web video "in the wild".Comment: Dataset available from http://download-dbis.dmi.unibas.ch/WWIN

QFD: an interactive algorithm for the prioritization of product's technical characteristics

The paper is concerned with the problem of the ``prioritization' ' of technical design characteristic s of a product. An interactive algorithm has been developed with the aim to better support the engineering design process by means of quality function deployment (QFD). The algorithm tries to soften customer approach to QFD in those situations in which customers are not able to give a ``significant' ' evaluation of the relative importance of their requirements . The method allows determining a ranking order of design characteristic s without the artificia l conversion of symbols contained in the relationshi p matrix, and without the use of explici t information concerning the relative degree of importance of customer requirements. A simple numerical applicatio n is also provide

Slow invariant manifold of heartbeat model

A new approach called Flow Curvature Method has been recently developed in a book entitled Differential Geometry Applied to Dynamical Systems. It consists in considering the trajectory curve, integral of any n-dimensional dynamical system as a curve in Euclidean n-space that enables to analytically compute the curvature of the trajectory - or the flow. Hence, it has been stated on the one hand that the location of the points where the curvature of the flow vanishes defines a manifold called flow curvature manifold and on the other hand that such a manifold associated with any n-dimensional dynamical system directly provides its slow manifold analytical equation the invariance of which has been proved according to Darboux theory. The Flow Curvature Method has been already applied to many types of autonomous dynamical systems either singularly perturbed such as Van der Pol Model, FitzHugh-Nagumo Model, Chua's Model, ...) or non-singularly perturbed such as Pikovskii-Rabinovich-Trakhtengerts Model, Rikitake Model, Lorenz Model,... More- over, it has been also applied to non-autonomous dynamical systems such as the Forced Van der Pol Model. In this article it will be used for the first time to analytically compute the slow invariant manifold analytical equation of the four-dimensional Unforced and Forced Heartbeat Model. Its slow invariant manifold equation which can be considered as a "state equation" linking all variables could then be used in heart prediction and control according to the strong correspondence between the model and the physiological cardiovascular system behavior.Comment: arXiv admin note: substantial text overlap with arXiv:1408.171

On the Derivation of Optimal Partial Successive Interference Cancellation

The necessity of accurate channel estimation for Successive and Parallel Interference Cancellation is well known. Iterative channel estimation and channel decoding (for instance by means of the Expectation-Maximization algorithm) is particularly important for these multiuser detection schemes in the presence of time varying channels, where a high density of pilots is necessary to track the channel. This paper designs a method to analytically derive a weighting factor $\alpha$, necessary to improve the efficiency of interference cancellation in the presence of poor channel estimates. Moreover, this weighting factor effectively mitigates the presence of incorrect decisions at the output of the channel decoder. The analysis provides insight into the properties of such interference cancellation scheme and the proposed approach significantly increases the effectiveness of Successive Interference Cancellation under the presence of channel estimation errors, which leads to gains of up to 3 dB.Comment: IEEE GLOBECOM 201