Control of continuous sedimentation of ideal suspensions as an initial and boundary value problem

We present the control of continuous sedimentation in an ideal thickener as an initial and boundary value problem and construct the entropy solution.     

Multicuts in unweighted graphs and digraphs with bounded degree and bounded tree-width

The Multicut problem can be defined as: given a graph G and a collection of pairs of distinct vertices {s_i,t_i} of G, find a minimum set of edges of G whose removal disconnects each s_i from the corresponding t_i. Multicut is known to be NP-hard and Max SNP-hard even when the input graph is restricted to being a tree. The main result of the paper is a polynomial-time approximation scheme (PTAS) for Multicut in unweighted graphs with bounded degree and bounded tree-width. That is, for any ε>0, we present a polynomial-time (1+ε)-approximation algorithm. In the particular case when the input is a bounded-degree tree, we have a linear-time implementation of the algorithm. We also provide some hardness results: we prove that Multicut is still NP-hard for binary trees and that it is Max SNP-hard if we drop any of the three conditions (unweighted, bounded-degree, bounded tree-width). Finally we show that some of these results extend to the vertex version of Multicut and to a directed version of Multicut.     

On distributive modules and rings

In this paper we study ω-distributive modules, where ω is a cardinal number. We extend a characterization of distributive modules to ω-distributive modules. In particular, the case in which ω = n is a finite cardinal is considered. We apply the results to the case n = 2, obtaining new characterizations for distributive modules and rings. Special attention is given to saturated submodules and ideals.     

Randomised circular means of Fourier transforms of measures

We explore decay estimates for circular means of the Fourier transform of a measure on in terms of its -dimensional energy. We find new upper bounds for the decay exponent. We also prove sharp estimates for a certain family of randomised versions of this problem.

     

A longitudinal study of MR diffusion changes in normal appearing white matter of patients with early multiple sclerosis

BACKGROUND AND PURPOSE: The stage at which normal appearing white matter (NAWM) abnormalities first appear in multiple sclerosis (MS) is not clear. The aim of our study was to monitor water diffusion changes over time in NAWM of patients with early MS.METHODS: Out of a consecutive series of patients enrolled in a MR study on clinically isolated syndrome (CIS), we selected 19 subjects who had completed a one year follow-up. The MR scans obtained at baseline and at 12 months were reviewed according to the new criteria on the diagnosis of MS. Lesion load on T2 and T1 weighted images and the trace of the apparent diffusion coefficient in NAWM were measured both at baseline and at 12 months in patients and in 12 healthy controls.RESULTS: In three patients the diagnosis of MS was done at baseline based on MR. Thirteen patients developed MS during the study and in three patients the diagnosis remained "possible MS." TADC in NAWM in patients was significantly higher than in controls at the 12 months' follow-up but not at baseline (controls mean tADC +/- sd = 0.745 +/- 0.02 mm(2)/sec x 10(-3); patients mean tADC(12) +/- sd = 0.767 +/- 0.02 mm(2)/sec x 10(-3); p < 0.02). TADC and T2 lesion load at 12 months were significantly correlated (p < 0.01). Patients exhibiting tADC(12) above a confidence interval had a significantly greater EDSS score at the same time period (EDSS(12) +/- sd = 1.9 +/- 0.5 and = 1.1 +/- 0.4 respectively; p < 0.01).CONCLUSIONS: This study suggests that diffusion MR cannot detect alterations in NAWM of patients with a CIS suggestive of MS. After one year, when most patients develop MS, diffusion MR abnormalities in NAWM become apparent. These abnormalities are correlated with T2 lesion load and may contribute to neurological impairment.     

The Role of Information in Managing Interactions from a Multifractal Perspective

In the framework of the multifractal hydrodynamic model, the correlations informational entropy–cross-entropy manages attractive and repulsive interactions through a multifractal specific potential. The classical dynamics associated with them imply Hubble-type effects, Galilei-type effects, and dependences of interaction constants with multifractal degrees at various scale resolutions, while the insertion of the relativistic amendments in the same dynamics imply multifractal transformations of a generalized Lorentz-type, multifractal metrics invariant to these transformations, and an estimation of the dimension of the multifractal Universe. In such a context, some correspondences with standard cosmologies are analyzed. Since the same types of interactions can also be obtained as harmonics mapping between the usual space and the hyperbolic plane, two measures with uniform and non-uniform temporal flows become functional, temporal measures analogous with Milne’s temporal measures in a more general manner. This work furthers the analysis published recently by our group in “Towards Interactions through Information in a Multifractal Paradigm”.     

Deep Learning for Walking Behaviour Detection in Elderly People Using Smart Footwear

The increase in the proportion of elderly in Europe brings with it certain challenges that society needs to address, such as custodial care. We propose a scalable, easily modulated and live assistive technology system, based on a comfortable smart footwear capable of detecting walking behaviour, in order to prevent possible health problems in the elderly, facilitating their urban life as independently and safety as possible. This brings with it the challenge of handling the large amounts of data generated, transmitting and pre-processing that information and analysing it with the aim of obtaining useful information in real/near-real time. This is the basis of information theory. This work presents a complete system aiming at elderly people that can detect different user behaviours/events (sitting, standing without imbalance, standing with imbalance, walking, running, tripping) through information acquired from 20 types of sensor measurements (16 piezoelectric pressure sensors, one accelerometer returning reading for the 3 axis and one temperature sensor) and warn the relatives about possible risks in near-real time. For the detection of these events, a hierarchical structure of cascading binary models is designed and applied using artificial neural network (ANN) algorithms and deep learning techniques. The best models are achieved with convolutional layered ANN and multilayer perceptrons. The overall event detection performance achieves an average accuracy and area under the ROC curve of 0.84 and 0.96, respectively.     

Analysis of mural paintings using in situ non‐invasive XRF,FTIR spectroscopy and optical microscopy

An analytical protocol consisting of X‐ray fluorescence spectroscopy, optical microscopy and Fourier transform infrared spectroscopy was used to study the origin and the nature of the materials (pigments, binders and coating preparation) of the Fundenii Doamnei church mural paint from Bucharest. The main interest of the present study consisted in the original votive paint from narthex, painted in 1757 in a secco technique. During analysis, an unexpected pigment in the votive paint could be detected by the combined analytical techniques: ultramarine blue. Along with this pigment, the presence of gypsum binder based on egg and flax seed oil could also be evidenced. These results demonstrated a secco execution technique of the votive paint and also the presence of a restoration treatment. Moreover, during the present study, the components of the preparation layer and the constitutive pigments from both 1699 and 1757 years mural paints have been analyzed. Hence, the following pigments could be identified: vermilion, azurite, cinnabar, lead white, ochre, natural umber and gold, by using the combination of the analytical techniques. The novelty of our results consists in detecting the composition of the materials used in this church painting (fresco and a secco) during these 254 years since its first restoration. The results of these investigations pointed to the suitability of the non‐destructive and semi‐destructive analytical techniques in the complex characterization of the paints realized in different techniques, at different periods. Copyright © 2013 John Wiley & Sons, Ltd.