Search results for "DIMENSION"

Topology guaranteeing manifold reconstruction using distance function to noisy data

2006

Given a smooth compact codimension one submanifold S of Rk and a compact approximation K of S, we prove that it is possible to reconstruct S and to approximate the medial axis of S with topological guarantees using unions of balls centered on K. We consider two notions of noisy-approximation that generalize sampling conditions introduced by Amenta & al. and Dey & al. Our results are based upon critical point theory for distance functions. For the two approximation conditions, we prove that the connected components of the boundary of unions of balls centered on K are isotopic to S. Our results allow to consider balls of different radii. For the first approximation condition, we also prove th…

The Kuratowski convergence and connected components

2012

International audience; We investigate the Kuratowski convergence of the connected components of the sections of a definable set applying the result obtained to semialgebraic approximation of subanalytic sets. We are led to some considerations concerning the connectedness of the limit set in general. We discuss also the behaviour of the dimension of converging sections and prove some general facts about the Kuratowski convergence in tame geometry.

Separation properties of continuous maps in codimension 1 and geometrical applications

1992

Abstract Nuno Ballesteros, J.J. and M.C. Romero Fuster, Separation properties of continuous maps in codimension 1 and geometrical applications, Topology and its Applications 46 (1992) 107-111. We show that the image of a proper closed continuous map, f , from an n -manifold X to an ( n + 1)-manifold Y , such that H 1 (Y; Z 2 ) =0 , separates Y into at least two connected components provided the self-intersections set of f is not dense in any connected component of Y . We also obtain some geometrical applications.

A system of conservation laws with discontinuous flux modelling flotation with sedimentation

2019

Abstract The continuous unit operation of flotation is extensively used in mineral processing, wastewater treatment and other applications for selectively separating hydrophobic particles (or droplets) from hydrophilic ones, where both are suspended in a viscous fluid. Within a flotation column, the hydrophobic particles are attached to gas bubbles that are injected and float as aggregates forming a foam or froth at the top that is skimmed. The hydrophilic particles sediment and are discharged at the bottom. The hydrodynamics of a flotation column is described in simplified form by studying three phases, namely the fluid, the aggregates and solid particles, in one space dimension. The relat…

2021

Recent studies on the economic dimensions of sports and physical activity in Germany have revealed that sport-related tourism is one of the important contributors to private household consumption. Due to a lack of representative and large-scale data sets, this topic has never been displayed in detail before. By using computer assisted telephone and web interviews, we collected a total data set of n=19,396 persons living in Germany. The expenditures for active sport tourism were isolated, which is understood as travelling to take part in different sporting activities. Data are provided on the overall spending of German households for sport trips, with skiing (€ 3.4 bn) and scuba diving (€ 2.…

Finding condensed descriptions for multi-dimensional data.

1976

Abstract We describe two programs that may be used to find condensed descriptions for data available in a contingency table or in a covariance matrix in the case that these data follow a multinomial or a multivariate normal distribution, respectively. The programs perform a stepwise model search among multiplicative models by computing appropriate likelihood-ratio test statistics.

The Reduction of Dimension in the Study of Economic Growth Models

2002

We examine the dimension reduction method and prove that it could be misleading if we try to get some insight into the dynamics of the original system from the dynamics of the transformed system alone. The reduced system seemingly may give rise to a continuum multiplicity of steady states when, actually, it does exist a unique and isolated steady state or even it does not exist a steady state at all. We show how the dynamics for the primary variables that is recovered from the solution to the reduced system may be refuted by solving the original one. In our opinion there is no alternative because nothing can be regarded as a close substitute for the study of the original system. Although th…

The Playing Brain. The Impact of Video Games on Cognition and Behavior in Pediatric Age at the Time of Lockdown: A Systematic Review

2021

A growing number of children and adolescents play video games (VGs) for long amounts of time. The current outbreak of the Coronavirus pandemic has significantly reduced outdoor activities and direct interpersonal relationships. Therefore, a higher use of VGs can become the response to stress and fear of illness. VGs and their practical, academic, vocational and educational implications have become an issue of increasing interest for scholars, parents, teachers, pediatricians and youth public policy makers. The current systematic review aims to identify, in recent literature, the most relevant problems of the complex issue of playing VGs in children and adolescents in order to provide sugges…

In-situ monitoring by Raman spectroscopy of the thermal doping of graphene and MoS2 in O-2-controlled atmosphere

2017

The effects of temperature and atmosphere (air and O2) on the doping of monolayers of graphene (Gr) on SiO2 and Si substrates, and on the doping of MoS2 multilayer flakes transferred on the same substrates have been investigated. The investigations were carried out by in situ micro-Raman spectroscopy during thermal treatments up to 430 °C, and by atomic force microscopy (AFM). The spectral positions of the G and 2D Raman bands of Gr undergo only minor changes during treatment, while their amplitude and full width at half maximum (FWHM) vary as a function of the temperature and the used atmosphere. The thermal treatments in oxygen atmosphere show, in addition to a thermal effect, an effect a…

Quantifying brain tumor tissue abundance in HR-MAS spectra using non-negative blind source separation techniques

2012

Given high-resolution magic angle spinning (HR-MAS) spectra from several glial tumor subjects, our goal is to differentiate between tumor tissue types by separating the different sources that contribute to the profile of each spectrum. Blind source separation techniques are applied for obtaining characteristic profiles for necrosis, highly cellular tumor and border tumor tissue and providing the contribution (abundance) of each of these tumor tissue types to the profile of each spectrum. The problem is formulated as a non-negative source separation problem. Non-negative matrix factorization, convex analysis of non-negative sources and non-negative independent component analysis methods are …