The effect of round-off error on long memory processes

We study how the round-off (or discretization) error changes the statistical properties of a Gaussian long memory process. We show that the autocovariance and the spectral density of the discretized process are asymptotically rescaled by a factor smaller than one, and we compute exactly this scaling factor. Consequently, we find that the discretized process is also long memory with the same Hurst exponent as the original process. We consider the properties of two estimators of the Hurst exponent, namely the local Whittle (LW) estimator and the Detrended Fluctuation Analysis (DFA). By using analytical considerations and numerical simulations we show that, in presence of round-off error, both estimators are severely negatively biased in finite samples. Under regularity conditions we prove that the LW estimator applied to discretized processes is consistent and asymptotically normal. Moreover, we compute the asymptotic properties of the DFA for a generic (i.e. non Gaussian) long memory process and we apply the result to discretized processes.Comment: 44 pages, 4 figures, 4 table

The Relationship Among Children’s Reading Achievement, Parental Attitudes Towards Reading, and Parental Reading Habits

The purpose of this study was to investigate the relationships among children\u27s reading achievement, parental attitudes towards reading, and parental reading habits. Fifty-seven students enrolled in grades 3, 4, 5, and 6 of a suburban parochial school in Western New York State and their parents constituted the subjects of this study. Specific questions to be answered were: 1. Does a strong relationship exist between parental reading habits and their child\u27s reading achievement? 2. Does a strong relationship exist between parental attitudes towards reading and their child\u27s reading achievement? .. 3. Does a strong relationship exist between parental attitudes towards reading and parental reading habits? Parents were asked to respond to two questionnaires; one to measure parental reading habits, the other to measure parental attitudes towards reading. A total score was obtained for each questionnaire by giving a weighted value to each response. Parental reading attitude scores and parental reading habit scores were compared to their children\u27s Stanford Achievement Test scores using a Pearson Product-Moment Correlation. Results revealed that a significant correlation did not exist between parental reading habits and children\u27s reading achievement. Results also revealed no significant correlation between parental attitudes towards reading and children\u27s reading achievement. Further analysis of the data showed that no significant correlation existed between mothers\u27 attitudes towards reading and mothers\u27 reading habits, although a moderately strong correlation did exist between fathers\u27 attitudes towards reading and fathers\u27 reading habits

long term follow up of hepatitis c virus positive patients with persistently normal serum transaminases

Material and methods. This study prospectively evaluated the progression of liver disease in a group of anti-HCV-positive patients with persistently normal ALT levels (PNALT) who were HCV-RNA positive. Patients selected for this study were those who presented with PNALT according to the Italian Association for the Study of the Liver (AISF) criteria in the year 1995/96 and underwent liver biopsy. They were divided into two groups according to their ALT evolution. Forty-five patients were included in this study. Results. After a median follow-up time of 180 months twenty-five of them maintained PNALT, but two of these developed liver cirrhosis (LC) in a mean time of 174 and 202 months, respectively. Twenty patients had flares of ALT and three of them developed LC in a mean time of 162-178 months. Twelve of these patients underwent current antiviral treatment; six patients were SVR. At baseline, the 5 patients who progressed to LC had age and BMI significantly higher than patients without LC (P < 0.005 and P < 0.01, respectively). Grading (P < 0.006) and staging (P < 0.003) were also more severe at histology, while serum HDL-C levels were statistically lower (P < 0.002). Comparing patients with flares of transaminases with and without LC, we found a significant difference at baseline for age, BMI, HDL-C, grading and staging (P < 0.05; P < 0.01 and P < 0.003, respectively). Conclusion. In HCV-RNA positive patients associated with PNALT the grade of disease activity increased over the years in only half of patients and a higher degree of liver fibrosis at baseline was the major relevant factor for progression

response to comment on the paper electromagnetic modeling of ellipsoidal nanoparticles for sensing applications

The authors respond to the comments by Mackay and Lakhtakia. First of all, we would like to thank Mackay and Lakhtakia1 who have carefully read our paper and for their valuable comments on our manuscript. We agree that the polarizability is a dyadic. For our aims (analytical models, full-wave simulations, and sensitivity analysis), we have assumed the impinging electromagnetic field as a plane wave having the electric field E parallel to the nanoparticle principal axis (x -axis as depicted in the Fig. 1 of the paper). In this case, Eq. (1) and the following equations refer only to scalar component x ^ x ^ of the dyadic polarizability α − − − − (sufficient to evaluate the nanoparticle response under the aforementioned excitation condition). We have to point out that for sensing applications the analyzed polarization is crucial in order to obtain the best sensitivity performances

Electromagnetic Modeling of Dielectric Mixtures

Electromagnetic modeling of dielectric materials allows us to study the effects of electromagnetic wave propagation and how such electromagnetic fields influence and interact with them.Dielectric materials are composites or mixtures, which often are made up of at least two constituents or phases. Modelling the electromagnetic behaviour of dielectric mixtures is crucial to understand how geometrical factors (shape and concentration), electromagnetic properties of inclusions and background medium, influence the permittivity of the overall material.The aim of this work is to develop new analytical models for dielectric mixtures, in order to describe their electromagnetic behaviour and design them with desired electromagnetic properties, for specific required applications. In particular, in this paper a new general expression for the effective permittivity of dielectric mixture is presented. The mixtures consist of inclusions, with arbitrary shapes, embedded in a surrounding dielectric environment. We consider the hosting environment and the hosted material as real dielectrics, both of them as dispersive dielectrics.The proposed analytical models simplify practical design tasks for dielectric mixtures and allow us to understand their physical phenomena and electromagnetic behaviours

The FE-Meshless multiscale approach applied to masonry structures

Heterogeneous structures have an overall response that is strongly dependent on the inelastic events developing at the local level. In these structures, the most relevant kinematical and mechanical phenomena take place at a scale which is small if compared to the dimensions of the entire structure. In literature, a mesoscopic and a macroscopic scales of interest are distinguished, directly linked to as many theoretical approaches. The mesoscopic approach [1] considers materials and their interfaces individually, but many difficulties arise in the mesh creation and a fine discretization of the structure is needed, which leads to prohibitive computational costs. The macroscopic approach considers the structure as constituted by a fictitious homogeneous and continuous material. The multiscale techniques belong to the second approach and couple different scales of interest by means of apposite transition laws capable to exchange informations between different consecutive scales [2]. This work relates with the multiscale first order computational homogenization technique applied to masonry structures. A unit cell (UC) is assumed constituted by an elastic bulk volume surrounded by weak joints, which are simulated by zero-thickness elasto-plastic interface models. At a single time step, the FE solution of the fictitious homogenized structure provides strains at all quadrature points. The corresponding macrostress field associated to the strain is obtained by solving a Boundary Value Problem (BVP) of the UC at the mesoscale level. The solution of the BVP is approached by means of a meshless strategy [3] instead of a classical finite element procedure, that is usually time-consuming. By imposing Taylor-Voigt type boundary conditions on the UC, the macroscopic stress is evaluated averaging the UC boundary tractions, according to the Hill-Mandel principle. Localization is faced at both the quadrature point level and at the element level. At the quadrature point level plastic bands are localized applying a continuous-discontinuous bifurcation theory [4] based on the spectral analysis of the acoustic tensor associated to the stiffness matrix. At the element level inelastic response is obtained smearing the plastic zones at the quadrature points over the element area, considering the localized and not localized fraction areas. The proposed model has been implemented on a research oriented finite element analysis pro- gram to run 2D simulations in plane-stress conditions for heterogeneous periodic structures. Quali- tatively good results are obtained in comparison with numerical data available in literature

CH of masonry materials via meshless meso-modeling

In the present study a multi-scale computational strategy for the analysis of masonry structures is presented. The structural macroscopic behaviour is obtained making use of the Computational Homogenization (CH) technique based on the solution of the boundary value problem (BVP) of a detailed Unit Cell (UC) chosen at the meso-scale and representative of the heterogeneous material. The smallest UC is composed by a brick and half of its surrounding joints, the former assumed to behave elastically while the latter considered with an elastoplastic softening response. The governing equations at the macroscopic level are formulated in the framework of finite element method while the Meshless Method (MM) is adopted to solve the BVP at the mesoscopic level. The work focuses on the BVP solution. The consistent tangent stiffness matrix at a macroscopic quadrature point is evaluated on the base of BVP results for the UC together with a localisation procedure. Validation of the MM procedure at the meso-scale level is demonstrated by numerical examples that show the results of the BVP for the simple cases of normal and shear loading of the UC

A FE-Meshless Multiscale Approach for Masonry Materials

AbstractA FE-Meshless multiscale computational strategy for the analysis of running bond masonry is presented. The Meshless Method (MM) is adopted to solve the boundary value problem (BVP) at the mesoscopic level. The representative unit cell is composed by the aggregate and the surrounding joints, the former assumed to behave elastically while the latter are simulated as non-associated elastic-plastic zero-thickness interfaces with a softening response. Macroscopic localization of plastic bands is obtained performing a spectral analysis of the tangent stiffness matrix. Localized plastic bands are embedded into the quadrature points area of the macroscopic finite elements