Fourier analysis of stationary time series in function space

We develop the basic building blocks of a frequency domain framework for drawing statistical inferences on the second-order structure of a stationary sequence of functional data. The key element in such a context is the spectral density operator, which generalises the notion of a spectral density matrix to the functional setting, and characterises the second-order dynamics of the process. Our main tool is the functional Discrete Fourier Transform (fDFT). We derive an asymptotic Gaussian representation of the fDFT, thus allowing the transformation of the original collection of dependent random functions into a collection of approximately independent complex-valued Gaussian random functions. Our results are then employed in order to construct estimators of the spectral density operator based on smoothed versions of the periodogram kernel, the functional generalisation of the periodogram matrix. The consistency and asymptotic law of these estimators are studied in detail. As immediate consequences, we obtain central limit theorems for the mean and the long-run covariance operator of a stationary functional time series. Our results do not depend on structural modelling assumptions, but only functional versions of classical cumulant mixing conditions, and are shown to be stable under discrete observation of the individual curves.Comment: Published in at http://dx.doi.org/10.1214/13-AOS1086 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Reconstruction of Directed Networks from Consensus Dynamics

This paper addresses the problem of identifying the topology of an unknown, weighted, directed network running a consensus dynamics. We propose a methodology to reconstruct the network topology from the dynamic response when the system is stimulated by a wide-sense stationary noise of unknown power spectral density. The method is based on a node-knockout, or grounding, procedure wherein the grounded node broadcasts zero without being eliminated from the network. In this direction, we measure the empirical cross-power spectral densities of the outputs between every pair of nodes for both grounded and ungrounded consensus to reconstruct the unknown topology of the network. We also establish that in the special cases of undirected or purely unidirectional networks, the reconstruction does not need grounding. Finally, we extend our results to the case of a directed network assuming a general dynamics, and prove that the developed method can detect edges and their direction.Comment: 6 page

Tackling the Declining Number of Participants in Youth Tackle Football Through the Creation of an Awareness Website

There are many benefits to youth who participate in tackle football. Unfortunately, there has been a decline in participation over the years. Fear surrounding concussions and Chronic Traumatic Encephalopathy (CTE) has been mostly to blame for the dramatic decrease. Research has shown that there are many physical, social, emotional and health benefits associated with those who do participate. The researcher used statistical data from many varying studies and multiple other resources to create an awareness website. The awareness website is a tool that would benefit those who are undecided about allowing their child to participate in youth tackle football. Through qualitative research, the researcher created an online survey using both Likert scale and open-ended questions. The data collected from these surveys was used two fold. First, it was used to validate that the information provided on the website was accurate and perceived to be helpful for those who may be researching more about the sport. Secondly, the feedback provided by way of the open-ended questions will be used to continuously enhance the website for future use. After analyzing survey results, the researcher was able to gather enough input to research ways to enhance the website for future use. After analyzing survey results, the researcher was able to gather enough input to research ways to enhance the website for future use

The influence of hydrodynamics and particle size on the rejection properties of ultrafiltration membranes

A mathematical model based on the flow hydrodynamics is developed to calculate the treatment efficiency of ultrafiltration process. This model relates the treatment efficiency with the consideration of both fixed parameters and variable parameters. The fixed parameters are function of the intrinsic rejection coefficient, diffusion coefficient, and viscosity whereas the variable parameters can be related to the fluid velocity, volume flux, and cartridge dimensions. The model has been examined by solutions with solutes that have different molecular weights. The experimental data fits the proposed mathematical model very closely suggesting its suitability to evaluate the rejection efficiency in ultrafiltration. As such the mathematical model can be used to evaluate the intrinsic rejection coefficient that can be used to determine the solvent flux in Kedem Katchalisky model. The role of the particle size is investigated by using a log -log plot of the intrinsic rejection coefficient and the solute molecular weight. Results shows that modeling of the intrinsic rejection coefficient as log normal probability distribution function is possible. Fluid velocity on the membrane cartridge as an important parameter in the design of ultrafiltration systems

Shear Behaviour of Misurata Wet Sand

The foundation design of buildings depends on the bearing capacity of soil and foundation shaft resistance, upon this reason, for buildings safety, the study of shear behaviour of soil is very important to analyse and evaluate the foundation settlement and friction between soil and foundation surface. especially in the case of deep foundation. The paper is to study and evaluate the shear behaviour of Misurata wet sand around foundation surface under the effect of different axial loads by using direct shear box test. This study contains nine laboratory tests were done to measure the Sand-Aluminum interface of smooth surfaces, and other nine tests for Sand-Aluminum interface of rough surfaces, to simulate foundation surface in the site. Also, another nine tests were done to measure Sand-Sand interface shear behaviour resulting from friction between wet sand grains under different normal loads, soil type and initial sand density in three cases of soil, loose, medium  and dense wet sand. The test results showed that the value of soil displacement and interface friction angle (d) are very important for foundation design, especially for deep foundations. Also, from the evaluation of experimental test results we found that the interface friction angle (d) depends on roughness of the foundation, initial compactness, water content and porosity of sand

Three-dimensional numerical modelling of ballasted railway track foundations for high-speed trains with special reference to critical speed

Due to recent congestion of highways in many countries around the world, railways have become the most popular means of public transportation, which has increased the demand for heavier and faster trains. High speeds and heavy loads of trains are usually accompanied with large vibrations in the train-track-ground system, especially when train speed reaches its critical value, leading to possible train derailment and track damages. This unwanted scenario makes it important for railway geotechnical engineers to investigate the behaviour of ballasted railway track foundations for high-speed trains, with special reference to critical speed. In the current paper, a sophisticated three-dimensional (3D) finite element (FE) modelling was developed to simulate the dynamic response of ballasted railway tracks subjected to train moving loads, and the critical speed was investigated for various train-track-ground system conditions. The results were presented in terms of the evolution of the coefficient of dynamic amplification of sleeper deflection versus train speed, which have been synthesized into simple sensitivity charts that can be used to determine the critical speed corresponding to the conditions of a particular train-track-ground system