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The objective of this chapter is to demonstrate the linkage between convolution and filtering and to discuss preliminary filtering with examples. The simplest low-pass filtering that allows low frequency to pass to the output is a “moving average,” which is essentially through a computation involving a rectangular window function (in this case, it is a filter), with a length determined by the cutoff frequency. The filtering action is accomplished by a convolution between the filter and the time series. However, moving average has its drawbacks because of the rectangular window effect or the side lobe effect. It is considered as a “poor man’s filter” because of the lack of sophistication in getting rid of the leakage from side lobes. One improvement over the moving average is using a non-rectangular window function in the convolution to reduce the sharp change at the edges. The basic ideas and examples presented here are useful in demonstrating how to do filtering with several MATLAB functions. When a low-pass filter is designed, a high-pass filter can be defined. With two or more low-pass filters, one can also design band-pass and band-stop filters. There are also other filters that can have various controls on the results.
This chapter discusses the transition between Fourier series and Fourier Transform, which is the tool for spectrum analysis. Generally, the use of linearly independent base functions allows a wide range of linear regression models that work in a least square sense such that the total error squared is minimized in finding the coefficients of the base functions. A special case is sinusoidal functions based on a fundamental frequency and all its harmonics up to infinity. This leads to the Fourier series for periodic functions. In this chapter, we start from the original Fourier series expression and convert the sinusoidal base functions to exponential functions. We can then consider the limit when the length of the function and the period of the original function approach infinity (so that the fundamental frequency approaches 0, including aperiodic functions), leading to the Fourier integral and Fourier Transform. We can then define the inverse Fourier Transform and establish the relationship between the coefficients of Fourier series and the discrete form Fourier Transform. All these are preparations for the fast Fourier Transform (FFT), an efficient algorithm of computation of the discrete Fourier Transform that is widely used in data analysis for oceanography and other applications.
This chapter discusses the drawback of Fourier analysis and the methods that can overcome its limitations. In general, Fourier analysis does not include information about time, particularly events. A slight modification of Fourier analysis can allow the addition of a dimension in time: by dividing the time series into smaller segments and doing the Fourier Transform for each segment, a method called short-time Fourier Transform (STFT) is introduced. Wavelet analysis is then discussed as a much better alternative to or replacement for STFT. It involves scaled and translated convolution with a short base function (short in the sense that it is essentially non-zero only in a finite interval). Wavelet analysis uses different base functions than the Fourier Transform. They are limited in time (unlike the infinitely long sinusoidal functions) and can be stretched or compressed to represent different scales (equivalent to frequencies). This method will allow the resolution of events at different times and different scales.
Backyard chickens are increasingly popular, and their husbandry varies widely. How backyard chickens are housed may influence the accessibility of chicken feed and water to wild birds, and thus, the contact rates between both groups. Increased contacts have implications for pathogen transmission; for instance, Newcastle disease virus or avian influenza virus may be transmitted to and from backyard chickens from contaminated water or feed. Given this potentially increased pathogen risk to wild birds and backyard chickens, we examined which wild bird species are likely to encounter backyard chickens and their resources. We performed a supplemental feeding experiment followed by observations at three sites associated with backyard chickens in North Georgia, USA. At each site, we identified the species of wild birds that: (a) shared habitat with the chickens, (b) had a higher frequency of detection relative to other species and (c) encountered the coops. We identified 14 wild bird species that entered the coops to consume supplemental feed and were considered high-risk for pathogen transmission. Our results provide evidence that contact between wild birds and backyard chickens is frequent and more common than previously believed, which has crucial epidemiological implications for wildlife managers and backyard chicken owners.
In this introductory chapter, we briefly go over the definitions of terms and tools we need for data analysis. Among the tools, MATLAB is the software package to use. The other tool is mathematics. Although much of the mathematics are not absolutely required before using this book, a person with a background in the relevant mathematics will always be better positioned with insight to learn the data analysis skills for real applications.
This chapter discusses some basic spherical trigonometry applicable to distance computations between points on the surface of the Earth, including in the ocean, particularly for large-scale problems in oceanography. Because of the curvature of the Earth, the plane geometry is not applicable.
The objective of this chapter is to discuss the concept of base functions and the basics of using some simple base functions to represent other functions. These base functions are needed in many commonly used analyses. An example of using base functions to approximate an almost arbitrary target function is the Taylor series expansion we have discussed. Here we say that an “almost arbitrary function” is not really arbitrary because, in theory, the target function must be differentiable an arbitrary number of times for the Taylor series expansion to be valid. The concept of linear independence of functions is important in understanding the selection of base functions.
We review the difference between real-world and risk-neutral processes. We illustrate asset processes using two years of daily returns from the S\&P 500 stock index, and with 30 years of monthly data from the S\&P/TSX (Toronto Stock Exchange) stock index. We describe three models for modelling asset prices in discrete time: the independent lognormal model, the GARCH model, and the regime-switching lognormal model. We describe how the models are fitted to data, and briefly discuss how to choose between models.
Fraud analytics refers to the use of advanced analytics (data mining, big data analysis, or artificial intelligence) to detect fraud. While fraud analytics offers the promise of more efficiency in fighting fraud, it also raises legal challenges related to data protection and administrative law. These legal requirements are well documented but the concrete way in which public administrations have integrated them remains unexplored. Due to the complexity of the techniques applied, it is crucial to understand the current state of practice and the accompanying challenges to develop appropriate governance mechanisms. The use of advanced analytics in organizations without appropriate organizational change can lead to ethical challenges and privacy issues. The goal of this article is to examine how these legal requirements are addressed in public administrations and to identify the challenges that emerge in doing so. For this, we examined two case studies related to fraud analytics from the Belgian Federal administration: the detection of tax frauds and social security infringements. This article details 15 governance practices that have been used in administrations. Furthermore, it highlights the complexity of integrating legal requirements with advanced analytics by identifying six key trade-offs between fraud analytics opportunities and legal requirements.
Contact with livestock and consumption of unpasteurised dairy products are associated with an increased risk of zoonotic and foodborne infection, particularly among populations with close animal contact, including pastoralists and semi-pastoralists. However, there are limited data on disease risk factors among pastoralists and other populations where livestock herding, particularly of dromedary camels, is common. This cross-sectional study used a previously validated survey instrument to identify risk factors for self-reported symptoms. Adults (n = 304) were randomly selected from households (n = 171) in the Somali Region of Ethiopia, a region characterised by chronic food insecurity, population displacement, recurrent droughts and large semi-pastoralist and pastoralist populations. Multivariable logistic regression assessed associations between self-reported symptoms and type of milk consumed, controlling for demographics and human-animal interaction. Consumption of days-old unrefrigerated raw camel milk was significantly associated with symptoms in the 30 days prior to the survey (AOR = 5.07; 95% CI 2.41–10.66), after controlling for age, refugee status, sanitation, camel ownership and source of drinking water and accounting for clustering. Consumption of days-old unrefrigerated raw ruminant milk was significantly associated with symptoms (AOR = 4.00, 95% CI 1.27–12.58). Source of drinking water and camel ownership, a proxy for camel contact, were significantly associated with the outcome in each model. There were no significant associations between self-reported symptoms and fresh or soured animal milk consumption. Research is needed to identify pathogens and major routes of transmission. Tailored communication campaigns to encourage safe food preparation should also be considered.
For a uniform random labelled tree, we find the limiting distribution of tree parameters which are stable (in some sense) with respect to local perturbations of the tree structure. The proof is based on the martingale central limit theorem and the Aldous–Broder algorithm. In particular, our general result implies the asymptotic normality of the number of occurrences of any given small pattern and the asymptotic log-normality of the number of automorphisms.
Reproducibility of a deep-learning fully convolutional neural network is evaluated by training several times the same network on identical conditions (database, hyperparameters, and hardware) with nondeterministic graphics processing unit operations. The network is trained to model three typical time–space-evolving physical systems in two dimensions: heat, Burgers’, and wave equations. The behavior of the networks is evaluated on both recursive and nonrecursive tasks. Significant changes in models’ properties (weights and feature fields) are observed. When tested on various benchmarks, these models systematically return estimations with a high level of deviation, especially for the recurrent analysis which strongly amplifies variability due to the nondeterminism. Trainings performed with double floating-point precision provide slightly better estimations and a significant reduction of the variability of both the network parameters and its testing error range.