Wavelets in Statistics

In this paper we give the main uses of wavelets in statistics, with emphasis in time series analysis. We include the fundamental work on non parametric regression, which motivated the development of techniques used in the estimation of the spectral density of stationary processes and of the evolutionary spectrum of locally stationary processes

Indirect inference for locally stationary ARMA processes with stable innovations

The class of locally stationary processes assumes that there is a time-varying spectral representation, that is, the existence of finite second moment. We propose the $\alpha$-stable locally stationary process by modifying the innovations into stable distributions and the indirect inference to estimate this type of model. Due to the infinite variance, some of interesting properties such as time-varying auto-correlation cannot be defined. However, since the $\alpha$-stable family of distributions is closed under linear combination which includes the possibility of handling asymmetry and thicker tails, the proposed model has the same tail behavior throughout the time. In this paper, we propose this new model, present theoretical properties of the process and carry out simulations related to the indirect inference in order to estimate the parametric form of the model. Finally, an empirical application is illustrated.Comment: 31 pages, 14 figures. Submitted to the Journal of Statistical Computation and Simulatio

Welder’s Maculopathy; a Case Report

Background: Outer retinal damage can occur when excessive ultraviolet (UV) radiation reaches the retina. The most common etiology is from the sun, known as solar retinopathy, especially when individuals observe solar eclipses without appropriate eye protection. Another cause of UV retinopathy that is not frequently encountered in practice is arc welding, causing Welder’s Maculopathy. Fortunately, the prognosis of the UV retinopathies is quite favourable, as many fully recover after the initial insult to the retina. This retrospective case review aims to outline the clinical manifestation of this maculopathy and current opinions on its etiology and diagnosis. Case Report: A 45-year-old patient presented for a comprehensive eye examination with an occupational history of arc welding. Best corrected visual acuities were 20/20 OD, OS. Dilated fundus examination revealed central red macular retinal pigment epithelium (RPE) disruption in the right and left eyes. Spectral domain optical coherence tomography (SD-OCT) demonstrated no defects OD and foveal loss of the ellipsoid portion of the photoreceptor inner segment (ISe) band with atrophy in the RPE OS. Conclusion: Welder’s Maculopathy is an established, but infrequently encountered, cause of UV retinopathy. Most cases are self-limiting and cause no long-term functional sequelae. SD-OCT findings from photochemical injury to the photoreceptors and RPE lead to a box-shaped outer retinal hole that can interrupt the ISe band; which is a determinant of visual prognosis. Careful occupational education should be discussed with each patient

Symbolic Logic meets Machine Learning: A Brief Survey in Infinite Domains

The tension between deduction and induction is perhaps the most fundamental issue in areas such as philosophy, cognition and artificial intelligence (AI). The deduction camp concerns itself with questions about the expressiveness of formal languages for capturing knowledge about the world, together with proof systems for reasoning from such knowledge bases. The learning camp attempts to generalize from examples about partial descriptions about the world. In AI, historically, these camps have loosely divided the development of the field, but advances in cross-over areas such as statistical relational learning, neuro-symbolic systems, and high-level control have illustrated that the dichotomy is not very constructive, and perhaps even ill-formed. In this article, we survey work that provides further evidence for the connections between logic and learning. Our narrative is structured in terms of three strands: logic versus learning, machine learning for logic, and logic for machine learning, but naturally, there is considerable overlap. We place an emphasis on the following "sore" point: there is a common misconception that logic is for discrete properties, whereas probability theory and machine learning, more generally, is for continuous properties. We report on results that challenge this view on the limitations of logic, and expose the role that logic can play for learning in infinite domains

Aberrant methylation of Polo-like kinase CpG islands in Plk4 heterozygous mice

<p>Abstract</p> <p>Background</p> <p>Hepatocellular carcinoma (HCC), one of the most common cancers world-wide occurs twice as often in men compared to women. Predisposing conditions such as alcoholism, chronic viral hepatitis, aflatoxin B1 ingestion, and cirrhosis all contribute to the development of HCC.</p> <p>Methods</p> <p>We used a combination of methylation specific PCR and bisulfite sequencing, qReal-Time PCR (qPCR), and Western blot analysis to examine epigenetic changes for the <it>Polo-like kinases </it>(<it>Plks</it>) during the development of hepatocellular carcinoma (HCC) in <it>Plk4 </it>heterozygous mice and murine embryonic fibroblasts (MEFs).</p> <p>Results</p> <p>Here we report that the promoter methylation of <it>Plk4 </it>CpG islands increases with age, was more prevalent in males and that <it>Plk4 </it>epigenetic modification and subsequent downregulation of expression was associated with the development of HCC in <it>Plk4 </it>mutant mice. Interestingly, the opposite occurs with another Plk family member, <it>Plk1 </it>which was typically hypermethylated in normal liver tissue but became hypomethylated and upregulated in liver tumours. Furthermore, upon alcohol exposure murine embryonic fibroblasts exhibited increased <it>Plk4 </it>hypermethylation and downregulation along with increased centrosome numbers and multinucleation.</p> <p>Conclusions</p> <p>These results suggest that aberrant <it>Plk </it>methylation is correlated with the development of HCC in mice.</p