Homology groups of embedded fractional Brownian motion.

A well-known class of nonstationary self-similar time series is the fractional Brownian motion (fBm) considered to model ubiquitous stochastic processes in nature. Due to noise and trends superimposed on data and even sample size and irregularity impacts, the well-known computational algorithm to compute the Hurst exponent (H) has encountered superior results. Motivated by this discrepancy, we examine the homology groups of high-dimensional point cloud data (PCD), a subset of the unit D-dimensional cube, constructed from synthetic fBm data as a pipeline to compute the H exponent. We compute topological measures for embedded PCD as a function of the associated Hurst exponent for different embedding dimensions, time delays, and amount of irregularity existing in the dataset in various scales. Our results show that for a regular synthetic fBm, the higher value of the embedding dimension leads to increasing the H dependency of topological measures based on zeroth and first homology groups. To achieve a reliable classification of fBm, we should consider the small value of time delay irrespective of the irregularity presented in the data. More interestingly, the value of the scale for which the PCD to be path connected and the postloopless regime scale are more robust concerning irregularity for distinguishing the fBm signal. Such robustness becomes less for the higher value of the embedding dimension. Finally, the associated Hurst exponents for our topological feature vector for the S&P500 were computed, and the results are consistent with the detrended fluctuation analysis method.

Three novel mutations in CYBA among 22 Iranians with Chronic granulomatous disease.

Chronic granulomatous disease (CGD) is a rare primary immunodeficiency caused by defect in one of the components of nicotinamide adenine dinucleotide phosphate (NADPH)-oxidase enzyme. The enzyme is at least composed of membrane-bound subunits gp91-phox and p22-phox (also named cytochrome b558 ), and cytosolic ones p40-phox, p47-phox and p67-phox. A defect in the enzyme activity leads to impaired intracellular killing of phagocytic cells. The CYBA gene encoding p22-phox is located on chromosome 16q24. In this study, new genetic changes of CYBA gene in 22 Iranian patients with autosomal recessive-CGD (AR-CGD) were identified. Twenty-two patients with CGD were referred to Immunology, Asthma and Allergy Research Institute (IAARI) and enrolled in this study based on defect in NADPH oxidase activity, demographic data and clinical histories. All patients had p22-phox deficiency based on Western blotting. Genomic DNA was extracted from peripheral blood mononuclear cells (PBMCs), and PCR followed by direct sequencing was performed to find p22-phox mutations. Mutation analysis of CYBA revealed 12 different mutations, including three novel mutations: one was deletion of exon 1, and two were point mutations in exon 3 (c.136G>A (p.Gly46Ser)), and exon 6 (c.388C>T (p.Gln130X)). Three new mutations of CYBA gene in four of 22 Iranian patients with AR-CGD were found. These three novel mutations can partly complete the database of Human Gene Mutation Database (HGMD) and other related ones. It can also be helpful for further prenatal diagnosis in the affected families. Given that currently bone marrow transplantation is considered to be the curative treatment for patients with CGD, finding mutations will also be useful for timely decision-making in bone marrow transplantation.