Statistical Modeling of RPCA-FCM in Spatiotemporal Rainfall Patterns Recognition

This study was conducted to identify the spatiotemporal torrential rainfall patterns of the East Coast of Peninsular Malaysia, as it is the region most affected by the torrential rainfall of the Northeast Monsoon season. Dimension reduction, such as the classical Principal Components Analysis (PCA) coupled with the clustering approach, is often applied to reduce the dimension of the data while simultaneously performing cluster partitions. However, the classical PCA is highly insensitive to outliers, as it assigns equal weights to each set of observations. Hence, applying the classical PCA could affect the cluster partitions of the rainfall patterns. Furthermore, traditional clustering algorithms only allow each element to exclusively belong to one cluster, thus observations within overlapping clusters of the torrential rainfall datasets might not be captured effectively. In this study, a statistical model of torrential rainfall pattern recognition was proposed to alleviate these issues. Here, a Robust PCA (RPCA) based on Tukey’s biweight correlation was introduced and the optimum breakdown point to extract the number of components was identified. A breakdown point of 0.4 at 85% cumulative variance percentage efficiently extracted the number of components to avoid low-frequency variations or insignificant clusters on a spatial scale. Based on the extracted components, the rainfall patterns were further characterized based on cluster solutions attained using Fuzzy C-means clustering (FCM) to allow data elements to belong to more than one cluster, as the rainfall data structure permits this. Lastly, data generated using a Monte Carlo simulation were used to evaluate the performance of the proposed statistical modeling. It was found that the proposed RPCA-FCM performed better using RPCA-FCM compared to the classical PCA coupled with FCM in identifying the torrential rainfall patterns of Peninsular Malaysia’s East Coast.

Scientific Study of Types of Network Architecture and Discussing Advantages Disadvantages

This paper will explain the theory of network architecture. The concept of network architecture is the combination of different layers of the network infrastructure. Each layer has specific roles. This paper will also discuss about the challenges in the implementation of any type of network architecture. The two types of networks will be discussed. There are number of components which are used to implement the network

Improvement of cottage cheese technology

In recent years, the prospect of improving the technology of cereal cottage cheese using linseed oil has been widely used to improve and maintain their quality, increase the biological and nutritional value of the finished product, and increase the shelf life. In the course of the work, the number of components of the cottage cheese with the addition of linseed oil was selected, a technological scheme was developed. Physicochemical and microbiological changes were investigated, and the energy value of the resulting product was calculated. (per 100 g of product: 774kj/178 kcal: fats 10.42 g (52%); protein 18 g (40%); carbohydrates 3.3 g (8%)).

A Combinatorial Bijection on di-sk Trees

A di-sk tree is a rooted binary tree whose nodes are labeled by $\oplus$ or $\ominus$, and no node has the same label as its right child. The di-sk trees are in natural bijection with separable permutations. We construct a combinatorial bijection on di-sk trees proving the two quintuples $(\mathrm{LMAX},\mathrm{LMIN},\mathrm{DESB},\mathsf{iar},\mathsf{comp})$ and $(\mathrm{LMAX},\mathrm{LMIN},\mathrm{DESB},\mathsf{comp},\mathsf{iar})$ have the same distribution over separable permutations. Here for a permutation $\pi$, $\mathrm{LMAX}(\pi)/\mathrm{LMIN}(\pi)$ is the set of values of the left-to-right maxima/minima of $\pi$ and $\mathrm{DESB}(\pi)$ is the set of descent bottoms of $\pi$, while $\mathsf{comp}(\pi)$ and $\mathsf{iar}(\pi)$ are respectively the number of components of $\pi$ and the length of initial ascending run of $\pi$. Interestingly, our bijection specializes to a bijection on $312$-avoiding permutations, which provides (up to the classical Knuth–Richards bijection) an alternative approach to a result of Rubey (2016) that asserts the two triples $(\mathrm{LMAX},\mathsf{iar},\mathsf{comp})$ and $(\mathrm{LMAX},\mathsf{comp},\mathsf{iar})$ are equidistributed on $321$-avoiding permutations. Rubey's result is a symmetric extension of an equidistribution due to Adin–Bagno–Roichman, which implies the class of $321$-avoiding permutations with a prescribed number of components is Schur positive. Some equidistribution results for various statistics concerning tree traversal are presented in the end.

Rethinking the Integrative Dimension of Theology with Science: Syntheses and Congruences

If we want to define today's society in one word, trying to capture its meaning, it would be polarization. The interdependence between all social segments, articulated by globalization, has a double function: unpacking the identitary elements that enter in the structure of society (religion, politics, culture, science, etc.) and framing them in a relational dynamic. In this situation are Theology and Science, which, of course, maintain a number of components under their general names. Can we talk about a congruence between these two dimensions of human knowledge? Or they are developing completely separately and antagonistic in social progress? According to Ian G. Barbour there are four types of relation between Science and Religion: conflict, independence, dialogue, integration. This article intends to highlight the congruence between Theology and Science in the paradigm of neo-patristic synthesis , which explores in a phenomenological, theological and philosophical way the relationship between these two. Neo-patristic synthesis is a theological movement from the 20th century, generated by the initiative of the orthodox theologian G. Florovsky.