Application of Hierarchical Agglomerative Clustering (HAC) for Systemic Classification of Pop-Up Housing (PUH) Environments

This paper is the result of the first-phase, inter-disciplinary work of a multi-disciplinary research project (“Urban pop-up housing environments and their potential as local innovation systems”) consisting of energy engineers and waste managers, landscape architects and spatial planners, innovation researchers and technology assessors. The project is aiming at globally analyzing and describing existing pop-up housings (PUH), developing modeling and assessment tools for sustainable, energy-efficient and socially innovative temporary housing solutions (THS), especially for sustainable and resilient urban structures. The present paper presents an effective application of hierarchical agglomerative clustering (HAC) for analyses of large datasets typically derived from field studies. As can be shown, the method, although well-known and successfully established in (soft) computing science, can also be used very constructively as a potential urban planning tool. The main aim of the underlying multi-disciplinary research project was to deeply analyze and structure THS and PUE. Multiple aspects are to be considered when it comes to the characterization and classification of such environments. A thorough (global) web survey of PUH and analysis of scientific literature concerning descriptive work of PUH and THS has been performed. Moreover, out of several tested different approaches and methods for classifying PUH, hierarchical clustering algorithms functioned well when properly selected metrics and cut-off criteria were applied. To be specific, the ‘Minkowski’-metric and the ‘Calinski-Harabasz’-criteria, as clustering indices, have shown the best overall results in clustering the inhomogeneous data concerning PUH. Several additional algorithms/functions derived from the field of hierarchical clustering have also been tested to exploit their potential in interpreting and graphically analyzing particular structures and dependencies in the resulting clusters. Hereby, (math.) the significance ‘S’ and (math.) proportion ‘P’ have been concluded to yield the best interpretable and comprehensible results when it comes to analyzing the given set (objects n = 85) of researched PUH-objects together with their properties (n > 190). The resulting easily readable graphs clearly demonstrate the applicability and usability of hierarchical clustering- and their derivative algorithms for scientifically profound building classification tasks in Urban Planning by effectively managing huge inhomogeneous building datasets.

Curvature

The mathematics of Riemannian curvature is presented. The Riemann curvature tensor and its role in parallel transport, in the metric, and in geodesic deviation are expounded at length. We begin by defining the curvature tensor and the torsion tensor by relating them to covariant derivatives. Then the local metric is obtained up to second order in terms of Minkowski metric and curvature tensor. Geometric issues such as the closure or non-closure of parallelograms are discussed. Next, the relation between curvature and parallel transport around a loop is derived. Then we proceed to geodesic deviation. The influence of global properties of the manifold on parallel transport is briefly expounded. The Lie derivative is then defined, and isometries of spacetime are discussed. Killing’s equation and properties of Killing vectors are obtained. Finally, the Weyl tensor (conformal tensor) is introduced.

Constraints on General Relativity Geodesics by a Covariant Geometric Uncertainty Principle

The classical uncertainty principle inequalities are imposed over the general relativity geodesic equation as a mathematical constraint. In this way, the uncertainty principle is reformulated in terms of proper space–time length element, Planck length and a geodesic-derived scalar, leading to a geometric expression for the uncertainty principle (GeUP). This re-formulation confirms the need for a minimum length of space–time line element in the geodesic, which depends on a Lorentz-covariant geodesic-derived scalar. In agreement with quantum gravity theories, GeUP imposes a perturbation over the background Minkowski metric unrelated to classical gravity. When applied to the Schwarzschild metric, a geodesic exclusion zone is found around the singularity where uncertainty in space-time diverged to infinity.

Constraints on General Relativity Geodesics by a Covariant Geometric Uncertainty Principle

The classical uncertainty principle inequalities were imposed as a mathematical constraint over the general relativity geodesic equation. In this way, the uncertainty principle was reformulated in terms of the proper space-time length element, Planck length and a geodesic-derived scalar, leading to a geometric expression for the uncertainty principle (GeUP). This re-formulation confirmed the necessity for a minimum length for the space-time line element in the geodesic, dependent on a geodesic-derived scalar which made the expression Lorentz-covariant. In agreement with quantum gravity theories, GeUP required the imposition of a perturbation over the background Minkowski metric unrelated to classical gravity. When applied to the Schwarzschild metric, a geodesic exclusion zone was found around the singularity where uncertainty in space-time diverged to infinity.

Devising an entropy-based approach for identifying patterns in multilingual texts

Even though the plagiarism identification issue remains relevant, modern detection methods are still resource-intensive. This paper reports a more efficient alternative to existing solutions. The devised system for identifying patterns in multilingual texts compares two texts and determines, by using different approaches, whether the second text is a translation of the first or not. This study's approach is based on Renyi entropy. The original text from an English writer's work and five texts in the Russian language were selected for this research. The real and "fake" translations that were chosen included translations by Google Translator and Yandex Translator, an author's book translation, a text from another work by an English writer, and a fake text. The fake text represents a text compiled with the same frequency of keywords as in the authentic text. Upon forming a key series of high-frequency words for the original text, the relevant key series for other texts were identified. Then the entropies for the texts were calculated when they were divided into "sentences" and "paragraphs". A Minkowski metric was used to calculate the proximity of the texts. It underlies the calculations of a Hamming distance, the Cartesian distance, the distance between the centers of masses, the distance between the geometric centers, and the distance between the centers of parametric means. It was found that the proximity of texts is best determined by calculating the relative distances between the centers of parametric means (for "fake" texts ‒ exceeding 3, for translations ‒ less than 1). Calculating the proximity of texts by using the algorithm based on Renyi entropy, reported in this work, makes it possible to save resources and time compared to methods based on neural networks. All the raw data and an example of the entropy calculation on php are publicly available

An Analysis of Gravitational waves

The September 14, 2015 gravitational wave observations showed the inspiral of two black holes observed from Hanford and Livingston LIGO observatories. This detection was significant for two reasons: firstly, it coupled the result and avoided the possibility of a false alarm by 5σ , meaning that the detected “noise” was indeed from an astronomical source of gravitational waves. We will discuss the primary landscape of gravitational waves, their mathematical structure and how they can be used to predict the masses of the merger system. We will also discuss gravitational wave detector optimisations, and then we will consider the results from the detected merger GW150914. We will consider a straight-forward mathematical approach, and we will primarily be interested in the mathematical modelling of gravitational waves from General Relativity (Section 1). We will first consider a “perturbed” Minkowski metric, and then we will discuss the properties of the perturbation addition tensor. We will then discuss on the gravitational field tensor, and how it arises from the perturbation tensor. We will then talk about the gauge condition, essentially the gauge “freedom” , and then we will talk about the curvature tensor, leading eventually to the effect of gravitational waves on a ring of particles. We will consider the polarisation tensor, which maps the amplitude and polarisation details. The polarisation splits into plus polarised and cross polarised waves, which is technically the effect of a propagating gravitational wave through a ring of particles. We will then talk about the linearized Einstein Field Equations, and how the physical system of merger is encoded into the mathematical structural unity of the metric. We will then talk about the detection of these gravitational waves and how the detector can be optimised, or how the detector can be set so that any “noise” detected can fall in the error margins, and how the detector can prevent the interferometric “photon-noise” from being detected (Section 2.2). Then, we will discuss data results from the source GW150914 detection by LIGO (Section 3).

Counterexamples to inverse problems for the wave equation

<p style='text-indent:20px;'>We construct counterexamples to inverse problems for the wave operator on domains in <inline-formula><tex-math id="M1">\begin{document}$ \mathbb{R}^{n+1} $\end{document}</tex-math></inline-formula>, <inline-formula><tex-math id="M2">\begin{document}$ n \ge 2 $\end{document}</tex-math></inline-formula>, and on Lorentzian manifolds. We show that non-isometric Lorentzian metrics can lead to same partial data measurements, which are formulated in terms certain restrictions of the Dirichlet-to-Neumann map. The Lorentzian metrics giving counterexamples are time-dependent, but they are smooth and non-degenerate. On <inline-formula><tex-math id="M3">\begin{document}$ \mathbb{R}^{n+1} $\end{document}</tex-math></inline-formula> the metrics are conformal to the Minkowski metric.</p>

A cans waste classification system based on RGB images using different distances of k-means clustering

This study aims to build a classify the cans waste based on the pixel of captured Red, Green, and Blue (RGB) image by implement different metric 3 distances of k-means clustering; Manhattan, Euclidean, and Minkowski metric distance. The image capturing is designed using combinations of two the conveyor belt speeds of 0.181 m/sec and 0.086 m/sec, two the lightings of halogen and incandescent lamps, and four lighting angles of 300, 450, 600, and 900. The classification results note that the implementation of Manhattan distance on the k-means clustering method for classifying the cans waste into three can types has the highest level of accuracy in the majority of data. The highest accuracy level of classification is obtained from data of captured image on the conveyor belt speeds of 0.181 m/sec, the lightings of halogen lamp, and the lighting angles of 450 by implementing the Euclidean distance, while the lowest accuracy level of classification is obtained from data of captured image on the lighting angles of 300 with the same speeds and the lamp by implementing the Manhattan distance. The highest average accuracy is obtained by implementing the Euclidean distance, that derived from the average accuracy at lighting angle of 450.