Multidimensional scaling visualization of earthquake phenomena

Earthquakes are associated with negative events, such as large number of casualties, destruction of buildings and infrastructures, or emergence of tsunamis. In this paper, we apply the Multidimensional Scaling (MDS) analysis to earthquake data. MDS is a set of techniques that produce spatial or geometric representations of complex objects, such that, objects perceived to be similar/distinct in some sense are placed nearby/distant on the MDS maps. The interpretation of the charts is based on the resulting clusters since MDS produces a different locus for each similarity measure. In this study, over three million seismic occurrences, covering the period from January 1, 1904 up to March 14, 2012 are analyzed. The events, characterized by their magnitude and spatiotemporal distributions, are divided into groups, either according to the Flinn–Engdahl seismic regions of Earth or using a rectangular grid based in latitude and longitude coordinates. Space-time and Space-frequency correlation indices are proposed to quantify the similarities among events. MDS has the advantage of avoiding sensitivity to the non-uniform spatial distribution of seismic data, resulting from poorly instrumented areas, and is well suited for accessing dynamics of complex systems. MDS maps are proven as an intuitive and useful visual representation of the complex relationships that are present among seismic events, which may not be perceived on traditional geographic maps. Therefore, MDS constitutes a valid alternative to classic visualization tools, for understanding the global behavior of earthquakes.

Analysis of Forest Fires by means of Pseudo Phase Plane and Multidimensional Scaling Methods

Forest fires dynamics is often characterized by the absence of a characteristic length-scale, long range correlations in space and time, and long memory, which are features also associated with fractional order systems. In this paper a public domain forest fires catalogue, containing information of events for Portugal, covering the period from 1980 up to 2012, is tackled. The events are modelled as time series of Dirac impulses with amplitude proportional to the burnt area. The time series are viewed as the system output and are interpreted as a manifestation of the system dynamics. In the first phase we use the pseudo phase plane (PPP) technique to describe forest fires dynamics. In the second phase we use multidimensional scaling (MDS) visualization tools. The PPP allows the representation of forest fires dynamics in two-dimensional space, by taking time series representative of the phenomena. The MDS approach generates maps where objects that are perceived to be similar to each other are placed on the map forming clusters. The results are analysed in order to extract relationships among the data and to better understand forest fires behaviour.

Analysis of World Economic Variables Using Multidimensional Scaling

Waves of globalization reflect the historical technical progress and modern economic growth. The dynamics of this process are here approached using the multidimensional scaling (MDS) methodology to analyze the evolution of GDP per capita, international trade openness, life expectancy, and education tertiary enrollment in 14 countries. MDS provides the appropriate theoretical concepts and the exact mathematical tools to describe the joint evolution of these indicators of economic growth, globalization, welfare and human development of the world economy from 1977 up to 2012. The polarization dance of countries enlightens the convergence paths, potential warfare and present-day rivalries in the global geopolitical scene.

Multi-dimensional scaling applied to histogram-based DNA analysis

This paper aims to study the relationships between chromosomal DNA sequences of twenty species. We propose a methodology combining DNA-based word frequency histograms, correlation methods, and an MDS technique to visualize structural information underlying chromosomes (CRs) and species. Four statistical measures are tested (Minkowski, Cosine, Pearson product-moment, and Kendall τ rank correlations) to analyze the information content of 421 nuclear CRs from twenty species. The proposed methodology is built on mathematical tools and allows the analysis and visualization of very large amounts of stream data, like DNA sequences, with almost no assumptions other than the predefined DNA “word length.” This methodology is able to produce comprehensible three-dimensional visualizations of CR clustering and related spatial and structural patterns. The results of the four test correlation scenarios show that the high-level information clusterings produced by the MDS tool are qualitatively similar, with small variations due to each correlation method characteristics, and that the clusterings are a consequence of the input data and not method’s artifacts.

A multidimensional scaling analysis of musical sounds based on pseudo phase plane

This paper studies musical opus from the point of view of three mathematical tools: entropy, pseudo phase plane (PPP), and multidimensional scaling (MDS). The experiments analyze ten sets of different musical styles. First, for each musical composition, the PPP is produced using the time series lags captured by the average mutual information. Second, to unravel hidden relationships between the musical styles the MDS technique is used. The MDS is calculated based on two alternative metrics obtained from the PPP, namely, the average mutual information and the fractal dimension. The results reveal significant differences in the musical styles, demonstrating the feasibility of the proposed strategy and motivating further developments towards a dynamical analysis of musical sounds.

PPO Reaction Scale-up

O óxido de polifenileno com a marca comercial PPO® é uma das resinas principais produzidas na SABIC IP e o ingrediente principal do plástico de engenharia com a marca registada, Noryl®. A equipa de tecnologia de processo de PPO® desenvolve uma série de novos produtos em reactores de pequena escala, tanto em Selkirk como em Bergen op Zoom. Para se efectuar uma transição rápida da escala laboratorial para a fábrica, é necessário um conhecimento completo do reactor. O objectivo deste projecto consiste em esboçar linhas gerais para o scale-up de novos produtos de PPO1, do laboratório para a escala industrial, baseado no estudo de um tipo de PPO, PPO 803. Este estudo pode ser dividido em duas fases. Numa primeira fase, as receitas e os perfis da reacção são comparados, de onde se retiram as primeiras conclusões. Posteriormente, com base nestas conclusões, é realizado um planeamento experimental. O estudo inicial sugeriu que a receita, a temperatura inicial do reactor e a velocidade do agitador poderiam influenciar o tempo da reacção bem como a queda da velocidade intrínseca do polímero (IV drop). As reacções experimentais mostraram que a receita é o principal factor que influencia, tanto o tempo de reacção, como a queda de viscosidade intrínseca. O tempo de reacção será tanto maior quanto menor a agitação devido à má dispersão do oxigénio na mistura. O uso de temperaturas iniciais elevadas conduz a uma queda maior da viscosidade intrínseca devido à desactivação do catalisador. O método experimental utilizado no laboratório de Bergen op Zoom é um bom exemplo, simulador, do procedimento utilizado na fábrica.

Soil remediation time to achieve clean-up goals I: influence of soil water content

The current models are not simple enough to allow a quick estimation of the remediation time. This work reports the development of an easy and relatively rapid procedure for the forecasting of the remediation time using vapour extraction. Sandy soils contaminated with cyclohexane and prepared with different water contents were studied. The remediation times estimated through the mathematical fitting of experimental results were compared with those of real soils. The main objectives were: (i) to predict, through a simple mathematical fitting, the remediation time of soils with water contents different from those used in the experiments; (ii) to analyse the influence of soil water content on the: (ii1) remediation time; (ii2) remediation efficiency; and (ii3) distribution of contaminants in the different phases present into the soil matrix after the remediation process. For sandy soils with negligible contents of clay and natural organic matter, artificially contaminated with cyclohexane before vapour extraction, it was concluded that (i) if the soil water content belonged to the range considered in the experiments with the prepared soils, then the remediation time of real soils of similar characteristics could be successfully predicted, with relative differences not higher than 10%, through a simple mathematical fitting of experimental results; (ii) increasing soil water content from 0% to 6% had the following consequences: (ii1) increased remediation time (1.8–4.9 h, respectively); (ii2) decreased remediation efficiency (99–97%, respectively); and (ii3) decreased the amount of contaminant adsorbed onto the soil and in the non-aqueous liquid phase, thus increasing the amount of contaminant in the aqueous and gaseous phases.

Soil remediation time to achieve clean-up goals II: influence of natural organic matter and water contents

This work reports a relatively rapid procedure for the forecasting of the remediation time (RT) of sandy soils contaminated with cyclohexane using vapour extraction. The RT estimated through the mathematical fitting of experimental results was compared with that of real soils. The main objectives were: (i) to predict the RT of soils with natural organic matter (NOM) and water contents different from those used in experiments; and (ii) to analyse the time and efficiency of remediation, and the distribution of contaminants into the soil matrix after the remediation process, according to the soil contents of: (ii1) NOM; and (ii2) water. For sandy soils with negligible clay contents, artificially contaminated with cyclohexane before vapour extraction, it was concluded that: (i) if the NOM and water contents belonged to the range of the prepared soils, the RT of real soils could be predicted with relative differences not higher than 12%; (ii1) the increase of NOM content from 0% to 7.5% increased the RT (1.8–13 h) and decreased the remediation efficiency (RE) (99–90%) and (ii2) the increase of soil water content from 0% to 6% increased the RT (1.8–4.9 h) and decreased the RE (99–97%). NOM increases the monolayer capacity leading to a higher sorption into the solid phase. Increasing of soil water content reduces the mass transfer coefficient between phases. Concluding, NOM and water contents influence negatively the remediation process, turning it less efficient and more time consuming, and consequently more expensive.

Fractional dynamics and MDS visualization of earthquake phenomena

This paper analyses earthquake data in the perspective of dynamical systems and fractional calculus (FC). This new standpoint uses Multidimensional Scaling (MDS) as a powerful clustering and visualization tool. FC extends the concepts of integrals and derivatives to non-integer and complex orders. MDS is a technique that produces spatial or geometric representations of complex objects, such that those objects that are perceived to be similar in some sense are placed on the MDS maps forming clusters. In this study, over three million seismic occurrences, covering the period from January 1, 1904 up to March 14, 2012 are analysed. The events are characterized by their magnitude and spatiotemporal distributions and are divided into fifty groups, according to the Flinn–Engdahl (F–E) seismic regions of Earth. Several correlation indices are proposed to quantify the similarities among regions. MDS maps are proven as an intuitive and useful visual representation of the complex relationships that are present among seismic events, which may not be perceived on traditional geographic maps. Therefore, MDS constitutes a valid alternative to classic visualization tools for understanding the global behaviour of earthquakes.

Biocomplementation of SVE to achieve clean-up goals in soils contaminated with toluene and xylene

Soil vapor extraction (SVE) and bioremediation (BR) are two of the most common soil remediation technologies. Their application is widespread; however, both present limitations, namely related to the efficiencies of SVE on organic soils and to the remediation times of some BR processes. This work aimed to study the combination of these two technologies in order to verify the achievement of the legal clean-up goals in soil remediation projects involving seven different simulated soils separately contaminated with toluene and xylene. The remediations consisted of the application of SVE followed by biostimulation. The results show that the combination of these two technologies is effective and manages to achieve the clean-up goals imposed by the Spanish Legislation. Under the experimental conditions used in this work, SVE is sufficient for the remediation of soils, contaminated separately with toluene and xylene, with organic matter contents (OMC) below 4 %. In soils with higher OMC, the use of BR, as a complementary technology, and when the concentration of contaminant in the gas phase of the soil reaches values near 1 mg/L, allows the achievement of the clean-up goals. The OMC was a key parameter because it hindered SVE due to adsorption phenomena but enhanced the BR process because it acted as a microorganism and nutrient source.

Multidimensional scaling analysis of the dynamics of a country economy

This paper analyzes the Portuguese short-run business cycles over the last 150 years and presents the multidimensional scaling (MDS) for visualizing the results. The analytical and numerical assessment of this long-run perspective reveals periods with close connections between the macroeconomic variables related to government accounts equilibrium, balance of payments equilibrium, and economic growth. The MDS method is adopted for a quantitative statistical analysis. In this way, similarity clusters of several historical periods emerge in the MDS maps, namely, in identifying similarities and dissimilarities that identify periods of prosperity and crises, growth, and stagnation. Such features are major aspects of collective national achievement, to which can be associated the impact of international problems such as the World Wars, the Great Depression, or the current global financial crisis, as well as national events in the context of broad political blueprints for the Portuguese society in the rising globalization process.

Multidimensional scaling for orthodontic root resorption

The paper investigates the risk factors for the severity of orthodontic root resorption. The multidimensional scaling (MDS) visualization method is used to investigate the experimental data from patients who received orthodontic treatment at the Department of Orthodontics and Dentofacial Orthopedics, Faculty of Dentistry, “Carol Davila” University of Medicine and Pharmacy, during a period of 4 years. The clusters emerging in the MDS plots reveal features and properties not easily captured by classical statistical tools. The results support the adoption of MDS for tackling the dentistry information and overcoming noise embedded into the data. The method introduced in this paper is rapid, efficient, and very useful for treating the risk factors for the severity of orthodontic root resorption.

Analysis of stock market indices with multidimensional scaling and wavelets

Stock market indices SMIs are important measures of financial and economical performance. Considerable research efforts during the last years demonstrated that these signals have a chaotic nature and require sophisticated mathematical tools for analyzing their characteristics. Classical methods, such as the Fourier transform, reveal considerable limitations in discriminating different periods of time. This paper studies the dynamics of SMI by combining the wavelet transform and the multidimensional scaling MDS . Six continuous wavelets are tested for analyzing the information content of the stock signals. In a first phase, the real Shannon wavelet is adopted for performing the evaluation of the SMI dynamics, while their comparison is visualized by means of the MDS. In a second phase, the other wavelets are also tested, and the corresponding MDS plots are analyzed.

Analysis of UV spectral bands using multidimensional scaling

This study describes the change of the ultraviolet spectral bands starting from 0.1 to 5.0 nm slit width in the spectral range of 200–400 nm. The analysis of the spectral bands is carried out by using the multidimensional scaling (MDS) approach to reach the latent spectral background. This approach indicates that 0.1 nm slit width gives higher-order noise together with better spectral details. Thus, 5.0 nm slit width possesses the higher peak amplitude and lower-order noise together with poor spectral details. In the above-mentioned conditions, the main problem is to find the relationship between the spectral band properties and the slit width. For this aim, the MDS tool is to used recognize the hidden information of the ultraviolet spectra of sildenafil citrate by using a ShimadzuUV–VIS 2550, which is in theworld the best double monochromator instrument. In this study, the proposed mathematical approach gives the rich findings for the efficient use of the spectrophotometer in the qualitative and quantitative studies.