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.

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.

Multidimensional scaling analysis of fractional systems

This paper investigates the use of multidimensional scaling in the evaluation of fractional system. Several algorithms are analysed based on the time response of the closed loop system under the action of a reference step input signal. Two alternative performance indices, based on the time and frequency domains, are tested. The numerical experiments demonstrate the feasibility of the proposed visualization method.

Analysis of stock market indices through multidimensional scaling

We propose a graphical method to visualize possible time-varying correlations between fifteen stock market values. The method is useful for observing stable or emerging clusters of stock markets with similar behaviour. The graphs, originated from applying multidimensional scaling techniques (MDS), may also guide the construction of multivariate econometric models.

Is multidimensional scaling suitable for mapping the input respiratory impedance in subjects and patients?

This paper presents the application of multidimensional scaling (MDS) analysis to data emerging from noninvasive lung function tests, namely the input respiratory impedance. The aim is to obtain a geometrical mapping of the diseases in a 3D space representation, allowing analysis of (dis)similarities between subjects within the same pathology groups, as well as between the various groups. The adult patient groups investigated were healthy, diagnosed chronic obstructive pulmonary disease (COPD) and diagnosed kyphoscoliosis, respectively. The children patient groups were healthy, asthma and cystic fibrosis. The results suggest that MDS can be successfully employed for mapping purposes of restrictive (kyphoscoliosis) and obstructive (COPD) pathologies. Hence, MDS tools can be further examined to define clear limits between pools of patients for clinical classification, and used as a training aid for medical traineeship.

Analysis of financial data series using fractional Fourier transform and multidimensional scaling

The goal of this study is the analysis of the dynamical properties of financial data series from worldwide stock market indexes during the period 2000–2009. We analyze, under a regional criterium, ten main indexes at a daily time horizon. The methods and algorithms that have been explored for the description of dynamical phenomena become an effective background in the analysis of economical data. We start by applying the classical concepts of signal analysis, fractional Fourier transform, and methods of fractional calculus. In a second phase we adopt the multidimensional scaling approach. Stock market indexes are examples of complex interacting systems for which a huge amount of data exists. Therefore, these indexes, viewed from a different perspectives, lead to new classification patterns.

Identifying economic periods and crisis with the multidimensional scaling

This paper applied MDS and Fourier transform to analyze different periods of the business cycle. With such purpose, four important stock market indexes (Dow Jones, Nasdaq, NYSE, S&P500) were studied over time. The analysis under the lens of the Fourier transform showed that the indexes have characteristics similar to those of fractional noise. By the other side, the analysis under the MDS lens identified patterns in the stock markets specific to each economic expansion period. Although the identification of patterns characteristic to each expansion period is interesting to practitioners (even if only in a posteriori fashion), further research should explore the meaning of such regularities and target to find a method to estimate future crisis.

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 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 Shimadzu UV–VIS 2550, which is in the world 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.

Analysis of Electricity Market Prices Using Multidimensional Scaling

This paper studies the impact of the energy upon electricity markets using Multidimensional Scaling (MDS). Data from major energy and electricity markets is considered. Several maps produced by MDS are presented and discussed revealing that this method is useful for understanding the correlation between them. Furthermore, the results help electricity markets agents hedging against Market Clearing Price (MCP) volatility.

Wavelet analysis of human DNA

This paper studies the human DNA in the perspective of signal processing. Six wavelets are tested for analyzing the information content of the human DNA. By adopting real Shannon wavelet several fundamental properties of the code are revealed. A quantitative comparison of the chromosomes and visualization through multidimensional and dendograms is developed.

Analysis and visualization of chromosome information

This paper analyzes the DNA code of several species in the perspective of information content. For that purpose several concepts and mathematical tools are selected towards establishing a quantitative method without a priori distorting the alphabet represented by the sequence of DNA bases. The synergies of associating Gray code, histogram characterization and multidimensional scaling visualization lead to a collection of plots with a categorical representation of species and chromosomes.

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.

Relativistic time effects in financial dynamics

Financial time series have a complex dynamic nature. Many techniques were adopted having in mind standard paradigms of time flow. This paper explores an alternative route involving relativistic effects. It is observed that the measuring perspective influences the results and that we can have different time textures.