Shannon, rényie and tsallis entropy analysis of DNA using phase plane

This paper analyzes DNA information using entropy and phase plane concepts. First, the DNA code is converted into a numerical format by means of histograms that capture DNA sequence length ranging from one up to ten bases. This strategy measures dynamical evolutions from 4 up to 410 signal states. The resulting histograms are analyzed using three distinct entropy formulations namely the Shannon, Rényie and Tsallis definitions. Charts of entropy versus sequence length are applied to a set of twenty four species, characterizing 486 chromosomes. The information is synthesized and visualized by adapting phase plane concepts leading to a categorical representation of chromosomes and species.

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.

Dynamic analysis of earthquake phenomena by means of pseudo phase plane

This paper analyses earthquake data in the perspective of dynamical systems and its Pseudo Phase Plane representation. The seismic data is collected from the Bulletin of the International Seismological Centre. The geological events are characterised by their magnitude and geographical location and described by means of time series of sequences of Dirac impulses. Fifty groups of data series are considered, according to the Flinn-Engdahl seismic regions of Earth. For each region, Pearson’s correlation coefficient is used to find the optimal time delay for reconstructing the Pseudo Phase Plane. The Pseudo Phase Plane plots are then analysed and characterised.

Analysis of the nano-surface of a modified glassy carbon electrode by pseudo phase plane method

This paper presents the Pseudo phase plane (PPP) method for detecting the existence of a nanofilm on the nitroazobenzene-modified glassy carbon electrode (NAB-GC) system. This modified electrode systems and nitroazobenze-nanofilm were prepared by the electrochemical reduction of diazonium salt of NAB at the glassy carbon electrodes (GCE) in nonaqueous media. The IR spectra of the bare glassy carbon electrodes (GCE), the NAB-GC electrode system and the organic NAB film were recorded. The IR data of the bare GC, NAB-GC and NAB film were categorized into five series consisting of FILM1, GC-NAB1, GC1; FILM2, GC-NAB2, GC2; FILM3, GC-NAB3, GC3 and FILM4, GC-NAB4, GC4 respectively. The PPP approach was applied to each group of the data of unmodified and modified electrode systems with nanofilm. The results provided by PPP method show the existence of the NAB film on the modified GC electrode.

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.

Shoulder Kinematics Is Not Influenced by External Load During Elevation in the Scapular Plane

The current study aimed to compare the shoulder kinematics (3D scapular orientation, scapular angular displacement and scapulohumeral rhythm) of asymptomatic participants under unloaded and loaded conditions during unilateral shoulder elevation in the scapular plane. We used a repeated-measures design with a convenience sample. Eleven male participants with an age range of 21–28 years with no recent history of shoulder injury participated in the study. The participants performed isometric shoulder elevation from a neutral position to approximately 150 degrees of elevation in the scapular plane in intervals of approximately 30 degrees during unloaded and loaded conditions. Shoulder kinematic data were obtained with videogrammetry. During shoulder elevation, the scapula rotated upwardly and externally, and tilted posteriorly. The addition of an external load did not affect 3D scapular orientation, scapular angular displacement, or scapulohumeral rhythm throughout shoulder elevation (P > .05). In clinical practice, clinicians should expect to observe upward and external rotation and posterior tilt of the scapula during their assessments of shoulder elevation. Such behavior was not influenced by an external load normalized to 5% of body weight when performed in an asymptomatic population.

Pseudo Phase Plane and Fractional Calculus Modelling of Western Global Economic Downturn

This paper applies Pseudo Phase Plane (PPP) and Fractional Calculus (FC) mathematical tools for modeling world economies. A challenging global rivalry among the largest international economies began in the early 1970s, when the post-war prosperity declined. It went on, up to now. If some worrying threatens may exist actually in terms of possible ambitious military aggression, invasion, or hegemony, countries’ PPP relative positions can tell something on the current global peaceful equilibrium. A global political downturn of the USA on global hegemony in favor of Asian partners is possible, but can still be not accomplished in the next decades. If the 1973 oil chock has represented the beginning of a long-run recession, the PPP analysis of the last four decades (1972–2012) does not conclude for other partners’ global dominance (Russian, Brazil, Japan, and Germany) in reaching high degrees of similarity with the most developed world countries. The synergies of the proposed mathematical tools lead to a better understanding of the dynamics underlying world economies and point towards the estimation of future states based on the memory of each time series.

Fractional Dynamics Representation in the Pseudo Phase Plane

Proceedings of the 10th Conference on Dynamical Systems Theory and Applications

Analysis of the Out-Of-Plane Seismic Behavior of Unreinforced Masonry: A Literature Review

Although the issue of the out-of-plane response of unreinforced masonry structures under earthquake excitation is well known with consensus among the research community, this issue is simultaneously one of the more complex and most neglected areas on the seismic assessment of existing buildings. Nonetheless, its characterization should be found on the solid knowledge of the phenomenon and on the complete understanding of methodologies currently used to describe it. Based on this assumption, this article presents a general framework on the issue of the out-of-plane performance of unreinforced masonry structures, beginning with a brief introduction to the topic, followed by a compact state of art in which the principal methodologies proposed to assess the out-of-plane behavior of unreinforced masonry structures are presented. Different analytical approaches are presented, namely force and displacement-based, complemented with the presentation of existing numerical tools for the purpose presented above. Moreover, the most relevant experimental campaigns carried out in order to reproduce the phenomenon are reviewed and briefly discussed.

A simplified four-branch model for the analytical study of the out-of-plane performance of regular stone URM walls

During the last years, several studies have been made aiming to assess the out-of-plane seismic response of unreinforced stone masonry structures. This fact led to the development of a wide variety of models and approaches, ranging from simple kinematic based analytical models up to complex numerical simulations. Nevertheless, for the sake of simplicity, the out-of-plane seismic response of a masonry wall pier may be obtained by means of a simple single-degree-of-freedom system while still providing good results. In fact, despite the assumptions associated with such a simple formulation, it is also true that the epistemic uncertainty inherent with the selection of appropriate input parameters in more complex models may render them truly ineffective. In this framework, this paper focuses on the study of the out-of-plane bending of unreinforced stone masonry walls (cantilevers) by proposing a simplified analytical approach based on the construction of a linearized four-branch model, which is used to characterize the linear and nonlinear response of such structural elements through an overturning moment-rotation relationship. The formulation of the four-branch model is presented and described in detail and the meaningful parameters used for its construction are obtained from a set of experimental laboratory tests performed on six full-scale unreinforced regular sacco stone masonry specimens. Moreover, a parametric analysis aiming to evaluate the effect of these parameters’ variation on the final configuration of the model is presented and critically discussed. Finally, the results obtained from the application of the developed four-branch model on real unreinforced regular sacco stone masonry walls are thoroughly analysed and the main conclusions obtained from its application are summarized.

Experimental characterization of the out-of-plane performance of regular stone masonry walls, including test setups and axial load influence

Stone masonry is one of the oldest and most worldwide used building techniques. Nevertheless, the structural response of masonry structures is complex and the effective knowledge about their mechanical behaviour is still limited. This fact is particularly notorious when dealing with the description of their out-of-plane behaviour under horizontal loadings, as is the case of the earthquake action. In this context, this paper describes an experimental program, conducted in laboratory environment, aiming at characterizing the out-of-plane behaviour of traditional unreinforced stone masonry walls. In the scope of this campaign, six full-scale sacco stone masonry specimens were fully characterised regarding their most important mechanic, geometric and dynamic features and were tested resorting to two different loading techniques under three distinct vertical pre-compression states; three of the specimens were subjected to an out-of-plane surface load by means of a system of airbags and the remaining were subjected to an out-of-plane horizontal line-load at the top. From the experiments it was possible to observe that both test setups were able to globally mobilize the out-of-plane response of the walls, which presented substantial displacement capacity, with ratios of ultimate displacement to the wall thickness ranging between 26 and 45 %, as well as good energy dissipation capacity. Finally, very interesting results were also obtained from a simple analytical model used herein to compute a set of experimental-based ratios, namely between the maximum stability displacement and the wall thickness for which a mean value of about 60 % was found.

Simulation of masonry out-of-plane failure modes by multi-body dynamics

The seismic assessment of the local failure modes in existing masonry buildings is currently based on the identification of the so-called local mechanisms, often associated with the out-of-plane wall behavior, whose stability is evaluated by static force-based approaches and, more recently, by some displacement-based proposals. Local mechanisms consist of kinematic chains of masonry portions, often regarded as rigid bodies, with geometric nonlinearity and concentrated nonlinearity in predefined contact regions (unilateral no-tension behavior, possible sliding with friction). In this work, the dynamic behavior of local mechanisms is simulated through multi-body dynamics, to obtain the nonlinear response with efficient time history analyses that directly take into account the characteristics of the ground motion. The amplification/filtering effects of the structure are considered within the input motion. The proposed approach is validated with experimental results of two full-scale shaking-table tests on stone masonry buildings: a sacco-stone masonry façade tested at Laboratório Nacional de Engenharia Civil and a two-storey double-leaf masonry building tested at European Centre for Training and Research in Earthquake Engineering (EUCENTRE).