Influence of long-term wearing of unstable shoes on compensatory control of posture: An electromyography-based analysis

Purpose: This study investigated the influence of long-term wearing of unstable shoes (WUS) on compensatory postural adjustments (CPA) to an external perturbation. Methods: Participants were divided into two groups: one wore unstable shoes while the other wore conventional shoes for 8 weeks. The ground reaction force signal was used to calculate the anterior– posterior (AP) displacement of the centre of pressure (CoP) and the electromyographic signal of gastrocnemius medialis (GM), tibialis anterior (TA), rectus femoris (RF) and biceps femoris (BF) muscles was used to assess individual muscle activity, antagonist co-activation and reciprocal activation at the joint (TA/GM and RF/(BF + GM) pairs) and muscle group levels (ventral (TA + RF)/dorsal (GM + BF) pair) within time intervals typical for CPA. The electromyographic signal was also used to assess muscle latency. The variables described were evaluated before and after the 8-week period while wearing the unstable shoes and barefoot. Results: Long-term WUS led to: an increase of BF activity in both conditions (barefoot and wearing the unstable shoes); a decrease of GM activity; an increase of antagonist co-activation and a decrease of reciprocal activation level at the TA/GM and ventral/dorsal pairs in the unstable shoe condition. Additionally, WUS led to a decrease in CoP displacement. However, no differences were observed in muscle onset and offset. Conclusion: Results suggest that the prolonged use of unstable shoes leads to increased ankle and muscle groups’ antagonist co-activation levels and higher performance by the postural control system.

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.

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 State Space Analysis of Economy Systems

This paper examines modern economic growth according to the multidimensional scaling (MDS) method and state space portrait (SSP) analysis. Electing GDP per capita as the main indicator for economic growth and prosperity, the long-run perspective from 1870 to 2010 identifies the main similarities among 34 world partners’ modern economic growth and exemplifies the historical waving mechanics of the largest world economy, the USA. MDS reveals two main clusters among the European countries and their old offshore territories, and SSP identifies the Great Depression as a mild challenge to the American global performance, when compared to the Second World War and the 2008 crisis.