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.

Integer/fractional decomposition of the impulse response of fractional linear systems

The decomposition of a fractional linear system is discussed in this paper. It is shown that it can be decomposed into an integer order part, corresponding to possible existing poles, and a fractional part. The first and second parts are responsible for the short and long memory behaviors of the system, respectively, known as characteristic of fractional systems.

Numerical calculation of the left and right fractional derivatives

The calculation of fractional derivatives is an important topic in scientific research. While formal definitions are clear from the mathematical point of view, they pose limitations in applied sciences that have not been yet tackled. This paper addresses the problem of obtaining left and right side derivatives when adopting numerical approximations. The results reveal the relationship between the resulting distinct values for different fractional orders and types of signals.

Fractional Order Description of DNA

This study addresses the deoxyribonucleic acid (DNA) and proposes a procedure based on the association of statistics, information theory, signal processing, Fourier analysis and fractional calculus for describing fundamental characteristics of the DNA. In a first phase the 24 chromosomes of the Human are evaluated. In a second phase, 10 chromosomes for different species are also processed and the results compared. The results reveal invariance in the description and close resemblances with fractional Brownian motion.

What is a fractional derivative?

This paper discusses the concepts underlying the formulation of operators capable of being interpreted as fractional derivatives or fractional integrals. Two criteria for required by a fractional operator are formulated. The Grünwald–Letnikov, Riemann–Liouville and Caputo fractional derivatives and the Riesz potential are accessed in the light of the proposed criteria. A Leibniz rule is also obtained for the Riesz potential.

Discrete fractional order system vibrations

A theory of free vibrations of discrete fractional order (FO) systems with a finite number of degrees of freedom (dof) is developed. A FO system with a finite number of dof is defined by means of three matrices: mass inertia, system rigidity and FO elements. By adopting a matrix formulation, a mathematical description of FO discrete system free vibrations is determined in the form of coupled fractional order differential equations (FODE). The corresponding solutions in analytical form, for the special case of the matrix of FO properties elements, are determined and expressed as a polynomial series along time. For the eigen characteristic numbers, the system eigen main coordinates and the independent eigen FO modes are determined. A generalized function of visoelastic creep FO dissipation of energy and generalized forces of system with no ideal visoelastic creep FO dissipation of energy for generalized coordinates are formulated. Extended Lagrange FODE of second kind, for FO system dynamics, are also introduced. Two examples of FO chain systems are analyzed and the corresponding eigen characteristic numbers determined. It is shown that the oscillatory phenomena of a FO mechanical chain have analogies to electrical FO circuits. A FO electrical resistor is introduced and its constitutive voltage–current is formulated. Also a function of thermal energy FO dissipation of a FO electrical relation is discussed.

An Extension of Estimation of Domain of Attraction for Fractional Order Linear System Subject to Saturation Control

This paper employs the Lyapunov direct method for the stability analysis of fractional order linear systems subject to input saturation. A new stability condition based on saturation function is adopted for estimating the domain of attraction via ellipsoid approach. To further improve this estimation, the auxiliary feedback is also supported by the concept of stability region. The advantages of the proposed method are twofold: (1) it is straightforward to handle the problem both in analysis and design because of using Lyapunov method, (2) the estimation leads to less conservative results. A numerical example illustrates the feasibility of the proposed method.

Fractional Dynamics in the Rayleigh's Piston

This paper studies the dynamics of the Rayleigh piston using the modeling tools of Fractional Calculus. Several numerical experiments examine the effect of distinct values of the parameters. The time responses are transformed into the Fourier domain and approximated by means of power law approximations. The description reveals characteristics usual in Fractional Brownian phenomena.

Influence of dual-task on sit-to-stand-to-sit postural control in Parkinson's disease

Postural control deficits are the most disabling aspects of Parkinson's disease (PD), resulting in decreased mobility and functional independence. The aim of this study was to assess the postural control stability, revealed by variables based on the centre of pressure (CoP), in individuals with PD while performing a sit-to-stand-to-sit sequence under single- and dual-task conditions. An observational, analytical and cross-sectional study was performed. The sample consisted of 9 individuals with PD and 9 healthy controls. A force platform was used to measure the CoP displacement and velocity during the sit-to-stand-to-sit sequence. The results were statistically analysed. Individuals with PD required greater durations for the sit-to-stand-to-sit sequence than the controls (p < 0.05). The anteroposterior and mediolateral CoP displacement were higher in the individuals with PD (p < 0.05). However, only the anteroposterior CoP velocity in the stand-to-sit phase (p = 0.006) was lower in the same individuals. Comparing the single- and dual-task conditions in both groups, the duration, the anteroposterior CoP displacement and velocity were higher in the dual-task condition (p < 0.05). The individuals with PD presented reduced postural control stability during the sit-to-stand-to-sit sequence, especially when under the dual-task condition. These individuals have deficits not only in motor performance, but also in cognitive performance when performing the sit-to-stand-to-sit sequence in their daily life tasks. Moreover, both deficits tend to be intensified when two tasks are performed simultaneously.

Standing balance in individuals with Parkinson's disease during single and dual-task conditions

This study aimed to examine the differences in standing balance between individuals with Parkinson's disease (PD) and subjects without PD (control group), under single and dual-task conditions. A cross-sectional study was designed using a non-probabilistic sample of 110 individuals (50 participants with PD and 60 controls) aged 50 years old and over. The individuals with PD were in the early or middle stages of the disease (characterized by Hoehn and Yahr as stages 1-3). The standing balance was assessed by measuring the centre of pressure (CoP) displacement in single-task (eyes-open/eyes-closed) and dual-task (while performing two different verbal fluency tasks). No significant differences were found between the groups regarding sociodemographic variables. In general, the standing balance of the individuals with PD was worse than the controls, as the CoP displacement across tasks was significantly higher for the individuals with PD (p<0.01), both in anteroposterior and mediolateral directions. Moreover, there were significant differences in the CoP displacement based parameters between the conditions, mainly between the eyes-open condition and the remaining conditions. However, there was no significant interaction found between group and condition, which suggests that changes in the CoP displacement between tasks were not influenced by having PD. In conclusion, this study shows that, although individuals with PD had a worse overall standing balance than individuals without the disease, the impact of performing an additional task on the CoP displacement is similar for both groups.

The hyperaccumulator Sedum plumbizincicola harbors metal-resistant endophytic bacteria that improve its phytoextraction capacity in multi-metal contaminated soil

Endophyte-assisted phytoremediation has recently been suggested as a successful approach for ecological restoration of metal contaminated soils, however little information is available on the influence of endophytic bacteria on the phytoextraction capacity of metal hyperaccumulating plants in multi-metal polluted soils. The aims of our study were to isolate and characterize metal-resistant and 1-aminocyclopropane-1-carboxylate (ACC) utilizing endophytic bacteria from tissues of the newly discovered Zn/Cd hyperaccumulator Sedum plumbizincicola and to examine if these endophytic bacterial strains could improve the efficiency of phytoextraction of multi-metal contaminated soils. Among a collection of 42 metal resistant bacterial strains isolated from the tissues of S. plumbizincicola grown on Pb/Zn mine tailings, five plant growth promoting endophytic bacterial strains (PGPE) were selected due to their ability to promote plant growth and to utilize ACC as the sole nitrogen source. The five isolates were identified as Bacillus pumilus E2S2, Bacillus sp. E1S2, Bacillus sp. E4S1, Achromobacter sp. E4L5 and Stenotrophomonas sp. E1L and subsequent testing revealed that they all exhibited traits associated with plant growth promotion, such as production of indole-3-acetic acid and siderophores and solubilization of phosphorus. These five strains showed high resistance to heavy metals (Cd, Zn and Pb) and various antibiotics. Further, inoculation of these ACC utilizing strains significantly increased the concentrations of water extractable Cd and Zn in soil. Moreover, a pot experiment was conducted to elucidate the effects of inoculating metal-resistant ACC utilizing strains on the growth of S. plumbizincicola and its uptake of Cd, Zn and Pb in multi-metal contaminated soils. Out of the five strains, B. pumilus E2S2 significantly increased root (146%) and shoot (17%) length, fresh (37%) and dry biomass (32%) of S. plumbizincicola as well as plant Cd uptake (43%), whereas Bacillus sp. E1S2 significantly enhanced the accumulation of Zn (18%) in plants compared with non-inoculated controls. The inoculated strains also showed high levels of colonization in rhizosphere and plant tissues. Results demonstrate the potential to improve phytoextraction of soils contaminated with multiple heavy metals by inoculating metal hyperaccumulating plants with their own selected functional endophytic bacterial strains.

Task partitioning and priority assignment for distributed hard real-time systems

In this paper, we propose the Distributed using Optimal Priority Assignment (DOPA) heuristic that finds a feasible partitioning and priority assignment for distributed applications based on the linear transactional model. DOPA partitions the tasks and messages in the distributed system, and makes use of the Optimal Priority Assignment (OPA) algorithm known as Audsley’s algorithm, to find the priorities for that partition. The experimental results show how the use of the OPA algorithm increases in average the number of schedulable tasks and messages in a distributed system when compared to the use of Deadline Monotonic (DM) usually favoured in other works. Afterwards, we extend these results to the assignment of Parallel/Distributed applications and present a second heuristic named Parallel-DOPA (P-DOPA). In that case, we show how the partitioning process can be simplified by using the Distributed Stretch Transformation (DST), a parallel transaction transformation algorithm introduced in [1].

P-SOCRATES: A parallel software framework for time-critical many-core systems

Article in Press, Corrected Proof

Scalable and Efficient Configuration of TimeDivision Multiplexed Resources

Consumer-electronics systems are becoming increasingly complex as the number of integrated applications is growing. Some of these applications have real-time requirements, while other non-real-time applications only require good average performance. For cost-efficient design, contemporary platforms feature an increasing number of cores that share resources, such as memories and interconnects. However, resource sharing causes contention that must be resolved by a resource arbiter, such as Time-Division Multiplexing. A key challenge is to configure this arbiter to satisfy the bandwidth and latency requirements of the real-time applications, while maximizing the slack capacity to improve performance of their non-real-time counterparts. As this configuration problem is NP-hard, a sophisticated automated configuration method is required to avoid negatively impacting design time. The main contributions of this article are: 1) An optimal approach that takes an existing integer linear programming (ILP) model addressing the problem and wraps it in a branch-and-price framework to improve scalability. 2) A faster heuristic algorithm that typically provides near-optimal solutions. 3) An experimental evaluation that quantitatively compares the branch-and-price approach to the previously formulated ILP model and the proposed heuristic. 4) A case study of an HD video and graphics processing system that demonstrates the practical applicability of the approach.

Formation Control Driven by Cooperative Object Tracking

In this paper we introduce a formation control loop that maximizes the performance of the cooperative perception of a tracked target by a team of mobile robots, while maintaining the team in formation, with a dynamically adjustable geometry which is a function of the quality of the target perception by the team. In the formation control loop, the controller module is a distributed non-linear model predictive controller and the estimator module fuses local estimates of the target state, obtained by a particle filter at each robot. The two modules and their integration are described in detail, including a real-time database associated to a wireless communication protocol that facilitates the exchange of state data while reducing collisions among team members. Simulation and real robot results for indoor and outdoor teams of different robots are presented. The results highlight how our method successfully enables a team of homogeneous robots to minimize the total uncertainty of the tracked target cooperative estimate while complying with performance criteria such as keeping a pre-set distance between the teammates and the target, avoiding collisions with teammates and/or surrounding obstacles.