Stability of fractional order systems

The theory and applications of fractional calculus (FC) had a considerable progress during the last years. Dynamical systems and control are one of the most active areas, and several authors focused on the stability of fractional order systems. Nevertheless, due to the multitude of efforts in a short period of time, contributions are scattered along the literature, and it becomes difficult for researchers to have a complete and systematic picture of the present day knowledge. This paper is an attempt to overcome this situation by reviewing the state of the art and putting this topic in a systematic form. While the problem is formulated with rigour, from the mathematical point of view, the exposition intends to be easy to read by the applied researchers. Different types of systems are considered, namely, linear/nonlinear, positive, with delay, distributed, and continuous/discrete. Several possible routes of future progress that emerge are also tackled.

Dynamic adaptation of stability periods for service level agreements

A QoS adaptation to dynamically changing system conditions that takes into consideration the user’s constraints on the stability of service provisioning is presented. The goal is to allow the system to make QoS adaptation decisions in response to fluctuations in task traffic flow, under the control of the user. We pay special attention to the case where monitoring the stability period and resource load variation of Service Level Agreements for different types of services is used to dynamically adapt future stability periods, according to a feedback control scheme. System’s adaptation behaviour can be configured according to a desired confidence level on future resource usage. The viability of the proposed approach is validated by preliminary experiments.

Fresh-cut aromatic herbs: Nutritional quality stability during shelf-life

Fresh-cut vegetables are a successful convenient healthy food. Nowadays, the presence of new varieties of minimally processed vegetables in the market is common in response to the consumers demand for new flavours and high quality products. Within the most recent fresh-cut products are the aromatic herbs. In this work, the objective was to evaluate the nutritional quality and stability of four fresh-cut aromatic herbs. Several physicochemical quality characteristics (colour, pH, total soluble solids, and total titratable acidity) were monitored in fresh-cut chives, coriander, spearmint and parsley leaves, stored under refrigeration (3 ± 1 ºC) during 10 days. Their nutritional composition was determined, including mineral composition (phosphorous, potassium, sodium, calcium, magnesium, iron, zinc, manganese and copper) and fat- and water-soluble vitamin contents. Total soluble phenolics, flavonoids and the antioxidant capacity were determined by spectrophotometric methods. The aromatic herbs kept their fresh appearance during the storage, maintaining their colour throughout shelf-life. Their macronutrient composition and mineral content were stable during storage. Coriander had the highest mineral and fatsoluble vitamin content, while spearmint showed the best scores in the phenolic, flavonoid and antioxidant capacity assays. Vitamins and antioxidant capacity showed some variation during storage, with a differential behaviour of each compound according to the sample.

Dynamical Stability and Predictability of Football Players: The Study of One Match

The game of football demands new computational approaches to measure individual and collective performance. Understanding the phenomena involved in the game may foster the identification of strengths and weaknesses, not only of each player, but also of the whole team. The development of assertive quantitative methodologies constitutes a key element in sports training. In football, the predictability and stability inherent in the motion of a given player may be seen as one of the most important concepts to fully characterise the variability of the whole team. This paper characterises the predictability and stability levels of players during an official football match. A Fractional Calculus (FC) approach to define a player’s trajectory. By applying FC, one can benefit from newly considered modeling perspectives, such as the fractional coefficient, to estimate a player’s predictability and stability. This paper also formulates the concept of attraction domain, related to the tactical region of each player, inspired by stability theory principles. To compare the variability inherent in the player’s process variables (e.g., distance covered) and to assess his predictability and stability, entropy measures are considered. Experimental results suggest that the most predictable player is the goalkeeper while, conversely, the most unpredictable players are the midfielders. We also conclude that, despite his predictability, the goalkeeper is the most unstable player, while lateral defenders are the most stable during the match.

Stability of the Transthyretin Molecule as a Key Factor in

Transthyretin (TTR) protects against A-Beta toxicity by binding the peptide thus inhibiting its aggregation. Previous work showed different TTR mutations interact differently with A-Beta, with increasing affinities correlating with decreasing amyloidogenecity of the TTR mutant; this did not impact on the levels of inhibition of A-Beta aggregation, as assessed by transmission electron microscopy. Our work aimed at probing differences in binding to A-Beta by WT, T119M and L55P TTR using quantitative assays, and at identifying factors affecting this interaction. We addressed the impact of such factors in TTR ability to degrade A-Beta. Using a dot blot approach with the anti-oligomeric antibody A11, we showed that A-Beta formed oligomers transiently, indicating aggregation and fibril formation, whereas in the presence of WT and T119M TTR the oligomers persisted longer, indicative that these variants avoided further aggregation into fibrils. In contrast, L55PTTR was not able to inhibit oligomerization or to prevent evolution to aggregates and fibrils. Furthermore, apoptosis assessment showed WT and T119M TTR were able to protect against A-Beta toxicity. Because the amyloidogenic potential of TTR is inversely correlated with its stability, the use of drugs able to stabilize TTR tetrameric fold could result in increased TTR/ABeta binding. Here we showed that iododiflunisal, 3-dinitrophenol, resveratrol, [2-(3,5-dichlorophenyl)amino] (DCPA) and [4- (3,5-difluorophenyl)] (DFPB) were able to increase TTR binding to A-Beta; however only DCPA and DFPB improved TTR proteolytic activity. Thyroxine, a TTR ligand, did not influence TTR/A-Beta interaction and A-Beta degradation by TTR, whereas RBP, another TTR ligand, not only obstructed the interaction but also inhibited TTR proteolytic activity. Our results showed differences between WT and T119M TTR, and L55PTTR mutant regarding their interaction with A-Beta and prompt the stability of TTR as a key factor in this interaction, which may be relevant in AD pathogenesis and for the design of therapeutic TTR-based therapies.

Dynamic stability metrics for the container loading problem

The Container Loading Problem (CLP) literature has traditionally evaluated the dynamic stability of cargo by applying two metrics to box arrangements: the mean number of boxes supporting the items excluding those placed directly on the floor (M1) and the percentage of boxes with insufficient lateral support (M2). However, these metrics, that aim to be proxies for cargo stability during transportation, fail to translate real-world cargo conditions of dynamic stability. In this paper two new performance indicators are proposed to evaluate the dynamic stability of cargo arrangements: the number of fallen boxes (NFB) and the number of boxes within the Damage Boundary Curve fragility test (NB_DBC). Using 1500 solutions for well-known problem instances found in the literature, these new performance indicators are evaluated using a physics simulation tool (StableCargo), replacing the real-world transportation by a truck with a simulation of the dynamic behaviour of container loading arrangements. Two new dynamic stability metrics that can be integrated within any container loading algorithm are also proposed. The metrics are analytical models of the proposed stability performance indicators, computed by multiple linear regression. Pearson’s r correlation coefficient was used as an evaluation parameter for the performance of the models. The extensive computational results show that the proposed metrics are better proxies for dynamic stability in the CLP than the previous widely used metrics.