Stochastic perturbations to dynamical systems: a response theory approach

Using the formalism of the Ruelle response theory, we study how the invariant measure of an Axiom A dynamical system changes as a result of adding noise, and describe how the stochastic perturbation can be used to explore the properties of the underlying deterministic dynamics. We first find the expression for the change in the expectation value of a general observable when a white noise forcing is introduced in the system, both in the additive and in the multiplicative case. We also show that the difference between the expectation value of the power spectrum of an observable in the stochastically perturbed case and of the same observable in the unperturbed case is equal to the variance of the noise times the square of the modulus of the linear susceptibility describing the frequency-dependent response of the system to perturbations with the same spatial patterns as the considered stochastic forcing. This provides a conceptual bridge between the change in the fluctuation properties of the system due to the presence of noise and the response of the unperturbed system to deterministic forcings. Using Kramers-Kronig theory, it is then possible to derive the real and imaginary part of the susceptibility and thus deduce the Green function of the system for any desired observable. We then extend our results to rather general patterns of random forcing, from the case of several white noise forcings, to noise terms with memory, up to the case of a space-time random field. Explicit formulas are provided for each relevant case analysed. As a general result, we find, using an argument of positive-definiteness, that the power spectrum of the stochastically perturbed system is larger at all frequencies than the power spectrum of the unperturbed system. We provide an example of application of our results by considering the spatially extended chaotic Lorenz 96 model. These results clarify the property of stochastic stability of SRB measures in Axiom A flows, provide tools for analysing stochastic parameterisations and related closure ansatz to be implemented in modelling studies, and introduce new ways to study the response of a system to external perturbations. Taking into account the chaotic hypothesis, we expect that our results have practical relevance for a more general class of system than those belonging to Axiom A.

Grain quality of upland rice cultivars in response to cropping systems in the Brazilian tropical savanna

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Response of human pulps capped with different self-etch adhesive systems

The aim of this study was to evaluate the response of human pulps capped with a calcium hydroxide hard-setting cement or with two-step self-etch adhesive systems. Pulp exposures were performed on the occlusal floor, and the bleeding control was performed with saline solution. The exposed pulp tissue was capped with Clearfil LB 2V (2V) or Clearfil SE Bond (SE) and restored with a composite resin. In control group, the pulpal wound was capped with Ca(OH)(2) cement and restored with Clearfil LB 2V or Clearfil SE Bond + composite resin. After 30 and 90 days, the teeth were extracted, processed for hematoxylin and eosin, and categorized in a histological score system. The pulpal response was worse for groups capped with the self-etch adhesive systems (2V and SE) in both periods of evaluation, when compared to their respective control groups at 90 days (p < 0.05). For both self-etch systems evaluated, the pulp tissue exhibited moderate to severe inflammatory cell infiltrate involving the coronal pulp with chronic abscesses. Dentin bridging was observed in a few specimens. For the calcium hydroxide groups, almost all specimens showed dentin bridge formation, with few scattered inflammatory cells and normal tissue below the pulp exposure site. Calcium hydroxide should be used as the material of choice for pulp capping, and the use of two-step self-etch adhesives for human pulp capping is contraindicated.

Response of human dental pulp to dentin adhesive systems

Many in vivo studies have stated that the response of the dentin/pulp complex does not depend on the dental material used as the liner or pulp-capping agent. However, several in vitro studies have reported the metabolic cytotoxic effects of resin components applied to fibroblast and odontoblast cell lines. The aim of this study was to evaluate the human pulp response following direct pulp capping with current bonding agents and calcium hydroxide (CH). Sound premolars scheduled for orthodontic extraction had their pulp tissue mechanically exposed. After hemorrhage control and total acid conditioning, the experimental bonding agents, including All Bond 2, Scotchbond MP-Plus, Clearfil Liner Bond 2, and Prime & Bond 2.1 were applied on the pulp exposure site. CH saline paste was used as the control pulp-capping agent. All cavities were restored with Z-100 resin composite according to the manufacturer's instructions. Following extractions, the teeth were processed for microscopic evaluation. In the short term, the bonding agents elicited a moderate inflammatory pulp response with associated dilated and congested blood vessels adjacent to the pulp exposure site. A mild inflammatory pulp response was observed when Clearfil Liner Bond 2 or CH was applied on the pulp exposures. With time, macrophages and giant cells engulfing globules and components of all experimental bonding agents displaced into the pulp space were seen. This chronic inflammatory response did not allow complete pulp repair, which interfered with the dentin bridge formation. Pulp exposures capped with CH exhibited an initial organization of elongated pulp cells underneath the coagulation necrosis. CH stimulated early pulp repair and dentin bridging that extended into the longest period. The bonding agents evaluated in the present study cannot be recommended for pulp therapy on sound human teeth.

New approach to four-phase transmission systems: analysis of the transient response and the possible voltage surges

This study describes a technical analysis of a four-phase line as a transmission system alternative. An analysis in the frequency and the time domains is performed to evaluate the electrical characteristics and the transient response of a generic four-phase system compared with those of a conventional three-phase transmission system. The technical features of this non-conventional system are discussed and reviewed based on the current literature. Thus, a new analysis of the four-phase system is presented that emphasises several technical characteristics that have not been discussed in previous studies.

Sufficients conditions for analysis of extrema in the step-response of the linear control systems

This note deals whith the problem of extrema which may occur in the step-response of a stable linear system with real zeros and poles. Some simple sufficients conditions and necessary conditions are presented for analyses when zeros located between the dominant and fastest pole does not cause extrema in the step-response. These conditions require knowledge of the pole-zero configuration of the corresponding transfer-function.

Non linear response of planar asymmetric systems

The seismic behaviour of one-storey asymmetric structures has been studied since 1970s by a number of researches studies which identified the coupled nature of the translational-to-torsional response of those class of systems leading to severe displacement magnifications at the perimeter frames and therefore to significant increase of local peak seismic demand to the structural elements with respect to those of equivalent not-eccentric systems (Kan and Chopra 1987). These studies identified the fundamental parameters (such as the fundamental period TL normalized eccentricity e and the torsional-to-lateral frequency ratio Ωϑ) governing the torsional behavior of in-plan asymmetric structures and trends of behavior. It has been clearly recognized that asymmetric structures characterized by Ωϑ >1, referred to as torsionally-stiff systems, behave quite different form structures with Ωϑ <1, referred to as torsionally-flexible systems. Previous research works by some of the authors proposed a simple closed-form estimation of the maximum torsional response of one-storey elastic systems (Trombetti et al. 2005 and Palermo et al. 2010) leading to the so called “Alpha-method” for the evaluation of the displacement magnification factors at the corner sides. The present paper provides an upgrade of the “Alpha Method” removing the assumption of linear elastic response of the system. The main objective is to evaluate how the excursion of the structural elements in the inelastic field (due to the reaching of yield strength) affects the displacement demand of one-storey in-plan asymmetric structures. The system proposed by Chopra and Goel in 2007, which is claimed to be able to capture the main features of the non-linear response of in-plan asymmetric system, is used to perform a large parametric analysis varying all the fundamental parameters of the system, including the inelastic demand by varying the force reduction factor from 2 to 5. Magnification factors for different force reduction factor are proposed and comparisons with the results obtained from linear analysis are provided.

In vivo degradation of magnesium plate/screw osteosynthesis implant systems: Soft and hard tissue response in a calvarial model in miniature pigs.

Biodegradable magnesium plate/screw osteosynthesis systems were implanted on the frontal bone of adult miniature pigs. The chosen implant geometries were based on existing titanium systems used for the treatment of facial fractures. The aim of this study was to evaluate the in vivo degradation and tissue response of the magnesium alloy WE43 with and without a plasma electrolytic surface coating. Of 14 animals, 6 received magnesium implants with surface modification (coated), 6 without surface modification (uncoated), and 2 titanium implants. Radiological examination of the skull was performed at 1, 4, and 8 weeks post-implantation. After euthanasia at 12 and 24 weeks, X-ray, computed tomography, and microfocus computed tomography analyses and histological and histomorphological examinations of the bone/implant blocks were performed. The results showed a good tolerance of the plate/screw system without wound healing disturbance. In the radiological examination, gas pocket formation was found mainly around the uncoated plates 4 weeks after surgery. The micro-CT and histological analyses showed significantly lower corrosion rates and increased bone density and bone implant contact area around the coated screws compared to the uncoated screws at both endpoints. This study shows promising results for the further development of coated magnesium implants for the osteosynthesis of the facial skeleton.

Response threshold models, stochastic learning automata and ant colony optimization-based decentralized self-coordination algorithms for heterogeneous multi-tasks distribution in multi-robot systems

In recent decades, there has been an increasing interest in systems comprised of several autonomous mobile robots, and as a result, there has been a substantial amount of development in the eld of Articial Intelligence, especially in Robotics. There are several studies in the literature by some researchers from the scientic community that focus on the creation of intelligent machines and devices capable to imitate the functions and movements of living beings. Multi-Robot Systems (MRS) can often deal with tasks that are dicult, if not impossible, to be accomplished by a single robot. In the context of MRS, one of the main challenges is the need to control, coordinate and synchronize the operation of multiple robots to perform a specic task. This requires the development of new strategies and methods which allow us to obtain the desired system behavior in a formal and concise way. This PhD thesis aims to study the coordination of multi-robot systems, in particular, addresses the problem of the distribution of heterogeneous multi-tasks. The main interest in these systems is to understand how from simple rules inspired by the division of labor in social insects, a group of robots can perform tasks in an organized and coordinated way. We are mainly interested on truly distributed or decentralized solutions in which the robots themselves, autonomously and in an individual manner, select a particular task so that all tasks are optimally distributed. In general, to perform the multi-tasks distribution among a team of robots, they have to synchronize their actions and exchange information. Under this approach we can speak of multi-tasks selection instead of multi-tasks assignment, which means, that the agents or robots select the tasks instead of being assigned a task by a central controller. The key element in these algorithms is the estimation ix of the stimuli and the adaptive update of the thresholds. This means that each robot performs this estimate locally depending on the load or the number of pending tasks to be performed. In addition, it is very interesting the evaluation of the results in function in each approach, comparing the results obtained by the introducing noise in the number of pending loads, with the purpose of simulate the robot's error in estimating the real number of pending tasks. The main contribution of this thesis can be found in the approach based on self-organization and division of labor in social insects. An experimental scenario for the coordination problem among multiple robots, the robustness of the approaches and the generation of dynamic tasks have been presented and discussed. The particular issues studied are: Threshold models: It presents the experiments conducted to test the response threshold model with the objective to analyze the system performance index, for the problem of the distribution of heterogeneous multitasks in multi-robot systems; also has been introduced additive noise in the number of pending loads and has been generated dynamic tasks over time. Learning automata methods: It describes the experiments to test the learning automata-based probabilistic algorithms. The approach was tested to evaluate the system performance index with additive noise and with dynamic tasks generation for the same problem of the distribution of heterogeneous multi-tasks in multi-robot systems. Ant colony optimization: The goal of the experiments presented is to test the ant colony optimization-based deterministic algorithms, to achieve the distribution of heterogeneous multi-tasks in multi-robot systems. In the experiments performed, the system performance index is evaluated by introducing additive noise and dynamic tasks generation over time.