Rest Points Research Articles

Nodes and energy flow in the transverse oscillations of resonantly end-driven stretched strings with viscous damping

Abstract Most of the works that analyze the forced oscillations of strings assume that, although they can support a tension T, they are perfectly elastic/flexible entities that do not have losses. In this work we will show that the incorporation of losses, even maintaining the analysis in a linear regime, allows us to clarify some details of the behavior that is observed in the forced oscillations of a real string. By introducing a dissipative force into the analysis, it is possible to predict not only the resonance frequencies but also how the oscillation amplitudes depend on the strength of the driving force. We can also analyze the variation of the amplitude of the antinodes when the excitation frequency approaches the resonance frequency. This amplitude variation has a behavior very similar to that of the resonance amplitude of a spring-mass oscillator. It is generally recognized that the nodes of a string, in forced oscillation, are not points of absolute rest because the energy of vibration must be transmitted through these points. However, it is difficult to find works that analyze the peculiar properties of this small movement. In this work we calculate the amplitudes of the nodes and deduce the peculiar properties of their movement. We also calculate the time averaged energy that flows along the string, from its excitation point to its fixed end.

Optimising the reintroduction of a specialist peatland butterfly Coenonympha tullia onto peatland restoration sites

The two main goals of peatland restoration are habitat improvement and climate change mitigation by reducing greenhouse gas emissions from damaged peatlands and providing a net carbon sink. The biodiversity of specialist peatland species is threatened because of habitat destruction and the large heath butterfly Coenonympha tullia has become a flagship species for peatland ecosystem restoration, with a species reintroduction programme currently underway on a peatland restoration site within Chat Moss, Greater Manchester, UK. The aim of this study was to improve our quantitative understanding of C. tullia habitat resource requirements to optimise habitat restoration for further reintroduction attempts. We monitored butterfly micro-distribution and dispersal during the first three flight seasons (2020, 2021 and 2022) of the reintroduction using high-accuracy GPS, combined with a distance-bearing protocol. Analysis of butterfly flight points and rest points in relation to plant species distribution and abundance, identified the most important habitat resources. Using logistic regression, treatment-response curves were constructed, enabling us to identify critical thresholds for the abundance of these important habitat resources. The break of slope near the top of the logistic curve was identified using segmented regression, giving an estimate of the near-optimal abundance; fourteen Eriophorum vaginatum tussocks per 2 m quadrat and 13.4% Erica tetralix cover.Implications for insect conservationDuring ecosystem restorations, prior to the reintroduction of species with specialist habitat requirements, it is necessary to have a clear understanding of the abundance of the important habitat resources that need to be provided. The quantitative approach we describe defines the most significant environmental factors and habitat resources, then uses segmented regression to estimate the near-optimal habitat resource requirements; increasing the likelihood of reintroduced populations thriving and reintroduction programmes achieving long-term success.

Global Stabilization of a Bounded Controlled Lorenz System

In this work, we present a method for the Global Asymptotic Stabilization (GAS) of an affine control chaotic Lorenz system, via admissible (bounded and regular) feedback controls, where the control bounds are given by a class of (convex) polytopes. The proposed control design method is based on the control Lyapunov function (CLF) theory introduced in [Artstein, 1983; Sontag, 1998]. Hence, we first recall, with parameters including those in [Lorenz, 1963], that these equations are point-dissipative, i.e. there is an explicit absorbing ball [Formula: see text] given by the level set of a certain Lyapunov function, [Formula: see text]. However, since the minimum point of [Formula: see text] does not coincide with any rest point of Lorenz system, we apply a modified solution to the “uniting CLF problem” (to unify local (possibly optimal) controls with global ones, proposed in [Andrieu & Prieur, 2010]) in order to obtain a CLF [Formula: see text] for the affine system with minimum at a desired equilibrium point. Finally, we achieve the GAS of “any” rest point of this system via bounded and regular feedback controls by using the proposed CLF method, which also contains the following controllers: (i) damping controls outside [Formula: see text], so they collaborate with the beneficial stable free dynamics, and (ii) (possibly optimal) feedback controls inside [Formula: see text] that stabilize the control system at “any” desired rest point of the (unforced) Lorenz system.

Global stabilization of a bounded controlled system based on the Rössler system

In this work we present a method for the global asymptotic stabilization of an affine control system based on a Rössler system (which is well known by its chaotic behavior), through regular feedback controls constrained to control value sets given by (convex) polytopes U. The proposed method for control designing is based on the control Lyapunov function (clf) theory due to Artstein and Sontag. To this aim, we construct first an explicit absorbing ballB to “trap” the global attractor of Rössler system: we show that the affine system is the feedback interconnection of two subsystems, that leads to obtain B as the level set of a Lyapunov function, V∞(x). However, since the minimum point of V∞(x) is not a rest point of Rössler system, we apply a modified solution to the “uniting clf problem” (to unite local (possibly optimal) controls with global ones, proposed in Andrieu and Prieur (2010)) in order to obtain a clfV(x) for the affine system with minimum at a desired rest point. Finally, we achieve the global asymptotic stabilization of “any” rest point of this system via bounded and regular feedback controls by using the proposed clf method, also obtaining that controls are: (i) damping controls outside B, so they collaborate with the beneficial stable free dynamics, and (ii) (possibly optimal) feedback controls inside B that stabilize the control system at “any” desired equilibrium point of the (unforced) Rössler system.

Changes in Cerebral Oxygenation in the Prefrontal Cortex During Cardiopulmonary Exercise Testing in Patients After Cardiovascular Surgery.

Oxygenated haemoglobin (O2Hb) and total haemoglobin (THb) concentrations rise with increasing exercise load during the cardiopulmonary exercise test (CPX); however, this elevated response is impaired in patients with chronic heart failure. Furthermore, the changes occurring in patients during the acute phase of cardiac surgery are unknown. This study aimed to measure cerebral oxygenation in the prefrontal cortex (PFC) during CPX in patients during the acute post-operative phase following cardiovascular surgery. Fourteen patients in the acute phase of post-cardiovascular surgery period were enrolled. CPX was administered between the post-operative period and discharge. The protocol employed the ramp method (10W/min) after 3-min rest and 3-min warm-up periods. Levels of O2Hb, deoxygenated haemoglobin (HHb), THb, and the regional cerebral oxygen saturation (rSO2) in the PFC were measured from the resting state through the end of CPX using near-infrared spectroscopy. The mean values of O2Hb, HHb, and THb levels and rSO2 were compared at rest, warm-up, anaerobic threshold, and peak points. At the peak, O2Hb and rSO2 declined significantly, and HHb rose significantly compared to the respective values at rest; no significant changes were observed in THb. These findings suggest that the oxygen supply to the PFC is reduced in patients with reduced cardiac function following cardiovascular surgery.

Cervical Disc Arthroplasties Fail to Maintain Physiological Kinematics Under Lateral Eccentric Loads.

In vitro human cadaveric biomechanical analysis. Optimization of prostheses for cervical disc arthroplasties (CDA) reduces the risk of complications. The instantaneous helical axis (IHA) is a superior parameter for examining the kinematics of functional spinal units. There is no comprehensive study about the IHA after CDA considering all 3 motion dimensions. Ten human functional spinal units C4-5 (83.2 ± 7.9yrs.) were examined with an established measuring apparatus in intact conditions (IC), and after CDA, with 2 different types of prostheses during axial rotation, lateral bending, and flexion/extension. Eccentric preloads simulated strains. The IHA orientation and its position at the point of rest (IHA0-position) were analyzed. The results confirmed the existing data for IHA in IC. Lateral preloads showed structural alterations of kinematics after CDA: During axial rotation and lateral bending, the shift of the IHA0-position was corresponding with the lateral preloads' applied site in IC, while after CDAs, it was vice versa. During lateral bending, the lateral IHA orientation was inclined, corresponding with the lateral preloads' applied site in the IC and oppositely after the CDAs. During flexion/extension, the lateral IHA orientation was nearly vertical in the IC, while after CDA, it inclined, corresponding with the lateral preloads' applied site. The axial IHA orientation rotated to the lateral preloads' corresponding site in the IC; after CDA, it was vice versa. Both CDAs failed to maintain physiological IHA characteristics under lateral preloads, revealing a new aspect for improving prostheses' design and optimizing their kinematics.

A new 4-D dynamical system exhibiting chaos with a line of rest points, its synchronization and circuit model

A new 4-D dynamical system exhibiting chaos with a line of rest points, its synchronization and circuit model

A new 4‐D hyperchaotic two‐scroll system with hidden attractor and its field‐programmable gate array implementation

SummaryThis research work reports the finding of a new 4‐D hyperchaotic two‐scroll system having three second‐order nonlinear terms. It is detailed that the system does not have any rest point for non‐zero values of the system parameters. Thus, we deduce that the new hyperchaotic system has a hidden attractor. The main findings of the new hyperchaotic system include a detailed bifurcation analysis, coexisting attractors, and offset‐boosting control. The new 4‐D hyperchaotic two‐scroll system with hidden attractor is prototyped using the field‐programmable gate array (FPGA) Zybo Z7‐20 development board, Xilinx Vivado tool, and the hardware description by VHDL. It is highlighted that the simulation of the circuit design, and the experimental results from the FPGA synthesis, all of them are in good agreement with theoretical simulations.

Pigouvian algorithmic platform design

There are rising concerns that reinforcement algorithms might learn tacit collusion in oligopolistic pricing, and moreover that the resulting ‘black box’ strategies would be difficult to regulate. Here, I exploit a strong connection between evolutionary game theory and reinforcement learning to show when the latter’s rest points are Bayes–Nash equilibria, but also to derive a system of Pigouvian taxes guaranteed to implement an (unknown) socially optimal outcome of an oligopoly pricing game. Finally, I illustrate reinforcement learning of equilibrium play via simulation, which provides evidence of the capacity of reinforcement algorithms to collude in a very simple setting, but the introduction of the optimal tax scheme induces a competitive outcome.

Minimum time control of a gantry crane system with rate constraints

This paper focuses on the development of minimum time control profiles for point-to-point motion of a gantry crane system in the presence of uncertainties in modal parameters. Assuming that the velocity of the trolley of the crane can be commanded and is subject to limits, an optimal control problem is posed to determine the bang-off-bang control profile to transition the system from a point of rest to the terminal states with no residual vibrations. Both undamped and underdamped systems are considered and the variation of the structure of the optimal control profiles as a function of the final displacement is studied. As the magnitude of the rigid body displacement is increased, the collapse and birthing of switches in the optimal control profile are observed and explained. Robustness to uncertainties in modal parameters is accounted for by forcing the state sensitivities at the terminal time to zero. The observation that the time-optimal control profile merges with the robust time-optimal control is noted for specific terminal displacements and the migration of zeros of the time-delay filter parameterizing the optimal control profile are used to explain this counter intuitive result. As a comparison to the proposed controller, an acceleration constrained time-optimal control is analyzed which as expected demands a larger maneuver time. A two degree of freedom gantry crane system is used to experimentally validate the observations of the numerical studies and the tradeoff of increase in maneuver time to the reduction of residual vibrations is experimentally illustrated.

Strategy sets closed under payoff sampling

We consider population games played by procedurally rational players who, when revising their current strategy, test each of their available strategies independently in a series of random matches –i.e., a battery of tests–, and then choose the strategy that performed best in this battery of tests. This revision protocol leads to the so-called payoff-sampling dynamics (aka test-all Best Experienced Payoff dynamics).In this paper we characterize the support of all the rest points of these dynamics in any game and analyze the asymptotic stability of the faces to which they belong. We do this by defining strategy sets closed under payoff sampling, and by proving that the identification of these sets can be made in terms of simple comparisons between some of the payoffs of the game.

Emerging Spiral Waves and Coexisting Attractors in Memductance-Based Tabu Learning Neurons

Understanding neuron function may aid in determining the complex collective behavior of brain systems. To delineate the collective behavior of the neural network, we consider modified tabu learning neurons (MTLN) with magnetic flux. Primarily, we explore the rest points and stability of the isolated MTLN, as well as its dynamical characteristics using maximal Lyapunov exponents. Surprisingly, we discover that for a given set of parameter values with distinct initial conditions, the periodic and the chaotic attractors may coexist. In addition, experimental analysis is carried out using a microcontroller-based implementation technique to support the observed complex behavior of the MTLN. We demonstrate that the observed numerical results are in good agreement with the experimental verification. Eventually, the collective behaviors of the considered MTLN are investigated by extending them to the network of the lattice array. We discover that when the magnetic flux coupling coefficient is varied in the presence of an external stimulus, the transition from spiral waves to traveling plane waves occurs. Finally, we manifest the formation of spiral waves in the absence of an external stimulus in contrast to previous observations.

Some examples for stable and historic behavior in replicator equations

The evolutionary dynamics of zero-sum and non zero-sum games under replicator equations could be drastically different from each other. In zero-sum games, heteroclinic cycles naturally occur whenever the species of the population supersede each other in cyclic fashion (like for the Rock–Paper–Scissors game). In this case, the highly erratic oscillations may cause the divergence of the time averages. In contrast, it is a common belief that all “reasonable” replicator equations of non-zero sum games satisfy “The Folk Theorem of Evolutionary Game Theory” which asserts that (i)a Nash equilibrium is a rest point; (ii)a stable rest point is a Nash equilibrium; (iii)a strictly Nash equilibrium is asymptotically stable; (iv)any interior convergent orbit evolves to a Nash equilibrium. In this paper, we propose two distinct classes of replicator equations generated by Schur-convex potential functions which exhibit two opposing phenomena: stable/predictable and historic/unpredictable behavior. In the latter case, the time averages of the orbit will slowly oscillate during the evolution of the system and do not converge to any limit. This will eventually cause the divergence of higher-order repeated time averages.

Stability of strict equilibria in best experienced payoff dynamics: Simple formulas and applications

We consider a family of population game dynamics known as Best Experienced Payoff Dynamics. Under these dynamics, when agents are given the opportunity to revise their strategy, they test some of their possible strategies a fixed number of times. Crucially, each strategy is tested against a new randomly drawn set of opponents. The revising agent then chooses the strategy whose total payoff was highest in the test, breaking ties according to a given tie-breaking rule. Strict Nash equilibria are rest points of these dynamics, but need not be stable. We provide some simple formulas and algorithms to determine the stability or instability of strict Nash equilibria.

A novel point cloud simplification method using local conditional information

In three-dimensional measurement of large-scale parts, such as car bodies and aircraft wings, massive points (up to hundreds of millions) are collected. If all point cloud data is processed, a large amount of computing resources and storage space will be consumed. It is an important task to reduce the burden of processing while maintaining the feature of the point cloud as much as possible. This paper proposes a novel point cloud simplification method using local conditional information that is utilized to evaluate the features of each point in point clouds.The proposed method can reduce the size of point clouds while reserving significant features. Firstly, the original information of each point is evaluated by calculating the curvature of the original point cloud. Secondly, the point with the maximal information is selected and reserved in the target point cloud that will be updated as the alternative point cloud after simplification. The conditional information of each rest point is evaluated by the neighborhood and updated to the information of the current point, which attenuates with the distance from the other reserved points. Finally, the point with the maximal information is reserved iteratively until the number of points reserved satisfies the requirements of simplification according to enterprise needs. Experiments verify the effectiveness and performance of the proposed method. The experimental results indicate that the proposed method performs much better on feature retention than Voxel simplification and Curvature simplification.

Stability Analysis, Hopf Bifurcation and Drug Therapy Control of an HIV Viral Infection Model with Logistic Growth Rate and Cell-to-Cell and Cell-Free Transmissions

It is well known that dynamical systems are very useful tools to study viral diseases such as HIV, HBV, HCV, Ebola and Influenza. This paper focuses on a mathematical model of the cell-to-cell and the cell-free spread of HIV with both linear and nonlinear functional responses and logistic target cell growth. The reproduction number of each mode of transmission has been calculated and their sum has been considered as the basic reproduction number. Based on the values of the reproduction number, the local and global stabilities of the rest points are investigated. Choosing a suitable bifurcation parameter, some conditions for the occurrence of Hopf bifurcation are also obtained. Moreover, numerical simulations are presented to support the analytical results. Finally, to study the effect of the drug on the disease process, some control conditions are determined. Since two modes of transmission and both linear and nonlinear functional responses have been included in this manuscript, our obtained results are a generalization of those in the literature. Moreover, the results are obtained with weaker assumptions in comparison with the previous ones.

INTERPRETIVE TRAILS AND ENVIRONMENTAL EDUCATION IN CAATINGA: A PROPOSAL FOR THE AÇU NATIONAL FOREST - RN

The National Forest of Açú – Flona of Açu is located in the municipality of Assú/Rio Grande do Norte, It has Caatinga vegetation and its total territorial area borders the Piató lagoon. The headquarters of this conservation unit – UC is inserted in the urban portion. These characteristics, as well as all the biodiversity and scenic beauty, provide a rich and diverse environment for field classes, ecological trails and for environmental education activities. The Flona of Açu already has actions aimed at environmental education, but activities and actions developed today are insufficient and do not cover its potential, as the unit's management plan highlights. In front of the potential that the trails have for conducting field classes and for environmental education actions related to the caatinga and semi-arid region, this work aims to propose a trail roudmap for the Flona of Açu, highlighting its potential for environmental education through the interpretation of natural elements and the importance of the unit for the preservation of Caatinga. The methodology used for producing the work consisted of the following steps: theoretical framework; field visits in the Flona of Açu; selection and interpretation of attractive points based on the IAPI method (Attractiveness Indicators of Interpretive Points) planning the interpretive trails roadmap based on (Furlan, 2011); analysis and interpretation of data. As a result, the main trail was selected for scripting. Through the IAPI Method, four main points were selected in the attractive infrastructure zone, a rest point and nine attractive points along the trail walk, a visit itinerary was planned based on the interpretation of the selected point. The expected results of the method are important, as well as for different similar results, improving the different characteristics of the different method, improving the different characteristics of the local method.

Distributed Population Dynamics for Searching Generalized Nash Equilibria of Population Games With Graphical Strategy Interactions

Evolutionary games and population dynamics are finding increasing applications in design learning and control protocols for a variety of resource allocation problems. The implicit requirement for full communication has been the main limitation of the evolutionary game dynamic approach in engineering tasks with various information constraints. This article intends to build population games and dynamics with both static and dynamical graphical communication structures. To this end, we formulate a population game model with graphical strategy interactions and derive its corresponding population dynamics. In particular, we first introduce the concept of generalized Nash equilibria for population games with graphical strategy interactions, and establish the equivalence between the set of generalized Nash equilibria and the set of rest points of its distributed population dynamics. Furthermore, the conditions for convergence to generalized Nash equilibrium and particularly to Nash equilibrium are obtained for the distributed population dynamics with both static and dynamical graphical structures. These results provide a new approach to design distributed Nash equilibrium seeking algorithms for population games with both static and dynamical communication networks, and hence, expand the applicability of the population game dynamics in the design of learning and control protocols under distributed circumstances.

Global stability analysis of viral infection model with logistic growth rate, general incidence function and cellular immunity

It is well known that the mathematical biology and dynamical systems give very important information for the study and research of viral infection models such as HIV, HBV, HCV, Ebola and Influenza. This paper deals with the global dynamics of generalized virus model with logistic growth rate for target cells, general incidence rate and cellular immunity. The results will be obtained by using Lyapunov’s second method and LaSalle’s invariance principle. We prove the global stability of the rest points of the system by the value of basic reproduction number (R0) and the immune response reproduction number (RCTL). We have found that if R0<1, then the infection-free equilibrium is globally asymptotically stable. For R0>1 and RCTL<1, under certain conditions on incidence rate function, immune-free equilibrium is globally asymptotically stable. Finally, we prove that if R0>1 and RCTL>1, then under certain conditions on incidence rate function the endemic equilibrium is globally asymptotically stable. Since the logistic growth rate for target cells and general incidence rate have been included in this manuscript, our obtained results are the generalization of those in the previous literatures. Moreover, the results have been obtained with weaker assumptions in comparison with the previous ones. Numerical simulations are presented to support and illustrate our analytical results.

Stable sampling in repeated games

This paper considers finitely repeated games played by procedurally rational players, who sample their available alternatives and use realized payoffs as a basis for strategy selection. The corresponding solution concept is that of (payoff) sampling equilibrium, which is a distribution over strategies that is self-replicating under the sampling procedure. Sampling equilibria are rest points of a disequilibrium dynamic process, and stability with respect to this process can be used as an equilibrium selection criterion. The structure of stable sampling equilibria in symmetric, finitely repeated games is characterized, and illustrated with applications to cooperation and coordination over time.