Quadratic Evolution Research Articles

RESEARCH ON THE SEQUENTIAL QUADRATIC PROGRAMMING DIFFERENTIAL EVOLUTION, JAYA, AND JAYA'S EVOLUTIONARY ALGORITHM

This study focuses on researching and comparing optimization algorithms such as Sequential Quadratic Programming, Differential Evolution, Jaya, and Jaya's evolutionary algorithm. Sequential Quadratic Programming is an optimization method based on mathematical programming, where constraints and objective functions are represented by convex and differentiable functions. Differential Evolution is a combinatorial evolutionary algorithm that utilizes genetic operators such as crossover and mutation to generate new generations of individuals. Jaya is an optimization algorithm based on continuous improvement of the population, where individuals are updated based on the current best solution. This study focuses on the specific application of the Jaya evolutionary algorithm (iJaya) compared to other algorithms and compares the performance of these algorithms in solving optimization problems through real-world examples of fiber orientation optimization in stiffened composite plates. Experiments on popular optimization problems and measure factors such as runtime, accuracy, and the ability to search for optimal solutions were conducted. The research results will provide an overview of the performance and advantages of each algorithm, thereby providing recommendations for selecting the appropriate algorithm for corresponding problems in the construction field.

Gains of integrability and local smoothing effects for quadratic evolution equations

We characterize geometrically the semigroups generated by non-selfadjoint quadratic differential operators (e−tqw)t≥0 enjoying local smoothing effects and providing gains of integrability. More precisely, we prove that the evolution operators e−tqw map Lp on Lq∩C∞, for all 1≤p≤q≤∞, if and only if the singular space of the quadratic operator qw is included in the graph of a linear map. We also provide quantitative estimates for the associated operator norms in the short-time asymptotics 0<t≪1.

Water–air interface deformation by transient acoustic radiation pressure

The deformation of a fluid interface by the acoustic radiation pressure has been used for surface tension measurements or to design exotic structures such as acoustic diodes. However, few studies focus on the characterization of the spatial characteristics of deformation induced by transient excitation, making research requiring precise spatial control of deformation challenging. This paper investigates experimentally and numerically the effects of transient excitation on deformation generated by an acoustic radiation pressure at the water–air interface. A numerical model using the finite-element method and based on theoretical background for permanent excitation is generalized to transient excitation. An experimental setup is developed to evaluate the maximum height of interface deformation for different durations and amplitudes of ultrasonic excitation using two complementary methods: the first using a camera and an edge detection algorithm and the other using a multichromatic confocal displacement sensor. Numerical and experimental results for a non-steady-state excitation show a quadratic evolution of the height of deformation as a function of incident pressure and also a linear increase as a function of the excitation duration. The evaluation of the deformation height induced by acoustic radiation pressure at a water–air interface for a transient excitation paves the way to applications requiring noncontact space-time interface modulation, such as subwavelength phenomena.

Semigroups for quadratic evolution equations acting on Shubin–Sobolev and Gelfand–Shilov spaces

We consider the initial value Cauchy problem for a class of evolution equations whose Hamiltonian is the Weyl quantization of a homogeneous quadratic form with non-negative definite real part. The solution semigroup is shown to be strongly continuous on several spaces: the Shubin-Sobolev spaces, the Schwartz space, the tempered distributions, the equal index Beurling type Gelfand-Shilov spaces and their dual ultradistribution spaces.

Forecasting nonlinear vibrations of patches of granular materials by elastic interactions between spheres

A particle model devoted to the study of three-dimensional grain packages in a dynamic setting is presented and discussed. The proposed approach considers each grain as a rigid sphere immersed in an elastically deformable medium. The motion of the grains is described by using as Lagrangian parameters the grain centroid displacement and the grain rotation. In this framework, strain and kinetic energies are described in a fully nonlinear way. The motion evolution is reconstructed by using a stepwise time integration scheme based on a quadratic evolution of the displacement in the chosen time step and on a discrete form of the momentum–impulse relationship. A numerical simulation of a package containing few grains gives an idea of the proposed model performances.

Maximum aerobic speed as a way to improve social interactions in rugby union

During the last decades, rugby union focused on players’ physical development as the main way of performance optimization. Consequently, a tremendous amount of research attention has been devoted to better understanding the main training parameters, neglecting however to study the effects of physical conditioning on group dynamics. In the present research, a quasi-experimental design in ecological conditions was used to analyze the effects of effort intensity on social interactions, especially during the rest periods of physical training. Semiprofessional rugby union players (N = 61; Mage = 23.78, SD = 7.03 years) participated in this study. They were randomly assigned to four conditions consisting of three 5-min runs. With counterbalancing, the participant sample was divided into four groups. A control group ran at 50% Maximum Aerobic Speed (MAS) while the three experimental groups ran at three different effort intensities (80%, 90%, and 100% MAS) in a counterbalanced order (i.e., linear increase/linear decrease/and quadratic evolution of effort intensity). The results showed a positive relationship between effort intensity and the number of intragroup social interactions during rest periods, this result being accrued at the end of the training session. Interestingly, the results suggested that ending a conditioning session at 100% MAS after a linear progression of effort intensity might influence social identity mobility between different levels of self-abstraction, leading to more cooperation between group members. Overall, this research offers a psychosocial view of training effects that invites academics and coaches to consider effort intensity as a way to develop social bonding in rugby. Lay summary: This study supports the perspective that “working hard” during conditioning influence social interactions between players. As a consequence, our results suggest that conditioning may be a powerful approach to build a feeling of “us-ness” that participates in optimizing group dynamics, and ultimately, performance in rugby. IMPLICATIONS FOR PRACTICE In order to benefit from the positive influence of conditioning on social interactions within a team coach should: • Prefer incremental conditioning ending at the highest intensity, to non-linear training • Encourage emotional expression norms by appointing congratulating behaviors during rest periods and more particularly at the end of the training session • Employ rest zone on the pitch so as to facilitate social bonding between players

Scattering mechanism for quadratic evolution of depolarization

It was recently demonstrated theoretically, when the polarimetric properties of a material depend only upon the direction transverse to that of propagation (long coherence length regime), depolarization in transmission evolves quadratically with material thickness. This behavior was observed in several experimental studies. However, some of these studies unlikely satisfy the long coherence length condition under which the theory applies. Here, we demonstrate that abandoning a unidirectional approach to the propagation of light through a medium, i.e., introducing scatter, causes quadratic depolarization to occur in the short coherence length regime.

Medical imaging based in silico head model for ischaemic stroke simulation

Stroke is one of the most common causes of death and a leading factor of disability in adults worldwide. It occurs when the blood supply to part of the brain is significantly reduced, potentially leading to the formation of brain oedema. Owing to the rigid nature of the skull, brain expansion results in the shifting of tissue structure, often captured by measurement of the midline shift (MLS). Clinically, MLS has been used in practice as an indication of stroke severity, potential tissue damage and as a way to assess whether decompressive surgery should be performed. However, a growing body of research points towards limitations in such predictive ability. Inspired by the recent progress made in traumatic brain injury simulations, in silico experiments appear as the ideal candidate to elucidate stroke consequences on brain tissues, e.g., morphological changes, in particular in the overarching context of computer model assisted clinical decision making support. To this end, two biologically-informed finite element head models, human and rat, were constructed to support such analysis. The main components of the models include magnetic resonance imaging-derived grey matter, white matter, cerebrospinal fluid and skull, while the human head model also includes the vasculature, additional cerebral components and axonal tractography. Constitutive models representing the mechanical behaviour of each component account in particular for the behaviour of brain tissues during the swelling process accompanying oedema development. The rat model was leveraged for the calibration of the swelling parameters, in turn used for the simulation of human stroke. Human oedema development as a result of stroke was simulated at three frequent locations: basal ganglia, fronto-opercular/anterior insula and temporo-parietal. All three cases exhibit a quadratic MLS evolution with time with the basal ganglia and temporo-parietal showing the largest and smallest values, respectively, at any given time. A proposed injury criterion for axonal tract damage was shown to be larger in the temporo-parietal case. Taken together, these results point towards i) the importance of considering stroke location when using the MLS as an indication of stroke severity, and ii) the potential lack of correlation between MLS value and tissue damage. Ultimately, we propose an in silico methodology that may hold promise in predicting stroke evolution based on an estimate of MLS and stroke location at a given time.

Optimal Discrete-time Integral Sliding Mode Control for Piecewise Affine Systems

This paper presents an optimal discrete-time integral sliding mode control for constrained piecewise affine systems. The proposed scheme is developed on the basis of linear quadratic regulator approach and differential evolution algorithm in order to ensure the stability of the closed-loop system in discrete-time sliding mode and the optimization of response characteristics in presence of control input constraints. Moreover, the controller is designed such that chattering phenomenon is avoided and finite-time convergence to the sliding surface is guaranteed. The follow-up of a reference model is also ensured. The efficiency of the proposed method is illustrated with an inverted pendulum system.

Optimization of temperature compensation model on angle sensor based on nonlinear fitting

In industrial measurement, the accuracy of accelerometer is much sensitive to the change of environmental temperature. Although previous work can achieve good performance about reducing the temperature impact, all of them cannot achieve a high accuracy. A new nonlinear fitting method is proposed to eliminate temperature influence on the accuracy of accelerometer. When using an accelerometer to calculate an object’s tilt angle, the change of temperature will lead to drift on the value of accelerometer. This drift will lead to the increase of angle calculation bias. In order to solve this problem, this paper proposes a new experimental nonlinear fitting temperature compensation method. With the measurement data and the quadratic model evolution, this method can effectively eliminate the influence of temperature on the accuracy of accelerometer and improve the precision and the accuracy of angle calculating. The experimental results show that this method has an advantage of high compensation accuracy.

A dynamical system of temperature-dependent sex linked inheritance

Recently, R.Varro introduced a gonosomal algebra of the temperature-dependent sex determination system which is controlled by three temperature ranges. In this paper we study dynamical systems which are given by quadratic evolution operators of the gonosomal algebras of sex-liked populations. We show that this evolution operator can be reduced to an evolution operator of free population. Then using behavior of the free population we describe the set of limit points for trajectories of several evolution operators of the sex-linked populations.

Generalized Mehler formula for time-dependent non-selfadjoint quadratic operators and propagation of singularities

We study evolution equations associated to time-dependent dissipative non-selfadjoint quadratic operators. We prove that the solution operators to these non-autonomous evolution equations are given by Fourier integral operators whose kernels are Gaussian tempered distributions associated to non-negative complex symplectic linear transformations, and we derive a generalized Mehler formula for their Weyl symbols. Some applications to the study of the propagation of Gabor singularities (characterizing the lack of Schwartz regularity) for the solutions to non-autonomous quadratic evolution equations are given.

The influence of meteorological variables on CO2 and CH4 trends recorded at a semi-natural station

CO2 and CH4 evolution is usually linked with sources, sinks and their changes. However, this study highlights the role of meteorological variables. It aims to quantify their contribution to the trend of these greenhouse gases and to determine which contribute most. Six years of measurements at a semi-natural site in northern Spain were considered. Three sections are established: the first focuses on monthly deciles, the second explores the relationship between pairs of meteorological variables, and the third investigates the relationship between meteorological variables and changes in CO2 and CH4. In the first section, monthly outliers were more marked for CO2 than for CH4. The evolution of monthly deciles was fitted to three simple expressions, linear, quadratic and exponential. The linear and exponential are similar, whereas the quadratic evolution is the most flexible since it provided a variable rate of concentration change and a better fit. With this last evolution, a decrease in the change rate was observed for low CO2 deciles, whereas an increasing change rate prevailed for the rest and was more accentuated for CH4. In the second section, meteorological variables were provided by a trajectory model. Backward trajectories from 1-day prior to reaching the measurement site were used to calculate distance and direction averages as well as the recirculation factor. Terciles of these variables were determined in order to establish three intervals with low, medium and high values. These intervals were used to classify the variables following their interval widths and skewnesses. The best correlation between pairs of meteorological variables was observed for the average distance, in particular with horizontal wind speed. Sinusoidal relationships with the average direction were obtained for average distance and for vertical wind speed. Finally, in the third section, the quadratic evolution was considered in each interval of all the meteorological variables. As regards the main result, the greatest increases were obtained for high potential temperature for both gases followed by low and medium boundary layer height for CO2 and CH4, respectively. Combining both meteorological variables provided increases of 22 ± 9 and 0.070 ± 0.019 ppm for CO2 and CH4, respectively, although the number of observations affected is small, around 7%.

Redox Levels through Constant Fermi-Level ab Initio Molecular Dynamics.

We develop a method to determine redox levels of half reactions through the use of ab initio molecular dynamics evolving at constant Fermi energy. This scheme models the effect of an electrode by controlling the charge transfer between the single-particle energy levels of the system and an electron reservoir set at a given potential during the dynamics. Like the thermodynamic integration method, our scheme does not require a priori knowledge of the products of the reaction, which can simply be obtained by driving the reaction through the variation of the Fermi level. The simulations are performed subject to periodic boundary conditions in the absence of any counterelectrode. We extract the redox level from the evolution of the Kohn-Sham energies upon charging (or discharging) the system. Using Janak's theorem and assuming a quadratic evolution of the Kohn-Sham energy of the highest occupied state upon charging, we demonstrate that our scheme for the determination of redox levels is equivalent to the thermodynamic integration method. The approach is illustrated for the redox couples Fe2+/Fe3+, HO2•/HO2-, and MnO4-/MnO4-2 in aqueous solution and yields redox potentials differing by less than 0.1 eV from respective ones achieved with the thermodynamic integration method.

Reconfigurable Mechanical System Design for Tracking an Ankle Trajectory Using an Evolutionary Optimization Algorithm

This paper presents a procedure for designing a mechanical training and rehabilitation gait system centered on ankle trajectories for children with cerebral palsy or any other psycho-motor limitation. With the aim of developing a reconfigurable device adjustable to the anthropometric characteristics of the user, an analytic model for the generation of ankle trajectories was elaborated, taking as a base the experimental data reported in literature. A dimensional synthesis for a mechanism to follow the drop type trajectories was carried out as a constrained numerical optimization problem that was solved with both the mathematical programming method and an evolutive algorithm, sequential quadratic programming (SQP) and differential evolution (DE), respectively. The comparative analysis of the results from both methods for this case study shows that DE outperforms SQP because of the limited feasibility space derived from the problem constrains and boundaries. The best result from DE was simulated with a computer-aided design package using a real size model for manufacturing.

Quadratic dissipative evolution of Gaussian states with drift

The solution of the Cauchy problem for the Gorini–Kossakowski–Sudarshan–Lindblad equation describing the irreversible quantum evolution of an n-particle system with a generator, which is a quadratic function in creation-annihilation operators, is reduced to the calculation of standard algebraic functions of 2n × 2n matrices.

Quadratic dissipative evolution of Gaussian states

Quadratic dissipative evolution of Gaussian states

Constrained evolution algebras and dynamical systems of a bisexual population

Consider a bisexual population such that the set of females can be partitioned into finitely many different types indexed by {1,2,…,n} and, similarly, that the male types are indexed by {1,2,…,ν}. Recently an evolution algebra of bisexual population was introduced by identifying the coefficients of inheritance of a bisexual population as the structure constants of the algebra. In this paper we study constrained evolution algebra of bisexual population in which type “1” of females and males have preference. For such algebras sets of idempotent and absolute nilpotent elements are known. We consider two particular cases of this algebra, giving more constraints on the structural constants of the algebra. By the first our constraint we obtain an n+ν-dimensional algebra with a matrix of structural constants containing only 0 and 1. In the second case we consider n=ν=2 but with general constraints. In both cases we study dynamical systems generated by the quadratic evolution operators of corresponding constrained algebras. We find all fixed points, limit points and some 2-periodic points of the dynamical systems. Moreover we study several properties of the constrained algebras connecting them to the dynamical systems. We give some biological interpretation of our results.

Extracellular Neural Microstimulation May Activate Much Larger Regions than Expected by Simulations: A Combined Experimental and Modeling Study

Electrical stimulation of the central nervous system has been widely used for decades for either fundamental research purposes or clinical treatment applications. Yet, very little is known regarding the spatial extent of an electrical stimulation. If pioneering experimental studies reported that activation threshold currents (TCs) increase with the square of the neuron-to-electrode distance over a few hundreds of microns, there is no evidence that this quadratic law remains valid for larger distances. Moreover, nowadays, numerical simulation approaches have supplanted experimental studies for estimating TCs. However, model predictions have not yet been validated directly with experiments within a common paradigm. Here, we present a direct comparison between experimental determination and modeling prediction of TCs up to distances of several millimeters. First, we combined patch-clamp recording and microelectrode array stimulation in whole embryonic mouse spinal cords to determine TCs. Experimental thresholds did not follow a quadratic law beyond 1 millimeter, but rather tended to remain constant for distances larger than 1 millimeter. We next built a combined finite element – compartment model of the same experimental paradigm to predict TCs. While theoretical TCs closely matched experimental TCs for distances <250 microns, they were highly overestimated for larger distances. This discrepancy remained even after modifications of the finite element model of the potential field, taking into account anisotropic, heterogeneous or dielectric properties of the tissue. In conclusion, these results show that quadratic evolution of TCs does not always hold for large distances between the electrode and the neuron and that classical models may underestimate volumes of tissue activated by electrical stimulation.

Static analysis of functionally graded sandwich plates according to a hyperbolic theory considering Zig-Zag and warping effects

In this paper, a variation of Murakami’s Zig-Zag theory is proposed for the analysis of functionally graded plates. The new theory includes a hyperbolic sine term for the in-plane displacements expansion and accounts for through-the-thickness deformation, by considering a quadratic evolution of the transverse displacement with the thickness coordinate. The governing equations and the boundary conditions are obtained by a generalization of Carrera’s Unified Formulation, and further interpolated by collocation with radial basis functions. Numerical examples on the static analysis of functionally graded sandwich plates demonstrate the accuracy of the present approach. The thickness stretching effect on such problems is studied.