Improvement of a temperature response function for divertor heat flux monitoring in fusion devices

Temperature response functions have been developed to investigate sensor design and divertor heat flux estimation in magnetically confined plasmas. The time-dependent heat flux can be derived by fitting the response function to experimental thermocouple(TC) data. Because the TC signals have a time delay to transit events such as discharge start or confinement transition, the time delay is taken into account in a temperature response function. Such a function accurately describes the signal from each TC channel with time delay in a sensor test using a neutral beam injection. Measurement for commercial TCs shows that the time delay is caused by the finite heat capacity of TC wire and contact heat resistance between TC and target surface.

Tool Condition Monitoring Based on Nonlinear Output Frequency Response Functions and Multivariate Control Chart

Tool condition monitoring(TCM)is a key technology for intelligent manufacturing.The objective is to monitor the tool operation status and detect tool breakage so that the tool can be changed in time to avoid significant damage to workpieces and reduce manufacturing costs.Recently,an innovative TCM approach based on sensor data modelling and model frequency analysis has been proposed.Different from traditional signal feature-based monitoring,the data from sensors are utilized to build a dynamic process model.Then,the nonlinear output frequency response functions,a concept which extends the linear system frequency response function to the nonlinear case,over the frequency range of the tooth passing frequency of the machining process are extracted to reveal tool health conditions.In order to extend the novel sensor data modelling and model frequency analysis to unsupervised condition monitoring of cutting tools,in the present study,a multivariate control chart is proposed for TCM based on the frequency domain properties of machining processes derived from the innovative sensor data modelling and model frequency analysis.The feature dimension is reduced by principal component analysis first.Then the moving average strategy is exploited to generate monitoring variables and overcome the effects of noises.The milling experiments of titanium alloys are conducted to verify the effectiveness of the proposed approach in detecting excessive flank wear of solid carbide end mills.The results demonstrate the advantages of the new approach over conventional TCM techniques and its potential in industrial applications.

Nutrient Response Functions of Sorghum for Miesso District Central Rift Valley of Ethiopia

This study was executed to offer the basis for optimized profit from fertilizer use for sorghum yield and to determine robust crop nutrient response function and economic rate for the production of sorghum at Miesso Central Rift Valley of Ethiopia. Trails were conducted at six experimental sites, sorghum yield response to N and P fertilizers application and economically optimum rates of nitrogen (EONR) and phosphorus (EOPR) were evaluated on a vertisols within the semi-arid Miesso districts west Hararge zone of Oromia region. The nutrient rates in 2014 cropping season four levels of Nitrogen (N) alone, these levels with 20 kg·ha−1 Phosphorus (P) and without N, 69 kg·ha−1 N with three levels of P treatments including the zero control were evaluated. In 2015, cropping season similar rates of N alone, the same rate N with 20 kg·ha−1 P, 92 kg·ha−1 N with three rates of P including the zero control were evaluated. The treatments were arranged in a randomized complete block with three replications in factorial design. Nutrient responses of sorghum were determined using asymptotic quadratic plateau functions. The significantly highest nitrogen rate was 46 kg·ha−1 alone in 2014 season, which gave grain yield of 2.56 Mg·ha−1 with a maximum yield advantage of 43%. P rates in both seasons and combined (sites + seasons) were not significantly influenced sorghum yield. Nitrogen agronomic and partial factor productivity peaked at 23 kg N ha−1 but declined with increasing N rate. The EONR combined (sites + seasons) were 37, 45, 52 and 60 kg·ha−1 and for the profit to cost ratio (PCR) were 2.43, 3.65, 4.86 and 5.79 at difference cost to grain price ratios (CP) = 3.6, 2.3, 1.6 and 1.2 respectively at Miesso Ethiopia. Nitrogen application had economically profitable than P. The study concluded that the application of N at 37 or 60 kg N ha−1 to sorghum production could be economically profitable for those economically constrained farmers or economically not constrained farmers. Validation should be farther conducted on farmers’ fields for refining the results obtained.

Near-optimal control of a stochastic rumor spreading model with Holling II functional response function and imprecise parameters

In recent years,rumor spreading has caused widespread public panic and affected the whole social harmony and stability.Consequently,how to control the rumor spreading effectively and reduce its negative influence urgently needs people to pay much attention.In this paper,we mainly study the near-optimal control of a stochastic rumor spreading model with Holling II functional response function and imprecise parameters.Firstly,the science knowledge propagation and the refutation mechanism as the control strategies are introduced into a stochastic rumor spreading model.Then,some sufficient and necessary conditions for the near-optimal control of the stochastic rumor spreading model are discussed respectively.Finally,through some numerical simulations,the validity and availability of theoretical analysis is verified.Meanwhile,it shows the significance and effectiveness of the proposed control strategies on controlling rumor spreading,and demonstrates the influence of stochastic disturbance and imprecise parameters on the process of rumor spreading.

Continuous-Time and Discrete-Time Singular Value Decomposition of an Impulse Response Function

This paper proposes the continuous-time singular value decomposition (SVD) for the impulse response function, a special kind of Green’s functions, in order to find a set of singular functions and singular values so that the convolutions of such function with the set of singular functions on a specified domain are the solutions to the inhomogeneous differential equations for those singular functions. A numerical example was illustrated to verify the proposed method. Besides the continuous-time SVD, a discrete-time SVD is also presented for the impulse response function, which is modeled using a Toeplitz matrix in the discrete system. The proposed method has broad applications in signal processing, dynamic system analysis, acoustic analysis, thermal analysis, as well as macroeconomic modeling.

Pilot study on the Non-Invasive Detectability of Femoral Neck Fractures with Frequency Response Functions

A suspicion of a femoral neck fracture is a frequently recurring situation, especially in nursing homes. For the clarification of such a suspicion normally imaging techniques are used. Such equipment is expensive and therefore is located in hospitals. In addition to the costs, a transport causes stress for the patient. This pilot study is devoted to the question whether the detection of a femoral neck fracture with vibration measurements is possible in principal. In such a case, the clarification could be done on-site by an ordinary person using much cheaper equipment. This would reduce the stress for the patient and save money. For this purpose vibration measurements on a dead body with intact, with partially fractured and with complete cut femoral neck have been performed. Two different methods for the vibration initiation have been investigated, the so called impact testing and the shaker testing. The frequency response function has been determined for all combinations on both sides of the body. It turned out that there is a clear difference in the frequency response functions of the fractured bone with respect to the intact bone when shaker testing is used. This indicates that the method could have the potential to be a cost-saving alternative to imaging techniques. However, in a next step a statistically reliable clinical survey on living persons needs to be done.

AB052.A standardized quantification of the visual contrast response function

Background:All neurons of the visual system exhibit response to differences in luminance.This neural response to visual contrast,also known as the contrast response function(CRF),follows a characteristic sigmoid shape that can be fitted with the Naka-Rushton equation.Four parameters define the CRF,and they are often used in different visual research disciplines,since they describe selective variations of neural responses.As novel technologies have grown,the capacity to record thousands of neurons simultaneously brings new challenges:processing and robustly analyzing larger amounts of data to maximize the outcomes of our experimental measurements.Nevertheless,current guidelines to fit neural activity based on the Naka-Rushton equation have been poorly discussed in depth.In this study,we explore several methods of boundary-setting and least-square curve-fitting for the CRF in order to avoid the pitfalls of blind curve-fitting.Furthermore,we intend to provide recommendations for experimenters to better prepare a solid quantification of CRF parameters that also minimize the time of the data acquisition.For this purpose,we have created a simplified theoretical model of spike-response dynamics,in which the firing rate of neurons is generated by a Poisson process.The spike trains generated by the theoretical model depending on visual contrast intensities were then fitted with the Naka-Rushton equation.This allowed us to identify combinations of parameters that were more important to adjust before performing experiments,to optimize the precision and efficiency of curve fitting(e.g.,boundaries of CRF parameters,number of trials,number of contrast tested,metric of contrast used and the effect of including multi-unit spikes into a single CRF,among others).Several goodness-of-fit methods were also examined in order to achieve ideal fits.With this approach,it is possible to anticipate the minimal requirements to gather and analyze data in a more efficient way in order to build stronger functional models.Methods:Spike-trains were randomly generated following a Poisson distribution in order to draw both an underlying theoretical curve and an empirical one.Random noise was added to the fit to simulate empirical conditions.The correlation function was recreated on the simulated data and re-fit using the Naka-Rushton equation.The two curves were compared:the idea being to determine the most advantageous boundaries and conditions for the curve-fit to be optimal.Statistical analysis was performed on the data to determine those conditions for experiments.Experiments were then conducted to acquire data from mice and cats to verify the model.Results:Results were obtained successfully and a model was proposed to assess the goodness of the fit of the contrast response function.Various parametres and their influence of the model were tested.Other similar models were proposed and their performance was assessed and compared to the previous ones.The fit was optimized to give semi-strict guidelines for scientists to follow in order to maximize their efficiency while obtaining the contrast tuning of a neuron.Conclusions:The aim of the study was to assess the optimal testing parametres of the neuronal response to visual gratings with various luminance,also called the CRF.As technology gets more powerful and potent,one must make choices when experimenting.With a strong model,robust boundaries,and strong experimental conditioning,the best fit to a function can lead to more efficient analysis and stronger cognitive models.

Stability Analysis of a Self-Memory Prey-Predator Diffusion Model Based on Bazykin Functional Response

To investigate the effects of self-memory diffusion on predator-prey models, we consider a predator-prey model with Bazykin functional response of self- memory diffusion. The uniqueness, boundedness, positivity, existence and stability of equilibrium point of the model are studied. In this paper, the uniqueness of the solution is discussed under the non-negative initial function and Neumann boundary conditions satisfying a specific space. The boundness of the solution is proved by the comparison principle of parabolic equations, and the positivity of the solution is proved by the strong maximum principle of parabolic equations. Hurwitz criterion and Lyapunov function construction are used to analyze the local stability and global stability of feasible equilibrium points. The results show that the system solution is unique non-negative and bounded. The model is unstable at the trivial equilibrium point E0 and the boundary equilibrium point E1, and the condition of whether the positive equilibrium point E2 is stable under certain conditions is given.

Dynamic Analysis of a Predator-Prey Model with Holling-II Functional Response

A predator-prey model with linear capture term Holling-II functional response was studied by using differential equation theory. The existence and the stabilities of non-negative equilibrium points of the model were discussed. The results show that under certain limited conditions, these two groups can maintain a balanced position, which provides a theoretical reference for relevant departments to make decisions on ecological protection.

Dynamics Analysis of Active Variable Stiffness Vibration Isolator for Whole-Spacecraft Systems Based on Nonlinear Output Frequency Response Functions

In order to improve the harsh dynamic environment experienced by heavy rockets during different external excitations,this study presents a novel active variable stiffness vibration isolator(AVS-VI)used as the vibration isolation device to reduce excessive vibration of the whole-spacecraft isolation system.The AVS-VI is composed of horizontal stiffness spring,positive stiffness spring,parallelogram linkage mechanism,piezoelectric actuator,acceleration sensor,viscoelastic damping,and PID active controller.Based on the AVS-VI,the generalized vibration transmissibility determined by the nonlinear output frequency response functions and the energy absorption rate is applied to analyze the isolation performance of the whole-spacecraft system with AVS-VI.The AVS-VI can conduct adaptive vibration suppression with variable stiffness to the whole-spacecraft system,and the analysis results indicate that the AVS-VI is efTective in reducing the extravagant vibration of the whole-spacecraft system,where the vibration isolation is decreased up to above 65%under different acceleration excitations.Finally,different parameters of AVS-VI are considered to optimize the whole-spacecraft system based on the generalized vibration transmissibility and the energy absorption rate.

AB050.Neuronal response to visual contrast varies as function of the cortical layer

Background:For years,studies using several animal models have highlighted the predominant role of the primary visual area in visual information processing.Its six cortical layers have morphological,hodological and physiological differences,although their roles regarding the integration of visual contrast and the messages sent by the layers to other brain regions have been poorly explored.Given that cortical layers have distinct properties,this study aims to understand these differences and how they are affected by a changing visual contrast.Methods:A linear multi-channel electrode was placed in the primary visual cortex(V1)of the anesthetized mouse to record neuronal activity across the different cortical layers.The laminar position of the electrode was verified in real time by measuring the current source density(CSD)and the multi-unit activity(MUA),and confirmed post-mortem by histological analysis.Drifting gratings varying in contrast enabled the measurement of the firing rate of neurons throughout layers.We fitted this data to the Naka-Rushton equations,which generated the contrast response function(CRF)of neurons.Results:The analysis revealed that the baseline activity as well as the rate of change of neural discharges(the slope of the CRF)had a positive correlation across the cortical layers.In addition,we found a trend between the cortical position and the contrast evoking the semi-saturation of the activity.A significant difference in the maximum discharge rate was also found between layers II/III and IV,as well as between layers II/III and V.Conclusions:Since layers II/III and V process visual contrast differently,our results suggest that higher cortical visual areas,as well subcortical regions,receive different information regarding a change in visual contrast.Thus,a contrast may be processed differently throughout the different areas of the visual cortex.

Protection zone in a diffusive predator-prey model with Ivlev-type functional response

The effect of a protection zone on a diffusion predator-prey model with Ivlev-type functional response is considered.We discuss the existence and non-existence of positive steady state solutions by using the bifurcation theory.It is shown that the protection zone for prey has beneficial effects on the coexistence of the two species when the growth rate of predator is positive.Moreover,we examine the dependence of the coexistence region on the efficiency of the predator capture of the prey and the protection zone.

Impulsive Predator-Prey Dynamic Systems with Beddington-DeAngelis Type Functional Response on the Unification of Discrete and Continuous Systems

In this study, the impulsive predator-prey dynamic systems on time scales calculus are studied. When the system has periodic solution is investigated, and three different conditions have been found, which are necessary for the periodic solution of the predator-prey dynamic systems with Beddington-DeAngelis type functional response. For this study the main tools are time scales calculus and coincidence degree theory. Also the findings are beneficial for continuous case, discrete case and the unification of both these cases. Additionally, unification of continuous and discrete case is a good example for the modeling of the life cycle of insects.

Bifurcationing Analysis of Predator-Prey Diffusive System Based on Bazykin Functional Response

A predator-prey diffusion system with a Bazykin functional response is studied. The existence of equilibrium points, the stability of normal number equilibrium points and the existence of Hopf bifurcationes are investigated for the proposed system, the existence of positive solutions in the system is discussed under Neumann boundary conditions, and the stability of constant equilibrium points is focused on under the condition of Hurwitz criterion. The results show that there exist positive equilibrium points in the system under Neumann boundary conditions, and the normal number equilibrium points are stable when specific conditions are satisfied, and the bifurcation points of Hopf bifurcationes and their orders are given.

Examining approaches for modeling individual tree growth response to thinning in Norway spruce

Using periodic measurements from permanent plots in non-thinned and thinned Norway spruce(Picea abies(L.)H.Karst.)stands in Norway,individual-tree growth models were developed to predict annual diameter increment,height increment,and height to crown base increment.Based on long-term data across a range of thinning regimes and stand conditions,alternative approaches for modeling response to treatment were assessed.Dynamic thinning response functions in the form of multiplicative modifiers that predict no effect at the time of thinning,a rapid increase followed by an early maximum before the effect gradually declines to zero could not be fitted to initially derived baseline models without thinning related predictors.However,alternative approaches were used and found to perform well.Specifically,indicator variables representing varying time periods after thinning were statistically significant and behaved in a robust manner as well as consistent with general expectations.In addition,they improved overall prediction accuracy when incorporated as fixed effects into the baseline models for diameter and height to crown base increment.Further,more simply,including exponentially decreasing multiplicative thinning response functions improved prediction accuracy for height increment and height to crown base increment.Irrespective of studied attribute and modelling approach,improvement in performance of these extended models was relatively limited when compared to the corresponding baseline models and more pronounced in trees from thinned stands.We conclude that the largely varying and often multi-year measurement intervals of the periodic data used in this study likely prevented the development of more sophisticated thinning response functions.However,based on the evaluation of the final models’overall performance such complex response functions may not to be necessary to reliably predict individual tree growth after thinning for certain conditions or species,which should be further considered in future analyses of similar nature.

AB001.How to optimize the visual contrast response of cortical neurons

Background:In the visual system,one of the most explored neural behaviors is the response of cells to changes in visual contrast.This neural response to visual contrast,also known as the contrast response function(CRF),can be fitted with the Naka-Rushton equation(NRE).Assessing the CRF of many neurons at the same time is critical to establishing functional visual properties.However,maximizing the performance of neurons to fit the NRE,while minimizing their time acquisitions is a challenge.We present a method to accurately obtain reliable NRE fits from experimental data,that ensure a reasonable time of record acquisition.Methods:We simulated CRF of cortical neurons with a toy model based on the response of Poisson spike trains to varied levels of contrasts.We first tested whether mean values or the whole set of contrast responses fit better the NRE.Then,we analyzed what were the boundaries to optimize the fit of the NRE,and after we explore the consequences of fitting the NRE with single-or multi-units.With these outcomes,we varied experimental parameters such as the number of trials,number of input contrasts and length of time acquisition to calculate the errors of fitting CRFs.Those data sets that maximize the CRF fit but minimize the time of recording were selected.The selected data set was then evaluated in visual cortical neurons of anesthetized cats from areas 17,18 and 21a.Results:First,we found that is always better to fit the NRE with mean values rather than the whole set of points.Then,we noticed that either removing or imposing loose boundaries to the CRF parameters lead to an increase in the performance of the NRE fit.Afterward,we found that single units(SU)or assume multi-unit formed of several SUs(>30)adjusted considerably better the NRE fit.Finally,the experiments showed that specific sets of patterns(number of trials,number of input contrasts and length of time acquisition)satisfied our two constraints:minimize the error of the NRE fit while maximizing the acquisition time of recording.The most characteristic pattern was the one with 6 points,15 repetitions and 1 second of duration.However,cortical areas varied in the representation of the patterns.Conclusions:Theoretical simulations of many different sets of patterns and their following experimental validation suggest strongly that a particular set of patterns can satisfy the imposed constraints.With this approach,we provided a tool that allows an optimal design of stimuli to assess the CRF of large neuronal populations and guarantees the finest fit for each unit analyzed.

Fear and delay effects on a food chain system with two kinds of different functional responses

For food chain system with three populations,direct predation is the basic interaction between species.Different species often have different predation functional responses,so a food chain system with Holling-II response for middle predator and Beddinton-DeAngelis response for top predator is proposed.Apart from direct predation,predator population can significantly impact the survival of prey population by inducing the prey's fear,but the impact often possesses a time delay.This paper is concentrated to explore how the fear and time delay affect the system stability and the species persistence.By use of Lyapunov functional method and bifurcation theory,the positiveness and boundedness of solutions,local and global behavior of species,the system stability around the equilibrium states and various kinds of bifurcation are investigated.Numerically,some simulations are carried out to validate the main findings and the critical values of the bifurcation parameters of fear and conversion rate are obtained.It is observed that fear and delay can not only stabilize,but also destabilize the system,which depends on the magnitude of the fear and delay.The system varies from unstable to stable due to the continuous increase of the prey's fear by middle predator.Small fear induced by top predator or small delay of the prey's fear can stabilize the system,while they are sufficiently large,the system stability is to be destroyed.Simultaneously,the conversion rate can also change the stability and even make the species to be extinct.Some rich dynamics like multiple stabilities and various types of bistability behaviors are also exhibited,which results in the convergence of the species from one stable equilibrium to another.

Dynamic analysis of a predator-prey model of Gause type with Allee effect and non-Lipschitzian hyperbolic-type functional response

In this work,we study a predator-prey model of Gause type,in which the prey growth rate is subject to an Allee effect and the action of the predator over the prey is determined by a generalized hyperbolic-type functional response,which is neither differentiable nor locally Lipschitz at the predator axis.This kind of functional response is an extension of the so-called square root functional response,used to model systems in which the prey have a strong herd structure.We study the behavior of the solutions in the first quadrant and the existence of limit cycles.We prove that,for a wide choice of parameters,the solutions arrive at the predator axis in finite time.We also characterize the existence of an equilibrium point and,when it exists,we provide necessary and sufficient conditions for it to be a center-type equilibrium.In fact,we show that the set of parameters that yield a center-type equilibrium,is the graph of a function with an open domain.We also prove that any center-type equilibrium is stable and it always possesses a supercritical Hopf bifurcation.In particular,we guarantee the existence of a unique limit cycle,for small perturbations of the system.

Dynamical Behavior of Discrete Ratio-Dependent Predator-Prey System

In this paper, we propose a discrete ratio-dependent predator-prey system. The stability of the fixed points of this model is studied. At the same time, it is shown that the discrete model undergoes fold bifurcation and flip bifurcation by using bifurcation theory and the method of approximation by a flow. Numerical simulations are presented not only to demonstrate the consistence with our theoretical analyses, but also to exhibit the complex dynamical behaviors, such as the cascade of period-doubling bifurcation in period-2 and the chaotic sets. The Maximum Lyapunov exponents are numerically computed to confirm further the complexity of the dynamical behaviors. These results show that the direct discrete method has more rich dynamic behaviors than the discrete model obtained by Euler method.

Statistical Analysis and Evaluation of Macroeconomic Policies: A Selective Review

In this paper,we highlight some recent developments of a new route to evaluate macroeconomic policy effects,which are investigated under the framework with potential outcomes.First,this paper begins with a brief introduction of the basic model setup in modern econometric analysis of program evaluation.Secondly,primary attention goes to the focus on causal effect estimation of macroeconomic policy with single time series data together with some extensions to multiple time series data.Furthermore,we examine the connection of this new approach to traditional macroeconomic models for policy analysis and evaluation.Finally,we conclude by addressing some possible future research directions in statistics and econometrics.