Nonlinear terms produced by passing amplitude-modulated sinusoids through a hair cell transducer function

We derive mathematically the output of Corey and Hudspeth's hair cell transducer function for the following cases: (1) the input is a single carrier whose output is modulated by the sum of two sinusoids; (2) the input is the sum of two carriers, each of which is amplitude-modulated by a single sinusoid. The theoretical results are similar to the results of an experiment in which field potentials were recorded from the human scalp while one ear was stimulated with auditory waveform (1) and with auditory waveform (2) of the cases above.     

Material flow analysis (MFA) of an eco-economic system:a case study of Wujin District,Changzhou,China

The economic and ecological aspects of a social system are coherently linked and can be examined by its material and energy flows.In this study,we used the material flow analysis (MFA) to model the material input and output of the Wujin District of Changzhou City,Jiangsu Province in China.It was revealed that:(1) total material input and material input per capita increased with economic development,while the total material out-put and material output per capita decreased consistently;(2) except for water,the total material input continued to increase.Input of solid materials grew faster than that of gaseous materials,while the total material output declined.The gas output accounted for the largest pro-portion of the output resulting in primary environmental pollution as burned fossil fuel; (3) water use in agriculture continued with an increasing trend while that in industrial and residential sectors decreased per capita.The total wastewater discharge and wastewater discharge per capita decreased with a faster decreasing rate of residential was-tewater discharge followed by industrial wastewater dis-charge; (4) material input per unit GDP fluctuated and material output per unit GDP decreased.A decreasing trend in both water use and wastewater discharge per unit GDP was disclosed.These results suggest that the effi-ciency of resource use in the Wujin District has improved.This weakened the direct link between economic develop-ment and environmental deterioration.Additionally,we discussed the harmonic development between environ-ment and economy.Potential limitations of MFA's application were also discussed.It is suggested that effec-tive measures should be taken for the enforcement of cir-cular economic strategies and the construction of a resource-saving economy     

Gamma oscillations as a mechanism for selective information transmission

In the past decades, many studies have focussed on the relation between the input and output of neurons with the aim to understand information processing by neurons. A particular aspect of neuronal information, which has not received much attention so far, concerns the problem of information transfer when a neuron or a population of neurons receives input from two or more (populations of) neurons, in particular when these (populations of) neurons carry different types of information. The aim of the present study is to investigate the responses of neurons to multiple inputs modulated in the gamma frequency range. By a combination of theoretical approaches and computer simulations, we test the hypothesis that enhanced modulation of synchronized excitatory neuronal activity in the gamma frequency range provides an advantage over a less synchronized input for various types of neurons. The results of this study show that the spike output of various types of neurons [i.e. the leaky integrate and fire neuron, the quadratic integrate and fire neuron and the Hodgkin–Huxley (HH) neuron] and that of excitatory–inhibitory coupled pairs of neurons, like the Pyramidal Interneuronal Network Gamma (PING) model, is highly phase-locked to the larger of two gamma-modulated input signals. This implies that the neuron selectively responds to the input with the larger gamma modulation if the amplitude of the gamma modulation exceeds that of the other signals by a certain amount. In that case, the output of the neuron is entrained by one of multiple inputs and that other inputs are not represented in the output. This mechanism for selective information transmission is enhanced for short membrane time constants of the neuron.     

The response of a model neurone to a white noise input

We consider a simple model of a neurone in which the input voltage is integrated to form the somatic potential, and a pulse is emitted when this reaches a threshold; the somatic potential is then reset to its resting value. We subject this model to a white-noise input, and evaluate the cross correlation between input white noise and the output pulse train; this is proportional to the small-signal impulse response of the model. Some numerical estimations are presented.     

Predicting the synaptic information efficacy in cortical layer 5 pyramidal neurons using a minimal integrate-and-fire model

Synaptic information efficacy (SIE) is a statistical measure to quantify the efficacy of a synapse. It measures how much information is gained, on the average, about the output spike train of a postsynaptic neuron if the input spike train is known. It is a particularly appropriate measure for assessing the input–output relationship of neurons receiving dynamic stimuli. Here, we compare the SIE of simulated synaptic inputs measured experimentally in layer 5 cortical pyramidal neurons in vitro with the SIE computed from a minimal model constructed to fit the recorded data. We show that even with a simple model that is far from perfect in predicting the precise timing of the output spikes of the real neuron, the SIE can still be accurately predicted. This arises from the ability of the model to predict output spikes influenced by the input more accurately than those driven by the background current. This indicates that in this context, some spikes may be more important than others. Lastly we demonstrate another aspect where using mutual information could be beneficial in evaluating the quality of a model, by measuring the mutual information between the model’s output and the neuron’s output. The SIE, thus, could be a useful tool for assessing the quality of models of single neurons in preserving input–output relationship, a property that becomes crucial when we start connecting these reduced models to construct complex realistic neuronal networks.     

Activation of command fibres to the stomatogastric ganglion by input from a gastric mill proprioceptor in the crab,Cancer pagurus †

In semi‐intact preparations of the crab Cancer pagurus the normal output from the stomatogastric ganglion (StG) was a regular pyloric cycle (Figure 4). Repeated stimulation of the posterior stomach nerve (psn) of the posterior gastric mill proprioceptor (PSR) often induced series of spontaneous gastric cycles. We were therefore able to describe the normal gastric cycle as recorded in the output nerves from StG and to identify most of the relevant motor neurones by reference to the muscles that they innervate (Figure 10). The gastric cycle output was variable (Figures 5, 6), although in many preparations one complex type of output predominated (Figure 7). The basic feature of the gastric cycle was an alternation of activity between the single cardio‐pyloric neurone (CP) and a complex variable burst in the lateral cardiac (LC), the gastro‐pyloric (GP), the gastric (GM), and other associated neurones. During this normally occurring complex gastric burst significant changes occurred in the pyloric cycle, notably an increase in activity of the pacemaker pyloric dilator (PD) group and an inhibition of the lateral pyloric (LP), inferior cardiac (IC) and ventricular dilator (VD) neurones (Figures 6, 7, 8, 9). These changes are probably associated with an opening of the cardio‐pyloric valve and food passage into the pyloric filter. The gastric output was related to the normally observed movements of the dorsal ossicles of the gastric mill and thus to the operation of the teeth of the mill (Figure 11). Increased input from the PSR is associated with the grinding action of the teeth which is caused by the complex gastric burst (Figure 12).

Stimulation of the psn during an ongoing regular pyloric output caused changes in the cycle which mimicked those occurring during the spontaneous gastric cycle (Figure 13; Table 1). Stimulation of the psn during ongoing gastric activity also affected the gastric units (Figure 14). The input pathway from the PSR is shown to be through the stomatogastric nerve (sgn), the connection between the commissural ganglia and the stomatogastric ganglion (Figure 15). The commissural ganglia are known to receive most of the sensory input from the foregut and PSR input is probably processed there. Recordings from the sgn show that psn stimulation activates a small number of centrally originating units, and that the activity of these units coincides with the pyloric output changes (Figures 15, 16). We therefore label the units command interneurones. Their effects could be mediated by direct connections to only the PD pacemaker neurones of the pyloric cycle. Control experiments showed that PSR input is not necessary for the pyloric output changes to occur during gastric output but that similar output changes can be evoked by input resulting from induced gastric movements (Figure 15(E)). We think that the pyloric cycle output changes are normally controlled by a number of mechanisms at different levels (Figure 17). We cannot easily explain the effects of PSR input on the gastric cycle neurones.

These findings are important because they allow us to study a specific input to the StG without disrupting its normal input‐output pathways to the central nervous system. Further experiments on the system designed to test the assumption that the sgn units are in fact responsible for the pyloric output changes, and to investigate the processing of the PSR input are outlined.     

Material flow analysis (MFA) of an eco-economic system: a case study of Wujin District, Changzhou, China

The economic and ecological aspects of a social system are coherently linked and can be examined by its material and energy flows. In this study, we used the material flow analysis (MFA) to model the material input and output of the Wujin District of Changzhou City, Jiangsu Province in China. It was revealed that: (1) total material input and material input per capita increased with economic development, while the total material output and material output per capita decreased consistently; (2) except for water, the total material input continued to increase. Input of solid materials grew faster than that of gaseous materials, while the total material output declined. The gas output accounted for the largest proportion of the output resulting in primary environmental pollution as burned fossil fuel; (3) water use in agriculture continued with an increasing trend while that in industrial and residential sectors decreased per capita. The total wastewater discharge and wastewater discharge per capita decreased with a faster decreasing rate of residential wastewater discharge followed by industrial wastewater discharge; (4) material input per unit GDP fluctuated and material output per unit GDP decreased. A decreasing trend in both water use and wastewater discharge per unit GDP was disclosed. These results suggest that the efficiency of resource use in the Wujin District has improved. This weakened the direct link between economic development and environmental deterioration. Additionally, we discussed the harmonic development between environment and economy. Potential limitations of MFA’s application were also discussed. It is suggested that effective measures should be taken for the enforcement of circular economic strategies and the construction of a resource-saving economy __________ Translated from Acta Ecologica Sinica, 2006, (8): 2578–2586 [译自:生态学报]     

Rectification of correlation by a sigmoid nonlinearity

We investigated the normalized autocovariance (correlation coefficient) function of the output of an erf( ) function nonlinearity subject to non-zero mean Gaussian noise input. When the sigmoid is wide compared to the input, or the input mean is close to the midpoint of the sigmoid, the output correlation coefficient function is very close to the input correlation coefficient function. When the noise mean and variance are such that there is a significant probability of operating in the saturation region and the sigmoid is not too flat, the correlation coefficient output function is less than that of the input. This difference is much greater when the correlation coefficient is negative than when it is positive. The sigmoid partially rectifies the correlation coefficient function. The analysis does not depend on the spectral properties of the input noise. All that is required is that the input at times t and (t+τ) be jointly Gaussian with the same mean and autocovariance. The analysis therefore applies equally well to the case of two identical sigmoids with jointly Gaussian inputs. This correlational rectification could help explain the parameter sensitivity of "neural network" models. If biological neurons share this property it could explain why few negative correlations between spike trains have been observed. Received: 1 July 1992/Accepted in revised form: 6 July 1993     

高产池塘混养鱼类相互关系及主体鱼资金投入产出模型的建立

应用灰色关联度分析法对顺德高产池塘的多品种混养鱼类关系进行分析,各种不同鱼类的放养对产量的关系为：鲮放养量对镛的净产量影响最大（Ｇ３４＝０．７９２１）,其次为草鱼放养对鲮的净产量影响（Ｇ１３＝０．７４１５）,最小为鲢的放养对草鱼的净产量关系（０．５９３２）。鲮的放养为优势母因子,鳙的收获为优势子因子。应用灰色动态模型ＧＭ（１,２）建模法建立了高产池塘主体鱼的产投关系模型,在该模型的基础上建立了系统     

An examination of current Hg deposition and export in Fenno-Scandian catchments

The input and output flux data of total Hg (THg) and methylmercury (MeHg) from three catchments located in different geographical regions in Sweden and one catchment in southern Finland were compared to elucidate the role of current atmospheric Hg/MeHg deposition with regard to waterborne Hg/MeHg output.There was a negative co-variaton between the open field THg inputs and the ratio of THg output to open field input. The highest ratio (and lowest input) occurring in N. Sweden and S. Finland, while the lowest output ratio (and highest inputs) occurred in southwest Sweden. A much larger variation was found in the ratio of output to open field input for MeHg (14 to 160%). Examinations of MeHg input/output data in relation to catchment charateristics suggest that riparian peat, mires and wet organic soil contributed to the large MeHg output from certain catchments, probably due to in situ production of MeHg. This finding is consistent with other studies which have found that catchment characteristics such as wetland area, flow pathways, seasonal temperature and water flow are important in controlling the output of MeHg. These catchment characteristics govern the fate of the contemporary input of Hg and MeHg as well as the mobilization of the soil pools.     

Computation of a stabilizing set of feedback matrices of a large-scale nonlinear musculoskeletal dynamic model

The purpose of this study is to present a general mathematical framework to compute a set of feedback matrices which stabilize an unstable nonlinear anthropomorphic musculoskeletal dynamic model. This method is activity specific and involves four fundamental stages. First, from muscle activation data (input) and motion degrees-of-freedom (output) a dynamic experimental model is obtained using system identification schemes. Second, a nonlinear musculoskeletal dynamic model which contains the same number of muscles and degrees-of-freedom and best represents the activity being considered is proposed. Third, the nonlinear musculoskeletal model (anthropomorphic model) is replaced by a family of linear systems, parameterized by the same set of input/output data (nominal points) used in the identification of the experimental model. Finally, a set of stabilizing output feedback matrices, parameterized again by the same set of nominal points, is computed such that when combined with the anthropomorphic model, the combined system resembles the structural form of the experimental model. The method is illustrated in regard to the human squat activity.     

Computation of a Stabilizing Set of Feedback Matrices bf a Large-scale Nonlinear Musculoskeletal Dynamic Model

The purpose of this study is to present a general mathematical framework to compute a set of feedback matrices which stabilize an unstable nonlinear anthropomorphic musculoskeletal dynamic model. This method is activity specific and involves four fundamental stages. First, from muscle activation data (input) and motion degrees-of-freedom (output) a dynamic experimental model is obtained using system identification schemes. Second, a nonlinear musculoskeletal dynamic model which contains the same number of muscles and degrees-of-freedom and best represents the activity being considered is proposed. Third, the nonlinear musculoskeletal model (anthropomorphic model) is replaced by a family of linear systems, parameterized by the same set of input/ output data (nominal points) used in the identification of the experimental model. Finally, a set of stabilizing output feedback matrices, parameterized again by the same set of nominal points, is computed such that when combined with the anthropomorphic model, the combined system resembles the structural form of the experimental model. The method is illustrated in regard to the human squat activity.     

Population modeling for a captive squirrel monkey colony

Population modeling for a squirrel monkey colony breeding in a captive laboratory environment was approached with the use of two different mathematical modeling techniques. Deterministic modeling was used initially on a spreadsheet to estimate future census figures for animals in various age/sex classes. Historical data were taken as input parameters for the model, combined with harvesting policies to calculate future population figures in the colony. This was followed by a more sophisticated stochastic model that is capable of accommodating random variations in biological phenomena, as well as smoothing out measurement errors. Point estimates (means) for input parameters used in the deterministic model are replaced by probability distributions fitted into historical data from colony records. With the use of Crystal Ball (Decisioneering, Inc., Denver, CO) software, user-selected distributions are embedded in appropriate cells in the spreadsheet model. A Monte Carlo simulation scheme running within the spreadsheet draws (on each cycle) random values for input parameters from the distribution embedded in each relevant cell, and thus generates output values for forecast variables. After several thousand runs, a distribution is formed at the output end representing estimates for population figures (forecast variables) in the form of probability distributions. Such distributions provide the decision-maker with a mathematical habitat for statistical analysis in a stochastic setting. In addition to providing standard statistical measures (e.g., mean, variance, and range) that describe the location and shape of the distribution, this approach offers the potential for investigating crucial issues such as conditions surrounding the plausibility of extinction.     

Linear and quadratic models of point process systems: Contributions of patterned input to output

In the 1880's Volterra characterised a nonlinear system using a functional series connecting continuous input and continuous output. Norbert Wiener, in the 1940's, circumvented problems associated with the application of Volterra series to physical problems by deriving from it a new series of terms that are mutually uncorrelated with respect to Gaussian processes. Subsequently, Brillinger, in the 1970's, introduced a point-process analogue of Volterra's series connecting point-process inputs to the instantaneous rate of point-process output. We derive here a new series from this analogue in which its terms are mutually uncorrelated with respect to Poisson processes. This new series expresses how patterned input in a spike train, represented by third-order cross-cumulants, is converted into the instantaneous rate of an output point-process. Given experimental records of suitable duration, the contribution of arbitrary patterned input to an output process can, in principle, be determined. Solutions for linear and quadratic point-process models with one and two inputs and a single output are investigated. Our theoretical results are applied to isolated muscle spindle data in which the spike trains from the primary and secondary endings from the same muscle spindle are recorded in response to stimulation of one and then two static fusimotor axons in the absence and presence of a random length change imposed on the parent muscle. For a fixed mean rate of input spikes, the analysis of the experimental data makes explicit which patterns of two input spikes contribute to an output spike.     

Design of Mechanical Frequency Regulator for Predictable Uniform Power from Triboelectric Nanogenerators

Mechanical energy scavengers convert irregular input mechanical energy into irregular electrical output. There is a need to enable uniform and predictable electric output from energy scavengers regardless of the variability in the mechanical input. So, in this work, a mechanical frequency regulator is proposed that fixes the input forces and input frequency acting on a triboelectric nanogenerator, thus enabling predictable electric output. The irregular low frequency mechanical input energy is first stored in a spiral spring following which the energy is released at the desired frequency by means of an appropriate design of gear train, cam, and flywheel. By regulating the nanogenerator output at 50 Hz, a standard power transformer can be optimally driven to increase the output current to 6.5 mA and reduce its voltage to 17 V. This output is highly compatible for powering wireless node sensors as is demonstrated in this work.     

Membrane voltage changes in a compartmental chain model of a neurone

A mathematical model of the neurone has been developed using the method of subdivision of the neurone into a number of equivalent circuit compartments. Compartmental characteristics have been investigated by calculating the shape indices of the output produced in response to a given somatic input conductance change. A generalised form of compartmental chain has been chosen to allow calculation of the shape indices produced by a variety of geometrical configurations including the straight and tapering chain forms. Equations have been deduced from the computations made on a CDC 6600 computer relating the peak amplitude of the output response to the compartmental diameter for both the straight and tapering chain forms. The effect of variation in the location of the input conductance injection site has also been related to the peak amplitude of the somatic response. The optimum characteristics of the input conductance pulse shape have been computed initially using a rectangular pulse and later the more physiologically relevant double exponential shape. The effect of alteration in the end compartmental terminal impedances over the range from open to short circuit conditions was also calculated. The establishment of optimum single compartmental chain criteria allows the future investigation of multiple chain and pyramidal cell configurations.     

Measures of transinformation for multiple input/single output neuronal systems

This paper presents a method for the calculation of the information transfer, or transinformation, in multiple input/single output neuronal systems. Our approach is an extension of an approach introduced by Eckhorn and Poepel in 1974. These authors computed the transinformation in single input/single output neuronal channels by regarding the spike (or stimulus) trains involved as finite Markov chains. The expressions for multiple input systems presented here are derived in close analogy to formulae in linear systems theory which show explicity the correlations between the different input channels. A number of equivalent forms for the transinformation are discussed.     

The interspike interval of a cable model neuron with white noise input

The firing time of a cable model neuron in response to white noise current injection is investigated with various methods. The Fourier decomposition of the depolarization leads to partial differential equations for the moments of the firing time. These are solved by perturbation and numerical methods, and the results obtained are in excellent agreement with those obtained by Monte Carlo simulation. The convergence of the random Fourier series is found to be very slow for small times so that when the firing time is small it is more efficient to simulate the solution of the stochastic cable equation directly using the two different representations of the Green's function, one which converges rapidly for small times and the other which converges rapidly for large times. The shape of the interspike interval density is found to depend strongly on input position. The various shapes obtained for different input positions resemble those for real neurons. The coefficient of variation of the interspike interval decreases monotonically as the distance between the input and trigger zone increases. A diffusion approximation for a nerve cell receiving Poisson input is considered and input/output frequency relations obtained for different input sites. The cases of multiple trigger zones and multiple input sites are briefly discussed.     

Generalized Make and Use Framework for Allocation in Life Cycle Assessment

Allocation in life cycle inventory (LCI) analysis is one of the long‐standing methodological issues in life cycle assessment (LCA). Discussion on allocation among LCA researchers has taken place almost in complete isolation from the series of closely related discussions from the 1960s in the field of input?output economics, regarding the supply and use framework. This article aims at developing a coherent mathematical framework for allocation in LCA by connecting the parallel developments of the LCA and the input?output communities. In doing so, the article shows that the partitioning method in LCA is equivalent to the industry‐technology model in input?output economics, and system expansion in LCA is equivalent to the by‐product‐technology model in input?output output economics. Furthermore, we argue that the commodity‐technology model and the by‐product‐technology model, which have been considered as two different models in input?output economics for more than 40 years, are essentially equivalent when it comes to practical applications. It is shown that the matrix‐based approach used for system expansion successfully solves the endless regression problem that has been raised in LCA literature. A numerical example is introduced to demonstrate the use of allocation models. The relationship of these approaches with consequential and attributional LCA models is also discussed.