A discrete time neural network model with spiking neurons

We derive rigorous results describing the asymptotic dynamics of a discrete time model of spiking neurons introduced in Soula et al. (Neural Comput. 18, 1, 2006). Using symbolic dynamic techniques we show how the dynamics of membrane potential has a one to one correspondence with sequences of spikes patterns (“raster plots”). Moreover, though the dynamics is generically periodic, it has a weak form of initial conditions sensitivity due to the presence of a sharp threshold in the model definition. As a consequence, the model exhibits a dynamical regime indistinguishable from chaos in numerical experiments.      

基于替代数据思想的复杂度归一化方法及其在心电信号分析中的应用

基于替代数据(Surrogate)思想的复杂度归一化方法,克服了一般复杂度对信号采样长度与采样频率的敏感性。文章对在生物医学信号复杂度分析中最有潜在应用价值的近似熵和C0复杂度进行了归一化。应用该方法可以有效地反映人体心脏某些病理状态之间的差别。同时,通过比较各种复杂度指标发现,C0复杂度和近似熵对采样长度的敏感性最弱,适用于短数据量的信号分析。     

A training whole-heart model for simulating propagation and ECG patterns

The forward problem of electrocardiography describes the spatio-temporal source–field relationship generating the body surface potential (BSP) and, thus, the electrocardiogram (ECG). The paper presents a ventricular and atrial model for simulating cardiac de- and repolarization and the P-, QRS- and T-wave. The atria and the ventricles are coupled, so that electroanatomical function can be simulated at ones. Movement and contraction are not taken into account while an individual geometry, fibre architecture and ECG sensor arrangement including the Wilson central terminal (WCT) as common reference were considered. This in silico whole-heart model can be used for detailed investigations of the nature of the ECG for the normal beat, arrhythmias, ischemia and infarction. In addition, this model was used as a reference tool for developing and testing different electrocardiographic inverse approaches.     

Wavelet threshold based TDL and TDR algorithms for real-time ECG signal compression

In this paper, two novel and simple, target distortion level (TDL) and target data rate (TDR), Wavelet threshold based ECG compression algorithms are proposed for real-time applications. The issues on the use of objective error measures, such as percentage root mean square difference (PRD) and root mean square error (RMSE) as a quality measures, in quality controlled/guranteed algorithm are investigated with different sets of experiments. For the proposed TDL and TDR algorithm, data rate variability and reconstructed signal quality is evaluated under different ECG signal test conditions. Experimental results show that the TDR algorithm achieves the required compression data rate to meet the demands of wire/wireless link while the TDL algorithm does not. The compression performance is assessed in terms of number of iterations required to achieve convergence and accuracy, reconstructed signal quality and coding delay. The reconstructed signal quality is evaluated by correct diagnosis (CD) test through visual inspection. Three sets of ECG data from three different databases, the MIT-BIH Arrhythmia (mita) (F_s=360 Hz, 11 b/sample), the Creighton University Ventricular Tachyarrhythmia (cuvt) (F_s=250 Hz, 12 b/sample) and the MIT-BIH Supraventricular Arrhythmia (mitsva) (F_s=128 Hz, 10 b/sample), are used for this work. For each set of ECG data, the compression ratio (CR) range is defined. The CD value of 100% is achieved for CR ≤12, CR ≤ 8 and CR ≤ 4 for data from mita, cuvt and mitsva databases, respectively. The experimental results demonstrate that the proposed TDR algorithm is suitable for real-time applications.     

Dynamical systems analysis of arterial blood pressure signals in relation to heart rate fluctuations in chick embryos

We attempted a new approach based on a modern dynamical system theory to reconstruct the arterial blood pressure signals in relation to heart rate fluctuations of developing chick embryos. The dynamical systems approach in general is to model a phenomenon that is presented by a single time series record and approximate the dynamical property (e.g. heart rate fluctuations) of a system based only on information contained in a single-variable (arterial blood pressure) of the system. The time-series data of the arterial blood pressure was reconstructed in 3-dimensional space to draw characteristic orbits. Since the reconstructed orbits of the blood pressure should retain information contained in the pressure signals, we attempted to derive instantaneous heart rate (IHR) from the reconstructed orbits. The derived IHR presenting HR fluctuations coincided well with the IHR obtained conventionally from the peak-to-peak time intervals of the maximum blood pressure. Movements of the reconstructed orbits of the arterial blood pressure in 3-dimensional space reflected HR fluctuations (i.e. transient decelerations and accelerations).     

A novel approach for removing ECG interferences from surface EMG signals using a combined ANFIS and wavelet

In recent years, the removal of electrocardiogram (ECG) interferences from electromyogram (EMG) signals has been given large consideration. Where the quality of EMG signal is of interest, it is important to remove ECG interferences from EMG signals. In this paper, an efficient method based on a combination of adaptive neuro-fuzzy inference system (ANFIS) and wavelet transform is proposed to effectively eliminate ECG interferences from surface EMG signals. The proposed approach is compared with other common methods such as high-pass filter, artificial neural network, adaptive noise canceller, wavelet transform, subtraction method and ANFIS. It is found that the performance of the proposed ANFIS–wavelet method is superior to the other methods with the signal to noise ratio and relative error of 14.97 dB and 0.02 respectively and a significantly higher correlation coefficient (p < 0.05).     

A mathematical model for progression and heterogeneity in colorectal cancer dynamics

This paper deals with the development of a mathematical model that describes cancer dynamics at the cellular scale.The selected case study concerns colon and rectum cancer, which originates in colorectal crypts. Cells inside the crypts are assumed to be organized according to a compartmental-like arrangement and to be homogeneously mixing. A mathematical model for cancer progression is proposed here. This model describes the generation of multiple clonal sub-populations of cells at different progression stages in a single crypt.Asymptotic analysis and simulations are developed with an exploratory aim. The obtained results offer some insights into the role played by mutation, proliferation and differentiation phenomena on cancer dynamics. In particular, the acquisition of an additional growing power and a reduction for cellular differentiation seem more likely to be the driving force behind carcinogenesis rather than an increase in the mutation rate. The mutation rate instead seems to affect progression dynamics and intra-tumor heterogeneity. The role played by cells, at different differentiation stages, in the onset and progression of colorectal cancer is highlighted. The results support the fact that stem cells play a key role in cancer development and the idea that transit-amplifying cells could also take on an active role in carcinogenesis.     

A distance-based dynamical transition analysis of time series signals and application to biological systems

This study demonstrates an application of distance-based numerical measures to the phase space of time series signals, in order to obtain a temporal analysis of complex dynamical systems. This method is capable of detecting alterations appearing in the characters of the deterministic dynamical systems and provides a simple tool for the real-time analysis of time series data obtained from a complex dynamical system even with black box functionality. The study presents a possible application of the method in the dynamical transition analysis of real EEG records from epilepsy patients.     

生态足迹改进模型及在江苏省耕地利用评价中的应用

将能值分析理论引入生态足迹的研究中,建立了改进的生态足迹模型,并应用于江苏省耕地利用的可持续性评价,同时用改进模型和传统模型对江苏省耕地生态足迹进行比较。结果表明:改进模型和传统模型的江苏省耕地生态赤字分别为0.224和0.06hm2·人-1;耕地生态可持续指数分别为0.29和0.41;江苏省的耕地利用处于不可持续状态。与传统模型相比,改进生态足迹模型的研究结果更接近江苏省的实际情况。     

Dynalets: A new method for modelling and compressing biological signals. Applications to physiological and molecular signals

The biological information coming from electrophysiologic sensors like ECG, pulse sensor or from molecular signal devices like NMR spectrometry has to be visualized and manipulated in a compressed way for an efficient medical use by clinicians, if stored in scientific data bases or in personalized patient records repositories. Here, we define a new transform called Dynalet based on Liénard ordinary differential equations susceptible to model the mechanism at the source of the studied signal, and we propose to apply this new technique first to the modelling and compression of real biological periodic signals like ECG and pulse rhythm. We consider that the cardiovascular activity results from the summation of cellular oscillators located in the cardiac sinus node and we show that, as a result, the van der Pol oscillator (a particular Liénard system) fits well the ECG signal and the pulse signal. The reconstruction of the original signal (pulse or ECG) using Dynalet transform is then compared with that of Fourier, counting the number of parameters to be set for obtaining an expected signal-to-noise ratio. Then, we apply the Dynalet transform to the modelling and compression of molecular spectra obtained by protein NMR spectroscopy. The reconstruction of the original signal (peak) using Dynalet transform is again compared with that of Fourier. After reconstructing visually the peak, we propose to periodize the signal and give it to hear, the whole process being called the protein “stethoscope”.     

A model for slow axonal transport and its application to neurofilamentous neuropathies

A model for slow axonal transport is developed in which the essential features are reversible binding of cytoskeletal elements and of soluble cytosolic proteins to each other and to motile elements such as actin microfilaments. Computer simulation of the equations of the model demonstrate that the model can account for many of the features of the SCa and SCb waves observed in pulse experiments. The model also provides a unified explanation for the increase and decrease of neurofilament transport rates observed in various toxicant-induced neuropathies.     

A model for one-dimensional morphoelasticity and its application to fibroblast-populated collagen lattices

The mechanical behaviour of solid biological tissues has long been described using models based on classical continuum mechanics. However, the classical continuum theories of elasticity and viscoelasticity cannot easily capture the continual remodelling and associated structural changes in biological tissues. Furthermore, models drawn from plasticity theory are difficult to apply and interpret in this context, where there is no equivalent of a yield stress or flow rule. In this work, we describe a novel one-dimensional mathematical model of tissue remodelling based on the multiplicative decomposition of the deformation gradient. We express the mechanical effects of remodelling as an evolution equation for the effective strain, a measure of the difference between the current state and a hypothetical mechanically relaxed state of the tissue. This morphoelastic model combines the simplicity and interpretability of classical viscoelastic models with the versatility of plasticity theory. A novel feature of our model is that while most models describe growth as a continuous quantity, here we begin with discrete cells and develop a continuum representation of lattice remodelling based on an appropriate limit of the behaviour of discrete cells. To demonstrate the utility of our approach, we use this framework to capture qualitative aspects of the continual remodelling observed in fibroblast-populated collagen lattices, in particular its contraction and its subsequent sudden re-expansion when remodelling is interrupted.     

A modified active Brownian dynamics model using asymmetric energy conversion and its application to the molecular motor system

We consider a modified energy depot model in the overdamped limit using an asymmetric energy conversion rate, which consists of linear and quadratic terms in an active particle’s velocity. In order to analyze our model, we adopt a system of molecular motors on a microtubule and employ a flashing ratchet potential synchronized to a stochastic energy supply. By performing an active Brownian dynamics simulation, we investigate effects of the active force, thermal noise, external load, and energy-supply rate. Our model yields the stepping and stalling behaviors of the conventional molecular motor. The active force is found to facilitate the forwardly processive stepping motion, while the thermal noise reduces the stall force by enhancing relatively the backward stepping motion under external loads. The stall force in our model decreases as the energy-supply rate is decreased. Hence, assuming the Michaelis–Menten relation between the energy-supply rate and the an ATP concentration, our model describes ATP-dependent stall force in contrast to kinesin-1.     

A novel method for quantifying overdispersion in count data and its application to farmland birds

The statistical modelling of count data permeates the discipline of ecology. Such data often exhibit overdispersion compared with a standard Poisson distribution, so that the variance of the counts is greater than that of the mean. Whereas modelling to reveal the effects of explanatory variables on the mean is commonplace, overdispersion is generally regarded as a nuisance parameter to be accounted for and subsequently ignored. Instead, we propose a method that models the overdispersion as a biologically interesting property of a data set and show how novel inference is provided as a result. We adapted the double hierarchical generalized linear model approach to create an easily extendible model structure that quantifies the influence of explanatory variables on the overdispersion of count data, and apply it to farmland birds. These data were from a study within Irish agricultural ecosystems, in which total bird species abundance and the abundance of farmland indicator species were compared on dairy and non‐dairy farms in the winter and breeding seasons. In general, overdispersion in bird counts was greater on dairy farms than on non‐dairy farms, and for total bird numbers, overdispersion was greatest on dairy farms in winter. Our code is fitted using the Bayesian package Rstan, and we make all code and data available in a GitHub repository. Within a Bayesian framework, this approach facilitates a meaningful quantification of the effects of categorical explanatory variables on any response variable with a tendency to overdispersion that has a meaningful biological or ecological explanation.     

A constitutive model for two-dimensional soft tissues and its application to experimental data

A constitutive relation proposed by Shoemaker (Ph.D. dissertation, 1984) to model the mechanical behavior of membraneous or two-dimensional soft tissues is described. Experiments by Schneider (Ph.D. dissertation, 1982) on human skin and Lee et al. (Am. J. Physiol., 249, H222-H230, 1985) on canine pericardium, and the application of the constitutive model to biaxial stress-strain data from these experiments, are discussed. Some experimental data and predictions of the model obtained by curvefitting are presented for comparison. Values of material parameters are also presented. It is concluded that the constitutive model is well able to fit results of individual tests, and that its generality (judged by consistency of parameters from test to test of the same specimen), though not complete, does compare favorably with some other results presented in the literature.     

A hydraulic-photosynthetic model based on extended HLH and its application to Coast redwood (Sequoia sempervirens)

Although recent investigations [Ryan, M.G., Yoder, B.J., 1997. Hydraulic limits to tree height and tree growth. Bioscience 47, 235-242; Koch, G.W., Sillett, S.C.,Jennings, G.M.,Davis, S.D., 2004. The limits to tree height. Nature 428, 851-854; Niklas, K.J., Spatz, H., 2004. Growth and hydraulic (not mechanical) constraints govern the scaling of tree height and mass. Proc. Natl Acad. Sci. 101, 15661-15663; Ryan, M.G., Phillips, N., Bond, B.J., 2006. Hydraulic limitation hypothesis revisited. Plant Cell Environ. 29, 367-381; Niklas, K.J., 2007. Maximum plant height and the biophysical factors that limit it. Tree Physiol. 27, 433-440; Burgess, S.S.O., Dawson, T.E., 2007. Predicting the limits to tree height using statistical regressions of leaf traits. New Phytol. 174, 626-636] suggested that the hydraulic limitation hypothesis (HLH) is the most plausible theory to explain the biophysical limits to maximum tree height and the decline in tree growth rate with age, the analysis is largely qualitative or based on statistical regression. Here we present an integrated biophysical model based on the principle that trees develop physiological compensations (e.g. the declined leaf water potential and the tapering of conduits with heights [West, G.B., Brown, J.H., Enquist, B.J., 1999. A general model for the structure and allometry of plant vascular systems. Nature 400, 664-667]) to resist the increasing water stress with height, the classical HLH and the biochemical limitations on photosynthesis [von Caemmerer, S., 2000. Biochemical Models of Leaf Photosynthesis. CSIRO Publishing, Australia]. The model has been applied to the tallest trees in the world (viz. Coast redwood (Sequoia sempervirens)). Xylem water potential, leaf carbon isotope composition, leaf mass to area ratio at different heights derived from the model show good agreements with the experimental measurements of Koch et al. [2004. The limits to tree height. Nature 428, 851-854]. The model also well explains the universal trend of declining growth rate with age.     

A block-free hidden Markov model for genotypes and its application to disease association.

We present a new stochastic model for genotype generation. The model offers a compromise between rigid block structure and no structure altogether: It reflects a general blocky structure of haplotypes, but also allows for "exchange" of haplotypes at nonboundary SNP sites; it also accommodates rare haplotypes and mutations. We use a hidden Markov model and infer its parameters by an expectation-maximization algorithm. The algorithm was implemented in a software package called HINT (haplotype inference tool) and tested on 58 datasets of genotypes. To evaluate the utility of the model in association studies, we used biological human data to create a simple disease association search scenario. When comparing HINT to three other models, HINT predicted association most accurately.     

A validated bioenergetics model for ruffe Gymnocephalus cernuus and its application to a northern lake

A bioenergetics model was constructed for ruffe Gymnocephalus cernuus , and the model was used to estimate the food consumption of a native G. cernuus stock in Pyhäjärvi, a large mesotrophic lake in south-west Finland. The parameters for the bioenergetics model were determined through laboratory experiments conducted at several temperatures between 5 and 22° C for different sized G. cernuus (from 6 to 27 g). The model was verified and validated with independent laboratory growth experiments. The validated model was applied to field data from Pyhäjärvi to estimate the food consumption of G. cernuus and its effects on the zoobenthos community during the years 2002–2004. The total annual food consumption of the G. cernuus stock ranged from 11·6 to 15·7 g m⁻² (wet mass). Chironomidae was the most abundant prey, 81% of the total consumption. The annual total production of zoobenthos in Pyhäjärvi was 15·2 g m⁻² (wet mass). Therefore, it can be concluded that G. cernuus stock is likely to exert a significant influence on the zoobenthos community in this lake, indicating a potential role of G. cernuus as an influential invasive species in many freshwater ecosystems in Europe and North America.     

A Poisson model of sequence comparison and its application to coronavirus phylogeny

In this paper, we propose two metrics to compare DNA and protein sequences based on a Poisson model of word occurrences. Instead of comparing the frequencies of all fixed-length words in two sequences, we consider (1) the probability of ‘generating’ one sequence under the Poisson model estimated from the other; (2) their different expression levels of words. Phylogenetic trees of 25 viruses including SARS-CoVs are constructed to illustrate our approach.