A mathematical study of a two-regional population growth model

The paper provides a mathematical study of a model of urban dynamics, adjusting to an ecological model proposed by Lotka and Volterra. The model is a system of two first-order non-linear ordinary differential equations. The study proposed here completes the original proof by using the main tools such as a Lyapunov function.     

Automated image segmentation by fractal grey tone functions

A new image segmentation method is presented. It is based on mathematical derivations stemming from both mathematical morphology and fractal geometry. Structures of different nature are most often characterized by a fractal grey tone function, in a certain range of resolutions, with a particular value of the fractal dimension. Our method allows the isolation of such structures. It only requires a series of dilated and eroded grey tone images.     

Medical image segmentation based on level set and isoperimetric constraint

Level set based methods are being increasingly used in image segmentation. In these methods, various shape constraints can be incorporated into the energy functionals to obtain the desired shapes of the contours represented by their zero level sets of functions. Motivated by the isoperimetric inequality in differential geometry, we propose a segmentation method in which the isoperimetric constrain is integrated into a level set framework to penalize the ratio of its squared perimeter to its enclosed area of an active contour. The new model can ensure the compactness of segmenting objects and complete missing or/and blurred parts of their boundaries simultaneously. The isoperimetric shape constraint is free of explicit expressions of shapes and scale-invariant. As a result, the proposed method can handle various objects with different scales and does not need to estimate parameters of shapes. Our method can segment lesions with blurred or/and partially missing boundaries in ultrasound, Computed Tomography (CT) and Magnetic Resonance (MR) images efficiently. Quantitative evaluation also confirms that the proposed method can provide more accurate segmentation than two well-known level set methods. Therefore, our proposed method shows potential of accurate segmentation of lesions for applying in diagnoses and surgical planning.     

Modelling of signalling via G-protein coupled receptors: pathway-dependent agonist potency and efficacy

A mathematical model is constructed to study promiscuous coupling of receptors to G-proteins and to simulate events leading to the activation of multiple effector pathways within a cell. The model is directed at a better understanding of the factors that determine the efficacy and potency of a drug. Assuming that the receptors can exist in multiple conformational states, and allowing for agonist specific conformation, a system of ordinary differential equations is constructed and subsequently pathway-dependent agonist efficacy and potency order is predicted. A simple case of the compartmentalization of receptors and G-proteins is also given, using the current model to illustrate the effects of spatial heterogeneity on the predicted response.     

A SIMPLIFIED METHOD OF DNA DISTRIBUTION ANALYSIS

Current methods of analysing DNA distributions utilize complex mathematical expressions that require the use of large non-linear curve fitting methods and, consequently, large computers. This paper presents a new method of analysing DNA distributions of asynchronously growing or mildly perturbed cells. The S phase fraction is obtained by fitting a second degree polynomial to that part of the distribution, mid S phase, which is not influenced by either the G₁ or the G₂+ M peaks. The method is simple and fast, it exceeds the accuracy of other methods and it can be used on a large desk calculator or mini-computer.     

Reducing activity and differential thermal analysis of enterococci

The reducing activity of 100 Streptococcus faecalis strains, 100 Streptococcus faecium strains and 100 enterococcal strains were studied by the quantitative method. The study revealed that all mobile enterococci, in contrast to S. faecium, reduce 2,3,5-triphenyltetrazolium chloride with the formation of triphenylformasan. Differential thermal analysis also indicated that S. faecalis, S. faecium and mobile enterococci had thermograms with definite mathematical characteristics and could be best differentiated by the indices of their form and the size of S3 areas. The quantitative methods of the investigation of reducing activity and differential thermal analysis can be used for the differentiation of enterococcal species. Mobile enterococci have definite characteristics allowing one to sharply differentiate them from S. faecium and S. faecalis.     

Differential polarization imaging. II. Symmetry properties and calculations

Various differential polarization images or Mueller images of model objects are generated using the equations derived in the previous paper (paper I of this series). These calculated images include models of the higher-order organization of metaphase chromosomes, and show the applicability of the differential polarization imaging method to the elucidation of complex molecular organizations. Then, the symmetry behavior of the Mueller matrix elements upon infinitesimal rotations of the optical components about the optical axis of the imaging system is presented. It is shown that the rotational properties of the Mueller images can be used to eliminate the linear polarization contributions to the M14 and M44 images, which appear when these images are generated with imperfect circular polarizations. The relationships between the 16 bright-field Mueller images for four different media, i.e., linearly and circularly isotropic, circularly anisotropic, linearly anisotropic, and linearly and circularly anisotropic, are also derived. For the first three cases simple relationships between the Mueller images are found and phenomenological equations in terms of the optical coefficients are derived. In the last case there are no specific relationships between the Mueller images and instead we briefly present Schellman and Jensen's method for treating this type of medium. The criterion of spatial resolution between adjacent domains of different optical anisotropy is then derived. It is found that in transitions between domains of opposite anisotropy the classical Rayleigh limit must be replaced by a magnitude criterion which depends on the limits of the sensitivity of the detection. Finally, the feasibility of optical sectioning in differential polarization imaging is demonstrated.     

Analytical stereophotogrammetric determination of three-dimensional knee-joint geometry

An analytical stereophotogrammetric method is introduced to measure the three-dimensional geometry of articular surfaces in vitro. Information of this kind is particularly useful for mathematical joint models and anthropological studies. The method requires no specific equipment, such as a stereocomparator, contrarily to other techniques reported (e.g. Ghosh, 1983) and is relatively simple and inexpensive. The background of the method is outlined in the present paper, and results of accuracy and precision tests are presented. It is shown that an accuracy on the order of 0.2 mm (95% confidence interval) is well feasible in actual knee-joint evaluations, if the measuring procedure is conducted carefully. The method is illustrated by measuring and comparing the articular surface geometries of a bilateral pair of knee joints.     

Untangling the Interplay between Epidemic Spread and Transmission Network Dynamics

The epidemic spread of infectious diseases is ubiquitous and often has a considerable impact on public health and economic wealth. The large variability in the spatio-temporal patterns of epidemics prohibits simple interventions and requires a detailed analysis of each epidemic with respect to its infectious agent and the corresponding routes of transmission. To facilitate this analysis, we introduce a mathematical framework which links epidemic patterns to the topology and dynamics of the underlying transmission network. The evolution, both in disease prevalence and transmission network topology, is derived from a closed set of partial differential equations for infections without allowing for recovery. The predictions are in excellent agreement with complementarily conducted agent-based simulations. The capacity of this new method is demonstrated in several case studies on HIV epidemics in synthetic populations: it allows us to monitor the evolution of contact behavior among healthy and infected individuals and the contributions of different disease stages to the spreading of the epidemic. This gives both direction to and a test bed for targeted intervention strategies for epidemic control. In conclusion, this mathematical framework provides a capable toolbox for the analysis of epidemics from first principles. This allows for fast, in silico modeling--and manipulation--of epidemics and is especially powerful if complemented with adequate empirical data for parameterization.     

基于邻域最大差值与区域合并的油茶毒蛾幼虫图像分割

【目的】油茶树害虫的种类较多,其中油茶毒蛾Euproctis pseudoconspersa幼虫是危害较大的害虫之一。为完成油茶毒蛾幼虫的自动检测需要对其图像进行分割,油茶毒蛾幼虫图像的分割效果直接影响到图像的自动识别。【方法】本文提出了基于邻域最大差值与区域合并的油茶毒蛾幼虫图像分割算法,该方法主要是对相邻像素RGB的3个分量进行差值运算,最大差值若为0,则进行相邻像素合并得出初始的分割图像,根据合并准则进一步合并,得到最终分割结果。【结果】实验结果表明,该算法可以快速有效地将油茶毒蛾幼虫图像中的背景和虫体分割开来。【结论】使用JSEG分割算法、K均值聚类分割算法、快速几何可变形分割算法和本文算法对油茶毒蛾幼虫图像进行分割,将结果进行对比发现本文方法的分割效果最佳,且处理时间较短。     

A Novel Vision Localization Method of Automated Micro-Polishing Robot

Based on photogrammetry technology,a novel localization method of micro-polishing robot,which is restricted withincertain working space,is presented in this paper.On the basis of pinhole camera model,a new mathematical model of visionlocalization of automated polishing robot is established.The vision localization is based on the distance-constraints of featurepoints.The method to solve the mathematical model is discussed.According to the characteristics of gray image,an adaptivemethod of automatic threshold selection based on connected components is presented.The center coordinate of the featureimage point is resolved by bilinear interpolation gray square weighted algorithm.Finally,the mathematical model of testingsystem is verified by global localization test.The experimental results show that the vision localization system in working spacehas high precision.     

用去卷积法提高超声调制光学成像的空间分辨率

超声调制光学成像的空间分辨率取决于光在组织中的散射程度和扫描超声束的聚焦大小。由于组织是强散射介质,实际应用中的超声束都有一定的聚焦宽度(通常是毫米数量级),所以该技术成像空间分辨率一直无法提高。针对这个问题,首次将去卷积图像处理法运用在超声调制光学成像技术中,有效地解决了扫描超声束带来的信号展开,分辨率下降的影响。理论和防真结果表明,处理后的成像分辨率大大提高,图像质量明显改善。该方法无须对系统装置做任何改动,只利用适当的数据处理,就实现了成像超分辨,具有应用价值。     

Making biology count: integrating mathematics into the teaching of inheritance

In this paper, I explore how seamless embedding of four mathematical concepts: counting, ratio, distribution, and statistical significance, into a unit on inheritance enables students to gain a deeper insight into biological phenomena than a qualitative only approach achieves. The topic of Mendelian inheritance is used to illustrate this proposal. An introductory activity is presented that separates the specialized genetics vocabulary from the inheritance process, allowing the initial mathematical relationship to be developed and subsequently followed by the language requirements.     

Differential polarization imaging. I. Theory

A theory of differential polarization imaging is derived using Mueller calculus. It is shown that, for any arbitrary object, 16 images (in general different) can be obtained by combining different incident polarizations of light and measuring the specific polarization components transmitted or scattered by the object. These are called the Mueller images of the object. Mathematical expressions of these images for an object of arbitrary geometry are derived using classical vector diffraction theory and the paraxial and thin lens approximations. The object is described as a collection of point polarizable groups. The electromagnetic fields are calculated using the first Born-Approximation, but extension of the theory to higher-order approximations is shown to be straightforward. These expressions are obtained for the transmission, or bright-field, geometry, and the scattering, or dark-field, configuration. In both cases, the contributions of scattering, absorption, and background illumination to the Mueller images are characterized. The contributions of linear dichroism, circular dichroism, and linear and circular intensity differential scattering to certain Mueller images are established. It is shown that the Mueller images represent a complete two-dimensional mapping of the molecular anisotropy of the object.     

A Neuro-Muscular Elasto-Dynamic Model of the Human Arm Part 1: Model Development

In this paper we develop an elasto-dynamic model of the human arm for use in neuro-muscular control and dynamic interactionstudies.The motivation for this work is to present a case for developing and using non-quasistatic models of humanmusculo-skeletal biomechanics.The model is based on hybrid parameter multiple body system(HPMBS)variational projectionprinciples.In this paper,we present an overview of the HPMBS variational principle applied to the full elasto-dynamic model ofthe arm.The generality of the model allows one to incorporate muscle effects as either loads transmitted through the tendon atpoints of origin and insertion or as an effective torque at a joint.Though the technique is suitable for detailed bone and jointmodeling,we present in this initial effort only simple geometry with the bones discretized as Rayleigh beams with elongation,while allowing for large deflections.Simulations demonstrate the viability of the mcthod for use in the companion paper and infuture studies.     

基于知识的颅内出血（ICH）三维医学图像分割方法

本文描述一种基于知识的三维医学图像自动分割方法,用于进行人体颅内出血(Intracranial Hemorrhage,ICH)的分割和分析。首先,数字化CT胶片,并自动对数字化后的胶片按照有无异常分类。然后,阀值结合模糊C均值聚类算法将图像分类成多个具有统一亮度的区域。最后,在先验知识以及预定义的规则的基础上,借助基于知识的专家系统将各个区域标记为背景、钙化点、血肿、颅骨、脑干。     

An iterative procedure to estimate muscle lines of action in vivo

A method is described to estimate the line of action of muscles in the three-dimensional space from serial images of parallel muscle sections obtained in vivo by means of CT or MRI scanning. The external shape of a muscle, reconstructed from the series of parallel sections, is mathematically divided into a series of imaginary slices directed arbitrarily in the three-dimensional space. The line of action is estimated initially as a regression line through the centroids of these mathematical slices. A new series of mathematical slices is constructed perpendicular to the regression line and a new estimate of the line of action is obtained from their centroids. This procedure is repeated until the estimated line of action is perpendicular to the mathematical slices; it can then be considered as a reliable estimate of the line of action. The accuracy of the method has been tested for various reconstruction parameters and muscle shapes. The results of these tests show that the accuracy is relatively independent of the direction in which the sectional images have been made and that, except for relatively short and thick muscles, the estimated lines of action deviated less than about 2 degrees from the theoretical one. The presented method is a relatively simple mathematical technique which can be used easily for muscles reconstructed in vivo from routinely obtained sectional MRI or CT images.     

EXTRACT: A program to extract three-dimensional coordinates from stereo diagrams of proteins

The program EXTRACT has been developed to extract accurate three-dimensional coordinates from published stereo α-carbon diagrams of protein structures. The approach is based on the display of scanned images of the left and right eye views of the diagram on a stereo-equipped workstation, allowing construction of a molecular model using the diagram as a guide. A number of structural checks assess the building, including probability maps derived for α-carbon geometry in protein structures. The procedure has also been extended to produce less accurate models from mono images.