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In this paper, we consider a class of expanding flows of closed, smooth, uniformly convex hypersurfaces in Euclidean Rn+1 with speed uα ƒβ (α, β ∈ R1), where u is the support function of the hypersurface, ƒ is a smooth, symmetric, homogenous of degree one, positive function of the principal curvature radii of the hypersurface. If α ≤ 0 < β ≤ 1−α, we prove that the flow has a unique smooth and uniformly convex solution for all time, and converges smoothly after normalization, to a round sphere centered at the origin. [ABSTRACT FROM AUTHOR]

In the 3-D Minkowski space， the spacelike curves can be divided into the spacelike curves of the first kind， the second kind and the pseudo null curves according to the nature of their principal normal vectors. The representation forms of pseudo null curves were surveyed. First， two structure functions were defined by the concept of pseudo null curves. Then the Frenet frames and the curvature functions were expressed by the defined structure functions. At the same time， the relationship between the two structure functions were found. Finally， the representation forms of pseudo null curves with constant curvatures and their structure functions were given， furthermore， the corresponding examples and their graphs were given. [ABSTRACT FROM AUTHOR]

• Centromere identification by concave function and weighted shortest path calculation. • SVM for classifying centromere and non-centromere region in chromosomes. • Chromosome abnormality detection based on centromere position. • Comparative analysis of MAT, Projection vector and concavity function. The most significant information of the shape of any image/object is concentrated in curvature regions along the contour and objects boundaries rather than uniformly distributed contour. The points belonging to greater magnitude of curvature gives more meaningful information about the shape of an object. The sign of the curvature can be positive (convex) and negative (concave), the negative curvature information is most significant for segmentation. The contour and region based geometry gives a better visual representation of the shape of an object and helps in identifying the centromere position in chromosomes. Centromere of a chromosome is the constriction point which divides the chromosome into two sections or arms. The two arms are p arm (short arm) and q arm (long arm). The size of the arms are calculated with respect to the position of the centromere. The centromere is identified using boundary concavity method which helps in detecting the dominant points (centromere points) in chromosomes. The method uses the concave function and weighted shortest path calculation for centromere detection. SVM classifier is used for improving the accuracy in detecting the centromere of the chromosomes. As the classifier is binary classifier, it helps in recognizing the centromere and non-centromere regions in chromosomes. Comparative analysis is performed with two other methods (i) Medial Axis Transform (MAT) and (ii) Projection Vector. Boundary concavity proves to be efficient for straight, bent and severely bent chromosomes. [ABSTRACT FROM AUTHOR]

In this work, we define a quaternionic osculating curves and give the conditions for curves to be osculating with the help of curvature functions. [ABSTRACT FROM AUTHOR]

In this paper, we propose a method how to manage the convergence of Newton's method if its iteration process encounters a local extremum. This idea establishes the osculating circle at a local extremum. It then uses the radius of the osculating circle also known as the radius of curvature as an additional number of the local extremum. It then takes that additional number and combines it with the local extremum. This is then used as an initial guess in finding a root near to that local extremum. This paper will provide several examples which demonstrate that the proposed idea is successful and they perform to fulfill the aim of this paper. [ABSTRACT FROM AUTHOR]

We investigate the elliptic curves, expressed in the Weierstrass form, from a differential geometric viewpoint. The curvature function is carefully studied and bounds for the number of vertices of the elliptic curves are given. As a generalization, a program for the classification of algebraic curves is sketched, using geometric invariants. [ABSTRACT FROM AUTHOR]

In this paper, we first consider a class of expanding flows of closed, smooth, star-shaped hypersurface in Euclidean space R n + 1 with speed u α f − β , where u is the support function of the hypersurface, f is a smooth, symmetric, homogenous of degree one, positive function of the principal curvatures of the hypersurface on a convex cone. For α ⩽ 0 < β ⩽ 1 − α , we prove that the flow has a unique smooth solution for all time, and converges smoothly after normalization, to a sphere centered at the origin. In particular, the results of Gerhardt [16] and Urbas [40] can be recovered by putting α = 0 and β = 1 in our first result. If the initial hypersurface is convex, this is our previous work [11]. If α ⩽ 0 < β < 1 − α and the ambient space is hyperbolic space H n + 1 , we prove that the flow ∂ X ∂ t = (u α f − β − η u) ν has a longtime existence and smooth convergence to a coordinate slice. The flow in H n + 1 is equivalent (up to an isomorphism) to a re-parametrization of the original flow in R n + 1 case. Finally, we find a family of monotone quantities along the flows in R n + 1. As applications, we give a new proof of a family of inequalities involving the weighted integral of k th elementary symmetric function for k -convex, star-shaped hypersurfaces, which is an extension of the quermassintegral inequalities in [20]. [ABSTRACT FROM AUTHOR]

This paper addresses the problem of scan matching which is highly indispensable for mobile robot systems based on range sensors. Recently, polar scan matching (PSM) has been used in solving the problem because it is accurate and fast enough to be performed in real time. However, the performance of PSM degenerates when the portion of scan data from dynamic objects is excessively large. This paper proposes a scan restoration method to overcome this problem and improve the performance of PSM in dynamic environments. The proposed method restores the scan data from dynamic objects to appropriate scan data from static objects. First, whole scan data is segmented and classified as static and dynamic objects. Next, curvature functions are extracted from the classified segments and smoothed by interpolating the segments indicating dynamic obstacles. PSM with the proposed method was tested and evaluated in various real dynamic environments, which reveals that the proposed method can improve the performance of PSM in dynamic environments. [ABSTRACT FROM AUTHOR]

This paper, retrieving surgical data recorded in the Pediatric Cardiac Care Consortium between 1985-2004, identifies an inverse relationship between in-hospital mortality and pediatric cardiac surgical volume in small and medium-sized centers. Similar inverse relationship was found for both low and high complexity cases after stratifying the data by risk category using the Risk Adjustment for Congenital Heart Surgery (RACHS). Given the relationship, a threshold on the volume to reach the lowest attainment of surgical mortality is suggested when is attainable. [ABSTRACT FROM AUTHOR]

Abstract: The diode ideality factor is an important parameter in the description of device’s electrical behavior. Our goal in this work is to find a practical procedure for determination of diode ideality factors of heterojunction devices which contain parallel connected diodes series with resistance in the equivalent circuit. For this purpose, Beta (β) model is applied to experimental current–voltage (I–V) data of the heterojunction (wenrun 10mm white LED) structure. Diodes’ ideality factors are easily determined by using β model. This model lights on potential barrier number in the device without making any additional experimental measurements. Analyzing the LED’s I–V curves with the help of β model shows the ideality factors larger than unity to result from lateral fluctuations of the local characteristic tunneling energies. Results obtained from β model are consistent with experimental data. [Copyright &y& Elsevier]

Abstract: Most of the techniques have been developed to extract diode ideality factor utilize the one-exponential diode model. However, for a correct description of two linear regions in the log I–V (current–voltage) graph of unipolar devices, one-exponential diode model is not sufficient. We have derived a new model which is named Beta (β) model for the calculation of diode ideality factor from dark current–voltage characteristic of the device (p–i–n device). Results obtained from our model are considerably in compliance with the experimental data. [Copyright &y& Elsevier]

Through an investigation of normal curvature functions for influence graphs of a family of perturbed models, we develop the concept of local conditional influence. This concept can be used to study masking and boosting effects in local influence. We identify the situation under which the influence graph of the unperturbed model contains all the information on these effects. The linear regression model is used for illustration and it is shown that the concept developed is consistent with Lawrance's (1995) approach of conditional influence in Cook's distance. [ABSTRACT FROM AUTHOR]

This paper presents a method to segment, characterise and pair a set of chromosomes in a cell of an eukaryotic organism. This method yields several new features: (i) chromosomes are captured at non-uniform resolution to minimise the problem instance; (ii) segmentation is adaptively conducted by means of a hierarchical structure in a fast way; (iii) the curvature of each chromosome is studied at high resolution by means of attentive steps; (iv) a very short and uncorrelated feature vector is extracted from curvature by analysing its spectral components; and (v) a multistage benchmark classifier is used to pair chromosomes according to shape and banding. The method has been tested with publicly available databases. Results were successfully compared to manual karyotypes. [ABSTRACT FROM AUTHOR]

This paper presents a planar shape recognition method for content-based image retrieval in multimedia databases. Shapes are characterised by their corners, which are extracted from the curvature function of their contours. Then, corner sequences are compared by using Hidden Markov Models so that the process is resistant against corner shifting and loss. The proposed method has been successfully tested over publicly available databases. [Copyright &y& Elsevier]