On geometry of spherical image in Minkowski space-time with timelike type-2 parallel transport frame

In this paper, we investigate a different type of the parallel transport frame in 3-dimensional Minkowski space R^3_1 by using the binormal vector field of a timelike regular curve as common vector field to introduce, and we recall this frame as timelike type-2 parallel transport frame . Also, we present new spherical images and call them as timelike type-2 parallel transport spherical images by translating the induced frame vectors to the center of unit Lorentzian sphere in 3-dimensional Minkowski space R^3_1. Additionally, we obtain the Frenet apparatus of these new spherical images in terms of base curves timelike type-2 parallel transport invariants. Finally, interesting relations are expressed and illustrate an example of the results

(R1977) On Geometry of Equiform Smarandache Ruled Surfaces via Equiform Frame in Minkowski 3-Space

In this paper, some geometric properties of equiform Smarandache ruled surfaces in Minkowski space E13 using an equiform frame are investigated. Also, we give the sufficient conditions that make these surfaces are equiform developable and equiform minimal related to the equiform curvatures and when the equiform base curve contained in a plane or general helix. Finally, we provide an example, such as these surfaces

Special equiform Smarandache curves in Minkowski space-time

A regular non-null curve in Minkowski space-time, whose posi- tion vector is composed by Frenet frame vectors on another regular curve, is called a Smarandache curve [1] . Recently special Smaran- dache curves have been studied by some authors [2–5]

Generalized Smarandache curves of spacelike and equiform spacelike curves via timelike second binormal in

In this paper, we investigate spacelike Smarandache curves recording to the Frenet and the equiform Frenet frame of spacelike base curve with timelike second binormal vector in fourdimensional Minkowski space. Also, we compute the formulas of Frenet and equiform Frenet apparatus recording to the base curve. Furthermore, we give the geometric properties to these curves when is general helix

(R1519) On Some Geometric Properties of Non-null Curves via its Position Vectors in \mathbb{R}_1^3

In this work, the geometric properties of non-null curves lying completely on spacelike surface via its position vectors in the dimensional Minkowski 3-space \mathbb{R}_1^3 are studied. Also, we give a few portrayals for the spacelike curves which lie on certain subspaces of \mathbb{R}_1^3. Finally, we present an application to demonstrate our insights

Family of ruled surfaces generated by equiform Bishop spherical image in Minkowski 3-space

The study of a family of equiform Bishop spherical image ruled surfaces created by some specific curves such as spherical image in Minkowski 3-space using equiform Bishop frame of that curve is presented in this paper. We also offer the necessary criteria for these surfaces to be equiform Bishop developable and equiform Bishop minimum in relation to equiform Bishop curvatures, as well as when the curve is enclosed in a plane. Finally, we provide an example, such as these surfaces

Retinal Vessels Segmentation Techniques and Algorithms: A Survey

Retinal vessels identification and localization aim to separate the different retinal vasculature structure tissues, either wide or narrow ones, from the fundus image background and other retinal anatomical structures such as optic disc, macula, and abnormal lesions. Retinal vessels identification studies are attracting more and more attention in recent years due to non-invasive fundus imaging and the crucial information contained in vasculature structure which is helpful for the detection and diagnosis of a variety of retinal pathologies included but not limited to: Diabetic Retinopathy (DR), glaucoma, hypertension, and Age-related Macular Degeneration (AMD). With the development of almost two decades, the innovative approaches applying computer-aided techniques for segmenting retinal vessels are becoming more and more crucial and coming closer to routine clinical applications. The purpose of this paper is to provide a comprehensive overview for retinal vessels segmentation techniques. Firstly, a brief introduction to retinal fundus photography and imaging modalities of retinal images is given. Then, the preprocessing operations and the state of the art methods of retinal vessels identification are introduced. Moreover, the evaluation and validation of the results of retinal vessels segmentation are discussed. Finally, an objective assessment is presented and future developments and trends are addressed for retinal vessels identification techniques.https://doi.org/10.3390/app802015

Construction of gene regulatory networks using biclustering and bayesian networks

<p>Abstract</p> <p>Background</p> <p>Understanding gene interactions in complex living systems can be seen as the ultimate goal of the systems biology revolution. Hence, to elucidate disease ontology fully and to reduce the cost of drug development, gene regulatory networks (GRNs) have to be constructed. During the last decade, many GRN inference algorithms based on genome-wide data have been developed to unravel the complexity of gene regulation. Time series transcriptomic data measured by genome-wide DNA microarrays are traditionally used for GRN modelling. One of the major problems with microarrays is that a dataset consists of relatively few time points with respect to the large number of genes. Dimensionality is one of the interesting problems in GRN modelling.</p> <p>Results</p> <p>In this paper, we develop a biclustering function enrichment analysis toolbox (BicAT-plus) to study the effect of biclustering in reducing data dimensions. The network generated from our system was validated via available interaction databases and was compared with previous methods. The results revealed the performance of our proposed method.</p> <p>Conclusions</p> <p>Because of the sparse nature of GRNs, the results of biclustering techniques differ significantly from those of previous methods.</p

Two dimensional kinematic surface in Lorentz-Minkowski 5-space with constant scalar curvature

In this paper we analyzed the problem of investigating locally the scalar curvature of the two dimensional kinematic surfaces foliated by the homothetic motion of an eight curve in Lorentz-Minkowski 5-space Ls. We express the scalar curvature of the corresponding two dimensional kinematic surfaces as the quotient of hyperbolic functions {sinh mv, cosh mv }. From that point, we derive the necessary and sufficient conditions that the coefficients of hyperbolic functions vanished identically. Additionally, an example is given to show two dimensional kinematic surfaces with constant scalar curvature

Ex Vivo Optical Properties Estimation for Reliable Tissue Characterization

: Lasers are demonstrating high impact in many medical and biological applications. They have different interaction mechanisms within tissues depending on operational parameters, particularly the wavelength. In addition, the optical properties of the examined tissue (i.e., absorption and scattering properties) influence the efficacy of the applied laser. The development of optical biomedical techniques relies on the examination of tissues’ optical properties, which describe the viability of tissue optical evaluation and the effect of light on the tissue. Understanding the optical properties of tissues is necessary for the interpretation and evaluation of diagnostic data, as well as the prediction of light and energy absorption for therapeutic and surgical applications. Moreover, the accuracy of many applications, including tissue removal and coagulation, depends on the tissues' spectroscopic characteristics. In the current paper, a set of ex vivo absorption and scattering coefficients of different types of biological samples (skin, skull, liver and muscle) at 650 nm laser irradiation were retrieved using an integrating phere system paired with the Kubelka–Munk model. The obtained optical parameters were utilized to acquire the local fluence rate within the irradiated tissues based on the Monte Carlo simulation method and the diffusion approximation of the radiative transfer equation. The obtained results reveal that the optical absorption and scattering coefficients control the light propagation and distribution within biological tissues. Such an understanding refers to system design optimization, light delivery accuracy and the minimization of undesirable physiological effects such as phototoxicity or photobleaching