Constitutive laws for strong geometric non-linearity

This paper is divided into two different parts. The first one provides a brief introduction to the fractal geometry with some simple illustrations in fluid mechanics. We thought it would be helpful to introduce the reader into this relatively new approach to mechanics that has not been sufficiently explored by engineers yet. Although in fluid mechanics, mainly in problems of percolation and binary flows, the use of fractals has gained some attention, the same is not true for solid mechanics, from the best of our knowledge. The second part deals with the mechanical behavior of thin wires subjected to very large deformations. It is shown that starting to a plausible conjecture it is possible to find global constitutive equations correlating geometrical end energy variables with the fractal dimension of the solid subjected to large deformations. It is pointed out the need to complement the present proposal with experimental work.

Nuclear morphometry, apoptotic and mitotic indices, and tubular differentiation in Libyan breast cancer

Aims of this study were to evaluate the relations of nuclear morphometry, mitotic and apoptotic indices, and tubular differentiation with clinicopathological features and survival rate in Libyan women. The data were compared with corresponding results on Finnish, and Nigerian female breast cancer patients. Histological samples of breast cancer (BC) from 131 patients were retrospectively studied. Mitotic activity indices (MAI and SMI), apoptotic index (AI), and fraction of fields with tubular differentiation (FTD) were estimated. Samples were also studied by computerized nuclear morphometry, such as mean nuclear area (MNA). Demographic and clinicopathological features were analyzed from 234 patients. The Libyan BC was dominantly premenopausal, and aggressive in behavior. There were statistically significant correlations between the mean nuclear area, fraction of fields with tubular differentiation, apoptotic index and proliferative indices, and most clinicopathological features. The highest significances were shown between lymph node status and the proliferative and apoptotic indices (p=0.003 with SMI, and p=0.005 with AI). There were significant associations between clinical stage and SMI and AI (p=0.002 and 0.009, respectively). The most significant associations with grade were observed with MNA and FTD (p<0.0001 and 0.001, respectively). The proliferative differences between Libyan, Nigerian and Finnish populations were prominent. These indices in Libyan were lower than in Nigerian, but higher than in Finnish patients. The Libyan patients’ AI is slightly higher than in Nigeria, but much higher than in Finland. The differences between countries may be associated with the known variation in the distribution of genetic markers in these populations. The results also indicated that morphometric factors can be reliable prognostic indicators in Libyan BC patients.

Morphometry and acetylcholinesterase activity of the myenteric plexus of the wild mouse Calomys callosus

The myenteric plexus of the digestive tract of the wild mouse Calomys callosus was examined using a histochemical method that selectively stains nerve cells, and the acetylcholinesterase (AChE) histochemical technique in whole-mount preparations. Neuronal density was 1,500 ± 116 neurons/cm2 (mean ± SEM) in the esophagus, 8,900 ± 1,518 in the stomach, 9,000 ± 711 in the jejunum and 13,100 ± 2,089 in the colon. The difference in neuronal density between the esophagus and other regions was statistically significant. The neuron profile area ranged from 45 to 1,100 µm2. The difference in nerve cell size between the jejunum and other regions was statistically significant. AChE-positive nerve fibers were distributed within the myenteric plexus which is formed by a primary meshwork of large nerve bundles and a secondary meshwork of finer nerve bundles. Most of the nerve cells displayed AChE activity in the cytoplasm of different reaction intensities. These results are important in order to understand the changes occurring in the myenteric plexus in experimental Chagas' disease

Coronary fat content evaluated by morphometry in patients with severe atherosclerosis has no relation with serum lipid levels

The relationship between lipid serum levels and coronary atherosclerotic plaque fat content was studied in 51 necropsy patients. Serum lipids were measured by standard techniques, during life, in the absence of lipid-lowering drugs. Intima, intimal fat and media areas were measured using a computerized system in cryosections of the odd segments of the right, anterior descending and circumflex coronary arteries stained with Sudan-IV. Mean intimal and lipid areas were 5.74 ± 1.98 and 1.22 ± 0.55 mm² (22.12 ± 8.48%) in 26 cases with high cholesterol (³200 mg/dL) and 4.98 ± 1.94 and 1.16 ± 0.66 mm² (22.75 ± 9.06%) in 25 cases with normal cholesterol (<200 mg/dL; P > 0.05). Patients with high levels of low-density lipoprotein (³130 mg/dL, N = 15) had a higher intima/media area ratio than those with normal levels of low-density lipoprotein (<130 mg/dL, N = 13, P < 0.01). No significant difference in the morphometrical variables was found in groups with high or low serum levels of triglycerides (³200 mg/dL, N = 13 vs <200 mg/dL, N = 36) or high-density lipoprotein (³35 mg/dL, N = 11 vs <35 mg/dL, N = 17). The association between the morphological measurements and serum levels of cholesterol, its fractions, and triglycerides was also tested and the correlation coefficients were low. Although high cholesterol is a risk factor, we show here that in patients with severe atherosclerosis blood cholesterol and triglyceride levels seem to have little influence on coronary lipid content, indicating that other factors may contribute to arterial lipid deposition and plaque formation.

Longitudinal brain volumetric changes during one year in non-elderly healthy adults: a voxel-based morphometry study

Previous cross-sectional magnetic resonance imaging (MRI) studies of healthy aging in young adults have indicated the presence of significant inverse correlations between age and gray matter volumes, although not homogeneously across all brain regions. However, such cross-sectional studies have important limitations and there is a scarcity of detailed longitudinal MRI studies with repeated measures obtained in the same individuals in order to investigate regional gray matter changes during short periods of time in non-elderly healthy adults. In the present study, 52 healthy young adults aged 18 to 50 years (27 males and 25 females) were followed with repeated MRI acquisitions over approximately 15 months. Gray matter volumes were compared between the two times using voxel-based morphometry, with the prediction that volume changes would be detectable in the frontal lobe, temporal neocortex and hippocampus. Voxel-wise analyses showed significant (P < 0.05, family-wise error corrected) relative volume reductions of gray matter in two small foci located in the right orbitofrontal cortex and left hippocampus. Separate comparisons for males and females showed bilateral gray matter relative reductions in the orbitofrontal cortex over time only in males. We conclude that, in non-elderly healthy adults, subtle gray matter volume alterations are detectable after short periods of time. This underscores the dynamic nature of gray matter changes in the brain during adult life, with regional volume reductions being detectable in brain regions that are relevant to cognitive and emotional processes.

Reliable computation for geometric models

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A Cryptosystem Using the Concepts of Algebraic Geometric Code

Cryptosystem using linear codes was developed in 1978 by Mc-Eliece. Later in 1985 Niederreiter and others developed a modified version of cryptosystem using concepts of linear codes. But these systems were not used frequently because of its larger key size. In this study we were designing a cryptosystem using the concepts of algebraic geometric codes with smaller key size. Error detection and correction can be done efficiently by simple decoding methods using the cryptosystem developed. Approach: Algebraic geometric codes are codes, generated using curves. The cryptosystem use basic concepts of elliptic curves cryptography and generator matrix. Decrypted information takes the form of a repetition code. Due to this complexity of decoding procedure is reduced. Error detection and correction can be carried out efficiently by solving a simple system of linear equations, there by imposing the concepts of security along with error detection and correction. Results: Implementation of the algorithm is done on MATLAB and comparative analysis is also done on various parameters of the system. Attacks are common to all cryptosystems. But by securely choosing curve, field and representation of elements in field, we can overcome the attacks and a stable system can be generated. Conclusion: The algorithm defined here protects the information from an intruder and also from the error in communication channel by efficient error correction methods.

Geometric Algebra and Einstein’s Electron

This thesis entitled Geometric algebra and einsteins electron: Deterministic field theories .The work in this thesis clarifies an important part of Koga’s theory.Koga also developed a theory of the electron incorporating its gravitational field, using his substitutes for Einstein’s equation.The third chapter deals with the application of geometric algebra to Koga’s approach of the Dirac equation. In chapter 4 we study some aspects of the work of mendel sachs (35,36,37,).Sachs stated aim is to show how quantum mechanics is a limiting case of a general relativistic unified field theory.Chapter 5 contains a critical study and comparison of the work of Koga and Sachs. In particular, we conclude that the incorporation of Mach’s principle is not necessary in Sachs’s treatment of the Dirac equation.

Some characterization problems associated with the bivariate exponential and geometric distributions

It is highly desirable that any multivariate distribution possessescharacteristic properties that are generalisation in some sense of the corresponding results in the univariate case. Therefore it is of interest to examine whether a multivariate distribution can admit such characterizations. In the exponential context, the question to be answered is, in what meaning— ful way can one extend the unique properties in the univariate case in a bivariate set up? Since the lack of memory property is the best studied and most useful property of the exponential law, our first endeavour in the present thesis, is to suitably extend this property and its equivalent forms so as to characterize the Gumbel's bivariate exponential distribution. Though there are many forms of bivariate exponential distributions, a matching interest has not been shown in developing corresponding discrete versions in the form of bivariate geometric distributions. Accordingly, attempt is also made to introduce the geometric version of the Gumbel distribution and examine several of its characteristic properties. A major area where exponential models are successfully applied being reliability theory, we also look into the role of these bivariate laws in that context. The present thesis is organised into five Chapters

Algebraic Geometric Codes and their relation to Cryptography using Elliptic Curves

Communication is the process of transmitting data across channel. Whenever data is transmitted across a channel, errors are likely to occur. Coding theory is a stream of science that deals with finding efficient ways to encode and decode data, so that any likely errors can be detected and corrected. There are many methods to achieve coding and decoding. One among them is Algebraic Geometric Codes that can be constructed from curves. Cryptography is the science ol‘ security of transmitting messages from a sender to a receiver. The objective is to encrypt message in such a way that an eavesdropper would not be able to read it. A eryptosystem is a set of algorithms for encrypting and decrypting for the purpose of the process of encryption and decryption. Public key eryptosystem such as RSA and DSS are traditionally being prel‘en‘ec| for the purpose of secure communication through the channel. llowever Elliptic Curve eryptosystem have become a viable altemative since they provide greater security and also because of their usage of key of smaller length compared to other existing crypto systems. Elliptic curve cryptography is based on group of points on an elliptic curve over a finite field. This thesis deals with Algebraic Geometric codes and their relation to Cryptography using elliptic curves. Here Goppa codes are used and the curves used are elliptic curve over a finite field. We are relating Algebraic Geometric code to Cryptography by developing a cryptographic algorithm, which includes the process of encryption and decryption of messages. We are making use of fundamental properties of Elliptic curve cryptography for generating the algorithm and is used here to relate both.

Length-weight relationship, relative condition factor (Kn) and morphometry of Arius subrostratus (Valenciennes, 1840) from a coastal wetland in Kerala

The length – weight relationship and relative condition factor of the shovel nose catfish, Arius subrostratus (Valenciennes, 1840) from Champakkara backwater were studied by examination of 392 specimens collected during June to September 2008. These fishes ranged from 6 to 29 cm in total length and 5.6 to 218 g in weight. The relation between the total length and weight of Arius subrostratus is described as Log W = -1.530+2.6224 log L for males, Log W = - 2.131 + 3.0914 log L for females and Log W = - 1.742 + 2.8067 log L for sexes combined. The mean relative condition factor (Kn) values ranged from 0.75 to 1.07 for males, 0.944 to 1.407 for females and 0.96 to 1.196 for combined sexes. The length-weight relationship and relative condition factor showed that the well-being of A. subrostratus is good. The morphometric measurements of various body parts and meristic counts were recorded. The morphometric measurements were found to be non-linear and there is no significant difference observed between the two sexes. From the present investigation, the fin formula can be written as D: I, 7; P: I, 12; A: 17 – 20; C: 26 – 32. There is no change in meristic counts with the increase in body length.

Internal Camera Calibration Using Rotation and Geometric Shapes

This paper describes a simple method for internal camera calibration for computer vision. This method is based on tracking image features through a sequence of images while the camera undergoes pure rotation. The location of the features relative to the camera or to each other need not be known and therefore this method can be used both for laboratory calibration and for self calibration in autonomous robots working in unstructured environments. A second method of calibration is also presented. This method uses simple geometric objects such as spheres and straight lines to The camera parameters. Calibration is performed using both methods and the results compared.

Geometric Structure of the Adaptive Controller of the Human Arm

The objects with which the hand interacts with may significantly change the dynamics of the arm. How does the brain adapt control of arm movements to this new dynamic? We show that adaptation is via composition of a model of the task's dynamics. By exploring generalization capabilities of this adaptation we infer some of the properties of the computational elements with which the brain formed this model: the elements have broad receptive fields and encode the learned dynamics as a map structured in an intrinsic coordinate system closely related to the geometry of the skeletomusculature. The low--level nature of these elements suggests that they may represent asset of primitives with which a movement is represented in the CNS.

Geometric and Algebraic Aspects of 3D Affine and Projective Structures from Perspective 2D Views

We investigate the differences --- conceptually and algorithmically --- between affine and projective frameworks for the tasks of visual recognition and reconstruction from perspective views. It is shown that an affine invariant exists between any view and a fixed view chosen as a reference view. This implies that for tasks for which a reference view can be chosen, such as in alignment schemes for visual recognition, projective invariants are not really necessary. We then use the affine invariant to derive new algebraic connections between perspective views. It is shown that three perspective views of an object are connected by certain algebraic functions of image coordinates alone (no structure or camera geometry needs to be involved).