On the approximate parametrization problem of algebraic curves.

The problem of parameterizing approximately algebraic curves and surfaces is an active research field, with many implications in practical applications. The problem can be treated locally or globally. We formally state the problem, in its global version for the case of algebraic curves (planar or spatial), and we report on some algorithms approaching it, as well as on the associated error distance analysis.

The birational transformations of algebraic curves of genus four.

Thesis (Ph.D.)--Cornell University, 1908.

Teorema de Riemann-Roch e aplicações

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Unfolding physics from the algebraic classification of spinor fields

After reviewing the Lounesto spinor field classification, according to the bilinear covariants associated to a spinor field, we call attention and unravel some prominent features involving unexpected properties about spinor fields under such classification. In particular, we pithily focus on the new aspects - as well as current concrete possibilities. They mainly arise when we deal with some non-standard spinor fields concerning, in particular, their applications in physics. © 2012 Elsevier B.V.

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.

Automatic Detection and Classification of Glioma Tumors using Statistical Features

The characterization and grading of glioma tumors, via image derived features, for diagnosis, prognosis, and treatment response has been an active research area in medical image computing. This paper presents a novel method for automatic detection and classification of glioma from conventional T2 weighted MR images. Automatic detection of the tumor was established using newly developed method called Adaptive Gray level Algebraic set Segmentation Algorithm (AGASA).Statistical Features were extracted from the detected tumor texture using first order statistics and gray level co-occurrence matrix (GLCM) based second order statistical methods. Statistical significance of the features was determined by t-test and its corresponding p-value. A decision system was developed for the grade detection of glioma using these selected features and its p-value. The detection performance of the decision system was validated using the receiver operating characteristic (ROC) curve. The diagnosis and grading of glioma using this non-invasive method can contribute promising results in medical image computing

Constructions of algebraic lattices

In this work we present constructions of algebraic lattices in Euclidean space with optimal center density in dimensions 2, 3, 4, 6, 8 and 12, which are rotated versions of the lattices Λn, for n = 2,3,4,6,8 and K12. These algebraic lattices are constructed through twisted canonical homomorphism via ideals of a ring of algebraic integers. Mathematical subject classification: 18B35, 94A15, 20H10.

Signal classification of submerged aquatic vegetation based on the hemispherical-conical reflectance factor spectrum shape in the yellow and red regions

The water column overlying the submerged aquatic vegetation (SAV) canopy presents difficulties when using remote sensing images for mapping such vegetation. Inherent and apparent water optical properties and its optically active components, which are commonly present in natural waters, in addition to the water column height over the canopy, and plant characteristics are some of the factors that affect the signal from SAV mainly due to its strong energy absorption in the near-infrared. By considering these interferences, a hypothesis was developed that the vegetation signal is better conserved and less absorbed by the water column in certain intervals of the visible region of the spectrum; as a consequence, it is possible to distinguish the SAV signal. To distinguish the signal from SAV, two types of classification approaches were selected. Both of these methods consider the hemispherical-conical reflectance factor (HCRF) spectrum shape, although one type was supervised and the other one was not. The first method adopts cluster analysis and uses the parameters of the band (absorption, asymmetry, height and width) obtained by continuum removal as the input of the classification. The spectral angle mapper (SAM) was adopted as the supervised classification approach. Both approaches tested different wavelength intervals in the visible and near-infrared spectra. It was demonstrated that the 585 to 685-nm interval, corresponding to the green, yellow and red wavelength bands, offered the best results in both classification approaches. However, SAM classification showed better results relative to cluster analysis and correctly separated all spectral curves with or without SAV. Based on this research, it can be concluded that it is possible to discriminate areas with and without SAV using remote sensing. © 2013 by the authors; licensee MDPI, Basel, Switzerland.

Classification of masses in mammographic image using wavelet domain features and polynomial classifier

Breast cancer is the most common cancer among women. In CAD systems, several studies have investigated the use of wavelet transform as a multiresolution analysis tool for texture analysis and could be interpreted as inputs to a classifier. In classification, polynomial classifier has been used due to the advantages of providing only one model for optimal separation of classes and to consider this as the solution of the problem. In this paper, a system is proposed for texture analysis and classification of lesions in mammographic images. Multiresolution analysis features were extracted from the region of interest of a given image. These features were computed based on three different wavelet functions, Daubechies 8, Symlet 8 and bi-orthogonal 3.7. For classification, we used the polynomial classification algorithm to define the mammogram images as normal or abnormal. We also made a comparison with other artificial intelligence algorithms (Decision Tree, SVM, K-NN). A Receiver Operating Characteristics (ROC) curve is used to evaluate the performance of the proposed system. Our system is evaluated using 360 digitized mammograms from DDSM database and the result shows that the algorithm has an area under the ROC curve Az of 0.98 ± 0.03. The performance of the polynomial classifier has proved to be better in comparison to other classification algorithms. © 2013 Elsevier Ltd. All rights reserved.

A comparison of CA125, HE4, risk ovarian malignancy algorithm (ROMA), and risk malignancy index (RMI) for the classification of ovarian masses

OBJECTIVE: Differentiation between benign and malignant ovarian neoplasms is essential for creating a system for patient referrals. Therefore, the contributions of the tumor markers CA125 and human epididymis protein 4 (HE4) as well as the risk ovarian malignancy algorithm (ROMA) and risk malignancy index (RMI) values were considered individually and in combination to evaluate their utility for establishing this type of patient referral system. METHODS: Patients who had been diagnosed with ovarian masses through imaging analyses (n = 128) were assessed for their expression of the tumor markers CA125 and HE4. The ROMA and RMI values were also determined. The sensitivity and specificity of each parameter were calculated using receiver operating characteristic curves according to the area under the curve (AUC) for each method. RESULTS: The sensitivities associated with the ability of CA125, HE4, ROMA, or RMI to distinguish between malignant versus benign ovarian masses were 70.4%, 79.6%, 74.1%, and 63%, respectively. Among carcinomas, the sensitivities of CA125, HE4, ROMA (pre-and post-menopausal), and RMI were 93.5%, 87.1%, 80%, 95.2%, and 87.1%, respectively. The most accurate numerical values were obtained with RMI, although the four parameters were shown to be statistically equivalent. CONCLUSION: There were no differences in accuracy between CA125, HE4, ROMA, and RMI for differentiating between types of ovarian masses. RMI had the lowest sensitivity but was the most numerically accurate method. HE4 demonstrated the best overall sensitivity for the evaluation of malignant ovarian tumors and the differential diagnosis of endometriosis. All of the parameters demonstrated increased sensitivity when tumors with low malignancy potential were considered low-risk, which may be used as an acceptable assessment method for referring patients to reference centers.

Determination of absorption curves, dissolution profiles and establishment of in vitro-in vivo correlation by in silico methods using GastroPlusTM and DDDPlusTM

The use of computer programs to predict drug absorption in humans and to simulate dissolution profiles has become a valuable tool in the pharmaceutical area. The objective of this study was to use in silico methods through software GastroPlusTM and DDDPlusTM to simulate drug absorption curves and dissolution profiles, and to establish in vitro-in vivo correlations (IVIVCs). The work presented herein is divided into five chapters and includes the drugs ketoprofen, pyrimethamine, metronidazole, fluconazole, carvedilol and doxazosin. In Chapter 1, simulated plasma curves for ketoprofen matrix tablets are presented and IVIVC was established. The use of simulated intrinsic dissolution tests for pyrimethamine and metronidazole as a tool for biopharmaceutics classification is detailed in Chapter 2. In Chapter 3, simulation of plasma curves for fluconazole capsules with different dissolution profiles is demonstrated as a tool for biowaiver. IVIVC studies were also conducted for carvedilol immediate-release tablets from dissolution profiles in Chapter 4. Chapter 5 covers the application of simulated dissolution tests for development of doxazosin extended-release formulations. Simulation of plasma curves and IVIVC using the software GastroPlusTM as well as intrinsic dissolution tests and dissolution profiles using the software DDDPlusTM proved to be a tool of wide application in predicting biopharmaceutical characteristics of drugs and formulations, allowing the reduction of time and costs of experimental laboratory work.

Computational aspects of modular parametrizations of elliptic curves

Thesis (Ph.D.)--University of Washington, 2016-06

Triangular Models and Asymptotics of Continuous Curves with Bounded and Unbounded Semigroup Generators

2000 Mathematics Subject Classification: Primary 47A48, Secondary 60G12.

A Note on the L2-norm of the Second Fundamental Form of Algebraic Manifolds

2000 Mathematics Subject Classification: 53C42, 53C55.

Very special divisors on 4-gonal real algebraic curves

International audience