An application of lattice basis reduction to polynomial identities for algebraic structures

The authors` recent classification of trilinear operations includes, among other cases, a fourth family of operations with parameter q epsilon Q boolean OR {infinity}, and weakly commutative and weakly anticommutative operations. These operations satisfy polynomial identities in degree 3 and further identities in degree 5. For each operation, using the row canonical form of the expansion matrix E to find the identities in degree 5 gives extremely complicated results. We use lattice basis reduction to simplify these identities: we compute the Hermite normal form H of E(t), obtain a basis of the nullspace lattice from the last rows of a matrix U for which UE(t) = H, and then use the LLL algorithm to reduce the basis. (C) 2008 Elsevier Inc. All rights reserved.

The classification and the conjugacy classes of the finite subgroups of the sphere braid groups

Let n >= 3. We classify the finite groups which are realised as subgroups of the sphere braid group B(n)(S(2)). Such groups must be of cohomological period 2 or 4. Depending on the value of n, we show that the following are the maximal finite subgroups of B(n)(S(2)): Z(2(n-1)); the dicyclic groups of order 4n and 4(n - 2); the binary tetrahedral group T*; the binary octahedral group O*; and the binary icosahedral group I(*). We give geometric as well as some explicit algebraic constructions of these groups in B(n)(S(2)) and determine the number of conjugacy classes of such finite subgroups. We also reprove Murasugi`s classification of the torsion elements of B(n)(S(2)) and explain how the finite subgroups of B(n)(S(2)) are related to this classification, as well as to the lower central and derived series of B(n)(S(2)).

Lesion detection and classification in breast cancer: evaluation of approaches based on morphological features, tracer kinetic modelling and semi-quantitative parameters in MR functional imaging (DCE-MRI)

The diagnosis, grading and classification of tumours has benefited considerably from the development of DCE-MRI which is now essential to the adequate clinical management of many tumour types due to its capability in detecting active angiogenesis. Several strategies have been proposed for DCE-MRI evaluation. Visual inspection of contrast agent concentration curves vs time is a very simple yet operator dependent procedure, therefore more objective approaches have been developed in order to facilitate comparison between studies. In so called model free approaches, descriptive or heuristic information extracted from time series raw data have been used for tissue classification. The main issue concerning these schemes is that they have not a direct interpretation in terms of physiological properties of the tissues. On the other hand, model based investigations typically involve compartmental tracer kinetic modelling and pixel-by-pixel estimation of kinetic parameters via non-linear regression applied on region of interests opportunely selected by the physician. This approach has the advantage to provide parameters directly related to the pathophysiological properties of the tissue such as vessel permeability, local regional blood flow, extraction fraction, concentration gradient between plasma and extravascular-extracellular space. Anyway, nonlinear modelling is computational demanding and the accuracy of the estimates can be affected by the signal-to-noise ratio and by the initial solutions. The principal aim of this thesis is investigate the use of semi-quantitative and quantitative parameters for segmentation and classification of breast lesion. The objectives can be subdivided as follow: describe the principal techniques to evaluate time intensity curve in DCE-MRI with focus on kinetic model proposed in literature; to evaluate the influence in parametrization choice for a classic bi-compartmental kinetic models; to evaluate the performance of a method for simultaneous tracer kinetic modelling and pixel classification; to evaluate performance of machine learning techniques training for segmentation and classification of breast lesion.

Short anterior correction of the thoracolumbar/lumbar curve in King 1 idiopathic scoliosis: the behaviour of the instrumented and non-instrumented curves and the trunk balance

This is a retrospective clinical, radiological and patient outcome assessment of 21 consecutive patients with King 1 idiopathic adolescent scoliosis treated by short anterior selective fusion of the major thoracolumbar/lumbar (TL/L) curve. Three-dimensional changes of both curves, changes in trunk balance and rib hump were evaluated. The minimal follow-up was 24 months (max. 83). The Cobb angle of the TL/L curve was 52 degrees (45-67 degrees) with a flexibility of 72% (40-100%). The average length of the main curve was 5 (3-8) segments. An average of 3 (2-4) segments was fused using rigid single rod implants with side-loading screws. The Cobb angle of the thoracic curve was 33 degrees (18-50 degrees) with a flexibility of 69% (29-100%). The thoracic curve in bending was less than 20 degrees in 17 patients, and 20-25 degrees in 4 patients. In the TL/L curve there was an improvement of the Cobb angle of 67%, of the apex vertebral rotation of 51% and of the apex vertebral translation of 74%. The Cobb angle of the thoracic curve improved 29% spontaneously. Shoulder balance improved significantly from an average preoperative imbalance of 14.5-3.1 mm at the last follow-up. Seventy-five percent of the patients with preoperative positive shoulder imbalance (higher on the side of the thoracic curve) had levelled shoulders at the last follow-up. C7 offset improved from a preoperative 19.8 (0-40) to 4.8 (0-18) mm at the last follow-up. There were no significant changes in rotation, translation of the thoracic curve and the clinical rib hump. There were no significant changes in thoracic kyphosis or lumbar lordosis. The average score of the SRS-24 questionnaire at the last follow-up was 91 points (max. 120). We conclude that short anterior selective fusion of the TL/L curve in King 1 scoliosis with a thoracic curve bending to 25 degrees or less (Type 5 according to Lenke classification) results in a satisfactory correction and a balanced spine. Short fusions leave enough mobile lumbar segments for the establishment of global spinal balance. A positive shoulder imbalance is not a contraindication for this procedure. Structural interbody grafts are not necessary to maintain lumbar lordosis.

Symplectic Representation of a Braid Group on 3-Sheeted Covers of the Riemann Sphere

We define Picard cycles on each smooth three-sheeted Galois cover C of the Riemann sphere. The moduli space of all these algebraic curves is a nice Shimura surface, namely a symmetric quotient of the projective plane uniformized by the complex two-dimensional unit ball. We show that all Picard cycles on C form a simple orbit of the Picard modular group of Eisenstein numbers. The proof uses a special surface classification in connection with the uniformization of a classical Picard-Fuchs system. It yields an explicit symplectic representation of the braid groups (coloured or not) of four strings.

Linearly Normal Curves in P^n

2000 Mathematics Subject Classification: 14H45, 14H50, 14J26.

Algebro-Geometric Aspects of the Classical Yang-Baxter Equation

In this thesis we consider algebro-geometric aspects of the Classical Yang-Baxter Equation and the Generalised Classical Yang-Baxter Equation. In chapter one we present a method to construct solutions of the Generalised Classical Yang-Baxter Equation starting with certain sheaves of Lie algebras on algebraic curves. Furthermore we discuss a criterion to check unitarity of such solutions. In chapter two we consider the special class of solutions coming from sheaves of traceless endomorphisms of simple vector bundles on the nodal cubic curve. These solutions are quasi-trigonometric and we describe how they fit into the classification scheme of such solutions. Moreover, we describe a concrete formula for these solutions. In the third and final chapter we show that any unitary, rational solution of the Classical Yang-Baxter Equation can be obtained via the method of chapter one applied to a sheaf of Lie algebras on the cuspidal cubic curve.

Transmission Of Intra-cellular Genetic Information: A System Proposal.

One of the great challenges of the scientific community on theories of genetic information, genetic communication and genetic coding is to determine a mathematical structure related to DNA sequences. In this paper we propose a model of an intra-cellular transmission system of genetic information similar to a model of a power and bandwidth efficient digital communication system in order to identify a mathematical structure in DNA sequences where such sequences are biologically relevant. The model of a transmission system of genetic information is concerned with the identification, reproduction and mathematical classification of the nucleotide sequence of single stranded DNA by the genetic encoder. Hence, a genetic encoder is devised where labelings and cyclic codes are established. The establishment of the algebraic structure of the corresponding codes alphabets, mappings, labelings, primitive polynomials (p(x)) and code generator polynomials (g(x)) are quite important in characterizing error-correcting codes subclasses of G-linear codes. These latter codes are useful for the identification, reproduction and mathematical classification of DNA sequences. The characterization of this model may contribute to the development of a methodology that can be applied in mutational analysis and polymorphisms, production of new drugs and genetic improvement, among other things, resulting in the reduction of time and laboratory costs.

[pediatric Patient Classification System: Improvement Of An Instrument].

Improve the content validity of the instrument for classification of pediatric patients and evaluate its construct validity. A descriptive exploratory study in the measurement of the content validity index, and correlational design for construct validation through exploratory factor analysis. The content validity index for indicators was 0.99 and it was 0.97 for graded situations. Three domains were extracted in the construct validation, namely: patient, family and therapeutic procedures, with 74.97% of explained variance. The instrument showed evidences of content and construct validity. The validation of the instrument occurred under the approach of family-centered care, and allowed incorporating some essential needs of childhood such as playing, interaction and affection in the content of the instrument.

A classification methodology for the risk of weed infestation using fuzzy logic

Despite modern weed control practices, weeds continue to be a threat to agricultural production. Considering the variability of weeds, a classification methodology for the risk of infestation in agricultural zones using fuzzy logic is proposed. The inputs for the classification are attributes extracted from estimated maps for weed seed production and weed coverage using kriging and map analysis and from the percentage of surface infested by grass weeds, in order to account for the presence of weed species with a high rate of development and proliferation. The output for the classification predicts the risk of infestation of regions of the field for the next crop. The risk classification methodology described in this paper integrates analysis techniques which may help to reduce costs and improve weed control practices. Results for the risk classification of the infestation in a maize crop field are presented. To illustrate the effectiveness of the proposed system, the risk of infestation over the entire field is checked against the yield loss map estimated by kriging and also with the average yield loss estimated from a hyperbolic model.

Effect of the Novel Thienopyridine Prasugrel Compared With Clopidogrel on Spontaneous and Procedural Myocardial Infarction in the Trial to Assess Improvement in Therapeutic Outcomes by Optimizing Platelet Inhibition With Prasugrel-Thrombolysis in Myocardial Infarction 38 An Application of the Classification System From the Universal Definition of Myocardial Infarction

Background-Prasugrel is a novel thienopyridine that reduces new or recurrent myocardial infarctions (MIs) compared with clopidogrel in patients with acute coronary syndrome undergoing percutaneous coronary intervention. This effect must be balanced against an increased bleeding risk. We aimed to characterize the effect of prasugrel with respect to the type, size, and timing of MI using the universal classification of MI. Methods and Results-We studied 13 608 patients with acute coronary syndrome undergoing percutaneous coronary intervention randomized to prasugrel or clopidogrel and treated for 6 to 15 months in the Trial to Assess Improvement in Therapeutic Outcomes by Optimizing Platelet Inhibition With Prasugrel-Thrombolysis in Myocardial Infarction (TRITON-TIMI 38). Each MI underwent supplemental classification as spontaneous, secondary, or sudden cardiac death (types 1, 2, and 3) or procedure related (Types 4 and 5) and examined events occurring early and after 30 days. Prasugrel significantly reduced the overall risk of MI (7.4% versus 9.7%; hazard ratio [HR], 0.76; 95% confidence interval [CI], 0.67 to 0.85; P < 0.0001). This benefit was present for procedure-related MIs (4.9% versus 6.4%; HR, 0.76; 95% CI, 0.66 to 0.88; P = 0.0002) and nonprocedural (type 1, 2, or 3) MIs (2.8% versus 3.7%; HR, 0.72; 95% CI, 0.59 to 0.88; P = 0.0013) and consistently across MI size, including MIs with a biomarker peak >= 5 times the reference limit (HR. 0.74; 95% CI, 0.64 to 0.86; P = 0.0001). In landmark analyses starting at 30 days, patients treated with prasugrel had a lower risk of any MI (2.9% versus 3.7%; HR, 0.77; P = 0.014), including nonprocedural MI (2.3% versus 3.1%; HR, 0.74; 95% CI, 0.60 to 0.92; P = 0.0069). Conclusion-Treatment with prasugrel compared with clopidogrel for up to 15 months in patients with acute coronary syndrome undergoing percutaneous coronary intervention significantly reduces the risk of MIs that are procedure related and spontaneous and those that are small and large, including new MIs occurring during maintenance therapy. (Circulation. 2009; 119: 2758-2764.)

Classification System of Raman Spectra using Cluster Analysis to Diagnose Coronary Artery Lesions

The traditional methods employed to detect atherosclerotic lesions allow for the identification of lesions; however, they do not provide specific characterization of the lesion`s biochemistry. Currently, Raman spectroscopy techniques are widely used as a characterization method for unknown substances, which makes this technique very important for detecting atherosclerotic lesions. The spectral interpretation is based on the analysis of frequency peaks present in the signal; however, spectra obtained from the same substance can show peaks slightly different and these differences make difficult the creation of an automatic method for spectral signal analysis. This paper presents a signal analysis method based on a clustering technique that allows for the classification of spectra as well as the inference of a diagnosis about the arterial wall condition. The objective is to develop a computational tool that is able to create clusters of spectra according to the arterial wall state and, after data collection, to allow for the classification of a specific spectrum into its correct cluster.

Classification model based on Raman spectra of selected morphological and biochemical tissue constituents for identification of atherosclerosis in human coronary arteries

This study presents the results of Raman spectroscopy applied to the classification of arterial tissue based on a simplified model using basal morphological and biochemical information extracted from the Raman spectra of arteries. The Raman spectrograph uses an 830-nm diode laser, imaging spectrograph, and a CCD camera. A total of 111 Raman spectra from arterial fragments were used to develop the model, and those spectra were compared to the spectra of collagen, fat cells, smooth muscle cells, calcification, and cholesterol in a linear fit model. Non-atherosclerotic (NA), fatty and fibrous-fatty atherosclerotic plaques (A) and calcified (C) arteries exhibited different spectral signatures related to different morphological structures presented in each tissue type. Discriminant analysis based on Mahalanobis distance was employed to classify the tissue type with respect to the relative intensity of each compound. This model was subsequently tested prospectively in a set of 55 spectra. The simplified diagnostic model showed that cholesterol, collagen, and adipocytes were the tissue constituents that gave the best classification capability and that those changes were correlated to histopathology. The simplified model, using spectra obtained from a few tissue morphological and biochemical constituents, showed feasibility by using a small amount of variables, easily extracted from gross samples.

Assessment of the quality of brain regions and neuroimaging metrics as biomarkers of Alzheimer’s disease

Alzheimer Disease (AD) is characterized by progressive cognitive decline and dementia. Earlier diagnosis and classification of different stages of the disease are currently the main challenges and can be assessed by neuroimaging. With this work we aim to evaluate the quality of brain regions and neuroimaging metrics as biomarkers of AD. Multimodal Imaging Brain Connectivity Analysis (MIBCA) toolbox functionalities were used to study AD by T1weighted, Diffusion Tensor Imaging and 18FAV45 PET, with data obtained from the AD Neuroimaging Initiative database, specifically 12 healthy controls (CTRL) and 33 patients with early mild cognitive impairment (EMCI), late MCI (LMCI) and AD (11 patients/group). The metrics evaluated were gray-matter volume (GMV), cortical thickness (CThk), mean diffusivity (MD), fractional anisotropy (FA), fiber count (FiberConn), node degree (Deg), cluster coefficient (ClusC) and relative standard-uptake-values (rSUV). Receiver Operating Characteristic (ROC) curves were used to evaluate and compare the diagnostic accuracy of the most significant metrics and brain regions and expressed as area under the curve (AUC). Comparisons were performed between groups. The RH-Accumbens/Deg demonstrated the highest AUC when differentiating between CTRLEMCI (82%), whether rSUV presented it in several brain regions when distinguishing CTRL-LMCI (99%). Regarding CTRL-AD, highest AUC were found with LH-STG/FiberConn and RH-FP/FiberConn (~100%). A larger number of neuroimaging metrics related with cortical atrophy with AUC>70% was found in CTRL-AD in both hemispheres, while in earlier stages, cortical metrics showed in more confined areas of the temporal region and mainly in LH, indicating an increasing of the spread of cortical atrophy that is characteristic of disease progression. In CTRL-EMCI several brain regions and neuroimaging metrics presented AUC>70% with a worst result in later stages suggesting these indicators as biomarkers for an earlier stage of MCI, although further research is necessary.

The contribution of multitemporal information from multispectral satellite images for automatic land cover classification at the national scale

Thesis submitted to the Instituto Superior de Estatística e Gestão de Informação da Universidade Nova de Lisboa in partial fulfillment of the requirements for the Degree of Doctor of Philosophy in Information Management – Geographic Information Systems