On the Remainders Obtained in Finding the Greatest Common Divisor of Two Polynomials

In 1917 Pell (1) and Gordon used sylvester2, Sylvester’s little known and hardly ever used matrix of 1853, to compute(2) the coefficients of a Sturmian remainder — obtained in applying in Q[x], Sturm’s algorithm on two polynomials f, g ∈ Z[x] of degree n — in terms of the determinants (3) of the corresponding submatrices of sylvester2. Thus, they solved a problem that had eluded both J. J. Sylvester, in 1853, and E. B. Van Vleck, in 1900. (4) In this paper we extend the work by Pell and Gordon and show how to compute (2) the coefficients of an Euclidean remainder — obtained in finding in Q[x], the greatest common divisor of f, g ∈ Z[x] of degree n — in terms of the determinants (5) of the corresponding submatrices of sylvester1, Sylvester’s widely known and used matrix of 1840. (1) See the link http://en.wikipedia.org/wiki/Anna_Johnson_Pell_Wheeler for her biography (2) Both for complete and incomplete sequences, as defined in the sequel. (3) Also known as modified subresultants. (4) Using determinants Sylvester and Van Vleck were able to compute the coefficients of Sturmian remainders only for the case of complete sequences. (5) Also known as (proper) subresultants.

A Bayesian neural network algorithm identifies patients in whom post-EVAR surveillance may be unnecessary

Lifelong surveillance is not cost-effective after endovascular aneurysm repair (EVAR), but is required to detect aortic complications which are fatal if untreated (type 1/3 endoleak, sac expansion, device migration). Aneurysm morphology determines the probability of aortic complications and therefore the need for surveillance, but existing analyses have proven incapable of identifying patients at sufficiently low risk to justify abandoning surveillance. This study aimed to improve the prediction of aortic complications, through the application of machine-learning techniques. Patients undergoing EVAR at 2 centres were studied from 2004–2010. Aneurysm morphology had previously been studied to derive the SGVI Score for predicting aortic complications. Bayesian Neural Networks were designed using the same data, to dichotomise patients into groups at low- or high-risk of aortic complications. Network training was performed only on patients treated at centre 1. External validation was performed by assessing network performance independently of network training, on patients treated at centre 2. Discrimination was assessed by Kaplan-Meier analysis to compare aortic complications in predicted low-risk versus predicted high-risk patients. 761 patients aged 75 +/− 7 years underwent EVAR in 2 centres. Mean follow-up was 36+/− 20 months. Neural networks were created incorporating neck angu- lation/length/diameter/volume; AAA diameter/area/volume/length/tortuosity; and common iliac tortuosity/diameter. A 19-feature network predicted aor- tic complications with excellent discrimination and external validation (5-year freedom from aortic complications in predicted low-risk vs predicted high-risk patients: 97.9% vs. 63%; p < 0.0001). A Bayesian Neural-Network algorithm can identify patients in whom it may be safe to abandon surveillance after EVAR. This proposal requires prospective study.

BRAF mutation testing algorithm for vemurafenib treatment in melanoma: recommendations from an expert panel.

The incidence of melanoma has increased rapidly over the past 30 years, and the disease is now the sixth most common cancer among men and women in the U.K. Many patients are diagnosed with or develop metastatic disease, and survival is substantially reduced in these patients. Mutations in the BRAF gene have been identified as key drivers of melanoma cells and are found in around 50% of cutaneous melanomas. Vemurafenib (Zelboraf(®) ; Roche Molecular Systems Inc., Pleasanton, CA, U.S.A.) is the first licensed inhibitor of mutated BRAF, and offers a new first-line option for patients with unresectable or metastatic melanoma who harbour BRAF mutations. Vemurafenib was developed in conjunction with a companion diagnostic, the cobas(®) 4800 BRAF V600 Mutation Test. The purpose of this paper is to make evidence-based recommendations to facilitate the implementation of BRAF mutation testing and targeted therapy in patients with metastatic melanoma in the U.K. The recommendations are the result of a meeting of an expert panel and have been reviewed by melanoma specialists and representatives of the National Cancer Research Network Clinical Study Group on behalf of the wider melanoma community. This article is intended to be a starting point for practical advice and recommendations, which will no doubt be updated as we gain further experience in personalizing therapy for patients with melanoma.

Parallel Cyclostationarity-Exploiting Algorithm for Energy-Efficient Spectrum Sensing

The evolution of wireless communication systems leads to Dynamic Spectrum Allocation for Cognitive Radio, which requires reliable spectrum sensing techniques. Among the spectrum sensing methods proposed in the literature, those that exploit cyclostationary characteristics of radio signals are particularly suitable for communication environments with low signal-to-noise ratios, or with non-stationary noise. However, such methods have high computational complexity that directly raises the power consumption of devices which often have very stringent low-power requirements. We propose a strategy for cyclostationary spectrum sensing with reduced energy consumption. This strategy is based on the principle that p processors working at slower frequencies consume less power than a single processor for the same execution time. We devise a strict relation between the energy savings and common parallel system metrics. The results of simulations show that our strategy promises very significant savings in actual devices.

Parallel Cyclostationarity-Exploiting Algorithm for Energy-Efficient Spectrum Sensing

The evolution of wireless communication systems leads to Dynamic Spectrum Allocation for Cognitive Radio, which requires reliable spectrum sensing techniques. Among the spectrum sensing methods proposed in the literature, those that exploit cyclostationary characteristics of radio signals are particularly suitable for communication environments with low signal-to-noise ratios, or with non-stationary noise. However, such methods have high computational complexity that directly raises the power consumption of devices which often have very stringent low-power requirements. We propose a strategy for cyclostationary spectrum sensing with reduced energy consumption. This strategy is based on the principle that p processors working at slower frequencies consume less power than a single processor for the same execution time. We devise a strict relation between the energy savings and common parallel system metrics. The results of simulations show that our strategy promises very significant savings in actual devices.

Age estimation in common sole Solea solea larvae: validation of daily increments and evaluation of a pattern recognition technique

Close similarities have been found between the otoliths of sea-caught and laboratory-reared larvae of the common sole Solea solea (L.), given appropriate temperatures and nourishment of the latter. But from hatching to mouth formation. and during metamorphosis, sole otoliths have proven difficult to read because the increments may be less regular and low contrast. In this study, the growth increments in otoliths of larvae reared at 12 degrees C were counted by light microscopy to test the hypothesis of daily deposition, with some results verified using scanning electron microscopy (SEM), and by image analysis in order to compare the reliability of the 2 methods in age estimation. Age was first estimated (in days posthatch) from light micrographs of whole mounted otoliths. Counts were initiated from the increment formed at the time of month opening (Day 4). The average incremental deposition rate was consistent with the daily hypothesis. However, the light-micrograph readings tended to underestimate the mean ages of the larvae. Errors were probably associated with the low-contrast increments: those deposited after the mouth formation during the transition to first feeding, and those deposited from the onset of eye migration (about 20 d posthatch) during metamorphosis. SEM failed to resolve these low-contrast areas accurately because of poor etching. A method using image analysis was applied to a subsample of micrograph-counted otoliths. The image analysis was supported by an algorithm of pattern recognition (Growth Demodulation Algorithm, GDA). On each otolith, the GDA method integrated the growth pattern of these larval otoliths to averaged data from different radial profiles, in order to demodulate the exponential trend of the signal before spectral analysis (Fast Fourier Transformation, FFT). This second method both allowed more precise designation of increments, particularly for low-contrast areas, and more accurate readings but increased error in mean age estimation. The variability is probably due to a still rough perception of otolith increments by the GDA method, counting being achieved through a theoretical exponential pattern and mean estimates being given by FFT. Although this error variability was greater than expected, the method provides for improvement in both speed and accuracy in otolith readings.

Advancing Bag-of-visual-words Representations For Lesion Classification In Retinal Images.

Diabetic Retinopathy (DR) is a complication of diabetes that can lead to blindness if not readily discovered. Automated screening algorithms have the potential to improve identification of patients who need further medical attention. However, the identification of lesions must be accurate to be useful for clinical application. The bag-of-visual-words (BoVW) algorithm employs a maximum-margin classifier in a flexible framework that is able to detect the most common DR-related lesions such as microaneurysms, cotton-wool spots and hard exudates. BoVW allows to bypass the need for pre- and post-processing of the retinographic images, as well as the need of specific ad hoc techniques for identification of each type of lesion. An extensive evaluation of the BoVW model, using three large retinograph datasets (DR1, DR2 and Messidor) with different resolution and collected by different healthcare personnel, was performed. The results demonstrate that the BoVW classification approach can identify different lesions within an image without having to utilize different algorithms for each lesion reducing processing time and providing a more flexible diagnostic system. Our BoVW scheme is based on sparse low-level feature detection with a Speeded-Up Robust Features (SURF) local descriptor, and mid-level features based on semi-soft coding with max pooling. The best BoVW representation for retinal image classification was an area under the receiver operating characteristic curve (AUC-ROC) of 97.8% (exudates) and 93.5% (red lesions), applying a cross-dataset validation protocol. To assess the accuracy for detecting cases that require referral within one year, the sparse extraction technique associated with semi-soft coding and max pooling obtained an AUC of 94.2 ± 2.0%, outperforming current methods. Those results indicate that, for retinal image classification tasks in clinical practice, BoVW is equal and, in some instances, surpasses results obtained using dense detection (widely believed to be the best choice in many vision problems) for the low-level descriptors.

The Crystal-t Algorithm: A New Approach To Calculate The Sle Of Lipidic Mixtures Presenting Solid Solutions.

Lipidic mixtures present a particular phase change profile highly affected by their unique crystalline structure. However, classical solid-liquid equilibrium (SLE) thermodynamic modeling approaches, which assume the solid phase to be a pure component, sometimes fail in the correct description of the phase behavior. In addition, their inability increases with the complexity of the system. To overcome some of these problems, this study describes a new procedure to depict the SLE of fatty binary mixtures presenting solid solutions, namely the Crystal-T algorithm. Considering the non-ideality of both liquid and solid phases, this algorithm is aimed at the determination of the temperature in which the first and last crystal of the mixture melts. The evaluation is focused on experimental data measured and reported in this work for systems composed of triacylglycerols and fatty alcohols. The liquidus and solidus lines of the SLE phase diagrams were described by using excess Gibbs energy based equations, and the group contribution UNIFAC model for the calculation of the activity coefficients of both liquid and solid phases. Very low deviations of theoretical and experimental data evidenced the strength of the algorithm, contributing to the enlargement of the scope of the SLE modeling.

Occurrence Of Isoflavonoids In Brazilian Common Bean Germplasm (phaseolus Vulgaris L.).

Common bean (Phaseolus vulgaris) is present in the daily diet of various countries and, as for other legumes, has been investigated for its nutraceutical potential. Thus, 16 genotypes from different gene pools, representing seven types of seed coats and different responses to pathogens and pests, were selected to verify their isoflavone contents. The isoflavonoids daidzein and genistein and the flavonols kaempferol, myricetin, and quercetin were found. Grains of the black type showed the highest concentrations of isoflavonoids and were the only ones to exhibit daidzein. IAC Formoso, with high protein content and source of resistance to anthracnose, showed the greatest concentration of genistein, representing around 11% of the content present in soybean, as well as high levels of kaempferol. Arc 1, Raz 55, and IAC Una genotypes showed high content of coumestrol. The results suggest the use of IAC Formoso to increase the nutraceutical characteristics in common bean.

Censored Linear Regression Models For Irregularly Observed Longitudinal Data Using The Multivariate-t Distribution.

In acquired immunodeficiency syndrome (AIDS) studies it is quite common to observe viral load measurements collected irregularly over time. Moreover, these measurements can be subjected to some upper and/or lower detection limits depending on the quantification assays. A complication arises when these continuous repeated measures have a heavy-tailed behavior. For such data structures, we propose a robust structure for a censored linear model based on the multivariate Student's t-distribution. To compensate for the autocorrelation existing among irregularly observed measures, a damped exponential correlation structure is employed. An efficient expectation maximization type algorithm is developed for computing the maximum likelihood estimates, obtaining as a by-product the standard errors of the fixed effects and the log-likelihood function. The proposed algorithm uses closed-form expressions at the E-step that rely on formulas for the mean and variance of a truncated multivariate Student's t-distribution. The methodology is illustrated through an application to an Human Immunodeficiency Virus-AIDS (HIV-AIDS) study and several simulation studies.

Brazilian multicentre study of common mental disorders in primary care: rates and related social and demographic factors

Mental health problems are common in primary health care, particularly anxiety and depression. This study aims to estimate the prevalence of common mental disorders and their associations with socio-demographic characteristics in primary care in Brazil (Family Health Strategy). It involved a multicenter cross-sectional study with patients from Rio de Janeiro, São Paulo, Fortaleza (Ceará State) and Porto Alegre (Rio Grande do Sul State), assessed using the General Health Questionnaire (GHQ-12) and the Hospital Anxiety and Depression Scale (HAD). The rate of mental disorders in patients from Rio de Janeiro, São Paulo, Fortaleza and Porto Alegre were found to be, respectively, 51.9%, 53.3%, 64.3% and 57.7% with significant differences between Porto Alegre and Fortaleza compared to Rio de Janeiro after adjusting for confounders. Prevalence proportions of mental problems were especially common for females, the unemployed, those with less education and those with lower incomes. In the context of the Brazilian government's moves towards developing primary health care and reorganizing mental health policies it is relevant to consider common mental disorders as a priority alongside other chronic health conditions.

Análise bayesiana do modelo de herança monogênica no melhoramento vegetal: um exemplo com abobrinha

A common breeding strategy is to carry out basic studies to investigate the hypothesis of a single gene controlling the trait (major gene) with or without polygenes of minor effect. In this study we used Bayesian inference to fit genetic additive-dominance models of inheritance to plant breeding experiments with multiple generations. Normal densities with different means, according to the major gene genotype, were considered in a linear model in which the design matrix of the genetic effects had unknown coefficients (which were estimated in individual basis). An actual data set from an inheritance study of partenocarpy in zucchini (Cucurbita pepo L.) was used for illustration. Model fitting included posterior probabilities for all individual genotypes. Analysis agrees with results in the literature but this approach was far more efficient than previous alternatives assuming that design matrix was known for the generations. Partenocarpy in zucchini is controlled by a major gene with important additive effect and partial dominance.

Full threshold vs. Swedish interactive threshold algorithm (SITA) em pacientes glaucomatosos submetidos à perimetria computadorizada pela primeira vez

PURPOSE: To compare the Full Threshold (FT) and SITA Standard (SS) strategies in glaucomatous patients undergoing automated perimetry for the first time. METHODS: Thirty-one glaucomatous patients who had never undergone perimetry underwent automated perimetry (Humphrey, program 30-2) with both FT and SS on the same day, with an interval of at least 15 minutes. The order of the examination was randomized, and only one eye per patient was analyzed. Three analyses were performed: a) all the examinations, regardless of the order of application; b) only the first examinations; c) only the second examinations. In order to calculate the sensitivity of both strategies, the following criteria were used to define abnormality: glaucoma hemifield test (GHT) outside normal limits, pattern standard deviation (PSD) <5%, or a cluster of 3 adjacent points with p<5% at the pattern deviation probability plot. RESULTS: When the results of all examinations were analyzed regardless of the order in which they were performed, the number of depressed points with p<0.5% in the pattern deviation probability map was significantly greater with SS (p=0.037), and the sensitivities were 87.1% for SS and 77.4% for FT (p=0.506). When only the first examinations were compared, there were no statistically significant differences regarding the number of depressed points, but the sensitivity of SS (100%) was significantly greater than that obtained with FT (70.6%) (p=0.048). When only the second examinations were compared, there were no statistically significant differences regarding the number of depressed points, and the sensitivities of SS (76.5%) and FT (85.7%) (p=0.664). CONCLUSION: SS may have a higher sensitivity than FT in glaucomatous patients undergoing automated perimetry for the first time. However, this difference tends to disappear in subsequent examinations.

Combining Legendre's Polynomials and Genetic Algorithm in the Solution of Nonlinear Initial-Value Problems

This work develops a method for solving ordinary differential equations, that is, initial-value problems, with solutions approximated by using Legendre's polynomials. An iterative procedure for the adjustment of the polynomial coefficients is developed, based on the genetic algorithm. This procedure is applied to several examples providing comparisons between its results and the best polynomial fitting when numerical solutions by the traditional Runge-Kutta or Adams methods are available. The resulting algorithm provides reliable solutions even if the numerical solutions are not available, that is, when the mass matrix is singular or the equation produces unstable running processes.

Skewed Distribution of Circulating Activated Natural Killer T (NKT) Cells in Patients with Common Variable Immunodeficiency Disorders (CVID)

Common variable immunodeficiency disorder (CVID) is the commonest cause of primary antibody failure in adults and children, and characterized clinically by recurrent bacterial infections and autoimmune manifestations. Several innate immune defects have been described in CVID, but no study has yet investigated the frequency, phenotype or function of the key regulatory cell population, natural killer T (NKT) cells. We measured the frequencies and subsets of NKT cells in patients with CVID and compared these to healthy controls. Our results show a skewing of NKT cell subsets, with CD4+ NKT cells at higher frequencies, and CD8+ NKT cells at lower frequencies. However, these cells were highly activated and expression CD161. The NKT cells had a higher expression of CCR5 and concomitantly expression of CCR5+CD69+CXCR6 suggesting a compensation of the remaining population of NKT cells for rapid effector action.