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Significance Prostate cancer is the most common cancer among men. An accurate diagnosis of its severity at detection plays a major role in improving their survival. Recently, machine learning models using biomarkers identified from Raman micro-spectroscopy discriminated intraductal carcinoma of the prostate (IDC-P) from cancer tissue with a ≥85 % detection accuracy and differentiated high-grade prostatic intraepithelial neoplasia (HGPIN) from IDC-P with a ≥97.8 % accuracy. Aim To improve the classification performance of machine learning models identifying different types of prostate cancer tissue using a new dimensional reduction technique. Approach A radial basis function (RBF) kernel support vector machine (SVM) model was trained on Raman spectra of prostate tissue from a 272-patient cohort (Centre hospitalier de l'Universite de Montreal, CHUM) and tested on two independent cohorts of 76 patients [University Health Network (UHN)] and 135 patients (Centre hospitalier universitaire de Quebec-Universite Laval, CHUQc-UL). Two types of engineered features were used. Individual intensity features, i.e., Raman signal intensity measured at particular wavelengths and novel Raman spectra fitted peak features consisting of peak heights and widths. Results Combining engineered features improved classification performance for the three aforementioned classification tasks. The improvements for IDC-P/cancer classification for the UHN and CHUQc-UL testing sets in accuracy, sensitivity, specificity, and area under the curve (AUC) are (numbers in parenthesis are associated with the CHUQc-UL testing set): +4 % (+8 % ), +7 % (+9 % ), +2 % (6%), +9 (+9) with respect to the current best models. Discrimination between HGPIN and IDC-P was also improved in both testing cohorts: +2.2 % (+1.7 % ), +4.5 % (+3.6 % ), +0 % (+0 % ), +2.3 (+0). While no global improvements were obtained for the normal versus cancer classification task [+0 % (-2 % ), +0 % (-3 % ), +2 % (-2 % ), +4 (+3)], the AUC was improved in both testing sets. Conclusions Combining individual intensity features and novel Raman fitted peak features, improved the classification performance on two independent and multicenter testing sets in comparison to using only individual intensity features.

In this paper, we introduce the notion of an Evertse–Ferretti Nevanlinna constant and compare it with the birational Nevanlinna constant introduced by the authors in a recent joint paper. We then use it to recover several previously known results. This includes a 1999 example of Faltings from his Baker’s Garden article. We also extend the theory of these Nevanlinna constants to what we call “multidivisor Nevanlinna constants,” which allow the proximity function to involve the maximum of Weil functions for finitely many divisors.

Author(s): Oh, Sung-Jin; Tataru, Daniel | Abstract: This article represents the fourth and final part of a four-paper sequence whose aim is to prove the Threshold Conjecture as well as the more general Dichotomy Theorem for the energy critical $4+1$ dimensional hyperbolic Yang--Mills equation. The Threshold Theorem asserts that topologically trivial solutions with energy below twice the ground state energy are global and scatter. The Dichotomy Theorem applies to solutions in arbitrary topological class with large energy, and provides two exclusive alternatives: Either the solution is global and scatters, or it bubbles off a soliton in either finite time or infinite time. Using the caloric gauge developed in the first paper, the continuation/scattering criteria established in the second paper, and the large data analysis in an arbitrary topological class at optimal regularity in the third paper, here we perform a blow-up analysis which shows that the failure of global well-posedness and scattering implies either the existence of a soliton with at most the same energy bubbling off, or the existence existence of a nontrivial self-similar solution. The proof is completed by showing that the latter solutions do not exist.

Laser ultrasonic techniques (LUTs) are becoming widely used for damage detection based on full-field ultrasonic data. In general, LUTs provide threedimensional (3-D) ultrasonic signals from which significant informative features may be extracted about the health condition of a structure. In this paper, statistical convariance method is proposed to investigate 3-D ultrasonic features. A laser ultrasonic interrogation method based on a Q-switched laser scanning system was used to interrogate 3-D ultrasonic signals in to a 2 mm aluminum plate. The ultrasonic signals in three-dimensional (3-D) space were generated, indexed by spatial N (xdirection), spatial M (y-direction), and temporal K (t-direction) samples, respectively. Then, two sets of covariance matrices were obtained based on the vector variables in x-direction and y-direction respectively for all k time samples respectively. The covariance imaging and the corresponding variance map were obtained. The wavelength and group velocity of S0 and A0 modes were able estimated from the variance map. The wavelength of the S0 and A0 modes were estimated with the deviation error of 2.3% and 11% respectively. The group velocities of S0 and A0 modes were estimated with the deviation error of 1.8% and 0.9%. The analysis will be further performed to develop group velocity curves for a range of frequency in metal and composite plates.

Various regression methods have been proposed for analyzing recurrent event data. Among them, the semiparametric additive rates model is particularly appealing because the regression coefficients quantify the absolute difference in the occurrence rate of the recurrent events between different groups. Estimation of the additive rates model requires the values of time-dependent covariates being observed throughout the entire follow-up period. In practice, however, the time-dependent covariates are usually only measured at intermittent follow-up visits. In this paper, we propose to kernel smooth functions involving time-dependent covariates across subjects in the estimating function, as opposed to imputing individual covariate trajectories. Simulation studies show that the proposed method outperforms simple imputation methods. The proposed method is illustrated with data from an epidemiologic study of the effect of streptococcal infections on recurrent pharyngitis episodes.

This paper establishes non-asymptotic concentration bound and Bahadur representation for the quantile regression estimator and its multiplier bootstrap counterpart in the random design setting. The non-asymptotic analysis keeps track of the impact of the parameter dimension $d$ and sample size $n$ in the rate of convergence, as well as in normal and bootstrap approximation errors. These results represent a useful complement to the asymptotic results under fixed design and provide theoretical guarantees for the validity of Rademacher multiplier bootstrap in the problems of confidence construction and goodness-of-fit testing. Numerical studies lend strong support to our theory and highlight the effectiveness of Rademacher bootstrap in terms of accuracy, reliability and computational efficiency.