Related papers: ROC curves for LDA classifiers
We consider the locus of irreducible nonsingular rational curves of degree d Pn, n>2, meeting a generic collection of linear subspaces. When this locus is 0 (resp 1)- dimensional, we compute (recursively) its degree (resp. geometric genus).…
Accurate diagnosis of disease is of fundamental importance in clinical practice and medical research. Before a medical diagnostic test is routinely used in practice, its ability to distinguish between diseased and nondiseased states must be…
Medical images differ from natural images in significantly higher resolutions and smaller regions of interest. Because of these differences, neural network architectures that work well for natural images might not be applicable to medical…
Ultrasound image diagnosis of breast tumors has been widely used in recent years. However, there are some problems of it, for instance, poor quality, intense noise and uneven echo distribution, which has created a huge obstacle to…
We consider Jordan curves of the form $\gamma=\cup_{j=1}^n \gamma_j$ on the Riemann sphere for which each $\gamma_j$ is a hyperbolic geodesic in $(\widehat{\mathbb C} \smallsetminus \gamma)\cup \gamma_j$. These Jordan curves are…
We establish H\"ormander-type $L^2$-estimates for the $\overline{\partial}$-operators that hold uniformly for all nontrivial flat holomorphic line bundles on compact K\"ahler manifolds. Our result can be regarded as a…
Accurate breast lesion risk estimation can significantly reduce unnecessary biopsies and help doctors decide optimal treatment plans. Most existing computer-aided systems rely solely on mammogram features to classify breast lesions. While…
A closed-form expression for the amplitudes of source waves in 2D discrete lattice with local and linear (waveguides) defects is derived. The numerical implementation of this analytic expression is demonstrated by several examples.
We show that there is an equivalence of $\infty$-categories between Lie algebroids and certain kinds of curved Lie algebras. For this we develop a method to study the $\infty$-category of curved Lie algebras using the homotopy theory of…
The receiver operating characteristic (ROC) curve is the most popular tool used to evaluate the discriminatory capability of diagnostic tests/biomarkers measured on a continuous scale when distinguishing between two alternative disease…
The area under the ROC curve (AUC) is one of the most widely used performance measures for classification models in machine learning. However, it summarizes the true positive rates (TPRs) over all false positive rates (FPRs) in the ROC…
Under an assumption of normal genericity, we show that a stable J-holomorphic curve has, in the space of homologous curves of the same genus, a locally Euclidean neighbourhood of the expected dimension given by Riemann-Roch. In dimension 4,…
Background Identifying the right cut-off for continuous biomarkers in clinical trials is important to identify subgroups of patients who are at greater risk of disease or more likely to benefit from a drug. The literature in this area tends…
We characterize the extendibility of the normal curvature on frontals and we give a representation formula of this type of frontals. Also we give representation formulas for wavefronts on all types of singularities and others sub classes of…
In this paper we obtain an explicit formula for the number of curves in two dimensional complex projective space, of degree d, passing through d(d+3)/2-(k+1) generic points and having one node and one codimension k singularity, where k is…
We present a new construction of Radon curves which only uses convexity methods. In other words, it does not rely on an auxiliary Euclidean background metric (as in the classical works of J. Radon, W. Blaschke, G. Birkhoff, and M. M. Day),…
We generalize the formula for the log canonical threshold(LCT) of plane curves over the complex numbers to arbitrary characteristics. Our proof relies purely on valuation theory, instead of on the theory of $D$-modules.
This is an expository note to give a brief review of classical elastica theory, mainly prepared for giving a more detailed proof of the author's Li--Yau type inequality for self-intersecting curves in Euclidean space. We also discuss some…
Two different approaches to analysis of data from diagnostic biomarker studies are commonly employed. Logistic regression is used to fit models for probability of disease given marker values, while ROC curves and risk distributions are used…
The study of a receptor-ligand system generally relies on the analysis of its dose-response (or concentration-effect) curve, which quantifies the relation between ligand concentration and the biological effect (or cellular response) induced…