Positively curved

In work "Convexity of ROC curves", interested in the accuracy measures of binary classifiers in the context of artificial intelligence. More specifically, we will be interested in the receiver operating characteristic (ROC) curves. By using analytical and optimization, we prove the main result of the paper which is “ROC curves of optimal machines are convex”.

4p tuongtrihoai 23-07-2024 5 2   Download

Nghiên cứu nhằm so sánh giá trị tiên lượng chỉ số thở nhanh nông (RSBI) và nhịp thở trong quá trình cai máy thở của 64 bệnh nhân hồi sức ngoại khoa phải thở máy qua ống nội khí quản (NKQ). Độ nhạy (sensitivity, Se), độ đặc hiệu (specificity, Sp), đường cong ROC (receiver operator characteristic), diện tích dưới đường cong AUC (area under the curve), giá trị dự đoán dương tính (positive predictive value, PPV) và âm tính (negative predictive value, NPV) của hai chỉ số trong quá trình cai thở máy của các bệnh nhân.

8p vijersey2711 03-03-2021 40 2   Download

Sums of two squares near perfect squares by R. C. Vaughan∗∗∗ In memory of Pritish Limani (1983–2003) Abstract Let C be a nondegenerate planar curve and for a real, positive decreasing function ψ let C(ψ) denote the set of simultaneously ψ-approximable points lying on C. We show that C is of Khintchine type for divergence; i.e. if a certain sum diverges then the one-dimensional Lebesgue measure on C of C(ψ) is full. We also obtain the Hausdorff measure analogue of the divergent Khintchine type result. ...

61p noel_noel 17-01-2013 52 7   Download

There are very few examples of Riemannian manifolds with positive sectional curvature known. In fact in dimensions above 24 all known examples are diffeomorphic to locally rank one symmetric spaces. We give a partial explanation of this phenomenon by showing that a positively curved, simply connected, compact manifold (M, g) is up to homotopy given by a rank one symmetric space, provided that its isometry group Iso(M, g) is large. More precisely we prove first that if dim(Iso(M, g)) ≥ 2 dim(M ) − 6, then M is tangentially homotopically equivalent to a rank one symmetric space or M...

63p noel_noel 17-01-2013 55 5   Download

Web geometry is devoted to the study of families of foliations which are in general position. We restrict ourselves to the local situation, in the neighborhood of the origin in C2 , with d ≥ 1 complex analytic foliations of curves in general position. We are interested in the geometry of such configurations, that is, properties of planar d-webs which are invariant with respect to analytic local isomorphisms of C2 . The initiators of the subject are W. Blaschke, G. Thomsen and G. Bol in the 1930’s (cf. [B-B], [B] and for instance [H1]). ...

22p tuanloccuoi 04-01-2013 52 6   Download

Tuyển tập các báo cáo nghiên cứu khoa học ngành toán học tạp chí Department of Mathematic dành cho các bạn yêu thích môn toán học đề tài: Positively Curved Combinatorial 3-Manifolds...

23p thulanh7 04-10-2011 35 3   Download

Calculating sensitivity and specificity requires selection of a decision value for the test to define the threshold value at or above which the test is considered "positive." For any given test, as this cut point is moved to improve sensitivity, specificity typically falls and vice versa. This dynamic tradeoff between more accurate identification of subjects with disease versus those without disease is often displayed graphically as a receiver operating characteristic (ROC) curve (Fig. 3-1). An ROC curve plots sensitivity (y-axis) versus 1 – specificity (x-axis).

5p tubreakdance 26-11-2010 82 6   Download