scholarly journals Streaming Algorithm for Euler Characteristic Curves of Multidimensional Images

2017 ◽  
pp. 397-409 ◽  
Author(s):  
Teresa Heiss ◽  
Hubert Wagner
Keyword(s):  
Euler Characteristic ◽  
Characteristic Curves ◽  
Streaming Algorithm ◽  
Multidimensional Images

scholarly journals Vortices over Riemann surfaces and dominated splittings

2021 ◽  
pp. 1-26
Author(s):  
THOMAS METTLER ◽  
GABRIEL P. PATERNAIN
Keyword(s):  
Euler Characteristic ◽  
Tangent Bundle ◽  
Riemann Surfaces ◽  
Dominated Splitting ◽  
Vortex Equations ◽  
Special Cases ◽  
Unit Tangent Bundle ◽  
Anosov Flows

Abstract We associate a flow $\phi $ with a solution of the vortex equations on a closed oriented Riemannian 2-manifold $(M,g)$ of negative Euler characteristic and investigate its properties. We show that $\phi $ always admits a dominated splitting and identify special cases in which $\phi $ is Anosov. In particular, starting from holomorphic differentials of fractional degree, we produce novel examples of Anosov flows on suitable roots of the unit tangent bundle of $(M,g)$ .

A conditional approach for the receiver operating characteristic curve construction to evaluate diagnostic test performance in a family-matched case–control design

2021 ◽  
pp. 096228022199595
Author(s):  
Yalda Zarnegarnia ◽  
Shari Messinger
Keyword(s):  
Receiver Operating Characteristic Curve ◽  
Receiver Operating Characteristic ◽  
Operating Characteristic ◽  
Characteristic Curve ◽  
Case Control ◽  
Paired Data ◽  
Characteristic Curves ◽  
Receiver Operating Characteristic Curves ◽  
Operating Characteristic Curve ◽  
Receiver Operating

Receiver operating characteristic curves are widely used in medical research to illustrate biomarker performance in binary classification, particularly with respect to disease or health status. Study designs that include related subjects, such as siblings, usually have common environmental or genetic factors giving rise to correlated biomarker data. The design could be used to improve detection of biomarkers informative of increased risk, allowing initiation of treatment to stop or slow disease progression. Available methods for receiver operating characteristic construction do not take advantage of correlation inherent in this design to improve biomarker performance. This paper will briefly review some developed methods for receiver operating characteristic curve estimation in settings with correlated data from case–control designs and will discuss the limitations of current methods for analyzing correlated familial paired data. An alternative approach using conditional receiver operating characteristic curves will be demonstrated. The proposed approach will use information about correlation among biomarker values, producing conditional receiver operating characteristic curves that evaluate the ability of a biomarker to discriminate between affected and unaffected subjects in a familial paired design.

scholarly journals Derivation of water flooding characteristic curve for offshore low-amplitude structural reservoir with strong bottom water

2021 ◽  
Author(s):  
Ying-xian Liu ◽  
Jie Tan ◽  
Hui Cai ◽  
Yan-lai Li ◽  
Chun-yan Liu
Keyword(s):  
Bottom Water ◽  
Characteristic Curve ◽  
Calculated Data ◽  
Oil Production ◽  
Water Flooding ◽  
Characteristic Curves ◽  
Recoverable Reserves ◽  
Curve Method ◽  
Water Cut ◽  
Low Amplitude

AbstractThe water flooding characteristic curve method is one of the essential techniques to predict recoverable reserves. However, the recoverable reserves indicated by the existing water flooding characteristic curves of low-amplitude reservoirs with strong bottom water increase gradually, and the current local recovery degree of some areas has exceeded the predicted recovery rate. The applicability of the existing water flooding characteristic curves in low-amplitude reservoirs with strong bottom water is lacking, which affects the accurate prediction of development performance. By analyzing the derivation process of the conventional water flooding characteristic curve method, this manuscript finds out the reasons for the poor applicability of the existing water flooding characteristic curve in low-amplitude reservoir with strong bottom water and corrects the existing water flooding characteristic curve according to the actual situation of the oilfield and obtains the improvement method of water flooding characteristic curve in low-amplitude reservoir with strong bottom water. After correction, the correlation coefficient between $$\frac{{k_{ro} }}{{k_{rw} }}$$ k ro k rw and $$S_{w}$$ S w is 95.92%. According to the comparison between the actual data and the calculated data, in 2021/3, the actual water cut is 97.29%, the water cut predicted by the formula is 97.27%, the actual cumulative oil production is 31.19 × 104t, and the predicted cumulative oil production is 31.31 × 104t. The predicted value is consistent with the actual value. It provides a more reliable method for predicting low-amplitude reservoirs' recoverable ability with strong bottom water and guides the oilfield's subsequent decision-making.

scholarly journals Tropical geometry and the motivic nearby fiber

2011 ◽  
Vol 148 (1) ◽  
pp. 269-294 ◽  
Author(s):  
Eric Katz ◽  
Alan Stapledon
Keyword(s):  
Euler Characteristic ◽  
Hodge Structure ◽  
Tropical Geometry ◽  
Mixed Hodge Structure ◽  
General Fiber ◽  
Algebraic Torus ◽  
Tropical Varieties

AbstractWe construct motivic invariants of a subvariety of an algebraic torus from its tropicalization and initial degenerations. More specifically, we introduce an invariant of a compactification of such a variety called the ‘tropical motivic nearby fiber’. This invariant specializes in the schön case to the Hodge–Deligne polynomial of the limit mixed Hodge structure of a corresponding degeneration. We give purely combinatorial expressions for this Hodge–Deligne polynomial in the cases of schön hypersurfaces and matroidal tropical varieties. We also deduce a formula for the Euler characteristic of a general fiber of the degeneration.

scholarly journals Topology of Subvarieties of Complex Semi-abelian Varieties

2020 ◽  
Author(s):  
Yongqiang Liu ◽  
Laurentiu Maxim ◽  
Botong Wang
Keyword(s):  
Euler Characteristic ◽  
Morse Theory ◽  
Characteristic Property ◽  
Abelian Varieties ◽  
Betti Numbers ◽  
Local Systems ◽  
Affine Manifolds ◽  
Cyclic Covers ◽  
Rank One ◽  
Generic Vanishing

Abstract We use the non-proper Morse theory of Palais–Smale to investigate the topology of smooth closed subvarieties of complex semi-abelian varieties and that of their infinite cyclic covers. As main applications, we obtain the finite generation (except in the middle degree) of the corresponding integral Alexander modules as well as the signed Euler characteristic property and generic vanishing for rank-one local systems on such subvarieties. Furthermore, we give a more conceptual (topological) interpretation of the signed Euler characteristic property in terms of vanishing of Novikov homology. As a byproduct, we prove a generic vanishing result for the $L^2$-Betti numbers of very affine manifolds. Our methods also recast June Huh’s extension of Varchenko’s conjecture to very affine manifolds and provide a generalization of this result in the context of smooth closed sub-varieties of semi-abelian varieties.

scholarly journals Kinematic formula and tube formula in space of constant curvature

1990 ◽  
Vol 33 (1) ◽  
pp. 79-88
Author(s):  
Sungyun Lee
Keyword(s):  
Euclidean Space ◽  
Euler Characteristic ◽  
Constant Curvature ◽  
Kinematic Formula ◽  
Curvature Invariants ◽  
Space Of Constant Curvature

The Euler characteristic of an even dimensional submanifold in a space of constant curvature is given in terms of Weyl's curvature invariants. A derivation of Chern's kinematic formula in non-Euclidean space is completed. As an application of above results Weyl's tube formula about an odd-dimensional submanifold in a space of constant curvature is obtained.

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