292 research outputs found
Identifying prognostic structural features in tissue sections of colon cancer patients using point pattern analysis
Diagnosis and prognosis of cancer is informed by the architecture inherent in cancer patient tissue sections. This architecture is typically identified by pathologists, yet advances in computational image analysis facilitate quantitative assessment of this structure. In this article we develop a spatial point process approach in order to describe patterns in cell distribution within tissue samples taken from colorectal cancer (CRC) patients. In particular, our approach is centered on the Palm intensity function. This leads to taking an approximate-likelihood technique in fitting point processes models. We consider two Neyman-Scott point processes and a void process, fitting these point process models to the CRC patient data. We find that the parameter estimates of these models may be used to quantify the spatial arrangement of cells. Importantly, we observe characteristic differences in the spatial arrangement of cells between patients who died from CRC and those alive at follow-up
Opposite Antipodal Fundamental Solution of Laplace's Equation in Hyperspherical Geometry
Due to the isotropy of -dimensional hyperspherical space, one expects
there to exist a spherically symmetric opposite antipodal fundamental solution
for its corresponding Laplace-Beltrami operator. The -radius hypersphere
with , represents a Riemannian manifold with
positive-constant sectional curvature. We obtain a spherically symmetric
opposite antipodal fundamental solution of Laplace's equation on this manifold
in terms of its geodesic radius. We give several matching expressions for this
fundamental solution including a definite integral over reciprocal powers of
the trigonometric sine, finite summation expressions over trigonometric
functions, Gauss hypergeometric functions, and in terms of the Ferrers function
of the second with degree and order given by and respectively,
with real argument .Comment: essentially corrected versio
Digital Analytical Geometry: How do I define a digital analytical object?
International audienceThis paper is meant as a short survey on analytically de-ned digital geometric objects. We will start by giving some elements on digitizations and its relations to continuous geometry. We will then explain how, from simple assumptions about properties a digital object should have, one can build mathematical sound digital objects. We will end with open problems and challenges for the future
Basic Understanding of Condensed Phases of Matter via Packing Models
Packing problems have been a source of fascination for millenia and their
study has produced a rich literature that spans numerous disciplines.
Investigations of hard-particle packing models have provided basic insights
into the structure and bulk properties of condensed phases of matter, including
low-temperature states (e.g., molecular and colloidal liquids, crystals and
glasses), multiphase heterogeneous media, granular media, and biological
systems. The densest packings are of great interest in pure mathematics,
including discrete geometry and number theory. This perspective reviews
pertinent theoretical and computational literature concerning the equilibrium,
metastable and nonequilibrium packings of hard-particle packings in various
Euclidean space dimensions. In the case of jammed packings, emphasis will be
placed on the "geometric-structure" approach, which provides a powerful and
unified means to quantitatively characterize individual packings via jamming
categories and "order" maps. It incorporates extremal jammed states, including
the densest packings, maximally random jammed states, and lowest-density jammed
structures. Packings of identical spheres, spheres with a size distribution,
and nonspherical particles are also surveyed. We close this review by
identifying challenges and open questions for future research.Comment: 33 pages, 20 figures, Invited "Perspective" submitted to the Journal
of Chemical Physics. arXiv admin note: text overlap with arXiv:1008.298
Optimal Consensus set for nD Fixed Width Annulus Fitting
International audienceThis paper presents a method for fitting a nD fixed width spherical shell to a given set of nD points in an image in the presence of noise by maximizing the number of inliers, namely the consensus set. We present an algorithm, that provides the optimal solution(s) within a time complexity O(N n+1 log N) for dimension n, N being the number of points. Our algorithm guarantees optimal solution(s) and has lower complexity than previous known methods
Iris Codes Classification Using Discriminant and Witness Directions
The main topic discussed in this paper is how to use intelligence for
biometric decision defuzzification. A neural training model is proposed and
tested here as a possible solution for dealing with natural fuzzification that
appears between the intra- and inter-class distribution of scores computed
during iris recognition tests. It is shown here that the use of proposed neural
network support leads to an improvement in the artificial perception of the
separation between the intra- and inter-class score distributions by moving
them away from each other.Comment: 6 pages, 5 figures, Proc. 5th IEEE Int. Symp. on Computational
Intelligence and Intelligent Informatics (Floriana, Malta, September 15-17),
ISBN: 978-1-4577-1861-8 (electronic), 978-1-4577-1860-1 (print
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