Results 41 to 50 of about 4,356 (253)
On the α-connections and the α-conformal equivalence on statistical manifolds [PDF]
Arab Journal of Mathematical SciencesPurpose – In this paper, we give some properties of the α-connections on statistical manifolds and we study the α-conformal equivalence where we develop an expression of curvature R¯ for ∇¯ in relation to those for ∇ and ∇^. Design/methodology/approach –
Khadidja Addad, Seddik Ouakkas
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An Alzheimer’s disease category progression sub-grouping analysis using manifold learning on ADNI
Scientific Reports, 2023 Many current statistical and machine learning methods have been used to explore Alzheimer’s disease (AD) and its associated patterns that contribute to the disease.
Dustin van der Haar +4 more
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Hypersurfaces in statistical manifolds
Differential Geometry and its Applications, 2009 A statistical structure on a manifold \(M\) consists of a Riemannian metric \(g\) and a torsion-free affine connection \(\nabla\) that satisfies \( (\nabla_Xg)(Y,Z) = (\nabla_Yg)(X,Z)\) for all vector fields \(X\), \(Y\), and \(Z\) on \(M\). The statistical manifold \((M, \nabla, g)\) has constant curvature \(k\) if \[ R^\nabla(X,Y)Z = k(g(Y,Z)X-g(X,Z ...
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SYMPLECTIC STRUCTURES ON STATISTICAL MANIFOLDS [PDF]
Journal of the Australian Mathematical Society, 2011 AbstractA relationship between symplectic geometry and information geometry is studied. The square of a dually flat space admits a natural symplectic structure that is the pullback of the canonical symplectic structure on the cotangent bundle of the dually flat space via the canonical divergence. With respect to the symplectic structure, there exists a
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Molecular Oncology, EarlyView.Tumors contain diverse cellular states whose behavior is shaped by context‐dependent gene coordination. By comparing gene–gene relationships across biological contexts, we identify adaptive transcriptional modules that reorganize into distinct vulnerability axes.
Brian Nelson +9 more
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Robustness of statistical manifolds
Topology and its Applications, 2023 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Loi, A., Matta, S.
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Molecular Oncology, EarlyView.Pre‐analytical handling critically determines liquid biopsy performance. This study defines practical best‐practice conditions for cell‐free DNA (cfDNA) and extracellular vesicle–derived DNA (evDNA), showing how processing time, storage conditions, tube type, and plasma input volume affect DNA integrity and mutation detection.
Jonas Dohmen +11 more
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Molecular Oncology, EarlyView.Glioma cells mainly express the endothelin receptor EDNRB, while EDNRA is restricted to a perivascular tumor subpopulation. Endothelin signaling reduces glioma cell proliferation while promoting migration and a proneural‐to‐mesenchymal transition associated with poor prognosis. This pathway activates Ca2+, K+, ERK, and STAT3 signalings and is regulated
Donovan Pineau +36 more
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Classification and Geometry of General Perceptual Manifolds
Physical Review X, 2018 Perceptual manifolds arise when a neural population responds to an ensemble of sensory signals associated with different physical features (e.g., orientation, pose, scale, location, and intensity) of the same perceptual object.
SueYeon Chung +2 more
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Tensor Balancing on Statistical Manifold
CoRR, 2017 We solve tensor balancing, rescaling an Nth order nonnegative tensor by multiplying N tensors of order N - 1 so that every fiber sums to one. This generalizes a fundamental process of matrix balancing used to compare matrices in a wide range of applications from biology to economics.
Mahito Sugiyama +2 more
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