Some Information Geometric Aspects of Cyber Security by Face Recognition by C. T. J. Dodson, John Soldera, Jacob Scharcanski

“…The important provision is of a natural geometric measure structure on families of probability distributions by representing them as Riemannian manifolds. Then the distributions are points lying in this geometrical manifold, different features can be identified and dissimilarities computed, so that neighbourhoods of objects nearby a given example object can be constructed. …”
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Geometry of <em>k</em>-Yamabe Solitons on Euclidean Spaces and Its Applications to Concurrent Vector Fields by Akram Ali, Fatemah Mofarreh, Pişcoran Laurian-Ioan, Nadia Alluhaibi

“…In several results on <i>k</i>-Yamabe solitons with a concurrent vector field on submanifolds in Riemannian manifolds, is proved that a <i>k</i>-Yamabe soliton <inline-formula><math display="inline"><semantics><mrow><mo>(</mo><msup><mi>M</mi><mi>n</mi></msup><mo>,</mo><mi>g</mi><mo>,</mo><msup><mi>v</mi><mi>T</mi></msup><mo>,</mo><mi>λ</mi><mo>)</mo></mrow></semantics></math></inline-formula> on a hypersurface in the Euclidean space <inline-formula><math display="inline"><semantics><msup><mi mathvariant="double-struck">R</mi><mrow><mi>n</mi><mo>+</mo><mn>1</mn></mrow></msup></semantics></math></inline-formula> is contained either in a hypersphere or a hyperplane. …”
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Geometry of sample spaces by Harms, Philipp, Michor, Peter W., Pennec, Xavier, Sommer, Stefan

“…We aim at deriving a general mathematical setting for studying the behavior of empirical and population means in spaces ranging from smooth Riemannian manifolds to general stratified spaces. We fully describe the orbifold and path-metric structure of the sample space when M is a manifold or path-metric space, respectively. …”
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Topics in non-convex optimization and learning by Zhang, Hongyi,Ph. D.Massachusetts Institute of Technology.

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Bounds for Eigenvalues of <i>q</i>-Laplacian on Contact Submanifolds of Sasakian Space Forms by Yanlin Li, Fatemah Mofarreh, Abimbola Abolarinwa, Norah Alshehri, Akram Ali

“…This study establishes new upper bounds for the mean curvature and constant sectional curvature on Riemannian manifolds for the first positive eigenvalue of the <i>q</i>-Laplacian. …”
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On an isoperimetric-isodiametric inequality by Mondino, A, Spadaro, E

“…The goal of the paper is to investigate such mixed isoperimetric-isodiametric inequalities in Riemannian manifolds. We first prove that the same inequality, with the sharp Euclidean constants, holds on Cartan-Hadamard spaces as well as on minimal submanifolds of ℝn. …”

Acceleration in first-order optimization methods: promenading beyond convexity or smoothness, and applications by Martinez Rubio, D

“…In this thesis, we investigate the acceleration phenomenon and its applications for three previously studied research questions in optimization and online learning: geodesically convex accelerated optimization in Riemannian manifolds, approximation of a proportional fair solution under positive linear constraints, also known as the 1-fair packing problem, and regret minimization in a decentralized cooperative stochastic multi-armed bandit problem with no reward collisions. …”

Lower bounds on Ricci curvature and quantitative behavior of singular sets by Cheeger, Jeff, Naber, Aaron Charles

“…Let Yn denote the Gromov-Hausdorff limit M[superscript n][subscript i][d[subscript GH] over ⟶]Y[superscript n] of v-noncollapsed Riemannian manifolds with Ric[subscript M[superscript n][subscript i]] ≥ −(n−1). …”
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Prime Geodesic Theorems for Compact Locally Symmetric Spaces of Real Rank One by Dženan Gušić

“…Our basic objects will be compact, even-dimensional, locally symmetric Riemannian manifolds with strictly negative sectional curvature. …”
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Harmonic maps and associated energy functionals by Tošić, O

“…There have been many results in this vein, culminating in the result of Benoist–Hulin asserting the existence of a harmonic map at a finite distance from an arbitrary quasi-isometry between pinched Hadamard manifolds (i.e. complete simply connected Riemannian manifolds with sectional curvatures bounded between two negative constants). …”

Advanced topics in learning to hash for large-scale retrieval by Huang, Long-Kai

“…The local approximation objective is solved by Riemannian optimization and its convergence is analyzed using the property of the objective function on Riemannian manifolds. To sum up, in this dissertation, we propose a series of learning to hash methods to address the challenge of training hash models in large-scale applications and we verify the state-of-the-art performances of all the proposed learning to hash models through extensive experiments on benchmark datasets.…”
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Poisson Doubly Warped Product Manifolds by Ibrahim Al-Dayel, Foued Aloui, Sharief Deshmukh

“…This article generalizes some geometric structures on warped product manifolds equipped with a Poisson structure to doubly warped products of pseudo-Riemannian manifolds equipped with a doubly warped Poisson structure. …”
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