New manifold types defined on quotient spaces.
problem Characterizing specific manifold structures.
method Introducing decomposable LCP manifolds and studying their properties.
result Characterized LCP manifolds on quotient spaces.
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16 results for “LCP”
Conformal vector fields on LCP manifolds are orthogonal and Killing.
problem Understanding conformal vector fields on specific geometric manifolds.
method Analyzing properties of conformal vector fields on compact locally conformally product manifolds.
result Conformal vector fields are orthogonal to the flat distribution and Killing.
This paper shows the reduced characteristic group of Lie LCP manifolds is simply connected.
problem Understanding the structure of Lie LCP manifolds and their characteristic groups.
method Restricting the action of the fundamental group to the non-flat factor of the universal cover and taking the connected component of the identity in the closure of this restriction.
result The reduced characteristic group of any Lie LCP manifold is simply connected.
Locally conformally product structures defined on compact manifolds.
problem Defining and characterizing locally conformally product structures on compact manifolds.
method Using reducible, non-flat, incomplete Riemannian metrics and connections with specific properties.
result Construction of new LCP structures from existing ones and links to number field theory.
This paper describes the characteristic group of LCP structures and their construction.
problem Understanding the characteristic group of LCP structures and their construction.
method Analyzing the characteristic group and constructing LCP structures.
result It is possible to endow certain quotients with LCP structures.
Study LCP structures on solvmanifolds, complete list up to 5 dimensions.
problem Characterize LCP structures on solvable Lie groups.
method Classify LCP structures on Lie groups, focus on solvable unimodular case.
result Complete list of solvable unimodular Lie algebras up to dimension 5 with LCP structures.
In this paper, we present a novel unsupervised feature learning architecture, which consists of a multi-clustering integration module and a variant of RBM termed multi-clustering integration RBM (MIRBM). In the multi-clustering integration module, we apply three unsupervised K-means, affinity propagation and spectral c…
New projection techniques reduce the frequency of projections in solving LCPs.
problem Solving linearly constrained problems efficiently with reduced projection frequency.
method Delayed projection technique to call a projection less frequently.
result Theoretical and practical improvements in convergence rates and efficiency.
Locally conformally product Lie algebras are characterized and constructed.
problem Characterizing and constructing compact locally conformally product Lie algebras.
method Characterization via closed 1-forms and non-unimodular Lie algebras acting on abelian ones.
result Explicit examples of compact LCP manifolds that are not solvmanifolds.
Paper proposes LCP for structural encodings, outperforming existing methods.
problem Improving Graph Neural Networks performance through effective structural encodings.
method Geometric perspective, Local Curvature Profiles (LCP) for structural encodings, combining with global positional encodings, comparing with rewiring techniques.
result LCP significantly outperforms existing structural encodings and combining LCP with global positional encodings improves performance.
The abstract discusses compact quotients of Riemannian products by discrete subgroups, generalizing Inoue-Bombieri surfaces.
problem Compact quotients of Riemannian products by discrete subgroups.
method Study of compact quotients of a Riemannian product by discrete subgroups of .
result The construction is equivalent to LCP manifolds and provides a Bieberbach-type rigidity result.
Classifies Weyl structures on compact conformal manifolds with special holonomy.
problem Classifying Weyl structures on compact conformal manifolds with specific holonomy properties.
method Analyzes the properties of connections preserving the conformal structure and classifies structures based on their holonomy.
result Local classification of Weyl structures on compact conformal manifolds with special holonomy.
European options can be priced by solving parabolic partial(-integro) differential equations under stochastic volatility and jump-diffusion models like Heston, Merton, and Bates models. American option prices can be obtained by solving linear complementary problems (LCPs) with the same operators. A finite difference di…
In this paper, we demonstrate that policy iteration, introduced in the context of HJB equations in [Forsyth & Labahn, 2007], is an extremely simple generic algorithm for solving linear complementarity problems resulting from the finite difference and finite element approximation of American options. We show that, in ge…
Two DRL policies collaborate to solve NP-hard routing problems.
problem Solving complex routing problems like TSP without expert knowledge.
method Learning Collaborative Policies (LCP) using seeder and reviser policies.
result Improves solution quality over single-policy DRL on various NP-hard routing problems.
Banach's fixed point theorem for contraction maps has been widely used to analyze the convergence of iterative methods in non-convex problems. It is a common experience, however, that iterative maps fail to be globally contracting under the natural metric in their domain, making the applicability of Banach's theorem li…