Sparse eigenproblems are important for various applications in computer graphics. The spectrum and eigenfunctions of the Laplace--Beltrami operator, example, fundamental methods shape analysis mesh processing. Subspace Iteration Method is a robust solver these problems. In practice, however, Lanczos schemes often faster. this paper, we introduce Hierarchical (HSIM), novel sparse that operates o...

Abstract In this paper, we present a limited-memory common-directions method for smooth optimization that interpolates between first- and second-order methods. At each iteration, subspace of limited dimension size is constructed using first-order information from previous iterations, an efficient Newton deployed to find approximate minimizer within subspace. With properly selected as small two,...

Clustering techniques are used in database mining for nding interesting patterns in high dimensional data. These are useful in various applications of knowledge discovery in databases. Some challenges in clustering for large data sets in terms of scalability, data distribution, understanding end-results, and sensitivity to input order, have received attention in the recent past. Recent approach...

The increasing availability of network data is creating a great potential for knowledge discovery from graph data. In many applications, feature vectors are given in addition to graph data, where nodes represent entities, edges relationships between entities, and feature vectors associated with the nodes represent properties of entities. Often features and edges contain complementary informatio...

Each space C N = {f ∈ C c (R) : sptf ⊂ [−N,N ]} ⊂ C[−N,N ] is strictly smaller than the space C[−N,N ] of all continuous functions on the interval [−N,N ], since functions in C N must vanish at the endpoints. Still, C o N is a closed subspace of the Banach space C [−N,N ] (with sup norm), since a sup-norm limit of functions vanishing at ±N must also vanish there. Thus, each individual C N is a ...

The interactions between topological covering spaces, homotopy and group structures in a fibered space exhibit an array of interesting properties. This paper proposes the formulation finite components compact Lindelof variety (C, R) spaces. spaces form Noetherian structure under injective embeddings. locally path-connected establish set groups, maintaining homomorphism. homeomorphic embedding b...

Discrete return (DR) Laser Detection and Ranging (Ladar) systems provide a series of echoes that reflect from objects in a scene. These can be first, last or multi-echo returns. In contrast, Full-Waveform (FW)-Ladar systems measure the intensity of light reflected from objects continuously over a period of time. In a camouflaged scenario, e.g., objects hidden behind dense foliage, a FW-Ladar pe...

For any degenerating Calabi–Yau family, we introduce a new limit space which call galaxy, whose dense subspace is the disjoint union of countably infinite open varieties, parametrized by rational points Kontsevich–Soibelman’s essential skeleton, while dominated Huber adification over Puiseux series field. Other topics include: projective limits toroidal compactifications (Sect. 3), locally mode...

A subset S of a paratopological group G is suitable set for G, if discrete subspace $$S\cup \{e\}$$ ∪ { e } closed, and the subgroup $$\langle S\rangle $$ ⟨ ⟩ generated by dense in G. Suitable sets topological groups were studied many authors. The aim present paper to provide start-up general investigation groups, looking what extent we can (by proving propositions) or cannot constructing examp...

Let Cb(K) be the set of all bounded continuous (real or complex) functions on a complete metric space K and A a closed subspace of Cb(K). Using the variational method, it is shown that the set of all strong peak functions in A is dense if and only if the set of all strong peak points is a norming subset of A. As a corollary we show that if X is a locally uniformly convex, complex Banach space, ...