We present an evolution-based method for optimal mechanism synthesis. It is based on the embedding of the Euclidean motion group in the space of affine displacements upon which an object-oriented Euclidean metric is imposed. This Euclidean structure allows the use of curve and surface evolution techniques from computer aided design and image processing. We demonstrate the algorithm by synthesiz...

We study the linearization of three dimensional Regge calculus around Euclidean metric. We provide an explicit formula for the corresponding quadratic form and relate it to the curlt curl operator which appears in the quadratic part of the Einstein-Hilbert action and also in the linear elasticity complex. We insert Regge metrics in a discrete version of this complex, equipped with densily defin...

Let B be the closed unit ball in R and S its boundary. We define a family of pseudo metrics on B. As an application, we prove that for any countable-to-one function f : S → [0, a], the set NMnf = {x ∈ S 2 | there exists y ∈ S2 such that f(x)−f(y) > ndE(x, y)} is uncountable for all n ∈ N, where dE is the Euclidean metric on R . 2000 Mathematics Subject Classification ; 57N05, 57M40 1 The family...

We prove that, building upon the universal-existential orthogonality-based axiom system for metric planes presented in [28], one can provide universal-existential axiom systems – expressed solely in terms of the ternary predicate I, with I(abc) standing for ‘ab is congruent to ac’, which Pieri has introduced 100 years ago – for metric planes, for absolute geometry with the circle axiom, for Euc...

Diffusion tensor imaging has become an important research and clinical tool, owing to its unique ability to infer microstructural properties of living tissue. Increased use has led to a demand for statistical tools to analyze diffusion tensor data and perform, for example, confidence estimates, ROI analysis, and group comparisons. A first step towards developing a statistical framework is estab...

Previous methods for accelerating Tanimoto queries have been based on using bit strings for representing molecules. No work has gone into examining accelerating Tanimoto queries on real valued descriptors, even though these offer a much more fine grained measure of similarity between molecules. This study utilises a recently discovered reduction from Tanimoto queries to distance queries in Eucl...

We consider the stochastic quantization method for scalar fields defined in a curved manifold. The two-point function associated to a massive self-interacting scalar field is evaluated, up to the first order level in the coupling constant λ, for the case of de Sitter Euclidean metric. Its value for the asymptotic limit of the Markov parameter τ → ∞ is exhibited. We discuss in detail the covaria...

We first investigate the combined effect of data complexity, curse of dimensionality and the definition of the Euclidean distance on the distance measure between points. Then, based on the concepts underlying manifold learning algorithms and the minimum volume ellipsoid metric, we design an algorithm that learns a local metric on the lower dimensional manifold on which the data is lying. Experi...

(1.2) PIH : C(Sn−1) −→ C(B) ∩ C∞(Bn), such that u = PIH f solves (1.2A) ∆Hu = 0 on B, u ∣∣ Sn−1 = f. Here, ∆H is the Laplace-Beltrami operator on B, with metric tensor (1.1). We will establish further regularity on u = PIH f when f has some further smoothness on Sn−1, and estimate du(x), in the hyperbolic metric, as x → ∂B. If n = 2, then ∆Hu = 0 if and only if ∆u = 0, where ∆ = ∂ 1 +∂ 2 2 is t...

We give a new proof of the complete integrability of the geodesic flow on the ellipsoid (in Euclidean, spherical or hyperbolic space). The proof is based on the construction of a metric on the ellipsoid whose non-parameterized geodesics coincide with those of the standard metric. This new metric is induced by the hyperbolic metric inside the ellipsoid (Klein’s model). Mathematics Subject Classi...