According to [9, 8], the initial datum of noncommutative differential geometry is a spectral triple (A,H, D) (see Section 3.1 for the definition), which provides a description of the corresponding geometrical space in terms of spectral data of geometrical operators on this space. The purpose of this paper is to construct spectral triples given by transversally elliptic operators with respect to...

We show that the spectral dimension on non-generic branched polymer models with susceptibility exponent γ > 0 is given by ds = 2/(1 + γ). For those models with γ < 0 we find that ds = 2. PACS: 04.60.Nc, 5.20.-y, 5.60.+w

Learning probabilistic models over strings is an important issue for many applications. Spectral methods propose elegant solutions to the problem of inferring weighted automata from finite samples of variable-length strings drawn from an unknown target distribution. These methods rely on a singular value decomposition of a matrix HS , called the Hankel matrix, that records the frequencies of (s...

As a novel clustering algorithm, spectral clustering is applied in machine learning extensively. Spectral clustering is built upon spectral graph theory, and has the ability to process the clustering of non-convex sample spaces. Most of the existing spectral clustering algorithms are based on k-means algorithm, and k-means algorithm uses the iterative optimization method to find the optimal sol...

Random delays and dynamic frequency switching are widely adopted in smartcards and embedded systems as temporal hiding countermeasures to side channel attack.Temporal hiding is regarded as efficient to enhance the security of cryptographic devices. However, spectral analysis with Fast Fourier Transform is a powerful method to defeat temporal hiding countermeasures. Spectral analysis shares the ...

Using McMullen’s Hausdorff dimension algorithm, we study numerically the dimension of the limit set of groups generated by reflections along three geodesics on the hyperbolic plane. Varying these geodesics, we found four minima in the two-dimensional parameter space, leading to a rigorous result why this must be so. Extending the algorithm to compute the limit measure and its moments, we study ...

Face retrieval has received much attention in recent years. This paper comparatively studied five feature description methods for face representation, including Local Binary Pattern (LBP), Gabor feature, Gray Level Co-occurrence Matrices (GLCM), Pyramid Histogram of Oriented Gradient (PHOG) and Curvelet Transform (CT). The problem of large dimensionalities of the extracted features was addresse...

A genericity condition is removed from a result of Agler and Young which reduces the spectral Nevanlinna-Pick problem in two dimensions to a family of classical Nevanlinna-Pick problems. Unlike the original approach, the argument presented here does not involve state-space methods.

We prove asymptotic equidistribution results for pieces of large closed horospheres in cofinite hyperbolic manifolds of arbitrary dimension. This extends earlier results by Hejhal [10] and Strömbergsson [34] in dimension 2. Our proofs use spectral methods, and lead to precise estimates on the rate of convergence to equidistribution.

The dynamics of networks of neuronal cultures has been recently shown to be strongly dependent on the network geometry and in particular on their dimensionality. However, this phenomenon has been so far mostly unexplored from the theoretical point of view. Here we reveal the rich interplay between network geometry and synchronization of coupled oscillators in the context of a simplicial complex...