Results presented in this paper represent part of an ongoing research programme dedicated to the resolution enhancement of Fourier domain magnetic resonance (MR) data. Here we explore the use of selfsimilarity methods that may aid in frequency extrapolation of such data. To this end, we present analytical and empirical results demonstrating the self similarity of complex, Fourier domain MR data.

We consider self-similar statistical ensembles with the phase space whose volume is invariant under the deformation that squeezes (expands) the coordinate and expands (squeezes) the momentum. Related probability distribution function is shown to possess a discrete symmetry with respect to manifold action of the Jackson derivative to be a homogeneous function with a self-similarity degree q fixe...

In this paper, new binary extremal self-dual codes are presented. A number of new extremal singly-even self-dual codes of lengths 48; 64 and 78, and extremal doubly-even self-dual codes of lengths 80 and 88, are constructed. We also relate an extremal doubly-even self-dual code of length divisible by 24 to an extremal singly-even self-dual code of that length. New singly-even self-dual codes of...

This paper presents a compact and efficient shape signature that can be applied to shape retrieval from handdrawn sketches. The two proposed invariant features that constitute our affine invariant signature are: (a) angle between spoke vectors, and (b) cumulated normalized area between consecutive spoke vectors. The signature can be computed efficiently from an input shape and supports fast sim...

In this work, new construction methods for self-dual codes are given. The methods use the short Kharaghani array and a variation of it. These are applicable to any commutative Frobenius ring. We apply the constructions over the ring F2 + uF2 and self-dual Type I [64, 32, 12]2-codes with various weight enumerators obtained as Gray images. By the use of an extension theorem for self-dual codes we...

“We introduce a new family of expanding wave solutions of the Einstein equations, and argue that they could account for the observed anomalous acceleration of the galaxies without Dark Energy. Currently, the anomalous acceleration is accounted for by adding in the cosmological constant (Dark Energy) to the Einstein equations, an artificial correction term that speeds up the expansion rate. In c...

Popular music segmentation plays an important role in popular music content retrieval, melody extraction and semantic understanding etc. Segmentation boundary detection is one of the key technologies in lots of conventional algorithms. In this paper, we propose an automatic segmentation approach that combines SVM classification and audio self-similarity segmentation, which firstly separate the ...

“We introduce a new family of expanding wave solutions of the Einstein equations, and argue that they could account for the observed anomalous acceleration of the galaxies without Dark Energy. Currently, the anomalous acceleration is accounted for by adding in the cosmological constant (Dark Energy) to the Einstein equations, an artificial correction term that speeds up the expansion rate. In c...

We prove that the rescaled costs of partial match queries in a random two-dimensional quadtree converge almost surely towards a random limit which is identified as the terminal value of a martingale. Our approach shares many similarities with the theory of self-similar fragmentations.