Robotics research has made extensive use of techniques based on the Moore-Penrose inverse, or generalized-inverse, of matrices. Recently, it has been pointed out how non-invariant results may, in general, be obtained applying these techniques to some areas of robotics, namely hybrid control and inverse velocity kinematics. Unfortunately, the problems are not restricted to just these particular ...

It is known that there is a only one invariant metric, and only one family of invariant affine connections on the the space of probability measures on finite sample spaces. Under certain conditions this may also true for finite measures on finite sample spaces. We extends these results to finite measures on arbitrary sample spaces. It is shown that the generalization of these structures are uni...

In the paper, preliminary results for the classification of microcalcifications (MCs) into the three BIRADSTM morphologic categories (punctate, pleomorphic and linear) have been presented. To classify the microcalcifications into morphologic types the set of 27 shape descriptors has been constructed. The morphology of the cluster has been determined as the mean values of shape descriptors for s...

In a graph or complex network, communities and anti-communities are node sets whose modularity attains extremely large values, positive and negative, respectively. We consider the simultaneous detection of communities and anti-communities, by looking at spectral methods based on various matrixbased definitions of the modularity of a vertex set. Invariant subspaces associated to extreme eigenval...

We study cohomology theories of strongly homotopy algebras, namely A∞, C∞ and L∞-algebras and establish the Hodge decomposition of Hochschild and cyclic cohomology of C∞-algebras thus generalising previous work by Loday and Gerstenhaber-Schack. These results are then used to show that a C∞-algebra with an invariant inner product on its cohomology can be uniquely extended to a symplectic C∞-alge...

We propose a new adaptive filtering algorithm whose convergence rate is very fast even for a highly correlated input signal. It is well-known that convergence rate gets worse when the input signal to an adaptive filter is correlated. Introducing an orthogonal constraint between successive input signal vectors makes us overcome the slow convergence caused by the correlated input signal. It is sh...

We use the theory of pseudo-Hermitian operators to address the problem of the construction and classification of positive-definite invariant inner-products on the space of solutions of a Klein-Gordon type evolution equation. This involves dealing with the peculiarities of formulating a unitary quantum dynamics in a Hilbert space with a timedependent inner product. We apply our general results t...

We study hamiltonian actions of compact groups in the presence of compatible involutions. We show that the lagrangian fixed point set on the symplectically reduced space is isomorphic to the disjoint union of the involutively reduced spaces corresponding to involutions on the group strongly inner to the given one. Our techniques imply that the solution to the eigenvalues of a sum problem for a ...

We consider a singularly perturbed elliptic equation with superlinear nonlinearity on an annulus in R, and look for solutions which are invariant under a fixed point free 1-parameter group action. We show that this problem can be reduced to a non-homogeneous equation on a related annulus in dimension R. The ground state solutions of this equation are single peak solutions which concentrate near...

here, the concept of electric capacity on finsler spaces is introduced and the fundamentalconformal invariant property is proved, i.e. the capacity of a compact set on a connected non-compact finslermanifold is conformal invariant. this work enables mathematicians and theoretical physicists to become morefamiliar with the global finsler geometry and one of its new applications.