Prototype based learning offers an intuitive interface to inspect large quantities of electronic data in supervised or unsupervised settings. Recently, many techniques have been extended to data described by general dissimilarities rather than Euclidean vectors, so-called relational data settings. Unlike the Euclidean counterparts, the techniques have quadratic time complexity due to the underl...

It is well known that synchronously full parallel Boltzmann machines do not converge to the minima of the quadratic energy but to a so called pseudo energy. So far the pseudo energy was treated as a defect disturbing the convergence of these Boltzmann machines. Various simulations suggest that convergence can be ensured if one reduces the degree of parallelism. Another approach that we follow i...

Consider a dynamical system generated by a quadratic mapping of the plane (x, y) 7−→ (λx + xy, μy + x) with parameters λ, μ ∈ R. This 2-parameter family arises as a finite-difference approximation of an ODE system with special quadratic nonlinearity and also as a leading part of a map on a center manifold (in some problems of intersections of bifurcations). Computer experiments on attractors wi...

Ramanujans Ternary Quadratic Form represents a series of numbers that satisfy a tripartite quadratic relation. In the present work, we examine the sequence of numbers generated by such forms and other related forms obtained by varying the coefficients and exponents to other values. Chaotic characterization using standard techniques such as Lyapunov Exponents, Kolmogorov Entropy, Fractal Dimensi...

I show that if an agent is risk neutral over a set of alternatives contained in a Euclidean space, then her utility function decreases linearly in the city block distance to her ideal point. Given a set of alternatives which is not contained in a Euclidean space, I find simple necessary and sufficient conditions on preferences such that, for any p ≥ 1, there exists a mapping of the set of alter...

We present a novel approach for the inverse problem in electrical impedance tomography based on regularized quadratic regression. Our contribution introduces a new formulation for the forward model in the form of a nonlinear integral transform, that maps changes in the electrical properties of a domain to their respective variations in boundary data. Using perturbation theory results the kernel...

We consider the optical flow estimation problem with lp sub-quadratic regularization, where 0 ≤ p ≤ 1. As in other image analysis tasks based on functional minimization, sub-quadratic regularization is expected to admit discontinuities and avoid oversmoothing of the estimated optical flow field. The problem is mathematically challenging, since the regularization term is non-differentiable. It i...