We study the chaotic behavior of order parameters in two coupled ensembles of self-sustained oscillators. Coupling within each of these ensembles is switched on and off alternately, while the mutual interaction between these two subsystems is arranged through quadratic nonlinear coupling. We show numerically that in the course of alternating Kuramoto transitions to synchrony and back to asynchr...

In this paper, the abstract computational principles underlying topographic maps are discussed. We give a definition of a “perfectly neighbourhood preserving” map, which we call a topographic homeomorphism, and we prove that this has certain desirable properties. It is argued that when a topographic homeomorphism does not exist (the usual case), many equally valid choices are available for quan...

We investigate Poisson properties of Postnikov’s map from the space of edge weights of a planar directed network into the Grassmannian. We show that this map is Poisson if the space of edge weights is equipped with a representative of a 6-parameter family of universal quadratic Poisson brackets and the Grasmannian is viewed as a Poisson homogeneous space of the general linear group equipped wit...

We present a spatiotemporally integrated formulation of the optimal fractionation problem using the standard log-linear-quadratic survival model. Our objective is to choose a fluencemap and a number of fractions so as to maximize the biological effect of tumor dose averaged over its voxels subject to maximum dose, mean dose, and dose-volume constraints for various normal tissues. Constrains are...

Assume both X and Y are Riemann surfaces which are subsets of compact Riemann surfaces X1 and Y1, respectively, and that the set X1 −X has infinitely many points. We show that the only surjective complex linear isometries between the spaces of integrable holomorphic quadratic differentials on X and Y are the ones induced by conformal homeomorphisms and complex constants of modulus 1. It follows...

Piece in Hand method is a security enhancement method for Multivariate Public Key Cryptosystems (MPKCs). Since 2004, many types of this method have been proposed. In this paper, we consider the 2-layer nonlinear Piece in Hand method as proposed by Tsuji et al. in 2009. The key point of this method is to introduce an invertible quadratic polynomial map on the plaintext variables to construct per...

Graph matching and MAP inference are essential problems in computer vision and machine learning. We introduce a novel algorithm that can accommodate both problems and solve them efficiently. Recent graph matching algorithms are based on a general quadratic programming formulation, which takes in consideration both unary and second-order terms reflecting the similarities in local appearance as w...

A new method for anatomically labeling the vasculature is presented and applied to the Circle of Willis. Our method converts the segmented vasculature into a graph that is matched with an annotated graph atlas in a maximum a posteriori (MAP) way. The MAP matching is formulated as a quadratic binary programming problem which can be solved efficiently. Unlike previous methods, our approach can ha...

We consider the inversion of a linear operator with centered Gaussian white noise by MAP estimation with a Gaussian prior distribution on the solution. The actual estimator is computed approximately by a numerical method. We propose a relation between the stationarity measure of this approximate solution to the mean square error of the exact solution. This relation enables the formulation of a ...

We report on a type of scaling behavior in quasiperiodically forced systems. On the parameter plane the critical point appears as a terminal point of the tori-collision bifurcation curve; its location is found numerically with high precision for two basic models, the forced supercritical circle map and the forced quadratic map. The hypothesis of universality, based on renormalization group argu...