The direction of neurite elongation is controlled by various environmental cues. However, it has been reported that even in the absence of any extrinsic directional signals, neurites turn clockwise on two-dimensional substrates. In this study, we have discovered autonomous rotational motility of the growth cone, which provides a cellular basis for inherent neurite turning. We have developed a t...

In this work we are interested in nonlinear symmetric cone problems (NSCPs), which contain as special cases nonlinear semidefinite programming, nonlinear second order cone programming and the classical nonlinear programming problems. We explore the possibility of reformulating NSCPs as common nonlinear programs (NLPs), with the aid of squared slack variables. Through this connection, we show ho...

In this paper, we study iteration complexities of Mizuno-Todd-Ye predictor-corrector (MTY-PC) algorithms in SDP and symmetric cone programs by way of curvature integrals. The curvature integral is defined along the central path, reflecting the geometric structure of the central path. The idea to exploit the curvature of the central path for the analysis of iteration complexities is based on the...

Based on an inverse function theorem for a system of semismooth equations, this paper establishes several necessary and sufficient conditions for an isolated solution of a complementarity problem defined on the cone of symmetric positive semidefinite matrices to be strongly regular/stable. We show further that for a parametric complementarity problem of this kind, if a solution corresponding to...

A receptor cone-1 based on a hexahomotrioxacalix[3]arene bearing three pyridyl groups was successfully synthesized, which has a C₃-symmetric conformation and is capable of binding alkylammonium and metal ions simultaneously in a cooperative fashion. It can bind alkylammonium ions through the -cavity formed by three aryl rings. This behaviour is consistent with the cone-in/cone-out conformation...

In this note, we obtain a recursive formula for the spherical functions associated with the symmetric cone of a formally real Jordan algebra. We use this formula as an inspiration for a similar recursive formula involving the Jack polynomials.

In this paper, we consider a sparse program with symmetric cone constrained parameterized generalized equations (SPSCC). Such problem is analogue vector optimization, and aim to provide smoothing framework for dealing SPSCC that includes classical complementarity problems the nonnegative cone, semidefinite second-order cone. An effective approximation given focus on solving perturbation problem...

This article deals with linear complementarity problems over symmetric cones. Our objective here is to characterize global uniqueness and solvability properties for linear transformations that leave the symmetric cone invariant. Specifically, we show that, for algebra automorphisms on the Lorentz space Ln and for quadratic representations on any Euclidean Jordan algebra, global uniqueness, glob...