Asymptotic net is an important concept in discrete differential geometry. In this paper, we show that we can associate affine discrete geometric concepts to an arbitrary non-degenerate asymptotic net. These concepts include discrete affine area, mean curvature, normal and co-normal vector fields and cubic form, and they are related by structural and compatibility equations. We consider also the...

The statistical bundle is the set of couples (Q, W) of a probability density Q and a random 1 variable W such that EQ [W] = 0. On a finite state space, we assume Q to be a probability density with 2 respect to the uniform probability and give an affine atlas of charts such that the resulting manifold is 3 a model for Information Geometry. Velocity and accelleration of a one-dimensional statisti...

This article provides new developments in characterizing the class of regime-switching exponential affine interest rate processes context pricing a zero-coupon bond. A finite-state Markov chain continuous time dictates random switching time-dependent parameters such processes. We present exact and approximate bond formulas by solving system partial differential equations minimizing an error fun...

This paper studies output feedback control of pure-feedback systems with immeasurable states and completely non-affine property. Since availability of all the states is usually impossible in the actual process, we assume that just the system output is measurable and the system states are not available. First, to estimate the immeasurable states a state observer is designed. Relatively fewer res...

We find and study a five-parameter family of four-dimensional coupled Painlevé V systems with affine Weyl group symmetry of type D (1) 5 . We then give an explicit description of a confluence from those systems to a four-parameter family of four-dimensional coupled Painlevé III systems with affine Weyl group symmetry of type B (1) 4 . 0. Introduction It is well-known that the Painlevé systems P...

The problem of simultaneously estimating affine deformations between multiple objects occur in many applications. Herein, a direct method is proposed which provides the result as a solution of a linear system of equations without establishing correspondences between the objects. The key idea is to construct enough linearly independent equations using covariant functions, and then finding the so...

We develop a convergence analysis of a multi-level algorithm combining higher order quasi-Monte Carlo (QMC) quadratures with general Petrov-Galerkin discretizations of countably affine parametric operator equations of elliptic and parabolic type, extending both the multi-level first order analysis in [F.Y. Kuo, Ch. Schwab, and I.H. Sloan, Multi-level quasi-Monte Carlo finite element methods for...

Most work on the problem of scheduling computations onto a systolic array is restricted to systems of uniform recurrence equations. In this paper, this restriction is relaxed to include systems of affine recurrence equations. In this broader class, a sufficient condition is given for the system to be computable. Necessary and sufficient conditions are given for the existence of an affine schedu...