The purpose of this article is to present the theory of higher order connections on vector bundles from a viewpoint inspired by projective differential geometry.

We have designed agents to participate in one of the internet auctions|Michigan AuctionBot. The agents communicate with the AuctionBot through API. For the inference mechanism underlying the agent, we use regression methods for online derivation of functional relations between other agents' actions and their internal states. The functional form of a regression model is based on an agent's assum...

We studied the mathematical relations between species abundance distributions (SADs) and species-area relationships (SARs) and found that a power-law SAR can be generally derived from a power-law SAD without a special assumption such as the “canonical hypothesis”. In the present analysis, an SAR-exponent is obtained as a function of an SAD-exponent for a finite number of species. We also studie...

A method for dynamically updating running code is described. The method is "principled" in that old functionality is not destroyed. Rather, new functionality is added which can selectively and dynamically change the overall behavior of the system, yet all formal properties of the original system are guaranteed to still hold. Higher-order functions are the key to making this work, and an impleme...

We introduce a solvable model of randomly growing systems consisted of many independent subunits. Scaling relations and growth rate distributions in the limit of infinite subunits are analyzed theoretically. Various types of scaling properties and distributions reported for growth rates of complex systems in wide fields can be derived from this basic physical model. Statistical data of growth r...

The slow roll approximation is studied for cosmological models in Hyperextended Scalar-Tensor Theories of Gravity. A procedure to obtain slow roll solutions in non-minimally coupled gravity is outlined and some examples are provided. An integral condition over the functional form of the non-minimal coupling is imposed in order to obtain intermediate inflationary behavior. e-mail: dtorres@venus....

Two major degradations, edge displacement and comer erosion, change the appearance of bilevel images. The displacement of an edge determines stroke width, and the erosion ofa comer affects crispness. These degradations are functions of the system parameters: the point spread function (PSF) width and functional form, and the binarization threshold. Changing each of these parameters will affect a...

Abs t rac t . In [3] a general fohl ol)eration has been introduced for definite programs wrt computed answer substitution semantics. It differs from the fold operation defined by Tama.ki and Sato in [26,25] because its application does not depend on the tra.~sformation history. This paper extends the results in [3] by giving a more powerful sufficient condition for the preservation of computed ...

A natural algebraic approach to the KdV hierarchy and its algebro-geometric finite-gap solutions is developed. In addition, a new derivation of associated higher-order trace formulas in connection with one-dimensional Schrödinger operators is presented.

We introduce a regularization method for mean curvature flow of a submanifold of arbitrary codimension in the Euclidean space, through higher order equations. We prove that the regularized problems converge to the mean curvature flow for all times before the first singularity.