This paper introduces the ―min-additive‖ (also called ―min-average‖) utility function. This function is a weighted combination of an additive utility function and a minimization over a set of single attribute utility functions. The weighting is accomplished by exploiting information already contained in the additive and minimization models. Four forms of the min-additive (MA) model are presente...

We explore a method for computing admissible heuristic evaluation functions for search problems. It utilizes pattern databases (Culberson & Schaeffer, 1998), which are precomputed tables of the exact cost of solving various subproblems of an existing problem. Unlike standard pattern database heuristics, however, we partition our problems into disjoint subproblems, so that the costs of solving t...

In this paper, we solve the additive ρ-functional inequalities ‖f(x+ y)− f(x)− f(y)‖ ≤ ∥∥∥∥ρ(2f (x+ y 2 ) − f(x)− f(y) )∥∥∥∥ , (1) ∥∥∥∥2f (x+ y 2 ) − f(x)− f(y) ∥∥∥∥ ≤ ‖ρ (f(x+ y)− f(x)− f(y))‖ , (2) where ρ is a fixed non-Archimedean number with |ρ| < 1 or ρ is a fixed complex number with |ρ| < 1. Using the direct method, we prove the Hyers-Ulam stability of the additive ρ-functional inequalit...

For A,B subsets of an additive group Z, we define A + B to be the sumset {a + b : a ∈ A, b ∈ B}, and kA to be the k-fold sum A + A + · · · + A of A. We also let A−B = {a−b : a ∈ A, b ∈ B} and b+A = {b}+A for a single element set {b}, a translate of A. Note that A − A is not 0 unless |A| = 1. We let k ¦ A = {ka : a ∈ A}, a dilate of A. There are many obvious properties of “+” that can be checked...

Let A be an asymptotic basis for N0 of some order. By an essentiality of A one means a subset P such that A\P is no longer an asymptotic basis of any order and such that P is minimal among all subsets of A with this property. A finite essentiality of A is called an essential subset. In a recent paper, Deschamps and Farhi asked the following two questions : (i) does every asymptotic basis of N0 ...

as a fragmentation of unit mass into clusters of masses xi. The additive coalescent of Evans and Pitman is the -valued Markov process in which pairs of clusters of masses xi xj merge into a cluster of mass xi + xj at rate xi + xj. They showed that a version X∞ t −∞ < t < ∞ of this process arises as a n → ∞ weak limit of the process started at time − 2 log n with n clusters of mass 1/n. We show ...

This is essentially the talk I gave on definable additive categories; I define these categories, say where they came from, describe some of what is around them and then point out the 2-category which

We propose an extensive framework for additive regression models for correlated functional responses, allowing for multiple partially nested or crossed functional random effects with flexible correlation structures for, e.g., spatial, temporal, or longitudinal functional data. Additionally, our framework includes linear and nonlinear effects of functional and scalar covariates that may vary smo...