Varieties of Cost Functions.

Regular cost functions were introduced as a quantitative generalisation of regular languages, retaining many of their equivalent characterisations and decidability properties. For instance, stabilisation monoids play the same role for cost functions as monoids do for regular languages. The purpose of this article is to further extend this algebraic approach by generalising two results on regular languages to cost functions: Eilenberg's varieties theorem and profinite equational characterisations of lattices of regular languages. This opens interesting new perspectives, but the specificities of cost functions introduce difficulties that prevent these generalisations to be straightforward. In contrast, although syntactic algebras can be defined for formal power series over a commutative ring, no such notion is known for series over semirings and in particular over the tropical semiring

Comparing Cost Functions in Resource Analysis

Cost functions provide information about the amount of resources required to execute a program in terms of the sizes of input arguments. They can provide an upper-bound, a lower-bound, or the average-case cost. Motivated by the existence of a number of automatic cost analyzers which produce cost functions, we propose an approach for automatically proving that a cost function is smaller than another one. In all applications of resource analysis, such as resource-usage verification, program synthesis and optimization, etc., it is essential to compare cost functions. This allows choosing an implementation with smaller cost or guaranteeing that the given resource-usage bounds are preserved. Unfortunately, automatically generated cost functions for realistic programs tend to be rather intricate, defined by multiple cases, involving non-linear subexpressions (e.g., exponential, polynomial and logarithmic) and they can contain multiple variables, possibly related by means of constraints. Thus, comparing cost functions is far from trivial. Our approach first syntactically transforms functions into simpler forms and then applies a number of su!cient conditions which guarantee that a set of expressions is smaller than another expression. Our preliminary implementation in the COSTA system indicates that the approach can be useful in practic

Cost functions for pairwise data clustering

Cost functions for non-hierarchical pairwise clustering are introduced, in the probabilistic autoencoder framework, by the request of maximal average similarity between the input and the output of the autoencoder. The partition provided by these cost functions identifies clusters with dense connected regions in data space; differences and similarities with respect to a well known cost function for pairwise clustering are outlined.Comment: 5 pages, 4 figure

Price of Anarchy for Non-atomic Congestion Games with Stochastic Demands

We generalize the notions of user equilibrium and system optimum to non-atomic congestion games with stochastic demands. We establish upper bounds on the price of anarchy for three different settings of link cost functions and demand distributions, namely, (a) affine cost functions and general distributions, (b) polynomial cost functions and general positive-valued distributions, and (c) polynomial cost functions and the normal distributions. All the upper bounds are tight in some special cases, including the case of deterministic demands.Comment: 31 page

Hospital cost functions for developing countries

There is extensive literature on hospital cost functions for industrial countries, but very little literature for developing countries. Yet the issues facing policy-makers in all countries are much the same: are hospitals overcapitalized, as is often claimed of U.S. hospitals? Are hospitals inefficient in other respects? Do hospitals vary in efficiency? Are private hospitals more efficient than their public counterparts? Should hospitals specialize or provide a broad range of services? Should costs be reduced by concentrating cases in fewer hospitals? The authors critically survey the techniques available for analyzing hospital costs and review the few hospital cost-function studies undertaken for developing countries. Although the paper is intended primarily for those working in developing countries, the discussion for cost function methodology has broad implications for interpreting econometric cost functions and for examining economies of scale and scope in both developing and industrial countries. The authors survey of econometric techniques is not uncritical. They question, for example, the validity of recent tests of over-capitalization undertaken on American hospitals. They also make general observations about the methods used to investigate economies of scope and economies of scale.Economic Theory&Research,Environmental Economics&Policies,Business in Development,Business Environment,Banks&Banking Reform