Dual-context multicategories as models for implicit computational complexity

In this thesis we study dual-context type systems and their models. A dual-context type system is one in which the context of a term is split into two parts, a normal part and a safe part. This separation allows one to put different kinds of usage restrictions on the two types of variable. For example, in implicit computational complexity, such a separation is used to implement resource-free characterisations of complexity classes. A similar separation between two kinds of variable occurs in type systems for linear logic, where different structural operations are permitted in the normal and safe parts of the context.We start by defining two basic dual-context calculi II(Σ) and IL(Σ) of typed terms, built using two kinds of free variables and dual-typed function symbols. In the IL(Σ) calculus we use safe variables in a 'linear' fashion, forbidding any weakening and contraction, while, in the II(Σ) calculus, contraction and weakening are allowed for both safe and normal variables.We then consider models for II(Σ) and IL(Σ) with basic equational judgements. Rather than following the traditional approach of encoding dual-contexts through additional structure on a category, we consider dual-context multicategories in which dual-contexts are built into the definition. The main advantage this approach is that it covers a wider class of models, including some particularly natural models from the field of implicit computational complexity.Next we enrich our basic calculi with different type constructions such as products and sums and provide their multicategorical interpretation. We consider a dual-context list type constructor together with a type-theoretic analogue of the safe recursion of Bellantoni and Cook's system ß, which characterises polynomial time computability on natural numbers. We define an interpretation for such dual-context lists using safe list objects. We show that the polytime computable functions are exactly the functions definable in every dual-context multicategory with safe binary list object.Finally, motivated by the standard approach to the categorical interpretation of primitive recursion using the notion of initial algebra, we develop a notion of safe initial algebra, which generalises the safe recursion scheme and provides us with insights about the choice of initial functions in system ß

Cascade search principle and its applications to the coincidence problems of n one-valued or multi-valued mappings

AbstractThe problem of the construction of a multi-cascade with a given limit subset A is considered in a metric space X. A multi-cascade is a discrete multi-valued dynamic system with the translation semigroup (Z⩾0,+). The cascade search principle using so-called search functionals is suggested. It gives a solution of the problem. Also, an estimation is obtained for the distance between any initial point x and every correspondent limit point. Several applications of one-valued and multi-valued versions of the mentioned cascade search principle are given for the cases when the limit subset A is (1) the full (or expanded) preimage of a closed subspace under a mapping from X to another metric space; (2) the coincidence set (or expanded coincidence set) of n mappings from X to another metric space (n>1); (3) the common preimage (or the expanded one) of a closed subspace under n mappings; and (4) the common fixed point set of n mappings of the space X into itself (n⩾1). Generalizations of the previous authors results are obtained. And, in particular cases, generalizations of some recent results by A.V. Arutyunov on coincidences of two mappings and a generalization of Banach fixed point principle are obtained

Claims-shifting: The problem of parallel reimbursement regimes

Parallel reimbursement regimes, under which providers have some discretion over which payer gets billed for patient treatment, are a common feature of health care markets. In the U.S., the largest such system is under Workers’ Compensation (WC), where the treatment workers with injuries that are not definitively tied to a work accident may be billed either under group health insurance plans or under WC. We document that there is significant reclassification of injuries from group health plans into WC, or “claims shifting”, when the financial incentives to do so are strongest. In particular, we find that injuries to workers enrolled in capitated group health plans (such as HMOs) see a higher incidence of their claims for soft-tissue injuries (which are hard to classify specifically as work related) under WC than under group health, relative to those in non-capitated plans. Such a pattern is not evident for workers with traumatic injuries. Moreover, we find that such reclassification is more common in states with higher WC fees, once again for soft tissue but not traumatic injuries. Our results imply that a significant shift towards capitated reimbursement, or reimbursement reductions, under GH could lead to a large rise in the cost of WC plans

Future development of focus group method in marketing system

The aim of the article. The article investigates the prospects of development of the focus groups method in the contemporary economy, discussed the theoretical background and features of the this method, identified the new properties and scope of implementation, justified the possibility of focus groups method using as a tool of indirect communication. The results of the analysis. We offer to look at the focus group - a qualitative method of marketing research as a specific tool of marketing communications. What can be used in situations where a certain organization or a product have a negative image and consumers were not much familiar with its functions and features. And then during the focus group using such techniques as personalization, role play and hypothetical scenarios that make the respondent feel the full seriousness of the situation and cause vivid emotions during work . Thus this understanding will remain in the memory of the participant for a long period. And good emotions and memories is always a pleasure to share with your loved ones. Conclusions and directions of further researches. After analysis of the data, we concluded that the method of focus group research can be regarded as a specific tool of marketing communications. It is specific because of certain indications for use such as the need to improve the image of the company, informing consumers about the functions performed by the organization and rapid change of views on the enterprise from the point of view of consumers

Recursion formulas for the Lie integral

AbstractAn explicit definition is given of a non-linear integral which is termed the Lie integral. This integral is defined for Lie algebra valued functions in terms of the representations of the algebra. Various properties of the integral are investigated, and applications are given to differential equations. Applications to differential geometry will be given elsewhere

Complexity and Heegaard genus of an infinite class of compact 3-manifolds

Using the theory of hyperbolic manifolds with totally geodesic boundary, we provide for every integer n greater than 1 a class of such manifolds all having Matveev complexity equal to n and Heegaard genus equal to n+1. All the elements of this class have a single boundary component of genus n, and the numbers of distinct members of the class grows at least exponentially with n.Comment: 15 pages, 7 figure