The East Midlands in 2006: executive summary

The East Midlands in 2006 is the evidence base that was produced to underpin the development of the regional economic strategy, A Flourishing Region. It presents a statistical portrait of the region covering demography, economy & productivity, the labour market, deprivation & economic inclusion, transport, infrastructure & development and the environment. This document is the executive summary

Adjoint exactness

Plato's ideas and Aristotle's real types from the classical age, Nominalism and Realism of the mediaeval period and Whitehead's modern view of the world as pro- cess all come together in the formal representation by category theory of exactness in adjointness (a). Concepts of exactness and co-exactness arise naturally from ad- jointness and are needed in current global problems of science. If a right co-exact valued left-adjoint functor ( ) in a cartesian closed category has a right-adjoint left- exact functor ( ), then physical stability is satis ed if itself is also a right co-exact left-adjoint functor for the right-adjoint left exact functor ( ): a a . These concepts are discussed here with examples in nuclear fusion, in database interroga- tion and in the cosmological ne structure constant by the Frederick construction

Don't confuse left and right exactness! A note correcting the distinction in the Proceedings of ANPA 27

A note correcting and enlarging on the distinction between the parities of exactness and adjointness in our paper Process as a World Transaction in the proceedings of ANPA 27

Conditions for interoperability

Interoperability for information systems remains a challenge both at the semantic and organisational levels. The original three-level architecture for local databases needs to be replaced by a categorical four-level one based on concepts, constructions, schema types and data together with the mappings between them. Such an architecture provides natural closure as further levels are superfluous even in a global environment. The architecture is traversed by means of the Godement calculus: arrows may be composed at any level as well as across levles. The necessary and sufficient conditions for interoperability are satisfied by composable (formal) diagrams both for intension and extension in categories that are cartesian closed and locally cartesian closed. Methods like partial categories and sketches in schema design can benefit from Freyd’s punctured diagrams to identify precisely type-forcing natural transformations. Closure is better achieved in standard full categories. Global interoperability of extension can be achieved through semantic annotation but only if applied at run time

Anticipation as prediction in the predication of data types

Every object in existence has its type. Every subject in language has its predicate. Every intension in logic has its extension. Each therefore has two levels but with the fundamental problem of the relationship between the two. The formalism of set theory cannot guarantee the two are co-extensive. That has to be imposed by the axiom of extensibility, which is inadequate for types as shown by Bertrand Russell's rami ed type theory, for language as by Henri Poincar e's impredication and for intension unless satisfying Port Royal's de nitive concept. An anticipatory system is usually de ned to contain its own future state. What is its type? What is its predicate? What is its extension? Set theory can well represent formally the weak anticipatory system, that is in a model of itself. However we have previously shown that the metaphysics of process category theory is needed to represent strong anticipation. Time belongs to extension not intension. The apparent prediction of strong anticipation is really in the structure of its predication. The typing of anticipation arises from a combination of and | respectively (co) multiplication of the (co)monad induced by adjointness of the system's own process. As a property of cartesian closed categories this predication has signi cance for all typing in general systems theory including even in the de nition of time itself

Property Owners in Australia: A Snapshot

Property represents more than half of all household assets in Australia and its share has been rising in recent years. Since most property purchases require debt financing because of the size of the purchase, property makes up a large part of both sides of households’ balance sheets. This paper uses household-level data to examine what determines the ownership of residential property and the holding of property debt by households in Australia. We examine these decisions for both owner-occupied and investment property. The results suggest that the household’s age, composition, income and wealth are important factors determining property ownership and gearing decisions. Income and wealth are found to be more influential in determining the value of property owned, while the household’s age is more influential in determining the gearing. Household composition is important for decisions on owner-occupied property, but has a limited influence on investment property decisions.home ownership; investment property; gearing

Process as a world transaction

Transaction is process closure: for a transaction is the limiting process of process itself. In the process world view the universe is the ultimate (intensional) transaction of all its extensional limiting processes that we call reality. ANPA’s PROGRAM UNIVERSE is a computational model which can be explored empirically in commercial database transactions where there has been a wealth of activity over the real world for the last 40 years. Process category theory demonstrates formally the fundamental distinctions between the classical model of a transaction as in PROGRAM UNIVERSE and physical reality. The paper concludes with a short technical summary for those who do not wish to read all the detail