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

Measurement Bias in the Canadian Consumer Price Index

The consumer price index (CPI) is the most commonly used measure of inflation in Canada. As an indicator of changes in the cost of living, however, the CPI is subject to various types of measurement bias. The author updates previous Bank of Canada estimates of the bias in the Canadian CPI by examining four different sources of potential bias. He finds that the total measurement bias has increased only slightly in recent years to 0.6 percentage points per year, and is low when compared with other countries.Inflation et prix; Cibles en matière d'inflation

Process categories: the metaphysics, methodology & mathematics, philosophy of nature and process philosophy

To apply the metaphysical methodology of mathematics to the logic and form of process in natural philosophy requires a metaphysics above modelling, a methodology more than method and a mathematics beyond the set based topics of arithmetic, algebra, geometry and topology. At the start of the twentieth century Alfred North Whitehead together with his former student Bertrand Russell was able to expound the form and logic of the mathematics of his day by the extensive treatment of axioms and theorems. The technical quality of this work found world acclaim and became the foundation for the advancement of science by the application of models still with us today

A new process foundation for the applied topos

The world is in turmoil for want of sound reasoning. Economics and the environment are but two of many areas of human endeavour badly betrayed through a failed combination of physical and information science and the rule of law. Logic is the fabric of pure mathematics as the foundation of applied mathematics on which all science is based from the physical through biological and medical to the social sciences. However the symbolic logic of today seems of scarce more use than the syllogisms of Aristotle as observed by Francis Bacon nearly 400 years ago: The logic now in use serves rather to fix and give stability to the errors which have their foundation in commonly received notions than to help the search after truth. So it does more harm than good [Novum Organon Aphorism XII, 1620]

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