Independence – the study of what is relevant to a given problem of reasoning – is an important AI topic. In this paper, we investigate several notions of conditional independence in propositional logic: Darwiche and Pearl’s conditional independence, and two more restricted forms of it, called strong conditional independence and perfect conditional independence. Many characterizations and proper...

Extended BRS symmetry is used to prove gauge independence of the fermion renormalization constant Z2 in on-shell QED renormalization schemes. A necessary condition for gauge independence of Z2 in on-shell QCD renormalization schemes is formulated. Satisfying this necessary condition appears to be problematic at the three-loop level in QCD. In on-shell schemes, the fermion mass renormalization Z...

adjudication independence can be studied in two areas namely independency of judicial power and independency of judge. the first one is based on the separation of powers theory but judge independence means its freedom from parties and their attorneys and its independence in intern of judiciary power. this sense of independence has two objectives: 1) judge's freedom in applying the law to f...

We consider the approximations behind the typical mean-field model derived for a class of systems made up of type II excitable units influenced by noise and coupling delays. The formulation of the two approximations, referred to as the Gaussian and the quasi-independence approximation, as well as the fashion in which their validity is verified, are adapted to reflect the essential properties of...

We examine fields in which model theoretic algebraic closure coincides with relative field theoretic algebraic closure. These are perfect fields with nice model theoretic behaviour. For example, they are exactly the fields in which algebraic independence is an abstract independence relation in the sense of Kim and Pillay. Classes of examples are perfect PAC fields, model complete large fields a...

the angular dependent magnetoresistance oscillation (admro) of the stage-2 ibr graphiteintercalation compound (gic) was studied between 1.8 k and 110 k in magnetic fields between 1 and 9t. there was a series of peaks in the c-axis resistance as the field direction was changed from the c axisto the (001) plane. the field independence of the angular positions of the peaks, showing that theoscilla...