The fractional weak discrepancy of a poset P , written wdF (P ), is the least k such that some f : P → R satisfies f(y)− f(x) ≥ 1 for x ≺ y and |f(y)− f(x)| ≤ k for x‖y. We determine the minimal forbidden subposets for the property wdF (P ) ≤ k when k is an integer.

In the first part of the paper we recall the coalgebraic approach to handling the so-called invisible transitions that appear in different state-based systems semantics. We claim that these transitions are always part of the unit of a certain monad. Hence, coalgebras with internal moves are exactly coalgebras over a monadic type. The rest of the paper is devoted to supporting our claim by study...

We prove a cancellation theorem for simple refinement monoids satisfying the weak comparability condition, first introduced by K.C. O’Meara in the context of von Neumann regular rings. This result is then applied to von Neumann regular rings and C∗-algebras of real rank zero via the monoid of isomorphism classes of finitely generated projective modules. Introduction Let M be an (abelian) monoid...

This paper is part of the program of reverse mathematics. We assume the reader is familiar with this program as well as with RCA,, and WKL,, the two weak subsystems of second-order arithmetic we are going to work with here. (If not, a good place to start is [2].) In [2], [3], [4], many well-known theorems about countable rings, countable fields, etc. were studied in the context of reverse mathe...

In this paper we associate to each multivariate polynomial f that is homogeneous relative to a subset of its variables a series of polynomial families Pλ(f) of m-tuples of homogeneous polynomials of equal degree such that the circuit size of any member in Pλ(f) is bounded from above by the circuit size of f . This provides a method for obtaining lower bounds for the circuit size of f by proving...

In this paper we extend the Bayesian model fitting shape measurement method presented in Miller et al. (2007) and use the method to estimate the shear from the Shear TEsting Programme simulations (STEP). The method uses a fast model fitting algorithm which uses realistic galaxy profiles and analytically marginalises over the position and amplitude of the model by doing the model fitting in Four...

In this paper we associate to each multivariate polynomial f that is homogeneous relative to a subset of its variables a series of polynomial families Pλ(f) of m-tuples of homogeneous polynomials of equal degree such that the circuit size of any member in Pλ(f) is bounded from above by the circuit size of f . This provides a method for obtaining lower bounds for the circuit size of f by proving...

Weak states on posets are defined which are in some analogy to states on orthomodular posets used in axiomatic quantum mechanics. It is shown how certain properties of the set of weak states characterize certain properties of the underlying poset. Orthomodular posets serve as algebraic models for logics in axiomatic quantum mechanics. States on them are considered which reflect the properties o...

In this paper we study the notion of strong non-reeection, and its contrapositive weak reeection. We say strongly non-reeects at ii there is a function F : ! such that for all < with cf() = there is C club in such that F C is strictly increasing. We prove that it is consistent to have a cardinal such that strong non-reeection and weak reeection each hold on an unbounded set of cardinals less th...

Definition 1.1. A weak factorization system (L,R) in a category K consists of two classes L and R of morphisms of K such that (1) R = L , L = R and (2) any morphism h of K has a factorization h = gf with f ∈ L and g ∈ R. Definition 1.2. A model category is a complete and cocomplete category K together with three classes of morphisms F , C and W called fibrations, cofibrations and weak equivalen...