The Third Trick

We prove a result, similar to the ones known as Ishihara's First and Second Trick, for sequences of functions

Improving exploration in Ant Colony Optimisation with antennation

Ant Colony Optimisation (ACO) algorithms use two heuristics to solve computational problems: one long-term (pheromone) and the other short-term (local heuristic). This paper details the development of antennation, a mid-term heuristic based on an analogous process in real ants. This is incorporated into ACO for the Travelling Salesman Problem (TSP). Antennation involves sharing information of the previous paths taken by ants, including information gained from previous meetings. Antennation was added to the Ant System (AS), Ant Colony System (ACS) and Ant Multi-Tour System (AMTS) algorithms. Tests were conducted on symmetric TSPs of varying size. Antennation provides an advantage when incorporated into algorithms without an inbuilt exploration mechanism and a disadvantage to those that do. AS and AMTS with antennation have superior performance when compared to their canonical form, with the effect increasing as problem size increases.IEEE Computational Intelligence Societ

SEPARATING FRAGMENTS OF WLEM, LPO, AND MP

Abstract. We separate many of the basic fragments of classical logic which are used in reverse constructive mathematics. A group of related Kripke and topological models is used to show that various fragments of the Weak Law of the Excluded Middle, the Limited Principle of Omniscience, and Markov's Principle, including Weak Markov's Principle, do not imply each other. §1. Introduction. At the beginning of the twentieth century, Brouwer identified a number of constructively dubious principles, which Bishop later, in his 1967 monograph Omniscience principles are commonly used to show the independence of more subject specific theorems: if a (classical) result constructively implies an omniscience principle, then it cannot be proved using constructive techniques. By separating different omniscience principles over IZF we make this task easier: if under the assumption of a classical result together with an omniscience principle we can derive a stronger omniscience principle, then we can still conclude that the classical theorem is nonconstructive. More generally, implications among these principles and theorems of mainstream mathematics have been studied for a long time. Often this is the motivation for introducing these principles (some references being provided with the principles below), and often this study is done for foundational reasons after the principles are already established (as, for instance, in In this paper we present many models, often related to each other, that separate a large number of the omniscience principles defined in terms of binary sequences and related principles. The genesis of this work was the first author's question to the second of whether Richman's LLPO n hierarchy [23] could be separated, a question about results. Since then, much interest has shifted to technique: could an argumen

Reverse mathematics, well-quasi-orders, and Noetherian spaces

A quasi-order Q induces two natural quasi-orders on P(Q) P(Q) , but if Q is a well-quasi-order, then these quasi-orders need not necessarily be well-quasi-orders. Nevertheless, Goubault-Larrecq (Proceedings of the 22nd Annual IEEE Symposium 4 on Logic in Computer Science (LICS’07), pp. 453–462, 2007) showed that moving from a well-quasi-order Q to the quasi-orders on P(Q) P(Q) preserves well-quasi-orderedness in a topological sense. Specifically, Goubault-Larrecq proved that the upper topologies of the induced quasi-orders on P(Q) P(Q) are Noetherian, which means that they contain no infinite strictly descending sequences of closed sets. We analyze various theorems of the form “if Q is a well-quasi-order then a certain topology on (a subset of) P(Q) P(Q) is Noetherian” in the style of reverse mathematics, proving that these theorems are equivalent to ACA0 over RCA0. To state these theorems in RCA0 we introduce a new framework for dealing with second-countable topological spaces

Multi-objective improvement of software using co-evolution and smart seeding

Optimising non-functional properties of software is an important part of the implementation process. One such property is execution time, and compilers target a reduction in execution time using a variety of optimisation techniques. Compiler optimisation is not always able to produce semantically equivalent alternatives that improve execution times, even if such alternatives are known to exist. Often, this is due to the local nature of such optimisations. In this paper we present a novel framework for optimising existing software using a hybrid of evolutionary optimisation techniques. Given as input the implementation of a program or function, we use Genetic Programming to evolve a new semantically equivalent version, optimised to reduce execution time subject to a given probability distribution of inputs. We employ a co-evolved population of test cases to encourage the preservation of the program’s semantics, and exploit the original program through seeding of the population in order to focus the search. We carry out experiments to identify the important factors in maximising efficiency gains. Although in this work we have optimised execution time, other non-functional criteria could be optimised in a similar manner

Bull terrier hereditary nephritis: A model for autosomal dominant Alport syndrome

Bull terrier hereditary nephritis: A model for autosomal dominant Alport syndrome. Bull terrier hereditary nephritis is inherited as an autosomal dominant disease and causes renal failure at variable ages in affected dogs. The aims of this study were to compare the clinical, ultrastructural and immunohistochemical features of bull terrier hereditary nephritis with the characteristics of the human forms of Alport syndrome. Many animals with bull terrier hereditary nephritis have hematuria, and some have anterior lenticonus. However, deafness is not associated with the renal disease, and affected dogs do not have the large platelets that are occasionally seen in patients with autosomal Alport syndrome. The glomerular capillary basement membrane (GCBM) in affected bull terriers has an identical ultrastructural appearance to that seen in X-linked Alport syndrome, with lamellations and intramembranous electron-dense deposits. However, both the Goodpasture and the Alport antigens, which represent parts of the alpha 3(IV) and alpha 5 (IV) collagen chains, respectively, are present in the GCBM of affected dogs. Bull terrier hereditary nephritis represents an animal model for autosomal dominant Alport syndrome, and can be used to further examine how genetic mutations affect a basement membrane protein and the corresponding membrane structure