David Joyce

Bio: David Joyce is an academic researcher from Clark University. The author has contributed to research in topics: Matrix polynomial & Locale (computer hardware). The author has an hindex of 3, co-authored 5 publications receiving 952 citations.

My Way or the Highway: a More Naturalistic Model of Altruism Tested in an Iterative Prisoners' Dilemma

Abstract: There are three prominent solutions to the Darwinian problem of altruism, kin selection, reciprocal altruism, and trait group selection. Only one, reciprocal altruism, most commonly implemented in game theory as a TIT FOR TAT strategy, is not based on the principle of conditional association. On the contrary, TIT FOR TAT implements conditional altruism in the context of unconditionally determined associates. Simulations based on Axelrod's famous tournament have led many to conclude that conditional altruism among unconditional partners lies at the core of much human and animal social behavior. But the results that have been used to support this conclusion are largely artifacts of the structure of the Axelrod tournament, which explicitly disallowed conditional association as a strategy. In this study, we modify the rules of the tournament to permit competition between conditional associates and conditional altruists. We provide evidence that when unconditional altruism is paired with conditional association, a strategy we called MOTH, it can outcompete TIT FOR TAT under a wide range of conditions.

Mathematical concepts for analyzing ambiguous situations

Abstract: We examine some mathematical tools for dealing with ambiguous situations. The main tool is the use of non-standard logic with truth-values in what is called a locale. This approach is related to fuzzy set theory, which we briefly discuss. We also consider probabilistic concepts. We include specific examples and describe the way a researcher can set up a suitable locale to analyse a concrete situation.

Animal Intelligence: Experimental Studies

Abstract: ONE of the most remarkable examples of sudden and rapid development of a new scientific method and a new and extensive body of scientific fact is to be seen in the growth of the study of animal psychology during the last ten or a dozen years. As in the case of the general science of psychology, the change came with the introduction of experiment as the fundamental method of investigation, but the transition was accentuated by a craving for objectivity of results, which focussed the attention upon the objective performance or behaviour of the animal under examination, not only to the detriment, but even, in the case of many observers, to the complete neglect of speculation as to its psychical life. If the new psychology claimed to be a psychology without a soul, the new animal psychology threatened, and still threatens, to become an animal psychology without consciousness. Many investigators have indeed openly declared for this ideal-not denying the presence of consciousness, but regarding it as of no importance or value in an explanatory scientific system. Nevertheless signs are not wanting in the most recent work of a healthy reaction from this extreme view, based as much upon observed fact as upon a priori speculation. Animal Intelligence: Experimental Studies. By E. L. Thorndike. Pp. viii + 297. (New York: The Macmillan Co.; London: Macmillan and Co., Ltd., 1911.) Price 7s. net.

Quandle cohomology and state-sum invariants of knotted curves and surfaces

Abstract: The 2-twist spun trefoil is an example of a sphere that is knotted in 4-dimensional space. A proof is given in this paper that this sphere is distinct from the same sphere with its orientation reversed. Our proof is based on a state-sum invariant for knotted surfaces developed via a cohomology theory of racks and quandles (also known as distributive groupoids). A quandle is a set with a binary operation - the axioms of which model the Reidemeister moves in classical knot theory. Colorings of diagrams of knotted curves and surfaces by quandle elements, together with cocycles of quandles, are used to define state-sum invariants for knotted circles in 3-space and knotted surfaces in 4-space. Cohomology groups of various quandles are computed herein and applied to the study of the state-sum invariants. Non-triviality of the invariants is proved for a variety of knots and links, and conversely, knot invariants are used to prove non-triviality of cohomology for a variety of quandles.

An Introduction to Knot Theory

Abstract: This paper concentrates on the construction of invariants of knots, such as the Jones polynomials and the Vassiliev invariants, and the relationships of these invariants to other mathematics (such as Lie algebras).