Light-Cone Operator-Product Expansions Revisited: I

We again consider the problem of the light-cone expansion for products of currents and explain the motivations making a rethinking of old results relevant today.     

Vagueness as Semantic Indecision: Metaphysical Vagueness vs Indeterminate Reference

After presenting a negative characterization of metaphysical vagueness and the main tenets of the view of vagueness as semantic indecision, the paper critically discusses the objection that such a view requires that at least some vagueness not be just constituted by semantic indecision—but rather by the metaphysical vagueness of some semantic relations themselves submitted by Trenton Merricks and, more recently, Nathan Salmon.     

Tolerance Spaces Revisited I: Almost Solutions

Mathematical Notes - The paper deals with sequences of positive numbers (dn) such that, multiplying the Fourier coefficients (Cn(f)) of functions from given function classes by these numbers, one...     

Fitting-Attitude Analyses: The Dual-Reason Analysis Revisited

Classical fitting-attitude analyses understand value in terms of its being fitting, or more generally, there being a reason to favour the bearer of value. Recently, such analyses have been interpreted as referring to two reason-notions rather than to only one. The idea is that the properties of the object provide reason not only for a certain kind of favouring(s) vis-à-vis the object, but the very same properties should also figure in the intentional content of the favouring; the agent should favour the object on account of those properties that provide reason for favouring the object in the first place. While this expansion of the original proposal might seem intuitive given that favourings are discerning attitudes, it is nonetheless argued that proponents of the fitting-attitude analysis are in fact not served by such an expansion of the classical analysis. The objections raised here are relevant not only for advocates and critics of fitting-attitude analyses, but for anyone interested in the relation between normative reasons and motivation.     

Order-Compactifications of Totally Ordered Spaces: Revisited

Order-compactifications of totally ordered spaces were described by Blatter (J Approx Theory 13:56–65, 1975) and by Kent and Richmond (J Math Math Sci 11(4):683–694, 1988). Their results generalize a similar characterization of order-compactifications of linearly ordered spaces, obtained independently by Fedorčuk (Soviet Math Dokl 7:1011–1014, 1966; Sib Math J 10:124–132, 1969) and Kaufman (Colloq Math 17:35–39, 1967). In this note we give a simple characterization of the topology of a totally ordered space, as well as give a new simplified proof of the main results of Blatter (J Approx Theory 13:56–65, 1975) and Kent and Richmond (J Math Math Sci 11(4):683–694, 1988). Our main tool will be an order-topological modification of the Dedekind-MacNeille completion. In addition, for a zero-dimensional totally ordered space X, we determine which order-compactifications of X are Priestley order-compactifications.     

Inverting Random Functions III: Discrete MLE Revisited

This paper continues our earlier investigations into the inversion of random functions in a general (abstract) setting. In Section 2, we investigate a concept of invertibility and the invertibility of the composition of random functions defined on finite sets. In Section 3, we resolve some questions concerning the number of samples required to ensure the accuracy of maximum likelihood estimation (MLE) in the presence of ‘nuisance’ parameters. A direct application to phylogeny reconstruction is given.     

Universal graphs without instances of CH: Revisited

We give a complete proof of the consistency of the existence of a universal graph of powerλ, whereκ =κ ^<κ <λ = cfλ < 2 ^κ are arbitrary. The author would like to thank the NSF for partially supporting this research, Alice Leonhardt for the beautiful typing, and M. Kojman for proofreading. Publication No. 175A. The proof in the second section of [9] is flawed.     

Appollonius Revisited: Supporting Spheres for Sundered Systems

When C is a ball in and S is the sphere , we say that S supports a convex body B if S intersects B and either (then S is a far support) or the interior of C is disjoint from B (then S is a near support). The focus here is on common supports for a system of d+1 bodies in such that for each way of selecting a point from each member of , the selected points are affinely independent and hence form the vertex-set of a d-simplex. The main result asserts that if is an arbitrary partition of , then there exists a unique Euclidean sphere that is simultaneously a near support for each member of and a far support for each member of . Received August 2, 1995, and in revised form November 30, 1995.     

Packet Models Revisited: Tandem and Priority Systems

We examine two extensions of traditional single-node packet-scale queueing models: tandem networks and (strict) priority systems. Two generic input processes are considered: periodic and Poisson arrivals. For the two-node tandem, an exact expression is derived for the joint distribution of the total queue length, and the queue length of the first queue, implicitly determining the distribution of the second queue. Similarly we derive the distribution of the low-priority queue in a two-class priority system. We also provide explicit approximations based on the Brownian bridge.     

Production Bonus Schemes: A Cautionary Tale

A case study is presented showing how a simple logical analysis of the causes of a problem, rather than its symptoms, efficiently solved some production and accounting difficulties.Discrepancies between accounting records and physical stocks, and substandard production were found to be caused by a badly designed factory bonus scheme. Modification of the scheme solved both problems.     

Conceptual mathematics: An application to education

This paper presents an alternative proposal concerning the teaching of mathematics. The present paper can be placed within the broader framework of the teaching of mathematics, but also within the more specific framework of category theory (CT). In other words, new ways will be investigated in which CT can be best developed within the broader framework of the teaching of mathematics. Following the research at the end of this paper, the outcome of this investigation is that CT can successfully be used as a background for the foundation and teaching of mathematics.     

Noncommutative Symmetric Functions VII: Free Quasi-Symmetric Functions Revisited

We prove a Cauchy identity for free quasi-symmetric functions and apply it to the study of various bases. A free Weyl formula and a generalization of the splitting formula are also discussed.     

Iterative Proportional Scaling Revisited: A Modern Optimization Perspective

This article revisits the classic iterative proportional scaling (IPS) from a modern optimization perspective. In contrast to the criticisms made in the literature, we show that based on a coordinate descent characterization, IPS can be slightly modified to deliver coefficient estimates, and from a majorization-minimization standpoint, IPS can be extended to handle log-affine models with features not necessarily binary-valued or nonnegative. Furthermore, some state-of-the-art optimization techniques such as block-wise computation, randomization, and momentum-based acceleration can be employed to provide more scalable IPS algorithms, as well as some regularized variants of IPS for concurrent feature selection. Supplementary material for this article is available online.     

Understanding Social Reforms: A Conceptual Analysis

We attempt here to explain why reforming social systems is not an easy job and what can be done about it. Vickers' concept of ‘appreciative systems’ is re-examined and further developed. It is argued that appreciative systems are socially established ways of perceiving, consisting of a set of cognitive categories, values and interests which are grounded on social practices. The latter are constituted by certain historically developed self-understandings shared by individuals. Social practices are self-referential and, therefore, particularly resistant to reform. It is argued that the role of policy makers should be seen as consisting of two components. First, inventing and supplying social systems with new appreciative systems, and secondly, regularly providing social systems with information about their own functioning as well as the functioning of other systems. That information, spread throughout a system, has potentially reforming effects. These claims are illustrated with examples from UK and American public life.     

Asynchronous Teams: Cooperation Schemes for Autonomous Agents

Experiments over a variety of optimization problems indicate that scale-effective convergence is an emergent behavior of certain computer-based agents, provided these agents are organized into an asynchronous team (A-Team). An A-Team is a problem-solving architecture in which the agents are autonomous and cooperate by modifying one another's trial solutions. These solutions circulate continually. Convergence is said to occur if and when a persistent solution appears. Convergence is said to be scale-effective if the quality of the persistent solution increases with the number of agents, and the speed of its appearance increases with the number of computers. This paper uses a traveling salesman problem to illustrate scale-effective behavior and develops Markov models that explain its occurrence in A-Teams, particularly, how autonomous agents, without strategic planning or centralized coordination, can converge to solutions of arbitrarily high quality. The models also perdict two properties that remain to be experimentally confirmed: construction and destruction are dual processes. In other words, adept destruction can compensate for inept construction in an A-Team, and vice-versa. (Construction refers to the process of creating or changing solutions, destruction, to the process of erasing solutions.) solution quality is independent of agent-phylum. In other words, A-Teams provide an organizational framework in which humans and autonomous mechanical agents can cooperate effectively.     

Birkhoff interpolation on some perturbed roots of unity: Revisited

We consider the regularity of Birkhoff interpolation on some non-uniformly distributed roots of unity. We determine the range of values of in the complex plane which makes the problem of lacunary interpolation on the zeros of (z ⁿ +1)(z–) regular.