Robert Milson

Bio: Robert Milson is an academic researcher from Dalhousie University. The author has contributed to research in topics: Invariant (mathematics) & Orthogonal polynomials. The author has an hindex of 30, co-authored 112 publications receiving 4307 citations. Previous affiliations of Robert Milson include McGill University & Halifax.

Classification of the Weyl tensor in higher dimensions

Abstract: We discuss the algebraic classification of the Weyl tensor in higher-dimensional Lorentzian manifolds. This is done by characterizing algebraically special Weyl tensors by means of the existence of aligned null vectors of various orders of alignment. Further classification is obtained by specifying the alignment type and utilizing the notion of reducibility. For a complete classification it is then necessary to count aligned directions, the dimension of the alignment variety and the multiplicity of principal directions. The present classification reduces to the classical Petrov classification in four dimensions. Some applications are briefly discussed.

Rational extensions of the quantum harmonic oscillator and exceptional Hermite polynomials

Abstract: We prove that every rational extension of the quantum harmonic oscillator that is exactly solvable by polynomials is monodromy free, and therefore can be obtained by applying a finite number of state-deleting Darboux transformations on the harmonic oscillator. Equivalently, every exceptional orthogonal polynomial system of Hermite type can be obtained by applying a Darboux-Crum transformation to the classical Hermite polynomials. Exceptional Hermite polynomial systems only exist for even codimension 2m, and they are indexed by the partitions λ of m. We provide explicit expressions for their corresponding orthogonality weights and differential operators and a separate proof of their completeness. Exceptional Hermite polynomials satisfy a 2l + 3 recurrence relation where l is the length of the partition λ. Explicit expressions for such recurrence relations are given.

Simple Heuristics That Make Us Smart

Abstract: Fast and frugal heuristics - simple rules for making decisions with realistic mental resources - are presented here. These heuristics can enable both living organisms and artificial systems to make smart choices, classifications, and predictions by employing bounded rationality. But when and how can such fast and frugal heuristics work? What heuristics are in the mind's adaptive toolbox, and what building blocks compose them? Can judgments based simply on a single reason be as accurate as those based on many reasons? Could less knowledge even lead to systematically better predictions than more knowledge? This book explores these questions by developing computational models of heuristics and testing them through experiments and analysis. It shows how fast and frugal heuristics can yield adaptive decisions in situations as varied as choosing a mate, dividing resources among offspring, predicting high school drop-out rates, and playing the stock market.

Reflections of the Environment in Memory

Abstract: Availability of human memories for specific items shows reliable relationships to frequency, recency, and pattern of prior exposures to the item. These relationships have defied a systematic theoretical treatment. A number of environmental sources (New York Times, parental speech, electronic mail) are examined to show that the probability that a memory will be needed also shows reliable relationships to frequency, recency, and pattern of prior exposures. Moreover, the environmental relationships are the same as the memory relationships. It is argued that human memory has the form it does because it is adapted to these environmental relationships. Models for both the environment and human memory are described. Among the memory phenomena addressed are the practice function, the retention function, the effect of spacing of practice, and the relationship between degree of practice and retention.

The seven sins of memory. Insights from psychology and cognitive neuroscience.

Abstract: Though often reliable, human memory is also fallible. This article examines how and why memory can get us into trouble. It is suggested that memory's misdeeds can be classified into 7 basic "sins": transience, absentmindedness, blocking, misattribution, suggestibility, bias, and persistence. The first three sins involve different types of forgetting, the next three refer to different types of distortions, and the final sin concerns intrusive recollections that are difficult to forget. Evidence is reviewed concerning each of the 7 sins from relevant sectors of psychology (cognitive, social, and clinical) and from cognitive neuroscience studies that include patients with focal brain damage or make use of recently developed neuroimaging techniques. Although the 7 sins may appear to reflect flaws in system design, it is argued instead that they are by-products of otherwise adaptive features of memory.