An Interview With Albert W. Tucker

The mathematical career of Albert W. Tucker, Professor Emeritus at Princeton University, spans more than 50 years. Best known today for his work in mathematical programming and the theory of games (e.g., the Kuhn-Tucker theorem, Tucker tableaux, and the Prisoner\u27s Dilemma), he was also in his earlier years prominent in topology. Outstanding teacher, administrator and leader, he has been President of the MAA, Chairman of the Princeton Mathematics Department, and course instructor, thesis advisor or general mentor to scores of active mathematicians. He is also known for his views on mathematics education and the proper interplay between teaching and research. Tucker took an active interest in this interview, helping with both the planning and the editing. The interviewer, Professor Maurer, received his Ph.D. under Tucker in 1972 and teaches at Swarthmore College

Distributed Hierarchical SVD in the Hierarchical Tucker Format

We consider tensors in the Hierarchical Tucker format and suppose the tensor data to be distributed among several compute nodes. We assume the compute nodes to be in a one-to-one correspondence with the nodes of the Hierarchical Tucker format such that connected nodes can communicate with each other. An appropriate tree structure in the Hierarchical Tucker format then allows for the parallelization of basic arithmetic operations between tensors with a parallel runtime which grows like $\log(d)$, where $d$ is the tensor dimension. We introduce parallel algorithms for several tensor operations, some of which can be applied to solve linear equations $\mathcal{A}X=B$ directly in the Hierarchical Tucker format using iterative methods like conjugate gradients or multigrid. We present weak scaling studies, which provide evidence that the runtime of our algorithms indeed grows like $\log(d)$. Furthermore, we present numerical experiments in which we apply our algorithms to solve a parameter-dependent diffusion equation in the Hierarchical Tucker format by means of a multigrid algorithm

[Review of] William H. Tucker. The Science and Politics of Racial Research

Since there is usually a two year period of time that elapses between the acceptance of a manuscript by a university press and its publication, we must commend William H. Tucker, who is an associate professor of psychology at Rutgers University, in his anticipation of contemporary controversies in reference to the relative abilities of races. Tucker argues that there is continuity in the thought of racists, which over the past two centuries include anthropometricians, eugenicists, and segregationists. ”The imprimatur of science,“ Tucker argues cogently, ”has been offered to justify, first slavery and, later, segregation, nativism, socio-political inequality, class subordination, poverty, and the general futility of social and economic reform. For Tucker, the attempt to demonstrate that one race is genetically less intelligent than others has been scientifically valueless and socially harmful. Scientific research into racial differences has, in essence, resulted in the “legitimation” of racist ideology. Nevertheless, Tucker is not pessimistic about winning the battle with racists. ”America\u27s democratic political traditions, he writes, ”have prevailed, and today universal suffrage, equal rights under law, and the guarantee of other civil liberties to all citizens are no longer up for debate; where demonstrable infringement has occurred, there is generally outrage and prompt redress

ON NECESSARY CONDITIONS FOR EFFICIENCY IN DIRECTIONALLY DIFFERENTIABLE OPTIMIZATION PROBLEMS

This paper deals with multiobjective programming problems with in- equality, equality and set constraints involving Dini or Hadamard differentiable func- tions. A theorem of the alternative of Tucker type is established, and from which Kuhn-Tucker necessary conditions for local Pareto minima with positive Lagrange multipliers associated with all the components of objective functions are derived.Theorem of the alternative, Kuhn-Tucker necessary conditions, direc- tionally differentiable functions.

The Borsuk-Ulam-property, Tucker-property and constructive proofs in combinatorics

This article is concerned with a general scheme on how to obtain constructive proofs for combinatorial theorems that have topological proofs so far. To this end the combinatorial concept of Tucker-property of a finite group $G$ is introduced and its relation to the topological Borsuk-Ulam-property is discussed. Applications of the Tucker-property in combinatorics are demonstrated.Comment: 12 pages, 0 figure

Kuhn-Tucker Estimation of Recreation Demand – A Study of Temporal Stability

The paper examines the Kuhn Tucker model in the context of estimating recreation demand when the choice set it very large. It examines the temporal stability of parameter estimates using multiple years of data on trips to 127 lakes in Iowa made by households in Iowa. The study finds that for the given dataset, the estimates derived from a Kuhn-Tucker model are largely stable over time.Recreation demand, Kuhn-Tucker, Temporal Stability, Environmental Economics and Policy, C2, Q2,