Some additional results on principal components analysis of three-mode data by means of alternating least squares algorithms

Kroonenberg and de Leeuw (1980) have developed an alternating least-squares method TUCKALS-3 as a solution for Tucker's three-way principal components model. The present paper offers some additional features of their method. Starting from a reanalysis of Tucker's problem in terms of a rank-constrained regression problem, it is shown that the fitted sum of squares in TUCKALS-3 can be partitioned according to elements of each mode of the three-way data matrix. An upper bound to the total fitted sum of squares is derived. Finally, a special case of TUCKALS-3 is related to the Carroll/Harshman CANDECOMP/PARAFAC model.     

On Intermediate Predicate Logics of some Finite Kripke Frames,I. Levelwise Uniform Trees

An intermediate predicate logic L is called finite iff it is characterized by a finite partially ordered set M, i.e., iff L is the logic of the class of all predicate Kripke frames based on M. In this paper we study axiomatizability of logics of this kind. Namely, we consider logics characterized by finite trees M of a certain type (levelwise uniform trees) and establish the finite axiomatizability criterion for this case.     

On Modal Logics of Partial Recursive Functions

The classical propositional logic is known to be sound and complete with respect to the set semantics that interprets connectives as set operations. The paper extends propositional language by a new binary modality that corresponds to partial recursive function type constructor under the above interpretation. The cases of deterministic and non-deterministic functions are considered and for both of them semantically complete modal logics are described and decidability of these logics is established. Presented by Melvin Fitting     

Levels of theory‐of‐mind reasoning in competitive games

The literature on recursive theory of mind (TOM) reasoning in interactive decision making (reasoning of the type “I think that you think that I think…”) has been pessimistic, suggesting that adults attribute to others levels of reasoning that are low and slow to increase with learning. In four experiments with college‐age adults playing sequential games, we examined whether choices and predictions were consistent with believing that others pursue their immediate self‐interest, or with believing that others reason through their own decision making, with fixed‐sum games that were simpler and more competitive. This manipulation led to higher‐level default TOM reasoning; indeed, reasoning against a lower‐level opponent was frequently consistent with assuming the opponent's reasoning to be higher‐level, leading to sub‐optimal choices. We conclude that TOM reasoning is not of a low level in all game settings; rather, individuals may display effective TOM reasoning, reflecting realistic assumptions about their opponents, in competitive and relatively simple games. Copyright © 2010 John Wiley & Sons, Ltd.     

Constructing robust crew schedules with bicriteria optimization

Optimization‐based computer systems are used by many airlines to solve crew planning problems by constructing minimal cost tours of duty. However, today airlines do not only require cost effective solutions, but are also very interested in robust solutions. A more robust solution is understood to be one where disruptions in the schedule (due to delays) are less likely to be propagated into the future, causing delays of subsequent flights. Current scheduling systems based solely on cost do not automatically provide robust solutions. These considerations lead to a multiobjective framework, as the maximization of robustness will be in conflict with the minimization of cost. For example crew changing aircraft within a duty period is discouraged if inadequate ground time is provided. We develop a bicriteria optimization framework to generate Pareto optimal schedules for the domestic airline. A Pareto optimal schedule is one which does not allow an improvement in cost and robustness at the same time. We developed a method to solve the bicriteria problem, implemented it and tested it with actual airline data. Our results show that considerable gain in robustness can be achieved with a small increase in cost. The additional cost is mainly due to an increase in overnights, which allows for a reduction of the number of aircraft changes. Copyright © 2003 John Wiley & Sons, Ltd.     

Can Constructive Mathematics be Applied in Physics?

The nature of modern constructive mathematics, and its applications, actual and potential, to classical and quantum physics, are discussed.     

A scale-invariant treatment for recursive path models

A reparameterization is formulated that yields estimates of scale-invariant parameters in recursive path models with latent variables, and (asymptotically) correct standard errors, without the use of constrained optimization. The method is based on the logical structure of the reticular action model.     

Equality and Monodic First-Order Temporal Logic

It has been shown recently that monodic first-order temporal logic without functional symbols but with equality is incomplete, i.e., the set of the valid formulae of this logic is not recursively enumerable. In this paper we show that an even simpler fragment consisting of monodic monadic two-variable formulae is not recursively enumerable.     

Nanoscale partitioning of Mn between austenite and martensite revealed by Curie temperature variations

The partitioning of Mn between deformation-induced martensite and austenite phases of a Fe?18Mn?2Al?2Si?0.04C high-Mn steel was studied by tracking variations in the Curie temperature of martensite after exposure to successively higher annealing temperatures. The increase in Curie temperature was justified by the Mn depletion of martensite. Assuming a linear relationship between the Curie temperature and Mn concentration, the average Mn concentration of martensite was expressed as a function of annealing temperature. The proposed method, which is applicable in a dilatometer with inductive heating, enables the ready estimation of Mn partitioning in intercritically annealed medium- and high-Mn steels.