From Zero to Sixty: Calibrating Real-Time Responses

Recent advances in data recording technology have given researchers new ways of collecting on-line and continuous data for analyzing input-output systems. For example, continuous response digital interfaces are increasingly used in psychophysics. The statistical problem related to these input-output systems reduces to linking time-varying covariates to a continuous response variate. Using real-time data obtained from an experiment in psychoacoustics, we showcase new statistical tools that incorporate dynamical elements of an input-output system. We employ functional data analysis (FDA) methods and a simple differential equation to analyze and model the continuous responses. Furthermore, we outline the issues involved in analyzing input-output systems when the exact form of the underlying mathematical model is not known. Finally, we develop a calibration method to facilitate inter-subject and intra-subject comparisons. This work was supported by grants from the National Sciences and Engineering Research Council (NSERC) to J. O. Ramsay and to D. J. Levitin, and by a grant from the Social Sciences and Humanities Research Council (SSHRC) to D. J. Levitin. We would like to thank Bennett Smith for designing and implementing the software used to conduct the pitch tracking experiment. Also, we wish to thank the research assistants in the Levitin Laboratory involved in the data collection: Catherine Chapados, Andrew Schaaf and Carla Himmelman. We would also like to acknowledge Giles Hooker’s work on implementing the generalized profiling software used within this paper.     

The Variety of Lattice Effect Algebras Generated by MV-algebras and the Horizontal Sum of Two 3-element Chains

It has been recently shown [4] that the lattice effect algebras can be treated as a subvariety of the variety of so-called basic algebras. The open problem whether all subdirectly irreducible distributive lattice effect algebras are just subdirectly irreducible MV-chains and the horizontal sum of two 3-element chains is in the paper transferred into a more tractable one. We prove that modulo distributive lattice effect algebras, the variety generated by MV-algebras and is definable by three simple identities and the problem now is to check if these identities are satisfied by all distributive lattice effect algebras or not. Presented by Daniele Mundici     

Combined reasoning by automated cooperation

Different reasoning systems have different strengths and weaknesses, and often it is useful to combine these systems to gain as much as possible from their strengths and retain as little as possible from their weaknesses. Of particular interest is the integration of first-order and higher-order techniques. First-order reasoning systems, on the one hand, have reached considerable strength in some niches, but in many areas of mathematics they still cannot reliably solve relatively simple problems, for example, when reasoning about sets, relations, or functions. Higher-order reasoning systems, on the other hand, can solve problems of this kind automatically. But the complexity inherent in their calculi prevents them from solving a whole range of problems. However, while many problems cannot be solved by any one system alone, they can be solved by a combination of these systems.We present a general agent-based methodology for integrating different reasoning systems. It provides a generic integration framework which facilitates the cooperation between diverse reasoners, but can also be refined to enable more efficient, specialist integrations. We empirically evaluate its usefulness, effectiveness and efficiency by case studies involving the integration of first-order and higher-order automated theorem provers, computer algebra systems, and model generators.     

Weakly higher order cylindric algebras and finite axiomatization of the representables

We show that the variety of n-dimensional weakly higher order cylindric algebras, introduced in Németi [9], [8], is finitely axiomatizable when n > 2. Our result implies that in certain non-well-founded set theories the finitization problem of algebraic logic admits a positive solution; and it shows that this variety is a good candidate for being the cylindric algebra theoretic counterpart of Tarski’s quasi-projective relation algebras. Supported by the Hungarian National Foundation for Scientific Research grant T73601.     

The Hennessy–Milner equivalence for continuous time stochastic logic with mu-operator

A continuous stochastic logic with a μ-operator μCSL is defined, and an interpretation through stochastic relations is proposed. We investigate morphisms for models of μCSL, showing that the associated congruences can be used for an investigation of bisimilarity. The Hennessy–Milner equivalence for μCSL is discussed, and it is shown that models are equivalent iff they are bisimilar, using a general criterion for bisimilarity from the theory of stochastic relations.     

On the Nature of Continuous Physical Quantities in Classical and Quantum Mechanics

Journal of Philosophical Logic - Within the traditional Hilbert space formalism of quantum mechanics, it is not possible to describe a particle as possessing, simultaneously, a sharp position value...     

A Comparison of Methods for Creating Multiple Imputations of Nominal Variables

Many variables that are analyzed by social scientists are nominal in nature. When missing data occur on these variables, optimal recovery of the analysis model's parameters is a challenging endeavor. One of the most popular methods to deal with missing nominal data is multiple imputation (MI). This study evaluated the capabilities of five MI methods that can be used to treat incomplete nominal variables: multiple imputation with chained equations (MICE) using polytomous regression as the elementary imputation method; MICE based on classification and regression trees (CART); MICE based on nested logistic regressions; the ranking procedure described by Allison (2002 Allison, P. D. (2002). Missing data. Thousand Oaks, CA: Sage Publications. https://doi.org/10.4135/9780857020994.n4[Crossref] , [Google Scholar]); and a joint modeling approach based on the general location model. We first motivate our inquiry with an applied example and then present the results of a Monte Carlo simulation study that compared the performance of the five imputation methods under conditions of varying sample size, percentage of missing data, and number of nominal response categories. We found that MICE with polytomous regression was the strongest performer while the Allison (2002 Allison, P. D. (2002). Missing data. Thousand Oaks, CA: Sage Publications. https://doi.org/10.4135/9780857020994.n4[Crossref] , [Google Scholar]) ranking procedure and MICE with CART performed poorly in most conditions.     

Fragments of R-Mingle

The logic RM and its basic fragments (always with implication) are considered here as entire consequence relations, rather than as sets of theorems. A new observation made here is that the disjunction of RM is definable in terms of its other positive propositional connectives, unlike that of R. The basic fragments of RM therefore fall naturally into two classes, according to whether disjunction is or is not definable. In the equivalent quasivariety semantics of these fragments, which consist of subreducts of Sugihara algebras, this corresponds to a distinction between strong and weak congruence properties. The distinction is explored here. A result of Avron is used to provide a local deduction-detachment theorem for the fragments without disjunction. Together with results of Sobociski, Parks and Meyer (which concern theorems only), this leads to axiomatizations of these entire fragments — not merely their theorems. These axiomatizations then form the basis of a proof that all of the basic fragments of RM with implication are finitely axiomatized consequence relations.Special issue of Studia Logica: Algebraic Theory of Quasivarieties Presented by M. E. Adams, K. V. Adaricheva, W. Dziobiak, and A. V. Kravchenko     

Dominions in quasivarieties of universal algebras

The dominion of a subalgebra H in an universal algebra A (in a class ) is the set of all elements such that for all homomorphisms if f, g coincide on H, then a^f = a^g. We investigate the connection between dominions and quasivarieties. We show that if a class is closed under ultraproducts, then the dominion in is equal to the dominion in a quasivariety generated by . Also we find conditions when dominions in a universal algebra form a lattice and study this lattice.Special issue of Studia Logica: Algebraic Theory of Quasivarieties Presented by M. E. Adams, K. V. Adaricheva, W. Dziobiak, and A. V. Kravchenko