Relating first-order set theories and elementary toposes

We show how to interpret the language of first-order set theory in an elementary topos endowed with, as extra structure, a directed structural system of inclusions (dssi). As our main result, we obtain a complete axiomatization of the intuitionistic set theory validated by all such interpretations. Since every elementary topos is equivalent to one carrying a dssi, we thus obtain a first-order set theory whose associated categories of sets are exactly the elementary toposes. In addition, we show that the full axiom of Separation is validated whenever the dssi is superdirected. This gives a uniform explanation for the known facts that cocomplete and realizability toposes provide models for Intuitionistic Zermelo-Fraenkel set theory (IZF)

Is there evidence for cross-domain congruency sequence effect? A replication of Kan et al. (2013)

Exploring the mechanisms of cognitive control is central to understanding how we control our behaviour. These mechanisms can be studied in conflict paradigms, which require the inhibition of irrelevant responses to perform the task. It has been suggested that in these tasks, the detection of conflict enhances cognitive control resulting in improved conflict resolution of subsequent trials. If this is the case, then this so-called congruency sequence effect can be expected to occur in cross-domain tasks. Previous research on the domain-generality of the effect presented inconsistent results. In this study, we provide a multi-site replication of three previous experiments of Kan et al. (Kan IP, Teubner-Rhodes S, Drummey AB, Nutile L, Krupa L, Novick JM 2013 Cognition 129, 637-651) which test congruency sequence effect between very different domains: from a syntactic to a non-syntactic domain (Experiment 1), and from a perceptual to a verbal domain (Experiments 2 and 3). Despite all our efforts, we found only partial support for the claims of the original study. With a single exception, we could not replicate the original findings; the data remained inconclusive or went against the theoretical hypothesis. We discuss the compatibility of the results with alternative theoretical frameworks

Reviews

Adam Makkai (ed.): In Quest of the 'Miracle Stag': The Poetry of Hungary. An Anthology of Hungarian Poetry from the 13th Century to the Present in English Translation. Vol. I. Chicago-Budapest: Atlantis-Centaur, M. Szivárvány and Corvina, 1996. LXVI + 964 pp. ; Der literaturgeschichtliche Fahrplan ; The Kiss: 20th Century Hungarian Short Stories Selected by István Bart. Budapest: Corvina Books, 1993. Fourth Printing, 1998. ; László Kósa (ed.): A Cultural History of Hungary Translated by Tünde Vajda. Budapest: Corvina Books/Osiris Kiadó, 1999. ; Gábor Tolcsvai-Nagy: A magyar nyelv stilisztikája [Hungarian Stylistics]. Budapest: Nemzeti Tankönyvkiadó, 1996

Symmetry structure in discrete models of biochemical systems : natural subsystems and the weak control hierarchy in a new model of computation driven by interactions

© 2015 The Authors. Published by the Royal Society under the terms of the Creative Commons Attribution License http://creativecommons.org/licenses/by/4.0/, which permits unrestricted use, provided the original author and source are credited.Interaction Computing (IC) is inspired by the observation that cell metabolic/regulatory systems construct order dynamically, through constrained interactions between their components and based on a wide range of possible inputs and environmental conditions. The goals of this work are (1) to identify and understand mathematically the natural subsystems and hierarchical relations in natural systems enabling this, and (2) to use the resulting insights to define a new model of computation based on interactions that is useful for both biology and computation. The dynamical characteristics of the cellular pathways studied in Systems Biology relate, mathematically, to the computational characteristics of automata derived from them, and their internal symmetry structures to computational power. Finite discrete automata models of biological systems such as the lac operon, Krebs cycle, and p53-mdm2 genetic regulation constructed from Systems Biology models have canonically associated algebraic structures { transformation semigroups. These contain permutation groups (local substructures exhibiting symmetry) that correspond to "pools of reversibility". These natural subsystems are related to one another in a hierarchical manner by the notion of "weak control ". We present natural subsystems arising from several biological examples and their weak control hierarchies in detail. Finite simple non-abelian groups (SNAGs) are found in biological examples and can be harnessed to realize nitary universal computation. This allows ensembles of cells to achieve any desired finitary computational transformation, depending on external inputs, via suitably constrained interactions. Based on this, interaction machines that grow and change their structure recursively are introduced and applied, providing a natural model of computation driven by interactions.Peer reviewe

Continuous Symmetries of Difference Equations

Lie group theory was originally created more than 100 years ago as a tool for solving ordinary and partial differential equations. In this article we review the results of a much more recent program: the use of Lie groups to study difference equations. We show that the mismatch between continuous symmetries and discrete equations can be resolved in at least two manners. One is to use generalized symmetries acting on solutions of difference equations, but leaving the lattice invariant. The other is to restrict to point symmetries, but to allow them to also transform the lattice.Comment: Review articl

The Psychological Science Accelerator: Advancing Psychology through a Distributed Collaborative Network

Concerns have been growing about the veracity of psychological research. Many findings in psychological science are based on studies with insufficient statistical power and nonrepresentative samples, or may otherwise be limited to specific, ungeneralizable settings or populations. Crowdsourced research, a type of large-scale collaboration in which one or more research projects are conducted across multiple lab sites, offers a pragmatic solution to these and other current methodological challenges. The Psychological Science Accelerator (PSA) is a distributed network of laboratories designed to enable and support crowdsourced research projects. These projects can focus on novel research questions, or attempt to replicate prior research, in large, diverse samples. The PSA\u27s mission is to accelerate the accumulation of reliable and generalizable evidence in psychological science. Here, we describe the background, structure, principles, procedures, benefits, and challenges of the PSA. In contrast to other crowdsourced research networks, the PSA is ongoing (as opposed to time-limited), efficient (in terms of re-using structures and principles for different projects), decentralized, diverse (in terms of participants and researchers), and inclusive (of proposals, contributions, and other relevant input from anyone inside or outside of the network). The PSA and other approaches to crowdsourced psychological science will advance our understanding of mental processes and behaviors by enabling rigorous research and systematically examining its generalizability

The Psychological Science Accelerator: Advancing Psychology Through a Distributed Collaborative Network

Source at https://doi.org/10.1177/2515245918797607.Concerns about the veracity of psychological research have been growing. Many findings in psychological science are based on studies with insufficient statistical power and nonrepresentative samples, or may otherwise be limited to specific, ungeneralizable settings or populations. Crowdsourced research, a type of large-scale collaboration in which one or more research projects are conducted across multiple lab sites, offers a pragmatic solution to these and other current methodological challenges. The Psychological Science Accelerator (PSA) is a distributed network of laboratories designed to enable and support crowdsourced research projects. These projects can focus on novel research questions or replicate prior research in large, diverse samples. The PSA’s mission is to accelerate the accumulation of reliable and generalizable evidence in psychological science. Here, we describe the background, structure, principles, procedures, benefits, and challenges of the PSA. In contrast to other crowdsourced research networks, the PSA is ongoing (as opposed to time limited), efficient (in that structures and principles are reused for different projects), decentralized, diverse (in both subjects and researchers), and inclusive (of proposals, contributions, and other relevant input from anyone inside or outside the network). The PSA and other approaches to crowdsourced psychological science will advance understanding of mental processes and behaviors by enabling rigorous research and systematic examination of its generalizability