Results for ' Martin-Löf randomness'

992 found
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  1.  13
    A Nonstandard Counterpart of WWKL.Stephen G. Simpson & Keita Yokoyama - 2011 - Notre Dame Journal of Formal Logic 52 (3):229-243.
    In this paper, we introduce a system of nonstandard second-order arithmetic $\mathsf{ns}$-$\mathsf{WWKL_0}$ which consists of $\mathsf{ns}$-$\mathsf{BASIC}$ plus Loeb measure property. Then we show that $\mathsf{ns}$-$\mathsf{WWKL_0}$ is a conservative extension of $\mathsf{WWKL_0}$ and we do Reverse Mathematics for this system.
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  2.  9
    Martin-Löf Randomness Implies Multiple Recurrence in Effectively Closed Sets.Rodney G. Downey, Satyadev Nandakumar & André Nies - 2019 - Notre Dame Journal of Formal Logic 60 (3):491-502.
    This work contributes to the program of studying effective versions of “almost-everywhere” theorems in analysis and ergodic theory via algorithmic randomness. Consider the setting of Cantor space {0,1}N with the uniform measure and the usual shift. We determine the level of randomness needed for a point so that multiple recurrence in the sense of Furstenberg into effectively closed sets P of positive measure holds for iterations starting at the point. This means that for each k∈N there is an (...)
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  3.  5
    Martin-löf randomness in spaces of closed sets.Logan M. Axon - 2015 - Journal of Symbolic Logic 80 (2):359-383.
  4.  3
    Quanta, Randomness, and Explanation.Martin E. Gerwin - 1988 - Philosophie Et Culture: Actes du XVIIe Congrès Mondial de Philosophie 3:86-91.
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  5.  5
    Martin–Löf random generalized Poisson processes.Logan Axon - 2018 - Annals of Pure and Applied Logic 169 (4):261-276.
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  6.  13
    Martin-Löf randomness and Galton–Watson processes.David Diamondstone & Bjørn Kjos-Hanssen - 2012 - Annals of Pure and Applied Logic 163 (5):519-529.
  7. Rules, Regularities, Randomness. Festschrift for Michiel van Lambalgen.Keith Stenning & Martin Stokhof (eds.) - 2022 - Amsterdam, The Netherlands: Institute for Logic, Language and Computation.
    Festschrift for Michiel van Lambalgen on the occasion of his retirement as professor of logic and cognitive science at the University of Amsterdam.
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  8.  3
    On the Creation of Representative Samples of Random Quasi-Orders.Martin Schrepp & Ali Ünlü - 2015 - Frontiers in Psychology 6.
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  9.  6
    Π11‐Martin‐Löf randomness and Π11‐Solovay completeness.Claude Sureson - 2019 - Mathematical Logic Quarterly 65 (3):265-279.
    Developing an analogue of Solovay reducibility in the higher recursion setting, we show that results from the classical computably enumerable case can be extended to the new context.
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  10.  5
    The moral importance of selecting people randomly.Martin Peterson - 2008 - Bioethics 22 (6):321–327.
    This article discusses some ethical principles for distributing pandemic influenza vaccine and other indivisible goods. I argue that a number of principles for distributing pandemic influenza vaccine recently adopted by several national governments are morally unacceptable because they put too much emphasis on utilitarian considerations, such as the ability of the individual to contribute to society. Instead, it would be better to distribute vaccine by setting up a lottery. The argument for this view is based on a purely consequentialist account (...)
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  11.  2
    From Typical Areas to Random Sampling: Sampling Methods in Russia from 1875 to 1930.Martine Mespoulet - 2002 - Science in Context 15 (3):411-425.
  12.  48
    A learning-theoretic characterisation of Martin-Löf randomness and Schnorr randomness.Francesca Zaffora Blando - 2021 - Review of Symbolic Logic 14 (2):531-549.
    Numerous learning tasks can be described as the process of extrapolating patterns from observed data. One of the driving intuitions behind the theory of algorithmic randomness is that randomness amounts to the absence of any effectively detectable patterns: it is thus natural to regard randomness as antithetical to inductive learning. Osherson and Weinstein [11] draw upon the identification of randomness with unlearnability to introduce a learning-theoretic framework (in the spirit of formal learning theory) for modelling algorithmic (...)
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  13.  5
    Memory for random shapes: A dual-task analysis.Richard T. Kelly & David W. Martin - 1974 - Journal of Experimental Psychology 103 (2):224.
  14.  4
    Ethics in the Gray Area.Martin Peterson - 2023 - Cambridge, UK: Cambridge University Press.
    What should morally conscientious agents do if they must choose among options that are somewhat right and somewhat wrong? Should one select an option that is right to the highest degree, or would it perhaps be more rational to choose randomly among all somewhat right options? And how should lawmakers and courts address behaviour that is neither entirely right nor entirely wrong? In this first book-length discussion of the 'gray area' in ethics, Martin Peterson challenges the assumption that rightness (...)
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  15.  15
    Jorge Mario Bergoglio & Abraham Skorka, On Heaven and Earth: Pope Francis on Faith, Family, and the Church in the Twenty-First Century, Translated by Alejandro Bermudez and Howard Goodman, New York: Random House/Image, 2013, 236 hlm. [REVIEW]Martin Harun - 2020 - Diskursus - Jurnal Filsafat dan Teologi STF Driyarkara 13 (2):282-284.
    Dalam buku ini Kardinal Jorge Mario Bergoglio—saat itu masih Uskup Agung Buenos Aires dan sejak 13 Maret 2013 menjadi Paus Fransiskus—dan Rabi Abraham Skorka berdialog tentang sejumlah masalah agama, kehidupan, keluarga, politik, dan masyarakat yang mereka lihat sebagai tantangan besar pada abad ke-21 ini. Dialog itu mulai dan berakhir dengan penukaran pandangan tentang topik dialog sendiri sebagaimana mereka usahakan. Latarnya adalah Argentina yang karena sejarahnya telah lupa akan seni untuk saling mendengarkan dan berbicara dengan satu sama lain. Di tengah kebuntuan (...)
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  16.  6
    Serial versus random presentation of paired associates.Clessen J. Martin & Eli Saltz - 1963 - Journal of Experimental Psychology 65 (6):609.
  17.  11
    Freedom as a Natural Phenomenon.Martin Zwick - 2017 - Foundations of Science 22 (1):1-10.
    “Freedom” is a phenomenon in the natural world. This phenomenon—and indirectly the question of free will—is explored using a variety of systems-theoretic ideas. It is argued that freedom can emerge only in systems that are partially determined and partially random, and that freedom is a matter of degree. The paper considers types of freedom and their conditions of possibility in simple living systems and in complex living systems that have modeling subsystems. In simple living systems, types of freedom include independence (...)
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  18.  95
    Freedom as a Natural Phenomenon.Martin Zwick - 2015 - Foundations of Science 20 (3):1-10.
    “Freedom” is a phenomenon in the natural world. This phenomenon—and indirectly the question of free will—is explored using a variety of systems-theoretic ideas. It is argued that freedom can emerge only in systems that are partially determined and partially random, and that freedom is a matter of degree. The paper considers types of freedom and their conditions of possibility in simple living systems and in complex living systems that have modeling subsystems. In simple living systems, types of freedom include independence (...)
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  19.  5
    Characterizing strong randomness via Martin-Löf randomness.Liang Yu - 2012 - Annals of Pure and Applied Logic 163 (3):214-224.
  20.  65
    Explanation in mathematical conversations: An empirical investigation.Alison Pease, Andrew Aberdein & Ursula Martin - 2019 - Philosophical Transactions of the Royal Society A 377.
    Analysis of online mathematics forums can help reveal how explanation is used by mathematicians; we contend that this use of explanation may help to provide an informal conceptualization of simplicity. We extracted six conjectures from recent philosophical work on the occurrence and characteristics of explanation in mathematics. We then tested these conjectures against a corpus derived from online mathematical discussions. To this end, we employed two techniques, one based on indicator terms, the other on a random sample of comments lacking (...)
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  21.  5
    Cascade Theory.Martin Cohen - 2010 - In Mind Games: 31 Days to Rediscover Your Brain. Malden, MA: Wiley-Blackwell. pp. 52–53.
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  22.  14
    Supervised Speaker Diarization Using Random Forests: A Tool for Psychotherapy Process Research.Lukas Fürer, Nathalie Schenk, Volker Roth, Martin Steppan, Klaus Schmeck & Ronan Zimmermann - 2020 - Frontiers in Psychology 11.
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  23.  4
    The Fallacy of the Lonely Fact.Martin Cohen - 2010 - In Mind Games: 31 Days to Rediscover Your Brain. Malden, MA: Wiley-Blackwell. pp. 7–7.
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  24.  20
    The second law of probability dynamics.Martin Barrett & Elliott Sober - 1994 - British Journal for the Philosophy of Science 45 (4):941-953.
  25.  8
    Michael Sandel. Lo que el dinero no puede comprar: Los límites morales del mercado. Trad. del inglés de Joaquín Chamorro Mielke. Barcelona: Random House Mondadori, 2013. [REVIEW]Alan Martin - 2014 - Revista de filosofía (Chile) 70:196-198.
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  26.  21
    The Pathosome: A Dynamic Three‐Dimensional View of Disease–Environment Interaction.Peter Lenart, Martin Scheringer & Julie Bienertova-Vasku - 2019 - Bioessays 41 (6):1900014.
    Most contemporary models of disease development consider the interaction between genotype and environment as static. The authors argue that because time is a key factor in genotype–environment interaction, this approach oversimplifies the pathology analysis and may lead to wrong conclusions. In reviewing the field, the authors suggest that the history of genotype–environment interactions plays an important role in the development of diseases and that this history may be analyzed using the phenotype as a proxy. Furthermore, a theoretical and experimental framework (...)
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  27.  56
    The Arbitrariness of Belief.Martin Smith - 2013 - In Dylan Dodd & Elia Zardini (eds.), Scepticism and Perceptual Justification. New York: Oxford University Press.
    In Knowledge and Lotteries, John Hawthorne offers a diagnosis of our unwillingness to believe, of a given lottery ticket, that it will lose a fair lottery – no matter how many tickets are involved. According to Hawthorne, it is natural to employ parity reasoning when thinking about lottery outcomes: Put roughly, to believe that a given ticket will lose, no matter how likely that is, is to make an arbitrary choice between alternatives that are perfectly balanced given one’s evidence. It’s (...)
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  28.  10
    ‘I Just Stopped Going’: A Mixed Methods Investigation Into Types of Therapy Dropout in Adolescents With Depression.Sally O’Keeffe, Peter Martin, Mary Target & Nick Midgley - 2019 - Frontiers in Psychology 10.
    What does it mean to ‘drop out’ of therapy? Many definitions of ‘dropout’ have been proposed, but the most widely accepted is the client ending treatment without agreement of their therapist. However, this is in some ways an external criterion that does not take into account the client’s experience of therapy, or reasons for ending it prematurely. This study aimed to identify whether there were more meaningful categories of dropout than the existing dropout definition, and to test whether this refined (...)
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  29.  1
    Guidelines for Community-based Ethics Review of Children’s Science Fair Projects.Martin Tolich - 2008 - Journal of Bioethical Inquiry 5 (4):303-310.
    Low-level community based ethics committees staffed by teachers, parents and community representatives can readily review children’s science fair projects subject to the revision of two core assumptions currently governing children’s Science Fairs. The first part of the paper recasts the New Zealand Royal Society guidelines from its primary emphasis on risk to a new assumption, without benefit there can be no risk. Equally, this revision gives more prominence to the participant information sheet, allowing it to act as a quasi application (...)
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  30.  83
    Positive Development Based on the Teaching of Personal and Social Responsibility: An Intervention Program With Institutionalized Youngsters.Paulo Martins, António-José Gonzalez, Margarida Pedroso de Lima, João Faleiro & Luís Preto - 2022 - Frontiers in Psychology 13.
    From the standpoint of the school settings, sport participation constitutes a key strategy concerning the manifestation of positive behaviors that result from the development of personal and social responsibility. Based on the TPSR model, the goal of this study was to evaluate the effects of an intervention geared toward teaching life skills through sport to youngsters who had been committed. The participants were evaluated before and after the intervention. After the initial evaluation, they were randomly assigned to the experimental and (...)
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  31.  4
    Theorems as meaningful cultural artifacts: Making the world additive.Martin H. Krieger - 1991 - Synthese 88 (2):135 - 154.
    Mathematical theorems are cultural artifacts and may be interpreted much as works of art, literature, and tool-and-craft are interpreted. The Fundamental Theorem of the Calculus, the Central Limit Theorem of Statistics, and the Statistical Continuum Limit of field theories, all show how the world may be put together through the arithmetic addition of suitably prescribed parts (velocities, variances, and renormalizations and scaled blocks, respectively). In the limit — of smoothness, statistical independence, and large N — higher-order parts, such as accelerations, (...)
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  32.  13
    Idiosyncratic Characteristics of Postural Sway in Normal and Perturbed Standing.Tania E. Sakanaka, Martin Lakie & Raymond F. Reynolds - 2021 - Frontiers in Human Neuroscience 15:660470.
    ObjectiveAre people with a characteristically large physiological sway rendered particularly unstable when standing on a moving surface? Is postural sway in standing individuals idiosyncratic? In this study, we examine postural sway in individuals standing normally, and when subtle continuous sinusoidal disturbances are applied to their support platform. We calculate consistency between conditions to verify if sway can be considered characteristic of each individual. We also correlate two different aspects of participants’ responses to disturbance; their sway velocity and their regulation of (...)
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  33.  5
    Does Social Exclusion Improve Detection of Real and Fake Smiles? A Replication Study.Simon Schindler & Martin Trede - 2021 - Frontiers in Psychology 12.
    Research on social exclusion suggests an increased attention of excluded persons to subtle social cues. In one study (N= 32), published inPsychological Science,Bernstein et al. (2008)provided evidence for this idea by showing that participants in the social exclusion condition were better in correctly categorizing a target person’s smile as real or fake. Although highly cited, this finding has never been directly replicated. The present study aimed to fill that gap. 201 participants (79.1% female) were randomly assigned to a social exclusion, (...)
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  34.  5
    Dealing with elite sport competition demands: an exploration of the dynamic relationships between stress appraisal, coping, emotion, and performance during fencing matches.Julie Doron & Guillaume Martinent - 2021 - Cognition and Emotion 35 (7):1365-1381.
    The present research aimed to provide a more holistic analysis of stressful experiences in sport by examining how stress appraisal, coping and emotion are dynamically inter-related constructs and the extent to which their dynamic relationship is associated with objective performance. Based on process-oriented methods, two studies were conducted with elite athletes in order to investigate the dynamic relationship between these constructs and performance in highly demanding sport situations (Study 1: simulated competitive fencing matches during a training session; Study 2: real-life (...)
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  35.  13
    La escala del tiempo. El concepto pitagórico de analogía en la definición de tiempo platónicoaristotélica.Martín Simesen de Bielke - 2017 - Eidos: Revista de Filosofía de la Universidad Del Norte 27:96-124.
    RESUMEN Este artículo apunta a someter a consideración si existe o no un fundamento histórico-filosófico para la hipótesis de una homonimia no azarosa entre "escala de tiempo" y "escala musical". Un examen minucioso de ciertos pasajes del diálogo Timeo muestra que Platón fue el primero en sentar las bases para el concepto de tiempo, definido como número, al incorporar el concepto de 'analogía' o proporción, el cual fue desarrollado por los pitagóricos en el marco místico y teórico de los principios (...)
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  36. A Computer Simulation of the Argument from Disagreement.Johan E. Gustafsson & Martin Peterson - 2012 - Synthese 184 (3):387-405.
    In this paper we shed new light on the Argument from Disagreement by putting it to test in a computer simulation. According to this argument widespread and persistent disagreement on ethical issues indicates that our moral opinions are not influenced by any moral facts, either because no such facts exist or because they are epistemically inaccessible or inefficacious for some other reason. Our simulation shows that if our moral opinions were influenced at least a little bit by moral facts, we (...)
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  37.  9
    What characterizes life story memories? A diary study of Freshmen’s first term.Dorthe Kirkegaard Thomsen, Martin Hammershøj Olesen, Anette Schnieber, Thomas Jensen & Jan Tønnesvang - 2012 - Consciousness and Cognition 21 (1):366-382.
    We investigated whether memories are selected for the life story based on event characteristics. Sixty-one students completed weekly diaries over their first term at university. They described, dated and rated two events each week. Three months after the end of the term they completed an unexpected memory test. They recalled three memories from the diary period that were important to their life story. Three randomly selected events scoring low on importance to the life story functioned as control memories. Life story (...)
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  38.  5
    A Categorical Approach to Probability Theory.Roman Frič & Martin Papčo - 2010 - Studia Logica 94 (2):215-230.
    First, we discuss basic probability notions from the viewpoint of category theory. Our approach is based on the following four “sine quibus non” conditions: 1. (elementary) category theory is efficient (and suffices); 2. random variables, observables, probability measures, and states are morphisms; 3. classical probability theory and fuzzy probability theory in the sense of S. Gudder and S. Bugajski are special cases of a more general model; 4. a good model allows natural modifications.
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  39.  9
    George Barmpalias, Andrew E. M. Lewis and Keng Meng NG. The importance of Π 0 1 classes in effective randomness. The Journal of Symbolic Logic, vol. 75 (2010), pp. 387–400. - George Barmpalias, Andrew E. M. Lewis and Frank Stephan. Π 0 1 classes, LR degrees and Turing degrees. Annals of Pure and Applied Logic, vol. 156 (2008), pp. 21–38. - Antonin Kučera. Measure, Π 0 1 classes and complete extensions of PA. Recursion Theory Week (Oberwofach, 1984). Lecture Notes in Mathematics, vol. 1141. Springer, Berlin, 1985, pp. 245–259. - Frank Stephan. Martin-Löf randomness and PA complete sets. Logic Colloquium '02. Lecture Notes in Logic, vol. 27, Association for Symbolic Logic, La Jolla, CA, 2006, pp. 342–348. [REVIEW]Douglas Cenzer - 2012 - Bulletin of Symbolic Logic 18 (3):409-412.
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  40.  21
    Quantitative approaches to empirical legal research.Lee Epstein & Andrew D. Martin - 2010 - In Peter Cane & Herbert M. Kritzer (eds.), The Oxford handbook of empirical legal research. New York: Oxford University Press.
    This article deals with the objective nuances of empirical research, within the ambit of the quantitative kind. It begins with an overview of conducting empirical legal research, discussing its research design, implementation, and challenges faced. Theorizing in empirical legal scholarship comes in different forms: in some projects theories seek to provide insight into a wide range of phenomena, others are tailored to fit particular situations. In the clarification process the researcher translates abstract notions into concrete ones. To convert the data (...)
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  41.  95
    Trust in Intrusion Detection Systems: An Investigation of Performance Analysis for Machine Learning and Deep Learning Models.Basim Mahbooba, Radhya Sahal, Martin Serrano & Wael Alosaimi - 2021 - Complexity 2021:1-23.
    To design and develop AI-based cybersecurity systems ), users can justifiably trust, one needs to evaluate the impact of trust using machine learning and deep learning technologies. To guide the design and implementation of trusted AI-based systems in IDS, this paper provides a comparison among machine learning and deep learning models to investigate the trust impact based on the accuracy of the trusted AI-based systems regarding the malicious data in IDs. The four machine learning techniques are decision tree, K nearest (...)
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  42.  11
    Context and Perceptual Salience Influence the Formation of Novel Stereotypes via Cumulative Cultural Evolution.Jacqui Hutchison, Sheila J. Cunningham, Gillian Slessor, James Urquhart, Kenny Smith & Douglas Martin - 2018 - Cognitive Science 42 (S1):186-212.
    We use a transmission chain method to establish how context and category salience influence the formation of novel stereotypes through cumulative cultural evolution. We created novel alien targets by combining features from three category dimensions—color, movement, and shape—thereby creating social targets that were individually unique but that also shared category membership with other aliens (e.g., two aliens might be the same color and shape but move differently). At the start of the transmission chains each alien was randomly assigned attributes that (...)
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  43.  2
    Scientific writing: a professional upgrading need for health sciences professors.Laura María Pérez de Valdivia, Ener Raúl Rivera Martín & Geycell Emma Guevara Fernández - 2016 - Humanidades Médicas 16 (3):504-518.
    El presente trabajo es un estudio descriptivo y con un enfoque sincrónico que da muestra de las deficiencias de los profesores universitarios al redactar textos científicos. Este estudio tiene como objetivo proponer varias acciones de superación para perfeccionar el manejo del lenguaje y el arte de redactar de los docentes de la Universidad de Ciencias Médicas "Dr. Faustino Pérez Hernández" de la provincia Sancti Spíritus que cursan la octava edición de la Maestría en Ciencias de la Educación de la Universidad (...)
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  44.  6
    Jevons e o Papel da Analogia na Arte da Descoberta Experimental: o Caso da Descoberta dos Raios x e sua Investigação Pré-Teórica.Roberto de Andrade Martins - 1998 - Episteme 6:222-249.
    This paper discusses the role of analogy in pre-theoretical experimental research, studying a particular historical case (the discovery and early investigation of X rays) and using the methodological ideas of William Stanley Jevons. The historical data and Jevons’ analysis suggest that the discovery of a completely new phenomenon is due to chance, but soon afterwards it is necessary that some assumptions provide a guidance to the research – otherwise, observations and experiments would occur at random, and that would sendom lead (...)
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  45.  13
    Testing the Treatment Integrity of the Managing Cancer and Living Meaningfully Psychotherapeutic Intervention for Patients With Advanced Cancer.Susan Koranyi, Rebecca Philipp, Leonhard Quintero Garzón, Katharina Scheffold, Frank Schulz-Kindermann, Martin Härter, Gary Rodin & Anja Mehnert-Theuerkauf - 2020 - Frontiers in Psychology 11.
    IntroductionThe Managing Cancer and Living Meaningfully therapy for patients with advanced cancer was tested against a supportive psycho-oncological counseling intervention in a randomized controlled trial. We investigated whether CALM was delivered as intended ; whether CALM therapists with less experience in psycho-oncological care show higher adherence scores; and whether potential overlapping treatment elements between CALM and SPI can be identified.MethodsTwo trained and blinded raters assessed on 19 items four subscales of the Treatment Integrity Scale covering treatment domains of CALM. A (...)
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  46. Measuring Mindfulness: A Psychophysiological Approach.Vladimir Bostanov, Lilian Ohlrogge, Rita Britz, Martin Hautzinger & Boris Kotchoubey - 2018 - Frontiers in Human Neuroscience 12:325019.
    Mindfulness-based interventions have proved effective in reducing various clinical symptoms and in improving general mental health and well-being. The investigation of the mechanisms of therapeutic change needs methods for assessment of mindfulness. Existing self-report measures have, however, been strongly criticized on various grounds, including distortion of the original concept, response bias, and other. We propose a psychophysiological method for the assessment of the mindfulness learned through time-limited mindfulness-based therapy by people who undergo meditation training for the first time. We use (...)
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  47.  5
    The Energetic Dimension of Emotions: An Evolution-Based Computer Simulation with General Implications.Luc Ciompi & Martin Baatz - 2008 - Biological Theory 3 (1):42-50.
    Viewed from an evolutionary standpoint, emotions can be understood as situation-specific patterns of energy consumption related to behaviors that have been selected by evolution for their survival value, such as environmental exploration, flight or fight, and socialization. In the present article, the energy linked with emotions is investigated by a strictly energy-based simulation of the evolution of simple autonomous agents provided with random cognitive and motor capacities and operating among food and predators. Emotions are translated into evolving patterns of energy (...)
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  48.  13
    Low test–retest reliability of a protocol for assessing somatosensory cortex excitability generated from sensory nerves of the lower back.Katja Ehrenbrusthoff, Cormac G. Ryan, Denis J. Martin, Volker Milnik, Hubert R. Dinse & Christian Grüneberg - 2022 - Frontiers in Human Neuroscience 16.
    In people with chronic low back pain, maladaptive structural and functional changes on a cortical level have been identified. On a functional level, somatosensory cortical excitability has been shown to be reduced in chronic pain conditions, resulting in cortical disinhibition. The occurrence of structural and/or functional maladaptive cortical changes in people with CLBP could play a role in maintaining the pain. There is currently no measurement protocol for cortical excitability that employs stimulation directly to the lower back. We developed a (...)
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  49.  10
    Computable randomness and betting for computable probability spaces.Jason Rute - 2016 - Mathematical Logic Quarterly 62 (4-5):335-366.
    Unlike Martin‐Löf randomness and Schnorr randomness, computable randomness has not been defined, except for a few ad hoc cases, outside of Cantor space. This paper offers such a definition (actually, several equivalent definitions), and further, provides a general method for abstracting “bit‐wise” definitions of randomness from Cantor space to arbitrary computable probability spaces. This same method is also applied to give machine characterizations of computable and Schnorr randomness for computable probability spaces, extending the previously (...)
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  50.  3
    Randomness and Semimeasures.Laurent Bienvenu, Rupert Hölzl, Christopher P. Porter & Paul Shafer - 2017 - Notre Dame Journal of Formal Logic 58 (3):301-328.
    A semimeasure is a generalization of a probability measure obtained by relaxing the additivity requirement to superadditivity. We introduce and study several randomness notions for left-c.e. semimeasures, a natural class of effectively approximable semimeasures induced by Turing functionals. Among the randomness notions we consider, the generalization of weak 2-randomness to left-c.e. semimeasures is the most compelling, as it best reflects Martin-Löf randomness with respect to a computable measure. Additionally, we analyze a question of Shen, a (...)
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