Descartes' Apple Sorting Problem (The Problem of the Criterion)

Educación y valores

Foro Educacional ◽

10.29344/07180772.19.855 ◽

2014 ◽

pp. 83

Author(s):

Sabino de Juan López

Keyword(s):

Key Words ◽

A Priori ◽

Palabras Clave ◽

The Subject ◽

The Relationship ◽

Problem Of The Criterion

RESUMEN En el artículo se ofrece una reflexión en torno a la educación y valores. Tras una referencia a los diferentes sentidos en que se puede plantear el problema en función de la forma como se puede entender la relación entre los dos sustantivos “educación” y “valores”, la reflexión se centra en algunos problemas relacionados con los valores en cuanto contenidos de la educación. Primeramente se refiere al problema del criterio en función del cual determinar los valores de la educación, concluyendo en que el criterio no podía ser ni de carácter a priori, ni empírico, sino “sintético”. A continuación, se afronta el problema del principio, de la fuente de los valores, o la concreción del criterio de los valores de la educación, entendiendo que éstos deberían ser determinados a partir del sujeto de la educación. Se concluye con la referencia a una exigencia de los valores de la educación, la configuración de una totalidad unitaria e interactiva. Palabras clave: educación, valores, fuente de valores, integración, cultura EDUCATION AND VALUES ABSTRACT The article offers a reflection on education and values. After a reference to the different senses in which one can pose the problem in terms of how you can understand the relationship between the two nouns “education” and “values”, reflection focuses on some problems related to the values in the contents of education. First, it concerns the problem of the criterion against which to determine the values of education, concluding that the criterion could be neither a priori in nature, not empirical, but “synthetic”. Herein, the problem of principle is faced, the source of values, or the realization of the criterion of the values of education, understanding that these should be determined from the subject of education. It concludes with the reference of a requirement of the values in education, setting up a unitary and interactive whole. Key Words: education, values , power values , integration, culture

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Core Criteria I

10.1093/oso/9780198793670.003.0004 ◽

2018 ◽

Author(s):

Sanford C. Goldberg

Keyword(s):

Cognitive Processes ◽

Point Of View ◽

Infinite Regress ◽

Belief Formation ◽

Forming Process ◽

Epistemic Criteria ◽

Problem Of The Criterion

Chapter 3 deals with the first issue one faces in the task of articulating the explicit epistemic criteria for belief: the problem of the criterion. It is tempting to suppose that a belief can be normatively proper from the epistemic point of view only if the believer can certify for herself the reliability of every belief-forming process on which she relied. But insisting on this quickly leads to the threat of an infinite regress. This chapter defends a foundationalist response to this problem, according to which we enjoy a default (albeit defeasible) permission to rely on certain cognitive processes in belief-formation. These are processes that satisfy what the author calls the Reliabilist Rationale. Importantly, our permissions here are social: any one of us is permitted to rely on any token process that satisfies this rationale, whether the token process resides in one’s own mind/brain or that of another epistemic subject.

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Exact Markov chain-based runtime analysis of a discrete particle swarm optimization algorithm on sorting and OneMax

Natural Computing ◽

10.1007/s11047-021-09856-0 ◽

2021 ◽

Author(s):

Moritz Mühlenthaler ◽

Alexander Raß ◽

Manuel Schmitt ◽

Rolf Wanka

Keyword(s):

Particle Swarm Optimization ◽

Markov Chain ◽

Markov Model ◽

Optimization Problems ◽

Formal Analysis ◽

Particle Swarm ◽

Upper And Lower Bounds ◽

Swarm Optimization ◽

Local Optima ◽

Sorting Problem

AbstractMeta-heuristics are powerful tools for solving optimization problems whose structural properties are unknown or cannot be exploited algorithmically. We propose such a meta-heuristic for a large class of optimization problems over discrete domains based on the particle swarm optimization (PSO) paradigm. We provide a comprehensive formal analysis of the performance of this algorithm on certain “easy” reference problems in a black-box setting, namely the sorting problem and the problem OneMax. In our analysis we use a Markov model of the proposed algorithm to obtain upper and lower bounds on its expected optimization time. Our bounds are essentially tight with respect to the Markov model. We show that for a suitable choice of algorithm parameters the expected optimization time is comparable to that of known algorithms and, furthermore, for other parameter regimes, the algorithm behaves less greedy and more explorative, which can be desirable in practice in order to escape local optima. Our analysis provides a precise insight on the tradeoff between optimization time and exploration. To obtain our results we introduce the notion of indistinguishability of states of a Markov chain and provide bounds on the solution of a recurrence equation with non-constant coefficients by integration.

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T-SNE visualization of large-scale neural recordings

10.1101/087395 ◽

2016 ◽

Cited By ~ 5

Author(s):

George Dimitriadis ◽

Joana Neto ◽

Adam R. Kampff

Keyword(s):

Large Scale ◽

New Technologies ◽

Dimensional Space ◽

Clustering Algorithms ◽

Brain Regions ◽

Data Sets ◽

Neural Recordings ◽

Sorting Problem ◽

Feature Spaces ◽

High Degree

AbstractElectrophysiology is entering the era of ‘Big Data’. Multiple probes, each with hundreds to thousands of individual electrodes, are now capable of simultaneously recording from many brain regions. The major challenge confronting these new technologies is transforming the raw data into physiologically meaningful signals, i.e. single unit spikes. Sorting the spike events of individual neurons from a spatiotemporally dense sampling of the extracellular electric field is a problem that has attracted much attention [22, 23], but is still far from solved. Current methods still rely on human input and thus become unfeasible as the size of the data sets grow exponentially.Here we introduce the t-student stochastic neighbor embedding (t-sne) dimensionality reduction method [27] as a visualization tool in the spike sorting process. T-sne embeds the n-dimensional extracellular spikes (n = number of features by which each spike is decomposed) into a low (usually two) dimensional space. We show that such embeddings, even starting from different feature spaces, form obvious clusters of spikes that can be easily visualized and manually delineated with a high degree of precision. We propose that these clusters represent single units and test this assertion by applying our algorithm on labeled data sets both from hybrid [23] and paired juxtacellular/extracellular recordings [15]. We have released a graphical user interface (gui) written in python as a tool for the manual clustering of the t-sne embedded spikes and as a tool for an informed overview and fast manual curration of results from other clustering algorithms. Furthermore, the generated visualizations offer evidence in favor of the use of probes with higher density and smaller electrodes. They also graphically demonstrate the diverse nature of the sorting problem when spikes are recorded with different methods and arise from regions with different background spiking statistics.

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