Maximal Nucleus Clusters in Pawlak Paintings. Nerves as approximating tools in Visual Arts

Peters, James F.; Ramanna, Sheela

doi:10.15439/2016f004

Cited by 3 publications

(4 citation statements)

References 6 publications

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“…Indeed, FedCSIS 2016 (Gdańsk, Poland) hosted the international panel discussion in memoriam of the 90th anniversary of the birth and the 10th anniversary of the death of Professor Pawlak 12 . The previously-cited publications [4], [8], [100] were prepared specially for that panel.…”

Section: Discussionmentioning

confidence: 99%

“…The second considered event is the PP-RAI 2022 conference held this year in Gdynia, Poland 8 . The chairs of PP-RAI 2022 decided to celebrate the 40th anniversary of rough sets by organizing the contest for the most influential article on rough sets co-authored by Polish researchers in 2020 or later 9 .…”

Section: B Rough Set Contest At Pp-rai 2022mentioning

confidence: 99%

“…It is also interesting to note that the basic models he used working in different fields, such as conflict analysis [6] or concurrency [7], were based on information systems. In the same time, his personal interests were going far beyond computer science and science in general [8].…”

Section: Introduction and Basic Conceptsmentioning

confidence: 99%

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Rough Sets Turn 40: From Information Systems to Intelligent Systems

Skowron¹,

Ślęzak²

2022

Annals of Computer Science and Information Systems

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The theory of rough sets was founded by Zdzisław Pawlak as a framework for data and knowledge exploration. His seminal paper titled "Rough Sets" was published in 1982, in International Journal of Computer and Information Sciences. One of the key aspects that lets us use rough sets in practical scenarios is the notion of information system, which comes from even earlier Professor Pawlak's works. Information systems are the means for data and knowledge representation. They constitute the input to rough set mechanisms aimed at computing approximations of concepts and deriving compacted, interpretable decision models. In particular, the fundamental notion of the indiscernibility relation is defined on the basis of a given information system. Accordingly, we discuss to what extent information systems can serve as the basis for intelligent systems. We claim that in many cases it is not enough to treat a data set -represented as an information system -as a purely abstract object with no linkage to the data origins. Oppositely, we should give ourselves a technical possibility to construct information systems dynamically, taking into account interaction with physical environments where the data comes from. With this respect, we refer to the notions of interactive granular computing and we generally consider together the paradigms of rough sets, information systems, and information granulation.

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Section: Discussionmentioning

confidence: 99%

Section: B Rough Set Contest At Pp-rai 2022mentioning

confidence: 99%

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Rough Sets Turn 40: From Information Systems to Intelligent Systems

Skowron¹,

Ślęzak²

2022

Annals of Computer Science and Information Systems

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“…For the purpose of this paper, the toy at rest stands for a given brain scale-free exponent, and its shadows for the corresponding Shannon entropy. In turn, the changes in location of the moving toy stand for changes in brain scale-free exponents, while the modifications in shadow's shape and its undulating contour stand for the corresponding Re ´nyi entropy (Re ´nyi 1961(Re ´nyi , 1966Peters 2017;Peters and Ramanna 2016).…”

Section: Introductionmentioning

confidence: 99%

The informational entropy endowed in cortical oscillations

2018

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A two-dimensional shadow may encompass more information than its corresponding three-dimensional object. Indeed, if we rotate the object, we achieve a pool of observed shadows from different angulations, gradients, shapes and variable length contours that make it possible for us to increase our available information. Starting from this simple observation, we show how informational entropies might turn out to be useful in the evaluation of scale-free dynamics in the brain. Indeed, brain activity exhibits a scale-free distribution that leads to the variations in the power law exponent typical of different functional neurophysiological states. Here we show that modifications in scaling slope are associated with variations in Rényi entropy, a generalization of Shannon informational entropy. From a three-dimensional object's perspective, by changing its orientation (standing for the cortical scale-free exponent), we detect different two-dimensional shadows from different perception angles (standing for Rényi entropy in different brain areas). We show how, starting from known values of Rényi entropy (easily detectable in brain fMRIs or EEG traces), it is feasible to calculate the scaling slope in a given moment and in a given brain area. Because changes in scale-free cortical dynamics modify brain activity, this issue points towards novel approaches to mind reading and description of the forces required for transcranial stimulation.

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Shape Descriptions and Classes of Shapes. A Proximal Physical Geometry Approach

Peters

Ramanna

2017

Advances in Feature Selection for Data and Pattern Recognition

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This article introduces proximalCech nerves andCech complexes, restricted to finite, bounded regions K of the Euclidean plane. ACech nerve is a collection of intersecting balls. ACech complex is a collection of nerves that cover K.Cech nerves are proximal, provided the nerves are close to each other, either spatially or descriptively. ACech nerve has an advantage over the usual Alexandroff nerve, since we need only identify the center and fixed radius of each ball in aCech nerve instead of identifying the three vertices of intersecting filled triangles (2-simplexes) in an Alexandroff nerve. As a result,Cech nerves more easily cover K and facilitate approximation of the shapes of irregular finite, bounded planar regions. A main result of this article is extension of the Edelsbrunner-Harer Nerve Theorem for descriptive and non-descriptiveCech nerves andCech complexes, covering K.2010 Mathematics Subject Classification. Primary 54E05 (Proximity); Secondary 68U05 (Computational Geometry).

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Maximal Nucleus Clusters in Pawlak Paintings. Nerves as approximating tools in Visual Arts

Cited by 3 publications

References 6 publications

Rough Sets Turn 40: From Information Systems to Intelligent Systems

Rough Sets Turn 40: From Information Systems to Intelligent Systems

The informational entropy endowed in cortical oscillations

Shape Descriptions and Classes of Shapes. A Proximal Physical Geometry Approach

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