ON THE MINIMAL TEACHING SETS OF TWO-DIMENSIONAL THRESHOLD FUNCTIONS.
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| Title: | ON THE MINIMAL TEACHING SETS OF TWO-DIMENSIONAL THRESHOLD FUNCTIONS. |
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| Authors: | ALEKSEYEV, MAX A.1 maxal@gwu.edu, BASOVA, MARINA G.2 mbas@inbox.ru, ZOLOTYKH, NIKOLAI YU.3 olotykh@vmk.unn.ru |
| Source: | SIAM Journal on Discrete Mathematics. 2015, Vol. 29 Issue 1, p157-165. 9p. |
| Subjects: | Function point analysis, Functional analysis, Functional differential equations, Calculus of variations, Functional equations |
| Abstract: | It is known that a minimal teaching set of any threshold function on the two-dimensional rectangular grid consists of 3 or 4 points. We derive exact formulae for the numbers of functions corresponding to these values and further refine them in the case of a minimal teaching set of size 3. We also prove that the average cardinality of the minimal teaching sets of threshold functions is asymptotically 7/2. We further present corollaries of these results concerning some special arrangements of lines in the plane. [ABSTRACT FROM AUTHOR] |
| Copyright of SIAM Journal on Discrete Mathematics is the property of Society for Industrial & Applied Mathematics and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.) | |
| Database: | Engineering Source |
| FullText | Text: Availability: 0 |
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| Header | DbId: egs DbLabel: Engineering Source An: 108644228 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
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| Items | – Name: Title Label: Title Group: Ti Data: ON THE MINIMAL TEACHING SETS OF TWO-DIMENSIONAL THRESHOLD FUNCTIONS. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22ALEKSEYEV%2C+MAX+A%2E%22">ALEKSEYEV, MAX A.</searchLink><relatesTo>1</relatesTo><i> maxal@gwu.edu</i><br /><searchLink fieldCode="AR" term="%22BASOVA%2C+MARINA+G%2E%22">BASOVA, MARINA G.</searchLink><relatesTo>2</relatesTo><i> mbas@inbox.ru</i><br /><searchLink fieldCode="AR" term="%22ZOLOTYKH%2C+NIKOLAI+YU%2E%22">ZOLOTYKH, NIKOLAI YU.</searchLink><relatesTo>3</relatesTo><i> olotykh@vmk.unn.ru</i> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22SIAM+Journal+on+Discrete+Mathematics%22">SIAM Journal on Discrete Mathematics</searchLink>. 2015, Vol. 29 Issue 1, p157-165. 9p. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Function+point+analysis%22">Function point analysis</searchLink><br /><searchLink fieldCode="DE" term="%22Functional+analysis%22">Functional analysis</searchLink><br /><searchLink fieldCode="DE" term="%22Functional+differential+equations%22">Functional differential equations</searchLink><br /><searchLink fieldCode="DE" term="%22Calculus+of+variations%22">Calculus of variations</searchLink><br /><searchLink fieldCode="DE" term="%22Functional+equations%22">Functional equations</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: It is known that a minimal teaching set of any threshold function on the two-dimensional rectangular grid consists of 3 or 4 points. We derive exact formulae for the numbers of functions corresponding to these values and further refine them in the case of a minimal teaching set of size 3. We also prove that the average cardinality of the minimal teaching sets of threshold functions is asymptotically 7/2. We further present corollaries of these results concerning some special arrangements of lines in the plane. [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of SIAM Journal on Discrete Mathematics is the property of Society for Industrial & Applied Mathematics and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.) |
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| RecordInfo | BibRecord: BibEntity: Identifiers: – Type: doi Value: 10.1137/140978090 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 9 StartPage: 157 Subjects: – SubjectFull: Function point analysis Type: general – SubjectFull: Functional analysis Type: general – SubjectFull: Functional differential equations Type: general – SubjectFull: Calculus of variations Type: general – SubjectFull: Functional equations Type: general Titles: – TitleFull: ON THE MINIMAL TEACHING SETS OF TWO-DIMENSIONAL THRESHOLD FUNCTIONS. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: ALEKSEYEV, MAX A. – PersonEntity: Name: NameFull: BASOVA, MARINA G. – PersonEntity: Name: NameFull: ZOLOTYKH, NIKOLAI YU. IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 01 Text: 2015 Type: published Y: 2015 Identifiers: – Type: issn-print Value: 08954801 Numbering: – Type: volume Value: 29 – Type: issue Value: 1 Titles: – TitleFull: SIAM Journal on Discrete Mathematics Type: main |
| ResultId | 1 |
