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Visualizing Transfer Learning [article]

Róbert Szabó, Dániel Katona, Márton Csillag, Adrián Csiszárik, Dániel Varga
2020 arXiv   pre-print
Acknowledgements We thank Dániel Feles for designing the website for the project.  ...  Correspondence to: Dániel Varga <daniel@renyi.hu>.  ... 
arXiv:2007.07628v1 fatcat:ej326ne33vdpvm6yzrfccbfxci

Union-intersecting set systems [article]

Gyula O. H. Katona, Dániel T. Nagy
2014 arXiv   pre-print
(De Bonis-Katona, [2])  ...  (Katona, [7] , formula (12)) Let F be a t-intersecting system of subsets of [n] .  ... 
arXiv:1403.0088v1 fatcat:wj5l567k3nhbdaendmf2ob3yqi

Majority and Plurality Problems [article]

Dániel Gerbner, Gyula O.H. Katona, Dömötör Pálvölgyi and Balázs Patkós
2012 arXiv   pre-print
Given a set of n balls each colored with a color, a ball is said to be majority, k-majority, plurality if its color class has size larger than half of the number of balls, has size at least k, has size larger than any other color class; respectively. We address the problem of finding the minimum number of queries (a comparison of a pair of balls if they have the same color or not) that is needed to decide whether a majority, k-majority or plurality ball exists and if so then show one such ball.
more » ... We consider both adaptive and non-adaptive strategies and in certain cases, we also address weighted versions of the problems.
arXiv:1203.1398v1 fatcat:nid2fh2ftjhwjbw25vtukdhiv4

Incomparable copies of a poset in the Boolean lattice [article]

Gyula O. H. Katona, Dániel T. Nagy
2013 arXiv   pre-print
Katona and Tarján proved that a subset of B n containing none of the posets {V 2 , Λ 2 } has at most n−1 ⌊ n−1 2 ⌋ elements, and this bound is sharp [8] .  ... 
arXiv:1309.7379v1 fatcat:i6yd5nlddjblbluvgzlaw6xo7a

Union-Intersecting Set Systems

Gyula O. H. Katona, Dániel T. Nagy
2014 Graphs and Combinatorics  
(De Bonis-Katona, [2]) Assume that G is a K xy -free family of subsets of [n]. Then  ...  (Katona-Tarján, [10] ) Assume that G is a family of subsets of [n] that is K 12 -free andTheorem 4. (De Bonis-Katona, [2]) Assume that G is a K 1y -free family of subsets of [n]. Then K 21 -free.  ... 
doi:10.1007/s00373-014-1456-7 fatcat:bpfkglaqxzhvxlhoz7ez2gvnfy

Properties of minimally t-tough graphs [article]

Gyula Y. Katona, Dániel Soltész, Kitti Varga
2017 arXiv   pre-print
A graph G is minimally t-tough if the toughness of G is t and the deletion of any edge from G decreases the toughness. Kriesell conjectured that for every minimally 1-tough graph the minimum degree δ(G)=2. We show that in every minimally 1-tough graph δ(G)<n+2/3. We also prove that every minimally 1-tough claw-free graph is a cycle. On the other hand, we show that for every t ∈Q any graph can be embedded as an induced subgraph into a minimally t-tough graph.
arXiv:1604.02746v2 fatcat:d5eolkm3mvaejf3o565o5t4cb4

Majority and plurality problems

Dániel Gerbner, Gyula O.H. Katona, Dömötör Pálvölgyi, Balázs Patkós
2013 Discrete Applied Mathematics  
Given a set of n balls each colored with a color, a ball is said to be majority, k-majority, plurality if its color class has size larger than half of the number of balls, has size at least k, has size larger than any other color class; respectively. We address the problem of finding the minimum number of queries (a comparison of a pair of balls if they have the same color or not) that is needed to decide whether a majority, k-majority or plurality ball exists and if so then show one such ball.
more » ... We consider both adaptive and non-adaptive strategies and in certain cases, we also address weighted versions of the problems.
doi:10.1016/j.dam.2012.10.023 fatcat:e3wmzt3epbg3tpgi4knuxljqtq

Properties of minimally t-tough graphs

Gyula Y. Katona, Dániel Soltész, Kitti Varga
2018 Discrete Mathematics  
A graph G is minimally t-tough if the toughness of G is t and the deletion of any edge from G decreases the toughness. Kriesell conjectured that for every minimally 1-tough graph the minimum degree δ(G) = 2. We show that in every minimally 1-tough graph δ(G) ≤ n 3 + 1. We also prove that every minimally 1-tough, claw-free graph is a cycle. On the other hand, we show that for every positive rational number t any graph can be embedded as an induced subgraph into a minimally t-tough graph.
doi:10.1016/j.disc.2017.08.033 fatcat:qjafkqrx35hbnn2sk5z7kpc7t4

Role of Endogenous Cannabinoids in Synaptic Signaling

TAMÁS F. FREUND, ISTVÁN KATONA, DANIELE PIOMELLI
2003 Physiological Reviews  
[Modified from Katona et al. (188) and Há jos et al. (138).]  ...  [Modified from Katona et al. (188) and Há jos et al. (138) .] grouped according to their levels of CB 1 mRNA (225, 231, 235) .  ... 
doi:10.1152/physrev.00004.2003 pmid:12843414 fatcat:rk65ipt3lzaypmmlpwndfh7n4a

Teachers' Point of View in Teaching Mathematical Problem-Solving

András Ambrus, Dániel Katona
2018 Magistra Iadertina  
There is still a deep gap between the theories of the didactics of mathematics and mathematics teaching practice worldwide. In our article, we analyse our trial to reach practicing mathematics teachers and summarize their opinion about some basic issues of teaching mathematics problem-solving from the point of view of cognitive load theory, what is a quite new topic in mathematics didactics society. We asked on the one hand, teachers from a small town in Hungary, and on the other hand, expert
more » ... achers and four young teachers from elite schools in the capital. The four young teachers have also started their PhD studies in mathematics education, besides school teaching. The opinions of the two groups of teachers reflect different attitudes towards teaching problem-solving, but in both cases relevant and important perspectives of the Hungarian school reality. The base of our study was a talk and an article of the first author, related to the role of human memory in learning and teaching mathematical problem-solving. We have been interested in how classroom teachers can take into consideration some results of the cognitive load theory, e.g. the split-attention effect and schema automation in their teaching practice, as well as in their attitudes to the use of worked examples and distributed practice. We analyse the results mostly from the perspective of desirable developments in in-service teacher training in Hungary.
doi:10.15291/magistra.1489 fatcat:mzqdkqfbgnahzaplk4rqedpupa

Incomparable Copies of a Poset in the Boolean Lattice

Gyula O. H. Katona, Dániel T. Nagy
2015 Order  
Katona and Tarján proved that a subset of B n containing none of the posets {V 2 , Λ 2 } has at most n−1 n− 1 2 elements, and this bound is sharp [10] .  ... 
doi:10.1007/s11083-014-9342-8 fatcat:7oiq2qiaw5dbxmt6ps5ceb6qfu

Categorising question question relationships in the Pósa method

Dániel Katona
2020 Teaching Mathematics and Computer Science  
For a sample of the Pósa WPT, see (Katona & Szűcs, 2017) .  ...  Model for analysing Q-Q relationships during task-design Basically the same problem is in(Katona & Szűcs, 2017, pp. 22-23)  ... 
doi:10.5485/tmcs.2020.0495 fatcat:37vogkabxvcodenaetd23go6uu

Adaptive Majority Problems for Restricted Query Graphs and for Weighted Sets [article]

Gábor Damásdi, Dániel Gerbner, Gyula O.H. Katona, Balázs Keszegh, Dániel Lenger, Abhishek Methuku, Dániel T. Nagy, Dömötör Pálvölgyi, Balázs Patkós, Máté Vizer, Gábor Wiener
2020 arXiv   pre-print
Suppose that the vertices of a graph G are colored with two colors in an unknown way. The color that occurs on more than half of the vertices is called the majority color (if it exists), and any vertex of this color is called a majority vertex. We study the problem of finding a majority vertex (or show that none exists) if we can query edges to learn whether their endpoints have the same or different colors. Denote the least number of queries needed in the worst case by m(G). It was shown by
more » ... s and Werman that m(K_n)=n-b(n), where b(n) is the number of 1's in the binary representation of n. In this paper, we initiate the study of the problem for general graphs. The obvious bounds for a connected graph G on n vertices are n-b(n)< m(G)< n-1. We show that for any tree T on an even number of vertices we have m(T)=n-1 and that for any tree T on an odd number of vertices, we have n-65< m(T)< n-2. Our proof uses results about the weighted version of the problem for K_n, which may be of independent interest. We also exhibit a sequence G_n of graphs with m(G_n)=n-b(n) such that G_n has O(nb(n)) edges and n vertices.
arXiv:1903.08383v2 fatcat:ejjtft2rk5gvjefgrufsobwhoe

Majority and plurality problems [chapter]

Dániel Gerbner, Gyula O. H. Katona, Dömötör Pålvölgyi, Balázs Patkós
2013 The Seventh European Conference on Combinatorics, Graph Theory and Applications  
Given a set of n balls each colored with a color, a ball is said to be majority, k-majority, plurality if its color class has size larger than half of the number of balls, has size at least k, has size larger than any other color class; respectively. We address the problem of finding the minimum number of queries (a comparison of a pair of balls if they have the same color or not) that is needed to decide whether a majority, k-majority or plurality ball exists and if so then show one such ball.
more » ... We consider both adaptive and non-adaptive strategies and in certain cases, we also address weighted versions of the problems.
doi:10.1007/978-88-7642-475-5_89 fatcat:izq7ycpoprblpbon2akhhh6c2y

COVID-19 disruptions to endoscopic surveillance in Lynch syndrome

Danielle B McKenna, Christina M Dudzik, Shria Kumar, Nadim Mahmud, Bryson W Katona
2021 Cancer Prevention Research  
Katona reports grants from NIH/NIDDK during the conduct of the study; other from Janssen and Exact Sciences outside the submitted work. No disclosures were reported by the other authors.  ... 
doi:10.1158/1940-6207.capr-20-0565 pmid:33627398 fatcat:wzq4kfrhynb63n2uqganrrjxhy
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