# Search Results

###### On scores in tournaments

References [1] P. Avery, Score sequences of oriented graphs, J. Graph Theory , 15, 3 (1991) 251–257. ⇒257 [2] R. A. Brualdi and J. Shen, Landau’s inequalities for tournament scores and a short proof of a Theorem on transitive sub-tournaments, J. Graph Theory , 38 (2001) 244–254. ⇒258 [3] R. A. Brualdi and J. Shen, Landau’s inequalities for tournament scores and a short proof of a Theorem on transitive sub-tournaments, J. Graph Theory , 38 (2001) 244–254. ⇒258 [4] J. R. Griggs and K. B. Reid, Landau’s theorem revisited

###### Reconstruction of score sets

References [1] G. Chartrand, L. Lesniak, J. Roberts, Degree sets for digraphs, Periodica Math. Hung., 7 (1976) 77-85. ⇒212 [2] T. H. Cormen, Ch. E. Leiserson, R. L. Rivest, C. Stein, Introduction to Algorithms (third edition), The MIT Press/McGraw Hill, Cambridge/New York, 2009. ⇒216 [3] J. L. Gross, J. Yellen, P. Zhang, Handbook of Graph Theory, CRC Press, Boca Raton, FL, 2013. ⇒210 [4] M. Hager. On score sets for tournaments, Discrete Math., 58 (1986) 25-34. ⇒ 210, 212 [5] A

###### On the scores and degrees in hypertournaments

[5] G. Gutin, A. Yeo, Hamiltonian paths and cycles in hypertournaments, J. Graph Theory 25 (1997), 277–286. ⇒201 [6] K. K. Kayibi, M. A. Khan, S. Pirzada, Uniform sampling of k -hypertournaments, Linear and Multilinear Algebra 61, 1 (2013), 123–138. ⇒201 [7] Y. Koh, S. Ree, On k -hypertournament matrices, Lin. Alg. Appl. 373 (2002) 183–195. ⇒202, 203 [8] M. A. Khan, S. Pirzada, K. K. Kayibii, Scores, Inequalities and regular hypertournaments, J. Math. Inequal. Appl. 15, 2 (2012) 343–351. ⇒203, 204 [9] H. G. Landau, On

###### On linear programming duality and Landau’s characterization of tournament

References [1] G. G. Alway, Matrices and sequences, Math. Gazette 46 (1962) 208-213. ⇒21 [2] C. M. Bang, H. Sharp, An elementary proof of Moon’s theorem on generalized tournaments, J. Comb. Theory, Ser. B 22, 3 (1977) 299-301. ⇒21 [3] C. M. Bang, H. Sharp, Score vectors of tournaments, J. Comb. Theory, Ser. B 26, 1, (1979) 81-84. ⇒31 [4] A. Brauer, I. C. Gentry, K. Shaw, A new proof of a theorem by H. G. Landau on tournament matrices, J. Comb. Theory 5, 3 (1968) 289-292. ⇒21 [5] R

###### Tripartite graphs with given degree set

. On score sets for tournaments, Discrete Math. , 58 (1986) 25–34. ⇒99, 100 [13] S. L. Hakimi, On the realizability of a set of integers as degrees of the vertices of a simple graph. J. SIAM Appl. Math. 10 (1962) 496–506. ⇒79 [14] S. L. Hakimi, On the degrees of the vertices of a graph, F. Franklin Institute, 279, (4) (1965) 290–308. ⇒ [15] F. Harary, On the notion of balance of a signed graph, Michigan Math. J. 2, 2 (1953), 143–146. ⇒78, 79 [16] F. Harary, The number of linear, directed, rooted and connected graphs, Trans

###### Automatic detection of hard and soft exudates from retinal fundus images

## Abstract

According to WHO estimates, 400 million people suffer from diabetes, and this number is likely to double by year 2030. Unfortunately, diabetes can have severe complications like glaucoma or retinopathy, which both can cause blindness. The main goal of our research is to provide an automated procedure that can detect retinopathy-related lesions of the retina from fundus images. This paper focuses on the segmentation of so-called white lesions of the retina that include hard and soft exudates. The established procedure consists of three main phases. The preprocessing step compensates the various luminosity patterns found in retinal images, using background and foreground pixel extraction and a data normalization operator similar to Z-transform. This is followed by a modified SLIC algorithm that provides homogeneous superpixels in the image. The final step is an ANN-based classification of pixels using fifteen features extracted from the neighborhood of the pixels taken from the equalized images and from the properties of the superpixel where the pixel belongs. The proposed methodology was tested using high-resolution fundus images originating from the IDRiD database. Pixelwise accuracy is characterized by a 54% Dice score in average, but the presence of exudates is detected with 94% precision.

###### Low and high grade glioma segmentation in multispectral brain MRI data

## Abstract

Several hundreds of thousand humans are diagnosed with brain cancer every year, and the majority dies within the next two years. The chances of survival could be easiest improved by early diagnosis. This is why there is a strong need for reliable algorithms that can detect the presence of gliomas in their early stage. While an automatic tumor detection algorithm can support a mass screening system, the precise segmentation of the tumor can assist medical staff at therapy planning and patient monitoring. This paper presents a random forest based procedure trained to segment gliomas in multispectral volumetric MRI records. Beside the four observed features, the proposed solution uses 100 further features extracted via morphological operations and Gabor wavelet filtering. A neighborhood-based post-processing was designed to regularize and improve the output of the classifier. The proposed algorithm was trained and tested separately with the 54 low-grade and 220 high-grade tumor volumes of the MICCAI BRATS 2016 training database. For both data sets, the achieved accuracy is characterized by an overall mean Dice score > 83%, sensitivity > 85%, and specificity > 98%. The proposed method is likely to detect all gliomas larger than 10 mL.

###### On partial sorting in restricted rounds

[36] A. Hollosi, M. Pahle, Tie Breaker, in Sensei's Library, Graz, 2013, http://senseis.xmp.net/?SwissPairing, Downloaded June 6, 2017. )21, 23 [37] A. Iványi, Reconstruction of complete interval tournaments, Acta Univ. Sapientiae, Inform., 1, 1 (2009) 71–88. )18 [38] A. Iványi, Reconstruction of complete interval tournaments II., Acta Univ. Sapientiae, Math., 2, 1 (2010) 47–71. )18 [39] A. Iványi, Directed graphs with prescribed score sequences, in: The 7th Hungarian-Japanese Symposium on Discrete Mathematics and

###### On vertex independence number of uniform hypergraphs

. In: Proc. Twenty-fourth Annual ACM Symp. Theory Comp. (STOC’92), ACM New York, NY, 1992, 339-350. ⇒138, 142 [108] L. Khachiyan, E. Boros, V. Gurvich, K. Elbassioni, Computing many maximal independent sets for hypergraphs in parallel, Parallel Process. Lett. 17, 2 (2007) 141-152. ⇒141 [109] I. Khan, Perfect matchings in 3-uniform hypergraphs with large vertex degree. SIAM J. Discrete Math. 27, 2 (2013) 1021-1039. ⇒141 [110] M. A. Khan, S. , K. K. Kayibi, Scores, inequalities and regular hypertournaments, Math. Inequal

###### Parallel enumeration of degree sequences of simple graphs II

. L. Erdős, L. A. Székely: Degree-based graph construction, J. Physics: Math. Theor. A 42 (2009), 392001, 10 pages. ⇒ [58] Z. Király, Recognizing graphic degree sequences and generating all realizations. Egres Technical Reports, TR-2011-11 April 23, 2012, 12 pages. ⇒246, 250 [59] D. J. Kleitman, D. Wang, Algorithms for constructing graphs and digraphs with given valences and factors, Discrete Math. 6 (1973) 79-88. ⇒250 [60] D. J. Kleitman, K. J. Winston, Forests and score vectors. Combinatorica 1 (1981) 49-51. ⇒250