TY - JOUR AU - Buczolich, Zoltán AU - Hanson, Bruce AU - Maga, Balázs AU - Vértesy, Gáspár TI - Strong one-sided density without uniform density JF - PERIODICA MATHEMATICA HUNGARICA J2 - PERIOD MATH HUNG VL - 86 PY - 2023 SP - 13 EP - 23 PG - 11 SN - 0031-5303 DO - 10.1007/s10998-022-00455-9 UR - https://m2.mtmt.hu/api/publication/32750764 ID - 32750764 N1 - Department of Analysis, ELTE Eötvös Loránd University, Pázmány Péter Sétány 1/c, Budapest, 1117, Hungary Department of Mathematics, Statistics and Computer Science, St. Olaf College, Northfield, MN 55057, United States Alfréd Rényi Institute of Mathematics, Reáltanoda utca 13-15, Budapest, 1053, Hungary Export Date: 8 September 2022 Correspondence Address: Buczolich, Z.; Department of Analysis, Pázmány Péter Sétány 1/c, Hungary; email: zoltan.buczolich@ttk.elte.hu LA - English DB - MTMT ER - TY - JOUR AU - Buczolich, Zoltán AU - Maga, Balázs AU - Vértesy, Gáspár TI - Generic Hölder level sets and fractal conductivity JF - CHAOS SOLITONS & FRACTALS J2 - CHAOS SOLITON FRACT VL - 164 PY - 2022 SN - 0960-0779 DO - 10.1016/j.chaos.2022.112696 UR - https://m2.mtmt.hu/api/publication/33124160 ID - 33124160 N1 - Department of Analysis, ELTE Eötvös Loránd, University, Pázmány Péter Sétány 1/c, Budapest, 1117, Hungary Alfréd Rényi Institute of Mathematics, Reáltanoda street 13-15, Budapest, 1053, Hungary Export Date: 4 October 2022 CODEN: CSFOE Correspondence Address: Buczolich, Z.; Department of Analysis, Pázmány Péter Sétány 1/c, Hungary; email: zoltan.buczolich@ttk.elte.hu LA - English DB - MTMT ER - TY - CONF AU - Maga, Balázs TI - Valós analízisbeli problémák T2 - Intézményi ÚNKP Konferencia 2022 PB - Eötvös Loránd Tudományegyetem (ELTE) C1 - Budapest PY - 2022 SP - 165 UR - https://m2.mtmt.hu/api/publication/33099660 ID - 33099660 LA - Hungarian DB - MTMT ER - TY - JOUR AU - Buczolich, Zoltán AU - Maga, Balázs AU - Vértesy, Gáspár TI - Generic Hölder level sets on fractals JF - JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS J2 - J MATH ANAL APPL VL - 516 PY - 2022 IS - 2 SN - 0022-247X DO - 10.1016/j.jmaa.2022.126543 UR - https://m2.mtmt.hu/api/publication/33072066 ID - 33072066 AB - Hausdorff dimensions of level sets of generic continuous functions defined on fractals were considered in two papers by R. Balka, Z. Buczolich and M. Elekes. In those papers the topological Hausdorff dimension of fractals was defined. In this paper we start to study level sets of generic 1-Hölder-α functions defined on fractals. This is related to some sort of “thickness”, “conductivity” properties of fractals. The main concept of our paper is D⁎(α,F) which is the essential supremum of the Hausdorff dimensions of the level sets of a generic 1-Hölder-α function defined on the fractal F. We prove some basic properties of D⁎(α,F), we calculate its value for an example of a “thick fractal sponge”, we show that for connected self similar sets D⁎(α,F) it equals the Hausdorff dimension of almost every level in the range of a generic 1-Hölder-α function. © 2022 The Author(s) LA - English DB - MTMT ER - TY - JOUR AU - Maga, Balázs AU - Maga, Péter TI - Generic power series on subsets of the unit disk JF - CZECHOSLOVAK MATHEMATICAL JOURNAL J2 - CZECH MATH J VL - 72 PY - 2022 IS - 3 SP - 637 EP - 652 PG - 16 SN - 0011-4642 DO - 10.21136/CMJ.2022.0021-21 UR - https://m2.mtmt.hu/api/publication/32704811 ID - 32704811 LA - English DB - MTMT ER - TY - CHAP AU - Gellert, Karolyi AU - Melinda, Kiss AU - Adrián, Csiszárik AU - Ákos, Matszangosz AU - Maga, Balázs AU - Dániel, Varga ED - Csuhaj-Varjú, Erzsébet ED - Sziklai, Péter TI - Global Sinkhorn Autoencoder - Optimal transport on the latent representation of the full dataset T2 - Conference on Developments in Computer Science PB - Eötvös Loránd University, Faculty of Informatics CY - Budapest SN - 9789634893882 PY - 2021 SP - 199 EP - 202 PG - 4 UR - https://m2.mtmt.hu/api/publication/32627793 ID - 32627793 LA - English DB - MTMT ER - TY - JOUR AU - Buczolich, Zoltán AU - Hanson, Bruce AU - Maga, Balázs AU - Vértesy, Gáspár TI - Big and little Lipschitz one sets JF - EUROPEAN JOURNAL OF MATHEMATICS J2 - EUR J MATH VL - 7 PY - 2021 IS - 2 SP - 464 EP - 488 PG - 25 SN - 2199-675X DO - 10.1007/s40879-021-00458-9 UR - https://m2.mtmt.hu/api/publication/31981091 ID - 31981091 N1 - Department of Analysis, ELTE Eötvös Loránd, University, Pázmány Péter Sétány 1/c, Budapest, 1117, Hungary Department of Mathematics, Statistics and Computer Science, St. Olaf College, Northfield, MN 55057, United States Cited By :1 Export Date: 8 September 2022 Correspondence Address: Buczolich, Z.; Department of Analysis, Pázmány Péter Sétány 1/c, Hungary; email: zoltan.buczolich@ttk.elte.hu LA - English DB - MTMT ER - TY - CONF AU - Gaál, G. AU - Maga, Balázs AU - Lukács, András ED - Hayes, J. ED - Gurrin, C. ED - Pini, A. ED - Keane, M. TI - Attention U-net based adversarial architectures for chest X-ray lung segmentation T2 - 2020 Workshop on Applied Deep Generative Networks, ADGN 2020 VL - 2692 PB - CEUR Workshop Proceedings T3 - CEUR Workshop Proceedings, ISSN 1613-0073 ; 2692. PY - 2020 UR - https://m2.mtmt.hu/api/publication/31849361 ID - 31849361 N1 - Conference code: 163425 Export Date: 5 February 2021 Scopus:hiba:85096649584 2022-10-12 11:40 típus nem egyezik AB - X-ray is by far the most common among medical imaging modalities, being faster, more accessible, and more cost-effective compared to other radiographic methods. Chest X-ray (CXR) is the most commonly requested test due to its contribution to the early detection of lung cancer. The most important biomarker in detecting cancer of the lung are nodules, and in finding those, lung segmentation of chest X-rays is essential. Another goal is interpretability, helping radiologists integrate computer-aided detection methods into their diagnostic pipeline, greatly reducing their workload. For this reason, a robust algorithm to perform this otherwise arduous segmentation task is much desired in the field of medical imaging. In this work, we present a novel deep learning approach that uses state-of-the-art fully convolutional neural networks in conjunction with an adversarial critic model. Our network generalized well to CXR images of unseen datasets with different patient profiles, achieving a final DSC of 97.5% on the JSRT CXR dataset. Copyright © 2020 for this paper by its authors. Use permitted under Creative Commons License Attribution 4.0 International (CC BY 4.0) LA - English DB - MTMT ER - TY - JOUR AU - Buczolich, Zoltán AU - Maga, Balázs AU - Moore, Ryo TI - Generic Birkhoff spectra JF - DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS SERIES A J2 - DISCRETE CONT DYN S VL - 40 PY - 2020 IS - 12 SP - 6649 EP - 6679 PG - 31 SN - 1078-0947 DO - 10.3934/dcds.2020131 UR - https://m2.mtmt.hu/api/publication/31596965 ID - 31596965 N1 - Funding Agency and Grant Number: CONICYT PIA ACT [172001] Funding text: This project was initiated in October 2018, during the first author's visit to Facultad de Matematicas at Pontificia Universidad Catolica de Chile, which was partially supported by CONICYT PIA ACT 172001. The first author would like to thank the hospitality of PUC. Department of Analysis, ELTE Eötvös Loránd University, Pázmány Péter Sétány 1/c, Budapest, 1117, Hungary Facultad de Matemáticas, Pontificia Universidad Católica de Chile, Avda. Vicuña Mackenna, Santiago, 4860, Chile Export Date: 5 February 2021 Correspondence Address: Buczolich, Z.; Department of Analysis, Pázmány Péter Sétány 1/c, Hungary; email: buczo@caesar.elte.hu Funding details: 3170279 Funding details: 124749 Funding details: Nemzeti Kutatási Fejlesztési és Innovációs Hivatal, NKFIH, 124003 Funding details: Comisión Nacional de Investigación Científica y Tecnológica, CONICYT, PIA ACT 172001 Funding text 1: 2020 Mathematics Subject Classification. Primary: 37A30; Secondary: 28A80, 37B10, 37C45. Key words and phrases. Birkhoff spectrum, multifractal analysis, Hausdorff dimension, generic/typical continuous functions, symbolic dynamics. ZB was supported by the Hungarian National Research, Development and Innovation Office– NKFIH, Grant 124003. BM was supported by the ÚNKP-18-2 New National Excellence of the Hungarian Ministry of Human Capacities, and by the Hungarian National Research, Development and Innovation Office–NKFIH, Grant 124749. RM was partially supported by CONICYT-FONDECYT Postdoctorado 3170279. ∗ Corresponding author. Funding text 2: author’s visit to Facultad de Matemáticas at Pontificia Universidad Católica de Chile, which was partially supported by CONICYT PIA ACT 172001. The first author would like to thank the hospitality of PUC. The second author is thankful to MátéFellner for the valuable discussion. AB - Suppose that Omega = {0, 1}(N) and sigma is the one-sided shift. The Birkhoff spectrum S-f(alpha) = dim(H) {omega is an element of Omega : lim(N ->infinity) 1/N Sigma(N)(n=1) f(sigma(n)omega) = alpha} where dim H is the Hausdorff dimension. It is well-known that the support of S-f(alpha) is a bounded and closed interval L-f = [alpha(f,min)* ,alpha(f,max)*]and S-f(alpha) on L-f is concave and upper semicontinuous. We are interested in possible shapes/properties of the spectrum, especially for generic/typical f is an element of C(Omega) in the sense of Baire category. For a dense set in C(Omega) the spectrum is not continuous on R, though for the generic f is an element of C(Omega) the spectrum is continuous on R, but has infinite one-sided derivatives at the endpoints of L-f. We give an example of a function which has continuous S-f on R, but with finite one-sided derivatives at the endpoints of L-f. The spectrum of this function can be as close as possible to a "minimal spectrum". We use that if two functions f and g are close in C(Omega) then S-f and S-g are close on L-f apart from neighborhoods of the endpoints. LA - English DB - MTMT ER - TY - JOUR AU - Buczolich, Zoltán AU - Hanson, Bruce AU - Maga, Balázs AU - Vértesy, Gáspár TI - LIPSCHITZ ONE SETS MODULO SETS OF MEASURE ZERO JF - MATHEMATICA SLOVACA J2 - MATH SLOVACA VL - 70 PY - 2020 IS - 3 SP - 567 EP - 584 PG - 18 SN - 0139-9918 DO - 10.1515/ms-2017-0372 UR - https://m2.mtmt.hu/api/publication/31350038 ID - 31350038 N1 - Funding Agency and Grant Number: Hungarian National Research, Development and Innovation Office-NKFIH [124003, 124749]; New National Excellence of the Hungarian Ministry of Human Capacities [UNKP-18-2, UNKP-18-3]; New National Excellence Program of the Ministry for Innovation and Technology [UNKP-19-3] Funding text: Zoltan Buczolich was supported by the Hungarian National Research, Development and Innovation Office-NKFIH, Grant 124003.; Balazs Maga was initially supported by the UNKP-18-2 New National Excellence of the Hungarian Ministry of Human Capacities, later on by the UNKP-19-3 New National Excellence Program of the Ministry for Innovation and Technology, and during the entire period by the Hungarian National Research, Development and Innovation Office-NKFIH, Grant 124749.; Gaspar Vertesy was supported by the UNKP-18-3 New National Excellence Program of the Ministry of Human Capacities, and by the Hungarian National Research, Development and Innovation Office-NKFIH, Grant 124749. Department of Analysis, ELTE Eötvös Loránd University, Pazmany Péter Sétány 1/c, Budapest, 1117, Hungary Department of Mathematics, Statistics and Computer Science, St. Olaf College, Northfield, MN 55057, United States Cited By :1 Export Date: 5 February 2021 Funding details: Emberi Eroforrások Minisztériuma, EMMI Funding details: 124003 Funding details: Ministry for Innovation and Technology, 124749 Funding text 1: Zoltan Buczolich was supported by the Hungarian National Research, Development and Innovation Office-NKFIH, Grant 124003. Balazs Maga was initially supported by the UNKP-18-2 New National Excellence of the Hungarian Ministry of Human Capacities, later on by the UNKP-19-3 New National Excellence Program of the Ministry for Innovation and Technology, and during the entire period by the Hungarian National Research, Development and Innovation Office-NKFIH, Grant 124749. Gaspar Vertesy was supported by the UNKP-18-3 New National Excellence Program of the Ministry of Human Capacities, and by the Hungarian National Research, Development and Innovation Office-NKFIH, Grant 124749. AB - We denote the local "little" and "big" Lipschitz functions of a function f : R -> R by lip f and Lip f. In this paper we continue our research concerning the following question. Given a set E subset of R is it possible to find a continuous function f such that lip f = 1(E) or Lip f = 1(E)? In giving some partial answers to this question uniform density type (UDT) and strong uniform density type (SUDT) sets play an important role. In this paper we show that modulo sets of zero Lebesgue measure any measurable set coincides with a Lip1 set. On the other hand, we prove that there exists a measurable SUDT set E such that for any G(delta) set (E) over tilde satisfying vertical bar E Delta(E) over tilde vertical bar = 0 the set (E) over tilde does not have UDT. Combining these two results we obtain that there exist Lip1 sets not having UDT, that is, the converse of one of our earlier results does not hold. (C) 2020 Mathematical Institute Slovak Academy of Sciences LA - English DB - MTMT ER -