doc. RNDr. Jan Vybíral, Ph.D.

e-mail:	zobrazit e-mail
telefon:	+420 778 546 165
místnost:	33c
www:	http://kmlinux.fjfi.cvut.cz/~vybirja2/

rozvrh
témata prací
publikace

Structured matrices in compressed sensing

školitel:	doc. RNDr. Jan Vybíral, Ph.D.
e-mail:	zobrazit e-mail
typ práce:	bakalářská práce, diplomová práce
zaměření:	MI_AMSM, MINF
klíčová slova:	Random matrices, compressed sensing, Johnson-Lindenstrauss Lemma
popis:	The student will review some basic properties of random matrices in the area of compressed sensing. Then (s)he will discuss the role of structured random matrices - the speed up of matrix-vector multiplication, the reduced amount of random bits needed, theoretical guarantees for their performance, real-life performance for some specific problems.
literatura:	H. Boche, R. Calderbank, and G. Kutyniok, A Survey of Compressed Sensing, First chapter in Compressed Sensing and its Applications, Birkhäuser, Springer, 2015 F. Krahmer and R. Ward, New and improved Johnson–Lindenstrauss embeddings via the restricted isometry property, SIAM Journal on Mathematical Analysis, 2011
poznámka:	The preferred language of the thesis is English.
naposledy změněno:	14.07.2022 09:20:08

Impact of delay on pattern formation and stability in the attraction-repulsion model

školitel:	Dr. Jan Haškovec, doc. Jan Vybíral
e-mail:	zobrazit e-mail
typ práce:	bakalářská práce
zaměření:	MI_MM, MI_AMSM, MINF, APIN
klíčová slova:	attraction-repulsion model, pattern formation, delay differential equations
přiložený soubor:	pdf
popis:	See the pdf file for description.
naposledy změněno:	05.10.2022 20:58:57

Bases of ReLU Neural Networks

školitel:	doc. RNDr. Jan Vybíral, Ph.D.
e-mail:	zobrazit e-mail
typ práce:	bakalářská práce, diplomová práce
zaměření:	MI_MM, MI_AMSM, MINF
klíčová slova:	ReLU, Neural Networks, Riesz Basis, Frame
popis:	The astonishing performance of neural networks in multivariate problems still lacks satisfactory mathematical explanation. In a recent work of I. Daubechies and her co-authors, they proposed a univariate system of piecewise linear functions, which resemble very much the trigonometric system and which form the so-called Riesz basis. Moreover, these functions are easily reproducible as ReLU Neural Networks. In a follow-up work of C. Schneider and J. Vybiral, this was generalized to the multivariate setting. The task of this work will be to investigate further potential improvements of the recent research, both on theoretical as well as practical side. This includes a) optimization of the Riesz constants of the system b) application of an orthonormalization procedure c) numerical implementation of the proposed NN-architecture and the study of its performance in approximation of multivariate functions.
literatura:	C. Schneider and J. Vybiral, Multivariate Riesz basis of ReLU neural networks, submitted I. Daubechies, R. DeVore, S. Foucart, B. Hanin, and G. Petrova, Nonlinear Approximation and (Deep) ReLU Networks, Constr. Appr. 55 (2022), 127–172 P. Beneventano, P. Cheridito, R. Graeber, A. Jentzen, and B. Kuckuck, Deep neural network approximation theory for high-dimensional functions, available at arXiv:2112.14523
naposledy změněno:	10.03.2023 14:14:49

Databáze V3S

Aplikace V3S eviduje výsledky vědy a výzkumu a další aktivity vědecko-výzkumných pracovníků ve vědecké komunitě. Aplikace V3S slouží k odesílání výsledků do RIV, exportům pro statistické analýzy i k interním hodnocením vědecko-výzkumné činnosti.

Seznam publikaci ve V3S

Články v časopisech

2017

A. Kolleck and J. Vybiral, Non-asymptotic Analysis of l_1-norm Support Vector Machines, IEEE Transactions on Information Theory (2017)
BiBTeX

@ARTICLE{kolleck2017n,
  title = {Non-asymptotic Analysis of l_1-norm Support Vector Machines},
  author = {A. Kolleck and J. Vybiral},
  journal = {IEEE Transactions on Information Theory},
  publisher = {IEEE},
  year = {2017}
}

T. Conrad, M. Genzel, N. Cvetkovic, N. Wulkow, A. Leichtle, J. Vybiral, G. Kutyniok, and Ch. Sch\"utte, Sparse Proteomics Analysis-a compressed sensing-based approach for feature selection and classification of high-dimensional proteomics mass spectrometry data, BMC bioinformatics 18 (2017) , 160
BiBTeX

@ARTICLE{conrad2017sp,
  title = {Sparse Proteomics Analysis--a compressed sensing-based approach for feature selection and classification of high-dimensional proteomics mass spectrometry data},
  author = {T. Conrad, M. Genzel, N. Cvetkovic, N. Wulkow, A. Leichtle, J. Vybiral, G. Kutyniok, and Ch. Sch{\"u}tte},
  journal = {BMC bioinformatics},
  publisher = {BioMed Central},
  year = {2017},
  volume = {18},
  number = {1},
  pages = {160}
}

A. Hinrichs, J. Prochno, and J. Vybiral, Entropy numbers of embeddings of Schatten classes, Journal of Functional Analysis 273 (2017) , 3241-3261
BiBTeX

@ARTICLE{hinrichs2017,
  title = {Entropy numbers of embeddings of Schatten classes},
  author = {A. Hinrichs, J. Prochno, and J. Vybiral},
  journal = {Journal of Functional Analysis},
  publisher = {Elsevier},
  year = {2017},
  volume = {273},
  number = {10},
  pages = {3241--3261}
}

L.M. Ghiringhelli, J. Vybiral, E. Ahmetcik, R. Ouyang, S.V. Levchenko, C. Draxl, and M. Scheffler, Learning physical descriptors for materials science by compressed sensing, New Journal of Physics 19 (2017) , 023017
BiBTeX

@ARTICLE{ghiringhelli,
  title = {Learning physical descriptors for materials science by compressed sensing},
  author = {L.M. Ghiringhelli, J. Vybiral, E. Ahmetcik, R. Ouyang, S.V. Levchenko, C. Draxl, and M. Scheffler},
  journal = {New Journal of Physics},
  publisher = {IOP Publishing},
  year = {2017},
  volume = {19},
  number = {2},
  pages = {023017}
}

H. Kempka and J. Vybíral, Volumes of unit balls of mixed sequence spaces, Mathematische Nachrichten 290 (2017) , 1317-1327
BiBTeX

@ARTICLE{kempka2017vo,
  title = {Volumes of unit balls of mixed sequence spaces},
  author = {H. Kempka and J. Vyb{\'\i}ral},
  journal = {Mathematische Nachrichten},
  publisher = {Wiley Online Library},
  year = {2017},
  volume = {290},
  number = {8-9},
  pages = {1317--1327}
}

za obsah této stránky zodpovídá: Radek Fučík | naposledy změněno: 7.8.2011