doc. RNDr. Jan Vybíral, Ph.D.

e-mail:	show e-mail
telephone:	+420 778 546 165
room:	33c
www:	http://kmlinux.fjfi.cvut.cz/~vybirja2/

timetable
topics
publications

Structured matrices in compressed sensing

advisor:	doc. RNDr. Jan Vybíral, Ph.D.
e-mail:	show e-mail
type:	bachelor thesis, master thesis
branch of study:	MI_AMSM, MINF
key words:	Random matrices, compressed sensing, Johnson-Lindenstrauss Lemma
description:	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.
references:	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
note:	The preferred language of the thesis is English.
last update:	14.07.2022 09:20:08

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

advisor:	Dr. Jan Haškovec, doc. Jan Vybíral
e-mail:	show e-mail
type:	bachelor thesis
branch of study:	MI_MM, MI_AMSM, MINF, APIN
key words:	attraction-repulsion model, pattern formation, delay differential equations
attached file:	pdf
description:	See the pdf file for description.
last update:	05.10.2022 20:58:57

Bases of ReLU Neural Networks

advisor:	doc. RNDr. Jan Vybíral, Ph.D.
e-mail:	show e-mail
type:	bachelor thesis, master thesis
branch of study:	MI_MM, MI_AMSM, MINF
key words:	ReLU, Neural Networks, Riesz Basis, Frame
description:	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.
references:	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
last update:	10.03.2023 14:14:49

V3S Database

The application records results of science and research, and other academic activities. The V3S application serves as a tool for submitting data to the RIV database, exporting data for statistic analyses, and internal evaluation of research.

List of publications in V3S

Articles

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}
}

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