dr Jarosław Duda
Assistant professor at Institute of Computer Science, Jagiellonian University
2015- Jagiellonian University, Institute of Computer Science, assistant professor,
2013-2014 Purdue University, Center for Science of Information, Postdoctoral researcher,
2006-2012 Jagiellonian University, Cracow, PhD in Theoretical Physics (thesis)
2004-2010 Jagiellonian University, Cracow, PhD in Theoretical Computer Science (thesis)
2001-2006 Jagiellonian University, Cracow, MSc in Theoretical Physics (thesis)
2000-2005 Jagiellonian University, Cracow, MSc in Theoretical Mathematics (thesis)
1999-2004 Jagiellonian University, Cracow, MSc in Computer Science (thesis)
Main research areas:
Information theory/statistical physics - for my last MSc ( is its translation) I have worked on optimal encoding with constraints on a lattice (kind of generalization of Fibonacci coding), for example to improve storage media capacity by more precise head positioning. The maximizing capacity way to choose the stochastic matrix (Maximal Entropy Random Walk) was further developed for applications in physics as my second PhD. This thesis has also started ANS and lead to my work on a few new coding approaches (slides):
- Asymmetric Numeral Systems (ANS, slides, PCS article): new approach to entropy coding. Previously, Huffman coding allowed for fast but suboptimal compression, arithmetic coding for nearly optimal but slow. ANS offers nearly optimal compression ratio at even better speeds than Huffman coding. Here is a list of implementations and compressors switched to ANS. For example Apple LZFSE (= Lempel-Ziv + Finite State Entropy) compressor uses Finite State Entropy implementation of tANS variant, CRAM 3.0 genetic data compressor of European Bioinformatics Institute uses rANS variant. Additionally, chaotic behavior of tANS makes it also perfect for simultaneous encryption.
- Correction Trees philosophy as improvement of sequential decoding for convolutional codes: using larger state and bidirectional decoding, making it complementary alternative for state-of-art method (implementation). It also allows to handle synchronization errors like deletion channel
- Constrained Coding: generalization of the Kuznetsov-Tsybakov problem: allowing to encode a message under some constraints, which are known only to the sender. This generalization allows to use statistical constraints, for example enforcing resemblance to a picture (grayness of a pixel becomes probability of using 1 at this position). It can be used for various watermarking/steganography purposes, like to generate QR-like codes resembling given picture (implementation , ICIP article),
- Joint Reconstruction Codes (JRC, implementation): enhancement of the Fountain Codes concept, which allows to reconstruct a message from any large enough subset of packets. JRC additionally doesn’t need the sender to know the final damage levels of packets – this knowledge is required in standard approach to choose redundancy level, but is often inaccurate or unavailable in real-life scenarios. For example while writing a storage medium we usually don’t know how badly it will be damaged while reading. JRC allows the receivers to adapt to the actual noise levels, treated as independent trust level for each packet while their joint reconstruction/error correction. Continuous family of rates based on Renyi entropy allow to estimate statistical behavior of decoding (Pareto coefficient).
Maximal Entropy Random Walk (last PhD, here is preliminary version, here is presentation): standard stochastic models are based on philosophy that the object performs succeeding random decisions using probabilities assumed by us, while in thermodynamics this randomness only represents our lack of knowledge. Such models should be based on the maximal entropy principle, or equivalently: choosing e.g. canonical ensemble, getting recent Maximal Entropy Random Walk (MERW) and its expansions. Thanks of constructing models finally fulfilling these universal mathematical principles, in opposite to standard approach (which can be seen as approximation), we finally get agreement with thermodynamical expectations of quantum mechanics, like thermalization to the quantum mechanical ground state probability density and Born rule: ‘squares’ relating amplitudes and probabilities. My work on this subject has started with my physics MSc thesis ( is its translation), where the equations were found for information theory applications. The topic is continued in , ,  and . Here is conductance simulator to compare both philosophies.
soliton particle models (slides): Skyrme has made popular the search for alternative approach to particle models – starting not as usually with leading to many mathematical problems QFT perturbative approximation, but with trying to understand the configuration of fields building the particle (e.g. electromagnetic), which generally should maintain its structure (be a soliton), for example because of topological constraints for spin and charge. Standard skyrmion approach introduces separate fields to model single mesons or baryons – the perfect situation would be having just a single field, which soliton family corresponds to our whole particle menagerie and their dynamics with topological charges as quantum numbers. Working on MERW has lead me to simple model which surprisingly well fulfills these requirements – ellipsoid field (). Here is short essay about it and presentation.
Complex Base Numeral Systems (first two MSc-s) : probably complete family of positional numeral systems with complex base, which are ‘proper’ – representation function from digit sequences into a complex plane is surjective and injective everywhere but a zero measure set (it’s unavoidable, like 0.999(9)=1.000(0) ). Fractional part occurs to be simple Iterated Function System (fractal). I have also introduced practical methods for arithmetic in this representation, analytical tool to work with convex hull of such simple fractals, to get analytical formulas for Hausdorff dimension of boundary of such sets and briefly generalization into higher dimensions. It is described in  and , here is presentation about it.
Other interests and hobbies:
algorithm complexity – family of new simple invariants for graph isomorphism problem , approaches to P=NP problem (like translating into just continuous global optimization of low degree polynomial – forum post), to understand the strength of quantum computation (forum post), searching for new physical computation concepts (like continuous-time loop computers – forum post),
biology – evolutionism, neurobiology, biochemistry (e.g. chiral life concept – forum post),
Others: climbing, salsa, biking, fencing, photography
 J. Duda, Optimal encoding on discrete lattice with translational invariant constrains using statistical algorithms, arXiv:0710.3861 (2007),
 J. Duda, Analysis of the convex hull of the attractor of an IFS, arXiv:0710.3863 (2007),
 J. Duda, Complex base numeral systems, arXiv:0712.1309 (2007),
 J. Duda, Combinatorial invariants for graph isomorphism problem, arXiv:0804.3615 (2008),
 Z. Burda, J. Duda, J. M. Luck, B. Wacław, Localization of the Maximal Entropy Random Walk, Phys. Rev. Lett. 102, 160602 (2009),
 J. Duda, Asymmetric numeral systems, arXiv:0902.0271 (2009),
 J. Duda, Four-dimensional understanding of quantum mechanics, arXiv:0910.2724 (2009),
 Z. Burda, J. Duda, J. M. Luck, B. Wacław, The various facets of random walk entropy, Acta Phys. Polon. B. 41/5 (2010),
 J. Duda, P. Korus, Correction Trees as an Alternative to Turbo Codes and Low Density Parity Check Codes, arXiv: 1204.5317 (2012),
 Y. Baryshnikov, J. Duda, W. Szpankowski, Types of Markov Fields and Tilings, submitted to IEEE Transactions of Information Theory (PDF) (2014),
 J. Duda, Joint error correction enhancement of the Fountain Codes concept, arXiv:1505.07056 (2015),
 J. Duda, From Maximal Entropy Random Walk to quantum thermodynamics, J. Phys.: Conf. Ser. 361 012039 (2012),
 Y. Baryshnikov, J. Duda, W. Szpankowski, Markov Fields Types and Tilings, ISIT 2014 (2014),
 J. Duda, N. Gadgil, K. Tahboud, E. J. Delp, Generalizations of the Kuznetsov-Tsybakov problem for generating image-like 2D barcodes, ICIP 2014 (2014),
 J. Duda, W. Szpankowski, A. Grama, Fundamental Bounds and Approaches to Sequence Reconstruction from Nanopore Sequencers, submitted to ISMB 2015 (PDF) (2015).
Here are 6 simulators presenting subjects I worked on in intuitive, interactive way:
Some my implementations: https://github.com/JarekDuda