Dr Jarosław
Duda (Jarek Duda)
Assistant professor at Institute of
Computer Science (adiunkt),
Jagiellonian University
email:
jaroslaw.duda[at]uj.edu.pl
Short CV:
2015 Jagiellonian
University, Institute of Computer Science, assistant professor,
20132014 Purdue
University, NSF Center for Science of Information, Postdoctoral researcher (webpage),
20062012 Jagiellonian
University, Cracow, PhD in Theoretical Physics (thesis)
20042010 Jagiellonian
University, Cracow, PhD in Theoretical Computer Science (thesis)
20012006 Jagiellonian
University, Cracow, MSc in Theoretical Physics (thesis)
20002005 Jagiellonian
University, Cracow, MSc in Theoretical Mathematics (thesis)
19992004 Jagiellonian
University, Cracow, MSc in Computer Science (thesis)
Main research areas:
Information theory/statistical physics  for my last MSc ([1] is its
translation) I have worked on optimal encoding with constraints on a lattice
(multidimensional 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 – Wikipedia
article) was further developed for applications in physics as my second
PhD. This 2006 MSc thesis has also started ANS coding and has lead me to a few new coding approaches (slides):

Asymmetric Numeral Systems (ANS,
Wikipedia
article, slides, PCS article) family of entropy
coders (heart of data compressors). Previously, a compromise was required:
Huffman coding allowed for fast but suboptimal compression, arithmetic coding
for nearly optimal but slow (costly). ANS offers compression ratio as
arithmetic coding, at similar speed as Huffman coding. Here is a list of implementations and compressors switched to
ANS. For example Facebook
ZSTD and Apple LZFSE use Finite State Entropy implementation of tANS
variant, CRAM
3.0 genetic data compressor of European Bioinformatics Institute and experimental
branch of Google VP10 video codec use rANS
variant. Additionally, chaotic behavior of tANS
makes it also perfect for simultaneous
encryption,

Constrained Coding: generalization of the KuznetsovTsybakov 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 with a
given picture (grayness of a pixel becomes probability of using 1 in its
position). Natural applications are various watermarking/steganography purposes, for example to generate QRlike codes resembling a chosen image
(implementation , ICIP paper, IEEE
Forensics & Security paper),

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 individual damage levels of packets – this knowledge is required
in standard approach to choose redundancy levels, but is often inaccurate or
unavailable in reallife 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
levels for each packet while their joint reconstruction/error correction.
Introduced continuous family of rates based on Renyi
entropy allow to estimate statistical behavior of decoding (Pareto
coefficient),

Correction trees philosophy as improvement of sequential decoding for
convolutional codes: using larger state and bidirectional decoding, making it
complementary alternative for stateofart method (implementation). It also allows to handle synchronization errors
like deletion channel.
Maximal Entropy Random Walk (Wikipedia,
last
PhD, arXiv version, slides):
standard stochastic models are based on philosophy that the object performs
successive random decisions using probabilities chosen arbitrarily by us. In
contrast, in statistical physics this randomness only represents our lack of
knowledge. Such models should be based on the maximal entropy principle (Jaynes), or equivalently: choosing e.g.
canonical ensemble, getting recent Maximal Entropy Random Walk (MERW) and its
extensions. Thanks of constructing models finally fulfilling this fundamental
mathematical requirement, in contrast 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 ([1] is its translation), where the equations were found for
information theory applications. The topic is continued in [5], [7], [8] and
[9]. 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 ([7]). Here is short
essay about it
and presentation.
Complex Base Numeral Systems (first two MScs, slides) :
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 [2] and [3], here is presentation about it.
Other interests and hobbies:
algorithm complexity – family of new
simple invariants for graph isomorphism problem [4], 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 continuoustime loop computers – forum post),
biology – evolutionism, neurobiology,
biochemistry (e.g. chiral life concept
– forum post),
Others: climbing, salsa, biking, fencing,
photography
Articles:
[1] J. Duda, Optimal
encoding on discrete lattice with translational invariant constrains using
statistical algorithms, arXiv:0710.3861
(2007),
[2] J. Duda,
Analysis of the convex hull of the attractor of an IFS, arXiv:0710.3863 (2007),
[3] J. Duda,
Complex base numeral systems, arXiv:0712.1309
(2007),
[4] J. Duda,
Combinatorial invariants for graph isomorphism problem, arXiv:0804.3615 (2008),
[5] Z. Burda, J.
Duda, J. M. Luck, B. Wacław,
Localization of the Maximal Entropy Random Walk, Phys. Rev. Lett.
102, 160602 (2009),
[6] J. Duda,
Asymmetric numeral systems, arXiv:0902.0271
(2009),
[7] J. Duda,
Fourdimensional understanding of quantum mechanics, arXiv:0910.2724 (2009),
[8] Z. Burda, J.
Duda, J. M. Luck, B. Wacław,
The various facets of random walk entropy, Acta Phys. Polon.
B. 41/5 (2010),
[9] J. Duda,
From Maximal Entropy Random Walk to quantum thermodynamics, arXiv:1111.2253
(2011) (slides),
[10] J. Duda, P.
Korus, Correction Trees as an Alternative to Turbo Codes and Low Density Parity
Check Codes, arXiv: 1204.5317 (2012),
[11] J. Duda,
Optimal compression of hashorigin prefix trees, arXiv:1206.4555 (2012) (slides),
[12] J. Duda,
Embedding grayscale halftone pictures in QR Codes using Correction Trees, arXiv:1211.1572
(2012) (slides),
[13] J. Duda,
Asymmetric numeral systems: entropy coding combining speed of Huffman coding
with compression rate of arithmetic coding, arXiv:1311.2540 (2013) (slides),
[14] J. Duda,
Joint error correction enhancement of the Fountain Codes concept, arXiv:1505.07056 (2015),
[15] J. Duda,
Normalized rotation shape descriptors and lossy compression of molecular shape, arXiv:1505:09211
(2015) (slides),
[16] J. Duda, G.
Korcyl, Designing dedicated data compression for
physics experiments within FPGA already used for data acquisition, arXiv:1511.00856
(2015),
[17] J. Duda, P.
Korus, N. J. Gadgil, K. Tahboub,
E. J. Delp, ImageLike 2D Barcodes Using
Generalizations Of The KuznetsovTsybakov Problem, IEEE
Transactions on Information Forensics & Security volume 11, issue 4
(2016),
[18] J. Duda, W. Szpankowski, A. Grama, Fundamental Bounds and Approaches to Sequence
Reconstruction from Nanopore Sequencers, arXiv:1601.02420 (2016),
[19] J. Duda,
DistortionResistant Hashing for rapid
search of similar DNA subsequence, arXiv:1602.05889 (2016),
[20] Y. Baryshnikov, J. Duda, W. Szpankowski,
Types of Markov Fields and Tilings, IEEE
Transactions of Information Theory volume 62, issue 8 (PDF) (2016),
[21] J. Duda,
Nonuniform
probability modulation for reducing energy consumption of remote sensors, arXiv:1608.04271
(2016),
[22] J. Duda,
Practical estimation of rotation distance
and induced partial order for binary trees, arXiv:1610.06023 (2016),
[23] A. Magner,
J. Duda, W. Szpankowski, A.
Grama, Fundamental Bounds for Sequence
Reconstruction from Nanopore Sequencers, accepted for Shannon Centennial
Special Issue of IEEE Transactions on Molecular, Biological, and MultiScale
Communications (PDF)
(2016),
[27] J. Duda,
Improving Pyrami Vector Quantizer with power
projection, https://arxiv.org/abs/1705.05285
(2017).
Conference papers:
[1] J. Duda,
From Maximal Entropy Random Walk to quantum thermodynamics, J. Phys.: Conf. Ser. 361 012039 (2012),
[2] Y. Baryshnikov, J. Duda,
W. Szpankowski, Markov Fields Types and Tilings, ISIT
2014 (2014),
[3] J. Duda, N. Gadgil, K. Tahboud, E. J. Delp, Generalizations of the KuznetsovTsybakov
problem for generating imagelike 2D barcodes, ICIP
2014 (2014),
[4] J. Duda, N. Gadgil, K. Tahboud, E. J. Delp, The use of Asymmetric Numeral Systems as an accurate
replacement for Huffman coding, PCS 2015, (PDF),
Here are 10 simulators presenting subjects
I worked on in intuitive, interactive way:
http://demonstrations.wolfram.com/author.html?author=Jarek+Duda
Some my implementations: https://github.com/JarekDuda