dr Jarosław
Duda
Assistant
professor at Institute of Computer Science, Jagiellonian
University
email: jaroslaw.duda[at]uj.edu.pl
Short CV:
2015 Jagiellonian
University, Institute of Computer Science, assistant professor,
20132014 Purdue University, Center for Science of
Information, Postdoctoral researcher,
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 (kind of a 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) family of entropy coders. Previously a compromised was required: Huffman
coding allowed for fast but suboptimal compression, arithmetic coding for
nearly optimal but slow (costly). ANS offers nearly optimal compression ratio
at similar speed as Huffman coding. Here is a list of implementations and
compressors switched to ANS. For example Apple LZFSE (= LempelZiv + Finite
State Entropy), which is
the default compressor since iOS9 and OS X 10.11, uses 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.

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.

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 also use statistical constraints, for example enforcing resemblance
to a given picture (grayness of a pixel becomes probability of using 1 at this
position). It can be used for various watermarking/steganography purposes, for
example to generate QRlike codes resembling a given picture (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 level, 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 level 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).
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 (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 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 ([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) : 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) (presentation),
[13] J. Duda, Asymmetric numeral systems: entropy coding combining
speed of Huffman coding with compression rate of arithmetic coding, arXiv:1311.2540 (2013) (presentation),
[14] J. Duda,
Joint error correction enhancement of the Fountain Codes concept, arXiv:1505.07056
(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),
[20] Y. Baryshnikov, J. Duda, W. Szpankowski, Types of Markov Fields and Tilings, IEEE
Transactions of Information Theory volume 62, issue 8 (PDF)
(2016).
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 6
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