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 capacity by more precise head positioning. The maximizing capacity way
to choose statistical model (Maximal
Entropy Random Walk – Wikipedia,
2017 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,
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/cost as Huffman coding. Here is a list of implementations and compressors using ANS. For example Facebook
ZSTD (also used e.g. in
Linux kernel, ongoing MIME (email) standardization) and Apple LZFSE use Finite State Entropy implementation of tANS
variant, CRAM
3.0 DNA compressor of European Bioinformatics Institute and Google Draco and PIK 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.
Machine learning – searching for mathematically more sophisticated, but
still practical methods. For example molecular
shape descriptors (slides) for
virtual screening – parametrization of shape by fitting general bending of
molecule, then crosssection as evolving ellipse. More general rapid
parametric density estimation models density as just linear combination
of chosen functions, what allows for very inexpensive estimation, for example hierarchical
correlation reconstruction for multiple variables, decomposing into
correlations between subsets of coefficients, perfect for example for modelling
and imputation in missing data case (slides).
Maximal Entropy Random Walk (Wikipedia,
last
PhD, 2017 paper, 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:

Machine learning (e.g. molecular shape descriptors using
manifold learning, rapid parametric
density estimation/nonlinear
classification), P vs NP
problem (also for quantum
computing), Markov fields, DNA reconstruction.

Biology, e.g. evolutionism, neurobiology, biochemistry. For
example chiral life concept (Wikipedia) –
as a computer scientist, while starting studying genetics I thought about modifying
the rules how triples of nucleotides are translated into aminoacids, to get
immunity by incompatibility with our viruses. This approach has a lot of
issues, but later in 2007 it has lead me to the possibility of synthesizing
mirror version of standard cells (original forum post). It turns out that the race has recently started,
e.g. in 2016 reaching synthesis of mirror polymerase (enantiomer). While mirror
life carries enormous new possibilities including pathogenimmune humans, the
dangers of such synthetic life may include eradication of our life – mirror
photosynthesizing cyanobacteria could dominate our ecosystem. Hence, I believe
there is now required a wide discussion about the ongoing race to this
synthesis.

Others: dancing, climbing, 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,
IEEE Transactions on
Molecular, Biological, and MultiScale Communications (2016),
[27] J. Duda, Improving Pyramid Vector
Quantizer with power projection, arXiv:1705.05285 (2017),
[28] J. Duda, Fourdimensional
understanding of quantum mechanics and computation, arXiv:0910.2724v2
(2017),
[29] J. Duda, Polynomialbased rotation
invariant features, arXiv:1801.01058 (2018),
[30] J. Duda, Hierarchical correlation
reconstruction with missing data, for example for biologyinspired neuron, arXiv:1804.06218
(2018) (slides).
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