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,

2013-2014 Purdue University, Center for Science of
Information, Postdoctoral researcher (webpage),

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 ([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 compromise was required: Huffman
coding allowed for fast but suboptimal compression, arithmetic coding for
nearly optimal but slow (costly). ANS offers compression ratios 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 (= Lempel-Ziv +
Finite State Entropy) 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 **Kuznetsov-Tsybakov**** 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). A natural application are various **watermarking/steganography **purposes, for example to generate **QR-like 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 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. 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 state-of-art
method (implementation). It also allows to handle
synchronization errors like **deletion channel**.

**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
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 [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 continuous-time 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, Four-dimensional 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 hash-origin 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**, **Image-Like 2D Barcodes Using Generalizations Of** **The Kuznetsov-Tsybakov 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),

[21] J. Duda, Nonuniform
probability modulation for reducing energy consumption of remote sensors, *arXiv:1608.04271*
(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 Kuznetsov-Tsybakov problem for
generating image-like 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 7
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