# CSoI-UJ 2023 Seminar Series: Dynamic Networks, Machine Learning, AI for Classical and Quantum Data

**When**: November 6 till November 24 every day at 17:00 EU time and 11am EST USA time.

All lectures are recoreder and can be viewed on CSoI YouTube playlist containing all videos of this seminar series.

For personal discussion at the beginning and the end of the seminar, we shall use the following zoom: https://purdue-edu.zoom.us/j/548154976

A three week seminar series by CSoI together with faculty and students at Jagiellonian University, Poland .

The following unpublished yet book will be used and students are encouraged to brose through it:

"*Analytic Information Theory: From Compression to Learning*" by M. Drmota and W. Szpankowski

(see https://www.cs.purdue.edu/homes/spa/temp/ait22.pdf )

The following two books will be useful:

1 "*Analysis of Algorithms on Sequence*s" by W. Szpankowski, Willey 2001

(see https://www.cs.purdue.edu/homes/spa/mybook.pdf).

2 "*Analytic Pattern Matching: From DNA to Twitter*", by P. Jacquet and W. Szpankowski

(see https://www.cs.purdue.edu/homes/spa/temp/words15.pdf)

Nov 6 , at 11:00/17:00

W. Szpankowski (Purdue) and K. Turowski (UJ)

Organizational Meeting, pls use this zoom: : https://purdue-edu.zoom.us/j/548154976

Nov 7 at 11:00/17:00

W. Szpankowski (Purdue)

"Structural and Temporal Information"

View Video of the Seminar

Nov 8, at 11:00/17:00

A. Magner (U. Albany, NY)

"Fundamental Limits of Deep Graph Convolutional Networks for Graph

Classification"

View Video of the Seminar

Nov 9 at 11:00/17:00. At 11am please use zoom : https://purdue-edu.zoom.us/j/548154976

W. Szpankowski (Purdue)

Online & Supervised Learning: Analysis and Algorithms

View Video of the Seminar

Nov 10 at 11:00/17:00

K. Turowski (UJ)

Dynamic Networks: Duplication Divergence Model - Part I

View Video of this seminar

Nov 13 , at 11:00/17:00

K. Turowski (UJ)

Dynamic Networks: Duplication Divergence Model - Part II

View Video of this seminar

Nov 14 at 11:00/17:00

A. Padakandla (U. Tennessee, Knoxville)

Introduction to Quantum Information and Computation

View Video of this seminar

**View also the Quantum Computing Workshop**

Nov 15 at 11:00/17:00

A. Padakandla (U. Tennessee, Knoxville)

Learning of Quantum Measurement Classes

View Video of this seminar

Nov 16 at 11:00/17:00

M. Heidari (Purdue)

Feature Selection With Discrete Fourier Expansion

View Video of this Seminar

Nov 17 at 11:00/17:00. At 11am pls use zoom: : https://purdue-edu.zoom.us/j/548154976

M. Heidari (Purdue)

Physically Realizable Quantum Algorithms

View Video of this Seminar

Nov 17 at 11:00/17:00

M. Heidari (Purdue)

“Toward Physically Realizable Quantum Algorithms”

View Video of this Seminar

Nov 20-23 at 11:00/17:00**Students' zoom seminar**, use https://purdue-edu.zoom.us/j/548154976

Potential topics are listed below. Please discuss before with prof. K. Turowski if you are interested in any of below topic:

**1**. *The degree distribution and diameter for the preferential attachment model:*

**a.** compare methods in Bollobas, Riordan - Mathematical results on

scale-free random graphs and Bollobas et al. - The Degree Sequence of

a Scale-Free Random Graph Process

**Bonus:** apply differential equation method from Bennett, Dudek - A

gentle introduction to the differential equation method and dynamic

concentration to the master equation (17.1) for PA model from Frieze,

Karonski - Introduction to Random Graphs**2.** *Counting chordal and split graphs*

**a.** compare Bender, Richmond, Wormald - Almost all chordal graphs

split and Troyka - Split graphs: combinatorial species and asymptotics

**Bonus:** apply binomial sums method from Szpanowski, Weinberger -

Minimax Pointwise Redundancy for Memoryless Models Over Large

Alphabets to obtain precise asymptotics on the number of chordal and split graphs**3.** *The power law in partial duplication model*

**a**. explain derivations from Jacquet et al. - Power-law degree

distribution in the connected component of a duplication graph

**Bonus:** check power law hypothesis for the duplication model from

Chung, Lu - Complex Graphs and Networks, section 4.5 + use Mellin

transform to the equation (4.5)**4**. *Discuss parameter estimation in duplication models*

**a**. refer the results from Sreedharan et al. - Revisiting parameter

estimation in biological networks: Influence of symmetries

**Bonus:** compute exact asymptotics of clustering coefficient (local and

global) for Pastor-Satorras model e.g. using differential equation

method from Bennett, Dudek - A gentle introduction to the differential

equation method and dynamic concentration**5**. *The degree distribution, power law, and concentration for the linear copying model*

**a**. see Kumar et al. - Stochastic models for the web graph + provide

proofs for general d

**Bonus:** extend the analysis to the case, when we do not distinguish

between in- and out-degrees during copying**6.** *Number of isolated vertices, cherries, twins, and the asymmetry and entropy for Erdos-Renyi graphs*

**a.** for the latter refer to Choi, Szpankowski - Compression of

graphical structures: Fundamental limits, algorithms, and experiments

**Bonus:** provide a similar analysis for the special case of

Pastor-Satorras model with p = 0