FLAT VIRTUAL KNOTS AND REPRESENTATIONS OF FLAT VIRTUAL KNOTS

Decent English language skills (understanding English from the

Everybody have met braids one way or another. Intuitively, a braid is a set of several strands which are tangled with each other. Braids can often be found as a decorative element of hair. Braids never go out of fashion, it is a universal detail which can improve every fashion.

However, not everybody knows that there exists an extensive mathematical theory which studies braids from the mathematical point of view. This theory has many applications in various fields of mathematics, computer science, biological and medical research and mathematical physics. During the project we are going to work on the problems which connect the mathematical theory of braids with the matrix theory.

mentor

Doctor of science, NSU, TSU, Sobolev Institute of Mathematics

mentor, tutor

Doctor of science, NSU, Sobolev Institute of Mathematics

tutor

Candidate of science, NSU, Sobolev Institute of Mathematics

1.

Mahender Singh

lecturer

Ph.D., Indian Institute of Science Education and Research, Mohali, India

VACUUM EXISTENCE

PROBLEM

PROBLEM

Creativity and imagination when solving problems

Theoretical high-energy physics, in its quest to uncover the laws of the microscopic world, often runs into purely mathematical challenges, which are not always easy to solve with the methods the physicists are used to. But it does not mean that the problem is unsolvable — creativity often helps tackle a challenge when straightforward approaches fail.

In this project, you will help physicists solve a challenging issue which arises in theoretical models with several Higgs bosons. The mathematical essence of the problem is rather simple: derive necessary and sufficient conditions for a certain real-valued polynomial to be bounded from below. But it has profound physics implications: these conditions will tell when a stable vacuum can exist at all in a given class of models. Solving this problem will be of much support to physicists when they build and explore New Physics models at the Large Hadron Collider.

Igor Ivanov

mentor

Ph.D., Instituto Superior Tecnico, Lisbon, Portugal

2.

Valery Churkin

mentor

Candidate of science, NSU, Sobolev Institute of Mathematics

Nikolay Buskin

tutor

Candidate of science, NSU, Sobolev Institute of Mathematics

Results (in Russian)

DEVELOPMENT OF ALGORITHMS FOR OPTIMIZING THE WORK OF HUAWEI AUTOMATED WAREHOUSE

The main warehouse of the Huawei company - one of the world's largest manufacturers in telecommunications - has a high level of automation. However, the constant increase in demand and, accordingly, load, requires the development of an effective warehouse planning and scheduling system.

The project proposes to solve the problem of constructing a schedule for the assembly and packaging of orders, received at the warehouse for processing. This two-stage process is organized on several parallel lines, which allows to execute multiple orders simultaneously.

It is required to develop an algorithm that allows to process all orders in the shortest possible time.

Yury Kochetov

mentor

Doctor of science, NSU, Sobolev Institute of Mathematics

3.

Ivan Davydov

tutor

Candidate of science, NSU, Sobolev Institute of Mathematics

Polina Kononova

lecturer

Candidate of science, NSU, Sobolev Institute of Mathematics

Alexander Kononov

lecturer

Doctor of science, NSU, Sobolev Institute of Mathematics

Results (in Russian)

BEHAVIORAL ANALYSIS OF UNDESIRABLE ACTIVITY WITH ELEMENTS OF GAMIFICATION TO THE PURPOSE OF RAISING SECURITY AWARENESS

Programming skills, the ability to write <Python or other programming language> code at a level, sufficient to understand and use the materials mentioned below

Technical English (Be ready to read articles and communicate in English)

Familiarization with the materials in

ATT&CK is a structured list of known attacker behaviors that have been compiled into tactics and techniques. Since this list is a fairly comprehensive representation of behaviors attackers employ when compromising networks, it is useful for a variety of offensive and defensive measurements, representations, and other mechanisms.

ATT&CK can be useful to cyber threat intelligence as it allows for describing adversarial behaviors in a

standard fashion.

This gives a roadmap to defenders to apply against their operational controls to see where they have

weaknesses against certain actors and where they have strengths.

During the project, it is planned to work on the task of simulating behavior for the attacking and / or defending sides, towards the creation of a model that allows raising security awareness (for example, games, tests, tests on ATT&CK and security basics) with elements of gamification (maps, achievements, ratings).

Valery Boronin

mentor

Cloud Security Team Lead, Novosibirsk RC Huawei

+ members of Huawei team

4.

BIGDATA – OPEN SOURCE PROJECT APACHE FLINK

Basic knowledge of one of the programming languages

Knowledge of algorithms and data structures

Interest in machine learning

It is advisable to have basic knowledge in the following areas: metrics, clustering, embeddings, graph theory

During the work of the section, it is planned to study the problems associated with one popular component of BigData - the open source project Apache Flink.

The list of tasks is given below. During the workshop it is supposed to focus on one of them.

All the tasks are aimed at optimizing the framework for streaming computing. To achieve the goal we will use the basic theory of algorithms and data structures.

In addition, it is planned to actively use machine learning methods, which will be studied under this section also.

Igor Solodov

mentor

Senior Expert, Team Lead, BigData Research Team, Novosibirsk RC Huawei

5.

Alexey Pauls

tutor

BigData Research Team,

Novosibirsk RC Huawei

Leonid Anisutin

tutor

BigData Research Team,

Novosibirsk RC Huawei

OPTIMIZATION AND TESTING OF ELEMENTARY MATHEMATICAL FUNCTIONS FOR HIGH-PERFORMANCE CALCULATIONS ON THE BASIS OF HUAWEI

PROCESSORS (ARMv8)

PROCESSORS (ARMv8)

The main requirement is the desire and ability to learn

Successful completion of the courses

"Higher Algebra" and "Mathematical Analysis" of any university is sufficient to understand the

project materials

Basic programming skills in some simple programming language are also

required. If you know C, technical English and the Linux command line, you will have less to

learn in the process of working on a project

Tamara Kashevarova

mentor

Candidate of science, leading engineer, Novosibirsk RC Huawei

6.

6.1

Developing of elementary functions library using

Chebyshev polynomials

Chebyshev polynomials

In light of recent events, Huawei Company has begun a deep development of high-performance libraries, including mathematical libraries, for its own architecture that based on ARM-technologies. Under this project, you are invited to develop some elementary mathematical function and using a specified server speed its execution up. You will work on the project under the guidance of a specialist from the Novosibirsk technology center of the Huawei Company and a competent specialist from the Novosibirsk State University. It will be possible to choose a function that corresponds to the level of any student team, starting from elementary mathematical functions such as sine, logarithm or exponent and ending with advanced algorithms of computational linear algebra such as multiplication of two matrices, Gauss method, or calculation of eigenvalues and vectors. Under the project you will have an opportunity to use Huawei cloud services and get skills in developing professional C software (and maybe assembler) under Linux OS.

6.2

6.3

Alexander Panasenko

tutor

NSU, Sobolev Institute of Mathematics

Alexey Staroletov

tutor

Candidate of science, Sobolev Institute of Mathematics

Fedor Dudkin

tutor

Candidate of science, NSU, Sobolev Institute of Mathematics

Sergey Gololobov

mentor

Candidate of science, NSU, leading engineer, Novosibirsk RC Huawei

ANALYSIS OF GENOMES BY METHODS OF BIOINFORMATICS AND SYSTEMS BIOLOGY

departments of any universities and common knowledge of matrix calculations and linear

equation systems

Knowledge of the principles of biology

Basic skills in one of the languages: Python, C++, or Java

Bioinformatics is a fast-paced interdisciplinary field, whose tasks demand close cooperation of experts in various areas of activity: geneticists, biologists, IT specialists, and, of course, mathematicians. Owing to the quantum leap in the power of experimental facilities, which provides supermassive volumes of

biological information and to advances in applied math and data analysis, development of mathematical algorithms and approaches to programming, supported by a considerable growth of computer performance, the recent 10–20 years have witnessed a progress in bioinformatics and a surge of interest

in it.

You can enter this fascinating field by participating in the work of one of two groups: Modeling of biologic systems and Machine learning and image recognition. Members of the groups will take training and try their brains in solving problems in genome analysis and computer systems biology, from genome assembly to construction of mathematical models of biologic processes.

Dmitriy A. Afonnikov

tutor

Cand. Sci. (Biol.), Institute of Cytology and Genetics, Siberian Branch of Russian Academy of

Sciences

Sergey A. Lashin,

tutor

Cand. Sci. (Biol.), Institute of Cytology and Genetics, Siberian Branch of Russian Academy of

Sciences

Alexey V. Kochetov

mentor

Dr. Sci. (Biol.) Corresponding Member of the RAS, Director of the Institute of Cytology and Genetics, Siberian Branch of Russian Academy of Sciences

Nikolay A. Kolchanov

mentor

Dr. Sci. (Biol.) Full Member of the RAS, Academic Advisor of the Institute of Cytology and Genetics, Siberian Branch of Russian Academy of Sciences

7.

Interested students are welcome to the Master's course on bioinformatics at the Department of Mechanics and Mathematics, Novosibirsk State University.

__Presentation of the Master's course on bioinformatics__

MODEL OF OPINION DYNAMICS IN COMPLEX SYSTEMS WITH ONE CENTRALIZED COMMUNICATION CHANNEL

People talk. Share opinions. Opinions change. This phenomenon lies in the basis of collective social behaviour and relatively not long ago it started to be studied by social sciences. Now, with appearance of the data from online social networks we got the possibility and necessity in modelling of the process of opinion formation. Substantial literature is dedicated to the models of opinion dynamics in networks, a.k.a. graphs, where interaction is limited to pairwise communication between a relatively small sets of friends. However, the models, where interaction would happen through a common news feed, like in a well-known platform Reddit, have not been yet considered. Within the project framework we propose to close this gap and study how one can steer the people's opinion in Reddit communities.

Alexey Medvedev

tutor

Ph.D., Catholic University of Louvain, Belgium

Andreagiovanni Reina

lecturer, mentor

Ph.D., University of Sheffield, UK

Mengbin Ye

lecturer, mentor

Ph.D., Curtin University, Australia

8.

lecturer, mentor

Ph.D., University of Oxford, UK

English language (level sufficient for reading of articles and listening to technical lectures)

Ability to program in Python (having an idea about the environment of Jupyter Notebooks, about the packages numpy, scipy, matplotlib, networkx)

Knowledge of the basics of linear algebra (matrices, systems of linear equations, the meaning of eigenvalues)

Knowledge of the fundamentals of probability theory (the ability to count the probabilities of events, knowledge of the main distributions, the properties of the exponential distribution, the Poisson process)

Mastery of the fundamentals of differential equations (systems of linear differential equations, knowledge of methods and types of solutions)

Results (in Russian)

PERFECT STRUCTURES AND DESIGNS

Perfect structures arise when local constraints on some discrete optimization problems surprisingly crystallize into an object with additional global uniformity and regularity. Perfect codes, Steiner systems, Hadamard matrices, and bent-functions have exactly this nature. Another example is a perfect coloring of a graph, in which all vertices of a given color have the same colored neighborhood. We are planning to research several seemingly different discrete problems and the resulting perfect structures. Moreover, we study connections between these structures and the world of combinatorial designs.

Sergey Avgustinovich

mentor, lecturer

Candidate of science, Sobolev Institute of Mathematics

Vladimir Potapov

mentor, lecturer

Candidate of science, Sobolev Institute of Mathematics

Anna Taranenko

tutor, lecturer

Candidate of science, NSU, Sobolev Institute of Mathematics

9.

High school math knowledge. Almost everything necessary will be mastered during the workshop

Knowledge of the basics of combinatorics and discrete mathematics: discrete probability, combinatorial numbers, basic concepts of graph theory (optional)

Mastery of the standard course in linear algebra and group theory (optional)

Results (in Russian)

PREDICTION OF THE ESTIMATED TIME OF ORDERS DELIVERY USING RANDOM GRAPH THEORY. ILLUSTRATED BY THE EXAMPLE OF NAIROBI, KENYA

According to many specialists we now live in the era of big data. With the rapid growth of the amount of information people create every day we need new methods to process it – and here machine learning comes to our rescue.

Imagine that you come across a table with some company's data on the delivery of parcels over the past few years. Is it possible to predict the time it would take to complete the new order given the available data? "Of course!" – happily exclaims a specialist in machine learning and immediately starts constructing decision trees. But, unfortunately, machine learning has a "black box" problem, meaning that in many cases it is impossible to know how exactly an algorithm comes to its conclusions, even though it shows remarkable results on a specific data set. What we propose is to approach the problem from the different angle – namely to create a probabilistic model that allows you to model, predict, and, most importantly, explain the nature of the phenomena.

Evgeny Prokopenko

mentor

Ph.D., NSU, Sobolev Institute of Mathematics, ESSEC Business School, Mathematical Center in Akademgorodok

Timofey Prasolov

tutor, lecturer

Ph.D., NSU, Mathematical Center in

Akademgorodok

Ekaterina Savinkina

tutor, lecturer

Ph.D. Student, Sobolev Institute of Mathematics, Mathematical Center in Akademgorodok

10.

Konstantin Avrachenkov

expert

PhD, Habilitation Degree, INRIA, Paris

Basic Python programming skills Knowledge of the basic course in Probability theory The idea of required level of proficiency in both disciplines is given by the first two weeks of the

STUDY OF SYSTEMS OF DIFFERENTIAL EQUATIONS MODELING THE DYNAMICS OF BIOLOGICAL PROCESSES. ANALYSIS OF REDUCTION OF THEIR DIMENSIONALITY IN ORDER TO SIMPLIFY COMPUTATIONAL EXPERIMENTS.

Sophomores of all depatements are welcome

Qualitative, not restricted by just computational experiments description of behavior of differential equations' systems trajectories lets us predict basic characteristics of various models. For example, in the process of modeling phenomena of molecular biology scientists run into the question of existence and properties of periodic solutions of specific systems of differential equations, which corresponds to periodic nature of plenty of biological systems - from cells to populations, including the spread of infectious diseases.

At the same time these problems of existence, uniqueness and stability of such periodic trajectories appear in "pure mathematics" as well, e. g. in the Hilbert's sixteenth problem or in the Poincare's "center-focus" problem.

We will study the behavior of trajectories of differential equations' systems that model biological processes. To be more precise, we will search for cycles in these systems.

Nataliya Kirillova

tutor

Ph.D.-student, Sobolev Institute of Mathematics

Vadim Efimov

mentor, lecturer

Doctor of science, professor, Institute of Cytology and Genetics

Vladimir

mentor, lecturer

Doctor of science, professor, NSU, Sobolev Institute of Mathematics

11.

Results (in Russian)

DEVELOPMENT OF ALGORITHMS FOR SOLVING THE PROBLEM OF GAS PREPARATION AND TRANSPORT

(GAZPROMNEFT STC)

(GAZPROMNEFT STC)

The gas producing company is required to develop an effective algorithm for solving the problem of minimizing the costs of gas processing and transportation in a gas field. Participants are invited to develop the desired solution algorithm based on well-known and successfully applied methods for solving optimization problems, for example, metaheuristics.

Alexander Plyasunov

mentor, lecturer

Candidate of science, NSU, Sobolev Institute of Mathematics

Roman Plotnikov

lecturer

Candidate of science, Sobolev Institute of Mathematics

Artem Panin

tutor, lecturer

Candidate of science, NSU, Sobolev Institute of Mathematics

12.

Adil Erzin

lecturer

Doctor of science, NSU, Sobolev Institute of Mathematics

Yuri Kochetov

lecturer

Doctor of science, NSU, Sobolev Institute of Mathematics

Ivan Davydov

lecturer

Candidate of science, NSU, Sobolev Institute of Mathematics

ALGEBRAIC COMBINATORICS. COMBINATORIAL METHODS FOR CHECKING GRAPH ISOMORPHISM

Basic knowledge of graph theory, knowledge of all operations on matrices, understanding

of the terms "group" and "algebra"

Python programming skills (optional)

A new section called "computer chemistry" has recently appeared in organic chemistry, in

which methods of discrete mathematics are applied to chemical problems. In these problems, substances are modeled by molecular graphs. One of the trends in this area is the task of recognition of chemical structures by reference to the chemical and physico-chemical databases. For solving this problem, it is necessary to be able to check the Isomorphism of graphs, which means understanding whether there exists a correspondence between the two graphs that

preserves the structure. As part of the project, we plan to study the problem of graph

isomorphism.

Leonid Shalaginov

mentor

PhD in Physical and Mathematical Sciences, Chelyabinsk State University, N.N. Krasovskii

Institute of Mathematics and Mechanics (IMM UB RAS), Mathematical Center in

Akademgorodok

13.

Ilya Ponomarenko

teacher

D.Sc. in Physical and Mathematical Sciences, St. Petersburg Department of Steklov Mathematical Institute of Russian Academy of Sciences, Mathematical Center in Akademgorodok

Vladislav Kabanov

lecturer

D.Sc. in Physical and Mathematical Sciences, N.N. Krasovskii Institute of Mathematics and Mechanics (IMM UB RAS), Mathematical Center in Akademgorodok

Elena Konstantinova

lecturer

PhD in Engineering Sciences, Steklov Mathematical Institute of Russian Academy of Sciences, Mathematical Center in Akademgorodok

Grigory Ryabov

lecturer

PhD in Physical and Mathematical Sciences, Steklov Mathematical Institute of Russian Academy of Sciences, Mathematical Center in Akademgorodok

Dmitry Panasenko

tutor

Chelyabinsk State University, Mathematical Center in Akademgorodok

Results (in Russian)

ОNLINE DIMENSION OF ALGEBRAIC STRUCTURES

Knowing the basics of Turing machines and partial computable functions

Computability theory studies the following questions. When does a mathematical object have an algorithmic presentation? How can one compare the complexity of different algorithmic presentations?

A simple example of an algorithmic presentation is provided by the codes of rational numbers: computer memory stores rational numbers as binary strings. Addition of rational numbers is implemented via an algorithm that given codes of numbers a and b, computes the binary code of their sum a+b.

The classical approach to algorithmic presentations is based on Turing machines. Our project aims to work on problems related to a new approach, which is based on online algorithms. In contrast to the classical "offline" situation, where an algorithm "knows everything" about input data, online algorithms work with data, which is given in a step-by-step fashion.

Nikolay Bazhenov

mentor, lecturer

Candidate of science, NSU, Sobolev Institute of Mathematics, Mathematical Center in Akademgorodok

14.

Alexander Melnikov

mentor, lecturer

Doctor of science, Massey University, Auckland, New Zealand

Sergey Goncharov

lecturer

Doctor of science, RAS Academician, NSU, director of Sobolev Institute of Mathematics

Manat Mustafa

mentor

Ph.D., Nazarbayev University, Kazakhstan

Iskander Kalimullin

lecturer

Doctor of science, professor, Kazan Federal University

Keng Meng Ng

lecturer

Ph.D., Nanyang Technological University, Singapore

Ruslan Kornev

tutor

NSU, Sobolev Institute of Mathematics, Mathematical Center in Akademgorodok

Results (in Russian)

SEMANTIC

PROGRAMMING

PROGRAMMING

Knowledge of the basics of mathematical logics

Understanding of the distinction between

Understanding of the principals behind

How often during yet another "existence" task you sadly thought: "What a pity that there is no algorithm that would proof it for me"? We have a solution! That are the automatic proof methods and semantic programming*. You just submit the initial data and result conditions. The process of proof is fully determined by the algorithm without your interference. Join this project and just in 6 days and 23 hours you will learn how to code without actually coding, what are solvers that let programmers do less work, how to apply the approach of semantic programming to modern tasks, for example creation of intelligent chat-bots.

Denis Ponomarev

project lead, lecturer

Candidate of science, NSU, Mathematical Center in Akademgorodok, Yershov Institute of Informatic Systems

15.

Sergey Ospichev

tutor

Candidate of science, NSU, Sobolev Institute of Mathematics, Mathematical Center in Akademgorodok

Dmitry Luppov

tutor, mentor

NSU, director of Dialogue Systems

Dmitry Vlasov

mentor, lecturer

Candidate of science, NSU, Sobolev Institute of Mathematics, leading developer of Lanit Terkom (St. Petersburg)

Sergey Goncharov

lecturer

Doctor of science, RAS Academician, NSU, director of Sobolev Institute of Mathematics

Dmitry Sviridenko

lecturer

Doctor of science, NSU, Sobolev Institute of Mathematics

Evgeny Vityaev

lecturer

Doctor of science, NSU, Sobolev Institute of Mathematics

*lets us automate *some* proofs of *some* tasks

** second part and interperiod are not included

** second part and interperiod are not included

Results (in Russian)

ALGORITHMS OF DATA REDUCTION WITH PERFORMANCE GUARANTEES

Basic knowledge of the graph theory and analysis of algorithm complexity

A popular example of successful application of data reduction is the following problem of public transport optimization: it is required to place minimal number of depots so that there is at least a single depot on each route. T`his problem in NP-compex, which means that intensity of solving algorithms grows with the increase in input data exponentially. However, this task can be easily solved using algorithms of data reduction: these algorithms try to reduce the volume of input data at polynomial time while preserving the optimal solvability. Participants will work on data reduction algorithms for a more general task of Hypergraph vertex coverage, which is also spread in bioinformatics, data analysis, program engineering and artificial intelligence. The aim of the project is to outline the properties of data that can be used in data reduction algorithms with guaranteed performance. Workshop participants will construct algorithms that provably reduce the volume of data to the dimensions that do not depend on initial ones.

Rene van Bevern

mentor, tutor

Dr. rer. nat., NSU, Mathemaical Center in Akademgorodok

16.

Results (in Russian)

AUTOECODER NEURAL NETWORKS FOR PROCESSING ANTENNA ARRAY SIGNALS

The Deep Learning technique develops rapidly during last years. The complex neural network architectures are being developed and testing as well as software for their training, evaluation and application.

In the frame of present project, we propose problem of optimization of autoecoder neural network, which is used for the analysis of real data of astrophysical experiment.

Dmitry Kostunin

mentor

Ph.D., DESY Zeuthen

Yulia Kazarina

project lead

Candidate of science, Irkutsk State University

17.

Pavel Bezyazykov

tutor

Ph.D.-student, Irkutsk State University

Python programming language (particularly

DIGITAL URBANISM: **GEOSPACIALDATA** **ANALYSIS****,** **URBAN MODELLING AND MACHINE LEARNING**

Basic knowledge of machine learning (data pre-processing; problem types, such as regression, classification, clustering, dimensionality reduction, etc.) and ML algorithms

Knowledge of the basics of Calculus, linear algebra (vector and matrix data representation), statistics (main distribution types and their properties, parametric and non-parametric estimates) is beneficial

Knowledge of Python or PHP. Experience with PostGIS, PostgreSQL, Django, Linux,

Installed

Everyone who lives in a block of flats has thought at least once about how their courtyard can be changed – and whom they should contact to ensure that these changes are implemented in a functional and elegant manner. At the same time, there are many architectural bureaus and design think-tanks in Russia which can support citizens with the improvement of the adjacent outdoor areas. During the project the students will connect the supply of the services offered by such bureaus and think-tanks and demand of citizens. They should solve the problem of automating a process of citizen enquiries collection, define functional zones taking into consideration their preferences, and analyze geospatial data of the corresponding areas.

In the course of the project the students will be engaged in working on the problem of recognition of various urban objects, such as houses, roads, adjacent areas, parks, and the like. Afterwards, they will build a model encompassing socio-economic indicators in the form of a geotag-based heatmap. The teams will be working on tasks related to statistical and intellectual processing of both geospatial and user data, as well as modeling dynamic changes in urban areas.

Alexey Platonov

mentor

Ph.D. in Technical Sciences,

ITMO University

18.

Ekaterina Danilina

tutor

student, Kurgan State University

Anna Avdyushina

tutor

student, ITMO University

Tatiana Zmyzgova

project lead

Ph.D. in Technical Sciences,

Associate Professor,

Vice-rector on Computerization

Kurgan State University

DEVELOPMENT OF ALGEBRAIC ATTACKS ON LRX - AND ARX - CIPHERS

Programming skills (to check the hypothesis)

Be ready to read articles and communicate in English

Having a motivation to create something modern and new (the most important)

We use cryptography in our daily devices without even thinking, even though it has been around us since the early existence of mankind as a mean of secret messaging, that should be understood only by the right person.

The core of cryptography is its universe of ciphers, among which we emphasize symmetric ciphers, where the same secret key is used for encryption and decryption. An attack on them comes down to analysis of the operation of the cipher and finding the secret key. This analysis (cryptanalysis) comprises the solutions of different mathematical and programming tasks.

So, the goal of this project is to develop effective attacks on symmetric ciphers! The project can help to find weakness within a certain type of ciphers in order to improve them, thus making these ciphers more resilient to algebraic attacks.

This may seem a bit confusing, and it should be! Cryptography is not an easy subject, and this is for a good reason – if everyone knew everything about it, that would mean that our secrets are not safe enough!

So in this project you will at least understand more about the power of cryptography and even try to find its weaknesses!

Sergey Agievich

mentor

Ph.D., Head of IT Security Research Laboratory at Research Institute for Applied Problems of Mathematics and Informatics in Belarusian State University, the main developer of the several governmental standards in area of cryptography and information security

Aleksandr Kutsenko

tutor

PhD-student, NSU, Mathematical Center in Akademgorodok

Natalia Tokareva

project lead

Candidate of physics and mathematics, Institute of Mathematics SB RAS, NSU, Mathematical Center in Akademgorodok

19.

Results (in Russian)

DIFFERENTIAL CHARACTERISTICS OF THE MODERN SYMMETRIC CIPHERS

Basic course of linear algebra

Ability to read papers and communicate with mentor in English

Optional: Familiarity with discrete mathematics

If you can't wait to get started, look through

Only during this workshop! Immerse yourself in the mysterious world of cryptanalysis of symmetric ciphers! Our main focus are the ciphers of ARX architecture. Their primitives are just familiar operations – modulo 2

The solution to the problem that you will be working on is not yet known and is expected to have a significant impact on the understanding of widely deployed modern cryptographic ciphers. You will work together with Dr. Nicky Mouha, who is currently working for NIST while confined to the balcony of his home in Washington, D.C. due to the pandemic. He spent most of his career breaking ciphers, but has recently felt confident enough to dabble into cipher design. In the past few months his Chaskey cipher was internationally standardized in ISO/IEC 29192-6. It's also an ARX cipher and, moreover, one of the fastest ciphers in the entire world!

We will analyze the differences of the XOR operation relative to the modulo addition, since they affect the efficiency of differential cryptanalysis. What is differential cryptanalysis will be discussed in a lecture. If you know what a block cipher is, then this topic is for you!

Nicky Mouha

mentor

Ph.D., Researcher at the Computer Security Division of NIST (USA), a member of crypto standartization committees at NIST, ISO/IEC JTC1 SC27, and ASC X9F; a co-author of 3DES standard, which is one of only two block ciphers that are approved for use by the U.S. government

Nikolay Kolomeec

tutor

candidate of physics and mathematics, Institute of Mathematics SB RAS, NSU

Natalia Tokareva

project lead

Candidate of physics and mathematics, Institute of Mathematics SB RAS, NSU, Mathematical Center in Akademgorodok

20.

HOW TO DEVELOP OPEN SOURCE INTELLIGENCE FRAMEWORK FROM SCRATCH

A good level of English (ability to read documentation and communicate)

Software engineering skills (Python/Golang, Git) and familiarity with machine learning techniques from a software engineering perspective

The absence of some knowledge or skills is not a big problem, if you are ready to work hard

This workshop is for you, if you satisfy one or several requirements that are as follows:

You have been programming in Python

You have mental models of how network protocols (e.g., TCP, HTTP, TLS) behave and are used

You have hacker's intuition and like to "hack" things (in a good sense)

You like to automate security checks.

It would be good (but not required) if you are familiar with:

Docker and docker-compose

Git (Github, Gitlab) version control system

Security scanners (e.g., Burp, Nmap, Shodan, Masscan)

REST API and how to work with one

References:

Some heroes don't wear capes, and if you wanted to get secret information from the best special agent in the world you would not need to become one — learning basic principles of open source intelligence will be enough. If the glory of Edward Snowden haunted you, and Mr. Robot is your hero, then this workshop is for you. We, like the super-top-secret-agents à-la "007", will shake all fields of computer security, computer science, and software engineering in the process of work to learn how to gather information on the Internet within well-established Open Source Intelligence (OSINT) approach.

This workshop for you, if you are interested in these topics:

How to find top-secret documents?

How to find the missing persons and try to assist Liza Alert team?

How to ask someone their pet's name and email address and not look suspicious?

How to get all the information about a person based only on a photo?

How to make an investigation better than the Bloomberg agency?

How to become ears and eyes of the world, from the coffee machines to the refrigerators?

How to find out who is this person who follows your couple on Instagram this whole year?

How to automate all these things and analyze the gathered information using machine learning algorithms?

How to provide anonymity and confidentiality for you and your team in this process?

Our task will be to answer all of these questions, and we will develop an analytical framework to search and analyze information from various sources. This framework will help us to find and link different events, people, places in one full image and will open for us new edges of modern Open Source Intelligence.

Besides all that, we will also learn new stuff related to the advanced methodology of intelligence and searching, together with taking a look at the security level of different modern appliances, like nuclear power plants, machine learning systems, different servers, and cloud platforms, fitness trackers, scales, refrigerators and many more things that you never think about in this perspective of view.

So, if you are interested in all of this, welcome on board!

Denis Kolegov

mentor

Ph.D., associate professor at the Department of Computer Security in Tomsk State University, principal security developer at Bi.Zone

Anton Nikolaev

tutor

security developer at Bi.Zone

Natalia Tokareva

project lead

Candidate of physics and mathematics, Institute of Mathematics SB RAS, NSU

21.

Knowledge of calculus

Knowledge of a standard course on partial differential equations is welcome as well as a course on functional analysis

English proficiency (in terms of reading mathematical papers) is a plus

Progress in many advanced industries such as mechanical, airspace, and civil engineering, is significantly driven by design and implementation of composite materials. This is because composite materials amplify strength properties and bearing capacity of structural elements, as the weight of the construction decreases at the same time. Composites themselves are heterogeneous continuous media consisting of several distinct components whose mechanical properties and behavior can drastically differ from each other. Also, notice that nowadays the composite materials incorporating nanotubes are widely in use, since they possess high strength and stiffness. Therefore, an adequate mathematical simulation of composite bodies is in high demand. Such simulation allows to predict the behavior of composite bodies, to describe their characteristics accurately, to consider impact of the environment, and to derive criteria for the occurrence and propagation of cracks.

Sergey Sazhenkov

mentor, lecturer

Doctor of science, NSU, Lavrentyev Institute of Hydrodynamics

Evgeny Rudoy

mentor, lecturer

Doctor of science, NSU, Lavrentyev Institute of Hydrodynamics, Mathematical Center in Akademgorodok

22.

Sergey Golushko

mentor

Doctor of science, NSU vice-rector for economics, finance and innovation

Alexey Furtcev

tutor

Lavrentyev Institute of Hydrodynamics

MATHEMATICAL MODELS OF ELECTRICITY SYSTEMS

Mathematical modeling is based on a graph, where vertices contain consumers and/or producers of electric or thermal power. Edges of the graph refer to electric transmission lines or pipelines. The main goal is to deliver electric or thermal power from sources to consumers with, for example, minimal losses and transmission costs. The source structure (e.g. types of power plants), constraints on productive capacity, the graph topology and transmission capacity of the lines had to be taken into account. The 1st and the 2nd Kirchhoff's laws and other physical constraints must be fulfilled. Such research is of great theoretical and applied value.

Oleg Khamisov

mentor

Doctor of science, Melentiev Energy Systems Institute

23.

Anton Kolosnitcyn

mentor, tutor

Melentiev Energy Systems Institute

Ilya Minarchenko

mentor, tutor

Melentiev Energy Systems Institute

WAVELET ANALYSIS AND ITS APPLICATION TO FORECASTING PROBLEMS

Basic knowledge of mathematical analysis and linear algebra (e.g. integral, series, basis)

Skills in MATLAB or any other similar system (Scilab, Octave) are welcome

For an introduction to the subject we suggest you to complete the fourth week of the course

For an introduction to the subject we suggest you to complete the fourth week of the course

Do you know that with only 5-10% of the original information, using wavelets you can reconstruct an image with a good accuracy? A wavelet is a special function that looks like a "small wave". Wavelet analysis appeared about 40 years ago as an alternative to the Fourier analysis. Having certain advantages, the wavelet analysis has many applications in approximation, numerical methods, engineering, signal and image processing. While working on our project, we will learn how to analyze signals using wavelets and predict certain events based on the received information.

Evgeniya

mentor, lecturer

Candidate of science, NSU, Sobolev Institute of Mathematics

24.

Dariya Vozhdaeva

tutor

NSU

THE TRUTH COMES OUT: HOW MATHEMATICS HELPS FIND HIDDEN MEANING IN SPECIFIC TERMINOLOGY

Have you ever run into a situation where what is meant does not correspond with what is written? Or where something is called very sophisticatedly when it has a more easy name? Have you ever thought how long will a mathematical proof be if it had no auxiliary terms?

We will look into these questions from mathematical point of view and will see that plenty of both hidden and apparent problems with terms' descriptions can be solved elegantly and naturally. We will learn how to formulate definitions of terms (e. g. dictionaries, thesauruses, taxonomy) using computer language, how to search for hidden definitions and how long/short they can be. Together we will work on creation of algorithms that compute hidden definitions using machine reasoning methods, which are widely used in the field of artificial intelligence.

Denis Ponomarev

project lead

Candidate of science, NSU, Mathematical Center in Akademgorodok, Yershov Institute of Informatic Systems

project lead

Candidate of science, NSU, Mathematical Center in Akademgorodok, Yershov Institute of Informatic Systems

Sergey Odintsov

lecturer, mentor

Doctor of science, NSU, Sobolev Institute of Mathematics

lecturer, mentor

Doctor of science, NSU, Sobolev Institute of Mathematics

Stepan Yakovenko

lecturer, mentor

Leading developer, Visitele (Bratislava, Slovakia)

lecturer, mentor

Leading developer, Visitele (Bratislava, Slovakia)

Dmitry Vlasov

mentor, lecturer

Candidate of science, NSU, Sobolev Institute of Mathematics, leading developer of Lanit Terkom (St. Petersburg)

mentor, lecturer

Candidate of science, NSU, Sobolev Institute of Mathematics, leading developer of Lanit Terkom (St. Petersburg)

Sergey Drobyshevich

tutor

Candidate of science, NSU, Sobolev Institute of Mathematics

tutor

Candidate of science, NSU, Sobolev Institute of Mathematics

25.

Results (in Russian)

MATHEMATICAL APPROACH TO LINGUISTIC EXPERISE

Knowledge of Python (especially libraries of working with natural languages)

Understanding of mathematical bonds theory

You can start by looking into these courses:

1.

2.

3.

4.

5.

Harassment on the Net is one of the modern phenomena. You do not have to seach long for an example, just open any discussion or Trump's Twitter. Insult is an offence that is hard to proof because the law allows subjective reasoning and the judicial case comes down to a single expert's opinion. So an uncertainty rises: the same insult in a chat can «defame someone's honor», «harass» or even «humiliate human dignity». In the framework of this project we will create a model that would distinct insults among other genres of speech and remove the uncertainty in the legal field. We will use methods of mathematical linguistics and machine learning. Exact detection of aggression will not only objectify the guilt identification but also will protect human rights.

Liliya Komalova

project lead, lecturer

Doctor of science, Institute of Scientific Information on Social Sciences

Tatyana Goloshapova

mentor

Candidate of science

Ekaterina Mayorova

mentor

Institute of Scientific Information on Social Sciences

26.

Leonid Motovskikh

mentor

programmer, Ph.D.-student of Moscow State Linguistic University

Dmitry Morozov

tutor

Institute for Information Transmission Problems