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Международные научные проекты

В 2021-22 учебном году у студентов ФКН есть возможность выбрать иностранного научного руководителя курсовой или выпускной квалификационной работы. Список руководителей и предлагаемых ими тем представлен ниже.

Исследователь Аффилиация Название проекта на английском языке Название проекта на русском языке Требования Длительность Описание

Tommaso Dorigo

National Institute of Nuclear Physics (Padova section)

Performance studies of an optimized, overparametrized kNN regressor applied to the measurement of TeV-muon energies in a segmented calorimeter

Исследования производительности оптимизированного, сверхпараметризованного kNN-регрессора в применении к измерению энергии ТэВ-мюонов в сегментированном калориметре

С++ programming, notions on machine learning. Some prior knowledge of the root (root.cern.ch) application not required but useful.

Time involvement: from 2 months to six months.

Time frame: June 2021 – December 2021

A KNN regressor that associates a weight and a bias to each training event, similar to what a neural network would do, has been applied to the difficult problem of inferring the energy of muons in a highly-segmented calorimeter, exploiting their detected radiation loss. The student would study the optimization of the algorithm and produce results for a publication.

Possibility to co-author a publication on the method.

Tommaso Dorigo

National Institute of Nuclear Physics (Padova section)

End-to-end optimization of the design of a muon tomography apparatus

Сквозная оптимизация аппарата для мюонной томографии

Python programming, notions of machine learning. Some prior knowledge of PyTorch is useful.

Time involvement: from 3 months to six months.

Time frame: June 2021 – June 2022

By using differentiable programming libraries of PyTorch we are developing a pipeline for the optimization of the performance of a muon tomography detector in estimating the atomic number of an unknown volume of material, by choosing a layout, geometry, and cost of detection elements. The student would help code some of the modules of the pipeline and extend its functionality.

Possibility to co-author a publication of the proof-of-principle software.

Tommaso Dorigo

National Institute of Nuclear Physics (Padova section)

End-to-end optimization of the design of a hybrid calorimeter

Сквозная оптимизация гибридного калориметра

Python programming, notions of machine learning. Some prior knowledge of PyTorch or TensorFlow is useful.

Time involvement: six months or more.

Time frame: October 2021 –
 

Differentiable programming may enable the investigation of design choices for a calorimeter for a particle physics experiment. In this open-ended study, the student will consider possible layouts of a device comprised of tracking as well as scintillation layers, with the purpose of understanding the existence of novel design solutions to the problem of inferring the energy and direction of particle showers.

Possibility to co-author a publication on the studies performed.

Tommaso Dorigo

National Institute of Nuclear Physics (Padova section)

Anomaly detection in the copula space

Обнаружение аномалий в пространстве копул

С++ programming.

Time involvement: 2 to 4 months.

Time frame: June 2021 - June 2022
 

By standardizing the features of multi-dimensional data and applying the integral transform to each coordinate, one may study a dataset in search of localized overdensities without any need for a model of the background distribution. An algorithm has been designed to scan the space iteratively or in subspaces. The student would improve the gradient descent routines of the algorithm and benchmark the method with different datasets.

Jie-Hong Roland Jiang

National Taiwan University

Language and string constraint solving

Boolean circuit learning

Quantified decision procedures

Решение языковых и строковых ограничений

Обучение булевым схемам

Количественные процедуры принятия решений

Davide Bresolin

University of Padova

Automata theory, formal methods, model checking, cyberphysical-systems (precise topics upon inquiry)

Теория автоматов, формальные методы, проверка моделей, киберфизические системы (точные темы по запросу)

Up to two master students

On-site supervision

Paolo Baldan

University of Padova

Semantic foundations and formal methods for software systems

Семантические основы и формальные методы для программных систем

Up to two master students

On-site supervision

Mauro Conti

University of Padova

Cybersecurity

Кибербезопасность

Up to three master students

Both remote and on-site supervision

Massimiliano de Leoni

University of Padova

(Multi-perspective) Process Mining and Conformance Checking

(Многоперспективный) поиск процессов и проверка соответствия

Up to two master students

Preferably on-site supervision; if not, remotely, or dual

Francesco Rinaldi

University of Padova

Optimization Methods for Data Science and Complex Systems

Методы оптимизации для науки о данных и сложных систем

Up to four master students

Both remote and on-site supervision

Paolo Guiotto

University of Padova

Optimal Decisions in Integrated Operations Management

Оптимальные решения в интегрированном управлении операциями

Up to two master students

Both remote and on-site supervision

Maria Emilia Maietti

University of Padova

Categorical logic and type theory

Категориальная логика и теория типов

Up to three master students

Both remote and on-site supervision

Claudio Marchi

University of Padova

Mean Field Games systems: first order or second order case

Partial Differential Equation on networks

Системы игр со средним полем: случай первого или второго порядка

Частные дифференциальные уравнения в сетях

One bachelor or master student

Both remote and on-site supervision

Fabio Paronetto

University of Padova

Harnack's inequality for elliptic and parabolic equations

Gamma-convergence and/or G-convergence

Неравенство Харнака для эллиптических и параболических уравнений

Гамма-конвергенция и/или G-конвергенция

One bachelor and one master student

Both remote and on-site supervision

Paolo Rossi

University of Padova

Integrable systems and moduli space of curves

Интегрируемые системы и модульное пространство кривых

Up to two master students

On-site supervision

The moduli space of curves classifies all possible complex smooth algebraic curves (Riemann surfaces) and can be compactified to produce a closed compact space (a complex orbifold, to be precise). Each point represents a Riemann surface, up to reparametrization. Given the centrality of Riemann surface geometry in several fields of mathematics, from geometry to mathematical physics, the study of the topology of their moduli space is an important classical problem. Since the 90s and Witten's conjecture (a surprising intuition coming from string theory, later proved by Kontsevich) it has been known that integrable systems of Hamiltonian PDEs (an infinite-dimensional application of Arnold-Liouville integrability) control intersection theory of the moduli space of curves. This interaction has been fruitful both for geometry and mathematical physics. There are several special and very modern topics that use beautiful mathematics and could form the heart of a research-oriented master thesis. The details can be discussed and decided with the interested student.

Angelos Anadiotis

Ioana Manolescu

Ecole Polytechnique, Institut Polytechnique de Paris

Distributed Big Data & ML architecture for ConnectionLens

Распределенная архитектура больших данных и машинного обучения для ConnectionLens

One master student or a group of two students

• Relational database management systems

• Graph data management

• Distributed systems

• Machine learning techniques for natural language processing

Both remote and on-site supervision

ConnectionLens is a system that finds connections between user-specified search terms across heterogeneous data sources. ConnectionLens treats a set of heterogeneous, independently authored
data sources as a single virtual graph, where nodes represent fine-grained data items (relational tuples, attributes, key-value pairs, RDF, JSON or XML nodes…) and edges correspond either to structural connections (e.g., a tuple is in a database, an attribute is in a tuple, a JSON node has a parent) or to similarity (sameAs) links.
Currently, the pipeline is centralized, that is, it is deployed on a single, scale-up server. The goal of the thesis is to scale the end-to-end graph construction pipeline, to leverage a distributed computational
infrastructure (i.e., cluster). Achieving this goal requires two main tasks:
• Design and implement a distributed version of the graph construction algorithm, including database and Machine Learning (Information Extraction) computations
• Store the graph in a distributed store, such as Impala, Cassandra, HBase, while also considering pure graph stores such as MongoDB and Neo4j.

Full description and references (PDF, 79 Кб)

Jesse Read

LIX Laboratory, Ecole Polytechnique, Institute Polytechnique de Paris

Bayesian-Neural Methods for Missing Data Imputation with Applications in Bioinformatics

Байесовско-нейронные методы для введения отсутствующих данных с приложениями в биоинформатике

The project can be adapted to either bachelor or master level.

Knowledge of and experience in machine learning, including at least one deep-learning framework (e.g., TensorFlow
or PyTorch) and scientific programming in Python (including use of libraries such as Numpy), and specifically
awareness of probabilistic views of inference, including Bayesian methods.

Some relevant bioinformatics knowledge could make the topic more appreciable.

The mode of
work will be initially online, but travel and stay at the LIX laboratory will be a possibility to explore,

Missing data is a universal problem in data science and machine learning, and impacts many domains. Imputation can be approached as a machine learning task itself, by building models and using them to predict the missing values. These models can predict single or multiple values, either within a common row-instance or across the dataset within a common feature-column. Deep neural networks are a popular and successful class of model in general, particularly when multiple outputs are involved, yet usually, these methods only provide point estimates.
This proposed topic balances between the areas of machine learning and Bayesian inference. There are a number of methods found on this boundary that can be of interest, and among them, this project would target specifically Bayesian Neural Networks. We want not only to test and further develop this approach for missing values imputation (and specifically, in the domain of interest of SNP data), but also explore ways to leverage uncertainty information from the imputation task in a separate classification/regression task (using the imputed data). Although the main application domain is SNP datasets, methods can be tested in other domains including medical data (which we have available) and other tasks related to imputation, such as anomaly detection and recommendation systems.

Full description and references (PDF, 117 Кб)

Eric Goubault

Sylvie Putot 

Ecole Polytechnique, Institute Polytechnique de Paris

Verification of neural network based controllers 

Верификация контроллеров на основе нейронных сетей

Mostly master, but end bachelor for some parts of the project as well. No more than two.

Ideally, some knowledge on verification, formal methods, set-based methods, basic control theory and basic AI (neural nets)

Both remote and on-site supervision

The student will look into one or more, of these subjects:

- set-based abstractions of RELU activation functions, even swish, soft relu etc. 
(We already have sigmoids, tanh etc.) for inner and outer set approximation approaches, implemented in RINO https://github.com/cosynus-lix/RINO

- an interpretation of network architectures more general than feedforward neural nets (with CNN blocks etc., at least an important fragment of ONNX)

- abstractions for recurrent networks (initially, zonotopic interpretations and the use of our fixed point computation methods in the zonotopic domain see e.g. https://arxiv.org/abs/0910.1763)

- a better implementation (in particular with an external and not internal representation) of the interpretation of RELU networks by tropical polyhedra, cf. 
http://www.lix.polytechnique.fr/Labo/Sylvie.Putot/Publications/sas21.pdf

- extensions to this SAS21 paper (in particular, tropical polynomials, by simple techniques of linear representation on a monomial basis, improvement of the interpretation of multi-layer networks, e.g. by using intermediate zonotopes instead of hypercubes etc.)

- develop examples of neural network controllers for RINO and various tools (NNV, ReachNN, Verisig, flowstar in particular) around the F1/10tenth cf. https://arxiv.org/pdf/1910.11309.pdf and https://github.com/rivapp/autonomous_car_verification


 

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