HEИндивидуална стипендия2024–2026

RAND-COMB-DESIGN · Random Combinatorial Designs

„Хоризонт Европа“ — Действия „Мария Склодовска-Кюри“

Период: 2024-04-01 → 2026-03-31
Финансиране от ЕС: 181 153 €
Участници: 1
Схема: HORIZON-TMA-MSCA-PF-EF

Линиите свързват координатора с партньорите.

Накратко на български

Случайните комбинаторни структури съчетават математическия ред, подобен на судоку, с произволното разпределение на променливите. Това помага за създаването на по-справедливи и ефективни научни експерименти, като се избягват грешки и излишни разходи.

Този кратък обзор е генериран от изкуствен интелект

Кратко обяснение, генерирано от езиков модел по текста на CORDIS. Оригиналът е по-долу.

Резултати накратко

Random Combinatorial Designs

Experiments are used across many scientific fields to test various factors, and mathematics provides the tools to ensure these tests are both fair and efficient. Randomness is employed to make experiments fair by avoiding unintended biases, while combinatorial designs (highly regular patterns like those in a completed Sudoku square) make experiments efficient by testing every variable in the most resource-effective way. Purely random layouts can be wasteful, while ordered designs may have symmetries that reintroduce bias. This project investigated random designs to capture the benefits of both approaches. The main objectives were to advance the understanding of the properties of large designs from a probabilistic perspective and to develop new mathematical pathways toward efficient ways to sample these designs. The project also explored other high-level directions in discrete mathematics, including graph bootstrap percolation, which studies how information spreads through a network, and canonical Ramsey theory in random environments, which identifies inescapable regular patterns. A secondary goal was the professional development of the researcher to ensure a successful transition to an independent research career in Europe.

Текст от CORDIS, на английски · Данни: CORDIS, © Европейски съюз

Цел на проекта

The objective of this proposal is to develop fundamental and influential research into combinatorial designs. These objects have fascinated pure mathematicians for over 200 years and have also found many applications, for example in biological experiment design or in the design of strong error correcting codes in order to transmit data securely. The majority of research in design theory has focused on the existence and construction of designs. However recent breakthroughs have opened up exciting new perspectives, allowing for a much deeper understanding of these objects. The aim of this project is to develop these new directions by adopting a probabilistic stance and studying random designs. Our key objectives explore the existence and statistics of global structures in large designs and the longstanding problem of efficient algorithms for random sampling of designs. Through this, the project will foster connections between areas of pure mathematics, in particular extremal and probabilistic combinatorics, and the field of randomized algorithms in theoretical computer science. In order to achieve the proposal's objectives, the researchers will build upon a range of powerful novel methods, drawing on the expertise of the experienced researcher in absorption techniques and spanning structures and that of the host in rainbow structures and Markov chains. This will foster an exchange of knowledge between the two parties and greatly enhance the research potential of the experienced researcher. This project thus provides a pivotal opportunity for the development of his career as a young scientist, enabling him to push this exciting branch of design theory forward, broaden his knowledge and cement himself as a prominent researcher in several disciplines.

Оригинален текст от CORDIS (на английски).

Участници

UNIVERSITAT POLITECNICA DE CATALUNYA · BARCELONAКоординаторИспания