Les axes de recherche développés par l’équipe CORNET (*Complex systems, Operations Research for Networks and Text*) sont les suivants :

## Complex Systems

**Overview:** A *system *is often defined as a set of interacting elements that are relatively isolated from their environment. It is called *complex *when it possesses some *emerging *properties. These are properties that cannot be defined at the level of isolated elements, but require considering several interacting elements, or even the whole system at once. Consequently, these systems cannot be reliably studied and understood using reductionist approaches (i.e. thoroughly studying a single element and extrapolating the behavior of the system): they require specifically designed tools and methods. The goal of this research axis is to design such tools and methods.

**Topics: **

- Extraction and analysis of complex networks
- Diffusion of epidemics and gossip over complex networks
- Opinion dynamics over social networks
- Centrality measures and their distributed estimation

## Operations Research

**Overview:** Operations research (OR) can be understood to be a range of scientific tools employed to analyse decision options. Multidisciplinary in nature, it borrows techniques from disciplines such as mathematics, computer science and economics. It can be applied in regional, national and local governance, public policymaking as well as in enhancing operational strategy and decision-making in civil and industrial society organizations. It uses in particular mathematical optimization models and methods at the heart of our activities. Our research has two components. A fundamental part, where solution methods to solve fundamental NP-Hard problems are developed, and an applied one, dealing with real-life applications.

**Topics: **

- Problems: combinatorial optimization, quadratic 0-1, graphs, assignment and location, partitioning, scheduling.
- Méthods: mathematical programming, polytopes, decomposition methods, metaheuristics.
- Applications: urban planning, ressources allocation, social network

## Performance Evaluation

**Overview:** Our research activities focus on modeling and optimization of problems arising from telecommunication networks and in particular wireless networks. Indeed, mathematical models play a crucial role in the study of wireless and mobile networks, ad hoc networks, cellular networks and fixed networks. They allow for better analysis of the following problems : network resource allocation, cooperation or competition between agents, Internet protocols, wireless network protocols, network dynamics, and network topology. The models are used to identify network performance limits and evaluate trade-offs, and to design algorithms and mechanisms for managing networks. This modeling work is based on queueing theory, game theory, evolutionary games, stochastic processes, and distributed algorithms, and must take into account the emergence of new applications and infrastructures. The issues addressed in these different types of networks concern quality of service, admission control, resource reservation, deterministic boundary computation, and energy consumption management.

**Topics:**

- Parallel computing applications in datacenters
- Network Economics
- Edge Fog
- Wireless networks

## Machine Learning

**Overview:** The theory of learning involves several methodological aspects of optimization theory and control which are of interest for the group. To this respect, a core field of research which is routinely addressed is the convergence and the stability of stochastic learning algorithms, which complements naturally the modeling activities of the group. The design of stable and robust algorithms is indeed key for all applied fields where they are used to perform system prediction and/or control. Actually, the application of learning algorithms permits the operation systems under uncertainty or partial information on the state and/or its parameters. This is the case of e.g., queuing systems and multiagent systems, or more in general, of socio-technical systems where model parameters are unknown at runtime.

**Topics:**

- Stochastic Approximations: design, convergence and stability
- Reinforcement learning techniques: constrained and unconstrained RL
- Federated Learning: selection of computing nodes and message complexity
- Representation learning: text, graph and multimodal embedding methods

## Graphs & Graph Algorithms

**Overview:** This research axis focuses on graphs and graph algorithms. Optimization problems on graphs are addressed and algorithms are designed for those problems and thoroughly analyzed both on a theoretical and experimental point of view. Therefore this research axis is related to the Operations Research axis.

We are also interested in different types of graphs, such as signed graphs and temporal graphs. Models and methods specific to those kinds of graphs are studied. This implies a connection to the complex systems axis.

**Topics: **

- Graph models analysis and design
- Graph/network optimization
- Algorithms design for optimization problems on graphs
- Dynamic and/or temporal graphs
- Signed graphs