The general scientific focus of DYOGENE is on the development of network mathematics. The following theories lie within our research interest: dynamical systems, queuing theory, optimization and control, information theory, stochastic processes, random graphs, stochastic geometry.

Our theoretical developments are motivated by and applied in the context of communication networks (Internet, wireless, mobile, cellular, peer-to-peer), social and economic networks, power grids.

We collaborate with many industrial partners. Our current industrial relations involve EDF, Huawei, Microsoft, Nokia, Orange, Safran.

More specifically, the scientific focus of DYOGENE defined in 2013 was on geometric network dynamics arising in communications. By geometric networks we understand networks with a nontrivial, discrete or continuous, geometric definition of the existence of links between the nodes. In stochastic geometric networks, this definition leads to random graphs or stochastic geometric models.

A first type of geometric network dynamics is the one where the nodes or the links change over time according to an exogeneous dynamics (e.g. node motion and geometric definition of the links). We will refer to this as dynamics of geometric networks below. A second type is that where links and/or nodes are fixed but harbor local dynamical systems (in our case, stemming from e.g. information theory, queuing theory, social and economic sciences). This will be called dynamics on geometric networks. A third type is that where the dynamics of the network geometry and the local dynamics interplay. Our motivations for studying these systems stem from many fields of communications where they play a central role, and in particular: message passing algorithms; epidemic algorithms; wireless networks and information theory; device to device networking; distributed content delivery; social and economic networks, power grids.

The following research axes have been defined in 2013 when the project-team was created.

Algorithms for network performance analysis, led by A. Bouillard and A. Busic.

Stochastic geometry and information theory for wireless network, led by F. Baccelli and B. Blaszczyszyn.

The cavity method for network algorithms, led by M. Lelarge.

Our scientific interests keep evolving. Research areas which received the most of our attention in 2019 are summarized in the following sections.

Theory and algorithms for distributed control of networks with applications to the stabilization of power grids subject to high volatility of renewable energy production are being developed by A. Busic in collaboration with Sean Meyn [Prof. at University of Florida and Inria International Chair].

A comprehensive approach involving information theory, queueing and stochastic geometry to model and analyze the performance of large cellular networks, validated and implemented by Orange is being led by B. Blaszczyszyn in collaboration with F. Baccelli and M. K. Karray [Orange Labs]. A new collaboration between the Standardization and Research Lab at Nokia Bell Labs and ERC NEMO led by F. Baccelli has been started in 2019.

We computed information theoretic bounds for unsupervised and semi-supervised learning and proved complexity bounds for distributed optimization of convex functions using a network of computing units.

In collaboration with Mir-Omid Haji-Mirsadeghi [Sharif University, Tehran, Iran] and Ali Khezeli [School of Mathematical Sciences, Tehran, Iran] F. Baccelli develops a theory of unimodular random metric spaces.

The distortion properties of unconstrained one-bit compression were analyzed by F. Baccelli in collaboration with E. O'Reilly [Caltech] using high dimensional hyperplane tessellations.

In collaboration with D. Yogeshwaran [Indian Statistical Institute, Bangalore] and J. E. Yukich [Lehigh University] B. Błaszczyszyn develops a limit theory (Laws of Large Numbers and Central Limit Theorems) for functionals of spatially correlated point processes.

Internet, wireless, mobile, cellular networks, transportation networks, distributed systems (cloud, call centers). In collaboration with Nokia Bell Labs and Orange Labs.

Social interactions, human communities, economic networks.

Energy networks. In collaboration with EDF.

**ERC NEMO**

ERC NEMO, led by F. Baccelli, started in January 2019; see .

**Inria International Chair**

Sean Meyn obtained Inria International Chair for the period 2019–2023 and joined Dyogene.

**Markov Lecture**

L. Massoulié gave the Markov Lecture at the Annual Meeting of the INFORMS society, in October in Seattle https://

Cellular network dimensioning toolbox *CapRadio* is being developed by
Orange in a long-term collaboration between TREC/DYOGENE represented
by B. Błaszczyszyn, and Orange Labs, represented by
M. K. Karray. This year we are working on taking into account the
“massive MIMO” in 5G cellular networks; see .

** 1.**** Distributed Control of Thermostatically Controlled Loads: Kullback-Leibler Optimal Control in Continuous Time**
The paper develops distributed control techniques to obtain grid services from flexible loads. The Individual Perspective Design (IPD) for local (load level) control is extended to piecewise deterministic and diffusion models for thermostatically controlled load models. The IPD design is formulated as an infinite horizon average reward optimal control problem, in which the reward function contains a term that uses relative entropy rate to model deviation from nominal dynamics. In the piecewise deterministic model, the optimal solution is obtained via the solution to an eigenfunction problem, similar to what is obtained in prior work. For a jump diffusion model this simple structure is absent. The structure for the optimal solution is obtained, which suggests an ODE technique for computation that is likely far more efficient than policy-or value-iteration.

** 36.**** Robustness of spectral
methods for community detection**
This work is concerned with community detection. Specifically, we consider a
random graph drawn according to the stochastic block model: its vertex set is partitioned
into blocks, or communities, and edges are placed randomly and independently of each other with
probability depending only on the communities of their two endpoints. In this context, our aim is
to recover the community labels better than by random guess, based only on the observation of the
graph.

In the sparse case, where edge probabilities are in

We then study the sensitivity of the eigendecomposition of

Our proposed spectral method therefore: i) is robust to larger perturbations than prior spectral methods, while semi-definite programming (or SDP) methods can tolerate yet larger perturbations; ii) achieves non-trivial detection down to the KS threshold, which is conjectured to be optimal and is beyond reach of existing SDP approaches; iii) is faster than SDP approaches.

** 41.**** On the Dimension of Unimodular Discrete Spaces, Part II: Relations with Growth Rate**
The notions of unimodular Minkowski and Hausdorff dimensions are defined in for unimodular random discrete metric spaces. This work is focused on the connections between these notions and the polynomial growth rate of the underlying space. It is shown that bounding the dimension is closely related to finding suitable equivariant weight functions (i.e., measures) on the underlying discrete space. The main results are unimodular versions of the mass distribution principle and Billingsley's lemma, which allow one to derive upper bounds on the unimodular Hausdorff dimension from the growth rate of suitable equivariant weight functions. Also, a unimodular version of Frostman's lemma is provided, which shows that the upper bound given by the unimodular Billingsley lemma is sharp. These results allow one to compute or bound both types of unimodular dimensions in a large set of examples in the theory of point processes, unimodular random graphs, and self-similarity. Further results of independent interest are also presented, like a version of the max-flow min-cut theorem for unimodular one-ended trees.

Two year contract titled *Taking into account the “massive MIMO”
in the assessment of QoS and the dimensioning of 5G cellular
networks* between Inria and Orange Labs started 2018. It is a part
of a long-term collaboration between TREC/DYOGENE, represented by
B. Błaszczyszyn and Orange Labs, represented by M. K. Karray
on the development of analytic tools and methods allowing one to capture
macroscopic relation between antennas roll-out,
frequency allocation, volume of traffic carried on the network and
quality of service parameters such as the average and the variation of
bandwidth available to end users. This work addresses crucial technical and economical issues related
to the operator core business, particularly related to the current evolution of the cellular network technology
(4G*CapRadio* (see ) and used by the Direction of Regulatory Affairs of Orange.

Collaborative research in the area of demand dispatch of flexible loads. PI : A. Busic.

Contract with Orange started in 2017 and continued in 2018 for the co-advising by B. Błaszczyszyn of a PhD student of Orange, Quentin Le Gall.

Dyogene participates in LINCS https://

Dyogene participates in the PGMO (Gaspard Monge Program for Optimization, operations research, and their interactions with data science) via the project a 2 year project “Distributed control of flexible loads” funded through the ICODE/IROE call. This is a collaborative project between University Paris-Sud (PI: Gilles Stoltz) and Inria (PI: Ana Busic).

Members of Dyogene participate in Research Group GeoSto
(Groupement de recherche, GdR 3477)
http://

This is a collaboration framework for all French research teams working in the domain of spatial stochastic modeling, both on theory development and in applications.

Members of Dyogene participate in GdR-RO (Recherche Opérationelle;
GdR CNRS 3002), http://

Probabilistic Approach for Renewable Energy Integration: Virtual Storage from Flexible Loads. The project started in January 2017. PI — A. Bušić. This project is motivated by current and projected needs of a power grid with significant renewable energy integration. Renewable energy sources such as wind and solar have a high degree of unpredictability and time variation, which makes balancing demand and supply challenging. There is an increased need for ancillary services to smooth the volatility of renewable power. In the absence of large, expensive batteries, we may have to increase our inventory of responsive fossil-fuel generators, negating the environmental benefits of renewable energy. The proposed approach addresses this challenge by harnessing the inherent flexibility in demand of many types of loads. The objective of the project is to develop decentralized control for automated demand dispatch, that can be used by grid operators as ancillary service to regulate demand-supply balance at low cost. We call the resource obtained from these techniques virtual energy storage (VES). Our goal is to create the necessary ancillary services for the grid that are environmentally friendly, that have low cost and that do not impact the quality of service (QoS) for the consumers. Besides respecting the needs of the loads, the aim of the project is to design local control solutions that require minimal communications from the loads to the centralized entity. This is possible through a systems architecture that includes the following elements: i) local control at each load based on local measurements combined with a grid-level signal; ii) frequency decomposition of the regulation signal based on QoS and physical constraints for each class of loads.

NEMO, NEtwork MOtion
https://*Processus ponctuels et graphes aléatoires unimodulaires* https://

Partner: VITO (Belgium); https://

Co-advising of PhD student I. Shilov. Started: Nov 2019. Topic: “Algorithmic Games and Distributed Learning for Peer-to-Peer Energy Trading”. PhD scholarship by VITO.

University of Florida; Collaborations with Prof Sean Meyn (ECE), Associate Prof Prabir Barooah (MAE), and the PhD students: A. Devraj (ECE), A. Coffman (MAE), N. Cammardella (ECE), J. Mathias (ECE).

Sharif University, Tehran; Collaborations with O. Mirsadeghi.

UC Berkeley; Collaborations with V. Anantharam.

Indian Statistical Institute (ISI), Bangalore; Collaborations with Yogeshwaran D.

IFCAM Project “Geometric statistics of stationary point processes” B. Błaszczyszyn and Yogeshwaran D. from Indian Statistical Institute (ISI), Bangalore, have got in 2018 the approval from Indo-French Centre for Applied Mathematics (IFCAM), for their joint project on “Geometric statistics of stationary point processes" for the period 2018–2021. Yogeshwaran D. was visiting Dyogene for two weeks in March and November 2019.

Microsoft Research-Inria collaboration: Laurent Massoulié heads the Microsoft Research-Inria Joint Centre, and also participates to the “Distributed Machine Learning” project of the Joint Centre, together with Francis Bach (Inria), Sébastien Bubeck and Lin Xiao (MSR Redmond), and PhD student Hadrien Hendrikx.

** IIC- MEYN Sean**

Title: Distributed Control and Smart Grid

International Partner (Institution - Laboratory - Researcher):

University of Florida (United States) - Department of Electrical and Computer Engineering - Sean Meyn

Duration: 2019 – 2023

Start year: 2019

See also: https://

TOPIC: “Distributed Control and Smart Grid’’

Ali Khezeli [School of Mathematical Sciences, Tehran, Iran],

Christian Hirsch [Bernoulli Institute, University of Groningen,

David Métivier [Los Alamos National Laboratory, USA]

Deepjyoti Deka [Los Alamos National Laboratory, USA]

Guenter Last [Karlsruhe Institute of Technology, Germany],

Hermann Thorisson [University of Islande],

Holger Keeler [University of Melbourne, Australia] ,

Hrvoje Pandžić [University of Zagreb, Croatia]

Itai Benjamini [Weizmann Institute of Science, Rehovot, Israel],

Joe Yukich [Lehigh University, Bethelem, PA, USA],

Josu Doncel [University of the Basque Country, Spain],

Lucas Pereira [Técnico Lisboa, Portugal]

Miklós Abért [MTA Renyi Institute, Budapest, Hungary],

Mir-Omid Haji-Mirsadeghi [Sharif University, Tehran, Iran],

Natasa Dragovic [The University of Texas at Austin, TX, USA],

Nelson Antunes [University of Faro, Portugal],

Venkatachalam Anantharam [University of California, Berkeley, CA USA],

Yogeshwaran D. [ISI, Bangalore, India],

Bastien Dubail [École Normale Supérieure de Lyon],

Emmanuel Kravitzch [Inria],

Erwan Pichon [Inria].

Ge Jin [Inria],

Maxence Lefort [Inria].

C. Fricker: University of Faro, Portugal (one week).

A.Busic: program participant (5 weeks in total) of “The mathematics of energy systems’’, Isaac Newton Institute for Mathematical Sciences, Cambridge, UK. Spring 2019, https://

In collaboration with M. Vojnovic (London School of Economics), A. Busic and L. Massoulié organized an international workshop on Machine Learning and User Decision Making https://

Members of Dyogene (co-)organized the following events:

ERC inaugural workshop *Processus ponctuels et graphes aléatoires
unimodulaires*
https://

Scientific session *Modélisation et analyse des systèmes de vélo-partage*
at RFTM2019 (2emes Rencontres
Francophones Transport et Mobilité, 11-13/06/2019 Montréal);
https://

A. Busic: co-lead (with E. Hyon, LIP 6) of the research group COSMOS (Stochastic optimization and control, modeling and simulation) of the GDR-RO; http://

A. Busic: one week workshop “Flexible operation and advanced control for energy systems” within INI Cambridge program “The mathematics of energy systems”, January 2019, Cambridge, UK, https://

All members of the team act as reviewers for numerous scientific journals.

Mathematics Colloquium at *Paris-Descartes*, November
2019, F. Baccelli (talk on high dimensional stochastic geometry);

Mathematics Colloquium at *Karlsruhe Institute of
Technology*, July 2019, F. Baccelli (talk on unimodular dimensions);

Invited lecture at the workshop *Modern Applied
Probability, in celebration of Sergey Foss' 65th birthday*, ICMS,
Edinburgh, May 2019 F. Baccelli (talk on particle systems); https://

Invited lecture at the workshop *Point processes in space,
time, and beyond*, Aalborg University, May 2019 F. Baccelli (talk on random graphs); http://

Mathematics Colloquium at *Institut Elie Cartan de
Lorraine*, April 2019 F. Baccelli (on unimodular random metric spaces);

Colloquium at **CEA LETI**, Grenoble, January 2019,
F. Baccelli (talk on wireless stochastic geometry);

Training School on Machine Learning for Communications,
ISEP, Paris, B. Błaszczyszyn;
https://

“STAR workshop on random graphs”, Groningen
Netherlands, B. Błaszczyszyn;
http://

invited talk in the Department of Statistics and Data Science Yale University, September 2019, M. Lelarge;

Isaac Newton Institute for Mathematical Sciences, Cambridge, UK, April 2019, A. Busic (on grid balancing through distributed control of flexible loads) ; video: https://

Simons Institute, UC Berkeley, June 2019, A. Busic (on optimizing mean-field dynamics for distributed control of flexible loads)

Journées Scientifiques Inria, Lyon, June 2019, A. Busic (Optimisation/contrôle dans des réseaux électriques)

CWI – Inria workshop, September 2019, Ana Busic (Optimizing mean-field dynamics for flexible loads control in power systems)

CMAP seminar, École Politechnique, December 2019, A. Busic (on optimal control in dynamic matching systems)

Licence: B. Błaszczyszyn (Cours) Théorie de l'information et du codage 24 heqTD, L3, ENS Paris.

Licence: A. Busic (Cours) and S. Samain (TD) Structures et algorithmes aléatoires 60heqTD, L3, ENS Paris.

Licence: L. Massoulié (Cours) Social and Communication networks 60heqTD, L3, l'X.

Master: B. Błaszczyszyn (Cours) Processus ponctuels, graphes aléatoires et géeométrie stochastique 39heqTD, M2 Probabilités et Modèles Aléatoires, UPMC.

Master: A. Busic (Cours) and L. Stephan (TD) Modèles et algorithmes de réseaux 60heqTD, M1, ENS Paris.

Master: A. Busic (Cours) Fondements de la modélisation des réseaux 18 heqTD, M2 MPRI.

Master: M. Lelarge (Cours) Deep Learning Do it Yourself, M1, ENS Paris.
X, X-HEC https://

Master: M. Lelarge (Cours) Deep Learning Do it Yourself, M1, ENS Paris.

Master: L. Massoulié (Cours) Inference in large random graphs, M2 Université d'Orsay.

Summer school: M. Lelarge (Cours) HANDS-ON TOUR TO DEEP LEARNING
WITH PYTORCH,
https://

Invited mini-course: L. Massoulié at Journée spéciale Stat Math 2019 of Société Française de Statistiques, Institut Henri Poincaré.

PhD: Léo Miolane, “High dimensional statistics”, defended in 2019, advised by M. Lelarge.

PhD: Md Umar Hashmi, “Decentralized control for renewable integration in smartgrids”, defended in 2019, advised by A. Busic.

PhD in progress: Alexis Galland, Deep Learning on Graphs, since 2017, advised by M. Lelarge.

PhD in progress: Quentin Le Gall “Crowd networking : modélisation de la connectivité D2D” since October 2017; PhD CIFRE co-advised by B. Błaszczyszyn and E. Cali (Orange).

PhD in progress: Antoine Brochard “Signal processing for point processes and statistical learning for telecommunications”, since September 2018; PhD CIFRE co-advised by B. Błaszczyszyn and Georgios Paschos (Huawei).

PhD in progress: Sébastien Samain, “Monte Carlo methods for performance evaluation and reinforcement learning”, since November 2016, advised by A. Busic,

PhD in progress: Arnaud Cadas, “Dynamic matching models”, since October 2017, supervised by A. Busic.

PhD in progress: Michel Davydov, since September 2019, F. Baccelli.

PhD in progress: Luca Ganassali, since September 2019.

PhD in progress: Hadrien Hendrikx, since 2019

PhD in progress: Sayeh Khaniha, form 2019, supervised by F. Baccelli.

PhD in progress: Edouard Pineau, since 2019,

PhD in progress: Bharath Roy, since 2019, supervised by F. Baccelli and B. Błaszczyszyn,

PhD in progress: Ilia Shilov, since 2019, supervised by A. Busic,

PhD in progress: Ludovic Stephan, since 2019.

F. Baccelli: PhD reviewer of **Gourab GHATAK**, Télécom Paris;
HDR reviewer of **Marios KOUNTOURIS**, Université Paris-Sud 1;
HDR jury member of **Raphaël LACHIEZE-REY**, Université Paris-Descartes.

B. Blaszczyszyn: PhD reviewer of: **Sanjoy Kumar JHAWAR**, Indian Institute of Science
Bangalore, India; **Arnaud POINAS**, Université de Rennes 1;
HDR reviewer of: **Marious KOUNTOURIS**, Université Paris-Sud 1;
PhD jury member of : **Jalal RACHAD**, Télécom Paris.

C. Fricker: PhD reviewer of: **Celine COMTE**, Université
Paris-Saclay; PhD jury member of: **Hamza BEN AMMAR**, Université de Rennes 1.

M. Lelarge: PhD jury member Xiaoyi MAI, Université Paris-Saclay.