As every researcher knows, there is generally a gap between all what we know/master about, all what we are interested in and what finally appears scarcely in some of our published papers. Often it is also just challenging to find people to work with on some specific topic that is a bit off your main research stream. So here I want to list some topics/keywords/questions I would love working on. Some are kind of linked to my field, some are definitely not, sometimes I manage to work on them a little bit, often I am just too busy with another exciting project. The purpose of this list is that you, as a researcher or a student, get in touch with me about one topic so that we can start collaborating on this together. If you feel like being interested by one of these projects, feel free to contact me, and I would be happy to guide you more.
- Information reconstruction in resource networks:
In this project, we study a large network of agents who produce, transfer and consumate resources. Only transfer of resources can be observed but neither production nor consumptions. Under some assumptions such that a production can only start if the resources needed for production have been received by the agent, and that transfer of resources systematically occur when a production cannot start, the goal is to study to which point it is possible to reconstruct the information of production and consumption, with quantitive bounds, as well as the network of effective dependency of a specific production.
- Stable and self-moving structures on weakly-differentiable manifolds:
Motivated by the loss of differentiability occurring in shocks between « particles » we study manifolds that are only weakly-differentiable, with respective extensions of the tangent space, geodesics, curvature, currents, etc. Also, for certain types of dynamical systems governed by a « flattening » dynamics, we study initial conditions that ensure the existence of stable and « self-moving » structures.
- Co-articulation Optimization:
Given a dynamical dystem (known dynamics) and a finite set of landmark points as inputs, we want to compute, for each finite sequence of landmark points, an optimal interpolation path passing maximally close to the targeted landmark points in the given order while being maximally distinct from the other landmark points. Then, we want to do the same when the dynamics is unknown.
This model naturally applies to the computation of co-articulation complexity of words, each landmark point corresponding to the prononciation parameters of one phoneme for a given speech apparatus. Then, based on a corpus of documents in some natural language, we can for instance compute the average co-articulation complexity of a language with respect to a given model of speech aparatus. In case we moreover have access to a grammar generator, we may generate a new natural language that minimizes the co-articulation complexity of most frequent grammatical structures while ensuring that the phoneme distance (geodesic distance in the parametric model of speech apparatus) between two grammatical structures increases with their co-occurrence frequency.
- Associative Memories with massive storage capabilities, Maximal no-hallucination capacity and optimal reconstruction:
An associative memory stores a signal into a (hyper-)graph by creating a (hyper-)clique structure, leading to a sparse and robust representation.
Optimal reconstruction can be done via the use of random matrices under some conditions. We want to investigate basic properties of associatove memories with hyper graph of a given size, like how to avoid hallucination (either creation or reconstruction of a clique corresponding to no signal), what is the maximal capacity of the memory, and what are the guarantees of optimal reconstruction under the constraint of avoiding hallucinations.
There are also other projects such as:
- Automatic music composer.
- Study of some generic arithmetic operator in number theory.
- Closed-loop economy.