Search results for " Mathematics"
showing 10 items of 10797 documents
Graph-theoretical derivation of brain structural connectivity
2020
Brain connectivity at the single neuron level can provide fundamental insights into how information is integrated and propagated within and between brain regions. However, it is almost impossible to adequately study this problem experimentally and, despite intense efforts in the field, no mathematical description has been obtained so far. Here, we present a mathematical framework based on a graph-theoretical approach that, starting from experimental data obtained from a few small subsets of neurons, can quantitatively explain and predict the corresponding full network properties. This model also changes the paradigm with which large-scale model networks can be built, from using probabilisti…
Consensus via multi-population robust mean-field games
2017
In less prescriptive environments where individuals are told ‘what to do’\ud but not ‘how to do’, synchronization can be a byproduct of strategic thinking,\ud prediction, and local interactions. We prove this in the context of multipopulation\ud robust mean-field games. The model sheds light on a multi-scale\ud phenomenon involving fast synchronization within the same population and\ud slow inter-cluster oscillation between different populations.
On stability of linear dynamic systems with hysteresis feedback
2020
The stability of linear dynamic systems with hysteresis in feedback is considered. While the absolute stability for memoryless nonlinearities (known as Lure's problem) can be proved by the well-known circle criterion, the multivalued rate-independent hysteresis poses significant challenges for feedback systems, especially for proof of convergence to an equilibrium state correspondingly set. The dissipative behavior of clockwise input-output hysteresis is considered with two boundary cases of energy losses at reversal cycles. For upper boundary cases of maximal (parallelogram shape) hysteresis loop, an equivalent transformation of the closed-loop system is provided. This allows for the appli…
Global sensitivity analysis in welding simulations -- what are the material data you really need ?
2011
In this paper, the sensitivity analysis methodology is applied to numerical welding simulation in order to rank the importance of input variables on the outputs of the code like distorsions or residual stresses. The numerical welding simulation uses the finite element method, with a thermal computation followed by a mechanical one. Classically, a local sensitivity analysis is performed, hence the validity of the results is limited to the neighbourhood of a nominal point, and cross effects cannot be detected. This study implements a global sensitivity analysis which allows to screen the whole material space of the steel family mechanical properties. A set of inputs of the mechanical model-ma…
VARIABLE SELECTION FOR NOISY DATA APPLIED IN PROTEOMICS
2014
International audience; The paper proposes a variable selection method for pro-teomics. It aims at selecting, among a set of proteins, those (named biomarkers) which enable to discriminate between two groups of individuals (healthy and pathological). To this end, data is available for a cohort of individuals: the biological state and a measurement of concentrations for a list of proteins. The proposed approach is based on a Bayesian hierarchical model for the dependencies between biological and instrumental variables. The optimal selection function minimizes the Bayesian risk, that is to say the selected set of variables maximizes the posterior probability. The two main contributions are: (…
Robust Mean Field Games with Application to Production of an Exhaustible Resource
2012
International audience; In this paper, we study mean field games under uncertainty. We consider a population of players with individual states driven by a standard Brownian motion and a disturbance term. The contribution is three-fold: First, we establish a mean field system for such robust games. Second, we apply the methodology to an exhaustible resource production. Third, we show that the dimension of the mean field system can be significantly reduced by considering a functional of the first moment of the mean field process.
Opinion dynamics in social networks through mean field games
2016
Emulation, mimicry, and herding behaviors are phenomena that are observed when multiple social groups interact. To study such phenomena, we consider in this paper a large population of homogeneous social networks. Each such network is characterized by a vector state, a vector-valued controlled input, and a vector-valued exogenous disturbance. The controlled input of each network aims to align its state to the mean distribution of other networks' states in spite of the actions of the disturbance. One of the contributions of this paper is a detailed analysis of the resulting mean-field game for the cases of both polytopic and $mathcal L_2$ bounds on controls and disturbances. A second contrib…
New delay-dependent stability of Markovian jump neutral stochastic systems with general unknown transition rates
2015
This paper investigates the delay-dependent stability problem for neutral Markovian jump systems with generally unknown transition rates GUTRs. In this neutral GUTR model, each transition rate is completely unknown or only its estimate value is known. Based on the study of expectations of the stochastic cross-terms containing the integral, a new stability criterion is derived in terms of linear matrix inequalities. In the mathematical derivation process, bounding stochastic cross-terms, model transformation and free-weighting matrix are not employed for less conservatism. Finally, an example is provided to demonstrate the effectiveness of the proposed results.
A Hybrid Control Strategy for Quadratic Boost Converters with Inductor Currents Estimation
2020
International audience; This paper deals with a control strategy for a DC-DC quadratic boost converter. In particular, a hybrid control scheme is proposed to encompass a control law and an observer for the estimation of the system states, based only on the measurements of the input and output voltages. Differently from classical control methods, where the controller is designed from a small-signal model, here the real model of the system is examined without considering the average values of the discrete variables. Using hybrid dynamical system theory, asymptotic stability of a neighborhood of the equilibrium point is established, ensuring practical stability of the origin, which contains es…
P-FCM: a proximity-based fuzzy clustering for user-centered web applications
2003
Abstract In last years, the Internet and the web have been evolved in an astonishing way. Standard web search services play an important role as useful tools for the Internet community even though they suffer from a certain difficulty. The web continues its growth, making the reliability of Internet-based information and retrieval systems more complex. Nevertheless there has been a substantial analysis of the gap between the expected information and the returned information, the work of web search engine is still very hard. There are different problems concerning web searching activity, one among these falls in the query phase. Each engine provide an interface which the user is forced to le…