arXiv subjects

Ibrahima Faye

Publications and source records attributed to Ibrahima Faye.

15 recordsLinked to original sources

arXiv2025

Averaging principle for slow-fast fractional stochastic differential equations

We prove the averaging principle for a class of stochastic systems. The slow component is solution to a fractional differential equation, which is coupled with a fast component considered as solution to an ergodic stochastic differential equation driven by a standard Brownian motion. We establish the convergence of the slow component when the time-scale separation vanishes to the solution of the so-called averaged equation, which is an autonomous fractional differential equation, in the mean-square sense. Moreover, when the fast component does not depend on the slow component, we provide a rate of convergence depending on the order of the fractional derivative.

math.PR↗

arXiv2024

A Machine Learning Approach for Identifying Anatomical Biomarkers of Early Mild Cognitive Impairment

Alzheimer Disease poses a significant challenge, necessitating early detection for effective intervention. MRI is a key neuroimaging tool due to its ease of use and cost effectiveness. This study analyzes machine learning methods for MRI based biomarker selection and classification to distinguish between healthy controls and those who develop mild cognitive impairment within five years. Using 3 Tesla MRI data from ADNI and OASIS 3, we applied various machine learning techniques, including MATLAB Classification Learner app, nested cross validation, and Bayesian optimization. Data harmonization with polynomial regression improved performance. Consistent features identified were the entorhinal, hippocampus, lateral ventricle, and lateral orbitofrontal regions. For balanced ADNI data, Naive Bayes with z score harmonization performed best. For balanced OASIS 3, SVM with z score correction excelled. In imbalanced data, RUSBoost showed strong performance on ADNI and OASIS 3. Z score harmonization highlighted the potential of a semi automatic pipeline for early AD detection using MRI.

q-bio.NC↗

arXiv2024

Towards improving Alzheimer's intervention: a machine learning approach for biomarker detection through combining MEG and MRI pipelines

MEG are non invasive neuroimaging techniques with excellent temporal and spatial resolution, crucial for studying brain function in dementia and Alzheimer Disease. They identify changes in brain activity at various Alzheimer stages, including preclinical and prodromal phases. MEG may detect pathological changes before clinical symptoms, offering potential biomarkers for intervention. This study evaluates classification techniques using MEG features to distinguish between healthy controls and mild cognitive impairment participants from the BioFIND study. We compare MEG based biomarkers with MRI based anatomical features, both independently and combined. We used 3 Tesla MRI and MEG data from 324 BioFIND participants;158 MCI and 166 HC. Analyses were performed using MATLAB with SPM12 and OSL toolboxes. Machine learning analyses, including 100 Monte Carlo replications of 10 fold cross validation, were conducted on sensor and source spaces. Combining MRI with MEG features achieved the best performance; 0.76 accuracy and AUC of 0.82 for GLMNET using LCMV source based MEG. MEG only analyses using LCMV and eLORETA also performed well, suggesting that combining uncorrected MEG with z-score-corrected MRI features is optimal.

cs.LG↗

arXiv2023

Topological Derivative for Shallow Water Equations

Coastal erosion is a major and growing environmental problem describing the movement of sand caused by tides, waves or currents. Several phenomena contribute to the significant advance of the sea. These include climate change, with rising sea levels due to the melting of ice at the Earth's poles, the amplification of the tidal effect, leading to the transport of large masses of sand, storms, etc. We contribute to this problem by using topological shape optimization techniques applied to an PDE describing coastal erosion. We use Shallow water equations as a model.

math.NA↗

arXiv2023

Mathematical Modeling and Optimal Control of Untrue Information : Dynamic SEIZ in Online Social Networks

We propose to model the phenomenon of the spread of a rumor in this paper. We manipulate a model that is based on SEIR model that specializes in spreading rumors. In the second part, we introduce a control strategy to fight against the diffusion of the rumor. Our main objective is to characterize the three optimal controls that minimize the number of spreaders, susceptibles who enter and spread the rumor, and skeptics. For that matter, using the maximum principle of Pontryagin, we prove the existence and give characterization of our controls. To illustrate the theoretical results obtained, numerical simulations are given to concretize our approach.

cs.CY↗

arXiv2022

Min max method, shape, topological derivatives, averaged Lagrangian, homogenization, two scale convergence, Helmholtz equation

In this paper, we perform a rigourous version of shape and topological derivatives for optimizations problems under constraint Helmoltz problems. A shape and topological optimization problem is formulated by introducing cost functional. We derive first by considering the lagradian method the shape derivative of the functional. It is also proven a topological derivative with the same approach. An application to several unconstrained shape functions arising from differential geometry are also given.

math.OC↗

arXiv2022

Stochastic differential equations driven by relative martingales

This paper contributes to the study of relative martingales. Specifically, for a closed random set $H$, they are processes null on $H$ which decompose as $M=m+v$, where $m$ is a càdlàg uniformly integrable martingale and, $v$ is a continuous process with integrable variations such that $v_{0}=0$ and $dv$ is carried by $H$. First, we extend this notion to stochastic processes not necessarily null on $H$, where $m$ is considered local martingale instead of a uniformly integrable martingale. Thus, we provide a general framework for the new larger class of relative martingales by presenting some structural properties. Second, as applications, we construct solutions for skew Brownian motion equations using continuous stochastic processes of the above mentioned new class. In addition, we investigate stochastic differential equations driven by a relative martingale.

math.PR↗

arXiv2022

On shape and topological optimization problems with constraints Helmholtz equation and spectral problems

Coastal erosion describes the displacement of sand caused by the movement induced by tides, waves or currents. Some of its wave phenomena are modeled by Helmholtz-type equations. Our purposes, in this paper are, first, to study optimal shapes obstacles to mitigate sand transport under the constraint of the Helmholtz equation. And the second side of this work is related to Dirichlet and Neumann spectral problems.We show the existence of optimal shapes in a general admissible set of quasi open sets. And necessary optimality conditions of first order are given in a regular framework.

math.NA↗

arXiv2021

Averaging Principle for Backward Stochastic Differential Equations driven both standard and fractional Brownian motions

Stochastic averaging for a class of backward stochastic differential equations driven by both standard and fractional Brownian motions (SFrBSDEs in short), is investigated. An averaged SFrBSDEs for the original SFrBSDEs is proposed, and their solutions are quantitatively compared. Under some appropriate assumptions, the solutions to original systems can be approximated by the solutions to averaged stochastic systems in the sense of mean square and also in probability.

math.PR↗

arXiv2016

Homogenization and transport equations: the case of desert and sand piles

In this paper we build models for short-term, mean-term and long-term dynamics of dune in desert. They are models that are degenerated parabolic equations which are, moreover, singularly perturbed. We, then give existence and uniqueness results for the models, followed by homogenization ones and a corrector result is given.

math.AP↗

arXiv2015

Some New Generalized Results on Ostrowski Type Integral Inequalities With Application

The aim of this paper is to establish some new inequalities similar to the Ostrowski's inequalities which are more generalized than the inequalities of Dragomir and Cerone. The current article obtains bounds for the deviation of a function from a combination of integral means over the end intervals covering the entire interval. Some new purterbed results are obtained. Application for cumulative distribution function is also discussed.

math.CA↗

arXiv2015

A generalization of Ostrowski type inequality for mappings whose second derivatives belong to L$_{1}\left(a,b\right) $ and applications

In this paper, we will improve and generalize inequality of Ostrowski type for mappings whose second derivatives belong to L$_{1}\left(a,b\right) $ . Some well known inequalities can be derived as special cases. In addition, perturbed mid-point inequality and perturbed trapezoid inequality are also obtained. The obtained inequalities have immediate applications in numerical integration where new estimates are obtained for the remainder term of the trapezoid and midpoint formula. Applications to some special means are also investigated.

math.CA↗

arXiv2013

Two-Scale numerical simulation of sand transport problems

In this paper we consider a model for short term dynamics of dunes in tidal area. We construct a Two-Scale Numerical Method based on the fact that the solution of the equation which has oscillations Two-Scale converges to the solution of a well-posed problem. This numerical method uses on Fourier series.

math.NA↗

arXiv2011

Long term behaviour of singularly perturbed parabolic degenerated equation

In this paper we consider models for short-term, mean-term and long-term morphodynamics of dunes and megariples. We give an existence and uniqueness result for long term dynamics of dunes. This result is based on a time-space periodic solution existence result for degenerated parabolic equation that we set out. Finally the mean-term and long-term models are homogenized.

math.AP↗

arXiv2010

Singularly perturbed degenerated parabolic equations and application to seabed morphodynamics in tided environment

In this paper we build models for short-term, mean-term and long-term dynamics of dune and megariple morphodynamics. They are models that are degenerated parabolic equations which are, moreover, singularly perturbed. We, then give an existence and uniqueness result for the short-term and mean-term models. This result is based on a time-space periodic solution existence result for degenerated parabolic equation that we set out. Finally the short-term model is homogenized.

math.AP↗