arXiv subjects

Ryad Ghanam

Publications and source records attributed to Ryad Ghanam.

13 recordsLinked to original sources

arXiv2026

Nilpotent Lie algebras of vector fields in three variables

We give a complete constructive description of all finite dimensional nilpotent Lie algebras of smooth vector fields in three variables, including intransitive algebras. The description is organized by the rank and dimension of the center, which serves as the key invariant. Since every nonabelian solvable algebra lives in the normalizer of a nilpotent algebra, our normal forms provide the essential building blocks for the study of all solvable algebras of vector fields in three variables.

math.RT↗

arXiv2026

Linear Models, Variable Selection, Artificial Intelligence

Variable selection in linear regression models has been a problem since hypothesis testing began. Which variables to include or exclude from a model is not an easy task. Techniques such as Forward, Back ward, Stepwise Regression sequentially add or delete variables from a model. Penalized likelihood methods such as AIC, BIC, etc. seek to choose variables that have a significant contribution to the likelihood. Penalized sum of square methods such as LASSO and Elastic Net have been used to penalize small coefficients to only allow variables with large coefficients in the model. This work introduces an Artificial Intelligence approach to model selection where an ANN is trained to determine the significance of the variables based on OLS estimates. A simulation study shows the accuracy across various sample sizes and variances. Furthermore, a simulation study is conducted to compare the performance of the approach against Forward, Backward, AIC, BIC and LASSO. The approach is illustrated using a dataset from the World Health Organization regarding Life Expectancy. A github link is provided to the pretrained ANN that can handle up to 100 predictor variables, the original WHO dataset and the subset used in this work.

stat.ME↗

arXiv2025

Essential Workers at Risk: An Agent-Based Model (SAFE-ABM) with Bayesian Uncertainty Quantification

Essential workers face elevated infection risks due to their critical roles during pandemics, and protecting them remains a significant challenge for public health planning. This study develops SAFE-ABM, a simulation-based framework using Agent-Based Modeling (ABM), to evaluate targeted intervention strategies, explicitly capturing structured interactions across families, workplaces, and schools. We simulate key scenarios such as unrestricted movement, school closures, mobility restrictions specific to essential workers, and workforce rotation, to assess their impact on disease transmission dynamics. To ensure robust uncertainty assessment, we integrate a novel Bayesian Uncertainty Quantification (UQ) framework, systematically capturing variability in transmission rates, recovery times, and mortality estimates. Our comparative analysis demonstrates that while general mobility restrictions reduce overall transmission, a workforce rotation strategy for essential workers, when combined with quarantine enforcement, most effectively limits workplace outbreaks and secondary family infections. Unlike other interventions, this approach preserves a portion of the susceptible population, resulting in a more controlled and sustainable epidemic trajectory. These findings offer critical insights for optimizing intervention strategies that mitigate disease spread while maintaining essential societal functions.

q-bio.QM↗

arXiv2023

Studying Disease Reinfection Rates, Vaccine Efficacy and the Timing of Vaccine Rollout in the context of Infectious Diseases

Qatar has undergone distinct waves of COVID-19 infections, compounded by the emergence of variants, posing additional complexities. This research uniquely delves into the varied efficacy of existing vaccines and the pivotal role of vaccination timing in the context of COVID-19. Departing from conventional modeling, we introduce two models that account for the impact of vaccines on infections, reinfections, and deaths. Recognizing the intricacy of these models, we use the Bayesian framework and specifically utilize the Metropolis-Hastings Sampler for estimation of model parameters. The study conducts scenario analyses on two models, quantifying the duration during which the healthcare system in Qatar could have potentially been overwhelmed by an influx of new COVID-19 cases surpassing the available hospital beds. Additionally, the research explores similarities in predictive probability distributions of cumulative infections, reinfections, and deaths, employing the Hellinger distance metric. Comparative analysis, employing the Bayes factor, underscores the plausibility of a model assuming a different susceptibility rate to reinfection, as opposed to assuming the same susceptibility rate for both infections and reinfections. Results highlight the adverse outcomes associated with delayed vaccination, emphasizing the efficacy of early vaccination in reducing infections, reinfections, and deaths. Our research advocates prioritizing early vaccination as a key strategy in effectively combating future pandemics. This study contributes vital insights for evidence-based public health interventions, providing clarity on vaccination strategies and reinforcing preparedness for challenges posed by infectious diseases. The data set and implementation code for this project is made available at \url{https://github.com/elizabethamona/VaccinationTiming}.

stat.AP↗

arXiv2021

Algorithms for Simultaneous Block Triangularization and Block Diagonalization of Sets of Matrices

In a recent paper, a new method was proposed to find the common invariant subspaces of a set of matrices. This paper invstigates the more general problem of putting a set of matrices into block triangular or block-diagonal form simultaneously. Based on common invariant subspaces, two algorithms for simultaneous block triangularization and block diagonalization of sets of matrices are presented. As an alternate approach for simultaneous block diagonalization of sets of matrices by an invertible matrix, a new algorithm is developed based on the generalized eigen vectors of a commuting matrix. Moreover, a new characterization for the simultaneous block diagonalization by an invertible matrix is provided. The algorithms are applied to concrete examples using the symbolic manipulation system Maple.

math.GM↗

arXiv2021

A novel procedure for constructing invariant subspaces of a set of matrices

A problem that is frequently encountered in a variety of mathematical contexts, is to find the common invariant subspaces of a single, or set of matrices. A new method is proposed that gives a definitive answer to this problem. The key idea consists of finding common eigenvectors for exterior powers of the matrices concerned. A convenient formulation of the Pl\"ucker relations is then used to ensure that these eigenvectors actually correspond to subspaces or provide the initial constraints for eigenvectors involving parameters. A procedure for computing the divisors of totally decomposable vector is also provided. Several examples are given for which the calculations are too tedious to do by hand and are performed by coding the conditions found into Maple.

math.GM↗

arXiv2021

Monitoring SEIRD model parameters using MEWMA for the COVID-19 pandemic with application to the State of Qatar

During the current COVID-19 pandemic, decision makers are tasked with implementing and evaluating strategies for both treatment and disease prevention. In order to make effective decisions, they need to simultaneously monitor various attributes of the pandemic such as transmission rate and infection rate for disease prevention, recovery rate which indicates treatment effectiveness as well as the mortality rate and others. This work presents a technique for monitoring the pandemic by employing an Susceptible, Exposed, Infected, Recovered Death model regularly estimated by an augmented particle Markov chain Monte Carlo scheme in which the posterior distribution samples are monitored via Multivariate Exponentially Weighted Average process monitoring. This is illustrated on the COVID-19 data for the State of Qatar.

stat.ME↗

arXiv2021

Lie symmetries of the canonical connection: codimension one abelian nilradical case

This paper studies the canonical symmetric connection $\nabla$ associated to any Lie group $G$. The salient properties of $\nabla$ are stated and proved. The Lie symmetries of the geodesic system of a general linear connection are formulated. The results are then applied to $\nabla$ in the special case where the Lie algebra $\g$ of $G$, has a codimension one abelian nilradical. The conditions that determine a Lie symmetry in such a case are completely integrated. Finally the results obtained are compared with some four-dimensional Lie groups whose Lie algebras have three-dimensional abelian nilradicals, for which the calculations were performed by MAPLE.

math.DG↗

arXiv2020

SEIRD Model for Qatar Covid-19 Outbreak: A Case Study

The Covid-19 outbreak of 2020 has required many governments to develop mathematical-statistical models of the outbreak for policy and planning purposes. This work provides a tutorial on building a compartmental model using Susceptibles, Exposed, Infected, Recovered and Deaths status through time. A Bayesian Framework is utilized to perform both parameter estimation and predictions. This model uses interventions to quantify the impact of various government attempts to slow the spread of the virus. Predictions are also made to determine when the peak Active Infections will occur.

stat.AP↗

arXiv2017

A Bayesian Estimation for the Fractional Order of the Differential Equation that Models Transport in Unconventional Hydrocarbon Reservoirs

The extraction of natural gas from the earth has been shown to be governed by differential equations concerning flow through a porous material. Recently, models such as fractional differential equations have been developed to model this phenomenon. One key issue with these models is estimating the fraction of the differential equation. Traditional methods such as maximum likelihood, least squares and even method of moments are not available to estimate this parameter as traditional calculus methods do not apply. We develop a Bayesian approach to estimate the fraction of the order of the differential equation that models transport in unconventional hydrocarbon reservoirs. In this paper, we use this approach to adequately quantify the uncertainties associated with the error and predictions. A simulation study is presented as well to assess the utility of the modeling approach.

stat.AP↗

arXiv2017

Embedding algorithms and applications to differential equations

Algorithms for embedding certain types of nilpotent subalgebras in maximal subalgebras of the same type are developed, using methods of real algebraic groups. These algorithms are applied to determine non-conjugate subalgebras of the symmetry algebra of the wave equation, which in turn are used to determine a large class of invariant solutions of the wave equation. The algorithms are also illustrated for the symmetry algebra of a classical system of differential equations considered by Cartan in the context of contact geometry.

math.RT↗

arXiv2017

Minimal Representations of Lie Algebras With Non-Trivial Levi Decomposition

We obtain minimal dimension matrix representations for each of the Lie algebras of dimension five, six, seven, and eight obtained by Turkowski that have a non-trivial Levi decomposition. The Key technique involves using subspace associated to a particular representation of semi-simple Lie algebra to help in the construction of the radical in the putative Levi decomposition.

math.RT↗

arXiv2014

Minimal matrix representations of five-dimensional Lie algebras

We obtain minimal dimension matrix representations for each indecomposable five-dimensional Lie algebra over $\R$ and justify in each case that they are minimal. In each case a matrix Lie group is given whose matrix Lie algebra provides the required representation.

math.DG↗