arXiv subjects

Ibrahim Hassan

Publications and source records attributed to Ibrahim Hassan.

3 recordsLinked to original sources

arXiv2026

Tropical Bi-Objective Pseudolinear Optimization as Parametric Mean-Payoff Games

We extend the parametric mean-payoff game framework of Parsons et al. to bi-objective tropical pseudolinear optimization with general two-sided constraints. The problem is to simultaneously minimize two tropical pseudolinear objectives over the feasible set of a general two-sided system U otimes x oplus b is less than or equal to V otimes x oplus d, we characterize the Pareto front via a parametric mean-payoff game in two parameters ( lambda 1, lambda 2). The feasibility region R is convex and the Pareto front P is a convex piecewise-linear curve with finitely many breakpoints, these properties are natural extensions of the single-parameter case to two parameters. In addition, we give as a new result, the joint denominator bound: the cycle coefficients satisfy k 1( gamma ) + k 2( gamma ) is less than or equal to 2 for any elementary cycle gamma, yielding | Delta | is less than or equal to 2 for every 2 times 2 Newton system, except in the fully decoupled case, and implying that all breakpoints have half-integer coordinates for integer data. Optimality and infeasibility certificates are given in terms of the cycle structure of the parametric game. Two algorithms are developed, a directional bisection algorithm (O(n squared (n+m) log M) per direction) and a Newton scheme tracing the complete Pareto front via 2 times 2 linear solves in at most | S | steps, independent of M. The directional bisection algorithm is pseudo-polynomial in n, m and M. The Newton scheme is independent of M but requires up to |S| steps, where |S| is exponential in n. Lastly, we give numerical experiments on random instances to confirm the directional bisection complexity bound exactly; the Newton scheme's worst-case bound is not attained by random instances but is shown to be tight via explicit adversarial constructions.

math.OC↗

arXiv2020

Systematic Comparison of the Influence of Different Data Preprocessing Methods on the Performance of Gait Classifications Using Machine Learning

Human movements are characterized by highly non-linear and multi-dimensional interactions within the motor system. Recently, an increasing emphasis on machine-learning applications has led to a significant contribution to the field of gait analysis, e.g., in increasing the classification performance. In order to ensure the generalizability of the machine-learning models, different data preprocessing steps are usually carried out to process the measured raw data before the classifications. In the past, various methods have been used for each of these preprocessing steps. However, there are hardly any standard procedures or rather systematic comparisons of these different methods and their impact on the classification performance. Therefore, the aim of this analysis is to compare different combinations of commonly applied data preprocessing steps and test their effects on the classification performance of gait patterns. A publicly available dataset on intra-individual changes of gait patterns was used for this analysis. Forty-two healthy participants performed 6 sessions of 15 gait trials for 1 day. For each trial, two force plates recorded the 3D ground reaction forces (GRFs). The data was preprocessed with the following steps: GRF filtering, time derivative, time normalization, data reduction, weight normalization and data scaling. Subsequently, combinations of all methods from each preprocessing step were analyzed by comparing their prediction performance in a six-session classification using Support Vector Machines, Random Forest Classifiers, Multi-Layer Perceptrons, and Convolutional Neural Networks. In conclusion, the present results provide first domain-specific recommendations for commonly applied data preprocessing methods and might help to build more comparable and more robust classification models based on machine learning that are suitable for a practical application.

cs.LG↗

arXiv2020

Stochastic homogenization of Hamilton-Jacobi equations on a junction

We consider the specified stochastic homogenization of first order evolutive Hamilton-Jacobi equations on a very simple junction, i.e the real line with a junction at the origin. Far from the origin, we assume that the considered hamiltonian is closed to given stationary ergodic hamiltonians (which are different on the left and on the right). Near the origin, there is a perturbation zone which allows to pass from one hamiltonian to the other. The main result of this paper is a stochastic homogenization as the length of the transition zone goes to zero. More precisely, at the limit we get two deterministic right and left hamiltonians with a deterministic junction condition at the origin. The main difficulty and novelty of the paper come from the fact that the hamiltonian is not stationary ergodic. Up to our knowledge, this is the first specified stochastic homogenization result. This work is motivated by traffic flow applications.

math.AP↗