arXiv subjects

Shahid Khan

Publications and source records attributed to Shahid Khan.

5 recordsLinked to original sources

arXiv2026

Multiscale Asymptotic Analysis of Kernel-Smoothed Solutions to Fractional Riesz-Bessel Equations with Random Initial Conditions

This paper investigates fractional Riesz-Bessel equations with random initial conditions that exhibit either classical or cyclic long-range dependence. It studies zoom-in asymptotics for the corresponding solutions and establishes multiscaling limit theorems. It is known that for similar problems, non-degenerate multiscaling limits may not exist in general. The paper develops a kernel-smoothing approach for these equations and obtains non-degenerate limit fields under suitable normalisation and rescaling. It proves that the kernel-smoothed solutions converge weakly to Gaussian random fields, which are non-stationary in both time and space. Their spectral representations and covariance functions are derived. The paper also analyses the regularity and dependence structure of the limit fields. In particular, under appropriate general assumptions on the smoothing kernel, the limits exhibit long-range dependence in time and short-range dependence in space. Numerical examples for the case of Mat\'ern-type kernels are provided to illustrate the theoretical results.

math.PR↗

arXiv2022

BDDs Strike Back: Efficient Analysis of Static and Dynamic Fault Trees

Fault trees are a key model in reliability analysis. Classical static fault trees (SFT) can best be analysed using binary decision diagrams (BDD). State-based techniques are favorable for the more expressive dynamic fault trees (DFT). This paper combines the best of both worlds by following Dugan's approach: dynamic sub-trees are analysed via model checking Markov models and replaced by basic events capturing the obtained failure probabilities. The resulting SFT is then analysed via BDDs. We implemented this approach in the Storm model checker. Extensive experiments (a) compare our pure BDD-based analysis of SFTs to various existing SFT analysis tools, (b) indicate the benefits of our efficient calculations for multiple time points and the assessment of the mean-time-to-failure, and (c) show that our implementation of Dugan's approach significantly outperforms pure Markovian analysis of DFTs. Our implementation Storm-dft is currently the only tool supporting efficient analysis for both SFTs and DFTs.

cs.SE↗

arXiv2021

Machine Learning Application for $\mathbfΛ$ Hyperon Reconstruction in CBM at FAIR

The Compressed Baryonic Matter experiment at FAIR will investigate the QCD phase diagram in the region of high net-baryon densities. Enhanced production of strange baryons, such as the most abundantly produced $Λ$ hyperons, can signal transition to a new phase of the QCD matter. In this work, the CBM performance for reconstruction of the $Λ$ hyperon via its decay to proton and $π^{-}$ is presented. Decay topology reconstruction is implemented in the Particle-Finder Simple (PFSimple) package with Machine Learning algorithms providing efficient selection of the decays and high signal to background ratio.

physics.ins-det↗

arXiv2020

Various Ways to Quantify BDMPs

A Boolean logic driven Markov process (BDMP) is a dependability analysis model that defines a continuous-time Markov chain (CTMC). This formalism has high expressive power, yet it remains readable because its graphical representation stays close to standard fault trees. The size of a BDMP is roughly speaking proportional to the size of the system it models, whereas the size of the CTMC specified by this BDMP suffers from exponential growth. Thus quantifying large BDMPs can be a challenging task. The most general method to quantify them is Monte Carlo simulation, but this may be intractable for highly reliable systems. On the other hand, some subcategories of BDMPs can be processed with much more efficient methods. For example, BDMPs without repairs can be translated into dynamic fault trees, a formalism accepted as an input of the STORM model checker, that performs numerical calculations on sparse matrices, or they can be processed with the tool FIGSEQ that explores paths going to a failure state and calculates their probabilities. BDMPs with repairs can be quantified by FIGSEQ (BDMPs capturing quickly and completely repairable behaviors are solved by a different algorithm), and by the I&AB (Initiator and All Barriers) method, recently published and implemented in a prototype version of RISKSPECTRUM PSA. This tool, based exclusively on Boolean representations looks for and quantifies minimal cut sets of the system, i.e., minimal combinations of component failures that induce the loss of the system. This allows a quick quantification of large models with repairable components, standby redundancies and some other types of dependencies between omponents. All these quantification methods have been tried on a benchmark whose definition was published at the MARS 2017 workshop: the model of emergency power supplies of a nuclear power plant. In this paper, after a recall of the theoretical principles of the various quantification methods, we compare their performances on that benchmark.

cs.CE↗

arXiv2018

Supervised classification for object identification in urban areas using satellite imagery

This paper presents a useful method to achieve classification in satellite imagery. The approach is based on pixel level study employing various features such as correlation, homogeneity, energy and contrast. In this study gray-scale images are used for training the classification model. For supervised classification, two classification techniques are employed namely the Support Vector Machine (SVM) and the Naive Bayes. With textural features used for gray-scale images, Naive Bayes performs better with an overall accuracy of 76% compared to 68% achieved by SVM. The computational time is evaluated while performing the experiment with two different window sizes i.e., 50x50 and 70x70. The required computational time on a single image is found to be 27 seconds for a window size of 70x70 and 45 seconds for a window size of 50x50.

cs.LG↗