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Abdul Wahab

Publications and source records attributed to Abdul Wahab.

At least 37 records · Page 2Linked to original sources
arXiv2020

Comments on "Generalization of the gradient method with fractional order gradient direction"

In this paper, a detrimental mathematical mistake is pointed out in the proof of \textit{Theorem 1} presented in the paper\textit{ [Generalization of the gradient method with fractional order gradient direction, J. Franklin Inst., 357 (2020) 2514-2532]}. It is highlighted that the way the authors prove the convergence of the fractional extreme points of a real valued function to its integer order extreme points lacks correct and valid mathematical argument. Rest of the theorems contained in the paper are mostly announced without any proof relaying on that of Theorem 1.

math.OC↗
arXiv2020

Comments on "Design of fractional-order variants of complex LMS and NLMS algorithms for adaptive channel equalization"

The purpose of this note is to discuss some aspects of recently proposed fractional-order variants of complex least mean square (CLMS) and normalized least mean square (NLMS) algorithms in ``Design of Fractional-order Variants of Complex LMS and Normalized LMS Algorithms for Adaptive Channel Equalization'' [Nonlinear Dyn. 88(2), 839-858 (2017)]. It is observed that these algorithms do not always converge whereas they have apparently no advantage over the CLMS and NLMS algorithms whenever they converge. Our claims are based on analytical reasoning and are supported by numerical simulations.

math.OC↗
arXiv2020

E3-targetPred: Prediction of E3-Target Proteins Using Deep Latent Space Encoding

Understanding E3 ligase and target substrate interactions are important for cell biology and therapeutic development. However, experimental identification of E3 target relationships is not an easy task due to the labor-intensive nature of the experiments. In this article, a sequence-based E3-target prediction model is proposed for the first time. The proposed framework utilizes composition of k-spaced amino acid pairs (CKSAAP) to learn the relationship between E3 ligases and their target protein. A class separable latent space encoding scheme is also devised that provides a compressed representation of feature space. A thorough ablation study is performed to identify an optimal gap size for CKSAAP and the number of latent variables that can represent the E3-target relationship successfully. The proposed scheme is evaluated on an independent dataset for a variety of standard quantitative measures. In particular, it achieves an average accuracy of $70.63\%$ on an independent dataset. The source code and datasets used in the study are available at the author's GitHub page (https://github.com/psychemistz/E3targetPred).

q-bio.BM↗
arXiv2019

Smart Parking: IoT and Blockchain

Distributed ledger technology and IoT has revolutionized the world by finding its application in all the domains. It promises to transform the digital infrastructure which powers extensive evolutions and impacts a lot of areas. Vehicle parking is a major problem in major cities around the world in both developed and developing countries. The common problems are unavailability or shortage of parking spaces, no information about tariff and no mean of searching availability of parking space online. The struggle doesn't end even if an individual finds a spot, he is required to pay in cash. This traditional and manual process takes a lot of time and causes a lot of hassle. In this paper, we provide a novel solution to the parking problem using IoT and distributed ledger technology. This system is based on pervasive computing and provides auto check-in and check-out. The user can control the system and their profile using the app on their smartphone. The major advantage of the system is an easy and online payment method. Users can pay for their parking tickets using their credit cards from their smartphone app. This decreases their hassle of carrying cash and coins for purchasing parking tickets. Smart Parking will optimize the parking mechanism, save time, reduce traffic and pollution, and provide an enhanced user experience. It is robust, secure, scalable and automated using the combination of cutting-edge technologies.

cs.DC↗
arXiv2019

Deep Learning Diffuse Optical Tomography

Diffuse optical tomography (DOT) has been investigated as an alternative imaging modality for breast cancer detection thanks to its excellent contrast to hemoglobin oxidization level. However, due to the complicated non-linear photon scattering physics and ill-posedness, the conventional reconstruction algorithms are sensitive to imaging parameters such as boundary conditions. To address this, here we propose a novel deep learning approach that learns non-linear photon scattering physics and obtains an accurate three dimensional (3D) distribution of optical anomalies. In contrast to the traditional black-box deep learning approaches, our deep network is designed to invert the Lippman-Schwinger integral equation using the recent mathematical theory of deep convolutional framelets. As an example of clinical relevance, we applied the method to our prototype DOT system. We show that our deep neural network, trained with only simulation data, can accurately recover the location of anomalies within biomimetic phantoms and live animals without the use of an exogenous contrast agent.

cs.CV↗
arXiv2019

Comments on "Fractional Extreme Value Adaptive Training Method: Fractional Steepest Descent Approach"

In this comment, we raise serious concerns over the derivation of the rate of convergence of fractional steepest descent algorithm in Fractional Adaptive Learning (FAL) approach presented in `Fractional Extreme Value Adaptive Training Method: Fractional Steepest Descent Approach' [IEEE Trans. Neural Netw. Learn. Syst., vol. 26, no. 4, pp. 653--662, April 2015]. We substantiate that the estimate of the rate of convergence is grandiloquent. We also draw attention towards a critical flaw in the design of the algorithm stymieing its applicability for broad adaptive learning problems. Our claims are based on analytical reasoning supported by experimental results.

math.OC↗
arXiv2018

Survey of Consensus Protocols

Distributed ledger technology has gained wide popularity and adoption since the emergence of bitcoin in 2008 which is based on proof of work (PoW). It is a distributed, transparent and immutable database of records of all the transactions or events that have been shared and executed among the participants. All the transactions are verified and maintained by multiple nodes across a network without a central authority through a distributed cryptographic mechanism, a consensus protocol. It forms the core of this technology that not only validates the information appended to the ledger but also ensures the order in which it is appended across all the nodes. It is the foundation of its security, accountability and trust. While many researchers are working on improving the current protocol to be quantum resistant, fault-tolerant, and energy-efficient. Others are focused on developing different variants of the protocol, best suited for specific use cases. In this paper, we shall review different consensus protocols of distributed ledger technologies and their implementations. We shall also review their properties, concept and similar-work followed by a brief analysis.

cs.DC↗
arXiv2018

A Mathematical Framework for Deep Learning in Elastic Source Imaging

An inverse elastic source problem with sparse measurements is of concern. A generic mathematical framework is proposed which incorporates a low- dimensional manifold regularization in the conventional source reconstruction algorithms thereby enhancing their performance with sparse datasets. It is rigorously established that the proposed framework is equivalent to the so-called \emph{deep convolutional framelet expansion} in machine learning literature for inverse problems. Apposite numerical examples are furnished to substantiate the efficacy of the proposed framework.

math.OC↗
arXiv2017

Topological Sensitivity Based Far-Field Detection of Elastic Inclusions

The aim of this article is to present and rigorously analyze topological sensitivity based algorithms for detection of diametrically small inclusions in an isotropic homogeneous elastic formation using single and multiple measurements of the far-field scattering amplitudes. A $L^2-$cost functional is considered and a location indicator is constructed from its topological derivative. The performance of the indicator is analyzed in terms of the topological sensitivity for location detection and stability with respect to measurement and medium noises. It is established that the location indicator does not guarantee inclusion detection and achieves only a low resolution when there is mode-conversion in an elastic formation. Accordingly, a weighted location indicator is designed to tackle the mode-conversion phenomenon. It is substantiated that the weighted function renders the location of an inclusion stably with resolution as per Rayleigh criterion.

math.NA↗
arXiv2017

Detection of Electromagnetic Inclusions using Topological Sensitivity

In this article a topological sensitivity framework for far field detection of a diametrically small electromagnetic inclusion is established. The cases of single and multiple measurements of the electric far field scattering amplitude at a fixed frequency are taken into account. The performance of the algorithm is analyzed theoretically in terms of its resolution and sensitivity for locating an inclusion. The stability of the framework with respect to measurement and medium noises is discussed. Moreover, the quantitative results for signal-to-noise ratio are presented. A few numerical results are presented to illustrate the detection capabilities of the proposed framework with single and multiple measurements.

math.NA↗
arXiv2017

A Joint Sparse Recovery Framework for Accurate Reconstruction of Inclusions in Elastic Media

A robust algorithm is proposed to reconstruct the spatial support and the Lamé parameters of multiple inclusions in a homogeneous background elastic material using a few measurements of the displacement field over a finite collection of boundary points. The algorithm does not require any linearization or iterative update of Green's function but still allows very accurate reconstruction. The breakthrough comes from a novel interpretation of Lippmann-Schwinger type integral representation of the displacement field in terms of unknown densities having common sparse support on the location of inclusions. Accordingly, the proposed algorithm consists of a two-step approach. First, the localization problem is recast as a joint sparse recovery problem that renders the densities and the inclusion support simultaneously. Then, a noise robust constrained optimization problem is formulated for the reconstruction of elastic parameters. An efficient algorithm is designed for numerical implementation using the Multiple Sparse Bayesian Learning (M-SBL) for joint sparse recovery problem and the Constrained Split Augmented Lagrangian Shrinkage Algorithm (C-SALSA) for the constrained optimization problem. The efficacy of the proposed framework is manifested through extensive numerical simulations. To the best of our knowledge, this is the first algorithm tailored for parameter reconstruction problems in elastic media using highly under-sampled data in the sense of Nyquist rate.

math.NA↗
arXiv2017

Two-Dimensional Elastic Scattering Coefficients and Enhancement of Nearly Elastic Cloaking

The concept of scattering coefficients has played a pivotal role in a broad range of inverse scattering and imaging problems in acoustic, and electromagnetic media. In view of their promising applications in inverse problems related to mathematical imaging and elastic cloaking, the notion of elastic scattering coefficients of an inclusion is presented from the perspective of boundary layer potentials and a few properties are discussed. A reconstruction algorithm is developed and analyzed for extracting the elastic scattering coefficients from multi-static response measurements of the scattered field in order to cater to inverse scattering problems. The decay rate, stability and error analyses, and the estimate of maximal resolving order in terms of the signal-to-noise ratio are discussed. Moreover, scattering-coefficients-vanishing structures are designed and their utility for enhancement of nearly elastic cloaking is elucidated.

math-ph↗
arXiv2015

Far field imaging of a dielectric inclusion

A non-iterative topological sensitivity framework for guaranteed far field detection of a dielectric inclusion is presented. The cases of single and multiple measurements of the electric far field scattering amplitude at a fixed frequency are taken into account. The performance of the algorithm is analyzed theoretically in terms of resolution, stability, and signal-to-noise ratio.

math-ph↗
arXiv2015

Stability and Resolution Analysis of Topological Derivative Based Localization of Small Electromagnetic Inclusions

The aim of this article is to elaborate and rigorously analyze a topological derivative based imaging framework for locating an electromagnetic inclusion of diminishing size from boundary measurements of the tangential component of scattered magnetic field at a fixed frequency. The inverse problem of inclusion detection is formulated as an optimization problem in terms of a filtered discrepancy functional and the topological derivative based imaging functional obtained therefrom. The sensitivity and resolution analysis of the imaging functional is rigorously performed. It is substantiated that the Rayleigh resolution limit is achieved. Further, the stability of the reconstruction with respect to measurement and medium noises is investigated and the signal-to-noise ratio is evaluated in terms of the imaginary part of free space fundamental magnetic solution.

math.OC↗
arXiv2014

Electromagnetic source localization with finite set of frequency measurements

A phase conjugation algorithm for localizing an extended radiating electromagnetic source from boundary measurements of the electric field is presented. Measurements are taken over a finite number of frequencies. The artifacts related to the finite frequency data are tackled with $l_1-$regularization blended with the fast iterative shrinkage-thresholding algorithm with backtracking of Beck & Teboulle.

math-ph↗
arXiv2014

Electromagnetic time reversal algorithms and source localization in lossy dielectric media

The problem of reconstructing the spatial support of an extended radiating electric current source density in a lossy dielectric medium from transient boundary measurements of the electric fields is studied. A time reversal algorithm is proposed to localize a source density from loss-less wave-field measurements. Further, in order to recover source densities in a lossy medium, we first build attenuation operators thereby relating loss-less waves with lossy ones. Then based on asymptotic expansions of attenuation operators with respect to attenuation parameter, we propose two time reversal strategies for localization. The losses in electromagnetic wave propagation are incorporated using the Debye's complex permittivity, which is well-adopted for low frequencies (radio and microwave) associated with polarization in dielectrics.

math-ph↗
arXiv2012

Localization, Stability, and Resolution of Topological Derivative Based Imaging Functionals in Elasticity

The focus of this work is on rigorous mathematical analysis of the topological derivative based detection algorithms for the localization of an elastic inclusion of vanishing characteristic size. A filtered quadratic misfit is considered and the performance of the topological derivative imaging functional resulting therefrom is analyzed. Our analysis reveals that the imaging functional may not attain its maximum at the location of the inclusion. Moreover, the resolution of the image is below the diffraction limit. Both phenomena are due to the coupling of pressure and shear waves propagating with different wave speeds and polarization directions. A novel imaging functional based on the weighted Helmholtz decomposition of the topological derivative is, therefore, introduced. It is thereby substantiated that the maximum of the imaging functional is attained at the location of the inclusion and the resolution is enhanced and it proves to be the diffraction limit. Finally, we investigate the stability of the proposed imaging functionals with respect to measurement and medium noises.

math.AP↗