Abdullah Malik

Abdullah Malik

Graph Data Scientist

Publications

Simplicial Methods in Graph Machine Learning

Published in Florida State University, 2024

The Weisfeiler-Leman algorithm is a powerful test of graph isomorphism, and works by iteratively isolating clusters of nodes via a coloring scheme based on binary relationships. This refinement process is akin to message passing on graph neural networks. Graph neural networks are paradigms of computation that yield powerful results for structured data based on binary relationships, and therefore their expressivity shares the limitations of the Weisfeiler-Leman test. One way to circumvent this limitation relies on identifying and working with higher relationships within the data, or by finding a better refinement criterion that can be implemented on a machine. In this thesis, we put forward data structures closely based on the identification of such higher relationships via Kan Extensions of structured data built on binary relations. These data structures are well known in algebraic topology as Simplicial Sets; the theoretical underpinnings based on the combinatorics of simplicial sets and directed graphs are explored in this thesis and, based on of it, algorithms are introduced that can identify higher-order relations. A metric that can serve as a quantification for community detection tools is also introduced, as well as the notion of a pseudoterminal vertex as a proxy for these higher relations. This helps us balance the variance-bias tradeoff necessary for generalizability of the architecture. We introduce functors that show how these higher relationships can be modelled and expanded. Finally, we propose three neural networks that benefit from the topology of these nonbinary relations. These neural networks can be ported into the standard graph neural network library to augment feature classification in a semisupervised manner. All source code is available at https://github.com/abdullahnaeemmalik/simplicial-methods-in-graph-machine-learning

Recommended citation: Malik, A.N. Simplicial Methods in Graph Machine Learning. Diss. Florida State University, 2024. https://www.proquest.com/dissertations-theses/simplicial-methods-graph-machine-learning/docview/3064071895/se-2?accountid=4840

Technology Embedded Hybrid Learning

Published in Preprints.org, 2018

This preprint is a culmination of the proposal that marked the introduction of hybrid courses to COMSATS Institute of Information Technology, and the evolution of its model as an amalgam of the traditional class room model augmented with the aid of state-of-the-art online learning technologies. Two hybrid courses were offered to full-time students, with all the courses in traditional classroom mode, except one course offered as hybrid course, with both synchornous and asynchronous learning modalities. A survey and its results of the pilot program are presented.

Recommended citation: Behzad, M.; Adnan, N.; Malik, A.N..; Merchant, S.A. Technology-Embedded Hybrid Learning. Preprints 2018, 2018030229. https://doi.org/10.20944/preprints201803.0229.v2 https://www.preprints.org/manuscript/201803.0229/v2

Effects of Gender on the Performance of Microenterprises in Pakistan

Published in The International Journal of Humanities & Social Studies, 2017

In Pakistan, there has been a surge in women entrepreneurship, either as a sole proprietorship or joint partnership mostly with male family members. Using non-randomized data, in this paper we compare the impact of gender of owner on the performance of the enterprise in Pakistan. Our results show an intricate association between the gender of the owner and the performance of the enterprise. While there is no significant difference in the performance with respect to profitability of the business, however, female owned enterprises have shown more employment growth as compared to male owned enterprises. Results of OLS regression on the basis of gender show that common factors that affect the performance of the enterprises have assorted effects for male-owned and female-owned enterprises. For female entrepreneurs, education in the most significant factor in their business success.

Recommended citation: Xing, Y. H., Farooq, M. U., & Malik, A. N. Effects of Gender on the Performance of Microenterprises in Pakistan. The International Journal of Humanities & Social Studies, 5(11). 2017 https://www.internationaljournalcorner.com/index.php/theijhss/article/view/125536

Orthomodularity and the incompatibility of Relativity and Quantum mechanics

Published in Springer, 2016

We show that orthomodularity in general and non-existence of isotropic vectors in particular decisively yield the geometry of quantum mechanics and that a fundamental reason why quantum mechanics and relativity cannot be unified is because of the non-existence of isotropic vectors

Recommended citation: Malik, A.N., Kamran, T. Orthomodularity and the incompatibility of relativity and quantum mechanics. Quantum Stud.: Math. Found. 4, 171–179 (2017). https://doi.org/10.1007/s40509-016-0092-8 https://link.springer.com/article/10.1007/s40509-016-0092-8

Operator Algebras and the Foundations of Quantum Mechanics

Published in Quaid-i-Azam University, 2016

The purpose of this thesis is to analyse the Hilbert Space requirement for Quantum Mechanics. In particular, we justify sharp observables but question the requirement of completeness of the inner product space and the underlying field. We view our mathematical framework as a dynamical theory but with a mysterious probabilistic interpretation instead of the otherway round. Whenever we speak of Quantum Mechanics, we mean Non-relativistic Quantum Mechanics. To make things less messy, we assume associativity through-out. No attempt has been made to refer to QFT and statistical quantum mechanics and we use conventional mathematical symbols instead of Dirac’s formalism.

Recommended citation: Malik, A.N. Operator Algebras and Foundations of Quantum Mechanics. Diss. Quaid-e-Azam University, Islamabad, 2016 http://abdullahnaeemmalik.github.io/files/Operator Algebras and the Foundations of Quantum Mechanics.pdf

Engineering Deutsch-Jozsa Algorithm in Cavity QED via Bragg Regime

Published in COMSATS Institute of Information Technology, 2012

The theory of quantum mechanics, developed as a limiting case to classical mechanics, notwithstanding its interpretive difficulties, has with it the elegance for paving way to a variety of applications. One such application is the implementation of a working Quantum Computer. The push one receives for using quantum principles as a measure of information and execution of algorithms is from quantum parallelism. It seems as though nature hides its enormous calculations. One such realisation of the power of Quantum Parallelism can be seen with quantum optics when one considers engineering a Quantum Computer, choosing techniques of cavity QED amongst many other competitors. The Deutsch-Josza algorithm, although of little practical signi cance, is an encouraging example which greatly reduces the time required for a specific function to be determined completely, when compared with its classical counterpart. The Hadamard gate has been physically realised, and so has the other unitary transformations in the Deutsch-Jozsa algorithm using different times of interactions in the cavity. Also, a generalisation of the Deutsch-Jozsa algorithm has been discussed, which might pave way for a working model of a Quantum Computer.

Recommended citation: Malik, A.N. Engineering Deutsch-Jozsa Algorithm in Cavity QED via Bragg Regime. Diss. COMSATS Institute of Information Technology, Islamabad, 2012. http://abdullahnaeemmalik.github.io/files/Engineering the Deutsch-Jozsa Algorithm.pdf