Projects & Research
My work in Mathematics, artificial intelligence and machine learning
Papers
This paper proposes a novel physics-inspired framework for generating Infinitely differentiable (C∞) smooth curves by continuously deforming a base curve (initially a straight line segment) under the influence of dynamically modulated gravitational fields. The deformation is driven by multiple gravitational control points, each defined by an adjustable magnitude and location.
This paper presents a comprehensive framework for approaching the long-standing Lonely Runner Conjecture (LRC). Originating in Diophantine approximation and ge- ometric view-obstruction problems, the conjecture posits that for any set of n runners on a unit circle with distinct constant speeds, each runner will, at some time, be at a distance of at least 1/(n+1) from all other runners.
This paper introduces a novel cryptographic framework leveraging high-dimensional po- lar coordinates to create quantum-resistant security mechanisms. Our proposed system, which we call PolarCrypt, provides robust encryption, key exchange, and digital signature capabilities while demonstrating superior computational efficiency compared to existing post-quantum alternatives.
Current Projects
This research introduces the Temporal-KAN-LSTM with Option-specific Attention (TKLA), a novel neural architecture for financial derivatives pricing that synergistically combines Kolmogorov- Arnold Networks (KANs) with Long Short-Term Memory (LSTM) networks.
This paper introduces Bézier Neural Networks (BNNs), a novel architecture paradigm designed to address these limitations. BNNs replace the standard affine transformations within neurons with the evaluation of parametric Bézier curves, whose shapes are intuitively controlled by learnable control points. This work provides a formal definition of the BNN architecture.