Akshit Sharma | Searcharxiv

arXiv2026

Quadratic Gauge Transformation

Symmetries plays a significant role in understanding the conservation laws in Quantum field theories. Here, we attempted a quadratic type dimensionless gauge transformation to achieve the invariance in QFTs. We have shown the extensive study of invariance of complex scalar, Abelian and Non- Abelian theories and established the conservation laws. We included an explicit graphical analysis to invoke the invariance. This is studied in a physical context, where different field configurations correspond to the same physical state. The necessity of the covariant derivative is studied in detail, highlighting how it ensures consistent transformation under local symmetry operations. The meaning of covariance is clarified as the preservation of the form of physical laws under transformations.

hep-th↗

arXiv2024

FLEXIS: FLEXible Frequent Subgraph Mining using Maximal Independent Sets

Frequent Subgraph Mining (FSM) is the process of identifying common subgraph patterns that surpass a predefined frequency threshold. While FSM is widely applicable in fields like bioinformatics, chemical analysis, and social network anomaly detection, its execution remains time-consuming and complex. This complexity stems from the need to recognize high-frequency subgraphs and ascertain if they exceed the set threshold. Current approaches to identifying these patterns often rely on edge or vertex extension methods. However, these strategies can introduce redundancies and cause increased latency. To address these challenges, this paper introduces a novel approach for identifying potential k-vertex patterns by combining two frequently observed (k - 1)-vertex patterns. This method optimizes the breadth-]first search, which allows for quicker search termination based on vertices count and support value. Another challenge in FSM is the validation of the presumed pattern against a specific threshold. Existing metrics, such as Maximum Independent Set (MIS) and Minimum Node Image (MNI), either demand significant computational time or risk overestimating pattern counts. Our innovative approach aligns with the MIS and identifies independent subgraphs. Through the "Maximal Independent Set" metric, this paper offers an efficient solution that minimizes latency and provides users with control over pattern overlap. Through extensive experimentation, our proposed method achieves an average of 10.58x speedup when compared to GraMi and an average 3x speedup when compared to T-FSM

cs.DB↗