Freedom PreethaminMathematical MusingsThe Timeless Elegance of Mathematics“Why, oh why, do you use math equations in your writings?”1d ago1d ago

Freedom PreethaminMathematical MusingsUnderstanding Green’s Theorem: A Comprehensive GuideGreen’s Theorem is one of the cornerstone results in vector calculus, bridging the concepts of line integrals and double integrals. It…2d ago2d ago

Freedom PreethaminAutonomous AgentsPart 2 : SciML — A Mathematical account of PDE Solvers, Discoverers and Operator LearningThe integration of machine learning with scientific modeling, known as Scientific Machine Learning (SciML), has ushered in transformative…2d ago2d ago

Freedom PreethaminQuantum MysteriesThe Quantum-Classical Boundary: Exploring Decoherence and the Emergence of ClassicalityThe transition from quantum to classical behavior remains one of the most profound and challenging issues in quantum mechanics. At its…4d ago4d ago

Freedom PreethaminAutonomous AgentsPart 3: Biological Operators to Math Operators ~ Mixture of Operators for Modeling Genomic…Nature is modular and multi-scale. While natural systems exhibit chaos and complexity in the codomain with high variability, the natural…5d ago5d ago

Freedom PreethaminMeta MultiomicsPart 2: Biological Operators ~ Capturing the Effects of Synonymous SNPs Using Genomic AssaysAs an example of how to use foundational biological operators as discussed in Part 1, let us consider synonymous SNPs.5d ago5d ago

Freedom PreethaminMeta MultiomicsPart 1: Biological Operators ~ Genomic-Level Perturbations and Their Downstream Effects5d ago5d ago

Freedom PreethaminThe SimulacrumWhy You Should Never Ask a Biologist How to Cross the Road6d ago6d ago

Freedom PreethaminAutonomous AgentsPart 1: SciML — Why Transformers Fall Short in Scientific ComputingTransformer based models like LLMs have demonstrated remarkable prowess in natural language processing tasks. However, their limitations…Jul 7Jul 7

Freedom PreethaminMathematical MusingsMathematical Intuition for Gene Expression Modeling using Graph Dynamical SystemsGene expression analysis through the lens of graph dynamical systems offers profound insights into the complex interactions that govern…Jul 6Jul 6