Problem

Retail inventory forecasting lacks a rigorous multi-dimensional benchmark evaluating accuracy, complexity, robustness, and stability simultaneously.

Approach

• ›Designed 4-dimension evaluation framework: RMSE accuracy, forecast stability under noise, model complexity cost, cross-dataset generalizability
• ›Applied to primary retail dataset and Walmart secondary validation
• ›Identified ARIMA optimal hyperparameter regimes across all four dimensions simultaneously

Problem

RL agents trained on stationary environments fail in deployment when the environment drifts — distribution shift at episode boundaries is the root cause.

Approach

• ›Formalized using forecast posterior as initial-state distribution each episode (Theorem 3.7: SNRf sample complexity bound)
• ›Proved Trajectory-Tube Contraction (Lemma 3.5): variance contracts uniformly across full episode horizon
• ›Validated on M5 benchmark — 3,049 SKUs, 5.4M records, 20 random seeds, p < 0.001

Problem

Drug discovery lacks a unified survey mapping how GNNs and topological data analysis jointly reshape molecular screening pipelines.

Approach

• ›Surveyed TDA persistent homology methods for molecular property prediction and binding affinity estimation
• ›Analyzed GNN architecture families (MPNN, SchNet, DimeNet) for atomistic and crystallographic modeling
• ›Mapped mathematical abstractions to experimental validation workflows and wet-lab feedback loops

Problem

There is no systematic review of how AI is augmenting discovery in pure mathematics and theoretical physics.

Approach

• ›Analyzed AI conjecture generation across the Langlands program and topological quantum field theory
• ›Reviewed transformer-based formal proof assistants (Lean4, Coq) combined with LLM guidance
• ›Mapped AI impact on elliptic curve cryptography and algebraic geometry research workflows

Problem

Transit surveys introduce detection bias that can distort estimates of habitable-zone exoplanet occurrence.

Approach

• ›Built a three-model framework combining Bayesian MCMC, Random Forest, and Logistic Regression
• ›Corrected survey bias across NASA exoplanet records and identified PLATO mission candidates
• ›Evaluated habitability classification with recall-focused metrics

Problem

Modern supply chains need a practical architecture connecting forecasting, automation, traceability, and ERP operations.

Approach

• ›Mapped ARIMA/LSTM/Transformer forecasting into an end-to-end digital supply chain blueprint
• ›Integrated IoT sensing, blockchain traceability, RPA automation, and SAP S/4HANA ERP concepts
• ›Outlined implementation layers for operational decision-making and resilience

Problem

Existing RL state representations ignore probabilistic demand structure, causing poor generalization under uncertainty.

Approach

• ›Modeled state as a density matrix (quantum-inspired) to encode distributional information compactly
• ›Derived theoretical guarantees for convergence and sample complexity in demand-uncertain MDPs
• ›Benchmarked on retail demand datasets against standard MDP baselines

Problem

ARIMA and modern forecasting methods are compared without controlling for demand regime, masking when each method is actually superior.

Approach

• ›Segmented retail demand data by regime (stable, seasonal, volatile, sparse)
• ›Benchmarked ARIMA, ETS, LightGBM, LSTM, and TFT across all regimes on small-scale retail data
• ›Identified statistically significant regime-performance interactions

Problem

Practitioners lack a principled heuristic for selecting which forecasting model to use on short retail demand series.

Approach

• ›Computed autocorrelation features across a corpus of short retail demand series
• ›Benchmarked ARIMA, ETS, LightGBM, and LSTM as a function of autocorrelation structure
• ›Demonstrated autocorrelation is the dominant first-order predictor of model ranking

Problem

Retail optimization needs decisions that stay robust when demand, stockouts, and replenishment constraints move together.

Approach

• ›Combined Temporal Fusion Transformers for demand forecasting with QAOA for combinatorial allocation
• ›Used Conservative Q-Learning to keep policies grounded in observed operational data
• ›Wrapped the system in a FastAPI and Docker stack for repeatable experimentation

Problem

Competitive applications require tailored CVs and follow-through, but manual customization does not scale.

Approach

• ›Built an autonomous workflow for generating role-specific CV material
• ›Stored generated assets in S3 so outputs are reproducible and easy to retrieve
• ›Designed the system as an end-to-end deployed Next.js application

Problem

Exoplanet habitability estimates can be distorted by transit-survey detection bias.

Approach

• ›Combined Bayesian MCMC, Random Forest, and Logistic Regression into a three-model framework
• ›Corrected bias across 4,510 NASA exoplanets before ranking candidate planets
• ›Prioritized recall for habitable-zone candidates to avoid missing promising targets

Problem

Model evaluation pipelines need reliable scoring and simulation infrastructure beyond one-off notebooks.

Approach

• ›Implemented a custom Neural Bradley-Terry architecture for comparative prediction
• ›Ran Monte Carlo simulation at 10K iterations to stress-test outcomes
• ›Used cloud-backed persistence for experiment tracking and reproducibility

Problem

Biophysical neuron simulation becomes slow when detailed models are run at large scale.

Approach

• ›Designed GPU-parallel simulation paths for computationally heavy neuron dynamics
• ›Used Python and Julia to balance rapid iteration with numerical performance
• ›Targeted CUDA acceleration for throughput-sensitive simulation workloads

Problem

Portfolio allocation is sequential and non-stationary, making static rebalancing rules brittle.

Approach

• ›Modeled allocation as a reinforcement learning problem over changing market states
• ›Used deep RL tooling to learn dynamic rebalancing policies
• ›Compared policy behavior against conventional portfolio optimization baselines