Skill UI

Offers MATLAB and GNU Octave guidance for matrix math, data import/export, visualizations, statistics, signal processing, differential equations, and general scripting—helpful when writing or translating MATLAB/Octave code and running scripts under either interpreter.

Guides symbolic mathematics work in Python, covering algebraic simplification, calculus, equation solving, linear algebra, physics, number theory, geometry, and code generation to deliver exact symbolic results instead of numeric approximations.

Rigorously dissects code and architecture through advanced mathematics—graph theory, category theory, stochastic systems, information theory, and formal invariants—to uncover hidden structure and optimize performance.

This skill automates the complex and tedious process of porting academic papers written in LaTeX from one publisher's journal template (e.g., Springer) to another (e.g., MDPI, IEEE). It executes a structured multi-stage workflow, including content extraction, structural mapping, systematic fixing of common LaTeX issues (like float placement and math environments), and final compilation to ensure the output adheres to the target journal's specifications.

polars-bio accelerates genomic interval math and bioinformatics I/O by combining Polars, Arrow, and DataFusion to handle BED/VCF/BAM/GFF/FASTA streams, SQL queries, and cloud storage with overlap, coverage, and nearest APIs plus streaming fallbacks.

This skill structures and derives research formulas, building coherent derivation packages from scattered notes. It helps users formalize theory lines, organize assumptions, and produce paper-ready derivation documents. Ideal for researchers and students who need to clarify mathematical derivations or rewrite theory notes into structured, coherent presentations.

Manim is a powerful Python library used for creating high-quality mathematical and scientific animations. This skill facilitates the generation of educational videos and complex visualizations for presentations. It is ideal for researchers, educators, or content creators who need to visualize complex concepts in an engaging animated format. Note: This specific file is related to localization/translation.

SymPy is a Python library for exact symbolic mathematics, enabling algebra, calculus, equation solving, and linear algebra without numerical approximations. Ideal for physics calculations, code generation, and generating LaTeX output. Use when precision matters over speed.

Invariant-Guard enforces a correctness-first approach to algorithm design. Instead of writing code and hoping it works, this skill mandates defining the function contract, loop invariants, termination arguments, and all potential edge cases *before* implementation. It is essential for complex algorithms where subtle bugs (like off-by-one errors or missed post-conditions) are common, ensuring mathematically rigorous and verifiable code.

A specialized skill for achieving asymptotic performance gains when classical algorithms are already near optimal. It leverages advanced mathematical techniques and probabilistic data structures (e.g., Bloom Filters, HyperLogLog, FFT, MinHash/LSH) to handle massive datasets (n ≥ 10⁶) by accepting bounded approximations or exploiting deep structural properties. Requires strict adherence to error parameter and complexity justification protocols.

This skill simulates a world-class Senior System Design Engineer with 20+ years of experience at top tech companies. It helps users design, review, and scale complex, highly available, and resilient distributed systems. It covers every aspect from database sharding and microservices decomposition to caching strategies, observability stacks, and CI/CD pipelines, providing detailed blueprints and mathematical scaling estimates.

This skill guides authors and researchers on how to strategically position their computer graphics, rendering, or visual computing work for the ACM SIGGRAPH conference. It covers core fit assessment, required evidence (visual, mathematical, or system), manuscript reframing from journal/arXiv styles, and navigating venue-specific submission requirements. Use this tool to improve your conference submission strategy and maximize visibility among top graphics reviewers.