Network and Computational Biology

1. Cospectrality and duality (forthcoming)
2. Complex Networks (random, scale-free and small world)
3. Breadth-First Search Enumeration
4. Euler’s Polyhedral Formula
5. World Metro Networks
6. Generating Random DNA Sequences (with GC content per species)
7. Network motifs and graphlets

Discrete Math, Mathematical Logic & Combinatorics

1. Truth Tables
2. Fundamental Theorem of Arithmetic
3. Golden Ratio by the Fibonacci Sequence
4. Visualizing the Goldbach Conjecture
5. Predicate Calculus Formula Generator
6. Skolemization of Quantified Formulae
7. Applying the Pólya-Burnside Enumeration Theorem

Information Theory, Computational Lingustics & Complexity Theory

1. Shannon’s Noisy-Channel Coding Theorem
2. Cellular Automaton Compressibility
3. Kolmogorov Complexity of 3×3 and 4×4 Squares
4. Prediction and Entropy of Languages
5. Zipf’s Law Applied to Word and Letter Frequencies
6. Multilanguage Word Lengths
7. Borel’s Infinite Money Theorem and Algorithmic Probability
8. Speedup and Slowdown Phenomena in Turing Machines
9. Fractal Dimension versus Time Computational Complexity in Turing Machines
10. Complexity: an R-package to enable measures of algorithmic complexity (with N.Gauvrit, H.Singmann and F.Soler)
11. Block Decomposition Method (soon available in Perl, Python, Java, C++, Pascal and Mathematica, w/F.Soler)

Automata, Normality & Pseudorandomness

1. Busy Beaver Turing Machines
2. John von Neumann’s First Pseudorandom Number Generator(middle-square method)
3. Random Number Generation and Testing
4. Country Data and Benford’s Law
5. Champernowne Constant
6. Prime Numbers Gaps
7. Collatz Sequence Paths
8. Distribution of Primes
9. Digit Frequencies in the Copeland-Erdos Constant
10. Unveiling Mathematica’s TuringMachine Function Step by Step
11. Small Turing Machines with Halting State: Enumeration and Running on a Blank Tape