Research, published and explored.

Publications by our team and commentary on methods shaping optimization, modelling and decision science.

Team publications

Papers and preprints by the mathematicians behind Meromorphic.

  1. Preprint 2026

    Equilibrium in the Canonical Stackelberg Triopoly via Response Functions and Fixed Point Theory

    Response-function and fixed-point analysis of equilibrium in a canonical Stackelberg triopoly.

    Anton Badev, Martin Pavlov, Boyan Zlatanov

    arXiv:2604.26487. Under review at Decisions in Economics and Finance.

    Read on arXiv

  2. Preprint 2026

    A Failed Cartel: When Collusive Firms Become Competitors

    A model of competition that emerges when one firm leaves a cartel.

    Anton Badev, Vanya Ivanova, Diana Nedelcheva, Martin Pavlov, Boyan Zlatanov

    Preprints.org manuscript 202608.0988 (2026).

    Read the preprint

  3. Preprint 2026

    Equilibrium in a Failed Cartel: Set-Valued Reactions and Sources of Market Asymmetry

    Set-valued reaction models for equilibrium and market asymmetry after a cartel member exits.

    Anton Badev, Vanya Ivanova, Diana Nedelcheva, Martin Pavlov, Boyan Zlatanov

    Preprints.org manuscript 202608.0503 (2026).

    Read the preprint

  4. Publication 2025

    A Fixed Point Approach to the Stackelberg Model in Oligopoly Markets

    Fixed point methods applied to leader–follower competition in oligopoly markets.

    Martin Pavlov, Vasil Zhelinski, Boyan Zlatanov

    Scientific Works of the University of Plovdiv, Mathematics, Vol. 40, Book 3, pp. 55–68. ISSN 0204–5249.

    Read the paper (PDF)

Commentary on external research

Technical explanations of published methods, their applications and the conditions that shape their use.

  1. Container rows, cranes and access roads beside a harbour, seen from above.
    Haris IllahiUnsplash LicenseIllustrative photograph of a container terminal.

    Better routes. Real constraints.

    PyVRP connects a practical routing solver to the capacity and timing rules that make delivery planning difficult.

    Based on Niels A. Wouda, Leon Lan and Wouter Kool. INFORMS Journal on Computing 36(4), 943–955 (2024).

  2. Diagonal rows of blue solar panels separated by grass and service tracks.
    Andreas GücklhornUnsplash LicenseIllustrative photograph of solar arrays in Offingen, Germany.

    Predict for the decision.

    Smart Predict, then Optimize asks a better question than forecast accuracy alone: what happens to the decision?

    Based on Adam N. Elmachtoub and Paul Grigas. Management Science (2022); first published online in 2021.

  3. An industrial hall containing pipework, machinery and production equipment.
    Shavr IKUnsplash LicenseIllustrative photograph of industrial machinery.

    Choose the next experiment.

    BoFire brings Bayesian optimisation and experimental design closer to the constraints of practical chemistry.

    Based on Johannes P. Dürholt and coauthors. Journal of Machine Learning Research 26(204), 1–7 (2025).

  4. Candidate solutions plotted against two objectives, with a Pareto frontier and two competing choices A and B.
    Johann Dréo / NojhanCC BY-SA 3.0Pareto frontier: a trade-off between two objectives.Unmodified artwork, scaled to fit. Artwork remains CC BY-SA 3.0.

    Plan beyond one forecast.

    Wasserstein distributionally robust optimisation makes uncertainty about the data-generating distribution part of the decision.

    Based on Peyman Mohajerin Esfahani and Daniel Kuhn. Mathematical Programming 171, 115–166 (2018); online 2017.

  5. A trajectory winds around two lobes of the Lorenz attractor.
    CepheusPublic domainLorenz attractor: an illustration of nonlinear dynamics.Unmodified artwork, scaled to fit.

    Find equations in the data.

    SINDy searches for compact dynamical models that can be inspected, rather than only returning a prediction.

    Based on Steven L. Brunton, Joshua L. Proctor and J. Nathan Kutz. Proceedings of the National Academy of Sciences 113(15), 3932–3937 (2016).

From sine waves to a square wave.

Explore how adding harmonics improves a Fourier approximation, and why an overshoot persists near a discontinuity.

Fourier convergence · square wave

Sₙ(x) = 4/π Σ sin((2k+1)x)/(2k+1)

Target square waveSuccessive partial sums: 1, 3, 7, 15 terms
Smooth sine waves progressively reconstruct the discontinuous target. The persistent overshoot near the jump is the Gibbs phenomenon, so convergence improves without pretending the discontinuity becomes uniformly smooth.

Develop an idea into a working method.

Partner with us on mathematical research, algorithm development or an applied prototype.

Discuss your project