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Krzysztof Domino

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Computational Engineering, Finance, and Science Computer Vision Numerical Analysis q-fin.PM quant-ph

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preprint2026arXiv

Assessment of the quantitative impact of occlusal positioning splints on temporomandibular joint conditions

A computational method for quantitative analysis of temporomandibular joint (TMJ) configuration using occlusal positioning splints is proposed and demonstrated. The method models a positioning splint as a physical realization of a predefined rigid transformation of the mandible, derived from multimodal data, including CBCT, facial motion acquisition, and dental scans integrated within a common coordinate system. Splints corresponding to selected mandibular positions are designed and fabricated, and their positioning accuracy is evaluated using repeated scans of plaster models. Discrepancies are represented as error transformations and analyzed statistically in the space of rigid motions. The estimated transformations are propagated to segmented TMJ structures, enabling simulation-based evaluation of joint space changes. Transformation-based error analysis and surface distance metrics are used to quantify differences between planned and achieved configurations. The method enables indirect assessment of TMJ configuration using a single anatomical model and transformation data, reducing the need for repeated imaging across multiple mandibular positions. This study is intended as a methodological demonstration, supported by a clear step-by-step graphical presentation, and does not aim to provide clinical validation.

preprint2026arXiv

Thermodynamic significance of QUBO encoding on quantum annealers

Quadratic unconstrained binary optimization (QUBO) is the standard interface to quantum annealers, yet a single constrained task admits many QUBO encodings whose penalty choices reshape the energy landscape experienced by hardware. We study a Job Shop Scheduling instance using a two-parameter family of encodings controlled by penalty weights $p_{\rm sum}$ (one-hot/sum constraints) and $p_{\rm pair}$ (precedence constraints). Sweeping $(p_{\rm sum},p_{\rm pair})$, we observe sharp transitions in feasibility and solver success across classical annealing-inspired heuristics and on a D-Wave Advantage processor. Going beyond solution probability, we treat the annealer as an open thermodynamic system and perform cyclic reverse-annealing experiments initialized from thermal samples, measuring the stochastic processor energy change. From the first two moments of this energy change we infer lower bounds on entropy production, work, and exchanged heat via thermodynamic uncertainty relations, and corroborate the observed trends with adiabatic master equation simulations. We find that the same encoding transitions that govern computational hardness also reorganize dissipation: weak penalties generate low-energy infeasible manifolds, while overly strong penalties suppress the effective problem energy scale and increase irreversibility, reducing the thermodynamic efficiency. Our results establish QUBO penalties as thermodynamic control knobs and motivate thermodynamics-aware encoding strategies for noisy intermediate-scale quantum annealers.

preprint2016arXiv

The use of the multi-cumulant tensor analysis for the algorithmic optimisation of investment portfolios

The cumulant analysis plays an important role in non Gaussian distributed data analysis. The shares' prices returns are good example of such data. The purpose of this research is to develop the cumulant based algorithm and use it to determine eigenvectors that represent investment portfolios with low variability. Such algorithm is based on the Alternating Least Square method and involves the simultaneous minimisation 2'nd -- 6'th cumulants of the multidimensional random variable (percentage shares' returns of many companies). Then the algorithm was tested during the recent crash on the Warsaw Stock Exchange. To determine incoming crash and provide enter and exit signal for the investment strategy the Hurst exponent was calculated using the local DFA. It was shown that introduced algorithm is on average better that benchmark and other portfolio determination methods, but only within examination window determined by low values of the Hurst exponent. Remark that the algorithm of is based on cumulant tensors up to the 6'th order calculated for a multidimensional random variable, what is the novel idea. It can be expected that the algorithm would be useful in the financial data analysis on the world wide scale as well as in the analysis of other types of non Gaussian distributed data.