arXiv subjects

Zbigniew Drogosz

Publications and source records attributed to Zbigniew Drogosz.

At least 19 recordsLinked to original sources

arXiv2026

Multifractal Signatures of Ageing and Dementia Development: A Multifractal Space-Filling Curve Analysis

Multifractality is an effective formalism for quantifying the nonlinear, scale-free properties of complex data. In this study, we propose a novel and efficient methodology, termed Multifractal Space-filling Curve Analysis (MFSCA), for quantifying the correlation structure of multidimensional data. Within this framework, the original multidimensional data - while preserving both local and long-range organisational properties - are projected onto a one-dimensional representation using a fractal space-filling curve. The resulting one-dimensional signal is then analysed using multifractal algorithms. We demonstrate the utility of the method using both artificially generated multifractal structures and real data. In particular, we apply MFSCA to analyse magnetic resonance imaging (MRI) data from Alzheimer patients at different stages of dementia. Based on the results, we estimate the multifractal profiles of the brain for healthy subjects of different ages as well as for dementia patients. The analysis reveals that the spatial organization of brain structures, as measured by the degree of multifractality, progressively weakens with age and the development of dementia. A transition from multifractality to monofractality is observed both in control groups, when comparing the Young Control and Elderly Control groups, and among dementia subjects of similar age but at different stages of the disease, namely early dementia and mild cognitive impairment. Thus, from the perspective of multiscaling properties, the heterogeneous characteristics of spatial brain organization deteriorate under worsening conditions, leading to a homogeneous and weakly correlated structure. These findings not only effectively capture key aspects of brain organisation, but also demonstrate that the multifractality of MRI data can serve as a marker of structural brain changes.

q-bio.NC↗

arXiv2026

Boost-invariant and cylindrically symmetric perfect spin hydrodynamics

Equations of a boost-invariant and cylindrically symmetric perfect hydrodynamics are solved numerically for initial conditions inspired by the wounded nucleon model. The energy-momentum and spin tensors are used in the form that describes a relativistic massive gas governed by Boltzmann statistics. In contrast to one dimensional boost-invariant expansion, we find a coupling between the azimuthal and longitudinal components of the electric and magnetic components of the spin polarization tensor. This feature is similar to that found earlier for the Gubser symmetry, however, our treatment allows for a more general form of initial conditions and expansion geometry. Defining the freeze-out hypersurface by the constant temperature condition, we evaluate the Pauli-Luba\'nski four-vector and find that for the assumed geometry the only nonzero total polarization may be induced by the longitudinal component of the magnetic part of the spin polarization tensor coupled with the azimuthal electric component. The obtained results may serve as a reference point for more realistic models of hydrodynamic expansion.

hep-ph↗

arXiv2026

Boost-invariant perfect Fermi-Dirac spin hydrodynamics

We analyze the effect of using the Fermi-Dirac statistics, rather than its Boltzmann approximation, in numerical simulations of perfect spin hydrodynamics of particles with spin 1/2. The system considered is boost invariant, transversely homogeneous, with corrections to the baryon current and the energy-momentum tensor that are second order in the spin polarization tensor $\omega$, and the spin tensor considered is first order in $\omega$. The study shows the feasibility of this approach, as the special functions defined by integrals that appear in the coefficients in the Fermi-Dirac case can be conveniently parametrized. For sets of initial conditions used in previous works, the differences in parameter evolution between the two underlying particle statistics are about one order of magnitude smaller than corrections coming from spin feedback. We also discuss when and why the numerical solutions of the equations of perfect spin hydrodynamics break down for very large values of spin polarization in one of the geometric configurations considered.

hep-ph↗

arXiv2025

Nonlinear causality and stability of perfect spin hydrodynamics and its nonperturbative character

Four formulations of perfect spin hydrodynamics for spin-1/2 particles, distinguished by their treatment of spin (classical vs. quantum) and by the underlying particle statistics (Boltzmann vs. Fermi-Dirac), are analyzed and shown to satisfy the requirements of a divergence-type theory. Moreover, for all the formulations, we define the generating functions associated with the relevant thermodynamic currents and demonstrate that the constructed hydrodynamic theory is nonlinearly causal and stable. The latter is achieved by employing the exact expressions for the distribution functions, indicating a nonperturbative character of our approach.

hep-ph↗

arXiv2025

Machine learning in phase transition analysis of lattice quantum gravity

Using numerical data coming from Monte Carlo simulations of four-dimensional Causal Dynamical Triangulations, we study how automated machine learning algorithms can be used to recognize transitions between different phases of quantum geometries observed in lattice quantum gravity. We tested seven supervised and seven unsupervised machine learning models and found that most of them were very successful in that task, even outperforming standard methods based on order parameters.

hep-lat↗

arXiv2025

Local equilibrium Wigner function for spin-1/2 particles

Formal connections between the spin density matrix and the Wigner function for spin-1/2 particles forming a relativistic gas are explored to determine their general structures. They suggest that the commonly used form of the local equilibrium Wigner function should be replaced by a new expression. The latter fulfills the necessary condition for the normalization of the mean spin polarization, which the former fails to reproduce. The new definition of the Wigner function leads to generalized thermodynamic relations for perfect spin hydrodynamics, identical to those obtained earlier using the classical concept of spin. Moreover, one can prove that the perfect spin hydrodynamics based on the new equilibrium Wigner function is nonlinearly causal and stable. Finally, the selection rule for the Lagrange multipliers, which is satisfied by real systems, is discussed.

hep-ph↗

arXiv2025

Perfect spin hydrodynamics at all orders in spin polarization

We compare two recently developed frameworks of perfect spin hydrodynamics for spin-$1/2$ particles, based respectively on classical kinetic theory and the Wigner function. We show that the conserved currents in both approaches have the same form at each order of the expansion in the components of the spin polarization tensor $\omega$. The only difference is a relative multiplicative factor, which is equal to 1 at the lowest nontrivial order and increases monotonically with the expansion order.

hep-ph↗

arXiv2025

Spin hydrodynamics -- recent developments

After briefly touching on relativistic hydrodynamics, we provide a detailed description of recent developments in spin hydrodynamics. We discuss the theory of perfect spin hydrodynamics within two different approaches, which lead to identical generalized thermodynamic relations. We also indicate the applicability range of the theory, finding it compatible with the conditions existing in the late stages of heavy-ion collisions. Finally, we discuss the near-equilibrium dynamics.

hep-ph↗

arXiv2025

Application range of perfect spin hydrodynamics

The application range of perfect spin hydrodynamics is studied in two cases: one based on the classical spin description and the other using a quantum spin density matrix (Wigner function). Different forms of the conditions connecting the components of the spin polarization tensor, particle mass, temperature, and hydrodynamic flow are introduced, and their mutual relations are explained. The results obtained are important for practical applications of spin hydrodynamics to model heavy-ion collisions.

hep-ph↗

arXiv2025

Hybrid framework of Fermi-Dirac spin hydrodynamics

We outline the hybrid framework of spin hydrodynamics, combining classical kinetic theory with the Israel-Stewart method of introducing dissipation. We obtain the local equilibrium expressions for the baryon current, the energy-momentum tensor, and the spin tensor of particles with spin 1/2 following the Fermi-Dirac statistics and compare them with the previously derived versions where the Boltzmann approximation was used. The expressions in the two cases have the same form, but the coefficients are governed by different functions. The relative differences between the tensor coefficients in the Fermi-Dirac and Boltzmann cases are found to grow exponentially with the baryon chemical potential. In the proposed formalism, nonequilibrium processes are studied including mathematically possible dissipative corrections. Standard conservation laws are applied, and the condition of positive entropy production allows for transfer between the spin and orbital parts of angular momentum.

hep-ph↗

arXiv2025

$^3$H and $^3$He nuclei production in a combined thermal and coalescence framework for heavy-ion collisions in the few-GeV energy regime

A thermal model describing hadron production in heavy-ion collisions in the few-GeV energy regime is combined with the idea of nucleon coalescence to make predictions for the $^3$H and $^3$He nuclei production. A realistic parametrization of the freeze-out conditions is used, which reproduces well the spectra of protons and pions. It also correctly predicts the deuteron yield that agrees with the experimental value. The predicted yields of $^3$H and $^3$He appear to be smaller by about a factor of two compared to the experimental results. The model predictions for the spectra can be compared with future experimental data.

hep-ph↗

arXiv2025

Using Space-Filling Curves and Fractals to Reveal Spatial and Temporal Patterns in Neuroimaging Data

We present a novel method, Fractal Space-Curve Analysis (FSCA), which combines Space-Filling Curve (SFC) mapping for dimensionality reduction with fractal Detrended Fluctuation Analysis (DFA). The method is suitable for multidimensional geometrically embedded data, especially for neuroimaging data which is highly correlated temporally and spatially. We conduct extensive feasibility studies on diverse, artificially generated data with known fractal characteristics: the fractional Brownian motion, Cantor sets, and Gaussian processes. We compare the suitability of dimensionality reduction via Hilbert SFC and a data-driven alternative. FSCA is then successfully applied to real-world magnetic resonance imaging (MRI) and functional MRI (fMRI) scans. The method utilizing Hilbert curves is optimized for computational efficiency, proven robust against boundary effects typical in experimental data analysis, and resistant to data sub-sampling. It is able to correctly quantify and discern correlations in both stationary and dynamic two-dimensional images. In MRI Alzheimer's dataset, patients reveal a progression of the disease associated with a systematic decrease of the Hurst exponent. In fMRI recording of breath-holding task, the change in the exponent allows distinguishing different experimental phases. This study introduces a robust method for fractal characterization of spatial and temporal correlations in many types of multidimensional neuroimaging data. Very few assumptions allow it to be generalized to more dimensions than typical for neuroimaging and utilized in other scientific fields. The method can be particularly useful in analyzing fMRI experiments to compute markers of pathological conditions resulting from neurodegeneration. We also showcase its potential for providing insights into brain dynamics in task-related experiments.

q-bio.NC↗

arXiv2025

Dynamical constraints on pseudo-gauge transformations

Classical pseudo-gauge transformations are discussed in the context of hydrodynamic models of heavy-ion collisions. A decomposition of the pseudo-gauge transformation into Lorentz-invariant tensors is made, which allows for better interpretation of its physical consequences. For pseudo-gauge transformations connecting two symmetric energy-momentum tensors, we find that the super-potential $Φ^{λμν}$ must obey a conservation law of the form $\partial_λΦ^{λμν} = 0$. This equation, referred to below as the STS condition, represents a constraint that is hardly possible to be satisfied for tensors constructed out of the basic hydrodynamic variables such as temperature, baryon chemical potential, and the hydrodynamic flow. However, in a special case of the boost-invariant flow, the STS condition is automatically fulfilled and a non-trivial residual pseudo-gauge transformation defined by a single scalar field is allowed. In this case the bulk and shear viscosity coefficients become pseudo-gauge dependent; however, their specific linear combination appearing in the equations of motion remains pseudo-gauge invariant. This finding provides new insights into the role of pseudo-gauge transformations and pseudo-gauge invariance.

hep-ph↗

arXiv2024

Hybrid approach to perfect and dissipative spin hydrodynamics

A hybrid framework of spin hydrodynamics is proposed that combines the results of kinetic theory for particles with spin 1/2 with the Israel-Stewart method of introducing nonequilibrium dynamics. The framework of kinetic theory is used to define the perfect-fluid description that conserves baryon number, energy, linear momentum and spin part of angular momentum. This leads to the entropy conservation although, in the presence of spin degrees of freedom, the perfect-fluid formalism includes extra terms whose structure is usually attributed to dissipation. The genuine dissipative terms appear from the condition of positive entropy production in nonequilibrium processes. They are responsible for the transfer between the spin and orbital parts of angular momentum, with the total angular momentum being conserved.

hep-ph↗

arXiv2024

Boost-invariant spin hydrodynamics with spin feedback effects

A recently formulated extension of perfect spin hydrodynamics, which includes second-order corrections in the spin polarization tensor to the energy-momentum tensor and baryon current, is studied in the case of a one-dimensional boost-invariant expansion. The presence of second-order corrections introduces feedback from spin dynamics on the hydrodynamic background, constraining possible spin polarization configurations. However, as long as the magnitude of the spin polarization tensor remains small (below unity in natural units), the permitted spin dynamics differs very little from that found in the case without the second-order corrections.

hep-ph↗

arXiv2023

Investigating structural and functional aspects of the brain's criticality in stroke

This paper addresses the question of the brain's critical dynamics after an injury such as a stroke. It is hypothesized that the healthy brain operates near a phase transition (critical point), which provides optimal conditions for information transmission and responses to inputs. If structural damage could cause the critical point to disappear and thus make self-organized criticality unachievable, it would offer the theoretical explanation for the post-stroke impairment of brain function. In our contribution, however, we demonstrate using network models of the brain, that the dynamics remain critical even after a stroke. In cases where the average size of the second-largest cluster of active nodes, which is one of the commonly used indicators of criticality, shows an anomalous behavior, it results from the loss of integrity of the network, quantifiable within graph theory, and not from genuine non-critical dynamics. We propose a new simple model of an artificial stroke that explains this anomaly. The proposed interpretation of the results is confirmed by an analysis of real connectomes acquired from post-stroke patients and a control group. The results presented refer to neurobiological data; however, the conclusions reached apply to a broad class of complex systems that admit a critical state.

q-bio.NC↗

arXiv2021

New topological observables in a model of Causal Dynamical Triangulations on a torus

The structure of simplicial manifolds in a model of Causal Dynamical Triangulations in 3+1 dimensions with the spatial topology of a 3-torus is analyzed with the help of topological observables, such as loops with nonzero winding numbers and coordinates based on scalar fields with jumps at the boundaries of the elementary cell of the torus. The results are given an interpretation and used in the measurements of a more local observable that is the quantum Ricci curvature. We moreover analyze the influence of scalar matter fields on the geometry of CDT spacetimes.

hep-th↗

arXiv2021

Scalar fields in Causal Dynamical Triangulations

A typical geometry extracted from the path integral of a quantum theory of gravity might be quite complicated in the UV region. Even if such a configuration is not physical, it may be of interest to understand the details of its nature, since some universal features can be important for the physics of the model. If the formalism describing the geometry is coordinate independent, such understanding may be facilitated by the use of suitable coordinate systems. In this article we use scalar fields that solve Laplace's equation to introduce coordinates on geometries with a toroidal topology. Using these coordinates we observe what we denote as the "cosmic voids and filaments" structure, even if no matter is present in the theory. We also show that if the scalar fields we used as coordinates are dynamically coupled to geometry, they can change it in a dramatic way.

gr-qc↗