arXiv subjects

Zbigniew R. Struzik

Publications and source records attributed to Zbigniew R. Struzik.

10 recordsLinked to original sources

arXiv2026

Wavelet Localisation and Local Modulation Freezing in MRW Unwrapping

We develop a localised wavelet formulation of multifractal random walk unwrapping based on the local multiplicative modulation freezing. The framework is motivated by the observation that finite-support wavelet localisation may induce approximate local factorisation of multiplicatively modulated stochastic fields, allowing the modulation component to become effectively frozen within sufficiently localised probing domains. Within this regime, logarithmic wavelet amplitudes admit an approximate additive decomposition linking local wavelet statistics directly to the underlying modulation field. This viewpoint reformulates covariance-based MRW unwrapping as a localised multiscale operator problem in which wavelet coefficients act as finite-support probes of multiplicative organisation. The validity of the approximation depends explicitly on support geometry, scale-dependent overlap, and residual multiscale mixing generated by internal modulation variability. We show that these effects naturally produce finite-scale deviations from ideal logarithmic covariance scaling and lead to structured covariance distortions whose form depends on the interaction between the modulation field and the geometry of the wavelet representation. In the resulting framework, localisation itself becomes the operational mechanism enabling multiscale probing of local stochastic organisation. Numerical investigations using orthonormal wavelet decompositions support the proposed interpretation and demonstrate the emergence of scale-dependent freezing regimes, residual covariance mixing, and finite-support breakdown effects consistent with the theory. The proposed framework suggests a broader connection between wavelet localisation, local regularity organisation, and finite-support multiscale stochastic operators. Wavelet localisation becomes an operational mechanism for probing localised multiscale structure.

cond-mat.stat-mech↗

arXiv2020

Towards a Universal Measure of Complexity

Recently it has been argued that entropy can be a direct measure of complexity, where the smaller value of entropy indicates lower system complexity, while its larger value indicates higher system complexity. We dispute this view and propose a universal measure of complexity based on the Gell-Mann's view of complexity. Our universal measure of complexity bases on a non-linear transformation of time-dependent entropy, where the system state with the highest complexity is the most distant from all the states of the system of lesser or no complexity. We have shown that the most complex is optimally mixed states consisting of pure states i.e., of the most regular and most disordered which the space of states of a given system allows. A parsimonious paradigmatic example of the simplest system with a small and a large number of degrees of freedom, is shown to support this methodology. Several important features of this universal measure are pointed out, especially its flexibility (i.e., its openness to extensions), ability to the analysis of a system critical behavior, and ability to study the dynamic complexity.

cond-mat.stat-mech↗

arXiv2020

The new face of multifractality: Multi-branchedness and the phase transitions in time series of mean inter-event times

Empirical time series of inter-event or waiting times are investigated using a modified Multifractal Detrended Fluctuation Analysis operating on fluctuations of mean detrended dynamics. The core of the extended multifractal analysis is the non-monotonic behavior of the generalized Hurst exponent $h(q)$ -- the fundamental exponent in the study of multifractals. The consequence of this behavior is the non-monotonic behavior of the coarse Hölder exponent $α(q)$ leading to multi-branchedness of the spectrum of dimensions. The Legendre-Fenchel transform is used instead of the routinely used canonical Legendre (single-branched) contact transform. Thermodynamic consequences of the multi-branched multifractality are revealed. These are directly expressed in the language of phase transitions between thermally stable, metastable, and unstable phases. These phase transitions are of the first and second orders according to Mandelbrot's modified Ehrenfest classification. The discovery of multi-branchedness is tantamount in significance to extending multifractal analysis.

q-fin.ST↗

arXiv2018

Adaptive Decision Making via Entropy Minimization

An agent choosing between various actions tends to take the one with the lowest cost. But this choice is arguably too rigid (not adaptive) to be useful in complex situations, e.g., where exploration-exploitation trade-off is relevant in creative task solving or when stated preferences differ from revealed ones. Here we study an agent who is willing to sacrifice a fixed amount of expected utility for adaptation. How can/ought our agent choose an optimal (in a technical sense) mixed action? We explore consequences of making this choice via entropy minimization, which is argued to be a specific example of risk-aversion. This recovers the $ε$-greedy probabilities known in reinforcement learning. We show that the entropy minimization leads to rudimentary forms of intelligent behavior: (i) the agent assigns a non-negligible probability to costly events; but (ii) chooses with a sizable probability the action related to less cost (lesser of two evils) when confronted with two actions with comparable costs; (iii) the agent is subject to effects similar to cognitive dissonance and frustration. Neither of these features are shown by entropy maximization.

physics.data-an↗

arXiv2014

Visualization of short-term heart period variability with network tools as a method for quantifying autonomic drive

Signals from heart transplant recipients can be considered to be a natural source of information for a better understanding of the impact of the autonomic nervous system on the complexity of heart rate variability. Beat-to-beat heart rate variability can be represented as a network of increments between subsequent $RR$-intervals, which makes possible the visualization of short-term heart period fluctuations. A network is constructed of vertices representing increments between subsequent $RR$-intervals, and edges which connect adjacent $RR$-increments. Two modes of visualization of such a network are proposed. The method described is applied to nocturnal Holter signals recorded from healthy young people and from cardiac transplant recipients. Additionally, the analysis is performed on surrogate data: shuffled RR-intervals (to display short-range dependence), and shuffled phases of the Fourier Transform of RR-intervals (to filter out linear dependences). Important nonlinear properties of autonomic nocturnal regulation in short-term variability in healthy young persons are associated with $RR$-increments: accelerations and decelerations of a size greater than about 35 ms. They reveal that large accelerations are more likely antipersistent, while large decelerations are more likely persistent. Changes in $RR$-increments in a heart deprived of autonomic supervision are much lower than in a healthy individual, and appear to be maintained around a homeostatic state, but there are indications that this dynamics is nonlinear. The method is fruitful in the evaluation of the vagal activity - the quantity and quality of the vagal tone - during the nocturnal rest of healthy young people. The method also successfully extracts nonlinear effects related to intrinsic mechanisms of the heart regulation.

physics.data-an↗

arXiv2013

Multi-command Tactile Brain Computer Interface: A Feasibility Study

The study presented explores the extent to which tactile stimuli delivered to the ten digits of a BCI-naive subject can serve as a platform for a brain computer interface (BCI) that could be used in an interactive application such as robotic vehicle operation. The ten fingertips are used to evoke somatosensory brain responses, thus defining a tactile brain computer interface (tBCI). Experimental results on subjects performing online (real-time) tBCI, using stimuli with a moderately fast inter-stimulus-interval (ISI), provide a validation of the tBCI prototype, while the feasibility of the concept is illuminated through information-transfer rates obtained through the case study.

q-bio.NC↗

arXiv2013

Multicommand Tactile Brain Computer Interface based on Fingertips or Head Stimulation

The paper presents results from a computational neuroscience study conducted to test vibrotactile stimuli delivered to subject fingertips and head areas in order to evoke the somatosensory brain responses utilized in a haptic brain computer interface (hBCI) paradigm. We present the preliminary and very encouraging results, with subjects conducting online hBCI interfacing experiments, ranging from 40% to 90% with a very fast inter-stimulus-interval (ISI) of 250ms. The presented results confirm our hypothesis that the hBCI paradigm concept is valid and it allows for rapid stimuli presentation in order to achieve a satisfactory information-transfer-rate of the novel BCI.

q-bio.NC↗

arXiv2004

1/f Scaling in Heart Rate Requires Antagonistic Autonomic Control

We present the first systematic evidence for the origins of 1/f-type temporal scaling in human heart rate. The heart rate is regulated by the activity of two branches of the autonomic nervous system: the parasympathetic (PNS) and the sympathetic (SNS) nervous systems. We examine alterations in the scaling property when the balance between PNS and SNS activity is modified, and find that the relative PNS suppression by congestive heart failure results in a substantial increase in the Hurst exponent H towards random walk scaling $1/f^{2}$ and a similar breakdown is observed with relative SNS suppression by primary autonomic failure. These results suggest that 1/f scaling in heart rate requires the intricate balance between the antagonistic activity of PNS and SNS.

q-bio.OT↗

arXiv2004

Critical Scale-invariance in Healthy Human Heart Rate

We demonstrate the robust scale-invariance in the probability density function (PDF) of detrended healthy human heart rate increments, which is preserved not only in a quiescent condition, but also in a dynamic state where the mean level of heart rate is dramatically changing. This scale-independent and fractal structure is markedly different from the scale-dependent PDF evolution observed in a turbulent-like, cascade heart rate model. These results strongly support the view that healthy human heart rate is controlled to converge continually to a critical state.

q-bio.TO↗

arXiv2004

1/f Noise in a one-dimensional charge density wave system

The current noise in a classical one-dimensional charge density wave system is studied in the weak pinning regime by solving the overdamped equation of motion numerically. At low temperatures and just above the zero temperature depinning threshold, the power spectrum of the current noise $S(f)$ was found to scale with frequency $f$ as $S(f) \sim f^{-γ}$, where $γ\approx 1$, suggesting the existence of {\it flicker noise}. Our result is in agreement with experimental findings for quasi-one-dimensional charge density wave systems and provides the first evidence of $1/f$ behavior obtained from first principles.

cond-mat.dis-nn↗