arXiv subjects

Jeremi K. Ochab

Publications and source records attributed to Jeremi K. Ochab.

16 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↗

arXiv2025

StylOch at PAN: Gradient-Boosted Trees with Frequency-Based Stylometric Features

This submission to the binary AI detection task is based on a modular stylometric pipeline, where: public spaCy models are used for text preprocessing (including tokenisation, named entity recognition, dependency parsing, part-of-speech tagging, and morphology annotation) and extracting several thousand features (frequencies of n-grams of the above linguistic annotations); light-gradient boosting machines are used as the classifier. We collect a large corpus of more than 500 000 machine-generated texts for the classifier's training. We explore several parameter options to increase the classifier's capacity and take advantage of that training set. Our approach follows the non-neural, computationally inexpensive but explainable approach found effective previously.

cs.CL↗

arXiv2025

Stylometry recognizes human and LLM-generated texts in short samples

The paper explores stylometry as a method to distinguish between texts created by Large Language Models (LLMs) and humans, addressing issues of model attribution, intellectual property, and ethical AI use. Stylometry has been used extensively to characterise the style and attribute authorship of texts. By applying it to LLM-generated texts, we identify their emergent writing patterns. The paper involves creating a benchmark dataset based on Wikipedia, with (a) human-written term summaries, (b) texts generated purely by LLMs (GPT-3.5/4, LLaMa 2/3, Orca, and Falcon), (c) processed through multiple text summarisation methods (T5, BART, Gensim, and Sumy), and (d) rephrasing methods (Dipper, T5). The 10-sentence long texts were classified by tree-based models (decision trees and LightGBM) using human-designed (StyloMetrix) and n-gram-based (our own pipeline) stylometric features that encode lexical, grammatical, syntactic, and punctuation patterns. The cross-validated results reached a performance of up to .87 Matthews correlation coefficient in the multiclass scenario with 7 classes, and accuracy between .79 and 1. in binary classification, with the particular example of Wikipedia and GPT-4 reaching up to .98 accuracy on a balanced dataset. Shapley Additive Explanations pinpointed features characteristic of the encyclopaedic text type, individual overused words, as well as a greater grammatical standardisation of LLMs with respect to human-written texts. These results show -- crucially, in the context of the increasingly sophisticated LLMs -- that it is possible to distinguish machine- from human-generated texts at least for a well-defined text type.

cs.CL↗

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↗

arXiv2024

Multifractal organization of EEG signals in Multiple Sclerosis

Quantifying the complex/multifractal organization of the brain signals is crucial to fully understanding the brain processes and structure. In this contribution, we performed the multifractal analysis of the electroencephalographic (EEG) data obtained from a controlled multiple sclerosis (MS) study, focusing on the correlation between the degree of multifractality, disease duration, and disability level. Our results reveal a significant correspondence between the complexity of the time series and multiple sclerosis development, quantified respectively by scaling exponents and the Expanded Disability Status Scale (EDSS). Namely, for some brain regions, a well-developed multifractality and little persistence of the time series were identified in patients with a high level of disability, whereas the control group and patients with low EDSS were characterised by persistence and monofractality of the signals. The analysis of the cross-correlations between EEG signals supported these results, with the most significant differences identified for patients with EDSS $> 1$ and the combined group of patients with EDSS $\leq 1$ and controls. No association between the multifractality and disease duration was observed, indicating that the multifractal organisation of the data is a hallmark of developing the disease. The observed complexity/multifractality of EEG signals is hypothetically a result of neuronal compensation -- i.e., of optimizing neural processes in the presence of structural brain degeneration. The presented study is highly relevant due to the multifractal formalism used to quantify complexity and due to scarce resting-state EEG evidence for cortical reorganization associated with compensation.

q-bio.NC↗

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↗

arXiv2022

Task-dependent fractal patterns of information processing in working memory

We applied detrended fluctuation analysis, power spectral density, and eigenanalysis of detrended cross-correlations to investigate fMRI data representing a diurnal variation of working memory in four visual tasks: two verbal and two nonverbal. We show that the degree of fractal scaling is regionally dependent on engagement in cognitive tasks. A particularly apparent difference was found between memorisation in verbal and nonverbal tasks. Furthermore, the detrended cross-correlations between brain areas were predominantly indicative of differences between resting state and other tasks, between memorisation and retrieval, and between verbal and nonverbal tasks. The fractal and spectral analyses presented in our study are consistent with previous research related to visuospatial and verbal information processing, working memory (encoding and retrieval), and executive functions, but they were found to be more sensitive than Pearson correlations and showed the potential to obtain other subtler results. We conclude that regionally dependent cognitive task engagement can be distinguished based on the fractal characteristics of BOLD signals and their detrended cross-correlation structure.

q-bio.NC↗

arXiv2021

Untangling the brain web: from the early days of complex functional networks to the non-linear dynamical directed functional connectivity measures

Already two decades passed since the first applications of graph theory to brain neuroimaging. Since that early description, the characterization of the brain as a very large interacting complex network has evolved in several directions. In this brief review we discuss our contributions to this topic and discuss some perspective for future work.

q-bio.NC↗

arXiv2020

From synaptic interactions to collective dynamics in random neuronal networks models: critical role of eigenvectors and transient behavior

The study of neuronal interactions is currently at the center of several big collaborative neuroscience projects (including the Human Connectome Project, the Blue Brain Project, the Brainome, etc.) which attempt to obtain a detailed map of the entire brain. Under certain constraints, mathematical theory can advance predictions of the expected neural dynamics based solely on the statistical properties of the synaptic interaction matrix. This work explores the application of free random variables to the study of large synaptic interaction matrices. Besides recovering in a straightforward way known results on eigenspectra in types of models of neural networks proposed by Rajan and Abbott, we extend them to heavy-tailed distributions of interactions. More importantly, we derive analytically the behavior of eigenvector overlaps, which determine the stability of the spectra. We observe that upon imposing the neuronal excitation/inhibition balance, despite the eigenvalues remaining unchanged, their stability dramatically decreases due to the strong non-orthogonality of associated eigenvectors. It leads us to the conclusion that the understanding of the temporal evolution of asymmetric neural networks requires considering the entangled dynamics of both eigenvectors and eigenvalues, which might bear consequences for learning and memory processes in these models. Considering the success of free random variables theory in a wide variety of disciplines, we hope that the results presented here foster the additional application of these ideas in the area of brain sciences.

q-bio.NC↗

arXiv2020

Revisiting non-linear functional brain co-activations: directed, dynamic and delayed

The center stage of neuro-imaging is currently occupied by studies of functional correlations between brain regions. These correlations define the brain functional networks, which are the most frequently used framework to represent and interpret a variety of experimental findings. In previous work we first demonstrated that the relatively stronger BOLD activations contain most of the information relevant to understand functional connectivity and subsequent work confirmed that a large compression of the original signals can be obtained without significant loss of information. In this work we revisit the correlation properties of these epochs to define a measure of nonlinear dynamic directed functional connectivity (nldFC) across regions of interest. We show that the proposed metric provides at once, without extensive numerical complications, directed information of the functional correlations, as well as a measure of temporal lags across regions, overall offering a different perspective in the analysis of brain co-activation patterns. In this paper we provide for a proof of concept, based on replicating and completing existing results on an Autism database, to discuss the main features and advantages of the proposed strategy for the study of brain functional correlations. These results show new interpretations of the correlations found on this sample.

q-bio.NC↗

arXiv2019

Classifying attention deficit hyperactivity disorder in children with non-linearities in actigraphy

Objective This study provides an objective measure based on actigraphy for Attention Deficit Hyperactivity Disorder (ADHD) diagnosis in children. We search for motor activity features that could allow further investigation into their association with other neurophysiological disordered traits. Method The study involved $n=29$ (48 eligible) male participants aged $9.89\pm0.92$ years (8 controls, and 7 in each group: ADHD combined subtype, ADHD hyperactive-impulsive subtype, and autism spectrum disorder, ASD) wearing a wristwatch actigraph continuously for a week ($9\%$ losses in daily records) in two acquisition modes. We analyzed 47 quantities: from sleep duration or movement intensity to theory-driven scaling exponents or non-linear prediction errors of both diurnal and nocturnal activity. We used them in supervised classification to obtain cross-validated diagnostic performance. Results We report the best performing measures, including a nearest neighbors 4-feature classifier providing $69.4\pm1.6\%$ accuracy, $78.0\pm2.2\%$ sensitivity and $60.8\pm2.6\%$ specificity in a binary ADHD vs control classification and $46.5\pm1.1\%$ accuracy (against $25\%$ baseline), $61.8\pm1.4\%$ sensitivity and $79.30 \pm0.43\%$ specificity in 4-class task (two ADHD subtypes, ASD, and control). The most informative feature is skewness of the shape of Zero Crossing Mode (ZCM) activity. Mean and standard deviation of nocturnal activity are among the least informative. Conclusion Actigraphy causes only minor discomfort to the subjects and is inexpensive. The range of existing mathematical and machine learning tools also allow it to be a useful add-on test for ADHD or differential diagnosis between ADHD subtypes. The study was limited to a small, male sample without the inattentive ADHD subtype.

q-bio.QM↗

arXiv2018

On the pros and cons of using temporal derivatives to assess brain functional connectivity

The study of correlations between brain regions is an important chapter of the analysis of large-scale brain spatiotemporal dynamics. In particular, novel methods suited to extract dynamic changes in mutual correlations are needed. Here we scrutinize a recently reported metric dubbed "Multiplication of Temporal Derivatives" (MTD) which is based on the temporal derivative of each time series. The formal comparison of the MTD formula with the Pearson correlation of the derivatives reveals only minor differences, which we find negligible in practice. A comparison with the sliding window Pearson correlation of the raw time series in several stationary and non-stationary set-ups, including a realistic stationary network detection, reveals lower sensitivity of derivatives to low frequency drifts and to autocorrelations but also lower signal-to-noise ratio. It does not indicate any evident mathematical advantages of the proposed metric over commonly used correlation methods.

q-bio.NC↗

arXiv2015

How we move is universal: scaling in the average shape of human activity

Human motor activity is constrained by the rhythmicity of the 24 hours circadian cycle, including the usual 12-15 hours sleep-wake cycle. However, activity fluctuations also appear over a wide range of temporal scales, from days to a few seconds, resulting from the concatenation of a myriad of individual smaller motor events. Furthermore, individuals present different propensity to wakefulness and thus to motor activity throughout the circadian cycle. Are activity fluctuations across temporal scales intrinsically different, or is there a universal description encompassing them? Is this description also universal across individuals, considering the aforementioned variability? Here we establish the presence of universality in motor activity fluctuations based on the empirical study of a month of continuous wristwatch accelerometer recordings. We study the scaling of average fluctuations across temporal scales and determine a universal law characterized by critical exponents $α$, $τ$ and $1/μ$. Results are highly reminiscent of the universality described for the average shape of avalanches in systems exhibiting crackling noise. Beyond its theoretical relevance, the present results can be important for developing objective markers of healthy as well as pathological human motor behavior.

q-bio.NC↗

arXiv2015

Reinventing the Triangles: Rule of Thumb for Assessing Detectability

Statistical significance of network clustering has been an unresolved problem since it was observed that community detection algorithms produce false positives even in random graphs. After a phase transition between undetectable and detectable cluster structures was discovered, the connection between spectra of adjacency matrices and detectability limits were shown, and both were calculated for a wide range of networks with arbitrary degree distributions and community structure. In practice the full eigenspectrum is not known, and whether a given network has any communities within detectability regime cannot be easily established. Based on the global clustering coefficient we construct a criterion telling whether in an undirected, unweighted network there is some/no detectable community structure, or if the network is in a transient regime. The method is simple and faster than methods involving bootstrapping.

cs.SI↗

arXiv2012

Maximal entropy random walk in community finding

The aim of this paper is to check feasibility of using the maximal-entropy random walk in algorithms finding communities in complex networks. A number of such algorithms exploit an ordinary or a biased random walk for this purpose. Their key part is a (dis)similarity matrix, according to which nodes are grouped. This study encompasses the use of the stochastic matrix of a random walk, its mean first-passage time matrix, and a matrix of weighted paths count. We briefly indicate the connection between those quantities and propose substituting the maximal-entropy random walk for the previously chosen models. This unique random walk maximises the entropy of ensembles of paths of given length and endpoints, which results in equiprobability of those paths. We compare performance of the selected algorithms on LFR benchmark graphs. The results show that the change in performance depends very strongly on the particular algorithm, and can lead to slight improvements as well as significant deterioration.

physics.soc-ph↗

arXiv2012

Maximal Entropy Random Walk: solvable cases of dynamics

We focus on the study of dynamics of two kinds of random walk: generic random walk (GRW) and maximal entropy random walk (MERW) on two model networks: Cayley trees and ladder graphs. The stationary probability distribution for MERW is given by the squared components of the eigenvector associated with the largest eigenvalue λ_0 of the adjacency matrix of a graph, while the dynamics of the probability distribution approaching to the stationary state depends on the second largest eigenvalue λ_1. Firstly, we give analytic solutions for Cayley trees with arbitrary branching number, root degree, and number of generations. We determine three regimes of a tree structure that result in different statics and dynamics of MERW, which are due to strongly, critically, and weakly branched roots. We show how the relaxation times, generically shorter for MERW than for GRW, scale with the graph size. Secondly, we give numerical results for ladder graphs with symmetric defects. MERW shows a clear exponential growth of the relaxation time with the size of defective regions, which indicates trapping of a particle within highly entropic intact region and its escaping that resembles quantum tunneling through a potential barrier. GRW shows standard diffusive dependence irrespective of the defects.

cond-mat.stat-mech↗