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Abstract: Equation discovery, also known as symbolic regression, is the field of machine learning that studies algorithms for discovering quantitative laws, expressed as closed-form equations or formulas, in collections of observed data. The latter is expected to come from measurements of physical systems and, therefore, noisy, moving the focus of equation discovery algorithms towards discovering approximate equations. These loosely match the noisy observed data, rendering them inappropriate for applications in mathematics. In this article, we introduce Diofantos, an algorithm for discovering equations in the ring of integers that exactly match the training data. Diofantos is based on a reformulation of the equation discovery task into the task of solving linear Diophantine equations. We empirically evaluate the performance of Diofantos on reconstructing known equations for more than 27,000 sequences from the online encyclopedia of integer sequences, OEIS. Diofantos successfully reconstructs more than 90% of these equations and clearly outperforms SINDy, a state-of-the-art method for discovering approximate equations, that achieves a reconstruction rate of less than 70%.
Keywords: symbolic regression, equation discovery, online encyclopedia of integer sequences
Published in DiRROS: 27.03.2025; Views: 259; Downloads: 137
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Abstract: — Introduction: Parkinson’s disease (PD) is characterized by enhanced beta-band activity (13–30 Hz) in the motor control regions. Simultaneously, corticomuscular (CM) connectivity in the beta-band during isometric contractions tends to decline with age, in various diseases, and under dual-task conditions. Objective: This study aimed to characterize electroencephalograph (EEG) and electromyograph (EMG) power spectra during a motor task, assess CM phase connectivity, and explore how these measures are modulated by an additional cognitive task. Specifically, we focused on the beta-band to explore the relationship between heightened beta amplitude and reduced beta CM connectivity. Methodology: Early-stage people with PD and age-matched controls performed an isometric knee extension task, a cognitive task, and a combined dual task, while EEG (128ch) and EMG (2x32ch) were recorded. CM phase connectivity was assessed through phase coherence and a phase dynamics model. Results: The EEG power spectrum revealed no cohort differences in the beta-band. EMG also showed no differences up to 80 Hz. However, the combined EEG-EMG analysis uncovered reduced beta phase coherence in people with early PD during the motor task. CM phase coherence exhibited distinct scalp topography and frequency ranges compared to the EEG power spectrum, suggesting different mechanisms for pathological beta increase and CM connectivity. Additionally, phase dynamics modelling indicated stronger directional coupling from the cortex to the active muscle and less prominent phase coupling across people with PD. Despite high inter-individual variability, these metrics may prove useful for personalized assessments, particularly in people with heightened CM connectivity.
Keywords: electroencephalography, brain modeling, electromiography, coherence, motors, diseases, couplings, electrodes, oscillators, protocols
Published in DiRROS: 13.01.2025; Views: 352; Downloads: 187
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Abstract: Montane temperate forests in central and southern Europe host diverse small mammal assemblages, but the fluctuations in these assemblages in correlation with owl predators are still poorly explored. The key questions of our study were how coexisting owls responded to different prey fluctuations and whether any particular small mammal species governed predator–prey co-dynamics. We conducted a long-term study (2004–2020) in low-elevation (300–1100 m above sea level) mixed Beech and Silver Fir forest in the northern Dinaric Alps (central Slovenia). Monitoring data on the main small mammal groups – mice Muridae, voles Cricetidae, dormice Gliridae and shrews Soricidae – and three owl species – the Ural Owl Strix uralensis, Tawny Owl Strix aluco and Boreal Owl Aegolius funereus – were collected annually. To find relationships between prey and predator populations, we used two types of supervised machine learning approaches and addressed three predictive modelling tasks of multi-target regression. The dominant species in the small mammal assemblage, the Yellow-necked Mouse Apodemus flavicollis, had a key role in determining predator populations and their breeding performance. We noted higher sensitivity to small mammal fluctuations in boreal zone owl species (Boreal Owl and Ural Owl), which reach their southern distribution limit in the Dinaric Alps, whereas the temperate zone species (Tawny Owl) seemed to be less affected. In years of prey shortage, the Boreal Owl was found to presumably abandon its territories, the Ural Owl suppressed breeding and the Tawny Owl sustained breeding activity by shifting prey selection. Low-elevation forests appeared to be suboptimal habitat for the competitive subordinate Boreal Owl, which may exploit occasional outbreaks of small mammal populations in these habitats even in the presence of larger competitors. Whether low-elevation forests can play a role in maintaining threatened and cold-adapted Boreal Owl populations in central and southern Europe in the face of recent ecosystem changes due to climate and environmental changes remains an open scientific question.
Keywords: sove, mali sesalci, populacijska dinamika, strojno učenje
Published in DiRROS: 16.07.2024; Views: 744; Downloads: 360
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Abstract: In this study, we estimate the generalization of the performance of previously proposed predictive models for nutrient value prediction across different recipe datasets. For this purpose, we introduce a quantitative indicator that determines the level of generalization of using the developed predictive model for new unseen data not presented in the training process. On a predefined corpus of recipe embeddings from six publicly available recipe datasets (i.e., projecting them in the same meta-feature vector space), we train predictive models on one of the six recipe datasets and test the models on the rest of the datasets. In parallel, we define and calculate generalizability indexes which are numbers that indicate how generalizable a predictive model is i.e., how well will a predictive model learned on one dataset perform on another one not involved in the training. The evaluation results prove the validity of these indexes – their relation with the accuracy of the predictions. Further, we define three sampling techniques for selecting representative data instances that will cover all parts from the feature space uniformly (involving data from all datasets) and further will improve the generalization of a predictive model. We train predictive models with these generalized datasets and test them on instances from the six recipe datasets that are not selected and included in the generalized datasets. The results from the evaluation of these predictive models show improvement compared to the results from the predictive models trained on one recipe dataset and tested on the others separately.
Keywords: ML pipeline, predictive modeling, nutrient prediction, recipe datasets
Published in DiRROS: 25.09.2023; Views: 1026; Downloads: 568
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Abstract: The utilization of a non-invasive electroencephalogram (EEG) as an input sensor is a common approach in the field of the brain–computer interfaces (BCI). However, the collected EEG data pose many challenges, one of which may be the age-related variability of event-related potentials (ERPs), which are often used as primary EEG BCI signal features. To assess the potential effects of aging, a sample of 27 young and 43 older healthy individuals participated in a visual oddball study, in which they passively viewed frequent stimuli among randomly occurring rare stimuli while being recorded with a 32-channel EEG set. Two types of EEG datasets were created to train the classifiers, one consisting of amplitude and spectral features in time and another with extracted time-independent statistical ERP features. Among the nine classifiers tested, linear classifiers performed best. Furthermore, we show that classification performance differs between dataset types. When temporal features were used, maximum individuals’ performance scores were higher, had lower variance, and were less affected overall by within-class differences such as age. Finally, we found that the effect of aging on classification performance depends on the classifier and its internal feature ranking. Accordingly, performance will differ if the model favors features with large within-class differences. With this in mind, care must be taken in feature extraction and selection to find the correct features and consequently avoid potential age-related performance degradation in practice.
Keywords: aging, elderly, machine learning, visual oddball study, brain-computer interface
Published in DiRROS: 01.02.2023; Views: 1006; Downloads: 532
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