Concept: Chaos theory
The mathematical structure of Sudoku puzzles is akin to hard constraint satisfaction problems lying at the basis of many applications, including protein folding and the ground-state problem of glassy spin systems. Via an exact mapping of Sudoku into a deterministic, continuous-time dynamical system, here we show that the difficulty of Sudoku translates into transient chaotic behavior exhibited by this system. We also show that the escape rate κ, an invariant of transient chaos, provides a scalar measure of the puzzle’s hardness that correlates well with human difficulty ratings. Accordingly, η = -log(10)κ can be used to define a “Richter”-type scale for puzzle hardness, with easy puzzles having 0 < η ≤ 1, medium ones 1 < η ≤ 2, hard with 2 < η ≤ 3 and ultra-hard with η > 3. To our best knowledge, there are no known puzzles with η > 4.
Individual participant data (IPD) meta-analyses that obtain “raw” data from studies rather than summary data typically adopt a “two-stage” approach to analysis whereby IPD within trials generate summary measures, which are combined using standard meta-analytical methods. Recently, a range of “one-stage” approaches which combine all individual participant data in a single meta-analysis have been suggested as providing a more powerful and flexible approach. However, they are more complex to implement and require statistical support. This study uses a dataset to compare “two-stage” and “one-stage” models of varying complexity, to ascertain whether results obtained from the approaches differ in a clinically meaningful way.
- Journal of the Royal Society, Interface / the Royal Society
- Published over 6 years ago
A new tool for visualization and analysis of system dynamics is introduced: the phasegram. Its application is illustrated with both classical nonlinear systems (logistic map and Lorenz system) and with biological voice signals. Phasegrams combine the advantages of sliding-window analysis (such as the spectrogram) with well-established visualization techniques from the domain of nonlinear dynamics. In a phasegram, time is mapped onto the x-axis, and various vibratory regimes, such as periodic oscillation, subharmonics or chaos, are identified within the generated graph by the number and stability of horizontal lines. A phasegram can be interpreted as a bifurcation diagram in time. In contrast to other analysis techniques, it can be automatically constructed from time-series data alone: no additional system parameter needs to be known. Phasegrams show great potential for signal classification and can act as the quantitative basis for further analysis of oscillating systems in many scientific fields, such as physics (particularly acoustics), biology or medicine.
An important challenge in heart research is to make the relation between the features of external stimuli and heart activity. Olfactory stimulation is an important type of stimulation that affects the heart activity, which is mapped on Electrocardiogram (ECG) signal. Yet, no one has discovered any relation between the structures of olfactory stimuli and the ECG signal. This study investigates the relation between the structures of heart rate and the olfactory stimulus (odorant). We show that the complexity of the heart rate is coupled with the molecular complexity of the odorant, where more structurally complex odorant causes less fractal heart rate. Also, odorant having higher entropy causes the heart rate having lower approximate entropy. The method discussed here can be applied and investigated in case of patients with heart diseases as the rehabilitation purpose.
In this paper we explore the specific role of randomness in financial markets, inspired by the beneficial role of noise in many physical systems and in previous applications to complex socio-economic systems. After a short introduction, we study the performance of some of the most used trading strategies in predicting the dynamics of financial markets for different international stock exchange indexes, with the goal of comparing them to the performance of a completely random strategy. In this respect, historical data for FTSE-UK, FTSE-MIB, DAX, and S & P500 indexes are taken into account for a period of about 15-20 years (since their creation until today).
- Computer methods in biomechanics and biomedical engineering
- Published about 8 years ago
Electrocardiogram (ECG) signals are difficult to interpret, and clinicians must undertake a long training process to learn to diagnose diabetes from subtle abnormalities in these signals. To facilitate these diagnoses, we have developed a technique based on the heart rate variability signal obtained from ECG signals. This technique uses digital signal processing methods and, therefore, automates the detection of diabetes from ECG signals. In this paper, we describe the signal processing techniques that extract features from heart rate (HR) signals and present an analysis procedure that uses these features to diagnose diabetes. Through statistical analysis, we have identified the correlation dimension, Poincaré geometry properties (SD2), and recurrence plot properties (REC, DET, L (mean)) as useful features. These features differentiate the HR data of diabetic patients from those of patients who do not have the illness, and have been validated by using the AdaBoost classifier with the perceptron weak learner (yielding a classification accuracy of 86%). We then developed a novel diabetic integrated index (DII) that is a combination of these nonlinear features. The DII indicates whether a particular HR signal was taken from a person with diabetes. This index aids the automatic detection of diabetes, thereby allowing a more objective assessment and freeing medical professionals for other tasks.
Tactile stimulation of the hand evokes highly precise and repeatable patterns of activity in mechanoreceptive afferents; the strength (i.e., firing rate, Muniak et al. 2007) and timing (Johansson and Birznieks 2004; Mackevicius et al. 2012; Saal et al. 2009) of these responses have been shown to convey stimulus information. To achieve an understanding of the mechanisms underlying the representation of tactile stimuli in the nerve, we developed a two-stage computational model consisting of a nonlinear mechanical transduction stage followed by a generalized integrate-and-fire mechanism. The model improves upon a recently published counterpart (Kim et al. 2010) in two important ways. First, complexity is dramatically reduced (at least one order of magnitude fewer parameters). Second, the model comprises a saturating non-linearity and therefore can be applied to a much wider range of stimuli. We show that both the rate and timing of afferent responses are predicted with remarkable precision, and observed adaptation patterns and threshold behavior are well captured. We conclude that the responses of mechanoreceptive afferents can be understood using a very parsimonious mechanistic model, which can then be used to accurately simulate the responses of afferent populations.
BACKGROUND: The prognostic value of evoked potentials (EPs) in multiple sclerosis (MS) has not been fully established. The correlations between the Expanded Disability Status Scale (EDSS) at First Neurological Evaluation (FNE) and the duration of the disease, as well as between EDSS and EPs, have influenced the outcome of most previous studies. To overcome this confounding relations, we propose to test the prognostic value of EPs within an appropriate patient population which should be based on patients with low EDSS at FNE and short disease duration. METHODS: We retrospectively selected a sample of 143 early relapsing remitting MS (RRMS) patients with an EDSS < 3.5 from a larger database spanning 20 years. By means of bivariate logistic regressions, the best predictors of worsening were selected among several demographic and clinical variables. The best multivariate logistic model was statistically validated and prospectively applied to 50 patients examined during 2009--2011. RESULTS: The Evoked Potentials score (EP score) and the Time to EDSS 2.0 (TT2) were the best predictors of worsening in our sample (Odds Ratio 1.10 and 0.82 respectively, p=0.001). Low EP score (below 15--20 points), short TT2 (lower than 3--5 years) and their interaction resulted to be the most useful for the identification of worsening patterns. Moreover, in patients with an EP score at FNE below 6 points and a TT2 greater than 3 years the probability of worsening was 10% after 4--5 years and rapidly decreased thereafter. CONCLUSIONS: In an appropriate population of early RRMS patients, the EP score at FNE is a good predictor of disability at low values as well as in combination with a rapid buildup of disability. Interestingly, an EP score at FNE under the median together with a clinical stability lasting more than 3 years turned out to be a protective pattern. This finding may contribute to an early identification of benign patients, well before the term required to diagnose Benign MS (BMS).
Breathing dynamics vary between infant sleep states, and are likely to exhibit non-linear behaviour. This study applied the non-linear analytical tool recurrence quantification analysis (RQA) to 400 breath interval periods of REM and N-REM sleep, and then using an overlapping moving window. The RQA variables were different between sleep states, with REM radius 150% greater than N-REM radius, and REM laminarity 79% greater than N-REM laminarity. RQA allowed the observation of temporal variations in non-linear breathing dynamics across a night’s sleep at 30s resolution, and provides a basis for quantifying changes in complex breathing dynamics with physiology and pathology.
Characterizing brain dynamics during anesthesia is a main current challenge in anesthesia study. Several single channel Electroencephalogram (EEG) -based commercial monitors like the Bispectral index (BIS) have suggested to examine EEG signal. But, the BIS index has obtained numerous critiques. In this study, we evaluate the concentration-dependent effect of the propofol on long-range frontal-temporal synchronization of EEG signals collected from eight subjects during a controlled induction and recovery design. We used order patterns cross recurrence plot and provide an index named order pattern laminarity (OPL) to assess changes in neuronal synchronization as the mechanism forming the foundation of conscious perception. The prediction probability of 0.9 and 0.84 for OPL and BIS specified that the OPL index correlated more strongly with effect-site propofol concentration. Also, our new index makes faster reaction to transients in EEG recordings based on pharmacokinetic and pharmacodynamic model parameters and demonstrates less variability at the point of loss of consciousness (standard deviation of 0.04 for OPL compared with 0.09 for BIS index). The result show that the OPL index can estimate anesthetic state of patient more efficiently than the BIS index in lightly sedated state with more tolerant of artifacts.