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 7 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.
The purpose of this study was to compare the effectiveness and recovery times of 0.3 and 0.5 mg/kg intranasal midazolam (INM) administered with a mucosal atomizer device (MAD) in a pediatric emergency dental hospital clinic. One hundred eighteen children aged from 4 to 6 years were randomly administered either 0.3 or 0.5 mg/kg INM via an MAD in a triple-blinded randomized controlled trial. Sedation was achieved to some degree in 100% of the sample. The pulse rate and oxygen saturation were within the normal range in 99% of the patients. A burning sensation was reported in 9% of children. The recovery time of the 0.5 mg/kg group was statistically longer than that of the 0.3 mg/kg group (16.5 vs 18.8 minutes) but the difference was not clinically significant. The findings of this study show that 0.3 or 0.5 mg/kg doses of INM resulted in safe and effective sedation. The 0.5 mg/kg dose was more effective than the 0.3 mg/kg dose in reducing anxiety.
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).
Physiological processes are regulated by nonlinear dynamical systems. Various nonlinear measures have frequently been used for characterizing the complexity of fractal time signals to detect system features that cannot be derived from linear analyses. We analysed human balance dynamics ranging from simple standing to balancing on one foot with closed eyes to study the inherent methodological problems when applying fractal dimension analysis to real-world signals. Higuchi dimension was used as an example. Choice of measurement and analysis parameters has a distinct influence on the computed dimension. Noise increases the fractional dimension which may be misinterpreted as a higher complexity of the signal. Publications without specifying the parameter setting, or without analysing the noise-sensitivity are not comparable to findings of others and therefore of limited scientific value.
- Computer methods in biomechanics and biomedical engineering
- Published almost 9 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).