Irregularity, volatility, risk, and financial market time series

Random forest-based prediction of intracranial hypertension in patients with traumatic brain injury

BACKGROUND

Treatment and prevention of intracranial hypertension (IH) to minimize secondary brain injury are central to the neurocritical care management of traumatic brain injury (TBI). Predicting the onset of IH in advance allows for a more aggressive prophylactic treatment. This study aimed to develop random forest (RF) models for predicting IH events in TBI patients.

METHODS

We analyzed prospectively collected data from patients admitted to the intensive care unit with invasive intracranial pressure (ICP) monitoring. Patients with persistent ICP > 22 mmHg in the early postoperative period (first 6 h) were excluded to focus on IH events that had not yet occurred. ICP-related data from the initial 6 h were used to extract linear (ICP, cerebral perfusion pressure, pressure reactivity index, and cerebrospinal fluid compensatory reserve index) and nonlinear features (complexity of ICP and cerebral perfusion pressure). IH was defined as ICP > 22 mmHg for > 5 min, and severe IH (SIH) as ICP > 22 mmHg for > 1 h during the subsequent ICP monitoring period. RF models were then developed using baseline characteristics (age, sex, and initial Glasgow Coma Scale score) along with linear and nonlinear features. Fivefold cross-validation was performed to avoid overfitting.

RESULTS

The study included 69 patients. Forty-three patients (62.3%) experienced an IH event, of whom 30 (43%) progressed to SIH. The median time to IH events was 9.83 h, and to SIH events, it was 11.22 h. The RF model showed acceptable performance in predicting IH with an area under the curve (AUC) of 0.76 and excellent performance in predicting SIH (AUC = 0.84). Cross-validation analysis confirmed the stability of the results.

CONCLUSIONS

The presented RF model can forecast subsequent IH events, particularly severe ones, in TBI patients using ICP data from the early postoperative period. It provides researchers and clinicians with a potentially predictive pathway and framework that could help triage patients requiring more intensive neurological treatment at an early stage.

Predicting the Severity and Discharge Prognosis of Traumatic Brain Injury Based on Intracranial Pressure Data Using Machine Learning Algorithms

OBJECTIVE

This study aimed to explore the potential of employing machine learning algorithms based on intracranial pressure (ICP), ICP-derived parameters, and their complexity to predict the severity and short-term prognosis of traumatic brain injury (TBI).

METHODS

A single-center prospectively collected cohort of neurosurgical intensive care unit admissions was analyzed. We extracted ICP-related data within the first 6 hours and processed them using complex algorithms. To indicate TBI severity and short-term prognosis, Glasgow Coma Scale score on the first postoperative day and Glasgow Outcome Scale-Extended score at discharge were used as binary outcome variables. A univariate logistic regression model was developed to predict TBI severity using only mean ICP values. Subsequently, 3 multivariate Random Forest (RF) models were constructed using different combinations of mean and complexity metrics of ICP-related data. To avoid overfitting, five-fold cross-validations were performed. Finally, the best-performing multivariate RF model was used to predict patients' discharge Glasgow Outcome Scale-Extended score.

RESULTS

The logistic regression model exhibited limited predictive ability with an area under the curve (AUC) of 0.558. Among multivariate models, the RF model, combining the mean and complexity metrics of ICP-related data, achieved the most robust ability with an AUC of 0.815. Finally, in terms of predicting discharge Glasgow Outcome Scale-Extended score, this model had a consistent performance with an AUC of 0.822. Cross-validation analysis confirmed the performance.

CONCLUSIONS

This study demonstrates the clinical utility of the RF model, which integrates the mean and complexity metrics of ICP data, in accurately predicting the TBI severity and short-term prognosis.

Multiscale two-dimensional permutation entropy to analyze encrypted images

Multiscale versions of weighted (and non-weighted) permutation entropy for two dimensions are considered in order to compare and analyze the results when different experiments are conducted. We propose the application of these measures to analyze encrypted images with different security levels and encryption methods.

Exploiting deterministic features in apparently stochastic data

Many processes in nature are the result of many coupled individual subsystems (like population dynamics or neurosystems). Not always such systems exhibit simple stable behaviors that in the past science has mostly focused on. Often, these systems are characterized by bursts of seemingly stochastic activity, interrupted by quieter periods. The hypothesis is that the presence of a strong deterministic ingredient is often obscured by the stochastic features. We test this by modeling classically stochastic considered real-world data from both, the stochastic as well as the deterministic approaches to find that the deterministic approach's results level with those from the stochastic side. Moreover, the deterministic approach is shown to reveal the full dynamical systems landscape, which can be exploited for steering the dynamics into a desired regime.

Regularity in Stock Market Indices within Turbulence Periods: The Sample Entropy Approach

The aim of this study is to assess and compare changes in regularity in the 36 European and the U.S. stock market indices within major turbulence periods. Two periods are investigated: the Global Financial Crisis in 2007–2009 and the COVID-19 pandemic outbreak in 2020–2021. The proposed research hypothesis states that entropy of an equity market index decreases during turbulence periods, which implies that regularity and predictability of a stock market index returns increase in such cases. To capture sequential regularity in daily time series of stock market indices, the Sample Entropy algorithm (SampEn) is used. Changes in the SampEn values before and during the particular turbulence period are estimated. The empirical findings are unambiguous and confirm no reason to reject the research hypothesis. Moreover, additional formal statistical analyses indicate that the SampEn results are similar both for developed and emerging European economies. Furthermore, the rolling-window procedure is utilized to assess the evolution of SampEn over time.

An Entropy Approach to Measure the Dynamic Stock Market Efficiency

We measure stock market efficiency by drawing the comprehensive sample from Asia, Europe, Africa, North-South America, and Pacific Ocean regions and rank the cross-regional stock markets according to their level of informational efficiency. The study period spans from January 1, 1994, to August 3, 2017. We employ the approximate entropy approach and find that stock market efficiency evolves over the period. The degree and nature of evolution vary across regions and the development stage of the markets. The global, regional, domestic economic, and non-economic factors influence the adaptive nature of the stock markets. The emerging stock markets have improved efficiency by financial liberalization policy but are adversely affected by global shocks. The estimates validate the relevance of the adaptive market framework to describe the rejection of random walk without excess returns. The results suggest the growing presence of technical analysis and active portfolio managers. The emerging markets in Asia hold policy lessons for their peers. The findings suggest that global investors need to overcome the homogeneity bias as returns opportunities exist within the region and types of markets.

Radionuclide ventriculography phase analysis for risk stratification of patients undergoing cardiotoxic cancer therapy

BACKGROUND

Accurate diagnostic tools to identify patients at risk of cancer therapy-related cardiac dysfunction (CTRCD) are critical. For patients undergoing cardiotoxic cancer therapy, ejection fraction assessment using radionuclide ventriculography (RNVG) is commonly used for serial assessment of left ventricular (LV) function.

METHODS

In this retrospective study, approximate entropy (ApEn), synchrony, entropy, and standard deviation from the phase histogram (phase SD) were investigated as potential early markers of LV dysfunction to predict CTRCD. These phase parameters were calculated from the baseline RNVG phase image for 177 breast cancer patients before commencing cardiotoxic therapy.

RESULTS

Of the 177 patients, 11 had a decline in left ventricular ejection fraction (LVEF) of over 10% to an LVEF below 50% after treatment had commenced. This patient group had a significantly higher ApEn at baseline to those who maintained a normal LVEF throughout treatment. Of the parameters investigated, ApEn was superior for predicting the risk of CTRCD. Combining ApEn with the baseline LVEF further improved the discrimination between the groups.

CONCLUSIONS

The results suggest that RNVG phase analysis using approximate entropy may aid in the detection of sub-clinical LV contraction abnormalities, not detectable by baseline LVEF measurement, predicting a subsequent decline in LVEF.

Financial markets' deterministic aspects modeled by a low-dimensional equation

We ask whether empirical finance market data (Financial Stress Index, swap and equity, emerging and developed, corporate and government, short and long maturity), with their recently observed alternations between calm periods and financial turmoil, could be described by a low-dimensional deterministic model, or whether this requests a stochastic approach. We find that a deterministic model performs at least as well as one of the best stochastic models, but may offer additional insight into the essential mechanisms that drive financial markets.

Statistical physics approaches to the complex Earth system

Global warming, extreme climate events, earthquakes and their accompanying socioeconomic disasters pose significant risks to humanity. Yet due to the nonlinear feedbacks, multiple interactions and complex structures of the Earth system, the understanding and, in particular, the prediction of such disruptive events represent formidable challenges to both scientific and policy communities. During the past years, the emergence and evolution of Earth system science has attracted much attention and produced new concepts and frameworks. Especially, novel statistical physics and complex networks-based techniques have been developed and implemented to substantially advance our knowledge of the Earth system, including climate extreme events, earthquakes and geological relief features, leading to substantially improved predictive performances. We present here a comprehensive review on the recent scientific progress in the development and application of how combined statistical physics and complex systems science approaches such as critical phenomena, network theory, percolation, tipping points analysis, and entropy can be applied to complex Earth systems. Notably, these integrating tools and approaches provide new insights and perspectives for understanding the dynamics of the Earth systems. The overall aim of this review is to offer readers the knowledge on how statistical physics concepts and theories can be useful in the field of Earth system science.

The interplay between executive control, behavioural variability and mind wandering: Insights from a high-definition transcranial direct-current stimulation study

While the involvement of executive processes in mind wandering is largely undebated, their exact relationship is subject to an ongoing debate and rarely studied dynamically within-subject. Several brain-stimulation studies using transcranial direct current stimulation (tDCS) have attempted to modulate mind-wandering propensity by stimulating the left dorsolateral prefrontal cortex (DLPFC) which is an important hub in the prefrontal control network. In a series of three studies testing a total of N = 100 participants, we develop a novel task that allows to study the dynamic interplay of mind wandering, behavioural varibility and the flexible recruitment of executive resources as indexed by the randomness (entropy) of movement sequences generated by our participants. We consistently find that behavioural variability is increased and randomness is decreased during periods of mind wandering. Interestingly, we also find that behavioural variability interacts with the entropy-MW effect, opening up the possibility to detect distinct states of off-focus cognition. When applying a high-definition transcranial direct-current stimulation (HD-tDCS) montage to the left DLPFC, we find that propensity to mind wander is reduced relative to a group receiving sham stimulation.

Uncovering transitions in paleoclimate time series and the climate driven demise of an ancient civilization

We present a hybrid framework appropriate for identifying distinct dynamical regimes and transitions in a paleoclimate time series. Our framework combines three powerful techniques used independently of each other in time series analysis: a recurrence plot, manifold learning through Laplacian eigenmaps, and Fisher information metric. The resulting hybrid approach achieves a more automated classification and visualization of dynamical regimes and transitions, including in the presence of missing values, observational noise, and short time series. We illustrate the capabilities of the method through several pragmatic numerical examples. Furthermore, to demonstrate the practical usefulness of the method, we apply it to a recently published paleoclimate dataset: a speleothem oxygen isotope record from North India covering the past 5700 years. This record encodes the patterns of monsoon rainfall over the region and covers the critically important period during which the Indus Valley Civilization matured and declined. We identify a transition in monsoon dynamics, indicating a possible connection between climate change and the decline of the Indus Valley Civilization.

Analyzing changes in the complexity of climate in the last four decades using MERRA-2 radiation data

The energy balance of the Earth is controlled by the shortwave and longwave radiation emitted to space. Changes in the thermodynamic state of the system over time affect climate and are noticeable when viewing the system as a whole. In this paper, we study the changes in the complexity of climate in the last four decades using data from the Modern-Era Retrospective analysis for Research and Applications, Version 2 (MERRA-2). First, we study the complexity of the shortwave and longwave radiation fields independently using Approximate Entropy and Sample Entropy, observing that the rate of complexity change is faster for shortwave radiation. Then, we study the causality of those changes using Transfer Entropy to capture the non-linear dynamics of climate, showing that the changes are mainly driven by the variations in shortwave radiation. The observed behavior of climatic complexity could be explained by the changes in cloud amount, and we research that possibility by investigating its evolution from a complexity perspective using data from the International Satellite Cloud Climatology Project (ISCCP).

Quantifying the randomness of the stock markets

Randomness has been mathematically defined and quantified in time series using algorithms such as Approximate Entropy (ApEn). Even though ApEn is independent of any model and can be used with any time series, as the markets have different statistical values, it cannot be applied directly to make comparisons between series of financial data. In this paper, we develop further the use of Approximate Entropy to quantify the existence of patterns in evolving data series, defining a measure to allow comparisons between time series and epochs using a maximum entropy approach. We apply the methodology to the stock markets as an example of its application, showing that the number of patterns changed for the six analyzed markets depending on the economic situation, in agreement with the Adaptive Markets Hypothesis.

Approximate Entropy and Sample Entropy: A Comprehensive Tutorial

Approximate Entropy and Sample Entropy are two algorithms for determining the regularity of series of data based on the existence of patterns. Despite their similarities, the theoretical ideas behind those techniques are different but usually ignored. This paper aims to be a complete guideline of the theory and application of the algorithms, intended to explain their characteristics in detail to researchers from different fields. While initially developed for physiological applications, both algorithms have been used in other fields such as medicine, telecommunications, economics or Earth sciences. In this paper, we explain the theoretical aspects involving Information Theory and Chaos Theory, provide simple source codes for their computation, and illustrate the techniques with a step by step example of how to use the algorithms properly. This paper is not intended to be an exhaustive review of all previous applications of the algorithms but rather a comprehensive tutorial where no previous knowledge is required to understand the methodology.

Data-driven inference of hidden nodes in networks

The explosion of activity in finding interactions in complex systems is driven by availability of copious observations of complex natural systems. However, such systems, e.g., the human brain, are rarely completely observable. Interaction network inference must then contend with hidden variables affecting the behavior of the observed parts of the system. We present an effective approach for model inference with hidden variables. From configurations of observed variables, we identify the observed-to-observed, hidden-to-observed, observed-to-hidden, and hidden-to-hidden interactions, the configurations of hidden variables, and the number of hidden variables. We demonstrate the performance of our method by simulating a kinetic Ising model, and show that our method outperforms existing methods. Turning to real data, we infer the hidden nodes in a neuronal network in the salamander retina and a stock market network. We show that predictive modeling with hidden variables is significantly more accurate than that without hidden variables. Finally, an important hidden variable problem is to find the number of clusters in a dataset. We apply our method to classify MNIST handwritten digits. We find that there are about 60 clusters which are roughly equally distributed among the digits.

Network inference in stochastic systems from neurons to currencies: Improved performance at small sample size

The fundamental problem in modeling complex phenomena such as human perception using probabilistic methods is that of deducing a stochastic model of interactions between the constituents of a system from observed configurations. Even in this era of big data, the complexity of the systems being modeled implies that inference methods must be effective in the difficult regimes of small sample sizes and large coupling variability. Thus, model inference by means of minimization of a cost function requires additional assumptions such as sparsity of interactions to avoid overfitting. In this paper, we completely divorce iterative model updates from the value of a cost function quantifying goodness of fit. This separation enables the use of goodness of fit as a natural rationale for terminating model updates, thereby avoiding overfitting. We do this within the mathematical formalism of statistical physics by defining a formal free energy of observations from a partition function with an energy function chosen precisely to enable an iterative model update. Minimizing this free energy, we demonstrate coupling strength inference in nonequilibrium kinetic Ising models, and show that our method outperforms other existing methods in the regimes of interest. Our method has no tunable learning rate, scales to large system sizes, and has a systematic expansion to obtain higher-order interactions. As applications, we infer a functional connectivity network in the salamander retina and a currency exchange rate network from time-series data of neuronal spiking and currency exchange rates, respectively. Accurate small sample size inference is critical for devising a profitable currency hedging strategy.

The evolving cobweb of relations among partially rational investors

To overcome the limitations of neoclassical economics, researchers have leveraged tools of statistical physics to build novel theories. The idea was to elucidate the macroscopic features of financial markets from the interaction of its microscopic constituents, the investors. In this framework, the model of the financial agents has been kept separate from that of their interaction. Here, instead, we explore the possibility of letting the interaction topology emerge from the model of the agents’ behavior. Then, we investigate how the emerging cobweb of relationship affects the overall market dynamics. To this aim, we leverage tools from complex systems analysis and nonlinear dynamics, and model the network of mutual influence as the output of a dynamical system describing the edge evolution. In this work, the driver of the link evolution is the relative reputation between possibly coupled agents. The reputation is built differently depending on the extent of rationality of the investors. The continuous edge activation or deactivation induces the emergence of leaders and of peculiar network structures, typical of real influence networks. The subsequent impact on the market dynamics is investigated through extensive numerical simulations in selected scenarios populated by partially rational investors.

Optimizing human activity patterns using global sensitivity analysis

Implementing realistic activity patterns for a population is crucial for modeling, for example, disease spread, supply and demand, and disaster response. Using the dynamic activity simulation engine, DASim, we generate schedules for a population that capture regular (e.g., working, eating, and sleeping) and irregular activities (e.g., shopping or going to the doctor). We use the sample entropy (SampEn) statistic to quantify a schedule's regularity for a population. We show how to tune an activity's regularity by adjusting SampEn, thereby making it possible to realistically design activities when creating a schedule. The tuning process sets up a computationally intractable high-dimensional optimization problem. To reduce the computational demand, we use Bayesian Gaussian process regression to compute global sensitivity indices and identify the parameters that have the greatest effect on the variance of SampEn. We use the harmony search (HS) global optimization algorithm to locate global optima. Our results show that HS combined with global sensitivity analysis can efficiently tune the SampEn statistic with few search iterations. We demonstrate how global sensitivity analysis can guide statistical emulation and global optimization algorithms to efficiently tune activities and generate realistic activity patterns. Though our tuning methods are applied to dynamic activity schedule generation, they are general and represent a significant step in the direction of automated tuning and optimization of high-dimensional computer simulations.

Non-linear dynamics in parkinsonism

Over the last 30 years, the functions (and dysfunctions) of the sensory-motor circuitry have been mostly conceptualized using linear modelizations which have resulted in two main models: the “rate hypothesis” and the “oscillatory hypothesis.” In these two models, the basal ganglia data stream is envisaged as a random temporal combination of independent simple patterns issued from its probability distribution of interval interspikes or its spectrum of frequencies respectively. More recently, non-linear analyses have been introduced in the modelization of motor circuitry activities, and they have provided evidences that complex temporal organizations exist in basal ganglia neuronal activities. Regarding movement disorders, these complex temporal organizations in the basal ganglia data stream differ between conditions (i.e., parkinsonism, dyskinesia, healthy control) and are responsive to treatments (i.e., l-DOPA, deep brain stimulation). A body of evidence has reported that basal ganglia neuronal entropy (a marker for complexity/irregularity in time series) is higher in hypokinetic state. In line with these findings, an entropy-based model has been recently formulated to introduce basal ganglia entropy as a marker for the alteration of motor processing and a factor of motor inhibition. Importantly, non-linear features have also been identified as a marker of condition and/or treatment effects in brain global signals (EEG), muscular activities (EMG), or kinetic of motor symptoms (tremor, gait) of patients with movement disorders. It is therefore warranted that the non-linear dynamics of motor circuitry will contribute to a better understanding of the neuronal dysfunctions underlying the spectrum of parkinsonian motor symptoms including tremor, rigidity, and hypokinesia.

Temporal Complexity in Team Coordination Associated with Increased Performance in a Fast-Paced Puzzle Task

Coordination is a critical component of team performance. Nonlinear time-series measures, such as Sample Entropy (SEn), provide a novel means to examine temporal structure in team coordination. The goal for this study was to apply SEn to the continuous motor responses (gamepad button presses) of dyadic teams who performed a fast-paced puzzle task (Quadra – a variant of videogame Tetris). Inferential analyses were used to: a) determine if meaningful (i.e., deterministic) temporal structure existed in team responses using SEn, and b) examine correlations between team performance and coordination metrics (including SEn). Results confirmed that meaningful temporal structure existed in the sequential type and time of team motor responses. In addition, SEn was the only coordination metric to exhibit a significant relationship with team performance outcomes. Together, these findings support the viability and salience of nonlinear measures such as SEn in assessment of team coordination.

Approximate entropy of network parameters

We study the notion of approximate entropy within the framework of network theory. Approximate entropy is an uncertainty measure originally proposed in the context of dynamical systems and time series. We first define a purely structural entropy obtained by computing the approximate entropy of the so-called slide sequence. This is a surrogate of the degree sequence and it is suggested by the frequency partition of a graph. We examine this quantity for standard scale-free and Erdös-Rényi networks. By using classical results of Pincus, we show that our entropy measure often converges with network size to a certain binary Shannon entropy. As a second step, with specific attention to networks generated by dynamical processes, we investigate approximate entropy of horizontal visibility graphs. Visibility graphs allow us to naturally associate with a network the notion of temporal correlations, therefore providing the measure a dynamical garment. We show that approximate entropy distinguishes visibility graphs generated by processes with different complexity. The result probes to a greater extent these networks for the study of dynamical systems. Applications to certain biological data arising in cancer genomics are finally considered in the light of both approaches.

Oscillations in joint synchrony of reproductive hormones in healthy men

Negative-feedback (inhibitory) and positive-feedforward (stimulatory) processes regulate physiological systems. Whether such processes are themselves rhythmic is not known. Here, we apply cross-approximate entropy (cross-ApEn), a noninvasive measurement of joint (pairwise) signal synchrony, to inferentially assess hypothesized circadian and ultradian variations in feedback coupling. The data comprised simultaneous measurements of three pituitary and one peripheral hormone (LH, FSH, prolactin, and testosterone) in 12 healthy men each sampled every 10 min for 4 days (5,760 min). Ergodicity, due to the time series stationarity of the measurements over the 4 days, allows for effective estimation of parameters based upon the 12 subjects. Cross-ApEn changes were quantified via moving-window estimates applied to 4-day time series pairs. The resultant ordered windowed cross-ApEn series (in time) were subjected to power spectrum analysis. Rhythmicity was assessed against the null hypothesis of randomness using 1,000 simulated periodograms derived by shuffling the interpulse-interval hormone-concentration segments and redoing cross-ApEn windows and spectral analysis. By forward cross-ApEn analysis, paired LH-testosterone, LH-prolactin, and LH-FSH synchrony maintained dominant rhythms with periodicities of 18-22.5, 18, and 22.5 h, respectively (each P < 0.001). By reverse (feedback) cross-ApEn analysis, testosterone-LH, testosterone-prolactin, and testosterone-FSH synchrony cycles were 30, 18, and 30-45 h, respectively (each P ≤ 0.001). Significant 8- or 24-h rhythms were also detected in most linkages, and maximal bihormonal synchrony occurred consistently at ∼0400-0500. Collectively, these analyses demonstrate significant ultradian (<24 h), circadian (∼24 h), and infradian (>24 h) oscillations in pituitary-testis synchrony, wherein maximal biglandular coordination is strongly constrained to the early morning hours.

Evaluation of eye metrics as a detector of fatigue

OBJECTIVES

This study evaluated oculometrics as a detector of fatigue in Air Force-relevant tasks after sleep deprivation. Using the metrics of total eye closure duration (PERCLOS) and approximate entropy (ApEn), the relation between these eye metrics and fatigue-induced performance decrements was investigated.

BACKGROUND

One damaging effect to the successful outcome of operational military missions is that attributed to sleep deprivation-induced fatigue. Consequently, there is interest in the development of reliable monitoring devices that can assess when an operator is overly fatigued.

METHOD

Ten civilian participants volunteered to serve in this study. Each was trained on three performance tasks: target identification, unmanned aerial vehicle landing, and the psychomotor vigilance task (PVT). Experimental testing began after 14 hr awake and continued every 2 hr until 28 hr of sleep deprivation was reached.

RESULTS

Performance on the PVT and target identification tasks declined significantly as the level of sleep deprivation increased.These performance declines were paralleled more closely by changes in the ApEn compared to the PERCLOS measure.

CONCLUSION

The results provide evidence that the ApEn eye metric can be used to detect fatigue in relevant military aviation tasks.

APPLICATION

Military and commercial operators could benefit from an alertness monitoring device.

Volatility, irregularity, and predictable degree of accumulative return series

Recently it was shown that financial time series are not completely random process but exhibit long-term or short-term dependences, which offer promises for predictability. However, we do not clearly understand the potential relationship between serial structure and predictability. This paper proposed a framework to magnify the correlations and regularities contained in financial time series through constructing accumulative return series. This method can help us distinguish the real world financial time series from random-walk process effectively by examining the change patterns of volatility, Hurst exponent, and approximate entropy. Furthermore, we have found that the predictable degree increases continually with the increasing length of accumulative return. Our results suggest that financial time series are predictable to some extent and approximate entropy is a good indicator to characterize the predictable degree of financial time series if we take the influence of their volatility into account.

Fast computation of approximate entropy

The approximate entropy (ApEn) is a measure of systems complexity. The implementation of the method is computationally expensive and requires execution time analogous to the square of the size of the input signal. We propose here a fast algorithm which speeds up the computation of approximate entropy by detecting early some vectors that are not similar and by excluding them from the similarity test. Experimental analysis with various biomedical signals revealed a significant improvement in execution times.

Estimating the stability of Escherichia coli O157:H7 survival in manure-amended soils with different management histories

The objective of this study is to describe survival of Escherichia coli O157:H7 populations in manure-amended soils in terms of population stability, i.e. the temporal variation around the decline curve, in relation to soil characteristics indicative of soil health. Cow manure inoculated with E. coli O157:H7 was mixed with 18 pairs of organically and conventionally managed soils (10% of manure, kg kg(-1)). For four of the soil pairs, also three different manure densities (5%, 10% and 20%) were compared. All soil-manure mixtures were incubated for 2 months, and population densities of E. coli O157:H7 were quantified weekly. De-trending of survival data was done by modified logistic regression. The residual values were used to assess variation in the changes of E. coli O157:H7 populations by performing the approximate entropy (ApEn) procedure. The term irregularity is used to describe this variation in ApEn literature. On average, the decline of E. coli O157:H7 was more irregular in conventional and loamy soils than in organic and sandy soils (P < 0.05). Multiple regression analysis of irregularity of E. coli O157:H7 survival on 13 soil characteristics showed a positive relation with the ratio of copiotrophic/oligotrophic bacteria, suggesting greater instability at higher available substrate concentrations. Incremental rates of manure application significantly changed the irregularity for conventional soils only. Estimation of temporal variation of enteropathogen populations by the ApEn procedure can increase the accuracy of predicted survival time and may form an important indication for soil health.

Approximate entropy as a measure of irregularity for psychiatric serial metrics

OBJECTIVES

The quantification of subtle patterns in sequential data, and their changes, has considerable potential utility throughout psychiatry, including the analyses of mood ratings, heart rate, respiratory, and electroencephalographic recordings.

METHODS

Approximate entropy (ApEn), a relatively recently developed statistic quantifying serial irregularity, has been applied in numerous studies throughout mathematics and other fields of study, especially biology.

RESULTS

We discussed applications of ApEn, both extant and potential, of most relevance to psychiatrists. We provided a mechanistic interpretation of lowered ApEn values, and discusses the relationship between ApEn and other (both classical and complexity) measures of serial dynamics. We also briefly discussed cross-ApEn, a thematically similar quantification of two-variable asynchrony that can aid in uncovering subtle disruptions in complicated network dynamics.

CONCLUSIONS

ApEn and cross-ApEn have significant potential to consequentially enhance present statistical methodologies of analysis of psychiatric data, in both clinical and in research settings.