Conditional Entropic Approach to Nonequilibrium Complex Systems with Weak Fluctuation Correlation

A conditional entropic approach is discussed for nonequilibrium complex systems with a weak correlation between spatiotemporally fluctuating quantities on a large time scale. The weak correlation is found to constitute the fluctuation distribution that maximizes the entropy associated with the conditional fluctuations. The approach is illustrated in diffusion phenomenon of proteins inside bacteria. A further possible illustration is also presented for membraneless organelles in embryos and beads in cell extracts, which share common natures of fluctuations in their diffusion.

Feasibility of Ultra-Short-Term Analysis of Heart Rate and Systolic Arterial Pressure Variability at Rest and during Stress via Time-Domain and Entropy-Based Measures

Heart Rate Variability (HRV) and Blood Pressure Variability (BPV) are widely employed tools for characterizing the complex behavior of cardiovascular dynamics. Usually, HRV and BPV analyses are carried out through short-term (ST) measurements, which exploit ~five-minute-long recordings. Recent research efforts are focused on reducing the time series length, assessing whether and to what extent Ultra-Short-Term (UST) analysis is capable of extracting information about cardiovascular variability from very short recordings. In this work, we compare ST and UST measures computed on electrocardiographic R-R intervals and systolic arterial pressure time series obtained at rest and during both postural and mental stress. Standard time-domain indices are computed, together with entropy-based measures able to assess the regularity and complexity of cardiovascular dynamics, on time series lasting down to 60 samples, employing either a faster linear parametric estimator or a more reliable but time-consuming model-free method based on nearest neighbor estimates. Our results are evidence that shorter time series down to 120 samples still exhibit an acceptable agreement with the ST reference and can also be exploited to discriminate between stress and rest. Moreover, despite neglecting nonlinearities inherent to short-term cardiovascular dynamics, the faster linear estimator is still capable of detecting differences among the conditions, thus resulting in its suitability to be implemented on wearable devices.

Belavkin-Staszewski Relative Entropy, Conditional Entropy, and Mutual Information

Belavkin–Staszewski relative entropy can naturally characterize the effects of the possible noncommutativity of quantum states. In this paper, two new conditional entropy terms and four new mutual information terms are first defined by replacing quantum relative entropy with Belavkin–Staszewski relative entropy. Next, their basic properties are investigated, especially in classical-quantum settings. In particular, we show the weak concavity of the Belavkin–Staszewski conditional entropy and obtain the chain rule for the Belavkin–Staszewski mutual information. Finally, the subadditivity of the Belavkin–Staszewski relative entropy is established, i.e., the Belavkin–Staszewski relative entropy of a joint system is less than the sum of that of its corresponding subsystems with the help of some multiplicative and additive factors. Meanwhile, we also provide a certain subadditivity of the geometric Rényi relative entropy.

Categorical Nature of Major Factor Selection via Information Theoretic Measurements

Without assuming any functional or distributional structure, we select collections of major factors embedded within response-versus-covariate (Re-Co) dynamics via selection criteria [C1: confirmable] and [C2: irrepaceable], which are based on information theoretic measurements. The two criteria are constructed based on the computing paradigm called Categorical Exploratory Data Analysis (CEDA) and linked to Wiener–Granger causality. All the information theoretical measurements, including conditional mutual information and entropy, are evaluated through the contingency table platform, which primarily rests on the categorical nature within all involved features of any data types: quantitative or qualitative. Our selection task identifies one chief collection, together with several secondary collections of major factors of various orders underlying the targeted Re-Co dynamics. Each selected collection is checked with algorithmically computed reliability against the finite sample phenomenon, and so is each member’s major factor individually. The developments of our selection protocol are illustrated in detail through two experimental examples: a simple one and a complex one. We then apply this protocol on two data sets pertaining to two somewhat related but distinct pitching dynamics of two pitch types: slider and fastball. In particular, we refer to a specific Major League Baseball (MLB) pitcher and we consider data of multiple seasons.

Life Worth Mentioning: Complexity in Life-Like Cellular Automata

Cellular automata (CA) have been lauded for their ability to generate complex global patterns from simple local rules. The late English mathematician, John Horton Conway, developed his illustrious Game of Life (Life) CA in 1970, which has since remained one of the most quintessential CA constructions-capable of producing a myriad of complex dynamic patterns and computational universality. Life and several other Life-like rules have been classified in the same group of aesthetically and dynamically interesting CA rules characterized by their complex behaviors. However, a rigorous quantitative comparison among similarly classified Life-like rules has not yet been fully established. Here we show that Life is capable of maintaining as much complexity as similar rules while remaining the most parsimonious. In other words, Life contains a consistent amount of complexity throughout its evolution, with the least number of rule conditions compared to other Life-like rules. We also found that the complexity of higher density Life-like rules, which themselves contain the Life rule as a subset, form a distinct concave density-complexity relationship whereby an optimal complexity candidate is proposed. Our results also support the notion that Life functions as the basic ingredient for cultivating the balance between structure and randomness to maintain complexity in 2D CA for low- and high-density regimes, especially over many iterations. This work highlights the genius of John Horton Conway and serves as a testament to his timeless marvel, which is referred to simply as: Life.

Information Flow Between Heart Rhythm, Repolarization, and the Diastolic Interval Series for Healthy Individuals and LQTS1 Patients

Using information theoretic measures, relations between heart rhythm, repolarization in the tissue of the heart, and the diastolic interval time series are analyzed. These processes are a fragment of the cardiovascular physiological network. A comparison is made between the results for 84 (42 women) healthy individuals and 65 (45 women) long QT syndrome type 1 (LQTS1) patients. Self-entropy, transfer entropy, and joint transfer entropy are calculated for the three time series and their combinations. The results for self-entropy indicate the well-known result that regularity of heart rhythm for healthy individuals is larger than that of QT interval series. The flow of information depends on the direction with the flow from the heart rhythm to QT dominating. In LQTS1 patients, however, our results indicate that information flow in the opposite direction may occur—a new result. The information flow from the heart rhythm to QT dominates, which verifies the asymmetry seen by Porta et al. in the variable tilt angle experiment. The amount of new information and self-entropy for LQTS1 patients is smaller than that for healthy individuals. However, information transfers from RR to QT and from DI to QT are larger in the case of LQTS1 patients.

Conditional Entropy: A Potential Digital Marker for Stress

Recent decades have witnessed a substantial progress in the utilization of brain activity for the identification of stress digital markers. In particular, the success of entropic measures for this purpose is very appealing, considering (1) their suitability for capturing both linear and non-linear characteristics of brain activity recordings and (2) their direct association with the brain signal variability. These findings rely on external stimuli to induce the brain stress response. On the other hand, research suggests that the use of different types of experimentally induced psychological and physical stressors could potentially yield differential impacts on the brain response to stress and therefore should be dissociated from more general patterns. The present study takes a step toward addressing this issue by introducing conditional entropy (CE) as a potential electroencephalography (EEG)-based resting-state digital marker of stress. For this purpose, we use the resting-state multi-channel EEG recordings of 20 individuals whose responses to stress-related questionnaires show significantly higher and lower level of stress. Through the application of representational similarity analysis (RSA) and K-nearest-neighbor (KNN) classification, we verify the potential that the use of CE can offer to the solution concept of finding an effective digital marker for stress.

Working Memory Decline in Alzheimer's Disease Is Detected by Complexity Analysis of Multimodal EEG-fNIRS

Alzheimer's disease (AD) is characterized by working memory (WM) failures that can be assessed at early stages through administering clinical tests. Ecological neuroimaging, such as Electroencephalography (EEG) and functional Near Infrared Spectroscopy (fNIRS), may be employed during these tests to support AD early diagnosis within clinical settings. Multimodal EEG-fNIRS could measure brain activity along with neurovascular coupling (NC) and detect their modifications associated with AD. Data analysis procedures based on signal complexity are suitable to estimate electrical and hemodynamic brain activity or their mutual information (NC) during non-structured experimental paradigms. In this study, sample entropy of whole-head EEG and frontal/prefrontal cortex fNIRS was evaluated to assess brain activity in early AD and healthy controls (HC) during WM tasks (i.e., Rey-Osterrieth complex figure and Raven's progressive matrices). Moreover, conditional entropy between EEG and fNIRS was evaluated as indicative of NC. The findings demonstrated the capability of complexity analysis of multimodal EEG-fNIRS to detect WM decline in AD. Furthermore, a multivariate data-driven analysis, performed on these entropy metrics and based on the General Linear Model, allowed classifying AD and HC with an AUC up to 0.88. EEG-fNIRS may represent a powerful tool for the clinical evaluation of WM decline in early AD.

New Service Virtualisation Approach to Generate the Categorical Fields in the Service Response

Software services communicate with different requisite services over the computer network to accomplish their tasks. The requisite services may not be readily available to test a specific service. Thus, service virtualisation has been proposed as an industry solution to ensure availability of the interactive behaviour of the requisite services. However, the existing techniques of virtualisation cannot satisfy the required accuracy or time constraints to keep up with the competitive business world. These constraints sacrifices quality and testing coverage, thereby delaying the delivery of software. We proposed a novel technique to improve the accuracy of the existing service virtualisation solutions without sacrificing time. This method generates the service response and predicts categorical fields in virtualised responses, extending existing research with lower complexity and higher accuracy. The proposed service virtualisation approach uses conditional entropy to identify the fields that can be used to drive the value of each categorical field based on the historical messages. Then, it uses joint probability distribution to find the best values for the categorical fields. The experimental evaluation illustrates that the proposed approach can generate responses with the required fields and accurate values for categorical fields over four data sets with stateful nature.

Conditional entropy approach to analyze cognitive dynamics in autism spectrum disorder

OBJECTIVE

Preliminary evidence has documented functional connectivity during the cognitive task in Autism Spectrum Disorder (ASD). However, evidence of effective neural connectivity with respect to information flow between different brain regions during complex tasks is missing. The present paper aims to provide insights into the cognition-based neural dynamics reflecting information exchange in brain network under cognitive load in ASD.

METHODS

Twenty-two individuals with ASD (8-18 years) and 18 Typically Developing (TD; 6-17 years) individuals participated in the cognitive task of differentiating risky from neutral stimuli. The Conditional Entropy (CE) technique is applied upon task-activated Electroencephalogram (EEG) to measure the causal influence of the activity of brain's one Region of interest (ROI) over another.

RESULTS

A higher CE in frontal ROI and left hemisphere reflected atypical brain complexity in ASD. The absence of causal effect, poor Coupling Strength (CS; measured using CE) and hemisphere lateralization is responsible for lower cognition in ASD. However, the persistent information exchange during the task reflects the existence of certain alternative paths when other direct paths remained disconnected due to cognitive impairment. The Support Vector Machine (SVM) classifier showed that CE can identify the atypical information exchange with an accuracy of 96.89% and area under curve = 0.987.

DISCUSSION

The statistical results reflect a significant change in the information flow between different ROIs in ASD. A correlation of CS and behavioral domain suggests that the cognitive decline could be predicted from the connectivity patterns. Thus, CS could be a potential biomarker to identify cognitive status at a higher discrimination rate in ASD.

Are Strategies Favoring Pattern Matching a Viable Way to Improve Complexity Estimation Based on Sample Entropy?

It has been suggested that a viable strategy to improve complexity estimation based on the assessment of pattern similarity is to increase the pattern matching rate without enlarging the series length. We tested this hypothesis over short simulations of nonlinear deterministic and linear stochastic dynamics affected by various noise amounts. Several transformations featuring a different ability to increase the pattern matching rate were tested and compared to the usual strategy adopted in sample entropy (SampEn) computation. The approaches were applied to evaluate the complexity of short-term cardiac and vascular controls from the beat-to-beat variability of heart period (HP) and systolic arterial pressure (SAP) in 12 Parkinson disease patients and 12 age- and gender-matched healthy subjects at supine resting and during head-up tilt. Over simulations, the strategies estimated a larger complexity over nonlinear deterministic signals and a greater regularity over linear stochastic series or deterministic dynamics importantly contaminated by noise. Over short HP and SAP series the techniques did not produce any practical advantage, with an unvaried ability to discriminate groups and experimental conditions compared to the traditional SampEn. Procedures designed to artificially increase the number of matches are of no methodological and practical value when applied to assess complexity indexes.

Sharp Second-Order Pointwise Asymptotics for Lossless Compression with Side Information

The problem of determining the best achievable performance of arbitrary lossless compression algorithms is examined, when correlated side information is available at both the encoder and decoder. For arbitrary source-side information pairs, the conditional information density is shown to provide a sharp asymptotic lower bound for the description lengths achieved by an arbitrary sequence of compressors. This implies that for ergodic source-side information pairs, the conditional entropy rate is the best achievable asymptotic lower bound to the rate, not just in expectation but with probability one. Under appropriate mixing conditions, a central limit theorem and a law of the iterated logarithm are proved, describing the inevitable fluctuations of the second-order asymptotically best possible rate. An idealised version of Lempel-Ziv coding with side information is shown to be universally first- and second-order asymptotically optimal, under the same conditions. These results are in part based on a new almost-sure invariance principle for the conditional information density, which may be of independent interest.

Weighted Mutual Information for Aggregated Kernel Clustering

Background: A common task in machine learning is clustering data into different groups based on similarities. Clustering methods can be divided in two groups: linear and nonlinear. A commonly used linear clustering method is K-means. Its extension, kernel K-means, is a non-linear technique that utilizes a kernel function to project the data to a higher dimensional space. The projected data will then be clustered in different groups. Different kernels do not perform similarly when they are applied to different datasets. Methods: A kernel function might be relevant for one application but perform poorly to project data for another application. In turn choosing the right kernel for an arbitrary dataset is a challenging task. To address this challenge, a potential approach is aggregating the clustering results to obtain an impartial clustering result regardless of the selected kernel function. To this end, the main challenge is how to aggregate the clustering results. A potential solution is to combine the clustering results using a weight function. In this work, we introduce Weighted Mutual Information (WMI) for calculating the weights for different clustering methods based on their performance to combine the results. The performance of each method is evaluated using a training set with known labels. Results: We applied the proposed Weighted Mutual Information to four data sets that cannot be linearly separated. We also tested the method in different noise conditions. Conclusions: Our results show that the proposed Weighted Mutual Information method is impartial, does not rely on a single kernel, and performs better than each individual kernel specially in high noise.

Multi-Harmonic Source Localization Based on Sparse Component Analysis and Minimum Conditional Entropy

Aiming at the fact that the independent component analysis algorithm requires more measurement points and cannot solve the problem of harmonic source location under underdetermined conditions, a new method based on sparse component analysis and minimum conditional entropy for identifying multiple harmonic source locations in a distribution system is proposed. Under the condition that the network impedance is unknown and the number of harmonic sources is undetermined, the measurement node configuration algorithm selects the node position to make the separated harmonic current more accurate. Then, using the harmonic voltage data of the selected node as the input, the sparse component analysis is used to solve the harmonic current waveform under underdetermination. Finally, the conditional entropy between the harmonic current and the system node is calculated, and the node corresponding to the minimum condition entropy is the location of the harmonic source. In order to verify the effectiveness and accuracy of the proposed method, the simulation was performed in an IEEE 14-node system. Moreover, compared with the results of independent component analysis algorithms. Simulation results verify the correctness and effectiveness of the proposed algorithm.

Ordinal Pattern Based Entropies and the Kolmogorov-Sinai Entropy: An Update

Different authors have shown strong relationships between ordinal pattern based entropies and the Kolmogorov–Sinai entropy, including equality of the latter one and the permutation entropy, the whole picture is however far from being complete. This paper is updating the picture by summarizing some results and discussing some mainly combinatorial aspects behind the dependence of Kolmogorov–Sinai entropy from ordinal pattern distributions on a theoretical level. The paper is more than a review paper. A new statement concerning the conditional permutation entropy will be given as well as a new proof for the fact that the permutation entropy is an upper bound for the Kolmogorov–Sinai entropy. As a main result, general conditions for the permutation entropy being a lower bound for the Kolmogorov–Sinai entropy will be stated. Additionally, a previously introduced method to analyze the relationship between permutation and Kolmogorov–Sinai entropies as well as its limitations will be investigated.

Refined Multiscale Entropy Using Fuzzy Metrics: Validation and Application to Nociception Assessment

The refined multiscale entropy (RMSE) approach is commonly applied to assess complexity as a function of the time scale. RMSE is normally based on the computation of sample entropy (SampEn) estimating complexity as conditional entropy. However, SampEn is dependent on the length and standard deviation of the data. Recently, fuzzy entropy (FuzEn) has been proposed, including several refinements, as an alternative to counteract these limitations. In this work, FuzEn, translated FuzEn (TFuzEn), translated-reflected FuzEn (TRFuzEn), inherent FuzEn (IFuzEn), and inherent translated FuzEn (ITFuzEn) were exploited as entropy-based measures in the computation of RMSE and their performance was compared to that of SampEn. FuzEn metrics were applied to synthetic time series of different lengths to evaluate the consistency of the different approaches. In addition, electroencephalograms of patients under sedation-analgesia procedure were analyzed based on the patient’s response after the application of painful stimulation, such as nail bed compression or endoscopy tube insertion. Significant differences in FuzEn metrics were observed over simulations and real data as a function of the data length and the pain responses. Findings indicated that FuzEn, when exploited in RMSE applications, showed similar behavior to SampEn in long series, but its consistency was better than that of SampEn in short series both over simulations and real data. Conversely, its variants should be utilized with more caution, especially whether processes exhibit an important deterministic component and/or in nociception prediction at long scales.

Double-Granule Conditional-Entropies Based on Three-Level Granular Structures

Rough set theory is an important approach for data mining, and it refers to Shannon's information measures for uncertainty measurements. The existing local conditional-entropies have both the second-order feature and application limitation. By improvements of hierarchical granulation, this paper establishes double-granule conditional-entropies based on three-level granular structures (i.e., micro-bottom, meso-middle, macro-top ), and then investigates the relevant properties. In terms of the decision table and its decision classification, double-granule conditional-entropies are proposed at micro-bottom by the dual condition-granule system. By virtue of successive granular summation integrations, they hierarchically evolve to meso-middle and macro-top, to respectively have part and complete condition-granulations. Then, the new measures acquire their number distribution, calculation algorithm, three bounds, and granulation non-monotonicity at three corresponding levels. Finally, the hierarchical constructions and achieved properties are effectively verified by decision table examples and data set experiments. Double-granule conditional-entropies carry the second-order characteristic and hierarchical granulation to deepen both the classical entropy system and local conditional-entropies, and thus they become novel uncertainty measures for information processing and knowledge reasoning.

An Information-Theoretic Approach to Quantitative Analysis of the Correspondence Between Skin Blood Flow and Functional Near-Infrared Spectroscopy Measurement in Prefrontal Cortex Activity

Effect of Skin blood flow (SBF) on functional near-infrared spectroscopy (fNIRS) measurement of cortical activity proves to be an illusive subject matter with divided stances in the neuroscientific literature on its extent. Whereas, some reports on its non-significant influence on fNIRS time series of cortical activity, others consider its impact misleading, even detrimental, in analysis of the brain activity as measured by fNIRS. This situation is further escalated by the fact that almost all analytical studies are based on comparison with functional Magnetic Resonance Imaging (fMRI). In this article, we pinpoint the lack of perspective in previous studies on preservation of information content of resulting fNIRS time series once the SBF is attenuated. In doing so, we propose information-theoretic criteria to quantify the necessary and sufficient conditions for SBF attenuation such that the information content of frontal brain activity in resulting fNIRS times series is preserved. We verify these criteria through evaluation of their utility in comparative analysis of principal component (PCA) and independent component (ICA) SBF attenuation algorithms. Our contributions are 2-fold. First, we show that mere reduction of SBF influence on fNIRS time series of frontal activity is insufficient to warrant preservation of cortical activity information. Second, we empirically justify a higher fidelity of PCA-based algorithm in preservation of the fontal activity's information content in comparison with ICA-based approach. Our results suggest that combination of the first two principal components of PCA-based algorithm results in most efficient SBF attenuation while preserving maximum frontal activity's information. These results contribute to the field by presenting a systematic approach to quantification of the SBF as an interfering process during fNIRS measurement, thereby drawing an informed conclusion on this debate. Furthermore, they provide evidence for a reliable choice among existing SBF attenuation algorithms and their inconclusive number of components, thereby ensuring minimum loss of cortical information during SBF attenuation process.

Entropy Measures in Analysis of Head up Tilt Test Outcome for Diagnosing Vasovagal Syncope

The paper presents possible applications of entropy measures in analysis of biosignals recorded during head up tilt testing (HUTT) in patients with suspected vasovagal syndrome. The study group comprised 80 patients who developed syncope during HUTT (57 in the passive phase of the test (HUTT(+) group) and 23 who had negative result of passive phase and developed syncope after provocation with nitroglycerine (HUTT(−) group)). The paper focuses on assessment of monitored signals’ complexity (heart rate expressed as R-R intervals (RRI), blood pressure (sBP, dBP) and stroke volume (SV)) using various types of entropy measures (Sample Entropy (SE), Fuzzy Entropy (FE), Shannon Entropy (Sh), Conditional Entropy (CE), Permutation Entropy (PE)). Assessment of the complexity of signals in supine position indicated presence of significant differences between HUTT(+) versus HUTT(−) patients only for Conditional Entropy (CE(RRI)). Values of CE(RRI) higher than 0.7 indicate likelihood of a positive result of HUTT already at the passive phase. During tilting, in the pre-syncope phase, significant differences were found for: (SE(sBP), SE(dBP), FE(RRI), FE(sBP), FE(dBP), FE(SV), Sh(sBP), Sh(SV), CE(sBP), CE(dBP)). HUTT(+) patients demonstrated significant changes in signals’ complexity more frequently than HUTT(−) patients. When comparing entropy measurements done in the supine position with those during tilting, SV assessed in HUTT(+) patients was the only parameter for which all tested measures of entropy (SE(SV), FE(SV), Sh(SV), CE(SV), PE(SV)) showed significant differences.

Change-Point Detection Using the Conditional Entropy of Ordinal Patterns

This paper is devoted to change-point detection using only the ordinal structure of a time series. A statistic based on the conditional entropy of ordinal patterns characterizing the local up and down in a time series is introduced and investigated. The statistic requires only minimal a priori information on given data and shows good performance in numerical experiments. By the nature of ordinal patterns, the proposed method does not detect pure level changes but changes in the intrinsic pattern structure of a time series and so it could be interesting in combination with other methods.

Transductive Feature Selection Using Clustering-Based Sample Entropy for Temperature Prediction in Weather Forecasting

Entropy measures have been a major interest of researchers to measure the information content of a dynamical system. One of the well-known methodologies is sample entropy, which is a model-free approach and can be deployed to measure the information transfer in time series. Sample entropy is based on the conditional entropy where a major concern is the number of past delays in the conditional term. In this study, we deploy a lag-specific conditional entropy to identify the informative past values. Moreover, considering the seasonality structure of data, we propose a clustering-based sample entropy to exploit the temporal information. Clustering-based sample entropy is based on the sample entropy definition while considering the clustering information of the training data and the membership of the test point to the clusters. In this study, we utilize the proposed method for transductive feature selection in black-box weather forecasting and conduct the experiments on minimum and maximum temperature prediction in Brussels for 1-6 days ahead. The results reveal that considering the local structure of the data can improve the feature selection performance. In addition, despite the large reduction in the number of features, the performance is competitive with the case of using all features.

Conditional Entropy and Location Error in Indoor Localization Using Probabilistic Wi-Fi Fingerprinting

Localization systems are increasingly valuable, but their location estimates are only useful when the uncertainty of the estimate is known. This uncertainty is currently calculated as the location error given a ground truth, which is then used as a static measure in sometimes very different environments. In contrast, we propose the use of the conditional entropy of a posterior probability distribution as a complementary measure of uncertainty. This measure has the advantage of being dynamic, i.e., it can be calculated during localization based on individual sensor measurements, does not require a ground truth, and can be applied to discrete localization algorithms. Furthermore, for every consistent location estimation algorithm, both the location error and the conditional entropy measures must be related, i.e., a low entropy should always correspond with a small location error, while a high entropy can correspond with either a small or large location error. We validate this relationship experimentally by calculating both measures of uncertainty in three publicly available datasets using probabilistic Wi-Fi fingerprinting with eight different implementations of the sensor model. We show that the discrepancy between these measures, i.e., many location estimates having a high location error while simultaneously having a low conditional entropy, is largest for the least realistic implementations of the probabilistic sensor model. Based on the results presented in this paper, we conclude that conditional entropy, being dynamic, complementary to location error, and applicable to both continuous and discrete localization, provides an important extra means of characterizing a localization method.

Conditional entropy in variation-adjusted windows detects selection signatures associated with expression quantitative trait loci (eQTLs)

BACKGROUND

Over the past 50,000 years, shifts in human-environmental or human-human interactions shaped genetic differences within and among human populations, including variants under positive selection. Shaped by environmental factors, such variants influence the genetics of modern health, disease, and treatment outcome. Because evolutionary processes tend to act on gene regulation, we test whether regulatory variants are under positive selection. We introduce a new approach to enhance detection of genetic markers undergoing positive selection, using conditional entropy to capture recent local selection signals.

RESULTS

We use conditional logistic regression to compare our Adjusted Haplotype Conditional Entropy (H|H) measure of positive selection to existing positive selection measures. H|H and existing measures were applied to published regulatory variants acting in cis (cis-eQTLs), with conditional logistic regression testing whether regulatory variants undergo stronger positive selection than the surrounding gene. These cis-eQTLs were drawn from six independent studies of genotype and RNA expression. The conditional logistic regression shows that, overall, H|H is substantially more powerful than existing positive-selection methods in identifying cis-eQTLs against other Single Nucleotide Polymorphisms (SNPs) in the same genes. When broken down by Gene Ontology, H|H predictions are particularly strong in some biological process categories, where regulatory variants are under strong positive selection compared to the bulk of the gene, distinct from those GO categories under overall positive selection. . However, cis-eQTLs in a second group of genes lack positive selection signatures detectable by H|H, consistent with ancient short haplotypes compared to the surrounding gene (for example, in innate immunity GO:0042742); under such other modes of selection, H|H would not be expected to be a strong predictor.. These conditional logistic regression models are adjusted for Minor allele frequency(MAF); otherwise, ascertainment bias is a huge factor in all eQTL data sets. Relationships between Gene Ontology categories, positive selection and eQTL specificity were replicated with H|H in a single larger data set. Our measure, Adjusted Haplotype Conditional Entropy (H|H), was essential in generating all of the results above because it: 1) is a stronger overall predictor for eQTLs than comparable existing approaches, and 2) shows low sequential auto-correlation, overcoming problems with convergence of these conditional regression statistical models.

CONCLUSIONS

Our new method, H|H, provides a consistently more robust signal associated with cis-eQTLs compared to existing methods. We interpret this to indicate that some cis-eQTLs are under positive selection compared to their surrounding genes. Conditional entropy indicative of a selective sweep is an especially strong predictor of eQTLs for genes in several biological processes of medical interest. Where conditional entropy is a weak or negative predictor of eQTLs, such as innate immune genes, this would be consistent with balancing selection acting on such eQTLs over long time periods. Different measures of selection may be needed for variant prioritization under other modes of evolutionary selection.

Assessing randomness and complexity in human motion trajectories through analysis of symbolic sequences

Complexity is a hallmark of intelligent behavior consisting both of regular patterns and random variation. To quantitatively assess the complexity and randomness of human motion, we designed a motor task in which we translated subjects' motion trajectories into strings of symbol sequences. In the first part of the experiment participants were asked to perform self-paced movements to create repetitive patterns, copy pre-specified letter sequences, and generate random movements. To investigate whether the degree of randomness can be manipulated, in the second part of the experiment participants were asked to perform unpredictable movements in the context of a pursuit game, where they received feedback from an online Bayesian predictor guessing their next move. We analyzed symbol sequences representing subjects' motion trajectories with five common complexity measures: predictability, compressibility, approximate entropy, Lempel-Ziv complexity, as well as effective measure complexity. We found that subjects' self-created patterns were the most complex, followed by drawing movements of letters and self-paced random motion. We also found that participants could change the randomness of their behavior depending on context and feedback. Our results suggest that humans can adjust both complexity and regularity in different movement types and contexts and that this can be assessed with information-theoretic measures of the symbolic sequences generated from movement trajectories.

Inferring Boolean network states from partial information

Networks of molecular interactions regulate key processes in living cells. Therefore, understanding their functionality is a high priority in advancing biological knowledge. Boolean networks are often used to describe cellular networks mathematically and are fitted to experimental datasets. The fitting often results in ambiguities since the interpretation of the measurements is not straightforward and since the data contain noise. In order to facilitate a more reliable mapping between datasets and Boolean networks, we develop an algorithm that infers network trajectories from a dataset distorted by noise. We analyze our algorithm theoretically and demonstrate its accuracy using simulation and microarray expression data.

Mechanisms of causal interaction between short-term RR interval and systolic arterial pressure oscillations during orthostatic challenge

The transition from the supine to the upright position requires a reorganization of the mechanisms of cardiovascular control that, if not properly accomplished, may lead to neurally mediated syncope. We investigated how the patterns of causality between systolic arterial pressure (SAP) and cardiac RR interval were modified by prolonged head-up tilt using a novel nonlinear approach based on corrected conditional entropy (CCE) compared with the standard approach exploiting the cross-correlation function (CCF). Measures of coupling strength and delay of the causal interactions from SAP to RR and from RR to SAP were obtained in 10 patients with recurrent, neurally mediated syncope (RNMS) and 10 healthy control (CO) subjects in the resting supine position (su) and after head-up tilting during early (et; ~2 min) and late (lt; ~15 min or before presyncope) epochs of upright posture. Main results were that 1) the coupling strength from SAP to RR increased significantly from su to et in both groups; by contrast, upon lt, the coupling strength was kept high in CO subjects and dropped to low values in RNMS patients; 2) in RNMS patients, the delay from SAP to RR was higher than in healthy controls and increased moving from et to lt. Although these trends were evident using the CCE approach, statistical significance was not attained using the CCF approach. These results indicate the necessity of dissecting causality between RR and SAP to properly assess directional mechanisms from the closed-loop cardiovascular regulation and suggest a weakened and slowed baroreflex as a major mechanism involved in the cardiovascular impairment associated to neurally mediated syncope.

Uncertainty in visual and auditory series is coded by modality-general and modality-specific neural systems

Coding for the degree of disorder in a temporally unfolding sensory input allows for optimized encoding of these inputs via information compression and predictive processing. Prior neuroimaging work has examined sensitivity to statistical regularities within single sensory modalities and has associated this function with the hippocampus, anterior cingulate, and lateral temporal cortex. Here we investigated to what extent sensitivity to input disorder, quantified by Markov entropy, is subserved by modality-general or modality-specific neural systems when participants are not required to monitor the input. Participants were presented with rapid (3.3 Hz) auditory and visual series varying over four levels of entropy, while monitoring an infrequently changing fixation cross. For visual series, sensitivity to the magnitude of disorder was found in early visual cortex, the anterior cingulate, and the intraparietal sulcus. For auditory series, sensitivity was found in inferior frontal, lateral temporal, and supplementary motor regions implicated in speech perception and sequencing. Ventral premotor and central cingulate cortices were identified as possible candidates for modality-general uncertainty processing, exhibiting marginal sensitivity to disorder in both modalities. The right temporal pole differentiated the highest and lowest levels of disorder in both modalities, but did not show general sensitivity to the parametric manipulation of disorder. Our results indicate that neural sensitivity to input disorder relies largely on modality-specific systems embedded in extended sensory cortices, though uncertainty-related processing in frontal regions may be driven by both input modalities.

Information domain approach to the investigation of cardio-vascular, cardio-pulmonary, and vasculo-pulmonary causal couplings

The physiological mechanisms related to cardio-vascular (CV), cardio-pulmonary (CP), and vasculo-pulmonary (VP) regulation may be probed through multivariate time series analysis tools. This study applied an information domain approach for the evaluation of non-linear causality to the beat-to-beat variability series of heart period (t), systolic arterial pressure (s), and respiration (r) measured during tilt testing and paced breathing (PB) protocols. The approach quantifies the causal coupling from the series i to the series j (C_ij) as the amount of information flowing from i to j. A measure of directionality is also obtained as the difference between two reciprocal causal couplings (D_i,j = C_ij − C_ji). Significant causal coupling and directionality were detected respectively when the median of C_ij over subjects was positive (C_ij > 0), and when D_i,j was statistically different from zero (D_i,j > 0 or D_i,j < 0). The method was applied on t, s, and r series measured in 15 healthy subjects (22–32 years, 8 males) in the supine (su) and upright (up) positions, and in further 15 subjects (21–29 years, 7 males) during spontaneous (sp) and paced (pa) breathing. In the control condition (su, sp), a significant causal coupling was observed for C_rs, C_rt, C_st, and C_ts, and significant directionality was present only from r to t (D_r,t > 0). During head-up tilt (up, sp), C_rs was preserved, C_rt decreased to zero median, and C_st and C_ts increased significantly; directionality vanished between r and t (D_r,t = 0) and raised from s to t (D_s,t > 0). During PB (su, pa), C_rs increased significantly, C_rt and C_ts were preserved, and C_st decreased to zero median; directionality was preserved from r to t (D_r,t > 0), and raised from r to s (D_r,s > 0). These results suggest that the approach may reflect modifications of CV, CP, and VP mechanisms consequent to altered physiological conditions, such as the baroreflex engagement and the dampening of respiratory sinus arrhythmia induced by tilt, or the respiratory driving on arterial pressure induced by PB. Thus, it could be suggested as a tool for the non-invasive monitoring of CV and cardiorespiratory control systems in normal and impaired conditions.