Sequence Of Intervals Research Articles

Specificity of the effect of double fractures of the rhythmogram on the daily variability of the sinus rhythm in patients with pulmonary and arterial hypertension

Introduction. In contrast to coronary heart disease (CHD), heart failure and a number of other diseases, in arterial and pulmonary hypertension, the deterioration of the functional state of the patient is often not accompanied by a decrease in the parameters of his sinus rhythm variability (SRV) for long periods of time. Moreover, an increase in age and an increase in blood pressure in patients with hypertension may lead not to a decrease, but to an increase in the parameters of daily SRV. It is noted that with hypertension on the sinus rhythm, the number of so-called double fractures of the rhythmogram (DFR) sequences of RR intervals short-long-short-long becomes greater, which can greatly affect the daily SRV.
 Aim. To study the specifics of the effect of DFR on daily SRV in arterial and pulmonary hypertension.
 Materials and methods. 300 Holter ECG records were analyzed, including 67 records of healthy persons, 20 records of CHD patients with CAG-confirmed vascular damage, 126 records of patients with arterial hypertension and 87 records of patients with idiopathic pulmonary hypertension. In the analysis of daily SRV, a modification of the SRV analysis method developed at the National Medical Research Center of Cardiology, taking into account the presence of DFR, was used.
 Results. It is shown that DFR reflects the processes of regulation of the sinus rhythm, which are affected differently by CHD and hypertension. In CHD, the frequency of DFR and its effect on the daily SRV significantly decreases (compared to the norm). With hypertension, the frequency of the appearance of DFR increases; there is a clear trend towards a decrease in SRV in comparison with the norm in the areas without DFR; in areas with DFR, this trend is less pronounced or absent, and at ages over 50 years, SRV increases.
 Conclusion. When studying the daily SRV of patients with arterial and idiopathic pulmonary hypertension, it is necessary to take into account the effect of DFR on the increase in SRV.

Variations of Time Irreversibility of Heart Rate Variability Under Normobaric Hypoxic Exposure.

In the field of biomedicine, time irreversibility is used to describe how imbalanced and asymmetric biological signals are. As an important feature of signals, the direction of time is always ignored. To find out the variation regularity of time irreversibility of heart rate variability (HRV) in the initial stage of hypoxic exposure, the present study implemented 2 h acute normobaric hypoxic exposure on six young subjects who have no plateau or hypoxia experiences; oxygen concentration was set as 12.9%. Electrocardiogram (ECG) signals were recorded in the whole process and RR interval sequences were extracted. Mathematical operations were executed to transform the difference of adjacent RR intervals into proportion and distance with delay time to conduct time irreversibility analysis of HRV. The same calculating method was implemented on six items randomly picked out from the MIT-BIH normal sinus rhythm database as a control group. Results show that variation of time irreversibility of HRV in a hypoxic environment is different from that in a normoxic environment, time irreversibility indices of a hypoxic group decreases continually at a delay time of 1 and 2, and indices curves of time irreversibility gradually tend to be steady and gather with each other at a delay time of 3 or 4. The control group shows no consistent tendency no matter what the delay time is in the range of 1–4. Our study indicates that in short-time hypoxic exposure, as hypoxic time goes by, regulation of the cardiovascular autonomic nervous system weakens; regulation times and intensity of sympathetic and parasympathetic nerves tend to be equal.

Development of a direct NGM(1,1) prediction model based on interval grey numbers

PurposeThe purpose of this paper is to construct an interval grey number NGM(1,1) direct prediction model (abbreviated as IGNGM(1,1)), which need not transform interval grey numbers sequences into real number sequences, and the Markov model is used to optimize residual sequences of IGNGM(1,1) model.Design/methodology/approachA definition equation of IGNGM(1,1) model is proposed in this paper, and its time response function is solved by recursive iteration method. Next, the optimal weight of development coefficients of two boundaries is obtained by genetic algorithm, which is designed by minimizing the average relative error based on time weighted. In addition to that, the Markov model is used to modify residual sequences.FindingsThe interval grey numbers’ sequences can be predicted directly by IGNGM(1,1) model and its residual sequences can be amended by Markov model. A case study shows that the proposed model has higher accuracy in prediction.Practical implicationsUncertainty and volatility information is widespread in practical applications, and the information can be characterized by interval grey numbers. In this paper, an interval grey numbers direct prediction model is proposed, which provides a method for predicting the uncertainty information in the real world.Originality/valueThe main contribution of this paper is to propose an IGNGM(1,1) model which can realize interval grey numbers prediction without transforming them into real number and solve the optimal weight of integral development coefficient by genetic algorithm so as to avoid the distortion of prediction results. Moreover, the Markov model is used to modify residual sequences to further improve the modeling accuracy.

Inverted central auditory hierarchies for encoding local intervals and global temporal patterns

In sensory systems, representational features of increasing complexity emerge at successive stages of processing. In the mammalian auditory pathway, the clearest change from brainstem to cortex is defined by what is lost, not by what is gained, in that high-fidelity temporal coding becomes increasingly restricted to slower acoustic modulation rates.1,2 Here, we explore the idea that sluggish temporal processing is more than just an inability for fast processing, but instead reflects an emergent specialization for encoding sound features that unfold on very slow timescales.3,4 We performed simultaneous single unit ensemble recordings from three hierarchical stages of auditory processing in awake mice - the inferior colliculus (IC), medial geniculate body of the thalamus (MGB) and primary auditory cortex (A1). As expected, temporal coding of brief local intervals (0.001 - 0.1 s) separating consecutive noise bursts was robust in the IC and declined across MGB and A1. By contrast, slowly developing (∼1s period) global rhythmic patterns of inter-burst interval sequences strongly modulated A1 spiking, were weakly captured by MGB neurons, and not at all by IC neurons. Shifts in stimulus regularity were not represented by changes in A1 spike rates, but rather in how the spikes were arranged in time. These findings show that low-level auditory neurons with fast timescales encode isolated sound features but not the longer gestalt, while the extended timescales in higher-level areas can facilitate sensitivity to slower contextual changes in the sensory environment.

Multiscale adaptive multifractal analysis and its applications.

To precisely analyze the fractal nature of a short-term time series under the multiscale framework, this study introduces multiscale adaptive multifractal analysis (MAMFA) combining the adaptive fractal analysis method with the multiscale multifractal analysis (MMA). MAMFA and MMA are both applied to the two kinds of simulation sequences, and the results show that the MAMFA method achieves better performances than MMA. MAMFA is also applied to the Chinese and American stock indexes and the R-R interval of heart rate data. It is found that the multifractal characteristics of stock sequences are related to the selection of the scale range s. There is a big difference in the Hurst surface's shape of Chinese and American stock indexes and Chinese stock indexes have more obvious multifractal characteristics. For the R-R interval sequence, we find that the subjects with abnormal heart rate have significant shape changes in three areas of Hurst surface compared with healthy subjects, thereby patients can be effectively distinguished from healthy subjects.

Terminal-Time Synchronization of Multivehicle Systems Under Sampled-Data Communications

This article presents a novel technique for terminal-time synchronization of multivehicle systems. Taking sampled-data communications into account, the terminal-time synchronization problem of multivehicle systems is formulated as three demands. An estimation of terminal time is introduced for each vehicle, and a cooperative algorithm is designed based on motion planning to synchronize all estimated terminal times by using only local sampled-data information. The proposed algorithm not only can ensure the consensus of estimated terminal times at appointed time, but also can make the estimates finally be equal to the actual terminal times. To avoid Zeno behavior, the explicit expression of the norm of the consensus error is formulated, based on which the sampling interval sequence is modified to realize appointed-time approximate consensus of the actual terminal times. Local controller is also designed for each vehicle to ensure the fixed-time convergence of the relative velocity normal to the line of sight, and thus the singularity of control input at terminal time instant is successfully avoided. Experiments are performed to verify the effectiveness of the algorithms.

Generative Adversarial Networks-Based Stochastic Approach to the Modeling of Individual Jumping Loads

Features of jumping loads are essentially high-dimensional random variables but have been simplistically modeled owing to the lack of proper mathematical tools. Generative adversarial networks (GANs) in conjunction with deep learning technology are adopted herein for modeling the jumping loads. Conditional GANs (CGANs) combined with Wasserstein GANs (WGANs) with gradient penalty (WGANs-GP) are adopted in the impulse modeling, where a multi-layer perceptron and a convolutional neural network are employed for the discriminator and generator, respectively. As for the impulse amplitude sequence and interval sequence modeling, similar CGANs combined with WGANs-GP are adopted, where recurrent neural networks are employed for both the generator and discriminator. A large amount of measured individual jumping loads are utilized in training GANs to ensure the generated samples can simulate the real ones well. After training, the individual jumping loads are simulated by connecting the generated impulse samples, based on the generated impulse amplitude sequence samples and interval sequence samples. The simulated jumping loads can be used to assess the vibration performance of assembly structures, such as grandstands, concert halls, and gym floors. Moreover, the established GANs can be extended to the modeling of other stochastic dynamic excitations.

Имплицитное запоминание последовательности временных интервалов

The article considers the studies performed in the «Sequence Learning» paradigm. A special case of this experimental approach is the method of temporal sequences memorization. The elements of such sequences are time intervals instead of stimulus or their spatial localization. The item of the conducted and described study was implicit learning of the time interval sequence. The goal of the experiment was to check the possibility of unconscious acquisition of the temporal sequences, not related to the sequences of another type of organization. To process the obtained results, mixed linear models were used. It was found that the learning of time interval sequences can occur regardless of the presence of regularity in the reaction order (motor sequence) and without rules in stimuli organization (structural sequence) or in the order of their localization (spatial sequence).

Optimization of Systems Repair Plans and Assessment of the Useful Life of Nuclear Power Plant Equipment

This paper presents a computer-aided method of planning the volumes of repairs of systems of nuclear power units and a method for calculating their gamma-percentile life. This planning is carried out on the basis of predicting the reliability indicator, the probability of no-failure operation for a certain time period, with the gamma-percentile life of the equipment being determined by solving the corresponding equations. The tasks considered are related to an important energy problem of extending the operation of nuclear power units. Its importance is determined mainly by economic feasibility: it is cheaper to assess the useful life of a nuclear power unit and, on this research basis, extend its operation, than create a new unit. It is also shown that the calculation of the probability of a radiation accident at a nuclear power unit is associated with the results of planning the repairs of its systems, with assessment of its useful life. An optimization problem is formulated: it is required to find such a plan for the volumes of repair of a system that, with limited repair costs, its reliability indicator for a given duration deviates least from the maximum permissible value. The solution to the problem is based on calculating the structural reliability of the system. A graphological image of the system is built in the form of a composition of graphological images of typical structures. After the reliability indicator of typical structures has been calculated, the structures are replaced with individual structural elements, which makes it possible to simplify the initial graphological image of the system in a computational scenario and calculate its reliability indicator. The determination of the repair volume is carried out by applying a version of the coordinate-wise optimization method. To assess the gamma-percentile life, a model is adopted, in which the recoverable equipment components have an unlimited life, although, of course, they "age", and the non-recoverable components spend their life up to the level when their replacement becomes conditioned by the violation of the requirement for the maximum permissible value of the system reliability indicator. Estimates of the gamma-percentile life of the equipment are calculated by planning system repairs on a sequence of intervals of annual energy production by a nuclear power unit.

Modeling fuzzy management processes of passenger transport systems

The main tasks of organizing route transportation when considering processes in transport systems are to ensure a high level of management and the introduction of advanced working methods to meet the needs of the commuters, to ensure the quality of passenger service, to use vehicles of the enterprises’ automobile fleet efficiently, to ensure transportation safety, as well as to reduce the cost of the necessary trips for the population. The main task of the passenger transport management should be the creation of schedules and the rational organization for the routes of vehicles. When looking for new effective methods and tools for managing passenger traffic, aimed at minimizing service time and achieving the maximum level of satisfaction of passengers, it is useful to consider the fuzzy logic methods. These methods provide and implement the mechanism of working with inaccurate concepts, introduce fuzzy sets of input data and allow performing logical actions with them as well as obtaining the final solution of the problem. While setting the task of integer programming for creating a schedule for a train route, the target function and the system of restrictions on the desired values of unknowns are replaced by the functions of belonging to fuzzy sets, which indicate the average degree of belonging to the selected sets. Finding the values of the variables that are the solution to the problem and grouping them gives us a schedule for the route, which optimizes the target function under given restrictions. As the objective function, namely, the function of belonging to multiple time intervals, which correspond to the fuzzy function of the target in the studies, the numerical expression of the average degree of satisfaction of the needs of passengers is chosen. The time intervals − the average degree of use of vehicles during service during the daily operation of the route is chosen as the system of restrictions on the desired variables. The algorithm for finding a solution space that is the basis for generating a schedule of vehicles on a route in the form of a sequence of service intervals corresponding to variable values has been developed. The fuzzy objectives of the problem should be subject to the main criterion for creating a traffic schedule and optimal route control. That criterion takes into account the cost of the operation time of vehicles and the cost of waiting time for passengers.

A Digital Electrocardiographic System for Assessing Myocardial Electrical Instability: Principles and Applications.

The aim of the study was to develop an ECG hardware and software system for monitoring electrical instability of the myocardium and to assess the diagnostic and prognostic capabilities of this setup in a cardiology clinic.Materials and Methods.The Intecard 7.3 software and hardware system developed in this study makes it possible to measure fluctuations of the ECG amplitude-time parameters using the beat-to-beat mode. Intecard 7.3 evaluates a number of ECG markers that reflect electrical instability of the myocardium. Among them are the fragmented QRS complex, the spatial QRS-T angle, the T-wave alternans, the duration, and dispersion of the QT interval, the turbulence and acceleration/deceleration of the heart rhythm.Clinical trials of Intecard 7.3 were carried out with 734 patients with ischemic heart disease or cardiomyopathy and 112 healthy individuals.Results.Intecard 7.3 reliably identifies fragmented QRS complexes by detecting short spikes of <25 ms in the ascending parts of the Q, R, and S waves. The QRS-T angle is determined from the reference amplitudes of the R and T waves in leads avF, V2, V5, and V6. Digital precision processing of the ECG signal improves its accuracy to microvolts and microseconds.The software was designed to measure the T-wave amplitude in each of 300–500 cardiobeats; T-wave alternans was estimated by the moving average method. In a typical cardiobeat, the QT dispersion was calculated based on 12 ECG leads. From the sequence of RR intervals, turbulence, and deceleration of the heart rhythm were determined.During the observation period of 5.0 [2.1; 5.9] years, 90 out of 734 patients (12.3%) experienced adverse cardiovascular events (ACVE). In this period, the myocardial electrical instability was recorded in patients with ACVE more frequently than in those without ACVE. Thus, the frequency of fragmented QRS was 72.2±4.7 vs 16.8±1.5% (p<0.01), the values of the QRS-T angle were 128 [55; 101] vs 80 [53; 121]° (p<0.001), the T-wave alternans — 36.9 [15.5; 62.1] vs 21.9 [10.2; 30.7] μV (p<0.005), the QT interval — 408 [383; 438] vs 376 [351; 400] ms (p<0.001), the QT dispersion — 76 [57; 96] vs 64 [50; 92] ms (p<0.005), respectively. In patients with ACVE, the threshold that triggers pathological rhythm turbulence was higher (>0%) than that in healthy controls (p<0.001); the deceleration of the heart rhythm was reduced from 19.2 [2.2; 38.0] to 8.8 [4.0; 16.8] ms (p<0.05).A personalized model for ACVE risk stratification has been developed. In this model, the area under the ROC curve was 0.856; sensitivity — 75%; specificity — 78%; predictive accuracy — 77%.Conclusion.Using the ECG markers of myocardial electrical instability, the Intecard 7.3 system allows one to predict life-threatening ventricular tachyarrhythmias and sudden cardiac death with an accuracy of 77%. The non-invasiveness, high productivity, and reasonable cost ensure the availability of this predictive technology in all levels of healthcare.

SMILE: a feature-based temporal abstraction framework for event-interval sequence classification

In this paper, we study the problem of classification of sequences of temporal intervals. Our main contribution is a novel framework, which we call SMILE, for extracting relevant features from interval sequences to construct classifiers.SMILE introduces the notion of utilizing random temporal abstraction features, we define as e-lets, as a means to capture information pertaining to class-discriminatory events which occur across the span of complete interval sequences. Our empirical evaluation is applied to a wide array of benchmark data sets and fourteen novel datasets for adverse drug event detection. We demonstrate how the introduction of simple sequential features, followed by progressively more complex features each improve classification performance. Importantly, this investigation demonstrates that SMILE significantly improves AUC performance over the current state-of-the-art. The investigation also reveals that the selection of underlying classification algorithm is important to achieve superior predictive performance, and how the number of features influences the performance of our framework.

Measuring the seismic risk along the Nazca–South American subduction front: Shannon entropy and mutability

Abstract. Four geographical zones are defined along the trench that is formed due to the subduction of the Nazca plate underneath the South American plate; they are denoted A, B, C and D from north to south; zones A, B and D had a major earthquake after 2010 (magnitude over 8.0), while zone C has not, thus offering a contrast for comparison. For each zone, a sequence of intervals between consecutive seisms with magnitudes greater than or equal to 3.0 is set up and then characterized by Shannon entropy and mutability. These methods show a correlation after a major earthquake in what is known as the aftershock regime but show independence otherwise. Exponential adjustments to these parameters reveal that mutability offers a wider range for the parameters to characterize the recovery compared to the values of the parameters defining the background activity for each zone before a large earthquake. It is found that the background activity is particularly high for zone A, still recovering for zone B, reaching values similar to those of zone A in the case of zone C (without recent major earthquake) and oscillating around moderate values for zone D. It is discussed how this can be an indication of more risk of an important future seism in the cases of zones A and C. The similarities and differences between Shannon entropy and mutability are discussed and explained.

An improved Poincaré plot-based method to detect atrial fibrillation from short single-lead ECG

PurposeWith the popularity of wearable mobile devices, increasing numbers of applications use single-lead electrocardiograms (ECGs), which provides information about heart rate and rhythm to detect cardiac diseases. Atrial fibrillation (AF) is the most common arrhythmia in clinical practice, it is very important to detect AF early. In this study, we propose a Poincaré plot-based method for AF detection that has the advantages of requiring few calculations and short detection segments. MethodOur method first extracts the first-order differential RR interval (ΔRRI) sequences from a segmented ECG data, and then the polar coordinate transformation is performed on the Poincaré plot of the ΔRRI to obtain the phase-based distribution. Two features, the distribution width Dw and the average distribution height Dh are extracted from the phase-based distribution to classify the AF and non-AF episodes. Five PhysioNet databases were used for the assessment, which contain 3,843.3 hours of data from 229 subjects. Long-Term AF Database was selected as the training set, and the remaining four databases were used as the testing sets. ResultsIn the testing sets, the results yield good sensitivity/specificity (97.91%/99.14%) with 60 second ECG signal segments, which are better than those of the existing the Poincaré plot-based methods, and the method also performs well with 20 second ECG signal segments (sensitivity/specificity of 97.28%/98.35%). ConclusionThe detection performance of this method is good under different condition, and has the advantage of easy implementation, which makes it promising for application in the detection and monitoring of AF.

Strip Layering Diagram-Based Optimum Continuously Varying Pulse Interval Sequence Design for Extremely High-Resolution Spaceborne Sliding Spotlight SAR

Applying a continuous varying pulse interval (CVPI) sequence is of significance for an extremely high-resolution (EHR) spaceborne sliding spotlight synthetic aperture radar (SAR) for complete data acquisition. An optimum CVPI sequence should be the one leading to the minimum movement of the echoes of interest in a pulse train. However, such an optimization can be hardly conducted using the traditional timing diagram. Aiming at solving this problem, this article introduces a new graphic tool, referred to as the strip layering diagram, to achieve an optimum CVPI sequence for an EHR spaceborne sliding spotlight SAR. The basic rationale is to explicitly employ a new parameter <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\eta $ </tex-math></inline-formula> to directly control the movement of the echoes of interest in a pulse train. The new strip layering diagram consists of two layered subdiagrams: one is the candidate subdiagram, consisting of the candidate strips presenting all the CVPI sequence candidates restricted by the data acquisition geometry; the other is the feasibility subdiagram, consisting of the feasibility strips marking all the feasible regions where the echoes of interest are not submerged by the transmitted pulses or contaminated by the nadir echoes. An optimum CVPI sequence can be accurately and efficiently achieved by sketching a line segment satisfying four conditions inside the strip layering diagram. The detailed comparisons between the new diagram and the traditional timing diagram are also provided, followed by computer simulations to validate the presented approaches.

An Explainable Fuzzy Theoretic Nonparametric Deep Model for Stress Assessment Using Heartbeat Intervals Analysis

This article presents an explainable fuzzy theoretic nonparametric deep model for an analysis of heart rate variability in application to stress assessment. We are concerned with the development of a model that evaluates and explains a short-time (3–5 min long) heartbeat interval sequence of an individual to estimate the level of acute perceived stress on a numerical scale from 0 to 100 via monitoring the functioning of the autonomic nervous system. The salient features of the approach are the following. 1) A deep model, consisting of a nested composition of mappings, discovers layers of increasingly abstract heartbeat interval data representation. 2) An analytical solution of the deep model's learning problem facilitates inducing a mapping from the noninterpretable heartbeat-interval-data-space onto another <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">interpretable</i> domain spanned by a stress index. A given noninterpretable R– R interval feature vector is explained by: 1) estimating the corresponding stress value; 2) providing the weights which must be assigned to the subjective ratings of stress; and 3) providing various information about the sympathetic and parasympathetic activities of autonomic nervous system by analyzing R-R interval sequence in frequency domain at different abstraction levels. The proof-of-concept is provided by experimentation on a previously studied dataset of 50 subjects and a new dataset of 100 subjects.

Dynamical complexity of FitzHugh–Nagumo neuron model driven by Lévy noise and Gaussian white noise

In this paper, on the basis of information theory measures (statistical complexity and normalized Shannon entropy), the dynamical complexity of FitzHugh–Nagumo (FHN) neuron model under the co-excitation of Lévy noise and Gaussian white noise is studied. Because the potential function of the neuron system is asymmetric, we consider not only the total residence time interval of the system, but also the residence time interval of the left and right potential wells respectively. Here, we use Bandt–Pompe algorithm to calculate the three interval sequences, and obtain the statistical complexity and normalized Shannon entropy of the total system as well as the left and right potential wells. Finally, the effects of additive noise intensity, multiplicative noise intensity and system parameter on complexity of system are analyzed. We find that the total dynamical complexity of the system is obviously different from that of a single potential well. In addition, Gaussian white noise and Lévy noise have different effects on the complexity of the system.

SOR-Like New Iterative Method for Solving the Epidemic Model and the Prey and Predator Problem

Our aim in this paper is to propose an SOR-like new iterative method by introducing a relaxation parameter ω to improve the new iterative method proposed by Daftardar-Gejji and Jafari (NIM) [J. Math. Anal. Appl. 316 (2006) 753–763] in order to solve two problems. The first one is the problem of the spread of a nonfatal disease in a population which is assumed to have constant size over the period of the epidemic, and the other one is the problem of prey and predator. The proposed method is not limited to these two problems but can be applicable to a wide range of systems of nonlinear functional problem. The results, for different values of ω, show that we found some known methods and our method compared to methods using the calculation of special polynomials and derivatives like the Adomian decomposition method (ADM), the calculation of the Lagrange multiplier as in the variational iterative method (VIM), or the construction of a homotopy as in the homotopy perturbation method (HPM) has several advantages, such as very effective and very simple to implement. Unfortunately, these methods do not guarantee a valid approximation in large time interval. To overcome this, we applied our method for approximating the solution of the problems in a sequence of time intervals as a multistage approach. Some numerical results are presented with plots according to the parameter ω.

Analysis of temporal correlation in heart rate variability through maximum entropy principle in a minimal pairwise glassy model

In this work we apply statistical mechanics tools to infer cardiac pathologies over a sample of M patients whose heart rate variability has been recorded via 24 h Holter device and that are divided in different classes according to their clinical status (providing a repository of labelled data). Considering the set of inter-beat interval sequences {mathbf {r}(i) } = { r_1(i), r_2(i), ldots , }, with i=1,ldots ,M, we estimate their probability distribution P(mathbf {r}) exploiting the maximum entropy principle. By setting constraints on the first and on the second moment we obtain an effective pairwise (r_n,r_m) model, whose parameters are shown to depend on the clinical status of the patient. In order to check this framework, we generate synthetic data from our model and we show that their distribution is in excellent agreement with the one obtained from experimental data. Further, our model can be related to a one-dimensional spin-glass with quenched long-range couplings decaying with the spin–spin distance as a power-law. This allows us to speculate that the 1/f noise typical of heart-rate variability may stem from the interplay between the parasympathetic and orthosympathetic systems.

Genome-wide association analysis of aluminum tolerance related traits in rapeseed (Brassica napus L.) during germination

With the increasing acidification of soil, aluminum (Al) toxicity has become one of the most important stress factors affecting seed germination quality and crop yield. To investigate the Al tolerance on seed germination, genome-wide association analysis (GWAS) of 19,949 SNPs with genome-wide coverage was used to identify the candidate genes, which were potentially related to germinate traits of rapeseed (Brassica napus L.) under Al stress. In the experiment, 169 rapeseed cultivars (lines) were treated with AlCl3 solution of 90 ppm, and distilled water was added to the control. At the 7th day, the phenotype data, including root length and dry weight, were measured and calculated. Using the TASSEL software, Al tolerance related traits were explored in rapeseed under germination with a 60 K Brassica Illumina® Infinium SNP array. Then, the structure of the population was analyzed with the STRUCTURE software, and the genetic relationship and LD attenuation were analyzed with the software TASSEL, respectively. The GWAS of relative root length (RRL) and relative dry weight (RDW) with SNP markers were carried out under the optimal model. Meanwhile, the candidate genes were predicted based on the LD interval sequence of the associated SNP locus. Subsequently, the homologous genes of rapeseed related to Al tolerance in the target genome region were screened in Arabidopsis thaliana (L.) Heynh. The results showed that 13 SNPs were significantly associated with these two traits. Among them, 8 SNPs were significantly associated with RRL and located on chromosomes A03, A07, A09, A10, C05, C06, and C09, respectively. Five SNPs were significantly associated with RDW and located on chromosomes A03, A04, A10, C05, and C07, respectively. Afterward, fifty-nine candidate genes related to Al tolerance were identified in the LD region of these SNP loci. Four of these genes were involved in the growth regulation about organic acid, ten were involved in growth-regulating substance, eleven were related to oxidative stress, and nineteen were involved in carbon and nitrogen metabolism. The results of this study provided a theoretical basis for Al tolerance in rapeseed and laid out a foundation for further functional verification of genes and cultivation of new Al tolerant rapeseed varieties.