基于Poincaré差值散点图的心率变异性分析方法研究

在心率变异性的非线性分析中, Poincaré散点图分析是一种重要手段.本文基于Poincaré差值散点图(modified Poincaré plot)提出了两个参数——区域分布熵和区域分布系数, 用于定量描述所考察区域内散点的分布趋势, 并提出对散点在4个象限中的分布进行分别计算.通过对MIT-BIH数据库中健康年轻人、健康老年人和充血性心力衰竭患者样本数据的分析, 发现两参数值均呈现显著的组间差异;同时, 不同象限的分析结果显示了四个象限具有不同的区分敏感性, 而其中尤以第一象限的区分度为最高, 反映出充血性心力衰竭患者相对健康人迷走神经调控功能的改变最为显著, 与以往的生理学研究结论相符.经验证, 该方法可用于短时数据, 更易于扩展至临床应用.     

心率变异性基本尺度熵的多尺度化研究

将基本尺度熵的方法在时间上做多尺度化的扩展,并将其应用到心跳间隔序列的分析研究中.研究发现,健康人的心率变异性是小时间尺度下的模式特定性与大时间尺度下的模式丰富性相结合的,而充盈性心衰患者则正好相反.这说明充盈性心衰患者在小时间尺度下心脏动力系统的控制不力,导致随机性增加,而在大时间尺度下对外界环境变化反应又不够丰富,从而导致生命更容易受威胁.据此提出了以小时间尺度下的基本尺度熵值相对于大时间尺度下平台区基本尺度熵值的变异参数δ作为区分健康人和充盈性心衰患者的诊断依据.通过对72例健康人和44例充盈性心衰患者的计算,发现两组样本差异显著,证明了参数δ的有效性. 关键词： 多尺度化的基本尺度熵 心跳间隔序列 心率变异性 充盈性心衰     

The growth rate for the number of singular and periodic orbits for a polygonal billiard

For any simply connected polygon in the plane, the number of billiard orbits which begin and end at a vertex grows subexponentially with respect to the length or to the number of reflections. This implies that the numbers of isolated periodic orbits and of families of parallel periodic orbits do grow subexponentially. The main technical device is a calculation showing that the topological entropy of the Poincaré map for the billiard flow is equal to zero.Supported in part by NSF Grant #DMS-8414400     

On the Variability of Heart Rate Variability—Evidence from Prospective Study of Healthy Young College Students

Heart rate variability (HRV) has been widely used as indices for autonomic regulation, including linear analyses, entropy and multi-scale entropy based nonlinear analyses, and however, it is strongly influenced by the conditions under which the signal is being recorded. To investigate the variability of healthy HRV under different settings, we recorded electrocardiograph (ECG) signals from 56 healthy young college students (20 h for each participant) at campus using wearable single-lead ECG device. Accurate R peak to R peak (RR) intervals were extracted by combing the advantages of five commonly used R-peak detection algorithms to eliminate data quality influence. Thorough and detailed linear and nonlinear HRV analyses were performed. Variability of HRV metrics were evaluated from five categories: (1) different states of daily activities; (2) different recording time period in the same day during free-running daily activities; (3) body postures of sitting and lying; (4) lying on the left, right and back; and (5) gender influence. For most of the analyzed HRV metrics, significant differences (p < 0.05) were found among different recording conditions within the five categories except lying on different positions. Results suggested that the standardization of ECG data collection and HRV analysis should be implemented in HRV related studies, especially for entropy and multi-scale entropy based analyses. Furthermore, this preliminary study provides reference values of HRV indices under various recording conditions of healthy young subjects that could be useful information for different applications (e.g., health monitoring and management).     

总体经验模态分解能量向量用于ECG能量分布的研究

总体经验模态分解(EEMD)改进了经验模态分解(EMD)存在的模态混叠问题, 依据信号自身的波动特点将信号分解, 特别适合非线性非平稳信号的分析处理. ECG信号能量分布有一定的规律, 疾病会引起能量分布的变化, 研究ECG能量分布的改变对心脏疾病的研究和临床诊断有重要意义. 本文将ECG信号通过EEMD方法分解为多个本征模态函数(IMF)分量, 观察IMF分量的波动规律, 指出了ECG信号在不同时间尺度上的波动特点和物理意义. 将IMF分量分别计算能量, 得到ECG的能量向量, 并对健康人和三种心脏疾病患者能量向量进行对比分析. 结果表明心脏疾病导致EEMD能量向量的高频分量显著降低, 尤其是p₁分量具有较好的区分度, 可以作为心脏疾病诊断的参考依据. 相比较传统的频域分析方法单纯关注频率而忽略信号自身特点和信号成分之间的相互作用, EEMD的分解结果依赖于ECG信号本身, 因此更能够反映ECG信号的真实情况, 揭示年龄和疾病对ECG能量分布的影响.     

Phytoplankton Temporal Strategies Increase Entropy Production in a Marine Food Web Model

We develop a trait-based model founded on the hypothesis that biological systems evolve and organize to maximize entropy production by dissipating chemical and electromagnetic free energy over longer time scales than abiotic processes by implementing temporal strategies. A marine food web consisting of phytoplankton, bacteria, and consumer functional groups is used to explore how temporal strategies, or the lack thereof, change entropy production in a shallow pond that receives a continuous flow of reduced organic carbon plus inorganic nitrogen and illumination from solar radiation with diel and seasonal dynamics. Results show that a temporal strategy that employs an explicit circadian clock produces more entropy than a passive strategy that uses internal carbon storage or a balanced growth strategy that requires phytoplankton to grow with fixed stoichiometry. When the community is forced to operate at high specific growth rates near 2 d⁻¹, the optimization-guided model selects for phytoplankton ecotypes that exhibit complementary for winter versus summer environmental conditions to increase entropy production. We also present a new type of trait-based modeling where trait values are determined by maximizing entropy production rather than by random selection.     

Short-Term Effect of Percutaneous Coronary Intervention on Heart Rate Variability in Patients with Coronary Artery Disease

Myocardial ischemia in patients with coronary artery disease (CAD) leads to imbalanced autonomic control that increases the risk of morbidity and mortality. To systematically examine how autonomic function responds to percutaneous coronary intervention (PCI) treatment, we analyzed data of 27 CAD patients who had admitted for PCI in this pilot study. For each patient, five-minute resting electrocardiogram (ECG) signals were collected before and after the PCI procedure. The time intervals between ECG collection and PCI were both within 24 h. To assess autonomic function, normal sinus RR intervals were extracted and were analyzed quantitatively using traditional linear time- and frequency-domain measures [i.e., standard deviation of the normal-normal intervals (SDNN), the root mean square of successive differences (RMSSD), powers of low frequency (LF) and high frequency (HF) components, LF/HF] and nonlinear entropy measures [i.e., sample entropy (SampEn), distribution entropy (DistEn), and conditional entropy (CE)], as well as graphical metrics derived from Poincaré plot [i.e., Porta’s index (PI), Guzik’s index (GI), slope index (SI) and area index (AI)]. Results showed that after PCI, AI and PI decreased significantly (p < 0.002 and 0.015, respectively) with effect sizes of 0.88 and 0.70 as measured by Cohen’s d static. These changes were independent of sex. The results suggest that graphical AI and PI metrics derived from Poincaré plot of short-term ECG may be potential for sensing the beneficial effect of PCI on cardiovascular autonomic control. Further studies with bigger sample sizes are warranted to verify these observations.     

Kac’s ring: Entropy and Poincaré recurrence

We study the entropy of an N$N$-site Kac ring in a non-equilibrium state. As the system dynamically evolves towards equilibrium and eventually to the initial state exhibiting Poincaré recurrence, we see that the entropy saturates over a period of time which is large for large N$N$. At about the time of order N$N$, the system starts to return to its initial state. We show that there is indeed a perfect “recurrence of statistical fluctuations”, which we are able to explore, as Kac’s ring possesses a finite recurrence time. Entropy is shown here to be a periodic function of the Poincaré recurrence time.     

The Systematic Bias of Entropy Calculation in the Multi-Scale Entropy Algorithm

Entropy indicates irregularity or randomness of a dynamic system. Over the decades, entropy calculated at different scales of the system through subsampling or coarse graining has been used as a surrogate measure of system complexity. One popular multi-scale entropy analysis is the multi-scale sample entropy (MSE), which calculates entropy through the sample entropy (SampEn) formula at each time scale. SampEn is defined by the “logarithmic likelihood” that a small section (within a window of a length m) of the data “matches” with other sections will still “match” the others if the section window length increases by one. “Match” is defined by a threshold of r times standard deviation of the entire time series. A problem of current MSE algorithm is that SampEn calculations at different scales are based on the same matching threshold defined by the original time series but data standard deviation actually changes with the subsampling scales. Using a fixed threshold will automatically introduce systematic bias to the calculation results. The purpose of this paper is to mathematically present this systematic bias and to provide methods for correcting it. Our work will help the large MSE user community avoiding introducing the bias to their multi-scale SampEn calculation results.     

Supergravity in (2 + 1) dimensionsfrom (3 + 1)-dimensional supergravity

In the context of the formalism proposed by Stelle-West and Grignani-Nardelli, it is shown that Chern-Simons supergravity can be consistently obtained as a dimensional reduction of (3 + 1)-dimensional supergravity, when written as a gauge theory of the Poincaré group. The dimensional reductions are consistent with the gauge symmetries, mapping (3 + 1)-dimensional Poincaré supergroup gauge transformations onto (2 + 1)-dimensional Poincaré supergroup ones.     

A class of nontrivial weakly local massive wightman fields with interpolating properties

It is shown that in a quantum field theory satisfying Wightman's axioms with locality replaced by weak locality and cyclicity by a weak irreducibility, every unitary Poincaré invariant and CPT-invariant operator is a scattering operator (in the LSZ-sense). The proof is given by explicit construction of a corresponding class of nontrivial weakly local massive Wightman fields. This result implies Jost's conjecture that only locality leads to nontrivial restrictions for the scattering operator and extends corresponding results of Schneider.     

Poincaré covariance and κ-Minkowski spacetime

A fully Poincaré covariant model is constructed as an extension of the κ-Minkowski spacetime. Covariance is implemented by a unitary representation of the Poincaré group, and thus complies with the original Wigner approach to quantum symmetries. This provides yet another example (besides the DFR model), where Poincaré covariance is realised à la Wigner in the presence of two characteristic dimensionful parameters: the light speed and the Planck length. In other words, a Doubly Special Relativity (DSR) framework may well be realised without deforming the meaning of “Poincaré covariance”.     

Effects of Cardiac Resynchronization Therapy on Cardio-Respiratory Coupling

In this study, the effect of cardiac resynchronization therapy (CRT) on the relationship between the cardiovascular and respiratory systems in heart failure subjects was examined for the first time. We hypothesized that alterations in cardio-respiratory interactions, after CRT implantation, quantified by signal complexity, could be a marker of a favorable CRT response. Sample entropy and scaling exponents were calculated from synchronously recorded cardiac and respiratory signals 20 min in duration, collected in 47 heart failure patients at rest, before and 9 months after CRT implantation. Further, cross-sample entropy between these signals was calculated. After CRT, all patients had lower heart rate and CRT responders had reduced breathing frequency. Results revealed that higher cardiac rhythm complexity in CRT non-responders was associated with weak correlations of cardiac rhythm at baseline measurement over long scales and over short scales at follow-up recording. Unlike CRT responders, in non-responders, a significant difference in respiratory rhythm complexity between measurements could be consequence of divergent changes in correlation properties of the respiratory signal over short and long scales. Asynchrony between cardiac and respiratory rhythm increased significantly in CRT non-responders during follow-up. Quantification of complexity and synchrony between cardiac and respiratory signals shows significant associations between CRT success and stability of cardio-respiratory coupling.     

The generalized parton distribution of the pion in a relativistic Bethe-Salpeter quark model

We present a Poincaré covariant calculation of the generalized parton distribution of the pion. Results for different values of the kinematical parameters are shown and discussed.     

Conformal invariance of relativistic equations for arbitrary spin particles

We show that any Poincaré-invariant equation for particles of zero mass and of discrete spin provide a unitary representation of the conformal group, and find an explicit expression of the conformal group generators in terms of Poincaré group generators.     

Half-sided modular inclusion and the construction of the Poincaré group

In this note we will give a construction of the Poincaré group out of the modular groups of the wedge algebras provided the groups act on the algebra of every double cone like the associated Lorentz boosts. This construction will use the concept of half-sided modular inclusions instead of the first and second cohomology of the Poincaré group as used by Brunetti, Guido and Longo. By our method we obtain directly the Poincaré group and not its covering group.     

On the response of a two-level quantum system to a class of time-dependent quasiperiodic perturbations

We study analytically the response of a two-level quantum system to a certain class of time-dependent quasiperiodic perturbations generated by a Fibonacci sequence. We show that the quasi-energy spectrum (Fourier transform of the evolution operator) generically is not a denumerable sum of delta functions. Hence the response is not quasiperiodic. Several numerical investigations (Poincaré sections, polarization fluctuation, etc.) suggest an intermediate kind of behavior between quasiperiodic and chaotic.     

Poincaré canonical momenta and nambu mechanics

We show that if certain Poincaré-like integrals are conserved, then to each configuration coordinate of a system an entity can be associated that is an acceptable generalization of the notion of canonical momentum: In the particular case of standard mechanics, the canonical momenta are retrieved. Under certain general restrictions, the Poincaré momenta make sense for either mechanical or general systems for which we do not have (or are not aware of) entities (like the Lagrangian) that are generally used to define the momentum. The Poincaré momentum may also make sense for systems whose characteristics are difficult, or impossible, to reconcile with the notion of the usual canonical momentum. It is also relevant for certain cases where a Lagrangian exists, but it leads to a mixture of physical and unphysical entities. In particular, we show that while physical canonical momenta do not generally exist in the new Nambu mechanics (because of the dimensionality of state vector space), the Poincaré momenta exist, they are physical, and have the properties we could have expected for the mechanics.     

The foundations of the poincaré group and the validity of general relativity

After discussions about accepted ideas concerning the nonlocalisability of the photon, the interpretation of the Minkowski space-time, the wave-corpuscle duality ideas of Niels Bohr and the concept of elementary particle by Eugene Wigner, the validity of the Poincaré group is brought into question and some other ideas are developed. Lukierski, Nowicki and Ruegg showed that the successes of the Poincaré group are preserved if we deform the group by introducing a constant κ. Such deformation replaces the Poincaré Hopf algebra by another one. We call such a deformation a mathematical deformation. The main inconvenience of this mathematical deformation is that the coproduct is not commutative. The consequence is that a two-particle state is defined in an ambiguous way because we must say which is the first particle and which is the second one. The only mathematical deformation of the Poincaré group which preserves the commutativity of the coproduct is the trivial one, that is the Poincaré Hopf algebra itself. That is why we reject the mathematical deformation of Lukierski, Nowicki and Ruegg. That is also why we propose what we call a physical deformation of the Poincaré group, which means that we reinterpret the Poincaré Hopf algebra, with the same constant κ. Our proposal has four advantages:

1.

1. The constant x has the dimensions of a mass. When this constant becomes infinite, we are left with the Poincaré group with its main successes.

2.

2. The two-particle states are unambiguously defined.

3.

3. The constant κ may be chosen in such a way that the search for a missing mass in the universe is useless.

4.

4. It consists in the disappearing of unphysical irreducible representations of the Poincaré group.

With the constant κ, we arrive at a reformulation of special relativity where the energy is no longer additive. This would imply a change in general relativity where the density of matter must be different from the density of energy. Unfortunately, we are not able to propose a substitute for the general relativity theory. Obviously, when the constant κ goes to infinity, the new general relativity would become the standard general relativity.