The interval neutrosophic uncertain linguistic variables can easily express the indeterminate and inconsistent information in real world, and TOPSIS is a very effective decision making method more and more extensive applications. In this paper, we will extend the TOPSIS method to deal with the interval neutrosophic uncertain linguistic information, and propose an extended TOPSIS method to solve the multiple attribute decision making problems in which the attribute value takes the form of the interval neutrosophic uncertain linguistic variables (...) and attribute weight is unknown. Firstly, the operational rules and properties for the interval neutrosophic variables are introduced. Then the distance between two interval neutrosophic uncertain linguistic variables is proposed and the attribute weight is calculated by the maximizing deviation method, and the closeness coefficients to the ideal solution for each alternatives. Finally, an illustrative example is given to illustrate the decision making steps and the effectiveness of the proposed method. (shrink)

ObjectiveNoisy galvanic vestibular stimulation (nGVS) is often used to improve postural stability in disorders, such as neurorehabilitation montage. For the safe use of nGVS, we investigated whether arterial pressure (AP) and heart rate vary during static supine and slow whole-body tilt with random nGVS (0.4 mA, 0.1–640 Hz, gaussian distribution) in a healthy elderly population.MethodsThis study was conducted with a double-blind, sham-controlled, cross-over design. Seventeen healthy older adults were recruited. They were asked to maintain a static supine position on a (...) bed for 10 min, and the bed was tilted up (TU) to 70 degrees within 30 s. After maintaining this position for 3 min, the bed was passively tilted down (TD) within 30 s. Real-nGVS or sham-nGVS was applied from 4 to 15 min. The time course of mean arterial pressure (MAP) and RR interval variability (RRIV) were analyzed to estimate the autonomic nervous activity.ResultnGVS and/or time, including pre-/post-event (nGVS-start, TU, and TD), had no impact on MAP and RRIV-related parameters. Further, there was no evidence supporting the argument that nGVS induces pain, vertigo/dizziness, and uncomfortable feeling.ConclusionnGVS may not affect the AP and RRIV during static position and whole-body tilting or cause pain, vertigo/dizziness, and discomfort in the elderly. (shrink)

Precise global solar radiation data are indispensable to the design, planning, operation, and management of solar radiation utilization equipment. Some examples prove that the uncertainty of the prediction of solar radiation provides more value than deterministic ones in the management of power systems. This study appraises the potential of random forest, V-support vector regression, and a resilient backpropagation artificial neural network for daily global solar radiation point prediction from average relative humidity, daily average temperature, and daily sunshine duration. To acquire (...) more accurate predictions of DGSR and examine the influence of historical DGSR on the performance of point prediction models, two different model inputs are considered: three meteorological variables and the lags of DGSR and three meteorological variables. Then, two interval prediction methods are developed by introducing the KDE to out-of-bag, introducing kernel density estimation to split conformal based on the three machine learning models. The two methods for interval prediction are denoted as OOB-KDE and SC-KDE. The mean absolute error, mean relative error, and Kendall rank correlation are used to assess the point prediction models. The performance of interval prediction methods is evaluated by the prediction interval coverage probability, prediction interval normalized average width, and coverage width criteria. The following conclusions are drawn from this study. First, the V-SVR model performs best with the lowest mean absolute error of 0.016 and mean relative error of 0.001. Second, the lags of DGSR improve the prediction accuracy by about 30%. Third, the OOB-KDE and SC-KDE methods improved the quality of the prediction interval. OOB-KDE improved CWC by 81%, and SC-KDE improved CWC by 99.99%. Fourth, the best interval prediction result is obtained using the SC-KDE method using the V-SVR model. The average difference between its PICP and prediction interval nominal coverage is only 3% of the PINC, and its PINAW is less than 0.007. (shrink)

Two experiments were conducted for the derivation of psychophysical scales of the following audio descriptors: spectral centroid, spectral spread, spectral skewness, odd-to-even harmonic ratio, spectral deviation, and spectral slope. The stimulus sets of each audio descriptor were synthesized and independently controlled through appropriate synthesis techniques. Partition scaling methods were used in both experiments, and the scales were constructed by fitting well-behaving functions to the listeners' ratings. In the first experiment, the listeners' task was the estimation of the relative differences between (...) successive levels of a particular audio descriptor. The median values of listeners' ratings increased with increasing feature values, which confirmed listeners' abilities to estimate intervals. However, there was a large variability in the reliability of the derived interval scales depending on the stimulus spacing in each trial. In the second experiment, listeners had control over the stimulus values and were asked to divide the presented range of values into perceptually equal intervals, which provides a ratio scale. For every descriptor, the reliability of the derived ratio scales was excellent. The unit of a particular ratio scale was assigned empirically so as to facilitate qualitative comparisons between the scales of all audio descriptors. The construction of psychophysical scales based on univariate stimuli allowed for the establishment of cause-and-effect relations between audio descriptors and perceptual dimensions, contrary to past research that has relied on multivariate stimuli and has only examined the correlations between the two. Most importantly, this study provides an understanding of the ways in which the sensation magnitudes of several audio descriptors are apprehended. (shrink)

We consider a new fragment of first-order logic with two variables. This logic is defined over interval structures. It constitutes unary predicates, a binary predicate and a function symbol. Considering such a fragment of first-order logic is motivated by defining a general framework for event-based interval temporal logics. In this paper, we present a sound, complete and terminating decision procedure for this logic. We show that the logic is decidable, and provide a NEXPTIME complexity bound for satisfiability. This (...) result shows that even a simple decidable fragment of first-order logic has NEXPTIME complexity. (shrink)

Heart rate variability (HRV), the change in the time intervals between adjacent heartbeats, is an emergent property of interdependent regulatory systems that operate on different time scales to adapt to challenges and achieve optimal performance. This article briefly reviews neural regulation of the heart, and its basic anatomy, the cardiac cycle, and the sinoatrial and atrioventricular pacemakers. The cardiovascular regulation center in the medulla integrates sensory information and input from higher brain centers, and afferent cardiovascular system inputs to adjust heart (...) rate and blood pressure via sympathetic and parasympathetic efferent pathways. This article reviews sympathetic and parasympathetic influences on the heart, and examines the interpretation of HRV and the association between reduced HRV, risk of disease and mortality, and the loss of regulatory capacity. This article also discusses the intrinsic cardiac nervous system and the heart-brain connection, through which afferent information can influence activity in the subcortical and frontocortical areas, and motor cortex. It also considers new perspectives on the putative underlying physiological mechanisms and properties of the ultra-low-frequency (ULF), very-low-frequency (VLF), low-frequency (LF), and high-frequency (HF) bands. Additionally, it reviews the most common time and frequency domain measurements as well as standardized data collection protocols. In its final section, this article integrates Porges' polyvagal theory, Thayer and colleagues' neurovisceral integration model, Lehrer et al.'s resonance frequency model, and the Institute of HeartMath's coherence model. The authors conclude that a coherent heart is not a metronome because its rhythms are characterized by both complexity and stability over longer time scales. Future research should expand understanding of how the heart and its intrinsic nervous system influence the brain. (shrink)

Cross entropy measure is one of the best way to calculate the divergence of any variable from the priori one variable. We define a new cross entropy measure under interval neutrosophic set environment.

According to the standard analysis of degree questions, the logical form of a degree question contains a variable that ranges over individual degrees and is bound by the degree question operator how. In contrast with this, we claim that the variable bound by the degree question operator how does not range over individual degrees but over intervals of degrees, by analogy with Schwarzschild and Wilkinson's proposal regarding the semantics of comparative clauses. Not only does the interval-based semantics (...) predict the existence of certain readings that are not predicted under the standard view, it is also able, together with other natural assumptions, to account for the sensitivity of degree questions to negative islands, as well as for the fact, uncovered by Fox and Hackl, that negative islands can be obviated by some properly placed modals. Like Fox and Hackl, we characterize negative island effects as arising from the fact that the relevant question, due to its meaning alone, can never have a maximally informative answer. Contrary to Fox and Hackl, however, we do not need to assume that scales are universally dense, nor that the notion of maximal informativity responsible for negative islands is blind to contextual parameters. (shrink)

It is important to increase computation efficiency of a system at a low cost while holding the system correct. For this realization, addition of new and efficient equivalent transformation rules, whose correctness is assured, is useful. As long as correct ET rules are added to a correct system, the computation result of the system is always correct. Improvement of rules is promoted further by improvement of data structure.In this paper, we improve data structure by introducing interval variables into the (...) usual term domain and add two correct and efficient ET rules, which are promoted by introduction of interval variables, for member constraints on interval variables. These rules are the candidate elimination rule and the common pattern specialization rule. We show by an experiment that computation efficiency is increased by using these rules. (shrink)

Introduction: The present study aimed to investigate the effects of two high-intensity interval training shuttle-run-based models, over ten weeks on aerobic, anaerobic, and neuromuscular parameters, and the association of the training load and heart rate variability with the change in the measures in young futsal players. Methods: Eleven young male futsal players participated in this study. This pre-post study design was performed during a typical 10 weeks training period. HIIT sessions were conducted at 86% and 100% of peak speed (...) of the FIET. Additionally, friendly and official matches, technical-tactical and strength-power training sessions were performed. Before and after the training period, all players performed the FIET, treadmill incremental, repeated sprint ability, sprint 15-m, and vertical jump tests, and the HRV was measured. Training load was monitored using the session rating of perceived effort. Data analysis was carried out using Bayesian inference methods. Results: The HIIT86 model showed clear improvements for the peak oxygen uptake, peak speed in the treadmill incremental test, first and second ventilatory thresholds, RSA best and mean times, CMJ, and SJ. The HIIT100 model presented distinct advances in VO2peak, peak speed in the treadmill incremental test, RSA mean time, and CMJ. Between HIIT models comparisons showed more favorable probabilities of improvement for HIIT86 than HIIT100 model in all parameters. TL data and HIIT models strongly explained the changes in the RSA mean and best times, as well as HRV changes, and HIIT models explained positively VO2peak changes. All other changes in the parameters were low to moderately explained. Conclusion: The HIIT86 proved to be more effective for improving aerobic, RSA, and neuromuscular parameters than HIIT100 during a typical 10-week futsal training period. So, strength and conditioning specialists prescribing shuttle-run intermittent exercises at submaximal intensities can manage the individual acceleration load imposed on athlete increasing or decreasing either the set duration or the frequency of change of direction during HIIT programming. (shrink)

Objective: Clock variance is an important statistic in many clinical and developmental studies. Existing methods require a large number of trials for accurate clock variability assessment, which is problematic in studies using clinical or either young or aged participants. Furthermore, these existing methods often implicitly convolute clock and memory processes, making it difficult to disentangle whether the clock or memory system are driving the observed deviations. Here we assessed whether twenty repeated productions of a well-engrained interval (1 second), a (...) task that does not incorporate memory updating nor the processing of feedback, could provide an accurate assessment of clock variability. Method: Sixty-eight undergraduate students completed two tasks: a 1-second production task in which they were asked to produce a 1-second duration by ending a tone by a keypress, and a multi-duration reproduction task. Durations presented in the reproduction task were tones lasting 1.17, 1.4 and 1.68 seconds. No feedback was presented in either task, and the order of presentation was counterbalanced between participants. Results: The observed central tendency in the reproduction task was better explained by models including the measures of clock variability derived from the 1-second production task than by models without it. Three clock variability measures were calculated for each participant (standard deviation, root mean squared residuals (RMSR) from an estimated linear slope, and RMSR scaled by mean production duration). The model including the scaled RMSR was prefered over the alternative models, and no notable effects of the order of presentation were observed. These results suggest that (1) measures of variability should account for drift, (2) the presentation of another timing task before a 1-second production task did not influence the assessment of the clock variability, and (3) the observed variability adheres to the scalar property and predicts temporal performance, and is thus a usable index of clock variability. Conclusion: This study shows that just 20 repeated productions of 1 second provide a reliable index of clock variability. As administering this task is fast and easy, it could prove to be useful in a large variety of developmental and clinical populations. (shrink)

A SEM-based approach using likelihood-based confidence interval has been proposed to form confidence intervals for unstandardized and standardized indirect effect in mediation models. However, when used with the maximum likelihood estimation, this approach requires that the variables are multivariate normally distributed. This can affect the LBCIs of unstandardized and standardized effect differently. In the present study, the robustness of this approach when the predictor is not normally distributed but the error terms are conditionally normal, which does not violate the (...) distributional assumption of ordinary least squares estimation, is compared to four other approaches: nonparametric bootstrapping, two variants of LBCI, LBCI assuming the predictor is fixed and LBCI based on ADF estimation, and Monte Carlo. A simulation study was conducted using a simple mediation model and a serial mediation model, manipulating the distribution of the predictor. The Monte Carlo method performed worst among the methods. LBCI and LBCI-Fixed-X had suboptimal performance when the distributions had high kurtosis and the population indirect effects were medium to large. In some conditions, the problem was severe even when the sample size was large. LBCI-ADF and nonparametric bootstrapping had coverage probabilities close to the nominal value in nearly all conditions, although the coverage probabilities were still suboptimal for the serial mediation model when the sample size was small with respect to the model. Implications of these findings in the context of this special case of nonnormal data were discussed. (shrink)

The Contextuality-by-Default approach to determining and measuring the (non)contextuality of a system of random variables requires that every random variable in the system be represented by an equivalent set of dichotomous random variables. In this paper we present general principles that justify the use of dichotomizations and determine their choice. The main idea in choosing dichotomizations is that if the set of possible values of a random variable is endowed with a pre-topology (V-space), then the allowable dichotomizations split (...) the space of possible values into two linked subsets (“linkedness” being a weak form of pre-topological connectedness). We primarily focus on two types of random variables most often encountered in practice: categorical and real-valued ones (including continuous random variables, greatly underrepresented in the contextuality literature). A categorical variable (one with a finite number of unordered values) is represented by all of its possible dichotomizations. If the values of a random variable are real numbers, then they are dichotomized by intervals above and below a variable cut point. (shrink)

We prove that the positive fragment of first-order intuitionistic logic in the language with two individual variables and a single monadic predicate letter, without functional symbols, constants, and equality, is undecidable. This holds true regardless of whether we consider semantics with expanding or constant domains. We then generalise this result to intervals \ and \, where QKC is the logic of the weak law of the excluded middle and QBL and QFL are first-order counterparts of Visser’s basic and formal logics, (...) respectively. We also show that, for most “natural” first-order modal logics, the two-variable fragment with a single monadic predicate letter, without functional symbols, constants, and equality, is undecidable, regardless of whether we consider semantics with expanding or constant domains. These include all sublogics of QKTB, QGL, and QGrz—among them, QK, QT, QKB, QD, QK4, and QS4. (shrink)

Epidemiological studies have confirmed that long-term exposure to road traffic noise can cause cardiovascular diseases, and when noise exposure reaches a certain level, the risk of related CDs significantly increases. Currently, a large number of Chinese residents are exposed to high noise exposure, which could greatly increase the risk of cardiovascular disease. On the other hand, relevant studies have found that people with high noise sensitivity are more susceptible to noise. And it is necessary to pay more attention to the (...) high noise-sensitive people. This study investigated the acute physiological effect of different noise-sensitive groups by indoor-level noise stimulus experiments under laboratory conditions, by observing heart rate variability indicators, including standard deviation of NN intervals, low frequency/high frequency, and heart rate. The results showed that there was no significant difference in HRV between the high-sensitive group and the low-sensitive group at the physiological baseline and the different stimulating noise levels. Then, based on the theory of cumulative effect of noise proposed by WHO Regional Office for Europe, non-significant but observable differences between groups were further discussed. By analyzing differences of the variation trends and the within-group significant changes of SDNN and HR between the two groups, the results tended to show that the high-sensitive group is more affected by road traffic noise. In addition, the values of SDNN and HR showed observable between-group differences at 55 dB and 65 dB which corresponding to the SPL associated with a significantly increased risk of cardiovascular disease concerned by epidemiological studies. According to the cumulative effect theory, these differences in HRV caused by short-term noise stimulation may have the potential to produce physiological response and lead to between-groups differences in prevalence after long-term recurrent effect, and deserve attention and further research. (shrink)

BackgroundRecurrent Major Depressive Disorder is one of the most disabling mental disorders in modern society. Prior research has shown that self-compassion protects against ruminative tendencies, a key feature of recurrent MDD. In addition, self-compassion has been found to be positively related to higher psychophysiological flexibility in young, healthy adults. To our knowledge, there is a lack of studies on how self-compassion relates to vmHRV in patients with recurrent MDD. The aim of the current study was to investigate whether higher self-compassion (...) would associate with lower ruminative tendencies and higher vmHRV in a sample of adults with recurrent MDD.MethodsWe included a sample of 63 patients between 20 and 71 years old with a history of three or more depressive episodes. They filled out the Self-Compassion Scale, Beck Depression Inventory, and Rumination Rating Scale. ECG was acquired while resting and the square root of the mean squared differences of successive RR interval values was calculated as measure of vmHRV.ResultsAs hypothesized, self-compassion was associated with lower ruminative tendencies. However, self-compassion was not associated with level of vmHRV. Several confounding variables were controlled for in the statistical analyses, and higher age predicted lower vmHRV across all statistical analyses.ConclusionThe results confirmed our hypothesis that higher self-compassion would be associated with lower ruminative tendencies in recurrent MDD. Contrary to our expectation, we did not find that the tendency to be more self-compassionate was associated with higher vmHRV. As such, higher self-compassion seems to relate with a lower tendency to ruminate about past mistakes and events but does not seem to relate to a flexible autonomic stress response. Other potential explanatory factors for lower vmHRV in recurrent MDD is suggested as focus for exploration in future studies. (shrink)

Background: Monitoring the daily change in resting heart rate variability can provide information regarding training adaptation and recovery status of the autonomic nervous system during training camps. However, it remains unclear whether postural stabilization is essential for valid and reliable ultra-short-term recordings in short-term overseas training camps.Design: Observational and longitudinal study.Purpose: This study aimed to investigate ultra-short-term heart rate variability recordings under stabilization or post-stabilization periods in four overseas training camps.Participant: Twenty-seven U-20 male national team futsal players voluntarily participated in (...) this study.Method: Resting HRV was evaluated for 10 min during the early morning of each training camp. The natural logarithm of the root mean square of successive normal-to-normal interval differences was used for comparisons. Time segments of HRV were divided into two periods with three measures within each: the first 30-s, the first 60-s, and the 5-min standard during stabilization; the first 30-s, the first 60-s, and the 5-min standard after stabilization.Result: The results demonstrated trivial to small ES, very large to nearly perfect ICC, and narrow range of SEM when all time segments of HRVUST were compared to the 1st_5 min and 2nd_5 min HRV. Furthermore, the magnitude of the correlation coefficients ranged from very high to nearly perfect for all the time segments. The HRVUST posted excellent agreement in all time segments with/without postural stabilization. Trivial to small levels of effect size in all time segments of LnRMSSDmean and LnRMSSDcv across overseas training camps was identified.Conclusion: The first 30 or 60-s LnRMSSD recordings can be used to evaluate daily cardiac-autonomic function during overseas training camps in futsal players. The process for stabilization seems to be unnecessary for measuring the morning resting LnRMSSD in overseas training camps among young adult futsal players. (shrink)

In alternating phases, pigeons received immediate and delayed food reinforcement under a variable-ratio schedule for pecking a key. A 3-sec delay produced less disruption in responding if the entire delay interval was signaled rather than unsignaled. Effects of signaling different.5-sec portions of the delay interval were also examined. Most birds showed little or no decrease in responding if the signal occurred at the beginning of the delay interval, but showed a substantial decrease in responding if the (...) signal occurred in the middle or at the end of the delay interval. (shrink)

We extend a result of Dubins [3] from bounded to unbounded random variables. Dubins [3] showed that a finitely additive expectation over the collection of bounded random variables can be written as an integral of conditional expectations (disintegrability) if and only if the marginal expectation is always within the smallest closed interval containing the conditional expectations (conglomerability). We give a sufficient condition to extend this result to the collection Z of all random variables that have finite expected value and (...) whose conditional expectations are finite and have finite expected value. The sufficient condition also allows the result to extend some, but not all, subcollections of Z. We give an example where the equivalence of disintegrability and conglomerability fails for a subcollection of Z that still contains all bounded random variables. (shrink)

We consider a one-dimensional translation invariant point process of density one with uniformly bounded variance of the number NI of particles in any interval I. Despite this suppression of fluctuations we obtain a large deviation principle with rate function F(ρ) −L−1 log Prob(ρ) for observing a macroscopic density profile ρ(x), x ∈ [0, 1], corresponding to the coarse-grained and rescaled density of the points of the original process in an interval of length L in the limit L → (...) ∞. F(ρ) is not convex and is discontinuous at ρ ≡ 1, the typical profile. (shrink)

To reason about continuous processes in some areas of artificial intelligence and embedded systems one has to express real-time properties. For such purpose a real-time logic has to be considered. Various such logics have been proposed. Some of these formalisms interpret formulas over intervals of time. These are called interval logics. Zhou Chaochen and Michael Hansen have introduced one such first-order interval logic called Neighborhood Logic (NL) which has two expanding modalities ◊r and ◊l. They have shown the (...) adequacy of these modalities by deriving other unary and binary modalities from them; in particular, they show that chop can be expressed in terms of these modalities. The logic is subsequently expanded to get a Duration Calculus (called DC/nl) by expressing temporal variables as integrals of state variables. Liveness and fairness properties of a computing system can now be expressed in DC/nl by means of neighborhood (expanding) modalities. We take up an investigation of DC/nl in detail. We present a proof system for it. We further show that most of the results that hold in the original Duration Calculus continue to hold in our logic with some modifications. In this process we discuss soundness, completeness, and decidability results for DC/nl. Thus this paper establishes DC/nl as a useful formalism for specifying and verifying properties of real-time computing systems. (shrink)

Symmetries play a major role in physics, in particular since the work by E. Noether and H. Weyl in the first half of last century. Herein, we briefly review their role by recalling how symmetry changes allow to conceptually move from classical to relativistic and quantum physics. We then introduce our ongoing theoretical analysis in biology and show that symmetries play a radically different role in this discipline, when compared to those in current physics. By this comparison, we stress that (...) symmetries must be understood in relation to conservation and stability properties, as represented in the theories. We posit that the dynamics of biological organisms, in their various levels of organization, are not just processes, but permanent (extended, in our terminology) critical transitions and, thus, symmetry changes. Within the limits of a relative structural stability (or interval of viability), variability is at the core of these transitions. (shrink)

In this book, for the first time, authors try to introduce the concept of linguistic variables as a continuum of linguistic terms/elements/words in par or similar to a real continuum. For instance, we have the linguistic variable, say the heights of people, then we place the heights in the linguistic continuum [shortest, tallest] unlike the real continuum (–∞, ∞) where both –∞ or +∞ is only a non-included symbols of the real continuum, but in case of the linguistic continuum (...) we generally include the ends or to be more mathematical say it is a closed interval, where shortest denotes the shortest height of a person, maybe the born infant who is very short from usual and the tallest will denote the tallest one usually very tall; however this linguistic continuum [shortest, tallest] in the real continuum will be the closed interval say [1 foot, 8 feet] or [1, 8] the measurement in terms of feet. So, the real interval is a subinterval with which we have associated the real continuum in terms of qualifying unit feet and inches in this case. (shrink)

The single-particle wave function ψ=ReiS/h has been interpreted classically: At a given point the particle momentum is ▽S, and the relative particle density in an ensemble is R 2 . It is first proposed to modify this interpretation by assuming that physical variables undergo rapid fluctuations, so that ▽S is the average of the momentum over a short time interval. However, it appears that this is not enough. It seems necessary to assume that the density also fluctuates. The fluctuations (...) are taken to be random and to satisfy conditions required for agreement with quantum mechanics. In some cases the fluctuating density may take on instantaneous negative values. One gets agreement with quantum mechanics for the spin correlations of two particles in a singlet state. This comes about because of the correlations between the fluctuations of the variables of the two particles, the effect of which is equivalent to an action at a distance. The relation to Bell's inequality is discussed. (shrink)

Writing and reading are closely related and are thus likely to have a common orthographic representation. A fundamental question in the literature on the production of written Chinese characters concerns the structure of orthographic representations. We report on a Chinese character handwriting pedagogical corpus involving a class of 22 persons, 232 composite character types, 1,913 tokens, and 13,057 stroke records, together with the inter-stroke interval (ISI), which reflects the parallel processing of multilevel orthographic representation during the writing execution, and (...) 50 orthographic variables from the whole character, logographeme, and stroke. The results of regression analyses show that orthographic representation has a hierarchy and that different representational levels are active simultaneously. In the multilevel structure of orthographic representation, the representation of the logographeme is absolutely dominant. Writing and reading have both commonalities and individual differences in their orthographic representations. The online processing of the logographeme unit probably occurs at the ISI before the initial stroke of the current logographeme, which may also cascade to the first subsequent logographeme. In addition, we propose a new effective character structure unit for describing orthographic complexity. (shrink)

A time operator, which incorporates the idea of time as a dynamical variable, was first introduced in the context of a theory of irreversible evolution. The existence of a time operator has interesting implications in several areas of physics. Here we demonstrate a close link between the existence of the time operator for relativistic particles and the existence of an indivisible time interval or chronons for dynamical evolution. More explicitly, we consider a Klein-Gordon particle and require the existence (...) of a time operator for its evolution. We also make a natural choice of the form of the time operator which expresses it in terms of the generators of the Poincaré group. These then imply that the physical time evolution group must be the discrete subgroup Unτ (n integers) of the originally given evolution group Ut of the Klein-Gordon particle and the constant τ is given by τ=h/2mc2. This means that the requirement of the existence of a time operator implies that the time evolution cannot be followed to time intervals smaller than τ and, as such, τ emerges as a chronon for the dynamical evolution. Expecting that the same results hold for a Dirac particle also, we conclude that the so-called Zitterbewegungdoes not occur in reality. Thus, possible confirmation of the existence of chronons would result if no observableconsequence of Zitterbewegungis actually realized in nature. This calls for a search of observable consequences of the Zitterbewegungand a re-examination of their agreement (if any) with experiments. A possible consequence of Zitterbewegung,the so-called Darwin term present in the Dirac Hamiltonian in an electric field, is briefly considered. (shrink)