Clock Variables Research Articles

Reduced phase space approach to Kasner universe and the problem of time in quantum theory

We apply the reduced phase space quantization to the Kasner universe. We construct the kinematical phase space, find solutions to the Hamilton equations of motion, identify Dirac observables and arrive at physical solutions in terms of Dirac observables and an internal clock. We obtain the physical Hilbert space, which is the carrier space of the self-adjoint representation of the Dirac observables. Then, we discuss the problem of time. We demonstrate that the inclusion of evolution in a gravitational system, at classical level as well as at quantum level, leads respectively to canonically and unitarily inequivalent theories. The example of Hubble operator in two different clock variables and with two distinct spectra is given.

Concurrency theory: timed automata, testing, program synthesis

Today, with the widespread use of Internet and with the increase in the complexity of the software, it becomes vital to develop methods for ensuring the quality of concurrent software systems. It is therefore natural that this area, broadly referred to as concurrency theory, be represented in the journal Distributed Computing. As a way of reassessing this relevance, the present issue of the journal is entirely devoted to concurrency theory. The four papers presented cover three important topics within concurrency theory: timed automata, automated program synthesis, and testing. I briefly comment on the contributions below. Traditional automata model the interactions between a system and its environment by retaining only the sequencing of events. The behaviour of a system is thus the tree, or the set of sequences, of such events. The strength of automata theory lies in the efficient algorithms and decision procedures for automatically manipulating and analyzing the resulting behaviors. Many verification theories, including model checking, are based on the theory of automata, in one of their various variants (deterministic, Meely machines, Buchi, pushdown, etc.). While the abstraction from quantitative time has had many advantages, it prevents the applicability of the techniques to cases in which real-time constraints are essential. Timed automata were introduced by Alur and Dill in 1994 as a formal notation to model the behavior of realtime systems. In its definition, state-transitions are annotated with timing constraints using finitely many real-valued clock variables. Timed automata accept timed words; these are infinite sequences in which each symbol is associated with a

Enhancement of a Fault Measure for AMSs Using Probabilistic Timed Automata

A novel approach for probabilistic timed structure that is based on combining the formalisms of timed automata and probabilistic automata representation of the system is proposed. Due to their real-valued clocks can measure the passage of time and transitions can be probabilistic such that it can be expressed as a discrete probability distribution on the set of target states. The usage of clock variables and the specification of state space are illustrated with real value time applications. The transitions between states are probabilistic by events which describe either the occurrence of faults or normal working conditions. Additionally, the passage of discrete time and transitions can be probabilistic by mean of the theory of expectation sets to obtain a unified measure reasoning strategy.

Analysis of Non-Linear Probabilistic Hybrid Systems

This paper shows how to compute, for probabilistic hybrid systems, the clock approximation and linear phase-portrait approximation that have been proposed for non probabilistic processes by Henzinger et al. The techniques permit to define a rectangular probabilistic process from a non rectangular one, hence allowing the model-checking of any class of systems. Clock approximation, which applies under some restrictions, aims at replacing a non rectangular variable by a clock variable. Linear phase-approximation applies without restriction and yields an approximation that simulates the original process. The conditions that we need for probabilistic processes are the same as those for the classic case.

Paced finger-tapping abnormalities in bipolar disorder indicate timing dysfunction

Theoretical and empirical evidence suggests that impaired time perception and the neural circuitry contributing to internal timing mechanisms may contribute to severe psychiatric disorders, including mood disorders. The structures that are involved in subsecond timing, i.e., cerebellum and basal ganglia, have also been implicated in the pathophysiology of bipolar disorder. However, the timing of subsecond intervals has infrequently been studied in this population. Paced finger-tapping tasks have been used to characterize internal timing processes in neuropsychiatric disorders. A total of 42 bipolar disorder patients (25 euthymic, 17 manic) and 42 age-matched healthy controls completed a finger-tapping task in which they tapped in time with a paced (500-ms intertap interval) auditory stimulus (synchronization), then continued tapping without auditory input while attempting to maintain the same pace (continuation). This procedure was followed using the dominant index finger, then with alternating thumbs. Bipolar disorder participants showed greater timing variability relative to controls regardless of pacing stimulus (synchronization versus continuation) or condition (dominant index finger versus alternating thumbs). Decomposition of timing variance into internal clock versus motor implementation components using the Wing-Kristofferson model showed higher clock variability in the bipolar disorder groups compared to controls, with no differences between groups on motor implementation variability. These findings suggest that internal timing mechanisms are disrupted in bipolar disorder patients, independent of symptom status. Increased clock variability in bipolar disorder may be related to abnormalities in cerebellar function.

Unimodular loop quantum cosmology

Unimodular gravity is based on a modification of the usual Einstein-Hilbert action that allows one to recover general relativity with a dynamical cosmological constant. It also has the interesting property of providing, as the momentum conjugate to the cosmological constant, an emergent clock variable. In this paper we investigate the cosmological reduction of unimodular gravity, and its quantization within the framework of flat homogeneous and isotropic loop quantum cosmology. It is shown that the unimodular clock can be used to construct the physical state space, and that the fundamental features of the previous models featuring scalar field clocks are reproduced. In particular, the classical singularity is replaced by a quantum bounce, which takes place in the same condition as obtained previously. We also find that requirement of semiclassicality demands the expectation value of the cosmological constant to be small (in Planck units). The relation to spin foam models is also studied, and we show that the use of the unimodular time variable leads to a unique vertex expansion.

The effect of entrainment on the timing of periodic eye movements

We performed an experiment in which eight healthy individuals made periodic eye movements at five pacing interval conditions (500ms, 750ms, 1000ms, 1250ms, and 1500ms). Three methods of entrainment were used in the synchronization phase: saccade, continuous pursuit and discontinuous pursuit. The stimulus train was extinguished and in the continuation phase, subjects made saccadic eye movements at the entrained movement frequencies between two static targets. Using the Wing–Kristofferson model, clock and motor variance were extracted from the time series of continuation trials for all three entrainment conditions. Our results revealed a main effect of time interval on total variance clock variance (as predicted by Weber's law) and on motor variance. We also report that the pursuit entrainment conditions resulted in and mean duration and variance to the saccade entrainment. These results suggest that the neural networks recruited to support a periodic motor timing task depend on the method used to establish the temporal reference.

Central and Peripheral Timing Variability in Children With Heavy Prenatal Alcohol Exposure

The study examined whether prenatal alcohol exposure is associated with increased motor timing variability when the timing response is partitioned into central clock variability, which indexes information processing at the central nervous system (CNS) level and motor delay variability, which reflects timing processes at the level of the peripheral nervous system. Eighteen children with histories of prenatal alcohol exposure and 22 control children were assigned to young (7 to 11 years) or older (12 to 17 years) groups. Children tapped a single response key with the index finger in synchrony with a series of externally generated tones (the paced phase). At the conclusion of these tones, children continued tapping (the continuation phase) while attempting to maintain the same rate of tapping imposed by the paced phase. Two blocks of tapping were completed with inter-tone-intervals set at either 400 or 900 milliseconds. Inter-response interval, central clock variability, and motor delay variability produced during the continuation phase were the dependent variables. Mean inter-response interval for the 4 groups did not differ for either time interval. Central clock variability produced by the young alcohol-exposed group was significantly greater than the two older groups for the 400 millisecond interval and all other groups for the 900 millisecond interval. Motor delay variability produced by the young alcohol-exposed group was significantly greater than the other three groups for both time intervals. Central and motor delay variability in children with and without alcohol exposure was directly related to the duration of the interval to be reproduced. Central and peripheral timing variability was significantly greater for the young alcohol-exposed children. This atypical timing may be related to the teratogenic effects of alcohol, although the negative effects are limited to younger alcohol-exposed children since there were no differences in central and peripheral timing variability between the older alcohol-exposed children and controls.

Assessment of Chronotype in Four- to Eleven-Year-Old Children: Reliability and Validity of the Children's ChronoType Questionnaire (CCTQ)

Individual differences in circadian phase preference (“chronotype”) are linked to sleep schedule variability, psychosocial functioning, and specific properties of the circadian clock. While much is known about the development, distribution, and variability of chronotype in adolescents and adults, assessment in prepubertal children has been hindered by a lack of appropriate, reliable, and valid measures. This study presents a detailed description of the assessment of children's chronotype by the Children's ChronoType Questionnaire (CCTQ). The CCTQ is a parent-report, 27-item mixed-format questionnaire resulting in multiple measures of chronotype in 4- to 11-yr-old children: the midsleep point on free days (MSF), a morningness/eveningness scale (M/E) score, and a five-point chronotype (CT) score. The study provides validity data using actigraphy as well as test-retest reliability data for all three chronotype measures and sleep/wake parameters. Overall, the findings indicate moderate to strong agreement between the three measures, adequate associations between chronotype measures and sleep/wake parameters assessed by actigraphy, and excellent temporal stability (reliability).

Tolerance for Clock Variance of LF-Band Wireless SS Communication Utilizing Peak Detection with Maximum Determination at the Center of Section Method

The authors devised a novel method to determine the position of correlation peaks resulting from a received spread spectrum signal. This method does not require any threshold or clock adjustment. A simulation and experimental evaluation of this method were performed with an LF-band wireless communication system. The result showed that the system has a clock tolerance of about 1000ppm and is useful for LF communication with limited circuit scale (e.g., an LF wireless tag).

Timed Automata Patterns

Timed automata have proven to be useful for specification and verification of real-time systems. System design using timed automata relies on explicit manipulation of clock variables. A number of automated analyzers for timed automata have been developed. However, timed automata lack composable patterns for high-level system design. Specification languages like Timed Communicating Sequential Process (CSP) and Timed Communicating Object-Z (TCOZ) are well suited for presenting compositional models of complex real-time systems. In this work, we define a set of composable Timed Automata patterns based on hierarchical constructs in time-enriched process algebras. The patterns facilitate the hierarchical design of complex systems using timed automata. They also allow a systematic translation from Timed CSP/TCOZ models to timed automata so that analyzers for timed automata can be used to reason about TCOZ models. A prototype has been developed to support system design using timed automata patterns or, if given a TCOZ specification, to automate the translation from TCOZ to timed automata.

Mapped Clock Oscillators as Ring Devices and Their Application to Neuronal Electrical Rhythms

The mapped clock oscillator (MCO) is a second-order, Winfree-type oscillator generating two instantaneous clock variables (amplitude and phase) that are mapped to an observable output variable (voltage) via a static nonlinearity. Two fundamental classes of ring devices are presented. Their respective dynamics give rise to two oscillator forms--the labile clock and the clock--which can be coupled together in various configurations to create higher-order systems with sufficient complexity to capture the dynamics of neuronal assemblies. To demonstrate the applicability of MCOs in modelling neuronal rhythms, a hippocampal network model of four coupled oscillators was constructed and shown to exhibit rhythmic activity of varying complexity, depending on model parameters. The dynamics of the network were quantified through estimation of the maximum lyapunov exponent and the correlation dimension. Synthesis of complex neuronal rhythms may have therapeutic implications. The modular and efficient design of the MCO should facilitate the process of implementing coupled MCO networks in electronic hardware as potential neural prostheses for treating dynamic diseases such as epilepsy.

The influence of dominant versus non-dominant hand on event and emergent motor timing

It has been hypothesized that timing in tapping utilizes event timing; a clock-like process, whereas timing in circle drawing is emergent. Three experiments examined timing in tapping and circle drawing by the dominant and non-dominant hand. Participants were right-hand dominant college aged males and females. The relationship between variance and the square of the timed interval (the Weber fraction), thought to capture clock-like timekeeping processes, was compared. Furthermore, timing variance was decomposed into a clock and a motor component. The slopes for timing were different for dominant hand tapping and circle drawing, but equal for non-dominant and dominant hand tapping. Negative lag one covariance, consistent with motor implementation variability, was found for non-dominant but not for dominant hand circle drawing (Experiment 1). Practice did not influence this relation (Experiment 2). A significant correlation for clock variability was found between non-dominant hand circle drawing and tapping (Experiment 3). Collectively, these findings indicate that event timing is shareable across hands while emergent timing is specific to an effector. Emergent timing does not appear to be obligatory for the non-dominant hand in circle drawing. We suggest that the use of emergent timing might depend upon the extensive practice experienced by a person’s dominant hand.

Prolonged cortical silent period but normal sensorimotor plasticity in spinocerebellar ataxia 6

Spinocerebellar ataxia 6 (SCA6) is a hereditary disease characterized by a trinucleotide repeat expansion in the CACNA1A gene and late-onset bilateral cerebellar atrophy. It is unclear if there is significant pathology outside of the cerebellum. We used transcranial magnetic stimulation to assess sensorimotor cortical circuits and cortical plasticity in 8 SCA6 patients and 8 age-matched controls. Behavioral performance was assessed using a rhythmic tapping task. Neurophysiological measures of SCA6 patients showed a prolonged cortical silent period (CSP) but normal MEP recruitment curve, short-latency afferent inhibition, long-latency afferent inhibition and ipsilateral silent period. Paired-associative stimulation induction also increased motor-evoked potentials normally. SCA6 patients had greater variability with cued rhythmic tapping than normals and deteriorated when the cue was removed; in comparison, normal subjects had similar variability between cued and uncued rhythmic tapping. Analysis using a Wing-Kristofferson timing model indicated that both clock variance and motor delay variance were abnormal. Conclusion. In SCA6, the circuits for sensorimotor integration and the mechanisms for LTP-like plasticity in the sensorimotor cortex are unimpaired. A prolonged CSP in SCA6 just like in other cerebellar atrophies would suggest that this neurophysiological change typifies cerebellar dysfunction.

Independence of Genetic Geographical Variation between Photoperiodic Diapause, Circadian Eclosion Rhythm, and Thr-Gly Repeat Region of the Period Gene inDrosophila littoralis

Drosophila littoralis is a latitudinally widespread European species of the Drosophila virilis group. The species has ample genetic variation in photoperiodism (adult diapause) and circadian rhythmicity (pupal eclosion rhythm), with adaptive latitudinal clines in both of them. The possible common genetic basis between the variability of photoperiodism and circadian rhythms was studied by a long-term crossing experiment. A northern strain (65 degrees N) having long critical day length (CDL = 19.9 h) for diapause, early phase of the entrained rhythm in LD 3:21 (psi(LD3:21) = 12.3 h), and short period (tau= 18.8 h) of the free-running rhythm for the eclosion rhythm was crossed with a southern strain (42 degrees N) having short CDL (12.4 h), late eclosion phase (psi(LD3:21) = 20.2 h), and long period (tau= 22.8 h). After 54 generations, including free recombination, artificial selection, and genetic drift, a novel strain resulted, having even more "southern" diapause and more "northern" eclosion rhythm characteristics than found in any of the geographical strains. The observed complete separation of eclosion rhythm characteristics from photoperiodism is a new finding in D. littoralis; in earlier studies followed for 16 generations, the changes had been mostly parallel. Evidently, the genes controlling the variability of the eclosion rhythm and photoperiodism in D. littoralis are different but closely linked. To test for the possible gene loci underlying the observed geographical variability, the period gene was studied in 10 strains covering all the known clock variability in D. littoralis. The authors sequenced the most suspected Thr-Gly region, which is known to take part in the adaptive clock variability in Drosophila melanogaster. No coding differences were found in the strains, showing that this region is not included in the adaptive clock variability in D. littoralis.

Remove Irrelevant Atomic Formulas for Timed Automaton Model Checking

Most of the timed automata reachability analysis algorithms in the literature explore the state spaces by enumeration of symbolic states, which use time constraints to represent a set of concrete states. A time constraint is a conjunction of atomic formulas which bound the differences of clock values. In this paper, it is shown that some atomic formulas of symbolic states generated by the algorithms can be removed to improve the model checking time- and space-efficiency. Such atomic formulas are called as irrelevant atomic formulas. A method is also presented to detect irrelevant formulas based on the test-reset information about clock variables. An optimized model-checking algorithm is designed based on these techniques. The case studies show that the techniques presented in this paper significantly improve the space- and time-efficiency of reachability analysis.

Reachability Checking of Finite Precision Timed Automata

To relieve the state space explosion problem, and accelerate the speed of model checking, this paper introduces the concept of finite precision timed automata (FPTAs) and proposes a data structure to represent its symbolic states. FPTAs only record the integer values of clock variables together with the order of their most recent resets to reduce the state space. The constraints under which the reachability checking of a timed automaton can be reduced to that of the corresponding FPTA are provided, and then an algorithm for reachability analysis is presented. Finally, the paper presents some preliminary experimental results, and analyzes the advantages and disadvantages of the new data structure.

Development and evaluation of symbolic model checker based on approximation for real‐time systems

AbstractIn this paper, the authors describe symbolic model checking for real‐time systems based on approximation. It is important to determine how to reduce the increase in verification cost due to timed‐state processing during symbolic model checking of a real‐time system. Verification techniques that use a set of approximate states instead of exact timed states in a reachability analysis of a real‐time system have been proposed to increase the effect in reducing the verification cost. Therefore, the authors propose a symbolic model checking technique for real‐time systems that uses a set of approximate states. The verification algorithm calculates the set of approximate states by performing fixpoint calculations based on an approximation corresponding to a computation tree logic (CTL) formula. The authors implemented the proposed algorithm and compared it with existing real‐time symbolic model checkers. They obtained results showing that the proposed technique is effective for verifying a large‐scale system that includes many clock variables. © 2004 Wiley Periodicals, Inc. Syst Comp Jpn, 35(10): 83–101, 2004; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/scj.10565

Neurobiology of perceptual and motor timing in children with spina bifida in relation to cerebellar volume.

The cerebellum is important for perceptual and motor timing in the mature brain, but the timing function of the cerebellum in the immature brain is less well understood. We investigated timing in children with spina bifida meningomyelocele (SB), a neural tube defect that involves cerebellar dysgenesis, and in age-matched controls. Specifically, we studied perceptual timing (judgements of 400 ms duration) and motor timing (isochronous motor tapping); measured cerebellar volumes; and related perceptual and motor timing to each other and to cerebellar volume measurements. Children with SB had impairments in the perception of duration (around 400 ms) but not frequency (around 3000 Hz), showing that their perceptual timing deficit was not a generalized auditory impairment. Children with SB had motor timing deficits on unpaced but not paced isochronous tapping, and their unpaced timing performance was associated with clock variance rather than with motor implementation. Perceptual and motor timing were correlated, suggesting that children with SB have impairments in a central timing mechanism. Children with SB, especially those with upper spinal cord lesions, had significant cerebellar volume reductions in grey and white matter, as well as different regional patterns of grey matter, white matter and CSF. Duration perception was correlated with cerebellar volumes, and the number of valid tapping trials was correlated with cerebellar volumes in the SB group, which data demonstrate structure-function relations between timing and cerebellar volumes.

Adding drift to the decomposition of simple isochronous tapping: an extension of the Wing-Kristofferson model.

The Wing-Kristofferson model (A. M. Wing & A. B. Kristofferson, (1973a, 1973b) decomposes the variance of isochronous finger tapping into 2 components: a central clock component and a peripheral motor component. The method assumes that there is no drift in the intertap intervals. A new method is introduced that further decomposes the clock component drift and drift-free clock variance. The method was studied through simulation and empirical analyses. Clock variance was the most prominent, followed by drift, and then motor variance. Individual and group differences were larger for the motor and drift variances than for the drift-free clock variance, so that group differences observed in the past may have been partially due to the failure to fully remove drift. The authors argue that the methods presented and extensions thereon show great promise in extending a method in wide use since 1973.