Clock Variables Research Articles

Reaching and stepping respond differently to medication and cueing in Parkinson’s disease

The basal ganglia contribute to internal timekeeping, and dopaminergic medication has been observed to moderate timing deficits associated with Parkinson’s Disease (PD) during single joint movements. However, it is unclear whether similar effects can be observed in multi-joint movements. Twenty-five people with PD and twelve healthy peers performed repetitive reaching and stepping-in-place tasks with and without auditory cues at their self-selected maximal cadence. The PD group was measured ON and OFF medication. Reduced cadence error was found for both groups and tasks when cued, and ON PD exhibited decreased cadence compared to OFF PD. Overall timing variability was no different from controls, but differences were found in estimates of clock and motor variance using the Wing-Kristofferson model of interval timing. A medication and cueing interaction during the reaching task produced increased clock variance in uncued, ON PD. During the stepping task, clock and motor variance of the PD group were unaffected by cues, in contrast to the control group. Serial lag-one correlation was reduced in both groups for cued reaching, but was unaffected by cueing or medication in the PD group when stepping-in-place. These findings suggest that overall timing variability may not capture timing deficits in PD.

A Network Analysis of Digital Clock Drawing for Command and Copy Conditions.

Graphomotor and time-based variables from the digital Clock Drawing Test (dCDT) characterize cognitive functions. However, no prior publications have quantified the strength of the associations between digital clock variables as they are produced. We hypothesized that analysis of the production of clock features and their interrelationships, as suggested, will differ between the command and copy test conditions. Older adults aged 65+ completed a digital clock drawing to command and copy conditions. Using a Bayesian hill-climbing algorithm and bootstrapping (10,000 samples), we derived directed acyclic graphs (DAGs) to examine network structure for command and copy dCDT variables. Although the command condition showed moderate associations between variables (= 0.34) relative to the copy condition ( = 0.25), the copy condition network had more connections (18/18 versus 15/18 command). Network connectivity across command and copy was most influenced by five of the 18 variables. The direction of dependencies followed the order of instructions better in the command condition network. Digitally acquired clock variables relate to one another but differ in network structure when derived from command or copy conditions. Continued analyses of clock drawing production should improve understanding of quintessential normal features to aid in early neurodegenerative disease detection.

Spontaneous collapse models lead to the emergence of classicality of the Universe

Assuming that Quantum Mechanics is universal and that it can be applied over all scales, then the Universe is allowed to be in a quantum superposition of states, where each of them can correspond to a different space-time geometry. How can one then describe the emergence of the classical, well-defined geometry that we observe? Considering that the decoherence-driven quantum-to-classical transition relies on external physical entities, this process cannot account for the emergence of the classical behaviour of the Universe. Here, we show how models of spontaneous collapse of the wavefunction can offer a viable mechanism for explaining such an emergence. We apply it to a simple General Relativity dynamical model for gravity and a perfect fluid. We show that, by starting from a general quantum superposition of different geometries, the collapse dynamics leads to a single geometry, thus providing a possible mechanism for the quantum-to-classical transition of the Universe. Similarly, when applying our dynamics to the physically-equivalent Parametrised Unimodular gravity model, we obtain a collapse on the basis of the cosmological constant, where eventually one precise value is selected, thus providing also a viable explanation for the cosmological constant problem. Our formalism can be easily applied to other quantum cosmological models where we can choose a well-defined clock variable.

Using digital assessment technology to detect neuropsychological problems in primary care settings.

Screening for neurocognitive impairment and psychological distress in ambulatory primary and specialty care medical settings is an increasing necessity. The Core Cognitive Evaluation™ (CCE) is administered/scored using an iPad, requires approximately 8 min, assesses 3- word free recall and clock drawing to command and copy, asks questions about lifestyle and health, and queries for psychological distress. This information is linked with patients' self- reported concerns about memory and their cardiovascular risks. A total of 199 ambulatory patients were screened with the CCE as part of their routine medical care. The CCE provides several summary indices, and scores on 44 individual digital clock variables across command and copy tests conditions. Subjective memory concerns were endorsed by 41% of participants. Approximately 31% of participants reported psychological distress involving loneliness, anxiety, or depression. Patients with self-reported memory concerns scored lower on a combined delay 3- word/ clock drawing index (p < 0.016), the total summary clock drawing command/ copy score (p < 0.050), and clock drawing to command Drawing Efficiency (p < 0.036) and Simple and Complex Motor (p < 0.029) indices. Patients treated for diabetes and atherosclerotic cardiovascular disease (ASCVD) scored lower on selected CCE outcome measures (p < 0.035). Factor analyses suggest that approximately 10 underlying variables can explain digital clock drawing performance. The CCE is a powerful neurocognitive assessment tool that is sensitive to patient's subjective concerns about possible decline in memory, mood symptoms, possible cognitive impairment, and cardiovascular risk. iPad administration ensures total reliability for test administration and scoring. The CCE is easily deployable in outpatient ambulatory primary care settings.

Internal clock variability, mood swings and working memory in bipolar disorder

BackgroundDistortions in time processing may be regarded as an endophenotypic marker of neuropsychiatric diseases; however, investigations addressing Bipolar Disorder (BD) are still scarce. MethodsThe present study compared timing abilities in 30 BD patients and 30 healthy controls (HC), and explored the relationship between time processing and affective-cognitive symptoms in BD, with the aim to determine whether timing difficulties are primary in bipolar patients or due to comorbid cognitive impairment. Four tasks measuring external timing were administered: a temporal and spatial orienting of attention task and a temporal and colour discrimination task, for assessing the ability to evaluate temporal properties of external events; two other tasks assessed the speed of the internal clock (i.e. temporal bisection and temporal production tasks). Attentional, executive and working memory (WM) demands were equated for controlling additional cognitive processes. ResultsBD patients did not show differences in external timing accuracy compared to HC; conversely, we found increased variability of the internal clock in BD and this performance was related to Major Depressive Episodes recurrence and WM functioning. Hence, variability of the internal clock is influenced by the progressive course of BD and impacted by variations in WM. LimitationsFuture studies including BD patients stratified by mood episode will further specify timing alterations conditional to the current affective state. ConclusionsOur results shed new light on the clinical phenotypes of BD, suggesting that timing might be used as a model system of the ongoing pathophysiological process.

Deriving homing sequences for Finite State Machines with timeouts

Abstract State identification is the well-known problem in the automata theory that is aimed to determining the current or initial state of a system under test and this fact is widely used in the model-based testing of software and hardware systems. When modern systems are modeled, it is necessary to take into account the timed aspects and for this reason classical Finite State Machines (FSM) are extended by clock variables. In this work, we study the homing problem for FSMs with timeouts (TFSM). For this purpose, we introduce the notion of a timed homing sequence (HS) that is different from that for classical FSMs and propose a method for checking the existence and deriving a timed HS if it exists. A proposed method is based on the FSM abstraction of a TFSM, i.e. on a classical FSM that partially describes the behavior of a corresponding TFSM and inherits many of its properties. Since timeouts allow the system to move from state to state without input impact, we define a timed HS as a sequence that sets a TFSM to a stable state where the system can stay infinitely long waiting for an input.

Relational evolution with oscillating clocks

A fundamental description of time can be consistent not only with the usual monotonic behavior but also with an oscillating physical clock variable, coupled to the degrees of freedom of a system evolving in time. Generically, one would in fact expect some kind of oscillating motion of a system that is dynamical and interacts with its surroundings, as required for a fundamental clock that can be noticed by any other system. Unitary evolution does not require a monotonic clock variable and can be achieved more generally by formally unwinding the oscillating clock movement, keeping track not only of the value of the clock variable but also of the number of cycles it has gone through at any moment. The specific treatment used here employs concatenations of evolution operators, alternating between forward and backward evolution of the oscillating clock. Because the clock and an evolving system have a common conserved energy, the clock is in different cycles for different energy eigenstates of the system state. As a result, the clock is generically in a quantum state with a superposition of different clock cycles, a key feature that distinguishes oscillating clocks from monotonic time. In addition, coherence could be lost faster than observed, for instance if a system that would be harmonic in isolation is made anharmonic by interactions with a fundamental clock, implying observational bounds on fundamental clocks. Numerical computations show that coherence is maintained over long timescales provided the clock period is much smaller than the system period. A small loss of coherence nevertheless remains and, measured in terms of the relative standard deviation of the system period, is proportional to the ratio of the system period and the clock period. Since the precision of atomic clocks could not be achieved if atomic frequencies would be subject to additional variations from coupling to a fundamental clock, an upper bound on the clock period can be obtained that turns out to be much smaller than currently available direct or indirect measurements of time.

Effective cosmology from one-body operators in group field theory

We propose a new method for obtaining an effective Friedmann–Lemaître–Robertson–Walker (FLRW) cosmology from the quantum gravity dynamics of group field theory (GFT), based on the idea that an FLRW universe is characterised by a few macroscopic observables. Rather than relying on assuming a particular type of quantum state and computing expectation values in such a state, here we directly start from relations between macroscopic observables (defined as one-body operators) and formulate dynamics only for those observables. We apply the effective approach to constrained quantum systems (as developed by Bojowald and collaborators) to GFT, providing a systematic expansion in powers of ℏ. We obtain a kinematical phase space of expectation values and moments, which does not require an a priori choice of clock variable. We identify a gauge fixing of the system which corresponds to choosing one of the cosmological variables (with the role of extrinsic curvature) as a clock and which allows us to rewrite the effective dynamics in relational form. We show necessary and sufficient conditions for the resulting dynamics of expectation values to be compatible with those of classical FLRW cosmology and discuss the impact of quantum fluctuations.

Clocks and Trajectories in Quantum Cosmology

We consider a simple cosmological model consisting of an empty Bianchi I Universe, whose Hamiltonian we deparametrise to provide a natural clock variable. The model thus effectively describes an isotropic universe with an induced clock given by the shear. By quantising this model, we obtain various different possible bouncing trajectories (semiquantum expectation values on coherent states or obtained by the de Broglie–Bohm formulation) and explicit their clock dependence, specifically emphasising the question of symmetry across the bounce.

A Bounded Model Checker for Timed Automata and Its Application to LTL Properties

Model checking with a time aspect is often used in verification on hardware and embedded systems. Timed automata are often used for such models. UPPAAL is a world-wide famous model checking tool for timed automata; however, UPPAAL is a Computational Tree Logic (CTL)-based model checking tool and cannot use Linear Temporal Logic (LTL) properties. Bounded model checking uses LTL (Linear Time Logic) for a checking formula. Bounded model checking specifies a boundary k and obtains counterexamples by searching from the initial state of a system to states reachable by k-steps. There are several studies on bounded model checking. Sorea has proposed a concrete algorithm for a timed automaton. There are, however, no clear details on how to implement bounded model checking tools for timed automata, and study the performance. Another problem is that the timed automaton covered by the method does not support general variables except for clock variables. The objective of this study is to implement a bounded model checking tool using LTL for timed automata. We also improve Sorea's method so that it can handle extended timed automata that handle general variables. This paper also presents some LTL examples from texts on requirement specifications for embedded systems and the results of applying the tool to them.

Deriving Homing Sequences for Finite State Machines with Timed Guards

State identification is the well-known problem in the theory of Finite State Machines (FSM) where homing sequences (HS) are used for the identification of a current FSM state, and this fact is widely used in the area of software and hardware testing and verification. For various kinds of FSMs, such as partial, complete, deterministic, non-deterministic, there exist sufficient and necessary conditions for the existence ofpreset and adaptive HS and algorithms for their derivation. Nowadays timed aspects become very important for hardware and software systems and for this reason classical FSMs are extended by clock variables. In this work, we address the problem of checking the existence and derivation of homing sequences for FSMs with timed guards and show that the length estimation for timed homing sequence coincides with that for untimed FSM. The investigation is based on the FSM abstraction of a Timed FSM, i.e. on a classical FSM which describes behavior of corresponding TFSM and inherits some of its properties. When solving state identification problems for timed FSMs, the existing FSM abstraction is properly optimized.

Configurable verification of timed automata with\xa0discrete\xa0variables

Algorithms and protocols with time dependent behavior are often specified formally using timed automata. For practical real-time systems, besides real-valued clock variables, these specifications typically contain discrete data variables with nontrivial data flow. In this paper, we propose a configurable lazy abstraction framework for the location reachability problem of timed automata that potentially contain discrete variables. Moreover, based on our previous work, we uniformly formalize in our framework several abstraction refinement strategies for both clock and discrete variables that can be freely combined, resulting in many distinct algorithm configurations. Besides the proposed refinement strategies, the configurability of the framework allows the integration of existing efficient lazy abstraction algorithms for clock variables based on {textit{LU}}-bounds. We demonstrate the applicability of the framework and the proposed refinement strategies by an empirical evaluation on a wide range of timed automata models, including ones that contain discrete variables or diagonal constraints.

0170 Association of HIF-1 Alpha and Beta Subunits with Clock and BMAL1 Proteins in Obstructive Sleep Apnea Patients

Abstract Introduction Obstructive sleep apnea (OSA) is a chronic condition that is characterized by intermittent hypoxia. Key regulator of oxygen metabolism is hypoxia inducible factor (HIF), which consists of oxygen sensitive subunit and continuously produced subunit. Circadian clock is composed of set of genes, which function as activators - CLOCK and BMAL 1, who similarly to HIF are basic helix-loop-helix-PER-ARNT-SIM transcription factors. Therefore, the aim of the study was to assess the relationship between HIF-1alpha, HIF-1beta, CLOCK, BMAL1 and polysomnography (PSG) variables in healthy individuals and severe OSA patients. Methods The study included 20 individuals, who underwent PSG and based on apnea-hypopnea index (AHI) were divided into severe OSA group (n=10; AHI30; 90% male) and healthy control (n=10; AHI&amp;lt;5; 70% male). All participants had their peripheral blood collected in the evening (9:00-10:00 pm) before and in the morning (6:00-7:00 am) after the PSG. HIF-1alpha, HIF-1beta, CLOCK and BMAL1 protein concertation measurements were performed using ELISA. Results Significant difference was observed in the following protein measurements between study groups: evening and morning HIF-1 (p=0.020 and p=0.043, respectively), evening HIF-1alpha (p=0.047), evening and morning CLOCK (p=0.037 and p=0.019, respectively) and morning BMAL1 (p=0.016). No differences were observed between morning and evening protein levels in both groups. Evening HIF-1beta corraleted with evening CLOCK and morning BMAL1 (R=0.511, p=0.21 and R=0.594, p=0.006, respectively), while morning HIF-1 with evening BMAL1 (R=474, p=0.35). Furthermore, evening and morning HIF-1 correlated with evening BMAL1 (R=564, p=0.010 and R=0.689, p=0.001, respectively). Additionally, morning CLOCK and BMAL1 correlated with AHI (R=0.510, p=0.022 and R=0.560, p=0.010, respectively) and desaturation index (R=0.487, p=0.209 and R=0.570, p=0.009, respectively). Conclusion There is significant correlation between both subunits of HIF-1 protein and circadian clock proteins: CLOCK and BMAL1, which further correlate with increased disease severity. This suggests OSA patients are in risk of circadian clock disruption due to present hypoxia. Support The study was financed by Polish National Centre Grant no. 2018/31/N/NZ5/03931.

Denotational semantics for guarded dependent type theory

AbstractWe present a new model of guarded dependent type theory (GDTT), a type theory with guarded recursion and multiple clocks in which one can program with and reason about coinductive types. Productivity of recursively defined coinductive programs and proofs is encoded in types using guarded recursion and can therefore be checked modularly, unlike the syntactic checks implemented in modern proof assistants. The model is based on a category of covariant presheaves over a category of time objects, and quantification over clocks is modelled using a presheaf of clocks. To model theclock irrelevance axiom, crucial for programming with coinductive types, types must be interpreted as presheaves internally right orthogonal to the object of clocks. In the case of dependent types, this translates to a lifting condition similar to the one found in homotopy theoretic models of type theory, but here with an additional requirement of uniqueness of lifts. Since the universes defined by the standard Hofmann–Streicher construction in this model do not satisfy this property, the universes in GDTT must be indexed by contexts of clock variables. We show how to model these universes in such a way that inclusions of clock contexts give rise to inclusions of universes commuting with type operations on the nose.

Visual feedback is not important for bimanual human interval timing.

The clock variance of intervals produced by one finger is reduced when that finger taps along with another finger (termed the bimanual advantage). The multiple-timekeeper model proposes a coupling of internal clocks, leading to reduced clock variance for bimanual timing. Alternatively, reduced variance for bimanual timing could result from additional sensory feedback from two fingers as opposed to one. We aimed to test the role of visual feedback in reducing temporal variability. Participants tapped unimanually and bimanually (with no table contact) in three conditions: full vision, blindfolded, and with additional visual feedback provided via a mirror reflecting the right hand. We predicted that temporal variability would be reduced for tapping with vision versus no vision, and when the left hand was represented by a mirror but did not actually tap. Additional, redundant visual information did not reduce temporal variability for any condition, suggesting that visual feedback is not crucial for bimanual advantage. These findings support the role of sensory feedback (namely, tactile, auditory, and proprioceptive) in reducing timekeeper variability during bimanual timing and argue against a strictly multiple-timekeeper model.

Deriving of Time Constants in Timed Automata for Hazard Transition Sequences for STAMP/STPA

Abstract In recent years, information systems have become large-scale and complicated. The demand for research on the cause analysis of information systems that can fail and the construction of countermeasures has been increasing. Systems Theoretic Accident Model and Processes (STAMP) is an accident model based on systems theory. STAMP has the feature that it can analyze not only failures of system components and human errors but also hazards caused by unsafe interaction between components and between components and humans. An analysis method based on the STAMP model System-Theoretic Process Analysis (STPA) is a method for analyzing in advance the possibility of a system accident for the interaction between a controller and a controlled device. As a preliminary study, we have performed STAMP/STPA to ‘Fallen Barrier Trap at Railroad Crossing,” which is an example of STAMP/STPA analysis. We have analyzed with the time automaton model checker UPPAAL in cooperation with STAMP Workbench, a STAMP/STPA support tool. From the preliminary study, we consider that the analysis procedure can be automated in order to reduce the burden on analysts. In this paper, we propose a method for deriving hazard transition sequences as a STAMP/STPA support method. Specifically, the model definition is described in STAMP Workbench, the method of deriving files that can be used in UPPAAL from the definition statement is described, and in order to automate model checking, the SAT/SMT solver is used. The constraints for the clock variables in each component are automatically derived. This paper describes a method for deriving the shortest path as a counterexample that does not satisfy the safety constraint equation by using the calculation method of the concrete value the constraints of and the binary search method. The proposed method is applied manually as the evaluation experiment. We confirmed that an effective sequence corresponding to some hazard scenarios derived by the conventional procedure could be derived.

On reduced forms of initialized Finite State Machines with timeouts

Trace models such as Finite State Machines (FSMs) are widely used in the area of analysis and synthesis of discrete event systems. FSM minimization is a well-known optimization problem which allows to reduce the number of FSM states by deriving the canonical form that is unique up to isomorphism. In particular, the latter is a base for FSM-based ‘black-box’ test derivation methods such as W-method and its modifications. Since nowadays the behavior of many software and hardware systems significantly depends on time aspects, classical FSMs are extended by clock variables including input and output timeouts. The minimization of a Timed Finite State Machine (TFSM) includes both state and time aspects reduction. Existing approaches allow to derive the canonical representation for non-initialized deterministic TFSMs while for initialized TFSMs, i.e., TFSMs with the designated initial state, several pair-wise non-isomorphic minimal forms can exist. In this paper, we determine initialized TFSM classes for which the minimal form is unique up to isomorphism.

Timing deficiencies in amnestic Mild Cognitive Impairment: Disentangling clock and memory processes

Interval timing performance in cognitive decline is typically characterized by decreased accuracy, precision, or both. One explanation for this decreased performance is a larger clock time variability. However, memory deficiencies associated with cognitive decline might also affect temporal performance in two alternative ways: First, memory deficiencies could lead to reduced encoding of just perceived durations, and thus a stronger reliance on the memory traces of previous experiences (the “prior”), yielding less precise reproductions of the most current experiences. Second, memory deficiencies could hamper the storage of perceived intervals, thus resulting in less influence of the prior.Here, we present data of 15 patients with amnestic Mild Cognitive Impairment (aMCI) and 44 healthy, aged controls, the latter split in two groups based on memory performance. All participants were tested on a temporal production task to assess clock time variability and a multi-duration reproduction task to assess the influence of memory traces reflecting current and previous experiences.Patients with aMCI showed the strongest regression towards the mean in a multi-duration reproduction task, followed by low-performing healthy controls and high-performing healthy controls, respectively. As no difference was observed between the groups in terms of clock time variability, and clock variability did not statistically contribute to the observed regression, this increased central tendency effect was not attributable to clock noise. We therefore, in line with the first explanation, conclude that memory deficiencies result in a stronger (relative) reliance on the prior.

From Real-time Logic to Timed Automata

We show how to construct temporal testers for the logic MITL, a prominent linear-time logic for real-time systems. A temporal tester is a transducer that inputs a signal holding the Boolean value of atomic propositions and outputs the truth value of a formula along time. Here we consider testers over continuous-time Boolean signals that use clock variables to enforce duration constraints, as in timed automata. We first rewrite the MITL formula into a “simple” formula using a limited set of temporal modalities. We then build testers for these specific modalities and show how to compose testers for simple formulae into complex ones. Temporal testers can be turned into acceptors, yielding a compositional translation from MITL to timed automata. This construction is much simpler than previously known and remains asymptotically optimal. It supports both past and future operators and can easily be extended.

Floquet time crystals in clock models

We construct a class of period-$n$-tupling discrete time crystals based on $\mathbb{Z}_n$ clock variables, for all the integers $n$. We consider two classes of systems where this phenomenology occurs, disordered models with short-range interactions and fully connected models. In the case of short-range models we provide a complete classification of time-crystal phases for generic $n$. For the specific cases of $n=3$ and $n=4$ we study in details the dynamics by means of exact diagonalisation. In both cases, through an extensive analysis of the Floquet spectrum, we are able to fully map the phase diagram. In the case of infinite-range models, the mapping onto an effective bosonic Hamiltonian allows us to investigate the scaling to the thermodynamic limit. After a general discussion of the problem, we focus on $n=3$ and $n=4$, representative examples of the generic behaviour. Remarkably, for $n=4$ we find clear evidence of a new crystal-to-crystal transition between period $n$-tupling and period $n/2$-tupling.