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This study presents bounds on transient variations of fundamental constants, with typical timescales ranging from minutes to months, using clocks in space. The underlying phenomenology describing such transient variations relies on models for Dark Matter (DM) which suggest possible encounters of macroscopic compact objects with the Earth, due to the motion of the solar system in the galactic halo. If such compact objects possess an effective feeble interaction with the ordinary matter beyond the gravitational one, it may result in effective transient variations of fundamental constants. Such variations leave signatures on clocks onboard GNSS satellites. In this paper, we introduce a phenomenological study dedicated to the search for such DM transient objects using the network of passive hydrogen masers (H-Masers) onboard Galileo satellites. We first model the signature of transient variations of fundamental constants as a frequency modulation in the difference between two satellite clocks, considering the satellite trajectories relative to the transient event. Then, we present first results based on a fast analysis method, the maximum reach analysis. The main result is a significant extension of the discovery range for DM transients, with a sensitivity never achieved before. We investigate indeed the range of transient sizes from 10 5 to 10 9 kilometres, which, apart from indirect and model-dependent non-transient effects, has never been explored previously. [ABSTRACT FROM AUTHOR]

Introduction Context Discussion Few sociocultural constructs exist that are so deeply embedded in our daily lives and able to influence our thoughts, behaviours and interactions than time itself. Time spans all cultures, and yet many of us have not critically engaged with how time effects what we do, how we perceive and the ways in which we interact. As such, our relationship to time remains almost invisible running in the background nearly unnoticed until it is somehow brought into conscious awareness.In this paper, we draw on Levine's concepts of clock time and event time as different perspectives on time, demonstrating how they play out in medical education and clinical practice within the United States and Brazil. Clock time treats time as something external to our lives, fixed by the natural world and measured by clocks. Event time is conceptualised more flexibly, where the duration of activities depends on internal cues related to the flow and progression of events rather than strict schedules.By contrasting these differences, we hope to make visible the way that time influences our choices for educating physicians and provide a foundation for medical education to begin questioning how time is positioned, experienced and understood as a powerful force in the shaping of our profession. Additionally, we consider these perspectives within the concepts of Taylorism and Slow Medicine to better understand their links to medicine's formal and hidden curriculum in hopes of raising awareness and create new visions for medical education. [ABSTRACT FROM AUTHOR]

Parametric timed automata (PTA) have been introduced by Alur, Henzinger, and Vardi as an extension of timed automata in which clocks can be compared against parameters. The reachability problem asks for the existence of an assignment of the parameters to the non-negative integers such that reachability holds in the underlying timed automaton. The reachability problem for PTA is long known to be undecidable, already over three parametric clocks. A few years ago, Bundala and Ouaknine proved that for PTA over two parametric clocks and one parameter the reachability problem is decidable and also showed a lower bound for the complexity class PSPACENEXP. Our main result is that the reachability problem for two-parametric timed automata with one parameter is EXPSPACE-complete. Our contribution is two-fold. For the EXPSPACE lower bound, inspired by [13-14], we make use of deep results from complexity theory, namely a serializability characterization of EXPSPACE (in turn based on Barrington's Theorem) and a logspace translation of numbers in Chinese remainder representation to binary representation due to Chiu, Davida, and Litow. It is shown that with small PTA over two parametric clocks and one parameter one can simulate serializability computations. For the EXPSPACE upper bound, we first give a careful exponential time reduction from PTA over two parametric clocks and one parameter to a (slight subclass of) parametric one-counter automata over one parameter based on a minor adjustment of a construction due to Bundala and Ouaknine. For solving the reachability problem for parametric one-counter automata with one parameter, we provide a series of techniques to partition a fictitious run into several carefully chosen subruns that allow us to prove that it is sufficient to consider a parameter value of exponential magnitude only. This allows us to show a doubly-exponential upper bound on the value of the only parameter of a PTA over two parametric clocks and one parameter. We hope that extensions of our techniques lead to finally establishing decidability of the long-standing open problem of reachability in parametric timed automata with two parametric clocks (and arbitrarily many parameters) and, if decidability holds, determinining its precise computational complexity. [ABSTRACT FROM AUTHOR]

The common requirement to set the time to "10 past 11" on the Clock Drawing Test is intended to elicit a stimulus bound response (SBR), in which the responder is "pulled" to the salient stimulus "10," resulting in hands set at "10 before 11." SBRs are considered markers of executive dysfunction, although this assumption has not yet been validated. We compared SBR and other time-setting errors on inhibitory control tests, hypothesizing that they represent related constructs. The role of semantic dysfunction in the formation of those errors was also investigated. We examined baseline test performance of participants with Mild Cognitive Impairment or a history of depression, and control participants, enrolled in a dementia prevention study. Among 258 participants, we identified clocks with SBRs (n = 16), other time errors (n = 22), or no errors at all (n = 42). Performance between the groups with SBRs and other time-setting errors did not differ on any of the executive tests, and both error groups performed significantly worse than the No Error group on the semantic tests. Control for covariates further supported semantic and executive components in time-setting errors. Both semantic and inhibitory control deficits may underlie time representation errors in general. [ABSTRACT FROM AUTHOR]

Stochastic clocks represent a class of time change methods for incorporating trading activity into continuous-time financial models, with the ability to deal with typical asymmetrical and tail risks in financial returns. In this paper we propose a significant improvement of stochastic clocks for the same objective but without decreasing the number of trades or changing the trading intensity. Our methodology targets any Lévy subordinator, or more generally any process of nonnegative independent increments, and is based on various choices of regulating kernels motivated from repeated averaging. By way of a hyperparameter linked to the degree of regulation, arbitrarily large skewness and excess kurtosis of returns can be easily achieved. Generic-time Laplace transforms, characterizing triplets, and cumulants of the regulated clocks and subsequent mixed models are analyzed, serving purposes ranging from statistical estimation and option price calibration to simulation techniques. Under specified jump–diffusion processes and tempered stable processes, a robust moment-based estimation procedure with profile likelihood is developed and a comprehensive empirical study involving S&P500 and Bitcoin daily returns is conducted to demonstrate a series of desirable effects of the proposed methods. [ABSTRACT FROM AUTHOR]

This article assesses the role and understanding of war's most inflexible factor—time—and its associated pressures and advantages in the Russo-Ukrainian War. While there seems to be no consensus on who might prevail (and of course the elements of what constitutes victory itself can vary), the passage of time—frequently understood in military terms as endurance and exhaustion—is a useful framework to assess the direction of the war, relative advantage at various stages, who may ultimately prevail, and under what conditions that may be possible. Although timetables and schedules have played an enormous role in military history, there appears to be no systematic assessment of the role of time in relation to strategy and victory in the Russo-Ukrainian war. This article sets out to fill that gap through a systematic comparison of time's passing and time pressures facing the combatants. [ABSTRACT FROM AUTHOR]

We present an additive-manufactured microwave cavity for a Ramsey-type, double resonance, compact cold-atom clock. Atoms can be laser cooled inside the cavity using a grating magneto-optic trap with the cavity providing an excellent TE011-like mode while maintaining sufficient optical access for atomic detection. The cavity features a low Q-factor of 360 which conveniently reduces the cavity pulling of the future clock. Despite the potential porosity of the additive-manufacturing process, we demonstrate that the cavity is well-suited for vacuum. A preliminary clock setup using cold atoms allows for measuring the Zeeman spectrum and Rabi oscillations in the cavity which enables us to infer excellent field uniformity and homogeneity, respectively, across the volume accessed by the cold atoms. Ramsey spectroscopy is demonstrated, indicating that the cavity is suitable for clock applications. Finally, we discuss the limitations of the future clock. [ABSTRACT FROM AUTHOR]

The application of rare earth (RE) doped crystals in quantum information processing has attracted more and more attention in the past decade. How to change the clock transitions of RE ion in crystal and control their lifetime of maintaining coherent quantum state is a valuable question. In this work, the trigonal 171Yb3+ centers in lithium niobate (LN) crystal are investigated theoretically to obtain their accurate ground and excited hyperfine sublevels under external magnetic field B by a combined method of density functional theory-based geometric optimization and parametric effective Hamiltonian modeling. An optical clock transition at |B| = 45.73 mT along the c axis of the LN crystal is successfully found by calculation. To show the pressure-dependent behavior of optical clock transition, the variation of such transition under hydrostatic pressure up to 3 GPa is also obtained theoretically. The calculated results show that applying external pressure is an effective way to control these transitions of RE ion doped crystal. Moreover, the optical coherence time T2 at zero magnetic field for 171Yb3+ ion with C3 symmetry in the LN crystal is estimated by our calculations. The calculated results indicate that if the magnetic field noise is 33 μT in the LN crystal, it is possible to find an optical clock transition with long coherence time T2 (≈382 μs) at the zero magnetic field. The present methods of seeking optical clock transition and calculating its coherence time T2 caused by a fluctuating magnetic field noise in the host crystal can be applied to other Kramers RE ions doped materials. [ABSTRACT FROM AUTHOR]

We present here a massively parallel implementation of the recently developed CPS(D-3) excitation energy model that is based on cluster perturbation theory. The new algorithm extends the one developed in Baudin et al. [J. Chem. Phys., 150, 134110 (2019)] to leverage multiple nodes and utilize graphical processing units for the acceleration of heavy tensor contractions. Furthermore, we show that the extended algorithm scales efficiently with increasing amounts of computational resources and that the developed code enables CPS(D-3) excitation energy calculations on large molecular systems with a low time-to-solution. More specifically, calculations on systems with over 100 atoms and 1000 basis functions are possible in a few hours of wall clock time. This establishes CPS(D-3) excitation energies as a computationally efficient alternative to those obtained from the coupled-cluster singles and doubles model. [ABSTRACT FROM AUTHOR]

A simple model is built to evaluate quantitatively the individual feeling of the passage of time using a sociophysics approach. Given an objective unit of time like the year, I introduce an individualized mirror-subjective counterpart, which is inversely proportional to the number of objective units of time already experienced by a person. An associated duration of time is then calculated. Past and future individual horizons are also defined together with a subjective speed of time. Furthermore, I rescale the subjective unit of time by activating additional clocks connected to ritualized socializations, which mark and shape the specific times of an individual throughout their life. The model shows that without any ritual socialization, an individual perceives their anticipated life as infinite via a "soft" infinity. The past horizon is also perceived at infinity but with a "hard" infinity. However, the price for the first ritualized socialization is to exit eternity in terms of the anticipated future with the simultaneous reward of experiencing a finite moment of infinity analogous to that related to birth. I then extend the model using a power law of the number of past objective units of time to mitigate the phenomenon of shrinking of time. The findings are sound and recover common feelings about the passage of time over a lifetime. In particular, the fact that time passes more quickly with aging with a concomitant slowing down of the speed of time. [ABSTRACT FROM AUTHOR]

Epigenetic aging clocks are computational models that predict age using DNA methylation information. Initially, first-generation clocks were developed to make predictions using CpGs that change with age. Over time, next-generation clocks were created using CpGs that relate to both age and health. Since existing next-generation clocks were constructed in blood, we sought to develop a next-generation clock optimized for prediction in cheek swabs, which are non-invasive and easy to collect. To do this, we collected MethylationEPIC data as well as lifestyle and health information from 8045 diverse adults. Using a novel simulated annealing approach that allowed us to incorporate lifestyle and health factors into training as well as a combination of CpG filtering, CpG clustering, and clock ensembling, we constructed CheekAge, an epigenetic aging clock that has a strong correlation with age, displays high test–retest reproducibility across replicates, and significantly associates with a plethora of lifestyle and health factors, such as BMI, smoking status, and alcohol intake. We validated CheekAge in an internal dataset and multiple publicly available datasets, including samples from patients with progeria or meningioma. In addition to exploring the underlying biology of the data and clock, we provide a free online tool that allows users to mine our methylomic data and predict epigenetic age. [ABSTRACT FROM AUTHOR]

Data acquisition based on network-on-chip (NoC) technology is a high-sampling-rate data acquisition scheme using low-sampling-rate analog–digital conversion (ADC) chips. It has the characteristics of multi-task parallel communication, being global asynchronous, local synchronous clock distribution, high throughput, low transmission latency, and strong scalability. High-speed data acquisition is realized through the combination of an on-chip network and time-interleaved data acquisition technology. In the time-interleaved sampling technique, the precision of clock synchronization directly affects the precision of sampling. Based on the proposed NOC data acquisition scheme, an improved White Rabbit clock synchronization protocol is applied to high-speed data acquisition to achieve high-precision synchronization of multi-channel time-interleaved sampling clocks. Firstly, the offset of the master clock and slave clock is determined by the PTP protocol, and the offset is corrected to achieve rough synchronization between the master clock and slave clock. Secondly, a digital dual-mixer time difference (DDMTD) is used to measure the phases of the master and slave clocks. After that, the phase of the slave clock is corrected through the dynamic phase-shift function of the clock's phase-locked loop (PLL). Finally, according to the simulation results in Modelsim, the average absolute error of a TI-ADC sampling clock can be less than 20 ps. [ABSTRACT FROM AUTHOR]

General relativity predicts that two counter-orbiting clocks around a spinning mass differ in the time required to complete the same orbit. The difference in these two values for the orbital period is generally referred to as the gravito-magnetic (GM) clock effect. It has been proposed to measure the GM clock effect using atomic clocks carried by satellites in prograde and retrograde orbits around the Earth. The precision and stability required for satellites to accurately perform this measurement remains a challenge for current instrumentation. One of the most accurate clocks in the Universe is a millisecond pulsar, which emits periodic radio pulses with high stability. Timing of the pulsed signals from millisecond pulsars has proven to be very successful in testing predictions of general relativity and the GM clock effect is potentially measurable in binary systems. In this work, we derive the generic GM clock effect by considering a slowly spinning binary system on an elliptical orbit, with both arbitrary mass ratio and arbitrary spin orientations. The spin–orbit interaction introduces a perturbation to the orbit, causing the orbital plane to precess and nutate. We identify several different contributions to the clock effects: the choice of spin supplementary condition and the observer-dependent definition of a full revolution and 'nearly identical' orbits. We discuss the impact of these subtle definitions on the formula for GM clock effects and show that most of the existing formulae in the literature can be recovered under appropriate assumptions. [ABSTRACT FROM AUTHOR]

Summary: Circadian rhythms are entrained by external factors such as sunlight and social cues, but also depend on internal factors such as age. Adolescents exhibit late chronotypes, but worldwide school starts early in the morning leading to unhealthy sleep habits. Several studies reported that adolescents benefit from later school start times. However, the effect of later school start time on different outcomes varies between studies, and most previous literature only takes into consideration the social clock (i.e. local time of school starting time) but not the solar clock (e.g. the distance between school start time and sunrise). Thus, there is an important gap in the literature: when assessing the effect of a school start time on chronotype and sleep of adolescents at different locations and/or seasons, the solar clock might differ and, consistently, the obtained results. For example, the earliest school start time for adolescents has been suggested to be 08:30 hours, but this school start time might correspond to different solar times at different times of the year, longitudes and latitudes. Here, we describe the available literature comparing different school start times, considering important factors such as geographic position, nationality, and the local school start time and its distance to sunrise. Then, we described and contrasted the relative role of both social and solar clocks on the chronotype and sleep of adolescents. As a whole, we point and discuss a gap in literature, suggesting that both clocks are relevant when addressing the effect of school start time on adolescents' chronotype and sleep. [ABSTRACT FROM AUTHOR]

The utilization of Low Earth Orbit (LEO) satellites is anticipated to augment various aspects of traditional GNSS-based Positioning, Navigation, and Timing (PNT) services. While the LEO satellite orbital products can nowadays be produced with rather high accuracy in real-time of a few centimeters, the precision of the LEO satellite clock products that can be achieved in real-time is less studied. The latter, however, plays an essential role in the LEO-augmented positioning and timing performances. In real-time, the users eventually use the predicted LEO satellite clocks, with their precision determined by both the near-real-time clock precision and the prediction time needed to match the time window for real-time applications, i.e., the precision loss during the prediction phase. In this study, a real-time LEO satellite clock determination method, consisting of near-real-time clock determination with ultra-short-term clock prediction is proposed and implemented. The principles and strategies of this method are discussed in detail. The proposed method utilized Kalman-filter-based processing, but supports restarts at pre-defined times, thus hampering continuous bias propagation and accumulation from ancient epochs. Based on the method, using Sentinel-3B GNSS observations and the real-time GNSS products from the National Center for Space Studies (CNES) in France, the near-real-time LEO satellite clocks can reach a precision of 0.2 to 0.3 ns, and the precision loss during the prediction phase is within 0.07 ns for a prediction time window from 30 to 90 s. This results in a total error budget in the real-time LEO satellite clocks of about 0.3 ns. [ABSTRACT FROM AUTHOR]

Living systems are built from microscopic components that function dynamically; they generate work with molecular motors, assemble and disassemble structures such as microtubules, keep time with circadian clocks, and catalyze the replication of DNA. How do we implement these functions in synthetic nanostructured materials to execute them before the onset of dissipative losses? Answering this question requires a quantitative understanding of when we can improve performance and speed while minimizing the dissipative losses associated with operating in a fluctuating environment. Here, we show that there are four modalities for optimizing dynamical functions that can guide the design of nanoscale systems. We analyze Markov models that span the design space: a clock, ratchet, replicator, and self-assembling system. Using stochastic thermodynamics and an exact expression for path probabilities, we classify these models of dynamical functions based on the correlation of speed with dissipation and with the chosen performance metric. We also analyze random networks to identify the model features that affect their classification and the optimization of their functionality. Overall, our results show that the possible nonequilibrium paths can determine our ability to optimize the performance of dynamical functions, despite ever-present dissipation, when there is a need for speed. [ABSTRACT FROM AUTHOR]

When a perturbed periodic oscillation dephases, the system edits it to retrieve the original clock. The inherent clock born during retrieval is the time crystal. Time crystals have been explored for five decades, and only one inherent clock was detected in biological and artificial systems. Only one type of atom is used in those time crystals, but two or more atom types would lead to multi-functional and programmable time crystals. No such concept was ever conceived. Here, we demonstrate a multi-clock time crystal or a polyatomic time crystal in the brain neuron-extracted microtubule nanowire using dielectric resonance and quantum optics experiments. Earlier, one used to artificially reset the phase of an inherent clock to find a time crystal. Instead, we map how a biomaterial spontaneously generates distinct new clocks at many time domains at a time. We observe multiple time-symmetry-breaking events at a time. Moreover, unlike conventional time crystal research, we searched for polyatomic time crystals at least 103 orders lower than the excitation frequency region. Conventional time crystals could be rejected, arguing that inherent clocks born after the breaking of time symmetry are harmonics of the external input, and such an argument will not hold for us. Moreover, quantum experiments revealed a method to synthesize and fuse distinct clocks in one hologram as a polyatomic time crystal and project it like an antenna meters away. The discovery of material-like holographic engineering of polyatomic time crystals would make them useful. [ABSTRACT FROM AUTHOR]

The motion of an ion in a radiofrequency (rf) Paul trap is described by the Mathieu equation and the associated stability parameters that are proportional to the rf and dc electric field gradients. Here, a higher-order, iterative method to accurately solve the stability parameters from measured secular frequencies is presented. It is then used to characterize an endcap trap by showing that the trap's radial asymmetry is dominated by the dc field gradients and by measuring the relation between the applied voltages and the gradients. The results are shown to be in good agreement with an electrostatic finite-element-method simulation of the trap. Furthermore, a method to determine the direction of the radial trap axes using a "tickler" voltage is presented, and the temperature dependence of the rf voltage is discussed. As an application for optical ion clocks, the method is used to predict and minimize the electric quadrupole shift (EQS) using the applied dc voltages. Finally, a lower limit of 1070 for the cancellation factor of the Zeeman-averaging EQS cancellation method is determined in an interleaved low-/high-EQS clock measurement. This reduces the EQS uncertainty of our 88 Sr + optical clock to ≲ 1 × 10 − 19 in fractional frequency units. [ABSTRACT FROM AUTHOR]

Circadian clocks impose daily periodicities to behavior, physiology, and metabolism. This control is mediated by a central clock and by peripheral clocks, which are synchronized to provide the organism with a unified time through mechanisms that are not fully understood. Here, we characterized in Drosophila the cellular and molecular mechanisms involved in coupling the central clock and the peripheral clock located in the prothoracic gland (PG), which together control the circadian rhythm of emergence of adult flies. The time signal from central clock neurons is transmitted via small neuropeptide F (sNPF) to neurons that produce the neuropeptide Prothoracicotropic Hormone (PTTH), which is then translated into daily oscillations of Ca2+ concentration and PTTH levels. PTTH signaling is required at the end of metamorphosis and transmits time information to the PG through changes in the expression of the PTTH receptor tyrosine kinase (RTK), TORSO, and of ERK phosphorylation, a key component of PTTH transduction. In addition to PTTH, we demonstrate that signaling mediated by other RTKs contributes to the rhythmicity of emergence. Interestingly, the ligand to one of these receptors (Pvf2) plays an autocrine role in the PG, which may explain why both central brain and PG clocks are required for the circadian gating of emergence. Our findings show that the coupling between the central and the PG clock is unexpectedly complex and involves several RTKs that act in concert and could serve as a paradigm to understand how circadian clocks are coordinated. [ABSTRACT FROM AUTHOR]

The explanation of Einstein’s special theory of relativity in his original 1905 paper is examined. His analysis is confusing, as terms x, y, z, t, etc., have different meanings at various points, and he presents equations based on different and inconsistent assumptions. Adding subscripts clarifies these issues but exposes errors in his reasoning. To calculate his transformation equations, he selects a combination of equations which gives results matching the Lorentz transformation but he ignores other possible valid solutions. Also his calculations contain serious errors. Therefore, he fails to prove that his theory leads to the Lorentz equations as a unique solution. Einstein’s analysis includes “moving” clocks which show “stationary” time t, so the idea that a moving clock should run slower than a stationary clock is incompatible with his theory. Also, his calculation of time dilation contains serious errors. As a result, he fails to provide a theoretical justification for his famous “clocks paradox.” [ABSTRACT FROM AUTHOR]

A sub-nanosecond clock synchronization scheme based on the field programmable gate array (FPGA) is proposed for the Fiber Channel (FC) communication system in this paper. The counter value of the slave node is synchronized to that of the master node through the embedded IEEE 1588 protocol over the communication link. In order to ensure the counter clocks have the same frequency in both nodes, which is recovered from the FC communication link, the clock phase difference is measured by the digital dual mixer time difference technique and the data recovery technique in the Gigabyte Transceiver, and then it is compensated by the mixed-mode clock manager in FPGAs. The proposed clock synchronization approach is evaluated with an FC communication system that has a serial rate of 12.5 Gbps, and the reported experimental results show that the proposed clock synchronization module can achieve a time difference lower than 1 ns. [ABSTRACT FROM AUTHOR]

The relative enrichment of s -process to α-elements ([ s /α]) has been linked with age, providing a potentially useful avenue in exploring the Milky Way's chemical evolution. However, the age–[ s /α] relationship is non-universal, with dependencies on metallicity and current location in the Galaxy. In this work, we examine these chemical clock tracers across birth radii (⁠|${R}_\text{birth}$|⁠), recovering the inherent trends between the variables. We derive |${R}_\text{birth}$| and explore the [ s /α]–age– |${R}_\text{birth}$| relationship for 36 652 APOGEE DR17 red giant and 24 467 GALAH DR3 main-sequence turn-off and subgiant branch disc stars using [Ce/Mg], [Ba/Mg], and [Y/Mg]. We discover that the age– |$\rm [{\it s}/Mg]$| relation is strongly dependent on birth location in the Milky Way, with stars born in the inner disc having the weakest correlation. This is congruent with the Galaxy's initially weak, negative |$\rm [{\it s}/Mg]$| radial gradient, which becomes positive and steep with time. We show that the non-universal relations of chemical clocks is caused by their fundamental trends with |${R}_\text{birth}$| over time, and suggest that the tight age– |$\rm [{\it s}/Mg]$| relation obtained with solar-like stars is due to similar |${R}_\text{birth}$| for a given age. Our results are put into context with a Galactic chemical evolution model, where we demonstrate the need for data-driven nucleosynthetic yields. [ABSTRACT FROM AUTHOR]

The article focuses on "The Great Historical Clock of America," an immense clock from 1890 exhibited in the Smithsonian's National Museum of American History. Topics include the clock's dimensions, intricate decorations depicting scenes from U.S. history, and its significance as an uncommon object with a life history that reveals connections between people and things. The article explores the concept of object biography, tracing the clock's journey through time and space.

Various oscillatory phenomena occur in the world. Because some are associated with abnormal states (e.g. epilepsy), it is important to establish ways to terminate oscillations by external stimuli. However, despite the prior development of techniques for stabilizing unstable oscillations, relatively few studies address the transition from oscillatory to resting state in nonlinear dynamics. This study mainly analyzes the oscillation-quenching of metronomes on a platform as an example of such transitions. To facilitate the analysis, we describe the impulsive force (escapement mechanism) of a metronome by a fifth-order polynomial. By performing both averaging approximation and numerical simulation, we obtain a phase diagram for synchronization and oscillation quenching. We find that quenching occurs when the feedback to the oscillator increases, which will help explore the general principle regarding the state transition from oscillatory to resting state. We also numerically investigate the bifurcation of out-of-phase synchronization and beat-like solution. Despite the simplicity, our model successfully reproduces essential phenomena in interacting mechanical clocks, such as the bistability of in-phase and anti-phase synchrony and oscillation quenching occurring for a large mass ratio between the oscillator and the platform. We believe that our simple model will contribute to future analyses of other dynamics of mechanical clocks. [ABSTRACT FROM AUTHOR]

This article maps out the lexical landscape of precision from the late seventeenth to the early eighteenth century and investigate the various meanings of precision, both as a word and a concept, within the Paris Observatory and beyond. It argues that precision was first an attribute of instruments supposed to produce numerical measurements, like clocks and divided circles or sectors attached to optical devices. Less often, precision was applied to observers, the handling of instruments, and observational methods, including mathematical corrections applied to raw data. When all these aspects were combined the numerical result finally was also deemed to be precise. Moving to the debate about the shape of the Earth that shook the Academy of Sciences in the 1730s, it follows the way in which wider audiences were conveyed the various meanings of precision. Between the Cartesian resistance to the emergence of a professional science of precision and the pedagogical approach followed by the Newtonians such as Maupertuis, it argues that Cassini III embraced the professionalism of modern science, but did not feel that methodological precision was out of the reach of an educated public. While Maupertuis has seemed content with a discussion focusing on the precision of instruments and results, Cassini III set himself the hefty task of producing an accessible account of precision as a method of inquiry. [ABSTRACT FROM AUTHOR]

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The Hafele-Keating experiment showed the occurrence of time dilation in clocks placed on two airplanes, one moving eastward and one moving westward relative to the Earth's rotation. However, the application of the special theory of relativity failed to account for the significant differences in the data. This problem is solved by a novel approach that focuses on the absolute velocities of the clocks with reference to the Earth's rotation and uses space as a fixed reference point. The basic idea here is that time dilatation is an experimental fact and, therefore, independent from the theory behind it, so it is independent from relativism. Time dilatation also can occur under absolute conditions. Up until now, it is not clear if the concept of relativism is correct or not. The existence of time dilatation cannot be proofs for relativism as time dilatation also can occur under absolute conditions. Here, it is established that the eastbound plane had a higher absolute velocity than its westbound counterpart, resulting in time dilation figures of 50 and 140 ns, respectively. [ABSTRACT FROM AUTHOR]

Nowadays, the BDS-3 satellites transmit new signals B1c and B2a that are compatible with GPS and Galileo, which is meaningful to fully take advantage of the BDS positioning capability. However, further research and analysis are needed to investigate the precise point positioning ambiguity resolution (PPP-AR) performance of the new BDS-3 signal combination. In this manuscript, the characteristics and quality of differential code bias (DCB), inter frequency clock bias (IFCB) and uncalibrated phase delay (UPD) of BDS-3 new signals are analyzed based on 30 days observation data from 70 multi GNSS experiment (MGEX) stations. The results show that the mean value of IFCB between B1I/B3I and B1C/B2a is 1.18 cm, which indicates that the IFCB can be ignored when performing the clock errors reference conversion of BDS-3 satellites. Besides, the DCB of the new BDS-3 signals varies within 0.2 ns over 30 days, and with a difference of 0.08 ns compared to the DCB product provided by chinese academy of science (CAS). The percentage of the estimated residuals less than 0.25 cycles for new signals WL UPD and less than 0.15 cycles for new signals NL UPD are 99.76% and 97.19%, respectively. The above results demonstrate the reliability of the DCB and UPD products, which can be used to estimate the carrier phase observable specific signal bias (OSB) product for the new signals. The average positioning errors of the BDS-3 new signals static PPP-AR in the N, E and U directions is 0.50 cm, 0.43 cm and 1.62 cm respectively, with an improvement of 18.3%, 28.3% and 11.5% compared to the ambiguity float static PPP. The average positioning errors of the kinematic PPP-AR are 2.09 cm, 2.67 cm and 4.79 cm in three directions, respectively, with an improvement of 17.1%, 23.9% and 15.7% compared to the ambiguity float PPP. The convergence time of the static and kinematic PPP-AR are 26.36 min and 29.12 min, respectively. [ABSTRACT FROM AUTHOR]