Clock Model Research Articles

Nondiagonal anisotropic quantum Hall states

We propose a family of Abelian quantum Hall states termed the non-diagonal states, which arise at filling factors $\nu=p/2q$ for bosonic systems and $\nu=p/(p+2q)$ for fermionic systems, with $p$ and $q$ being two coprime integers. Non-diagonal quantum Hall states are constructed in a coupled wire model, which shows an intimate relation to the non-diagonal conformal field theory and has a constrained pattern of motion for bulk quasiparticles, featuring a non-trivial interplay between charge symmetry and translation symmetry. The non-diagonal state is established as a distinctive symmetry-enriched topological order. Aside from the usual $U(1)$ charge sector, there is an additional symmetry-enriched neutral sector described by the quantum double model $\mathcal{D}(\mathbb{Z}_p)$, which relies on the presence of both the $U(1)$ charge symmetry and the $\mathbb{Z}$ translation symmetry of the wire model. Translation symmetry distinguishes non-diagonal states from Laughlin states, in a way similar to how it distinguishes weak topological insulators from trivial band insulators. Moreover, the translation symmetry in non-diagonal states can be associated to the $\mathbf{e}\leftrightarrow\mathbf{m}$ anyonic symmetry in $\mathcal{D}(\mathbb{Z}_p)$, implying the role of dislocations as two-fold twist-defects. The boundary theory of non-diagonal states is derived microscopically. For the edge perpendicular to the direction of wires, the effective Hamiltonian has two components: a chiral Luttinger liquid and a generalized $p$-state clock model. Importantly, translation symmetry in the bulk is realized as self-duality on the edge. The symmetric edge is thus either gapless or gapped with spontaneously broken symmetry. For $p=2,3$, the respective electron tunneling exponents are predicted for experimental probes.

Intrahost speciations and host switches played an important role in the evolution of herpesviruses.

In times when herpesvirus genomic data were scarce, the cospeciation between these viruses and their hosts was considered to be common knowledge. However, as more herpesviral sequences were made available, tree reconciliation analyses started to reveal topological incongruences between host and viral phylogenies, indicating that other cophylogenetic events, such as intrahost speciation and host switching, likely played important roles along more than 200 million years of evolutionary history of these viruses. Tree reconciliations performed with undated phylogenies can identify topological differences, but offer insufficient information to reveal temporal incongruences between the divergence timing of host and viral species. In this study, we performed cophylogenetic analyses using time-resolved trees of herpesviruses and their hosts, based on careful molecular clock modelling. This approach enabled us to infer cophylogenetic events over time and also integrate information on host biogeography to better understand host–virus evolutionary history. Given the increasing amount of sequence data now available, mismatches between host and viral phylogenies have become more evident, and to account for such phylogenetic differences, host switches, intrahost speciations and losses were frequently found in all tree reconciliations. For all subfamilies in Herpesviridae, under all scenarios we explored, intrahost speciation and host switching were more frequent than cospeciation, which was shown to be a rare event, restricted to contexts where topological and temporal patterns of viral and host evolution were in strict agreement.

Autonomous Ticking Clocks from Axiomatic Principles

There are many different types of time keeping devices. We use the phraseticking clockto describe those which – simply put – ``tick'' at approximately regular intervals. Various important results have been derived for ticking clocks, and more are in the pipeline. It is thus important to understand the underlying models on which these results are founded. The aim of this paper is to introduce a new ticking clock model from axiomatic principles that overcomes concerns in the community about the physicality of the assumptions made in previous models. The ticking clock model in \cite{woods2018quantum} achieves high accuracy, yet lacks the autonomy of the less accurate model in \cite{thermoClockErker}. Importantly, the model we introduce here achieves the best of both models: it retains the autonomy of \cite{thermoClockErker} while allowing for the high accuracies of \cite{woods2018quantum}. What is more, \cite{thermoClockErker} is revealed to be a special case of the new ticking clock model.

The Benefits of Receiver Clock Modelling in Satellite Timing

Satellite timing is an effective and convenient method that has been widely accepted in the time community. The key to satellite timing is obtaining a clean receiver clock offset. In this paper, instead of regarding the receiver clock offset as white noise, a two-state stochastic clock model involving three kinds of noise was conceived and used in PPP filter estimation. The influence of clock type and sampling time on satellite timing performance was first analysed. In addition, the kinematic scheme and static scheme were both investigated for meeting the demands of multi-occasional users. The values show that the model works well for both the kinematic scheme and static scheme; in contrast to that of the white noise model, the timing stability is enhanced at all the sampling times. For the six stations, especially when the averaging time is less than 1000 s, the average stability improvement values of the kinematic scheme are 75.53, 43.24, 75.00, 69.05, 40.57, and 25.45%, and the average improvement values of the static scheme are 65.49, 77.94, 56.71, 60.78, 64.41, and 39.41%. Furthermore, the enhancement magnitude is related to clock type. For a high-stability clock, the improvement of the kinematic scheme is greater than that of the static scheme, whereas for a low-stability clock, the improvement of the kinematic scheme is less than that of the static scheme.

Characteristics of Mandibular Canal Branches Related to Nociceptive Marker

It is difficult to correlate the direction of mandibular canal branches (MCBs) with altered sensation in dental treatments. In contrast, calcitonin gene–related peptide (CGRP) is related to vasodilation, bone formation, and the interaction with the peripheral nervous system. Therefore, we investigated the detailed morphological characteristics of MCBs using cone-beam computed tomography (CBCT) and observation of the CGRP distribution around the MCB. The MCB measurements were evaluated using principal component analysis (PCA) to identify morphological correlations. A total of 168 sides of mandibles from 84 cadavers were analyzed in this study. Most of the MCBs were primarily in the direction of the clock model from X to XI in sagittal sections and XII to I in coronal sections of the mandible. The structure of the MCB was divided into the fine canal branch (60.4%, 223/369), partial branch (24.4%, 90/369), and no canal branch (15.2%, 56/369). PCA indicated that the measurement element with the MCB and its structures were correlated in contrast to tooth factors. Positive CGRP reactions were clearly observed in the no-canal branch group compared to other groups. These data provide useful suggestions for MCB dynamics and information for clinical dental treatment.

Integrating oscillator-based circadian clocks with crop growth simulations

Abstract Circadian rhythms play critical roles in plant physiology, growth, development and survival, and their inclusion in crop growth models is essential for high-fidelity results, especially when considering climate change. Commonly used circadian clock models are often inflexible or result in complex outputs, limiting their use in general simulations. Here we present a new circadian clock model based on mathematical oscillators that easily adapts to different environmental conditions and produces intuitive outputs. We then demonstrate its utility as an input to Glycine max development models. This oscillator clock model has the power to simplify the inclusion of circadian cycles and photoperiodic effects in crop growth models and to unify experimental data from field and controlled environment observations.

Segmentation-clock synchronization in circular-lattice networks of embryonic presomitic-mesoderm cells

<abstract> Somitogenesis is the process by means of which a tissue known as presomitic mesoderm (PSM) is segmented in blocks of cells, called somites, along the anterior-posterior axis of the developing embryo in segmented animals. In vertebrates, somites give rise to axial skeleton, cartilage, tendons, skeletal muscle, and dermis. Somite formation occurs periodically, and this periodicity is driven by a genetic oscillator that operates within PSM cells and is known as the segmentation clock. The correct synchronization of the segmentation clock among PSM cells is essential for somitogenesis to develop normally. When synchronization is disrupted, somites form irregularly and, in consequence, the tissues that originate from them show clear malformations. In this work, based in a model for zebrafish segmentation clock, we investigate by means of a mathematical modeling approach, how PSM-cell synchronization is affected by factors like: the size of PSM-cell networks, the amount of cell-to-cell interactions per PSM cell, the strength of these interactions, and the inherent variability among PSM cells. Interestingly we found that very small PSM-cell networks are unable to synchronize. Moreover, the effect of decreasing the strength of interactions among PSM cells is corrected by increasing the network connectivity-level, and a moderated level of variability among cells can have a positive effect on synchronization, specially in large networks. </abstract>

Измерение времени с помощью благовоний в Восточной Азии

Spanning across thousands of years of aromatic culture development in the countries of East Asia, incense application has accumulated vast experience in various fields, including calendrical calculations and time measurement. Analysis of artifacts, objects of religious worship and everyday life indicates fragrant substances’ great versatility in terms of their use: in addition to sticks, spirals and cones, devices such as the Hundred Graduations Incense seals, alarm clocks, as well as clocks that measured night time, strictly dependent on the calendar season, were invented. Various types of aromatic clocks could be distinguished by their great functionality, finding application in many areas ‒ navigation, engineering, in court and religious ceremonies, scientists’ work, in monastic and private schools, tea houses, and were the subject of admiration for poets, artists and calligraphers. The study of the ways of using incense in East Asian countries (including for measuring time) is based on the analysis of a variety of sources ‒ written, artistic and ethnographic. Compared to the large number of Chinese and Japanese sources, the cultural heritage of the Korean Peninsula contains significant gaps, which significantly complicates the interpretation of the material. The use of incense burners, aromatic raw materials and various instruments for measuring time is a remarkable phenomenon in the fragrance culture of China, Korea and Japan, testifying to the high adaptability of symbols and images of traditional culture not only to everyday household needs, but also to various achievements of science and technology. This is confirmed at the present time, given the production of new models of aromatic clocks.

A mathematical model of the circadian clock and drug pharmacology to optimize irinotecan administration timing in colorectal cancer

Scheduling anticancer drug administration over 24 h may critically impact treatment success in a patient-specific manner. Here, we address personalization of treatment timing using a novel mathematical model of irinotecan cellular pharmacokinetics and –dynamics linked to a representation of the core clock and predict treatment toxicity in a colorectal cancer (CRC) cellular model. The mathematical model is fitted to three different scenarios: mouse liver, where the drug metabolism mainly occurs, and two human colorectal cancer cell lines representing an in vitro experimental system for human colorectal cancer progression. Our model successfully recapitulates quantitative circadian datasets of mRNA and protein expression together with timing-dependent irinotecan cytotoxicity data. The model also discriminates time-dependent toxicity between the different cells, suggesting that treatment can be optimized according to their cellular clock. Our results show that the time-dependent degradation of the protein mediating irinotecan activation, as well as an oscillation in the death rate may play an important role in the circadian variations of drug toxicity. In the future, this model can be used to support personalized treatment scheduling by predicting optimal drug timing based on the patient’s gene expression profile.

Clock Synchronization Algorithms Over PTP-Unaware Networks: Reproducible Comparison Using an FPGA Testbed

This work explores clock synchronization algorithms used to process timestamps from the IEEE 1588 precision time protocol (PTP). It focuses on the PTP-unaware network scenario, where the network nodes do not actively contribute to PTP’s operation. This scenario typically imposes a harsh environment for accurate clock distribution, primarily due to the packet delay variation experienced by PTP packets. In this context, it is essential to process the noisy PTP measurements using algorithms and strategies that consider the underlying clock and packet delay models. This work surveys some attractive algorithms and introduces an open-source analysis library that combines several of them for better performance. It also provides an unprecedented comparison of the algorithms based on datasets acquired from a sophisticated testbed composed of field-programmable gate arrays (FPGAs). The investigation provides insights regarding the synchronization performance under various scenarios of background traffic and oscillator stability.

The Metabolic Clock Model of B Cell Activation and Differentiation.

Recent advancements in the field of B cell immunometabolism have provided mechanistic insights to B cell activation and fate determination. Here, in this short article, I will explain the main principles of our novel metabolic clock model and how it may reshape our perspective on longstanding immunological questions related to pathologies arising from out of context B cell activation.

Two- and three-point functions at criticality: Monte Carlo simulations of the three-dimensional (q+1) -state clock model

We simulate the improved $(q+1)$-state clock model on the simple-cubic lattice at the critical point on lattices of a linear size up to $L=960$. We compute operator product expansion coefficients for the three-dimensional $XY$ universality class. These are compared with highly accurate estimates obtained by using the conformal bootstrap method. We find that the results are consistent.

Complete density calculations of q-state Potts and clock models: Reentrance of interface densities under symmetry breaking.

All local bond-state densities are calculated for q-state Potts and clock models in three spatial dimensions, d=3. The calculations are done by an exact renormalization group on a hierarchical lattice, including the density recursion relations, and simultaneously are the Migdal-Kadanoff approximation for the cubic lattice. Reentrant behavior is found in the interface densities under symmetry breaking, in the sense that upon lowering the temperature, the value of the density first increases and then decreases to its zero value at zero temperature. For this behavior, a physical mechanism is proposed. A contrast between the phase transition of the two models is found and explained by alignment and entropy, as the number of states q goes to infinity. For the clock models, the renormalization-group flows of up to 20 energies are used.

Monte Carlo study on domain wall dynamics of J1–J2 triangular spin system

Monte Carlo simulations are employed to study the model of a triangular Ising antiferromagnet with the next-nearest neighbor ferromagnetic interaction (TIAFF), which can be well mapped to a six-state clock model, and provide a new model to explore the excitation of a topological six-state domain vortex. The TIAFF model retains the symmetry of the lattice and provides more details of vortex excitations and micro dynamics. The crossover of the domain walls in three sub-lattices creates the topological six-state domain vortices. The attractive force between the vortex and the anti-vortex is proportional to the number of domain walls that connect them. The movement of the vortex in the lattice is along the domain walls to avoid creating new defects. Our simulation works reveal that vortices obeying Arrhenius law are difficult to excite at a low temperature. Therefore, the surviving vortices are generated through the Kibble–Zurek mechanism (KZM), which explains the formation of topological solitons in a nonequilibrium system. The existing vortices in the system go through a slow random walk and annihilate in the first-order kinetic process.

Sphenodontian phylogeny and the impact of model choice in Bayesian morphological clock estimates of divergence times and evolutionary rates

BackgroundThe vast majority of all life that ever existed on earth is now extinct and several aspects of their evolutionary history can only be assessed by using morphological data from the fossil record. Sphenodontian reptiles are a classic example, having an evolutionary history of at least 230 million years, but currently represented by a single living species (Sphenodon punctatus). Hence, it is imperative to improve the development and implementation of probabilistic models to estimate evolutionary trees from morphological data (e.g., morphological clocks), which has direct benefits to understanding relationships and evolutionary patterns for both fossil and living species. However, the impact of model choice on morphology-only datasets has been poorly explored.ResultsHere, we investigate the impact of a wide array of model choices on the inference of evolutionary trees and macroevolutionary parameters (divergence times and evolutionary rates) using a new data matrix on sphenodontian reptiles. Specifically, we tested different clock models, clock partitioning, taxon sampling strategies, sampling for ancestors, and variations on the fossilized birth-death (FBD) tree model parameters through time. We find a strong impact on divergence times and background evolutionary rates when applying widely utilized approaches, such as allowing for ancestors in the tree and the inappropriate assumption of diversification parameters being constant through time. We compare those results with previous studies on the impact of model choice to molecular data analysis and provide suggestions for improving the implementation of morphological clocks. Optimal model combinations find the radiation of most major lineages of sphenodontians to be in the Triassic and a gradual but continuous drop in morphological rates of evolution across distinct regions of the phenotype throughout the history of the group.ConclusionsWe provide a new hypothesis of sphenodontian classification, along with detailed macroevolutionary patterns in the evolutionary history of the group. Importantly, we provide suggestions to avoid overestimated divergence times and biased parameter estimates using morphological clocks. Partitioning relaxed clocks offers methodological limitations, but those can be at least partially circumvented to reveal a detailed assessment of rates of evolution across the phenotype and tests of evolutionary mosaicism.

Falling off a limit cycle using phase-agnostic stimuli: Definitions and conceptual framework.

Nearly a half-century of biomedical research has revealed methods and mechanisms by which an oscillator with bistable limit cycle kinetics can be stopped using critical stimuli applied at a specific phase. Is it possible to construct a stimulus that stops oscillation regardless of the phase at which the stimulus is applied? Using a radial isochron clock model, we demonstrate the existence of such stimulus waveforms, which can take on highly complex shapes but with a surprisingly simple mechanism of rhythm suppression. The perturbation, initiated at any phase of the limit cycle, first corrals the oscillator to a narrow range of new phases, then drives the oscillator to its phase singularity. We further constructed a library of waveforms having different durations, each achieving phase-agnostic suppression of rhythm but with varying rates of phase corralling prior to amplitude suppression. The optimal stimulus energy to achieve phase-agnostic suppression of rhythm is dependent on the rate of phase corralling and the configuration of the phaseless set. We speculate that these results are generic and suggest the existence of stimulus waveforms that can stop the rhythm of more complex oscillators irrespective of the applied phase.

A dual-feedback loop model of the mammalian circadian clock for multi-input control of circadian phase.

The molecular circadian clock is driven by interlocked transcriptional-translational feedback loops, producing oscillations in the expressions of genes and proteins to coordinate the timing of biological processes throughout the body. Modeling this system gives insight into the underlying processes driving oscillations in an activator-repressor architecture and allows us to make predictions about how to manipulate these oscillations. The knockdown or upregulation of different cellular components using small molecules can disrupt these rhythms, causing a phase shift, and we aim to determine the dosing of such molecules with a model-based control strategy. Mathematical models allow us to predict the phase response of the circadian clock to these interventions and time them appropriately but only if the model has enough physiological detail to describe these responses while maintaining enough simplicity for online optimization. We build a control-relevant, physiologically-based model of the two main feedback loops of the mammalian molecular clock, which provides sufficient detail to consider multi-input control. Our model captures experimentally observed peak to trough ratios, relative abundances, and phase differences in the model species, and we independently validate this model by showing that the in silico model reproduces much of the behavior that is observed in vitro under genetic knockout conditions. Because our model produces valid phase responses, it can be used in a model predictive control algorithm to determine inputs to shift phase. Our model allows us to consider multi-input control through small molecules that act on both feedback loops, and we find that changes to the parameters of the negative feedback loop are much stronger inputs for shifting phase. The strongest inputs predicted by this model provide targets for new experimental small molecules and suggest that the function of the positive feedback loop is to stabilize the oscillations while linking the circadian system to other clock-controlled processes.

Inclusion of GPS clock estimates for satellites Sentinel-3A/3B in DORIS geodetic solutions

A unique architecture of Sentinel-3A and Sentinel-3B satellites includes the shared ultra-stable oscillator (USO) by the DORIS and GPS receivers. This concept enables to apply onboard GPS clock estimates in the DORIS processing substituting the DORIS polynomial clock model by the GPS epoch-wise model, together with a DORIS-specific clock offset. Such an approach is particularly profitable for the mitigation of the South Atlantic Anomaly (SAA) effect affecting the short-term frequency stability of the USO oscillator in the South America and South Atlantic region. The GPS clock behavior precisely maps the SAA effect and enables us to demonstrate a difference of the USO sensitivity to the SAA for Sentinel-3A and Sentinel-3B. We present world grid maps of clock time derivatives for both Sentinels, displaying a different sign of the direct effect and other differences in the USO memory/recovery effect. Moreover, we present the impact of SAA on 3D positioning where the largest SAA-related bias reaches several centimeters. We also determine an effect of the precise clock modeling on the Earth rotation parameter estimates. In addition to these improvements, the elimination of the SAA effect gives us an opportunity to get an almost SAA-free DORIS solution from Sentinel-3A and Sentinel-3B satellites. Using the combined solution of both Sentinels as a reference, we estimate the SAA effect on the DORIS beacon positions also for satellites Jason-2, Jason-3, Saral, Cryosat-2 and Hy-2A and find significant positioning biases for all the recent satellites except Saral.

Seasonality and light phase-resetting in the mammalian circadian rhythm

We study the impact of light on the mammalian circadian system using the theory of phase response curves. Using a recently developed ansatz we derive a low-dimensional macroscopic model for the core circadian clock in mammals. Significantly, the variables and parameters in our model have physiological interpretations and may be compared with experimental results. We focus on the effect of four key factors which help shape the mammalian phase response to light: heterogeneity in the population of oscillators, the structure of the typical light phase response curve, the fraction of oscillators which receive direct light input and changes in the coupling strengths associated with seasonal day-lengths. We find these factors can explain several experimental results and provide insight into the processing of light information in the mammalian circadian system. In particular, we find that the sensitivity of the circadian system to light may be modulated by changes in the relative coupling forces between the light sensing and non-sensing populations. Finally, we show how seasonal day-length, after-effects to light entrainment and seasonal variations in light sensitivity in the mammalian circadian clock are interrelated.

Strong Zero Modes from Geometric Chirality in Quasi-One-Dimensional Mott Insulators.

Strong zero modes provide a paradigm for quantum many-body systems to encode local degrees of freedom that remain coherent far from the ground state. Example systems include Z_{n} chiral quantum clock models with strong zero modes related to Z_{n} parafermions. Here, we show how these models and their zero modes arise from geometric chirality in fermionic Mott insulators, focusing on n=3 where the Mott insulators are three-leg ladders. We link such ladders to Z_{3} chiral clock models by combining bosonization with general symmetry considerations. We also introduce a concrete lattice model which we show to map to the Z_{3} chiral clock model, perturbed by the Uimin-Lai-Sutherland Hamiltonian arising via superexchange. We demonstrate the presence of strong zero modes in this perturbed model by showing that correlators of clock operators at the edge remain close to their initial value for times exponentially long in the system size, even at infinite temperature.