Fixed Cycle Length Research Articles

Forecasting of Menstruation using a Calendar-based Method based on a Web Application

Accurately predicting menstrual dates is valuable for women, yet it poses a significant challenge, particularly for those with irregular cycles. This study introduces a web application that utilises a calendar-based method to predict upcoming menstrual dates while offering additional features such as tracking past periods, logging symptoms, and providing personalised health advice. Using the software development life cycle approach, the critical contribution of this work is the development of a user-friendly tool that not only aids in menstrual tracking but also highlights the limitations of calendar-based predictions, especially for women with irregular cycles. Our findings suggest that while the method provides accurate predictions for women with regular cycles, it is less reliable for those with irregular cycles due to its dependence on a fixed cycle length range. This study underscores the need for more adaptive models to improve prediction accuracy for a broader population.

Full dynamic control of dairy wastewater treatment by aerobic granular sludge using electric conductivity and oxygen uptake rate

Abstract The objective of the current study was to determine the applicability of a sensor-based dynamic control strategy for the treatment of real variable dairy wastewater by aerobic granular sludge (AGS) performing enhanced biological phosphorus removal (EBPR). Two parallel sequencing batch reactors (SBRs) were set up that used only an anaerobic feast/aerobic famine microbial selection strategy to successfully obtain sludge granulation. SBR-STA used a fixed cycle length, while the duration of the reaction steps in SBR-DYN was variable. The control strategy was based solely on (derived) signals from low-cost and common sensors. The profile of the electric conductivity during the anaerobic reaction step was related to the microbial release of phosphate (PO4-P) and the associated uptake of dissolved organic carbon (DOC) by polyphosphate-accumulating organisms (PAOs). Control of the aerobic reaction step was based on the oxygen uptake rate (OUR). This resulted in a dynamic reactor operation with significant efficiency gains, such as 32% shorter cycle times and 42% higher sludge loading rates without impairing the effluent quality. These results extend the existing potential of indirect control strategies to full biological nutrient removal processes, which may be of great assistance to the operators and designers of industrial installations.

Optimal Base-Stock Inventory-Management Policies of Cement Retailers under Supply-Side Disruptions

The current study aims to identify some optimal base-stock inventory-management policies that maximize the expected long-run profitability of cement retailers under potential supply-side disruptions. Unlike existing articles, the proposed economic order-quantity model considers periodically varying random demand rates of deteriorating items together with partially back-ordered shortages in the face of those random disruptions. This study computes the global concavity to execute the exemplary aspect for the optimal base-stock level under a slew of cost components and a fixed cycle length. Regarding the optimal pricing-related policies, this study proposes that cement retailers should stock from nearby supplier points. Unlike existing articles, we find that changes to either the unit-holding cost or the unit-lost sales cost have hardly any determining effect on the long-run profitability of retailers. When supply-side disruptions are more likely to occur during peak seasons, this study advocates for a planned capacity addition and higher base-stock levels of cement bags.

Atrial stimulation protocols to test inducibility of atrial fibrillation

Abstract Funding Acknowledgements Type of funding sources: None. Background The electrophysiological inducibility of atrial fibrillation (AF) after pulmonary vein isolation (PVI) has been identified as a predictor of future AF recurrence. Stimulation protocols have not been sufficiently studied prospectively with respect to their reliability for inducing AF. Methods and results We conducted a prospective monocentric randomized clinical trial to evaluate different standardized electrical stimulation protocols on their potential to induce AF. Patients with symptomatic AF presenting in sinus rhythm scheduled for PVI were enrolled. The primary outcome was induction of AF. A total of 30 patients (age=62±2 years, 17% female, 13% persistent AF, left atrial systolic volume (LASV) 93±5 ml) were enrolled and randomized. To one of three different stimulation protocols performed at the beginning of PVI. Atrial fibrillation was induced in 4 out of 10 patients (40%) with fixed cycle length stimulation followed by up to 3 extrastimuli (protocol A), 6 out of 10 patients (60%) with burst stimulation (protocol B) and 9 out of 10 patients (90%) with fixed stimulation using the shortest cycle length with 1:1 atrial capture (protocol C), respectively. Time from start of stimulation to inducibility of AF was significantly lower in protocol C vs. protocol B and A (29±10 sec vs 40±14 sec vs 366±71 sec; p<0.0001). Isoprenaline was used in 10% in protocol A, 40% in protocol B and 80% protocol C. Overall, there were no significant differences concerning age (61±3 vs. 63±4 years; p=0.74), LASV (93±6 vs. 94±8 ml; p=0.98) or other parameters between patients with inducible and non-inducible AF. Conclusion With systematic stimulation protocols AF can be induced in up to 90%. Further studies are warranted to assess the specifity of these stimulations.

The effect of basic cycle length stimuli on effective refractory period measurement

Background: Refractory periods are measured by the extrastimulus technique, whereby a single extrastimulus is introduced at progressively shorter coupling intervals until a response is no longer elicited. Purpose: As refractoriness of cardiac tissues depends on prior cycle length, refractory periods should be determined at a fixed cycle length within the physiologic range. The extrastimulus is delivered after a train of 8 to 10 paced complexes to allow time for reasonable stabilization of refractoriness, which is usually accomplished after the first 3 or 4 paced beats. Objectives: We conducted this study to compare the effect of 6 vs 8 stimuli in basic cycle length (BCL) in measurement of effective refractory period (ERP). Materials and Methods: During electrophysiologic study (EPS) of 100 consecutive patients, anterograde and retrograde ERP of atrioventricular node (AVN) were measured by introduction of 6 vs 8 stimuli in BCL and premature beat, then the results were compared. Results: Recorded anterograde and retrograde ERP of AVN applying 6 vs 8 stimuli in BCL were compared and no difference was detected. Conclusion: We concluded that for ERP measurement of AVN, 6 stimuli in BCL is comparable to 8 stimuli in reaching the steady state.

Reduction of mapping time in pulmonary vein isolation using atrial pacing during left atrial voltage map acquisition

Introduction3D mapping systems are used during radiofrequency (RF) pulmonary vein isolation (PVI) to facilitate catheter navigation and to provide additional electroanatomical information as a surrogate marker for the presence and location of fibrotic atrial myocardium.Electric voltage information can only be measured when the myocardium is depolarized. Low heart rates or frequent premature atrial beats can significantly prolong creation of detailed left atrial voltage maps. This study was designed to evaluate the potential advantage of voltage information collection during atrial pacing instead of acquisition during sinus rhythm. Methods and resultsA total of 40 patients were included in the study, in 20 consecutive patients voltage mapping was performed during sinus rhythm, and in the following 20 patients during atrial pacing. The average age of the included patients was 69.5 ± 9.4, 17 of 40 patients (43%) were male.All procedures were performed using the Carto 3D Mapping system. For LA voltage mapping, a multipolar circular mapping catheter was used. The atrium was paced via the proximal coronary sinus catheter electrodes with a fixed cycle length of 600 ms.By mapping during atrial pacing mapping time was reduced by 35% (441 s. (±141) vs.683 s. (±203) p = 0.029) while a higher number of total mapping points were acquired (908 ± 560 vs. 581 ± 150, p = 0.008). ConclusionAcquiring left atrial low voltage maps during atrial pacing significantly reduces mapping time. As pacing also improves comparability of left atrial electroanatomical maps we suggest that this approach may be considered as a standard during these procedures.

A Platoon-Based Adaptive Signal Control Method with Connected Vehicle Technology.

One important objective of urban traffic signal control is to reduce individual delay and improve safety for travelers in both private car and public bus transit. To achieve signal control optimization from the perspective of all users, this paper proposes a platoon-based adaptive signal control (PASC) strategy to provide multimodal signal control based on the online connected vehicle (CV) information. By introducing unified phase precedence constraints, PASC strategy is not restricted by fixed cycle length and offsets. A mixed-integer linear programming (MILP) model is proposed to optimize signal timings in a real-time manner, with platoon arrival and discharge dynamics at stop line modeled as constraints. Based on the individual passenger occupancy, the objective function aims at minimizing total personal delay for both buses and automobiles. With the communication between signals, PASC achieves to provide implicit coordination for the signalized arterials. Simulation results by VISSIM microsimulation indicate that PASC model successfully reduces around 40% bus passenger delay and 10% automobile delay, respectively, compared with signal timings optimized by SYNCHRO. Results from sensitivity analysis demonstrate that the model performance is not sensitive to the number fluctuation of bus passengers, and the requested CV penetration rate range is around 20% for the implementation.

Connected Vehicles Based Traffic Signal Timing Optimization

We study the traffic signal control problem with connected vehicles by assuming a fixed cycle length so that the proposed model can be extended readily for the coordination of multiple signals. The problem can be first formulated as a mixed-integer nonlinear program, by considering the information of individual vehicle’s trajectories (i.e., second-by-second vehicle locations and speeds) and their realistic driving/car-following behaviors. The objective function is to minimize the weighted sum of total fuel consumption and travel time. Due to the large dimension of the problem and the complexity of the nonlinear car-following model, solving the nonlinear program directly is challenging. We then reformulate the problem as a dynamic programming model by dividing the timing decisions into stages (one stage for a signal phase) and approximating the fuel consumption and travel time of a stage as functions of the state and decision variables of the stage. We also propose a two-step method to make sure that the obtained optimal solution can lead to the fixed cycle length. Numerical experiments are provided to test the performance of the proposed model using data generated by traffic simulation.

Multi-Agent Based Traffic Signal Optimization under Fully Actuated Control

This paper presents a multi-agent based distributed traffic control model to optimize the traffic signal for multiple intersections. Previous works in the area of traffic signal control suffer from a number of inadequacies, including the use of fixed cycle length, centralized mode of operations and dependency on historical data. Considering these, the aim of this work is to control the traffic signal timings by adjusting the phase sequence in order to minimize the delay in traffic at the intersections. To model the traffic network, a three-tier multi-agent system has been adopted in distributed mode. In addition, a fully actuated signal control algorithm is designed and it utilizes state-space equations to formulate the queue length at the green light phase and red light phase. The proposed model is simulated with SUMO simulator and a comparative analysis has been made between adaptive control method, multi-agent method based on collective learning and multi-agent based fully actuated control method on a similar platform. The results spectacle the proposed traffic control model outperforms that of other existing control methods in all condition; hence it can be deployed to control the tremendous traffic on the road network and to optimize the traffic signal in more effective manner.

Fuzzy Vehicle Control System for Single Intersection

Traffic light at the intersection is an important part of the daily life of the urban cities. Traffic light needs to be managed properly so that a large number of vehicles able to cross the intersection. Current traffic light system is not able to allot efficient traffic light cycle length to vehicles. It is because of the traffic system is based on the fixed cycle length. Today traffic is highly fluctuating. Number of vehicles in the traffic varies with respect to time and day. To handle this situation, the paper proposes a vehicle control system using fuzzy logic: Fuzzy Vehicle Control System (FVCS). FVCS allots dynamic cycle length signal duration to vehicles based on the present traffic available at the intersection. Experiments have been performed on the proposed FVCS architecture using MATLAB. Experiments show that a reduction of 28.92% can be achieved in the number of vehicles that are waiting at the intersection to cross it

Research of Intersection Traffic Signal Control and Simulation Based on Fuzzy Logic

In order to improve the traffic signal control for urban road intersection and reduce vehicle delay, the paper took the typical urban crossing signal control system as the research object and proposed a control algorithm based on fuzzy logic. Considering the traffic flow information as well as the length of vehicles on different approaches, the average delay hours had been selected out as the performance index. By using the control algorithm to improve the traditional fixed cycle length time distribution method of the intersection, the paper successfully designed a signal control system to adapt to various traffic conditions. By using Matlab software to analyze the data and simulate the effect, the results showed that this algorithm significantly reduced the traffic delay, achieved good control effect, and enhanced the capacity of the intersection. It has proved that the utilization of the control algorithm is a practical and effective method for the intelligent urban traffic control.

Beat-to-Beat Variability of Ventricular Action Potential Duration Oscillates at Low Frequency During Sympathetic Provocation in Humans.

Background: The temporal pattern of ventricular repolarization is of critical importance in arrhythmogenesis. Enhanced beat-to-beat variability (BBV) of ventricular action potential duration (APD) is pro-arrhythmic and is increased during sympathetic provocation. Since sympathetic nerve activity characteristically exhibits burst patterning in the low frequency range, we hypothesized that physiologically enhanced sympathetic activity may not only increase BBV of left ventricular APD but also impose a low frequency oscillation which further increases repolarization instability in humans.Methods and Results: Heart failure patients with cardiac resynchronization therapy defibrillator devices (n = 11) had activation recovery intervals (ARI, surrogate for APD) recorded from left ventricular epicardial electrodes alongside simultaneous non-invasive blood pressure and respiratory recordings. Fixed cycle length was achieved by right ventricular pacing. Recordings took place during resting conditions and following an autonomic stimulus (Valsalva). The variability of ARI and the normalized variability of ARI showed significant increases post Valsalva when compared to control (p = 0.019 and p = 0.032, respectively). The oscillatory behavior was quantified by spectral analysis. Significant increases in low frequency (LF) power (p = 0.002) and normalized LF power (p = 0.019) of ARI were seen following Valsalva. The Valsalva did not induce changes in conduction variability nor the LF oscillatory behavior of conduction. However, increases in the LF power of ARI were accompanied by increases in the LF power of systolic blood pressure (SBP) and the rate of systolic pressure increase (dP/dtmax). Positive correlations were found between LF-SBP and LF-dP/dtmax (rs = 0.933, p < 0.001), LF-ARI and LF-SBP (rs = 0.681, p = 0.001) and between LF-ARI and LF-dP/dtmax (rs = 0.623, p = 0.004). There was a strong positive correlation between the variability of ARI and LF power of ARI (rs = 0.679, p < 0.001).Conclusions: In heart failure patients, physiological sympathetic provocation induced low frequency oscillation (~0.1 Hz) of left ventricular APD with a strong positive correlation between the LF power of APD and the BBV of APD. These findings may be of importance in mechanisms underlying stability/instability of repolarization and arrhythmogenesis in humans.

Evaluation of Decentralized Feedback Traffic Light Control with Dynamic Cycle Length

An established rule of thumb in the field of traffic light control prescribes that, during periods of higher demand, it is convenient to have longer cycles. This is in order to reduce the fraction of the cycle length when no incoming lanes receive green light. In this paper, we simulate a novel, provably stable, decentralized feedback traffic light control policy with variable cycle length. The proposed control strategy is fully decentralized and does not require any information about the network structure or the turning rates. Through simulations on a micro simulator, we compare the performance of our variable cycle length policy to a similar feedback policy with fixed cycle length and with a fixed-time control policy. The simulations show that having dynamic cycle lengths allows one to significantly reduce the overall queue lengths in the network, in both medium and low demands.

Distance colouring without one cycle length

We consider distance colourings in graphs of maximum degree at most d and how excluding one fixed cycle length ℓ affects the number of colours required as d→∞. For vertex-colouring and t≥1, if any two distinct vertices connected by a path of at most t edges are required to be coloured differently, then a reduction by a logarithmic (in d) factor against the trivial bound O(dt) can be obtained by excluding an odd cycle length ℓ≥3t if t is odd or by excluding an even cycle length ℓ≥2t+2. For edge-colouring and t≥2, if any two distinct edges connected by a path of fewer than t edges are required to be coloured differently, then excluding an even cycle length ℓ≥2t is sufficient for a logarithmic factor reduction. For t≥2, neither of the above statements are possible for other parity combinations of ℓ and t. These results can be considered extensions of results due to Johansson (1996) and Mahdian (2000), and are related to open problems of Alon and Mohar (2002) and Kaiser and Kang (2014).

Person-Based Optimization of Signal Timing

Recent studies have proposed the use of person-based frameworks for the optimization of traffic signal timing to minimize the total passenger delay experienced by passenger cars and buses at signalized intersections. The efficiency and applicability of existing efforts, however, have been limited by an assumption of fixed cycle lengths and deterministic bus arrival times. An existing algorithm for person-based optimization of signal timing for isolated intersections was extended to accommodate flexible cycle lengths and uncertain bus arrival times. To accommodate flexible cycle lengths, the mathematical program was redefined to minimize total passenger delay within a fixed planning horizon that allowed cycle lengths to vary within a feasible range. Two strategies were proposed to accommodate uncertain bus arrival times: ( a) a robust optimization approach that conservatively minimized delays experienced in a worst-case scenario and ( b) a blended strategy that combined deterministic optimization and rule-based green extensions. The proposed strategies were tested with numerical simulations of an intersection in State College, Pennsylvania. Results revealed that the flexible cycle length algorithm could significantly reduce bus passenger delay and total passenger delay, with negligible increases in car passenger delay. These results were robust to changes in both bus and car flows. For bus arrival times, the robust optimization strategy seemed to be more effective at low levels of uncertainty and the blended strategy at higher levels of uncertainty. The anticipated benefits decreased with increases in the intersection flow ratio because of the lower flexibility of signal timing at the intersection.

Abstract 275: A Prediction Model for Acute Heart Failure Outcomes

Objectives: The Cox proportional hazard (PH) model is commonly used to evaluate the relative impact of risk factors on the baseline hazard of events in reference population. However Cox PH is limited in its ability to incorporate time dependent variables. While building models with fixed cycle lengths, where variable like medical history changes due to treatment intervention, a risk equation could help us better. Parameter risk equations, like Framingham Heart Study equations, can account for the shape of the baseline event rate which enables the estimation of future risk. The purpose of this study is to develop a set of risk equations that account for clinical evidence and biomarkers for acute heart failure (HF) patients to estimate time to discharge, time to in-hospital mortality, time to readmission and time to post-discharge mortality following an HF hospitalization Methods: We utilized data from the placebo arm population from Pro-B Type natriuretic peptide Outpatient Tailored Chronic heart failure Therapy (PROTECT) study to develop the risk equations. For each outcome, determining the best risk equation involved two steps, (a) selecting the appropriate underlying distribution, and (b) choosing the right set of risk-factors. Various distributions considered including Weibull, exponential, piecewise exponential, logistic, log normal and gamma distribution. The final distribution was chosen based on model fit and its AIC score. A variety of risk factors were considered including patient characteristics, relevant biomarkers and medical history. The best risk factors were chosen based on clinical relevance, systematic literature review, and how they performed on a maximum likelihood ratio test for the chosen distribution. The predicted value for each outcome was compared to observed values from PROTECT for internal validity and Efficacy and Safety of Relaxin for the Treatment of Acute Heart Failure (RELAX-AHF) study for external validity. Results: The gamma, Weibull, piecewise exponential and exponential distributions were selected for the time to discharge, in-hospital mortality, hospital readmission and post-discharge mortality, respectively. The key risk factors included gender, age, SBP, heart rate, ProBNP, GFR, NYHA class, in-hospital diuretic dosage, medication usage and cardiovascular comorbidities. The internal and external validity are confirmed by comparing predicted and observed values from PROTECT and RELAX-AHF study respectively. The predicted and observed LOS is 12.6 and 10.5 days. Although the predicted and observed 30 day post-discharge mortality are 1.20% and 3.30%, the difference between predicted and observed all-cause mortality is 0.1 (11.40% vs 11.3%). Conclusions: Since risk factors (i.e SBP and BNP) that change over time were identified as important risk-factors, parametric risk equations were superior to cox PH model.

Ivabradine and AV conduction

Ivabradine is a heart rate reducing agent that selectively inhibits the If current in the sinus node, without affecting heart contractility, relaxation and peripheral vascular resistance [1]. The clinical efficacy and safety of ivabradine have been confirmed in majormorbidity andmortality studies in patients with heart failure and coronary artery disease. Because the If current is mainly present in the sinus node, the effects of ivabradine can be observed during sinus rhythm. However, recent experimental [2] and clinical observations suggest that ivabradine significantly reduces the ventricular rate during atrial fibrillation [3,4]. In the context of this new and very important data we wish to submit our observation regarding the effects of ivabradine on the AV-node during fixed atrial pacing. A 60-year-old patient with a mechanical mitral valve was admitted with new-onset typical atrial flutter. The patient's only medication was an oral anticoagulant. The following day bidirectional block was created across the right atrial isthmus using radiofrequency ablation. After the termination of flutter, pacing was performed from a lateral tricuspid annulus site and from a coronary sinus ostium site to demonstrate permanent bidirectional block. The patient was given 5 mg oral ivabradine (“off-label”) after the ablation. Ivabradine caused a significant AH time prolongation during fixed cycle length stimulation after 30 min (Fig. 1), whereas the HV time remained unchanged. After the procedure, Holter monitoring showed no bradycardia episodes.

2 * Beta-blockers do not prevent the pro-arrhythmic action of high-level sympathetic stimulation: a role for neuropeptide Y?

Introduction: Beta-blockers (BB) are the only anti-arrhythmic drugs that improve mortality in patients with ischaemic heart disease, but a significant risk of arrhythmia remains. During high-level sympathetic drive, such as during myocardial infarction, co-transmitters including neuropeptide Y (NPY) can be released with norepinephrine. NPY is a potent vasoconstrictor that can also alter cardiac electrophysiology. We hypothesised that ventricular fibrillation threshold (VFT) would still be reduced following high-level sympathetic stimulation even in the presence of a BB. We also investigated whether NPY is independently pro-arrhythmic and decreases VFT, and if this mechanism is mediated by the Y1 receptor. Methods: Hearts with intact stellate ganglia (SG) and sympathetic innervation were isolated from male Sprague Dawley rats (250-300g) and Langendorff perfused in constant flow mode. VFT was determined by pacing at a fixed cycle length (150ms x 20 beats) followed by a 5sec 50Hz burst at increasing current amplitude (mA) until sustained VF was induced. VF was cardioverted with 1ml of potassium chloride solution (50mmol/L). A control experiment demonstrated that VFT remained constant over 3 successive inductions (n=6). SG were stimulated at 10Hz, 1msec pulse width (above capture voltage). Drugs were perfused for 15 minutes before stimulation. Electrical restitution (RT) was derived from optically mapped action potentials (RH237, 15 µL of 5mg/mL) in the presence of blebbistatin (10 µmol/L). All data are presented as mean±standard error. Results: Direct SG stimulation significantly (p<0.05) increased heart rate and left ventricular developed pressure (LVDP) and these changes were completely blocked by metoprolol (10 µmol/L). However, 2 mins of right SG stimulation in the presence of metoprolol still significantly reduced VFT (2.2±0.0.49 vs. 1.2±.0.26mA, n=6). VFT was also decreased by norepinephrine (1 µmol/L), however this effect was abolished by metoprolol (n=4). NPY (250nmol/L, n=6) mimicked the effect of SG stimulation and significantly reduced VFT by 50% (2.4±0.15 vs 1.2±0.12mA) and increased coronary vascular resistance and LVDP. The action of NPY on VFT, CVR and LVDP were abolished by the Y1 receptor antagonist BIBO3304 (1 µM, n=6). Preliminary analysis of RT by optical mapping is suggestive of a steepening of the curve with NPY 250nM (0.27±0.04 vs NPY 0.42±0.12). The Y1 receptor antagonist BIBO3304 (1 µM, n=6) also prevented the reduction in VFT in response to SG stimulation in the presence of metoprolol. Conclusion: Prolonged sympathetic stimulation remains pro-arrhythmic in the presence of BB, implicating sympathetic co-transmitters as a novel arrhythmic trigger. NPY can directly decrease VFT via a Y1 receptor mediated mechanism that steepens the RT curve. A combination of BB and Y1 receptor blockade is able to fully prevent the pro-arrhythmic action of prolonged sympathetic stimulation.

Self-organizing traffic signals using secondary extension and dynamic coordination

Actuated traffic signal control logic has many advantages because of its responsiveness to traffic demands, short cycles, effective use of capacity leading to and recovering from oversaturation, and amenability to aggressive transit priority. Its main drawback has been its inability to provide good progression along arterials. However, the traditional way of providing progression along arterials, coordinated–actuated control with a common, fixed cycle length, has many drawbacks stemming from its long cycle lengths, inflexibility in recovering from priority interruptions, and ineffective use of capacity during periods of oversaturation. This research explores a new paradigm for traffic signal control, “self-organizing signals,” based on local actuated control but with some additional rules that create coordination mechanisms. The primary new rules proposed are for secondary extensions, in which the green may be held to serve an imminently arriving platoon, and dynamic coordination, in which small groups of closely spaced signals communicate with one another to cycle synchronously with the group’s critical intersection. Simulation tests in VISSIM performed on arterial corridors in Massachusetts and Arizona show overall delay reductions of up to 14% compared to an optimized coordinated–actuated scheme where there is no transit priority, and more than 30% in scenarios with temporary oversaturation. Tests also show that with self-organizing control, transit signal priority can be more effective than with coordinated–actuated control, reducing transit delay by about 60%, or 12 to 14s per intersection with little impact on traffic delay.

Analysis of juggling data: Landmark and continuous registration of juggling trajectories

This paper focuses on the two one-dimensional summaries of the three-dimensional juggling data: tangential velocity and tangential acceleration. These are used jointly to define the beginnings and endings of the 123 cycles in the data divided unevenly over ten trials. Two levels of registration were used. The first was a landmark registration of each trial to a periodic image of itself with the period fixed at 712 milliseconds. The 123 tangential velocity cycles were then subjected to a continuous registration over this fixed cycle length. The amounts of across-trial and within-cycle phase variation, respectively, were surprisingly small, indicating tight neural control over the behavior. Within-cycle phase variation was primarily due to variation in the trajectories of the ball between throw and catch.