scholarly journals Non-repeated cycle lengths and Sidon sequences

Author(s):  
Jie Ma ◽  
Tianchi Yang
Keyword(s):  
1998 ◽  
Vol 29 (1) ◽  
pp. 11-15 ◽  
Author(s):  
Guantao Chen ◽  
Jen� Lehel ◽  
Michael S. Jacobson ◽  
Warren E. Shreve
Keyword(s):  

2021 ◽  
Vol 31 (1) ◽  
pp. 51-60
Author(s):  
Arsen L. Yakymiv

Abstract Dedicated to the memory of Alexander Ivanovich Pavlov. We consider the set of n-permutations with cycle lengths belonging to some fixed set A of natural numbers (so-called A-permutations). Let random permutation τ n be uniformly distributed on this set. For some class of sets A we find the asymptotics with remainder term for moments of total cycle number of τ n .


2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Sameera Senanayake ◽  
Nicholas Graves ◽  
Helen Healy ◽  
Keshwar Baboolal ◽  
Adrian Barnett ◽  
...  

Abstract Background Economic-evaluations using decision analytic models such as Markov-models (MM), and discrete-event-simulations (DES) are high value adds in allocating resources. The choice of modelling method is critical because an inappropriate model yields results that could lead to flawed decision making. The aim of this study was to compare cost-effectiveness when MM and DES were used to model results of transplanting a lower-quality kidney versus remaining waitlisted for a kidney. Methods Cost-effectiveness was assessed using MM and DES. We used parametric survival models to estimate the time-dependent transition probabilities of MM and distribution of time-to-event in DES. MMs were simulated in 12 and 6 monthly cycles, out to five and 20-year time horizon. Results DES model output had a close fit to the actual data. Irrespective of the modelling method, the cycle length of MM or the time horizon, transplanting a low-quality kidney as compared to remaining waitlisted was the dominant strategy. However, there were discrepancies in costs, effectiveness and net monetary benefit (NMB) among different modelling methods. The incremental NMB of the MM in the 6-months cycle lengths was a closer fit to the incremental NMB of the DES. The gap in the fit of the two cycle lengths to DES output reduced as the time horizon increased. Conclusion Different modelling methods were unlikely to influence the decision to accept a lower quality kidney transplant or remain waitlisted on dialysis. Both models produced similar results when time-dependant transition probabilities are used, most notable with shorter cycle lengths and longer time-horizons.


Author(s):  
A. M. Tahsin Emtenan ◽  
Christopher M. Day

During oversaturated conditions, common objectives of signal timing are to maximize vehicle throughput and manage queues. A common response to increases in vehicle volumes is to increase the cycle length. Because the clearance intervals are displayed less frequently with longer cycle lengths and fewer cycles, more of the total time is used for green indications, which implies that the signal timing is more efficient. However, previous studies have shown that throughput reaches a peak at a moderate cycle length and extending the cycle length beyond this actually decreases the total throughput. Part of the reason for this is that spillback caused by the turning traffic may cause starvation of the through lanes resulting in a reduction of the saturation flow rate within each lane. Gaps created by the turning traffic after a lane change may also reduce the saturation flow rate. There is a relationship between the proportions of turning traffic, the storage length of turning lanes, and the total throughput that can be achieved on an approach for a given cycle length and green time. This study seeks to explore this relationship to yield better signal timing strategies for oversaturated operations. A microsimulation model of an oversaturated left-turn movement with varying storage lengths and turning proportions is used to determine these relationships and establish a mathematical model of throughput as a function of the duration of green, storage length, and turning proportion. The model outcomes are compared against real-world data.


EP Europace ◽  
2021 ◽  
Author(s):  
Julius Obergassel ◽  
Molly O’Reilly ◽  
Laura C Sommerfeld ◽  
S Nashitha Kabir ◽  
Christopher O’Shea ◽  
...  

Abstract Aims Genetically altered mice are powerful models to investigate mechanisms of atrial arrhythmias, but normal ranges for murine atrial electrophysiology have not been robustly characterized. Methods and results We analyzed results from 221 electrophysiological (EP) studies in isolated, Langendorff-perfused hearts of wildtype mice (114 female, 107 male) from 2.5 to 17.7 months (mean 7 months) with different genetic backgrounds (C57BL/6, FVB/N, MF1, 129/Sv, Swiss agouti). Left atrial monophasic action potential duration (LA-APD), interatrial activation time (IA-AT), and atrial effective refractory period (ERP) were summarized at different pacing cycle lengths (PCLs). Factors influencing atrial electrophysiology including genetic background, sex, and age were determined. LA-APD70 was 18 ± 0.5 ms, atrial ERP was 27 ± 0.8 ms, and IA-AT was 17 ± 0.5 ms at 100 ms PCL. LA-APD was longer with longer PCL (+17% from 80 to 120 ms PCL for APD70), while IA-AT decreased (−7% from 80 to 120 ms PCL). Female sex was associated with longer ERP (+14% vs. males). Genetic background influenced atrial electrophysiology: LA-APD70 (−20% vs. average) and atrial ERP (−25% vs. average) were shorter in Swiss agouti background compared to others. LA-APD70 (+25% vs. average) and IA-AT (+44% vs. average) were longer in 129/Sv mice. Atrial ERP was longer in FVB/N (+34% vs. average) and in younger experimental groups below 6 months of age. Conclusion This work defines normal ranges for murine atrial EP parameters. Genetic background has a profound effect on these parameters, at least of the magnitude as those of sex and age. These results can inform the experimental design and interpretation of murine atrial electrophysiology.


Author(s):  
Daniel J. Cook

Along urban and suburban arterials, closely-spaced signalized intersections are commonly used to provide access to adjacent commercial developments. Often, these signalized intersections are designed to provide full access to developments on both sides of the arterial and permit through, left-turn, and right-turn movements from every intersection approach. Traffic signal timing is optimized to reduce vehicle delay or provide progression to vehicles on the arterial, or both. However, meeting both of these criteria can be cumbersome, if not impossible, under high-demand situations. This research proposes a new design that consolidates common movements at three consecutive signalized intersections into strategic fixed locations along the arterial. The consolidation of common movements allows the intersections to cycle between only two critical phases, which, in turn, promotes shorter cycle lengths, lower delay, and better progression. This research tested the consolidated intersection concept by modeling a real-world site in microsimulation software and obtaining values for delay and travel time for multiple vehicle paths along the corridor and adjacent commercial developments in both existing and proposed conditions. With the exception of unsignalized right turns at the periphery of the study area, all non-displaced routes showed a reduction in travel time and delay. Additional research is needed to understand how additional travel through the commercial developments adjacent to the arterial may effect travel time and delay. Other expected benefits of the proposed design include a major reduction in conflict points, shorter pedestrian crossing and wait times, and the opportunity to provide pedestrian refuge areas in the median.


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