Rate Change Point Research Articles

Psycho-physiological measures on a bicycle simulator in immersive virtual environments: how protected/curbside bike lanes may improve perceived safety

As a healthier and more sustainable way of mobility, cycling has been advocated by literature and policy. However, current trends in bicyclist crash fatalities suggest deficiencies in current roadway design in protecting these vulnerable road users. The lack of cycling data is a common challenge for studying bicyclists’ safety, behavior, and comfort levels under different design contexts. To understand bicyclists’ behavioral and physiological responses in an efficient and safe way, this study uses a bicycle simulator within an immersive virtual environment (IVE). Off-the-shelf sensors are utilized to evaluate bicyclists’ cycling performance (speed and lane position) and physiological responses (eye tracking and heart rate). Participants bike in a simulated virtual environment modeled to scale from a real-world street with a shared bike lane (sharrows) to evaluate how the introduction of a curbside bike lane and a protected bike lane with flexible delineators may impact perceptions of safety, as well as behavioral and psycho-physiological responses. Results from 50 participants (representing both genders and across a wide age range) show that the protected bike lane design received the highest perceived safety rating and exhibited the lowest average cycling speed. Furthermore, both the curbside bike lane and the protected bike lane scenarios show a less dispersed gaze distribution than the as-built sharrows scenario, reflecting a higher gaze focus among bicyclists on the biking task in the curbside bike lane and protected bike lane scenarios, compared to when bicyclists share right of way with vehicles. Additionally, heart rate change point results from the study suggest that creating dedicated zones for bicyclists (curbside bike lanes or protected bike lanes) has the potential to reduce bicyclists’ stress levels. Female participants show a higher preference on the protected bike lane design and a lower perceived safety rating on the sharrows. These findings are from participants riding a bicycle simulator in an immersive virtual environment and inform, but do not fully reflect, bicycling in the real world.

The Effect of Exercise Training on the Detection of Heart Rate and Body Temperature Sensors in Adolescents

The aim of this study is to study the effect of exercise training on heart rate and body temperature sensor detection in adolescents. For the methods of logical analysis, test, and mathematical statistics, this paper takes 60 students aged 13-15 in the experimental middle school as the research subjects to explore the characteristics of heart rate changes of middle school students under different high-intensity intermittent exercise schemes. Then, it analyzes the characteristics of heart rate change in exercise center and heart rate change in high-intensity intermittent exercise. The experimental results show that the high-intensity intermittent exercise of adolescents aged 13-15 presents the stage of rapid recovery and buffer recovery. Whether in the quiet heart rate buffer stage or the rapid heart rate increase stage, as well as the “extreme heart rate maintenance stage” and heart rate recovery stage, the heart rate change point of 15-year-old adolescents is 1-3 seconds later than that of 13-year-old and 14-year-old adolescents. In addition, in the heart rate maintenance stage of 15-year-old adolescents, the heart rate fluctuates greatly. The rapid recovery stage of boys is 1 minute, and the heart rate can reach the quiet heart rate after 4-5 minutes. The rapid recovery stage of girls is 1.5 minutes, and the heart rate can reach the quiet heart rate after 4-5 minutes. The older the age of high-intensity intermittent training of adolescents aged 13-15, the longer the rapid rise stage of heart rate change, and there was no significant change in quiet heart rate buffer stage and body temperature.

Strongly oversized fission yeast cells lack any size control and tend to grow linearly rather than bilinearly.

During the mitotic cycle, the rod-shaped fission yeast cells grow only at their tips. The newly born cells grow first unipolarly at their old end, but later in the cycle, the 'new end take-off' event occurs, resulting in bipolar growth. Photographs were taken of several steady-state and induction synchronous cultures of different cell cycle mutants of fission yeast, generally larger than wild type. Length measurements of many individual cells were performed from birth to division. For all the measured growth patterns, three different functions (linear, bilinear and exponential) were fitted, and the most adequate one was chosen by using specific statistical criteria, considering the altering parameter numbers. Although the growth patterns were heterogeneous in all the cultures studied, we could find some tendencies. In cultures with sufficiently wide size distribution, cells large enough at birth tend to grow linearly, whereas the other cells generally tend to grow bilinearly. We have found that among bilinearly growing cells, the larger they are at birth, the rate change point during their bilinear pattern occurs earlier in the cycle. This shifting near to the beginning of the cycle might finally cause a linear pattern, if the cells are even larger. In all of the steady-state cultures studied, a size control mechanism operates to maintain homeostasis. By contrast, strongly oversized cells of induction synchronous cultures lack any sizer, and their cycle rather behaves like an adder. We could determine the critical cell size for both the G1 and G2 size controls, where these mechanisms become cryptic. TAKE AWAY: Most individual fission yeast cells in steady-state cultures grow bilinearly. In strongly oversized fission yeast cells, linear growth dominates over bilinear. Above birth length thresholds, both the G1 and G2 size controls become cryptic.

The concepts of Ludwik Fleck and their application to the eukaryotic cell cycle

The concepts of Ludwik Fleck (1896–1961), a microbiologist, historian, and philosopher of medicine, can be used to analyze the conservative nature of scientific ideas. This is discussed and applied to ideas dominant in the understanding of the eukaryotic cell cycle. These are (a) the G1-phase restriction point as a regulatory element of the mammalian cell cycle, (b) the Rate Change Point proposed to exist in fission yeast, and (c) the proposal that a large number of genes are expressed in a cell-cycle-dependent manner. Fleck proposed that scientific ideas become fixed and difficult to change because criticisms of current and dominant models are either ignored or turned to support of the current model. The idea of a thought-collective leading to the stability of scientific ideas is a central theme of the theory of Ludwik Fleck.

Multi‐Scale Detection of Variance Changes in Renewal Processes in the Presence of Rate Change Points

Non‐stationarity of the rate or variance of events is a well‐known problem in the description and analysis of time series of events, such as neuronal spike trains. A multiple filter test (MFT) for rate homogeneity has been proposed earlier that detects change points on multiple time scales simultaneously. It is based on a filtered derivative approach, and the rejection threshold derives from a Gaussian limit process L which is independent of the point process parameters.Here, we extend the MFT to variance homogeneity of life times. When the rate is constant, the MFT extends directly to the null hypothesis of constant variance. In the presence of rate change points, we propose to incorporate estimates of these in the test for variance homogeneity, using an adaptation of the test statistic. The resulting limit process shows slight deviations from L that depend on unknown process parameters. However, these deviations are small and do not considerably change the properties of the statistical test. This allows practical application, for example, to neuronal spike trains, which indicates various profiles of rate and variance change points.

Optimum modified ramp-stress ALT plan with competing causes of failure

PurposeAccelerated life test is undertaken to induce early failure in high-reliability products likely to last for several years. Most of these products are exposed to several fatal risk factors and fail due to one of them. Examples include solar lighting device with two failure modes: capacitor failure, and controller failure. It is necessary to assess each risk factor in the presence of other risk factors as each one cannot be studied in isolation. The purpose of this paper is to explore formulation of optimum time-censored accelerated life test model under modified ramp-stress loading when different failure causes have independent exponential life distributions.Design/methodology/approachThe modified ramp-stress uses one test chamber in place of the various chambers used in the normal ramp-stress accelerate life test thus saving experimental cost. The stress-life relationship is modeled by inverse power law, and for each failure cause, a cumulative exposure model is assumed. The method of maximum likelihood is used for estimating design parameters. The optimal plan consists in finding out relevant experimental variables, namely, stress rate and stress rate change point(s).FindingsThe optimal plan is devised using D-optimality criterion which consists in finding out optimal stress rate and optimal stress rate change point by maximizing logarithm of determinant of Fisher information matrix to the base 10. This criterion is motivated by the fact that the volume of joint confidence region of model parameters is inversely proportional to square root of determinant of Fisher information matrix. The results of sensitivity analysis show that the plan is robust to small deviations from the true values of baseline parameters.Originality/valueThe model formulated can help reliability engineers obtain reliability estimates quickly of high-reliability products that are likely to last for several years.

The shark fin function: asymptotic behavior of the filtered derivative for point processes in case of change points

A multiple filter test for the analysis and detection of rate change points in point processes on the line has been proposed recently. The underlying statistical test investigates the null hypothesis of constant rate. For that purpose, multiple filtered derivative processes are observed simultaneously. Under the null hypothesis, each process G asymptotically takes the form $$\begin{aligned} G \sim L, \end{aligned}$$ while L is a zero-mean Gaussian process with unit variance. This result is used to derive a rejection threshold for statistical hypothesis testing. The purpose of this paper is to describe the behavior of G under the alternative hypothesis of rate changes and potential simultaneous variance changes. We derive the approximation $$\begin{aligned} G \sim \Delta \cdot \left( \Lambda + L\right) \!, \end{aligned}$$ with deterministic functions $$\Delta $$ and $$\Lambda $$ . The function $$\Lambda $$ accounts for the systematic deviation of G in the neighborhood of a change point. When only the rate changes, $$\Lambda $$ is hat shaped. When also the variance changes, $$\Lambda $$ takes the form of a shark’s fin. In addition, the parameter estimates required in practical application are not consistent in the neighborhood of a change point. Therefore, we derive the factor $$\Delta $$ termed here the distortion function. It accounts for the lack in consistency and describes the local parameter estimating process relative to the true scaling of the filtered derivative process.

Cell length growth patterns in fission yeast reveal a novel size control mechanism operating in late G2 phase.

Because cylindrically shaped fission yeast cells grow exclusively at their tips, cell volume is proportional to length and can be easily monitored by time-lapse microscopy. Here, we analysed the growth pattern of individual cells from several fission yeast strains to determine the growth function that describes them most adequately and to perform size control studies. The growth pattern of most cells during their growth period is best described by a bilinear function (i.e., two linear segments of different growth rates separated by a rate-change point). Linear growth patterns were also observed in several cases, but exponential ones only rarely. Since the bilinear patterns are separated into two segments by a breakpoint, we examined the existence of size control by regression analyses of the appropriate growth parameters in both segments. This confirmed the existence of known size controls in late G1, mid-G2 and late G2 during the fission yeast cycle. The present analyses also revealed that, contrary to the commonly accepted current view, late G2 size control is a general characteristic third event in the cycle. The level of the critical late G2 size that needs to be reached in an individual fission yeast cell is influenced by the growth rate of the cell in a manner similar to budding yeast, suggesting an evolutionary conserved mechanism. The present study of individual cell growth patterns in wild-type and several cell cycle mutant fission yeast strains confirmed that, for most cells, growth is best described by a bilinear function. Three different size control mechanisms were found to operate in the different strains, and, as a novel observation, cell size was always found to be monitored before mitotic onset, irrespective of the existence of any earlier size checkpoints. Studying the pattern of growth and the mechanism of size control helps to clarify the connections between cell growth and division, since their coordination must work properly to maintain size homeostasis. In this study, we argue that most individual fission yeast cells grow following a bilinear pattern, and we confirm the existence of three different size control mechanisms.

Optimum Time-Censored Modified Ramp-Stress ALT for the Burr Type XII Distribution with Warranty: A Goal Programming Approach

Accelerated life tests (ALTs) are used to make timely assessments of the life time distribution of highly reliable materials and components. Much of the previous work on ALTs has focused on constant-stress, step-stress, ramp-stress schemes and their various combinations. In the literature ramp-stress ALTs that have been formulated can be conducted when more than one test chambers are available; installation of which may prove to be costly. Even when one test chamber is used the stress rate remains constant throughout the duration of the experiment. It is not only necessary but imperative to examine if the test specimen is able to withstand differing stress conditions with the passage of time. This paper therefore, presents an optimal design of multi-objective modified ramp-stress ALT model with weighted goal programming approach. The modified ramp-stress uses one test chamber in place of the various chambers used in simple ramp-stress ALT thus saving experimental cost. With the market being increasingly competitive the emphasis today is on goal attainment with minimum deviations. Goal programming is a method to solve multi-objective problems that has applications in varied fields of engineering and operational research. The optimal plan consists in finding out relevant experimental variables, namely, stress rate, stress rate change point and warranty period, by using goal programming on weighted sum of variance of reliability function and expected warranty cost with pre-specified mission time under normal operating conditions. The Burr type XII life distribution and time-censored data have been used for the purpose. Burr type XII life distribution has been found appropriate for accelerated life testing experiments. The method developed has been explained using a numerical example and sensitivity analysis carried out. Comparative study has also been done to highlight the merits of the proposed model.

A model to analyze as-applied reports from variable rate applications

During variable rate operations, controller systems report information (as-applied files) about desired rates and real applied rates on georeferenced points along the machine tracks. These reports are useful for operation quality control but they have not been widely used to their potential. The goal of this study was to create a model to help analyzing as-applied files based on quantifying and locating off-rate errors and their probable related sources. The model calculates off-rate error at every point and classifies them as less than target rate, acceptable or over the target rate. Possible error sources are classified regarding three aspects: vehicle path position (inward, middle or outward), high rate change (step up or down) and vehicle acceleration or deceleration. A pulled type applicator (application 1) and a self-propelled applicator (application 2) were analyzed. An average of 30.6 % of the recorded points was considered application errors (10 % off the target rate). 70.5 % of them occurred on high rate change points on application 1 and 69.7 % on acceleration/deceleration points on application 2. The self-propelled applicator performed better during high transition rate than the pulled type which performed poorly when transition rate exceeded 10 %. The model determined the major and minor factors related to application error. It provided means to assess equipment limitations and its impact over the quality of application. The trials demonstrated its flexibility and how it can improve the use of as-applied files.

Application of joinpoint regression in determining breast cancer incidence rate change points by age and tumor characteristics in women aged 30-69 (years) and in Isfahan city from 2001 to 2010

Background and Objectives:Breast cancer is a major threat to women's health. Evaluation of the changes in trend of the incidence rate provides valuable information for the assessment and planning of development indicators of each country. The aim of the present study was to apply the JoinPoint regression model for determining changes in the trend of the breast cancer incidence rate in Isfahan.Materials and Methods:In this cross-sectional study, 3640 women with breast cancer referring to oncology and radiotherapy departments of Seyed-al-Shohada and Milad cancer treatment centers of Isfahan during 2001–2010 were studied and sampling was not done. Joinpoint regression model was used to investigate the pattern of breast cancer incidence rate. Response and independent variables were the natural logarithm of the age-standardized incidence rates and year of diagnosis of breast cancer, respectively, in which various levels of cancer tumor characteristics (P < 0.05) were analyzed.Results:The incidence rates increased annually in the age groups of 40–44 years (6.2%), 45–49 years (5.3%), and 55–59 years (5.3%). The trend of incidence rates in women with tumor size ≤2 cm (18.2%), well (moderately) differentiated tumor grade [8% (10.2%)], positive estrogen (progesterone) hormone receptor status [10.5% (6.9%)], and the proportion of positive lymph node to surgery node ≤25% (nonsignificant) was upward.Conclusion:The trend of incidence rates with tumor size ≤2 cm, well-differentiated tumor grade, moderately differentiated tumor grade, and positive estrogen and progesterone hormone receptors was upward. The pattern of breast cancer can help in cancer prevention and prognosis, and in selecting the best type of surgery.

Schizosaccharomyces pombegrows exponentially during the division cycle with no rate change points

Length measurements during the division cycle of 86 individual Schizosaccharomyces pombe cells demonstrate that length grows exponentially with no change in the growth rate and no rate change point (RCP) observed for any cell. These results support the proposal that length extension, or cell growth, is exponential during the division cycle. The finding of exponential growth during the cell cycle is significant because these results challenge and contradict the current, consensus, widely believed, and widely accepted view that growth of S.pombe during the division cycle is complex with ranges of linear growth changing at proposed RCPs. Biochemical synthetic patterns support and explain the observed exponential cell growth. Exponential growth of S.pombe is consistent with, and supports, the central tenets of the continuum model.

Cell length growth in fission yeast: an analysis of its bilinear character and the nature of its rate change transition

During their mitotic cycle, cylindrical fission yeast cells grow exclusively at their tips. Length growth starts at birth and halts at mitotic onset when the cells begin to prepare for division. While the growth pattern was initially considered to be exponential, during the last three decades an increasing amount of evidence indicated that it is rather a bilinear function [two linear segments separated by a rate change point (RCP)]. The main focus of this work was to clarify this and to elucidate the further question of whether the rate change occurs abruptly at the RCP or more smoothly during a transition period around it. We have analyzed the individual growth patterns obtained by time-lapse microscopy of 60 wild-type cells separately as well as that of the 'average' cell generated from their superposition. Linear, exponential, and bilinear functions were fitted to the data, and their suitability was compared using objective model selection criteria. This analysis found the overwhelming majority of the cells (70%) to have a bilinear growth pattern with close to half of them showing a smooth and not an abrupt transition. The growth pattern of the average cell was also found to be bilinear with a smooth transition.

A mathematical model for cell size control in fission yeast

Experimental investigations of cell size control in fission yeast Schizosaccharomyces pombe have illustrated that the cell cycle features ‘sizer’ and ‘timer’ phases which are distinguished by a growth rate changing point. Based on current biological knowledge of fission yeast size control, we propose here a model of ordinary differential equations (ODEs) for a possible explanation of the facts and control mechanism which is coupled with the cell cycle. Simulation results of the ODE model are demonstrated to agree with experimental data for the wild type and the cdc2-33 mutant. We show that the coupling of cell growth to cell division by translational control may account for observed properties of size control in fission yeast. As the translational control in the expression of cycle proteins Cdc13 and Cdc25 constructs positive feedback loops, the dynamical activities of the key components undergoes a rapid rising after a preliminary stage of slow increase. The coupling of this dynamical behavior to the elongation of the cell naturally gives rise to a rate change point and to ‘sizer’ and ‘timer’ phases, which characterize the cell cycle of fission yeast.

Growth Pattern of Single Fission Yeast Cells Is Bilinear and Depends on Temperature and DNA Synthesis

Cell growth and division have to be tightly coordinated to keep the cell size constant over generations. Changes in cell size can be easily studied in the fission yeast Schizosaccharomyces pombe because these cells have a cylindrical shape and grow only at the cell ends. However, the growth pattern of single cells is currently unclear. Linear, exponential, and bilinear growth models have been proposed. Here we measured the length of single fission yeast cells with high spatial precision and temporal resolution over the whole cell cycle by using time-lapse confocal microscopy of cells with green fluorescent protein-labeled plasma membrane. We show that the growth profile between cell separation and the subsequent mitosis is bilinear, consisting of two linear segments separated by a rate-change point (RCP). The change in growth rate occurred at the same relative time during the cell cycle and at the same relative extension for different temperatures. The growth rate before the RCP was independent of temperature, whereas the growth rate after the RCP increased with an increase in temperature, leading to clear bilinear growth profiles at higher temperatures. The RCP was not directly related to the initiation of growth at the new end (new end take-off). When DNA synthesis was inhibited by hydroxyurea, the RCP was not detected. This result suggests that completion of DNA synthesis is required for the increase in growth rate. We conclude that the growth of fission yeast cells is not a simple exponential growth, but a complex process with precise rates regulated by the events during the cell cycle.

Plastic deformation mechanism of pure aluminum at low homologous temperatures

Contemporary theory of metallic plastic deformation mechanism at low homologous temperatures is attributed to the physical processes of dislocations passing obstacles. Physically based deformation mechanism is generally considered as thermally activated motion of dislocations past obstacles and structural evolution of the obstacles. In order to verify the thermally activated deformation theory, stress rate change experiments, which give rapid stress changes, are conducted using pure aluminum at room temperature in this study. Incremental method is employed in the numerical simulation of above deformation mechanism. Excellent agreement is observed in the comparison between experimental data and numerical calculations, especially on the very abrupt change in strain rate at the stress rate change point. Sensitivity analyses are also performed to better understand the key parameters of both flow kinetics and structural evolution law. Simple kinetic model such as the regularly distributed rectangular obstacle is adequate enough. Obstacle structure is strongly influenced by the dislocation annihilation processes. Constant obstacle structure seems impossible to maintain once the loading condition changes.

Plastic deformation mechanism of pure copper at low homologous temperatures

Plastic deformation mechanism of pure metals at low homologous temperatures is attributed to the motion of dislocations and their interactions with each other or other kinds of obstacles. Physically based modeling of deformation mechanism is generally considered as thermally activated motion of dislocations past obstacles and structural evolution of the obstacles. In this study, stress rate change experiments, which give rapid stress changes, are conducted using pure copper at room temperature. Incremental method is employed in the numerical simulation of above modeling. Excellent agreement is observed in the comparison between experimental data and numerical calculations, especially on the very abrupt change in strain rate at the stress rate change point. Sensitivity analyses are also performed to better understand both flow kinetics and structural evolution law. Simple kinetic model such as the regular distributed rectangular obstacle is adequate enough. Obstacle structure is strongly influenced by the dislocation annihilation processes.

Growth During the Cell Cycle

During the cell cycle, major bulk parameters such as volume, dry mass, total protein, and total RNA double and such growth is a fundamental property of the cell cycle. The patterns of growth in volume and total protein or RNA provide an "envelope" that contains and may restrict the gear wheels. The main parameters of cell cycle growth were established in the earlier work when people moved from this field to the reductionist approaches of molecular biology, but very little is known on the patterns of metabolism. Most of the bulk properties of cells show a continuous increase during the cell cycle, although the exact pattern of this increase may vary. Since the earliest days, there have been two popular models, based on an exponential increase and linear increase. In the first, there is no sharp change in the rate of increase through the cycle but a smooth increase by a factor of two. In the second, the rate of increase stays constant through much of the cycle but it doubles sharply at a rate change point (RCP). It is thought that the exponential increase is caused by the steady growth of ribosome numbers and the linear pattern is caused by a doubling of the structural genes during the S period giving an RCP--a "gene dosage" effect. In budding yeast, there are experiments fitting both models but on balance slightly favoring "gene dosage." In fission yeast, there is no good evidence of exponential increase. All the bulk properties, except O2 consumption, appear to follow linear patterns with an RCP during the short S period. In addition, there is in wild-type cells a minor RCP in G2 where the rate increases by 70%. In mammalian cells, there is good but not extensive evidence of exponential increase. In Escherichia coli, exponential increase appears to be the pattern. There are two important points: First, some proteins do not show peaks of periodic synthesis. If they show patterns of exponential increase both they and the total protein pattern will not be cell cycle regulated. However, if the total protein pattern is not exponential, then a majority of the individual proteins will be so regulated. If this majority pattern is linear, then it can be detected from rate measurements on total protein. However, it would be much harder at the level of individual proteins where the methods are at present not sensitive enough to detect a rate change by a factor of two. At a simple level, it is only the exponential increase that is not cell cycle regulated in a synchronous culture. The existence of a "size control" is well known and the control has been studied for a long time, but it has been remarkably resistant to molecular analysis. The attainment of a critical size triggers the periodic events of the cycle such as the S period and mitosis. This control acts as a homeostatic effector that maintains a constant "average" cell size at division through successive cycles in a growing culture. It is a vital link coordinating cell growth with periodic events of the cycle. A size control is present in all the systems and appears to operate near the start of S or of mitosis when the cell has reached a critical size, but the molecular mechanism by which size is measured remains both obscure and a challenge. A simple version might be for the cell to detect a critical concentration of a gene product.

Reconstructing the history of forest fire frequency: Identifying hazard rate change points using the bayes information criterion

AbstractA problem in model selection, namely the identification of multiple change points for a piece‐wise constant hazard rate, is discussed. A methodology using the Bayes Information Criterion is developed in an overdispersed survival model (with corresponding quasi‐likelihood function). The technique is used to identify changes in the historical frequency of forest fire. It is applied to two datasets derived from time‐since‐fire maps in the Canadian Rockies.

The size control of fission yeast revisited.

An analysis was made of cell length and cycle time in time-lapse films of the fission yeast Schizosaccharomyces pombe using wild-type (WT) cells and those of various mutants. The more important conclusions about 'size controls' are: (1) there is a marker in G2 in WT cells provided by a rate change point (RCP) where the linear rate of length growth increases by approximately 30%. The period before this RCP is dependent on size and can be called a 'sizer'. The period after the RCP is nearly independent of size and can be called a 'timer'. The achievement of a critical threshold size is at or near the RCP which is on average at about 0.3 of the cycle (halfway through G2). This is much earlier than was previously believed. (2) The RCP is at about the time when H1 histone kinase activity and the B type cyclin cdc13 start to rise in preparation for mitosis. The RCP is also associated with other metabolic changes. (3) In wee1 mutants, the mitotic size control is replaced by a G1/S size control which is as strong as the mitotic control. As in WT cells, there is a sizer which precedes the RCP followed by a timer but the RCP is at about the G1/S boundary and has a larger increase (approximately 100%) in rate. (4) cdc25 is not an essential part of the size control at mitosis or at the G1/S boundary. (5) Three further situations have been examined in which the mitotic size control has been abolished. First, induction synchronisation by block and release of cdc2 and cdc10. In the largest oversize-cells which are produced, the RCP is pushed back to the beginning of the cycle. There is no sizer period but only a timer. Second, when both the antagonists wee1 and cdc25 are absent in the double mutant wee1-50 cdc25 delta. In this interesting situation there is apparently no mitotic size control and the cycle times are quantised. Third, in rum1 delta wee1-50 where the normal long G1 in wee1 is much reduced, there is probably no size control either in G1 or in G2 causing a continuous shortening of division length from cycle to cycle.