scholarly journals Estimating the division kernel of a size-structured population

2017 ◽  
Vol 21 ◽  
pp. 275-302
Author(s):  
Van Ha Hoang
Keyword(s):  
Bandwidth Selection ◽  
Random Measure ◽  
Time Interval ◽  
Constant Growth Rate ◽  
Adaptive Estimator ◽  
Daughter Cells ◽  
Structured Population ◽  
Symmetric Density ◽  
Constant Rate ◽  
Fragmentation Kernel

We consider a size-structured model describing a population of cells proliferating by division. Each cell contain a quantity of toxicity which grows linearly according to a constant growth rate α. At division, the cells divide at a constant rate R and share their content between the two daughter cells into fractions Γ and 1 − Γ where Γ has a symmetric density h on [ 0,1 ], since the daughter cells are exchangeable. We describe the cell population by a random measure and observe the cells on the time interval [ 0,T ] with fixed T. We address here the problem of estimating the division kernel h (or fragmentation kernel) when the division tree is completely observed. An adaptive estimator of h is constructed based on a kernel function K with a fully data-driven bandwidth selection method. We obtain an oracle inequality and an exponential convergence rate, for which optimality is considered.

scholarly journals CHLOROPLAST GENETICS OF CHLAMYDOMONAS. III. CLOSING THE CIRCLE

Genetics ◽  
1976 ◽  
Vol 83 (2) ◽  
pp. 341-354
Author(s):  
Burt Singer ◽  
Ruth Sager ◽  
Zenta Ramanis
Keyword(s):  
Genetic System ◽  
Time Interval ◽  
Data Sets ◽  
Mapping Data ◽  
Regression Problem ◽  
Mapping Procedure ◽  
Pooled Data ◽  
Constant Rate ◽  
Single Cross ◽  
Chloroplast Genetics

ABSTRACT A novel mapping procedure is presented for organelle genes or any other genetic system exhibiting a measurable frequency of exchanges occurring at a constant rate over a measurable time interval. For a set of markers in a multiply-marked cross, the exchange rates measure relative map distances from a centromere-like attachment point. With this method, we present mapping data and a linear map of genes in the chlcroplast genome of Chlamydomonas. The data are plotted as log (percent remaining heterozygotes) against time and map distances are taken as proportional to slope. A statistical method which is an adaptation of jackknife methodology to a regression problem was developed to estimate slope values. A single line is fitted to pooled data for each marker from several crosses, and then lines are re-fit to a series of pooled data sets in each of which the observations from a single cross have been omitted. From these data sets a final summary slope is computed as well as a statement of its variability. The relative positions of new markers present in single crosses can then be estimated utilizing data from many crosses. The method does not distinguish between one-armed and two-armed linear or circular maps. However, evaluation of this map in conjunction with cosegregation frequency data (Sager and Ramanis 1976b) provides unambiguous evidence of the genetic circularity of the Chlamydomonas chloroplast genome.

Brief cytochalasin-induced disruption of microfilaments during a critical interval in 1-cell C. elegans embryos alters the partitioning of developmental instructions to the 2-cell embryo

Development ◽  
1990 ◽  
Vol 108 (1) ◽  
pp. 159-172 ◽  
Author(s):  
D.P. Hill ◽  
S. Strome
Keyword(s):  
Cell Cycle ◽  
Asymmetric Cell Division ◽  
Critical Time ◽  
Time Interval ◽  
Critical Interval ◽  
Cell Stage ◽  
C Elegans ◽  
Daughter Cells ◽  
Correct Pattern ◽  
Cell Embryo

We are investigating the involvement of the microfilament cytoskeleton in the development of early Caenorhabditis elegans embryos. We previously reported that several cytoplasmic movements in the zygote require that the microfilament cytoskeleton remain intact during a narrow time interval approximately three-quarters of the way through the first cell cycle. In this study, we analyze the developmental consequences of brief, cytochalasin D-induced microfilament disruption during the 1-cell stage. Our results indicate that during the first cell cycle microfilaments are important only during the critical time interval for the 2-cell embryo to undergo the correct pattern of subsequent divisions and to initiate the differentiation of at least 4 tissue types. Disruption of microfilaments during the critical interval results in aberrant division and P-granule segregation patterns, generating some embryos that we classify as ‘reverse polarity’, ‘anterior duplication’, and ‘posterior duplication’ embryos. These altered patterns suggest that microfilament disruption during the critical interval leads to the incorrect distribution of developmental instructions responsible for early pattern formation. The strict correlation between unequal division, unequal germ-granule partitioning, and the generation of daughter cells with different cell cycle periods observed in these embryos suggests that the three processes are coupled. We hypothesize that (1) an ‘asymmetry determinant’, normally located at the posterior end of the zygote, governs asymmetric cell division, germ-granule segregation, and the segregation of cell cycle timing elements during the first cell cycle, and (2) the integrity or placement of this asymmetry determinant is sensitive to microfilament disruption during the critical time interval.

scholarly journals Hybrid systems approach to modeling stochastic dynamics of cell size

2016 ◽  
Author(s):  
Cesar Augusto Vargas-Garcia ◽  
Abhyudai Singh
Keyword(s):  
Growth Rate ◽  
Cell Size ◽  
Size Variation ◽  
Model Parameters ◽  
Constant Growth Rate ◽  
Division Rate ◽  
Size Dependent ◽  
Daughter Cells ◽  
Constant Growth ◽  
Over Time

A ubiquitous feature of all living cells is their growth over time followed by division into two daughter cells. How a population of genetically identical cells maintains size homeostasis, i.e., a narrow distribution of cell size, is an intriguing fundamental problem. We model size using a stochastic hybrid system, where a cell grows exponentially over time and probabilistic division events are triggered at discrete time intervals. Moreover, whenever these events occur, size is randomly partitioned among daughter cells. We first consider a scenario, where a timer (i.e., cell-cycle clock) that measures the time since the last division event regulates cellular growth and the rate of cell division. Analysis reveals that such a timer-driven system cannot achieve size homeostasis, in the sense that, the cell-to-cell size variation grows unboundedly with time. To explore biologically meaningful mechanisms for controlling size we consider three different classes of models: i) a size-dependent growth rate and timer-dependent division rate; ii) a constant growth rate and size-dependent division rate and iii) a constant growth rate and division rate that depends both on the cell size and timer. We show that each of these strategies can potentially achieve bounded intercellular size variation, and derive closed-form expressions for this variation in terms of underlying model parameters. Finally, we discuss how different organisms have adopted the above strategies for maintaining cell size homeostasis.

Reliability Analysis of Parallel Manufacturing Systems with Two Machines

1979 ◽  
Vol 101 (3) ◽  
pp. 250-254 ◽  
Author(s):  
K. Hitomi ◽  
M. Nakajima ◽  
N. Takahashi
Keyword(s):  
Manufacturing Systems ◽  
Manufacturing System ◽  
Cutting Tools ◽  
Reliability Theory ◽  
Continuous Operation ◽  
Time Interval ◽  
Time To Failure ◽  
Constant Rate ◽  
Tool Replacement ◽  
Two Machines

A stochastic mathematical model was built and analyzed by using the reliability theory for a manufacturing system in which two machines are arranged in parallel. Under the condition that the system is required to be operated at a constant rate of production, the variation of reliability and failure rate of cutting tools with the lapse of time were investigated, using the stress-strength model in failure physics. A time interval of tool replacement in the continuous operation and a time to failure for a manufacturing system which is composed of two lathes were also investigated.

Taking advantage of time-averaging

Paleobiology ◽  
1999 ◽  
Vol 25 (2) ◽  
pp. 226-238 ◽  
Author(s):  
Thomas Olszewski
Keyword(s):  
Temporal Resolution ◽  
Full Range ◽  
Exponential Model ◽  
Published Data ◽  
Time Interval ◽  
Time Averaging ◽  
Short Term ◽  
Constant Rate ◽  
Rapid Destruction

AbstractOne of the major obstacles in dealing with any form of data derived from fossils is the effects of time-averaging, which are the result of mixing the remains of organisms that did not live contemporaneously. Although this process results in loss of temporal resolution, it also serves to filter out short-term variations. Temporal resolution of a collection depends not only on the range of fossil ages, but also on their frequency distribution. Previous studies of marine molluscs indicate that most shells in an accumulation are relatively young. Such a distribution of shell ages can be fit by an exponential curve (assuming both a constant probability of shell loss and a constant rate of shell addition), which implies that 90% of the shells were added during the last 50% of the time interval represented by the collection. That is to say, differences between two collections can be discerned even if they overlap 50% in time, because the proportion of shells with shared ages is only 10%. Applying the exponential model to previously published data suggests that long-term rates of destruction are controlled by how frequently shells from the taphonomically active zone are re-exposed to rapid destruction. To take advantage of the “noise-filtering” property of time-averaging, samples need to be large enough to catch the full range of environmental variation recorded by an accumulation. A simple probability formula indicates that samples of easily achievable size can give satisfactory time-averaged results depending on the level of confidence and sampling density defined by the researcher.

The Fertilisation of Rabbit Ova in Relation to Time

1934 ◽  
Vol 11 (2) ◽  
pp. 140-161
Author(s):  
JOHN HAMMOND
Keyword(s):  
Litter Size ◽  
Metabolic Product ◽  
Time Interval ◽  
Fallopian Tubes ◽  
Male And Female ◽  
Constant Increase ◽  
Average Litter Size ◽  
Constant Rate ◽  
The Individual ◽  
Duration Of Pregnancy

1. By matings with fertile bucks at different intervals of time after a mating with a vasectomised buck (to induce ovulation) the time of insemination in the rabbit can be moved successively nearer to, at, and after the time of ovulation. 2. From inseminations 5 hours before to 2 hours after ovulation the percentage of matings which are fertile, the average litter size, and average number of young permating fall gradually and at a constant rate until absolute sterility is obtained. Does which produce large litters when mated normally (10 hours before ovulation) may be made to produce small litters by mating shortly before or after the time of ovulation. 3. The ova are only capable of fertilisation while they are in, or as they leave, the plug at the top of the Fallopian tubes, i.e. up to about 6 hours after ovulation. They are incapable of fertilisation as they begin to move down the tube and acquire a layer of albumen around them. 4. As a result of a mating made about the time of ovulation the apex of the "sperm swarm" arrives at the top of the tube in time to fertilise only those ova which still remain in the plug. The apex of the "sperm swarm" contains relatively few spermatozoa, and so small litters are produced. 5. By "double matings," of dominant and recessive coloured bucks on recessive coloured does, with a time interval between them, it is possible to measure the relative sizes of the "sperm swarms" at the tops of the tubes at different intervals of time after mating. 6. The size of the "sperm swarm," and so the interval of time over which it is possible to obtain fertilisation as a result of mating later than normal in relation to the time of ovulation, varies considerably in different males. 7. The speed at which the sperms ascend the female tract is apparently not affected by the presence in them of male and female sex-determining elements. 8. The duration of pregnancy is prolonged by reducing the size of the litter. With the prolongation of pregnancy the proportion of young born dead increases. Various possible causes for these facts are discussed. 9. While there is but little constant increase in the weight of the individual young due to the prolongation of pregnancy from 31 to 34 days, there is a large increase in the individual weight due to reduction in the number of young in the litter. 10. It is probable that the size of individual young is limited by the amount of some internal secretion or metabolic product of the mother.

scholarly journals Ecological specialization under multidimensional tradeoffs

2018 ◽  
Author(s):  
André Amado ◽  
Paulo R. A. Campos
Keyword(s):  
Resource Availability ◽  
Arbitrary Number ◽  
Essential Role ◽  
Ecological Specialization ◽  
Structured Population ◽  
Constant Rate ◽  
Population Sizes ◽  
Spatially Structured Population ◽  
Microbial Organisms

AbstractAlthough tradeoffs are expected to play an essential role in shaping the diversity in a community, their effects remain relatively nebulous and notoriously difficult to assess. This is especially true when multiple tradeoffs occur simultaneously. When dealing with single tradeoffs some information can be predicted based on their curvature. Does the same happen when dealing with multiple tradeoffs? What happens if the tradeoffs have opposing curvatures? To address these issues, we develop a resource-based model that encompasses multiple tradeoffs mediated by the acquisition and processing of the resources. The model considers a spatially structured population of microbial organisms that can grow on an arbitrary number of resources, which come into the system at a constant rate and diffuse through the environment. The individuals can adopt a variety of strategies through mutation constrained by tradeoffs, which renders the model adaptive. We assess population sizes and levels of ecological specialization. We find that when multiple tradeoffs are considered the classical intuition developed for single tradeoffs does not hold. The outcome can depend significantly not only on the curvature of the tradeoffs but also on resource availability.

scholarly journals SECOND-ORDER APPROXIMATION FOR ADAPTIVE REGRESSION ESTIMATORS

2001 ◽  
Vol 17 (5) ◽  
pp. 984-1024 ◽  
Author(s):  
Oliver Linton ◽  
Zhijie Xiao
Keyword(s):  
Mean Squared Error ◽  
Order Approximation ◽  
Bandwidth Selection ◽  
Order Effect ◽  
Order Theory ◽  
Second Order ◽  
Adaptive Estimator ◽  
Regression Estimators ◽  
Adaptive Regression ◽  
Error Density

We derive asymptotic expansions for semiparametric adaptive regression estimators. In particular, we derive the asymptotic distribution of the second-order effect of an adaptive estimator in a linear regression whose error density is of unknown functional form. We then show how the choice of smoothing parameters influences the estimator through higher order terms. A method of bandwidth selection is defined by minimizing the second-order mean squared error. We examine both independent and time series regressors; we also extend our results to a t-statistic. Monte Carlo simulations confirm the second order theory and the usefulness of the bandwidth selection method.

scholarly journals COMPLETENESS OF BOND MARKET DRIVEN BY LÉVY PROCESS

2010 ◽  
Vol 13 (05) ◽  
pp. 635-656 ◽  
Author(s):  
MICHAŁ BARSKI ◽  
JERZY ZABCZYK
Keyword(s):  
Dense Subset ◽  
Random Measure ◽  
Bond Market ◽  
Contingent Claims ◽  
Market Model ◽  
Time Interval ◽  
Poisson Random Measure ◽  
Finite Time Interval ◽  
Lévy Measure ◽  
Market Driven

The completeness problem of the bond market model with the random factors determined by a Wiener process and Poisson random measure is studied. Hedging portfolios use bonds with maturities in a countable, dense subset of a finite time interval. It is shown that under natural assumptions the market is not complete unless the support of the Lévy measure consists of a finite number of points. Explicit constructions of contingent claims which cannot be replicated are provided.

Stimulated Virus Production in Vinblastine and Cytochalasin-Induced Multinucleate Cells

1970 ◽  
Vol 28 ◽  
pp. 186-187
Author(s):  
Krishan Awtar
Keyword(s):  
Cell Division ◽  
Normal Cell ◽  
Virus Production ◽  
Multinucleate Cells ◽  
Daughter Cells ◽  
Cell Divisions ◽  
Nuclear Membranes ◽  
Division 2 ◽  
Vinblastine Sulfate

Exposure of cells to low sublethal but mitosis-arresting doses of vinblastine sulfate (Velban) results in the initial arrest of cells in mitosis followed by their subsequent return to an “interphase“-like stage. A large number of these cells reform their nuclear membranes and form large multimicronucleated cells, some containing as many as 25 or more micronuclei (1). Formation of large multinucleate cells is also caused by cytochalasin, by causing the fusion of daughter cells at the end of an otherwise .normal cell division (2). By the repetition of this process through subsequent cell divisions, large cells with 6 or more nuclei are formed.

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