scholarly journals Exponential growth rates of free and amalgamated products

2016 ◽  
Vol 212 (2) ◽  
pp. 521-546 ◽  
Author(s):  
Michelle Bucher ◽  
Alexey Talambutsa
Keyword(s):  
Growth Rates ◽  
Exponential Growth ◽  
Amalgamated Products

A multitype decomposable age-dependent branching process and its applications

1995 ◽  
Vol 32 (3) ◽  
pp. 591-608 ◽  
Author(s):  
Chinsan Lee ◽  
Grace L. Yang
Keyword(s):  
Tumor Growth ◽  
Life Span ◽  
Growth Rates ◽  
Exponential Growth ◽  
Branching Process ◽  
Asymptotic Formulas ◽  
Stage Model ◽  
Two Stage ◽  
Markov Branching Process ◽  
Age Dependent

Asymptotic formulas for means and variances of a multitype decomposable age-dependent supercritical branching process are derived. This process is a generalization of the Kendall–Neyman–Scott two-stage model for tumor growth. Both means and variances have exponential growth rates as in the case of the Markov branching process. But unlike Markov branching, these asymptotic moments depend on the age of the original individual at the start of the process and the life span distribution of the progenies.

scholarly journals High temperature decreases the PIC / POC ratio and increases phosphorus requirements in <i>Coccolithus pelagicus</i> (Haptophyta)

2014 ◽  
Vol 11 (1) ◽  
pp. 1021-1051 ◽  
Author(s):  
A. C. Gerecht ◽  
L. Šupraha ◽  
B. Edvardsen ◽  
I. Probert ◽  
J. Henderiks
Keyword(s):  
Elevated Temperature ◽  
Growth Rates ◽  
Exponential Growth ◽  
Phosphorus Limitation ◽  
Photic Zone ◽  
P Limitation ◽  
P Content ◽  
Phytoplankton Communities ◽  
Global Biogeochemical Cycles ◽  
Coccolithus Pelagicus

Abstract. Rising ocean temperatures will likely increase stratification of the water column and reduce nutrient input into the photic zone. This will increase the likelihood of nutrient limitation in marine microalgae, leading to changes in the abundance and composition of phytoplankton communities, which in turn will affect global biogeochemical cycles. Calcifying algae, such as coccolithophores, influence the carbon cycle by fixing CO2 into particulate organic carbon (POC) through photosynthesis and into particulate inorganic carbon (PIC) through calcification. As calcification produces a net release of CO2, the ratio of PIC / POC determines whether coccolithophores act as a source (PIC / POC > 1) or a sink (PIC / POC < 1) of atmospheric CO2. We studied the effect of phosphorus (P-) limitation and temperature stress on the physiology and PIC / POC ratios of two subspecies of Coccolithus pelagicus. This large and heavily calcified species (PIC / POC generally > 1.5) is a major contributor to calcite export from the photic zone into deep-sea reservoirs. Phosphorus limitation did not influence exponential growth rates in either subspecies, but P-limited cells had significantly lower cellular P-content. A 5 °C temperature increase did not affect exponential growth rates either, but nearly doubled cellular P-content under both high and low phosphate availability. The PIC / POC ratios did not differ between P-limited and nutrient-replete cultures, but at elevated temperature (from 10 to 15 °C) PIC / POC ratios decreased by 40–60%. Our results suggest that elevated temperature may intensify P-limitation due to a higher P-requirement to maintain growth and POC production rates, possibly reducing abundances in a warmer ocean. Under such a scenario C. pelagicus may decrease its calcification rate relative to photosynthesis, resulting in PIC / POC ratios < 1 and favouring CO2-sequestration over release. Phosphorus limitation by itself is unlikely to cause changes in the PIC / POC ratio in this species.

scholarly journals High temperature decreases the PIC / POC ratio and increases phosphorus requirements in <i>Coccolithus pelagicus</i> (Haptophyta)

2014 ◽  
Vol 11 (13) ◽  
pp. 3531-3545 ◽  
Author(s):  
A. C. Gerecht ◽  
L. Šupraha ◽  
B. Edvardsen ◽  
I. Probert ◽  
J. Henderiks
Keyword(s):  
High Temperature ◽  
Growth Rates ◽  
Exponential Growth ◽  
Temperature Increase ◽  
Phosphorus Limitation ◽  
Photic Zone ◽  
P Limitation ◽  
P Content ◽  
Phytoplankton Communities ◽  
Coccolithus Pelagicus

Abstract. Rising ocean temperatures will likely increase stratification of the water column and reduce nutrient input into the photic zone. This will increase the likelihood of nutrient limitation in marine microalgae, leading to changes in the abundance and composition of phytoplankton communities, which in turn will affect global biogeochemical cycles. Calcifying algae, such as coccolithophores, influence the carbon cycle by fixing CO2 into particulate organic carbon through photosynthesis (POC production) and into particulate inorganic carbon through calcification (PIC production). As calcification produces a net release of CO2, the ratio of PIC to POC production determines whether coccolithophores act as a source (high PIC / POC) or a sink (low PIC / POC) of atmospheric CO2. We studied the effect of phosphorus (P-) limitation and high temperature on the physiology and the PIC / POC ratio of two subspecies of Coccolithus pelagicus. This large and heavily calcified species is a major contributor to calcite export from the photic zone into deep-sea reservoirs. Phosphorus limitation did not influence exponential growth rates in either subspecies, but P-limited cells had significantly lower cellular P-content. One of the subspecies was subjected to a 5 °C temperature increase from 10 °C to 15 °C, which did not affect exponential growth rates either, but nearly doubled cellular P-content under both high and low phosphate availability. This temperature increase reduced the PIC / POC ratio by 40–60%, whereas the PIC / POC ratio did not differ between P-limited and nutrient-replete cultures when the subspecies were grown near their respective isolation temperature. Both P-limitation and elevated temperature significantly increased coccolith malformations. Our results suggest that a temperature increase may intensify P-limitation due to a higher P-requirement to maintain growth and POC production rates, possibly reducing abundances in a warmer ocean. Under such a scenario C. pelagicus may decrease its calcification rate relative to photosynthesis, thus favouring CO2 sequestration over release. It seems unlikely that P-limitation by itself causes changes in the PIC / POC ratio in this species.

scholarly journals Exponential growth rates in a typed branching diffusion

2007 ◽  
Vol 17 (2) ◽  
pp. 609-653 ◽  
Author(s):  
Y. Git ◽  
J. W. Harris ◽  
S. C. Harris
Keyword(s):  
Growth Rates ◽  
Exponential Growth ◽  
Branching Diffusion

A multitype decomposable age-dependent branching process and its applications

1995 ◽  
Vol 32 (03) ◽  
pp. 591-608
Author(s):  
Chinsan Lee ◽  
Grace L. Yang
Keyword(s):  
Tumor Growth ◽  
Life Span ◽  
Growth Rates ◽  
Exponential Growth ◽  
Branching Process ◽  
Asymptotic Formulas ◽  
Stage Model ◽  
Two Stage ◽  
Markov Branching Process ◽  
Age Dependent

Asymptotic formulas for means and variances of a multitype decomposable age-dependent supercritical branching process are derived. This process is a generalization of the Kendall–Neyman–Scott two-stage model for tumor growth. Both means and variances have exponential growth rates as in the case of the Markov branching process. But unlike Markov branching, these asymptotic moments depend on the age of the original individual at the start of the process and the life span distribution of the progenies.

Exponential Growth Rates of Periodic Asymmetric Oscillators

2008 ◽  
Vol 8 (4) ◽  
Author(s):  
Meirong Zhang ◽  
Zhe Zhou
Keyword(s):  
Lyapunov Exponents ◽  
Ergodic Theory ◽  
Growth Rates ◽  
Exponential Growth ◽  
Zero Solution ◽  
Unique Ergodicity ◽  
Topological Dynamics ◽  
Asymmetric Oscillator ◽  
Ergodicity Theorem

AbstractIn this paper we will study the dynamics of the periodic asymmetric oscillator xʺ + qdoes exist for each non-zero solution x(t) of the oscillator. The properties of these rates, or the Lyapunov exponents, will be given using the induced circle di®eomorphism of the oscillator. The proof is extensively based on the Denjoy theorem in topological dynamics and the unique ergodicity theorem in ergodic theory.

scholarly journals Statistical analysis of the impact of environmental temperature on the exponential growth rate of cases infected by COVID-19

2020 ◽  
Author(s):  
G. Livadiotis
Keyword(s):  
Growth Rate ◽  
Statistical Analysis ◽  
Growth Rates ◽  
Exponential Growth ◽  
Environmental Temperature ◽  
Exponential Growth Phase ◽  
Exponential Growth Rate ◽  
Statistical Confidence ◽  
Italian Regions ◽  
The Impact

AbstractWe perform a statistical analysis for understanding the effect of the environmental temperature on the exponential growth rate of the cases infected by COVID-19 for US and Italian regions. In particular, we analyze the datasets of regional infected cases, derive the growth rates for regions characterized by readable exponential growth phase in their evolution spread curve and plot them against the environmental temperatures averaged within the same regions, derive the relationship between temperature and growth rate, and evaluate its statistical confidence. The results clearly support the first reported statistically significant relationship of negative correlation between the average environmental temperature and exponential growth rates of the infected cases. The critical temperature, which eliminates the exponential growth, and thus the COVID-19 spread in US regions, is estimated to be TC = 86.1 ± 4.3 F0.

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