In this paper, we develop methods for inferring tumor growth rates from the observation of tumor volumes at two time points. We fit power law, exponential, Gompertz, and Spratt’s generalized logistic model to five data sets. Though the data sets are small and there are biases due to the way the samples were ascertained, there is a clear sign of exponential growth for the breast and liver cancer...

Extending Ireland’s (1994) model, this paper analyzes an international economy where cash or credit can be used for payment. Foreign trade credit is more costly than its domestic analog. A depreciation of the real exchange rate is associated with an external surplus and a reduced share of imports purchased with credit. Economic growth slows when foreign trade credit becomes the predominant mean...

The accurate measurement of growth-rate constants for bacteria in natural environments is generally found to be quite difficult. Estimation of growth rates for the chemoautotrophs concerned with nitrate production, however, may be made. Advantage is taken of the facts that chemoautotrophs are the major, if not the sole, agents concerned with nitrate production in nature, and that the oxidation ...

Throughout this thesis, we observe close correlations between values of the topological growth rates and various other fractal indices. These observations are based on both analytic derivations and numerical computations of the relevant exponents. In this chapter we derive inequalities that relate our topological growth rates to existing scaling indices such as the box-counting dimension and th...

McDANIEL, L. E. (Rutgers, The State University, New Brunswick, N.J.), E. G. BAILEY, AND A. ZIMMERL. Effect of oxygen-supply rates on growth of Escherichia coli. II. Comparison of results in shake flasks and 50-liter fermentor. Appl. Microbiol. 13: 115-119. 1965.-Growth of Escherichia coli and chemical changes in the medium were very similar in highly baffled flasks and in a 50-liter fermentor r...

In this paper we will study the dynamics of the periodic asymmetric oscillator x′′ + q(t)x+ + q−(t)x− = 0, where q, q− ∈ L(R/2πZ) and x+ = max(x, 0), x− = min(x, 0) for x ∈ R. It will be proved that the exponential growth rate χ(x) := lim t→+∞ 1 t log √ (x(t))2 + (x′(t))2 does exist for each non-zero solution x(t) of the oscillator. The properties of these rates, or the Lyapunov exponents, will...

McDANIEL, L. E. (Rutgers, The State University, New Brunswick, N.J.), E. G. BAILEY, AND A. ZIMMERL. Effect of oxygen-supply rates on growth of Escherichia coli. II. Comparison of results in shake flasks and 50-liter fermentor. Appl. Microbiol. 13: 115-119. 1965.-Growth of Escherichia coli and chemical changes in the medium were very similar in highly baffled flasks and in a 50-liter fermentor r...

In this paper, we describe a copy-and-paste method for constructing a class of infinite self-similar trees. A copy-paste tree is constructed by repeatedly attaching copies of a finite tree (called a generator) to certain designated attachment vertices. We show that each generator has an associated nonnegative matrix which can be used to determine a formula for the growth function of the copy-pa...

I consider how cell shape and environmental geometry affect the rate of nutrient capture and the consequent maximum growth rate of a cell, focusing on rod-like species like E. coli. Simple modeling immediately implies that it is the elongated profiles of such cells that allows for them to grow – as observed – at exponential rates in nutrient-rich media. Growth is strongly suppressed when nutrie...

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