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\"Completely updated and expanded new edition of this widely cited book, Modelling Forest Growth and Yield, 2nd Edition synthesizes current scientific literature, provides insights in how models are constructed, gives suggestions for future developments, and outlines keys for successful implementation of models.The book describes current modeling approaches for predicting forest growth and yield and explores the components that comprise the various modeling approaches. It provides the reader with the tools for evaluating and calibrating growth and yield models and outlines the steps necessary for developing a forest growth and yield model\"--

Although previous research has established the association between early-grade mathematics knowledge and later mathematics achievement, few studies have measured mathematical skills prior to school entry, and few have investigated the predictive power of early gains in mathematics ability. The current paper relates mathematical skills measured at 54 months to adolescent mathematics achievement using multisite longitudinal data. We find that preschool mathematics ability predicts mathematics achievement through age 15, even after accounting for early reading, cognitive skills, and family and child characteristics. Moreover, we find that growth in mathematical ability between age 54 months and first grade is an even stronger predictor of adolescent mathematics achievement. These results demonstrate the importance of prekindergarten mathematics knowledge and early math learning for later achievement.

Mathiness lets academic politics masquerade as science. Like mathematical theory, mathiness uses a mixture of words and symbols, but instead of making tight links, it leaves ample room for slippage between statements in the languages of words as opposed to symbols, and between statements with theoretical as opposed to empirical content. Because it is difficult to distinguish mathiness from mathematical theory, the market for lemons tells us that the market for mathematical theory might collapse, leaving only mathiness as entertainment that is worth little but cheap to produce.

Primary (budburst, foliage and shoot) growth and secondary (cambium and xylem) growth of plants play a vital role in sequestering atmospheric carbon. However, their potential relationships have never been mathematically quantified and the underlying physiological mechanisms are unclear. We monitored primary and secondary growth in Picea mariana and Abies balsamea on a weekly basis from 2010 to 2013 at four sites over an altitudinal gradient (25–900 m) in the eastern Canadian boreal forest. We determined the timings of onset and termination through the fitted functions and their first derivative. We quantified the potential relationships between primary growth and secondary growth using the mixed‐effects model. We found that xylem formation of boreal conifers can be modeled as a function of cambium activity, bud phenology, and shoot and needle growth, as well as species‐ and site‐specific factors. Our model reveals that there may be an optimal mechanism to simultaneously allocate the photosynthetic products and stored nonstructural carbon to growth of different organs at different times in the growing season. This mathematical link can bridge phenological modeling, forest ecosystem productivity and carbon cycle modeling, which will certainly contribute to an improved prediction of ecosystem productivity and carbon equilibrium.

We develop a new metric for the distribution of educational achievement across countries that can further track the cognitive skill distribution within countries and over time. Cross-country growth regressions generate a close relationship between educational achievement and GDP growth that is remarkably stable across extensive sensitivity analyses of specification, time period, and country samples. In a series of now-common microeconometric approaches for addressing causality, we narrow the range of plausible interpretations of this strong cognitive skills-growth relationship. These alternative estimation approaches, including instrumental variables, difference-in-differences among immigrants on the U.S. labor market, and longitudinal analysis of changes in cognitive skills and in growth rates, leave the stylized fact of a strong impact of cognitive skills unchanged. Moreover, the results indicate that school policy can be an important instrument to spur growth. The shares of basic literates and high performers have independent relationships with growth, the latter being larger in poorer countries.

In bacteria, the rate of cell proliferation and the level of gene expression are intimately intertwined. Elucidating these relations is important both for understanding the physiological functions of endogenous genetic circuits and for designing robust synthetic systems. We describe a phenomenological study that reveals intrinsic constraints governing the allocation of resources toward protein synthesis and other aspects of cell growth. A theory incorporating these constraints can accurately predict how cell proliferation and gene expression affect one another, quantitatively accounting for the effect of translation-inhibiting antibiotics on gene expression and the effect of gratuitous protein expression on cell growth. The use of such empirical relations, analogous to phenomenological laws, may facilitate our understanding and manipulation of complex biological systems before underlying regulatory circuits are elucidated.

We describe a new class of groups of Burnside type, by giving a procedure transforming an arbitrary non-free minimal action of the dihedral group on a Cantor set into an orbit-equivalent action of an infinite finitely generated periodic group. We show that if the associated Schreier graphs are linearly repetitive, then the group is of intermediate growth. In particular, this gives first examples of simple groups of intermediate growth.

Investors' subjective capital gains expectations are a key element explaining stock price fluctuations. Survey measures of these expectations display excessive optimism (pessimism) at market peaks (troughs). We formally reject the hypothesis that this is compatible with rational expectations. We then incorporate subjective price beliefs with such properties into a standard asset-pricing model with rational agents (internal rationality). The model gives rise to boom-bust cycles that temporarily delink stock prices from fundamentals and quantitatively replicates many asset-pricing moments. In particular, it matches the observed strong positive correlation between the price dividend ratio and survey return expectations, which cannot be matched by rational expectations.

We show that consumption-based asset pricing models with time-separable preferences generate realistic amounts of stock price volatility if one allows for small deviations from rational expectations. Rational investors with subjective beliefs about price behavior optimally learn from past price observations. This imparts momentum and mean reversion into stock prices. The model quantitatively accounts for the volatility of returns, the volatility and persistence of the price-dividend ratio, and the predictability of long-horizon returns. It passes a formal statistical test for the overall fit of a set of moments provided one excludes the equity premium.

Long leaves in terrestrial plants and their submarine counterparts, algal blades, have a typical, saddle-like midsurface and rippled edges. To understand the origin of these morphologies, we dissect leaves and differentially stretch foam ribbons to show that these shapes arise from a simple cause, the elastic relaxation via bending that follows either differential growth (in leaves) or differential stretching past the yield point (in ribbons). We quantify these different modalities in terms of a mathematical model for the shape of an initially flat elastic sheet with lateral gradients in longitudinal growth. By using a combination of scaling concepts, stability analysis, and numerical simulations, we map out the shape space for these growing ribbons and find that as the relative growth strain is increased, a long flat lamina deforms to a saddle shape and/or develops undulations that may lead to strongly localized ripples as the growth strain is localized to the edge of the leaf. Our theory delineates the geometric and growth control parameters that determine the shape space of finite laminae and thus allows for a comparative study of elongated leaf morphology.