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A length n word is (palindromic) rich if it contains the maximum possible number, which is n, of distinct non-empty palindromic factors. We prove both necessary and sufficient conditions for richness in terms of run-length encodings of words. Relating sufficient conditions to integer partitions, we prove a lower bound of order C n , where C ≈ 37.6 , on the growth function of the language of binary rich words. From experimental study we suggest that this growth function actually grows more slowly than n n , which makes our lower bound quite reasonable.

Growth functions see widespread application in animal production industries. These growth functions allow the prediction of body weight, or size, as a function of time. The Gompertz, logistic and von Bertalanffy see widespread application in the agricultural industry given their ability to describe the growth of terrestrial animals. Aquatic organisms, in contrast to terrestrial, display the ability to display indeterminate growth wherein growth continues past sexual maturation, in addition to growth being highly influenced by water temperature. Therefore, traditional growth equations are of limited use when applied to aquatic organisms. The purpose of this thesis was to advance the quantitative description of patterns of growth exhibited by aquatic organisms with reference to aquaculture and nutrition. This thesis proposes seven growth functions that were fitted to growth profiles of aquatic organisms exhibiting wide ranges of growth patterns using both empirical and mechanistically-inspired approaches. Growth trajectories of Pacific Whiteleg shrimp (Litopenaeus vannamei) were analyzed using two empirical models, specific growth rate (SGR) and Thermal-Unit Growth Coefficient (TGC). The indeterminate nature of growth exhibited by aquatic organisms was successfully described using equations akin to Michaelis-Menten and Mitscherlich. These equations are characterized by a lack of a point of inflexion and continuous growth, reflecting the true biological nature of indeterminate growth. The effect of water temperature on growth was described through modifying two elementary functions, representing exponential and asymptotic growth, using a sinusoidal function to account for the effect of fluctuating water temperature on growth rate. Finally, growth profiles of a bacterium were described through attenuating potential growth, represented by a logistic equation, using a dampening function. Dampening effects were represented by either a rectangular hyperbola, or a simple exponential, and represent the effect of a changes in environment on growth rate of the bacterium. In addition to providing researchers with models that have the ability to describe various patterns of growth exhibited by aquatic organisms, this thesis also provides insight into the modelling process. The importance of understanding model assumptions, data structure, strengths and weaknesses of empirical and mechanistic approaches, and the advantages of simple algebraic solutions are stressed. The Canadian Research Chairs program Grant#045867 (Natural Sciences and Engineering Research Council, Ottawa)

This work has been supported by the Ministerio de Economía y Competitividad grants MTM2014-56948-C2-2-P and MTM2017-84446-C2-2-R. Programa Oficial de Doctorado en Ingeniería Matemática Presidente: Fernando Varas Mérida.- Secretario: Manuel Carretero Cerrajero.- Vocal: Elena Cebrián de Barrio

Suppose $X$ and $Y$ are finite complexes, with $Y$ simply connected. Gromov conjectured that the number of mapping classes in $[X,Y]$ which can be realized by $L$-Lipschitz maps grows asymptotically as $L^\alpha$, where $\alpha$ is an integer determined by the rational homotopy type of $Y$ and the rational cohomology of $X$. This conjecture was disproved in a recent paper of the author and Weinberger; we gave an example where the `predicted' growth is $L^8$ but the true growth is $L^8\log L$. Here we show, via a different mechanism, that the universe of possible such growth functions is quite large. In particular, for every rational number $r \geq 4$, there is a pair $X,Y$ for which the growth of $[X,Y]$ is essentially $L^r$., Comment: 12 pages, 2 figures. Version accepted to J. Topol. Anal

Rastne funkcije so nepogrešljiv pripomoček pri sestavi donosnih tablic in postavitvi različnih modelov gospodarjenja. Rastna funkcija mora biti prilagodljiva,to pomeni, da mora kar se da najboljše ponazarjati dejansko rast sestojev, istočasno pa mora biti v takšni obliki, da vrednosti njenih parametrov neposredno podajajo karakteristične točke rasti sestoja in rastišča. V prispevku je podana tudi nova oblika rastne funkcije, ki dobro izpolnjuje pogoje, ki jih mora imeti tovrstna funkcija. Growth functions are an indispensable resource for making tablets and setting different models of management. The growth function has to be adaptable which means that it has to present as best as possible the actual growth of stands and at the same time to be in such a form, that the values of its parametres directly present the characteristical points of stand and site growth. The new form of growth funstion which fulfills well the conditions which a function of this kind has to have, is also presented in the paper.

13 páginas.

Cover crops are plants that are integrated in the crop rotation between two cash crops. The main objectives of cover cropping are organic matter input, mitigation of nitrate leaching and reduction of soil erosion. These benefits will only be achieved efficiently if the selected cover crop species are adapted to local environmental conditions and appropriate for the defined agro-ecological target. Therefore, a main limitation in cover cropping is the lack of a comprehensive species description. An improved cover crop characterization could be achieved with quantitative parameters derived from growth functions. Here, we show the use of this approach to assess plant traits relevant for erosion control by cover cropping. An experiment with four cover crop species (phacelia, vetch, rye and mustard) was performed over two years at a semi-arid site in Eastern Austria. Canopy cover was measured four times over the vegetation period. Root length density measurements were made to 40 cm soil depth before winter. Canopy dynamics were characterized by parameters from the asymptotic Gompertz function and from an extended logistic model that includes a parameter for decay after maximum coverage. Our results show that vetch had the lowest early vigor after dry conditions at sowing, with +45% longer time to attain maximum growth rate (parameter tmax) than the other species. Drought during the later autumn growing period led to the highest reduction in maximum canopy cover (parameter ymax) for phacelia (-41%). The rooting pattern was assessed by parameters from the exponential distribution function of Gerwitz and Page. The most intense rooting near the soil surface (parameter L0) was found for phacelia (9.7 cm cm −3 ). Vetch had the lowest L0 (4.6 cm cm −3 ) but highest root allocation to deeper soil layers. Mustard combined high average values in ymax (76%) and L0 (6.3 cm cm −3 ) with a stable growth over both years. The potential strengths of phacelia and vetch were more dependent on the particular year. Rye showed a stably high L0 (8.6 cm cm −3 ), but had only a low average value of ymax (55.1%). The quantitative parameter sets we derived for plant traits required for erosion control improved cover crop comparison and analysis of their local adaptation. Based on this extended species description our approach allows a better evaluation of cover crops and can be used for the optimization of management and decision support. cover crops / growth functions / species description / rooting pattern / rainfall distribution

This note addresses some questions that arise in the series of works by Kyoji Saito on the growth functions of graphs. We study "hyperbolike" graphs, which include Cayley graphs of hyperbolic groups. We generalize some well-known results on hyperbolic groups to the hyperbolike setting, including rationality of generating functions, and sharp estimates on the growth rate of vertices. We then apply these results to confirm a conjecture of Saito on the "opposite series", which was originally posed for hyperbolic groups., 12 pages

The paper 1 of this thesis is not available in Munin. Paper 1: Thyholdt, S. B. (2014) The Importance of Temperature in Farmed Salmon Growth: Regional Growth Functions for Norwegian Farmed Salmon. Available in Aquaculture Economics & Management 18(2):189–204. Submitted manuscript available in Munin at http://hdl.handle.net/10037/7184 Price and quantity numbers, which we are observing in a market place, occur because of an interaction between supply and demand. An understanding of what drives supply and demand is therefore important in order to understand the market in itself. This dissertation focuses on determining the impact of exogenous factors on salmon biomass growth and how producers respond to price changes. Furthermore, we determine the total demand growth and the factors affecting demand growth in the global salmon market. The first paper determines the importance of temperature in the growth of Norwegian farmed salmon for three different regions. The results show that sea temperature is a critical factor to explain growth. Periods with higher sea temperatures lead to faster growth in the North and Central regions, while leading to slower growth in the South. In the second paper, salmon farmers’ response to price changes are estimated for three different regions in Norway. We find that the salmon producers are responding to price changes in the long run, while there are limited responses to price changes in the short run. The long-run response differs from region to region, and the own-price supply elasticity is 1.22 for the Northern region, 1.39 for the Central region, and 0.58 for the Southern region, with a national average of 1.06. The third paper determines the magnitude of the shifts in annual demand across all major salmon importing regions in the world. Results indicate that demand varies considerably between years and regions and does not appear to follow a smooth trend, which is usually assumed in empirical analysis. The fourth paper extends the procedure of the third. We disentangle the impacts from income growth and price changes in substitute products from total demand shift. The remaining residual shift in demand is due to other unknown or omitted factors. Results indicate that demand shifts due to unknown factors account for a large portion of total demand growth in all regions, and this residual growth is not smooth in any region. The results demonstrate that any demand analysis focusing only on relative prices, income, and a trend variable will not appropriately account for the large variation in salmon demand in any region.

Este trabalho foi realizado com o objetivo de estudar o desempenho do Pinus elliottii Engelm. e Pinus taeda L. em áreas arenizadas e degradadas por ação antrópica, na região da fronteira oeste do estado do Rio Grande do Sul. Em povoamentos, foram selecionadas árvores médias, que foram abatidas e seccionadas pelo método de Smalian, a fim de obter discos de madeira para a análise dendrocronológica, para a obtenção do diâmetro por idade. O crescimento em diâmetro, quando comparado entre espécies, apresentou tendências diferentes de níveis de desenvolvimento no tempo. O uso de variáveis dummy no modelo de crescimento permitiu definir uma equação única para estimar o diâmetro em função da idade para ambas as espécies, considerando os níveis de degradação do solo médio e baixo, como variáveis necessárias para estimar o crescimento destas espécies nestes tipos de solos arenizados e degradados. This research aims to study the performance of Pinus elliottii Engelm. and Pinus taeda L. in the arenizated and degraded areas by antropic action in the western of Rio Grande do Sul state. In stands were selected medium trees, which were harvested and sectioned by Smalian method to obtain wood discs for dendro chronological analysis to determine the diameter by age. The diameter growth compared between species showed different levels of development over time. The use of dummy variables in the growth model enables a single equation to estimate the diameter as a function of age for both species, considering the medium and low levels of soil degradation, as variables necessary to estimate the growth of these species in these types of arenizated degraded soils.

International audience; We present a new framework for spatiotemporal analysis of parameterized functions attributed by properties of 4D longitudinal image data. Our driving application is the measurement of temporal change in white matter diffusivity of fiber tracts. A smooth temporal modeling of change from a discrete-time set of functions is obtained with an extension of the logistic growth model to time-dependent spline functions, capturing growth with only a few descriptive parameters. An unbiased template baseline function is also jointly estimated. Solution is demonstrated via energy minimization with an extension to simultaneous modeling of trajectories for multiple subjects. The new framework is validated with synthetic data and applied to longitudinal DTI from 15 infants. Interpretation of estimated model growth parameters is facilitated by visualization in the original coordinate space of fiber tracts.

Se propone un nuevo conjunto de curvas de índice de sitio para clasificar los terrenos ocupados con plantaciones coetáneas de Ciprés (Cupressus lusitánica Mill.) en la Región Central de Costa Rica. Se utilizó una muestra compuesta por 21 árboles, talados y seccionados en un estudio anterior y los promedios de altura dominante de 44 parcelas permanentes de muestreo, pertenecientes a cuatro ensayos de aclareo y rendimiento. A través del análisis fustal se generó información equivalente a un total de 373 árboles, con edades comprendidas entre 3 y 31 años de edad, cuyos diámetros con corteza (a 1,30 m) oscilan entre 7,88 cm y 47,80 cm y cuyas alturas totales van desde 4,59 m hasta 34,20 m. Las parcelas permanentes han sido medidas y conservadas durante 26 años, esto es desde los 8 hasta los 34 años de edad. Tanto los árboles como las parcelas provienen de la misma región comprendida en el estudio. La muestra total equivale a 1.104 pares de datos de altura dominante-edad, con la cual se ajustaron todos los modelos. Para escoger la ecuación más adecuada se probó un total de ocho ecuaciones lineales y no lineales (pero linealizables) y 12 modelos no lineales. La ecuación seleccionada fue la de Prodan (1.951), ya que presentó un buen ajuste estadístico y mostró un buen comportamiento cuando se graficó contra los valores observados; la ecuación tiene los siguientes estadísticos: r = 0,95; R2adj = 91,03; MSE = 7,432 y SEE = 2,726. A new set of site index curves is proposed to classify the land occupied with even-aged plantations of Mexican Cypress (Cupressus lusitanica Mill.) in the Central Region of Costa Rica. Sample used were 21 trees, cut down and sectioned in a previous study, and the averages of 44 permanent sampling plots belonging to four thinning and yield trials. Through the stem analysis it was generated information equivalent to a total of 373 trees, ranging 3 to 31 years of age, where diameters over bark (a.b.h.) ranged from 7,88 cm to 47,80 cm and total heights ranged from 4,59 m to 34,20 m. Permanent plots have been measured and maintained during 26 years, that is since the age of 8 until the age of 34. Both trees and plots came from the same region comprised in the study. The total sample is equivalent to 1104 pairs of dominant height-age data, used for adjust of models. In order to choose the best model, a total of eight equations linear and non-linear (but linealizable) and 12 non-linear models have been tested. The equation selected was that of Prodan (1951), since it presented a good statistical fit and showed a good graphical behavior when graphed against the observed values. This equation presented the following statistics: r = 0,95; R2adj = 91,03; MSE = 7,432 and SEE = 2,726. 7-26 fmora@una.ac.cr moraf2005@yahoo.com victor.meza.picado@una.cr orlando.chinchilla.mora@una.cr Semestral

Bacterial growth models are commonly used for the prediction of microbial safety and the shelf life of perishable foods. Growth is affected by several environmental factors such as temperature, acidity level and salt concentration. In this study, we develop two models to describe bacterial growth for multiple populations under both equal and different environmental conditions. First, a semi-parametric model based on the Gompertz equation is proposed. Assuming that the parameters of the Gompertz equation may vary in relation to the running conditions under which the experiment is performed, we use feedforward neural networks to model the influence of these environmental factors on the growth parameters. Second, we propose a more general model which does not assume any underlying parametric form for the growth function. Thus, we consider a neural network as a primary growth model which includes the influencing environmental factors as inputs to the network. One of the main disadvantages of neural networks models is that they are often very difficult to tune, which complicates fitting procedures. Here, we show that a simple Bayesian approach to fitting these models can be implemented via the software package WinBugs. Our approach is illustrated using real experimental Listeria monocytogenes growth data., Comment: Published in at http://dx.doi.org/10.1214/14-AOAS720 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org)

In the water supply of the city of Varazdin for many years there was a problem of too high nitrate concentrations in drinking water . The problem was solved in a way that well field where the nitrate concentration in groundwater was greatest was closed. At the same time new well fields were opened, so that today the wider area of the city of Varazdin groundwater pumped is in two locations: Vinokovščak and Bartolovec .In both well fields groundwater is pumped from alluvial strata of Quaternary age that are constructed mainly of sand and gravel . However , although the hydro geological conditions at both sites are equal, at the well field of Vinokovščak the nitrate concentrations were almost constantly increasing over the last ten years and have exceeded the maximum concentration recommended by the EU nitrate directive . Here we are modeling the annual average concentration of nitrate in groundwater at the well field Vinokovščak by polynomial functions of the first, second and third degree and by few nonlinear growth functions: general growth model, logistic function, Gompertz function and Richardson function. Since there are great oscilations in time series of nitrate concentrations, the time series is smoothed by method of moving average. Our hypothesis was that time series is going to be well adjusted to an increasing function that has asymptotic behaviour.

Bacterial growth models are commonly used for the prediction of microbial safety and the shelf life of perishable foods. Growth is affected by several environmental factors such as temperature, acidity level and salt concentration. In this study, we develop two models to describe bacterial growth for multiple populations under both equal and different environmental conditions. Firstly, a semi-parametric model based on the Gompertz equation is proposed. Assuming that the parameters of the Gompertz equation may vary in relation to the running conditions under which the experiment is performed, we use feed forward neural networks to model the influence of these environmental factors on the growth parameters. Secondly, we propose a more general model which does not assume any underlying parametric form for the growth function. Thus, we consider a neural network as a primary growth model which includes the influencing environmental factors as inputs to the network. One of the main disadvantages of neural networks models is that they are often very difficult to tune which complicates fitting procedures. Here, we show that a simple, Bayesian approach to fitting these models can be implemented via the software package WinBugs. Our approach is illustrated using real experimental Listeria Monocytogenes growth data.

Bacterial growth models are commonly used for the prediction of microbial safety and the shelf life of perishable foods. Growth is affected by several environmental factors such as temperature, acidity level and salt concentration. In this study, we develop two models to describe bacterial growth for multiple populations under both equal and different environmental conditions. Firstly, a semi-parametric model based on the Gompertz equation is proposed. Assuming that the parameters of the Gompertz equation may vary in relation to the running conditions under which the experiment is performed, we use feed forward neural networks to model the influence of these environmental factors on the growth parameters. Secondly, we propose a more general model which does not assume any underlying parametric form for the growth function. Thus, we consider a neural network as a primary growth model which includes the influencing environmental factors as inputs to the network. One of the main disadvantages of neural networks models is that they are often very difficult to tune which complicates fitting procedures. Here, we show that a simple, Bayesian approach to fitting these models can be implemented via the software package WinBugs. Our approach is illustrated using real experimental Listeria Monocytogenes growth data.

Context-free languages of sub-exponential growth were studied. The growth function was defined as the function whose value at each non-negative integer was the number of words of length n in a fixed formal language. The definition of a bounded language, which is a subset for some words, was also used in the analysis. Results showed that context-free languages of intermediate growth were nonexistent.

WOS:000228464800010 This study has focused on the comparison of Richards, Gompertz and Logistic growth models (functions) for describing the growth characteristics of three meat-type lines of Japanese quail. The live body weight data of wild-type, doted-white and extended-brown quail lines over time were collected and fitted to the three non-linear equations. The prediction performance of the models was evaluated by statistical error tests: mean percentage error (MPE), mean bias error (MBE), root mean square error (RMSE), and confidence interval test (CIT) using the data of three out bred lines of Japanese quails (dotted white, extended brown and wild in plumage colour). The prediction performance of the growth functions for the quail growth curves depends on the line and sex of quails as shown by the results of statistical error tests. In general, Richards function predicted the weight of quails better than other two growth functions. Commonly used statistical error tests (MPE, MBE and RMSE) may not reflect the prediction performance of growth models as accurately as confidence interval test. Confidence interval tests generated likeness percentage values between 82.35 and 100% for Richards growth function.

Funções de crescimento não-lineares foram ajustados a dados de peso-idade de 40 cordeiros das raças Santa Inês e Bergamácia. Pelos testes de Hartley e de Bartlett, verificou-se que os dados apresentavam heterogeneidade de variâncias; em função disso, ajustaram-se as funções de crescimento pelo método dos quadrados mínimos ponderado pelo inverso da variância dos pesos a cada pesagem utilizando a opção WEIGTH do PROC MODEL (SAS INSTITUTE, 1996). As funções de crescimento foram comparadas pela interpretação biológica dos parâmetros e pelos indicadores de qualidade do ajuste (coeficiente de determinação ajustado, quadrado médio do resíduo e teste de Durbin-Watson). As funções de von Bertalanffy e Gompertz apresentaram a melhor qualidade de ajuste, ao passo que as funções de Richards, Logística e Brody não se mostraram adequadas para descrever o crescimento dos animais por apresentarem estimativas não condizentes com a realidade. Non linear growth functions were fitted to weight-age data of 40 Santa Inês and Bergamacy lambs. The Hartley and Bartlett tests indicated that the data presented heteroscedastic variance, so the growth functions were fitted through weighted minimum square method by the inverse variance weight in each sampler using the WEIGHT option in PROC MODEL (SAS INSTITUTE, 1996). The functions were compared using the biological interpretation of the parameters and the quality indicators of fit (adjusted determination coefficient, mean square error and Durbin-Watson test). The von Bertalanffy and Gompertz functions provided the best fittings, whereas Richards, Logistic and Brody functions turned out not to be suitable for describing growth behavior, became estimates based on them do not agree with observation.

In this paper, a modeling of the mean value of the length of the red deer discarded antlers from region of Veliki Jastrebac is done. The modeling is based on the measurement done in region of Veliki Jastrebac and on data from region of Baranja and North-Western Bačka. The developed general model of the considered growth processes are based on data from region of Baranja and North- Western Bačka. The mentioned general models are developed using both the known maximum and mean values of the length of red deer antler. The new measured data from region of Veliki Jastrebac corresponds to 3, 4, 5 and 6 age of red deer. U radu je prikazano modeliranje srednjih vrednosti rasta dužine grana odbačenih parogova jelena iz regiona Veliki Jastrebac. Modeliranje je bazirano na merenjima koja su obavljena u regionu Veliki Jastrebac kao i na podacima iz regiona Baranje i severozapadne Bačke. Podaci koji važe za region Baranje i severozapadne Bačke iskorišćeni su za definisanje odgovarajućih opštih modela posmatranih procesa rasta. Pomenuti opšti modeli dobijeni su na osnovu srednjih i maksimalnih vrednosti dužine grana rogova jelena. Novi podaci odnosno merenja koja su obavljena u regionu Veliki Jastrebac obuhvataju trogodišnje, četvorogodišnje, petogodišnje i šestogodišnje jelene iz pomenutog regiona.

We start with finitely many1's and possibly some0's in between. Then each entry in the other rows is obtained from the Base2sum of the two numbers diagonally above it in the preceding row. We may formulate the game as follows: Defined1,jrecursively for1, a non-negative integer, andjan arbitrary integer by the rules:d0,j={1 for j=0,k (I)0 or 1 for 0k (II)di+1,j=di,j+1(mod2) for i≥0. (III)Now, if we interpret the number of1's in rowias the coefficientaiof a formal power series, then we obtain a growth function,f(x)=∑i=0∞aixi. It is interesting that there are cases for which this growth function factors into an infinite product of polynomials. Furthermore, we shall show that this power series never represents a rational function.

The phenomenon known as Watson–Crick complementarity is basic both in the experiments and theory of DNA computing. While the massive parallelism of DNA strands makes exhaustive searches possible, complementarity constitutes a powerful computational tool. It is also very fruitful to view complementarity as a language-theoretic operation: “bad” words obtained through a generative process are replaced by their complementary ones. This idea seems particularly suitable for Lindenmayer systems. D0L systems augmented with a specific complementarity transition, Watson–Crick D0L systems, have turned out to be a most interesting model and have already been extensively studied. A language is generated by a Watson–Crick D0L system as a sequence of words. Consequently, the systems can be applied also to compute functions in a natural way. In the present paper, attention is focused on uni-transitional systems, where at most one complementarity transition takes place in the generated sequence. In spite of their seeming simplicity, uni-transitional systems represent a vast extension of ordinary D0L systems. This becomes apparent in their capacity of defining functions. Quite remarkably, all basic decision problems for uni-transitional systems are algorithmically equivalent among themselves, as well as equivalent to a celebrated open problem. We investigate also a simpler case of systems with regular triggers, as well as pose some open problems.