Linear random knots and their scaling behavior

We present here a nonbiased probabilistic method that allows us to consistently analyze knottedness of linear random walks with up to several hundred noncorrelated steps. The method consists of analyzing the spectrum of knots formed by multiple closures of the same open walk through random points on a sphere enclosing the walk. Knottedness of individual "frozen" configurations of linear chains is therefore defined by a characteristic spectrum of realizable knots. We show that in the great majority of cases this method clearly defines the dominant knot type of a walk, i.e., the strongest component of the spectrum. In such cases, direct end-to-end closure creates a knot that usually coincides with the knot type that dominates the random closure spectrum. Interestingly, in a very small proportion of linear random walks, the knot type is not clearly defined. Such walks can be considered as residing in a border zone of the configuration space of two or more knot types. We also characterize the scaling behavior of linear random knots.

Precision and scaling in morphogen gradient read-out.

Morphogen gradients infer cell fate as a function of cellular position. Experiments in Drosophila embryos have shown that the Bicoid (Bcd) gradient is precise and exhibits some degree of scaling. We present experimental results on the precision of Bcd target genes for embryos with a single, double or quadruple dose of bicoid demonstrating that precision is highest at mid-embryo and position dependent, rather than gene dependent. This confirms that the major contribution to precision is achieved already at the Bcd gradient formation. Modeling this dynamic process, we investigate precision for inter-embryo fluctuations in different parameters affecting gradient formation. Within our modeling framework, the observed precision can only be achieved by a transient Bcd profile. Studying different extensions of our modeling framework reveals that scaling is generally position dependent and decreases toward the posterior pole. Our measurements confirm this trend, indicating almost perfect scaling except for anterior most expression domains, which overcompensate fluctuations in embryo length.

Solid phase crystallization under continuous heating: kinetic and microstructure scaling laws

The kinetics and microstructure of solid-phase crystallization under continuous heating conditions and random distribution of nuclei are analyzed. An Arrhenius temperature dependence is assumed for both nucleation and growth rates. Under these circumstances, the system has a scaling law such that the behavior of the scaled system is independent of the heating rate. Hence, the kinetics and microstructure obtained at different heating rates differ only in time and length scaling factors. Concerning the kinetics, it is shown that the extended volume evolves with time according to αex = [exp(κCt′)]m+1, where t′ is the dimensionless time. This scaled solution not only represents a significant simplification of the system description, it also provides new tools for its analysis. For instance, it has been possible to find an analytical dependence of the final average grain size on kinetic parameters. Concerning the microstructure, the existence of a length scaling factor has allowed the grain-size distribution to be numerically calculated as a function of the kinetic parameters

Emergence of Swiss metropole and scaling properties of urban clusters

Defining the limits of an urban agglomeration is essential both for fundamental and applied studies in quantitative and theoretical geography. A simple and consistent way for defining such urban clusters is important for performing different statistical analysis and comparisons. Traditionally, agglomerations are defined using a rather qualitative approach based on various statistical measures. This definition varies generally from one country to another, and the data taken into account are different. In this paper, we explore the use of the City Clustering Algorithm (CCA) for the agglomeration definition in Switzerland. This algorithm provides a systemic and easy way to define an urban area based only on population data. The CCA allows the specification of the spatial resolution for defining the urban clusters. The results from different resolutions are compared and analysed, and the effect of filtering the data investigated. Different scales and parameters allow highlighting different phenomena. The study of Zipf's law using the visual rank-size rule shows that it is valid only for some specific urban clusters, inside a narrow range of the spatial resolution of the CCA. The scale where emergence of one main cluster occurs can also be found in the analysis using Zipf's law. The study of the urban clusters at different scales using the lacunarity measure - a complementary measure to the fractal dimension - allows to highlight the change of scale at a given range.

Entropic transport: kinetics, scaling, and control mechanisms

We show that transport in the presence of entropic barriers exhibits peculiar characteristics which makes it distinctly different from that occurring through energy barriers. The constrained dynamics yields a scaling regime for the particle current and the diffusion coefficient in terms of the ratio between the work done to the particles and available thermal energy. This interesting property, genuine to the entropic nature of the barriers, can be utilized to effectively control transport through quasi-one-dimensional structures in which irregularities or tortuosity of the boundaries cause entropic effects. The accuracy of the kinetic description has been corroborated by simulations. Applications to different dynamic situations involving entropic barriers are outlined.

Problems of allometric scaling analysis: examples from mammalian reproductive biology.

Biological scaling analyses employing the widely used bivariate allometric model are beset by at least four interacting problems: (1) choice of an appropriate best-fit line with due attention to the influence of outliers; (2) objective recognition of divergent subsets in the data (allometric grades); (3) potential restrictions on statistical independence resulting from phylogenetic inertia; and (4) the need for extreme caution in inferring causation from correlation. A new non-parametric line-fitting technique has been developed that eliminates requirements for normality of distribution, greatly reduces the influence of outliers and permits objective recognition of grade shifts in substantial datasets. This technique is applied in scaling analyses of mammalian gestation periods and of neonatal body mass in primates. These analyses feed into a re-examination, conducted with partial correlation analysis, of the maternal energy hypothesis relating to mammalian brain evolution, which suggests links between body size and brain size in neonates and adults, gestation period and basal metabolic rate. Much has been made of the potential problem of phylogenetic inertia as a confounding factor in scaling analyses. However, this problem may be less severe than suspected earlier because nested analyses of variance conducted on residual variation (rather than on raw values) reveals that there is considerable variance at low taxonomic levels. In fact, limited divergence in body size between closely related species is one of the prime examples of phylogenetic inertia. One common approach to eliminating perceived problems of phylogenetic inertia in allometric analyses has been calculation of 'independent contrast values'. It is demonstrated that the reasoning behind this approach is flawed in several ways. Calculation of contrast values for closely related species of similar body size is, in fact, highly questionable, particularly when there are major deviations from the best-fit line for the scaling relationship under scrutiny.

Scaling behavior of random knots.

Using numerical simulations we investigate how overall dimensions of random knots scale with their length. We demonstrate that when closed non-self-avoiding random trajectories are divided into groups consisting of individual knot types, then each such group shows the scaling exponent of approximately 0.588 that is typical for self-avoiding walks. However, when all generated knots are grouped together, their scaling exponent becomes equal to 0.5 (as in non-self-avoiding random walks). We explain here this apparent paradox. We introduce the notion of the equilibrium length of individual types of knots and show its correlation with the length of ideal geometric representations of knots. We also demonstrate that overall dimensions of random knots with a given chain length follow the same order as dimensions of ideal geometric representations of knots.

Nonlinear principal and canonical directions from continuous extensions of multidimensional scaling

A continuous random variable is expanded as a sum of a sequence of uncorrelated random variables. These variables are principal dimensions in continuous scaling on a distance function, as an extension of classic scaling on a distance matrix. For a particular distance, these dimensions are principal components. Then some properties are studied and an inequality is obtained. Diagonal expansions are considered from the same continuous scaling point of view, by means of the chi-square distance. The geometric dimension of a bivariate distribution is defined and illustrated with copulas. It is shown that the dimension can have the power of continuum.

On convergence of transforms based on parabolic scaling

This thesis studies properties of transforms based on parabolic scaling, like Curvelet-, Contourlet-, Shearlet- and Hart-Smith-transform. Essentially, two di erent questions are considered: How these transforms can characterize H older regularity and how non-linear approximation of a piecewise smooth function converges. In study of Hölder regularities, several theorems that relate regularity of a function f : R2 → R to decay properties of its transform are presented. Of particular interest is the case where a function has lower regularity along some line segment than elsewhere. Theorems that give estimates for direction and location of this line, and regularity of the function are presented. Numerical demonstrations suggest also that similar theorems would hold for more general shape of segment of low regularity. Theorems related to uniform and pointwise Hölder regularity are presented as well. Although none of the theorems presented give full characterization of regularity, the su cient and necessary conditions are very similar. Another theme of the thesis is the study of convergence of non-linear M ─term approximation of functions that have discontinuous on some curves and otherwise are smooth. With particular smoothness assumptions, it is well known that squared L2 approximation error is O(M-2(logM)3) for curvelet, shearlet or contourlet bases. Here it is shown that assuming higher smoothness properties, the log-factor can be removed, even if the function still is discontinuous.

Hipsometric relationship modeling using data sampled in tree scaling and inventory plots

This work evaluated eight hypsometric models to represent tree height-diameter relationship, using data obtained from the scaling of 118 trees and 25 inventory plots. Residue graphic analysis and percent deviation mean criteria, qui-square test precision, residual standard error between real and estimated heights and the graybill f test were adopted. The identity of the hypsometric models was also verified by applying the F(Ho) test on the plot data grouped to the scaling data. It was concluded that better accuracy can be obtained by using the model prodan, with h and d1,3 data measured in 10 trees by plots grouped into these scaling data measurements of even-aged forest stands.

Challenges in scaling agile software development in offshoring environment

Corporate decision to scale Agile Software development methodologies in offshoring environment has been obstructed due to possible challenges in scaling agile as agile methodologies are regarded to be suitable for small project and co-located team only. Although model such as Agile Scaling Model (ASM) has been developed for scaling Agile with different factors, inabilities of companies to figure out challenges and addressing them lead to failure of project rather than gaining the benefits of using agile methodologies. This failure can be avoided, when scaling agile in IT offshoring environment, by determining key challenges associated in scaling agile in IT offshoring environment and then preparing strategies for addressing those key challenges. These key challenges in scaling agile with IT offshoring environment can be determined by studying issues related with Offshoring and Agile individually and also considering the positive impact of agile methodology in offshoring environment. Then, possible strategies to tackle these key challenges are developed according to the nature of individual challenges and utilizing the benefits of different agile methodologies to address individual situation. Thus, in this thesis, we proposed strategy of using hybrid agile method, which is increasing trend due to adaptive nature of Agile. Determination of the key challenges and possible strategies for tackling those challenges are supported with the survey conducted in the researched organization.

Scaling up stepwise feature introduction to construction of large software systems

Developing software is a difficult and error-prone activity. Furthermore, the complexity of modern computer applications is significant. Hence,an organised approach to software construction is crucial. Stepwise Feature Introduction – created by R.-J. Back – is a development paradigm, in which software is constructed by adding functionality in small increments. The resulting code has an organised, layered structure and can be easily reused. Moreover, the interaction with the users of the software and the correctness concerns are essential elements of the development process, contributing to high quality and functionality of the final product. The paradigm of Stepwise Feature Introduction has been successfully applied in an academic environment, to a number of small-scale developments. The thesis examines the paradigm and its suitability to construction of large and complex software systems by focusing on the development of two software systems of significant complexity. Throughout the thesis we propose a number of improvements and modifications that should be applied to the paradigm when developing or reengineering large and complex software systems. The discussion in the thesis covers various aspects of software development that relate to Stepwise Feature Introduction. More specifically, we evaluate the paradigm based on the common practices of object-oriented programming and design and agile development methodologies. We also outline the strategy to testing systems built with the paradigm of Stepwise Feature Introduction.