Narrow Results

We examine different generalizations of checking stack automata by allowing multiple input heads and multiple stacks, and characterize their computing power in terms of two-way multi-head finite automata and space-bounded Turing machines. For various models, we obtain hierarchies in terms of their computing power. Our characterizations and hierarchies expand or tighten some previously known results. We also discuss some decidability questions and the space/time complexity of the models.

We assume the market price to diffuse in a hierarchical comb of barriers, the heights of which represent the importance of new information entering the market. We find fat tails with the desired exponent for the price change distribution, and effective multifractality for intermediate times.

In this work, we extend the model of Bonabeau et al. in the case of scale-free networks. A sharp transition is observed from an egalitarian to an hierarchical society, with a very low population density threshold. The exact threshold value also depends on the network size. We find that in an hierarchical society the number of individuals with strong winning attitude is much lower than the number of the community members that have a low winning probability.

We reinvestigate the model of Bonabeau et al.¹ of self-organizing social hierarchies by including a distribution of attractive sites. Agents move randomly except in the case where an attractive site is located in its neighborhood. We find that the transition between an egalitarian society at low population density and a hierarchical one at high population density strongly depends on the distribution and percolation of the valuable sites. We also show how agent diffusivity is closely related to social hierarchy.

We study the maintenance of a simplicial grid or complex under changing density requirements. The proposed method works in any fixed dimension and generates grids by projecting cross-sections of a monotone simplicial complex that lives in one dimension higher than the grid. The density of the grid is adapted by locally moving the cross-section up or down along the extra dimension.

This article introduces a systemic theory of phyllotaxis (study of primordial patterns on plants) and updates a mathematical model which is central in the theory. The theory deals with the descriptive and the functional aspects of phyllotaxis, and studies the origins of patterns as well. The article concentrates on the formal aspects of the model and on its explanatory values. The model possesses biological foundations which will not be recalled here. It supposes a principle of optimal design and the representation of phyllotactic patterns with control hierarchies. These hierarchies can be generated with irreducible matrices and L-systems. In the hierarchies, parameters can be identified representing important characteristics of growth that is complexity, stability and rhythm. A formula linking those parameters allows us to calculate the numerical cost of each one of the phyllotactic patterns and to order the costs. The various types of patterns come out, including whorled patterns which are seen as special cases of spiral patterns. The model proposes predictions which can be compared to observations. It predicts the existence of improbable patterns which have been later identified and it possesses explanatory values which have been interestingly put to contribution in difficult problems of pattern recognition in botany. It also possesses mathematical by-products in the theory of growth functions of L-systems, thus related to Perron-Frobenius spectral theory.

We introduce a class of dynamical systems called Higher Order Cellular Automata (HOCA). These are based on ordinary CA, but have a hierarchical, or multi-level, structure and/or dynamics. We present a detailed formalism for HOCA and illustrate the concepts through four examples. Throughout the article we emphasize the principles and ideas behind the construction of HOCA, such that these easily can be applied to other types of dynamical systems. The article also presents new concepts and ideas for describing and studying hierarchial dynamics in general.

Models used in the understanding of complex entities, like organisations, are problematic in several respects. After an introductory discussion of this problem, this paper addresses the problems associated with the boundaries of complex systems, arguing that although boundaries do exist, they have a peculiar nature. Similarly, it is argued that although hierarchies form an important part of the structure of complex systems, they are not clearly defined or "nested" as is often assumed. Hierarchies should also in principle be transformable in a viable system. Finally, the usefulness of network models is investigated. The conclusion is that although network models have a structure similar to that of complex systems, they are subject to the same limitations all models of complexity are faced with. A few implications for our understanding of organisations are mentioned.

An abundant trait of biological protein materials are hierarchical nanostructures, ranging through atomistic, molecular to macroscopic scales. By utilizing the recently developed Hierarchical Bell Model, here we show that the use of hierarchical structures leads to an extended physical dimension in the material design space that resolves the conflict between disparate material properties such as strength and robustness, a limitation faced by many synthetic materials. We report materiomics studies in which we combine a large number of alpha-helical elements in all possible hierarchical combinations and measure their performance in the strength-robustness space while keeping the total material use constant. We find that for a large number of constitutive elements, most random structural combinations of elements (> 98%) lead to either high strength or high robustness, reflecting the so-called banana-curve performance in which strength and robustness are mutually exclusive properties. This banana-curve type behavior is common to most engineered materials. In contrast, for few, very specific types of combinations of the elements in hierarchies (< 2%) it is possible to maintain high strength at high robustness levels. This behavior is reminiscent of naturally observed material performance in biological materials, suggesting that the existence of particular hierarchical structures facilitates a fundamental change of the material performance. The results suggest that biological materials may have developed under evolutionary pressure to yield materials with multiple objectives, such as high strength and high robustness, a trait that can be achieved by utilization of hierarchical structures. Our results indicate that both the formation of hierarchies and the assembly of specific hierarchical structures play a crucial role in achieving these mechanical traits. Our findings may enable the development of self-assembled de novo bioinspired nanomaterials based on peptide and protein building blocks.

This chapter explains how cluster analysis organizes information in applications such as Computer Vision and Pattern Recognition. Information is represented as points in multidimensional feature spaces where each coordinate represents a measurement. Some tools from exploratory data analysis are discussed, with an emphasis on linear projections derived from the covariance matrix. Two types of clustering are reviewed — hierarchical and partitional. Hierarchical clustering leads to nested partitions of the data. SAHN algorithms for hierarchical clustering are defined and some of the common characteristics are explained. Partitional clustering arranges data in separate clusters, as with the K-Means algorithm. The chapter ends with a discussion of validation that centers on external and internal tests of validity and tests for the number of clusters. A bibliography is provided for further reading.

This chapter explains how cluster analysis organizes information in applications such as Computer Vision and Pattern Recognition. Information is represented as points in multidimensional feature spaces where each coordinate represents a measurement. Some tools from exploratory data analysis are discussed, with an emphasis on linear projections derived from the covariance matrix. Two types of clustering are reviewed—hierarchical and partitional. Hierarchical clustering leads to nested partitions of the data. SAHN algorithms for hierarchical clustering are defined and some of the common characteristics are explained. Partitional clustering arranges data in separate clusters, as with the K-Means algorithm. The chapter ends with a discussion of validation that centers on external and internal tests of validity and tests for the number of clusters. A bibliography is provided for further reading.