In this paper, we propose a novel algorithm for a decomposition of 3D binary shapes to rectangular blocks. The aim is to minimize the number of blocks. Theoretically optimal brute-force algorithm is known to be NP-hard and practically infeasible. We introduce its sub-optimal polynomial heuristic approximation, which transforms the decomposition problem onto a graph-theoretical problem. We compare its performance with the state of the art Octree and Delta methods. We show by extensive experiments that the proposed method outperforms the existing ones in terms of the number of blocks on statistically significant level. We also discuss potential applications of the method in image processing.
Arithmetic networks consist of neural, Boolean and fuzzy ones. Supposing the acyclic structure, decomposition of arithmetic network is possible. There are three results of our analysis: node unification, edge unification and network decomposition. We obtain only 14 node types and 4 edge types for realization of a wide class of traditional arithmetic networks from literature. The main result of our work is the splitting of the competitive neurons (nodes) to distance and soft extreme nodes. The side result of analysis is using the group of nodes instead of layer. It enables grouping the nodes of the same type but with the possibility of long interconnections. The main aiin of our work was to realize the system of arithmetic networks in the SQL language on any SQL server. The database realization enables not only saving, watching and editing the network structures and parameters but also studying the response of archived networks. The learning process was not included because of being iterative in general and unrealizable without loops on database server at that time.
We deal with decomposition theorems for modular measures $\mu \colon L\rightarrow G$ defined on a D-lattice with values in a Dedekind complete $\ell $-group. Using the celebrated band decomposition theorem of Riesz in Dedekind complete $\ell $-groups, several decomposition theorems including the Lebesgue decomposition theorem, the Hewitt-Yosida decomposition theorem and the Alexandroff decomposition theorem are derived. Our main result—also based on the band decomposition theorem of Riesz—is the Hammer-Sobczyk decomposition for $\ell $-group-valued modular measures on D-lattices. Recall that D-lattices (or equivalently lattice ordered effect algebras) are a common generalization of orthomodular lattices and of MV-algebras, and therefore of Boolean algebras. If $L$ is an MV-algebra, in particular if $L$ is a Boolean algebra, then the modular measures on $L$ are exactly the finitely additive measures in the usual sense, and thus our results contain results for finitely additive $G$-valued measures defined on Boolean algebras.
Despite the importance of saprophagous macroarthropods as key facilitators of plant litter decomposition within ecosystems and their likely sensitivity to global climate change and land-use change, a lack of ecological data has precluded attempts to explain their distribution patterns in terms of traits. Using an extensive set of large-scale and long-term biological records, the distribution patterns of 33 woodlice (Crustacea: Oniscidea) species in Britain were characterised by their range size (area of occupancy) and aggregation (degree to which occupied squares are clustered across the range). Body size and seven ecological traits were examined as correlates of range size and fill, while controlling for phylogeny and recording intensity, and comparing fine and broad-scale measures of habitat heterogeneity. Species that used a greater diversity of habitats had larger range sizes. Broad categorisation of habitats (by dominant vegetation) alongside other traits was less accurate in predicting range size than fine-scale habitat (microsites where individuals were discovered) data. The latter explained 25% more variance than broad-scale habitat data, highlighting the value of coupling biological recording of species with data on micro-habitat. Habitat use is an important trait in explaining distribution patterns and we conclude that ensuring land cover heterogeneity will favour conservation of saprophagous macro-arthropod diversity., Bethan V. Purse ... [et al.]., and Obsahuje seznam lileratury
In this paper we apply the notion of the product $MV$-algebra in accordance with the definition given by B. Riečan. We investigate the convex embeddability of an $MV$-algebra into a product $MV$-algebra. We found sufficient conditions under which any two direct product decompositions of a product $MV$-algebra have isomorphic refinements.
There are two basic types of artificial neural networks: Multi-Layer Perceptron (MLP) and Radial Basis Function network (RBF). The first type (MLP) consists of one type of neuron, which can be decomposed into a linear and sigmoid part. The second type (RBF) consists of two types of neurons: radial and linear ones. The radial basis function is analyzed and then used for decomposition of RBF network. The resulting Perceptron Radial Basis Function Network (PRBF) consists of two types of neurons: linear and extended sigmoid ones. Any RBF network can be directly converted to a four-layer PRBF network while any MLP network with three layers can be approximated by a five-layer PRBF network. The new PRBF network is then a generalization of MLP and RBF network abilities. Learning strategies are also discussed. The new type of PRBF network and its learning via repeated local optimization is demonstrated on a numerical example together with RBF and MLP for comparison. This paper is organized as follows: Basic properties of MLP and RBF neurons are summarized in the first two chapters. The third chapter includes novel relationship between sigmoidal and radial functions, which is useful for RBF decomposition and generalization. Description of new PRBF network, together with its properties, is subject of the fourth chapter. Numerical experiments with a PRBF and their requests are given in the last chapters.
Let $G$ be a multigraph. The star number ${\mathrm s}(G)$ of $G$ is the minimum number of stars needed to decompose the edges of $G$. The star arboricity ${\mathrm sa}(G)$ of $G$ is the minimum number of star forests needed to decompose the edges of $G$. As usual $\lambda K_n$ denote the $\lambda $-fold complete graph on $n$ vertices (i.e., the multigraph on $n$ vertices such that there are $\lambda $ edges between every pair of vertices). In this paper, we prove that for $n \ge 2$ \[ \begin{aligned} {\mathrm s}(\lambda K_n)&= \left\rbrace \begin{array}{ll}\frac{1}{2}\lambda n&\text{if}\ \lambda \ \text{is even}, \frac{1}{2}(\lambda +1)n-1&\text{if}\ \lambda \ \text{is odd,} \end{array}\right. {\vspace{2.0pt}} {\mathrm sa}(\lambda K_n)&= \left\rbrace \begin{array}{ll}\lceil \frac{1}{2}\lambda n \rceil &\text{if}\ \lambda \ \text{is odd},\ n = 2, 3 \ \text{or}\ \lambda \ \text{is even}, \lceil \frac{1}{2}\lambda n \rceil +1 &\text{if}\ \lambda \ \text{is odd},\ n\ge 4. \end{array}\right. \end{aligned} \qquad \mathrm{(1,2)}\].
While the key role of termites in the decomposition of litter in the tropics has been acknowledged for a long time, much less information exists on their importance in the recycling of dung of primary consumers, especially herbivores. A review of published studies shows that a diverse group of termites (at least 126 species) has been reported to feed on a wide range of mammalian dung (18 species). Predominantly, wood-feeding and polyphagous wood-litter feeding species were found to feed also frequently on dung. Moreover, we found that termites can quickly remove large amounts of mammalian dung, especially in the dry season, when on average about 1/3 of the dung deposited in a given habitat is removed by termites within one month (with the highest rates observed in savannas). No distinctive preference for mammalian dung over other organic food sources was observed for fungus-growing termites (Macrotermitinae), whereas the majority of the non-fungus growing taxa studied prefer dung over other food. As termites bring large quantities of dung below the soil surface, disturb and enrich soils with nutrients, dung feeding by termites appears to be a previously underestimated process important in the functioning of tropical ecosystems.
The purpose of the paper is to present existing and discuss modified optimization models and solution techniques which are suitable for engineering decision-making problems containing random elements with emphasis on two decision stages. The developed aproach is called two-stage stochastic programming and the paper links motivation, applicability, theoretical remarks, transformations, input data generation techniques, and selected decomposition algorithms for generalized class of engineering problems. The considered techniques have been found applicable by the experience of the authors in various areas of engineering problems. They have been applied to engineering design problems involving constraints based on differential equations to achieve reliable solutions. They have served for technological process control e.g. in melting, casting, and sustainable energy production. They have been used for industrial production technologies involving related logistics, as e.g. fixed interval scheduling under uncertainty. The paper originally introduces several recent improvements in the linked parts and it focuses on the unified two-stage stochastic programming approach to engineering problems in general. It utilizes authentic experience and ideas obtained in certain application areas and advises their fruitful utilization for other cases. The paper follows the paper published in 2000 which deals with the applicability of static stochastic programs to engineering design problems. Therefore, it refers to the basic concepts and notation introduced there and reviews only the principal ideas in the beginning. Then. it focuses on motivation of recourse concepts and two decision stages from engineering point of view. The principal models are introduced and selected theoretical features are reviewed. They are also accompanied by the discussion about difficulties caused by real-world cases. Scenario-based approach is detailed as the important one for the solution of engineering problems, discussion in data input generation is added together with model transformation remarks. Robust algorithms suitable for engineering problems involving nonlinearities and integer variable are selected and scenario-based decomposition is preferred. An original experience with using heuristics is shared. Several postprocessing remarks are added at the end of the paper, which is followed by an extensive literature review. and Obsahuje seznam literatury