Parametrization of translational surfaces

The algebraic translational surface is a typical modeling surface in computer aided design and architecture industry. In this paper, we give a necessary and sufficient condition for that algebraic surface having a standard parametric representation and our proof is constructive. If the given algebraic surface is translational, then we can compute a standard parametric representation for the surface

Rampant Arch and Its Optimum Geometrical Generation

Gothic art was developed in western Europe from the second half of the 12th century to the end of the 15th century. The most characteristic Gothic building is the cathedral. Gothic architecture uses well-carved stone ashlars, and its essential elements include the arch. The thrust is transferred by means of external arches (flying buttresses) to external buttresses that end in pinnacles, which accentuates the verticality. The evolution of the flying buttresses should not only be considered as an aesthetic consideration, but also from a constructive point of view as an element of transmission of forces or loads. Thus, one evolves from a beam-type buttress to a simple arch, and finally to a rampant arch. In this work, we study the geometry of the rampant arch to determine which is the optimum from the constructive point of view. The optimum rampant arch obtained is the one with the common tangent to the two arches parallel to the slope line. A computer program was created to determine this optimal rampant arch by means of a numerical or graphical input. It was applied to several well-known and representative cases of Gothic art in France (church of Saint Urbain de Troyes) and Spain (Cathedral of Palma de Mallorca), establishing if they were designs of optimal rampant arches or not

Parallel growing and training of neural networks using output parallelism

In order to find an appropriate architecture for a large-scale real-world application automatically and efficiently, a natural method is to divide the original problem into a set of sub-problems. In this paper, we propose a simple neural network task decomposition method based on output parallelism. By using this method, a problem can be divided flexibly into several sub-problems as chosen, each of which is composed of the whole input vector and a fraction of the output vector. Each module (for one sub-problem) is responsible for producing a fraction of the output vector of the original problem. The hidden structure for the original problem’s output units are decoupled. These modules can be grown and trained in parallel on parallel processing elements. Incorporated with a constructive learning algorithm, our method does not require excessive computation and any prior knowledge concerning decomposition. The feasibility of output parallelism is analyzed and proved. Some benchmarks are implemented to test the validity of this method. Their results show that this method can reduce computational time, increase learning speed and improve generalization accuracy for both classification and regression problems

Parameterization of rational translational surfaces

A rational translational surface is a typical modeling surface used in computer-aided design and the architecture industry. In this study, we determine whether a given algebraic surface implicitly defined as V is a rational translational surface or not. This problem is reduced to finding the rational parameterizations of two space curves. More important, our discussions are constructive, and thus if V is translational, we provide a parametric representation of V of the form P(t1,t2)=P1(t1)+P2(t2).Ministerio de Ciencia, Innovacion y Universidade

Evolutionary cellular configurations for designing feed-forward neural networks architectures

Proceeding of: 6th International Work-Conference on Artificial and Natural Neural Networks, IWANN 2001 Granada, Spain, June 13–15, 2001In the recent years, the interest to develop automatic methods to determine appropriate architectures of feed-forward neural networks has increased. Most of the methods are based on evolutionary computation paradigms. Some of the designed methods are based on direct representations of the parameters of the network. These representations do not allow scalability, so to represent large architectures, very large structures are required. An alternative more interesting are the indirect schemes. They codify a compact representation of the neural network. In this work, an indirect constructive encoding scheme is presented. This scheme is based on cellular automata representations in order to increase the scalability of the method

Combining constructive and equational geometric constraint solving techniques

In the past few years, there has been a strong trend towards developing parametric, computer aided design systems based on geometric constraint solving. An efective way to capture the design intent in these systems is to define relationships between geometric and technological variables. In general, geometric constraint solving including functional relationships requires a general approach and appropiate techniques toachieve the expected functional capabilities. This work reports on a hybrid method which combines two geometric constraint solving techniques: Constructive and equational. The hybrid solver has the capability of managing functional relationships between dimension variables and variables representing conditions external to the geometric problem. The hybrid solver is described as a rewriting system and is shown to be correct.Postprint (published version

Non-Direct Encoding Method Based on Cellular Automata to Design Neural Network Architectures

Architecture design is a fundamental step in the successful application of Feed forward Neural Networks. In most cases a large number of neural networks architectures suitable to solve a problem exist and the architecture design is, unfortunately, still a human expert’s job. It depends heavily on the expert and on a tedious trial-and-error process. In the last years, many works have been focused on automatic resolution of the design of neural network architectures. Most of the methods are based on evolutionary computation paradigms. Some of the designed methods are based on direct representations of the parameters of the network. These representations do not allow scalability; thus, for representing large architectures very large structures are required. More interesting alternatives are represented by indirect schemes. They codify a compact representation of the neural network. In this work, an indirect constructive encoding scheme is proposed. This scheme is based on cellular automata representations and is inspired by the idea that only a few seeds for the initial configuration of a cellular automaton can produce a wide variety of feed forward neural networks architectures. The cellular approach is experimentally validated in different domains and compared with a direct codification scheme.Publicad

Neural Network architectures design by Cellular Automata evolution

4th Conference of Systemics Cybernetics and Informatics. Orlando, 23-26 July 2000The design of the architecture is a crucial step in the successful application of a neural network. However, the architecture design is basically, in most cases, a human experts job. The design depends heavily on both, the expert experience and on a tedious trial-and-error process. Therefore, the development of automatic methods to determine the architecture of feedforward neural networks is a field of interest in the neural network community. These methods are generally based on search techniques, as genetic algorithms, simulated annealing or evolutionary strategies. Most of the designed methods are based on direct representation of the parameters of the network. This representation does not allow scalability, so to represent large architectures very large structures are required. In this work, an indirect constructive encoding scheme is proposed to find optimal architectures of feed-forward neural networks. This scheme is based on cellular automata representations in order to increase the scalability of the method.Publicad