Search results for "Calculus"
showing 10 items of 617 documents
The Local Fractional Derivative of Fractal Curves
2008
Fractal curves described by iterated function system (IFS) are generally non-integer derivative. For that we use fractional derivative to investigate differentiability of this curves. We propose a method to calculate local fractional derivative of a curve from IFS property. Also we give some examples of IFS representing the slopes of the right and left half-tangent of the fractal curves.
Vagueness and Roughness
2008
The paper proposes a new formal approach to vagueness and vague sets taking inspirations from Pawlak's rough set theory. Following a brief introduction to the problem of vagueness, an approach to conceptualization and representation of vague knowledge is presented from a number of different perspectives: those of logic, set theory, algebra, and computer science. The central notion of the vague set, in relation to the rough set, is defined as a family of sets approximated by the so called lower and upper limits. The family is simultaneously considered as a family of all denotations of sharp terms representing a suitable vague term, from the agent's point of view. Some algebraic operations on…
Aprendiendo Vibraciones Mec´anicas con Wolfram Mathematica
2015
[EN] Mechanical vibrations as subject can be found within many Engineering and Science Degrees. To achieve that the students understand the mathematics and its physical interpretation is the objective we should get as docents. In this paper we describe how to create a simple graphical model of a single degree of freedom vibrating system allowing us to visualize concepts like above concepts damping, resonance or forced vibrations. For that, we use the popular symbolic software Wolfram Mathematica with which, without an excessive programming complexity, we can obtain a very satisfactory visual model capable to move itself, controlled by parameters. In addition, the model incorporates the curv…
Mining Interpretable Rules for Sentiment and Semantic Relation Analysis Using Tsetlin Machines
2020
Tsetlin Machines (TMs) are an interpretable pattern recognition approach that captures patterns with high discriminative power from data. Patterns are represented as conjunctive clauses in propositional logic, produced using bandit-learning in the form of Tsetlin Automata. In this work, we propose a TM-based approach to two common Natural Language Processing (NLP) tasks, viz. Sentiment Analysis and Semantic Relation Categorization. By performing frequent itemset mining on the patterns produced, we show that they follow existing expert-verified rule-sets or lexicons. Further, our comparison with other widely used machine learning techniques indicates that the TM approach helps maintain inter…
Bounded approximation properties via integral and nuclear operators
2010
Published version of an article in the journal:Proceedings of the American Mathematical Society. Also available from the publisher, Open Access
Chapter 1 Amalgams, Colimits, and Conceptual Blending
2018
This chapter is a theoretical exploration of Joseph Goguen’s category-theoretic model of conceptual blending and presents an alternative proposal to model blending as amalgams, which were originally proposed as a method for knowledge transfer in case-based reasoning. The chapter concludes with a generalisation of the amalgam-based model by relating it to the notion of colimit, thus providing a category-theoretic characterisation of amalgams that is ultimately computationally realisable.
Anchoring symbols to conceptual spaces: the case of dynamic scenarios.
2003
In recent years, there have been several proposals for the realization of models inspired to biological solutions for pattern recognition. In this work we propose a new approach, based on a hierarchical modular structure, to realize a system capable to learn by examples and recognize objects in digital images. The adopted techniques are based on multiresolution image analysis and neural networks. Performance on two different data sets and experimental timings on a single instruction multiple data (SIMD) machine are also reported.
A fractional-order model for aging materials: An application to concrete
2018
Abstract In this paper, the hereditariness of aging materials is modeled within the framework of fractional calculus of variable order. A relevant application is made for the long-term behavior of concrete, for which the creep function is evaluated with the aid of Model B3. The corresponding relaxation function is derived through the Volterra iterated kernels and a comparison with the numerically-obtained relaxation function of Model B3 is also reported. The proposed fractional hereditary aging model (FHAM) for concretes leads to a relaxation function that fully agrees with the well-established Model B3. Furthermore, the FHAM takes full advantage of the formalism of fractional-order calculu…
Density-functional tight-binding for beginners
2009
This article is a pedagogical introduction to density-functional tight-binding (DFTB) method. We derive it from the density-functional theory, give the details behind the tight-binding formalism, and give practical recipes for parametrization: how to calculate pseudo-atomic orbitals and matrix elements, and especially how to systematically fit the short-range repulsions. Our scope is neither to provide a historical review nor to make performance comparisons, but to give beginner's guide for this approximate, but in many ways invaluable, electronic structure simulation method--now freely available as an open-source software package, hotbit.
Lattice-Boltzmann and finite difference simulations for the permeability of three-dimensional porous media
2002
Numerical micropermeametry is performed on three dimensional porous samples having a linear size of approximately 3 mm and a resolution of 7.5 $\mu$m. One of the samples is a microtomographic image of Fontainebleau sandstone. Two of the samples are stochastic reconstructions with the same porosity, specific surface area, and two-point correlation function as the Fontainebleau sample. The fourth sample is a physical model which mimics the processes of sedimentation, compaction and diagenesis of Fontainebleau sandstone. The permeabilities of these samples are determined by numerically solving at low Reynolds numbers the appropriate Stokes equations in the pore spaces of the samples. The physi…