Search results for "calculu"
showing 10 items of 642 documents
State-specific multireference coupled-cluster theory
2012
The multireference problem is considered one of the great challenges in coupled-cluster (CC) theory. Most recent developments are based on state-specific approaches, which focus on a single state and avoid some of the numerical problems of more general approaches. We review various state-of-the-art methods, including Mukherjee's state-specific multireference coupled-cluster (Mk-MRCC) theory, multireference Brillouin–Wigner coupled-cluster (MR-BWCC) theory, the MRexpT method, and internally contracted multireference coupled-cluster (ic-MRCC) theory. Related methods such as extended single-reference schemes [e.g., the complete active space coupled-cluster (CASCC) theory] and canonical transfo…
Descriptive Complexity, Lower Bounds and Linear Time
1999
This paper surveys two related lines of research: Logical characterizations of (non-deterministic) linear time complexity classes, and non-expressibility results concerning sublogics of existential second-order logic. Starting from Fagin’s fundamental work there has been steady progress in both fields with the effect that the weakest logics that are used in characterizations of linear time complexity classes are closely related to the strongest logics for which inexpressibility proofs for concrete problems have been obtained. The paper sketches these developments and highlights their connections as well as the obstacles that prevent us from closing the remaining gap between both kinds of lo…
An efficient distributed algorithm for generating and updating multicast trees
2006
As group applications are becoming widespread, efficient network utilization becomes a growing concern. Multicast transmission represents a necessary lower network service for the wide diffusion of new multimedia network applications. Multicast transmission may use network resources more efficiently than multiple point-to-point messages; however, creating optimal multicast trees (Steiner Tree Problem in networks) is prohibitively expensive. This paper proposes a distributed algorithm for the heuristic solution of the Steiner Tree Problem, allowing the construction of effective distribution trees using a coordination protocol among the network nodes. Furthermore, we propose a novel distribut…
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.