Search results for "General Mathematics"

Register data in sample allocations for small-area estimation

2018

The inadequate control of sample sizes in surveys using stratified sampling and area estimation may occur when the overall sample size is small or auxiliary information is insufficiently used. Very small sample sizes are possible for some areas. The proposed allocation based on multi-objective optimization uses a small-area model and estimation method and semi-collected empirical data annually collected empirical data. The assessment of its performance at the area and at the population levels is based on design-based sample simulations. Five previously developed allocations serve as references. The model-based estimator is more accurate than the design-based Horvitz–Thompson estimator and t…

Designing and implementing mathematical tasks: the T-shirt task

2010

Perspectives and reflections on teaching linear algebra

2020

Abstract This paper presents ‘expert opinions’ on what should be taught in a first-year linear algebra course at university; the aim is to gain a generic picture and general guiding principles for such a course. Drawing on a Delphi method, 14 university professors—called ‘experts’ in this study—addressed the following questions: What should be on a first-year linear algebra undergraduate course for engineering and/or mathematics students? How could such courses be taught? What tools (if any) are essential to these two groups of students? The results of the investigation, these experts’ opinions, mainly concern what should be in a linear algebra course (e.g. problem-solving and applications)…

On the application of the generalized means to construct multiresolution schemes satisfying certain inequalities proving stability

2021

Multiresolution representations of data are known to be powerful tools in data analysis and processing, and they are particularly interesting for data compression. In order to obtain a proper definition of the edges, a good option is to use nonlinear reconstructions. These nonlinear reconstruction are the heart of the prediction processes which appear in the definition of the nonlinear subdivision and multiresolution schemes. We define and study some nonlinear reconstructions based on the use of nonlinear means, more in concrete the so-called Generalized means. These means have two interesting properties that will allow us to get associated reconstruction operators adapted to the presence o…

On the advantages of combining differential algorithms and log-polar vision for detection of self-motion from a mobile robot

2001

Abstract This paper describes the design and implementation on programmable hardware (FPGAs) of an algorithm for the detection of self-mobile objects as seen from a mobile robot. In this context, ‘self-mobile’ refers to those objects that change in the image plane due to their own movement, and not to the movement of the camera on board of the mobile robot. The method consists on adapting the original algorithm from Chen and Nandhakumar [A simple scheme for motion boundary detection, in: Proceedings of the IEEE International Conference on Systems, Man and Cybernetics, 1994] by using foveal images obtained with a special camera whose optical axis points towards the direction of advance. It i…

Ontology-based state representations for intention recognition in human–robot collaborative environments

2013

In this paper, we describe a novel approach for representing state information for the purpose of intention recognition in cooperative human-robot environments. States are represented by a combination of spatial relationships in a Cartesian frame along with cardinal direction information. This approach is applied to a manufacturing kitting operation, where humans and robots are working together to develop kits. Based upon a set of predefined high-level state relationships that must be true for future actions to occur, a robot can use the detailed state information described in this paper to infer the probability of subsequent actions occurring. This would allow the robot to better help the …

A Cognitive Framework for Imitation Learning

2006

Abstract In order to have a robotic system able to effectively learn by imitation, and not merely reproduce the movements of a human teacher, the system should have the capabilities of deeply understanding the perceived actions to be imitated. This paper deals with the development of cognitive architecture for learning by imitation in which a rich conceptual representation of the observed actions is built. The purpose of the following discussion is to show how this Conceptual Area can be employed to efficiently organize perceptual data, to learn movement primitives from human demonstration and to generate complex actions by combining and sequencing simpler ones. The proposed architecture ha…

Indexing a sequence for mapping reads with a single mismatch

2014

Mapping reads against a genome sequence is an interesting and useful problem in computational molecular biology and bioinformatics. In this paper, we focus on the problem of indexing a sequence for mapping reads with a single mismatch. We first focus on a simpler problem where the length of the pattern is given beforehand during the data structure construction. This version of the problem is interesting in its own right in the context of the next generation sequencing. In the sequel, we show how to solve the more general problem. In both cases, our algorithm can construct an efficient data structure in time and space and can answer subsequent queries in time. Here, n is the length of the s…

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

Conceptual representations of actions for autonomous robots

2001

An autonomous robot involved in long and complex missions should be able to generate, update and process its own plans of action. In this perspective, it is not plausible that the meaning of the representations used by the robot is given from outside the system itself. Rather, the meaning of internal symbols must be firmly anchored to the world through the perceptual abilities and the overall activities of the robot. According to these premises, in this paper we present an approach to action representation that is based on a "conceptual" level of representation, acting as an intermediate level between symbols and data coming from sensors. Symbolic representations are interpreted by mapping …