Search results for "Generalized mean"

showing 3 items of 3 documents

Distributed Consensus in Networks of Dynamic Agents

2006

Stationary and distributed consensus protocols for a network of n dynamic agents under local information is considered. Consensus must be reached on a group decision value returned by a function of the agents' initial state values. As a main contribution we show that the agents can reach consensus if the value of such a function computed over the agents' state trajectories is time invariant. We use this basic result to introduce a protocol design rule allowing consensus on a quite general set of values. Such a set includes, e.g., any generalized mean of order p of the agents' initial states. We demonstrate that the asymptotical consensus is reached via a Lyapunov approach. Finally we perfor…

Asymptotic stability; Distributed consensus protocolsEngineeringMathematical optimizationAsymptotic stabilitybusiness.industryFunction (mathematics)Network topologyUniform consensusComputer Science::Multiagent SystemsLTI system theorySet (abstract data type)Distributed consensus protocolsConsensusExponential stabilityComputer Science::Systems and ControlControl theoryexperimental mechanics Fourier transform load stepping photoelasticityGeneralized meanbusinessProceedings of the 44th IEEE Conference on Decision and Control
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Exploring students’ proof comprehension of the Cauchy Generalized Mean Value Theorem

2019

AbstractUndergraduate students majoring in mathematics often face difficulties in comprehending mathematical proofs. Inspired by a number of studies related to students’ proof comprehension, and Mejia-Ramos et al.’s study in particular, a test was designed in relation to the proof comprehension of the Cauchy Generalized Mean Value Theorem (CGMVT). The test mainly focused on (a.) investigating students’ understanding of relations between the statements within the CGMVT proof and (b.) the relations between the CGMVT and other theorems. Thirty-five first-year university students voluntarily participated in this study. In addition, 10 of these students were subsequently interviewed to seek thei…

Mathematical logicGeneral MathematicsKnowledge level05 social sciences050301 educationCauchy distributionEducationComprehensionCalculus0501 psychology and cognitive sciencesGeneralized mean0503 educationValue (mathematics)050104 developmental & child psychologyMathematicsTeaching Mathematics and its Applications: An International Journal of the IMA
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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…

Computer scienceGeneral Mathematicslcsh:MathematicsStability (learning theory)010103 numerical & computational mathematicsConstruct (python library)Classification of discontinuitiesstability analysislcsh:QA1-93901 natural sciences010101 applied mathematicsNonlinear systemTensor productmultiresolutionScheme (mathematics)Computer Science (miscellaneous)Applied mathematicsnonlinearmeansGeneralized mean0101 mathematicssubdivision schemeEngineering (miscellaneous)data compressionData compression
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