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| = Dynamic Max Count = | \documentclass{article}[11pt] \usepackage[onehalfspacing]{setspace} \usepackage{times} \usepackage{amsmath} \usepackage{psfrag} \usepackage{graphicx} \usepackage{epsfig} \usepackage{geometry} |
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| This contains the ideas and notes for a Dynamic Max Count (Dynamic Max-in-time) agregate operator | \newtheorem{corollary1}{Corollary} \newtheorem{definition1}{Definition} \newtheorem{example1}{Example} \newtheorem{lemma1}{Lemma} \newtheorem{remark1}{Remark} \newtheorem{theorem1}{Theorem} \newtheorem{algorithm1}{Algorithm} |
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| == Concept == | \newenvironment{corollary}{\begin{corollary1} \rm}{\end{corollary1}} \newenvironment{definition}{\begin{definition1} \rm}{\end{definition1}} \newenvironment{example}{\begin{example1} \rm}{\end{example1}} \newenvironment{lemma}{\begin{lemma1} \rm}{\end{lemma1}} \newenvironment{remark}{\begin{remark1} \rm}{\end{remark1}} \newenvironment{theorem}{\begin{theorem1} \rm}{\end{theorem1}} \newenvironment{algorithm}{\begin{algorithm1} \rm}{\end{algorithm1}} \newenvironment{proof}[1][Proof]{\noindent\textbf{#1.} }{\ \rule{0.5em}{0.5em}} \geometry{left=1in,right=1in,top=1in,bottom=1in} |
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| Instead of using Hyper-buckets that have descrete boundaries and densities which can not be updated resonably using the MaxCountProgramNotes ideas, we propose a probabalistic method where by we put probability densities in space. Each probability density will need the following properties: | \begin{document} |
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| 1. Parameters that define the distribution e.g. 1. Center location 1. Spatial size 1. Standard deviation 1. A measure of symetry or skew 1. A multi-dimensional probability function preferably a function that specific types functions as parameters e.g. $p(x_u(t),x_l(t),y_u(t),y_l(t)[,z_u(t),z_l(t)])$ |
\section{Dynamic Max Count} This contains the ideas and notes for a Dynamic Max Count (Dynamic Max-in-time) aggregate operator \subsection{Concept} Instead of using Hyper-buckets that have discrete boundaries and densities which can not be updated reasonably using the MaxCountProgramNotes ideas, we propose a probabilistic method where by we put probability densities in space. Each probability density will need the following properties: \item A multi-dimensional probability function preferably a function that uses types functions as parameters e.g. $p(x_u(t),x_l(t),y_u(t),y_l(t)[,z_u(t),z_l(t)])$ \item A theory to update ({\em delete} or {\em insert} points) the distributions based on changes to points. \end{enumerate} Based on this last item, we must maintain a database of 4-dimensional points that we index using 4-dimensional, probability buckets. \end{document} |
\documentclass{article}[11pt] \usepackage[onehalfspacing]{setspace} \usepackage{times} \usepackage{amsmath} \usepackage{psfrag} \usepackage{graphicx} \usepackage{epsfig} \usepackage{geometry}
\newtheorem{corollary1}{Corollary} \newtheorem{definition1}{Definition} \newtheorem{example1}{Example} \newtheorem{lemma1}{Lemma} \newtheorem{remark1}{Remark} \newtheorem{theorem1}{Theorem} \newtheorem{algorithm1}{Algorithm}
\newenvironment{corollary}{\begin{corollary1} \rm}{\end{corollary1}} \newenvironment{definition}{\begin{definition1} \rm}{\end{definition1}} \newenvironment{example}{\begin{example1} \rm}{\end{example1}} \newenvironment{lemma}{\begin{lemma1} \rm}{\end{lemma1}} \newenvironment{remark}{\begin{remark1} \rm}{\end{remark1}} \newenvironment{theorem}{\begin{theorem1} \rm}{\end{theorem1}} \newenvironment{algorithm}{\begin{algorithm1} \rm}{\end{algorithm1}} \newenvironment{proof}[1][Proof]{\noindent\textbf{#1.} }{\ \rule{0.5em}{0.5em}} \geometry{left=1in,right=1in,top=1in,bottom=1in}
\begin{document}
\section{Dynamic Max Count}
This contains the ideas and notes for a Dynamic Max Count (Dynamic Max-in-time) aggregate operator
\subsection{Concept}
Instead of using Hyper-buckets that have discrete boundaries and densities which can not be updated reasonably using the MaxCountProgramNotes ideas, we propose a probabilistic method where by we put probability densities in space. Each probability density will need the following properties:
\begin{enumerate}
- \item Parameters that define the distribution e.g. \begin{enumerate}
- \item Center location \item Spatial size \item Standard deviation \item A measure of symmetry or skew
\end{enumerate}
Based on this last item, we must maintain a database of 4-dimensional points that we index using 4-dimensional, probability buckets.
\end{document}