Download Algorithmic Aspects of Analysis, Prediction, and Control in by Jaime Nava, Vladik Kreinovich PDF

By Jaime Nava, Vladik Kreinovich

This e-book demonstrates how one can describe and study a system's habit and extract the specified prediction and keep watch over algorithms from this research. a standard prediction is predicated on looking at related events long ago, realizing the results of those prior occasions, and looking forward to that the longer term consequence of the present state of affairs could be just like those prior saw results. In mathematical phrases, similarity corresponds to symmetry, and similarity of results to invariance.

This publication indicates how symmetries can be utilized in all periods of algorithmic difficulties of sciences and engineering: from research to prediction to manage. functions hide chemistry, geosciences, clever regulate, neural networks, quantum physics, and thermal physics. in particular, it's proven how the strategy in accordance with symmetry and similarity can be utilized within the research of real-life structures, within the algorithms of prediction, and within the algorithms of control.

Show description

Read or Download Algorithmic Aspects of Analysis, Prediction, and Control in Science and Engineering: An Approach Based on Symmetry and Similarity PDF

Best science books

The Universe in the Rearview Mirror: How Hidden Symmetries Shape Reality

A physicist speeds throughout house, time and every thing in among displaying that our stylish universe—from the Higgs boson to antimatter to the main enormous staff of galaxies—is formed via hidden symmetries that experience pushed all our contemporary discoveries concerning the universe and all of the ones to return.

Super Genes: Unlock the Astonishing Power of Your DNA for Optimum Health and Well-Being

The authors of the New York Times bestseller Super Brain present a daring new knowing of our genes and the way basic alterations in way of life can advance genetic job. The bounce into "radical well-being" is a promise ready to be fulfilled.  
 "You aren't easily the sum overall of the genes you have been born with," writes Deepak Chopra and Rudy Tanzi. "You are the consumer and controller of your genes, the writer of your organic tale. No prospect in self-care is extra intriguing. "
Learning the way to form your gene job is on the center of this interesting and eagerly-anticipated ebook from the bestselling duo behind Super Brain, which grew to become a national hit on public tv.  

For a long time scientific technology has believed that genes decided our organic future. Now the hot genetics has replaced that assumption perpetually. you'll always have the genes you have been born with, yet genes are dynamic, responding to every thing we predict, say, and do. all at once they've develop into our most powerful allies for private transformation. in the event you make way of life offerings that optimize how your genes behave, you could succeed in for a nation of healthiness and achievement undreamed of even a decade in the past.  The impression on prevention, immunity, nutrition, getting older, and persistent problems is exceptional.

Model-Based Control of Logistics Processes in Volatile Environments: Decision Support for Operations Planning in Supply Consortia

This monograph provides effects originating from a examine venture investigating self sufficient version of car schedules and systematically develops and evaluates cutting edge rules for the administration of transportation techniques in unstable situations. displaying the development made within the improvement of the methodological toolbox for determination aid in dynamic procedure administration is the most important motivation in the back of this ebook.

Additional resources for Algorithmic Aspects of Analysis, Prediction, and Control in Science and Engineering: An Approach Based on Symmetry and Similarity

Sample text

In this case, each state γ of the composite system is a pair γ = (γ1 , γ2 ) consisting of a state γ1 of the first subsystem and the state γ2 of the second subsystem. Often, these subsystems are independent. Due to this independence, the probability of going from a state γ = (γ1 , γ2 ) to a state γ = (γ1 , γ2 ) is equal to the product of the probabilities P1 and P2 corresponding to the first and to the second subsystems: P((γ1 , γ2 ) → (γ1 , γ2 )) = P1 (γ1 → γ1 ) · P2(γ2 → γ2 ). In order to describe how to satisfy this property, let us recall that in physics, independence of two subsystems is usually described by assuming that the corresponding action is equal to the sum of the actions corresponding to two subsystems: S((γ1 , γ2 )) = S1 (γ1 ) + S2(γ2 ).

Chemical interactions are, in effect, interaction of electrons. , [38]. In classical (pre-quantum) physics, to describe the state of a particle at any given moment of time, it is sufficient to describe its spatial location and momentum. We may not know the exact values of these quantities, but in principle, we can determine them with an arbitrarily high accuracy. In contrast, in quantum physics, it is impossible to uniquely determine both spatial location and momentum, we can only predict probabilities of different spatial locations (and different momentum values).

For which (s) (s) y(s) ≈ f x1 , . . , xn for all s from 1 to S. (The equality is usually approximate since the measurements are approximate and the value y is often only approximately determined by the values of the variables x1 , . . ) 46 3 Algorithmic Aspects of Prediction: An Approach Based on Symmetry and Similarity First Approximation: Linear Dependence. In many practical situations, the dependence f (x1 , . . , xn ) is smooth: informally, this means that small changes in xi lead to equally small changes in y.

Download PDF sample

Rated 4.94 of 5 – based on 8 votes