This document proposes and constructs new mathematical models based on fuzzy set theory and fuzzy systems. It presents two models: a Fuzzy Inference System (FIS) and an Adaptive Fuzzy System using neural networks. The models are applied to washing machine data and show good accuracy. Key aspects covered include: fuzzy rules, fuzzy inference systems, fuzzy logic operations, fuzzification and defuzzification methods, and constructing a 3-dimensional fuzzy system model. MATLAB is used to program and test the models.
A Mixed Binary-Real NSGA II Algorithm Ensuring Both Accuracy and Interpretabi...IJECEIAES
In this work, a Neuro-Fuzzy Controller network, called NFC that implements a Mamdani fuzzy inference system is proposed. This network includes neurons able to perform fundamental fuzzy operations. Connections between neurons are weighted through binary and real weights. Then a mixed binaryreal Non dominated Sorting Genetic Algorithm II (NSGA II) is used to perform both accuracy and interpretability of the NFC by minimizing two objective functions; one objective relates to the number of rules, for compactness, while the second is the mean square error, for accuracy. In order to preserve interpretability of fuzzy rules during the optimization process, some constraints are imposed. The approach is tested on two control examples: a single input single output (SISO) system and a multivariable (MIMO) system.
This document provides an introduction and overview of fuzzy logic, including:
- Fuzzy sets allow gradual membership rather than crisp membership in sets, addressing limitations of binary logic.
- A case study examines controlling the speed of a room cooler motor based on temperature and humidity using fuzzy logic rules and membership functions.
- Key fuzzy logic concepts covered include fuzzification, fuzzy rules and inference, and defuzzification to obtain a crisp output from fuzzy inputs and rules.
A Counterexample to the Forward Recursion in Fuzzy Critical Path Analysis Und...ijfls
This document presents a counterexample demonstrating that the fuzzy forward recursion method for determining critical paths does not always produce results consistent with the extension principle when discrete fuzzy sets are used to represent activity durations.
The document first provides background on fuzzy sets and critical path analysis. It then presents a proposition stating that the membership function for fuzzy critical path lengths can be determined by taking the maximum of the minimum membership values across all activity durations in each configuration.
The document goes on to present a counterexample using a simple series-parallel network with 18 configurations. It shows that applying the fuzzy forward recursion produces a different membership value for one critical path length compared to directly applying the extension principle. This difference proves the fuzzy forward
The document discusses modifications to the PC algorithm for constraint-based causal structure learning that remove its order-dependence, which can lead to highly variable results in high-dimensional settings; the modified algorithms are order-independent while maintaining consistency under the same conditions, and simulations and analysis of yeast gene expression data show they improve performance over the original PC algorithm in high-dimensional settings.
Markov model analyzing its behavior for uncertainty conditionsAlexander Decker
The document discusses analyzing the behavior of password guessing using Markov models under uncertainty. It introduces Markov models and fuzzy logic approaches. Specifically:
1) It explains how Markov models can represent password guessing by creating transition matrices from character prefixes.
2) It analyzes an example Markov model to identify possible guessable passwords and the probabilities of next characters.
3) It discusses using fuzzy logic rules and membership functions to generalize the analysis of states that output to the same state in the Markov model under uncertainty.
Investigations on Hybrid Learning in ANFISIJERA Editor
Neural networks have attractiveness to several researchers due to their great closeness to the structure of the brain, their characteristics not shared by many traditional systems. An Artificial Neural Network (ANN) is a network of interconnected artificial processing elements (called neurons) that co-operate with one another in order to solve specific issues. ANNs are inspired by the structure and functional aspects of biological nervous systems. Neural networks, which recognize patterns and adopt themselves to cope with changing environments. Fuzzy inference system incorporates human knowledge and performs inferencing and decision making. The integration of these two complementary approaches together with certain derivative free optimization techniques, results in a novel discipline called Neuro Fuzzy. In Neuro fuzzy development a specific approach is called Adaptive Neuro Fuzzy Inference System (ANFIS), which has shown significant results in modeling nonlinear functions. The basic idea behind the paper is to design a system that uses a fuzzy system to represent knowledge in an interpretable manner and have the learning ability derived from a Runge-Kutta learning method (RKLM) to adjust its membership functions and parameters in order to enhance the system performance. The problem of finding appropriate membership functions and fuzzy rules is often a tiring process of trial and error. It requires users to understand the data before training, which is usually difficult to achieve when the database is relatively large. To overcome these problems, a hybrid of Back Propagation Neural network (BPN) and RKLM can combine the advantages of two systems and avoid their disadvantages.
This document discusses using repeated simulations of a crisp neural network to obtain quasi-fuzzy weight sets (QFWS) that can be used to initialize fuzzy neural networks. The key points are:
1) A crisp neural network is repeatedly trained on input-output data to model an unknown function. The connection weights change with each simulation.
2) Recording the weights from multiple simulations produces quasi-fuzzy weight sets, where each weight is a fuzzy set rather than a single value.
3) These QFWS can provide initial solutions for training type-I fuzzy neural networks with reduced computational complexity compared to random initialization.
4) The QFWS follow fuzzy arithmetic and allow both numerical and linguistic data to
A Mixed Binary-Real NSGA II Algorithm Ensuring Both Accuracy and Interpretabi...IJECEIAES
In this work, a Neuro-Fuzzy Controller network, called NFC that implements a Mamdani fuzzy inference system is proposed. This network includes neurons able to perform fundamental fuzzy operations. Connections between neurons are weighted through binary and real weights. Then a mixed binaryreal Non dominated Sorting Genetic Algorithm II (NSGA II) is used to perform both accuracy and interpretability of the NFC by minimizing two objective functions; one objective relates to the number of rules, for compactness, while the second is the mean square error, for accuracy. In order to preserve interpretability of fuzzy rules during the optimization process, some constraints are imposed. The approach is tested on two control examples: a single input single output (SISO) system and a multivariable (MIMO) system.
This document provides an introduction and overview of fuzzy logic, including:
- Fuzzy sets allow gradual membership rather than crisp membership in sets, addressing limitations of binary logic.
- A case study examines controlling the speed of a room cooler motor based on temperature and humidity using fuzzy logic rules and membership functions.
- Key fuzzy logic concepts covered include fuzzification, fuzzy rules and inference, and defuzzification to obtain a crisp output from fuzzy inputs and rules.
A Counterexample to the Forward Recursion in Fuzzy Critical Path Analysis Und...ijfls
This document presents a counterexample demonstrating that the fuzzy forward recursion method for determining critical paths does not always produce results consistent with the extension principle when discrete fuzzy sets are used to represent activity durations.
The document first provides background on fuzzy sets and critical path analysis. It then presents a proposition stating that the membership function for fuzzy critical path lengths can be determined by taking the maximum of the minimum membership values across all activity durations in each configuration.
The document goes on to present a counterexample using a simple series-parallel network with 18 configurations. It shows that applying the fuzzy forward recursion produces a different membership value for one critical path length compared to directly applying the extension principle. This difference proves the fuzzy forward
The document discusses modifications to the PC algorithm for constraint-based causal structure learning that remove its order-dependence, which can lead to highly variable results in high-dimensional settings; the modified algorithms are order-independent while maintaining consistency under the same conditions, and simulations and analysis of yeast gene expression data show they improve performance over the original PC algorithm in high-dimensional settings.
Markov model analyzing its behavior for uncertainty conditionsAlexander Decker
The document discusses analyzing the behavior of password guessing using Markov models under uncertainty. It introduces Markov models and fuzzy logic approaches. Specifically:
1) It explains how Markov models can represent password guessing by creating transition matrices from character prefixes.
2) It analyzes an example Markov model to identify possible guessable passwords and the probabilities of next characters.
3) It discusses using fuzzy logic rules and membership functions to generalize the analysis of states that output to the same state in the Markov model under uncertainty.
Investigations on Hybrid Learning in ANFISIJERA Editor
Neural networks have attractiveness to several researchers due to their great closeness to the structure of the brain, their characteristics not shared by many traditional systems. An Artificial Neural Network (ANN) is a network of interconnected artificial processing elements (called neurons) that co-operate with one another in order to solve specific issues. ANNs are inspired by the structure and functional aspects of biological nervous systems. Neural networks, which recognize patterns and adopt themselves to cope with changing environments. Fuzzy inference system incorporates human knowledge and performs inferencing and decision making. The integration of these two complementary approaches together with certain derivative free optimization techniques, results in a novel discipline called Neuro Fuzzy. In Neuro fuzzy development a specific approach is called Adaptive Neuro Fuzzy Inference System (ANFIS), which has shown significant results in modeling nonlinear functions. The basic idea behind the paper is to design a system that uses a fuzzy system to represent knowledge in an interpretable manner and have the learning ability derived from a Runge-Kutta learning method (RKLM) to adjust its membership functions and parameters in order to enhance the system performance. The problem of finding appropriate membership functions and fuzzy rules is often a tiring process of trial and error. It requires users to understand the data before training, which is usually difficult to achieve when the database is relatively large. To overcome these problems, a hybrid of Back Propagation Neural network (BPN) and RKLM can combine the advantages of two systems and avoid their disadvantages.
This document discusses using repeated simulations of a crisp neural network to obtain quasi-fuzzy weight sets (QFWS) that can be used to initialize fuzzy neural networks. The key points are:
1) A crisp neural network is repeatedly trained on input-output data to model an unknown function. The connection weights change with each simulation.
2) Recording the weights from multiple simulations produces quasi-fuzzy weight sets, where each weight is a fuzzy set rather than a single value.
3) These QFWS can provide initial solutions for training type-I fuzzy neural networks with reduced computational complexity compared to random initialization.
4) The QFWS follow fuzzy arithmetic and allow both numerical and linguistic data to
The Positive Effects of Fuzzy C-Means Clustering on Supervised Learning Class...Waqas Tariq
Selection of inputs is one of the most substantial components of classification algorithms for data mining and pattern recognition problems since even the best classifier will perform badly if the inputs are not selected very well. Big data and computational complexity are main cause of bad performance and low accuracy for classical classifiers. In other words, the complexity of classifier method is inversely proportional with its classification efficiency. For this purpose, two hybrid classifiers have been developed by using both type-1 and type-2 fuzzy c-means clustering with cascaded a classifier. In this proposed classifier, a large number of data points are reduced by using fuzzy c-means clustering before applied to a classifier algorithm as inputs. The aim of this study is to investigate the effect of fuzzy clustering on well-known and useful classifiers such as artificial neural networks (ANN) and support vector machines (SVM). Then the role of positive effects of these proposed algorithms were investigated on applied different data sets.
Derivation of Convolutional Neural Network (ConvNet) from Fully Connected Net...Ahmed Gad
In image analysis, convolutional neural networks (CNNs or ConvNets for short) are time and memory efficient than fully connected (FC) networks. But why? What are the advantages of ConvNets over FC networks in image analysis? How is ConvNet derived from FC networks? Where the term convolution in CNNs came from? These questions are to be answered in this article.
Image analysis has a number of challenges such as classification, object detection, recognition, description, etc. If an image classifier, for example, is to be created, it should be able to work with a high accuracy even with variations such as occlusion, illumination changes, viewing angles, and others. The traditional pipeline of image classification with its main step of feature engineering is not suitable for working in rich environments. Even experts in the field won’t be able to give a single or a group of features that are able to reach high accuracy under different variations. Motivated by this problem, the idea of feature learning came out. The suitable features to work with images are learned automatically. This is the reason why artificial neural networks (ANNs) are one of the robust ways of image analysis. Based on a learning algorithm such as gradient descent (GD), ANN learns the image features automatically. The raw image is applied to the ANN and ANN is responsible for generating the features describing it.
-Reference
Aghdam, Hamed Habibi, and Elnaz Jahani Heravi. Guide to Convolutional Neural Networks: A Practical Application to Traffic-Sign Detection and Classification. Springer, 2017.
IJRET : International Journal of Research in Engineering and Technology is an international peer reviewed, online journal published by eSAT Publishing House for the enhancement of research in various disciplines of Engineering and Technology. The aim and scope of the journal is to provide an academic medium and an important reference for the advancement and dissemination of research results that support high-level learning, teaching and research in the fields of Engineering and Technology. We bring together Scientists, Academician, Field Engineers, Scholars and Students of related fields of Engineering and Technology.
Comparative analysis of dynamic programming algorithms to find similarity in ...eSAT Journals
Abstract There exist many computational methods for finding similarity in gene sequence, finding suitable methods that gives optimal similarity is difficult task. Objective of this project is to find an appropriate method to compute similarity in gene/protein sequence, both within the families and across the families. Many dynamic programming algorithms like Levenshtein edit distance; Longest Common Subsequence and Smith-waterman have used dynamic programming approach to find similarities between two sequences. But none of the method mentioned above have used real benchmark data sets. They have only used dynamic programming algorithms for synthetic data. We proposed a new method to compute similarity. The performance of the proposed algorithm is evaluated using number of data sets from various families, and similarity value is calculated both within the family and across the families. A comparative analysis and time complexity of the proposed method reveal that Smith-waterman approach is appropriate method when gene/protein sequence belongs to same family and Longest Common Subsequence is best suited when sequence belong to two different families. Keywords - Bioinformatics, Gene, Gene Sequencing, Edit distance, String Similarity.
This document presents an overview of a fuzzy logic control system for an automated accident prevention system in vehicles. It introduces fuzzy logic and how it is suited for control applications that involve imprecise human reasoning. It describes the differences between fuzzy and crisp sets, membership functions, fuzzification, and defuzzification. The document then provides an example of a fuzzy logic control system for braking that uses sensors to measure vehicle speed and distance to obstacles, defines input and output membership functions, and includes a set of rules to determine the braking level needed to prevent accidents. The conclusion states that such a fuzzy logic system can help relieve driver tension and prevent accidents, working towards an accident-free world.
MS SQL SERVER:Microsoft neural network and logistic regressionDataminingTools Inc
This document provides an overview of Microsoft Neural Network and Logistic Regression algorithms. It describes how neural networks can detect nonlinear relationships in data and are composed of an input, hidden and output layer. The Microsoft Neural Network algorithm uses backpropagation to update weights and minimize errors. Parameters like maximum inputs/outputs, sample size, and hidden node ratio can be configured. Examples of DMX queries are provided to create models for predicting customer attributes from demographic and technology usage data.
This document discusses manipulator mechanisms, including degrees of freedom, parallel manipulators, and teaching manipulators. It covers the following key points:
1) Degrees of freedom for serial manipulators is equal to the number of moving links. Closed chain mechanisms use Gubler's formula to determine degrees of freedom based on the number of links, revolute joints, and prismatic joints.
2) Parallel manipulators like the Stewart platform use six prismatic links connected to two rings by ball-and-socket and hook joints, giving it six degrees of freedom.
3) Manipulators can be used as measuring tools by knowing link lengths and joint angles to determine the position and orientation of the end effector
DESIGN AND IMPLEMENTATION OF BINARY NEURAL NETWORK LEARNING WITH FUZZY CLUSTE...cscpconf
In this paper, Design and Implementation of Binary Neural Network Learning with Fuzzy
Clustering (DIBNNFC), is proposed to classify semisupervised data, it is based on the
concept of binary neural network and geometrical expansion. Parameters are updated
according to the geometrical location of the training samples in the input space, and each
sample in the training set is learned only once. It’s a semisupervised based approach, the
training samples are semi-labelled i.e. for some samples, labels are known and for some
samples data labels are not known. The method starts with classification, which is done by
using the concept of ETL algorithm. In classification process various classes are formed.
These classes classify samples in to two classes after that considers each class as a region and calculates the average of the entire region separately. This average is centres of the region which is used for the purpose of clustering by using FCM algorithm. Once clustering process over labelling of semi supervised data is done, then whole samples would be classify by (DIBNNFC). The method proposes here is exhaustively tested with different benchmark datasets and it is found that, on increasing value of training parameters number of hidden neurons and training time both are getting decrease. The result reported, using real character recognition data set and result will compare with existing semi-supervised classifier, the proposed approach learned with semi-supervised leads to higher classification accuracy.
Dear students get fully solved assignments
Send your semester & Specialization name to our mail id :
“ help.mbaassignments@gmail.com ”
or
Call us at : 08263069601
The numerical solution of Huxley equation by the use of two finite difference methods is done. The first one is the explicit scheme and the second one is the Crank-Nicholson scheme. The comparison between the two methods showed that the explicit scheme is easier and has faster convergence while the Crank-Nicholson scheme is more accurate. In addition, the stability analysis using Fourier (von Neumann) method of two schemes is investigated. The resulting analysis showed that the first scheme
is conditionally stable if, r ≤ 2 − aβ∆t , ∆t ≤ 2(∆x)2 and the second
scheme is unconditionally stable.
The document discusses the history and applications of fuzzy logic control. It describes how fuzzy logic was first introduced in 1965 and began being applied in various industries starting in the 1970s. By the 1990s, fuzzy logic had become a standard control technique, especially for multi-variable control systems. The document outlines the basic elements of a fuzzy logic system and provides an example of how fuzzy logic can be used to control a container crane.
This document discusses fuzzy rules and fuzzy reasoning. It covers the extension principle, fuzzy relations, fuzzy if-then rules, the compositional rule of inference, and fuzzy reasoning using single and multiple rules with single and multiple antecedents. Methods like max-min and max-product composition are presented for combining fuzzy relations. Linguistic variables and terms that take linguistic values like "old" are also introduced.
This document provides an introduction to fuzzy logic, including its history and applications. It discusses classical logic and its limitations in dealing with uncertain propositions. Multi-valued logics are introduced as an approach to handle indeterminate truth values. Fuzzy logic then allows for gradual assessments between true and false by using membership functions and fuzzy set theory. Conditional and quantified fuzzy propositions are defined along with operations on them. The document concludes by mentioning applications of fuzzy logic in areas like controllers for washing machines and computer engineering.
This document provides an overview of fuzzy logic. It begins by defining fuzzy as not being clear or precise, unlike classical sets which have clear boundaries. It then explains fuzzy logic allows for partial set membership rather than binary membership. The document outlines fuzzy logic's ability to model imprecise or nonlinear systems using natural language-based rules. It details the key concepts of fuzzy logic including linguistic variables, membership functions, fuzzy set operations, fuzzy inference systems and the 5-step fuzzy inference process of fuzzifying inputs, applying fuzzy operations and implications, aggregating outputs and defuzzifying results.
Fuzzy logic provides a means of calculating intermediate values between absolute true and absolute false. It allows partial set membership and handles imprecise data. Fuzzy logic systems use membership functions to determine the degree to which inputs belong to sets and fuzzy inference systems to map inputs to outputs. Fuzzy logic has applications in devices like washing machines and cameras that require handling imprecise variables.
How can you deal with Fuzzy Logic. Fuzzy logic is a form of many-valued logic; it deals with reasoning that is approximate rather than fixed and exact. In contrast with traditional logic theory, where binary sets have two-valued logic: true or false, fuzzy logic variables may have a truth value that ranges in degree
between 0 and 1
- Fuzzy logic was developed by Lotfi Zadeh to address applications involving subjective or vague data like "attractive person" that cannot be easily analyzed using binary logic. It allows for partial truth values between completely true and completely false.
- Fuzzy logic controllers mimic human decision making and involve fuzzifying inputs, applying fuzzy rules, and defuzzifying outputs. This allows systems to be specified in human terms and automated.
- Fuzzy logic has many applications from industrial process control to consumer products like washing machines and microwaves. It offers an intuitive way to model real-world ambiguities compared to mathematical or logic-based approaches.
Pid controller tuning using fuzzy logicRoni Roshni
This document provides an overview of tuning a PID controller with fuzzy logic. It introduces fuzzy logic and discusses how it can be applied to PID tuning. Specifically, it discusses using fuzzy set-point weighting to tune the PID controller by determining the proportional weighting factor b(t) using a fuzzy inference system based on the error e(t) and change in error. It also discusses traditional Ziegler-Nichols tuning and compares the performance of fixed versus fuzzy set-point weighting tuning. The conclusion is that fuzzy logic provides benefits like balancing rise time and overshoot to obtain better performance than traditional methods.
The Positive Effects of Fuzzy C-Means Clustering on Supervised Learning Class...Waqas Tariq
Selection of inputs is one of the most substantial components of classification algorithms for data mining and pattern recognition problems since even the best classifier will perform badly if the inputs are not selected very well. Big data and computational complexity are main cause of bad performance and low accuracy for classical classifiers. In other words, the complexity of classifier method is inversely proportional with its classification efficiency. For this purpose, two hybrid classifiers have been developed by using both type-1 and type-2 fuzzy c-means clustering with cascaded a classifier. In this proposed classifier, a large number of data points are reduced by using fuzzy c-means clustering before applied to a classifier algorithm as inputs. The aim of this study is to investigate the effect of fuzzy clustering on well-known and useful classifiers such as artificial neural networks (ANN) and support vector machines (SVM). Then the role of positive effects of these proposed algorithms were investigated on applied different data sets.
Derivation of Convolutional Neural Network (ConvNet) from Fully Connected Net...Ahmed Gad
In image analysis, convolutional neural networks (CNNs or ConvNets for short) are time and memory efficient than fully connected (FC) networks. But why? What are the advantages of ConvNets over FC networks in image analysis? How is ConvNet derived from FC networks? Where the term convolution in CNNs came from? These questions are to be answered in this article.
Image analysis has a number of challenges such as classification, object detection, recognition, description, etc. If an image classifier, for example, is to be created, it should be able to work with a high accuracy even with variations such as occlusion, illumination changes, viewing angles, and others. The traditional pipeline of image classification with its main step of feature engineering is not suitable for working in rich environments. Even experts in the field won’t be able to give a single or a group of features that are able to reach high accuracy under different variations. Motivated by this problem, the idea of feature learning came out. The suitable features to work with images are learned automatically. This is the reason why artificial neural networks (ANNs) are one of the robust ways of image analysis. Based on a learning algorithm such as gradient descent (GD), ANN learns the image features automatically. The raw image is applied to the ANN and ANN is responsible for generating the features describing it.
-Reference
Aghdam, Hamed Habibi, and Elnaz Jahani Heravi. Guide to Convolutional Neural Networks: A Practical Application to Traffic-Sign Detection and Classification. Springer, 2017.
IJRET : International Journal of Research in Engineering and Technology is an international peer reviewed, online journal published by eSAT Publishing House for the enhancement of research in various disciplines of Engineering and Technology. The aim and scope of the journal is to provide an academic medium and an important reference for the advancement and dissemination of research results that support high-level learning, teaching and research in the fields of Engineering and Technology. We bring together Scientists, Academician, Field Engineers, Scholars and Students of related fields of Engineering and Technology.
Comparative analysis of dynamic programming algorithms to find similarity in ...eSAT Journals
Abstract There exist many computational methods for finding similarity in gene sequence, finding suitable methods that gives optimal similarity is difficult task. Objective of this project is to find an appropriate method to compute similarity in gene/protein sequence, both within the families and across the families. Many dynamic programming algorithms like Levenshtein edit distance; Longest Common Subsequence and Smith-waterman have used dynamic programming approach to find similarities between two sequences. But none of the method mentioned above have used real benchmark data sets. They have only used dynamic programming algorithms for synthetic data. We proposed a new method to compute similarity. The performance of the proposed algorithm is evaluated using number of data sets from various families, and similarity value is calculated both within the family and across the families. A comparative analysis and time complexity of the proposed method reveal that Smith-waterman approach is appropriate method when gene/protein sequence belongs to same family and Longest Common Subsequence is best suited when sequence belong to two different families. Keywords - Bioinformatics, Gene, Gene Sequencing, Edit distance, String Similarity.
This document presents an overview of a fuzzy logic control system for an automated accident prevention system in vehicles. It introduces fuzzy logic and how it is suited for control applications that involve imprecise human reasoning. It describes the differences between fuzzy and crisp sets, membership functions, fuzzification, and defuzzification. The document then provides an example of a fuzzy logic control system for braking that uses sensors to measure vehicle speed and distance to obstacles, defines input and output membership functions, and includes a set of rules to determine the braking level needed to prevent accidents. The conclusion states that such a fuzzy logic system can help relieve driver tension and prevent accidents, working towards an accident-free world.
MS SQL SERVER:Microsoft neural network and logistic regressionDataminingTools Inc
This document provides an overview of Microsoft Neural Network and Logistic Regression algorithms. It describes how neural networks can detect nonlinear relationships in data and are composed of an input, hidden and output layer. The Microsoft Neural Network algorithm uses backpropagation to update weights and minimize errors. Parameters like maximum inputs/outputs, sample size, and hidden node ratio can be configured. Examples of DMX queries are provided to create models for predicting customer attributes from demographic and technology usage data.
This document discusses manipulator mechanisms, including degrees of freedom, parallel manipulators, and teaching manipulators. It covers the following key points:
1) Degrees of freedom for serial manipulators is equal to the number of moving links. Closed chain mechanisms use Gubler's formula to determine degrees of freedom based on the number of links, revolute joints, and prismatic joints.
2) Parallel manipulators like the Stewart platform use six prismatic links connected to two rings by ball-and-socket and hook joints, giving it six degrees of freedom.
3) Manipulators can be used as measuring tools by knowing link lengths and joint angles to determine the position and orientation of the end effector
DESIGN AND IMPLEMENTATION OF BINARY NEURAL NETWORK LEARNING WITH FUZZY CLUSTE...cscpconf
In this paper, Design and Implementation of Binary Neural Network Learning with Fuzzy
Clustering (DIBNNFC), is proposed to classify semisupervised data, it is based on the
concept of binary neural network and geometrical expansion. Parameters are updated
according to the geometrical location of the training samples in the input space, and each
sample in the training set is learned only once. It’s a semisupervised based approach, the
training samples are semi-labelled i.e. for some samples, labels are known and for some
samples data labels are not known. The method starts with classification, which is done by
using the concept of ETL algorithm. In classification process various classes are formed.
These classes classify samples in to two classes after that considers each class as a region and calculates the average of the entire region separately. This average is centres of the region which is used for the purpose of clustering by using FCM algorithm. Once clustering process over labelling of semi supervised data is done, then whole samples would be classify by (DIBNNFC). The method proposes here is exhaustively tested with different benchmark datasets and it is found that, on increasing value of training parameters number of hidden neurons and training time both are getting decrease. The result reported, using real character recognition data set and result will compare with existing semi-supervised classifier, the proposed approach learned with semi-supervised leads to higher classification accuracy.
Dear students get fully solved assignments
Send your semester & Specialization name to our mail id :
“ help.mbaassignments@gmail.com ”
or
Call us at : 08263069601
The numerical solution of Huxley equation by the use of two finite difference methods is done. The first one is the explicit scheme and the second one is the Crank-Nicholson scheme. The comparison between the two methods showed that the explicit scheme is easier and has faster convergence while the Crank-Nicholson scheme is more accurate. In addition, the stability analysis using Fourier (von Neumann) method of two schemes is investigated. The resulting analysis showed that the first scheme
is conditionally stable if, r ≤ 2 − aβ∆t , ∆t ≤ 2(∆x)2 and the second
scheme is unconditionally stable.
The document discusses the history and applications of fuzzy logic control. It describes how fuzzy logic was first introduced in 1965 and began being applied in various industries starting in the 1970s. By the 1990s, fuzzy logic had become a standard control technique, especially for multi-variable control systems. The document outlines the basic elements of a fuzzy logic system and provides an example of how fuzzy logic can be used to control a container crane.
This document discusses fuzzy rules and fuzzy reasoning. It covers the extension principle, fuzzy relations, fuzzy if-then rules, the compositional rule of inference, and fuzzy reasoning using single and multiple rules with single and multiple antecedents. Methods like max-min and max-product composition are presented for combining fuzzy relations. Linguistic variables and terms that take linguistic values like "old" are also introduced.
This document provides an introduction to fuzzy logic, including its history and applications. It discusses classical logic and its limitations in dealing with uncertain propositions. Multi-valued logics are introduced as an approach to handle indeterminate truth values. Fuzzy logic then allows for gradual assessments between true and false by using membership functions and fuzzy set theory. Conditional and quantified fuzzy propositions are defined along with operations on them. The document concludes by mentioning applications of fuzzy logic in areas like controllers for washing machines and computer engineering.
This document provides an overview of fuzzy logic. It begins by defining fuzzy as not being clear or precise, unlike classical sets which have clear boundaries. It then explains fuzzy logic allows for partial set membership rather than binary membership. The document outlines fuzzy logic's ability to model imprecise or nonlinear systems using natural language-based rules. It details the key concepts of fuzzy logic including linguistic variables, membership functions, fuzzy set operations, fuzzy inference systems and the 5-step fuzzy inference process of fuzzifying inputs, applying fuzzy operations and implications, aggregating outputs and defuzzifying results.
Fuzzy logic provides a means of calculating intermediate values between absolute true and absolute false. It allows partial set membership and handles imprecise data. Fuzzy logic systems use membership functions to determine the degree to which inputs belong to sets and fuzzy inference systems to map inputs to outputs. Fuzzy logic has applications in devices like washing machines and cameras that require handling imprecise variables.
How can you deal with Fuzzy Logic. Fuzzy logic is a form of many-valued logic; it deals with reasoning that is approximate rather than fixed and exact. In contrast with traditional logic theory, where binary sets have two-valued logic: true or false, fuzzy logic variables may have a truth value that ranges in degree
between 0 and 1
- Fuzzy logic was developed by Lotfi Zadeh to address applications involving subjective or vague data like "attractive person" that cannot be easily analyzed using binary logic. It allows for partial truth values between completely true and completely false.
- Fuzzy logic controllers mimic human decision making and involve fuzzifying inputs, applying fuzzy rules, and defuzzifying outputs. This allows systems to be specified in human terms and automated.
- Fuzzy logic has many applications from industrial process control to consumer products like washing machines and microwaves. It offers an intuitive way to model real-world ambiguities compared to mathematical or logic-based approaches.
Pid controller tuning using fuzzy logicRoni Roshni
This document provides an overview of tuning a PID controller with fuzzy logic. It introduces fuzzy logic and discusses how it can be applied to PID tuning. Specifically, it discusses using fuzzy set-point weighting to tune the PID controller by determining the proportional weighting factor b(t) using a fuzzy inference system based on the error e(t) and change in error. It also discusses traditional Ziegler-Nichols tuning and compares the performance of fixed versus fuzzy set-point weighting tuning. The conclusion is that fuzzy logic provides benefits like balancing rise time and overshoot to obtain better performance than traditional methods.
The document discusses using clustering models like subtractive fuzzy clustering (SFC) and fuzzy c-means clustering (FCM) to generate an adaptive neuro-fuzzy inference system (ANFIS) for medical diagnoses. Experimental results on medical diagnosis datasets show that ANFIS models using SFC and FCM clustering (ANFIS-SFC and ANFIS-FCM) had better average training and checking errors compared to ANFIS without clustering. Specifically, ANFIS-SFC performed best using backpropagation learning, while ANFIS-FCM performed best using a hybrid learning model. Clustering the datasets without ANFIS was also able to identify different disease clusters.
INTERVAL TYPE-2 INTUITIONISTIC FUZZY LOGIC SYSTEM FOR TIME SERIES AND IDENTIF...ijfls
This paper proposes a sliding mode control-based learning of interval type-2 intuitionistic fuzzy logic system for time series and identification problems. Until now, derivative-based algorithms such as gradient descent back propagation, extended Kalman filter, decoupled extended Kalman filter and hybrid method of decoupled extended Kalman filter and gradient descent methods have been utilized for the optimization of the parameters of interval type-2 intuitionistic fuzzy logic systems. The proposed model is based on a Takagi-Sugeno-Kang inference system. The evaluations of the model are conducted using both real world and artificially generated datasets. Analysis of results reveals that the proposed interval type-2 intuitionistic fuzzy logic system trained with sliding mode control learning algorithm (derivative-free) do outperforms some existing models in terms of the test root mean squared error while competing favourable with other models in the literature. Moreover, the proposed model may stand as a good choice for real time applications where running time is paramount compared to the derivative-based models.
Although fuzzy systems demonstrate their ability to
solve different kinds of problems in various applications, there is an increasing interest on developing solid mathematical implementations suitable for control applications such as that used in fuzzy logic controllers (FLC). It is well known that, wide range of parameters is needed to be specified before the construction of a fuzzy system. To simplify in a systematic way the design and construction of a general fuzzy system, and without loss for generality a full parameterization process for a singleton type FLC is proposed in this paper. The resented methodology is very helpful in developing a universal computing algorithm for a standard fuzzy like PID controllers. An illustrative example shows the simplicity of applying the new paradigm.
Fuzzy Control of a Servomechanism: Practical Approach using Mamdani and Takag...ijfls
The main objective of this work is to propose two fuzzy controllers: one based on the Mamdani inference method and another controller based on the Takagi- Sugeno inference method, both will be designed for application in a position control system of a servomechanism. Some comparations between the methods mentioned above will be made with regard to the performance of the system in order to identify the advantages of the Takagi- Sugeno method in relation to the Mamdani method in the presence of disturbances and nonlinearities of the system. Some results of simulation and practical application are presented and results obtained showed that controllers based on Takagi- Sugeno method is more efficient than controllers based on Mamdani method for this specific application.
FUZZY CONTROL OF A SERVOMECHANISM: PRACTICAL APPROACH USING MAMDANI AND TAKAG...ijfls
The main objective of this work is to propose two fuzzy controllers: one based on the Mamdani inference
method and another controller based on the Takagi- Sugeno inference method, both will be designed for
application in a position control system of a servomechanism. Some comparations between the methods
mentioned above will be made with regard to the performance of the system in order to identify the
advantages of the Takagi- Sugeno method in relation to the Mamdani method in the presence of
disturbances and nonlinearities of the system. Some results of simulation and practical application are
presented and results obtained showed that controllers based on Takagi- Sugeno method is more efficient
than controllers based on Mamdani method for this specific application.
Interval Type-2 Intuitionistic Fuzzy Logic System for Time Series and Identif...ijfls
This paper proposes a sliding mode control-based learning of interval type-2 intuitionistic fuzzy logic system for time series and identification problems. Until now, derivative-based algorithms such as gradient descent back propagation, extended Kalman filter, decoupled extended Kalman filter and hybrid method of decoupled extended Kalman filter and gradient descent methods have been utilized for the optimization of the parameters of interval type-2 intuitionistic fuzzy logic systems. The proposed model is based on a Takagi-Sugeno-Kang inference system. The evaluations of the model are conducted using both real world and artificially generated datasets. Analysis of results reveals that the proposed interval type-2 intuitionistic fuzzy logic system trained with sliding mode control learning algorithm (derivative-free) do outperforms some existing models in terms of the test root mean squared error while competing favourable with other models in the literature. Moreover, the proposed model may stand as a good choice for real time applications where running time is paramount compared to the derivative-based models.
VALIDATION METHOD OF FUZZY ASSOCIATION RULES BASED ON FUZZY FORMAL CONCEPT AN...cscpconf
The document proposes a new validation method for fuzzy association rules based on three steps: (1) applying the EFAR-PN algorithm to extract a generic base of non-redundant fuzzy association rules using fuzzy formal concept analysis, (2) categorizing the extracted rules into groups, and (3) evaluating the relevance of the rules using structural equation modeling, specifically partial least squares. The method aims to address issues with existing fuzzy association rule extraction algorithms such as large numbers of extracted rules, redundancy, and difficulties with manual validation.
Compositional testing for fsm based modelsijseajournal
The contribution of this paper is threefold: first, it defines a framework for modelling component
-
based
systems, as well as a formalization of integration rules to combine their behaviour. This is based on fini
te
state machines (FSM). Second, it studies compositional conformance testing i.e. checking whether an
implementation made of conforming components combined with integration operators is conform to its
specification. Third, it shows the correctness of the
global system can be obtained by testing the
components involved into it towards the projection of the global specification on the specifications of the
components. This result is useful to build adequate test purposes for testing components taking into ac
count
the system where they are plugged in
Estimation of Air-Cooling Devices Run Time Via Fuzzy Logic and Adaptive Neuro...IRJET Journal
The document describes a study that uses fuzzy logic and adaptive neuro-fuzzy inference systems (ANFIS) to develop a system for predicting the optimal run time of air cooling devices. Fuzzy logic models were developed using temperature and door state as inputs and run time as the output. Three different membership functions were tested and the triangular function performed best. ANFIS combines fuzzy logic and neural networks and was able to more accurately predict run time compared to fuzzy logic alone. The developed models provide an efficient way to control air cooling device run times.
A Learning Linguistic Teaching Control for a Multi-Area Electric Power SystemCSCJournals
This paper presents a new methodology for designing a neuro-fuzzy control for complex physical systems. By developing a Neural -Fuzzy system learning with linguistic teaching signals. The advantage of this technique is that, produce a simple and well-performing system because it selects the fuzzy sets and the numerical numbers and process both numerical and linguistic information. This approach is able to process and learn numerical information as well as linguistic information. The proposed control scheme is applied to a multi-area power system with hydraulic and thermal turbines.
Fuzzy inference systems use fuzzy logic to map inputs to outputs. There are two main types:
Mamdani systems use fuzzy outputs and are well-suited for problems involving human expert knowledge. Sugeno systems have faster computation using linear or constant outputs.
The fuzzy inference process involves fuzzifying inputs, applying fuzzy logic operators, and using if-then rules. Outputs are determined through implication, aggregation, and defuzzification. Mamdani systems find the centroid of fuzzy outputs while Sugeno uses weighted averages, making it more efficient.
This document proposes a new method for extracting rules from trained multilayer artificial neural networks that can represent rules in both "if-then" and "M of N" formats. The method extracts an intermediate structure called a "generator list" from which both types of rules can be derived. This provides a more generic representation than existing methods that can only output one rule format. The generator list approach avoids preprocessing steps used in other methods that can modify the original network. It uses heuristics to prune the search space when extracting the generator list to address the computational complexity involved.
Modeling of LDO-fired Rotary Furnace Parameters using Adaptive Network-based ...theijes
In this paper a novel approach i.e. neuro-fuzzy technique is used for the first time in modeling rotary furnace parameters to predict the melting rate of the molten metal required to produce homogenous castings. The relationship between the process variables (input) viz. flame temperature, preheat air temperature, rotational speed of the furnace, excess air, melting time, and fuel consumption and melting rate (output) is very complex and is agreeable to neuro-fuzzy approach. The neuro-fuzzy model has been created out of training data obtained from the series of experimentation carried out on rotary furnace. The results provided by neuro-fuzzy model compares well with the experimental data. This work has considerable implications in selection and control of process variables in real time and ability to achieve energy and material savings, quality improvement and development of homogeneous properties throughout the casting and is a step towards agile manufacturing.
Fuzzy modeling require two main steps which are structure identification and parameter optimization, the
first one determines the numbers of membership functions and fuzzy if-then rules, while the second
identifies a feasible set of parameters under the given structure. However, the increase of input dimension,
rule numbers will have an exponential growth and there will cause problem of “rule disaster”. In this
paper, we have applied adaptive network fuzzy inference system ANFIS for phonemes recognition. The
appropriate learning algorithm is performed on TIMIT speech database supervised type, a pre-processing
of the acoustic signal and extracting the coefficients MFCCs parameters relevant to the recognition system.
First learning of the network structure by subtractive clustering, in order to define an optimal structure and
obtain small number of rules, then learning of parameters network by hybrid learning which combine the
gradient decent and least square estimation LSE to find a feasible set of antecedents and consequents
parameters. The results obtained show the effectiveness of the method in terms of recognition rate and
number of fuzzy rules generated.
SPECIFICATION OF THE STATE’S LIFETIME IN THE DEVS FORMALISM BY FUZZY CONTROLLERijait
This paper aims to develop a new approach to assess the duration of state in the DEVS formalism by fuzzy
controller. The idea is to define a set of fuzzy rules obtained from observers or expert knowledge and to
specify a fuzzy model which computes this duration, this latter is fed into the simulator to specify the new
value in the model. In conventional model, each state is defined by a mean lifetime value whereas our
method, calculates for each state the new lifetime according to inputs values. A wildfire case study is
presented at the end of the paper. It is a challenging task due to its complex behavior, dynamical weather
condition, and various variables involved. A global specification of the fuzzy controller and the forest fire
model are presented in the DEVS formalism and comparison between conventional and fuzzy method is
illustrated.
ROLE OF CERTAINTY FACTOR IN GENERATING ROUGH-FUZZY RULEIJCSEA Journal
The generation of effective feature-based rules is essential to the development of any intelligent system. This paper presents an approach that integrates a powerful fuzzy rule generation algorithm with a rough set-assisted feature reduction method to generate diagnostic rule with a certainty factor. Certainty factor of each rule is calculated by considering both the membership value of each linguistic term introduced at time of fuzzyfication of data as well as possibility values, due to inconsistent data, generated by rough set theory at time of rule generation. In time of knowledge inferencing in an intelligent system, certainty factor of each rule will play an important role to find out the appropriate rule to be selected. Experimental results demonstrate the superiority of our approach.
This document discusses fuzzy rule-based classification systems. There are three types of rules that can be formed: assignment statements, conditional statements, and unconditional statements. A fuzzy inference system uses a rule base of fuzzy rules to perform fuzzy reasoning and mapping of fuzzy inputs to outputs. The key components of a fuzzy inference system are fuzzification of inputs, a rule base, an inference engine, and defuzzification of outputs. Fuzzy rule-based systems find application in decision making problems.
This document summarizes an article about using an artificial bee colony (ABC) algorithm to extract knowledge from numerical data to generate fuzzy rules. The ABC algorithm is an optimization technique inspired by honeybee behavior that can be used for data-driven modeling when domain experts are unavailable. The article describes fuzzy systems and their components, defines the problem of generating fuzzy rules from data as a minimization problem, and provides an example of applying the ABC algorithm to generate rules for a rapid battery charger system based on temperature and charging rate data.
Travis Hills' Endeavors in Minnesota: Fostering Environmental and Economic Pr...Travis Hills MN
Travis Hills of Minnesota developed a method to convert waste into high-value dry fertilizer, significantly enriching soil quality. By providing farmers with a valuable resource derived from waste, Travis Hills helps enhance farm profitability while promoting environmental stewardship. Travis Hills' sustainable practices lead to cost savings and increased revenue for farmers by improving resource efficiency and reducing waste.
The ability to recreate computational results with minimal effort and actionable metrics provides a solid foundation for scientific research and software development. When people can replicate an analysis at the touch of a button using open-source software, open data, and methods to assess and compare proposals, it significantly eases verification of results, engagement with a diverse range of contributors, and progress. However, we have yet to fully achieve this; there are still many sociotechnical frictions.
Inspired by David Donoho's vision, this talk aims to revisit the three crucial pillars of frictionless reproducibility (data sharing, code sharing, and competitive challenges) with the perspective of deep software variability.
Our observation is that multiple layers — hardware, operating systems, third-party libraries, software versions, input data, compile-time options, and parameters — are subject to variability that exacerbates frictions but is also essential for achieving robust, generalizable results and fostering innovation. I will first review the literature, providing evidence of how the complex variability interactions across these layers affect qualitative and quantitative software properties, thereby complicating the reproduction and replication of scientific studies in various fields.
I will then present some software engineering and AI techniques that can support the strategic exploration of variability spaces. These include the use of abstractions and models (e.g., feature models), sampling strategies (e.g., uniform, random), cost-effective measurements (e.g., incremental build of software configurations), and dimensionality reduction methods (e.g., transfer learning, feature selection, software debloating).
I will finally argue that deep variability is both the problem and solution of frictionless reproducibility, calling the software science community to develop new methods and tools to manage variability and foster reproducibility in software systems.
Exposé invité Journées Nationales du GDR GPL 2024
Comparing Evolved Extractive Text Summary Scores of Bidirectional Encoder Rep...University of Maribor
Slides from:
11th International Conference on Electrical, Electronics and Computer Engineering (IcETRAN), Niš, 3-6 June 2024
Track: Artificial Intelligence
https://www.etran.rs/2024/en/home-english/
Nucleophilic Addition of carbonyl compounds.pptxSSR02
Nucleophilic addition is the most important reaction of carbonyls. Not just aldehydes and ketones, but also carboxylic acid derivatives in general.
Carbonyls undergo addition reactions with a large range of nucleophiles.
Comparing the relative basicity of the nucleophile and the product is extremely helpful in determining how reversible the addition reaction is. Reactions with Grignards and hydrides are irreversible. Reactions with weak bases like halides and carboxylates generally don’t happen.
Electronic effects (inductive effects, electron donation) have a large impact on reactivity.
Large groups adjacent to the carbonyl will slow the rate of reaction.
Neutral nucleophiles can also add to carbonyls, although their additions are generally slower and more reversible. Acid catalysis is sometimes employed to increase the rate of addition.
The use of Nauplii and metanauplii artemia in aquaculture (brine shrimp).pptxMAGOTI ERNEST
Although Artemia has been known to man for centuries, its use as a food for the culture of larval organisms apparently began only in the 1930s, when several investigators found that it made an excellent food for newly hatched fish larvae (Litvinenko et al., 2023). As aquaculture developed in the 1960s and ‘70s, the use of Artemia also became more widespread, due both to its convenience and to its nutritional value for larval organisms (Arenas-Pardo et al., 2024). The fact that Artemia dormant cysts can be stored for long periods in cans, and then used as an off-the-shelf food requiring only 24 h of incubation makes them the most convenient, least labor-intensive, live food available for aquaculture (Sorgeloos & Roubach, 2021). The nutritional value of Artemia, especially for marine organisms, is not constant, but varies both geographically and temporally. During the last decade, however, both the causes of Artemia nutritional variability and methods to improve poorquality Artemia have been identified (Loufi et al., 2024).
Brine shrimp (Artemia spp.) are used in marine aquaculture worldwide. Annually, more than 2,000 metric tons of dry cysts are used for cultivation of fish, crustacean, and shellfish larva. Brine shrimp are important to aquaculture because newly hatched brine shrimp nauplii (larvae) provide a food source for many fish fry (Mozanzadeh et al., 2021). Culture and harvesting of brine shrimp eggs represents another aspect of the aquaculture industry. Nauplii and metanauplii of Artemia, commonly known as brine shrimp, play a crucial role in aquaculture due to their nutritional value and suitability as live feed for many aquatic species, particularly in larval stages (Sorgeloos & Roubach, 2021).
Deep Behavioral Phenotyping in Systems Neuroscience for Functional Atlasing a...Ana Luísa Pinho
Functional Magnetic Resonance Imaging (fMRI) provides means to characterize brain activations in response to behavior. However, cognitive neuroscience has been limited to group-level effects referring to the performance of specific tasks. To obtain the functional profile of elementary cognitive mechanisms, the combination of brain responses to many tasks is required. Yet, to date, both structural atlases and parcellation-based activations do not fully account for cognitive function and still present several limitations. Further, they do not adapt overall to individual characteristics. In this talk, I will give an account of deep-behavioral phenotyping strategies, namely data-driven methods in large task-fMRI datasets, to optimize functional brain-data collection and improve inference of effects-of-interest related to mental processes. Key to this approach is the employment of fast multi-functional paradigms rich on features that can be well parametrized and, consequently, facilitate the creation of psycho-physiological constructs to be modelled with imaging data. Particular emphasis will be given to music stimuli when studying high-order cognitive mechanisms, due to their ecological nature and quality to enable complex behavior compounded by discrete entities. I will also discuss how deep-behavioral phenotyping and individualized models applied to neuroimaging data can better account for the subject-specific organization of domain-general cognitive systems in the human brain. Finally, the accumulation of functional brain signatures brings the possibility to clarify relationships among tasks and create a univocal link between brain systems and mental functions through: (1) the development of ontologies proposing an organization of cognitive processes; and (2) brain-network taxonomies describing functional specialization. To this end, tools to improve commensurability in cognitive science are necessary, such as public repositories, ontology-based platforms and automated meta-analysis tools. I will thus discuss some brain-atlasing resources currently under development, and their applicability in cognitive as well as clinical neuroscience.
The debris of the ‘last major merger’ is dynamically youngSérgio Sacani
The Milky Way’s (MW) inner stellar halo contains an [Fe/H]-rich component with highly eccentric orbits, often referred to as the
‘last major merger.’ Hypotheses for the origin of this component include Gaia-Sausage/Enceladus (GSE), where the progenitor
collided with the MW proto-disc 8–11 Gyr ago, and the Virgo Radial Merger (VRM), where the progenitor collided with the
MW disc within the last 3 Gyr. These two scenarios make different predictions about observable structure in local phase space,
because the morphology of debris depends on how long it has had to phase mix. The recently identified phase-space folds in Gaia
DR3 have positive caustic velocities, making them fundamentally different than the phase-mixed chevrons found in simulations
at late times. Roughly 20 per cent of the stars in the prograde local stellar halo are associated with the observed caustics. Based
on a simple phase-mixing model, the observed number of caustics are consistent with a merger that occurred 1–2 Gyr ago.
We also compare the observed phase-space distribution to FIRE-2 Latte simulations of GSE-like mergers, using a quantitative
measurement of phase mixing (2D causticality). The observed local phase-space distribution best matches the simulated data
1–2 Gyr after collision, and certainly not later than 3 Gyr. This is further evidence that the progenitor of the ‘last major merger’
did not collide with the MW proto-disc at early times, as is thought for the GSE, but instead collided with the MW disc within
the last few Gyr, consistent with the body of work surrounding the VRM.
The binding of cosmological structures by massless topological defectsSérgio Sacani
Assuming spherical symmetry and weak field, it is shown that if one solves the Poisson equation or the Einstein field
equations sourced by a topological defect, i.e. a singularity of a very specific form, the result is a localized gravitational
field capable of driving flat rotation (i.e. Keplerian circular orbits at a constant speed for all radii) of test masses on a thin
spherical shell without any underlying mass. Moreover, a large-scale structure which exploits this solution by assembling
concentrically a number of such topological defects can establish a flat stellar or galactic rotation curve, and can also deflect
light in the same manner as an equipotential (isothermal) sphere. Thus, the need for dark matter or modified gravity theory is
mitigated, at least in part.
What is greenhouse gasses and how many gasses are there to affect the Earth.moosaasad1975
What are greenhouse gasses how they affect the earth and its environment what is the future of the environment and earth how the weather and the climate effects.