Sometimes, an experimental situation may arise where experimental units are following smooth pattern of trend over time and space. In that situation, to eliminate the effect of uncontrollable variables that are correlated with the time, we use systematic run order instead of randomising the run order. An ordering of treatments, thus obtained is known as Trend free design. This article presents a method for constructing trend free fractional factorial design using parity check matrix of a linear code. The method provides a systematic approach to construct fractional and blocked fractional factorial design with trend free main effects and some two- factor interactions.
This document discusses lower bounds and limitations of algorithms. It begins by defining lower bounds and providing examples of problems where tight lower bounds have been established, such as sorting requiring Ω(nlogn) comparisons. It then discusses methods for establishing lower bounds, including trivial bounds, decision trees, adversary arguments, and problem reduction. The document explores different classes of problems based on complexity, such as P, NP, and NP-complete problems. It concludes by examining approaches for tackling difficult combinatorial problems that are NP-hard, such as using exact algorithms, approximation algorithms, and local search heuristics.
This document discusses dynamic programming and greedy algorithms. It begins by defining dynamic programming as a technique for solving problems with overlapping subproblems. Examples provided include computing the Fibonacci numbers and binomial coefficients. Greedy algorithms are introduced as constructing solutions piece by piece through locally optimal choices. Applications discussed are the change-making problem, minimum spanning trees using Prim's and Kruskal's algorithms, and single-source shortest paths. Floyd's algorithm for all pairs shortest paths and optimal binary search trees are also summarized.
This document discusses algorithms and their analysis. It defines an algorithm as a step-by-step procedure to solve a problem or calculate a quantity. Algorithm analysis involves evaluating memory usage and time complexity. Asymptotics, such as Big-O notation, are used to formalize the growth rates of algorithms. Common sorting algorithms like insertion sort and quicksort are analyzed using recurrence relations to determine their time complexities as O(n^2) and O(nlogn), respectively.
The document discusses algorithms and data structures using divide and conquer and greedy approaches. It covers topics like matrix multiplication, convex hull, binary search, activity selection problem, knapsack problem, and their algorithms and time complexities. Examples are provided for convex hull, binary search, activity selection, and knapsack problem algorithms. The document is intended as teaching material on design and analysis of algorithms.
Divide and Conquer - Part II - Quickselect and Closest Pair of PointsAmrinder Arora
This document discusses divide and conquer algorithms. It covers the closest pair of points problem, which can be solved in O(n log n) time using a divide and conquer approach. It also discusses selection algorithms like quickselect that can find the median or kth element of an unsorted array in linear time O(n) on average. The document provides pseudocode for these algorithms and analyzes their time complexity using recurrence relations. It also provides an overview of topics like mergesort, quicksort, and solving recurrence relations that were covered in previous lectures.
This document discusses hashing techniques for indexing and retrieving elements in a data structure. It begins by defining hashing and its components like hash functions, collisions, and collision handling. It then describes two common collision handling techniques - separate chaining and open addressing. Separate chaining uses linked lists to handle collisions while open addressing resolves collisions by probing to find alternate empty slots using techniques like linear probing and quadratic probing. The document provides examples and explanations of how these hashing techniques work.
This document discusses analyzing the efficiency of algorithms. It begins by explaining how to measure algorithm efficiency using Big O notation, which estimates how fast an algorithm's execution time grows as the input size increases. Common growth rates like constant, logarithmic, linear, and quadratic time are described. Examples are provided to demonstrate determining the Big O of various algorithms. Specific algorithms analyzed in more depth include binary search, selection sort, insertion sort, and Towers of Hanoi. The document aims to introduce techniques for developing efficient algorithms using approaches like dynamic programming, divide-and-conquer, and backtracking.
This document discusses lower bounds and limitations of algorithms. It begins by defining lower bounds and providing examples of problems where tight lower bounds have been established, such as sorting requiring Ω(nlogn) comparisons. It then discusses methods for establishing lower bounds, including trivial bounds, decision trees, adversary arguments, and problem reduction. The document explores different classes of problems based on complexity, such as P, NP, and NP-complete problems. It concludes by examining approaches for tackling difficult combinatorial problems that are NP-hard, such as using exact algorithms, approximation algorithms, and local search heuristics.
This document discusses dynamic programming and greedy algorithms. It begins by defining dynamic programming as a technique for solving problems with overlapping subproblems. Examples provided include computing the Fibonacci numbers and binomial coefficients. Greedy algorithms are introduced as constructing solutions piece by piece through locally optimal choices. Applications discussed are the change-making problem, minimum spanning trees using Prim's and Kruskal's algorithms, and single-source shortest paths. Floyd's algorithm for all pairs shortest paths and optimal binary search trees are also summarized.
This document discusses algorithms and their analysis. It defines an algorithm as a step-by-step procedure to solve a problem or calculate a quantity. Algorithm analysis involves evaluating memory usage and time complexity. Asymptotics, such as Big-O notation, are used to formalize the growth rates of algorithms. Common sorting algorithms like insertion sort and quicksort are analyzed using recurrence relations to determine their time complexities as O(n^2) and O(nlogn), respectively.
The document discusses algorithms and data structures using divide and conquer and greedy approaches. It covers topics like matrix multiplication, convex hull, binary search, activity selection problem, knapsack problem, and their algorithms and time complexities. Examples are provided for convex hull, binary search, activity selection, and knapsack problem algorithms. The document is intended as teaching material on design and analysis of algorithms.
Divide and Conquer - Part II - Quickselect and Closest Pair of PointsAmrinder Arora
This document discusses divide and conquer algorithms. It covers the closest pair of points problem, which can be solved in O(n log n) time using a divide and conquer approach. It also discusses selection algorithms like quickselect that can find the median or kth element of an unsorted array in linear time O(n) on average. The document provides pseudocode for these algorithms and analyzes their time complexity using recurrence relations. It also provides an overview of topics like mergesort, quicksort, and solving recurrence relations that were covered in previous lectures.
This document discusses hashing techniques for indexing and retrieving elements in a data structure. It begins by defining hashing and its components like hash functions, collisions, and collision handling. It then describes two common collision handling techniques - separate chaining and open addressing. Separate chaining uses linked lists to handle collisions while open addressing resolves collisions by probing to find alternate empty slots using techniques like linear probing and quadratic probing. The document provides examples and explanations of how these hashing techniques work.
This document discusses analyzing the efficiency of algorithms. It begins by explaining how to measure algorithm efficiency using Big O notation, which estimates how fast an algorithm's execution time grows as the input size increases. Common growth rates like constant, logarithmic, linear, and quadratic time are described. Examples are provided to demonstrate determining the Big O of various algorithms. Specific algorithms analyzed in more depth include binary search, selection sort, insertion sort, and Towers of Hanoi. The document aims to introduce techniques for developing efficient algorithms using approaches like dynamic programming, divide-and-conquer, and backtracking.
The document discusses the framework for analyzing the efficiency of algorithms by measuring how the running time and space requirements grow as the input size increases, focusing on determining the order of growth of the number of basic operations using asymptotic notation such as O(), Ω(), and Θ() to classify algorithms based on their worst-case, best-case, and average-case time complexities.
The document discusses the divide and conquer algorithm design strategy. It begins by explaining the general concept of divide and conquer, which involves splitting a problem into subproblems, solving the subproblems, and combining the solutions. It then provides pseudocode for a generic divide and conquer algorithm. Finally, it gives examples of divide and conquer algorithms like quicksort, binary search, and matrix multiplication.
The document discusses algorithm analysis and complexity. It covers key topics like asymptotic notation (Big-O, Big-Omega, Big-Theta), time and space complexity analysis, recurrence relations, and a case study on quicksort analysis. The outline presents introduction to algorithms, properties, studying algorithms, complexity concepts, asymptotic notation, recurrence relations, and a quicksort case study.
This document contains a past exam paper for the subject "Design and Analysis of Algorithms". It has 2 parts with a total of 15 questions. Part A covers basic algorithm concepts like recurrence relations, efficiency classes, minimum spanning trees, and more. Part B involves solving algorithm problems using techniques like dynamic programming, Huffman coding, shortest paths, and more. It also tests concepts like P vs NP, approximation algorithms, and analysis of algorithm efficiency.
The document discusses backtracking and branch and bound algorithms. Backtracking incrementally builds candidates and abandons them (backtracks) when they cannot lead to a valid solution. Branch and bound systematically enumerates solutions and discards branches that cannot produce a better solution than the best found so far based on upper bounds. Examples provided are the N-Queens problem solved with backtracking and the knapsack problem solved with branch and bound. Pseudocode is given for both algorithms.
Spline interpolation is a problem of "Numerical Methods".
This slide covers the basics of spline interpolation mostly the linear spline and cubic spline interpolation.
This document contains information about Kamalesh Karmakar, an assistant professor in the computer science department at Meghnad Saha Institute of Technology. It lists the algorithm topics he teaches, including algorithm analysis, design techniques, complexity theory, and more. It also provides references for algorithm textbooks and notes on time and space complexity analysis, asymptotic notation, and different algorithm design techniques like divide-and-conquer, dynamic programming, backtracking, and greedy methods.
The document discusses divide and conquer algorithms. It describes divide and conquer as a design strategy that involves dividing a problem into smaller subproblems, solving the subproblems recursively, and combining the solutions. It provides examples of divide and conquer algorithms like merge sort, quicksort, and binary search. Merge sort works by recursively sorting halves of an array until it is fully sorted. Quicksort selects a pivot element and partitions the array into subarrays of smaller and larger elements, recursively sorting the subarrays. Binary search recursively searches half-intervals of a sorted array to find a target value.
The document discusses the analysis of algorithms. It begins by defining an algorithm and describing different types. It then covers analyzing algorithms in terms of correctness, time efficiency, space efficiency, and optimality through theoretical and empirical analysis. The document discusses analyzing time efficiency by determining the number of repetitions of basic operations as a function of input size. It provides examples of input size, basic operations, and formulas for counting operations. It also covers analyzing best, worst, and average cases and establishes asymptotic efficiency classes. The document then analyzes several examples of non-recursive and recursive algorithms.
This document discusses various algorithms and problems including:
1) The Towers of Hanoi puzzle and its solution requiring 2n-1 moves for n disks.
2) Permutations and two methods for generating all possible permutations.
3) The n-queens problem of placing n queens on an n×n chessboard without any queens threatening each other, solved using backtracking.
4) Backtracking as a general method for constraint satisfaction problems.
Spline interpolation is a technique for generating new data points within the range of a discrete set of known data points. It uses piecewise polynomials, typically cubic polynomials, to fit curves to these data points. The document discusses linear and quadratic spline interpolation and provides an example of using quadratic splines to interpolate the velocity of a rocket at different times and calculate the velocity, distance, and acceleration at t=16 seconds.
This is the second lecture in the CS 6212 class. Covers asymptotic notation and data structures. Also outlines the coming lectures wherein we will study the various algorithm design techniques.
This document summarizes a research paper that proposes using motif discovery in time series data to make predictions. It begins by defining key concepts in time series analysis like motifs, distances, and ARIMA models. It then describes the specific approach taken - using the Chouakria index with CID similarity measure to identify motifs, which are then used to build prediction models. The results of this approach on several time series are compared to ARIMA models, finding the motif-based models provide better performance according to error metrics.
Analysis and design of algorithms part 4Deepak John
Complexity Theory - Introduction. P and NP. NP-Complete problems. Approximation algorithms. Bin packing, Graph coloring. Traveling salesperson Problem.
Dynamic programming is a mathematical optimization method and computer programming technique used to solve complex problems by breaking them down into simpler subproblems. It was developed by Richard Bellman in the 1950s and has been applied in many fields. Dynamic programming problems can be solved optimally by breaking them into subproblems with optimal substructures that can be solved recursively. It uses techniques like top-down or bottom-up approaches and storing results of subproblems to solve larger problems efficiently by avoiding recomputing the common subproblems. Multistage graphs are a type of problem well-suited for dynamic programming solutions using techniques like greedy algorithms, Dijkstra's algorithm, or dynamic programming to find shortest paths. Traversal and search algorithms like breadth-
Unit 1: Fundamentals of the Analysis of Algorithmic Efficiency, Units for Measuring Running Time, PROPERTIES OF AN ALGORITHM, Growth of Functions, Algorithm - Analysis, Asymptotic Notations, Recurrence Relation and problems
The document discusses approximation algorithms and genetic algorithms for solving optimization problems like the traveling salesman problem (TSP) and vertex cover problem. It provides examples of approximation algorithms for these NP-hard problems, including algorithms that find near-optimal solutions within polynomial time. Genetic algorithms are also presented as an approach to solve TSP and other problems by encoding potential solutions and applying genetic operators like crossover and mutation.
Einstein creía que debemos ser constantes en nuestros objetivos, pero flexibles en los medios para lograrlos. La toma de decisiones es el proceso de elegir entre opciones para resolver situaciones y problemas, requiriendo el análisis y comprensión del problema. Las decisiones deben ser lo más asertivas posible considerando tanto el pensamiento lógico como la intuición.
The document discusses the framework for analyzing the efficiency of algorithms by measuring how the running time and space requirements grow as the input size increases, focusing on determining the order of growth of the number of basic operations using asymptotic notation such as O(), Ω(), and Θ() to classify algorithms based on their worst-case, best-case, and average-case time complexities.
The document discusses the divide and conquer algorithm design strategy. It begins by explaining the general concept of divide and conquer, which involves splitting a problem into subproblems, solving the subproblems, and combining the solutions. It then provides pseudocode for a generic divide and conquer algorithm. Finally, it gives examples of divide and conquer algorithms like quicksort, binary search, and matrix multiplication.
The document discusses algorithm analysis and complexity. It covers key topics like asymptotic notation (Big-O, Big-Omega, Big-Theta), time and space complexity analysis, recurrence relations, and a case study on quicksort analysis. The outline presents introduction to algorithms, properties, studying algorithms, complexity concepts, asymptotic notation, recurrence relations, and a quicksort case study.
This document contains a past exam paper for the subject "Design and Analysis of Algorithms". It has 2 parts with a total of 15 questions. Part A covers basic algorithm concepts like recurrence relations, efficiency classes, minimum spanning trees, and more. Part B involves solving algorithm problems using techniques like dynamic programming, Huffman coding, shortest paths, and more. It also tests concepts like P vs NP, approximation algorithms, and analysis of algorithm efficiency.
The document discusses backtracking and branch and bound algorithms. Backtracking incrementally builds candidates and abandons them (backtracks) when they cannot lead to a valid solution. Branch and bound systematically enumerates solutions and discards branches that cannot produce a better solution than the best found so far based on upper bounds. Examples provided are the N-Queens problem solved with backtracking and the knapsack problem solved with branch and bound. Pseudocode is given for both algorithms.
Spline interpolation is a problem of "Numerical Methods".
This slide covers the basics of spline interpolation mostly the linear spline and cubic spline interpolation.
This document contains information about Kamalesh Karmakar, an assistant professor in the computer science department at Meghnad Saha Institute of Technology. It lists the algorithm topics he teaches, including algorithm analysis, design techniques, complexity theory, and more. It also provides references for algorithm textbooks and notes on time and space complexity analysis, asymptotic notation, and different algorithm design techniques like divide-and-conquer, dynamic programming, backtracking, and greedy methods.
The document discusses divide and conquer algorithms. It describes divide and conquer as a design strategy that involves dividing a problem into smaller subproblems, solving the subproblems recursively, and combining the solutions. It provides examples of divide and conquer algorithms like merge sort, quicksort, and binary search. Merge sort works by recursively sorting halves of an array until it is fully sorted. Quicksort selects a pivot element and partitions the array into subarrays of smaller and larger elements, recursively sorting the subarrays. Binary search recursively searches half-intervals of a sorted array to find a target value.
The document discusses the analysis of algorithms. It begins by defining an algorithm and describing different types. It then covers analyzing algorithms in terms of correctness, time efficiency, space efficiency, and optimality through theoretical and empirical analysis. The document discusses analyzing time efficiency by determining the number of repetitions of basic operations as a function of input size. It provides examples of input size, basic operations, and formulas for counting operations. It also covers analyzing best, worst, and average cases and establishes asymptotic efficiency classes. The document then analyzes several examples of non-recursive and recursive algorithms.
This document discusses various algorithms and problems including:
1) The Towers of Hanoi puzzle and its solution requiring 2n-1 moves for n disks.
2) Permutations and two methods for generating all possible permutations.
3) The n-queens problem of placing n queens on an n×n chessboard without any queens threatening each other, solved using backtracking.
4) Backtracking as a general method for constraint satisfaction problems.
Spline interpolation is a technique for generating new data points within the range of a discrete set of known data points. It uses piecewise polynomials, typically cubic polynomials, to fit curves to these data points. The document discusses linear and quadratic spline interpolation and provides an example of using quadratic splines to interpolate the velocity of a rocket at different times and calculate the velocity, distance, and acceleration at t=16 seconds.
This is the second lecture in the CS 6212 class. Covers asymptotic notation and data structures. Also outlines the coming lectures wherein we will study the various algorithm design techniques.
This document summarizes a research paper that proposes using motif discovery in time series data to make predictions. It begins by defining key concepts in time series analysis like motifs, distances, and ARIMA models. It then describes the specific approach taken - using the Chouakria index with CID similarity measure to identify motifs, which are then used to build prediction models. The results of this approach on several time series are compared to ARIMA models, finding the motif-based models provide better performance according to error metrics.
Analysis and design of algorithms part 4Deepak John
Complexity Theory - Introduction. P and NP. NP-Complete problems. Approximation algorithms. Bin packing, Graph coloring. Traveling salesperson Problem.
Dynamic programming is a mathematical optimization method and computer programming technique used to solve complex problems by breaking them down into simpler subproblems. It was developed by Richard Bellman in the 1950s and has been applied in many fields. Dynamic programming problems can be solved optimally by breaking them into subproblems with optimal substructures that can be solved recursively. It uses techniques like top-down or bottom-up approaches and storing results of subproblems to solve larger problems efficiently by avoiding recomputing the common subproblems. Multistage graphs are a type of problem well-suited for dynamic programming solutions using techniques like greedy algorithms, Dijkstra's algorithm, or dynamic programming to find shortest paths. Traversal and search algorithms like breadth-
Unit 1: Fundamentals of the Analysis of Algorithmic Efficiency, Units for Measuring Running Time, PROPERTIES OF AN ALGORITHM, Growth of Functions, Algorithm - Analysis, Asymptotic Notations, Recurrence Relation and problems
The document discusses approximation algorithms and genetic algorithms for solving optimization problems like the traveling salesman problem (TSP) and vertex cover problem. It provides examples of approximation algorithms for these NP-hard problems, including algorithms that find near-optimal solutions within polynomial time. Genetic algorithms are also presented as an approach to solve TSP and other problems by encoding potential solutions and applying genetic operators like crossover and mutation.
Einstein creía que debemos ser constantes en nuestros objetivos, pero flexibles en los medios para lograrlos. La toma de decisiones es el proceso de elegir entre opciones para resolver situaciones y problemas, requiriendo el análisis y comprensión del problema. Las decisiones deben ser lo más asertivas posible considerando tanto el pensamiento lógico como la intuición.
La amistad se define como un sentimiento compartido entre dos personas que están ahí el uno para el otro en los momentos difíciles y en todo momento, compartiendo secretos, aventuras y buenos tiempos juntos. Los amigos verdaderos son personas especiales en las que siempre se puede confiar y que no abandonan a uno sin importar lo que pase.
Este documento proporciona instrucciones sobre cómo usar Webs.com para crear y administrar un blog. Explica que Webs.com permite crear un blog de la ONU y luego gestionar el sitio y las páginas a través de botones como "Páginas Manage", "Sitio Web de edición", y "Modificar la plantilla". También describe cómo agregar nuevas páginas y elementos como calendarios y tiendas, y cambiar la plantilla y fondo del sitio.
Este documento define varios términos clave relacionados con el alojamiento web y el desarrollo de sitios. Explica que el hosting es dar alojamiento a una página web en un servidor para que sea accesible a nivel mundial, una URL es la dirección que identifica un recurso en internet, HTTP es el protocolo que permite solicitudes y respuestas entre clientes y servidores web, FTP permite transferir archivos entre computadoras en una red, y PHP es un lenguaje de programación usado principalmente para crear páginas web dinámicas
Strategy Inventory for Language Learning (SILL) surveyFazleen Jaffar
This document contains a strategy inventory for language learning (SILL) survey. The survey asks learners of a second language to rate statements about their language learning strategies and behaviors on a scale of 1 to 5, with 1 being "never or almost never true of me" and 5 being "always or almost always true of me". The survey is divided into 6 parts covering strategies like cognitive strategies, memory strategies, compensation strategies, metacognitive strategies, affective strategies, and social strategies. Respondents are asked to indicate how well each statement describes them as a language learner.
La voz de Jesús, susurrada con ternura en nuestro interior y en el encuentro con l@s herman@s... nos devuelve nuestro verdadero rostro: la imagen bella con que Dios nos creó.
Vibration Controller | Electrodynamic Vibration Systemsdyn India
Sdyn’s Vibration Controllers are tailored in 4/8/16 channel configuration to bring users the most advanced and complete range of vibration testing solutions. Our Vibration Controllers are compatible with any make of amplifier and shaker combination available worldwide.
http://sdyn.in/
Fritz Pfleumer was a German-Austrian inventor born in 1881 in Salzburg who died in 1945 in Radebeul. He invented the first practical magnetic tape recorder called the MagnetophonK1 in 1931 and granted rights to his invention to AEG in 1932, who then built the world's first practical tape recorder.
(Module: Modules as requirement specifications)
At the end of this lab you will be able to:
► Modify the attributes of a module
► Explore how a change effected the module’s history
Given
► Automated Meter Reader (Water) project (AMR)
Description
► In this lab, you log in as Bob the analyst and add a few details to a module by modifying its attributes. Then, you view the module’s history.
Closet Works Beautifully Designed Spacessuetrainor
The document discusses the benefits of exercise for mental health. Regular physical activity can help reduce anxiety and depression and improve mood and cognitive function. Exercise causes chemical changes in the brain that may help protect against mental illness and improve symptoms.
SQL Power Group provides a fully-integrated data collection and analytics platform that allows governments to collect machine-readable data through online forms. This platform automates government services and regulatory functions, providing a single portal for citizens to complete tax returns, applications, and other requests online. It enables real-time validation of submitted data and real-time analytics. The platform increases efficiencies, reduces costs, and provides governments with valuable data that can be analyzed across departments and jurisdictions.
1) The document describes a vehicle routing project that uses a multi-commodity network flow formulation to explore sub-optimal solutions for object classification with noisy sensors on a 2D grid.
2) It formulates the problem as assigning tasks to vehicles (commodities) that must flow through the graph in 4 directions while being constrained by boundaries and returning to base.
3) The algorithm uses a look-ahead window to consider future moves and a rollout step using linear programming to approximate costs farther in time and decide optimal vehicle movements.
Applying Model Checking Approach with Floating Point Arithmetic for Verificat...Sergey Staroletov
The document discusses applying model checking to verify a hybrid model of an air collision avoidance maneuver that involves floating point calculations. It proposes representing floating point numbers as integers in Promela to enable modeling the maneuver's dynamics and implementing trigonometric and other functions. The goal is to model check the system's safety property that the distance between aircraft remains above a safe threshold during the maneuver.
Super-resolution reconstruction is a method for reconstructing higher resolution images from a set of low resolution observations. The sub-pixel differences among different observations of the same scene allow to create higher resolution images with better quality. In the last thirty years, many methods for creating high resolution images have been proposed. However, hardware implementations of such methods are limited. Wiener filter design is one of the techniques we will use initially for this process. Wiener filter design involves matrix inversion. A novel method for the matrix inversion has been proposed in the report. QR decomposition will be the computational algorithm used using Givens Rotation.
In this paper generation of binary sequences derived from chaotic sequences defined over Z4 is proposed.
The six chaotic map equations considered in this paper are Logistic map, Tent Map, Cubic Map, Quadratic
Map and Bernoulli Map. Using these chaotic map equations, sequences over Z4 are generated which are
converted to binary sequences using polynomial mapping. Segments of sequences of different lengths are
tested for cross correlation and linear complexity properties. It is found that some segments of different
length of these sequences have good cross correlation and linear complexity properties. The Bit Error Rate
performance in DS-CDMA communication systems using these binary sequences is found to be better than
Gold sequences and Kasami sequences.
The key is the important part at any security system because it determines whether the system is strength or weakness. This paper aimed to proposed new way to generate keystream based on a combination between 3D Henoun map and 3D Cat map. The principle of the method consists in generating random numbers by using 3D Henon map and these numbers will transform to binary sequence. These sequence positions is permuted and Xoredusing 3D Cat map. The new key stream generator has successfully passed theNIST statistical test suite. The security analysisshows that it has large key space and its very sensitive initial conditions.
Propagation of Error Bounds due to Active Subspace ReductionMohammad
This document summarizes the propagation of error bounds due to active subspace reduction in computational models. It presents two algorithms for performing active subspace reduction: one that is gradient-free and reduces the response or state space, and one that is gradient-based and reduces the parameter space. It then develops a theorem for propagating error bounds across multiple reductions, both in the parameter and response spaces. Numerical experiments on an analytic function and a nuclear reactor pin cell model are used to validate the error bound approach.
Using QR Decomposition to calculate the sum of squares of a model has a limitation that the number of rows,
which is also the number of observations or responses, has to be greater than the total number of parameters used in the
model. The main goal in the experimental design model, as a part of the Linear Model, is to analyze the estimable function
of the parameters used in the model. In order not to deal with generalized invers, partitioned design matrix may be used
instead. This partitioned design matrix method may be used to calculate the sum of squares of the models whenever the total
number of parameters is greater than the number of observations. It can also be used to find the degrees of freedom of each
source of variation components. This method is discussed in a Balanced Nested-Factorial Experimental Design.
This document describes a quadratic assignment problem (QAP) involving assigning 358 constraints and 50 variables. It provides an example of a QAP with 3 facilities and 3 locations. The QAP aims to assign facilities to locations in a way that minimizes total cost, which is a function of the flow between facilities and the distance between locations. Several applications of QAP are discussed, including facility location, scheduling, and ergonomic design problems.
The International Journal of Engineering and Science (The IJES)theijes
The International Journal of Engineering & Science is aimed at providing a platform for researchers, engineers, scientists, or educators to publish their original research results, to exchange new ideas, to disseminate information in innovative designs, engineering experiences and technological skills. It is also the Journal's objective to promote engineering and technology education. All papers submitted to the Journal will be blind peer-reviewed. Only original articles will be published.
PCA is a dimensionality reduction technique that uses linear transformations to project high-dimensional data onto a lower-dimensional space while retaining as much information as possible. It works by identifying patterns in data and expressing the data in such a way as to highlight their similarities and differences. Specifically, PCA uses linear combinations of the original variables to extract the most important patterns from the data in the form of principal components. The first principal component accounts for as much of the variability in the data as possible, and each succeeding component accounts for as much of the remaining variability as possible.
The document describes a recursive algorithm for multi-step prediction with mixture models that have dynamic switching between components. It begins by introducing notations and reviewing individual models, including normal regression components and static/dynamic switching models. It then presents the mixture prediction algorithm, first for a static switching model by constructing a predictive distribution from weighted component predictions. For a dynamic switching model, it similarly takes point estimates from the previous time and substitutes them into components to make weighted averaged predictions over multiple steps. The algorithm is summarized as initializing component statistics and parameter estimates, then substituting previous estimates into components to obtain weighted mixture predictions for new data points.
Efficient Solution of Two-Stage Stochastic Linear Programs Using Interior Poi...SSA KPI
The document describes efficient solution methods for two-stage stochastic linear programs (SLPs) using interior point methods. Interior point methods require solving large, dense systems of linear equations at each iteration, which can be computationally difficult for SLPs due to their structure leading to dense matrices. The paper reviews methods for improving computational efficiency, including reformulating the problem, exploiting special structures like transpose products, and explicitly factorizing the matrices to solve smaller independent systems in parallel. Computational results show explicit factorizations generally require the least effort.
The document analyzes the use of the Tent map as a source of pseudorandom bits for generating binary codes. It evaluates the Tent map's period length, discrimination value, and merit factor. The Tent map is proposed as an alternative to traditional low-complexity pseudorandom bit generators. Different window functions are applied to the binary codes generated from the Tent map to reduce side lobes and improve performance. Results show discrimination increases with sequence length and some window functions perform better than others at different lengths.
A TRIANGLE-TRIANGLE INTERSECTION ALGORITHM csandit
This single algorithm can detect intersections between two triangles in 3D space, whether they are coplanar or crossing. It works by solving equations relating the triangles' vertices and finding values for parameters that satisfy constraints based on the triangles' geometry. The algorithm classifies any intersection found as a single point, line segment, or area. It was tested on different triangle pair configurations and intersection types, taking on average less than 0.1 seconds to compute.
Linear regression [Theory and Application (In physics point of view) using py...ANIRBANMAJUMDAR18
Machine-learning models are behind many recent technological advances, including high-accuracy translations of the text and self-driving cars. They are also increasingly used by researchers to help in solving physics problems, like Finding new phases of matter, Detecting interesting outliers
in data from high-energy physics experiments, Founding astronomical objects are known as gravitational lenses in maps of the night sky etc. The rudimentary algorithm that every Machine Learning enthusiast starts with is a linear regression algorithm. In statistics, linear regression is a linear approach to modelling the relationship between a scalar response (or dependent variable) and one or more explanatory variables (or independent
variables). Linear regression analysis (least squares) is used in a physics lab to prepare the computer-aided report and to fit data. In this article, the application is made to experiment: 'DETERMINATION OF DIELECTRIC CONSTANT OF NON-CONDUCTING LIQUIDS'. The entire computation is made through Python 3.6 programming language in this article.
Traveling Salesman Problem in Distributed Environmentcsandit
In this paper, we focus on developing parallel algorithms for solving the traveling salesman problem (TSP) based on Nicos Christofides algorithm released in 1976. The parallel algorithm
is built in the distributed environment with multi-processors (Master-Slave). The algorithm is installed on the computer cluster system of National University of Education in Hanoi,
Vietnam (ccs1.hnue.edu.vn) and uses the library PJ (Parallel Java). The results are evaluated and compared with other works.
TRAVELING SALESMAN PROBLEM IN DISTRIBUTED ENVIRONMENTcscpconf
The document describes developing a parallel algorithm for solving the traveling salesman problem (TSP) based on Christofides' algorithm. It discusses implementing Christofides' algorithm in a distributed environment using multiple processors. The parallel algorithm divides the graph vertices and distance matrix across slave processors, which calculate the minimum spanning tree in parallel. The master processor then finds odd-degree vertices, performs matching, and finds the Hamiltonian cycle to solve TSP. The algorithm is tested on a computer cluster using graphs of 20,000 and 30,000 nodes, showing improved runtime over the sequential algorithm.
The Catholic University of America School of Engineering .docxmattinsonjanel
The Catholic University of America
School of Engineering
Department of Electrical Engineering and Computer Science
CSC
513:
Fundamentals
of
Computer
Graphics
Assignment
1
1)
Write
the
parametric
form
of
a
ray
with
source
p
and
direction
d.
2)
Assuming
d
in
the
above
ray
is
a
unit
vector,
write
an
algorithm
that,
for
an
arbitrary
non-‐negative
integer
n,
generates
n
evenly
spaced
points
along
the
ray
at
1
unit
intervals.
3)
Write
the
parametric
form
of
the
unit
circle.
4)
Given
an
arbitrary
positive
integer
n,
write
an
algorithm
that
generates
n
evenly
spaced
points
that
are
sampled
along
the
unit
circle.
5)
Suppose
you
have
access
to
the
functions
scale(sx,
sy),
translate(tx,
ty),
and
rotate(α)
which
generate
the
corresponding
2D
homogeneous
transformation
matrices.
Using
these
functions,
write
the
expression
of
a
transformation
T
such
that
if
p
lies
on
the
unit
circle,
Tp
will
lie
on
an
ellipse
centered
at
c,
with
a
major
radius
r1,
minor
radius
r2
and
rotated
at
an
angle
of
α.
You
do
not
have
to
compute
the
full
matrix.
You
may
leave
it
expressed
using
the
above
functions.
Hint:
remember
that
order
is
important
and
that
operations
associate
from
the
"inside
out".
6)
Write
the
implicit
form
of
the
unit
sphere.
7)
Given
an
arbitrary
point
p,
write
a
test
to
determine
if
p
is
inside
the
unit
sphere.
8)
Suppose
you
are
given
an
affine
transformation
T
that
maps
the
unit
sphere
to
some
arbitrarily
located
and
oriented
ellipsoid.
Give
an
expression
which,
given
an
arbitrary
point
p,
determines
if
p
is
inside
said
ellipsoid.
Hint:
use
the
result
from
the
previous
exercise.
9)
You
are
given
the
vertices
of
a
convex
polygon
in
the
2D
plane
in
counter-‐clockwise
order
as
(p1,
...,
pn).
The
coordinates
of
vertex
pi
are
(xi,
yi).
9a)
(3
marks)
Give
an
expression
for
the
coordinates
of
the
outward-‐facing
normal
ni
of
the
edge
connecting
pi
and
pi+1.
9b)
(3
marks)
Let
q
=
(xq,
yq)
be
an
arbitrary
point
on
the
plane
containing
the
gi ...
Recurrent and Recursive Networks (Part 1)sohaib_alam
1. Recurrent neural networks (RNNs) can be represented as computational graphs that are unfolded through time. This unfolding allows the input size to remain fixed and for shared parameters to be used at each time step.
2. Common RNN architectures include those with recurrence between hidden units and those with recurrence from output to hidden units. Training RNNs involves backpropagation through time, which has linear time and memory costs with respect to the sequence length.
3. RNNs can be viewed as directed graphical models that represent the joint probability distribution over an output sequence conditioned on inputs. Introducing hidden units allows parameter sharing across time steps.
Similar to A technique to construct linear trend free fractional factorial design using some linear codes (20)
Evaluation of Agro-morphological Performances of Hybrid Varieties of Chili Pe...Premier Publishers
In Benin, chilli pepper is a widely consumed as vegetable whose production requires the use of performant varieties. This work assessed, at Parakou and Malanville, the performance of six F1 hybrids of chilli including five imported (Laali, Laser, Nandi, Kranti, Nandita) and one local (De cayenne), in completely randomized block design at four replications and 15 plants per elementary plot. Agro-morphological data were collected and submitted to analysis of variance and factor analysis of mixed data. The results showed the effects of variety, location and their interactions were highly significant for most of the growth, earliness and yield traits. Imported hybrid varieties showed the best performances compared to the local one. Multivariate analysis revealed that 'De cayenne' was earlier, short in size, thin-stemmed, red fruits and less yielding (≈ 1 t.ha-1). The imported hybrids LaaliF1 and KrantiF1 were of strong vegetative vigor, more yielding (> 6 t.ha-1) by developing larger, long and hard fruits. Other hybrids showed intermediate performances. This study highlighted the importance of imported hybrids in improving yield and preservation of chili fruits. However, stability and adaptation analyses to local conditions are necessary for their adoption.
An Empirical Approach for the Variation in Capital Market Price Changes Premier Publishers
The chances of an investor in the stock market depends mainly on some certain decisions in respect to equilibrium prices, which is the condition of a system competing favorably and effectively. This paper considered a stochastic model which was latter transformed to non-linear ordinary differential equation where stock volatility was used as a key parameter. The analytical solution was obtained which determined the equilibrium prices. A theorem was developed and proved to show that the proposed mathematical model follows a normal distribution since it has a symmetric property. Finally, graphical results were presented and the effects of the relevant parameters were discussed.
Influence of Nitrogen and Spacing on Growth and Yield of Chia (Salvia hispani...Premier Publishers
Chia is an emerging cash crop in Kenya and its production is inhibited by lack of agronomic management information. A field experiment was conducted in February-June and May-August 2021, to determine the influence of nitrogen and spacing on growth and yield of Chia. A randomized complete block design with a split plot arrangement was used with four nitrogen rates as the main plots (0, 40, 80, 120 kg N ha-1) and three spacing (30 cm x 15 cm (s1), 30 cm x 30 cm (s2), 50 cm x 50 cm (s3)). Application of 120 kg N ha-1 significantly increased (p≤0.05) vegetative growth and seed yield of Chia. Stem height, branches, stem diameter and leaves increased by 23-28%, 11-13%, 43-55% and 59-88% respectively. Spacing s3 significantly increased (p≤0.05) vegetative growth. An increase of 27-74%, 36-45% and 73-107% was recorded in number of leaves, stem diameter and dry weight, respectively. Chia yield per plant was significantly higher (p≤0.05) in s3. However, when expressed per unit area, s1 significantly produced higher yields. The study recommends 120 kg N ha-1 or higher nitrogen rates and a closer spacing of 15 cm x 30 cm as the best option for Chia production in Kenya.
Enhancing Social Capital During the Pandemic: A Case of the Rural Women in Bu...Premier Publishers
The document discusses a case study of enhancing social capital among rural women in Bukidnon Province, Philippines during the COVID-19 pandemic through a livelihood project. Key findings include:
1) Technical trainings provided by the project increased the women's knowledge, allowing them to generate additional household income through vegetable gardening during the pandemic.
2) The women's social capital, as measured by groups/networks, trust, and cooperation, increased by 15.5% from 2019 to 2020 through increased participation in their association.
3) Main occupations, income sources, and ethnicity influenced the women's social capital. The project enhanced social ties that empowered the rural women economically and socially despite challenges of the pandemic.
Impact of Provision of Litigation Supports through Forensic Investigations on...Premier Publishers
This paper presents an argument through the fraud triangle theory that the provision of litigation supports through forensic audits and investigations in relation to corporate fraud cases is adequate for effective prosecution of perpetrators as well as corporate fraud prevention. To support this argument, this study operationalized provision of litigation supports through forensic audit and investigations, data mining for trends and patterns, and fraud data collection and preparation. A sample of 500 respondents was drawn from the population of professional accountants and legal practitioners in Nigeria. Questionnaire was used as the instrument for data collection and this was mailed to the respective respondents. Resulting responses were analyzed using the OLS multiple regression techniques via the SPSS statistical software. The results reveal that the provision of litigation supports through forensic audits and investigations, fraud data mining for trends and patterns and fraud data collection and preparation for court proceedings have a positive and significant impact on corporate fraud prevention in Nigeria. This study therefore recommends that regulators should promote the provision of litigation supports through forensic audits and investigations in relation to corporate fraud cases in publicly listed firms in Nigeria, as this will help provide reports that are acceptable in court proceedings.
Improving the Efficiency of Ratio Estimators by Calibration WeightingsPremier Publishers
It is observed that the performances of most improved ratio estimators depend on some optimality conditions that need to be satisfied to guarantee better estimator. This paper develops a new approach to ratio estimation that produces a more efficient class of ratio estimators that do not depend on any optimality conditions for optimum performance using calibration weightings. The relative performances of the proposed calibration ratio estimators are compared with a corresponding global [Generalized Regression (GREG)] estimator. Results of analysis showed that the proposed calibration ratio estimators are substantially superior to the traditional GREG-estimator with relatively small bias, mean square error, average length of confidence interval and coverage probability. In general, the proposed calibration ratio estimators are more efficient than all existing estimators considered in the study.
Urban Liveability in the Context of Sustainable Development: A Perspective fr...Premier Publishers
Urbanization and quality of urban life are mutually related and however it varies geographically and regionally. With unprecedented growth of urban centres, challenge against urban development is more in terms of how to enhance quality of urban life and liveability. Making sense of and measuring urban liveability of urban places has become a crucial step in the context of sustainable development paradigm. Geographical regions depict variations in nature of urban development and consequently level of urban liveability. The coastal regain of West Bengal faces unusual challenges caused by increasing urbanization, uncontrolled growth, and expansion of economic activities like tourism and changing environmental quality. The present study offers a perspective on urban liveability of urban places located in coastal region comprising of Purba Medinipur and South 24 Parganas districts. The study uses the liveability standards covering four major pillars- institutional, social, economic and physical and their indicators. This leads to develop a City Liveability Index to rank urban places of the region, higher the index values better the urban liveability. The data for the purpose is collected from various secondary sources. Study finds that the eastern coastal region of the country covering state of West Bengal depicts variations in index of liveability determined by physical, economic, social and institutional indicators.
Transcript Level of Genes Involved in “Rebaudioside A” Biosynthesis Pathway u...Premier Publishers
Stevia rebaudiana Bertoni is a plant which has recently been used widely as a sweetener. This medicinal plant has some components such as diterpenoid glycosides called steviol glycosides [SGs]. Rebaudioside A is a diterpenoid steviol glycoside which is 300 times sweeter than table sugar. This study was done to investigate the effect of GA3 (50 mg/L) on the expression of 14 genes involved in Rebaudioside A biosynthesis pathway in Stevia rebaudiana under in vitro conditions. The expression of DXS remarkably decreased by day 3. Also, probably because of the negative feedback of GA3 on MEP-drived isoprenes, GGDS transcript level reached its lowest amount after GA3 treatment. The abundance of DXR, CMS, CMK, MCS, and CDPS transcripts showed a significant increase at various days after this treatment. A significant drop in the expression levels of KS and UGT85C2 is detected during the first day. However, expression changes of HDR and KD were not remarkable. Results revealed that the level of transcript of UGT74G1 and UGT76G1 up regulated significantly 4 and 2 times higher than control, respectively. However, more research needs to shed more light on the mechanism of GA3 on gene expression of MEP pathway.
Multivariate Analysis of Tea (Camellia sinensis (L.) O. Kuntze) Clones on Mor...Premier Publishers
Information on genetic variability for biochemical characters is a prerequisite for improvement of tea quality. Thirteen introduced tea clones characterized with objective; assessing tea clones based on morphological characters at Melko and Gera research stations. The study was conducted during 2017/18 cropping season on experimental plots in RCBD with three replications. Data recorded on morphological traits like days from pruning to harvest, height to first branch, stem diameter, leaf serration density, leaf length, leaf width, leaf size, petiole length, leaf ratio, internode length, shoot length, number of shoot, canopy diameter, hundred shoot weight, fresh leaf yield per tree. Cluster analysis of morphological trait grouped into four clusters indicated, the existence of divergence among the tested clones. The maximum inter-cluster distance was between clusters I and IV (35.27) while the minimum inter cluster distance was observed between clusters I and II (7.8).Principal components analysis showed that the first five principal components with eigenvalues greater than one accounted 86.45% for 15 morphological traits. Generally, the study indicated presence of variability for several morphological traits. However, high morphological variation between clones is not a guarantee for a high genetic variation; therefore, molecular studies need to be considered as complementary to biochemical studies.
Causes, Consequences and Remedies of Juvenile Delinquency in the Context of S...Premier Publishers
This research work was designed to examine nature of juvenile offences committed by juveniles, causes of juvenile delinquency, consequences of juvenile delinquency and remedies for juvenile delinquency in the context of Sub-Saharan Africa with specific reference to Eritrea. Left unchecked, juvenile delinquents on the streets engage in petty theft, take alcohol or drugs, rape women, rob people at night involve themselves in criminal gangs and threaten the public at night. To shed light on the problem of juvenile delinquency in the Sub-Saharan region data was collected through primary and secondary sources. A sample size of 70 juvenile delinquents was selected from among 112 juvenile delinquents in remand at the Asmara Juvenile Rehabilitation Center in the Eritrean capital. The study was carried out through coded self-administered questionnaires administered to a sample of 70 juvenile delinquents. The survey evidence indicates that the majority of the juvenile respondents come either from families constructed by unmarried couples or separated or divorced parents where largely the father is missing in the home or dead. The findings also indicate that children born out of wedlock, families led by single mothers, lack of fatherly role models, poor parental-child relationships and negative peer group influence as dominant causes of juvenile infractions. The implication is that broken and stressed families are highly likely to be the breeding grounds for juvenile delinquency. The survey evidence indicates that stealing, truancy or absenteeism from school, rowdy or unruly behavior at school, free-riding in public transportation, damaging the book of fellow students and beating other young persons are the most common forms of juvenile offenses. It is therefore, recommended that parents and guardians should exercise proper parental supervision and give adequate care to transmit positive societal values to children. In addition, the government, the police, prosecution and courts, non-government organizations, parents, teachers, religious leaders, education administrators and other stakeholders should develop a child justice system that strives to prevent children from entering deeper into the criminal justice process.
The Knowledge of and Attitude to and Beliefs about Causes and Treatments of M...Premier Publishers
Stigma and discrimination associated with mental illness are a common occurrence in the Sub-Saharan region including Eritrea. Numerous studies from Sub-Saharan Africa suggest that stigma and discrimination are major problems in the community, with negative attitudes and behavior towards people with mental illness being widespread. In order to assess the whether such negative attitudes persist in the context of Eritrea this study explored the knowledge and perceptions of 90 Eritrean university students at the College of Business and Economics, the University of Asmara regarding the causes and remedies of mental illness A qualitative method involving coded self-administered questionnaires administered to a sample of 90 university students to collecting data at the end of 2019. The survey evidence points that almost 50% of the respondents had contact with a mentally ill person suggesting that the significant number of the respondents experienced a first-hand encounter and knowledge of mental illness in their family and community. The findings show an overall greater science-based understanding of the causes of mental illness to be followed by recommended psychiatric treatments. The survey evidence indicates that the top three leading causes of mental illness in the context of Eritrea according to the respondents are brain disease (76%), bad events in the life of the mentally ill person (66%) and substance abuse or alcohol taking, smoking, taking drugs like hashish. (54%). The majority of the respondents have a very sympathetic and positive outlook towards mentally ill persons suggesting that mentally illness does not simply affect a chosen individual rather it can happen to anybody regardless of economic class, social status, ethnicity race and religion. Medical interventions cited by the majority of the respondents as being effective treatments for mental illness centered on the idea that hospitals and clinics for treatment and even cures for psychiatric disease. Changing perceptions of mental illnesses in Eritrea that paralleled the very caring and sympathetic attitudes of the sample university students would require raising public awareness regarding mental illness through education, using the mass media to raise public awareness, integrating mental health into the primary health care system, decentralizing mental health care services to increase access to treatment and providing affordable service to maintain positive treatment outcomes.
Effect of Phosphorus and Zinc on the Growth, Nodulation and Yield of Soybean ...Premier Publishers
This study investigated the effects of phosphorus and zinc on the growth, nodulation, and yield of two soybean varieties in Nigeria. Phosphorus application significantly affected growth, nodulation, yield, and some yield components, with 60 kg P2O5/ha giving the highest growth and yield. Phosphorus also increased nodulation, with 30 kg P2O5/ha providing the highest nodulation. Zinc application did not significantly affect most growth characters or nodulation, except for reducing plant height. Phosphorus increased soybean yield significantly to 1.9 t/ha compared to the control of 1.7 t/ha. Protein and oil contents were not significantly affected by phosphorus but were by zinc
Influence of Harvest Stage on Yield and Yield Components of Orange Fleshed Sw...Premier Publishers
A field experiment was conducted at Adami Tullu Agricultural Research Center in 2018 under rainfed condition with supplementary irrigation to determine the influence of harvest stage on vine yield and tuberous root yield of orange fleshed sweet potato varieties. The experiment consisted of four harvest stages (105, 120, 135 and 150 days after planting) and Kulfo, Tulla and Guntute varieties. A 4 X 3 factorial experiment arranged in randomized complete block design with three replications was used. Interaction of harvest stage and variety significantly influenced above ground fresh biomass, vine length, marketable tuberous root weight per hectare, commercial harvest index and harvest index. The highest mean values of above ground fresh biomass (66.12 t/ha) and marketable tuberous root weight (56.39 t/ha) were produced by Guntute variety harvested at 135 days after planting. Based on the results, it can be recommended that, farmers of the study area can grow Guntute variety by harvesting at 135 days after planting to obtain optimum vine and tuberous root yields.
Performance evaluation of upland rice (Oryza sativa L.) and variability study...Premier Publishers
This study evaluated 13 upland rice varieties over two locations in Ethiopia for yield and other traits. Significant differences were found among varieties for several traits. The highest yielding varieties were Chewaka, Hiddassie, and Fogera 1. Chewaka yielded 5395.8 kg/ha on average, 25.8-35% more than the check. Most varieties matured within 120-130 days. High heritability was found for days to heading, panicle length, and grain yield, indicating these traits can be easily improved through selection. Grain yield also had high genetic variation and heritability with genetic advance, suggesting yield can be improved through selection. This study identified variability that can be used
Response of Hot Pepper (Capsicum Annuum L.) to Deficit Irrigation in Bennatse...Premier Publishers
This study was conducted at Enchete kebele in Benna-Tsemay Woreda, South Omo Zone to evaluate the response of hot pepper to deficit irrigation on yield and water productivity under furrow irrigation system. The experiment comprised four treatments (100 % of ETc, 85% of ETc, 70 % of ETc and 50% of ETc), respectively. The experiment was laid out in RCBD and replicated four times. The two years combined yield results indicated that, the maximum total yield (20.38 t/ha) was obtained from 100% ETc while minimum yield (12.92 t/ha) was obtained from 50% of ETc deficit irrigation level. The highest WUE 5.22 kg/ha mm-1 was obtained from 50% of ETc. Treatment of 100% ETc irrigation application had highest benefit cost ratio (4.5) than all others treatments. Applying 50% of ETc reduce the yield by 37% when compared to 100 % ETc. Accordingly, to achieve maximum hot pepper yield in areas where water is not scarce, applying 100% ETc irrigation water application level throughout whole growing season under furrow irrigation system is recommended. But, in the study area water scarcity is the major limiting factor for crop production. So, it is possible to get better yield and water productivity of hot pepper when we apply 85% ETc irrigation water throughout growing season under furrow irrigation system.
Harnessing the Power of Agricultural Waste: A Study of Sabo Market, Ikorodu, ...Premier Publishers
Nigeria is still burdened with huge responsibilities of waste disposal because the potential for benefits of proper waste management is yet to be harnessed. The paper evaluates the capacity of the Sabo Cattle market in producing the required quantities of waste from animal dung alongside decomposed fruits with a view to generating renewable energy possibilities for lighting, security and other business activities of the market. It is estimated that about 998 million tons of agricultural waste is produced yearly in the country with organic wastes amounting to 80 percent of the total solid wastes. This can be categorized into biodegradable and non-biodegradable wastes. The paper evaluates the capacity of the Sabo Cattle market in producing the required quantities of waste from animal dung alongside decomposed fruits with a view to generating renewable energy possibilities for lighting, security and other business activities of the market. The Sabo market was treated as a study case with the adoption of in-depth examinations of the facility, animals and products for sale and waste generated. A combination of experimental, interviews (qualitative) and design simulation (for final phase) was adopted to extract, verify and analyse the data generated from the study. Animal waste samples were subjected to compositional and fibre analysis with results showing that the sample has high potency for biogas production. Biodegradable Wastes are human and animal excreta, agricultural and all degradable wastes. Availability of high quantity of waste generated being organic in Sabo market allows the use of anaerobic digestion to be proposed as a waste to energy technology due to its feasibility for conversion of moist biodegradable wastes into biogas. The study found that at peak supply period during the Islamic festivities, a conservative 300tonnes of animal waste is generated during the week which translates to over 800kilowatts of electricity.
Influence of Conferences and Job Rotation on Job Productivity of Library Staf...Premier Publishers
The general purpose of this study is to investigate the influence of conferences and job rotation on job productivity of library staff in tertiary institutions in Imo State, Nigeria. The survey research design was used for this study using questionnaire as an instrument for data collection. This study covered the entire population of 661. Out of these, 501 copies of the questionnaire representing 75.8% were duly completed and returned for analysis. Student’s t-test was used to analyze the research questions. The finding showed that conferences had no significant influence on the job productivity of library staff in tertiary institutions in Imo State, Nigeria (F cal= 7.86; t-vale =6.177; p >0.005). Finding also showed that job rotation significantly influences job productivity of library staff in tertiary institutions in Imo State, Nigeria (F-cal value= 18.65; t-value = 16.225; P<0.05). This study recommended that, government should ensure that library staff participate in conferences with themes and topics that are relevant to the job they perform and also ensure that there should be proper evaluation and feedback mechanism which aimed to ensuring control and minimize abuse of their development opportunities. Again, there should be written statement of objectives in order to sustain job rotation programmes. Also, that training and development needs of library staff must be identified and analyzed before embarking on job rotation processes as this would help to build skills, competences, specialization and high job productivity.
Scanning Electron Microscopic Structure and Composition of Urinary Calculi of...Premier Publishers
This document summarizes a study on the scanning electron microscopic structure and chemical composition of urinary calculi (stones) found in geriatric dogs. Microscopic examination of urine samples revealed increased numbers of blood cells, epithelial cells, pus cells, casts, bacteria and crystals of various shapes, predominantly struvite, calcium oxalate dihydrate and monohydrate, and ammonium urate. Scanning electron microscopy showed perpendicular columnar strata of struvite crystals and wavy phases of uric acid. Chemical analysis identified calcium phosphate, calcium oxalate and urea stones. The study characterized the microscopic and electron microscopic appearance of crystals and chemical composition of urinary calculi in geriatric dogs.
Gentrification and its Effects on Minority Communities – A Comparative Case S...Premier Publishers
This paper does a comparative analysis of four global cities and their minority districts which have been experiencing the same structural pressure of gentrification. The main contribution of this paper is providing a detailed comparison of four micro geographies worldwide and the impacts of gentrification on them: Barrio Logan in San Diego, Bo-Kaap in Cape Town, the Mission District in San Francisco, and the Rudolfsheim-Fünfhaus District in Vienna. All four cities have been experiencing the displacement of minority communities due to increases in property values. These cities were chosen because their governments enacted different policies to temper the gentrification process. It was found that cities which implemented social housing and cultural inclusionary policies were more successful in maintaining the cultural and demographic make-up of the districts.
Oil and Fatty Acid Composition Analysis of Ethiopian Mustard (Brasicacarinata...Premier Publishers
The experiments was conducted at Holetta Agricultural Research Center, to analyze forty nine Ethiopian Mustard land races for oil and fatty acid composition traits The experiment was carried out in a simple lattice design. The analysis of variance showed that there were highly significant differences among genotypes for all oil and fatty acid traits compared. The significant difference indicates the existence of genetic variability among the land races which is important for improvement
Beyond Degrees - Empowering the Workforce in the Context of Skills-First.pptxEduSkills OECD
Iván Bornacelly, Policy Analyst at the OECD Centre for Skills, OECD, presents at the webinar 'Tackling job market gaps with a skills-first approach' on 12 June 2024
Leveraging Generative AI to Drive Nonprofit InnovationTechSoup
In this webinar, participants learned how to utilize Generative AI to streamline operations and elevate member engagement. Amazon Web Service experts provided a customer specific use cases and dived into low/no-code tools that are quick and easy to deploy through Amazon Web Service (AWS.)
ISO/IEC 27001, ISO/IEC 42001, and GDPR: Best Practices for Implementation and...PECB
Denis is a dynamic and results-driven Chief Information Officer (CIO) with a distinguished career spanning information systems analysis and technical project management. With a proven track record of spearheading the design and delivery of cutting-edge Information Management solutions, he has consistently elevated business operations, streamlined reporting functions, and maximized process efficiency.
Certified as an ISO/IEC 27001: Information Security Management Systems (ISMS) Lead Implementer, Data Protection Officer, and Cyber Risks Analyst, Denis brings a heightened focus on data security, privacy, and cyber resilience to every endeavor.
His expertise extends across a diverse spectrum of reporting, database, and web development applications, underpinned by an exceptional grasp of data storage and virtualization technologies. His proficiency in application testing, database administration, and data cleansing ensures seamless execution of complex projects.
What sets Denis apart is his comprehensive understanding of Business and Systems Analysis technologies, honed through involvement in all phases of the Software Development Lifecycle (SDLC). From meticulous requirements gathering to precise analysis, innovative design, rigorous development, thorough testing, and successful implementation, he has consistently delivered exceptional results.
Throughout his career, he has taken on multifaceted roles, from leading technical project management teams to owning solutions that drive operational excellence. His conscientious and proactive approach is unwavering, whether he is working independently or collaboratively within a team. His ability to connect with colleagues on a personal level underscores his commitment to fostering a harmonious and productive workplace environment.
Date: May 29, 2024
Tags: Information Security, ISO/IEC 27001, ISO/IEC 42001, Artificial Intelligence, GDPR
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LAND USE LAND COVER AND NDVI OF MIRZAPUR DISTRICT, UPRAHUL
This Dissertation explores the particular circumstances of Mirzapur, a region located in the
core of India. Mirzapur, with its varied terrains and abundant biodiversity, offers an optimal
environment for investigating the changes in vegetation cover dynamics. Our study utilizes
advanced technologies such as GIS (Geographic Information Systems) and Remote sensing to
analyze the transformations that have taken place over the course of a decade.
The complex relationship between human activities and the environment has been the focus
of extensive research and worry. As the global community grapples with swift urbanization,
population expansion, and economic progress, the effects on natural ecosystems are becoming
more evident. A crucial element of this impact is the alteration of vegetation cover, which plays a
significant role in maintaining the ecological equilibrium of our planet.Land serves as the foundation for all human activities and provides the necessary materials for
these activities. As the most crucial natural resource, its utilization by humans results in different
'Land uses,' which are determined by both human activities and the physical characteristics of the
land.
The utilization of land is impacted by human needs and environmental factors. In countries
like India, rapid population growth and the emphasis on extensive resource exploitation can lead
to significant land degradation, adversely affecting the region's land cover.
Therefore, human intervention has significantly influenced land use patterns over many
centuries, evolving its structure over time and space. In the present era, these changes have
accelerated due to factors such as agriculture and urbanization. Information regarding land use and
cover is essential for various planning and management tasks related to the Earth's surface,
providing crucial environmental data for scientific, resource management, policy purposes, and
diverse human activities.
Accurate understanding of land use and cover is imperative for the development planning
of any area. Consequently, a wide range of professionals, including earth system scientists, land
and water managers, and urban planners, are interested in obtaining data on land use and cover
changes, conversion trends, and other related patterns. The spatial dimensions of land use and
cover support policymakers and scientists in making well-informed decisions, as alterations in
these patterns indicate shifts in economic and social conditions. Monitoring such changes with the
help of Advanced technologies like Remote Sensing and Geographic Information Systems is
crucial for coordinated efforts across different administrative levels. Advanced technologies like
Remote Sensing and Geographic Information Systems
9
Changes in vegetation cover refer to variations in the distribution, composition, and overall
structure of plant communities across different temporal and spatial scales. These changes can
occur natural.
This document provides an overview of wound healing, its functions, stages, mechanisms, factors affecting it, and complications.
A wound is a break in the integrity of the skin or tissues, which may be associated with disruption of the structure and function.
Healing is the body’s response to injury in an attempt to restore normal structure and functions.
Healing can occur in two ways: Regeneration and Repair
There are 4 phases of wound healing: hemostasis, inflammation, proliferation, and remodeling. This document also describes the mechanism of wound healing. Factors that affect healing include infection, uncontrolled diabetes, poor nutrition, age, anemia, the presence of foreign bodies, etc.
Complications of wound healing like infection, hyperpigmentation of scar, contractures, and keloid formation.
Communicating effectively and consistently with students can help them feel at ease during their learning experience and provide the instructor with a communication trail to track the course's progress. This workshop will take you through constructing an engaging course container to facilitate effective communication.
How to Setup Warehouse & Location in Odoo 17 InventoryCeline George
In this slide, we'll explore how to set up warehouses and locations in Odoo 17 Inventory. This will help us manage our stock effectively, track inventory levels, and streamline warehouse operations.
it describes the bony anatomy including the femoral head , acetabulum, labrum . also discusses the capsule , ligaments . muscle that act on the hip joint and the range of motion are outlined. factors affecting hip joint stability and weight transmission through the joint are summarized.
2. A technique to construct linear trend free fractional factorial design using some linear codes
Singh et al. 073
PRELIMINARIES
Fractional Factorial Design: Let D = (qr
n-p
) denote a q
-p
fraction of the q
n
factorial design in q
r
incomplete blocks. Let N
= q
n-p
be the number of treatment combinations, K=q
n-p-r
be the size of each block and B = q
r
be the number of
blocks.The linear model for the q
n
factorial design is given as
(1)
Where y is the N × 1 column vector of observations , X is the N× n design matrix of known constants; N is the n×1
column vector of regression coefficients and e is the N×1 column vector of random errors with zero means and
variance σ
2.
. When block effects are considered, the model is changed to
(2)
with B= is N×B block matrix with block size K and γ is the corresponding (K ×1) block .
Definition1: Let denotes the ordered vector of observations, for
x = 0,1,2,... be the N × 1 vector of trend coefficients and let ui be the contrast for main effect Ai ; i=1,2,...n, in the
run order. Then the quantity is known as the time count for the main effect Ai ..
A necessary and sufficient condition for a main effect contrast u to be trend free is that
(1.1)
In general, an N × 1 vector u is called trend free if equation(1.1) holds.
When the assumption of trend effect of different factors of the design is also considered, then this assumption changes
the model (2) to
(3)
Where , t is the (K ×1) linear vector and is the trend effect coefficient.The model (3) is a linear model
for factorial designs with trend. The first K rows of correspond to K treatment combinations in the
principal block, the next K rows to the treatment combinations in the second block and so on.
Definition 2: A run order is optimal for the estimation of the factor effects of interest in the presence of nuisance v-
degree polynomial trend iff
(1.2)
Where is an Nn matrix of factor effect coefficients and T is the Nv matrix of polynomial trend coefficients. If
equation(1.2) is satisfied then the run order is said to be v-trend free. If x is any column of nd t is any
column of T then the usual inner product is the time count between x and t. Criterion given in equation (1.2)
states that all the time count are zero for optimal run order.
Coster and Cheng(1988) introduced Generalised Foldover Scheme to generate systematic run order for full and
fractional factorial plans. We give here the definition of Generalised Foldover Scheme (Coster and Cheng(1988)).
Definition 3: Generalised Foldover Scheme (GFS): For a factorial design D= (qr
n-p
) with n factors A1, A2,…..An let G
be the generator matrix of design given by
3. A technique to construct linear trend free fractional factorial design using some linear codes
Int. J. Stat. Math. 074
Let be a 1×n matrix of zeros. Then the run order of design D is produced by the GFS with respect to the generator
sequence is given by where
for i = 1,2,…,n-p. In the run order , the principal block consists of the first q
n-p-r
runs; the second block consist of
the next q
n-p-r
runs, and so on. For a factorial design D1=(qr
n-p
), let be the n factors and G be the
generator matrix of design D1 given by Coster and Cheng (1988) derived following conditions for -trend free effects in
GFS. These conditions involve the generator matrix.
1. The main effect of a given factor is trend free if the corresponding letter appears at least ( +1) times in the
generator sequence.
2. A 2-factor interaction is -trend free if and only if there are at least ( +1) generator each of which exactly one of
the two factors appears at non-zero level.
For linear trend free design, the above conditions can be described in the following properties:
Property 1: For any factor , if there are at least two non zero elements , then all the main effect
components of factor are linear trend free.
Property 2:Forany factor ,if there are at least two pairs ,
such that one element is zero and the other element is non zero, then all components of the interaction are
linear trend free.
LINEAR CODES
A linear [n,k,d]q
code C over GF(q), where q is prime or prime power, n is the length, k is the dimension and d is the
minimum distance, is a k-dimensional subspace of the n-dimensional vector space V(n,q) over GF(q). The dual code
C
of an [n,k,d]q
code C is C
= { v V(n,q)/ v.w=0 for all w C}. This is an [n, n-k, d
]q
code and an (n-k) n generator
matrix H of C
is called a parity check matrix of C. If the generator matrix is given in the standard form, a
corresponding parity check matrix is given as
H = [
T
A knI ]
Any d
-1 columns in generator matrix G of C are linearly independent and any d-1 columns in parity check matrix
H are linearly independent.
FACTORIAL DESIGNS WITH SOME LINEAR TREND FREE EFFECTS
GFS provides a technique to construct linear trend free factional factorial designs using generator matrix, but there is
no general method to construct the generator matrix. We use the parity check matrix of a linear [n,k,d]q
code to obtain
the set of generators to construct the desired designs.
Method of Construction
1. Consider the parity check matrix Hn-k×n of a linear [n,k,d]q code.
2. Partition the matrix H in two submatrix F1 and F2, where F2 consists of the vectors with weight (w) one.
3. Let m denotes the number of columns in F2. If m <d-1, then select any d-1 columns from H to form a matrix M of
order n-k × d-1 otherwise select M such that there is at least one column from F2. The order of M is n-k × d-1.
4. Write the transpose of M and the transpose be denoted by MT of order (d-1×n-k). Delete the column with all zero
entries and repeated columns to form the matrix Gα of order ,say (d-1)×l
5. Retain Gα , if the number of columns (l ) in Gα>d-1 Otherwise go to step 3.
6. Apply GFS on Gα to obtain the fractional factorialdesign q
l-r
; where 1≤ r ≤ (n-k)-(d-1) & (d-1)+1 ≤l ≤ n-k .
The resultant fractional factorial designis such that some of the main effects and two factor interactions are linear
trend free.
4. A technique to construct linear trend free fractional factorial design using some linear codes
Singh et al. 075
Remark
1. The total number of possible choices of M matrices is
2. In case d-1 = l in step 5, we get the full factorial design q
l
with some main effects and two factor
interactions Linear trend free.
3. The design of trend freeness of the factors depends upon the weight (w) of the corresponding
column in Gα.
4. All the main effects will be trend free if the weight(w) of all columns in Gα is at least two.
Above method of construction can be summarized in following theorem. The proof of the theorem can be
obtained from the sequence of steps given in the construction method. The proof(*) is available with the authors.
*
Theorem1: Existence of a linear [n, k, d]q code implies the existence of q
l-r
{1≤ r ≤ (n-k)-(d-1) & (d-1)+1≤l≤ n-k
},fractional factorial design and q
l
( l=d-1) full factorial design in which all main effects and some of the two-factor
interactions are linear trend free, where (d-1) is number of linearly independent columns in matrix H and l is the
number of factors/columns in Gα.
LINEAR TREND FREE FRACTIONAL FACTORIAL DESIGNS USING DIFFERENT CODES
We consider different types of linear codes and generate linear trend free fractional factorial designs using the method
of construction described in previous section. For details see Hedayat et.al (1999).
a) Reed Muller Codes
The r
th
order binary Reed-Muller code R(r,a) of length n = 2
a
, for 0 r a, is the set of all vectors f, where f(i1,…..ia) is a
Boolean function which is a polynomial of degree at most r. For any a and any r, 0 ≤ r ≤ a, there is a binary r
th
order RM
code R(r,a) with the following properties:
Length n = 2
a
, dimension k = +…+ and minimum distance 2
a-r
. The parity check matrix of R(r,a) code is
the generator matrixof its dual code. The dual of RM(r,a) is RM(a-r-1,a) code.
Example 1: Consider a parity check matrix of RM(2,4)
H=
Any three columns in parity check matrix H matrix are linearly independent. Here d-1=3, and m =5 (in F2) and we get
the designs and corresponding generator matrices depending on the columns selected. According to the selection of
columns ,we have the following cases :
i)11 columns with none of the column having weight one and there are possible ways of selection where
none of the column is with weight (w) one and the corresponding factorial designs will have all main effects linear trend
free. All generated matrices and the table contains generator matrices, their corresponding designs, trend free effects
and defining relations are available with th authors.
5. A technique to construct linear trend free fractional factorial design using some linear codes
Int. J. Stat. Math. 076
ii) For m=5 and d-1=3, n-m=11.The possible choices of columns selected for generator matrix are
+ + . Suppose we choose the three columns 4
th
, 5
th
and 6
th
to form the matrix
MRM = On transposing we get matrix as GRM
in which all three rows d-1 =3 are independent. here d-1 =3 and l=5, Using the method of GFS on generator
matrix we get a resolution III, fractional factorial design with defining relation I =A1A3A5 = A1A2A3A4= A2A4A5.
Using the properties 1and 2 we observe that main effect component of A1, A3, A5 and the two factor interaction A1A2,
A1A3 and A2A4 and A3A4 are linear trend free.
Cyclic Codes
A linear code over GF(q) is said to be cyclic if whenever (c0
,c1
,…..,cn-2
,cn-1
) is a codeword so also is (c1
,c2
,…..,cn-1
,c0
).
Cyclic arrays can be described by a single generating vector z = ( z0
z1
……….zn-1
) such that the generator matrix consists
of this vector and its first ( k-1 ) cyclic shifts. The generating vector z is represented by a polynomial z(x) = z0 + z1X + …+zn-
1X
n-1
which is called a generator polynomial for the code. If a code is cyclic, so is its dual, and the generator
polynomial of its dual can be obtained by the following result given in Macwilliam and Sloane (1977).
Theorem 2: If C is a cyclic code of length n over GF(q), with generator polynomial z(x), then the dual code C
is also
cyclic and has generator polynomial
where z
*
(x) = X
deg.z
z(x
-1
) is reciprocal polynomial to z(x).
Example 2: Let = be the generator polynomial for
[15,7,5]2 code. Then the generator polynomial for the dual of this code is given as
h (x) = x
7
( 1+ x
-4
+x
-6
+x
-7
) = 1+x+x
3
+x
7
Hence the parity check matrix of [15,7,5]2 code is obtained by writing the coefficients and giving the cyclic shift to the
coefficients,as given below
Hcy= =
Any four columns in the H matrix are linearly independent, d-1 = 4 and m=5, n-m= 15-5 = 10 column with none of
them of weight(w) one. Then , there are 210 possible selection of such sets of columns from the matrix H. Following
the method of construction, we generated all generator matrices from the set of selected columns and listed
corresponding fractional factorial designs with their trend free effects and defining relations {available with the
authors}.The result of selecting columns 4
th
, 5
th
, 6
th
and 7
th
gives the matrix Mcy(8×4
Mcy(8×4=
6. A technique to construct linear trend free fractional factorial design using some linear codes
Singh et al. 077
Deleting column of zeroes and transposing
MT=
we get generator matrix as Gcy of order( (d-1)× l)
Gcy =
where l =7 and d-1 =4 . Using GFS, a 2
7-3
fractional factorial design is obtained with some main effects A3, A4, A5,
A6 and two factor interactions A1A2, A2A3, A2A6, A2A7, A3A4, A3A5, A3A6, A3A7, A5A4, A6A4, A5A6, A5A7 are linear trend
free.
BCH Codes
The BCH codes over GF(q) of length n = q
m
-1 and designed distance δ is the largest possible cyclic code having
zeroes α
b
,
,
α
b+1
,…,α
b+δ-2
where α є GF( q
m
) is the primitive n
th
root of unity, b is a non negative integer and m is the
multiplicative order of q mod n. The parity check matrix of a BCH code with b=1 is given by
C=
1n2222
1n5255
1n3233
1n2
)(.........)()(1
......
......
......
)(.........)(1
)(.........)(1
.........1
where each entry is replaced by the corresponding binary m-tuple.
Example 3.: The parity check matrix of [15,5,7]2 code is
H=
and we observe here that d-1=6 columns in above matrix are linearly independent. Since the matrix cannot be
partitioned into the sub matrices ,we consider all 15 columns to get the design and they are
Suppose we select columns 8
th
,9
th
,10
th
,11
th
,12
th
and 13
th
from above matrix H.The matrix obtained
by selection is
M =
7. A technique to construct linear trend free fractional factorial design using some linear codes
Int. J. Stat. Math. 078
On transposing and deleting columns of zeroes we get matrix GBCH as
GBCH =
Applying GFS on generator matrix with l = 10 and d-1 = 6 we get the design 2
10-4
fractional factorial design with all
main effects linear trend free. Some of the designs that can be generated by selecting different columns of the
generator matrix GBCH of the code [15,5,7]2 along with their defining relations are available with the author.
Ternary Golay Code
The Golay code were discovered by M.J.E.Golay in late 1940’s. The (unextended) Golay code are examples of perfect
codes. A q-nary code that attains the hamming ( or sphere packing) bound i.e. the one which has
codewords, is said to be perfect code. Consider the ternary Golay Code [11,6,5]3
over a ternary alphabet, the relative distance of the codes is as large as it possibly can be for a ternary code, and it
satisfies Hamming bound and is therefore a perfect ternary Golay [11,6,5]3 code. For perfect code its dual distance is
same as its covering radius. In terms of design the strength is same as the estimation index of an orthogonal array
obtained using this code. Golay codes are unique in the sense that binary or ternary codes with same parameters, can
be shown to be equivalent to them.
Example 4: Consider the parity check matrix of [11,6,5]3 and partition it into two submatrices as given in the method in
section 4, we get the matrix H as
H=
Any four columns in matrix H5×11 are linearly independent d-1 = 4 and m = 5 . Thus,
15 sets of column in which none of the columns has weight (w) one. Whereas the total possible selection of columns
to formmatrix M is 325.
Suppose we choose columns 1
st
,2
nd
,3
rd
and 4
th
from matrix H, we get the matrix
M = .
Next , we generate the matrices of order (4×5) that ensures the linear trend freeness of main effects and following
the steps of construction method , we get 3
5-1
fractional factorial design.
and then 3
5-1
fractional factorial design I= A1A2
2
A3A4
2
is generated using GFS on matrix Ggolay. The generated
design has all its main effects linear trend free with respect to the properties [1-3].
8. A technique to construct linear trend free fractional factorial design using some linear codes
Singh et al. 079
BLOCKING IN FRACTIONAL FACTORIAL DESIGN WITH SOME LINEAR TREND FREE EFFECTS.
When the block size is smaller than the number of treatment combinations in any factorial experiment, the technique of
blocking is used to carry out the analysis. The factorial/fractional factorial experiment thus obtained is known as
Blocked fractional factorial experiment. When we go for blocking of fractional factorial design, the block structure
affects the linear trend-freeness of the effects. We state here the result in continuation with the properties [1-3] . The
first h=n-p-r generates the principle block and let zv , h+1 ≤ v ≤ n-p be the generators of other blocks. Then the
following holds:
Property 4: For any given v, h+1 ≤ v ≤ n-p and factor say A1 , suppose z1v ≠ 0. Then
(a) All (q-1) main effect components are linear trend-free.
(b) If ziv = 0 , 2 ≤ i ≤ n-p, then all components of A1 × Ai interaction are linear trend-free.
(c)
The method described is used to construct Blocked fractional factorial designs with some linear trend free effects.
Reed Muller Code: We use here the generator matrix constructed in Example 1 by selecting columns 8
th
,9
th
and 10
th
We get 2
4-1
fractional factorial design, here q=2, n=3, p=1, r1=1, h=n-p-r1=1 independent generators. Using GFS, h=2
generators forms the principle block and remaining generators form the contents of the other block in which main
effects A and C are linear trend free. The confounded effect of the design is ABC.
Table 1. 24-1
fractional factorial design with
resolution III, I=ABC
Cyclic Code: We consider here generator matrix constructed in example 2 and by selecting 1
st
, 2
nd
,5
th
and 9
th
columns
We get Gcy=
Using GFS 2
5-1
fractional factorial design is obtained n=5, p1=1, s=2, r1=1, h = n-p-r1 = 5-1-1 = 3 independent
generators, generates the principal block and other generates the other block contents. Table 1 gives the design
generated.
Table 2 : 25-1
blocked fractional factorial design with resolution IV, I = ABCE
BCH Code: Consider the generator matrix in Example 3 by selecting columns 1
st
, 4
th
, 5
th
, 6
th
, 7
th
and 8
th
as
GBCH =
2
9-3
fractional factorial design is obtained, here n=9, p=3 , r1=1 and h = n-p-r1 = 9-3-1= 5 independent generators
forms the principal block and remaining generators the other block. Thus, Blocked 2
9-3
fractional factorial.design with
defining relation I = DEGJ= ABDEH = BCDF is obtained. Table 3 displays the first 16 runs of the design
constituting the principle block and the next 16 the other block and so on.
Block 1: (1) , acd , abd, bc
Block 2: c , ac, ab, bcd
Block 1: (1) , ab, bc, ac, acd, bcd, abd, d
Block 2: ce, abce, be, ae, ade, bde, abcde, cde
9. A technique to construct linear trend free fractional factorial design using some linear codes
Int. J. Stat. Math. 080
Table 3. 29-3
blocked fractional factorial design with resolution IV, I= DEFJ = ABDEH=BCDF
Block 1: (1), aej, dfhj, adefh, abefgh, bfghj, abdegj, bdg, bcej, abc, cdefh, abcdfhj, acfghj, cdhj, acdeh, cf,
acefj, abcdefj, bcdfg, abcegh, bcghj, bdeh, bdhj, bef, abf, adfg, defgj, aghj, egh.
Block 2: abdgh, bdeghj, abfgj, befg, def, adfj, ehj, ah, acdeghj, bcfg, acefg, cfgj, bcdfj, abcdef, bch, abcehj, abcgj,
abcdfgh, bcdefghj, cefhj, acfh, bcd, acdj, aeg, gj, adefg. dfgh, bfh, abefhj, bdj, abde.
Ternary Golay Code: Consider the generator matrix from Example 4 by selecting columns 1
st
,2
nd
, 3
rd
and 4
th
of
matrix H as
Ggolay =
3
5-1
fractional factorial design is obtained. Here n= 5, p1=1 and q=3 , r1=1 ,h=n-p-r1=3 independent generators are
obtained. Thus, principal block is generated by first three generators and remaining two generates the content of the
other block. First 3
3
treatment combinations in 3
5-1
fractional factorial design (given in Table 4 ) forms the principle
block and next 3
3
combinations forms the contents of second block and the remaining the third block contents. The
factors are denoted by A,B,C,D and E.
Table 4: 35-1
blocked fractional factorial design with resolution IV, I= ABCDE
Block 1: (1), abcde, a
2
b
2
c
2
d
2
e
2
, abc
2
d
2
, a
2
b
2
e, cde
2
, a
2
b
2
cd, c
2
d
2
e, abe
2
, ab
2
ce
2
, a
2
c
2
d , bd
2
e, a
2
d
2
e
2
, bc,
ab
2
c
2
de, bc
2
de
2
, ab
2
d, a
2
ce, a
2
bc
2
e, b
2
de
2
, acd
2
, b
2
cd
2
e, ac
2
d
2
, b
2
ce, ade, a
2
bcd
2
e
2
, b
2
d
2
.
Block 2: a
2
bde
2
, b
2
cd
2
, ac
2
e, b
2
c
2
e
2
, ad, a
2
bcd
2
e, acd
2
e
2
, a
2
bc
2
, b
2
de, cde, abc
2
d
2
e
2
, a
2
b
2
, abe, a
2
b
2
cde
2
, c
2
d
2
,
a
2
b
2
c
2
d
2
e, e
2
, abcd, ab
2
c
2
d, a
2
d
2
e, bce
2
, a
2
c, ab
2
cd, ab
2
d
2
e
2
, bd
2
, ab
2
de, a
2
c
2
de
2
.
Block 3: ab
2
d
2
e, a
2
ce
2
, bc
2
d, a
2
c
2
de, bd
2
e
2
, ab
2
c, bce, ab
2
c
2
de
2
, a
2
d
2
, a
2
bcd
2
, b
2
d
2
e, ade, b
2
d, acd
2
e, a
2
bc
2
e
2
, ac
2
,
a
2
bde, b
2
cd
2
e
2
, c
2
d
2
e
2
, ab, a
2
b
2
cde, abcde
2
, a
2
b
2
c
2
d
2
, e, a
2
b
2
e
2
, cd, abc
2
d
2
e.
CONCLUSION
A technique to construct fractional factorial designs with factors at q level, q>2, with some linear trend free effects
using parity check/generator matrix of linear code is developed. Since the generator matrix is not unique in nature,
therefore fractional factorial designs with linear trend free effects with same/ different resolution can be easily
constructed.
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