In this paper a new Binary-to-RNS converters for multi-moduli RNS based on conjugate-pair as
of the set { 2
n1
– 2, 2
n1
+ 2, 2
n2
– 2, 2
n2
+ 2, …, 2
nN
– 2, 2
nN
+ 2 } are presented. 2
n
– 2
and 2
n
+ 2 modulies are called conjugates of each other. Benefits of Multi-moduli RNS
processors are; relying on the sets with pairs of conjugate moduli : 1) Large dynamic ranges. 2)
Fast and balanced RNS arithmetic. 3) Simple and efficient RNS processing hardware. 4)
Efficient weighted-to-RNS and RNS-to-Weighted converters. [1] The dynamic range (M)
achieved by the set above is defined by the least common multiple (LCM) of the moduli. This
new non-coprime conjugate-pair is unique and the only one of its shape as to be shown.
The document describes a paper and pencil technique called Sureshchander's Search Technique (ST) for simplifying Boolean functions with more than 8 variables through prime implicant analysis. ST reduces the search space by generating essential prime implicants (EPIs) and other prime implicants with minimal effort, unlike Quine-McCluskey which generates all prime implicants. The technique involves identifying prime implicant terms that have proper consensus through the generation and checking of related minterms. Examples demonstrate how the technique is applied to identify prime implicants and minimize Boolean functions.
This document describes a numerical study involving the solution of Poisson's equation using the finite volume method. It presents results from solving Laplace's equation on square domains with mixed boundary conditions, as well as solving the pressure Poisson equation derived from incompressible flow equations. Gaussian elimination, successive over-relaxation, and second-order accuracy are discussed. Numerical experiments demonstrate that over-relaxation improves convergence and the method achieves second-order accuracy based on grid refinement studies.
The document discusses 2D arrays including their definition, implementation, and how to calculate the address of elements. It covers storing arrays in row-major and column-major order and includes formulas to calculate addresses based on the lower and upper bounds. Operations on 2D arrays like addition, subtraction, and multiplication are also explained. Some example problems are provided at the end to demonstrate calculating addresses of elements in 2D arrays stored in both row-major and column-major order.
This document describes a method called "k-means" for partitioning multivariate data into k groups based on minimizing within-group variance. It can be used for applications like classification, prediction, and testing independence among variables. The k-means process works by starting each group with a single data point, then iteratively assigning new points to the nearest group and updating group means. The document proves that the k-means values converge almost surely to a set of distinct points that minimize within-group variance. It also describes some applications and extensions of the k-means method.
A numerical solution for Sine-Gordon type system was done by the use of two finite difference schemes, the first is the explicit scheme and the second is the Crank-Nicholson scheme. A comparison between the two schemes showed that the explicit scheme is easier and has faster convergence than the Crank-Nicholson scheme which is more accurate. The MATLAB environment was used for the numerical computations.
The document presents a decomposition method for solving indefinite quadratic programming problems with n variables and m linear constraints. The method decomposes the original problem into at most m subproblems, each with dimension n-1 and m linear constraints. All global minima, isolated local minima, and some non-isolated local minima of the original problem can be obtained by combining the solutions of the subproblems. The subproblems can then be further decomposed into smaller subproblems until 1-dimensional subproblems are reached, which can be solved directly.
Numerical solution of fuzzy hybrid differential equation by third order runge...Alexander Decker
This document presents a numerical method for solving hybrid fuzzy differential equations using the third order Runge-Kutta Nystrom method. It begins with definitions of fuzzy numbers and fuzzy differential equations. It then describes hybrid fuzzy differential systems and develops the Runge-Kutta Nystrom method for approximating their solutions. The method is applied to an example hybrid fuzzy differential equation and results are presented in a table and figure comparing the approximate and exact solutions. The document concludes by discussing the accuracy of the method.
11.[8 17]numerical solution of fuzzy hybrid differential equation by third or...Alexander Decker
This document presents a numerical method called the third order Runge Kutta Nystrom method to solve fuzzy hybrid differential equations. It begins with definitions of fuzzy numbers and fuzzy functions. It then describes hybrid fuzzy differential systems and how they can be modeled as piecewise differentiable systems. The document goes on to develop the third order Runge Kutta Nystrom method for solving these systems numerically. It provides a convergence result and applies the method to a numerical example to illustrate the theory.
The document describes a paper and pencil technique called Sureshchander's Search Technique (ST) for simplifying Boolean functions with more than 8 variables through prime implicant analysis. ST reduces the search space by generating essential prime implicants (EPIs) and other prime implicants with minimal effort, unlike Quine-McCluskey which generates all prime implicants. The technique involves identifying prime implicant terms that have proper consensus through the generation and checking of related minterms. Examples demonstrate how the technique is applied to identify prime implicants and minimize Boolean functions.
This document describes a numerical study involving the solution of Poisson's equation using the finite volume method. It presents results from solving Laplace's equation on square domains with mixed boundary conditions, as well as solving the pressure Poisson equation derived from incompressible flow equations. Gaussian elimination, successive over-relaxation, and second-order accuracy are discussed. Numerical experiments demonstrate that over-relaxation improves convergence and the method achieves second-order accuracy based on grid refinement studies.
The document discusses 2D arrays including their definition, implementation, and how to calculate the address of elements. It covers storing arrays in row-major and column-major order and includes formulas to calculate addresses based on the lower and upper bounds. Operations on 2D arrays like addition, subtraction, and multiplication are also explained. Some example problems are provided at the end to demonstrate calculating addresses of elements in 2D arrays stored in both row-major and column-major order.
This document describes a method called "k-means" for partitioning multivariate data into k groups based on minimizing within-group variance. It can be used for applications like classification, prediction, and testing independence among variables. The k-means process works by starting each group with a single data point, then iteratively assigning new points to the nearest group and updating group means. The document proves that the k-means values converge almost surely to a set of distinct points that minimize within-group variance. It also describes some applications and extensions of the k-means method.
A numerical solution for Sine-Gordon type system was done by the use of two finite difference schemes, the first is the explicit scheme and the second is the Crank-Nicholson scheme. A comparison between the two schemes showed that the explicit scheme is easier and has faster convergence than the Crank-Nicholson scheme which is more accurate. The MATLAB environment was used for the numerical computations.
The document presents a decomposition method for solving indefinite quadratic programming problems with n variables and m linear constraints. The method decomposes the original problem into at most m subproblems, each with dimension n-1 and m linear constraints. All global minima, isolated local minima, and some non-isolated local minima of the original problem can be obtained by combining the solutions of the subproblems. The subproblems can then be further decomposed into smaller subproblems until 1-dimensional subproblems are reached, which can be solved directly.
Numerical solution of fuzzy hybrid differential equation by third order runge...Alexander Decker
This document presents a numerical method for solving hybrid fuzzy differential equations using the third order Runge-Kutta Nystrom method. It begins with definitions of fuzzy numbers and fuzzy differential equations. It then describes hybrid fuzzy differential systems and develops the Runge-Kutta Nystrom method for approximating their solutions. The method is applied to an example hybrid fuzzy differential equation and results are presented in a table and figure comparing the approximate and exact solutions. The document concludes by discussing the accuracy of the method.
11.[8 17]numerical solution of fuzzy hybrid differential equation by third or...Alexander Decker
This document presents a numerical method called the third order Runge Kutta Nystrom method to solve fuzzy hybrid differential equations. It begins with definitions of fuzzy numbers and fuzzy functions. It then describes hybrid fuzzy differential systems and how they can be modeled as piecewise differentiable systems. The document goes on to develop the third order Runge Kutta Nystrom method for solving these systems numerically. It provides a convergence result and applies the method to a numerical example to illustrate the theory.
11.numerical solution of fuzzy hybrid differential equation by third order ru...Alexander Decker
This document presents a numerical method for solving hybrid fuzzy differential equations using the third order Runge-Kutta Nystrom method. It begins with introductions to fuzzy numbers, fuzzy differential equations, and hybrid fuzzy differential systems. It then describes the third order Runge-Kutta Nystrom method for solving hybrid fuzzy differential equations. An example is provided to illustrate the method. Tables and figures compare the approximate solutions from this method to exact solutions. The method is shown to provide approximations close to the exact solutions.
PROBABILISTIC INTERPRETATION OF COMPLEX FUZZY SETIJCSEIT Journal
The document summarizes research on complex fuzzy sets. Complex fuzzy sets extend traditional fuzzy sets by allowing membership functions to range over the unit circle in the complex plane rather than just [0,1]. The paper defines complex fuzzy sets and operations like union, intersection, and complement. It presents examples and properties of these operations. It also introduces a probabilistic interpretation of complex fuzzy sets to distinguish them from probability.
We first consider a ternary matrix group related to the von Neumann regular semigroups and to the Artin braid group (in an algebraic way). The product of a special kind of ternary matrices (idempotent and of finite order) reproduces the regular semigroups and braid groups with their binary multiplication of components. We then generalize the construction to the higher arity case, which allows us to obtain some higher degree versions (in our sense) of the regular semigroups and braid groups. The latter are connected with the generalized polyadic braid equation and R-matrix introduced by the author, which differ from any version of the well-known tetrahedron equation and higher-dimensional analogs of the Yang-Baxter equation, n-simplex equations. The higher degree (in our sense) Coxeter group and symmetry groups are then defined, and it is shown that these are connected only in the non-higher case.
A COMPREHENSIVE ANALYSIS OF QUANTUM CLUSTERING : FINDING ALL THE POTENTIAL MI...IJDKP
Quantum clustering (QC), is a data clustering algorithm based on quantum mechanics which is
accomplished by substituting each point in a given dataset with a Gaussian. The width of the Gaussian is a
σ value, a hyper-parameter which can be manually defined and manipulated to suit the application.
Numerical methods are used to find all the minima of the quantum potential as they correspond to cluster
centers. Herein, we investigate the mathematical task of expressing and finding all the roots of the
exponential polynomial corresponding to the minima of a two-dimensional quantum potential. This is an
outstanding task because normally such expressions are impossible to solve analytically. However, we
prove that if the points are all included in a square region of size σ, there is only one minimum. This bound
is not only useful in the number of solutions to look for, by numerical means, it allows to to propose a new
numerical approach “per block”. This technique decreases the number of particles by approximating some
groups of particles to weighted particles. These findings are not only useful to the quantum clustering
problem but also for the exponential polynomials encountered in quantum chemistry, Solid-state Physics
and other applications.
A Counterexample to the Forward Recursion in Fuzzy Critical Path Analysis Und...ijfls
This document presents a counterexample demonstrating that the fuzzy forward recursion method for determining critical paths does not always produce results consistent with the extension principle when discrete fuzzy sets are used to represent activity durations.
The document first provides background on fuzzy sets and critical path analysis. It then presents a proposition stating that the membership function for fuzzy critical path lengths can be determined by taking the maximum of the minimum membership values across all activity durations in each configuration.
The document goes on to present a counterexample using a simple series-parallel network with 18 configurations. It shows that applying the fuzzy forward recursion produces a different membership value for one critical path length compared to directly applying the extension principle. This difference proves the fuzzy forward
This document discusses fast algorithms for computing the discrete cosine transform (DCT) and inverse discrete cosine transform (IDCT) using Winograd's method.
The conventional DCT and IDCT algorithms have high computational complexity due to cosine functions. Winograd's algorithm reduces the number of multiplications required for matrix multiplication by rearranging terms.
The document proposes applying Winograd's algorithm to DCT and IDCT computation by representing the transforms as matrix multiplications. This approach reduces the number of multiplications required for an 8x8 block from over 16,000 to just 736 multiplications, with fewer additions and subtractions as well. This leads to faster DCT and IDCT computation compared
CHN and Swap Heuristic to Solve the Maximum Independent Set ProblemIJECEIAES
We describe a new approach to solve the problem to find the maximum independent set in a given Graph, known also as Max-Stable set problem (MSSP). In this paper, we show how Max-Stable problem can be reformulated into a linear problem under quadratic constraints, and then we resolve the QP result by a hybrid approach based Continuous Hopfeild Neural Network (CHN) and Local Search. In a manner that the solution given by the CHN will be the starting point of the local search. The new approach showed a good performance than the original one which executes a suite of CHN runs, at each execution a new leaner constraint is added into the resolved model. To prove the efficiency of our approach, we present some computational experiments of solving random generated problem and typical MSSP instances of real life problem.
This document summarizes and implements an ordinary differential equation (ODE) neural network using the Diffeqflux.jl library. It begins with an introduction to deep learning and neural networks. It then provides the mathematics behind modeling a simple multi-layer perceptron neural network as a system of ODEs. This includes derivations of the forward and backward propagation algorithms. Finally, it describes implementing a simple example ODE neural network using Diffeqflux.jl to demonstrate the approach.
EXACT SOLUTIONS OF A FAMILY OF HIGHER-DIMENSIONAL SPACE-TIME FRACTIONAL KDV-T...cscpconf
In this paper, based on the definition of conformable fractional derivative, the functional
variable method (FVM) is proposed to seek the exact traveling wave solutions of two higherdimensional
space-time fractional KdV-type equations in mathematical physics, namely the
(3+1)-dimensional space–time fractional Zakharov-Kuznetsov (ZK) equation and the (2+1)-
dimensional space–time fractional Generalized Zakharov-Kuznetsov-Benjamin-Bona-Mahony
(GZK-BBM) equation. Some new solutions are procured and depicted. These solutions, which
contain kink-shaped, singular kink, bell-shaped soliton, singular soliton and periodic wave
solutions, have many potential applications in mathematical physics and engineering. The
simplicity and reliability of the proposed method is verified.
Quadratic programming (Tool of optimization)VARUN KUMAR
This document provides an overview of quadratic programming, including:
1. It defines quadratic programming as a special case of nonlinear programming where the objective function is quadratic and all constraints are linear.
2. It presents the general mathematical formulation of a quadratic programming problem and provides an example problem.
3. It discusses solutions to quadratic programs using the graphical method and the Karush-Kuhn-Tucker (KKT) conditions.
International Journal of Engineering Research and Applications (IJERA) is an open access online peer reviewed international journal that publishes research and review articles in the fields of Computer Science, Neural Networks, Electrical Engineering, Software Engineering, Information Technology, Mechanical Engineering, Chemical Engineering, Plastic Engineering, Food Technology, Textile Engineering, Nano Technology & science, Power Electronics, Electronics & Communication Engineering, Computational mathematics, Image processing, Civil Engineering, Structural Engineering, Environmental Engineering, VLSI Testing & Low Power VLSI Design etc.
FITTED OPERATOR FINITE DIFFERENCE METHOD FOR SINGULARLY PERTURBED PARABOLIC C...ieijjournal
In this paper, we study the numerical solution of singularly perturbed parabolic convection-diffusion type
with boundary layers at the right side. To solve this problem, the backward-Euler with Richardson
extrapolation method is applied on the time direction and the fitted operator finite difference method on the
spatial direction is used, on the uniform grids. The stability and consistency of the method were established
very well to guarantee the convergence of the method. Numerical experimentation is carried out on model
examples, and the results are presented both in tables and graphs. Further, the present method gives a more
accurate solution than some existing methods reported in the literature.
The Gaussian or normal distribution is one of the most widely used in statistics. Estimating its parameters using
Bayesian inference and conjugate priors is also widely used. The use of conjugate priors allows all the results to be
derived in closed form. Unfortunately, different books use different conventions on how to parameterize the various
distributions (e.g., put the prior on the precision or the variance, use an inverse gamma or inverse chi-squared, etc),
which can be very confusing for the student. In this report, we summarize all of the most commonly used forms. We
provide detailed derivations for some of these results; the rest can be obtained by simple reparameterization. See the
appendix for the definition the distributions that are used.
This document presents a new method for finding the fuzzy critical path in a project network using type-2 discrete fuzzy numbers and type reduction. The key steps are:
1. Represent the time span of each activity as a type-2 discrete fuzzy number.
2. Use type reduction and the center of gravity to calculate the earliest start time, latest finish time, and total slack fuzzy time for each activity.
3. Identify the fuzzy critical path as the path(s) with a total slack time of 0 based on the center of gravity calculations.
An example application of the method on a sample network is provided to demonstrate the approach. The proposed method allows identification of the fuzzy critical path when activity
This document contains solutions to problems from the MIT course 6.003 Signals and Systems. It includes solutions for manipulating complex numbers, determining periodicity of signals, representing signals as linear combinations of basis functions, identifying properties of linear time-invariant systems, and whether certain statements about systems are true or false. The problems cover a range of foundational concepts in signals and systems.
This document describes a new algorithm for dual tree kernel conditional density estimation (KCDE) that provides fast and accurate density predictions. The algorithm extends previous work on univariate KCDE to allow for multivariate labels (Y) and conditioning variables (X). It applies Gray's dual tree approach separately to the numerator and denominator of the KCDE formula, and uses error bounds to ensure the quotient estimates have bounded relative error. This new algorithm provides the fastest known method for kernel conditional density estimation for prediction tasks.
Simplified Solutions of the CLP and CCP Limiting Cases of the Problem of Apo...James Smith
The new solutions presented herein for the CLP and CCP limiting cases of the Problem of Apollonius are much shorter and more easily understood than those provided by the same author in References [1] and [2]. These improvements result from (1) a better selection of angle relationships as a starting point for the solution process; and (2) better use of GA identities to avoid forming troublesome combinations of terms within the resulting equations.
The document provides homework assignments and lesson material on finding the distance and midpoint between two points using formulas. It includes practice problems calculating distance between points with coordinates (6, -2) and (12, 8), (3, 0) and (6, -2), (-11, 9) and (3, -4), and finding midpoints between points with endpoints (2, -2) and (6, 2), (-4, 0) and (0, 14), (-1, -2) and (3, -4).
An Efficient Multiplierless Transform algorithm for Video CodingCSCJournals
This paper presents an efficient algorithm to accelerate software video encoders/decoders by reducing the number of arithmetic operations for Discrete Cosine Transform (DCT). A multiplierless Ramanujan Ordered Number DCT (RDCT) is presented which computes the coefficients using shifts and addition operations only. The reduction in computational complexity has improved the performance of the video codec by almost 58% compared with the commonly used integer DCT. The results show that significant computation reduction can be achieved with negligible average peak signal-to-noise ratio (PSNR) degradation. The average structural similarity index matrix (SSIM) also ensures that the degradation due to the approximation is minimal.
This document presents a methodology for mapping multidimensional transforms onto reconfigurable architectures like FPGAs. The methodology uses tensor product decompositions and permutation matrices to express transforms recursively in terms of lower-order blocks. This allows large transforms to be computed by combining many parallel, smaller transform blocks. Specific examples are given for mapping one-dimensional linear convolution and discrete cosine transforms. The overall goal is to provide a unified framework and design process for implementing multidimensional transforms in a modular, parallel architecture.
This document discusses widelinearly minimum mean square error (WLMMSE) estimation for unique word orthogonal frequency-division multiplexing (UW-OFDM). It first provides background on UW-OFDM and describes the system model. It then discusses the WLMMSE estimator and how it can outperform the linear MMSE estimator for improper constellations like binary phase-shift keying (BPSK). Simulation results are presented showing the WLMMSE estimator achieves around 1 dB gain over the LMMSE estimator for BPSK. The document concludes the WLMMSE/UW-OFDM scheme can achieve up to 1.9 dB gain over conventional IEEE 802.11 schemes.
Computer Science
Active and Programmable Networks
Active safety systems
Ad Hoc & Sensor Network
Ad hoc networks for pervasive communications
Adaptive, autonomic and context-aware computing
Advance Computing technology and their application
Advanced Computing Architectures and New Programming Models
Advanced control and measurement
Aeronautical Engineering,
Agent-based middleware
Alert applications
Automotive, marine and aero-space control and all other control applications
Autonomic and self-managing middleware
Autonomous vehicle
Biochemistry
Bioinformatics
BioTechnology(Chemistry, Mathematics, Statistics, Geology)
Broadband and intelligent networks
Broadband wireless technologies
CAD/CAM/CAT/CIM
Call admission and flow/congestion control
Capacity planning and dimensioning
Changing Access to Patient Information
Channel capacity modelling and analysis
Civil Engineering,
Cloud Computing and Applications
Collaborative applications
Communication application
Communication architectures for pervasive computing
Communication systems
Computational intelligence
Computer and microprocessor-based control
Computer Architecture and Embedded Systems
Computer Business
Computer Sciences and Applications
Computer Vision
Computer-based information systems in health care
Computing Ethics
Computing Practices & Applications
Congestion and/or Flow Control
Content Distribution
Context-awareness and middleware
Creativity in Internet management and retailing
Cross-layer design and Physical layer based issue
Cryptography
Data Base Management
Data fusion
Data Mining
Data retrieval
Data Storage Management
Decision analysis methods
Decision making
Digital Economy and Digital Divide
Digital signal processing theory
Distributed Sensor Networks
Drives automation
Drug Design,
Drug Development
DSP implementation
E-Business
E-Commerce
E-Government
Electronic transceiver device for Retail Marketing Industries
Electronics Engineering,
Embeded Computer System
Emerging advances in business and its applications
Emerging signal processing areas
Enabling technologies for pervasive systems
Energy-efficient and green pervasive computing
Environmental Engineering,
Estimation and identification techniques
Evaluation techniques for middleware solutions
Event-based, publish/subscribe, and message-oriented middleware
Evolutionary computing and intelligent systems
Expert approaches
Facilities planning and management
Flexible manufacturing systems
Formal methods and tools for designing
Fuzzy algorithms
Fuzzy logics
GPS and location-based app
11.numerical solution of fuzzy hybrid differential equation by third order ru...Alexander Decker
This document presents a numerical method for solving hybrid fuzzy differential equations using the third order Runge-Kutta Nystrom method. It begins with introductions to fuzzy numbers, fuzzy differential equations, and hybrid fuzzy differential systems. It then describes the third order Runge-Kutta Nystrom method for solving hybrid fuzzy differential equations. An example is provided to illustrate the method. Tables and figures compare the approximate solutions from this method to exact solutions. The method is shown to provide approximations close to the exact solutions.
PROBABILISTIC INTERPRETATION OF COMPLEX FUZZY SETIJCSEIT Journal
The document summarizes research on complex fuzzy sets. Complex fuzzy sets extend traditional fuzzy sets by allowing membership functions to range over the unit circle in the complex plane rather than just [0,1]. The paper defines complex fuzzy sets and operations like union, intersection, and complement. It presents examples and properties of these operations. It also introduces a probabilistic interpretation of complex fuzzy sets to distinguish them from probability.
We first consider a ternary matrix group related to the von Neumann regular semigroups and to the Artin braid group (in an algebraic way). The product of a special kind of ternary matrices (idempotent and of finite order) reproduces the regular semigroups and braid groups with their binary multiplication of components. We then generalize the construction to the higher arity case, which allows us to obtain some higher degree versions (in our sense) of the regular semigroups and braid groups. The latter are connected with the generalized polyadic braid equation and R-matrix introduced by the author, which differ from any version of the well-known tetrahedron equation and higher-dimensional analogs of the Yang-Baxter equation, n-simplex equations. The higher degree (in our sense) Coxeter group and symmetry groups are then defined, and it is shown that these are connected only in the non-higher case.
A COMPREHENSIVE ANALYSIS OF QUANTUM CLUSTERING : FINDING ALL THE POTENTIAL MI...IJDKP
Quantum clustering (QC), is a data clustering algorithm based on quantum mechanics which is
accomplished by substituting each point in a given dataset with a Gaussian. The width of the Gaussian is a
σ value, a hyper-parameter which can be manually defined and manipulated to suit the application.
Numerical methods are used to find all the minima of the quantum potential as they correspond to cluster
centers. Herein, we investigate the mathematical task of expressing and finding all the roots of the
exponential polynomial corresponding to the minima of a two-dimensional quantum potential. This is an
outstanding task because normally such expressions are impossible to solve analytically. However, we
prove that if the points are all included in a square region of size σ, there is only one minimum. This bound
is not only useful in the number of solutions to look for, by numerical means, it allows to to propose a new
numerical approach “per block”. This technique decreases the number of particles by approximating some
groups of particles to weighted particles. These findings are not only useful to the quantum clustering
problem but also for the exponential polynomials encountered in quantum chemistry, Solid-state Physics
and other applications.
A Counterexample to the Forward Recursion in Fuzzy Critical Path Analysis Und...ijfls
This document presents a counterexample demonstrating that the fuzzy forward recursion method for determining critical paths does not always produce results consistent with the extension principle when discrete fuzzy sets are used to represent activity durations.
The document first provides background on fuzzy sets and critical path analysis. It then presents a proposition stating that the membership function for fuzzy critical path lengths can be determined by taking the maximum of the minimum membership values across all activity durations in each configuration.
The document goes on to present a counterexample using a simple series-parallel network with 18 configurations. It shows that applying the fuzzy forward recursion produces a different membership value for one critical path length compared to directly applying the extension principle. This difference proves the fuzzy forward
This document discusses fast algorithms for computing the discrete cosine transform (DCT) and inverse discrete cosine transform (IDCT) using Winograd's method.
The conventional DCT and IDCT algorithms have high computational complexity due to cosine functions. Winograd's algorithm reduces the number of multiplications required for matrix multiplication by rearranging terms.
The document proposes applying Winograd's algorithm to DCT and IDCT computation by representing the transforms as matrix multiplications. This approach reduces the number of multiplications required for an 8x8 block from over 16,000 to just 736 multiplications, with fewer additions and subtractions as well. This leads to faster DCT and IDCT computation compared
CHN and Swap Heuristic to Solve the Maximum Independent Set ProblemIJECEIAES
We describe a new approach to solve the problem to find the maximum independent set in a given Graph, known also as Max-Stable set problem (MSSP). In this paper, we show how Max-Stable problem can be reformulated into a linear problem under quadratic constraints, and then we resolve the QP result by a hybrid approach based Continuous Hopfeild Neural Network (CHN) and Local Search. In a manner that the solution given by the CHN will be the starting point of the local search. The new approach showed a good performance than the original one which executes a suite of CHN runs, at each execution a new leaner constraint is added into the resolved model. To prove the efficiency of our approach, we present some computational experiments of solving random generated problem and typical MSSP instances of real life problem.
This document summarizes and implements an ordinary differential equation (ODE) neural network using the Diffeqflux.jl library. It begins with an introduction to deep learning and neural networks. It then provides the mathematics behind modeling a simple multi-layer perceptron neural network as a system of ODEs. This includes derivations of the forward and backward propagation algorithms. Finally, it describes implementing a simple example ODE neural network using Diffeqflux.jl to demonstrate the approach.
EXACT SOLUTIONS OF A FAMILY OF HIGHER-DIMENSIONAL SPACE-TIME FRACTIONAL KDV-T...cscpconf
In this paper, based on the definition of conformable fractional derivative, the functional
variable method (FVM) is proposed to seek the exact traveling wave solutions of two higherdimensional
space-time fractional KdV-type equations in mathematical physics, namely the
(3+1)-dimensional space–time fractional Zakharov-Kuznetsov (ZK) equation and the (2+1)-
dimensional space–time fractional Generalized Zakharov-Kuznetsov-Benjamin-Bona-Mahony
(GZK-BBM) equation. Some new solutions are procured and depicted. These solutions, which
contain kink-shaped, singular kink, bell-shaped soliton, singular soliton and periodic wave
solutions, have many potential applications in mathematical physics and engineering. The
simplicity and reliability of the proposed method is verified.
Quadratic programming (Tool of optimization)VARUN KUMAR
This document provides an overview of quadratic programming, including:
1. It defines quadratic programming as a special case of nonlinear programming where the objective function is quadratic and all constraints are linear.
2. It presents the general mathematical formulation of a quadratic programming problem and provides an example problem.
3. It discusses solutions to quadratic programs using the graphical method and the Karush-Kuhn-Tucker (KKT) conditions.
International Journal of Engineering Research and Applications (IJERA) is an open access online peer reviewed international journal that publishes research and review articles in the fields of Computer Science, Neural Networks, Electrical Engineering, Software Engineering, Information Technology, Mechanical Engineering, Chemical Engineering, Plastic Engineering, Food Technology, Textile Engineering, Nano Technology & science, Power Electronics, Electronics & Communication Engineering, Computational mathematics, Image processing, Civil Engineering, Structural Engineering, Environmental Engineering, VLSI Testing & Low Power VLSI Design etc.
FITTED OPERATOR FINITE DIFFERENCE METHOD FOR SINGULARLY PERTURBED PARABOLIC C...ieijjournal
In this paper, we study the numerical solution of singularly perturbed parabolic convection-diffusion type
with boundary layers at the right side. To solve this problem, the backward-Euler with Richardson
extrapolation method is applied on the time direction and the fitted operator finite difference method on the
spatial direction is used, on the uniform grids. The stability and consistency of the method were established
very well to guarantee the convergence of the method. Numerical experimentation is carried out on model
examples, and the results are presented both in tables and graphs. Further, the present method gives a more
accurate solution than some existing methods reported in the literature.
The Gaussian or normal distribution is one of the most widely used in statistics. Estimating its parameters using
Bayesian inference and conjugate priors is also widely used. The use of conjugate priors allows all the results to be
derived in closed form. Unfortunately, different books use different conventions on how to parameterize the various
distributions (e.g., put the prior on the precision or the variance, use an inverse gamma or inverse chi-squared, etc),
which can be very confusing for the student. In this report, we summarize all of the most commonly used forms. We
provide detailed derivations for some of these results; the rest can be obtained by simple reparameterization. See the
appendix for the definition the distributions that are used.
This document presents a new method for finding the fuzzy critical path in a project network using type-2 discrete fuzzy numbers and type reduction. The key steps are:
1. Represent the time span of each activity as a type-2 discrete fuzzy number.
2. Use type reduction and the center of gravity to calculate the earliest start time, latest finish time, and total slack fuzzy time for each activity.
3. Identify the fuzzy critical path as the path(s) with a total slack time of 0 based on the center of gravity calculations.
An example application of the method on a sample network is provided to demonstrate the approach. The proposed method allows identification of the fuzzy critical path when activity
This document contains solutions to problems from the MIT course 6.003 Signals and Systems. It includes solutions for manipulating complex numbers, determining periodicity of signals, representing signals as linear combinations of basis functions, identifying properties of linear time-invariant systems, and whether certain statements about systems are true or false. The problems cover a range of foundational concepts in signals and systems.
This document describes a new algorithm for dual tree kernel conditional density estimation (KCDE) that provides fast and accurate density predictions. The algorithm extends previous work on univariate KCDE to allow for multivariate labels (Y) and conditioning variables (X). It applies Gray's dual tree approach separately to the numerator and denominator of the KCDE formula, and uses error bounds to ensure the quotient estimates have bounded relative error. This new algorithm provides the fastest known method for kernel conditional density estimation for prediction tasks.
Simplified Solutions of the CLP and CCP Limiting Cases of the Problem of Apo...James Smith
The new solutions presented herein for the CLP and CCP limiting cases of the Problem of Apollonius are much shorter and more easily understood than those provided by the same author in References [1] and [2]. These improvements result from (1) a better selection of angle relationships as a starting point for the solution process; and (2) better use of GA identities to avoid forming troublesome combinations of terms within the resulting equations.
The document provides homework assignments and lesson material on finding the distance and midpoint between two points using formulas. It includes practice problems calculating distance between points with coordinates (6, -2) and (12, 8), (3, 0) and (6, -2), (-11, 9) and (3, -4), and finding midpoints between points with endpoints (2, -2) and (6, 2), (-4, 0) and (0, 14), (-1, -2) and (3, -4).
An Efficient Multiplierless Transform algorithm for Video CodingCSCJournals
This paper presents an efficient algorithm to accelerate software video encoders/decoders by reducing the number of arithmetic operations for Discrete Cosine Transform (DCT). A multiplierless Ramanujan Ordered Number DCT (RDCT) is presented which computes the coefficients using shifts and addition operations only. The reduction in computational complexity has improved the performance of the video codec by almost 58% compared with the commonly used integer DCT. The results show that significant computation reduction can be achieved with negligible average peak signal-to-noise ratio (PSNR) degradation. The average structural similarity index matrix (SSIM) also ensures that the degradation due to the approximation is minimal.
This document presents a methodology for mapping multidimensional transforms onto reconfigurable architectures like FPGAs. The methodology uses tensor product decompositions and permutation matrices to express transforms recursively in terms of lower-order blocks. This allows large transforms to be computed by combining many parallel, smaller transform blocks. Specific examples are given for mapping one-dimensional linear convolution and discrete cosine transforms. The overall goal is to provide a unified framework and design process for implementing multidimensional transforms in a modular, parallel architecture.
This document discusses widelinearly minimum mean square error (WLMMSE) estimation for unique word orthogonal frequency-division multiplexing (UW-OFDM). It first provides background on UW-OFDM and describes the system model. It then discusses the WLMMSE estimator and how it can outperform the linear MMSE estimator for improper constellations like binary phase-shift keying (BPSK). Simulation results are presented showing the WLMMSE estimator achieves around 1 dB gain over the LMMSE estimator for BPSK. The document concludes the WLMMSE/UW-OFDM scheme can achieve up to 1.9 dB gain over conventional IEEE 802.11 schemes.
Computer Science
Active and Programmable Networks
Active safety systems
Ad Hoc & Sensor Network
Ad hoc networks for pervasive communications
Adaptive, autonomic and context-aware computing
Advance Computing technology and their application
Advanced Computing Architectures and New Programming Models
Advanced control and measurement
Aeronautical Engineering,
Agent-based middleware
Alert applications
Automotive, marine and aero-space control and all other control applications
Autonomic and self-managing middleware
Autonomous vehicle
Biochemistry
Bioinformatics
BioTechnology(Chemistry, Mathematics, Statistics, Geology)
Broadband and intelligent networks
Broadband wireless technologies
CAD/CAM/CAT/CIM
Call admission and flow/congestion control
Capacity planning and dimensioning
Changing Access to Patient Information
Channel capacity modelling and analysis
Civil Engineering,
Cloud Computing and Applications
Collaborative applications
Communication application
Communication architectures for pervasive computing
Communication systems
Computational intelligence
Computer and microprocessor-based control
Computer Architecture and Embedded Systems
Computer Business
Computer Sciences and Applications
Computer Vision
Computer-based information systems in health care
Computing Ethics
Computing Practices & Applications
Congestion and/or Flow Control
Content Distribution
Context-awareness and middleware
Creativity in Internet management and retailing
Cross-layer design and Physical layer based issue
Cryptography
Data Base Management
Data fusion
Data Mining
Data retrieval
Data Storage Management
Decision analysis methods
Decision making
Digital Economy and Digital Divide
Digital signal processing theory
Distributed Sensor Networks
Drives automation
Drug Design,
Drug Development
DSP implementation
E-Business
E-Commerce
E-Government
Electronic transceiver device for Retail Marketing Industries
Electronics Engineering,
Embeded Computer System
Emerging advances in business and its applications
Emerging signal processing areas
Enabling technologies for pervasive systems
Energy-efficient and green pervasive computing
Environmental Engineering,
Estimation and identification techniques
Evaluation techniques for middleware solutions
Event-based, publish/subscribe, and message-oriented middleware
Evolutionary computing and intelligent systems
Expert approaches
Facilities planning and management
Flexible manufacturing systems
Formal methods and tools for designing
Fuzzy algorithms
Fuzzy logics
GPS and location-based app
IRJET- An Efficient Reverse Converter for the Three Non-Coprime Moduli Set {4...IRJET Journal
This paper proposes a new and efficient reverse converter for converting residue numbers to decimal numbers for the three moduli set {6, 10, 15} which shares the common factor of 5. The proposed converter replaces larger multipliers used in previous converters with smaller multipliers and adders, reducing the hardware requirements. The hardware implementation of the proposed converter is presented and compared to other state-of-the-art converters, showing it performs better with fewer adders and multipliers. The proposed converter efficiently implements reverse conversion for the non-coprime three moduli set while requiring less hardware than previous approaches.
Low power cost rns comparison via partitioning the dynamic rangeNexgen Technology
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Fast Algorithm for Computing the Discrete Hartley Transform of Type-IIijeei-iaes
This document presents a new fast algorithm for computing the discrete Hartley transform of type-II (DHT-II) using a radix-2 decimation-in-time approach. The algorithm decomposes the DHT-II computation into butterfly operations involving two DHT-IIs of length N/2. This allows an in-place implementation using a regular butterfly structure. The computational complexity of the new algorithm is analyzed and shown to require fewer operations than an existing DHT-II algorithm by Hu. A comparison of the algorithms demonstrates the new approach has better structural and computational complexity properties for real-time applications.
The document discusses the divide and conquer algorithm design paradigm. It begins by defining divide and conquer as recursively breaking down a problem into smaller sub-problems, solving the sub-problems, and then combining the solutions to solve the original problem. Some examples of problems that can be solved using divide and conquer include binary search, quicksort, merge sort, and the fast Fourier transform algorithm. The document then discusses control abstraction, efficiency analysis, and uses divide and conquer to provide algorithms for large integer multiplication and merge sort. It concludes by defining the convex hull problem and providing an example input and output.
The document discusses the divide and conquer algorithm design technique. It begins by defining divide and conquer as breaking a problem down into smaller subproblems, solving the subproblems, and then combining the solutions to solve the original problem. It then provides examples of applying divide and conquer to problems like matrix multiplication and finding the maximum subarray. The document also discusses analyzing divide and conquer recurrences using methods like recursion trees and the master theorem.
ON RUN-LENGTH-CONSTRAINED BINARY SEQUENCESijitjournal
A class of binary sequences, constrained with respect to the length of zero runs, is considered.
For such sequences, termed (d, k)-sequences, new combinatorial and computational results
are established. Explicit expressions for enumerating (d, k)-sequences of finite length are
obtained. Efficient computational procedures for calculating the capacity of a (d, k)-code are
given. A simple method for constructing a near-optimal (d, k)-code is proposed. Illustrative
numerical examples demonstrate further the theoretical results.
The document discusses several theorems related to twin prime conjectures:
- Theorem 1 states that a prime p can be written in the form 3k+1 or 3k-1, with k being even.
- Theorem 4 characterizes twin primes as pairs where n(n+2) satisfies a modular condition.
- Theorems aim to prove there are infinitely many twin primes, relying on the ratio of primes increasing without bound as n increases without bound.
Symmetric quadratic tetration interpolation using forward and backward opera...IJECEIAES
The existed interpolation method, based on the second-order tetration polynomial, has the asymmetric property. The interpolation results, for each considering region, give individual characteristics. Although the interpolation performance has been better than the conventional methods, the symmetric property for signal interpolation is also necessary. In this paper, we propose the symmetric interpolation formulas derived from the second-order tetration polynomial. The combination of the forward and backward operations was employed to construct two types of the symmetric interpolation. Several resolutions of the fundamental signals were used to evaluate the signal reconstruction performance. The results show that the proposed interpolations can be used to reconstruct the fundamental signal and its peak signal to noise ratio (PSNR) is superior to the conventional interpolation methods, except the cubic spline interpolation for the sine wave signal. However, the visual results show that it has a small difference. Moreover, our proposed interpolations converge to the steady-state faster than the cubic spline interpolation. In addition, the option number increasing will reinforce their sensitivity.
A Novel Multiplication Algorithm Based On Euclidean Division For Multiplying ...Jim Webb
This document presents a novel multiplication algorithm based on the Euclidean division algorithm (EDA) for multiplying large integers. The algorithm directly applies EDA when the integers are different sizes, and with a modification when they are the same size. It is supported by the property that the product of consecutive Fibonacci numbers is equal to the sum of squares of preceding terms. A Python implementation shows the algorithm can multiply integers with thousands to millions of digits. The algorithm is well-suited for multiplying unequal integers and could have applications in number theory.
FACTORING CRYPTOSYSTEM MODULI WHEN THE CO-FACTORS DIFFERENCE IS BOUNDEDZac Darcy
This document summarizes results from previous papers on factoring integers when the difference between the co-factors is bounded. It presents the following key points:
1. It improves on previous theorems which showed that if the difference between two prime factors P and Q of an integer N is bounded by 2k, where k is the bit-size of N, then P and Q can be computed efficiently in at most comparisons.
2. The document extends this to show that if the minimal distance between any two co-factors of N is bounded by 2k, then its weak decomposition can be found in at most comparisons.
3. An algorithm is provided that finds the weak decomposition of a composite integer N in
Enhance The K Means Algorithm On Spatial DatasetAlaaZ
The document describes an enhancement to the standard k-means clustering algorithm. The enhancement aims to improve computational speed by storing additional information from each iteration, such as the closest cluster and distance for each data point. This avoids needing to recompute distances to all cluster centers in subsequent iterations if a point does not change clusters. The complexity of the enhanced algorithm is reduced from O(nkl) to O(nk) where n is points, k is clusters, and l is iterations.
We have established a new general method to build doubly even
magic squares. New types of magic squares are built. The method
is aesthetic and easy to understand.
Composite Field Multiplier based on Look-Up Table for Elliptic Curve Cryptogr...Marisa Paryasto
This document discusses implementing elliptic curve cryptography using composite fields. It proposes using a 299-bit key represented in the composite field GF((213)23) instead of the conventional GF(2299). This breaks the finite field multiplication into smaller chunks by dividing the field into a ground field and extension field. A lookup table is used for multiplication in the ground field GF(213) while a classic multiplier is used for the extension field GF(23). This composite field approach aims to provide better time and area efficiency for implementation on FPGAs compared to a single large multiplier. The document provides background on elliptic curves, finite fields, and previous work on composite field representations.
This document presents radix-2 algorithms for computing type-II discrete cosine transform (DCT) and discrete sine transform (DST) of length N=2^n (n≥2). The algorithms decompose the computation into even and odd indexed output sequences. The even outputs are computed from two transforms of length N/2. Recursive relations are used to efficiently compute the odd outputs from the even outputs and additional terms, requiring fewer operations than existing methods. Pseudocode and complexity analysis are provided to demonstrate the algorithms.
International Journal of Engineering Research and Applications (IJERA) is an open access online peer reviewed international journal that publishes research and review articles in the fields of Computer Science, Neural Networks, Electrical Engineering, Software Engineering, Information Technology, Mechanical Engineering, Chemical Engineering, Plastic Engineering, Food Technology, Textile Engineering, Nano Technology & science, Power Electronics, Electronics & Communication Engineering, Computational mathematics, Image processing, Civil Engineering, Structural Engineering, Environmental Engineering, VLSI Testing & Low Power VLSI Design etc.
This document summarizes the finite difference method for numerically solving heat transfer problems. The method involves establishing a nodal network to discretize the domain, deriving finite difference approximations of the governing heat equation at each node, developing a system of simultaneous algebraic equations relating all nodal temperatures, and solving the system of equations using numerical techniques like matrix inversion or iterative methods. Examples are provided to illustrate the finite difference approximations, formation of the algebraic system, and solution via the Jacobi and Gauss-Seidel iteration methods.
Similar to NEW NON-COPRIME CONJUGATE-PAIR BINARY TO RNS MULTI-MODULI FOR RESIDUE NUMBER SYSTEM (20)
This talk will cover ScyllaDB Architecture from the cluster-level view and zoom in on data distribution and internal node architecture. In the process, we will learn the secret sauce used to get ScyllaDB's high availability and superior performance. We will also touch on the upcoming changes to ScyllaDB architecture, moving to strongly consistent metadata and tablets.
zkStudyClub - LatticeFold: A Lattice-based Folding Scheme and its Application...Alex Pruden
Folding is a recent technique for building efficient recursive SNARKs. Several elegant folding protocols have been proposed, such as Nova, Supernova, Hypernova, Protostar, and others. However, all of them rely on an additively homomorphic commitment scheme based on discrete log, and are therefore not post-quantum secure. In this work we present LatticeFold, the first lattice-based folding protocol based on the Module SIS problem. This folding protocol naturally leads to an efficient recursive lattice-based SNARK and an efficient PCD scheme. LatticeFold supports folding low-degree relations, such as R1CS, as well as high-degree relations, such as CCS. The key challenge is to construct a secure folding protocol that works with the Ajtai commitment scheme. The difficulty, is ensuring that extracted witnesses are low norm through many rounds of folding. We present a novel technique using the sumcheck protocol to ensure that extracted witnesses are always low norm no matter how many rounds of folding are used. Our evaluation of the final proof system suggests that it is as performant as Hypernova, while providing post-quantum security.
Paper Link: https://eprint.iacr.org/2024/257
How information systems are built or acquired puts information, which is what they should be about, in a secondary place. Our language adapted accordingly, and we no longer talk about information systems but applications. Applications evolved in a way to break data into diverse fragments, tightly coupled with applications and expensive to integrate. The result is technical debt, which is re-paid by taking even bigger "loans", resulting in an ever-increasing technical debt. Software engineering and procurement practices work in sync with market forces to maintain this trend. This talk demonstrates how natural this situation is. The question is: can something be done to reverse the trend?
From Natural Language to Structured Solr Queries using LLMsSease
This talk draws on experimentation to enable AI applications with Solr. One important use case is to use AI for better accessibility and discoverability of the data: while User eXperience techniques, lexical search improvements, and data harmonization can take organizations to a good level of accessibility, a structural (or “cognitive” gap) remains between the data user needs and the data producer constraints.
That is where AI – and most importantly, Natural Language Processing and Large Language Model techniques – could make a difference. This natural language, conversational engine could facilitate access and usage of the data leveraging the semantics of any data source.
The objective of the presentation is to propose a technical approach and a way forward to achieve this goal.
The key concept is to enable users to express their search queries in natural language, which the LLM then enriches, interprets, and translates into structured queries based on the Solr index’s metadata.
This approach leverages the LLM’s ability to understand the nuances of natural language and the structure of documents within Apache Solr.
The LLM acts as an intermediary agent, offering a transparent experience to users automatically and potentially uncovering relevant documents that conventional search methods might overlook. The presentation will include the results of this experimental work, lessons learned, best practices, and the scope of future work that should improve the approach and make it production-ready.
Conversational agents, or chatbots, are increasingly used to access all sorts of services using natural language. While open-domain chatbots - like ChatGPT - can converse on any topic, task-oriented chatbots - the focus of this paper - are designed for specific tasks, like booking a flight, obtaining customer support, or setting an appointment. Like any other software, task-oriented chatbots need to be properly tested, usually by defining and executing test scenarios (i.e., sequences of user-chatbot interactions). However, there is currently a lack of methods to quantify the completeness and strength of such test scenarios, which can lead to low-quality tests, and hence to buggy chatbots.
To fill this gap, we propose adapting mutation testing (MuT) for task-oriented chatbots. To this end, we introduce a set of mutation operators that emulate faults in chatbot designs, an architecture that enables MuT on chatbots built using heterogeneous technologies, and a practical realisation as an Eclipse plugin. Moreover, we evaluate the applicability, effectiveness and efficiency of our approach on open-source chatbots, with promising results.
[OReilly Superstream] Occupy the Space: A grassroots guide to engineering (an...Jason Yip
The typical problem in product engineering is not bad strategy, so much as “no strategy”. This leads to confusion, lack of motivation, and incoherent action. The next time you look for a strategy and find an empty space, instead of waiting for it to be filled, I will show you how to fill it in yourself. If you’re wrong, it forces a correction. If you’re right, it helps create focus. I’ll share how I’ve approached this in the past, both what works and lessons for what didn’t work so well.
ScyllaDB is making a major architecture shift. We’re moving from vNode replication to tablets – fragments of tables that are distributed independently, enabling dynamic data distribution and extreme elasticity. In this keynote, ScyllaDB co-founder and CTO Avi Kivity explains the reason for this shift, provides a look at the implementation and roadmap, and shares how this shift benefits ScyllaDB users.
Freshworks Rethinks NoSQL for Rapid Scaling & Cost-EfficiencyScyllaDB
Freshworks creates AI-boosted business software that helps employees work more efficiently and effectively. Managing data across multiple RDBMS and NoSQL databases was already a challenge at their current scale. To prepare for 10X growth, they knew it was time to rethink their database strategy. Learn how they architected a solution that would simplify scaling while keeping costs under control.
inQuba Webinar Mastering Customer Journey Management with Dr Graham HillLizaNolte
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In this webinar, we explored essential aspects of Customer Journey Management and personalization. Here’s a summary of the key insights and topics discussed:
Key Takeaways:
Understanding the Customer Journey: Dr. Hill emphasized the importance of mapping and understanding the complete customer journey to identify touchpoints and opportunities for improvement.
Personalization Strategies: We discussed how to leverage data and insights to create personalized experiences that resonate with customers.
Technology Integration: Insights were shared on how inQuba’s advanced technology can streamline customer interactions and drive operational efficiency.
Main news related to the CCS TSI 2023 (2023/1695)Jakub Marek
An English 🇬🇧 translation of a presentation to the speech I gave about the main changes brought by CCS TSI 2023 at the biggest Czech conference on Communications and signalling systems on Railways, which was held in Clarion Hotel Olomouc from 7th to 9th November 2023 (konferenceszt.cz). Attended by around 500 participants and 200 on-line followers.
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The videorecording (in Czech) from the presentation is available here: https://youtu.be/WzjJWm4IyPk?si=SImb06tuXGb30BEH .
"$10 thousand per minute of downtime: architecture, queues, streaming and fin...Fwdays
Direct losses from downtime in 1 minute = $5-$10 thousand dollars. Reputation is priceless.
As part of the talk, we will consider the architectural strategies necessary for the development of highly loaded fintech solutions. We will focus on using queues and streaming to efficiently work and manage large amounts of data in real-time and to minimize latency.
We will focus special attention on the architectural patterns used in the design of the fintech system, microservices and event-driven architecture, which ensure scalability, fault tolerance, and consistency of the entire system.
Must Know Postgres Extension for DBA and Developer during MigrationMydbops
Mydbops Opensource Database Meetup 16
Topic: Must-Know PostgreSQL Extensions for Developers and DBAs During Migration
Speaker: Deepak Mahto, Founder of DataCloudGaze Consulting
Date & Time: 8th June | 10 AM - 1 PM IST
Venue: Bangalore International Centre, Bangalore
Abstract: Discover how PostgreSQL extensions can be your secret weapon! This talk explores how key extensions enhance database capabilities and streamline the migration process for users moving from other relational databases like Oracle.
Key Takeaways:
* Learn about crucial extensions like oracle_fdw, pgtt, and pg_audit that ease migration complexities.
* Gain valuable strategies for implementing these extensions in PostgreSQL to achieve license freedom.
* Discover how these key extensions can empower both developers and DBAs during the migration process.
* Don't miss this chance to gain practical knowledge from an industry expert and stay updated on the latest open-source database trends.
Mydbops Managed Services specializes in taking the pain out of database management while optimizing performance. Since 2015, we have been providing top-notch support and assistance for the top three open-source databases: MySQL, MongoDB, and PostgreSQL.
Our team offers a wide range of services, including assistance, support, consulting, 24/7 operations, and expertise in all relevant technologies. We help organizations improve their database's performance, scalability, efficiency, and availability.
Contact us: info@mydbops.com
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LF Energy Webinar: Carbon Data Specifications: Mechanisms to Improve Data Acc...DanBrown980551
This LF Energy webinar took place June 20, 2024. It featured:
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Manufacturing custom quality metal nameplates and badges involves several standard operations. Processes include sheet prep, lithography, screening, coating, punch press and inspection. All decoration is completed in the flat sheet with adhesive and tooling operations following. The possibilities for creating unique durable nameplates are endless. How will you create your brand identity? We can help!
2. 106 Computer Science & Information Technology (CS & IT)
The new thing we come up with here is working with a full non-prime moduli set ( i.e. for this
case ) gcd (mi, mj ) ≠ 1 for i ≠ j (1)
RNS systems based on non coprime moduli have also been studied in literature [2] –[5].
Although as discussed in [2] that non-coprime has little studies upon, we still have strong sense
that it deserves to work on.
The rest of this paper is organized as follows. In Section 2, overview of the new Non-coprime
multi moduli is proposed. Section 3 presents the realization of the proposed forward converter of
the new non-coprime conjugate-pair multi-moduli , while the paper is concluded in Section 4.
2. OVERVIEW OF NEW NON-COPRIME MULTI –MODULI
Since almost all previous work stated that [1][3][5] " The basis for an RNS is a set of relatively
prime integers; that is :
S = { q1, q2, ... , qL }, where (qi , qj ) = 1 for i ≠j (2)
with (qi , qj ) indicating the greatest common divisor of qi and qj .
The set S is the moduli set while the dynamic range of the system ( i.e. M ) is the product Q of the
moduli qi in the set S. Any integer X belonging to ZQ = { 0, 1 2, .... , Q -1 } has an RNS
representation" .
X
RNS
( X1, X2, … , XL) (3)
Xi = < X >qi , i = 1, 2, .... , L (4)
Where <X>q is X mod q.
For our case of non-coprime , equation number 4 becomes :
Xi = < X >qi , i = 2, 3, .... , L (5)
For both cases ( i.e. Coprime and Non-coprime ), if X, Y have RNS representations { X1, …..,
XM}, { Y1, … , YM}, the RNS representation of W = X * Y ( * denotes addition, subtraction or
multiplication ) is
W RNS { W1, …. , WM }; Wi = < Xi * Yi > qi, i = 1, … , L (6)
Another thing to notice here is that our new proposed non-coprime conjugate-pair multi-moduli
set is also conjugate even by dividing it by the common factor among its moduli ( i.e. number 2 in
this case), the shape is to be discussed in another paper. However it has the following form :
3. Computer Science & Information Technology (CS & IT) 107
{ 2
n1-1
– 1, 2
n1-1
+ 1, 2
n2 - 1
– 1, 2
n2 - 1
+ 1, …, 2
nN- 1
– 1, 2
nN- 1
+ 1 }.
The proposed Non-coprime multi-moduli set form is :
S = { 2n1 – 2, 2n1 + 2, 2n2 – 2, 2n2 + 2, …, 2nN – 2, 2nN + 2 }.
It is clear that each conjugate-pair on the numbers line is 4 spaces apart. As discussed in [2] it was
shown that having the shape of the new non-coprime moduli set ( i.e. { 2n – 2, 2n , 2n + 2 } )
being 4 spaces apart from each other helped in the Forward conversion process (FC) of the
moduli. The same space for our new non-coprime multi-moduli is useful indeed.
Lets take an example to show what is meant by the spaces above.
Ex.1 Let n1 = 3 , n2 = 4 for the set S.
Then the set S = { 6, 10, 14, 18 }.
Numbers ( 6 , 10 ) and ( 14 , 18 ) are 4 spaces from each other on the numbers line. This is true
for any value taken for { n1, n2 … , nN }, notice that n1 < n2 < … < nN ; n1 >= 2.
This is need for the management process to prepare the multi-moduli in good shape.
Least Common Multiple (LCM) is must be used for the non-coprime case, since there is a
common factor among the modulus numbers.
3. NEW NON-COPRIME MULTI-MODULI PROPOSED FORWARD
CONVERTER
This section is preferred to be divided into two sections in order to show simply how it works.
Then from the multi-moduli shape provided it is generalized for size of (N).
In the first section, we are going to take N = 2, thus the multi-moduli would consist of 4 modulus
values. The second sub-section we are having N = 3, so there would be 6 modulus inside the
multi-moduli set. Forward conversion ( i.e. Binary to RNS ) is to be implemented for each case.
3.1 VALUES SET OF 4-MODULUS
The multi-moduli set will be of the form, when we take N = 2 :
S = { 2n1 – 2, 2n1 + 2, 2n2 – 2, 2n2 + 2 }.
If we take as the first example showed n1 = 3 , n2 = 4 . The shape of the set was :
S1 = { 6, 10, 14, 18 }.
M ( i.e. Dynamic Range of the set ) is calculated through the LCM. For the set S1 it is equal to
4. 108 Computer Science & Information Technology (CS & IT)
6 * 10 * 14 * 18 / 2L-1, where L = the size of the set. (7)
For this case L = 4, so M = 1890 .
That means any number in the range [ 0 – 1889 ] has a unique representation among the proposed
set. This dynamic range is larger than the range for { 2n1 – 2, 2n1 , 2n1 + 2 } which equals 120.
i.e. 1890 >> 120.
It is also having a larger range than the set { 2n2 – 2, 2n2 , 2n2 + 2 } which has M = 1008.
i.e. 1890 > 1008.
This is due we are working with 4-moduli set rather than 3-moduli set, and by neglecting the
middle modulus ( i.e. 2n ) and having the conjugate of n1 , n2 instead. Mathematically it could
be shown as :
M1 = 6 * 8 *10 / 4 , M2 = 14 * 16 * 18 / 4 while M3 = 6 * 10 * 14 * 18 / 8 .
Take for M2 case, as it has larger numbers than M1, 16 / 4 < 6 * 10 / 8 or by having 6 * 10 / 2 =
30, 30 > 16 when comparing them divided 4 ( i.e. having a common base of comparison ).
The conversion process works as the follow, each modulus having the shape 2n – 2 goes to
Converter number 1, while the 2n + 2 goes to Converter number 2 that works in parallel.
Converter 1 does its work just as figure 1 in [2] showed, figure 2 in the same paper shows
converter 2 work.
Hardware implementation for each case is shown in figures 3, 5 of [2].
3.2 VALUE SET OF 6-MODULUS
When we take N = 3, then the multi-moduli set will be on the form :
S = { 2n1 – 2, 2n1 + 2, 2n2 – 2, 2n2 + 2, 2n3 – 2, 2n3 + 2 }.
If we take n1 = 3 , n2 = 4 and n3 = 5 for simplicity. The shape of the set is :
S2 = { 6, 10, 14, 18, 30 , 34 }.
M ( i.e. Dynamic Range of the set ) is calculated through the LCM. For the set S2 it is equal to
6 * 10 * 14 * 18 * 30 * 34 / 2L-1, where L = the size of the set. (8)
For this case L = 6, so M = 481950.
5. Computer Science & Information Technology (CS & IT) 109
That means any number in the range [ 0 – 481949] has a unique representation among the
proposed set. This dynamic range is larger than the range for { 2n1 – 2, 2n1 , 2n1 + 2 } which
equals 120.
i.e. 481950 >> 120.
It is also having a very large range than the set { 2n2 – 2, 2n2 , 2n2 + 2 } which has M = 1008.
i.e. 481950>> 1008.
Finally it has larger range than the set { 2n3 – 2, 2n3 , 2n3 + 2 } which has M = 8160.
i.e. 481950>> 8160.
This is due we are working with 6-moduli set rather than 3-moduli set for each case, and by
neglecting the middle modulus ( i.e. 2n ) and having the conjugate of n1 , n2 and n3 instead.
Mathematically it could be shown as :
M1 = 6 * 8 *10 / 4 , M2 = 14 * 16 * 18 / 4 , M3 = 30 * 32 * 34 / 4 while
M4 = 6 * 10 * 14 * 18 * 30 * 34 / 32 .
Take for M3 case, as it has the largest numbers than M1 and M2, 32 / 4 < 6 * 10 * 14 * 18 / 32 or
by having 6 * 10 * 14 * 18 / 8 = 1890, 1890 > > 16 when comparing them divided 4 ( i.e. having
a common base of comparison ).
The conversion process works as the follow, each modulus having the shape 2n – 2 goes to
Converter number 1, while the 2n + 2 goes to Converter number 2 that both works in parallel.
Converter 1 does its work just as figure 1 in [2] showed, figure 2 in the same paper shows
converter 2 work.
Hardware implementation for each case is shown in figures 3, 5 of [2].
4. CONCLUSIONS
A new non-coprime multi-moduli set has been proposed. A general formula for the dynamic
range of it was derived. Algorithm of the special non-coprime multi-moduli set has been
suggested. Also a new mathematical algorithm for the new non-coprime multi-set has been
proposed.
This research revealed that non-coprime moduli set may be suitable for wide variety of cases not
limited to co-prime only ( i.e. Conjugate in multi-moduli ).
ACKNOWLEDGEMENTS
The author would like to thank everyone.
6. 110 Computer Science & Information Technology (CS & IT)
REFERENCES
[1] A. Skavantzos ; Y. Wang, "New efficient RNS-to-weighted decoders for conjugate-pair-moduli
residue number systems", IEEE Conference Record of the Thirty-Third Asilomar Conference on
Signals, Systems, and Computers, 1999..
[2] Mansour Bader, Andraws Swidan, Mazin Al-Hadidi and Baha Rababah, "A binary to residue
conversion using new proposed non-coprime moduli set", Signal & Image Processing : An
International Journal (SIPIJ) Vol.7, No.3, June 2016 .
[3] A. Skavantzos ; Yuke Wang, "Application of new Chinese Remainder Theorems to RNS with two
pairs of conjugate moduli", IEEE Pacific Rim Conference on Communications, Computers and Signal
Processing (PACRIM 1999). Conference Proceedings, 1999.
[4] M. Abdallah, A. Skavantzos, "On the binary quadratic residue system with non coprirne moduli",
IEEE Trans. On Signal Processing, vol. 45, no. 8, pp. 2085-2091, Aug. 1997.
[5] Y. Wang, "New Chinese Remainder Theorems", Proceedings of the Thirty Second Asilomar
Conference on Signals Systems and Computers, pp. 165-171, 1998-Nov.
[6] A. Skavantzos, M. Abdallah, "Implementation Issues of the Two-Level Residue Number System with
Pairs of Conjugate Moduli", IEEE Trans. On Signal Processing, vol. 47, no. 3, pp. 826-838, March
1999.
[7] A. Skavantzos, M. Abdallah, "Novel Residue Arithmetic Processors for High Speed Digital Signal
Processing", Proceedings of the Thirty Second Asilomar Conference on Signals Systems arid
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[8] A. Skavantzos ; T. Stouraitis, "Grouped-moduli residue number systems for fast signal processing",
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AUTHORS
Mansour Bader holds a MSc in computer engineering and networks, University of
Jordan, Jordan, 2016. BSc Computer Engineering, Al-Balqa Applied University,
Jordan, 2008. He is a technical support engineer of computer networks at computer
center of Al-Balqa Applied University for 8 years and a half.
7. Computer Science & Information Technology (CS & IT) 111
Dr. Andraws I. Swidan was born in Al-Karak Jordan in 1954. He received his
diploma in Computer Engineering (with honours) and Ph.D. in Computer
Engineering from LETI Ulianov Lenin, Sanct Peterburg (Leningrad), Russia in
1979 and 1982 respectively. He Joined the Electrical Engineering Department at
the University of Jordan in 1983 and was one of the founders of the Computer
Engineering Department at the University of Jordan in 1999. Since then he is a
professor at the department. He is also an Adjunct Professor with the ECE
department of the McGill University, Montreal, Canada. He holds several technical
certifications among which the CISSP. He is an IEEE member, Jordanian
Engineering Association member Quebec College of engineers member. He is a Canada Professional
Engineer (The province of Quebec). He was member of several national and international scientific
committees. He holds several patents and tens of publications. His main areas of research interest are:
computer arithmetic, computer security, encryption algorithms.
Mazin Al-hadidi has PhD. in Engineering Science (Computing Machines,
Systems and Networks), Institute of Problems of Simulation in Power Engineering
Academy of Science, Ukraine/Kiev .1990-1994, with grade Excellent. Bachelor
and Master Degrees in Engineering (Computer and intellectual systems and
networks) Kiev Institute of Civil Aviation Engineers, as a governmental
scholarship, Soviet Union / Kiev, 1984-1990, with grade very good. General
Secondary 12 Years Certificate in the Science branch, Jordan/Al-Salt, 1984, with
grade very good.