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Transmit Processing in MIMO Wireless Systems
IEEE 6th CAS Symp. on Emerging Technologies: Mobile and Wireless Comm Shanghai, China, May 31-June 2,2004 Transmit Processing in MIMO Wireless Systems Josef A. Nossek, Michael Joham, and Wolfgang Utschick Institute for Circuit Theory and Signal Processing, Munich University of Technology, 80333 Munich, Germany Phone: +49 (89) 289-28501, Email: [email protected] Abstract-By restricting the receive filter to he scalar, we weighted by a scalar in Section IV. In Section V, we compare derive the optimizations for linear transmit processing from the linear transmit and receive processing. respective joint optimizations of transmit and receive filters. We A popular nonlinear transmit processing scheme is Tom- can identify three filter types similar to receive processing: the nmamit matched filter (TxMF), the transmit zero-forcing filter linson Harashima precoding (THP) originally proposed for (TxZE), and the transmil Menerfilter (TxWF). The TxW has dispersive single inpur single output (SISO) systems in [IO], similar convergence properties as the receive Wiener filter, i.e. [Ill, but can also be applied to MlMO systems [12], [13]. it converges to the matched filter and the zero-forcing Pter for THP is similar to decision feedback equalization (DFE), hut low and high signal to noise ratio, respectively. Additionally, the contrary to DFE, THP feeds back the already transmitted mean square error (MSE) of the TxWF is a lower hound for the MSEs of the TxMF and the TxZF. symbols to reduce the interference caused by these symbols The optimizations for the linear transmit filters are extended at the receivers. Although THP is based on the application of to obtain the respective Tomlinson-Harashimp precoding (THP) nonlinear modulo operators at the receivers and the transmitter, solutions. -
A Category-Theoretic Approach to Representation and Analysis of Inconsistency in Graph-Based Viewpoints
A Category-Theoretic Approach to Representation and Analysis of Inconsistency in Graph-Based Viewpoints by Mehrdad Sabetzadeh A thesis submitted in conformity with the requirements for the degree of Master of Science Graduate Department of Computer Science University of Toronto Copyright c 2003 by Mehrdad Sabetzadeh Abstract A Category-Theoretic Approach to Representation and Analysis of Inconsistency in Graph-Based Viewpoints Mehrdad Sabetzadeh Master of Science Graduate Department of Computer Science University of Toronto 2003 Eliciting the requirements for a proposed system typically involves different stakeholders with different expertise, responsibilities, and perspectives. This may result in inconsis- tencies between the descriptions provided by stakeholders. Viewpoints-based approaches have been proposed as a way to manage incomplete and inconsistent models gathered from multiple sources. In this thesis, we propose a category-theoretic framework for the analysis of fuzzy viewpoints. Informally, a fuzzy viewpoint is a graph in which the elements of a lattice are used to specify the amount of knowledge available about the details of nodes and edges. By defining an appropriate notion of morphism between fuzzy viewpoints, we construct categories of fuzzy viewpoints and prove that these categories are (finitely) cocomplete. We then show how colimits can be employed to merge the viewpoints and detect the inconsistencies that arise independent of any particular choice of viewpoint semantics. Taking advantage of the same category-theoretic techniques used in defining fuzzy viewpoints, we will also introduce a more general graph-based formalism that may find applications in other contexts. ii To my mother and father with love and gratitude. Acknowledgements First of all, I wish to thank my supervisor Steve Easterbrook for his guidance, support, and patience. -
Download the Basketballplayer.Ngql Fle Here
Nebula Graph Database Manual v1.2.1 Min Wu, Amber Zhang, XiaoDan Huang 2021 Vesoft Inc. Table of contents Table of contents 1. Overview 4 1.1 About This Manual 4 1.2 Welcome to Nebula Graph 1.2.1 Documentation 5 1.3 Concepts 10 1.4 Quick Start 18 1.5 Design and Architecture 32 2. Query Language 43 2.1 Reader 43 2.2 Data Types 44 2.3 Functions and Operators 47 2.4 Language Structure 62 2.5 Statement Syntax 76 3. Build Develop and Administration 128 3.1 Build 128 3.2 Installation 134 3.3 Configuration 141 3.4 Account Management Statement 161 3.5 Batch Data Management 173 3.6 Monitoring and Statistics 192 3.7 Development and API 199 4. Data Migration 200 4.1 Nebula Exchange 200 5. Nebula Graph Studio 224 5.1 Change Log 224 5.2 About Nebula Graph Studio 228 5.3 Deploy and connect 232 5.4 Quick start 237 5.5 Operation guide 248 6. Contributions 272 6.1 Contribute to Documentation 272 6.2 Cpp Coding Style 273 6.3 How to Contribute 274 6.4 Pull Request and Commit Message Guidelines 277 7. Appendix 278 7.1 Comparison Between Cypher and nGQL 278 - 2/304 - 2021 Vesoft Inc. Table of contents 7.2 Comparison Between Gremlin and nGQL 283 7.3 Comparison Between SQL and nGQL 298 7.4 Vertex Identifier and Partition 303 - 3/304 - 2021 Vesoft Inc. 1. Overview 1. Overview 1.1 About This Manual This is the Nebula Graph User Manual. -
Modular Arithmetic
CS 70 Discrete Mathematics and Probability Theory Fall 2009 Satish Rao, David Tse Note 5 Modular Arithmetic One way to think of modular arithmetic is that it limits numbers to a predefined range f0;1;:::;N ¡ 1g, and wraps around whenever you try to leave this range — like the hand of a clock (where N = 12) or the days of the week (where N = 7). Example: Calculating the day of the week. Suppose that you have mapped the sequence of days of the week (Sunday, Monday, Tuesday, Wednesday, Thursday, Friday, Saturday) to the sequence of numbers (0;1;2;3;4;5;6) so that Sunday is 0, Monday is 1, etc. Suppose that today is Thursday (=4), and you want to calculate what day of the week will be 10 days from now. Intuitively, the answer is the remainder of 4 + 10 = 14 when divided by 7, that is, 0 —Sunday. In fact, it makes little sense to add a number like 10 in this context, you should probably find its remainder modulo 7, namely 3, and then add this to 4, to find 7, which is 0. What if we want to continue this in 10 day jumps? After 5 such jumps, we would have day 4 + 3 ¢ 5 = 19; which gives 5 modulo 7 (Friday). This example shows that in certain circumstances it makes sense to do arithmetic within the confines of a particular number (7 in this example), that is, to do arithmetic by always finding the remainder of each number modulo 7, say, and repeating this for the results, and so on. -
Three Methods of Finding Remainder on the Operation of Modular
Zin Mar Win, Khin Mar Cho; International Journal of Advance Research and Development (Volume 5, Issue 5) Available online at: www.ijarnd.com Three methods of finding remainder on the operation of modular exponentiation by using calculator 1Zin Mar Win, 2Khin Mar Cho 1University of Computer Studies, Myitkyina, Myanmar 2University of Computer Studies, Pyay, Myanmar ABSTRACT The primary purpose of this paper is that the contents of the paper were to become a learning aid for the learners. Learning aids enhance one's learning abilities and help to increase one's learning potential. They may include books, diagram, computer, recordings, notes, strategies, or any other appropriate items. In this paper we would review the types of modulo operations and represent the knowledge which we have been known with the easiest ways. The modulo operation is finding of the remainder when dividing. The modulus operator abbreviated “mod” or “%” in many programming languages is useful in a variety of circumstances. It is commonly used to take a randomly generated number and reduce that number to a random number on a smaller range, and it can also quickly tell us if one number is a factor of another. If we wanted to know if a number was odd or even, we could use modulus to quickly tell us by asking for the remainder of the number when divided by 2. Modular exponentiation is a type of exponentiation performed over a modulus. The operation of modular exponentiation calculates the remainder c when an integer b rose to the eth power, bᵉ, is divided by a positive integer m such as c = be mod m [1]. -
The Best of Both Worlds?
The Best of Both Worlds? Reimplementing an Object-Oriented System with Functional Programming on the .NET Platform and Comparing the Two Paradigms Erik Bugge Thesis submitted for the degree of Master in Informatics: Programming and Networks 60 credits Department of Informatics Faculty of mathematics and natural sciences UNIVERSITY OF OSLO Autumn 2019 The Best of Both Worlds? Reimplementing an Object-Oriented System with Functional Programming on the .NET Platform and Comparing the Two Paradigms Erik Bugge © 2019 Erik Bugge The Best of Both Worlds? http://www.duo.uio.no/ Printed: Reprosentralen, University of Oslo Abstract Programming paradigms are categories that classify languages based on their features. Each paradigm category contains rules about how the program is built. Comparing programming paradigms and languages is important, because it lets developers make more informed decisions when it comes to choosing the right technology for a system. Making meaningful comparisons between paradigms and languages is challenging, because the subjects of comparison are often so dissimilar that the process is not always straightforward, or does not always yield particularly valuable results. Therefore, multiple avenues of comparison must be explored in order to get meaningful information about the pros and cons of these technologies. This thesis looks at the difference between the object-oriented and functional programming paradigms on a higher level, before delving in detail into a development process that consisted of reimplementing parts of an object- oriented system into functional code. Using results from major comparative studies, exploring high-level differences between the two paradigms’ tools for modular programming and general program decompositions, and looking at the development process described in detail in this thesis in light of the aforementioned findings, a comparison on multiple levels was done. -
Functional C
Functional C Pieter Hartel Henk Muller January 3, 1999 i Functional C Pieter Hartel Henk Muller University of Southampton University of Bristol Revision: 6.7 ii To Marijke Pieter To my family and other sources of inspiration Henk Revision: 6.7 c 1995,1996 Pieter Hartel & Henk Muller, all rights reserved. Preface The Computer Science Departments of many universities teach a functional lan- guage as the first programming language. Using a functional language with its high level of abstraction helps to emphasize the principles of programming. Func- tional programming is only one of the paradigms with which a student should be acquainted. Imperative, Concurrent, Object-Oriented, and Logic programming are also important. Depending on the problem to be solved, one of the paradigms will be chosen as the most natural paradigm for that problem. This book is the course material to teach a second paradigm: imperative pro- gramming, using C as the programming language. The book has been written so that it builds on the knowledge that the students have acquired during their first course on functional programming, using SML. The prerequisite of this book is that the principles of programming are already understood; this book does not specifically aim to teach `problem solving' or `programming'. This book aims to: ¡ Familiarise the reader with imperative programming as another way of imple- menting programs. The aim is to preserve the programming style, that is, the programmer thinks functionally while implementing an imperative pro- gram. ¡ Provide understanding of the differences between functional and imperative pro- gramming. Functional programming is a high level activity. -
Fast Integer Division – a Differentiated Offering from C2000 Product Family
Application Report SPRACN6–July 2019 Fast Integer Division – A Differentiated Offering From C2000™ Product Family Prasanth Viswanathan Pillai, Himanshu Chaudhary, Aravindhan Karuppiah, Alex Tessarolo ABSTRACT This application report provides an overview of the different division and modulo (remainder) functions and its associated properties. Later, the document describes how the different division functions can be implemented using the C28x ISA and intrinsics supported by the compiler. Contents 1 Introduction ................................................................................................................... 2 2 Different Division Functions ................................................................................................ 2 3 Intrinsic Support Through TI C2000 Compiler ........................................................................... 4 4 Cycle Count................................................................................................................... 6 5 Summary...................................................................................................................... 6 6 References ................................................................................................................... 6 List of Figures 1 Truncated Division Function................................................................................................ 2 2 Floored Division Function................................................................................................... 3 3 Euclidean -
Modulo of a Negative Number1 1 Modular Arithmetic
Algologic Technical Report # 01/2017 Modulo of a negative number1 S. Parthasarathy [email protected] Ref.: negamodulo.tex Ver. code: 20170109e Abstract This short article discusses an enigmatic question in elementary num- ber theory { that of finding the modulo of a negative number. Is this feasible to compute ? If so, how do we compute this value ? 1 Modular arithmetic In mathematics, modular arithmetic is a system of arithmetic for integers, where numbers "wrap around" upon reaching a certain value - the modulus (plural moduli). The modern approach to modular arithmetic was developed by Carl Friedrich Gauss in his book Disquisitiones Arithmeticae, published in 1801. Modular arithmetic is a fascinating aspect of mathematics. The \modulo" operation is often called as the fifth arithmetic operation, and comes after + − ∗ and = . It has use in many practical situations, particu- larly in number theory and cryptology [1] [2]. If x and n are integers, n < x and n =6 0 , the operation \ x mod n " is the remainder we get when n divides x. In other words, (x mod n) = r if there exists some integer q such that x = q ∗ n + r 1This is a LATEX document. You can get the LATEX source of this document from [email protected]. Please mention the Reference Code, and Version code, given at the top of this document 1 When r = 0 , n is a factor of x. When n is a factor of x, we say n divides x evenly, and denote it by n j x . The modulo operation can be combined with other arithmetic operators. -
The Development and Understanding of the Concept of Quotient Group
HISTORIA MATHEMATICA 20 (1993), 68-88 The Development and Understanding of the Concept of Quotient Group JULIA NICHOLSON Merton College, Oxford University, Oxford OXI 4JD, United Kingdom This paper describes the way in which the concept of quotient group was discovered and developed during the 19th century, and examines possible reasons for this development. The contributions of seven mathematicians in particular are discussed: Galois, Betti, Jordan, Dedekind, Dyck, Frobenius, and H61der. The important link between the development of this concept and the abstraction of group theory is considered. © 1993 AcademicPress. Inc. Cet article decrit la d6couverte et le d6veloppement du concept du groupe quotient au cours du 19i~me si~cle, et examine les raisons possibles de ce d6veloppement. Les contributions de sept math6maticiens seront discut6es en particulier: Galois, Betti, Jordan, Dedekind, Dyck, Frobenius, et H61der. Le lien important entre le d6veloppement de ce concept et l'abstraction de la th6orie des groupes sera consider6e. © 1993 AcademicPress, Inc. Diese Arbeit stellt die Entdeckung beziehungsweise die Entwicklung des Begriffs der Faktorgruppe wfihrend des 19ten Jahrhunderts dar und untersucht die m/)glichen Griinde for diese Entwicklung. Die Beitrfi.ge von sieben Mathematikern werden vor allem diskutiert: Galois, Betti, Jordan, Dedekind, Dyck, Frobenius und H61der. Die wichtige Verbindung zwischen der Entwicklung dieses Begriffs und der Abstraktion der Gruppentheorie wird betrachtet. © 1993 AcademicPress. Inc. AMS subject classifications: 01A55, 20-03 KEY WORDS: quotient group, group theory, Galois theory I. INTRODUCTION Nowadays one can hardly conceive any more of a group theory without factor groups... B. L. van der Waerden, from his obituary of Otto H61der [1939] Although the concept of quotient group is now considered to be fundamental to the study of groups, it is a concept which was unknown to early group theorists. -
Grade 7/8 Math Circles Modular Arithmetic the Modulus Operator
Faculty of Mathematics Centre for Education in Waterloo, Ontario N2L 3G1 Mathematics and Computing Grade 7/8 Math Circles April 3, 2014 Modular Arithmetic The Modulus Operator The modulo operator has symbol \mod", is written as A mod N, and is read \A modulo N" or "A mod N". • A is our - what is being divided (just like in division) • N is our (the plural is ) When we divide two numbers A and N, we get a quotient and a remainder. • When we ask for A ÷ N, we look for the quotient of the division. • When we ask for A mod N, we are looking for the remainder of the division. • The remainder A mod N is always an integer between 0 and N − 1 (inclusive) Examples 1. 0 mod 4 = 0 since 0 ÷ 4 = 0 remainder 0 2. 1 mod 4 = 1 since 1 ÷ 4 = 0 remainder 1 3. 2 mod 4 = 2 since 2 ÷ 4 = 0 remainder 2 4. 3 mod 4 = 3 since 3 ÷ 4 = 0 remainder 3 5. 4 mod 4 = since 4 ÷ 4 = 1 remainder 6. 5 mod 4 = since 5 ÷ 4 = 1 remainder 7. 6 mod 4 = since 6 ÷ 4 = 1 remainder 8. 15 mod 4 = since 15 ÷ 4 = 3 remainder 9.* −15 mod 4 = since −15 ÷ 4 = −4 remainder Using a Calculator For really large numbers and/or moduli, sometimes we can use calculators to quickly find A mod N. This method only works if A ≥ 0. Example: Find 373 mod 6 1. Divide 373 by 6 ! 2. Round the number you got above down to the nearest integer ! 3. -
Strength Reduction of Integer Division and Modulo Operations
Strength Reduction of Integer Division and Modulo Operations Saman Amarasinghe, Walter Lee, Ben Greenwald M.I.T. Laboratory for Computer Science Cambridge, MA 02139, U.S.A. g fsaman,walt,beng @lcs.mit.edu http://www.cag.lcs.mit.edu/raw Abstract Integer division, modulo, and remainder operations are expressive and useful operations. They are logical candidates to express complex data accesses such as the wrap-around behavior in queues using ring buffers, array address calculations in data distribution, and cache locality compiler-optimizations. Experienced application programmers, however, avoid them because they are slow. Furthermore, while advances in both hardware and software have improved the performance of many parts of a program, few are applicable to division and modulo operations. This trend makes these operations increasingly detrimental to program performance. This paper describes a suite of optimizations for eliminating division, modulo, and remainder operations from programs. These techniques are analogous to strength reduction techniques used for multiplications. In addition to some algebraic simplifications, we present a set of optimization techniques which eliminates division and modulo operations that are functions of loop induction variables and loop constants. The optimizations rely on number theory, integer programming and loop transformations. 1 Introduction This paper describes a suite of optimizations for eliminating division, modulo, and remainder operations from pro- grams. In addition to some algebraic simplifications, we present a set of optimization techniques which eliminates division and modulo operations that are functions of loop induction variables and loop constants. These techniques are analogous to strength reduction techniques used for multiplications. Integer division, modulo, and remainder are expressive and useful operations.