Consensus Guidelines for the Use and Interpretation of Angiogenesis Assays
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Linear Systems and Control: a First Course (Course Notes for AAE 564)
Linear Systems and Control: A First Course (Course notes for AAE 564) Martin Corless School of Aeronautics & Astronautics Purdue University West Lafayette, Indiana [email protected] August 25, 2008 Contents 1 Introduction 1 1.1 Ingredients..................................... 4 1.2 Somenotation................................... 4 1.3 MATLAB ..................................... 4 2 State space representation of dynamical systems 5 2.1 Linearexamples.................................. 5 2.1.1 Afirstexample .............................. 5 2.1.2 Theunattachedmass........................... 6 2.1.3 Spring-mass-damper ........................... 6 2.1.4 Asimplestructure ............................ 7 2.2 Nonlinearexamples............................... 8 2.2.1 Afirstnonlinearsystem ......................... 8 2.2.2 Planarpendulum ............................. 9 2.2.3 Attitudedynamicsofarigidbody. .. 9 2.2.4 Bodyincentralforcemotion. 10 2.2.5 Ballisticsindrag ............................. 11 2.2.6 Doublependulumoncart . .. .. 12 2.2.7 Two-linkroboticmanipulator . .. 13 2.3 Discrete-timeexamples . ... 14 2.3.1 Thediscreteunattachedmass . 14 2.4 Generalrepresentation . ... 15 2.4.1 Continuous-time ............................. 15 2.4.2 Discrete-time ............................... 18 2.4.3 Exercises.................................. 20 2.5 Vectors....................................... 22 2.5.1 Vector spaces and IRn .......................... 22 2.5.2 IR2 andpictures.............................. 24 2.5.3 Derivatives ............................... -
Attachment 1
Appendix 1 Chemico-Biological Interactions 301 (2019) 2–5 Contents lists available at ScienceDirect Chemico-Biological Interactions journal homepage: www.elsevier.com/locate/chembioint An examination of the linear no-threshold hypothesis of cancer risk T assessment: Introduction to a series of reviews documenting the lack of biological plausibility of LNT R. Goldena,*, J. Busb, E. Calabresec a ToxLogic, Gaithersburg, MD, USA b Exponent, Midland, MI, USA c University of Massachusetts, Amherst, MA, USA The linear no-threshold (LNT) single-hit dose response model for evolution and the prominence of co-author Gilbert Lewis, who would be mutagenicity and carcinogenicity has dominated the field of regulatory nominated for the Nobel Prize some 42 times, this idea generated much risk assessment of carcinogenic agents since 1956 for radiation [8] and heat but little light. This hypothesis was soon found to be unable to 1977 for chemicals [11]. The fundamental biological assumptions upon account for spontaneous mutation rates, underestimating such events which the LNT model relied at its early adoption at best reflected a by a factor of greater than 1000-fold [19]. primitive understanding of key biological processes controlling muta- Despite this rather inauspicious start for the LNT model, Muller tion and development of cancer. However, breakthrough advancements would rescue it from obscurity, giving it vast public health and medical contributed by modern molecular biology over the last several decades implications, even proclaiming it a scientific principle by calling it the have provided experimental tools and evidence challenging the LNT Proportionality Rule [20]. While initially conceived as a driving force model for use in risk assessment of radiation or chemicals. -
Scientific Computing: an Introductory Survey
Eigenvalue Problems Existence, Uniqueness, and Conditioning Computing Eigenvalues and Eigenvectors Scientific Computing: An Introductory Survey Chapter 4 – Eigenvalue Problems Prof. Michael T. Heath Department of Computer Science University of Illinois at Urbana-Champaign Copyright c 2002. Reproduction permitted for noncommercial, educational use only. Michael T. Heath Scientific Computing 1 / 87 Eigenvalue Problems Existence, Uniqueness, and Conditioning Computing Eigenvalues and Eigenvectors Outline 1 Eigenvalue Problems 2 Existence, Uniqueness, and Conditioning 3 Computing Eigenvalues and Eigenvectors Michael T. Heath Scientific Computing 2 / 87 Eigenvalue Problems Eigenvalue Problems Existence, Uniqueness, and Conditioning Eigenvalues and Eigenvectors Computing Eigenvalues and Eigenvectors Geometric Interpretation Eigenvalue Problems Eigenvalue problems occur in many areas of science and engineering, such as structural analysis Eigenvalues are also important in analyzing numerical methods Theory and algorithms apply to complex matrices as well as real matrices With complex matrices, we use conjugate transpose, AH , instead of usual transpose, AT Michael T. Heath Scientific Computing 3 / 87 Eigenvalue Problems Eigenvalue Problems Existence, Uniqueness, and Conditioning Eigenvalues and Eigenvectors Computing Eigenvalues and Eigenvectors Geometric Interpretation Eigenvalues and Eigenvectors Standard eigenvalue problem : Given n × n matrix A, find scalar λ and nonzero vector x such that A x = λ x λ is eigenvalue, and x is corresponding eigenvector -
Diagonalizable Matrix - Wikipedia, the Free Encyclopedia
Diagonalizable matrix - Wikipedia, the free encyclopedia http://en.wikipedia.org/wiki/Matrix_diagonalization Diagonalizable matrix From Wikipedia, the free encyclopedia (Redirected from Matrix diagonalization) In linear algebra, a square matrix A is called diagonalizable if it is similar to a diagonal matrix, i.e., if there exists an invertible matrix P such that P −1AP is a diagonal matrix. If V is a finite-dimensional vector space, then a linear map T : V → V is called diagonalizable if there exists a basis of V with respect to which T is represented by a diagonal matrix. Diagonalization is the process of finding a corresponding diagonal matrix for a diagonalizable matrix or linear map.[1] A square matrix which is not diagonalizable is called defective. Diagonalizable matrices and maps are of interest because diagonal matrices are especially easy to handle: their eigenvalues and eigenvectors are known and one can raise a diagonal matrix to a power by simply raising the diagonal entries to that same power. Geometrically, a diagonalizable matrix is an inhomogeneous dilation (or anisotropic scaling) — it scales the space, as does a homogeneous dilation, but by a different factor in each direction, determined by the scale factors on each axis (diagonal entries). Contents 1 Characterisation 2 Diagonalization 3 Simultaneous diagonalization 4 Examples 4.1 Diagonalizable matrices 4.2 Matrices that are not diagonalizable 4.3 How to diagonalize a matrix 4.3.1 Alternative Method 5 An application 5.1 Particular application 6 Quantum mechanical application 7 See also 8 Notes 9 References 10 External links Characterisation The fundamental fact about diagonalizable maps and matrices is expressed by the following: An n-by-n matrix A over the field F is diagonalizable if and only if the sum of the dimensions of its eigenspaces is equal to n, which is the case if and only if there exists a basis of Fn consisting of eigenvectors of A. -
Mata Glossary of Common Terms
Title stata.com Glossary Description Commonly used terms are defined here. Mata glossary arguments The values a function receives are called the function’s arguments. For instance, in lud(A, L, U), A, L, and U are the arguments. array An array is any indexed object that holds other objects as elements. Vectors are examples of 1- dimensional arrays. Vector v is an array, and v[1] is its first element. Matrices are 2-dimensional arrays. Matrix X is an array, and X[1; 1] is its first element. In theory, one can have 3-dimensional, 4-dimensional, and higher arrays, although Mata does not directly provide them. See[ M-2] Subscripts for more information on arrays in Mata. Arrays are usually indexed by sequential integers, but in associative arrays, the indices are strings that have no natural ordering. Associative arrays can be 1-dimensional, 2-dimensional, or higher. If A were an associative array, then A[\first"] might be one of its elements. See[ M-5] asarray( ) for associative arrays in Mata. binary operator A binary operator is an operator applied to two arguments. In 2-3, the minus sign is a binary operator, as opposed to the minus sign in -9, which is a unary operator. broad type Two matrices are said to be of the same broad type if the elements in each are numeric, are string, or are pointers. Mata provides two numeric types, real and complex. The term broad type is used to mask the distinction within numeric and is often used when discussing operators or functions. -
The Jacobian of the Exponential Function
A Service of Leibniz-Informationszentrum econstor Wirtschaft Leibniz Information Centre Make Your Publications Visible. zbw for Economics Magnus, Jan R.; Pijls, Henk G.J.; Sentana, Enrique Working Paper The Jacobian of the exponential function Tinbergen Institute Discussion Paper, No. TI 2020-035/III Provided in Cooperation with: Tinbergen Institute, Amsterdam and Rotterdam Suggested Citation: Magnus, Jan R.; Pijls, Henk G.J.; Sentana, Enrique (2020) : The Jacobian of the exponential function, Tinbergen Institute Discussion Paper, No. TI 2020-035/III, Tinbergen Institute, Amsterdam and Rotterdam This Version is available at: http://hdl.handle.net/10419/220072 Standard-Nutzungsbedingungen: Terms of use: Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Documents in EconStor may be saved and copied for your Zwecken und zum Privatgebrauch gespeichert und kopiert werden. personal and scholarly purposes. Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle You are not to copy documents for public or commercial Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich purposes, to exhibit the documents publicly, to make them machen, vertreiben oder anderweitig nutzen. publicly available on the internet, or to distribute or otherwise use the documents in public. Sofern die Verfasser die Dokumente unter Open-Content-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, If the documents have been made available under an Open gelten abweichend von diesen Nutzungsbedingungen die in der dort Content Licence (especially Creative Commons Licences), you genannten Lizenz gewährten Nutzungsrechte. may exercise further usage rights as specified in the indicated licence. www.econstor.eu TI 2020-035/III Tinbergen Institute Discussion Paper The Jacobian of the exponential function Jan R. -
The Interface Between English and the Celtic Languages
Universität Potsdam Hildegard L. C. Tristram (ed.) The Celtic Englishes IV The Interface between English and the Celtic Languages Potsdam University Press In memoriam Alan R. Thomas Contents Hildegard L.C. Tristram Inroduction .................................................................................................... 1 Alan M. Kent “Bringin’ the Dunkey Down from the Carn:” Cornu-English in Context 1549-2005 – A Provisional Analysis.................. 6 Gary German Anthroponyms as Markers of Celticity in Brittany, Cornwall and Wales................................................................. 34 Liam Mac Mathúna What’s in an Irish Name? A Study of the Personal Naming Systems of Irish and Irish English ......... 64 John M. Kirk and Jeffrey L. Kallen Irish Standard English: How Celticised? How Standardised?.................... 88 Séamus Mac Mathúna Remarks on Standardisation in Irish English, Irish and Welsh ................ 114 Kevin McCafferty Be after V-ing on the Past Grammaticalisation Path: How Far Is It after Coming? ..................................................................... 130 Ailbhe Ó Corráin On the ‘After Perfect’ in Irish and Hiberno-English................................. 152 II Contents Elvira Veselinovi How to put up with cur suas le rud and the Bidirectionality of Contact .................................................................. 173 Erich Poppe Celtic Influence on English Relative Clauses? ......................................... 191 Malcolm Williams Response to Erich Poppe’s Contribution -
0 Nonsymmetric Eigenvalue Problems 149
0 Nonsymmetric Eigenvalue Problems 4.1. Introduction We discuss canonical forms (in section 4.2), perturbation theory (in section 4.3), and algorithms for the eigenvalue problem for a single nonsymmetric matrix A (in section 4.4). Chapter 5 is devoted to the special case of real symmet- ric matrices A = A T (and the SVD). Section 4.5 discusses generalizations to eigenvalue problems involving more than one matrix, including motivating applications from the analysis of vibrating systems, the solution of linear differ- ential equations, and computational geometry. Finally, section 4.6 summarizes all the canonical forms, algorithms, costs, applications, and available software in a list. One can roughly divide the algorithms for the eigenproblem into two groups: direct methods and iterative methods. This chapter considers only direct meth- ods, which are intended to compute all of the eigenvalues, and (optionally) eigenvectors. Direct methods are typically used on dense matrices and cost O(n3 ) operations to compute all eigenvalues and eigenvectors; this cost is rel- atively insensitive to the actual matrix entries. The mail direct method used in practice is QR iteration with implicit shifts (see section 4.4.8). It is interesting that after more than 30 years of depend- able service, convergence failures of this algorithm have quite recently been observed, analyzed, and patched [25, 65]. But there is still no global conver- gence proof, even though the current algorithm is considered quite reliable. So the problem of devising an algorithm that is numerically stable and globally (and quickly!) convergent remains open. (Note that "direct" methods must still iterate, since finding eigenvalues is mathematically equivalent to finding zeros of polynomials, for which no noniterative methods can exist. -
Petition Signatories 12 November 2020 First Name Surname Country Capacity
Petition Signatories 12 November 2020 First name Surname Country Capacity 1 Ulisses Abade Brasil Vice Presidente Sindicato 2 Sandrine Abayou France salariée 3 HAYANI ABDEL BELGIUM trade union 4 Ariadna Abeltina Latvia Trade Union Officer General Secretary FSC 5 Roberto Abenia España CCOO Aragón 6 Pascal Abenza France Délégué Syndical Groupe 7 Jacques ADAM Luxembourg membre du syndicat 8 Lenka Adamcikova Slowakei Member of works 9 Ole Einar Adamsrød Norway Trade Union 10 Paula Adao Luxembourg Déléguée 11 Nicolae Adrian România Union member 12 Costache Adrian Alin Romania Trade union 13 Pana Adriana Laura România Member of works council 14 Bert Aerts Belgium member of works council 15 Annick Aerts Belgium trade union 16 Sascha Aerts België 200 Secrétaire Générale UL 17 Odile AGRAFEIL FRANCE CGT 18 Oscar Aguado España Miembro comité empresa 19 Fátima Aguado Queipo Spain Trade union 20 Agustin Aguila Mellado España Miembro del Sindicato SECRETARIO UGT ADIF 21 HERNANDEZ AGUILAR OSWALD BARCELONA 22 Antonio Angel Aguilar Fernández España Trade Union 23 Jaan Aiaots Estonia Trade union SYNDICAT SYNPTAC-CGT 24 Nora AINECHE FRANCE PARIS FRANCE 25 Raul Aira España miembro comité empresa 26 Alessandra Airaldi Italy TRADE union 27 Juan Miguel Aisa Spain Member of works council 28 Juan-Miguel AISA Spain EWC Membre élu du comité européen Driver Services 29 Sylvestre AISSI France Norauto 30 Sara Akervall Sweden EWC 31 Michiel Al Netherlands trade union official 32 Nickels Alain Luxemburg Trade Union 33 MAURO ALBANESE FRANCE SYNDICAT 34 Michela Albarello -
On the Construction of Nearest Defective Matrices to a Normal Matrix
On the construction of nearest defective matrices to a normal matrix Rafikul Alam∗ Department of Mathematics Indian Institute of Technology Guwahati Guwahati - 781 039, INDIA Abstract. Let A be an n-by-n normal matrix with n distinct eigenvalues. We describe a simple procedure to construct a defective matrix whose distance from A, among all the defective matrices, is the shortest. Our construction requires only an appropriate pair of eigenvalues of A and their corresponding eigenvectors. We also show that the nearest defective matrices influence the evolution of spectral projections of A. Keywords: Defective matrix, multiple eigenvalue, pseudospectra, eigenvector, spectral pro- jection. 1 Introduction Let A Cn×n be a normal matrix with n distinct eigenvalues. Let d(A) be the distance of A ∈ from the set of defective matrices, that is, d(A) := inf A A0 : A0 is defective , (1.1) {k − k } where is either the 2-norm or the Frobenius norm. For a non-normal B, the determination k·k of d(B) and a defective matrix B0 such that B B0 = d(B) is a nontrivial task and is widely k − k known as Wilkinson’s problem (see, for example, [8], [9], [10], [6], [2], [5], [4], [1]). By contrast, since A is normal, it is easy to see that for the 2-norm 1 d(A)= min λi λj (1.2) 2 i6=j | − | where λ1,...,λn are the eigenvalues of A. However, it appears that the construction of a defective matrix A0 such that A A0 = d(A) is nontrivial. Note that the existence of such an k − k A0 would imply that the infimum in (1.1) is actually the minimum. -
Full Catalogue
Catalogue of ELECTRA Papers and SESSION Papers 12/11/2007 Contents The catalogue lists the papers published in ELECTRA after 1967 and the papers discussed at CIGRE Sessions from 1968 on. ELECTRA Papers are listed in chronological order. They are of various nature. The catalogue displays: - the ELECTRA reference - the year of publication - the title of the paper - the nature of the paper - the author(s), either the Working Body which produced it, or the author(s),when it was not the result of a collective work. The Session papers are listed in chronological order also. For each paper are given: - the paper reference, with the year - the title of the paper - the author(s) Structure of the Catalogue -There is a Table of Contents at the beginning of the Catalogue, indexed per year, which helps accessing the right part of the catalogue -The ELECTRA papers follow -The Session papers section comes after. Getting the documents ELECTRA papers and Session papers can be delivered to CIGRE members only. Non members can only get the full sets of Session papers (see the catalogue of Publications) After selection of the papers, members are requested to use the Order Form, available on the Web and send it to the Central Office of CIGRE. This order form gives details on payment, when applying. Documents will be sent in electronic (preferably) or on paper. The service is usually charged for, and charge depends on the nature of the services provided (large number of papers, special request with search…) - Orders will be emailed ([email protected]), posted to: CIGRE (21 rue d’Artois – 75008 Paris) , or faxed (+33 1 53 89 12 99) - Enquiries should be directed to: [email protected], secretary- [email protected], [email protected] (for membership details) IMPORTANT: Intellectual ownership of CIGRE documents. -
Department of Mathematics, University of Utah Analysis of Numerical Methods I MTH6610 – Section 001 – Fall 2017 Lecture Notes – Eigenvalues Wednesday October 25, 2017
Department of Mathematics, University of Utah Analysis of Numerical Methods I MTH6610 { Section 001 { Fall 2017 Lecture notes { Eigenvalues Wednesday October 25, 2017 These notes are not a substitute for class attendance. Their main purpose is to provide a lecture overview summarizing the topics covered. Reading: Trefethen & Bau III, Lectures 24 n×n Let A 2 C . A scalar λ 2 C is an eigenvalue of A if there exists a nonzero vector v such that Av = λv n For a fixed eigenvalue λj, the subspace Vj ⊂ C containing vectors v satisfying the above equation is called the eigenspace associated to λj. The eigenspace Vj has dimension dj, and this dimension is called the geometric multiplicity of the eigenvalue λj. Let λ1; : : : ; λp be an enumeration of the eigenvalues of A, and let λj have corresponding eigenspace Vj of dimension dj ≥ 1. Let vj1; : : : ; vjdj be any basis for Vj. Then we have the matrix equality AV = V Λ; where the matrices V and Λ are defined as 0 1 λ1Id1 B λ2Id C Λ = B 2 C ;V = v ··· v v ··· v ··· v B .. C 11 1d1 21 2d2 pdp @ . A λpIdp If λ is an eigenvalue of A, the definition implies that pA(λ) := det(λI − A) = 0; and also any λ satisfying the above is an eigenvalue of A. The Laplace expansion of the determinant implies that z 7! pA(z) is a polynomial of degree n. pA is the called the characteristic polynomial of A. We see that A must therefore have exactly n eigenvalues corresponding to the n roots of pA, some of which may be repeated.